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A NUMERICAL ANALYSIS APPROACH FOR ESTIMATING THE MINIMUM TRAVELING WAVE SPEED FOR AN AUTOCATALYTIC REACTION
Title
A NUMERICAL ANALYSIS APPROACH FOR ESTIMATING THE MINIMUM TRAVELING WAVE SPEED FOR AN AUTOCATALYTIC REACTION.
Creator
Blanken, Erika, Qi, Yuan-wei, 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 auto-catalyst. 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 auto-catalyst. 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 fourth-order Runge-Kutta method (RK4).
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Date Issued
2008
Identifier
CFE0002061, ucf:47571
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0002061
computational study of traveling wave solutions and global stability of predator-prey models
Title
computational study of traveling wave solutions and global stability of predator-prey 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 reaction-diffusion 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 reaction-diffusion 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 reaction-diffusion 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 reaction-diffusion 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 auto-catalyst 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 predator-prey system of Leslie Type and Holling-Tanner Type in a bounded domain $\Omega\subset R^N$ with no-flux 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.
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Date Issued
2016
Identifier
CFE0006519, ucf:51359
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0006519
Optimization problem in single period markets
Title
Optimization problem in single period markets.
Creator
Jiang, Tian, Yong, Jiongmin, Qi, Yuanwei, Shuai, Zhisheng, University of Central Florida
Abstract / Description
There had been a number of researches that investigated on the security market without transactioncosts. The focus of this research is in the area that when the security market with transaction costsis fair and in such fair market how one chooses a suitable portfolio to optimize the financial goal.The research approach adopted in this thesis includes linear algebra and elementary probability.The thesis provides evidence that we can maximize expected utility function to achieve our goal...
Show moreThere had been a number of researches that investigated on the security market without transactioncosts. The focus of this research is in the area that when the security market with transaction costsis fair and in such fair market how one chooses a suitable portfolio to optimize the financial goal.The research approach adopted in this thesis includes linear algebra and elementary probability.The thesis provides evidence that we can maximize expected utility function to achieve our goal(maximize expected return under certain risk tolerance). The main conclusions drawn from thisstudy are under certain conditions the security market is arbitrage-free, and we can always find anoptimal portfolio maximizing certain expected utility function.
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Date Issued
2013
Identifier
CFE0004696, ucf:49875
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0004696
A mathematical model for feral cat ecology with application to disease.
Title
A mathematical model for feral cat ecology with application to disease.
Creator
Sharpe, Jeff, Nevai, A, Shuai, Zhisheng, Qi, Yuanwei, Quintana-Ascencio, Pedro, University of Central Florida
Abstract / Description
We formulate and analyze a mathematical model for feral cats living in an isolated colony. The model contains compartments for kittens, adult females and adult males. Kittens are born at a rate proportional to the population of adult females and mature at equal rates into adult females and adult males. Adults compete with each other in a manner analogous to Lotka-Volterra competition. This competition comes in four forms, classified by gender. Native house cats, and their effects are also...
Show moreWe formulate and analyze a mathematical model for feral cats living in an isolated colony. The model contains compartments for kittens, adult females and adult males. Kittens are born at a rate proportional to the population of adult females and mature at equal rates into adult females and adult males. Adults compete with each other in a manner analogous to Lotka-Volterra competition. This competition comes in four forms, classified by gender. Native house cats, and their effects are also considered, including additional competition and abandonment into the feral population. Control measures are also modeled in the form of per-capita removal rates. We compute the net reproduction number (R_0) for the colony and consider its influence. In the absence of abandonment, if R_0(>)1, the population always persists at a positive equilibrium and if R_0 (<)= 1, the population always tends toward local extinction. This work will be referred to as the core model.The model is then expanded to include a set of colonies (patches) such as those in the core model (this time neglecting the effect of abandonment). Adult females and kittens remain in their native patch while adult males spend a fixed proportion of their time in each patch. Adult females experience competition from both the adult females living in the same patch as well as the visiting adult males. The proportion of adult males in patch j suffer competition from both adult females resident to that patch as well the proportion of adult males also in the patch. We formulate a net reproduction number for each patch (a patch reproduction number) R_j. If R_j(>)1 for at least one patch, then the collective population always persists at some nontrivial (but possibly semitrivial) steady state. We consider the number of possible steady states and their properties. This work will be referred to as the patch model.Finally, the core model is expanded to include the introduction of the feline leukemia virus. Since this disease has many modes of transmission, each of which depends on the host's gender and life-stage, we regard this as a model disease. A basic reproduction number R_0 for the disease is defined and analyzed. Vaccination terms are included and their role in disease propagation is analyzed. Necessary and sufficient conditions are given under which the disease-free equilibrium is stable.
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Date Issued
2016
Identifier
CFE0006502, ucf:51389
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0006502
Calibration of Option Pricing in Reproducing Kernel Hilbert Space
Title
Calibration of Option Pricing in Reproducing Kernel Hilbert Space.
Creator
Ge, Lei, Nashed, M, Yong, Jiongmin, Qi, Yuanwei, Sun, Qiyu, Caputo, Michael, University of Central Florida
Abstract / Description
A parameter used in the Black-Scholes equation, volatility, is a measure for variation of the price of a financial instrument over time. Determining volatility is a fundamental issue in the valuation of financial instruments. This gives rise to an inverse problem known as the calibration problem for option pricing. This problem is shown to be ill-posed. We propose a regularization method and reformulate our calibration problem as a problem of finding the local volatility in a reproducing...
Show moreA parameter used in the Black-Scholes equation, volatility, is a measure for variation of the price of a financial instrument over time. Determining volatility is a fundamental issue in the valuation of financial instruments. This gives rise to an inverse problem known as the calibration problem for option pricing. This problem is shown to be ill-posed. We propose a regularization method and reformulate our calibration problem as a problem of finding the local volatility in a reproducing kernel Hilbert space. We defined a new volatility function which allows us to embrace both the financial and time factors of the options. We discuss the existence of the minimizer by using regu- larized reproducing kernel method and show that the regularizer resolves the numerical instability of the calibration problem. Finally, we apply our studied method to data sets of index options by simulation tests and discuss the empirical results obtained.
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Date Issued
2015
Identifier
CFE0005617, ucf:50211
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0005617