iMechanica - Comments for "Statistical Mechanics"
https://imechanica.org/node/288
Comments for "Statistical Mechanics"enRe : durability
https://imechanica.org/comment/27840#comment-27840
<a id="comment-27840"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/170#comment-170">Very interesting</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Hello Pr Gong,</p>
<p>If the reliability is known, you have to define your event and then to identify the corresponding stochastic variables. The analysis can be done easily with probabilistic methods in the case of independent events. In other cases you need to use conditional probabilities. Books using probabilitic methods correspond to your application. In the next semester, i will post the second section of my couse on "mechanical reliability" on campusvirtuel.usthb.dz. You can find statistical applications which can calculate the reliability of any system.</p>
</div></div></div><ul class="links inline"><li class="comment_forbidden first last"><span><a href="/user/login?destination=node/288%23comment-form">Log in</a> or <a href="/user/register?destination=node/288%23comment-form">register</a> to post comments</span></li>
</ul>Sun, 08 Nov 2015 11:36:41 +0000mohamedlaminecomment 27840 at https://imechanica.orgRe: Stat Mech for Elasticity
https://imechanica.org/comment/1328#comment-1328
<a id="comment-1328"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/1327#comment-1327">Stat Mech for Elasticity</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Thanks for the reference, Pradeep.</p>
</div></div></div><ul class="links inline"><li class="comment_forbidden first last"><span><a href="/user/login?destination=node/288%23comment-form">Log in</a> or <a href="/user/register?destination=node/288%23comment-form">register</a> to post comments</span></li>
</ul>Sun, 25 Feb 2007 01:14:29 +0000Kaushik Dayalcomment 1328 at https://imechanica.orgStat Mech for Elasticity
https://imechanica.org/comment/1327#comment-1327
<a id="comment-1327"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/1324#comment-1324">Re: Focus on the sections on isolated system and temperature</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Kaushik, in case you are interested in a viewpoint that is anchored to continuum mechanics, you may wish to check out the not-quite-widely-known book by Weiner, "Statistical Mechanics of Elasticity". It is now available in Dover ($ 25) and is in my opinion a true gem. </p>
<p>The first few chapters review classical continuum mechanics and thermodynamics which provide a nice warm-fuzzy feeling to mechanicians who are studying statistical mechanics for the first time. Some of my students, who have taken stat mech courses both in physics as well as gone through this book, tend to favor Weiner. </p>
</div></div></div><ul class="links inline"><li class="comment_forbidden first last"><span><a href="/user/login?destination=node/288%23comment-form">Log in</a> or <a href="/user/register?destination=node/288%23comment-form">register</a> to post comments</span></li>
</ul>Sat, 24 Feb 2007 23:28:49 +0000Pradeep Sharmacomment 1327 at https://imechanica.orgRe: Focus on the sections on isolated system and temperature
https://imechanica.org/comment/1324#comment-1324
<a id="comment-1324"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/1323#comment-1323">Focus on the sections on isolated system and temperature</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Dear Zhigang,</p>
<p>Thanks for the advice and warning. I'll probably supplement my reading of your notes with a regular text that's meant for self-study.</p>
<p>Kaushik </p>
</div></div></div><ul class="links inline"><li class="comment_forbidden first last"><span><a href="/user/login?destination=node/288%23comment-form">Log in</a> or <a href="/user/register?destination=node/288%23comment-form">register</a> to post comments</span></li>
</ul>Sat, 24 Feb 2007 20:53:59 +0000Kaushik Dayalcomment 1324 at https://imechanica.orgFocus on the sections on isolated system and temperature
https://imechanica.org/comment/1323#comment-1323
<a id="comment-1323"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/1322#comment-1322">Thank you very much</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Dear Kaushik: </p>
<p>I've just finished teaching these sections in my class on <a href="/node/725">Advanced Elasticity</a>. Each section roughly corresponded to one 90-minute lecture. I did not include the sections on probability and entropy in my lectures. </p>
<p>Please go very slow with the section on <a href="/node/290">isolated system</a> and the section on <a href="/node/291">temperature</a>. Once you see through these two sections, perhaps the myth of thermodynamics will disappear. The rest is rather charming and technical applications of the same ideas.</p>
<p>Please don't be too disappointed if my notes don't help you. They are written for myself to teach the subject in class. I'm not sure that they can be used for self study. </p>
