Dissertations / Theses on the topic 'Pattern formation'
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Parrott, J. A. "Pattern formation in soils." Thesis, University of Bristol, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.520596.
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Sumner, Robert Walker 1975. "Pattern formation in lichen." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/86757.
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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.Includes bibliographical references (p. 73-76).
by Robert Walker Sumner.
S.M.
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Bowman, Christopher 1969. "Pattern formation and wavelets." Diss., The University of Arizona, 1997. http://hdl.handle.net/10150/288741.
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This thesis is a collection of results associated with pattern formation, and consists of several novel results. A multi-scale analysis is carried out near the lasing bifurcation on equations which model the free carrier semiconductor laser. This analysis produces an amplitude equation which resembles the Swift-Hohenberg equation derived for the simpler two level laser, but with extra terms arising from the more complicated semiconductor system. New results are also presented in the analysis of phase equations for patterns, showing that defects are weak solutions of the phase diffusion equation, and that the Gaussian curvature of the phase surface condenses onto point and line defects. This latter fact allows for considerable simplification of the phase diffusion equation, and this analysis is presented as well. Finally, and most importantly, an algorithm is presented, based on the continuous wavelet transform, for the extraction of local phase and amplitude information from roll patterns. This algorithm allows a precise detection of phase grain boundaries and point defects, as well as the computation of soft modes like the mean flow. Several tests are conducted on numerically generated signals to demonstrate the applicability and precision of the algorithm. The algorithm is then applied to actual experimental convection patterns, and conclusions about the nature of the wave director field in such patterns are presented.
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Duran, Nebreda Salvador 1987. "Artificial multicellularity and pattern formation." Doctoral thesis, Universitat Pompeu Fabra, 2016. http://hdl.handle.net/10803/403584.
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En aquesta tesi hem intentat atacar preguntes relacionades amb els orígens de la vida multicel•lular i dels comportaments cooperatius a la nostra biosfera. Particularment hem fet ús de mètodes “no naturals”: la vida artificial i la biologia sintètica. A diferencia dels enfocs més tradicionals com la caracterització filogenètica i la biologia teòrica, aquests mètodes permeten observar les transicions en individualitat i complexitat a mesura que tenen lloc. Més concretament, en aquest projecte hem proposat noves regles per aconseguir sistemes de trencament de simetria espacial i com la multicel•lularitat amb diferenciació pot ser seleccionada des de genotips unicel•lulars amb les pressions selectives apropiades.This project has tackled unanswered questions regarding the origins of multicellular life and cooperation using artificial approaches, namely: artificial evolution and synthetic biology. These offer unique opportunities to watch the evolution of complexity unfold and complement the extensively used methods of characterization of extant multicellular systems and theoretical biology. In particular we have proposed new mechanisms to create periodical structures in synthetic systems and how differentiated multicellularity might arise from Darwinian entities.
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Katsev, Sergei. "Pattern formation in geochemical systems." Thesis, University of Ottawa (Canada), 2002. http://hdl.handle.net/10393/6237.
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Compositional patterns are extremely common in natural minerals. While, in many cases, variations in the solid mineral composition reflect the external changes in the environment at the time of the mineral formation, the role of self-organization is increasingly acknowledged. For example, in reaction-transport systems, the patterns may form spontaneously from an unpatterned state at the time of crystal growth and then become preserved by being "frozen" in the solid mineral. In this work, the pattern formation by self-organization is investigated by means of model construction and computer simulations in several minerals from different geologic environments. The impact of environmental noise is investigated on a model of oscillatory zoning in plagioclase feldspar. It is shown that environmental noise can lead to pattern formation such as oscillatory zoning, even when no deterministic periodic solutions exist. Coherence resonance close to the Hopf bifurcation is observed. Oscillatory zoning in barite-celestite system is simulated to quantitatively describe the results of the previously reported nucleation and growth experiments. The zoning is thought to be formed by autocatalytic growth from an aqueous solution. In addition to the description of the reaction-diffusion system in terns of partial and ordinary differential equations, a cellular automata model is proposed for the first time for this oscillatory crystallization type of problems. A quantitative model of banding in Mississippi Valley-type sphalerite is presented. Banded ring-like patterns are shown to arise due to a self-propagating sequence of growth and dissolution (coarsening wave). A two-dimensional model is presented for the first time and the conditions for the pattern generation and preservation are discussed. A number of time series analysis techniques are applied to characterize the compositional patterns observed in natural minerals as well as in the colored rythmites found in the marine clay sediments of the Ottawa Valley. Several caveats in interpreting the results of such analyses are outlined.
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Stannard, Andrew David. "Pattern Formation in Nanostructured Systems." Thesis, University of Nottingham, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.523471.
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McIntyre, Ross. "Pattern formation in nonlinear optics." Thesis, Heriot-Watt University, 1996. http://hdl.handle.net/10399/716.
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Welford, Chris. "The evolution of pattern formation." Thesis, University of Sheffield, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.364296.
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Denton, Richard Frederick Roger James. "Pattern formation from chemical oscillators." Thesis, University of Edinburgh, 2009. http://hdl.handle.net/1842/13622.
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Jhugroo, Eric. "Pattern formation in squares and rectangles." Thesis, City, University of London, 2007. http://openaccess.city.ac.uk/18271/.
