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Graduation date: 1999

Thesis (Ph. D.)--Oregon State University, 1999. / Typescript (photocopy). Includes bibliographical references (leaves 58-59). Also available on the World Wide Web.

Thesis (M. Phil.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

The transportation of mass is an inherently `non-equilibrium' process, relying on a current of mass between two or more locations. Life exists by necessity out of equilibrium and non-equilibrium transport processes are seen at all levels in living organisms, from DNA replication up to animal foraging. As such, biological processes are ideal candidates for modelling using non-equilibrium stochastic processes, but, unlike with equilibrium processes, there is as of yet no general framework for their analysis. In the absence of such a framework we must study specific models to learn more about the behaviours and bulk properties of systems that are out of equilibrium. In this work I present the analysis of three distinct models of non-equilibrium mass transport processes. Each transport process is conceptually distinct but all share close connections with each other through a set of fundamental nonequilibrium models, which are outlined in Chapter 2. In this thesis I endeavour to understand at a more fundamental level the role of stochasticity and fluctuations in non-equilibrium transport processes. In Chapter 3 I present a model of a diffusive search process with stochastic resetting of the searcher's position, and discuss the effects of an imperfection in the interaction between the searcher and its target. Diffusive search process are particularly relevant to the behaviour of searching proteins on strands of DNA, as well as more diverse applications such as animal foraging and computational search algorithms. The focus of this study was to calculate analytically the effects of the imperfection on the survival probability and the mean time to absorption at the target of the diffusive searcher. I find that the survival probability of the searcher decreases exponentially with time, with a decay constant which increases as the imperfection in the interaction decreases. This study also revealed the importance of the ratio of two length scales to the search process: the characteristic displacement of the searcher due to diffusion between reset events, and an effective attenuation depth related to the imperfection of the target. The second model, presented in Chapter 4, is a spatially discrete mass transport model of the same type as the well-known Zero-Range Process (ZRP). This model predicts a phase transition into a state where there is a macroscopically occupied `condensate' site. This condensate is static in the system, maintained by the balance of current of mass into and out of it. However in many physical contexts, such as traffic jams, gravitational clustering and droplet formation, the condensate is seen to be mobile rather than static. In this study I present a zero-range model which exhibits a moving condensate phase and analyse it's mechanism of formation. I find that, for certain parameter values in the mass `hopping' rate effectively all of the mass forms a single site condensate which propagates through the system followed closely by a short tail of small masses. This short tail is found to be crucial for maintaining the condensate, preventing it from falling apart. Finally, in Chapter 5, I present a model of an interface growing against an opposing, diffusive membrane. In lamellipodia in cells, the ratcheting effect of a growing interface of actin filaments against a membrane, which undergoes some thermal motion, allows the cell to extrude protrusions and move along a surface. The interface grows by way of polymerisation of actin monomers onto actin filaments which make up the structure that supports the interface. I model the growth of this interface by the stochastic polymerisation of monomers using a Kardar-Parisi-Zhang (KPZ) class interface against an obstructing wall that also performs a random walk. I find three phases in the dynamics of the membrane and interface as the bias in the membrane diffusion is varied from towards the interface to away from the interface. In the smooth phase, the interface is tightly bound to the wall and pushes it along at a velocity dependent on the membrane bias. In the rough phase the interface reaches its maximal growth velocity and pushes the membrane at this speed, independently of the membrane bias. The interface is rough, bound to the membrane at a subextensive number of contact points. Finally, in the unbound phase the membrane travels fast enough away from the interface for the two to become uncoupled, and the interface grows as a free KPZ interface. In all of these models stochasticity and fluctuations in the properties of the systems studied play important roles in the behaviours observed. We see modified search times, strong condensation and a dramatic change in interfacial properties, all of which are the consequence of just small modifications to the processes involved.

