No description available.

Thesis (Ph. D.)--Florida State University, 2005. / Advisor: Oliver Steinbock, Florida State University, College of Arts and Sciences, Dept. of Chemistry and Biochemistry. Title and description from dissertation home page (viewed Jan. 24, 2006). Document formatted into pages; contains xii, 123 pages. Includes bibliographical references.

Made available in DSpace on 2014-06-11T19:32:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-04-05Bitstream added on 2014-06-13T19:25:53Z : No. of bitstreams: 1 azevedo_fs_dr_ift.pdf: 964901 bytes, checksum: 0ded483f0f1fa4571a038df930452981 (MD5) / Este trabalho é composto de estudos independentes, mas seus temas são conectados entre si. Ele foi feito baseando-se no estudo de equações de reação-difusão e em reação-difusão-advecção. Vários modelos foram utilizados para representar populações e apresentam características em comum. As populações representadas por esses modelos difundem, crescem e saturam de forma semelhante a equação de Fisher-Kolmogorov e Lotka-Volterra e foram modeladas usando condições de contorno de Dirichlet. Domínios limitados e ilimitados foram usados para que melhor representassem as devidas e diferentes aplicações de dados coletados em campo e publicados em periódicos. Esse trabalho também leva em conta a aplicabilidade à habitats fragmentados, isoladas e não-isoladas. Como foco principal temos o estudo do movimento de populações que vivem nesses habitats mostrando que a qualidade e distribuição deles afeta no movimento das populações / This thesis consists on independent studies, but its subjects are interconnected. It has been based on the study of reaction-diffusion-advection equations. Several models were used to represent populations and have some characteristics in common. The populations represented by the models spread, grow, and saturate in a way similar to that described by the Fisher-Kolmogorov and Lotka-Volterra equations, and were modeled using Dirichlet boundary conditions. Limited and unlimited domains were used to better represent the necessary applications and different data collected in the field and published in journals. This work also takes into account the applicability to fragmented habitats, isolated and not isolated. As the main focus we study the movement of populations living in these habitats, showing that the quality and distribution affects them the movement of populations

Orientador: Marcelo Martins dos Santos / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-23T21:53:25Z (GMT). No. of bitstreams: 1 Santos_RonaldoAntoniodos_D.pdf: 739129 bytes, checksum: f677894f21ef1223fced35636869835d (MD5) Previous issue date: 2013 / Resumo: Neste trabalho provamos a existência de solução global para um sistema não linear constituído de duas equações parabólicas acopladas a duas equações diferenciais ordinárias. Tal sistema modela um processo de combustão em um meio poroso com duas camadas, em que os efeitos de compressibilidade são desprezados, mas a troca de calor entre as camadas, bem como a propagação de calor por convecção são levadas em conta. Supondo que os dados iniciais são lipschitzianos, limitados e pertencentes a algum espaço , 1 < < ?, obtivemos solução clássica para o problema / Abstract: In this work we prove the existence of a global solution for a nonlinear system consisting of two parabolic equations coupled to two ordinary differential equations. Such a system models a combustion process in a porous medium with two layers in which compressibility effects are neglected, but heat transfer between the layers as well as heat conduction are taken into a account. We obtained a classical solution under the assumptions that the initial data is bounded, Lipschitz and belongs to some space, with 1 < < ? / Doutorado / Matematica / Doutor em Matemática

The growing flow of people and goods around the globe has allowed new, non-native species to establish and spread in already fragile ecosystems. The introduction of invasive species can have a detrimental impact on the already established species. Thus, it is important that we understand the mechanisms that facilitate or prevent invasion. Since reaction-diffusion invasion models produce travelling waves we can study invasion by looking at the mechanisms that allow for wave propagation failure, or wave-blocking. In this thesis we consider a perturbed reaction-diffusion model in which the perturbation resides in either the reaction or diffusion term. In doing so we exploit the underlying symmetry of our problem to define a region in the appropriate parameter space that leads to wave blocking. As a demonstrative example we apply our theory to the bistable equation and consider the effects of various perturbations.