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This thesis considers pattern formation governed by the two dimensional Swift-Hohenberg equation in square and rectangular domains. For the square, the dependence of the solution on the size of the square relative to the characteristic wavelength of the pattern is investigated for periodic, non-periodic (rigid) and quasi-periodic boundary conditions. Linear and weakly nonlinear analysis is used together with numerical computation to identify the bifurcation structure of steady-state solutions and to track their nonlinear development as a function of the control parameter. Nonlinear solutions arising from secondary bifurcations and fold bifurcations are also found. Time-dependent computations are also carried out in order to investigate stability, and to find certain nonlinear steady states. The structure of solutions in the limit where the size of the square is much larger than the characteristic wavelength of the pattern is investigated using asymptotic methods. For the rectangle, the dependence of the solution on the size of the rectangle relative to the characteristic wavelength of the pattern is investigated for non-periodic (rigid) boundary conditions. Most results are obtained for two aspect ratios, 0.75 and 0.5. Linear analysis is used together with numerical computations to identify the bifurcation structure of steady-state solutions and to track their nonlinear development. Nonlinear solutions arising from secondary bifurcations and fold bifurcations are also found, again making use of time-dependent calculations where necessary. Finally, the structure of solutions in the limit where the size of the rectangle is much larger than the characteristic wavelength of the pattern is investigated using asymptotic methods. The results are discussed in relation to patterns observed in physical systems such as Rayleigh-Benard convection.
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Wang, Lei. "Pattern formation in mesophase carbon fibers." Thesis, McGill University, 1996. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=24045.
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The principles governing pattern formation in discotic nematic liquid crystalline fibers subjected to uniaxial extensional flows are established. Computational and analytical methods are used in conjunction with bifurcational techniques to simulate the structural characteristics of the orientational patterns that arise by stretching discotic nematic liquid crystalline materials. The analytical and numerical results are in excellent agreement with actual cross-sectional fiber textures obtained by melt spinning carbonaceous mesophases. This work reproduces the main structural features of the oscillatory zig-zag pattern commonly observed in mesophase carbon fibers, and identifies the process conditions that lead to this peculiar fiber texture. In addition, the temperature driven texture transitions and the emergence of random pattern also observed during the industrial manufacturing of mesophase carbon fibers are captured by the simulations and thoroughly explained using classical viscoelastic theories of liquid crystalline materials.
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Crawford, David Michael. "Analysis of biological pattern formation models." Thesis, University of Oxford, 1989. http://ora.ox.ac.uk/objects/uuid:aaa19d3b-c930-4cfa-adc6-8ea498fa5695.
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In this thesis we examine mathematical models which have been suggested as possibile mechanisms for forming certain biological patterns. We analyse them in detail attempting to produce the requisite patterns both analytically and numerically. A reaction diffusion system in two spatial dimensions with anisotropic diffusion is examined in detail and the results compared with certain snakeskin patterns. We examine two other variants to the standard reaction diffusion system: a system where the reaction kinetics and the diffusion coefficients depend upon the cell density suggested as a possible model for the segmentation sequence in Drosophila and a system where the model parameters have one dimensional spatial gradients. We also analyse a model derived from known cellular processes used to model the branching behaviour in bryozoans and show that, in one dimension, such a model can, in theory, give all the required solution behaviour. A genetic switch model for pattern elements on butterfly wings is also briefly examined to obtain expressions for the solution behaviour under coldshock.
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Ren, Xiaojing, and 任晓晶. "Modeling pattern formation of swimming E.coli." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B43704001.
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Winterbottom, David Mark. "Pattern formation with a conservation law." Thesis, University of Nottingham, 2006. http://eprints.nottingham.ac.uk/10180/.
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The evolution of many pattern-forming systems is strongly influenced by the presence of a conserved quantity. Diverse physical phenomena such as magnetoconvection, rotating fluid convection, binary fluid convection, vibrated granular and fluid layers, filament dynamics and sandbank formation, all possess a conservation law which plays a central role in their nonlinear dynamics. In this thesis, this influence of a conserved quantity is examined through analyses of three distinct pattern-formation problems. Firstly, the consequences of conservation of mass are investigated in a phenomenological model of a vibrated granular layer. A new weakly nonlinear analysis is performed that reveals the existence of modulational instabilities for patterns composed of either stripes and squares. The nonlinear evolution of these instabilities is numerically studied and a plethora of patterns and localised arrangements are exhibited. The second component of this work concerns an oscillatory bifurcation in the presence of a conserved quantity. Building upon existing theory for the corresponding stationary bifurcation, universal amplitude equations are constructed through symmetry and asymptotic considerations. Subsequently, the stability properties of travelling and standing waves are found to be significantly altered and new modulational instabilities are uncovered. Numerical simulations reveal that, in the presence of a conserved quantity, travelling and standing waves lose stability to spatially localised patterns, either coherent, time-periodic or chaotic. Finally, wave-like behaviour of large-scale modes is examined through an analysis of a model for Faraday waves, that has been modified to account for flnite fluid depth. Several approaches to the weakly nonlinear analysis are considered and two sets of amplitude equations are derived that account for the unusual wave-like behaviour of large-scale modes. Numerical simulations reveal amplitude-modulated and localised patterns away from the small-amplitude, weak-viscosity limit.
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Cruywagen, Gerhard C. "Tissue interaction and spatial pattern formation." Thesis, University of Oxford, 1992. http://ora.ox.ac.uk/objects/uuid:f242b785-9b46-4c21-a789-477b025ce4b3.
