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The stability of growing uni-lamellar vesicles is investigated using the formalism of nonequilibrium thermodynamics. The vesicles, which are assumed to be in an otherwise aqueous solution, are growing due to the accretion of lipids to the bilayer which forms the vesicle membrane. The thermodynamic description is based on the hydrodynamics of a water-lipid mixture together with a model of the vesicle as a discontinuous system in the sense of linear nonequilibrium thermodynamics. The approach assumes that the energy of the bilayer membrane is given by the spontaneous curvature model attributed to Helfrich. Furthermore, the rate at which lipids incorporate into the membrane is taken to be proportional to the surface area of the membrane. In this way, the relevant forces and fluxes of the system are identified in the context of a stability analysis. The resulting constitutive equation for the flux of water across the membrane is used to analyse the stability of spherical vesicles that are subject to different perturbations. First, a simplified approach is presented which restricts perturbations to axisymmetric ellipsoids. In that case, the analysis is carried out using an explicit Cartesian parametrisation. A perturbation theory which describes more general deformations is then developed and applied to the case of arbitrary axisymmetric perturbations. It is found that there are generically two critical radii at which changes of stability occur. For the case where the perturbation takes the form of a single zonal harmonic, only one of these radii is physical and is given by the ratio $2L_p / L_\gamma$, where $L_p$ is the hydraulic conductivity and $L_\gamma$ is the Onsager coefficient related to changes in membrane area due to lipid accretion. The stability of such perturbations is related to the value of l corresponding to the particular zonal harmonic: those with lower l are more unstable than those with higher l. The conditions under which general axisymmetric perturbations reduce to explicit ellipsoidal calculations are also found. A heuristic explanation for the results is proposed whilst possible extensions of the current work and the need for experimental input are also discussed.

Over the last few decades the interests of statistical physicists have broadened to include the detailed quantitative study of many systems - chemical, biological and even social - that were not traditionally part of the discipline. These systems can feature rich and complex spatiotemporal behaviour, often due to continued interaction with the environment and characterised by the dissipation of flows of energy and/or mass. This has led to vigorous research aimed at extending the established theoretical framework and adapting analytical methods that originate in the study of systems at thermodynamic equilibrium to deal with out-of-equilibrium situations, which are much more prevalent in nature. This thesis focuses on a microscopic model known as the asymmetric exclusion process, or ASEP, which describes the stochastic motion of particles on a one-dimensional lattice. Though in the first instance a model of a lattice gas, it is sufficiently general to have served as the basis to model a wide variety of phenomena. That, as well as substantial progress made in analysing its stationary behaviour, including the locations and nature of phase transitions, have led to it becoming a paradigmatic model of an exactly solvable nonequilibrium system. Recently an exact solution for the dynamics found a somewhat enigmatic transition, which has not been well understood. This thesis is an attempt to verify and better understand the nature of that dynamical transition, including its relation, if any, to the static phase transitions. I begin in Chapter 2 by reviewing known results for the ASEP, in particular the totally asymmetric variant (TASEP), driven at the boundaries. I present the exact dynamical transition as it was first derived, and a reduced description of the dynamics known as domain wall theory (DWT), which locates the transition at a different place. In Chapter 3, I investigate solutions of a nonlinear PDE that constitutes a mean-field, continuum approximation of the ASEP, namely the Burgers equation, and find that a similar dynamical transition occurs there at the same place as predicted by DWT but in disagreement with the exact result. Next, in Chapter 4 I report on efforts to observe and measure the dynamical transition through Monte Carlo simulation. No directly obvious physical manifestation of the transition was observed. The relaxation of three different observables was measured and found to agree well with each other but only slightly better with the exact transition than with DWT. In Chapter 5 I apply a numerical renormalisation scheme known as the Density Matrix Renormalisation Group (DMRG) method and find that it confirms the exact dynamical transition, ruling out the behaviour predicted by DWT. Finally in Chapter 6 I demonstrate that a perturbative calculation, involving the crossing of eigenvalues, allows us to rederive the location of the dynamical transition found exactly, thereby offering some insight into the nature of the transition.

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg / In this thesis we investigate the evolution of viscous FRW cosmological models for two different constitutive equations for the bulk viscous pressure a, namely (Abbreviation abstract) / Andrew Chakane 2018

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, / In this thesis we investigate the evolution of viscous FRW cosmological models for two different constitutive equations for the bulk viscous pressure a, namely: The truncated theory,,,,,,,,,,,,,,,, and the full (non-truncated] Israel-Stewart theory ...................We first review the relativistic theory of non-equilibrium thermodynamics developed by Eckart (1940) and the essentially equivalent formulation of the theory given by Landau and Lifshitz (1958). We give a, brief description of the relativistic second-order theories found by Israel and Stewart (1976) and subsequently developed by Pavon, Jou, and co-workers (1982, 1993). All this is done in order to develop the tools for the study of the evolution of FRW cosmological models in the context of causal thermodynamics. We find new exact and perturbative solutions of Einstein's field equations for the truncated Israel-Stewart theory of irreversible thermodynamics. We show that viscous effects speed up the expansion of the universe. We also consider a viscous fluid in the presence of a " non-interacting scalar field and show that inflationary solutions exist. The full theory of bulk viscosity is applied to dissipative FRW spacetimes. New causal viscous inflationary solutions are presented. These solutions extend the results obtained by Maartens (1995a) to cases where the coefficient of bulk viscosity e and the relaxation time r are independent. Power-law solutions for the scale factor are shown to exist. / Andrew Chakane 2018