The earth’s climate is increasing in temperature and as a result many species’ habitat ranges are shifting. The shift in habitat ranges threatens the local persistence of many species. Mathematical models that capture this phenomena of range shift do so by considering a bounded domain that has a time dependant location on the real line. The analysis on persistence conditions has been considered in both continuous-time and -space, and discrete-time, continuous-space settings. In both model types density was considered to be continuous across the boundaries. However it has been shown that many species exhibit particular behaviour at habitat edges, such as biased movement towards the more suitable habitat. This behaviour should be incorporated into the analysis to obtain more accurate persistence conditions. In this thesis persistence conditions are obtained for generalized boundary conditions with a continuous-time and -space model for a range-shifting habitat. It is shown that a high preference for the suitable habitat at the trailing edge can greatly reduce the size of suitable habitat required for species persistence. As well, for fast shifting ranges, a high preference at the trailing edge is crucial for persistence.

A fibrilação, atrial ou ventricular, é caracterizada por uma desorganização da atividade elétrica do músculo. O coração, que normalmente contrai-se globalmente, em uníssono e uniforme, durante a fibrilação contrai-se localmente em várias regiões, de modo descoordenado. Para estudar qualitativamente este fenômeno, é aqui proposto um novo modelo matemático, mais simples do que os demais existentes e que, principalmente, admite uma representação singela na forma de circuito elétrico equivalente. O modelo foi desenvolvido empiricamente, após estudo crítico dos modelos conhecidos, e após uma série de sucessivas tentativas, ajustes e correções. O modelo mostra-se eficaz na simulação dos fenômenos, que se traduzem em padrões espaciais e temporais das ondas de excitação normais e patológicas, propagando-se em uma grade de pontos que representa o tecido muscular. O trabalho aqui desenvolvido é a parte básica e essencial de um projeto em andamento no Departamento de Engenharia Elétrica da EESC-USP, que é a elaboração de uma rede elétrica ativa, tal que possa ser estudada utilizando recursos computacionais de simuladores usualmente aplicados em projetos de circuitos integrados / Atrial and ventricular fibrillation are characterized by a disorganized electrical activity of the cardiac muscle. While normal heart contracts uniformly as a whole, during fibrillation several small regions of the muscle contracts locally and uncoordinatedly. The present work introduces a new mathematical model for the qualitative study of fibrillation. The proposed model is simpler than other known models and, more importantly, it leads to a very simple electrical equivalent circuit of the excitable cell membrane. The final form of the model equations was established after a long process of trial runs and modifications. Simulation results using the new model are in accordance with those obtained using other (more complex) models found in the related literature. As usual, simulations are performed on a two-dimensional grid of points (representing a piece of heart tissue) where normal or pathological spatial and temporal wave patterns are produced. As a future work, the proposed model will be used as the building block of a large active electrical network representing the muscle tissue, in an integrated circuit simulator

Calcium signaling has been identified with triggering of gene transcriptions associated with learning and neuroprotection in neurons. Studies indicate that dysregulation of calcium signaling is correlated with severe Alzheimer Disease pathologies. A stable calcium wave or signal arising from triggers in dendritic synapses needs to reach soma with constant amplitude for proper functioning of neurons. In this study, we introduce "CalciumSim", a calcium dynamics simulator which works on dimensionally reduced model. Numerical analysis is conducted to obtain the best configuration of neuron geometry to make the code efficient and fast. Alongside, biologically important insights are derived by modulating and changing parameters of the simulation. The ability of "CalciumSim" to work with real neuron geometries allows user to study calcium signalling in a realistic model. / Mathematics