A formalism for modelling the dynamics of genetic algorithms using methods from statistical physics, originally due to Pr¨ugel-Bennett and Shapiro, is extended to ranking selection, a form of selection commonly used in the genetic algorithm community. The extension allows a reduction in the number of macroscopic variables required to model the mean behaviour of the genetic algorithm. This reduction allows a more qualitative understanding of the dynamics to be developed without sacrificing quantitative accuracy. The work is extended beyond modelling the dynamics of the genetic algorithm. A caricature of an optimisation problem with many local minima is considered — the basin with a barrier problem. The first passage time — the time required to escape the local minima to the global minimum — is calculated and insights gained as to how the genetic algorithm is searching the landscape. The interaction of the various genetic algorithm operators and how these interactions give rise to optimal parameters values is studied.

published_or_final_version / Physics / Master / Master of Philosophy

For systems that are in equilibrium, fluctuations can be understood through interactions with external heat reservoirs. For this reason these fluctuations are known as thermal noise, and they usually become vanishingly small in the thermodynamic limit. However, many systems comprising interacting constituents studied by physicists in recent years are both far from equilibrium, and sufficiently small so that they must be considered finite. The finite number of constituents gives rise to an inherent demographic noise in the system, a source of fluctuations that is always present in the stochastic dynamics. This thesis investigates the role of stochastic fluctuations in the macroscopically observable dynamical behaviour of non-equilibrium, finite systems. To facilitate such a study, we construct microscopic models using an individual based modelling approach, allowing the explicit form of the demographic noise to be identified. In many physical systems and theoretical models, absorbing states are a defining feature. Once a system enters one, it cannot leave. We study the dynamics of a system with two symmetric absorbing states, finding that the amplitude of the multiplicative noise can induce a transition between two universal modes of domain coarsening as the system evolves to one of the absorbing states. In biological and ecological systems, cycles are a ubiquitously observed phenomenon, but are di cult to predict analytically from stochastic models. We examine a potential mechanism for cycling behaviour due to the flow of probability currents, induced by the athermal nature of the demographic noise, in a single patch population comprising two competing species. We find that such a current by itself cannot generate macroscopic cycles, but when combined with deterministic dynamics which constrain the system to a closed circular manifold, gives rise to global quasicycles in the population densities. Finally, we examine a spatially extended system comprising many such patch populations, exploring the emergence of synchronisation between the different cycles. By a stability analysis of the global synchronised state, we probe the relationship between the synchronicity of the metapopulation and the magnitude of the coupling between patches due to species migration. In all cases, we conclude that the nature of the demographic noise can play a pivotal role in the macroscopically observed dynamical behaviour of the system.

