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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Fock space approach to schnakenberg model

LEANDRO, Marlon Oliveira Martins 24 May 2016 (has links)
Submitted by Irene Nascimento (irene.kessia@ufpe.br) on 2016-08-02T18:02:48Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Fock space approach to Schnakenberg model.pdf: 6802590 bytes, checksum: 388dea2a463bd63474eaab61feece049 (MD5) / Made available in DSpace on 2016-08-02T18:02:48Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Fock space approach to Schnakenberg model.pdf: 6802590 bytes, checksum: 388dea2a463bd63474eaab61feece049 (MD5) Previous issue date: 2016-05-24 / Capes / This work has as objective to study the relationship between Fock spaces, quantum operators and chemical reaction systems used to model many stochastic processes with biological motivation, such as population growth, heartbeats and cell metabolism. In particular, we work with a generalization of Schnakenberg model, in its deterministic and stochastic versions, and which is used to describe the process of cellular glycolysis. As it is a new and at the same time a interdisciplinary area, involving knowledge in stochastic processes, theoretical physics, chemistry and biomathematics, this text seeks to be self-contained, including all the elements needed for the study of theme, for the purpose of contribute to the better understanding between these diverse areas. / Este trabalho tem como objetivo estudar a relação entre espaços de Fock, operadores de mecânica quântica e sistemas de reações químicas usados para modelar diversos processos estocásticos com motivação biológica, como crescimento populacional, batimentos cardíacos e metabolismo celular. Em particular, vamos trabalhar com uma generalização do modelo de Schnakenberg, em suas versões determinística e estocástica, e que pode ser utilizado para descrever o processo de glicólise celular. Como é uma área recente e ao mesmo tempo interdisciplinar, envolvendo conhecimento em processos estocásticos, física teórica, química e biomatemática, este texto procura ser autocontido, incluindo todos os fundamentos necessários para o estudo do tema, visando contribuir para o melhor entendimento entre estas diversas áreas.
2

The Scientific Way to Simulate Pattern Formation in Reaction-Diffusion Equations

Cleary, Erin 09 May 2013 (has links)
For a uniquely defined subset of phase space, solutions of non-linear, coupled reaction-diffusion equations may converge to heterogeneous steady states, organic in appearance. Hence, many theoretical models for pattern formation, as in the theory of morphogenesis, include the mechanics of reaction-diffusion equations. The standard method of simulation for such pattern formation models does not facilitate reproducibility of results, or the verification of convergence to a solution of the problem via the method of mesh refinement. In this thesis we explore a new methodology circumventing the aforementioned issues, which is independent of the choice of programming language. While the new method allows more control over solutions, the user is required to make more choices, which may or may not have a determining effect on the nature of resulting patterns. In an attempt to quantify the extent of the possible effects, we study heterogeneous steady states for two well known reaction-diffusion models, the Gierer-Meinhardt model and the Schnakenberg model. / Alexander Graham Bell Canada Graduate Scholarship provides financial support to high calibre scholars who are engaged in master's or doctoral programs in the natural sciences or engineering. / Natural Sciences and Engineering Research Council of Canada
3

Turing's model for pattern formation

Forsström, Oskar, Falgén Nikula, Oskar January 2022 (has links)
In an attempt to describe how patterns emerge in biological systems, Alan Turing proposed a mathematical model encapsulating the properties of such processes. It details a partial differential equation governing the dynamics of two or more substances, called morphogens, reacting and diffusing in a specific manner, in turn generating what has now come to be denoted as Turing patterns. In recent years, evidence has accumulated to support Turing's claim and it has been proposed that it is responsible for the dynamical characteristics of phenomena such as skin pigmentation and branching of lungs in vertebrates. The aim of this paper is to study how the choice of model parameters and reaction kinetics influence the nature of patterns generated, as well as explore how boundary control can be employed to generate pre-defined patterns and the efficiency of this procedure. To simulate the patterns, the differential equation is solved in Python by means of a spectral method using discretized space and time domains. The model parameters were then studied to try to gain insight in their effects on the patterns yielded. The boundary control was implemented in MATLAB using a difference method. The metric used for efficiency was taken to be the energy expenditure of the boundary cells. The complex dynamics of the studied systems make it difficult to draw valuable conclusions on the influence of the parameters, but the results support the expected characteristics of the models used. The efficiency of the pattern generation is deemed to be closely related to the amount of boundary control utilized.

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