Global ETD Search
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Showing 1 to 20 of 36 for “"reaction-diffusion systems"”.
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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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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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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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A strong maximum principle for reaction-diffusion systems and a weak convergence scheme for reflected stochastic differential equations by Lawrence Christopher Evans.
… a strong maximum principle for certain parabolic systems of equations, 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 …
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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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Hopf Bifurcations and Horseshoes Especially Applied to the Brusselator
… which is a model of certain chemical reaction-diffusion systems. After a thorough exploration of what a bifurcation is and what classifications there are, we give graphic representations of an occurring Hopf bifurcation in the Brusselator. When an additional forcing term is added, …
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Aging processes in complex systems
… understanding of physical aging in nondisordered systems with slow, i.e. glassy-like dynamics. In many systems a single dynamical length L(t), that grows as a power-law of time t or, in much more complicated cases, as a logarithmic function of t, governs the dynamics out of equilibrium. In the …
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Coupled nonlinear dynamical systems
… we study coupled nonlinear dynamical systems that exhibit new types of complex behavior. We numerically and analytically examine a variety of dynamical models, ranging from systems of ordinary differential equations (ODE) with novel elements of feedback to systems of partial …
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Pattern formation through synchronization in systems of nonidentical autonomous oscillators
… Kuramoto model which reduces general oscillatory systems to phase dynamics. The symmetry of the coupling plays an important role for the formation of patterns. We have studied the ordering influence of an asymmetry (non-isochronicity) in the phase coupling function on the phase profile in …
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Stochastic dynamics in spatially extended physical and biological systems
… of stochastic nature in spatially extended systems: (1) a noise induced mechanism for the emergence of biological homochirality in early life self-replicators, (2) the amplification effect of nonnormality on stochastic Turing patterns in reaction diffusion systems, and (3) the velocity …
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A Stochastic Model for The Transmission Dynamics of Toxoplasma Gondii
… Turner et al. and extend their work to include diffusion of hosts. Most of researches focus on the deterministic models. However, some scientists have reported that deterministic models sometimes are inaccurate or even inapplicable to describe reaction-diffusion systems, such as gene expression. …
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Cellular automata models for excitable media
… "masks" as discrete approximations to the diffusion equation are examined, showing how to calculate the diffusion coefficient from the elements of the mask. The mask is then combined with a thresholding operation to simulate the propagation of waves (shock fronts) in excitable media, …
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Deterministic and stochastic modelling of a catalytic surface reaction
Catalytic surface reactions are of great importance both for chemical industry and as model systems for the study of pattern formation far from thermodynamic equilibrium. A reaction that has been investigated extensively in experiments is the oxidation of carbon monoxide on platinum.In the present …
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Travelling waves in Lotka-Volterra competition models
In this thesis, we study a class of multi-stable reaction-diffusion systems used to model competing species. Systems in this class possess uniform stable steady states representing semi-trivial solutions. We start by considering a bistable, interaction, where the interactions are of classic …
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Magnetic resonance studies of chemical reactions in microemulsions
The Belousov-Zhabotinsky (BZ) reaction is the preeminent oscillating chemical reaction for the study of pattern formation in reaction-diffusion systems. The dispersal of the reaction in a water-in-oil AOT microemulsion (BZ-AOT reaction) gives rise to an extended range of patterns, including dash …
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Fluctuation Relations for Stochastic Systems far from Equilibrium
Fluctuations are of great importance in systems of small length and energy scales. Measuring the pulling of single molecules or the stationary fiow of mesospheres dragged through a viscous media enables the direct analysis of work and entropy distributions. These probability distributions are the …
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Splitting schemes for nonlinear parabolic problems
… be applied to such diverse problems as nonlinear reaction-diffusion systems, nonlinear parabolic problems with delay, as well as differential Riccati equations. Within the second theme of structure preservation, an in-depth study of operator-valued differential Riccati equations has been carried …
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