Related papers: Highly scalable numerical simulation of coupled re…
We review the recent literature on the simulation of the structure and deformation of amorphous glasses, including oxide and metallic glasses. We consider simulations at different length and time scales. At the nanometer scale, we review…
The propagation of cracks driven by a pressurized fluid emerges in several areas of engineering, including structural, geotechnical, and petroleum engineering. We present a robust numerical framework to simulate fluid-driven fracture…
We study a reaction-diffusion model posed on two distinct spatial scales that accounts for diffusion, aggregation, fragmentation, and deposition of populations of colloidal particles within a porous material. In this model, the macroscopic…
Models that involve coupled dynamics in a mixed-dimensional geometry are of increasing interest in several applications. Here, we describe the development of a simulation model for flow in fractured porous media, where the fractures and…
A hybrid mesoscopic multi-particle collision model is used to study diffusion-influenced reaction kinetics. The mesoscopic particle dynamics conserves mass, momentum and energy so that hydrodynamic effects are fully taken into account.…
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…
A scattering model is developed for ultracold molecular collisions, which allows inelastic processes, chemical reactions, and complex formation to be treated in a unified way. All these scattering processes and various combinations of them…
Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model…
The equation which describes a particle diffusing in a logarithmic potential arises in diverse physical problems such as momentum diffusion of atoms in optical traps, condensation processes, and denaturation of DNA molecules. A detailed…
A variety of simulation methodologies have been used for modeling reaction-diffusion dynamics -- including approaches based on Differential Equations (DE), the Stochastic Simulation Algorithm (SSA), Brownian Dynamics (BD), Green's Function…
For problems in astrophysics, planetary science and beyond, numerical simulations are often limited to simulating fewer particles than in the real system. To model collisions, the simulated particles (aka superparticles) need to be inflated…
Chemo-mechanical coupled systems have been a subject of interest for many decades now. Previous attempts to solve such models have mainly focused on elastic materials without taking into account the plastic deformation beyond yield, thus…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
We consider the numerical solution of coupled volume-surface reaction-diffusion systems having a detailed balance equilibrium. Based on the conservation of mass, an appropriate quadratic entropy functional is identified and an…
Thermodynamics analysis of oxidation-reduction reactions between metal melt and slag (1) provides answers to certain practical issues such as the path of specific chemical reactions, final (equilibrium) phase composition, and the elements…
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…
Mixed-dimensional mathematical models for flow in fractured media have been prevalent in the modeling community for almost two decades, utilizing the explicit representation of fractures by lower-dimensional manifolds embedded in the…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…
Recent advances in random-walk particle-tracking have enabled direct simulation of mixing and reactions on particles by allowing the particles to interact with each other using a multi-point mass transfer scheme. The mass transfer scheme…
One-dimensional non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relation. We consider in this paper transport properties…