Related papers: A framework for coupled deformation-diffusion anal…
We present an \textit{ab initio} method of diffusion, relaxation and dephasing processes of arbitrary observables, and corresponding diffusion lengths and lifetimes in solids. The method is based on linearized density-matrix master…
This work outlines a diffuse interface method for the study of fracture and fragmentation in ductile metals at high strain-rates in Eulerian finite volume simulations. The work is based on an existing diffuse interface method capable of…
In this work, we investigate a numerical procedure for recovering a space-dependent diffusion coefficient in a (sub)diffusion model from the given terminal data, and provide a rigorous numerical analysis of the procedure. By exploiting…
Solvation effect might have a tremendous influence on chemical reactions. However, precise quantum chemistry calculations are most often done either in vacuum neglecting the role of the solvent or using continuum solvent model ignoring its…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
The open dynamics of quantum many-body systems involve not only the exchange of energy, but also of other conserved quantities, such as momentum. This leads to additional decoherence, which may have a profound impact in the dynamics.…
This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary…
Despite the widespread use of Scanning Transmission Electron Microscopy (STEM) for observing the structure of materials at the atomic scale, a detailed understanding of some relevant electron beam damage mechanisms is limited. Recent…
A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…
We develop a continuum model for the dynamics of grain boundaries in three dimensions that incorporates the motion and reaction of the constituent dislocations. The continuum model is based on a simple representation of densities of curved…
The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied…
We study the rheology of a suspension of soft deformable droplets subjected to a pressure-driven flow. Through computer simulations, we measure the apparent viscosity as a function of droplet concentration and pressure gradient, and provide…
In this paper, we present splitting algorithms to solve multicomponent transport models with Maxwell-Stefan-diffusion approaches. The multicomponent models are related to transport problems, while we consider plasma processes, in which the…
We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the…
We present a high-fidelity three dimensional computational framework for simulating the bulk mechanical behavior of granular aggregates composed of deformable brittle grains. Departing from classical discrete element methods (DEM), our…
The incremental stress-strain relation of dense packings of polygons is investigated here by using molecular dynamics simulations. The comparison of the simulation results to the continuous theories is performed using explicit expressions…
In this paper, we present a model based on a local thermodynamic equilibrium, weakly ionized plasma-mixture model used for medical and technical applications in etching processes. We consider a simplified model based on the Maxwell-Stefan…
We investigate a two-scale system featuring an upscaled parabolic dispersion-reaction equation intimately linked to a family of elliptic cell problems. The system is strongly coupled through a dispersion tensor, which depends on the…
Diffusion models have recently gained traction as a powerful class of deep generative priors, excelling in a wide range of image restoration tasks due to their exceptional ability to model data distributions. To solve image restoration…
A thermodynamically consistent visco-elastodynamical model at finite strains is derived that also allows for inelasticity (like plasticity or creep), thermal coupling, and poroelasticity with diffusion. The theory is developed in the…