Active nematic elastomers are a class of active materials that possess the elasticity of a rubber, and the orientational symmetry of a liquid crystal. Their constituent elements are typically elongated, cross-linked and active. The cross-linking of the elements leads to an elasticity that prevents the material to ow like a liquid. These elements are active in a sense that they continuously consume and dissipate energy, creating a state that is far-from-equilibrium. Active nematic elastomers may be a good physical model for biological systems such as the metaphase spindle, a complex biological machine that is made of an integrated assembly of microtubules and molecular motors. These motors not only cross-link the microtubules, but also actively slide them against each other, creating a highly dynamic, non-equilibrium state. The metaphase spindle, like other non-equilibrium structures in biology, has important functions to perform. During mitosis, the spindle is responsible for (1) capturing the sister chromatids, (2) bringing all the sister chromatids to the equator of the mother cell, and (3) segregating the daughter chromosome to the opposite poles of the cell. Thus, a fundamental challenge to biological physics is to understand the complex dynamics of the spindle, and similar systems, using the tools of non-equilibrium statistical mechanics. In this Thesis, we develop and explore a phenomenological model for an active nematic elastomer. We formulate the dynamics of this phenomenological model by incorporating the contribution of the active elements to the standard formulation of the hydrodynamic equations of a passive system. In a coarse-grained picture, the activity is taken into account as an extra active stress, proportional to the alignment tensor, added to the momentum equation of an otherwise passive nematic elastomer. Having obtained the equations of motion of an active nematic elastomer, we then investigate the response of the system to an external field by means of examining the structure and the stability of the modes. An active nematic elastomer has eight modes, in which six modes are propagating and two modes are massive. Out of the six propagating modes, two modes are in the longitudinal direction, linked to the density waves, and the other four modes are in the transverse direction, linked to the shear waves. The nature of these propagating modes transitions from dissipative and oscillatory, and vice versa, depending on the length scales. In particular, their stability is largely determined in the hydrodynamic limit, by a competition between the stabilizing effect of the elasticity and the destabilizing effect of the activity. In fact, the activity renormalizes the elastic coefficients down to even a negative value in some cases and thus, rendering the system linearly unstable. This is in contrast to the well-known instability of an active nematic liquid crystal, which is always linearly unstable. We then map out and discuss the stability phase diagram of the active nematic elastomer. Next, we compute and study various equal-time correlation functions of an active nematic elastomer, assuming that the noise spectra are thermal in origin. We find that they can be conveniently arranged into two terms. The first term has the exact mathematical structure of the equal-time correlation functions of a passive nematic elastomer, albeit with certain coefficients renormalized by activity. The second term, which is proportional to the activity, represents the non-equilibrium nature of an active nematic elastomer, and manifestly breaks the Fluctuation-Dissipation Theorem. We also find that (1) the displacement-displacement correlation function decays inversely with the square of the wave number for both the compressible and incompressible nematic elastomer, similar to that of a passive nematic elastomer, with elastic coefficients renormalized by the activity. (2) The density-density correlation function approaches a constant at the long wave-length limit, since the conservation of mass links the density to the rate of changes of the displacement in the longitudinal direction. (3) The director-displacement correlation function is purely imaginary, and thus the director is locked to the displacement with a (π/2) phase-shift. (3) The director-director correlation function approaches a constant value in the long-wavelength limit, instead of decaying inversely with the square of the wave number, like it would for a liquid crystal. This is because of the massive mode stems from the coupling energy, and it indicates that director in the large length scale is locked to a specific angle. These theoretical results are in qualitative agreement with the experimental measurements of the spindle. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection

We theoretically study steady-state nonequilibrium properties of various open electronic systems subject to time-independent external bias. A charge current is established across each system by its coupling to two external particle reservoirs maintained at different chemical potentials. We discuss the impact of intra-reservoir electron correlations on transport, and examine how reservoir-generated dissipation and nonequilibrium-induced decoherence influence these systems. The effect of intra-lead electron interactions on transport is investigated in the context of a phonon-coupled single molecule transistor driven by Luttinger-liquid source and drain leads. The semi-classical master equation approach is used to compute current and noise characteristics of the device for various interaction strengths in the leads. The results suggest the possibility of tuning the Fano factor of the device using intra-lead electron interactions. The Keldysh path integral formalism is used to theoretically formulate models that describe the remaining open nonequilibrium systems. We consider voltage-induced electron-phonon scattering and electron mass enhancement due to phonons in a model metallic system. The possibility of adjusting the acoustic phonon velocity and the Thomas-Fermi screening length with external voltage is discussed. The effects of dissipation is investigated in an open BCS superconducting graphene, where the dissipation-induced rearrangement of its ground state from the BCS superconductor to the Fermi liquid is examined. The results theoretically infer prospects for a voltage-tuned metal-to-BCS quantum phase transition in graphene. Lastly, we develop a theory of nonequilibrium quantum criticality in open itinerant Ising and Heisenberg magnets. Both departures from equilibrium at conventional quantum critical points and the physics of phase transitions induced by the nonequilibrium drive are analyzed.

