Biomedical subjects

Iliya V Karlin

Publications and source records attributed to Iliya V Karlin.

8 recordsLinked to original sources

PubMed2003

Galilean-invariant lattice-Boltzmann models with H theorem.

We demonstrate that the requirement of Galilean invariance determines the choice of H function for a wide class of entropic lattice-Boltzmann models for the incompressible Navier-Stokes equations. The required H function has the form of the Burg entropy for D=2, and of a Tsallis entropy with q=1-(2/D) for D>2, where D is the number of spatial dimensions. We use this observation to construct a fully explicit, unconditionally stable, Galilean-invariant, lattice-Boltzmann model for the incompressible Navier-Stokes equations, for which attainable Reynolds number is limited only by grid resolution.

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PubMed2003

Dynamic mean-field models from a nonequilibrium thermodynamics perspective.

Complicated dynamic models are often approximated by introducing mean-field approximations and closures. The focus here is on examining such mean-field models using nonequilibrium thermodynamics. Two illustrative examples are studied in terms of the double-generator general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) framework. First, it is shown that a model for the coil-stretch transition of long chains in strong elongation flows as proposed by de Gennes is thermodynamically admissible. In the second example, we study a Gaussian approximation, which is used to simplify the effect of hydrodynamic interactions in polymer solutions. This approximation, which is known to be in conflict with the fluctuation-dissipation theorem, is identified as defective directly when formulated in the thermodynamic formalism.

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PubMed2003

Family of additive entropy functions out of thermodynamic limit.

We derive a one-parametric family of entropy functions that respect the additivity condition, and which describe effects of finiteness of statistical systems, in particular, distribution functions with long tails. This one-parametric family is different from the Tsallis entropies, and is a convex combination of the Boltzmann-Gibbs-Shannon entropy and the entropy function proposed by Burg. An example of how longer tails are described within the present approach is worked out for the canonical ensemble. We also discuss a possible origin of a hidden statistical dependence, and give explicit recipes on how to construct corresponding generalizations of the master equation.

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PubMed2002

Kinetic boundary conditions in the lattice Boltzmann method.

Derivation of the lattice Boltzmann method from the continuous kinetic theory [X. He and L. S. Luo, Phys. Rev. E 55, R6333 (1997); X. Shan and X. He, Phys. Rev. Lett. 80, 65 (1998)] is extended in order to obtain boundary conditions for the method. For the model of a diffusively reflecting moving solid wall, the boundary condition for the discrete set of velocities is derived, and the error of the discretization is estimated. Numerical results are presented which demonstrate convergence to the hydrodynamic limit. In particular, the Knudsen layer in the Kramers' problem is reproduced correctly for small Knudsen numbers.

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PubMed2002

Boundary layer variational principles: a case study.

Considering the model heat conduction problem in the setting of Grad's moment equations, we demonstrate a crossover in the structure of minima of the entropy production within the boundary layer. Based on this observation, we formulate and compare variation principles for solving the problem of boundary conditions in nonequilibrium thermodynamics.

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PubMed2002

Single relaxation time model for entropic lattice Boltzmann methods.

For lattice Boltzmann methods based on entropy functions, we derive a collision integral which enables simple identification of transport coefficients, and which circumvents construction of the equilibrium. Implementation of the two-dimensional hydrodynamics demonstrates considerable increase of stability with respect to conventional lattice Boltzmann schemes.

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PubMed2002

Duality in nonextensive statistical mechanics.

We revisit recent derivations of kinetic equations based on Tsallis' entropy concept. The method of kinetic functions is introduced as a standard tool for extensions of classical kinetic equations in the framework of Tsallis' statistical mechanics. Our analysis of the Boltzmann equation demonstrates a remarkable relation between thermodynamics and kinetics caused by the deformation of macroscopic observables.

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PubMed2002

Macroscopic dynamics through coarse-graining: a solvable example.

The recently derived fluctuation-dissipation formula [A. N. Gorban et al., Phys. Rev. E 63, 066124 (2001)] is illustrated by the explicit computation for McKean's kinetic model [H. P. McKean, J. Math. Phys. 8, 547 (1967)]. It is demonstrated that the result is identical, on the one hand, to the sum of the Chapman-Enskog expansion, and, on the other hand, to the exact solution of the invariance equation. The equality between all three results holds up to the crossover from the hydrodynamic to the kinetic domain.

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