This thesis outlines the research I completed during my M.Sc. work. This research focuses on analyzing the deformations of an elastic film at an imposed boundary. Specifically, I prepared a trilayer thin film sample geometry where a glassy polymer thin film floats atop a liquid layer and a final liquid layer sits on the top and partially covers the films below. This thesis is organized into four chapters. The first chapter details main topics associated with the background knowledge necessary for understanding the results. This introductory chapter provides an overview of the polymers that create the thin films, fluid dynamics associated with the flow of these polymer films in their liquid state and capillarity, as the length scales and forces involved in the experiments are at a length scale where gravity can be neglected. The second chapter discusses the experimental design involving sample preparation and explanations of the techniques used for data collection. The third chapter presents the results of the experiments and discusses our understanding of these results. The fourth chapter concludes the thesis. / Thesis / Master of Science (MSc)

This is a ‘sandwich thesis’ consisting of a publication that I contributed to during my M.Sc. work. The thesis begins with an introduction section in Chapter 1 that discusses the relevant physical concepts to the work performed in the publication. These topics include, polymers in section 1.1, fluid dynamics in section 1.2, and capillary effects in section 1.3. Chapter 2 contains an experimental technique section that maps out the experiments performed in the manuscript. The manuscript, Chapter 3, details the capillary driven levelling of thin polymer step that is supported by an immiscible polymer film and the dissipation of the capillary energy of the system. We find that the dissipation mechanism depends strongly on the viscosity ratio between the top and the bottom films. We developed a model of the energy dissipation that agrees well with the experimental results. / Thesis / Master of Science (MSc)

A variety of two-dimensional fluid systems, known as dipole-mediated systems, exhibit a dipole-dipole interaction between their fluid constituents. The com- petition of this repulsive dipolar force with the cohesive fluid forces cause these systems to form intricate and patterned structures in their boundaries. In this thesis, we show that the microscopic details of any such system are irrelevant in the macroscopic limit and contribute only to a constant offset in the system’s energy. A numeric model is developed, and some important stable domain morphologies are characterized. Previously unresolved bifurcating branches are explored. Finally, by applying a random energy background to the numer- ics, we recover the smörgåsbord of diverse domain morphologies that are seen in experiment. We develop an empirical description of these domains and use it to demonstrate that the system's nondimensional parameter, which is the ratio of the line tension to the dipole–dipole density, can be extracted for any domain using only its shape.

The constituents of a quantum many-body system can be inextricably linked, a phenomenon known as quantum entanglement. Entanglement can be used as a resource for quantum computing, quantum communication and detecting phase transitions, among others. The amount of entanglement can be quantified via the von Neumann and Rényi entropies, which have their origins in information theory. In this work, the quantum entanglement between subsystems of a one dimen- sional lattice model of fermions is quantified. The von Neumann and Rényi entropies were calculated for two types of subsystems. In the first study, the subsystems were treated as two subsets of particles, and in the second, as two spatial subregions. Finally, by considering particle superselection rules, the amount of entanglement that can actually be accessed as a resource was calcu- lated. In all cases, the quantum entanglement served to detect phase transitions in the model.