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The development of spatial structure and form on vertebrate skin is a complex and poorly understood phenomenon. We consider here a new mechanochemical tissue interaction model for generating vertebrate skin patterns. Tissue interaction, which plays a crucial role in vertebrate skin morphogenesis, is modelled by reacting and diffusing signal morphogens. The model consists of seven coupled partial differential equations, one each for dermal and epidermal cell densities, four for the signal morphogen concentrations and one for describing epithelial mechanics. Because of its complexity, we reduce the full model to a small strain quasi-steady-state model, by making several simplifying assumptions. A steady state analysis demonstrates that our reduced system possesses stable time-independent steady state solutions on one-dimensional spatial domains. A linear analysis combined with a multiple time-scale perturbation procedure and numerical simulations are used to examine the range of patterns that the model can exhibit on both one- and two-dimensions domains. Spatial patterns, such as rolls, squares, rhombi and hexagons, which are remarkably similar to those observed on vertebrate skin, are obtained. Although much of the work on pattern formation is concerned with synchronous spatial patterning, many structures on vertebrate skin are laid down in a sequential fashion. Our tissue interaction model can account for such sequential pattern formation. A linear analysis and a regular perturbation analysis is used to examine propagating epithelial contraction waves coupled to dermal cell invasion waves. The results compare favourably with those obtained from numerical simulations of the model. Furthermore, sequential pattern formation on one-dimensional domains is analysed; first by an asymptotic technique, and then by a new method involving the envelopes of the spatio-temporal propagating solutions. Both methods provide analytical estimates for the speeds of the wave of propagating pattern which are in close agreement with those obtained numerically. Finally, by numerical simulations, we show that our tissue interaction model can account for two-dimensional sequential pattern formation. In particular, we show that complex two-dimensional patterns can be determined by simple quasi-one-dimensional patterns.
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COLOMBO, EDUARDO HENRIQUE FILIZZOLA. "SPATIAL PATTERN FORMATION IN POPULATION DYNAMICS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2014. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=24777@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
FUNDAÇÃO DE APOIO À PESQUISA DO ESTADO DO RIO DE JANEIRO
PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO
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Motivado pela riqueza de fenômenos produzidos pelos seres vivos, este trabalho busca estudar a formação de padrões espaciais de populações biológicas. De um ponto de vista mesoscópico, definimos os processos básicos que podem ocorrer na dinâmica, construindo uma equação diferencial parcial para a evolução da distribuição da população. Essa equação incorpora duas generalizações de um modelo pre-existente para a dinâmica de um espécie, que leva em conta interações de longo alcance (não locais). A primeira generalização consiste em considerar que a difusão é não linear, isto é, é afetada pela densidade local de tal modo que o coeficiente de difusão segue uma lei de potência. Por outro lado, visto a alta complexidade envolvida na natureza dos parâmetros do modelo, introduzimos como segunda generalização parâmetros que flutuam no tempo. Idealizamos estas flutuações como um ruído descorrelacionado temporalmente e que obedece uma distribuição gaussiana (ruído branco). Para estudar o modelo resultante, utilizamos uma abordagem analítica e numérica. As ferramentas analíticas se baseiam na linearização da equação de evolução e portanto são aproximadas. Todavia, complementadas com resultados numéricos, conseguimos extrair conclusões relevantes. A não localidade das interações induz a formação de padrões. O alcance dessas interações é o que determina o modo dominante presente nos padrões. Assim, para valores dos parâmetros acima de um limiar crítico, emergem padrões. Analiticamente, mostramos que, mesmo abaixo desse limiar, as flutuações nos parâmetros podem induzir a aparição de ordem espacial. Os efeitos da difusão não-linear são captados superficialmente pela análise linear. Numericamente, mostraremos que sua presença modifica a forma dos padrões. Observamos, especialmente, a existência de uma transição quando alternamos entre o caso em que a difusão é facilitada por altas densidades e o caso oposto. Para o primeiro caso, verificamos que os padrões se tornam fragmentados, ou seja, a população é agora composta de sub-grupos desconectados.
Motivated by the richness of phenomena produced by living beings, this work aims to study the formation of spatial patterns in biological populations. From the mesoscopic point of view, we define the basic processes that may occur in the dynamics, building a partial differential equation for the evolution of the population distribution. This equation incorporates two generalizations of a pre-existing model for the dynamics of one species, which takes into account long-range (nonlocal) interactions. The first generalization is to consider that diffusion is nonlinear, i.e., it is affected by the local density such that the diffusion coeficient follows a power law. On the other hand, because of the high complexity involved in the nature of model parameters, we introduced as a second generalization time-fluctuating parameters. We idealize these fluctuations as Gaussian temporally uncorrelated (white) noises. To study the resulting model, we use an analytical and numerical approach. Analytical tools are based on the linearization of the evolution equation and are therefore approximate. However, as evidenced by numerical results, we draw important conclusions. The nonlocal feature of the interaction is the main mechanism which induces pattern formation. We show that the extent of these interactions is what characterizes the dominant mode. Thus, for parameter values above a critical threshold patterns emerge. Analytically, we also show that even below this threshold, fluctuations in the parameters can induce the appearance of spatial order. The effects of nonlinear diffusion are only superficially captured by the linear analysis. Numerically, we show that their presence modifies the patterns shape. We mainly observed the existence of a qualitative difference between the cases when diffusion is facilitated or not by high densities. In the first case, we note that the patterns become fragmented, that is, population becomes composed of disconnected clusters.
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Malheiros, Marcelo de Gomensoro. "The mechanochemical basis of pattern formation." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2017. http://hdl.handle.net/10183/169104.
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Esta tese de doutorado descreve um novo modelo para o acoplamento de difusão química contínua e eventos celulares discretos dentro de um ambiente de simulação biologicamente inspirado. Nosso objetivo é definir e explorar um conjunto minimalista de recursos que também são expressivos, permitindo a criação de padrões 2D complexos usando apenas poucas regras. Por não nos restringirmos a uma grade estática ou regular, mostramos que muitos fenômenos diferentes podem ser simulados, como sistemas tradicionais de reação-difusão, autômatos celulares e padrões de pigmentação de seres vivos. Em particular, demonstramos que a adição de saturação química aumenta significativamente a gama de padrões simulados usando reação-difusão, incluindo padrões que não eram possíveis anteriormente. Nossos resultados sugerem um possível modelo universal que pode integrar abordagens de formação de padrões anteriores, fornecendo nova base para experimentação e texturas de aparência realista para uso geral em Computação Gráfica.This doctoral thesis describes a novel model for coupling continuous chemical diffusion and discrete cellular events inside a biologically inspired simulation environment. Our goal is to define and explore a minimalist set of features that are also expressive, enabling the creation of complex 2D patterns using just a few rules. By not being constrained into a static or regular grid, we show that many different phenomena can be simulated, such as traditional reaction-diffusion systems, cellular automata, and pigmentation patterns from living beings. In particular, we demonstrate that adding chemical saturation increases significantly the range of simulated patterns using reaction-diffusion, including patterns not possible before. Our results suggest a possible universal model that can integrate previous pattern formation approaches, providing new ground for experimentation and realistic-looking textures for general use in Computer Graphics.
