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Madhattan</title><description></description><link>http://docmadhattan.fieldofscience.com/</link><managingEditor>noreply@blogger.com (Gianluigi Filippelli)</managingEditor><generator>Blogger</generator><openSearch:totalResults>409</openSearch:totalResults><openSearch:startIndex>1</openSearch:startIndex><openSearch:itemsPerPage>25</openSearch:itemsPerPage><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-8856222405976926647</guid><pubDate>Tue, 19 Jul 2022 19:40:00 +0000</pubDate><atom:updated>2022-07-19T21:40:00.181+02:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">astronomy</category><category domain="http://www.blogger.com/atom/ns#">black hole</category><category domain="http://www.blogger.com/atom/ns#">eso</category><category domain="http://www.blogger.com/atom/ns#">large magellanic cloud</category><category domain="http://www.blogger.com/atom/ns#">tomer shenar</category><category domain="http://www.blogger.com/atom/ns#">video</category><title>The first extragalactic black hole</title><description><div align="center"><iframe width="560" height="315" src="https://www.youtube.com/embed/GS-qxNDnTzE" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div>
In the world of black hole researchers, there is a group led by <strong>Tomer Shenar</strong> that, so far, has mostly demonstrated the non-existence of black holes previously announced by other teams.<br/>
As Shenar himself recalled, however,
<blockquote>For the first time, our group has come together to discuss the discovery of a black hole, instead of eliminating one.</blockquote>
We are talking about <a href="News https://www.eso.org/public/unitedkingdom/news/eso2210/?lang" target="eso">a black hole found inside the Tarantula Nebula</a>, which is part of the Large Magellanic Cloud, one of the satellite galaxies of the Milky Way.<br/>
In particular, this black hole, of stellar mass, is of the "dormant" type, that is, it emits very low levels of X radiation, which are the radiations with which black holes are generally discovered.<br/>
This happens because the black hole interacts very little with its surroundings.<br/>
Another interesting aspect of the discovery is the absence of any trace of the star that generated the black hole.
<blockquote>[It] appears to have completely collapsed, with no sign of a previous explosion.</blockquote>
This black hole, the first extragalactic, was discovered orbiting a massive star thanks to six years of observations at ESO's <em>Very Large Telescope</em>.</description><link>http://docmadhattan.fieldofscience.com/2022/07/the-first-extragalactic-black-hole.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://img.youtube.com/vi/GS-qxNDnTzE/default.jpg" height="72" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-6181556624360585924</guid><pubDate>Wed, 06 Jul 2022 21:19:00 +0000</pubDate><atom:updated>2022-07-06T23:19:36.272+02:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">fields medal</category><category domain="http://www.blogger.com/atom/ns#">mathematics</category><title>Fields Medals 2022</title><description><div class="pic right"><img alt="" border="0" data-original-height="298" data-original-width="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_iG_zcEw4IC77DTLRl70yWS9h7mL0VIVZpQEwVilIGKnGGfRQureC8NRbxUPamLQBOmjAYEleafEc92oip830DugQw3EHQhKp-L4ak3ZyVWSY_9j17yC9vRfGwE0fT8WpRQm-quTySRHH7_6_IFBnsmAXy10SRSIHHfqHwNOSRipI6mGdwRExsA53/s1600/20220706-fields_medal.jpg"/></div>
I hope to write something about the Ising model in the next weeks, but in the meanwhile you can <a href="http://docmadhattan.fieldofscience.com/2011/09/universe-and-flowers.html" target="doc">read something about E8 group</a>. Below you can find the mathematicians that awarded the Field Medals 2022:
<hr/>
<strong> Hugo Duminil-Copin</strong>
<blockquote>For solving longstanding problems in the probabilistic theory of phase transitions in statistical physics, especially in dimensions three and four.</blockquote>
<strong>June Huh</strong>
<blockquote>For bringing the ideas of Hodge theory to combinatorics, the proof of the Dowling–Wilson conjecture for geometric lattices, the proof of the Heron–Rota–Welsh conjecture for matroids, the development of the theory of Lorentzian polynomials, and the proof of the strong Mason conjecture.</blockquote>
<strong>James Maynard</strong>
<blockquote>For contributions to analytic number theory, which have led to major advances in the understanding of the structure of prime numbers and in Diophantine approximation.</blockquote>
<strong>Maryna Viazovska</strong>
<blockquote>For the proof that the E8 lattice provides the densest packing of identical spheres in 8 dimensions, and further contributions to related extremal problems and interpolation problems in Fourier analysis.</blockquote></description><link>http://docmadhattan.fieldofscience.com/2022/07/fields-medals-2022.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_iG_zcEw4IC77DTLRl70yWS9h7mL0VIVZpQEwVilIGKnGGfRQureC8NRbxUPamLQBOmjAYEleafEc92oip830DugQw3EHQhKp-L4ak3ZyVWSY_9j17yC9vRfGwE0fT8WpRQm-quTySRHH7_6_IFBnsmAXy10SRSIHHfqHwNOSRipI6mGdwRExsA53/s72-c/20220706-fields_medal.jpg" height="72" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-8306587028159344057</guid><pubDate>Wed, 23 Mar 2022 22:12:00 +0000</pubDate><atom:updated>2022-03-23T23:12:31.876+01:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">emmy noether</category><category domain="http://www.blogger.com/atom/ns#">mathemaics</category><category domain="http://www.blogger.com/atom/ns#">physics</category><category domain="http://www.blogger.com/atom/ns#">symmetry</category><title>Noether's theorem</title><description><div style="float:right; padding:5px;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJ8awNg1i5dy0vvyocL3stVQAavjtupMvLCYSGaoGL0xOB7Kt_6pLGNKMVDn0q1k191IFX5OWpYABsSG9UYzsiBSJzGLTGTrNgBtZpHtpplqYGIqPHkLjCp2t9eqoQD3pqtiV2eQlNgD8/s280/20130325-emmy_noether.jpg" /></div>
The <a href="https://en.wikipedia.org/wiki/Noether%27s_theorem" target="wiki">Noether's theorem</a>, discovered by German mathematician <strong>Emmy Noether</strong>, is one of the most sophisticated theorems in physics, a way to see how group theory, a branch of mathematics believed by many to be abstract, can provide the basis for an important physical concept. The premises of the theory of groups, coupled with the calculus of variations, lead to the conclusions of the theorem: the existence, under certain conditions, of conserved quantities within physical systems.<br/>
First of all we start with symmetry, one of the most important concepts for physics, and also the subject og group theory studies.
To realize, therefore, this close link, it is enough to have in mind the statement of the theorem:
<blockquote>If a physical system exhibits some continuous symmetry, then there are corresponding observables whose values are constant over time.</blockquote>
A more sophisticated formulation of the theorem, on the other hand, goes something like this:
<blockquote>To every differentiable symmetry generated by local actions there corresponds a conserved current.</blockquote>
This more technical statement links the theorem and the symmetries with some of the most important groups for physics, the Lie groups. In the abstract of the Noether's paper, <em>Invariant Variationsprobleme</em>, in fact, we can read:
<blockquote>The problems in variation here concerned are such as to admit a continuous group (in Lie's sense); the conclusions that emerge for the corresponding differential equations find their more general expression in the theorems formulated in Section I and proved in the following sections.</blockquote>
The Noether's theorem, therefore, ensures that, when a physical system is invariant under the action of the transformations belonging to a Lie group, that is a group in which we are able to differentiate functions, then it certainly exists at least one conserved quantity, and this quantity and its invariance are expressed in the following equation:
\[\frac{\text{d}}{\text{d} t} \left ( \frac{\partial L}{\partial \dot x_k} \right ) = \frac{\text{d} p_k}{\text{d} t}\]
<div id="box">Emmy Noether (1918). Invariante Variationsprobleme. <a href="https://de.wikisource.org/wiki/Invariante_Variationsprobleme" target="de">de.wikisource</a>.<br/>
English translation by Mort Tavel on <a href="https://arxiv.org/abs/physics/0503066" target="arxiv">arXiv</a></div></description><link>http://docmadhattan.fieldofscience.com/2022/03/noethers-theorem.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJ8awNg1i5dy0vvyocL3stVQAavjtupMvLCYSGaoGL0xOB7Kt_6pLGNKMVDn0q1k191IFX5OWpYABsSG9UYzsiBSJzGLTGTrNgBtZpHtpplqYGIqPHkLjCp2t9eqoQD3pqtiV2eQlNgD8/s72-c/20130325-emmy_noether.jpg" height="72" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-4196476225803916902</guid><pubDate>Mon, 14 Mar 2022 17:00:00 +0000</pubDate><atom:updated>2022-03-14T18:00:00.186+01:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">francois viete</category><category domain="http://www.blogger.com/atom/ns#">mathemaics</category><category domain="http://www.blogger.com/atom/ns#">nilakantha somayaji</category><category domain="http://www.blogger.com/atom/ns#">pi</category><category domain="http://www.blogger.com/atom/ns#">pi day</category><title>Pi stories: Viète and the infinite series</title><description><div id="caption" align="center"><img border="0" src="https://4.bp.blogspot.com/-RKEI_sHOPYc/WMcys6Zy4sI/AAAAAAAAQHg/_fIotffMwtInRe7Fq4vknv2EGx9M7DgyQCPcB/s450/20170314-pi_day.jpg" /><br/>
<small><a href="http://spikedmath.com/490.html" target="comics"><em>Spiked Math</em></a></small></div>
<a href="http://docmadhattan.fieldofscience.com/2016/03/ludolph-van-ceulen-in-searching-of-pi.html" target="doc"><strong>Ludolph van Ceulen</strong></a> in 1596 using the polygon method, first came to calculate 20 decimal digits, then 35. Van Ceulen wasn't the last to use the method: for example <strong>Willebrord Snellius</strong> in 1621 calculated 34 digits, while the Austrian astronomer <strong>Christoph Grienberger</strong> in 1630 reached a record 38 digits using a 1040-sided polygon: this result is the most accurate ever achieved using the polygon method.<br/>
The infinite series supplanted this method: the first to use them in Europe was the French mathematician <strong>François Viète</strong> in 1593
\[\frac2\pi = \frac{\sqrt2}2 \cdot \frac{\sqrt{2+\sqrt2}}2 \cdot \frac{\sqrt{2+\sqrt{2+\sqrt2}}}2 \cdots\]
And in 1655 <strong>John Wallis</strong>
\[\frac{\pi}{2} = \frac{2}{1} \cdot \frac{2}{3} \cdot \frac{4}{3} \cdot \frac{4}{5} \cdot \frac{6}{5} \cdot \frac{6}{7} \cdot \frac{8}{7} \cdot \frac{8}{9} \cdots\]
European mathematics, however, had come to this method only after Indian mathematics, albeit independently. In India, in fact, there is evidence of first approaches of this kind between 1400 and 1500. The first infinite series used to calculate $\pi$ is found, in fact, on the pages of the <em>Tantrasamgraha</em> (literally "<em>compilation of systems</em>") of the Indian astronomer <strong>Nilakantha Somayaji</strong>, circa 1500-1501. The series, presented without any proof (later published in the <em>Yuktibhāṣā</em>, circa 1530), was attributed by Nilakantha to the mathematician <strong>Madhava of Sangamagrama</strong>, who lived between 1350 and 1425 circa. Apparently Madhava discovered several infinite series, including many that contain the sine, cosine, and tangent. The Indian mathematician used these series to reach up to 11 digits around 1400, a value that was improved around 1430 by the Persian mathematician <strong>Jamshīd al-Kāshī</strong> using the polygon method.</description><link>http://docmadhattan.fieldofscience.com/2022/03/pi-day-viete-infinite-series.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://4.bp.blogspot.com/-RKEI_sHOPYc/WMcys6Zy4sI/AAAAAAAAQHg/_fIotffMwtInRe7Fq4vknv2EGx9M7DgyQCPcB/s72-c/20170314-pi_day.jpg" height="72" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-1857738318298971155</guid><pubDate>Wed, 01 Dec 2021 19:30:00 +0000</pubDate><atom:updated>2021-12-01T20:30:00.191+01:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">aids</category><category domain="http://www.blogger.com/atom/ns#">aids day</category><category domain="http://www.blogger.com/atom/ns#">mathemaics</category><category domain="http://www.blogger.com/atom/ns#">notices of ams</category><title>Mathematics and HIV</title><description><div id="box" align="center"><a href="http://www.worldaidsday.org/" target="aids">World AIDS Day</a></div>
There is a link between mathematics and HIV that goes beyond the geometric structure of the virus, based on the icosahedron. <strong>Denise Kirschner</strong> describes this relationship very well in <em>Using Mathematics to Understand HIV Immune Dynamics</em>:
<blockquote>Since the early 1980s there has been a tremendous effort made in the mathematical modeling of the human immunodeficiency virus (HIV), the virus which causes AIDS (Acquired Immune Deficiency Syndrome). The approaches in this endeavor have been twofold; they can be separated into the epidemiology of AIDS as a disease and the immunology of HIV as a pathogen (a foreign substance detrimental to the body).<sup class="footnote-ref">(<a href="#fn1" id="fnref1">1</a>)</sup></blockquote>
The paper focuses on HIV immunology:
<blockquote>Our goal then is to better understand the interaction of HIV and the human immune system for the purpose of testing treatment strategies.<sup class="footnote-ref">(<a href="#fn1" id="fnref1:1">1</a>)</sup></blockquote>
The behavior of the immune system is schematized in this way:
<div align="center" style="padding-top: 5px;"><a href="https://lh3.googleusercontent.com/-20KHjRsk0v4/ULlRkVC8M2I/AAAAAAAAF94/rwrDzg9IX-8/s700/20121201-immune_system.jpg" target="img"><img src="https://lh3.googleusercontent.com/-20KHjRsk0v4/ULlRkVC8M2I/AAAAAAAAF94/rwrDzg9IX-8/s512/20121201-immune_system.jpg" width="400" /></a></div><a name='more'></a>
In the diagram, the cells that the HIV virus uses to reproduce itself are CD4<sup>+</sup> T, that is, the cells that play a key role in the immune system's response against invasions. In summary, this means that any type of treatment must interfere with the transcription mechanism of the virus' RNA into the host cell's DNA. In this way it is not possible to find definitive cures, but simply treatments that block the progression of the disease. The search for a treatment that is ever closer to being a cure is therefore an important step in the fight against AIDS and mathematics could play an important role, and not just with simple statistical studies, but with the creation of mathematical models, such as the deterministic approach proposed by Kirschner.