Temperature isoclines are shifting with global warming. To survive, species with thermal niches must shift their geographical ranges to stay within the bounds of their suitable habitat, or acclimate to a new environment. Mathematical models that study range shifts are called moving-habitat models. The literature is rich and includes modelling with reaction-diffusion equations. Much of this literature represents space by the real line, with a handful studying 2-dimensional domains that are unbounded in at least one direction. The suitable habitat is represented by the set over which the demographics (reaction term) has a positive net growth rate. In some cases, this is a bounded set, in others, it is not. The unsuitable habitat is represented by the set over which the net growth rate is negative. The environmental shift is captured by an imposed shift of the suitable habitat. Individuals respond to their environment via their movement behaviour and many display habitat-dependent dispersal rates and a habitat bias. Such behaviour corresponds to a jump in density across the interface of suitable and unsuitable habitat. The questions motivating moving-habitat models are: when can a species track its shifting habitat and what is the impact of an environmental shift on a persisting species. Without closed form solutions, researchers rely on numerical methods to study the latter, and depending on the movement of the interface, the former may require numerical tools as well. We construct and analyse two numerical methods, a finite difference (FD) scheme and a finite element (FE) method in 1- and 2-dimensional space, respectively. The FD scheme can capture arbitrary movement of the boundary, and the FE method rather general shapes for the suitable habitat. The difficulty arises in capturing the jump across a shifting interface. We construct a reference frame in which the interfaces are fixed in time. We capture the jump in density with a clever placing of the nodes in the FD scheme, and through a Lagrange multiplier in the FE method. With biological applications, we demonstrate the power of our solvers in advancing research for moving-habitat models.

This thesis represents a small contribution to our understanding of metastable patterns in various stochastic models from physics and biology. By a \emph{metastable pattern}, we mean a pattern that appears to persist in a regular fashion on some timescale, but disappears or undergoes an irregular change on a longer timescale. Metastable patterns frequently result from stochastic perturbations of patterns that are stable without perturbation. In this thesis, we study stochastic perturbations of stable spatiotemporal patterns in several classes of PDE and integral equations. In particular, we address two major questions: \begin{enumerate}[Q1.] \item When perturbed by noise, for how long does a pattern that is stable without noise persist? \item How does the stochastic perturbation affect the average behaviour of a pattern on the timescale where it appears to persist? \end{enumerate} To address these questions, we pursue two lines of inquiry: the first based on the theory of \emph{quasi-ergodic measures}, and the second based on \emph{phase decomposition techniques}. In our first line of inquiry we present novel, rigorous connections between metastability of general infinite dimensional stochastic evolution systems and the spectral properties of their sub-Markov generators using the theory of quasi-ergodic measures. To do so, we develop a novel $L^p$-approach to the study of quasi-ergodic measures. We are then able to draw conclusions about the metastability of travelling waves and other patterns in a class of stochastic reaction-diffusion equations. For instance, we obtain a rigorous definition of the \emph{quasi-asymptotic speed}~of a travelling wave in a stochastic PDE. We moreover find that stochastic perturbations of amplitude $\sigma>0$ cause the quasi-asymptotic speed of certain travelling waves to deviate from the deterministic wave speed by a constant that is approximately proportional to $\sigma^2$. In our second line of inquiry, the dynamics of our (infinite dimensional) stochastic evolution system are projected onto a finite dimensional manifold that captures some property of a metastable pattern. While most previous studies using phase reduction techniques have used the \emph{variational phase}, we take an approach based on the \emph{isochronal phase}, inspired by classical work on finite dimensional oscillatory systems. When the pattern in question is a travelling wave, the isochronal phase captures the position of the wave at a given point in time. By exploiting the regularity properties of the isochronal phase, we are able to prove several novel results about the metastable behaviour of the reduced dynamics in the small noise regime in a very large class of stochastic evolution systems. These results allow us to moreover compute the noise-induced changes in the speed of stochastically perturbed travelling waves and other patterns. The results we obtain using this approach are numerically precise, and may be applied to a very general class of stochastic evolution systems.