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Ren, Xiaojing. "Modeling pattern formation of swimming E.coli." Click to view the E-thesis via HKUTO, 2010. http://sunzi.lib.hku.hk/hkuto/record/B43704001.
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Sun, Zhiying. "Pattern formation and evolution on plants." Diss., The University of Arizona, 2009. http://hdl.handle.net/10150/194905.
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Phyllotaxis, namely the arrangement of phylla (leaves, florets, etc.) has intrigued natural scientists for over four hundred years. Statistics show that about 90\% of the spiral patterns has their numbers of spirals belonging to two consecutive members of the regular Fibonacci sequence. (Fibonacci(-like) sequences refer to any sequences constructed with the addition rule $a_{j+2}=a_{j}+a_{j+1}$, while the regular Fibonacci sequence refers to the particular sequences 1,1,2,3,5,8,13,...) Historical research on pattern formation on plants, tracing back to as early as four hundred years ago, was mostly geometry based. Current studies focus on the activities on the cellular level and study initiation of primordia (the initial undifferentiated form of phylla) as a morphogenesis process cued by some signal. The nature of the signal and the mechanisms governing the distribution of the signal are still under investigation. The two top candidates are the biochemical hormone auxin distribution and the mechanical stresses in the plant surface (tunica). We built a model which takes into consideration the interactions between these mechanisms. In addition, this dissertation explores both analytically and numerically the conditions for the Fibonacci-like patterns to continuously evolve (i.e. as the mean radius of the generative annulus changes over time, the numbers of spirals in the pattern increase or decreases along the same Fibonacci-like sequence), as well as for different types of pattern transitions to occur. The essential condition for the Fibonacci patterns to continuously evolve is that the patterns are formed annulus by annulus on a circular domain and the pattern-forming mechanism is dominated by a quadratic nonlinearity. The predominance of the regular Fibonacci pattern is determined by the pattern transitions at early stages of meristem growth. Furthermore, Fibonacci patterns have self-similar structures across different radii, and there exists a one-to-one mapping between any two Fibonacci-like patterns. The possibility of unifying the previous theory of optimal packing on phyllotaxis and the solutions of current mechanistic partial differential equations is discussed.
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Condette, Nicolas. "Pattern formation in magnetic thin films." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2011. http://dx.doi.org/10.18452/16336.
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Die vorliegende Arbeit beschäftigt sich mit einer Klasse von Variationsproblemen, die im Kontext des Ferromagnetismus entstehen. Es soll hierbei ein numerischer und analytischer Hintergrund zur Behandlung von harten magnetischen dünnen Filmen mit senkrechter Anisotropie gegeben werden. Bei magnetischen dünnen Filmen handelt es sich um Schichten von magnetischen Materialien mit Dicken von wenigen Mikrometern bis hin zu einigen Nanometern. Ausgangspunkt der Betrachtungen ist ein Modell von Landau und Lifshitz, das die Grundzustände der Magnetisierung in einem dreidimensionalen Körpers mit den Minimierer eines nichtkonvexen und nichtlokalen Energiefunktionals, der sogenannten mikromagnetischen Energie, verbindet. Unter der Annahme sehr kleiner Filmdicken wird aus dem betrachteten Modell ein zwei-dimensionales Modell hergeleitet. Anschließend wird mit Hilfe der Gamma-Konvergenz die Konvergenz zu einem Sharp-Interface-Modell gezeigt. Das resultierende Energiefunktional besteht aus konkurrierenden Interface- und Dipolenergieanteilen. Der zweite Teil der Arbeit beschäftigt sich mit der Analyse einer numerischen Methode, die die Lösungen des vorher hergeleiteten Modells approximiert. Hierbei stützen sich die Betrachtungen auf ein relaxiertes Modell, in dem der Interfaceenergiebeitrag durch seine Modica-Mortola Approximation ersetzt und dann der entsprechende L^2 Gradientenfluß betrachtet wird. Die daraus resultierende nichtlineare und nichtlokale parabolische Gleichung wird anschließend durch ein Crank-Nicolson-Verfahren in der Zeitvariablen und einem Fourieransatz für die Raumvariablen diskretisiert. Wir beweisen die Existenz und Eindeutigkeit von Lösungen des numerischen Verfahrens, sowie deren Konvergenz zu Lösungen des anfänglich betrachteten stetigen Modells. Ferner werden auch a priori Fehlerabschätzungen für die numerische Methode hergeleitet. Abschließend werden die analytischen Resultate anhand numerischer Experimente illustriert.This thesis is concerned with the study of a class of variational problems arising in the context of ferromagnetism. More precisely, it aims at providing a numerical and analytical background to the study of hard magnetic thin films with perpendicular anisotropy. Magnetic thin films are sheets of magnetic materials with thicknesses of a few micrometers down to a few nanometers used mainly in electronic industry, for example as magnetic data storage media for computers. Our initial considerations are based on a model of Landau and Lifshitz that associates the ground states of the magnetization within a three-dimensional body to the minimizers of a nonconvex and nonlocal energy functional, the so-called micromagnetic energy. Under film thickness considerations (thin film regime), we first reduce the aforementioned model to two dimensions and then carry out a Gamma-limit for a sharp-interface model. The resulting energy functional features a competition between an interfacial and a dipolar energy contribution. The second part of the thesis is concerned with the analysis of a numerical method to approximate solutions of the previously derived sharp-interface model. We base our considerations on a relaxed model in which we replace the interfacial energy contribution by its Modica-Mortola approximation, and then study the associated L^2 gradient flow. The resulting evolution equation, a nonlinear and nonlocal parabolic equation, is discretized by a Crank-Nicolson approximation for the time variable and a Fourier collocation method for the space variable. We prove the existence and uniqueness of the solutions of the numerical scheme, the convergence of these solutions towards solutions of the initial continuous model and also derive a-priori error estimates for the numerical method. Finally, we illustrate the analytical results by a series of numerical experiments.