<blockquote>Continuous dynamical systems, whether ordinary or partial differential equations, are lending new insights into HIV infection. Population models are most commonly used, and, given hypotheses about the interactions of those populations, models can be created, analyzed, and refined.<sup class="footnote-ref">(<a href="#fn1" id="fnref1:2">1</a>)</sup></blockquote>
The differential equations used modeling the dynamics within blood cells, both of the diseased and the healthy ones. The equations used are three:
The first equation represents the source of new T cells from the thymus.
<blockquote>Since it has been shown that virus can infect thymocytes, we choose a function describing the decreasing source as a function of viral load; assuming that the uninfected T cell populations are reduced by half.<sup class="footnote-ref">(<a href="#fn1" id="fnref1:3">1</a>)</sup></blockquote>
It is therefore necessary to model the stimulus to proliferation induced in T cells by the presence of the virus and finally the infection itself.
The second equation describes the changes within the infected cell population.
<blockquote>(...) infected cells are lost either by having finite life span or by being stimulated to proliferate. They are destroyed during the proliferation process by bursting due to the large viral load.<sup class="footnote-ref">(<a href="#fn1" id="fnref1:4">1</a>)</sup></blockquote>
Finally, in the third equation, we focus on virus and parameters such as the source of the virus itself or its growth rate.<br/>
It is very interesting to note how, starting from a series of three numerically solved differential equations, we can also arrive at the formulation of a treatment: it is actually more to show the approach and its possible effectiveness that Kirschner is interested in item. And we can see that mathematics is playing an increasingly important role in the field of medicine, as in some ways <strong>Avner Friedman</strong> tries to show in <em>What Is Mathematical Biology and How Useful Is It?</em>
<blockquote>Viewing the present trends in mathematical biology, I believe that the coming decade will demonstrate very clearly that mathematics is the future frontier of biology and biology is the future frontier of mathematics.<sup class="footnote-ref">(<a href="#fn2" id="fnref2">2</a>)</sup></blockquote>
In 2012 Rao, Thomas, Kurapati, and Bhat<sup class="footnote-ref">(<a href="#fn3" id="fnref3">3</a>)</sup>, based on Indian data, tried to create a model that was able to predict that, in the future, we would use the two different antiretroviral therapies present in India. And even in this case the equations used are just differential equations!
<hr/>
<section class="footnotes">
<ol class="footnotes-list">
<li id="fn1" class="footnote-item">Denise Kirschner (1996). Using Mathematics to Understand HIV Immune Dynamics, <em>Notices of the American Mathematical Society</em>, 43 (02) 191-202 (<a href="http://www.ams.org/notices/199602/kirschner.pdf" target="pdf" class="pdf">pdf</a>) <a href="#fnref1" class="footnote-backref">↩︎</a> <a href="#fnref1:1" class="footnote-backref">↩︎</a> <a href="#fnref1:2" class="footnote-backref">↩︎</a> <a href="#fnref1:3" class="footnote-backref">↩︎</a> <a href="#fnref1:4" class="footnote-backref">↩︎</a></li>
<li id="fn2" class="footnote-item">Avner Friedman (2010). What Is Mathematical Biology and How Useful Is It?, <em>Notices of the American Mathematical Society</em>, 57 (07) 851-857 (<a href="http://www.ams.org/notices/201007/rtx100700851p.pdf" target="pdf" class="pdf">pdf</a>) <a href="#fnref2" class="footnote-backref">↩︎</a></li>
<li id="fn3" class="footnote-item">Rao A.S.R.S., Thomas K., Kurapati S. &amp; Bhat R. (2012). Improvement in Survival of People Living with HIV/AIDS and Requirement for 1st- and 2nd-Line ART in India: A Mathematical Model, <em>Notices of the American Mathematical Society</em>, 59 (04) 560-562. doi:<a href="http://dx.doi.org/10.1090%2Fnoti835" target="doi" class="doi">10.1090/noti835</a> <a href="#fnref3" class="footnote-backref">↩︎</a></li>
</ol>
</section></description><link>http://docmadhattan.fieldofscience.com/2021/12/mathematics-and-hiv.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://lh3.googleusercontent.com/-20KHjRsk0v4/ULlRkVC8M2I/AAAAAAAAF94/rwrDzg9IX-8/s72-c/20121201-immune_system.jpg" height="72" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-38921564751232175</guid><pubDate>Thu, 25 Nov 2021 19:30:00 +0000</pubDate><atom:updated>2021-11-25T20:30:00.184+01:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">alan turing</category><category domain="http://www.blogger.com/atom/ns#">computer science</category><category domain="http://www.blogger.com/atom/ns#">entropy</category><category domain="http://www.blogger.com/atom/ns#">gregory chaitin</category><category domain="http://www.blogger.com/atom/ns#">mathematics</category><title>The entropy and the halting probability problem</title><description>The <a href="https://en.wikipedia.org/wiki/Third_law_of_thermodynamics" traget="wiki" class="wiki">third law of thermodynamics</a> states:
<blockquote>It is impossible for any procedure to lead to the isotherm $T = 0$ in a finite number of steps.</blockquote>
The theorem, discovered by <strong>Walther Nernst</strong>, is equal to say:
<blockquote>It is impossible for any process, no matter how idealized, to reduce the entropy of a system to its zero point value in a finite number of operations.</blockquote>
In classical thermodynamics we can define <a href="https://en.wikipedia.org/wiki/Entropy" target="wiki" class="wiki">entropy</a>, or the variation of entropy $\Delta S$, with the following equation:
\[\Delta S = \frac{\Delta Q}{T}\]
where $\Delta Q$ is the heat's variation and $T$ is the temperature.<br/><a name='more'></a>
In 1970s <strong>Ludwig Boltzmann</strong> developed the statistical mechanics definition of the entropy, well known like Boltzmann's equation:
\[S = - k_B \sum_i p_i \ln p_i\]
where $k_B$ is the Boltzmann's constant, $p_i$ is the probability that the system is in the $i$-th microstate.<br/>
Now we jump to 2007 when <a href="http://www.umcs.maine.edu/~chaitin/" target="uni"><strong>Gregory Chaitin</strong></a> defined the <a href="https://en.wikipedia.org/wiki/Halting_problem" target="wiki" class="wiki">halting probability problem</a>:
\[\Omega = \sum_{\{ p \}} 2^{-p} = \sum_i 2^{-p_i}\]
\[\Omega_i = 2^{-p_i}\]
\[p_i = - \lg_2 \Omega_i\]
\[p = \sum_i p_i = - \sum_i \lg_2 \Omega_i\]
<div class="pic right"><img src="https://lh6.googleusercontent.com/-9ZamKVdHBTw/T-OXVvDws1I/AAAAAAAAEpc/7lBzPrXY9EU/s441/20120621-alan_turing.jpg" width="200" /></div>
The halting problem is the need to determine, given an arbitrary computer program, whether it will ever finish its processing or go on forever (something not too different from Hilbert's tenth problem, in some ways).<br/>
<strong>Alan Turing</strong>, in 1936, proved that there is no algorithm capable of solving the halting problem for all possible programs. Fundamental to this proof is the Turing machine itself: within this context, taking up the work of <strong>Kurt Godel</strong>, the problem of stopping is undecidable.<br/>
Chaitin then defined a halting probability<sup class="footnote-ref">(<a href="#fn1" id="fnref1">1</a>)</sup>, a real number which basically represents the probability that a randomly generated program will stop. This number turns out to be normal and transcendental, which implies that it can be well defined but cannot be fully calculated.<br/>
This means that it can be used to prove that there are no algorithms that produce the digits of $\Omega$, although its first digits have been calculated for simple cases, for example in binary notation:
\[\Omega = .110110\cdots\]
<hr/>
<section class="footnotes">
<ol class="footnotes-list"><li id="fn1" class="footnote-item"><div id="box"><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.jtitle=Enriques+lecture&rft_id=info%3Aarxiv%2Fmath%2F0611740v1&rfr_id=info%3Asid%2Fresearchblogging.org&rft.atitle=The+Halting+Probability+Omega%3A+Irreducible+Complexity+in+Pure%0D%0A++Mathematics&rft.issn=&rft.date=2006&rft.volume=&rft.issue=&rft.spage=&rft.epage=&rft.artnum=&rft.au=G.+J.+Chaitin&rfe_dat=bpr3.included=1;bpr3.tags=Computer+Science+%2F+Engineering%2CMathematics%2CProbability+and+Statistics">G. J. Chaitin (2006). The Halting Probability Omega: Irreducible Complexity in Pure Mathematics <span style="font-style: italic;">Enriques lecture</span> arXiv: <a rev="review" href="http://arxiv.org/abs/math/0611740v1" target="arxiv">math/0611740v1</a></span></div>
<div id="box"><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.jtitle=Scientific+American&rft_id=info%3Adoi%2F10.1038%2Fscientificamerican0306-74&rfr_id=info%3Asid%2Fresearchblogging.org&rft.atitle=The+Limits+of+Reason&rft.issn=0036-8733&rft.date=2006&rft.volume=294&rft.issue=3&rft.spage=74&rft.epage=81&rft.artnum=http%3A%2F%2Fwww.nature.com%2Fdoifinder%2F10.1038%2Fscientificamerican0306-74&rft.au=Chaitin%2C+G.&rfe_dat=bpr3.included=1;bpr3.tags=Mathematics%2CProbability+and+Statistics%2C+Logic+and+Foundations">Chaitin, G. (2006). The Limits of Reason <span style="font-style: italic;">Scientific American, 294</span> (3), 74-81 DOI: <a rev="review" href="http://dx.doi.org/10.1038/scientificamerican0306-74">10.1038/scientificamerican0306-74</a></span></div>
<div id="box"><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.jtitle=Information+and+Computation&rft_id=info%3Adoi%2F10.1016%2Fj.ic.2006.07.003&rfr_id=info%3Asid%2Fresearchblogging.org&rft.atitle=Natural+halting+probabilities%2C+partial+randomness%2C+and+zeta+functions&rft.issn=08905401&rft.date=2006&rft.volume=204&rft.issue=11&rft.spage=1718&rft.epage=1739&rft.artnum=http%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS0890540106000848&rft.au=Calude%2C+C.&rft.au=Stay%2C+M.&rfe_dat=bpr3.included=1;bpr3.tags=Computer+Science+%2F+Engineering">Calude, C., & Stay, M. (2006). Natural halting probabilities, partial randomness, and zeta functions <span style="font-style: italic;">Information and Computation, 204</span> (11), 1718-1739 DOI: <a rev="review" href="http://dx.doi.org/10.1016/j.ic.2006.07.003">10.1016/j.ic.2006.07.003</a></span></div><a href="#fnref1" class="footnote-backref">↩︎</a></li></ol>
</section></description><link>http://docmadhattan.fieldofscience.com/2021/11/entropy-halting-problem.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://lh6.googleusercontent.com/-9ZamKVdHBTw/T-OXVvDws1I/AAAAAAAAEpc/7lBzPrXY9EU/s72-c/20120621-alan_turing.jpg" height="72" width="72"/><thr:total>1</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-1415616688760103462</guid><pubDate>Tue, 23 Nov 2021 19:30:00 +0000</pubDate><atom:updated>2021-11-23T20:30:00.175+01:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">berry phase</category><category domain="http://www.blogger.com/atom/ns#">black hole</category><category domain="http://www.blogger.com/atom/ns#">cosmology</category><category domain="http://www.blogger.com/atom/ns#">geometry</category><category domain="http://www.blogger.com/atom/ns#">mathematics</category><category domain="http://www.blogger.com/atom/ns#">michael berry</category><category domain="http://www.blogger.com/atom/ns#">parallel transport</category><category domain="http://www.blogger.com/atom/ns#">quantum mechanics</category><category domain="http://www.blogger.com/atom/ns#">shivaramakrishnan pancharatnam</category><title>The Berry's phase and the black hole</title><description>In quantum mechanics a <a href="https://en.wikipedia.org/wiki/Geometric_phase" target="wiki" class="wiki">geometric phase</a>, also called <em>Berry phase</em>, is a phase difference that a given physical system acquires during a cycle in which the system itself is under the action of an adiabatic process. This phase is linked to the geometric properties of the system itself (which is a simplification, but for our purposes there is no need to go into too much detail).<br/>
It was discovered independently by <strong>Shivaramakrishnan Pancharatnam</strong> in 1956<sup class="footnote-ref">(<a href="#fn1" id="fnref1">1</a>)</sup>, <strong>Hugh Christopher Longuet-Higgins</strong><sup class="footnote-ref">(<a href="#fn2" id="fnref2">2</a>)</sup> in 1958 and subsequently generalized by <strong>Michael Berry</strong><sup class="footnote-ref">(<a href="#fn3" id="fnref3">3</a>)</sup> in 1984. This phase, although geometric, has measurable physical effects, for example in an interference experiment. An example of a geometric phase is <em>Foucault's pendulum</em>.<br/>
The most famous version of this experiment, designed by <strong>Léon Foucault</strong>, dates back to 1851 when the French physicist, with the aim of showing the rotation of the Earth around its axis, suspended a ball of 28 kilograms of lead coated with brass over a surface of sand using a 67 meter cable hooked to the top of the dome of the <em>Panthéon</em> in Paris. The plane of the pendulum was observed to rotate clockwise at approximately 11.3 degrees per hour, completing a full circle in 31.8 hours. A more refined examination shows that after 24 hours there is a difference between the initial and final orientation of the trace left on Earth which is equal to<a name='more'></a>
\[\alpha = -2\pi \sin \varphi\]
where $\varphi$ is the latitude.