</div></div></div><ul class="links inline"><li class="comment_forbidden first last"><span><a href="/user/login?destination=node/288%23comment-form">Log in</a> or <a href="/user/register?destination=node/288%23comment-form">register</a> to post comments</span></li>
</ul>Sat, 24 Feb 2007 19:52:43 +0000Zhigang Suocomment 1323 at https://imechanica.orgThank you very much
https://imechanica.org/comment/1322#comment-1322
<a id="comment-1322"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/1321#comment-1321">PDFs of notes on Statistical Mechanics</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Dear Zhigang,</p>
<p>Thank you very much for taking the time to convert your notes to PDF. I'm interested in learning some statistical mechanics, but I've been confused by the usual texts. I'm hoping that your mechanics perspective will be more accessible to me.</p>
<p>Kaushik </p>
</div></div></div><ul class="links inline"><li class="comment_forbidden first last"><span><a href="/user/login?destination=node/288%23comment-form">Log in</a> or <a href="/user/register?destination=node/288%23comment-form">register</a> to post comments</span></li>
</ul>Sat, 24 Feb 2007 18:29:11 +0000Kaushik Dayalcomment 1322 at https://imechanica.orgPDFs of notes on Statistical Mechanics
https://imechanica.org/comment/1321#comment-1321
<a id="comment-1321"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/1318#comment-1318">PDFs?</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Dear Kaushik: Thank you very much for your interest. I've just uploaded the pdf files.</p>
</div></div></div><ul class="links inline"><li class="comment_forbidden first last"><span><a href="/user/login?destination=node/288%23comment-form">Log in</a> or <a href="/user/register?destination=node/288%23comment-form">register</a> to post comments</span></li>
</ul>Sat, 24 Feb 2007 16:03:41 +0000Zhigang Suocomment 1321 at https://imechanica.orgStatistical mechanics books
https://imechanica.org/comment/1320#comment-1320
<a id="comment-1320"></a>
<p><em>In reply to <a href="https://imechanica.org/node/288">Statistical Mechanics</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>It is quite interesting in that now the statistical mechanics course is provided in Engineering. As far as I know, statistical mechanics includes fundamental topics in physics - thermodynamics, phase transition, renormalization theory, hydrodynamics, etc. However, in recent years, since applied mechanics people have intrigued by nanomechanics, so that statistical mechanics has been regarded as a basic background for understanding machanics of nano-scale objects.</p>
<p>In my case, when I was in UT as a PhD student, I took the statistical mechanics provided in Physics department. During that time, the course used the text book "A Modern Course in Statistical Physics (ISBN 0-471-59520-9)" written by Linda E. Reichl, who lectured the course at that time. Reichl's book is quite readable to not only physics students but also engineering students.</p>
<p>Also, I like the book "Statistical Mechanics of Elasticity (ISBN 0-486-42260-7)" written by J. H. Weiner. This book includes the topics of thermoelasticity, rubber elasticity, crystal lattices, basic quantum mechanics, etc. This book is quite understandable, without any physics background, to engineering students.</p>
</div></div></div><ul class="links inline"><li class="comment_forbidden first last"><span><a href="/user/login?destination=node/288%23comment-form">Log in</a> or <a href="/user/register?destination=node/288%23comment-form">register</a> to post comments</span></li>
</ul>Sat, 24 Feb 2007 15:46:14 +0000Kilho Eomcomment 1320 at https://imechanica.orgPDFs?
https://imechanica.org/comment/1318#comment-1318
<a id="comment-1318"></a>
<p><em>In reply to <a href="https://imechanica.org/node/288">Statistical Mechanics</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Is it convenient for you to also post your notes in some format that is more portable than Doc, for instance PDF? My Doc reader messes up the symbols quite badly.</p>
<p> Thanks very much,</p>
<p>Kaushik </p>
</div></div></div><ul class="links inline"><li class="comment_forbidden first last"><span><a href="/user/login?destination=node/288%23comment-form">Log in</a> or <a href="/user/register?destination=node/288%23comment-form">register</a> to post comments</span></li>
</ul>Fri, 23 Feb 2007 16:48:30 +0000Kaushik Dayalcomment 1318 at https://imechanica.orgStatistical mechanics and thermodyanmics made easy
https://imechanica.org/comment/379#comment-379
<a id="comment-379"></a>
<p><em>In reply to <a href="https://imechanica.org/node/288">Statistical Mechanics</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>
I wish I did. People have given me warm feedback about these study notes, which I wrote to teach myself. For a college student in engineering and science, perhaps the right place to start is the section "Isolated Systems" The section reminds you of what a quantum state is, and tells you the fundamental postulate of statistical mechanics.
