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We introduce a Darcy-scale model to describe compressible multi-component flow in a fully saturated porous medium. In order to capture cross-diffusive effects between the different species correctly, we make use of the Maxwell--Stefan…
We consider an operator-theoretic approach to linear infinite-dimensional port-Hamiltonian systems. In particular, we use the theory of system nodes by Staffans to formulate a~suitable concept for port-Hamiltonian systems, which allows a…
We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…
We introduce a diffuse interface model describing the evolution of a mixture of two different viscous incompressible fluids of equal density. The main novelty of the present contribution consists in the fact that the effects of temperature…
The mathematical analysis on the behavior of the entropy for viscous, compressible, and heat conducting magnetohydrodynamic flows near the vacuum region is a challenging problem as the governing equation for entropy is highly degenerate and…
We consider the transport of conserved charges in spatially inhomogeneous quantum systems with a discrete lattice symmetry. We analyse the retarded two point functions involving the charge and the associated currents at long wavelengths,…
We derive a large-scale hydrodynamic equation, including diffusive and dissipative effects, for systems with generic static position-dependent driving forces coupling to local conserved quantities. We show that this equation predicts…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
Motivated by compartmental analysis in engineering and biophysical systems, we present a variational framework for the nonequilibrium thermodynamics of systems involving both distributed and discrete (finite dimensional) subsystems by…
We consider a general class of nonlinear diffusive models with bulk dissipation and boundary driving, and derive its hydrodynamic description in the large size limit. Both the average macroscopic behavior and the fluctuating properties of…
As a reduced representation of the nonlinear spectral fluxes of ideal invariants in incompressible magnetohydrodynamics, we construct a gradient-diffusion network model that combines phenomenological considerations and geometrical analysis…
We develop a geometric framework for irreversible transport phenomena in which macroscopic evolution equations arise from the combined structure of a thermodynamic state metric and an Onsager-based dissipation metric. The construction…
Current fluctuations in boundary-driven diffusive systems are, in many cases, studied using hydrodynamic theories. Their predictions are then expected to be valid for currents which scale inversely with the system size. To study this…
We present a symmetry-based formulation of nonlinear fluctuating hydrodynamics (NFH) for one-dimensional many-particle systems with generic homogeneous nearest-neighbor interactions. We derive the hydrodynamic equations solely from symmetry…
Mathematical modeling of real-world physical systems requires the consistent combination of a multitude of physical laws and phenomenological models. This challenging task can be greatly simplified by hierarchically decomposing systems into…
The modeling framework of port-Hamiltonian descriptor systems and their use in numerical simulation and control are discussed. The structure is ideal for automated network-based modeling since it is invariant under power-conserving…
Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density $\mathcal{H}$. In passing, we obtain generalisations for…
We derive analytical expressions for the spectral moments of the dynamical response functions of the Hubbard model using the high-temperature series expansion. We consider generic dimension $d$ as well as the infinite-$d$ limit, arbitrary…
We introduce a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations. In this scheme, the collective beam dynamics is described by time--reversal…
This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…