<div align="center"><a href="https://commons.wikimedia.org/wiki/File:Parallel_Transport.svg" target="commons"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6SBrh7FSVnllFlNeUSXEOH4xfLlG8ZgN0PC2S1b2eI1mL-wW8n0aWP2YPQZ5lg4exe3SIuCpPxpLjHjtF7X5lR2V3Qbyz2nit7eD9OfSU7tA37jaG5ZYJJw8prqB40KgiMHokIEhCf6A/s1600/20190703-trasporto_parallelo.jpg" data-original-width="500" data-original-height="559" /></a></div>
In other words, if on a closed path I associate a vector to the initial position and see how its orientation varies along the entire path, when I return to the starting point at the end of the tour, I find that the final orientation is different from the initial one.<br/>
All this to say that even black holes are subject to the existence of a Berry phase under the action of adiabatic variations of supergravity, which, as the name suggests, is linked to string theory and supersymmetry. And perhaps, then, it is no coincidence that this effect is practically impossible to measure for a black hole, an object that is itself difficult to detect...
<div id="box">de Boer, J., Papadodimas, K., &amp; Verlinde, E. (2009). Black hole berry phase. <em>Physical review letters</em>, 103(13), 131301. doi:<a href="https://doi.org/10.1103/PhysRevLett.103.131301" target="doi">10.1103/PhysRevLett.103.131301</a> (<a href="https://arxiv.org/abs/0809.5062" target="arxiv">arXiv</a>)</div>
<hr/>
<section class="footnotes">
<ol class="footnotes-list"><li id="fn1" class="footnote-item">Pancharatnam, S. (1956, December). Generalized theory of interference and its applications. In <em>Proceedings of the Indian Academy of Sciences-Section A</em> (Vol. 44, No. 6, pp. 398-417). Springer India. doi:<a href="https://doi.org/10.1007/BF03046050" target="doi">10.1007/BF03046050</a>. <a href="#fnref1" class="footnote-backref">↩︎</a></li>
<li id="fn2" class="footnote-item">Longuet-Higgins, H. C., Öpik, U., Pryce, M. H. L., &amp; Sack, R. A. (1958). Studies of the Jahn-Teller effect. II. The dynamical problem. <em>Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences</em>, 244(1236), 1-16. doi:<a href="https://doi.org/10.1098/rspa.1958.0022" target="doi">10.1098/rspa.1958.0022</a>. <a href="#fnref2" class="footnote-backref">↩︎</a></li>
<li id="fn3" class="footnote-item"><p>Berry, M. V. (1984). Quantal phase factors accompanying adiabatic changes. <em>Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences</em>, 392(1802), 45-57. doi:<a href="https://doi.org/10.1098/rspa.1984.0023" target="doi">10.1098/rspa.1984.0023</a>. <a href="#fnref3" class="footnote-backref">↩︎</a></li></ol>
</section></description><link>http://docmadhattan.fieldofscience.com/2021/11/berry-phase-black-hole.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6SBrh7FSVnllFlNeUSXEOH4xfLlG8ZgN0PC2S1b2eI1mL-wW8n0aWP2YPQZ5lg4exe3SIuCpPxpLjHjtF7X5lR2V3Qbyz2nit7eD9OfSU7tA37jaG5ZYJJw8prqB40KgiMHokIEhCf6A/s72-c/20190703-trasporto_parallelo.jpg" height="72" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-8579089147002653970</guid><pubDate>Sat, 20 Nov 2021 19:10:00 +0000</pubDate><atom:updated>2021-11-20T20:10:00.192+01:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">erno rubik</category><category domain="http://www.blogger.com/atom/ns#">marvel comics</category><category domain="http://www.blogger.com/atom/ns#">mathemaics</category><category domain="http://www.blogger.com/atom/ns#">spider-man</category><category domain="http://www.blogger.com/atom/ns#">superheroes</category><title>Spider-man's magical snake</title><description><div align="center"><img alt="" border="0" data-original-height="310" data-original-width="636" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgDphEQXJRgaUZv9pE44eB_kYfGZb74rxqHVw5V9mWCWTw6_vRKObaVvKE__GpPVP6sTx6qfbKxexCtrUjn9j75gxf1BAH9sgejEelKpnxtUgC7EpNfxk1lhB4gM91iwqv_pT4RA1REhY/s0/20211120-spiderman_snake.jpg"/></div>
<a href="https://en.wikipedia.org/wiki/Ern%C5%91_Rubik" target="wiki" class="wiki"><strong>Ernő Rubik</strong></a> is one of the best known puzzle creators of the last 45 years: his best known puzzle, the <em>Rubik's cube</em>, was invented in 1974 and then marketed first as <em>Hungarian Magic Cube</em> in 1977 and then as <em>Rubik's Cube</em> in 1980. Rubik designed a second puzzle, dates to 1981, also based on the same principle of the <em>Cube</em>. The puzzle also had an exceptional testimonial, Spider-Man, in a one-page story: <em>The mystery of the museum snakes</em>. During the story, Spider-Man used the puzzle as the best trap to catch a gang of thieves.<br/>
But what is this new puzzle? Let's read it in the words of its creator:<a name='more'></a>
<blockquote><a href="https://en.wikipedia.org/wiki/Rubik%27s_Snake" target="wiki" class="wiki">The snake</a> is not a problem to be solved; it offers infinite possibilities of combination. It is a tool to test out ideas of shape in space. Speaking theoretically, the number of the snake's combinations is limited. But speaking practically, that number is limitless, and a lifetime is not sufficient to realize all of its possibilities.</blockquote>
Snake is made of 24 prisms, lined up in a row with alternate orientation (up and upside down). Each prism can assume 4 different positions, each with a 90° deviation. Prisms usually have alternating colors.<br/>
The number of different forms that Snake can take is at least $4^{23} = 70368744177664$, over than 70 trillion. But the real number of shapes is lower, because some configurations are spatially impossible, since they would require more than one prism to occupy the same region of space.
<div align="center" style="padding-top: 5px;"><iframe width="560" height="315" src="https://www.youtube.com/embed/LX5k3afEwpc" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div>
<div id="caption"><img src='https://i.postimg.cc/5tLbrWVv/20211120-spiderman-rubik-snake-mystery.jpg' border='0' alt='20211120-spiderman-rubik-snake-mystery'/><br/>via <a href="https://www.flickr.com/photos/littlestuffedbull/3168201339/">flickr</a></div></description><link>http://docmadhattan.fieldofscience.com/2021/11/spider-man-erno-rubik-snake.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgDphEQXJRgaUZv9pE44eB_kYfGZb74rxqHVw5V9mWCWTw6_vRKObaVvKE__GpPVP6sTx6qfbKxexCtrUjn9j75gxf1BAH9sgejEelKpnxtUgC7EpNfxk1lhB4gM91iwqv_pT4RA1REhY/s72-c/20211120-spiderman_snake.jpg" height="72" width="72"/><thr:total>1</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-4809716885148815176</guid><pubDate>Fri, 19 Nov 2021 19:00:00 +0000</pubDate><atom:updated>2021-11-19T20:00:00.205+01:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">climate change</category><category domain="http://www.blogger.com/atom/ns#">earth</category><category domain="http://www.blogger.com/atom/ns#">geophysics</category><category domain="http://www.blogger.com/atom/ns#">global warming</category><title>Earth's albedo and global warming</title><description><div class="pic right" style="width:35%;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisQpzwokfBJ_-gnZP1axuRpQvtLCoJoqhz64BqJ5ESLk-OPEnWIpGa2KlQWO8yJnoOGF2my5hEnu-z5szIY-r-eEJpXQqn_vZ18O1qWITtd8KaPzOLZBmvSr7-mZnKn4uHTMwM2pKLWo4/s0/20211025-hot_earth.jpg" /></div>
<blockquote>It's actually quite concerning. For some time, many scientists had hoped that a warmer Earth might lead to more clouds and higher albedo, which would then help to moderate warming and balance the climate system. But this shows the opposite is true.</blockquote>
In this way <strong>Edward Schwieterman</strong><sup class="footnote-ref">(<a href="#fn1" id="fnref1">1</a>)</sup> commented the result of a new paper about the Earth's climate.
But first of all we must say what is <a href="https://en.wikipedia.org/wiki/Albedo" target="wiki">albedo</a>:
<blockquote>(...) is the measure of the diffuse reflection of solar radiation out of the total solar radiation and measured on a scale from 0, corresponding to a black body that absorbs all incident radiation, to 1, corresponding to a body that reflects all incident radiation.</blockquote>
Now, a black body, an idealized opaque, non-reflective body, emits a <a href="https://en.wikipedia.org/wiki/Black-body_radiation" target="wiki">thermal electromagnetic radiation</a> that we could estimate also for the Earth. If we modelled it as a perfect black body, we find a temperature about 254.356 K, or -18.8 °C. But if we consider also, for example, the albedo, we can find a temperature of 245 K for albedo equals to 0.4, and a temperature of 255 K for albedo equals to 0.3. So, if the albedo decreases, Earth's temperature increases. And this is exactly what the researchers found.
<div id="box">Goode, P. R., Pallé, E., Shoumko, A., Shoumko, S., Montañes‐Rodriguez, P., &amp; Koonin, S. E. (2021). Earth's Albedo 1998–2017 as Measured From Earthshine. <em>Geophysical Research Letters</em>, 48(17), e2021GL094888. doi:<a href="https://doi.org/10.1029/2021GL094888">10.1029/2021GL094888</a></div>
<hr/>
<section class="footnotes">
<ol class="footnotes-list"><li id="fn1" class="footnote-item"><a href="https://news.agu.org/press-release/earth-is-dimming-due-to-climate-change/" target="news">Earth is dimming due to climate change</a> <a href="#fnref1" class="footnote-backref">↩︎</a></li></ol>
</section></description><link>http://docmadhattan.fieldofscience.com/2021/11/earths-albedo-and-global-warming.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisQpzwokfBJ_-gnZP1axuRpQvtLCoJoqhz64BqJ5ESLk-OPEnWIpGa2KlQWO8yJnoOGF2my5hEnu-z5szIY-r-eEJpXQqn_vZ18O1qWITtd8KaPzOLZBmvSr7-mZnKn4uHTMwM2pKLWo4/s72-c/20211025-hot_earth.jpg" height="72" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-2802566247236962894</guid><pubDate>Tue, 16 Nov 2021 19:00:00 +0000</pubDate><atom:updated>2021-11-16T20:00:00.207+01:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">cosmology</category><category domain="http://www.blogger.com/atom/ns#">fractals</category><category domain="http://www.blogger.com/atom/ns#">john nash</category><category domain="http://www.blogger.com/atom/ns#">nicolaas kuiper</category><category domain="http://www.blogger.com/atom/ns#">universe</category><title>Our flat, fractal universe</title><description>In order to evaluate the curvature of a space, we drawn a triangle and measure its internal angles. If the value is approximately 180°, the space is flat; if it is greater than 180 degrees, the space is like a sphere; if less than 180°, the space is a kind of saddle. To evaluate the curvature of a space, however, we need to find sufficiently large triangles: if we try to draw a triangle on the ground, it will most likely be a flat triangle, but if we try to draw a triangle, from space, with the extremes of the Sicily, we will have a spherical triangle. Similarly, for the universe, we must determine a triangle as large as possible. At this point we could take three stars and draw a triangle: the only complication is finding three stars that are at the same time from the moment the cosmic expansion began, and this thing is not exactly easy to determine. This forces us to examine a widespread signal that we are certain is from the same period in the universe timeline: the <a href="https://en.wikipedia.org/wiki/Cosmic_microwave_background" target="wiki">cosmic microwave background</a>.
