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statistical mechanics

cemalbasaran's picture

A Nobel Prize worthy paper, unifying Mechanics and Thermodynamics with a mathematical basis

I highly recommend this paper to any mechanician who is familiar with the scientific efforst in the last 150 years to unify mechanics and thermodynamics. Sosnoskiy and Sherbakov and several others from the Russian Academy of Sciences listed in the Acknowledgemnsts have achieved it. Congratulations.

Sosnovskiy, L. Sherbakov, S.,”Mechanothermodynamic Entropy and Analysis of Damage State of Complex Systems”, Entropy, 2016, 18, 268.

cemalbasaran's picture

A Nobel prize worthy paper, unifying Mechanics and Thermodynamics with a Mathematical Basis

I highly recommend this paper to any mechanician who is familiar with the scientific efforst in the last 150 years to unify mechanics and thermodynamics. Sosnoskiy and Sherbakov and several others from the Russian Academy of Sciences listed in the Acknowledgemnsts have achieved it. Congratulations.

Sosnovskiy, L. Sherbakov, S.,”Mechanothermodynamic Entropy and Analysis of Damage State of Complex Systems”, Entropy, 2016, 18, 268.

karelmatous's picture

Extreme Particle Shape Effect for Packs of Platonic Solids

For centuries, great minds like Kepler, Maxwell and Einstein have investigated the statistical characterization of many-body systems, and implications of small-scale structures on the macroscopic transport and mechanical properties. In this work, an accurate statistical description of heterogeneous particulate materials is computed using novel adaptive interpolation/integration scheme. This statistical information is then utilized within mathematical theories for predicting the overall thermo-mechanical behavior.

Zhigang Suo's picture

Freely jointed chain

A single strand of polymer is a chain of a large number of monomers.  The monomers are joined by covalent bonds, and two bonded monomers may rotate relative to each other.  At a finite temperature, the polymer rapidly changes from one configuration to another.  When the two ends of the polymer are pulled by a force, the distance between the two ends changes.  The polymer is known as an entropic spring.  These notes are developed as part of statistical thermodynamics to supplement the course on advanced elasticity

Open Postdoctoral Position at Carnegie Mellon University (USA)

We are currently looking for a top candidate to join the System Level Design group at CMU (www.ece.cmu.edu/~sld/), as a Postdoctoral Associate, starting Spring 2013. Main responsibilities involve work on modeling and control of stochastic micro-robotic swarms targeting biological applications.

Amit Acharya's picture

Microcanonical Entropy and Mesoscale Dislocation Mechanics and Plasticity

(Journal of Elasticity, Carlson memorial Volume)

A methodology is devised to utilize the statistical mechanical entropy of an isolated, constrained atomistic system to define the dissipative driving-force and energetic fields in continuum thermomechanics. A thermodynamic model of dislocation mechanics is discussed. One outcome is a definition for the mesoscale back-stress tensor and the symmetric, polar dislocation density-dependent, Cauchy stress tensor from atomistic ingredients.

Zhigang Suo's picture

Free Energy

For a system in thermal contact with the rest of the world, we have described three quantities: entropy, energy, and temperature. We have also described the idea of a constraint internal to the system, and associated this constraint to an internal variable.

Cai Wei's picture

Lecture notes on "Elasticity" and "Statistical Mechanics"

The lecture notes of the two courses I taught at Stanford University during the last two quarters, "ME 340 Elasticity" and "ME 334 Introduction to Statistical Mechanics", are available in PDF format online at:

  http://micro.stanford.edu/~caiwei/me340/

  http://micro.stanford.edu/~caiwei/me334/

Perhaps it could be useful to you.

What is "randomness"?

Does the word "randomness" have antonym? If yes, what is it? Why? What view of randomness does that imply?

A book on mechanics that would pique your curiosity

I am happy to recommend the following book for your general reading.

Ranganath, G.S., ``Mysterious Motions and other Intriguing Phenomena in Physics," Hyderabad, India: Universities Press (2001)

Zhigang Suo's picture

Electric potential

  • Electric charge
  • Movements of charged particles
  • Elastic dielectric
  • Work done by a battery and by a weight
  • Electromechanical coupling
  • Conservative system
  • Experimental determination of electric potential
  • Lagendre transformation
  • parallel-plate capacitor

Return to the outline of Statistical Mechanics

Zhigang Suo's picture

Pressure

So far we have been mainly concerned with systems of a single independent variable: energy (node/4878). We now consider a system of two independent variables: energy and volume. A thermodynamic model of the system is prescribed by entropy as a function of energy and volume.

The partial derivatives of the function give the temperature and the pressure. This fact leads to an experimental procedure to determine the function for a given system.

The laws of ideal gases and osmosis are derived. The two phenomena illustrate entropic elasticity.

Zhigang Suo's picture

The Boltzmann Distribution

  • 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.

Zhigang Suo's picture

Entropy

  • A dissection of a sample space
  • Entropy of a dissection of a sample space
Zhigang Suo's picture

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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