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 Title
 A NUMERICAL ANALYSIS APPROACH FOR ESTIMATING THE MINIMUM TRAVELING WAVE SPEED FOR AN AUTOCATALYTIC REACTION.
 Creator

Blanken, Erika, Qi, Yuanwei, University of Central Florida
 Abstract / Description

This thesis studies the traveling wavefront created by the autocatalytic cubic chemical reaction A + 2B → 3B involving two chemical species A and B, where A is the reactant and B is the autocatalyst. The diffusion coefficients for A and B are given by and . These coefficients differ as a result of the chemical species having different size and/or weight. Theoretical results show there exist bounds, and , depending on , where for speeds , a traveling wave solution exists, while for speeds , a...
Show moreThis thesis studies the traveling wavefront created by the autocatalytic cubic chemical reaction A + 2B → 3B involving two chemical species A and B, where A is the reactant and B is the autocatalyst. The diffusion coefficients for A and B are given by and . These coefficients differ as a result of the chemical species having different size and/or weight. Theoretical results show there exist bounds, and , depending on , where for speeds , a traveling wave solution exists, while for speeds , a solution does not exist. Moreover, if , and are similar to one another and in the order of when it is small. On the other hand, when there exists a minimum speed vmin, such that there is a traveling wave solution if the speed v > vmin. The determination of vmin is very important in determining the dynamics of general solutions. To fill in the gap of the theoretical study, we use numerical methods to determine vmin for various cases. The numerical algorithm used is the fourthorder RungeKutta method (RK4).
Show less  Date Issued
 2008
 Identifier
 CFE0002061, ucf:47571
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0002061
 Title
 Smooth and NonSmooth Traveling Wave Solutions of Some Generalized CamassaHolm Equations.
 Creator

Rehman, Taslima, Choudhury, Sudipto, Nevai, Andrew, Rollins, David, University of Central Florida
 Abstract / Description

In this thesis we employ two recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of recently derived integrable family of generalized CamassaHolm (GCH) equations. In the first part, a novel application of phaseplane analysis is employed to analyze the singular traveling wave equations of four GCH equations, i.e. the possible nonsmooth peakon, cuspon and compacton solutions. Two of the GCH equations do no support singular traveling...
Show moreIn this thesis we employ two recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of recently derived integrable family of generalized CamassaHolm (GCH) equations. In the first part, a novel application of phaseplane analysis is employed to analyze the singular traveling wave equations of four GCH equations, i.e. the possible nonsmooth peakon, cuspon and compacton solutions. Two of the GCH equations do no support singular traveling waves. We generalize an existing theorem to establish the existence of peakon solutions of the third GCH equation. This equation is found to also support four segmented, nonsmooth Mwave solutions. While the fourth supports both solitary (peakon) and periodic (cuspon) cusp waves in different parameter regimes.In the second part of the thesis, smooth traveling waves of the four GCH equations are considered. Here, we use a recent technique to derive convergent multiinfinite series solutions for the homoclinic and heteroclinic orbits of their travelingwave equations, corresponding to pulse and front (kink or shock) solutions respectively of the original PDEs. Unlike the majority of unaccelerated convergent series, high accuracy is attained with relatively few terms. Of course, the convergence rate is not comparable to typical asymptotic series. However, asymptotic solutions for global behavior along a full homoclinic/heteroclinic orbit are currently not available.
Show less  Date Issued
 2013
 Identifier
 CFE0004918, ucf:49637
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004918
 Title
 computational study of traveling wave solutions and global stability of predatorprey models.
 Creator

Zhu, Yi, Qi, Yuanwei, Rollins, David, Shuai, Zhisheng, Zhai, Lei, University of Central Florida
 Abstract / Description

In this thesis, we study two types of reactiondiffusion systems which have direct applications in understanding wide range of phenomena in chemical reaction, biological pattern formation and theoretical ecology.The first part of this thesis is on propagating traveling waves in a class of reactiondiffusion systems which model isothermal autocatalytic chemical reactions as well as microbial growth and competition in a flow reactor. In the context of isothermal autocatalytic systems, two...
Show moreIn this thesis, we study two types of reactiondiffusion systems which have direct applications in understanding wide range of phenomena in chemical reaction, biological pattern formation and theoretical ecology.The first part of this thesis is on propagating traveling waves in a class of reactiondiffusion systems which model isothermal autocatalytic chemical reactions as well as microbial growth and competition in a flow reactor. In the context of isothermal autocatalytic systems, two different cases will bestudied. The first is autocatalytic chemical reaction of order $m$ without decay. The second is chemical reaction of order $m$ with a decay of order $l$, where $m$ and $l$ are positive integers and $m(>)l\ge1$. A typical system is $A + 2B \rightarrow3B$ and $B\rightarrow C$ involving three chemical species, a reactant A and an autocatalyst B and C an inert chemical species.We use numerical computation to give more accurate estimates on minimum speed of traveling waves for autocatalytic reaction without decay, providing useful insight in the study of stability of traveling waves. For autocatalytic reaction of order $m = 2$ with linear decay $l = 1$, which hasa particular important role in biological pattern formation, it is shown numerically that there exist multiple traveling waves with 1, 2 and 3 peaks with certain choices of parameters.The second part of this thesis is on the global stability of diffusive predatorprey system of Leslie Type and HollingTanner Type in a bounded domain $\Omega\subset R^N$ with noflux boundary condition. By using a new approach, we establish much improved global asymptotic stability of a unique positiveequilibrium solution. We also show the result can be extended to more general type of systems with heterogeneous environment and/or other kind of kinetic terms.
Show less  Date Issued
 2016
 Identifier
 CFE0006519, ucf:51359
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0006519