<div align="center"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYXNIZ1-P_C9E-oyji1CEOZVWsttEmEO6Nsq-zfJqCPPsdtz7UJ0ubFDEKRJS8WCo5xlX3m2gHAspjvTXx9lPjnD2xteK6CR9JZtpdTNwTSeDwvaPfYWnr3rHnzd44oM6ZCY4mW7f5SUQ/s500/20181212-microwave_triangle.jpg" data-original-width="500" data-original-height="552" /></div><a name='more'></a>
Examining this radiation led us to the conclusion that the universe is flat<sup id="fnref:flat">(<a class="footnote-ref" href="#fn:flat" rel="footnote">1</a>)</sup>, because taking a triangle on this map, it turns out to be a flat triangle. The cosmic background radiation, however, dates back to the so-called epoch of recombination, so it would be more correct to say that the universe <strong>was</strong> flat. Whether it has always been flat in the course of its evolution or whether it is now is a completely different story. Furthermore, it is not certain that a flat universe cannot have a curved shape: in the 1950s <strong>John Nash</strong> and <strong>Nicolaas Kuiper</strong> suggested the existence of a particular square flat torus, such as the <em>Pac-Man</em> plank, which was finally <a href="http://docmadhattan.fieldofscience.com/2012/04/flat-torus-in-three-dimensional-space.html" target="doc">visualized as a three-dimensional surface</a> in 2012<sup id="fnref:thorus">(<a class="footnote-ref" href="#fn:thorus" rel="footnote">2</a>)</sup>. So the universe could have a toroidal shape and be flat just like the figures of Nash and Kuiper, but it should also have a fractal structure, which at the moment has not been verified, but which would not be incompatible with cosmic inflation.<br/>
However, I wrote all this round of words to introduce an interesting article on arXiv, <em>The equivalence principle and QFT: Can a particle detector tell if we live inside a hollow shell?</em>:
<blockquote>We show that a particle detector can distinguish the interior of a hollow shell from flat space for switching times much shorter than the light-crossing time of the shell, even though the local metrics are indistinguishable. This shows that a particle detector can read out information about the non-local structure of spacetime even when switched on for scales much shorter than the characteristic scale of the non-locality.</blockquote>
But we must not forget that the portion of the universe that we are able to observe is much smaller than it could be, in particular if the model of cosmic inflation were correct. This would mean that the universe globally could easily not be flat, in spite of the flatness of the universe that we can observe and we should consider local, despite its dimension are a few tens of billions of light years.
<hr/>
<ol><li id="fn:flat">de Bernardis, P., Ade, P. A., Bock, J. J., Bond, J. R., Borrill, J., Boscaleri, A., ... &amp; Ferreira, P. G. (2000). A flat Universe from high-resolution maps of the cosmic microwave background radiation. Nature, 404(6781), 955. doi:<a href="https://doi.org/10.1038/35010035" target="doi">10.1038/35010035</a> (<a href="https://arxiv.org/abs/astro-ph/0004404" target="arxiv">arXiv</a>)&#160;<a class="footnote-backref" href="#fnref:flat" rev="footnote" title="Jump back to footnote 1 in the text">&#8617;</a></li>
<li id="fn:thorus">Borrelli, V., Jabrane, S., Lazarus, F., &amp; Thibert, B. (2012). Flat tori in three-dimensional space and convex integration Proceedings of the National Academy of Sciences doi:<a href="http://dx.doi.org/10.1073/pnas.1118478109" target="doi">10.1073/pnas.1118478109</a>&#160;<a class="footnote-backref" href="#fnref:thorus" rev="footnote" title="Jump back to footnote 2 in the text">&#8617;</a></li></ol></description><link>http://docmadhattan.fieldofscience.com/2012/11/our-flat-fractal-universe.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYXNIZ1-P_C9E-oyji1CEOZVWsttEmEO6Nsq-zfJqCPPsdtz7UJ0ubFDEKRJS8WCo5xlX3m2gHAspjvTXx9lPjnD2xteK6CR9JZtpdTNwTSeDwvaPfYWnr3rHnzd44oM6ZCY4mW7f5SUQ/s72-c/20181212-microwave_triangle.jpg" height="72" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-5417645704925162568</guid><pubDate>Sat, 13 Nov 2021 19:30:00 +0000</pubDate><atom:updated>2021-11-13T20:30:00.253+01:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">bob de groot</category><category domain="http://www.blogger.com/atom/ns#">comics</category><category domain="http://www.blogger.com/atom/ns#">europe comics</category><category domain="http://www.blogger.com/atom/ns#">leonardo da vinci</category><category domain="http://www.blogger.com/atom/ns#">philippe liegeois</category><category domain="http://www.blogger.com/atom/ns#">review</category><title>Leonardo, a comics genius</title><description><div align="center"><img src="https://i.postimg.cc/SK9GgCzx/20211106-leonardo-europe-comics.jpg" alt="20211106-leonardo-europe-comics"/></div>
<em>Léonard</em> by <strong>Turk</strong> & <strong>De Groot</strong> is a particularly long-lived humorous series: after having made its debut in 1975 on the pages of <em>Achille Talon</em> magazine, it was subsequently serialized starting from March 1977 in a series of volumes, now in its 51st edition. June 2020. Now the first two volumes are also available in english thanks to the digital edition of <em>Europe Comics</em> (<a href="https://www.europecomics.com/album/1-leonardo-the-genius/" target="europe">volume 1</a> and <a href="https://www.europecomics.com/album/2-leonardo-still-genius/" target="europe">volume 2</a>).<br/>
Originally <strong>Bob De Groot</strong>, the screenwriter, had imagined an inventor named Methuselah as the long-lived biblical character, but later opted to focus on <strong>Leonardo da Vinci</strong>. On the other hand, this initial idea leaves traces in the drawings of <strong>Philippe Liégeois</strong>, known as Turk: Leonardo, in fact, is outlined with a white bum constantly in motion.<br/>
The two authors focus above all on Leonardo the inventor, a choice that allows them to show the scientist's variety of interests and his brilliant and multifaceted mind. With an irreverent spirit, the two belgian cartoonists create a series of gags, some of a purely visual page, others developed over a dozen pages, in which one laughs not only with, but also about Leonardo.<br/>
A heartfelt tribute to one of the greatest geniuses in the history of Italy and the world.<a name='more'></a>
<div align="center" class="pic"><img src="https://i.postimg.cc/cL2m7XCz/20211106-leonardo-car-europe-comics.jpg" alt="20211106-leonardo-car-europe-comics"/></div>
I did not choise the strip above at random. The two authors, in fact, have simply transposed a Leonardo's project present in the <em>Codex Atlanticus</em> into modern terms. The project presents a chariot with a kind of motor, that is a series of gears that allow the wheels to move, and the equivalent of the rudder of boats, which had the purpose of changing the direction of the device (a sort of proto-steering wheel). To supply energy to the motor we find a rubber band: I like to remember that Hooke's law of elastic force was enunciated by <strong>Robert Hooke</strong> only in the seventeenth century.<br/>
In 2004, the <em>Museum of the History of Science</em> in Florence created a miniature and, apparently, working version of Leonardo's car, as we see in the video below:
<div align="center" style="padding-top: 5px;"><iframe width="560" height="315" src="https://www.youtube.com/embed/a2qeZrejZp0" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div></description><link>http://docmadhattan.fieldofscience.com/2021/11/leonardo-comics-genius.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://img.youtube.com/vi/a2qeZrejZp0/default.jpg" height="72" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-5908517540302149143</guid><pubDate>Tue, 09 Nov 2021 19:00:00 +0000</pubDate><atom:updated>2021-11-09T20:00:00.201+01:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">biology</category><category domain="http://www.blogger.com/atom/ns#">chaos theory</category><category domain="http://www.blogger.com/atom/ns#">logistic map</category><category domain="http://www.blogger.com/atom/ns#">mathematics</category><category domain="http://www.blogger.com/atom/ns#">robert may</category><title>A chaotic balance</title><description>Our mathematical history begins in a discipline that, apparently, has very little to do with mathematics: biology. In 1975 on the journal <em>Nature</em> <strong>Robert May</strong>, an australian ecologist, publishes a review article with a rather indicative title: <em>Simple mathematical models with very complicated dynamics</em><sup class="footnote-ref">(<a href="#fn1" id="fnref1">1</a>)</sup>. The heart of the paper is the following equation:
\[x_{t+1} = a x_t (1 - x_t)\]
The equation, or <em><strong>logistic map</strong></em>, this is its name, describes the rate of change of a population in function of the parameter $t$ (the time), that varies in a discrete rather than continuous way, while $a$ is a constant that identifies the growth rate of a population. Insteed $x_t$ is the ratio between the existing population and the maximum possible population at time $t$.<br/>
The model thus described is deterministic, i.e. the population at instant 0 determines the population at subsequent instants. The equation predicts the existence of a stationary state, i.e. a situation in which the population at time $t + 1$ is equal to the population at time $t$. This state is stable, that is, it is maintained for a sufficiently long time, but only for $a$ lower than or equal to 3. However when the growth rate exceeds this value, the size of the population begins to oscillate between 0 and 1, apparently in a random way. But if we observe carefully, we notice small more or less periodic recurrences, which show how the behavior of the equation is actually chaotic.<a name='more'></a>
<div align="center" id="caption"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPAG9xDxYA29mM5YWtv3eRH9FAN2Y5BHaCXgFv7n3dcn0ofxN4wzRz12Au9GIX6uB4aZPNLFchadbB0b4r6ZObGfH2556oV0H3ai7b9ygqMcr9w1uPryQiB2n1_rBlTO7Nls4XybB3yRA/s450/20200312-chaos_vs_random.png" data-original-width="611" data-original-height="393" /><br/>
Differences between chaotic and random behavior - via <a href="https://geoffboeing.com/2015/03/chaos-theory-logistic-map/" target="geoff"><strong>Geoff Boeing</strong></a>)</div>
And because the equation describes the growth of a population quite well, the conclusion is quite obvious: equilibrium, in nature, does not exist, or at least there is no stable condition in nature.
It is also possible to clearly see the so-called <a href="http://docmadhattan.fieldofscience.com/2021/10/butterflies-hurricanes-and-pools.html" target="doc"><em>butterfly effect</em></a>. This is typically told with the story of the flapping butterfly in Brazil that generates a tornado in New York. In mathematical terms, the flapping of the butterfly's wings is a variation, even a small one, of the initial conditions, for example of the population size at time 0. For example, a variation of just 1/10000 generates a variation that begins to become evident from the 30th generation.
<div align="center" id="caption"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkCRns5kTwclmE1ek00dH0ljNIZaDOcWXOV4VNDHRv8WDBgfyronXjkJFxk18dp6C4Q08rIGWeyBWabMr4xVMy45k3In_TsV2h8TkFou2LfYZ5bE_rHH_DEt_uUepmAzbvCjAFojkdQUU/s450/20200312-butterfly_effect.png" data-original-width="606" data-original-height="393" /><br/>
The butterfly effect in a single plot - via <a href="https://geoffboeing.com/2015/03/chaos-theory-logistic-map/" target="geoff"><strong>Geoff Boeing</strong></a>)</div>
In fact, May had started to deal with this topic in 1974 when <em>Biological Populations with Nonoverlapping Generations: Stable Points, Stable Cycles, and Chaos</em><sup class="footnote-ref">(<a href="#fn2" id="fnref2">2</a>)</sup> was published on <em>Science</em>. In this paper he presented some simple models of the growth of biological populations. In addition to some differential equations, May also presented a variation on the logistic map.<br/>
There are many examples of the presence of chaos in the most disparate systems, for example in the three-body problem, in general all of them can be studied within the theory of chaos.