</p>
<p>
The whole statistical mechanics is then a collection of elaborate applications of the fundamental postulate. A first prototypical application is the definition of Temperature, the section you might read as the second section. The section relates the fundamental postulate to how we measure temperature and basic quentities like heat and the number of quantum states. The section also reminds people that temperature should really have the same unit as energy, and Boltzmann's constant is just a conversion factor between two units of temperature, rather like 1.6 is the conversion factor between miles and kilometers. These units are made up by humans, and have no fundamental significance. To think Boltzmann constant as a fundamental constant of nature is an abuse of nature and of the man.
</p>
<p>
Then you are ready to read the section on the Boltzmann distribution.
</p>
<p>
The section on Probability is inserted for people who want to have a quick review of math, the kind of necessary evil as we often talk about tensors at the beginning of a solid mechanics course. Of course, both the theory of probability and the theory of tensors are beautiful subjects in their own rights. But there is no point to let them overshadow mechanics, which is even more beautiful. Perhaps I should list the section as an appendix.
</p>
<p>
The section on Entropy, however, is perhaps an unnecessary evil. You certainly don't need it to read the rest of the notes. I inserted it right after Probability simply to remind people that Entropy is a quantity associated with any probability distribution. I make no distinction between information entropy and thermodynamic entropy and entropy associated with rolling a die. Because there is no distinction. Entropy is just a number you calculate when you have a probability distribution. No more, no less. You may find many things about entropy to impress other people at a dinner table.
</p>
<p>
The situation is rather like taking differentiation of a function. This is a mathematical operation: you can take a differentiation if you have a smooth function. You may make interesting applications in engineering and economics, but there is no point to make a distinction about an engineer's differentiation and an economist's differentiation. The distinction is in the applications, not the concept of differentiation itself.
</p>
<p>
To sum up, an easy reading sequence is
</p>
<ul><li>Isolated systems</li>
<li>Temperature</li>
<li>Boltzmann distribution</li>
</ul><p>With a glance at Probability to refresh your memory, and at Entropy as an aside. Let me know if these notes help.</p>
</div></div></div><ul class="links inline"><li class="comment_forbidden first last"><span><a href="/user/login?destination=node/288%23comment-form">Log in</a> or <a href="/user/register?destination=node/288%23comment-form">register</a> to post comments</span></li>
</ul>Sat, 25 Nov 2006 15:01:49 +0000Zhigang Suocomment 379 at https://imechanica.orgStatistics reference (Bayesian approach)
https://imechanica.org/comment/251#comment-251
<a id="comment-251"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/170#comment-170">Very interesting</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Xiao-Yan, I'd recommend <a href="http://www.amazon.com/Data-Analysis-Bayesian-Tutorial-Publications/dp/0198518897/sr=8-2/qid=1163369514/ref=pd_bbs_sr_2/002-0843497-3712833?ie=UTF8&s=books" target="_blank">Sivia's book</a> on Bayesian data analysis for an intuitive look into data/statistical analysis. It uses the Bayesian approach (probability is a degree-of-belief and is always conditional) as opposed to the classical (frequentist) one. This book is uniformly recommended by all who subscribe to the Bayesian school of statistics, and on reading parts of the book I came away with the same conclusion. The book is concise (~200 pages), very well-written, and proceeds in a very systematic manner to de-mystify standard statistics as is taught in school. The above link is the 1996 edition; I noticed that a new edition (with Skilling as co-author) has come out in 2006, so that might be preferable if one wants to buy the book. Reviewers' comments are available on the 1996 edition, and hence I have provided a link to that. For one, I think a tool such as this might be relevant to estimate material parameters (e.g., for constitutive theories) from available experimental data. Given the fact that there exists inherent variabilities in real materials (structure, properties and ergo response), such a tool would seem to be useful. If not anything, it'll give you new perspectives and indicate that there are other options than classical statistics (and the many ad-hoc tests therein) to deal with data and uncertainty. In spite of my obvious bias, I hope this helps?</p>
