27 papers · ranked by Valyu relevance
K. Zhukovsky
We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal…
K. V. Zhukovsky
We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the operational exponent…
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…
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…
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…
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…
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…
Benjamin Anwasia
We study a kinetic model for non-reactive mixtures of monatomic gases with hard-sphere cross-sections under isothermal condition. By considering a diffusive scaling of the kinetic model and using the method of moments, we formally obtain from the continuity and momentum balance equations of the species, in the limit as…
Anton Peterlin
Very often a non-solvent diffuses into a glassy polymer with a steep concentration profile proceeding at an almost constant rate v yielding a weight gain proportional to time. Such a diffusion is called type II diffusion in order to distinguish it from the more usual “Fickian” diffusion proceeding without such a…
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…
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
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…
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…
Waipot Ngamsaad, Suthep Suantai
In this study, we investigate a porous medium-type flux limited reaction–diffusion equation that arises in morphogenesis modeling. This nonlinear partial differential equation is an extension of the generalized Fisher–Kolmogorov–Petrovsky–Piskunov (Fisher-KPP) equation in onedimensional space. The approximate…
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…
Anotida Madzvamuse, Andy H. W. Chung, Chandrasekhar Venkataraman
In this article, we formulate new models for coupled systems of bulk-surface reaction-diffusion equations on stationary volumes. The bulk reaction-diffusion equations are coupled to the surface reaction-diffusion equations through linear Robin-type boundary conditions. We then state and prove the necessary conditions…
Valery Doobko
- 1. ( ; ), ( ; ) , , С x t a x t i e i j - are bounded together with their first and second derivatives in x,t . - 2. There exists 0, such that for n (Z, AZ) Z ,Z R 2 . - 3. (0) 0( ), (0) (0), (0) (0), 4 3M y x x y y
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…
Andreas Buttenschön, Thomas Hillen, Alf Gerisch, Kevin J. Painter
Cellular adhesion provides one of the fundamental forms of biological interaction between cells and their surroundings, yet the continuum modelling of cellular adhesion has remained mathematically challenging. In 2006, Armstrong et al. proposed a mathematical model in the form of an integro-partial differential…
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…
Matthew J Simpson, Jesse A Sharp, Liam C Morrow, Ruth E Baker
Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions.…
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…