<hr/>
<section class="footnotes">
<ol class="footnotes-list"><li id="fn1" class="footnote-item">May, R. M. (1976). Simple mathematical models with very complicated dynamics. Nature, 261(5560), 459-467. doi:<a href="https://doi.org/10.1038/261459a0" target="doi">10.1038/261459a0</a> <a href="#fnref1" class="footnote-backref">↩︎</a></li>
<li id="fn2" class="footnote-item">May, R. M. (1974). Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos. Science, 186(4164), 645-647. doi:<a href="https://doi.org/10.1126/science.186.4164.645" target="doi">10.1126/science.186.4164.645</a> <a href="#fnref2" class="footnote-backref">↩︎</a></li></ol>
</section></description><link>http://docmadhattan.fieldofscience.com/2012/10/ray-bradbury-and-butterfly-effects.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPAG9xDxYA29mM5YWtv3eRH9FAN2Y5BHaCXgFv7n3dcn0ofxN4wzRz12Au9GIX6uB4aZPNLFchadbB0b4r6ZObGfH2556oV0H3ai7b9ygqMcr9w1uPryQiB2n1_rBlTO7Nls4XybB3yRA/s72-c/20200312-chaos_vs_random.png" height="72" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-8294707129374887427</guid><pubDate>Sat, 06 Nov 2021 19:30:00 +0000</pubDate><atom:updated>2021-11-06T20:30:00.220+01:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">bill molno</category><category domain="http://www.blogger.com/atom/ns#">comics</category><category domain="http://www.blogger.com/atom/ns#">joe gill</category><category domain="http://www.blogger.com/atom/ns#">laika</category><category domain="http://www.blogger.com/atom/ns#">review</category><category domain="http://www.blogger.com/atom/ns#">sputnik</category><title>Travelling on Sputnik 2</title><description><div align="center" class="pic"><img alt="" border="0" data-original-height="420" data-original-width="700" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGvDXYCZpxa8bYwUBZRLBAR_SrKLyGJyreZbQXTrPPs9ipWs05sadXH1PBMfsbO8CiUUXqEaoPGzGYANnw2xbFD8lM4brJfON7g7xqss-KLQDRpOwHilvKmzzRhT_tqZke32dokuhoeWE/s0/20211106-laika_comics.jpg"/></div>
<a href="https://en.wikipedia.org/wiki/The_Mysterious_Traveler" target="wiki"><em>The Mysterious Traveler</em></a> was a multimedia project as it could only be before the advent of the world wide web: it was a radio program, which started on the 5th december, 1943 and went on, with mixed fortunes, until the 16th september, 1952; an anthological magazine (on which <strong>Ray Bradbury</strong> among others wrote short stories), published between 1951 and 1952; and a comic book, also anthological, of which 13 issues were released every two months between august 1956 and june 1959 (not counting the two volumes of 1985). Published by <em>Charlton</em>, it had <strong>Steve Ditko</strong> as its leading artist (he was not the only one, anyway) and, like the other two products that preceded it, contained fantasy and science fiction stories with a hint of crime.<br/>
The protagonist of <em>Tales of the Mysterious Traveler</em> (this is the name of the comic book) is a... mysterious traveler in a raincoat and with a wide-brimmed hat pulled over his eyes. The mysterious traveler moved from the most disparate corners of the universe and there was no barrier capable stopping him, neither the boiling heart of a planet, nor the cold and dark desolation of outer space.<br/>
<a href="https://comicbookplus.com/?dlid=18064" target="comics">On #12</a>, the mysterious traveler is sent (perhaps) by <strong>Joe Gill</strong> and <strong>Bill Molno</strong> aboard <em>Sputnik</em> 2. This was the second object launched by the Soviets into space, and the first to bring a living being on board, <a href="http://docmadhattan.fieldofscience.com/2017/11/sputnik-2-or-laika-our-hero.html" target="doc">the dog <strong>Laika</strong></a>.<a name='more'></a>
<div align="center" class="pic"><img src="https://i.postimg.cc/1zzSk0Qs/20211106-mysterious-traveler-laika.jpg" alt="20211106-mysterious-traveler-laika"/></div>
<em>Sputnik</em> 2 had been launched on the 3rd november, 1957 and Laika had been chosen among various strays, proving to possess the qualities for the mission that was imposed on her. The mission, then, was practically suicidal: the soviets had not foreseen any system for the recovery of the dog. In partial defense it could be said that the time available to them was limited: under pressure from the then soviet president, <strong>Nikita Khrushchev</strong>, <em>Sputnik</em> 2 with Laika on board had to arrive by the end of 1957 to be able to worthily celebrate the fortieth anniversary of the october revolution.<br/>
In any case, as noticed by passers in the two-pages story <em>I was there!</em>, the dog died because of her heart that couldn't stand the stress of the journey. The final cartoon of the short story is certainly consoling, but it does not cancel the outcome of Laika's life, nor the uselessness of this sacrifice, as Laika's trainer <strong>Oleg Gazenko</strong> recalled:
<blockquote>We haven't learned enough from the mission to justify the dog's death.</blockquote>
<div align="center" class="pic"><img src="https://i.postimg.cc/43FGsKft/20211106-mysterious-traveler-laika-end.jpg" alt="20211106-mysterious-traveler-laika-end"/></div></description><link>http://docmadhattan.fieldofscience.com/2021/11/travelling-on-sputnik-2.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGvDXYCZpxa8bYwUBZRLBAR_SrKLyGJyreZbQXTrPPs9ipWs05sadXH1PBMfsbO8CiUUXqEaoPGzGYANnw2xbFD8lM4brJfON7g7xqss-KLQDRpOwHilvKmzzRhT_tqZke32dokuhoeWE/s72-c/20211106-laika_comics.jpg" height="72" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-1479471700441304047</guid><pubDate>Thu, 04 Nov 2021 17:00:00 +0000</pubDate><atom:updated>2021-11-09T20:47:03.979+01:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">astronomy</category><category domain="http://www.blogger.com/atom/ns#">chemistry</category><category domain="http://www.blogger.com/atom/ns#">eso</category><title>Fluorine in the early universe</title><description>Using ALMA (<em>Atacama Large Millimeter/submillimeter Array</em>), a team of astronomers has detected fluorine in a galaxy far,
far away: its light reached us after a journey of over 12 billion years.<br/>
What we see of the NGP-190387 galaxy is a large cloud of gas crystallized at the time when the universe was only 1.4 billion years old. And since stars shed chemical elements into their surroundings only when they reach the end of their life, which generally ends explosively, the detection of fluorine in the gases of NGP-190387 implies that the stars in the galaxy must have lived relatively short lives. In particular these characteristics are possessed by the Wolf–Rayet stars.<br/>
Furthermore, the levels of fluorine in NGP-190387 (the first galaxy after the Milky Way where this chemical element was observed) are comparable to those of our galaxy, with the difference that the latter is older than a dozen and more than billions of years compared to NGP-190387.
<blockquote>We have shown that Wolf–Rayet stars, which are among the most massive stars known and can explode violently as they reach the end of their lives, help us, in a way, to maintain good dental health!
<hr/>
- <strong>Maximilien Franco</strong> from the University of Hertfordshire in the UK</blockquote>
<div align="center" class="pic"><iframe width="560" height="315" sandbox="allow-same-origin allow-scripts allow-popups" title="Fluorine in the Universe" src="https://peertube.uno/videos/embed/3c45aa93-fb17-4b85-9a8b-8f097bdbb104" frameborder="0" allowfullscreen></iframe></div>
<small>(<a href="https://www.eso.org/public/unitedkingdom/news/eso2115/?lang" target="eso">ESO's press release</a>)</small></description><link>http://docmadhattan.fieldofscience.com/2021/11/fluorine-in-early-universe.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-4907943056205495504</guid><pubDate>Sun, 31 Oct 2021 20:00:00 +0000</pubDate><atom:updated>2021-10-31T21:00:00.209+01:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">astronomy</category><category domain="http://www.blogger.com/atom/ns#">debris disk</category><category domain="http://www.blogger.com/atom/ns#">fomalhaut</category><category domain="http://www.blogger.com/atom/ns#">halloween</category><category domain="http://www.blogger.com/atom/ns#">hubble</category><title>The space eye of Sauron</title><description><div align="center" class="pic"><img alt="" border="0" data-original-height="475" data-original-width="1000" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYqt6rCuFAvJOl1LvczE_Qwm8S4bi699FLAw7snaA70E1-Cv7GhPCfl9vOziD1t4osgVbDsSUoPmP1xrw5KxMSTd-nAfHezZAFv9lAi_owcBd0MODu0DkBWyi6Qar3TVEqr7ZTcqKE-F0/s0/fomalhaut-occhio_sauron.jpg"/></div>
When the first image of the black hole, M87*, was released, several memes circulated online that repositioned the photo in different contexts. One of the best known was the one that placed M87* in the center of Sauron's eye as it was displayed in <strong>Peter Jackson</strong>'s <em>The Lord of the Rings</em> trilogy.<br/>
The photo I present above, however, taken in 2008 by the <em>Hubble Space Telescope</em> is much more reminiscent of the evil eye of Sauron. It represents the debris disk around the star <a href="https://en.wikipedia.org/wiki/Fomalhaut" target="wiki" class="wiki">Fomalhaut</a>, a white star in the constellation of Piscis Austrinus approximately 25 light years away. In 2008, an exoplanet was also discovered, Fomalhaut b (also known as Dagon, a perfect name for Halloween parties!), although there are still doubts about its existence (probably it does not exist, at least not yet).<br/>
The curiosity about this star is that the protagonist of <strong>Stanislaw Lem</strong>'s <em>Return from the Universe</em> returns to Earth after a space exploration trip right around Fomalhaut: the book is dated 1961, almost fifty years before astronomers discovered clues about the possible existence of Dagon.</description><link>http://docmadhattan.fieldofscience.com/2017/06/time-travel.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYqt6rCuFAvJOl1LvczE_Qwm8S4bi699FLAw7snaA70E1-Cv7GhPCfl9vOziD1t4osgVbDsSUoPmP1xrw5KxMSTd-nAfHezZAFv9lAi_owcBd0MODu0DkBWyi6Qar3TVEqr7ZTcqKE-F0/s72-c/fomalhaut-occhio_sauron.jpg" height="72" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-3436801321330149355</guid><pubDate>Tue, 26 Oct 2021 18:53:00 +0000</pubDate><atom:updated>2021-11-09T10:48:42.847+01:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">abstract</category><category domain="http://www.blogger.com/atom/ns#">climate change</category><category domain="http://www.blogger.com/atom/ns#">earth</category><category domain="http://www.blogger.com/atom/ns#">global warming</category><title>Total's responses to global warming</title><description><div class="pic right" style="width:35%;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisQpzwokfBJ_-gnZP1axuRpQvtLCoJoqhz64BqJ5ESLk-OPEnWIpGa2KlQWO8yJnoOGF2my5hEnu-z5szIY-r-eEJpXQqn_vZ18O1qWITtd8KaPzOLZBmvSr7-mZnKn4uHTMwM2pKLWo4/s0/20211025-hot_earth.jpg" /></div>
<blockquote>Building upon recent work on other major fossil fuel companies, we report new archival research and primary source interviews describing how Total responded to evolving climate science and policy in the last 50 years. We show that Total personnel received warnings of the potential for catastrophic global warming from its products by 1971, became more fully informed of the issue in the 1980s, began promoting doubt regarding the scientific basis for global warming by the late 1980s, and ultimately settled on a position in the late 1990s of publicly accepting climate science while promoting policy delay or policies peripheral to fossil fuel control. Additionally, we find that Exxon, through the International Petroleum Industry Environmental Conservation Association (IPIECA), coordinated an international campaign to dispute climate science and weaken international climate policy, beginning in the 1980s. This represents one of the first longitudinal studies of a major fossil fuel company's responses to global warming to the present, describing historical stages of awareness, preparation, denial, and delay.</blockquote>
<div id="box">Bonneuil, C., Choquet, P. L., &amp; Franta, B. (2021). Early warnings and emerging accountability: Total’s responses to global warming, 1971–2021. <em>Global Environmental Change</em>, 102386. doi:<a href="https://doi.org/10.1016/j.gloenvcha.2021.102386" target="doi">10.1016/j.gloenvcha.2021.102386</a></div></description><link>http://docmadhattan.fieldofscience.com/2021/10/totals-responses-to-global-warming.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisQpzwokfBJ_-gnZP1axuRpQvtLCoJoqhz64BqJ5ESLk-OPEnWIpGa2KlQWO8yJnoOGF2my5hEnu-z5szIY-r-eEJpXQqn_vZ18O1qWITtd8KaPzOLZBmvSr7-mZnKn4uHTMwM2pKLWo4/s72-c/20211025-hot_earth.jpg" height="72" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-4194287659229562793</guid><pubDate>Wed, 20 Oct 2021 21:42:00 +0000</pubDate><atom:updated>2021-10-20T23:42:52.395+02:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">black hole</category><category domain="http://www.blogger.com/atom/ns#">radio astronomy</category><title>Rewind a black hole story</title><description><div class="caption" align="center"><img alt="" border="0" data-original-height="361" data-original-width="755" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjE1CjtsY5hFiOATk6qIL5jYV08Q3H78-hQNGykLK1LqG0eCnbvj7vElY34hHUkhAGBXRQ8tPMFVxEEkgnlnRPCp0zoE2SIuynjWPZpqnZOMx_nmZprYheAIKCsZfA1KxxKoQB1tzGrRpE/s0/20211020-black_hole_bubbles.jpg"/><br/>
Glass bubbles from black hole</div>
In terms of the length of human life, we can conclude that this is a bit impossible to reconstruct the story of a particular star. Observing all the star in the universe we can create a model about their evolution, but we observe with a great details cosmo only since a century or so. Now, thanks to a particular device, the <em>LoFar</em>, Low Frequency Array, a team of astronomers collected data about the last 100000 years of the black hole at the center of Nest200047.<br/>
LoFar is a radiotelescope that collects radiation produced by the oldest electrons that are in the neighbour of a cosmic object. In this way researchers can go literally back in time along the story of Nest200047*.<br/>
During its phases of activity, the black hole devours the surrounding material and in this process releases a large amount of energy, sometimes even in the form of jets of particles that move at the speed of light and emit radio waves. These jets generate bubbles of particles and magnetic fields which by expanding are able to heat and move the intergalactic medium that surrounds them, enormously influencing its evolution and therefore the rate at which stars are formed.<a name='more'></a>
<div align="center" class="caption"><img src='https://i.postimg.cc/ZRg6KMFX/20211020-back-in-time-black-hole.jpg' border='0' alt='20211020-back-in-time-black-hole'/><br/>
Back in time with the black hole</div>
Another unteresting discovery was the existence of thin filaments of gas that move at speeds close to that of light and magnetic fields that extend up to one million light years.<br/>
Researchers believe these filaments are the remnants of the first bubbles produced hundreds of millions of years ago by the black hole at the center of Nest200047 and are now breaking apart and mixing with the intergalactic medium. The study of these structures in the future will reveal important new details on the physical properties of intergalactic matter and on the physical mechanism that regulates the transfer of energy from bubbles to the external environment.
