Related papers: A reaction-diffusion model for the hydration/setti…
We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis in the right-hand side. The input of hysteresis is given by a vector-valued function of space and time. Such systems describe hysteretic…
This study concerns with singularly perturbed systems of second-order reaction-diffusion equations in ODE's. To handle this type of problems, a numerical-asymptotic hybrid method is employed. In this hybrid method, an efficient asymptotic…
In molecular simulation and fluid mechanics, the coupling of a particle domain with a continuum representation of its embedding environment is an ongoing challenge. In this work, we show a novel approach where the latest version of the…
We present a generalised framework for resolving the electrochemistry-diffusion interface and modelling hydrogen transport near a crack tip. The adsorption and absorption kinetics are captured by means of Neumann-type generalised boundary…
A two-phase two-component model is formulated for the advective-diffusive transport of methane in liquid phase through sediment with the accompanying formation and dissolution of methane hydrate. This free-boundary problem has a unique…
From soft polymeric gels to hardened cement paste, amorphous solids under constant load exhibit a pronounced time-dependent deformation called creep. The microscopic mechanism of such a phenomenon is poorly understood in amorphous materials…
A phase-field approach to the dynamics of liquid-solid interfaces that evolve due to precipitation and/or dissolution is presented. For the purpose of illustration and comparison with other methods, phase field simulations were carried out…
A formal derivation of linear hydrodynamics for a granular fluid is given. The linear response to small spatial perturbations of the homogeneous reference state is studied in detail using methods of non-equilibrium statistical mechanics. A…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
Reaction-diffusion systems have been proposed as a model for pattern formation and morphogenesis. The Fickian diffusion typically employed in these constructions model the Brownian motion of particles. The biological and chemical elements…
We propose Context Diffusion, a diffusion-based framework that enables image generation models to learn from visual examples presented in context. Recent work tackles such in-context learning for image generation, where a query image is…
First-principles atomistic molecular dynamics simulation in the micro-canonical and canonical ensembles has been used to study the diffusion of interstitial hydrogen in $\alpha$-iron. Hydrogen to Iron ratios between $\theta=1/16 and 1/2…
A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition…
A model for three dimensional detonation is proposed based on the approximation that the detonation thickness is small compared to the characteristic scales of the fluid motion. In this framework detonations are treated as a modified…
A one-dimensional reaction-diffusion model consisting of two species of particles and vacancies on a ring is introduced. The number of particles in one species is conserved while in the other species it can fluctuate because of creation and…
In this paper, we study a numerical approximation for a class of stationary states for reaction-diffusion system with m densities having disjoint support, which are governed by a minimization problem. We use quantitative properties of both…
We study an autocatalytic reaction-diffusion scheme, the Gray-Scott model, when the mixing processes do not homogenize the reactants. Starting from the master equation, we derive the resulting coupled, nonlinear, stochastic partial…
The practical description of disordered chemical reactions, where reactions involve multiple species at multiple sites, is presently challenge using correlated electronic structure methods. Here we describe the gradient theory of…
Motivated by a problem in heterogeneous catalysis, we study a model for irreversible first-order reactions in which gas transport occurs only by diffusion, and reaction occurs only at a small number of well-localized sites. The main problem…
We derive a model for the non-isothermal reaction-diffusion equation. Combining ideas from non-equilibrium thermodynamics with the energetic variational approach we obtain a general system modeling the evolution of a non-isothermal chemical…