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• A small system in thermal contact with a large system
• The Boltzmann factor
• Partition function
• The probability for a system in thermal equilibrium with a reservoir to be in a specific state
• The probability for a system in thermal equilibrium with a reservoir to be in a configuration
• Thermal fluctuation of an RNA molecule
• A matter of words
  

Return to the outline of Statistical Mechanics.

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

The notes are attached.  See related notes on thermodynamics.

• 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

I am a first year PhD student in Aeronautics and Astronautics department at MIT. I also have obtained B.S. and M.S. from the same department. I have taken one Solid Mechanics (graduate level) course at MIT, but since it did not cover waves/vibration or nonlinear plate theory, I look forward to these new topics later in the course very much. My most research work has been done at Technology Laboratory for Advanced Materials and Composites at MIT. My M.S. thesis topic was on micro solid oxide fuel cell. The goal was to design and fabricate thin film tri-layer fuel cell structure that is thermomechanically stable at high operation temperature. We started with mechanical testing to acquire properties, and designed membranes with von Karman plate theory. My PhD topic is nano-engineered composites with carbon nanotubes (CNTs). Solid mechanics is very directly related to these structural tasks including stiffness testing. Generally, having better sense of mechanics behind and having many analysis tools will be greatly helpful. So far I have been having much fun coming to Harvard, taking a little break from MIT (I have been there more than enough, although I still love it there). I hope to learn as much as possible from this course.

Hi everyone, I am Roxanne, a G-2 student in applied physics.  My major was chemical engineering when I was an undergraduate student in Taiwan.  I had no background on mechanics then.  When I was a G-1, I took AP 293 (Deformation of Solids).  This course gave me some ideas on the plastic flow, elastic properties, and dislocations of materials. Math, like partial differential equation and tensors are pretty challenging to me…always.

Currently, I am working with Frans, and my research focus is on studying the creep phenomena in metals.

http://deas.harvard.edu/matsci/

My name is Xuanhe Zhao, and I'm a first year student in DEAS. Before joining Harvard, I got my Master Degree in Materials Engineering from University of British Columbia, Canand. I have took one course on Computational Mechanics, and read a couple of books on theory of elasticity.

 The major goal for me taking ES 240 is to learn how to understand and solve engineering problems, both familiar and unfamiliar, in a intuitive way. In addition, I will further consolidate my background in solid mechanics.

I am a first year grad student in bioengineering working in Dr. Parker's Disesase Biophysics Group (http://www.deas.harvard.edu/diseasebiophysics/). I attended Washington University in St. Louis for undergrad, where I double majored in biomedical engineering and biology and minored in chemistry. The only courses I have taken related to solid mechanics are Biomechanics and Transport Phenomena, both of which covered basic mechanics. As an undergrad, I worked in a research lab that focused on cardiac electrophysiology. The lab I am in now is interested in how the mechanical and electrical behaviors of cardiac cells are related, so I need to gain a stronger background in mechanics to match my background in electrophysiology. I hope that this class will help me develop an intuition about the mechanical behavior of objects, which I can apply to the mechanics of cellular events.

I completed my undergraduate degree in Mechanical Engineering at The Cooper Union for the Advancement of Science and Art, in New York City. At the undergraduate level, I have taken two courses related to solid mechanics: Solid Mechanics and Stress & Applied Elasticity. Though these courses covered most of the same topics, the focus was not on working with developing the equations for different situations. The majority of the work was in knowing when to apply the equations and coming up with quantitative solutions. Thus my weaknesses will be related to coming up with equations to model various stress situations.

Concerning my research, I am working with Prof. Robert Wood in the microrobotics laboratory. My focus will be on aquatic robots on the order of several centimeters in length. Because of the restrictions inherent in working at this scale, it will be important not to over-design the systems. From studying solid mechanics, I hope to gain the ability to analyze the states of stress and strain in materials such that I can effectively develop efficient systems for microrobotics.

My name is Will Adams and I am a first year grad student in BME. I have no previous courses in solid mechanics or strength of materials but I have taken two fluid mechanics courses, ES220 and ES123, as an undergrad which contain many of the same lines of thinking. Hopefully the math formalisms of these classes will help in ES240 but having no solids background leaves me with little intuition about experimental results. Hopefully I can acquire this here. I was a BME major as an undergrad here in DEAS.

My name is Adrian Podpirka and I am a first year grad student studying applied physics. I came to Harvard after finishing my Bachelors in Material Science and Engineering at Columbia University. As an undergraduate I took Mechanics of Solids with Professor Xi Chen and Mechanical Properties of Materials with Professor Noyan.

Related to this course, my main weakness is the mathematics involved since it has been more then 3 years since I took differential equations. Also, both my undergraduate courses were not tensor based. My main strength in this course would be my understanding of material properties and the phenomenas involved.

My likely research direction will probably be in the field of fuel cell membranes with Professor Ramanathan.

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

The major challenge in medical implant industry is the knowledge about human body. Had we know the human body and its functions better, we can make better and reliable implants. Below are two examples that I have learned.

Let's start from stent, a small, lattice-shaped, metal tube that is inserted permanently into an artery. The stent opens the narrowed artery so that an adequate supply of blood can be restored. See this FDA site for further detail.

Stent has revolutionized the treatments for cardiovascular disease and the interventional system. However, stent fractures are commonly observed in-vivo in the past years and has become a concern for patient wellness and therefore a challenge/opportunity for mechanical engineering. Both the engineering and the medical care societies have to work together to solve this issue. It is very surprising that little publications are available to study the key issues such as artery deformation, motion, its mechanical properties and its variations among patient age, race, and other factors. As a result, current stents, even they have been proven to be lifesavers for many patients, they are not necessarily a satisfactory product for a mechanical engineer. We can not wait for the medical care society to give us the information because they often concern and focus on different issues than us. In addition, they can not work alone to come up with the necessary equipments. Therefore, we need proactive to interact and help each other to get what we want. The day we know our interventional system better is the day that we can make better stents because stents can only be as good as our knowledge to the interventional system.

 University of Michigan, tenure-track faculty positions

The Department of Mechanical Engineering, University of Michigan, Ann Arbor, invites applications for tenure-track faculty positions in various areas of mechanical engineering including design and manufacturing, dynamics, systems and controls, materials and solid mechanics and thermal/fluid sciences. Candidates with research interests in automotive engineering, biotechnology, eco/sustainable systems, energy-systems, manufacturing, and micro/nano systems are particularly encouraged to apply.

Applicants should have an earned Ph.D. in Mechanical Engineering or related fields, a demonstrated record for conducting independent research, and the potential for leadership and impact in teaching and research. Appointments at all levels will be considered. For best consideration, candidates should apply by February 28, 2007, but the positions will remain open until filled.

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.