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Entropy

  • A dissection of a sample space
  • Entropy of a dissection of a sample space
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Probability

  • An experiment that has many possible outcomes
  • Construct a sample space at a suitable level of detail
  • Probability of an event
  • Conditioning
  • Independent events
  • Random variable
  • Use a random variable to specify an event
  • Use a random variable to dissect a sample space
  • Probability distribution of a random variable
  • Variance of a random variable
  • A dimensionless measure of the fluctuation of a random variable

Return to the outline of Statistical Mechanics

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Statistical Mechanics

Update on 14 December 2019. By now I have taught undergraduate thermodynamics three times at Harvard. I have written up my lecture notes as a book, and posted the book online.

Here are sections that I have now:

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Solid Mechanics Homework 11-15

This set of homework relies on a few elementary facts of the algebra of vectors and tensors.  If you are vague about these facts, see some old notes I wrote when I taught ES 240 in 2006:  node/205/revisions/1385/view

11. Positive-definite elastic energy density
12. The coefficient of thermal expansion (CTE) is a second-rank tensor.
13. Hooke's law for anisotropic, linearly elastic solids
14. Invariants of a tensor
15. A "derivation" of the Mises (1913) yield criterion

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Solid Mechanics Homework 6-10

6. Post an entry in iMechanica to explain to your teaching staff and classmates why you take this class.

7. Residual stress around an inclusion
8. Lame Solution in Cylindrical Shape
9. Stress Concentration around a Circular Hole
10. Back-of-Envelope Calculation

Return to the outline of the course.

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7 reasons to post your original ideas in iMechanica

1. iMechanica is free for all to use. iMechanica is hosted on a server at the School of Engineering and Applied Sciences, of Harvard University, and is managed by a team of volunteers -- mechanicians just like you. You pay nothing to post, and readers pay nothing to read. The limit of each upload file is 50MB, and each user is given 1GB server space.

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Solid Mechanics Homework 1-5

Due 26 September 2008 in class

  1. Nothing Is Continuum, but...
  2. Hooke's law in various forms
  3. Compatibility: the strain-displacement relations
  4. Traction vector on a plane
  5. Turbine blade: centrifugal force and creep

Return to the outline of the course.

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A Fresh Look at a Beautiful Subject

This is a review on Thermal Physics by Charles Kittle and Herbert Kroemer. I posted the review on Amazon on 2 December 2001.

This is by far THE BEST textbook on the subject. As many people say, thermodynamics is a subject that one has to learn at least three times. I can easily understand the very negative review from the undergraduate student at Berkely. The subject itself is hard, and simply is not for everyone, not for the first run at least. I say this from experience. I earned a Ph.D. degree over ten years ago, and took courses on thermodynamics at both undergraduate and graduate levels. I didn't understand the subject at all, and didn't find much use in my thesis work. However, something about the subject has kept me going back to it ever since. I now own about 40 books on the subject, and use the ideas almost daily in my research.

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Elements of linear elasticity

Update on 26 September 2008: An updated file on elements of linear elasticity is posted. You can still access the older version by clicking "revisions".

Return to the outline of the course.

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The long tail of papers

(Initially posted in Applied Mechanics News on 25 July 2006)

In an entry on pay per paper, I alluded to Chris Anderson's new book, The Long Tail. It should be straightforward to collect page views or down loads or citations of individual papers in a journal. You can plot the numbers of hits of individual papers against the rankings of the papers. Here is the curve for articles in Slate. (Not sure why data stopped at top 500 hits. Why not go further to see a really long tail?) Hope someone in Applied Mechanics will show the same data for JMPS, IJSS, MOM, etc. It will be fun.

Here is the gist of Anderson's observation: If you care about the total sale, as a publisher might, then what matters is the area under the curve; the contribution of the tail may rival that of the head. This much is objective, and should not be controversial.

Now allow me to play a variation of the theme, which is admittedly subjective and possibly controversial. Let's say the net contribution of a journal to new knowledge is proportional to the area under the curve (the subjective part). Then numerous less cited papers may make a significant contribution comparable to the contribution made by the best cited papers.

If you are interested in this argument, you might as well generalize the analysis from a single journal to all journals in a field, or to all journals in science, engineering and medicine. I'm not sure if such a curve has ever been plotted, but the job should not be too hard.

Now, if you are an individual author, surely you'd like to have a lot of hits for your own papers, just as Anderson is celebrating his book becoming a best seller. However, if your job is to increase the total knowledge, as the NSF is set up to do, then you might as well pay as much attention to the long tail as to the tall head.

