Thesis (Ph. D.)--Physics, Georgia Institute of Technology, 2005. / Jean Bellissard, Committee Member ; Turgay Uzer, Committee Member ; Roman Grigoriev, Committee Member ; Konstantin Mischaikow, Committee Member ; Predrag Cvitanovic, Committee Chair. Vita. Includes bibliographical references.

Thesis (Ph. D. in Cell and Developmental Biology)--Vanderbilt University, May 2006. / Title from title screen. Includes bibliographical references.

In this thesis we use density functional theory (DFT) to study the solvent mediated interactions between solvophobic, solvophilic and patchy nanostructures namely rectangular cross section blocks. We calculate both the density profiles and local compressibility around the blocks and the results obtained for our model system provide a means to understanding the basic physics of solvent mediated interactions between nanostructures, and between objects such as proteins in water, that possess hydrophobic and hydrophilic patches. Our results give an improved understanding of the behaviour of liquids around solvophobic objects and solvophobicity (hydrophobicity) in general. Secondly, we look into the physics incorporated in standard mean-field DFT. This is normally derived by making what appears to be a rather drastic approximation for the two body density distribution function: ρ(2)(r,r′) ≈ ρ(r)ρ(r′), where ρ(r) is the one-body density distribution function. We provide a rationale for why the DFT often does better than this approximation would make you expect. Finally, we develop a lattice model to understand the nature of the pattern formation exhibited by certain systems of particles deposited on liquid-air interfaces and in particular the nature of the transitions between the different patterned structures that are observed. This is done using Monte Carlo computer simulations and DFT and links the observed microphase ordering with the micellisation process seen e.g. in surfactant systems.

No description available.

This thesis describes the comparison of time-lapse field observations of suncups on alpine snow with numerical simulations. The simulations consist of solutions to a nonlinear partial differential equation which exhibits spontaneous pattern formation from a low amplitude, random initial surface. Both the field observations and the numerical solutions are found to saturate at a characteristic height and fluctuate chaotically with time. The timescale of these fluctuations is found to be instrumental in determining the full set of parameters for the numerical model such that it mimics the nonlinear dynamics of suncups. These parameters in turn are related to the change in albedo of the snow surface caused by the presence of suncups. This suggests the more general importance of dynamical behaviour in gaining an understanding of pattern formation phenomena. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

This study considers the dynamical interaction of two predatory carnivores (Lions (Panthera leo) and Spotted Hyaenas (Crocuta crocuta)) and three of their common prey (Buffalo (Syncerus caffer), Warthog (Phacochoerus africanus) and Kudu (Tragelaphus strepsiceros)). The dependence on spatial structure of species’ interaction stimulated the author to formulate reaction-diffusion models to explain the dynamics of predator-prey relationships in ecology. These models were used to predict and explain the effect of threshold populations, predator additional food and prey refuge on the general species’ dynamics. Vital parameters that model additional food to predators, prey refuge and population thresholds were given due attention in the analyses. The stability of a predator-prey model for an ecosystem faced with a prey out-flux which is analogous to and modelled as an Allee effect was investigated. The results highlight the bounds for the conversion efficiency of prey biomass to predator biomass (fertility gain) for which stability of the three species ecosystem model can be attained. Global stability analysis results showed that the prey (warthog) population density should exceed the sum of its carrying capacity and threshold value minus its equilibrium value i.e., W >(Kw + $) −W . This result shows that the warthog’s equilibrium population density is bounded above by population thresholds, i.e., W < (Kw+$). Besides showing the occurrence under parameter space of the so-called paradox of enrichment, early indicators of chaos can also be deduced. In addition, numerical results revealed stable oscillatory behaviour and stable spirals of the species as predator fertility rate, mortality rate and prey threshold were varied. The stabilising effect of prey refuge due to variations in predator fertility and proportion of prey in the refuge was studied. Formulation and analysis of a robust mathematical model for two predators having an overlapping dietary niche were also done. The Beddington-DeAngelis functional and numerical responses which are relevant in addressing the Principle of Competitive Exclusion as species interact were incorporated in the model. The stabilizing effect of additional food in relation to the relative diffusivity D, and wave number k, was investigated. Stability, dissipativity, permanence, persistence and periodicity of the model were studied using the routine and limit cycle perturbation methods. The periodic solutions (b 1 and b 3), which influence the dispersal rate (') of the interacting species, have been shown to be controlled by the wave number. For stability, and in order to overcome predator natural mortality, the nutritional value of predator additional food has been shown to be of high quality that can enhance predator fertility gain. The threshold relationships between various ecosystem parameters and the carrying capacity of the game park for the prey species were also deduced to ensure ecosystem persistence. Besides revealing irregular periodic travelling wave behaviour due to predator interference, numerical results also show oscillatory temporal dynamics resulting from additional food supplements combined with high predation rates.