<div id="box">Brienza, M., Shimwell, T.W., de Gasperin, F. et al. A snapshot of the oldest active galactic nuclei feedback phases. <em>Nat Astron</em> (2021). doi:<a href="https://doi.org/10.1038/s41550-021-01491-0" target="doi">10.1038/s41550-021-01491-0</a></div></description><link>http://docmadhattan.fieldofscience.com/2021/10/rewind-black-hole-story.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjE1CjtsY5hFiOATk6qIL5jYV08Q3H78-hQNGykLK1LqG0eCnbvj7vElY34hHUkhAGBXRQ8tPMFVxEEkgnlnRPCp0zoE2SIuynjWPZpqnZOMx_nmZprYheAIKCsZfA1KxxKoQB1tzGrRpE/s72-c/20211020-black_hole_bubbles.jpg" height="72" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-3082524646077949447</guid><pubDate>Fri, 15 Oct 2021 19:50:00 +0000</pubDate><atom:updated>2021-10-16T18:58:38.975+02:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">chaos theory</category><category domain="http://www.blogger.com/atom/ns#">edward lorenz</category><category domain="http://www.blogger.com/atom/ns#">george david birkhoff</category><category domain="http://www.blogger.com/atom/ns#">mathematics</category><title>Butterflies, hurricanes and... pools!</title><description><blockquote>Chaos is nothing more than order seen from the opposite side.</blockquote>
This defintion by Fethry Duck in the italian story <em>Il mobile caotico</em> (<em>The chaotic furniture</em>) can be considered very centered on the heart of chaos. And the mathematical tool that we used to study it is the <strong>theory of chaos</strong>.
<div id="box" align="center"><strong>Flapping the wings</strong></div>
What best identifies chaos theory is the <em>butterfly effect</em>, which identifies in a simple and effective way the strong dependence of chaotic systems on initial conditions. The name was first used by <strong>Edward Lorentz</strong>, who published the first article on this effect in 1963<sup class="footnote-ref">(<a href="#fn1" id="fnref1">1</a>)</sup>.<br/>
The popular version of the butterfly effect goes something like this: <em>The flapping of a butterfly's wings in Brazil causes a hurricane in New York</em> and the use of the butterfly was probably suggested to Lorentz from <strong>Ray Bradbury</strong>'s 1952 short story <em>A sound of thunder</em> in which an unwary time traveler, stepping out of the path set by the travel agency and thus stepping on a butterfly, even manages to change the result of the last US presidential elections, allowing a fascist to become the most powerful man on the planet!<br/>
From a scientific point of view, one of the most typically chaotic problems is that of <strong>weather forecasts</strong>, because of the large amount of variables that are present. The appearance of chaotic behaviors, however, would not be so scientifically interesting if it were not for one of their particular characteristics: the fundamental laws that govern, for example, time are deterministic and individually easily solved, but by combining together a large number of such equations, not only the resolution of the system is more complicated, so much so that it is necessary to use electronic calculators, but also the solution shows a chaotic behavior graphically well identified by the <em>Lorentz attractors</em>:
<div align="center"><img alt="" border="0" data-original-height="309" data-original-width="500" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjW2R0ziAKbCzZIPX3gHlk7Z0mqVNiv0yGvym2P1yY6tPFt3q4hl6AivA3L9W8XADxMUYgb9lN22Ha4hnDo24Bkgh3XstYF3YBtpUZmTfytyAy6DPqhrwcheL3UH47vGxMQNA7ECQGr0Sw/s0/20160422-lorenz_attractor.jpg"/></div><a name='more'></a>
The image above shows the trend of a chaotic system. Its position is variable, even a lot, over time, but it has an interesting feature: the system oscillates around two stable points, the two attractors, for example good and bad weather, just to stay on the subject of weather forecasts, or two gravitational centers if we try to study the system of three bodies in space, such as the Sun, Earth and Moon.<br/>
Indeed the three-body problem is another typical example of a chaotic system, as emerged from the numerical resolution of the problem. Obviously the Sun-Earth-Moon does not show such ùchaotic patterns, but let's not forget that the solar system itself is much more complex than these three objects alone.<br/>
The central point of chaos theory is that, to obtain statistical behavior, it is not necessary to start from statistical laws, but it is the high number of variables that complicate the matter.
<div id="box" align="center"><strong>The statistical billiards</strong></div>
<div align="center" class="pic"><img src='https://i.postimg.cc/B6KMNmNg/20211014-bunimovich-billiard.jpg' border='0' alt='20211014-bunimovich-billiard'/></div>
An interesting mathematical system that exhibits chaotic behavior is <a href="https://en.wikipedia.org/wiki/Dynamical_billiards" target="wiki">dynamical billiards</a><sup class="footnote-ref">(<a href="#fn2" id="fnref2">2</a>)</sup>. As in real billiards, we have a table on which a ball is thrown. This, as in real billiards, will hit the edges bouncing according to the usual laws of billiards, but unlike the real one, there are no holes in which to fall or friction to slow down the motion of the ball, which will continue to move forever. Furthermore, a dynamical billiard table can also have edges with shapes different from the straight ones typical of the rectangle or even be multidimensional. What unites all these dynamical billiards is the chaotic behavior of the ball and the <a href="https://en.wikipedia.org/wiki/Ergodicity" target="wiki">ergodic</a> characteristic of its motion: the ball, in fact, sooner or later, will hit all points of the billiard's edge. This fact, however, does not make it easier to predict the behavior of the ball, on the contrary it complicates the prediction, precisely because the ball, and more generally a chaotic system, can do exactly what it likes according to the surrounding conditions.<br/>
But what somehow simplifies weather predictions, making them somehow more accurate, is an interesting result known as <em><strong>Birkhoff's ergodic theorem</strong></em>, discovered in 1931 by the american mathematician <strong>George David Birkhoff</strong>. The theorem states that, although it cannot exactly predict the trajectory of a ball in a dynamic pool, it is possible to accurately predict how much time the ball will spend in a given region of the table. For example, if we are observing a gas, then even if we are not able to say exactly where its particles will be found at all times, we will still be able to predict quantities such as pressure and temperature.
<div align="center" class="pic"><img src='https://i.postimg.cc/XJf9pmQT/20211214-wind-tree-model.jpg' border='0' alt='20211214-wind-tree-model'/></div>
Dynamical billiards, however, have not ceased to amaze mathematicians. Let's take the <em><strong>Ehrenfest model</strong></em>. Proposed in 1907 by <strong>Paul Ehrenfest</strong> and his wife <strong>Tatyana Afanasyeva</strong> to explain the second law of thermodynamics, it considers <em>N</em> particles in a container divided into two zones. The particles pass from one area to another independently according to a certain exchange rate. The two physicists, however, were not satisfied with this model and in 1912 proposed a variation of it, the <em>wind-tree model</em><sup class="footnote-ref">(<a href="#fn3" id="fnref3">3</a>)</sup>, that is a gas that moves inside an infinite container but with rectangular obstacles inside.<br/>
Well, in 2011 the two mathematicians <strong>Corinna Ulcigrai</strong> and <strong>Krzysztof Fraczek</strong> studied a generalized version of the model, obtaining an unexpected result<sup class="footnote-ref">(<a href="#fn4" id="fnref4">4</a>)</sup>: <strong>the trajectories were not ergodic</strong>! Therefore, complicating the situation does not necessarily lead to chaotic behavior.
<hr/>
<section class="footnotes">
<ol class="footnotes-list"><li id="fn1" class="footnote-item">Lorenz, E. N., 1963, Deterministic nonperiodic flow, Journal of the atmospheric sciences, vol.20, n.2, pp. 130-141 doi:<a href="https://dx.doi.org/10.1175/1520-0469(1963)020%3C0130:DNF%3E2.0.CO;2" target="doi">10.1175/1520-0469(1963)020&lt;0130:DNF&gt;2.0.CO;2</a> <a href="#fnref1" class="footnote-backref">↩︎</a></li>
<li id="fn2" class="footnote-item">Leggi anche <a href="https://plus.maths.org/content/chaos-billiard-table" target="math"><em>Chaos on the billiard table</em></a> di <strong>Marianne Freiberger</strong>. <a href="#fnref2" class="footnote-backref">↩︎</a></li>
<li id="fn3" class="footnote-item">P. and T. Ehrenfest, Begriffliche Grundlagen der statistischen Auffassung in der Mechanik <em>Encykl. d. Math. Wissensch</em>. IV 2 II, Heft 6, 90 S (1912). <a href="#fnref3" class="footnote-backref">↩︎</a></li>
<li id="fn4" class="footnote-item">Frączek, K., &amp; Ulcigrai, C. (2014). Non-ergodic $\mathbb {Z}$-periodic billiards and infinite translation surfaces. <em>Inventiones mathematicae</em>, 197(2), 241-298. doi:<a href="https://dx.doi.org/10.1007/s00222-013-0482-z" target="doi">10.1007/s00222-013-0482-z</a> <a href="#fnref4" class="footnote-backref">↩︎</a></li></ol>
</section></description><link>http://docmadhattan.fieldofscience.com/2021/10/butterflies-hurricanes-and-pools.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjW2R0ziAKbCzZIPX3gHlk7Z0mqVNiv0yGvym2P1yY6tPFt3q4hl6AivA3L9W8XADxMUYgb9lN22Ha4hnDo24Bkgh3XstYF3YBtpUZmTfytyAy6DPqhrwcheL3UH47vGxMQNA7ECQGr0Sw/s72-c/20160422-lorenz_attractor.jpg" height="72" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-5869122354246013085</guid><pubDate>Wed, 13 Oct 2021 18:55:00 +0000</pubDate><atom:updated>2021-10-13T20:55:52.253+02:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">asteroids</category><category domain="http://www.blogger.com/atom/ns#">astronomy</category><category domain="http://www.blogger.com/atom/ns#">eso</category><category domain="http://www.blogger.com/atom/ns#">solar system</category><title>42: A family portrait</title><description><div align="center" style="display: none;"><img alt="" border="0" data-original-height="300" data-original-width="600" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGJMy09h6nAc0zcpu59rKilpe9XwcISUDtQY_Xdl2MXBsH8OtwoyqgacGKa5mecNRwPrF0kRFYxwexxCE-6GM7eol22dffpy2UAGALbp8pxfkyqOy83xEY5oCTiorUNR5kERokOCIj6Z8/s0/20211013-42_asteroids_eso-title.jpg" /></div>
No, this is not the <em>towel day</em>, but what ESO released yesterday is undoubtedly something quite useful for any space tourist: a series of 42 detailed images of the largest asteroids in the solar system.<br/>
The main asteroid belt, located just beyond the orbit of Mars, is made up of rocky objects of various sizes, reaching up to 200 km in diameter, without forgetting the largest of all, Ceres and Vesta, respectively 940 and 520 kilometers in diameter.