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Bose, Sumit. "Pattern formation at semiconductor interfaces and surfaces." [S.l.] : [s.n.], 2001. http://edocs.tu-berlin.de/diss/2000/bose_sumit.pdf.
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Beato, Valentina. "Noise-induced pattern formation in excitable media." [S.l.] : [s.n.], 2006. http://opus.kobv.de/tuberlin/volltexte/2007/1419.
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Myerscough, Mary Ruth. "A chemotactic model of biological pattern formation." Thesis, University of Oxford, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329983.
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Martin, Christopher Paul. "Pattern formation in self-organised nanoparticle assemblies." Thesis, University of Nottingham, 2007. http://eprints.nottingham.ac.uk/10772/.
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An extremely wide variety of self-organised nanostructured patterns can be produced by spin-casting solutions of colloidal nanoparticles onto solid substrates. This is an experimental regime that is extremely far from thermodynamic equilibrium, due to the rapidity with which the solvent evaporates. It is the dynamics of flow and evaporation that lead to the formation of the complex structures that are observed by atomic force microscopy (AFM). The mechanisms involved in the formation of these patterns are not yet fully understood, largely because it is somewhat challenging to directly observe the evaporation dynamics during spin-casting. Monte Carlo simulations based on a modified version of the model of Rabani et al. [1] have allowed the study of the processes that lead to the production of particular nanoparticle morphologies. Morphological image analysis (MIA) techniques are applied to compare simulated and experimental structures, revealing a high degree of correspondence. Furthermore, these tools provide an insight into the level of order in these systems, and improve understanding of how a pattern’s specific morphology arises from its formation mechanisms. Modifying the properties of a substrate on the scale of a few hundred nanometres by AFM lithography has a profound effect on the processes of nanoparticle pattern formation. The simulation model of Rabani et al. was successfully modified to account for the effect of surface modification. The simulations were further modified to reproduce cellular structures on two distinct length scales– a phenomenon that is commonly seen in experiments. The dynamic behaviour of simulated nanoparticle structures is examined in the “scaling” regime in relation to recent experiments carried out by Blunt et al. [2] in an attempt to understand the coarsening mechanism. Finally, a genetic algorithm approach is applied to evolve the simulations to a target morphology. In this way, an experimental target image can be automatically analysed with MIA techniques and compared with an evolving population of simulations until a target “fitness” is reached.
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Tse, Dawn Po-Ling. "Spatial period-multiplying bifurcations in pattern formation." Thesis, University of Cambridge, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.616060.
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Feugier, François Gabriel. "Models of vascular pattern formation in leaves." Paris 6, 2006. http://www.theses.fr/2006PA066506.
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J’étudie la formation du système vasculaire des feuilles des plantes à l’aide de modèles mathématiques. L’hypothèse de canalisation d’une phytohormone, l’auxin, stipule que l’auto activation de son transport entre les cellules crée des chemins préférentiels qui se différencieront plus tard en système vasculaire. J’entreprends une analyse numérique de modèles de canalisation sur une grande matrice, et parviens à créer des motifs branchés dans lesquels circule l’auxin. Une analyse de stabilité d’un modèle simplifié nous éclaire sur les raisons de la formation de ces motifs et l’impossibilité de créer un réseau réticulé. La majorité des plantes ayant un système vasculaire réticulé, je modifie le modèle de façon à obtenir ce type de réseau. En ajoutant une variable biologiquement plausible, je parviens à créer un réseau réticulé dans lequel l’auxin circule uniformément. Enfin, je discute des relations entre la formation du système vasculaire et de la spirale de phyllotaxie.
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Rinaldi, Matteo. "Dynamics of Phase Separation and Pattern Formation." Research Showcase @ CMU, 2017. http://repository.cmu.edu/dissertations/946.
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The focus of this thesis is the study of the evolution of two models adopted in the context of phase separation and pattern formation, the Cahn-Hilliard model and the Swift-Hohenberg model. In the study of the Cahn-Hilliard model, the PDEs arising as the L2 and H-1 gradient flows in the higher dimensional setting n > 1 are studied, and estimates are provided on the evolution of solutions initiated close to configurations that globally or locally minimize the perimeter of the interface are provided. The results rely on a new regularity property of a local version of the well-known isoperimetric function. In the Swift-Hohenberg setting, the one dimensional model is considered, and the slow evolution of a particular class of solutions is established. In this context, existence and regularity of solutions in dimension n_< 3 are provided. In the last part of this thesis, two ongoing project and future research directions are presented.
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Lam, Woon-Kwan. "Pattern formation in non-linear chemical systems." Ann Arbor, Mich. : ProQuest, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3288932.
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Thesis (Ph.D. in Applied Mathematics)--S.M.U., 2007.Title from PDF title page (viewed Nov. 19, 2009). Source: Dissertation Abstracts International, Volume: 68-11, Section: B, page: 7376. Adviser: Peter K. Moore. Includes bibliographical references.