Prédiction théorique des structures localisées à une et à deux dimensions dans des cavité passives soumis à une injection optique. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

No description available.

This thesis focuses on the impact of spatially heterogeneous environments on the spatio-temporal behavior of planktonic systems. Specific emphasis placed is on the influence of spatial variations in the strength of random or chaotic movements (diffusion) of the organisms. Interaction between different species is described by ordinary differential equations. In order to describe movements in space, reaction–diffusion or advection–reaction–diffusion systems are studied. Examples are given for different approaches of diffusive motion as well as for the possible effects on the localized biological system. The results are discussed based on their biological and physical meanings. In doing so, different mechanisms are shown which are able to explain events of fast plankton growth near turbulent flows. In general, it is shown that local variation in the strength of vertical mixing can have global effects on the biological system, such as changing the stability of dynamical solutions and generating new spatiotemporal behavior. The thesis consists of five chapters. Three of them have been published in international peer-reviewed scientific journals. Chapter 1. Introduction: This chapter gives a general introduction to the history of plankton modeling and introduces basic ideas and concepts which are used in the following chapters. Chapter 2. Fokker-Planck law of diffusion: The influence of spatially in- homogeneous diffusion on several common ecological problems is analyzed. Dif- fusion is modeled with Fick’s law and the Fokker–Planck law of diffusion. A discussion is given about the differences between the two formalisms and when to use the one or the other. To do this, the discussion starts with a pure diffusion equation, then it turns to a reaction–diffusion system with one logistically growing component which invades the spatial domain. This chapter also provides a look at systems of two reacting components, namely a trimolecular oscillating chemical model system and an excitable predator–prey model. Contrary to Fickian diffusion, spatial inhomogeneities promote spatial and spatiotemporal pattern formation in the case of Fokker–Planck diffusion. A slightly modified version of this chapter has been published in the Journal of Mathematical Biology (Bengfort et al., 2016). Chapter 3. Plankton blooms and patchiness: Microscopic turbulent motions of water have been shown to influence the dynamics of microscopic species. Therefore, the number, stability, and excitability of stationary states in a predator– prey model of plankton species can change when the strength of turbulent motions varies. In a spatial system these microscopic turbulent motions are naturally of different strength and form a heterogeneous physical environment. Spatially neighboring plankton communities with different physical conditions can impact each other due to diffusive coupling. It is shown that local variations in the physical conditions can influence the global system in the form of propagating pulses of high population densities. For this, three local predator–prey models with different local responses to variation in the physical environment are considered. The degree of spatial heterogeneity can, depending on the model, promote or reduce the number of propagating pulses, which can be interpreted as patchy plankton distributions and recurrent blooms. This chapter has been published in the Journal Ecological Complexity (Bengfort et al., 2014). Chapter 4. Advection–reaction–diffusion model: Here, some of the models introduced in chapter 1 and 2 are modified to perform two dimensional spatial simulations including advection, reaction and diffusion. These models include assumptions about turbulent flows introduced in chapter 1. Chapter 5. Competition: Some plankton species, such as cyanobacteria, have an advantage in competition for light compared to other species because of their buoyancy. This advantage can be diminished by vertical mixing in the surround- ing water column. A non–spatial model, based on ordinary differential equations, which accounts for this effect is introduced. The main aim is to show that vertical mixing influences the outcome of competition between different species. Hystersis is possible for a certain range of parameters. Introducing a grazing predator, the system exhibits different dynamics depending on the strength of mixing. In a diffusively coupled horizontal spatial model, local vertical mixing can also have a global effect on the biological system, for instance, destabilization of a locally stable solution, or the generation of new spatiotemporal behavior. This chapter has been published in the Journal Ecological Modelling (Bengfort and Malchow, 2016).

