Thesis (Ph. D.)--University of Chicago, Department of Physics, December 2003. / CD-ROM contains entire thesis in PDF format. Includes bibliographical references. Also available on the Internet.

The recent success in economical production of US shales and other low permeability reservoirs is primarily due to advances in hydraulic fracturing. In this well stimulation technique, a fracturing fluid is injected into the reservoir at pressures high enough to break down the reservoir rock and form fractures. The fractures drain the hydrocarbons in the rock matrix and provide connected pathways for the transport of hydrocarbons to the wellbore. Given the low permeability of the matrix, recent studies of shale gas production suggest that nearly all of the production has to come from a ramified, well-connected network of fractures. A recent study has shown, however, that for reasons yet unknown, the production history of more than 8000 wells in the Barnett Shale can be fit with reasonable accuracy with a linear flow model based on parallel planar hydraulic fractures perpendicular to the wellbore and spaced 1-2 meters apart. The current study is carried out to provide insights into the formation and production properties of complex hydraulic fracture networks. The end goal here is optimization of hydraulic fracture treatments: creating better-connected, more productive fracture networks that can drain the reservoir more quickly. The study provides a mechanistic model of how complexity can emerge in the pattern of hydraulic fracture networks, and describes production from such networks. Invasion percolation has been used in this study to model how the pattern of hydraulic fracture networks develop. The algorithm was chosen because it allows quick testing of different “what if” scenarios while avoiding the high computation cost associated with numerical methods such as the finite element method. The rules that govern the invasion are based on a proposed geo-mechanical model of hydraulic fracture-natural fracture interactions. In the geo-mechanical model, development of fracture networks is modeled as a sequence of basic geo-mechanical events that take place as hydraulic fractures grow and interact with natural fractures. Analytical estimates are provided to predict the occurrence of each event. A complex network of connected fractures is the output of the invasion percolation algorithm and the geo-mechanical model. To predict gas production from the network, this study uses a random walk algorithm. The random walk algorithm was chosen over other numerical methods because of its advantage in handling the complex boundary conditions present in the problem, simplicity, accuracy and speed. / text

Through flume experiments we demonstrate the calcite precipitation process seen at geothermal hot springs in the lab setting. A series of four experiments were run, varying temperature and terrace ridge height while all other experimental parameters, including initial substrate slope, spring water discharge, and CO₂ input were kept constant. The goal of the experiments was to measure the temperature and terrace height control quantitatively in terms of the amount of overall travertine aggradation, aggradation rate changes in time and downstream direction, as well as to observe the effect of these parameters on processes occurring during precipitation. Using the final deposit thickness measured manually at the end of each experiment and elevation data obtained from a laser topographic profiler, I conclude that high temperature and small terrace heights favor increased precipitation of travertine. However, the amount of precipitation also depends on location within a terrace pond. Flow velocity increases as it approaches a terrace lip, resulting in enhanced precipitation and greater thicknesses in the downstream direction through increased CO₂ degassing, a process called downstream coarsening. / text

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.

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>

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.

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