28 papers · ranked by Valyu relevance
Przemysław Chełminiak
Resetting or restart, when applied to a stochastic process, usually brings its dynamics to a timeindependent stationary state. In turn, the optimal resetting rate makes the mean time to reach a target to be the shortest one. These and other intriguing problems have been intensively studied in the case of ordinary…
Przemysław Chełminiak
Evaluating the completion time of a random algorithm or a running stochastic process is a valuable tip not only from a purely theoretical, but also pragmatic point of view. In the formal sense, this kind of a task is specified in terms of the first-passage time statistics. Although first-passage properties of diffusive…
Henrik Stenlund
This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary function for diffusion is given having an interesting relationship with the…
M. A. F. dos Santos
This review article aims to stress and reunite some of the analytic formalism of the anomalous diffusive processes that have succeeded in their description. Also, it has the objective to discuss which of the new directions they have taken nowadays. The discussion is started by a brief historical report that starts with…
Giorgio Kaniadakis, Dionissios T. Hristopulos
Master equations define the dynamics that govern the time evolution of various physical processes on lattices. In the continuum limit, master equations lead to Fokker-Planck partial differential equations that represent the dynamics of physical systems in continuous spaces. Over the last few decades, nonlinear…
Gabriele Sicuro, Peter Rapčan, Constantino Tsallis
We extend a recently introduced free-energy formalism for homogeneous Fokker–Planck equations to a wide, and physically appealing, class of inhomogeneous nonlinear Fokker–Planck equations. In our approach, the free-energy functional is expressed in terms of an entropic functional and an auxiliary potential, both…
Arsalan Rahimabadi, Habib Benali
In a variety of practical applications, there is a need to investigate diffusion or reaction-diffusion processes on complex structures, including brain networks, that can be modeled as weighted undirected and directed graphs. As an instance, the celebrated Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP)…
A. Barletta, Pedro Vayssière Brandão, Florinda Capone, Roberta De Luca
Rayleigh number Authors: ['A. Barletta' 'Pedro Vayssière Brandão' 'Florinda Capone' 'Roberta De Luca'] This work investigates the influence of a generic anomalous diffusion model on mass convection in a fluid-saturated porous medium, focusing on superdiffusive regimes. A mathematical model is developed, and stability…
Rafael S. Zola, Ervin K. Lenzi, Luciano R. da Silva, Marcelo K. Lenzi + 3 more
'Marcelo K. Lenzi' 'Rainer Klages' 'Marco Aurélio Dos Santos Bernardes' 'Xinping Zhou'] We study the entropy production in a fractal system composed of two subsystems, each of which is subjected to an external force. This is achieved by using the H-theorem on the nonlinear Fokker-Planck equations (NFEs) characterizing…
Stuart T. Johnston, Ruth E. Baker, Sean D.L McElwain, Matthew J. Simpson
Invasion processes are ubiquitous throughout cell biology and ecology. During invasion, individuals can become isolated from the bulk population and behave differently. We present a discrete, exclusion-based process that models the birth, death and movement of individuals. The model distinguishes between individuals…
Hosein Nasrolahpour
Almost all phenomena and structures in nature exhibit some degrees of fractionality or fractality. Fractional calculus and fractal theory are two interrelated concepts. In this article we study the memory effects in nature and particularly in biological structures. Based on this fact that natural way to incorporate…
Jakub Spiechowicz, Ivan G. Marchenko, Peter Hänggi, Jerzy Łuczka + 1 more
'Antonio M. Scarfone'] The diffusion of small particles is omnipresent in many processes occurring in nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject of exploration that we opt here to narrow our survey to the case of the…
Gabriel G. da Rocha, Michely P. Rosseto, Rodrigo J. Jaronski, Derik W. Gryczak + 3 more
in Electrolytic Cells: A Generalized Poisson–Nernst–Planck Model with Memory Effects Authors: Gabriel G. da Rocha, Michely P. Rosseto, Rodrigo J. Jaronski, Derik W. Gryczak, Luiz R. Evangelista, Rafael S. Zola, Ervin K. Lenzi We present an extension of the standard Poisson-Nernst-Planck model by incorporating temporal…
Aishani Ghosal, Yu-Huan Wang, Nguyen Nguyen, Laura Troyer + 1 more
Advances in fluorescence microscopy have enabled high-resolution tracking of individual biomolecules in living cells. However, accurate estimation of diffusion parameters from single-particle trajectories remains challenging due to static and dynamic localization errors inherent in these measurements. While previous…
Kolja Klett, Andrey G. Cherstvy, Jaeoh Shin, Igor M. Sokolov + 1 more
We employ Langevin-dynamics simulations to unveil non-Brownian and non-Gaussian center-of-mass self-diffusion of massive flexible dumbbell-shaped particles in crowded two-dimensional solutions. We also study the intra-dumbbell dynamics due to the relative motion of the two constituent elastically-coupled disks. Our…
Nosrat Mohammadi, Wilson Truccolo, Sydney S Cash, Anne-Lise Giraud + 1 more
Modeling and interpreting the complex recurrent dynamics of neuronal spiking activity is essential to understanding how networks implement behavior and cognition. Nonlinear Hawkes process models can capture a large range of spiking dynamics, but remain difficult to interpret, due to their discontinuous and stochastic…
A. Bhattacharyay
Fick's law for coordinate dependent diffusivity is derived. Corresponding diffusion current in the presence of coordinate dependent diffusivity is consistent with the form as given by Kramers-Moyal expansion. We have obtained the equilibrium solution of the corresponding Smoluchowski equation. The equilibrium…
Kim R. Kristiansen, Bjørn Hafskjold, Miguel Rubi
Local equilibrium approximation (LEA) is a central assumption in many applications of non-equilibrium thermodynamics involving the transport of energy, mass, and momentum. However, assessing the validity of the LEA remains challenging due to the limited development of tools for characterizing non-equilibrium states…
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…
Dirk Gillespie, Francesco Pappalardo
The numerical integration of the time-dependent spherically-symmetric radial diffusion equation from a point source is considered. The flux through the source can vary in time, possibly stochastically based on the concentration produced by the source itself. Fick’s one-dimensional diffusion equation is integrated over…
Balázs Fábián, Matti Javanainen
Curved membranes are abundant and functionally relevant in living matter, yet they have eluded computational studies due to methodological limitations. With multiple approaches available for setting up simulations on such curved membranes, there is a growing need for efficient and versatile tools to analyze their…
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…
Jinggang Lan, David Wilkins, Vladimir Rybkin, Marcella Iannuzzi + 1 more
We report the static and dynamical properties of liquid water at second-order Møller-Plesset perturbation theory level (MP2) with classical and quantum dynamics simulations using a neural network potential. We examined the temperature-dependent radial distribution function, diffusion and vibrational dynamics. MP2…
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…
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…
Authors not listed
Two-dimensional electronic spectroscopy (2DES) is a powerful experimental technique, as it directly probes the nonlinear (third-order) response function of the system, providing key insights into ultrafast energy transfer and relaxation processes. However, 2DES experiments are generally difficult to interpret, often…
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…