Dans la première partie de cette thèse, nous étudierons l’impact de l’hétérogénéité tumorale sur les phénomènes d’invasion collective des cellules cancéreuses et de dissémination métastatique.L’hétérogénéité des populations cellulaires tumorales est observée dans la plupart des lésions cancéreuses solides. Cependant, son impact sur le phénomène de métastase – élément prépondérant dans l’établissement du pronostic vital du patient – demeure à ce jour mal compris. En utilisant un modèle numérique minimal de tumeur, nous avons cherché à déterminer quel était l’impact de l’hétérogénéité des propriétés mécaniques des cellules cancéreuses sur leur invasion dans les tissus sains entourant la tumeur. Nous nous sommes particulièrement intéressés aux différences de mobilité cellulaire au sein des diverses populations cellulaires composant une tumeur. Nos travaux établissent un lien de causalité entre l’hétérogénéité tumorale et la dissémination métastatique. De plus, ils permettent de reproduire un certain nombre de morphologie d’invasion cancéreuse telles que des protrusions pluricellulaires en forme de « doigts » ou d’agrégats. Nos expériences in silico démontrent que deux mécanismes complémentaires sont à l’œuvre au sein des tumeurs hétérogènes. Une faible proportion de cellules leaders, possédant une force mobile plus élevée, est capable d’initier et de diriger l’invasion cancéreuse, alors que les effets de mouvements collectifs au sein de la tumeur fournissent la coordination mécanique nécessaire à un phénomène d’invasion collectif continu. Ces résultats suggèrent que la dynamique d’invasion collective observée durant le processus de métastase est un phénomène universel. Celui-ci est propre aux populations de cellules aux propriétés mécaniques hétérogènes, et peut être décrit en se fondant sur un nombre limité d’hypothèses physiques, et ce malgré l’importante variabilité génétique et phénotypique qui caractérise les pathologies cancéreuses.Dans la seconde partie de cette thèse, nous continuerons à étudier l’impact de l’hétérogénéité des propriétés cellulaires, cette fois à l’échelle d’un organisme pluricellulaire et non pas seulement d’un tissu. Nous nous intéresserons au développement de l’amibe sociale Dictyostelium discoideum. Lorsque les amibes sont privées de nourriture, elles forment des agrégats pluricellulaires nommés slugs,dans lesquels les cellules initialement identiques se différencient et se ségrèguent en deux populations distinctes : les cellules prespores, à l’arrière, et les cellules prestalks, à l’avant. La formation de ce motif spatial est caractérisé par une homéostasie des proportions des types cellulaires, qui demeurent quasi constants malgré les variations importantes du nombre de cellules au sein des agrégats. Si différents modèles ont été proposés pour expliquer l’origine de ce phénomène, il demeurait nécessaire de mettre en place des expériences quantitatives afin de confirmer ou d’infirmer ces modèles. Dans ce but, nous avons développé et caractérisé une nouvelle souche cellulaire de Dictyostelium, AX2-PYR, utilisant des sondes fluorescentes génétiquement encodées permettant de distinguer les différents types cellulaires au sein des slugs. Nos résultats démontrent l’invariance du motif prespore/prestalk avec la taille des slugs sur quatre ordres de grandeur, et mettent en évidence l’existence d’un mécanisme actif de régulation des proportions reposant sur les communications intercellulaires. / In the first part of this thesis, we study the impact of tumour heterogeneity on cancer collective invasion and metastatic dissemination. Heterogeneity within tumour cell populations is commonly observed in most solid tumours, but its impact on metastasis, one of the primary determinants of the disease prognosis, remains poorly understood.Working with a simplified numerical model of tumour spheroids, weinvestigate the impact of mechanical heterogeneity of tumour cells on the onset of tumour invasion into surrounding tissues, focusing more particularly on the influence of differences in cell motility. Ourwork establishes a positive link between tumour heterogeneity and metastatic dissemination, and recapitulates a number of invasion patterns identified in vivo, such as multicellular finger-like protrusionsor tumour cell clusters. In our in silico experiments, we demonstrate that two complementary mechanisms are at play in heterogeneous tumours: a small proportion of stronger cells with a higher motile force are able to initiate and lead the escape from the tumour, while collective effects in the bulk of the tumour provide the coordination required to sustain the invasive process through multicellular streaming. This suggests that the multicellular dynamics observed during metastasis is a generic feature of mechanically heterogeneous cell populations and might rely on a limited and generic set of physical assumptions shared by most tumours in spite of the genetic and phenotypic variability amongst patients and pathologies.In the second part of our work, we continue to explore the impact of heterogeneity on population scale behaviours of multicellular systems, focusing on the development of the social amoeba Dictyosteliumdiscoideum. Under starvation Dictyostelium cells form multicellular aggregates named slugs where amoeba cells differentiate and segregate into two distinct spatial zones, the prespore (rear) and prestalk (front) cells regions. This developmental pattern is characterized by an homeostasis of cell-type proportions with respect to slug size and external perturbations. Different models have been proposed to explain theorigin and regulation of this pattern, but quantitative experiments were still needed to decipher between the proposed mechanisms. To quantitatively investigate cell differentiation and spatial patterning in live multicellular aggregates, we developed and characterized a new stable cell line, AX2-PYR, using genetically encoded fluorescent reporters of cell differentiation into prespore and prestalk cells. Our results demonstrate the scaling of the prespore/prestalk pattern over more than three orders of magnitude in slug size, and show the existence of a proportion regulation mechanism which might rely on cell-cell communications.