We theoretically study steady-state nonequilibrium properties of various open electronic systems subject to time-independent external bias. A charge current is established across each system by its coupling to two external particle reservoirs maintained at different chemical potentials. We discuss the impact of intra-reservoir electron correlations on transport, and examine how reservoir-generated dissipation and nonequilibrium-induced decoherence influence these systems. The effect of intra-lead electron interactions on transport is investigated in the context of a phonon-coupled single molecule transistor driven by Luttinger-liquid source and drain leads. The semi-classical master equation approach is used to compute current and noise characteristics of the device for various interaction strengths in the leads. The results suggest the possibility of tuning the Fano factor of the device using intra-lead electron interactions. The Keldysh path integral formalism is used to theoretically formulate models that describe the remaining open nonequilibrium systems. We consider voltage-induced electron-phonon scattering and electron mass enhancement due to phonons in a model metallic system. The possibility of adjusting the acoustic phonon velocity and the Thomas-Fermi screening length with external voltage is discussed. The effects of dissipation is investigated in an open BCS superconducting graphene, where the dissipation-induced rearrangement of its ground state from the BCS superconductor to the Fermi liquid is examined. The results theoretically infer prospects for a voltage-tuned metal-to-BCS quantum phase transition in graphene. Lastly, we develop a theory of nonequilibrium quantum criticality in open itinerant Ising and Heisenberg magnets. Both departures from equilibrium at conventional quantum critical points and the physics of phase transitions induced by the nonequilibrium drive are analyzed.

There has been a continuous effort to unveil the physics of hypersonic flows both experimentally and numerically, in order to achieve an efficient hypersonic vehicle design. With the advent of the high speed computers, a lot of focus has been given on research pertaining to numerical approach to understand this physics. The features of such flows are quite different from those of subsonic, transonic and supersonic ones and thus normal CFD methodologies fail to capture the high speed flows efficiently. Such calculations are made even more challenging by the presence of nonequilibrium thermodynamic and chemical effects. Thus further research in the field of nonequilibrium thermodynamics is required for the accurate prediction of such high enthalpy flows. The objective of this thesis is to develop improved computational tools for hypersonic aerodynamics accounting for non-equilibrium effects. A survey of the fundamental theory and mathematical modeling pertaining to modeling high temperature flow physics is presented. The computational approaches and numerical methods pertaining to high speed flows are discussed. In the first part of this work, the fundamental theory and mathematical modeling pertaining to modeling high temperature flow physics is presented. Continuum based approach (Navier Stokes) and Boltzmann equation based approach (Gas Kinetic) are discussed. It is shown mathematically that unlike the most popular continuum based methods, Gas Kinetic method presented in this work satisfies the entropy condition. In the second part of this work, the computational approaches and numerical methods pertaining to high speed flows is discussed. In the continuum methods, the Steger Warming schemes and Roe’s scheme are discussed. The kinetic approach discussed is the Boltzmann equation with Bhatnagar Gross Krook (BGK) collision operator. In the third part, the results from new computational fluid dynamics code developed are presented. A range of validation and verification test cases are presented. A comparison of the two common reconstruction techniques: Green Gauss gradient method and MUSCL scheme are discussed. Two of the most common failings of continuum based methods: excessive numerical dissipation and carbuncle phenomenon techniques, are investigated. It is found that for the blunt body problem, Boltzmann BGK method is free of these failings.

In this thesis I present a nonequilibrium quantum field theory that describes the production of molecular dimers from a two-component quantum-degenerate atomic Fermi gas, via a linear downward sweep of a magnetic field across an s-wave Feshbach resonance. This problem raises interest because it is presently unclear as to why deviations from the universal Landau-Zener formula for the transition probability at two-level crossing are observed in the experimentally measured production efficiencies. The approach is based on evaluating real-time Green functions within the Keldysh- Schwinger formalism. The effects of quantum statistics associated with Pauli blocking for fermions and induced emission for bosons, characteristic of particle scattering in a quantum-degenerate many-body medium, are fully accounted for. I show that the molecular conversion efficiency is represented by a power series in terms of a dimensionless parameter which, in the zero-temperature limit, depends solely on the initial gas density and the Landau-Zener parameter. This result reveals a hindrance of the canonical Landau-Zener transition probability due to many-body effects, and presents an explanation for the experimentally observed deviations. A second topic treated in this thesis concerns the study of non-adiabatic transitions in N-state Landau-Zener systems. In connection to this, I provide a proof of the conjecture put forth by Brundobler and Elser, regarding the survival probability on the diabatic levels with maximum/minimum slope.