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Boltzmann constant: The Boltzmann constant, k, is one of seven fixed constants defining the International System of Units, the SI, with k = 1.380 649 x 10 −23 J K −1. The Boltzmann constant is a proportionality constant between the quantities temperature (with unit kelvin) and energy (with unit joule).
The general equation can then be written as [6] = + + (),. where the "force" term corresponds to the forces exerted on the particles by an external influence (not by the particles themselves), the "diff" term represents the diffusion of particles, and "coll" is the collision term – accounting for the forces acting between particles in collisions.
APBS (previously also Advanced Poisson-Boltzmann Solver) is a free and open-source software for solving the equations of continuum electrostatics intended primarily for the large biomolecular systems. [1] [2] It is available under the BSD license. PDB2PQR prepares the protein structure files from Protein Data Bank for use with APBS.
Observing the previous equation, a trivial solution is found for the case dc/dξ = 0, that is when concentration is constant over ξ.This can be interpreted as the rate of advancement of a concentration front being proportional to the square root of time (), or, equivalently, to the time necessary for a concentration front to arrive at a certain position being proportional to the square of the ...
Chapman–Enskog theory provides a framework in which equations of hydrodynamics for a gas can be derived from the Boltzmann equation.The technique justifies the otherwise phenomenological constitutive relations appearing in hydrodynamical descriptions such as the Navier–Stokes equations.
The Boltzmann equation is notoriously difficult to integrate. David Hilbert spent years trying to solve it without any real success. The form of the collision term assumed by Boltzmann was approximate. However, for an ideal gas the standard Chapman–Enskog solution of the Boltzmann equation is
In statistical thermodynamics, thermodynamic beta, also known as coldness, [1] is the reciprocal of the thermodynamic temperature of a system: = (where T is the temperature and k B is Boltzmann constant).
A different interpretation of the lattice Boltzmann equation is that of a discrete-velocity Boltzmann equation. The numerical methods of solution of the system of partial differential equations then give rise to a discrete map, which can be interpreted as the propagation and collision of fictitious particles.