Thesis (Ph. D.)--Ohio State University, 2007. / Full text release at OhioLINK's ETD Center delayed at author's request

abstract: A new method for generating artificial fingerprints is presented. Due to their uniqueness and durability, fingerprints are invaluable tools for identification for law enforcement and other purposes. Large databases of varied, realistic artificial fingerprints are needed to aid in the development and evaluation of automated systems for criminal or biometric identification. Further, an effective method for simulating fingerprints may provide insight into the biological processes underlying print formation. However, previous attempts at simulating prints have been unsatisfactory. We approach the problem of creating artificial prints through a pattern formation model. We demonstrate how it is possible to generate distinctive patterns that strongly resemble real fingerprints via a system of partial differential equations with a suitable domain and initial conditions. / Dissertation/Thesis / M.A. Mathematics 2013

We study energy-driven nonlocal pattern forming systems with opposing interactions. Selections are drawn from the area of Quantum Physics, and nonlocalities are present via Coulombian type interactions. More precisely, we study Thomas-Fermi-Dirac-Von Weizsacker (TFDW) type models, which are mass-constrained variational problems. The TFDW model is a physical model describing ground state electron configurations of many-body systems. First, we consider minimization problems of the TFDW type, both for general external potentials and for perturbations of the Newtonian potential satisfying mild conditions. We describe the structure of minimizing sequences, and obtain a more precise characterization of patterns in minimizing sequences for the TFDW functionals regularized by long-range perturbations. Second, we consider the TFDW model and the Liquid Drop Model with external potential, a model proposed by Gamow in the context of nuclear structure. It has been observed that the TFDW model and the Liquid Drop Model exhibit many of the same properties, especially in regard to the existence and nonexistence of minimizers. We show that, under a "sharp interface'' scaling of the coefficients, the TFDW energy with constrained mass Gamma-converges to the Liquid Drop model, for a general class of external potentials. Finally, we present some consequences for global minimizers of each model. / Thesis / Doctor of Philosophy (PhD)

<p>Bioelectricity, or endogenous electrical signaling mediated by the dynamic distribution of charged molecules, is an ancient signaling mechanism conserved across living organisms. Increasing evidence has revealed that bioelectric signals play a critical role in many diverse aspects of biology such as embryonic development, cell migration, regeneration, cancer, and other diseases. However, direct visualization and manipulation of bioelectricity during development are lacking. Neuroscience has developed tools such as GEVIs (genetically encoded voltage indicators) and chemogenetics like DREADDs (designer receptor exclusively activated by designer drugs) which allow for real–time voltage monitoring and activation of mutated receptors by inert molecules for perturbing membrane potential (Vm). To uncover bioelectric activity during development, we generated a whole-zebrafish transgenic GEVI reporter line and characterized the electrical signaling during early embryogenesis using light sheet microscopy (LSM). Additionally, we generated tissue-specific transgenic lines that combined GEVIs and chemogenetic DREADD tools to manipulate Vm. We found zebrafish embryos display stage-specific characteristic bioelectric signals during the cleavage, blastula, gastrula, and segmentation periods. Furthermore, activation of DREADDs was able to alter cell-specific GEVI fluorescence intensity and could cause a melanophore hyperpigmentation phenotype. Ultimately, these results provide the first real-time systematic analysis of endogenous bioelectricity during vertebrate embryonic development. Additionally, we generated and tested zebrafish transgenic lines for simultaneous visualization and chemogenetic manipulation of Vm during development. These results provide a better understanding of developmental bioelectricity and new tools for future studies, which could eventually help uncover the cellular electric mechanisms behind tissue patterning and disease.</p>

京都大学 / 新制・課程博士 / 博士(工学) / 甲第24614号 / 工博第5120号 / 新制||工||1979(附属図書館) / 京都大学大学院工学研究科材料工学専攻 / (主査)教授 邑瀬 邦明, 教授 宇田 哲也, 教授 作花 哲夫 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