Thesis (Ph.D.)--University of the Witwatersrand, Science Faculty (Physics), 2000. / Percolation phenomena are studied in a series of composites, each with a cellular structure (small conductor particles embedded on the surfaces of large insulator particles). The DC and AC conductivities, l/f noise and magnetic properties (in some series) are measured in the systems consisting of Graphite, Graphite-Boron Nitride, Carbon Black, Niobium Carbide, Nickel and Magnetite (Fe304) as the conducting components with Talc-wax (Talc powder coated with 4% wax by volume) being the common insulating component. Compressed discs of 26mm diameter and about 3mm thickness (with various conductor volume fractions covering both the insulating and conducting region) were made from the respective powders at a pressure of 380MPa and all measurements were taken in the axial (pressure) direction. The conductivity (σm) and dielectric constant (εm) of percolation systems obey the equations: σm = σc( ɸ - ɸc)t for ɸ >ɸc; σm = σi( ɸc - ɸ-s and εm = εi( ɸc - ɸ-s' for ɸ < ɸc; outside of the crossover region given by ɸc± (δdc ~=(σi/σc)1/(t+s). Here ɸc is the critical volume fraction of the conductor (with conductivity σ = σc) and cri is the conductivity of the insulator, t and s are the conductivity exponents in the conducting and insulating regions respectively and S’ is the dielectric exponent. The values of s and t are obtained by fitting the DC conductivity results to the combined Percolation or the two exponent phenomenological equations. Both universal and non-universal values of the sand t exponents were obtained. The dielectric exponent S’, obtained from the low frequency AC measurements, is found to be frequency-dependent. The real part of the dielectric constant of the systems, has been studied as a function of the volume fraction (ɸ) of the conducting component. In systems where it is measurable beyond the DC percolation threshold, the dielectric constant has a peak at ɸ > ɸ, which differs from key predictions of the original Percolation Theory. This behaviour of the dielectric constant can be qualitatively modeled by the phenomenological two exponent equation given in Chapter two of this thesis. Even better fits to the data are obtained when the same equation is used in conjunction with ideas from Balberg's extensions to the Random Void model (Balberg 1998a and 1998b). At high frequency and closer to the percolation threshold, the AC conductivity and dielectric constant follow the power laws: σm( ɸ,שּׂ) ~ שּׂX and εm( ɸ,שּׂ) ~ שּׂ-Y respectively. In some of the systems studied, the x and y exponents do not sum up to unity as expected from the relation x + y = 1. Furthermore, the exponent q obtained from שּׂ x σm( ɸ,O)q in all but the Graphite-containing systems is greater than 1, which agrees with the inter-cluster model prediction (q = (s + t)/t). The Niobium Carbide system is the first to give an experimental q exponent greater than the value calculated from the measured DC s and t exponents. l/f or flicker noise (Sv) on the conducting side (ɸ > ɸc) of some of the systems has been measured, which gives the exponents k and w from the well-established relationships Sv/V2 = D(ɸ - ɸc)-k and Sv/V2 = KRw. V is the DC voltage across the sample with resistance R while D and K are constants. A change in the value of the exponent k and w has been observed with k taking the values kl ~ 0.92 - 5.30 close to ɸc and k2 ~ 2.55 - 3.65 further into the conducting region. Values of WI range from 0.36 -1.1 and W2 ~ 1.2 - 1.4. These values of ware generally well within the limits of the noise exponents proposed by Balberg (1998a and 1998b) for the Random Void model. The t exponents calculated from k2 and W2 (using t = k/w) are self-consistent with the t values from DC conductivity measurements. Magnetic measurements in two of the systems (Fe304 and Nickel) show unexpected behaviour of the coercive field and remnant magnetisation plotted as a function of magnetic volume fraction. Fitting the permeability results to the two exponent phenomenological equation gives t values much smaller than the corresponding DC conductivity exponents. A substantial amount of data was obtained and analysed as part of this thesis. Experimental results, mostly in the form of exponents obtained from the various scaling laws of Percolation Theory, are presented in tabular form throughout the relevant chapters. The results have been tested against various models and compare with previous studies. While there is some agreement with previous work, there are some serious discrepancies between the present work and some aspects of the standard or original Percolation Theory, for example the dielectric constant behaviour with conductor volume fraction close to but above ɸc. New results have also emerged from the present work. This includes the change in the noise exponent k with (ɸ - ɸc), the variation of the dielectric exponent s' with frequency and some DC scaling results from the Fe304 system. The present work has dealt with some intriguing aspects of Percolation Theory in real continuum composites and hopefully opened avenues for further theoretical and experimental research. / AC 2016

<p> Every organism contains a few hundred to thousands of proteins. A protein is made of a sequence of molecular building blocks named amino acids. Amino acids will be referred to as residues. Every protein performs one or more functions in the cell. In order for a protein to do its job, it requires to bind properly to other partner proteins. Many genetic diseases such as cancer are caused by mutations (changes) of specific residues which cause disturbances in the functions of those proteins. The problem of prediction of protein binding site is a crucial topic in computational biology. A protein is usually made up of 50 to a few thousand residues. A contact site can occur within a protein or with other proteins. By having a robust and accurate model for identifying residues that are involved in the binding site, scientists can investigate the impact of critical mutations and residues that can cause genetic diseases. </p><p> The main focus of this thesis is to propose a machine learning model for predicting the binding site between two proteins. By extracting structural information from a protein, we can have additional knowledge of binding sites. This structural information can be converted into a penalty matrix for a graphical model to be learned from the protein sequence. The second part of this thesis is mostly focused on motion planning algorithms for proteins and simulation of the protein pathway changes using a Monte Carlo based method. Later, by applying a novel geometry based scoring function, we cluster the intermediate conformations into corresponding subsets that may indicate interesting intermediate states.</p><p>