The family portrait of the 42 asteroids was made using the Very Large Telescope:<a name='more'></a>
<div align="center" style="padding-top: 5px;"><img src='https://i.postimg.cc/4yRN0PpP/20211013-42-asteroids-eso.jpg' border='0' alt='20211013-42-asteroids-eso'/></div>
<small>(<a href="https://www.eso.org/public/news/eso2114/?lang" target="eso">ESO's press release</a>)</small></description><link>http://docmadhattan.fieldofscience.com/2021/10/42-family-portrait.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGJMy09h6nAc0zcpu59rKilpe9XwcISUDtQY_Xdl2MXBsH8OtwoyqgacGKa5mecNRwPrF0kRFYxwexxCE-6GM7eol22dffpy2UAGALbp8pxfkyqOy83xEY5oCTiorUNR5kERokOCIj6Z8/s72-c/20211013-42_asteroids_eso-title.jpg" height="72" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-8851814435551635719</guid><pubDate>Wed, 06 Oct 2021 18:00:00 +0000</pubDate><atom:updated>2021-10-06T20:00:00.156+02:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">banjamin list</category><category domain="http://www.blogger.com/atom/ns#">chemistry</category><category domain="http://www.blogger.com/atom/ns#">david macmillan</category><category domain="http://www.blogger.com/atom/ns#">nobel prize</category><category domain="http://www.blogger.com/atom/ns#">richard feynman</category><title>Nobel Prize in Chemistry 2021: A scent of Feynman</title><description>One of the most famous speech by <strong>Richard Feynman</strong> is <em>There's plenty of room at the bottom</em>:
<blockquote>Now comes the interesting question: How do we make such a tiny mechanism? I leave that to you. However, let me suggest one weird possibility. You know, in the atomic energy plants they have materials and machines that they can’t handle directly because they have become radioactive. To unscrew nuts and put on bolts and so on, they have a set of master and slave hands, so that by operating a set of levers here, you control the “hands” there, and can turn them this way and that so you can handle things quite nicely.</blockquote>
The idea is to manipulate molecules to build, for example, an electric engine, or a book, or something else. The most curious fact about the <a href="https://www.nobelprize.org/prizes/chemistry/2021/press-release/" target="nobel">Nobel Prize in Chemistry 2021</a> is that <strong>Johan Jarnestad</strong> has illustrated the work of <strong>Benjamin List</strong> and <strong>David MacMillan</strong> using a couple of workers, an image that, in a particular way, is very similar to Feynman's idea.
<div align="center" style="padding-top: 5px;"><img alt="" border="0" data-original-height="331" data-original-width="500" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEic3C2vGsJvjQ1g7wAeoVYLtk0lXs68aUH2AVRuyRu0OddjOPymfqURJOlotU-e78-44Yvyv8M2YHYWlp4k92DtBl2dqMt6_3ZgZZoWrxNaWrsyDA-ImaPETRuikVa8in-fuGEFJJ4kIKY/s0/20211006-chemistry2021-nobel_prize-jarnestad.jpg"/></div>
<blockquote>Building molecules is a difficult art. Benjamin List and David MacMillan are awarded the Nobel Prize in Chemistry 2021 for their development of a precise new tool for molecular construction: organocatalysis. This has had a great impact on pharmaceutical research, and has made chemistry greener.</blockquote>
I hope to write soon an article about Feynman and miniaturization obviously from the physics point of view.<br/>
<strong><em>Stay tuned!</em></strong></description><link>http://docmadhattan.fieldofscience.com/2021/10/nobel-prize-in-chemistry-2021-scent-of-feynman.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEic3C2vGsJvjQ1g7wAeoVYLtk0lXs68aUH2AVRuyRu0OddjOPymfqURJOlotU-e78-44Yvyv8M2YHYWlp4k92DtBl2dqMt6_3ZgZZoWrxNaWrsyDA-ImaPETRuikVa8in-fuGEFJJ4kIKY/s72-c/20211006-chemistry2021-nobel_prize-jarnestad.jpg" height="72" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-484395123667841339</guid><pubDate>Tue, 05 Oct 2021 20:58:00 +0000</pubDate><atom:updated>2021-10-05T22:58:59.328+02:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">giorgio parisi</category><category domain="http://www.blogger.com/atom/ns#">guido altarelli</category><category domain="http://www.blogger.com/atom/ns#">nobel prize</category><title>Giorgio Parisi: A Nobel for complex systems</title><description>The last time an italian was awarded the Nobel Prize in physics was in 2002: <strong>Roberto Giacconi</strong> for his pioneering research in the field of X-ray radiation from the universe. Another italian research that probably could win the Prize was <strong>Adalberto Giazotto</strong>, who designed the VIRGO interferometer, that with LIGOs shared the first observation of gravitational waves. The Swedish Academy decided to assign the Prize to three of the LIGO's founders, <strong>Rainer Weiss</strong>, <strong>Barry Barish</strong> and <strong>Kip Thorne</strong>. But this is not a great problem: after all, the Nobel Prize serves to emphasize personal contributions, but also to establish key points in the knowledge, and in this sense, the role of Italy had already been indicated as fundamental.<br/>
Today, however, a long-awaited award arrives: <strong>Giorgio Parisi</strong>, theoretical physicist, whose works have provided important contributions to field theory and statistical physics, <a href="https://www.nobelprize.org/prizes/physics/2021/press-release/" target="nobel">won the Nobel Prize in physics</a>
<blockquote>for the discovery of the interplay of disorder and fluctuations in physical systems from atomic to planetary scales</blockquote>
<div align="center"><img alt="" border="0" data-original-height="333" data-original-width="500" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXUHec4ULfT9u5C7xWN3vMM5MIuHeiIPQfRswJon4PUIWbxPKOZIzpZNPoRMVj2AutQqvzVIPP2JoVPNpJdyqgS-qyj3UMD9KDPaffgcRDIxbzIClquulTZhaxvAq4do5M4Wk0seHpY5E/s0/20211005-giorgio_parisi-nobel_prize.jpg"/></div><a name='more'></a>
During my PhD (we are talking about twenty years ago), there were two "mythical" italian theoretical physicists, <strong>Guido Altarelli</strong> and, in fact, Giorgio Parisi. The aura of myth of the pair was due to the then-known <em>Altarelli-Parisi equation</em> (later we discovered that the russian physicists <strong>Juri Lwowitsch Dokschizer</strong>, <strong>Vladimir Gribov</strong> and <strong>Lev Lipatov</strong>, more or less in the same years as the italians, had discovered a similar equation). <a href="https://en.wikipedia.org/wiki/DGLAP" target="wiki">The equation</a>, which is "only" the fundamental one in quantum chromodynamics (the branch of physics that describes quarks, in short).<br/>
The physics of the Nobel Prize in Parisi, on the other hand,
On the other hand, I explained the physics of Parisi's Nobel Prize <a href="https://it.wikinews.org/wiki/Giorgio_Parisi_vince_il_Premio_Nobel_per_la_Fisica_2021" target="wikin">on italian wikinews</a> and I translate it here:<br/>
The Nobel Prize's research papers are published between 1979 and the early 1980s relating to <a href="https://en.wikipedia.org/wiki/Spin_glass" target="wiki">spin glass</a>, a particular metal alloy in which iron atoms are randomly mixed within, for example, a grid of copper atoms.<br/>
Due to the presence of the iron atoms, the material changes its magnetic properties. Each of the iron atoms behaves like a small magnet, influenced by the other nearby iron atoms. In a usual magnet all spins point in the same direction, but in a spin glass some pairs point in the same direction, others in the opposite direction. Parisi, in 1979, showed how the use of a particular mathematical technique, the <a href="https://en.wikipedia.org/wiki/Replica_trick" target="wiki">replica trick</a>, allowed to solve the spin glass problem.<br/>
In particular, the papers dedicated to spin glass can be found below:
<div id="box">Parisi, G. (1979). Infinite number of order parameters for spin-glasses. <em>Physical Review Letters</em>, 43(23), 1754. doi:<a href="https://doi.org/10.1103/PhysRevLett.43.1754" target="doi">10.1103/PhysRevLett.43.1754</a><br/>
Parisi, G. (1980). Magnetic properties of spin glasses in a new mean field theory. <em>Journal of Physics A: Mathematical and General</em>, 13(5), 1887. doi:<a href="https://doi.org/10.1088/0305-4470/13/5/047" target="doi">10.1088/0305-4470/13/5/047</a><br/>
Parisi, G. (1983). Order parameter for spin-glasses. <em>Physical Review Letters</em>, 50(24), 1946. doi:<a href="https://doi.org/10.1103/PhysRevLett.50.1946" target="doi">10.1103/PhysRevLett.50.1946</a></div>
In recent years, Parisi has been involved in climate change
<div id="box">Benzi, R., Parisi, G., Sutera, A., & Vulpiani, A. (1982). Stochastic resonance in climatic change. <em>Tellus</em>, 34(1), 10-16. doi:<a href="https://doi.org/10.1111/j.2153-3490.1982.tb01787.x" target="doi">10.1111/j.2153-3490.1982.tb01787.x</a></div>
a field that we can consider strictly connected with the study of <a href="https://arxiv.org/abs/cond-mat/0205297" target="arxiv">complex systems</a>.<br/>
This part takes us directly to the other half of the 2021 Prize, shared by <strong>Syukuro Manabe</strong> and <strong>Klaus Hasselmann</strong> precisely for their research on complex systems, which brings us straight to chaos theory. I hope to write soon some articles about this subject in the next weeks.<br/>
<strong><em>Stay tuned!</em></strong></description><link>http://docmadhattan.fieldofscience.com/2021/10/giorgio-parisi-nobel-for-complex-systems.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXUHec4ULfT9u5C7xWN3vMM5MIuHeiIPQfRswJon4PUIWbxPKOZIzpZNPoRMVj2AutQqvzVIPP2JoVPNpJdyqgS-qyj3UMD9KDPaffgcRDIxbzIClquulTZhaxvAq4do5M4Wk0seHpY5E/s72-c/20211005-giorgio_parisi-nobel_prize.jpg" height="72" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-3579357070745665018</guid><pubDate>Thu, 30 Sep 2021 18:51:00 +0000</pubDate><atom:updated>2021-09-30T20:51:00.801+02:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">chameleon particle</category><category domain="http://www.blogger.com/atom/ns#">dark matter</category><category domain="http://www.blogger.com/atom/ns#">infn</category><title>Dark scent</title><description><div align="center" id="caption"><img alt="" border="0" data-original-height="420" data-original-width="518" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgELU3wi4TSRFSduPeXcfbRvs-j-OMZwwytol7Ds0pogRyvFvX7CG1jfNN-uHqgH5Mfpt5fmgssVPOX6w8v0d220S_Bgv6pAiQuGwOxnWyekqxqVSQCCCQKaV5uPT3cmQ4TTQjuLCeX5yg/s0/20210930-hand_of_creation-green_lantern.jpg"/><br/><em>The hand of creation</em> by <strong>John Byrne</strong> from <em>Green Lantern: Ganthet's Tale</em></div>
The <a href="http://www.xenon1t.org/" target="lab">XENON1T experiment</a> at <a href="http://w3.lnf.infn.it/" target="infn">Gran Sasso's laboratories</a> in Italy is a liquid xenon detector designed for serach of the mysterious dark matter. About one year ago researchers <a href="https://www.lngs.infn.it/en/news/xenon1t-excess-events" target="lngs">observed an excess of events</a>: 53 more than the 232 predicted<sup class="footnote-ref">(<a href="#fn1" id="fnref1">1</a>)</sup>.<br/>
There are several explanations: an unexpected noise' source; the passage of some axions, an hypothetical particle predicted by <a href="https://en.wikipedia.org/wiki/Peccei%E2%80%93Quinn_theory" target="wiki"><strong>Roberto Peccei</strong> and <strong>Helen Quinn</strong> in 1977</a>; some neutrinos that interact with matter in a new way.<br/>
Or dark matter's traces<sup class="footnote-ref">(<a href="#fn2" id="fnref2">2</a>)</sup>. There are two new articles suggesting this; in particular the second suggests that the detected excess in XENON1T is dued by chameleons<sup class="footnote-ref">(<a href="#fn3" id="fnref3">3</a>)</sup>.<br/>
The <a href="https://en.wikipedia.org/wiki/Chameleon_particle" target="wiki">chameleon</a> is an(other) hypothetical particle proposed in 2003 by <strong>Justin Khoury</strong> and <strong>Amanda Weltman</strong>, that couples to matter more weakly than gravity, and so a candidate for dark matter. It has a variable mass, so the hypothetical fifth force mediated by the chameleons can evade the constraints deduced by experiments on the equivalence principle. In this way chameleons could drive the observed acceleration of the universe's expansion, but it's very difficult to verify experimentally.
