251 citations · 746 across the 16 of their papers we have counts for
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Constructive Methods of Invariant Manifolds for Kinetic Problems
A. N. Gorban, I. V. Karlin, A. Yu. Zinovyev
We present the Constructive Methods of Invariant Manifolds for model reduction in physical and chemical kinetics, developed during last two decades. The problem of reduced descript…
Kinetic Theory of Turbulence Modeling: Smallness Parameter, Scaling and Microscopic Derivation of Smagorinsky Model
Santosh Ansumali, Iliya V. Karlin, Sauro Succi
A mean-field approach (filtering out subgrid scales) is applied to the Boltzmann equation in order to derive a subgrid turbulence model based on kinetic theory. It is demonstrated…
Uniqueness of thermodynamic projector and kinetic basis of molecular individualism
A. N. Gorban, I. V. Karlin
Three results are presented: First, we solve the problem of persistence of dissipation for reduction of kinetic models. Kinetic equations with thermodynamic Lyapunov functions are…
Legendre Integrators, Post-Processing and Quasiequilibrium
A. N. Gorban, P. A. Gorban, I. V. Karlin
A toolbox for the development and reduction of the dynamical models of nonequilibrium systems is presented. The main components of this toolbox are: Legendre integrators, dynamical…
Geometry of irreversibility: The film of nonequilibrium states
A. N. Gorban, I. V. Karlin
A general geometrical framework of nonequilibrium thermodynamics is developed. The notion of macroscopically definable ensembles is developed. The thesis about macroscopically defi…
Existence of the H theorem for the athermal lattice Boltzmann models with nonpolynomial equilibria
Santosh Ansumali, Iliya V. Karlin
The entropy function is found for the two-dimensional seven-velocity lattice Boltzmann method on a triangular lattice. Some issues pertinent to the stability and accuracy of the se…