Moment closure hierarchies for kinetic theories

Levermore, C. David

doi:10.1007/bf02179552

Cited by 849 publications

(940 citation statements)

References 25 publications

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“…In general, in the case considered in this section as well as in that considered in Section 2, it is not possible to assure that such a procedure can be accomplished. The solvability of the MEP problem depends on the band structure and on the choice of the moments, as well known already in gas-dynamics [14,49]. For example, if the parabolic case (where the energy is a quadratic function of the wave vector) is considered, the same drawbacks of classical gas-dynamics arise regarding the lack of integrability of the MEP distribution function.…”

Section: Two-dimensional Electron Gases: the Case Of Quantum Confinementmentioning

confidence: 97%

“…Macroscopic models can be constructed starting from the BBP system by taking a suitable number of moments of the distribution functions [14]. The most common choice is that of considering the following functions of the carrier and phonon wave vectors…”

Section: The 3d Semiclassical Macroscopic Modelsmentioning

confidence: 99%

“…A systematic way to find these relations is founded on a universal physical principle: the maximum entropy principle [6,14,27,28]. It states that, if a certain number of moments is known, then the least biased distribution functions, which can be used for evaluating the unknown moments, are those maximizing the total entropy functional under the constraint that they reproduce the known moments.…”

Section: The 3d Semiclassical Macroscopic Modelsmentioning

confidence: 99%

“…The models also have nice mathematical properties, being symmetric hyperbolic. In particular, this assures the well-posedness of the Cauchy problems and the finite velocity of the propagation of disturbances [14].…”

Section: Introductionmentioning

confidence: 96%

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Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors

Mascali

Romano

2017

Entropy

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Abstract:In the last two decades, the Maximum Entropy Principle (MEP) has been successfully employed to construct macroscopic models able to describe the charge and heat transport in semiconductor devices. These models are obtained, starting from the Boltzmann transport equations, for the charge and the phonon distribution functions, by taking-as macroscopic variables-suitable moments of the distributions and exploiting MEP in order to close the evolution equations for the chosen moments. Important results have also been obtained for the description of charge transport in devices made both of elemental and compound semiconductors, in cases where charge confinement is present and the carrier flow is two-or one-dimensional.

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Section: Two-dimensional Electron Gases: the Case Of Quantum Confinementmentioning

confidence: 97%

Section: The 3d Semiclassical Macroscopic Modelsmentioning

confidence: 99%

Section: The 3d Semiclassical Macroscopic Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

See 2 more Smart Citations

Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors

Mascali

Romano

2017

Entropy

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“…A physically sound modeling approach for approximating the mixture collision term is thus needed in any discrete velocity formulation. Recently, a new approach to model kinetic equations has been developed (Gorban and Karlin (1994); Levermore (1996); Ansumali et al (2005); ). The basic idea (Gorban and Karlin (1994)) is a model representation on the fast-slow decomposition of motions near quasi-equilibrium states.…”

Section: Introductionmentioning

confidence: 99%

Entropic lattice Boltzmann method for simulation of binary mixtures

Arcidiacono

Ansumali

Karlin

et al. 2006

Mathematics and Computers in Simulation

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A new kinetic model for binary mixtures and its Lattice Boltzman (LB) discretization is presented. In the hydrodynamic limit the model recovers the Navier-Stokes and the Stefan-Maxwell binary diffusion equations. The thermodynamic consistency is ensured by the defined non-negative entropy production within the domain of applicability of the model. The present formulation is able to simulate mixtures with different Schmidt numbers and with a large molecular weight ratio of the components.

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A Hierarchy of Hyperbolic Models Linking Boltzmann to Navier Stokes Equations for Polyatomic Gases

Tallec

2000

Z. angew. Math. Mech.

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Moment closure hierarchies for kinetic theories

Cited by 849 publications

References 25 publications

Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors

Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors

Entropic lattice Boltzmann method for simulation of binary mixtures

A Hierarchy of Hyperbolic Models Linking Boltzmann to Navier Stokes Equations for Polyatomic Gases

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