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Isomura, Akihiro. "Spatiotemporal pattern formation in cardiac cell culture." 京都大学 (Kyoto University), 2009. http://hdl.handle.net/2433/124393.
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Bertram, Matthias. "Controlling turbulence and pattern formation in chemical reactions." [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=964948931.
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Plenge, Florian Moritz. "Theory of electrochemical pattern formation under global coupling." [S.l.] : [s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=968694535.
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Moyles, Iain. "Hybrid asymptotic-numerical analysis of pattern formation problems." Thesis, University of British Columbia, 2015. http://hdl.handle.net/2429/53715.
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In this thesis we present an analysis of the Gierer-Meinhardt model with saturation (GMS) on various curve geometries in ℝ². We derive a boundary fitted coordinate framework which translates an asymptotic two-component differential equation into a single component reaction diffusion equation with singular interface conditions. We create a numerical method that generalizes the solution of such a system to arbitrary two-dimensional curves and show how it extends to other models with singularity properties that are related to the Laplace operator. This numerical method is based on integrating logarithmic singularities which we handle by the method of product integration where logarithmic singularities are handled analytically with numerically interpolated densities. In parallel with the generalized numerical method, we present some analytical solutions to the GMS model on a circular and slightly perturbed circular curve geometry. We see that for the regular circle, saturation leads to a hysteresis effect for two dynamically stable branches of equilibrium radii. For the near circle we show that there are two distinct perturbations, one resulting from the introduction of a angular dependent radius, and one caused by Fourier mode interactions which causes a vertical shift to the solution. We perform a linear stability analysis to the true circle solution and show that there are two classes of eigenvalues leading to breakup or zigzag instabilities. For the breakup instabilities we show that the saturation parameter can completely stabilize perturbations that we show are always unstable without saturation and for the zigzag instabilities we show that the eigenvalues are given by the near circle curve normal velocity. The breakup analysis is based on the reduction of an implicit non-local eigenvalue problem (NLEP) to a root finding problem. We derive conditions for which this eigenvalue problem can be made explicit and use it to analyze a stripe and ring geometry. This formulation allows us to classify certain technical properties of NLEPs such as instability bands and a Hopf bifurcation condition analytically.Science, Faculty of
Mathematics, Department of
Graduate
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Da, Rocha Miranda Pontes José. "Pattern formation in spatially ramped Rayleigh-Bénard systems." Doctoral thesis, Universite Libre de Bruxelles, 1994. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/212711.
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Teng, Jing. "Pattern formation and growth kinetics in eutectic systems." [Ames, Iowa : Iowa State University], 2007.
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Rogers, Jeffrey L. "Modulated pattern formation : stabilization, complex-order, and symmetry." Diss., Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/30930.
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Bates, Wilfred Mark. "Pattern formation in models of charge density waves." Thesis, McGill University, 2000. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=31189.
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We investigate the phenomenon of phase organization in charge density waves. Coppersmith and Littlewood [87] have argued that charge density waves become organized into a "minimally stable" state when subject to a pulsed driving force. They have also proposed that the pulse duration memory effect, observed by Fleming and Schneemeyer [86], is evidence for this self organizing behaviour.We review the microscopic origins of charge density waves, experimental results, and theoretical models of charge density waves. We also review theories of complex systems, and, in particular, the phase organization theory proposed by Tang et al. [87]. We focus on how the phase organization theory applies to the dynamics of charge density waves.
We investigate phase organization in a model of elastically coupled particles subject to a periodic potential and a pulsed driving force. By numerical simulation of the model, we show that the phase organization behaviour is contingent on the existence of a large number of inequivalent metastable configurations in the model. We also show that this model is equivalent to a purely elastic model of charge density waves interacting with impurities.
We further investigate phase organization in a model of charge density waves that has been proposed by Karttunen et al. [99], in which the dynamical generation of phase slips is naturally accounted for. Based on the results of numerical simulations, we argue that phase slips reduce or eliminate the phase organization behaviour of charge density waves by breaking the elasticity of the system.
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Lewis, Mark A. "Analysis of dynamic and stationary biological pattern formation." Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.276976.
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Maini, P. K. "On mechano-chemical models for morphogenetic pattern formation." Thesis, University of Oxford, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.370285.
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Thompson, Alasdair Graham. "Lattice models of pattern formation in bacterial dynamics." Thesis, University of Edinburgh, 2012. http://hdl.handle.net/1842/6248.
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In this thesis I study a model of self propelled particles exhibiting run-and tumble dynamics on lattice. This non-Brownian diffusion is characterised by a random walk with a finite persistence length between changes of direction, and is inspired by the motion of bacteria such as Escherichia coli. By defining a class of models with multiple species of particle and transmutation between species we can recreate such dynamics. These models admit exact analytical results whilst also forming a counterpart to previous continuum models of run-and- tumble dynamics. I solve the externally driven non-interacting and zero-range versions of the model exactly and utilise a field theoretic approach to derive the continuum fluctuating hydrodynamics for more general interactions. I make contact with prior approaches to run-and-tumble dynamics of lattice and determine the steady state and linear stability for a class of crowding interactions, where the jump rate decreases as density increases. In addition to its interest from the perspective of nonequilibrium statistical mechanics, this lattice model constitutes an efficient tool to simulate a class of interacting run-and-tumble models relevant to bacterial motion. Pattern formation in bacterial colonies is confirmed to be able to stem solely from the interplay between a diffusivity that depends on the local bacterial density and regulated division of the cells, in particular without the need for any explicit chemotaxis. This simple and generic mechanism thus provides a null hypothesis for pattern formation in bacterial colonies which has to be falsified before appealing to more elaborate alternatives. Most of the literature on bacterial motility relies on models with instantaneous tumbles. As I show, however, the finite tumble duration can play a major role in the patterning process. Finally a connection is made to some real experimental results and the population ecology of multiple species of bacteria competing for the same resources is considered.
