26 papers · ranked by Valyu relevance
Rainer W. Alexandrowicz
Response time (RT) data play an important role in psychology. The diffusion model (DM) allows to analyze RT-data in a two-alternative-force-choice paradigm using a particle drift diffusion modeling approach. It accounts for right-skewed distributions in a natural way. However, the model incorporates seven parameters…
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…
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…
Mohammad Azimi, Yousef Jamali, Mohammad R. K. Mofrad, Nic D. Leipzig
Diffusion plays a key role in many biochemical reaction systems seen in nature. Scenarios where diffusion behavior is critical can be seen in the cell and subcellular compartments where molecular crowding limits the interaction between particles. We investigate the application of a computational method for modeling the…
Elliot J. Carr
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such transport processes are well established, they fail to account for randomness inherent…
Carlos Barajas, Domitilla Del Vecchio
Deterministic ordinary differential equation (ODE) models of genetic circuits, commonly assume a well-mixed ensemble of species inside the cell. However, intracellular spatial heterogeneity is frequently observed experimentally, with a circuit’s DNA location and volume occupied by the chromosome (excluded volume…
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…
Anna M. Langmüller, Courtney C. Murdock, Philipp W. Messer
Ordinary differential equation models such as the classical SIR model are widely used in epidemiology to study and predict infectious disease dynamics. However, these models typically assume that populations are homogeneously mixed, disregarding possible variations in disease prevalence due to spatial heterogeneity. To…
Jixin Chen
This report uses Monte Carlo simulations to connect stochastic single-molecule and ensemble surface adsorption of molecules from dilute solutions. Monte Carlo simulations often use a fundamental time resolution to simulate each discrete step for each molecule. The adsorption rate obtained from such a simulation…
М. Н. Овчинников
The fundamental solutions of diffusion equation for the local-equilibrium and nonlocal models are considered as the limiting cases of the solution of a problem related to consideration of the Brownian particles random walks. The differences between fundamental solutions were studied. It was shown that on the period of…
Jixin Chen
Diffusive adsorption/association is a fundamental step in almost all chemical reactions in diluted solutions, such as organic synthesis, polymerization, self-assembly, biomolecular interactions, electrode dynamics, catalysis, chromatography, air and water environmental dynamics, and social and market dynamics. However…
Saurabh Sivakumar, Ambarish Kulkarni
The advent of machine learning potentials (MLPs) provides a unique opportunity to access simulation timescales and to directly compute physiochemical properties that are typically intractable using density functional theory (DFT). In this study, we use an active learning curriculum to train a generalizable MLP using…
Sebastian Schmitt, Hans Hasse, Simon Stephan
Entropy scaling is a powerful technique that has been used successfully 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 have tackled this issue and present an entropy scaling framework for…
Sabeeha Hasnain, Upendra Harbola, Pradipta Bandyopadhyay
We study memory based random walk models to understand diffusive motion in crowded heterogeneous environment. The models considered are non-Markovian as the current move of the random walk models is determined by randomly selecting a move from history. At each step, particle can take right, left or stay moves which is…
Authors not listed
Predicting how often molecules collide in dilute solution remains a long-standing challenge often with several orders of magnitude difference between theoretical values and experimental values also among different experimental values. Traditional frameworks from Smoluchowski and Langmuir rely on the formation of stable…
Chih-Lung Chen, Tsing-Hai Wang, Ching-Hor Lee, Shi-Ping Teng
Diffusion is a dominant mechanism regulating the transport of released nuclides. The through-diffusion method is typically applied to determine the diffusion coefficients (D). Depending on the design of the experiment, the concentrations in the source term [i.e., inlet reservoir (IR)] or the end term [i.e., outlet…
Christophe Tournassat, Carl I. Steefel, Patricia M. Fox, Ruth M. Tinnacher
'Ruth M. Tinnacher'] The reactive transport code CrunchClay was used to derive effective diffusion coefficients (D*e), clay porosities (ε), and adsorption distribution coefficients (K**D) from through-diffusion data while considering accurately the influence of unavoidable experimental biases on the estimation of these…
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…
T. J. Sego, Josua O. Aponte-Serrano, Juliano F. Gianlupi, James A. Glazier
Background The biophysics of an organism span multiple scales from subcellular to organismal and include processes characterized by spatial properties, such as the diffusion of molecules, cell migration, and flow of intravenous fluids. Mathematical biology seeks to explain biophysical processes in mathematical terms…
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…
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…
Tresa M. Elias, Edward B. Brown Jr., Edward B. Brown III
Significance Multi-photon fluorescence recovery after photobleaching (MPFRAP) is a nonlinear microscopy technique used to measure the diffusion coefficient of fluorescently tagged molecules in solution. Previous MPFRAP fitting models calculate the diffusion coefficient in systems with diffusion or diffusion in laminar…
Cordula Reisch, Sandra Nickel, Hans‐Michael Tautenhahn
The paper presents an approach for overcoming modeling problems of typical life science applications with partly unknown mechanisms and lacking quantitative data: A model family of reaction diffusion equations is built up on a mesoscopic scale and uses classes of feasible functions for reaction and taxis terms. The…
Thomas Williams, James McCaw, James Osborne
There has been an increasing recognition of the utility of models of the spatial dynamics of viral spread within tissues. Multicellular models, where cells are represented as discrete regions of space coupled to a virus density surface, are a popular approach to capture these dynamics. Conventionally, such models 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…