PhD Thesis / In this thesis, experiments are described which study the elastocapillary interactions between liquids and taut solid films. The research employs contact angle measurements to elucidate how capillary forces deform compliant solid structures, but also to attain fundamental insight into the energy of interfaces involving amorphous solids. The majority of the work focuses on how capillary deformations of compliant elastic membranes introduce modifications to descriptions of common wetting phenomena. Particular focus is given to studying partial wetting in the presence of compliant membranes in various geometries: droplet on a free-standing membrane, droplet capped by a membrane but sessile on a rigid substrate, and droplet pressed between two free-standing membranes. The mechanical tension in these membranes is found to play an equivalent role as the interfacial tensions. As such, the mechanical tension is incorporated into Young-Dupre's law (capped droplet on a rigid substrate) or Neumann's triangle (droplet on free-standing membrane), leading to departures from the classical wetting descriptions. In addition, one study is conducted investigating how viscous dewetting is affected by the liquid film being capped by an elastic film. The results of this study show that the dewetting rate and rim morphology are dictated by the elastic tension. Another important aspect of the work is demonstrating the utility of anisotropic membrane tension for liquid patterning. A biaxial tension is shown to produce droplets and dewetting holes which are elongated along the high tension direction. The compliant membrane geometry can also be designed to produce droplets and holes with square morphology. In the final project, the surface energy of strained glassy and elastomeric solids is studied. Glassy solids are shown to have strain-dependent surface energies, which implies that surface energy (energy per unit area) and surface stress (force per unit length) are not equivalent for this class of materials by virtue of the Shuttleworth equation. On the other hand, this study provides strong evidence that surface energy and surface stress are equivalent for elastomeric interfaces. / Thesis / Doctor of Philosophy (PhD)

An important phenomenon of systems driven far-from-equilibrium is spatiotemporal chaos where the dynamics are aperiodic in both time and space. We explored this numerically for three systems: the Lorenz-96 model, the Swift-Hohenberg equation, and Rayleigh-Bénard convection. The Lorenz-96 model is a continuous in time and discrete in space phenomenological model that captures important features of atmosphere dynamics. We computed the fractal dimension as a function of system size and external forcing to estimate characteristic length and time scales describing the chaotic dynamics. We found extensive chaos with significant deviations from extensivity for small changes in system size and also the power-law growth of the dimension with increasing forcing. The Swift-Hohenberg equation is a partial differential equation for a scalar field, which has been widely used as a model for the study of pattern formation. We found that the magnitude of the mean flow in this model must be sufficiently large for spiral defect chaos to occur. We also explored the spatiotemporal chaos in experimentally accessible Rayleigh-Bénard convection using large-scale numerical simulations of the Boussinesq equations and the corresponding tangent space equations. We performed a careful study analyzing the impact of variations in the domain size, Rayleigh number, and Prandtl number on the system dynamics and fractal dimension. In addition, we quantified the dynamics of the spectrum of Lyapunov exponents and the leading order Lyapunov vector in an effort to connect directly with the dynamics of the flow field patterns. Further, we numerically studied the synchronization of chaos in convective flows by imposing time-dependent boundary conditions from a principal domain onto an initially quiescent target domain. We identified a synchronization length scale to quantify the size of a chaotic element using only information from the pattern dynamics. We also explored the relationship of this length scale with the pattern wavelength. Finally, we analyzed bioconvection which occurs as the result of the collective behavior of a suspension of swimming microorganisms. We developed a series of simulations to capture the gyrotactic pattern formation of the swimming algae. The results can be compared with the corresponding trend of pattern instabilities observed in the experimental studies. / Ph. D.

We study game theoretic ecological models with cyclic competition in the case where the strategies can be mixed or pure. For both projects, reported in [49] and [50], we employ Monte Carlo simulations to study finite systems. In chapter 3 the results of a previously published paper [49] are presented and expanded upon, where we study the extinction time of four cyclically competing species on different lattice structures using Lotka-Volterra dynamics. We find that the extinction time of a well mixed system goes linearly with respect to the system size and that the probability distribution approximately takes the shape of a shifted exponential. However, this is not true for when spatial structure is added to the model. In that case we find that instead the probability distribution takes on a non-trivial shape with two characteristic slopes and that the mean goes as a power law with an exponent greater than one. This is attributed to neutral species pairs, species who do not interact, forming domains and coarsening. In chapter 4 the results of [50] are reported and expanded, where we allow agents to choose cyclically competing strategies out of a distribution. We first study the case of three strategies and find through both simulation and mean field equations that the probability distributions of the agents synchronize and oscillate with time in the limit where the agents probability distributions can be approximated as continuous. However, when we simulate the system on a one-dimensional lattice and the probability distributions are small and discretized, it is found that there is a drastic transition in stability, where the average extinction time of a strategy goes from being a power law with respect to system size to an exponential. This transition can also be observed in space time images with the emergence of tile patterns. We also look into the case of four cyclically competing strategies and find results similar to that of [49], such as the coarsening of neutral domains. However, the transition from power law to exponential for the average extinction time seen for three strategies is not observed, but we do find a transition from one power law to another with a different slope. This work was supported by the United States National Science Foundation through grants DMR-0904999 and DMR-1205309. / Ph. D.

