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Quantum mechanical equations of motion are strictly linear in state descriptors, such as wavefunctions and density matrices, but equations describing chemical kinetics and hydrodynamics may be non-linear in concentrations. This…
A time domain finite element numerical study of impedance spectroscopy in composite electroceramics is presented. The simulations take into account the complexity of the realistic three dimensional granular structure including grains and…
Suspensions with fiber-like particles in the low Reynolds number regime are modeled by two different approaches that both use a Lagrangian representation of individual particles. The first method is the well-established formulation based on…
Fluid flow applications can involve a number of coupled problems. One is the simulation of free-surface flows, which require the solution of a free-boundary problem. Within this problem, the governing equations of fluid flow are coupled…
The purpose of the dynamics of moving systems is to search for the mathematical model that describes the link between the resultant applied force, that is the cause, and the speed of system that is the effect. This mathematical link…
We investigate an undamped random phase-space dynamics in deterministic external force fields (conservative and magnetic ones). By employing the hydrodynamical formalism for those stochastic processes we analyze microscopic kinetic-type…
In this paper we study thermo-electric transport in interacting two-dimensional Dirac-type systems using a phenomenological Boltzmann approach. We consider a setup that can accommodate electrons, holes, and collective modes. In the first…
We show that one can employ well-established numerical continuation methods to efficiently calculate the phase diagram for thermodynamic systems. In particular, this involves the determination of lines of phase coexistence related to first…
With the development of multi-layer elastic systems in the field of engineering mechanics, the corresponding variational inequality theory and algorithm design have received more attention and research. In this study, a class of equivalent…
The use of machine learning algorithms to predict behaviors of complex systems is booming. However, the key to an effective use of machine learning tools in multi-physics problems, including combustion, is to couple them to physical and…
In this work we present a mass conservative numerical scheme for two-phase flow in porous media. The model for flow consists on two fully coupled, non-linear equations: a degenerate parabolic equation and an elliptic equation. The proposed…
In this paper, we propose a new multiphysics finite element method for a Biot model with secondary consolidation in soil dynamics. To better describe the processes of deformation and diffusion underlying in the original model, we…
The properties of dense granular systems are analyzed from a hydrodynamical point of view, based on conservation laws for the particle number density and linear momentum. We discuss averaging problems associated with the nature of such…
The electroporoelasticity model, which couples Maxwell's equations with Biot's equations, plays a critical role in applications such as water conservancy exploration, earthquake early warning, and various other fields. This work focuses on…
We scrutinize the hydrodynamic approach for calculating dynamical correlations in one-dimensional superfluids near integrability and calculate the characteristic time scale {\tau} beyond which this approach is valid. For time scales shorter…
The moist shallow water equations offer a promising route for advancing understanding of the coupling of physical parametrisations and dynamics in numerical atmospheric models, an issue known as 'physics-dynamics coupling'. Without moist…
In this chapter, we aim at presenting the basic techniques necessary to go beyond the widely accepted paradigm of second-order numerics. We specifically focus on finite-volume schemes for hyperbolic conservation laws occuring in fluid…
Hybrid-kinetic simulations describe ion-scale kinetic phenomena in space plasmas by considering ions kinetically, i.e. as particles, while electrons are modelled as a fluid. Most of the existing hybrid-kinetic codes neglect the electron…
We consider the hydrodynamic modes for dense trapped ultracold gases, where the interparticle distance is comparable to the scattering length. We show that the experimental determination of the hydrodynamic mode frequencies allows to obtain…
This paper analyzes a space-time finite element method for fractional wave problems. The method uses a Petrov-Galerkin type time-stepping scheme to discretize the time fractional derivative of order $ \gamma $ ($1<\gamma<2$). We establish…