<hr/>
<section class="footnotes">
<ol class="footnotes-list"><li id="fn1" class="footnote-item">XENON collaboration. (2020). Excess electronic recoil events in XENON1T. <em>Physical Review D</em>, 102(7). doi:<a href="https://doi.org/10.1103/PhysRevD.102.072004" target="doi">10.1103/PhysRevD.102.072004</a> <a href="#fnref1" class="footnote-backref">↩︎</a></li>
<li id="fn2" class="footnote-item">Aboubrahim, A., Klasen, M., &amp; Nath, P. (2021). Xenon-1T excess as a possible signal of a sub-GeV hidden sector dark matter. <em>Journal of High Energy Physics</em>, 2021(2), 1-21. doi:<a href="https://doi.org/10.1007/JHEP02(2021)229" target="doi">10.1007/JHEP02(2021)229</a> <a href="#fnref2" class="footnote-backref">↩︎</a></li>
<li id="fn3" class="footnote-item">Vagnozzi, S., Visinelli, L., Brax, P., Davis, A. C., &amp; Sakstein, J. (2021). Direct detection of dark energy: the XENON1T excess and future prospects. <em>Physical Review D</em>, 104(6). doi:<a href="https://doi.org/10.1103/PhysRevD.104.063023" target="doi">10.1103/PhysRevD.104.063023</a> <a href="#fnref3" class="footnote-backref">↩︎</a></li></ol>
</section></description><link>http://docmadhattan.fieldofscience.com/2021/09/dark-scent.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgELU3wi4TSRFSduPeXcfbRvs-j-OMZwwytol7Ds0pogRyvFvX7CG1jfNN-uHqgH5Mfpt5fmgssVPOX6w8v0d220S_Bgv6pAiQuGwOxnWyekqxqVSQCCCQKaV5uPT3cmQ4TTQjuLCeX5yg/s72-c/20210930-hand_of_creation-green_lantern.jpg" height="72" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-6925185220423845724</guid><pubDate>Wed, 15 Sep 2021 15:00:00 +0000</pubDate><atom:updated>2021-09-15T17:00:00.191+02:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">asbtracts</category><category domain="http://www.blogger.com/atom/ns#">astrobiology</category><category domain="http://www.blogger.com/atom/ns#">astronomy</category><category domain="http://www.blogger.com/atom/ns#">exoplanets</category><title>The Case for Dwarf K Stars</title><description><div id="caption" align="center"><img src='https://i.postimg.cc/25vNcgny/20210914-61-cygni.jpg' border='0' alt='20210914-61-cygni' width="100%" /><br/>61 Cygni, a binary K-type star system - via <a href="https://commons.wikimedia.org/wiki/File:61_Cygni_Proper_Motion.gif" target="commons">commons</a></div>
The <a href="https://en.wikipedia.org/wiki/Main_sequence" target="wiki">stellar main-sequence</a> is a strip that cuts diagonally <a href="https://en.wikipedia.org/wiki/Hertzsprung%E2%80%93Russell_diagram" target="wiki">the Hertzsprung-Russell diagram</a>, a star's plot of stellar color versus brightness. The main feature of main-sequence stars is that they burn hydrogen. In this group the <a href="https://en.wikipedia.org/wiki/K-type_main-sequence_star" target="wiki">K dwarfs</a>, or orange dwarfs, are intermediate stars in size between red M stars (red dwarfs) and yellow G stars. Their mass is between 0.5 and 0.8 times the Sun's mass and surface temperature is bewteen 3900 and 5200 K.<br/>
In the last few years these type of stars have become particularly interesting to astronomers, as they appear to have the characteristics to host <em>life-as-we-know</em>:<a name='more'></a>
<blockquote>To be habitable, a world (planet or moon) does not need to be located in the stellar habitable zone (HZ), and worlds in the HZ are not necessarily habitable. Here, we illustrate how tidal heating can render terrestrial or icy worlds habitable beyond the stellar HZ. Scientists have developed a language that neglects the possible existence of worlds that offer more benign environments to life than Earth does. We call these objects “superhabitable” and discuss in which contexts this term could be used, that is to say, which worlds tend to be more habitable than Earth. In an appendix, we show why the principle of mediocracy cannot be used to logically explain why Earth should be a particularly habitable planet or why other inhabited worlds should be Earth-like.<br/>
Superhabitable worlds must be considered for future follow-up observations of signs of extraterrestrial life. Considering a range of physical effects, we conclude that they will tend to be slightly older and more massive than Earth and that their host stars will likely be K dwarfs. This makes Alpha Centauri B, which is a member of the closest stellar system to the Sun and is supposed to host an Earth-mass planet, an ideal target for searches for a superhabitable world.</blockquote>
<div id="box">Heller, R., &amp; Armstrong, J. (2014). Superhabitable worlds. <em>Astrobiology</em>, 14(1), 50-66. doi:<a href="https://doi.org/10.1089/ast.2013.1088" target="doi">10.1089/ast.2013.1088</a> (<a href="https://arxiv.org/abs/1401.2392" target="arxiv">arXiv</a>)</div>
<blockquote>One of the most fundamental topics of exobiology concerns the identification of stars with environments consistent with life. Although it is believed that most types of main-sequence stars might be able to support life, particularly extremophiles, special requirements appear to be necessary for the development and sustainability of advanced life forms. From our study, orange main-sequence stars, ranging from spectral type late-G to mid-K (with a maximum at early K), are most promising. Our analysis considers a variety of aspects, including<br/>
(1) the frequency of the various types of stars,<br/>
(2) the speed of stellar evolution in their lifetimes,<br/>
(3) the size of the stellar climatological habitable zones (CLI-HZs),<br/>
(4) the strengths and persistence of their magnetic-dynamo-generated X-ray–UV emissions, and<br/>
(5) the frequency and severity of flares, including superflares;<br/>
both (4) and (5) greatly reduce the suitability of red dwarfs to host life-bearing planets. The various phenomena show pronounced dependencies on the stellar key parameters such as effective temperature and mass, permitting the assessment of the astrobiological significance of various types of stars. Thus, we developed a &quot;Habitable-Planetary-Real-Estate Parameter&quot; (HabPREP) that provides a measure for stars that are most suitable for planets with life. Early K stars are found to have the highest HabPREP values, indicating that they may be &quot;Goldilocks&quot; stars for life-hosting planets. Red dwarfs are numerous, with long lifetimes, but their narrow CLI-HZs and hazards from magnetic activity make them less suitable for hosting exolife. Moreover, we provide X-ray–far-UV irradiances for G0 V–M5 V stars over a wide range of ages.</blockquote>
<div id="box">Cuntz, M., &amp; Guinan, E. F. (2016). About exobiology: the case for dwarf K stars. <em>The Astrophysical Journal</em>, 827(1), 79. doi:<a href="https://doi.org/10.3847/0004-637X/827/1/79" target="doi">10.3847/0004-637X/827/1/79</a> (<a href="https://arxiv.org/abs/1606.09580" target="arxiv">arXiv</a>)</div>
<strong>Read also:</strong>
<ul><li><a href="https://www.centauri-dreams.org/2020/01/13/orange-dwarfs-goldilocks-stars-for-life/" target="dream">Orange Dwarfs: ‘Goldilocks’ Stars for Life?</a></li>
<li><a href="https://www.nasa.gov/feature/goddard/2020/goldilocks-stars-are-best-places-to-look-for-life" target="nasa">Goldilocks Stars Are Best Places to Look for Life</a></li></ul></description><link>http://docmadhattan.fieldofscience.com/2021/09/the-case-for-dwarf-k-stars.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-6762986005582978614</guid><pubDate>Mon, 13 Sep 2021 18:37:00 +0000</pubDate><atom:updated>2021-09-13T20:37:12.793+02:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">astronomy</category><category domain="http://www.blogger.com/atom/ns#">dark energy</category><category domain="http://www.blogger.com/atom/ns#">dark matter</category><category domain="http://www.blogger.com/atom/ns#">simulation</category><category domain="http://www.blogger.com/atom/ns#">universe</category><title>Uchuu: Universes' creator</title><description>If you are a superheroes' comics readers, you probably know <em>All-Star Superman</em> by <strong>Grant Morrison</strong> and <strong>Frank Quitely</strong> (if you want, I could publish a review of this comic). At some point in the story, Superman designs a small cubic universe to see what would happen on a planet like Earth without his presence. The development of intelligent life was also included in the Superman's simulation, but in essence even those of astronomers are structured in the same way: a cube of space of finite dimensions whose evolution is driven by a network of dark matter and dark energy.<br/>
At the end of the july 2021 <a href="https://www.cfca.nao.ac.jp/en/pr/20210910?fbclid=IwAR29QbP_ilNmpvCTC8ss3GWofHrreDCW0z_DUPUS5g2SJjjHBhoW2ZDlagI" target="press">it was realased <em>Uchuu</em></a>, presented as a <em>suite of large high-resolution cosmological N-body simulations</em>, in practice, a simulation that shows the evolution of dark matter structures in a cube of 9.63 billion light years on each side and made up of 2.1 trillion particles.
<div align="center" style="padding-top: 5px;"><iframe width="560" height="315" src="https://www.youtube.com/embed/R7nV6JEMGAo" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe></div>
Uchuu's main goal is to shed light on the dark matter halos surrounding galaxies, but the researchers think that another field of use for their simulation is the study of gravitational lenses.<br/>
In any case, it is a tool that could be very useful for improving the algorithms generally used in astronomy to process the data collected by instruments such as satellites and telescopes.
<div id="box">Ishiyama, T., Prada, F., Klypin, A. A., Sinha, M., Metcalf, R. B., Jullo, E., ... & Vega-Martínez, C. A. (2021). The Uchuu simulations: Data Release 1 and dark matter halo concentrations. <em>Monthly Notices of the Royal Astronomical Society</em>, 506(3), 4210-4231. doi:<a href="https://doi.org/10.1093/mnras/stab1755" target="doi">10.1093/mnras/stab1755</a> (<a href="https://arxiv.org/abs/2007.14720" target="arxiv">arXiv</a>)</div>
<strong>Read also</strong>:<br/>
<a href="http://skiesanduniverses.iaa.es/" target="sky">Skies & Universes</a><br/>
<a href="https://github.com/uchuuproject" target="git">Uchuu project on Git-Hub</a></description><link>http://docmadhattan.fieldofscience.com/2021/09/uchuu-universes-creator.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://img.youtube.com/vi/R7nV6JEMGAo/default.jpg" height="72" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-1916701795973514807.post-8062973440619710383</guid><pubDate>Thu, 09 Sep 2021 14:07:00 +0000</pubDate><atom:updated>2021-09-09T16:07:01.600+02:00</atom:updated><category domain="http://www.blogger.com/atom/ns#">asteroids</category><category domain="http://www.blogger.com/atom/ns#">astronomy</category><title>The dog-bone asteroid</title><description><div align="center"><img src='https://i.postimg.cc/RZ5mdmrF/20210909-kleopatra-asteroid.jpg' border='0' alt='20210909-kleopatra-asteroid' width="100%" /></div>
<blockquote>Using the European Southern Observatory's Very Large Telescope (ESO's VLT), a team of astronomers have obtained the sharpest and most detailed images yet of the asteroid Kleopatra. The observations have allowed the team to constrain the 3D shape and mass of this peculiar asteroid, which resembles a dog bone, to a higher accuracy than ever before. Their research provides clues as to how this asteroid and the two moons that orbit it formed.</blockquote>
<a href="https://en.wikipedia.org/wiki/216_Kleopatra" target="wiki">Kleopatra</a> also possesses another characteristic: a two-moon system discovered in 2008 by <strong>Franck Marchis</strong>' team at the Keck Observatory.<br/>
It is interesting to observe that the dynamics of Kleopatra's three-body system and its moons turn out to be chaotic. I hope to soon publish an article on the problem of the three bodies to clarify this aspect.
<div align="center" style="padding-top: 5px;"><img src='https://i.postimg.cc/DzjWN0PF/20210909-kleopatra-three-body-system.png' border='0' alt='20210909-kleopatra-three-body-system' width="100%" /></div>
<hr/>
<strong>Read</strong> <a href="https://www.eso.org/public/unitedkingdom/news/eso2113/?lang" target="eso">ESO's press release</a>
<div id="box">Marchis, F., Jorda, L., Vernazza, P., Brož, M., Hanuš, J., Ferrais, M., ... & Yang, B. (2021). (216) Kleopatra, a low density critically rotating M-type asteroid. <em>Astronomy&Astrophysics</em>, 653. doi:<a href="https://doi.org/10.1051/0004-6361/202140874" target="doi">10.1051/0004-6361/202140874</a><br/>
Broz, M., Marchis, F., Jorda, L., Hanuš, J., Vernazza, P., Ferrais, M., ... & Yang, B. (2021). An advanced multipole model for (216) Kleopatra triple system. <em>Astronomy&Astrophysics</em>, 653. doi:<a href="https://doi.org/10.1051/0004-6361/202140901" target="doi">10.1051/0004-6361/202140901</a></div>
<div id="box">Descamps, P., Marchis, F., Berthier, J., Emery, J. P., Duchêne, G., De Pater, I., ... & Macomber, B. (2011). Triplicity and physical characteristics of Asteroid (216) Kleopatra. <em>Icarus</em>, 211(2), 1022-1033. doi:<a href="https://doi.org/10.1016/j.icarus.2010.11.016" target="doi">10.1016/j.icarus.2010.11.016</a></div></description><link>http://docmadhattan.fieldofscience.com/2021/09/the-dog-bone-asteroid.html</link><author>noreply@blogger.com (Gianluigi Filippelli)</author><thr:total>0</thr:total></item></channel></rss>

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