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Siggers, Jennifer Helen. "Pattern formation in a cylinder, and related topics." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.619819.
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Irvine, Michael Alastair. "Pattern formation and persistence in spatial plant ecology." Thesis, University of Warwick, 2014. http://wrap.warwick.ac.uk/67166/.
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The main aim of the thesis is to explore the interaction between pattern and process in vegetation ecology using a variety of mathematical and statistical methods. Of particular interest is what information about the dynamics of the underlying system can be gained through a single spatial snapshot, such as an aerial photograph or satellite image. The hypotheses are related to seagrass ecology, whose growth is primarily clonal and broadly exists as a monoculture and thus makes it an ideal candidate to study these interactions. The thesis broadly concerns two forms of spatial pattern and the underlying dynamics that give rise to them. The first concerns regular pattern formation, where the pattern has a characteristic length scale. Examples are abundant in natural systems, such as mussel beds, semi-arid ecosystems as well as seagrass. The developments concerned with regular pattern formation include methods of detection in a large spatial dataset, a novel stochastic model of vegetation that produces regular pattern with plausible mechanisms, the development of a new methodology to fit regular spatial pattern data to the model and the impact as well as evolutionary mechanisms of regular patterning in the presence of disease. The second form of spatial pattern exhibited in a wide variety of sessile species is scale-free or fractal patterning. Certain scaling heuristics, such as the boundary dimension of a vegetation cluster or the power-law exponent of the patch-size distribution have been used to infer properties of the dynamics. We explore these heuristics using a variety of plausible models of vegetation growth and find the circumstances under which there is a clear relationship between the spatial heuristics and the dynamics. These are then supplemented by viewing vegetation growth as an aggregation process. A novel model of vegetation aggregation with death is produced to find the origin of the ubiquitous power-law patch-size distribution found in nature. Finally the impact of scaling on the spread of disease is explored.
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Hunt, Gordon S. "Mathematical modelling of pattern formation in developmental biology." Thesis, Heriot-Watt University, 2013. http://hdl.handle.net/10399/2706.
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The transformation from a single cell to the adult form is one of the remarkable wonders of nature. However, the fundamental mechanisms and interactions involved in this metamorphic change still remain elusive. Due to the complexity of the process, researchers have attempted to exploit simpler systems and, in particular, have focussed on the emergence of varied and spectacular patterns in nature. A number of mathematical models have been proposed to study this problem with one of the most well studied and prominent being the novel concept provided by A.M. Turing in 1952. Turing's simple yet elegant idea consisted of a system of interacting chemicals that reacted and di used such that, under certain conditions, spatial patterns can arise from near homogeneity. However, the implicit assumption that cells respond to respective chemical levels, di erentiating accordingly, is an oversimpli cation and may not capture the true extent of the biology. Here, we propose mathematical models that explicitly introduce cell dynamics into pattern formation mechanisms. The models presented are formulated based on Turing's classical mechanism and are used to gain insight into the signi cance and impact that cells may have in biological phenomena. The rst part of this work considers cell di erentiation and incorporates two conceptually di erent cell commitment processes: asymmetric precursor di erentiation and precursor speci cation. A variety of possible feedback mechanisms are considered with the results of direct activator upregulation suggesting a relaxation of the two species Turing Instability requirement of long range inhibition, short range activation. Moreover, the results also suggest that the type of feedback mechanism should be considered to explain observed biological results. In a separate model, cell signalling is investigated using a discrete mathematical model that is derived from Turing's classical continuous framework. Within this, two types of cell signalling are considered, namely autocrine and juxtacrine signalling, with both showing the attainability of a variety of wavelength patterns that are illustrated and explainable through individual cell activity levels of receptor, ligand and inhibitor. Together with the full system, a reduced two species system is investigated that permits a direct comparison to the classical activator-inhibitor model and the results produce pattern formation in systems considering both one and two di usible species together with an autocrine and/or juxtacrine signalling mechanism. Formulating the model in this way shows a greater applicability to biology with fundamental cell signalling and the interactions involved in Turing type patterning described using clear and concise variables.
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Acharya, Gyanu R. "Electroconvection and Pattern Formation in Nematic Liquid Crystals." Kent State University / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=kent1239804049.
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Degen, Michael Merle. "Time-dependent pattern formation in fluid dynamical systems /." The Ohio State University, 1997. http://rave.ohiolink.edu/etdc/view?acc_num=osu148794815862621.
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Yang, Xige. "MATHEMATICAL MODELS OF PATTERN FORMATION IN CELL BIOLOGY." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1542236214346341.
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Arouh, Scott. "Pattern formation and morphology transitions in bacterial systems /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC IP addresses, 2000. http://wwwlib.umi.com/cr/ucsd/fullcit?p9970683.
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Masson, Jean-Loup Didier. "Pattern formation and evolution in thin polymer films." Access restricted to users with UT Austin EID Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3034981.
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Reed, Robert Dale Jr. "The evolution of pattern formation in butterfly wings." Diss., The University of Arizona, 2004. http://hdl.handle.net/10150/290156.
