55,545 research outputs found
Lie groups in nonequilibrium thermodynamics: Geometric structure behind viscoplasticity
Poisson brackets provide the mathematical structure required to identify the
reversible contribution to dynamic phenomena in nonequilibrium thermodynamics.
This mathematical structure is deeply linked to Lie groups and their Lie
algebras. From the characterization of all the Lie groups associated with a
given Lie algebra as quotients of a universal covering group, we obtain a
natural classification of rheological models based on the concept of discrete
reference states and, in particular, we find a clear-cut and deep distinction
between viscoplasticity and viscoelasticity. The abstract ideas are illustrated
by a naive toy model of crystal viscoplasticity, but similar kinetic models are
also used for modeling the viscoplastic behavior of glasses. We discuss some
implications for coarse graining and statistical mechanics.Comment: 11 pages, 1 figure, accepted for publication in J. Non-Newtonian
Fluid Mech. Keywords: Elastic-viscoplastic materials, Nonequilibrium
thermodynamics, GENERIC, Lie groups, Reference state
Dendritic to globular morphology transition in ternary alloy solidification
The evolution of solidification microstructures in ternary metallic alloys is
investigated by adaptive finite element simulations of a general multicomponent
phase-field model. A morphological transition from dendritic to globular growth
is found by varying the alloy composition at a fixed undercooling. The
dependence of the growth velocity and of the impurity segregation in the solid
phase on the composition is analyzed and indicates a smooth type of transition
between the dendritic and globular growth structures.Comment: 4 pages, 2 figure
Fluid Simulations with Localized Boltzmann Upscaling by Direct Simulation Monte-Carlo
In the present work, we present a novel numerical algorithm to couple the
Direct Simulation Monte Carlo method (DSMC) for the solution of the Boltzmann
equation with a finite volume like method for the solution of the Euler
equations. Recently we presented in [14],[16],[17] different methodologies
which permit to solve fluid dynamics problems with localized regions of
departure from thermodynamical equilibrium. The methods rely on the
introduction of buffer zones which realize a smooth transition between the
kinetic and the fluid regions. In this paper we extend the idea of buffer zones
and dynamic coupling to the case of the Monte Carlo methods. To facilitate the
coupling and avoid the onset of spurious oscillations in the fluid regions
which are consequences of the coupling with a stochastic numerical scheme, we
use a new technique which permits to reduce the variance of the particle
methods [11]. In addition, the use of this method permits to obtain estimations
of the breakdowns of the fluid models less affected by fluctuations and
consequently to reduce the kinetic regions and optimize the coupling. In the
last part of the paper several numerical examples are presented to validate the
method and measure its computational performances
Pattern formation in a diffusion-ODE model with hysteresis
Coupling diffusion process of signaling molecules with nonlinear interactions
of intracellular processes and cellular growth/transformation leads to a system
of reaction-diffusion equations coupled with ordinary differential equations
(diffusion-ODE models), which differ from the usual reaction-diffusion systems.
One of the mechanisms of pattern formation in such systems is based on the
existence of multiple steady states and hysteresis in the ODE subsystem.
Diffusion tries to average different states and is the cause of spatio-temporal
patterns. In this paper we provide a systematic description of stationary
solutions of such systems, having the form of transition or boundary layers.
The solutions are discontinuous in the case of non-diffusing variables whose
quasi-stationary dynamics exhibit hysteresis. The considered model is motivated
by biological applications and elucidates a possible mechanism of formation of
patterns with sharp transitions.Comment: 32 pages, 8 picture
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