The adhesion at solid/liquid interface plays a fundamental role in diverse fields and helps explain the structure and physical properties of interfaces, at the atomic scale, for example in catalysis, crystal growth, lubrication, electrochemistry, colloidal system, and in many biological reactions. Unraveling the atomic structure at the solid/liquid interface is, therefore, one of the major challenges facing the surface science today to understand the physical processes in the phenomena such as surface coating, self-cleaning, and oil recovery applications. In this thesis, a variety of theory/computational methods in statistical physics and statistical mechanics are used to improve understanding of water adhesion at solid/liquid interfaces. In here, we addressed two separated, but interconnected problems: First, we consider water adhesion on fiber/surface, responsible for the emergence of droplet residue upon droplet detachment. In this project, we study the mechanism of water droplet detachment and retention of residual water on smooth hydrophilic fibers and surfaces using nonequilibrium molecular dynamics simulations. We investigate how the applied force affects the breakup of a droplet and how the minimal detaching force per unit mass decreases with droplet size. We extract scaling relations that allow extrapolation of our findings to larger length scales that are not directly accessible by molecular models. We find that the volume of the residue on a fiber varies nonmonotonically with the detaching force, reaching the maximal size at an intermediate force and associated detachment time. The strength of this force decreases with the size of the drop, while the maximal residue increases with the droplet volume, V, sub-linearly, in proportion to the V2/3. Second, we address the adhesion on conducting graphene. We improved the graphene model by incorporating the conductivity of graphene sheet using the fluctuating charge technique of Constant Potential Molecular Dynamics (CPMD). We evaluated the wettability by measuring the contact angle of cylindrical water drops on a conducting graphene sheet. We found that the CA of a water droplet on a graphene sheet supported by water is lower than in the absence of water under graphene. Our calculations reveal effective attractions between partial charges of equal sign across the conducting graphene sheet. Attractive correlations are attributed to the formation of the highly localized image charges on carbon atoms between the partially charged sites of water molecules on both sides of graphene. By performing additional computations with nonpolar diiodomethane, we confirm that graphene transmits both polar and dispersive interactions. These findings are important in applications including sensors, fuel cell membranes, water filtration, and graphene-based electrode material to enhance the supercapacitor performance. A challenge for future work concerns dynamic polarization response of wetted graphene at alternating (AC) field condition.

The prediction and analysis of changes in the numbers of biological populations rest on mathematical formulations of demographic events (births and deaths) classified by the age of individuals. The development of demographic theory when birth and death rates vary statistically over time is the central theme of this work. A study of the standard Leslie model for the demographic dynamics of populations in variable environments is made. At each time interval a Leslie matrix of survival rates and fertilities of a population is chosen according to a Markov process and the population numbers in different age classes are computed. Analytical bounds are developed for the logarithmic growth rate and the age-structure of a population after long times. For a two dimensional case, it is shown analytically that a uniform distribution results for the age-structure if the survival rate from the first to the second age-class is a uniformly distributed random quantity with no serial auto correlation. Numerical studies are made which lead to similar conclusions when the survival rate obeys other distributions. It is found that the variance in the survival parameter is linearly related to the variance in the age structure. An efficient algorithm is developed for numerical simulations on a computer by considering a time sequence of births rather than whole populations. The algorithm is then applied to an example in three dimensions to calculate a sequence of births when the survival rate from the first to the second age-class is a random parameter. Numerical values for the logarithmic growth rate and the logarithmic variance for a population and the probability of extinction are obtained and then compared to the analytical results reported here and elsewhere.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19478号 / 理博第4138号 / 新制||理||1595(附属図書館) / 32514 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)講師 市川 正敏, 教授 佐々 真一, 教授 山本 潤 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Although dynamical systems have a multitude of classical uses in physics and applied mathematics, new research in theoretical computer science shows that dynamical systems can also be used as a highly secure method of encrypting data. Properties of Lorenz and similar systems of equations yield chaotic outputs that are good at masking the underlying data both physically and mathematically. This paper aims to show how Lorenz systems may be used to encrypt text and image data, as well as provide a framework for how physical mechanisms may be built using these properties to transmit encrypted wave signals.

The transport of a biomolecule through a nanopore occurs in many biological functions such as, DNA or RNA transport across nuclear pores and the translocation of proteins across the eukaryotic endoplasmic reticulum. In addition to the biological processes, it has potential applications in technology such as, drug delivery, gene therapy, and single molecule sensing. The DNA translocation through a synthetic nanopore device is considered as the basis for cheap and fast sequencing technology. Motivated by the experimental advances, many theoretical models have been developed. In this thesis, we explore the dynamics of driven translocation of a semiflexible polymer through a nanopore in two dimensions (2D) using Langevin dynamics (LD) simulation. By carrying out extensive simulation as a function of different parameters such as, driving force, length and rigidity of the chain, viscosity of the solvent, and diameter of the nanopore, we provide a detailed description of the translocation process. Our studies are relevant for fundamental understanding of the translocation process which is essential for making accurate nano-pore based devices.

The goal of this thesis has been to find a means of i) designing an active square particle, and ii) continuously varying its degree of activity with the objective of understanding the effects of activity on the various phases of granular matter. The motivations, results and limitations of our methods of creating active particles are discussed in this thesis. The applicability of a stochastic model based on the Langevin equation in 2D as well as implications for future experiments are also discussed.