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Whitesides on writing a scientific paper

George Whitesides wrote this handout in 1989, and then published it in Advanced Materials in 2004. It's a gem. He explains how to use writing to plan research. Although Advanced Materials does not give free access to this handout, a number of other sites do. See Google Scholar.

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Bring researchers from industries to iMechanica

Posts on mechanics in industries may attract considerable interest. The audience will be mechanicians working in industries, students planning industrial careers, and academics looking for industrial collaborations.

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How to make long distance phone calls for free

Like many other communities, we mechanicians are scattered all over the world, often separated from families and colleagues. The Internet has promised for years to make long dstances irrelevant: anybody anywhere is just a click away. While nothing will ever be the same as being together in person, many Internet services can facilitate distant communication and collaboration. For example, Skype, an Internet phone service, allows you make free phone calls around the world. The sound quality is excellent.

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Pay per paper (P3)

(Originally published on Applied Mechanics News on 22 July 2006, where many comments provided remarkable insight)

I’ve just stopped subscribing to Science. The magazine is great, but few papers in it interest me. The signal-to-noise ratio of Science, I guess, is just too low to most individuals. Instead, I’ve now subscribed to the RSS feed of Science. If any paper looks interesting, I can access to the full paper online through Harvard Libraries. Outside my office, a color printer is free to use for everyone. A library of an institution seems to be an ideal home for a journal like Science. Nearly every individual paper in Science is of high enough quality to appeal to someone in the institution.

Few journals can make that claim, however. Most journals are only relevant to several people in an institution. Furthermore, few researchers read any scholarly journal from cover to cover. Rather, we all read individual papers. However, libraries subscribe to journals, or even bundles of journals. As a result, the libraries pay for many papers that nobody reads, and miss other papers that someone would like to read.

This business model is bad for authors and readers, and possibly even bad for publishers. Technology now exists to distribute information far more efficiently, in a unit consistent with how people consume the information. For example, many people now prefer buying individual songs to albums. See a recent book, The Long Tail, by Chris Anderson, the editor-in-chief of Wired, for a remarkably perceptive analysis of media industries.

The same business model may apply to scholarly papers. One may argue that journals, like albums, were invented as a packaging technology to suit the old economics of delivery. As scholarly papers are all online, the name of a journal becomes simply a tag to the papers published in that journal. Maybe a powerful tag, but a tag nonetheless. So far as how papers should be distributed, the name of a journal should serve the same function as all other tag-like entities: keywords, names of authors, etc: the tags help readers to sort papers and set priorities. It makes no sense for anyone to insist that papers with any particular tag be delivered as a bundle.

Many publishers already offer individual papers for sale online; for example, the cost is at $30 per paper for many Elsevier journals. Once a reader buys a paper, it seems reasonable to share this paper with his close colleagues, and it also seems reasonable to store the paper for future use. Perhaps we can formalize this practice.

How about we treat a paper just like a book? With one click, a reader will have the paper, and his library will automatically pay for it. Once bought, the paper is accessible to every user of the library. We can also collect statistics. If the users of a library buy many papers in a journal, the library should subscribe to the journal. Libraries will set up an algorithm to minimize the total cost. Publishers will set up their algorithms to maximize profits. However, libraries and publishers do have a common ground: they both want to help people to find papers.

To support such a business model, a third party may provide a web service. It seems to be too wasteful to make every individual library and every individual publisher maintain a separate web service. Something like Amazon.com or Last.fm for papers might do. The service can also be an extension of services like EZproxy or CiteULike.

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The LibraryLookup Bookmarklet

(Opriginally posted on Applied Mechanics News on 8 July 2006)

Quick link added on 12 July 2006. Here is a list of LibraryLookup Bookmarklets for many libraries, along with an instruction to use them.

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Libraries and Amazon

(Originally posted on Applied Mechanics News on 25 June 2006)

Libraries take premium spaces, which will not grow and will likely shrink. As more and more books are stored in off-campus depositories, people miss the serendipity of browsing among shelves and discovering books that they don’t know they’d like to read. They can browse the catalogues of the libraries. However, a typical catalogue of a library contains meager information: the online catalogue is a clone of its ancestor on cards. Creating an information-rich and user-friendly online catalogue is too expensive for a library.

