相关论文: Generalized gradient flow structure of internal en…

This article is concerned with the existence of nonnegative weak solutions to a particular fourth-order partial differential equation: it is a formal gradient flow with respect to a generalized Wasserstein transportation distance with…

Aspects of the dynamical glass transition are considered within a mean field spin glass model. At the dynamical transition the the system condenses in a state of lower entropy. The difference, the information entropy or complexity, is…

We develop an optimization-based approach to the problem of reconstructing temperature-dependent material properties in complex thermo-fluid systems described by the equations for the conservation of mass, momentum and energy. Our goal is…

We study thermodynamical formalism of a discrete nonautonomous dynamical system determined by a sequence of continuous self-maps of a compact metric space. Using the methods of Convex Analysis we get variational principles for pressure…

Thermoelectricity is traditionally explained via Onsager's irreversible, flux-force framework. The coupled flows of heat and electric charge are modelled as steady-state flows, driven by the thermodynamic forces defined in terms of the…

This paper presents the continuous and discrete variational formulations of simple thermodynamical systems whose configuration space is a (finite dimensional) Lie group. We follow the variational approach to nonequilibrium thermodynamics…

This study uses continuum thermodynamics of pure thermoelastic fluids to examine their phase transformation. To examine phase transformation kinetics, a special emphasis is placed on the jump condition for the axiom of entropy inequality,…

We propose a thermodynamically consistent phase-field model for the flow of a mixture of two different viscous incompressible fluids of equal density in a bounded domain. We prove the well-posedness of local-in-time strong solutions by…

Dissipative particle dynamics (DPD) does not conserve energy and this precludes its use in the study of thermal processes in complex fluids. We present here a generalization of DPD that incorporates an internal energy and a temperature…

The equality between dissipation and energy drop is a structural property of gradient-flow dynamics. The classical implicit Euler scheme fails to reproduce this equality at the discrete level. We discuss two modifications of the Euler…

Phase transitions impose topological constraints on thermodynamic state variables, masking energetic fluctuations at the phase boundary. This constraint is most apparent in melting systems, where temperature remains pinned despite continued…

We develop the convex-analytic structure of the thermodynamic formalism for continuous maps on compact metric spaces. The pressure functional is the Legendre-Fenchel transform of the negative entropy, and the biconjugate recovery of the…

The GENERIC structure allows for a unified treatment of different discrete models of hydrodynamics. We first propose a finite volume Lagrangian discretization of the continuum equations of hydrodynamics through the Voronoi tessellation. We…

Optimal transport theory has been a powerful tool for the analysis of parabolic equationsviewed as gradient flows of volume forms according to suitable transportation metrics.In this paper, we present an example of gradient flows for closed…

A type-I model of non-isothermal multicomponent systems of gases describing mass diffusive and heat conductive phenomena is presented. The derivation of the model and a convergence result among thermomechanical theories in the smooth regime…

We revisit the sharp-interface continuum thermodynamics of two-phase multicomponent fluid systems, accounting for partial mass and partial momentum balances both in the bulk phases and on the interface. This allows to describe the transfer…

A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible…

We study the governing equations for the motion of the fluid particles near air-water interface from an energetic point of view. Since evaporation and condensation phenomena occur at the interface, we have to consider phase transition. This…

An extended Maxwell viscoelastic model with a relaxation parameter is studied from mathematical and numerical points of view. It is shown that the model has a gradient flow property with respect to a viscoelastic energy. Based on the…

An internal energy function of the mass density, the volumetric entropy and their gradients at n-order generates the representation of multi-gradient fluids. Thanks to Hamilton's principle, we obtain a thermodynamical form of the equation…