27 papers · ranked by Valyu relevance
Eeshwar Prasad Poudel, Pitambar Acharya, Jeevan Kafle, Shreeram Khadka
'Shreeram Khadka'] In this paper, we address a time-dependent one-dimensional linear advectiondiffusion equation with Dirichlet homogeneous boundary conditions. The equation is solved both analytically, using separation of variables, and numerically, employing the finite difference method. The computational output…
Ervin K. Lenzi, Rafael S. Zola, Michely P. Rosseto, Renio S. Mendes + 13 more
'Haroldo V. Ribeiro' 'Luciano R. da Silva' 'Luiz R. Evangelista' 'Ugur Tirnakli' 'Christian Beck' 'Hans J. Herrmann' 'Airton Deppman' 'Henrik Jeldtoft Jensen' 'Evaldo M. F. Curado' 'Fernando D. Nobre' 'Angelo Plastino' 'Astero Provata' 'Andrea Rapisarda'] In this study, we investigate a nonlinear diffusion process in…
Tadeusz Kosztołowicz, Aldona Dutkiewicz, Katarzyna D. Lewandowska
Normal and anomalous diffusion processes are characterized by the time evolution of the mean square displacement of a diffusing molecule $σ2(t)$. When $σ2(t)$ is a power function of time, the process is described by a fractional subdiffusion, fractional superdiffusion or normal diffusion equation. However, for other…
Imre Ferenc Barna, László Mátyás
We investigate diffusion equations which have concentration dependent diffusion coefficients with physically two relevant Ansätze, the self-similar and the traveling wave Ansatz. We found that for power-law concentration dependence some of the results can be expressed with a general analytic implicit formulas for both…
Guglielmo Macrelli
A review of solutions of solid-state diffusion problems in infinite and semi-infinite bodies is presented. Based on the identified solutions for the semi-infinite body a two-step diffusion problem is discussed in detail with the first step characterized by a Dirichlet constant concentration condition and the second…
Camila Bräutigam, Matteo Smerlak
Diffusion theory is a central tool of modern population genetics, yielding simple expressions for fixation probabilities and other quantities that are not easily derived from the underlying Wright-Fisher model. Unfortunately, the textbook derivation of diffusion equations as scaling limits requires evolutionary…
Gabriel Barreiro, Vladimir Pérez-Veloz
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local models. This paper investigates a nonlinear diffusion equation where the…
Keita Nakajima, Hirokazu Ninomiya
Biological diffusion processes are often influenced by environmental factors. In this study, we investigate the effects of variable diffusion, which depend on the point between the departure and the arrival points, on the propagation of bistable waves. This process includes neutral, repulsive, and attractive…
Zhansen Qian, Y. Qiu, L. Zhao, J. Wu
In this paper a Monte-Carlo method for simulating the motion of fluid flow moving along a solid wall is proposed. The random vortex method in the present paper is established by using the reflection technology and perturbation technique. The Monte-Carlo method based on this random vortex dynamic may be implemented, and…
Jixin Chen
Predicting the reaction kinetics, that is, how fast a reaction can happen in a solution, is essential information for many processes, such as industrial chemical manufacturing, refining, synthesis and separation of petroleum products, environmental processes in air and water, biological reactions in cells, biosensing…
Bérénice Grec, Srboljub Simić
> Abstract. The aim of the study is to compare the standard Maxwell-Stefan model of diffusion with the higher-order one recently derived. This higher-order model takes into account the influence of the complete pressure tensor. A numerical scheme is developed for comparing the two models through numerical simulations…
José M. Escorcia, Erwin Suazo
Equations with Variable Coefficients Through a Riccati System Authors: ['José M. Escorcia' 'Erwin Suazo'] Abstract. This work is concerned with the study of explicit solutions for generalized coupled reaction-diffusion and Burgers-type systems with variable coefficients. Including nonlinear models with variable…
Jixin Chen
Predicting the reaction kinetics, that is, how fast a reaction can happen in a solution, is essential information for many processes, such as industrial chemical manufacturing, refining, synthesis and separation of petroleum products, environmental processes in air and water, biological reactions in cells, biosensing…
Jixin Chen
Predicting the reaction kinetics, that is, how fast a reaction can happen in a solution, is essential information for many processes, such as industrial chemical manufacturing, refining, synthesis and separation of petroleum products, environmental processes in air and water, biological reactions in cells, biosensing…
