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Statistical weight
About: Statistical weight is a research topic. Over the lifetime, 245 publications have been published within this topic receiving 6518 citations.
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TL;DR: Implicit solvent models for biomolecular simulations are reviewed and their underlying statistical mechanical basis is discussed, and the relation between the solute fluctuations and its macroscopic dielectric constant(s) clarified.
874 citations
Book•
01 Jan 2006
TL;DR: In this article, the authors introduce statistical mechanics, including random walks and emergent properties, as well as phase-space dynamics and ergodicity, including free energy and entropy.
Abstract: 1. What is Statistical Mechanics? 2. Random walks and emergent properties 3. Temperature and equilibrium 4. Phase-space dynamics and ergodicity 5. Entropy 6. Free Energies 7. Quantum statistical mechanics 8. Calculation and computation 9. Order parameters, broken symmetry, and topology 10. Correlations, response, and dissipation 11. Abrupt phase transitions 12. Continuous phase transitions APPENDIX: FOURIER METHODS
614 citations
TL;DR: In this paper, a statistical model of the collision term in the Boltzmann equation is introduced which is similar in concept to the well-known Krook model but yields the correct Prandtl number of ⅔ for a monatomic gas.
Abstract: A statistical model of the collision term in the Boltzmann equation is introduced which is similar in concept to the well‐known Krook model but yields the correct Prandtl number of ⅔ for a monatomic gas. A new method for constructing kinetic models is presented which is based on the information theory concept of entropy or uncertainty. This method, which is applicable to quite general systems in nonequilibrium statistical mechanics, is used to construct statistical models for multicomponent gas mixtures and for gases consisting of molecules with internal degrees of freedom.
482 citations
TL;DR: In this paper, an equivalence between the discrete velocity method of solving the Boltzmann equation and the Hermite polynomial expansion of the distribution function has been shown, and it is shown that truncating the truncated part has no contribution to the moments of low orders and is negligible at small Mach numbers.
Abstract: We point out an equivalence between the discrete velocity method of solving the Boltzmann equation, of which the lattice Boltzmann equation method is a special example, and the approximations to the Boltzmann equation by a Hermite polynomial expansion. Discretizing the Boltzmann equation with a Bhatnagar-Gross-Krook collision term at the velocities that correspond to the nodes of a Hermite quadrature is shown to be equivalent to truncating the Hermite expansion of the distribution function to the corresponding order. The truncated part of the distribution has no contribution to the moments of low orders and is negligible at small Mach numbers.
377 citations
TL;DR: Phase transitions in one dimension are discussed from the point of view of order—disorder transitions in linear polymers using the formalism of sequence generating functions due to Lifson.
Abstract: Phase transitions in one dimension are discussed from the point of view of order—disorder transitions in linear polymers using the formalism of sequence generating functions due to Lifson. If the statistical weight vj of an ordered sequence of j units has the form (lnvj)/j=a—bj−α, then a phase transition occurs when 0<α<1. As demonstrated by Fisher, this will occur, for example, if certain many‐body interactions of short range are introduced. This behavior is obtained if we consider long‐range pair potentials of the form 1/r1+α, for 0<α<1, occurring between all the units of an ordered sequence. An exponential potential, e−γx, gives a phase transition in the limit γ→0 if interactions are restricted to the units in an ordered sequence. The occurence of a phase transition arises from the convergence of the sequence generating function and its first derivative at the value of the unit partition function equal to the statistical weight of the ordered unit. This gives rise to a bend in the curve of the unit par...
286 citations