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Full-Text Articles in Physical Sciences and Mathematics
Nonlocal Diffusion Models: Application To Rapid Solidification Of Binary Mixtures, Sergey Sobolev
Nonlocal Diffusion Models: Application To Rapid Solidification Of Binary Mixtures, Sergey Sobolev
Sergey Sobolev
Various theoretical treatments and models for nonlocal diffusion are briefly reviewed and discussed. The nonlocal effects arise in far from equilibrium processes, which involve extremely fast heat and mass transfer at very small time and length scales. With only diffusive dynamics, the nonlocal models result in a set of transfer equations of parabolic type with an infinite velocity of diffusive disturbances. With the wavelike dynamics, the models lead to a set of transfer equations of hyperbolic type with a finite velocity of diffusive disturbances. Rapid solidification of binary alloys has been used to illustrate the influence of the nonlocal diffusion …
Local Nonequilibrium Transport Models, Sergey Sobolev
Local Nonequilibrium Transport Models, Sergey Sobolev
Sergey Sobolev
No abstract provided.
Two-Temperature Discrete Model For Nonlocal Heat Conduction, Sergey Sobolev
Two-Temperature Discrete Model For Nonlocal Heat Conduction, Sergey Sobolev
Sergey Sobolev
The two-temperature discrete model for heat conduction in heterogeneous media is proposed. It is shown that the discrete model contains as limiting cases both hyperbolic and parabolic heat conduction equations for propagative and diffusive regimes, respectively. To obtain these limiting cases two different laws of continuum limit have been introduced. The evolution of the two-temperature system comprises three stages with distinct time scales : fast relaxation of each subsystem to local equilibrium, energy exchange between the subsystems and classical hydrodynamics.