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Showing 1 to 20 of 145 for “"reaction-diffusion"”.
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Reaction-Diffusion Models of Cancer Dispersion
… the study is the mathematical analysis of a reaction-diffusion model describing the interaction between cancer cells, normal cells and growth inhibitor. The model leads to several predictions, some of which are supported by experimental data and clinical observations $\lbrack25\rbrack$. We …
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Energy methods for reaction-diffusion problems
Nonlinear reaction-diffusion equations arise in many areas of applied sciences such as combustion modeling, population dynamics, chemical kinetics, etc. A fundamental problem in the studies of these equations is to understand the long time behavior of solutions of the associated Cauchy problem. …
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Noisy Transport in Reaction-Diffusion Systems With Quenched Disorder
In order to determine the nature of transport in this system analytically, I will use a variety of tools drawn from disparate sources, including the theory of hopping conduction in doped semiconductors and first passage percolation. These tools will allow for predictions to be made for a number of …
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Stochastic Modeling and Simulation of Reaction-Diffusion Biochemical Systems
Reaction Diffusion Master Equation (RDME) framework, characterized by the discretization of the spatial domain, is one of the most widely used methods in the stochastic simulation of reaction-diffusion systems. Discretization sizes for RDME have to be appropriately chosen such that each discrete …
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Interfaces between Competing Patterns in Reaction-diffusion Systems with Nonlocal Coupling
… exhibits a wave instability for slow inhibitor diffusion, while, for fast inhibitor diffusion, a Turing instability is found. For moderate values of the inhibitor diffusion these two instabilities occur simultaneously at a codimension-2 wave-Turing instability. We perform a weakly nonlinear …
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Stability of planar fronts for a class of reaction diffusion systems
… space-independent steady states for a class of reaction diffusion systems that arise in combustion theory and chemical-reaction models. We begin by extending the recent one-dimensional stability results for reaction diffusion equations of this type. Using spaces with exponential weights, we …
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Diffusion Processes, Metric Graphs and Boundary Value Problems for Reaction Diffusion Systems
… a mathematical model of a class of first order reaction-diffusion system, known as TAP systems, in which gas reactants and products diffuse in a domain and reaction takes place at a single relatively small catalytic site in the domain. The central problem is to determine the probability of …
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Applications of Field Theory to Reaction Diffusion Models and Driven Diffusive Systems
… density. Two of the fit parameters, namely the diffusion constant and the noise strength, deviate from their naive bare values [6]. In particular, the former increases significantly with the system size. Since this behavior can only be caused by nonlinear effects, we calculate the lowest order …
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Spatially coherent solutions of damped-driven nonlinear evolution equations and reaction-diffusion system
Bibliography: leaves 128-134.
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M-lattice, a system for signal synthesis and processing based on reaction-diffusion
Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1994.
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Contributions to the Analysis of Biochemical Reaction-Diffusion Networks Stability, Analysis, and Numerical Solutions
… load for the numerical solution of a class of reaction diffusion networks. This projection method will also be used to compute the time-integral of some species concentration in a class of reaction-diffusion networks. Since we chose a theoretical approach, our results provide analytical …
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Global Existence of solutions to Reaction-Diffusion Systems with Mass Transport type Boundary Conditions
We consider coupled reaction-diffusion models, where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We proved if vector fields are locally Lipschitz functions and satisfies …
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Radial, vortex, and spiral solutions to the nonlinear Schrödinger equation and other reaction--diffusion systems
… explores various solutions to nonlinear reaction-diffusion systems, focusing primarily on the nonlinear Schrödinger equation. Three types of solutions are investigated: radial solutions (with no angular dependence), vortex solutions (with angular dependence but no radial phase …
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First Exit Time Analysis for the Stochastic Reaction Diffusion Process in a One Dimensional Domain
Recent advances in modeling stochastic reaction–diffusion (RD) process have focused on particle-based and master equation formulations. While these models offer strong theoretical foundation, a practical challenge remains: how does the choice of spatial discretization affect the accuracy and …
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Asymptotic Analysis of Perturbations to Travelling Wave Solutions of Nonlinear Advection-Reaction-Diffusion Equations of Fisher Type
… this thesis we examine some nonlinear advection-diffusion-reaction equations of Fisher type. First we discuss the stability properties of the equations by writing each nonlinear equation as a system of two ordinary different equations and then analyzing the stability of their equilibrium …
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A strong maximum principle for reaction-diffusion systems and a weak convergence scheme for reflected stochastic differential equations by Lawrence Christopher Evans.
… which, for illustrative purposes, I consider as reaction-diffusion systems. Using the theory of viscosity solutions, I give a proof which extends the previous theorem to no longer require any regularity assumptions on the boundary of the convex set in which the system takes its values. The second …
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Non-Classical Symmetry Solutions to the Fitzhugh Nagumo Equation.
<p>In <em>Reaction-Diffusion</em> systems, some parameters can influence the behavior of other parameters in that system. Thus reaction diffusion equations are often used to model the behavior of biological phenomena. The Fitzhugh Nagumo partial differential equation is a reaction diffusion …
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Calibrating a Latent Order Book Model to Market Data
… formulation of the Latent Order Book (LOB) as a reaction diffusion Partial Differential Equation (PDE) and its subsequent numerical solution through an explicit method based on discrete stochastic processes. The numerical solution is calibrated using likelihood-free methods, Approximate Bayesian …
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Efficient computational models for pattern formation in fixed and evolving domains
… model spatial patterns formed by nonlinear reaction-diffusion equations for benchmark reaction kinetics. Computational methods for modeling reaction-diffusion equations have been presented extensively in literature. Efficiency in these computational methods, either higher convergence or …
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