</div></div></div><ul class="links inline"><li class="comment_forbidden first last"><span><a href="/user/login?destination=node/288%23comment-form">Log in</a> or <a href="/user/register?destination=node/288%23comment-form">register</a> to post comments</span></li>
</ul>Sun, 12 Nov 2006 22:45:04 +0000N. Sukumarcomment 251 at https://imechanica.orgA Dover book on statistics
https://imechanica.org/comment/171#comment-171
<a id="comment-171"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/170#comment-170">Very interesting</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Xiao-Yan:</p>
<p>I have not studied statistics systematically, and cannot recommend a good book. Here is a Dover book that I studied: <a href="http://www.amazon.com/Principles-Statistics-M-G-Bulmer/dp/0486637603/sr=1-3/qid=1160522969/ref=sr_1_3/002-9179678-2688828?ie=UTF8&s=books">Principles of Statistics, by M.G. Bulmer</a>. I just noticed that readers reviews on Amazon are excellent. Apparently other people have also benefited from reading it.</p>
<p>If you'd like to have some fun, <a href="http://www.amazon.com/Cartoon-Guide-Statistics-Larry-Gonick/dp/0062731025/sr=1-1/qid=1160524122/ref=pd_bbs_1/002-9179678-2688828?ie=UTF8&s=books">Cartoon Guide to Statistics</a> may give you a quick overview of the subject. As a cartoon book goes, this one covers serious stuff. </p>
<p>Maybe some other iMechanicians will give you more advice.</p>
</div></div></div><ul class="links inline"><li class="comment_forbidden first last"><span><a href="/user/login?destination=node/288%23comment-form">Log in</a> or <a href="/user/register?destination=node/288%23comment-form">register</a> to post comments</span></li>
</ul>Tue, 10 Oct 2006 23:41:11 +0000Zhigang Suocomment 171 at https://imechanica.orgVery interesting
https://imechanica.org/comment/170#comment-170
<a id="comment-170"></a>
<p><em>In reply to <a href="https://imechanica.org/node/288">Statistical Mechanics</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Thanks to both. Statistics is widely used in the field of durability. Does anyone has recommendation for a good book in that field?</p>
<p>Zhigang, any thought to include durability as a chapter in the book?</p>
<p> Xiao-Yan Gong, PhD</p>
</div></div></div><ul class="links inline"><li class="comment_forbidden first last"><span><a href="/user/login?destination=node/288%23comment-form">Log in</a> or <a href="/user/register?destination=node/288%23comment-form">register</a> to post comments</span></li>
</ul>Tue, 10 Oct 2006 22:35:56 +0000Xiao-Yan Gongcomment 170 at https://imechanica.orgI have just downloaded Sethna's book
https://imechanica.org/comment/167#comment-167
<a id="comment-167"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/166#comment-166">suggestion for a book</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Thank you Pradeep. I have just downloaded Sethna's book from the website you pointed out, using this <a href="http://www.google.com/url?sa=t&ct=res&cd=1&url=http%3A%2F%2Fwww.physics.cornell.edu%2Fsethna%2FStatMech%2FEntropyOrderParametersComplexity.pdf&ei=GZ8rRfDgPKvEaI-CrZ8C&sig=__e4klumjanKyuybIMi6GGEqHoQbU=&sig2=kNsYbTEkV6xtIwuxhCGP0g#search=%22EntropyOrderParametersComplexity%22">link</a>. It looks like a fun but demanding book to read. </p>
</div></div></div><ul class="links inline"><li class="comment_forbidden first last"><span><a href="/user/login?destination=node/288%23comment-form">Log in</a> or <a href="/user/register?destination=node/288%23comment-form">register</a> to post comments</span></li>
</ul>Tue, 10 Oct 2006 13:27:23 +0000Zhigang Suocomment 167 at https://imechanica.orgsuggestion for a book
https://imechanica.org/comment/166#comment-166
<a id="comment-166"></a>
<p><em>In reply to <a href="https://imechanica.org/node/288">Statistical Mechanics</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Zhigang,</p>
<p>There is a recently released book by JP Sethna on Statistical Mechanics. I found it to be quite good especially since it unifies the relevance of statmech to diverse subjects (black holes to econonics). It has a chapter on (after paraphrasing) "how to construct a landau model for anything" which is certainly worth reading-- especially for a student. For a long time, this book was available online on the authors website for free. The link appears <a href="http://www.physics.cornell.edu/sethna/StatMech/" target="_blank" title="statistical mechanics">here</a>.</p>
</div></div></div><ul class="links inline"><li class="comment_forbidden first last"><span><a href="/user/login?destination=node/288%23comment-form">Log in</a> or <a href="/user/register?destination=node/288%23comment-form">register</a> to post comments</span></li>
</ul>Tue, 10 Oct 2006 12:59:16 +0000Pradeep Sharmacomment 166 at https://imechanica.org