26 papers · ranked by Valyu relevance
Kai Trepka
Building models of organismal growth enables predictions of natural variability and responses to perturbations. Complex systems such as animal pattern development and bacterial colonies can be modeled numerically using a reaction-diffusion system with relatively few factors and yield qualitatively accurate results…
Yasir Nawaz, Muhammad Shoaib Arif, Kamaleldin Abodayeh, Wasfi Shatanawi
'Wasfi Shatanawi'] An explicit unconditionally stable scheme is proposed for solving time-dependent partial differential equations. The application of the proposed scheme is given to solve the COVID-19 epidemic model. This scheme is first-order accurate in time and second-order accurate in space and provides the…
Gráinne T Carroll, Paul D Devereux, David N Ku, Timothy M McGloughlin + 1 more
'Timothy M McGloughlin' 'Michael T Walsh'] Background The finite volume solver Fluent (Lebanon, NH, USA) is a computational fluid dynamics software employed to analyse biological mass-transport in the vasculature. A principal consideration for computational modelling of blood-side mass-transport is convection-diffusion…
Di Yang, Gang Peng, Zhiming Gao, Geert Verdoolaege
In this paper, we propose a new positivity-preserving finite volume scheme with fixed stencils for the nonequilibrium radiation diffusion equations on distorted meshes. This scheme is used to simulate the equations on meshes with both the cell-centered and cell-vertex unknowns. The cell-centered unknowns are the…
Authors not listed
Atomistic simulations provide essential mechanistic insights into chemical processes, yet many important phenomena in chemistry and materials science occur on timescales that are inaccessible to molecular dynamics. Existing computational approaches force a choice between atomic resolution on relatively short timescales…
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…
Rebecca Menssen, Madhav Mani
Modern biology is a treasure trove of data. With all this data, it is helpful to have analytical tools that are applicable regardless of context. One type of data that needs more quantitative analytical tools is particulate trajectories. This type of data appears in many different contexts and across scales in biology…
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…
Felipe A. Asenjo, Sergio A. Hojman
We report accelerating diffusive solutions to the diffusion equation with a constant diffusion tensor. The maximum values of the diffusion density evolve in an accelerating fashion described by Airy functions. We show the diffusive accelerating behavior for one–dimensional systems, as well as for a general…
Tao Guo
Prior studies have focused on the overall behavior of randomly moving particle swarms. However, the characteristics of the stochastic-constrained particles that form ubiquitously within these swarms remain oblivious. This study demonstrates a generalized diffusion equation for stochastic-constrained particles that…
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…
Hamsanandini Radhakrishnan, Chenying Zhao, Valerie J. Sydnor, Erica B. Baller + 14 more
Diffusion Spectrum Imaging (DSI) using dense Cartesian sampling of q-space has been shown to provide important advantages for modeling complex white matter architecture. However, its adoption has been limited by the lengthy acquisition time required. Sparser sampling of q-space combined with compressed sensing (CS)…
Mustaquim, S M, Dey, Asim K. + 2 more
This study provides essential insights into how diffusion processes unfold in complex networks, with a focus on cryptocurrency blockchains and infrastructure networks. The structural properties of these networks, such as hub-dominated, heavy-tailed topology, network motifs, and node centrality, significantly influence…
Srijana Pandey, Dinesh Gautam, Jixin Chen
Many interactions between small molecules and particles occur in solutions. They are surrounded by other molecules that do not react, for example, biological processes in water, chemical reactions in gas or liquid solutions, and environmental reactions in air and water. Predicting the rate of such interactions involves…
Natarajan Meghanathan
In this paper, we consider a random network such that there could be a link between any two nodes in the network with a certain probability (plink). Diffusion is the phenomenon of spreading information throughout the network, starting from one or more initial set of nodes (called the early adopters). Information…
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…
Hardi Veermäe, Marco Patriarca
We study a simple model of a random walker in d dimensions moving in the presence of a local heterogeneous attracting factor expressed in terms of an assigned space-dependent "attractiveness function", a situation frequently encountered in the study of various diffusion problems. The corresponding drift-diffusion…
Tadeusz Kosztołowicz
We present the model of a diffusion-absorption process in a system which consists of two media separated by a thin partially permeable membrane. The kind of diffusion as well as the parameters of the process may be different in both media. Based on a simply model of particle's random walk in a membrane system we derive…
Eirini Messaritaki, Stavros I. Dimitriadis, Derek K. Jones
Structural brain networks derived from diffusion magnetic resonance imaging data have been used extensively to describe the human brain, and graph theory has allowed quantification of their network properties. Schemes used to construct the graphs that represent the structural brain networks differ in the metrics they…
Gregory L. Eyink, Amir Homayoun Jafari
We discuss application of methods from the Kraichnan model of turbulent advection to the study of non-equilibrium concentration fluctuations arising during diffusion in liquid mixtures at high Schmidt numbers. This approach treats nonlinear advection of concentration fluctuations exactly, without linearization.…
Benjamin A. Dalton, Ivo F. Sbalzarini, Itsuo Hanasaki
We develop a theoretical foundation for a time-series analysis method suitable for revealing the spectrum of diffusion coefficients in mixed Brownian systems, for which no prior knowledge of particle distinction is required. This method is directly relevant for particle tracking in biological systems, in which…
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…
Jinshan Qi, Xun Liang, Yi Wang, Hengchao Cheng
Opinions shared publicly in online social networks spread broadly and at an extremely high speed. However, modelling information diffusion in online social networks is still a challenge that is intriguing to many researchers. To monitor public opinions online, it is necessary to model the process of information…
Authors not listed
We consider a heterogeneous diffusion equation and its corresponding generalization to the Cattaneo-Vernotte equation. It is derived by a combination of the continuity equation and the constitutive relation in various stochastic interpretations of the heterogeneous diffusion process. The heterogeneity in the system is…
Sergio Gómez, Alberto Fernández, Sandro Meloni, Alex Arenas
The networked structure of contacts shapes the spreading of epidemic processes. Recent advances on network theory have improved our understanding of the epidemic processes at large scale. The relevance of several considerations still needs to be evaluated in the study of epidemic spreading. One of them is that of…