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In this dissertation I employ a comparative gene expression approach to address the evolution of butterfly wing pattern formation at several levels, with emphasis on early pattern determination and pigment gene regulation during late development. Expression analysis of the receptor molecule Notch suggested previously unknown roles for Notch signaling in butterfly wing patterning. Notch upregulation was found to precede the activation of the transcription factor Distal-less during early eyespot color pattern determination. A phylogenetic comparison of expression time series from multiple moth and butterfly species suggested that changes in a Notch/Distal-less temporal pattern formation process were associated with the gain and loss of both eyespot and midline color patterns during wing pattern evolution. Additionally, Notch expression was found to occur in a grid-like pattern in the butterfly wing epithelium shortly after pupation. This observation, together with previous expression and simulation studies, support a Notch-mediated lateral inhibition model of wing scale organization. Tryptophan-derived ommochrome pigments are a derived feature of nymphalid butterfly wings. I found that multiple genes in the ommochrome biosynthetic pathway were expressed in the wings of selected nymphalid butterflies. Additionally, transcriptional regulation of genes encoding the ommochrome synthesis enzymes vermilion and cinnabar was found to be temporally and spatially associated with the polymorphism and development of forewing band patterns in the mimetic butterfly Heliconius erato. These findings provide evidence that changes in ommochrome gene regulation underlie the evolution and development of major nymphalid wing pattern elements.
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Mulholland, Anthony J. "The Eikonal approach to reaction-diffusion equations in multiply-connected domains." Thesis, Glasgow Caledonian University, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.359146.
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Formosa, Jordan Pau. "Pattern formation through lateral inhibition mediated by Notch signaling." Doctoral thesis, Universitat de Barcelona, 2013. http://hdl.handle.net/10803/116495.
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Multicellular organisms are constituted by different kinds of cells which are arranged in a particular way, forming tissues with specific functions. The organization of these different cells can give rise to regular spatiotemporal patterns.
In this Thesis we evaluate from a theoretical perspective the effects of different regulatory elements of the Notch signaling pathway in lateral inhibition patterning. These new elements under study are motivated by recent experimental observations. For studying them, we reformulate a phenomenological model proposed by Collier and colleagues (1996). Our modeling approach is based on coupled ordinary differential equations in hexagonal and irregular bidimensional lattices. We use both deterministic and stochastic approaches. We analyze the pattern formation capabilities of our proposed models by using different analytical tools and integrate numerically our dynamical equations.
We focus on four main topics. In the first topic we study how a neurogenic differentiation wavefront in the embryonic vertebrate retina depends on the state of the invaded tissue. Our results show that the properties (pattern formed, shape and velocity) of progressing fronts of lateral inhibition depend crucially on the presence of ligand ahead of the differentiation front. We find similar results in a planar growing wavefront that would mimic morphogenetic furrow progression in embryonic Drosophila eye. Hence, our results point to a mechanism for neurogenic front regulation, and to a potential new design principle.
In the second topic, we study the effects of a diffusible ligand in the context of lateral inhibition. We show that the diffusible ligand per se combined with its inhibition by Notch is not able to generate a pattern. Our results indicate that diffusible ligand with the classical lateral inhibition circuit softens and destroys the lateral inhibition pattern. At intermediate diffusion rates, diffusion can help to create perfect patterns.
The third topic focuses on the study of receptor-ligand interactions within the same cell, what is called cis-interactions. We study the effect of Notch signal-productive cis-interactions in combination with another signaling source in two different situations: (i) in a multicellular scenario, where the other signaling source would be provided by the trans-interactions, and (ii) in a single-cell scenario in which a basal ligand-independent signaling source would be provided. In both situations, we predict that cis-interactions can drive cis-inhibition - i.e. an effective depletion of the signal production rate - at weak cis-signaling rates when acting together with a stronger signaling source, e.g. trans-interactions or with a ligand-independent signaling source. Our work also shows that cis-inhibition in the single-cell system together with a basal signal production can drive bistability. In the multicellular case, we observe that by increasing the amount of cis-interactions in the cis-inhibition scenario the proportion of high-Delta fated cells in a tissue gradually increases.
In the fourth topic we study the case of hair cell differentiation in the embryonic chick inner ear. In this context, Notch pathway operates in two opposite modes with two different ligands: first, lateral induction through Jag1 ligand and afterwards, lateral inhibition through Dl1 ligand. We predict that relative signaling rates (or strengths) by Jag1 and Dl1 when bound to Notch are critical for the transit of operating modes. Also, we predict that in the lateral inhibition stage, competition between Dl1 and Jag1 ligands arise. This competition introduces an extra intercellular mutual inhibitory feedback loop, contributing to lateral inhibition.
Overall, this Thesis presents new theoretical results and predictions on pattern formation in the context of lateral inhibition mediated by Notch signaling.Els organismes multicel·lulars estan constituïts per diferents tipus cel·lulars ordenats d’una certa manera, formant teixits amb funcions específiques. L’organització de cèl·lules de tipus diferents pot donar lloc a patrons espacio-temporals Aquesta Tesi es basa en l’estudi de com a partir d’un teixit de cèl·lules equivalents — estat homogeni precursor — s’estableixen patrons ordenats de tipus cel·lulars diferents. En particular, ens hem centrat en l’estudi d’un tipus de patrons que sorgeixen en teixits animals que tenen dos tipus cel·lulars i que presenten un ordre fi en el teixit, i.e. de longitud d’ona de poques cèl·lules. Aquest tipus de patrons són formats degut al efecte de la inhibició lateral. La inhibició lateral és un fenomen en el qual cèl·lules precursores equivalents intenten adoptar un cert estat o destí cel·lular per a diferenciar-se en un tipus cel·lular en particular, i al mateix temps inhibeixen a les seves cèl·lules veïnes que adquireixin aquest mateix estat. Aquest procés dinàmic dóna lloc a un patró fi, on les cèl·lules que han finalment adoptat l’estat desitjat vénen rodejades per cèl·lules que són inhibides, i que acabaran diferenciant-se en un tipus cel·lular diferent. Aquest tipus de patró es troba en una àmplia varietat de teixits animals, com ara en la retina ,i en l’oïda interna de vertebrats, i en l’ull de la mosca Drosophila.