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Mathematically, the Maxwell–Boltzmann distribution is the chi distribution with three degrees of freedom (the components of the velocity vector in Euclidean space), with a scale parameter measuring speeds in units proportional to the square root of / (the ratio of temperature and particle mass).
A kinetic description is achieved by solving the Boltzmann equation or, when the correct description of long-range Coulomb interaction is necessary, by the Vlasov equation which contains self-consistent collective electromagnetic field, or by the Fokker–Planck equation, in which approximations have been used to derive manageable collision terms.
The Andersen thermostat is a proposal in molecular dynamics simulation for maintaining constant temperature conditions. [1] [2] It is based on periodic reassignment of the velocities of atoms or molecules. For each atom or molecule, the reassigned velocity is picked randomly according to Maxwell–Boltzmann statistics for the given
The Monte Carlo method for electron transport is a semiclassical Monte Carlo (MC) approach of modeling semiconductor transport. Assuming the carrier motion consists of free flights interrupted by scattering mechanisms, a computer is utilized to simulate the trajectories of particles as they move across the device under the influence of an electric field using classical mechanics.
Using the results from either Maxwell–Boltzmann statistics, Bose–Einstein statistics or Fermi–Dirac statistics we use the Thomas–Fermi approximation (gas in a box) and go to the limit of a very large trap, and express the degeneracy of the energy states as a differential, and summations over states as integrals.
Maxwell–Boltzmann statistics is used to derive the Maxwell–Boltzmann distribution of an ideal gas. However, it can also be used to extend that distribution to particles with a different energy–momentum relation, such as relativistic particles (resulting in Maxwell–Jüttner distribution), and to other than three-dimensional spaces.
Maxwell–Boltzmann may refer to: Maxwell–Boltzmann statistics, statistical distribution of material particles over various energy states in thermal equilibrium;
All quantities are in Gaussian units except energy and temperature which are in electronvolts.For the sake of simplicity, a single ionic species is assumed. The ion mass is expressed in units of the proton mass, = / and the ion charge in units of the elementary charge, = / (in the case of a fully ionized atom, equals to the respective atomic number).