Ph.D. Physicshttp://hdl.handle.net/10464/108082019-07-17T14:30:08Z2019-07-17T14:30:08ZNonlinear dynamics of granular assembliesPrzedborski, Michellehttp://hdl.handle.net/10464/129342018-10-05T17:14:27ZNonlinear dynamics of granular assemblies
Przedborski, Michelle
In this work we investigate granular chains, which are one-dimensional systems of discrete macroscopic particles interacting via the intrinsically nonlinear Hertz law. Such systems support the propagation of solitary waves (SWs), which are non-dispersive,
mobile bundles of energy. A comprehensive analysis into the dynamical behaviour of these systems and the properties of SW propagation is presented, and several interesting new results are obtained.
First, we find that the transition to the quasi-equilibrium (QEQ) phase in granular chains can be manipulated by altering the material properties of the system. We further use these results to develop a novel shock absorption device with a predictable
and tunable frequency response, making it useful also for energy harvesting applications.
Second, we show for the first time that granular chains with various nonlinearities of the contact potential can achieve thermal equilibrium at sufficiently long times, and thus QEQ is an intermediate phase of these systems. We characterize the equilibrium
phase by deriving approximate distribution functions for grain velocity and kinetic energy and system kinetic energy in a microcanonical ensemble of interacting particles. As a by-product, we derive the equilibrium specific heat, and a size-dependent
correction term, for such systems. We also show how these ideas extend to heterogeneous systems such as diatomic, tapered, and random-mass chains. Furthermore, we look closely at the transition to equilibrium by using statistical tests to show that the
long-term dynamics is ergodic, and by examining the behaviour of various correlation functions close to the onset of the transition.
Third, we solve a highly nonlinear, fourth-order wave equation that models the continuum theory of long-wavelength pulses in weakly compressed, homogeneous granular chains with a general power-law contact interaction, to characterize all travelling wave solutions admitted by the equation. This involves deriving conservation laws admitted by the wave equation, followed by a modified energy analysis. We find that the wave equation admits various types of travelling wave solutions, including SW solutions as well as nonlinear periodic wave solutions. Not only have the SW solutions not appeared before in the literature on granular chains, but they are also a new addition to the literature on SWs in general.
A Multi-Scale Molecular Dynamic Approach to the Study of the Outer Membrane of the Bacteria Psudomonas Aeruginosa PA01 and the Biocide ChlorhexidineVan Oosten, Bradhttp://hdl.handle.net/10464/104232018-10-05T17:14:27ZA Multi-Scale Molecular Dynamic Approach to the Study of the Outer Membrane of the Bacteria Psudomonas Aeruginosa PA01 and the Biocide Chlorhexidine
Van Oosten, Brad
The introductory chapters of this thesis contains an explanation to the methods and basic theory of the molecular dynamics approach. Together with the appendix section, in which a step by step tutorial how to set up and run basic simulations using the gromacs software is presented, this thesis can serve as an introductory aid in performing molecular dynamics simulations. In the research portion of this thesis, I provide several uses for the molecular dynamics approach applied to the biocide chlorhexidine as well as the study of membranes, including a mimic of the bacteria membrane of Pseudomonas Aeruginosa PA01.
The motivation for this research was previous work done in our lab which determined that chlorhexidine has a high affinity for DMPC and found the depth at which it resides in a model DMPC membrane. From this information, an all-atom representation of chlorhexidine was made, which was proven to reproduce the experimental results. While we learned much about chlorhexidine in a model DMPC membrane, this study lacked the destruction of the membrane as well as the study of chlorhexidine in a biologically relevant membrane. For these reasons coarse grained versions of the all-atom chlorhexidine models as well as a new lipopolysaccharide molecule was created. With the coarse grained model of chlorhexidine and the ability to create a bacterial membrane mimic, the study of chlorhexidine and other antibacterial agents can be further studied.
Conservation laws of magnetohydrodynamics and their symmetry transformation propertiesPshenitsin, Dmitryhttp://hdl.handle.net/10464/98012018-10-05T17:14:27ZConservation laws of magnetohydrodynamics and their symmetry transformation properties
Pshenitsin, Dmitry
All kinematic conservation laws along with their symmetry transformation properties are derived for the system of magnetohydrodynamic equations governing incompressible viscous plasmas (or any other conducting fluid) in which the dynamic and magnetic viscosities are constant. Reductions of this system under translation symmetries, axial rotation symmetries, and helical symmetries are considered. For each reduced system, all kinematic conservation laws and point symmetries are obtained. The results yields several new conservation laws which are expected to be relevant for physical applications of magnetohydrodynamics.
Theory and Application of a Pure-sampling Quantum Monte Carlo AlgorithmOspadov, Egorhttp://hdl.handle.net/10464/92892017-10-10T14:14:35ZTheory and Application of a Pure-sampling Quantum Monte Carlo Algorithm
Ospadov, Egor
The objective of pure-sampling quantum Monte Carlo is to calculate physical properties that are independent of the importance sampling function being employed in the calculation, save for the mismatch of its nodal hypersurface with that of the exact wave function. To achieve this objective, we describe a pure-sampling algorithm that combines features of forward-walking methods of pure-sampling and reptation quantum Monte Carlo. The importance sampling is performed by using a single-determinant basis set composed of Slater-type orbitals. We implement our algorithm by systematically increasing an algorithmic parameter until the properties sampled from the electron distributions converge to statistically equivalent values, extrapolated in the limit of zero time-step. In doing so, we are able to unambiguously determine the values for the ground-state fixed-node energies and one-electron properties of various molecules. These quantities are free from importance sampling bias, population control bias, time-step bias, extrapolation-model bias, and the finite-field approximation. We applied our algorithm to the ground-states of lithium hydride, water and ethylene molecules, and found excellent agreement with the accepted literature values for the energy and a variety of other properties for those systems. Some of our one-electron properties of ethylene had not been calculated before at any level of theory. In a detailed comparison, we found reptation quantum Monte Carlo, our closest competitor, to be less efficient by at least a factor of two. It requires different sets of time-steps to accurately determine the ground-state energy and one-electron properties, whereas our algorithm can achieve the same objective by using a single set of time-step values.