Related papers: Highly scalable numerical simulation of coupled re…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
Discrete element method simulations of confined bidisperse granular shear flows elucidate the balance between diffusion and segregation that can lead to either mixed or segregated states, depending on confining pressure. Results indicate…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…
Kinetic equations model the position-velocity distribution of particles subject to transport and collision effects. Under a diffusive scaling, these combined effects converge to a diffusion equation for the position density in the limit of…
This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive…
We investigate an optimization problem that arises when working within the paradigm of Data-Driven Computational Mechanics. In the context of the diffusion-reaction problem, such an optimization problem seeks for the continuous primal…
The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…
The diffusion model has demonstrated promising results in image generation, recently becoming mainstream and representing a notable advancement for many generative modeling tasks. Prior applications of the diffusion model for both fast…
We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish local…
We introduce a numerical workflow to model and simulate transient close-contact melting processes based on the space-time finite element method. That is, we aim at computing the velocity at which a forced heat source melts through a…
We introduce a simple and efficient algorithm for diffusion in smoothed particle hydrodynamics (SPH) simulations and apply it to the problem of chemical mixing. Based on the concept of turbulent diffusion, we link the diffusivity of a…
The paper deals with the homogenization of reaction-diffusion equations with large reaction terms in a multi-scale porous medium. We assume that the fractures and pores are equidistributed and that the coefficients of the equations are…
We present a computational approach for solving reaction-diffusion equations on evolving surfaces which have been obtained from cell image data. It is based on finite element spaces defined on surface triangulations extracted from time…
Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct…
A detailed description and validation of a recently developed integration scheme is here reported for one- and two-dimensional reaction-diffusion models. As paradigmatic examples of this class of partial differential equations the complex…
Having in mind as target audience beginner researchers working in the field of cultural heritage, we present succinctly the concept of two-scale modeling of reaction-diffusion problems as it fits to scenarios where the action of the…
Combined-resolution simulations are an effective way to study molecular properties across a range of length- and time-scales. These simulations can benefit from adaptive boundaries that allow the high-resolution region to adapt (change size…
We present the Multi-Particle-Collision (MPC) dynamics approach to simulate properties of low-dimensional systems. In particular, we illustrate the method for a simple model: a one-dimensional gas of point particles interacting through…
Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or…
Extensive simulations are performed of the diffusion-limited reaction A$+$B$\to 0$ in one dimension, with initially separated reagents. The reaction rate profile, and the probability distributions of the separation and midpoint of the…