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Particle beds are widely used in various systems and processes, such as particle heat exchangers, granular flow reactors, and additive manufacturing. Accurate modeling of thermal conductivity of particle beds and understanding of their heat…
We discuss a connection between a generative model, called the diffusion model, and nonequilibrium thermodynamics for the Fokker-Planck equation, called stochastic thermodynamics. Using techniques from stochastic thermodynamics, we derive…
The recently established connection between stochastic thermodynamics and fluctuating hydrodynamics is applied to a study of efficiencies in the coupled transport of heat and matter on a small scale. A stochastic model for a mesoscopic cell…
A hydrogeological model for the spread of pollution in an aquifer is considered. The model consists in a convection-diffusion-reaction equation involving the dispersion tensor which depends nonlinearly of the fluid velocity. We introduce an…
This work presents a comparative review and classification between some well-known thermodynamically consistent models of hydrogel behavior in a large deformation setting, specifically focusing on solvent absorption/desorption and its…
In this work, we review and analyze both the theoretical and numerical aspects of strongly and weakly coupled thermoelastic systems. By employing spectral analysis techniques and establishing uniform resolvent estimates, we derive uniform…
Exact and approximate expressions for thermodynamic characteristics of heated matter, which consists of particles with finite mass-widths, are constructed. They are expressed in terms of Fermi/Bose distributions and spectral functions,…
We study the effects of superfluidity on the monopole and quadrupole collective excitations of a dilute ultra-cold Fermi gas with an attractive interatomic interaction. The system is treated fully microscopically within the Bogoliubov-de…
We establish universal relations between pattern formation and dissipation with a geometric approach to nonequilibrium thermodynamics of deterministic reaction-diffusion systems. We first provide a way to systematically decompose the…
We present a finite element discretization of a non-linear diffusion equation used in the field of critical phenomena and, more recently, in the context of Dynamic Density Functional Theory. The discretized equation preserves the structure…
Charge and energy are expected to diffuse in interacting systems of fermions at finite temperatures, even in the absence of disorder, with the interactions inducing a crossover from the coherent and ballistic streaming of quasi-particles at…
We develop a low-order conserving approximation for the interacting resonant-level model (IRLM), and apply it to (i) thermal equilibrium, (ii) nonequilibrium steady state, and (iii) nonequilibrium quench dynamics. Thermal equilibrium is…
We consider the numerical approximation of the ill-posed data assimilation problem for stationary convection-diffusion equations and extend our previous analysis in [Numer. Math. 144, 451--477, 2020] to the convection-dominated regime.…
The gradient discretisation method (GDM) is a generic framework for designing and analysing numerical schemes for diffusion models. In this paper, we study the GDM for the porous medium equation, including fast diffusion and slow diffusion…
Although generative diffusion models (GDMs) are widely used in practice, their theoretical foundations remain limited, especially concerning the impact of different discretization schemes applied to the underlying stochastic differential…
Seifert derived an exact fluctuation relation for diffusion processes using the concept of "stochastic system entropy". In this note we extend his formalism to entropic transport. We introduce the notion of relative stochastic entropy, or…
Understanding microstructural evolution under extreme thermal conditions is essential for advancing metal additive manufacturing (AM). This work demonstrates the feasibility of employing micro-electro-mechanical system (MEMS) heating…
The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…
In this paper, we study stochastic homogenization of a coupled diffusion-reaction system. The diffusion-reaction system is coupled to stochastic differential equations, which govern the changes in the media properties. Though homogenization…
We propose thermodynamically consistent models for viscoelastic fluids with a stress diffusion term. In particular, we derive variants of compressible/incompressible Maxwell/Oldroyd-B models with a stress diffusion term in the evolution…