This thesis explores the Turing model for pattern formation and its applicationin controlling reaction-diffusion systems. The goal is to simulate both linear andnonlinear reaction-diffusion models, to understand how patterns emerge and toinvestigate the controllability of these systems with boundary controls. Using thefinite difference method (FDM) and other numerical methods on a discretizedgrid, we generated patterns with nonlinear reaction functions, validating Turing’shypothesis that nonlinear models are more applicable for pattern formation. Thenonlinear models produced stable, organized patterns, whereas linear models re-sulted in divergence, creating unrealistic patterns. In the controllability study, wediscovered that full controllability is achieved when all control inputs are active.Our findings suggest that the placement of minimal control inputs, derived fromspecific patterns, ensures full controllability in small systems, though further re-search is needed to generalize this method to larger grids. This work underscoresthe potential of simplified models like Turing’s to provide insights into the com-plex mechanisms governing natural pattern formation.

This dissertation unravels intricate biological dynamics in three distinct biological systems as the following. These studies combine mathematical models with experimental data to enhance our understanding of these complex processes. 1. Bipolar Spindle Assembly: Mitosis relies on the formation of a bipolar mitotic spindle, which ensures an even distribution of duplicated chromosomes to daughter cells. We address the issue of how the spindle can robustly recover bipolarity from the irregular forms caused by centrosome defects/perturbations. By developing a biophysical model based on experimental data, we uncover the mechanisms that guide the separation and/or clustering of centrosomes. Our model identifies key biophysical factors that play a critical role in achieving robust spindle bipolarization, when centrosomes initially organize a monopolar or multipolar spindle. These factors encompass force fluctuations between centrosomes, balance between repulsive and attractive inter-centrosomal forces, centrosome exclusion from the cell center, proper cell size and geometry, and limitation of the centrosome number. 2. Chromosome Oscillation: During mitotic metaphase, chromosomes align at the spindle equator in preparation for segregation, and form the metaphase plate. However, these chromosomes are not static; they exhibit continuous oscillations around the spindle equator. Notably, either increasing or decreasing centromeric stiffness in PtK1 cells can lead to prolonged metaphase chromosome oscillations. To understand this biphasic relationship, we employ a force-balance model to reveal how oscillation arises in the spindle, and how the amplitude and period of chromosome oscillations depend on the biological properties of spindle components, including centromeric stiffness. 3. Pattern Formation in Bacterial-Phage Systems: The coexistence of bacteriophages (phages) and their host bacteria is essential for maintaining microbial communities. In resource-limited environments, mobile bacteria actively move toward nutrient-rich areas, while phages, lacking mobility, infect these motile bacterial hosts and disperse spatially through them. We utilize a combination of experimental methods and mathematical modeling to explore the coexistence and co-propagation of lytic phages and their mobile host bacteria. Our mathematical model highlights the role of local nutrient depletion in shaping a sector-shaped lysis pattern in the 2D phage-bacteria system. Our model further shows that this pattern, characterized by straight radial boundaries, is a distinctive indicator of extended coexistence and co-propagation of bacteria and phages. Such patterns rely on a delicate balance among the intrinsic biological characteristics of phages and bacteria, which have likely arisen from the coevolution of cognate pairs of phages and bacteria. / Doctor of Philosophy / Mathematical modeling is a powerful tool for studying intricate biological dynamics, as modeling can provide a comprehensive and coherent picture about the system of interest that facilitates our understanding, and can provide ways to probe the system that are otherwise impossible through experiments. This dissertation includes three studies of biological dynamics using mathematical modeling: 1. Bipolar Spindle Assembly: Mitotic spindle is a bipolar subcellular structure that self-assembles during cell division. The spindle ensures an even distribution of duplicated chromosomes into two daughter cells. Certain perturbations can cause the spindle to assemble abnormally with one pole or more than two poles, which would cause the daughter cells to inherit incorrect number of chromosomes and die from the error. However, the cell is surprisingly good at correcting these spindle abnormalities and recovering the bipolar spindle. Here we build a model to explore how the cell achieves such recoveries and preferentially form a bipolar spindle to rescue itself. 2. Chromosome Oscillation: In mitotic metaphase, chromosomes are aligned at the spindle equator before they segregate. Interestingly, unlike the cartoon images in textbooks, the aligned chromosomes often move rhythmically around the spindle equator. We used a mathematical model to unravel how the chromosome oscillation arises and how it depends on the biological properties of the spindle components, such as stiffness of the centromere, the structure that connects the two halves of duplicated chromosomes. 3. Pattern Formation in Bacterial-Phage System: Phages are viruses that hijack their host bacteria for proliferation and spreading. In this study we developed a mathematical model to elucidate a common lysis pattern that forms when expanding host bacterial colony encounters phages. Interestingly, our model revealed that such a lysis pattern is a telltale sign that the bacterium-phage pair have achieved a delicate balance between each other and are capable of spreading together over a long period of time.