These problems have a solution. The primary source of data on books is Amazon. It contains publisher-supplied data such as cover images, table of contents, index, and sample material. Searchable full texts are within reach. Perhaps even more valuable, Amazon contains comments of users on books. Based on collective behavior of users, Amazon also recommends books to users. Amazon will no doubt continue relentless innovation.

In an ideal world, a user should not waste his time on the catalog of a library, nor should the library waste its resources on maintaining a stand-alone catalog. The user should simply browse on Amazon. Once he finds an interesting book, a single click should tell him if the book is in any of the libraries accessible to him. In this ideal world, to enter a book into the catalog of a library, a librarian only needs to enter a single number: the call number of the book. All other data of the book are not library-specific and are already in Amazon. What if the library owns a book not in Amazon? The librarian should enter a detailed description of the book, as if she were the publisher of the book.

This ideal world may not be far different from our world. The LibraryLookup Project allows a user to generate a bookmarklet, so that with one click he can look up a book in a library, while surfing on Amazon. The creator of the Project, Jon Udell, has developed a screencast to guide you through the process of generating your own bookmarklet.

A deeper integration of Amazon and libraries would harness more power. The statistics of borrowing books could be aggregated from all libraries and be used to recommend books to users. Amazon, libraries and some third party could collaborate on the business of print on demand. Libraries could send even more books to depositories and greatly simplify efforts in cataloging books. Users would have a seamless experience with books. Oh, if a book is not in a library, users could suggest, with a single click, that the library order the book.

Ending added on 26 June 2006, after reading a message from Zak Stone. Amazon.com is named after the Amazon River, the largest river in the world, carrying more water than the next six largest rivers combined. May the rivers of libraries and the streams of users contribute to the River of All Books. May Amazon.com nurture the civilization without drowning us with commercialism.

Note added on 10 July 2006. An entry describes my experience with LibraryLookup Bookmarklets.

Note added on 15 July 2006. Wall Street Journal (13 July 2006) on Rice University's Press on line and print on demand (POD). For an example of comercial POD, see lulu.com. Also see a recent product annoucement of e-reader.

Note added on 17 July 2006. OCLC and Amazon: A Connection Revealed.

Note added on 27 July 2006. Springer will offer all new titles in e-book form.

Note added on 20 August 2006. Amazon introduces library processing.

Note added on 31 August 2006. Google offers free download of books.

Note added on 31 August 2006. Stanford's vision for library.

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What's wrong with Applied Mechanics?

(Originally posted on Applied Mechanics News in 16 May 2006)

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Knowledge processing and the Internet

(Originally posted on Applied Mechanics News on 10 May 2006)

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Connexions: knowledge as commodities

(Originally posted on Applied Mechanics News on 2 May 2006)

A twelve-year old found a blueprint to assemble a computer in a magazine, and ordered parts on newegg.com, a website that listed parts from all vendors and comments on each part by customers. Both features were reassuring. When the parts arrived in mail a week or two later, the boy assembled the computer himself. In the process, he saved a substantial amount of money. He also learned a lot about computers, and about dealing with his parents.

The boy could do all these because computer parts are commodities, products that are produced by different companies but conforming to the same standards: all parts fit. Websites like newegg bring the parts from the companies directly to boys and girls of all ages, skipping middlemen like Dell.

Commoditization has also occurred in the software industry, largely due to the open-source movement that has produced the Linux operating system, as well as a large number of other software systems.

Can we also commoditize knowledge? This is precisely the mission of the Connexions Project, founded by the electrical engineer Richard Baraniuk, of Rice University, in 1999. The Project has been funded by the National Science Foundation and private donors, and has produced a system of software to enable anyone to author parts of knowledge (called modules). It also enables anyone to assemble parts into a functional product of knowledge (called a course), free of charge, under a Creative Commons open license. By January 2006, Connexions hosted over 2900 modules and 138 courses.

Connexions will likely have tremendous impact on the textbook industry, which has an annual revenue of 10 billion dollars in the US alone. The Project is also bringing free, up-to-date knowledge to developing countries, including North Karea.

Connexions will also likely to change the practice of scholarship. If you'd like to learn how Connexions works, you may visit the website of Connexions, or look at a course, or read a white paper written by the Connexions staff, or simply enjoy a video of an inspiring talk given by Professor Baraniuk to Google engineers.

Notes added on 15 July 2006. Wall Street Journal (13 July 2006) reported on Rice University's Press on line and print on demand.

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Wikipedia and Applied Mechanics

(Originally posted on Applied Mechanics News on 25 February 2006)

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