Paul C. Bressloff
There are many processes in cell biology that can be modeled in terms of particles diffusing in a two-dimensional (2D) or three-dimensional (3D) bounded domain $\varOmega \subset{\mathbb{R}}^d$ containing a set of small subdomains or interior compartments ${\mathcal{U}}_j$, $j=1,\ldots ,N$ (singularly-perturbed…
Sebastian Schmitt, Hans Hasse, Simon Stephan
Entropy scaling is a powerful technique that has been used for predicting transport properties of pure components over a wide range of states. However, modeling mixture diffusion coefficients by entropy scaling is an unresolved task. We tackle this issue and present an entropy scaling framework for predicting mixture…
Johanna Busch, Dietmar Paschek
In a recent paper [J. Phys. Chem.B 127, 7983-7987 (2023)] , we have shown that for molecular dynamics (MD) simulations using orthorhombic periodic boundary conditions with "magic" box length ratios of $L_z/L_x=L_z/L_y=2.7933596497$, the self-diffusion coefficients $D_x$ and $D_y$ in $x$- and $y$-direction are…
Authors not listed
Classical molecular dynamics (MD) simulation is the most computationally efficient way to model large molecular systems atomistically for extended periods; however, due to fixed forcefield parameters, incorporating on-the-fly quantum reactions is not straightforward. Reactive Step-Based Molecular Dynamics (RSMD) is a…
Jurgen Riedel, Chris P. Barnes
In this study we examine the emergence of complex biological patterns through the lens of reaction-diffusion systems. We introduce two novel complexity metrics — Diversity of Number of States (DNOS) and Diversity of Pattern Complexity (DPC)— which aim to quantify structural intricacies in pattern formation, enhancing…
Josephine Evans, Daniel Morris, Havva Yoldaş
We consider a class of nonlinear, spatially inhomogeneous kinetic equations of BGK-type with density dependent collision rates. These equations share the same superlinearity as the Boltzmann equation, and fall into the class of run and tumble equations appearing in mathematical biology. We prove that the Cauchy problem…
Antonio Agresti
This paper is concerned with the problem of regularization by noise of systems of reaction-diffusion equations with mass control. It is known that strong solutions to such systems of PDEs may blow-up in finite time. Moreover, for many systems of practical interest, establishing whether the blow-up occurs or not is an…
A. Girelli, G. Giantesio, A. Musesti, R. Penta
This work explores diffusion with scale-dependent coefficients, starting from a general advection-diffusion framework from a theoretical standpoint, and then focusing numerically on a purely diffusive regime. Advection-diffusion processes are central to modeling transport phenomena in natural and engineered systems.…
Fernando P. Duda, Francisco S. Forte Neto, Eliot Fried
We develop a continuum framework applicable to solid-state hydrogen storage, cell biology and other scenarios where the diffusion of a single constituent within a bulk region is coupled via adsorption/desorption to reactions and diffusion on the boundary of the region. We formulate content balances for all relevant…
Johannes G. Borgqvist, Philip Gerlee, Carl Lundholm
The formation of buds on the cell membrane of budding yeast cells is thought to be driven by reactions and diffusion involving the protein Cdc42. These processes can be described by a coupled system of partial differential equations known as the Schnakenberg system. The Schnakenberg system is known to exhibit…
Martin Kutscherauer, Scott Anderson, Sebastian Böcklein, Gerhard Mestl + 2 more
Modeling catalytic fixed bed reactors with a small tube-to-particle diameter ratio requires a detailed description of the interactions between fluid flow, intra-particle transport, and the chemical reaction(s) within the catalyst. Particle-resolved computational fluid dynamics (PRCFD) simulations are the most promising…
Antoine Diez, Andrew L. Krause, Philip K. Maini, Eamonn A. Gaffney + 1 more
Conditions for self-organisation via Turing’s mechanism in biological systems represented by reaction-diffusion or reaction-cross-diffusion models have been extensively studied. Nonetheless, the impact of tissue stratification in such systems is under-explored, despite its ubiquity in the context of a thin epithelium…
Soha Ben Tahar, Jose J Muñoz, Sandra J Shefelbine, Ester Comellas
Reaction-diffusion systems have been widely used to model pattern formation in biological systems. However, the emergence of Turing patterns in three-dimensional (3D) domains remains relatively unexplored. A few studies on this topic have shown that extending pattern formation from 2D to 3D is not straightforward.…