Master of Science / Department of Physics / Jeremy Schmit / In this work, we present a model for the kinetics of amyloid fibril aggregation. In the model we mapped the process of Hydrogen bond (H-bond) formation and breakage to a random-walk. we captured the effect of side chains using position dependent H-bonds free energies which allows us to calculated the residence time for different binding alignments with the fibril. The residence time can be compared to the diffusion-limited attachment rate to give net aggregation stability. This stability increases exponentially with increasing number of bonds or binding energy in homopolymer chains, however for chains with patterned sequences, the residence time shows strong effects of the binding alignment. Using the residence time for uniform structures combined with estimate of the diffusion rate, we modeled and simulated the kinetics of amyloid aggregation. Results of the simulations gives the bond energies and concentrations required for the onset of growth of aggregates.

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Finite-state automata are a central computational model in computer science, with numerous and diverse applications. In one such application, viz. model-checking, automata over infinite words play a central rˆole. In this thesis, we concentrate on B¨uchi automata (BA), which are arguably the simplest finite-state model recognizing languages of infinite words. Two algorithmic problems are paramount in the theory of automata: language inclusion and automata minimization. They are both PSPACE-complete, thus under standard complexity-theoretic assumptions no deterministic algorithm with worst case polynomial time can be expected. In this thesis, we develop techniques to tackle these problems. In automata minimization, one seeks the smallest automaton recognizing a given language (“small” means with few states). Despite PSPACE-hardness of minimization, the size of an automaton can often be reduced substantially by means of quotienting. In quotienting, states deemed equivalent according to a given equivalence are merged together; if this merging operation preserves the language, then the equivalence is said to be Good for Quotienting (GFQ). In general, quotienting cannot achieve exact minimization, but, in practice, it can still offer a very good reduction in size. The central topic of this thesis is the design of GFQ equivalences for B¨uchi automata. A particularly successful approach to the design of GFQ equivalences is based on simulation relations. Simulation relations are a powerful tool to compare the local behavior of automata. The main contribution of this thesis is to generalize simulations, by relaxing locality in three perpendicular ways: by fixing the input word in advance (fixed-word simulations, Ch. 3), by allowing jumps (jumping simulations, Ch. 4), and by using multiple pebbles (multipebble simulations for alternating BA, Ch. 5). In each case, we show that our generalized simulations induce GFQ equivalences. For fixed-word simulation, we argue that it is the coarsest GFQ simulation implying language inclusion, by showing that it subsumes a natural hierarchy of GFQ multipebble simulations. From a theoretical perspective, our study significantly extends the theory of simulations for BA; relaxing locality is a general principle, and it may find useful applications outside automata theory. From a practical perspective, we obtain GFQ equivalences coarser than previously possible. This yields smaller quotient automata, which is beneficial in applications. Finally, we show how simulation relations have recently been applied to significantly optimize exact (exponential) language inclusion algorithms (Ch. 6), thus extending their practical applicability.

Graduation date: 1988

This thesis is concerned with the study of electrode kinetics, which we shall examine via comparison between theory with experiment. As such the first two chapters outline the basic principles of electrochemical experiments and their simulation. First, we examine the properties of voltammetry at porous electrodes by means of both simulations and experiments. We then introduce the symmetric Marcus-Hush (SMH) model of electrode kinetics as an alternative to the empirical Butler-Volmer model. First, we examine different methods for modeling the voltammetry of kinetically inhomogeneous electroactive monolayers. Next, we perform a critical evaluation of the SMH model for solution-phase systems through extensive comparison to experiments under diffusion-only and convective mass transport conditions using both cyclic and square wave voltammetry. The model is compared with the Butler-Volmer model throughout and is ultimately found to be poorly suited to the parameterisation of electrode kinetics, despite its foundations in the microscopic Marcus theory. We then introduce the asymmetric Marcus-Hush model, which removes the assumption that the Gibbs energy curves for reactant and product have the same curvature. This modification results in an additional parameter which quantifies the asymmetry of the system. A similar evaluation of this model is then undertaken for both surface-bound and solution phase systems and the asymmetric model is found to be a great deal more successful than its symmetric predecessor. Finally we outline a novel technique for extracting kinetic information directly from experimental cyclic voltammetry. The method is simple to implement and is general to all electrode geometries with one-dimensional symmetry.

Thesis (MBA)--Stellenbosch University, 1999. / ENGLISH ABSTRACT: A mini-study project presented on the use of Microsoft Excel 2000 in the field of simulation. The mini-study project covers the principles of queuing and it’s outputs. The simulation model will test various scenario’s of queuing theory. Inputs can be changed to suit the users requirements. Results may be analysed to determine an optimal queuing environment. / AFRIKAANSE OPSOMMING: Hierdie mini-werkstuk illustreer die gebruik van Excel 2000 in die veld van simulasie. Die beginsels van toustaan modelle word gedek, asook die tipiese resultate. Die simulasiemodel modelleer en toets verskillende toustaan scenarios. Toevoere kan verander word na gelang van die gebruiker se keuse. Die resultate kan ontleed word om die optimale toustaan omgewing te bepaal.

Eine der Faustregeln der Kolloid- und Oberflächenphysik ist, dass die meisten Oberflächen geladen sind, wenn sie mit einem Lösungsmittel, normalerweise Wasser, in Kontakt treten. Dies ist zum Beispiel bei ladungsstabilisierten Kolloidalen Suspensionen der Fall, bei denen die Oberfläche der Kolloidteilchen geladen ist (gewöhnlich mit einer Ladung von mehreren Hunderttausend Elementarladungen), oder bei Monoschichten ionischer Tenside, die auf einer Luft-Wasser Grenzfläche sitzen (wobei die wasserliebenden Kopfgruppen durch die Freisetzung von Gegenionen geladen werden), sowie bei Doppelschichten, die geladene phospholipide enthalten (wie Zellmembranen). In dieser Arbeit betrachten wir einige Modellsysteme, die zwar eine vereinfachte Fassung der Realität darstellen, von denen wir aber dennoch erwarten koennen, dass wir mit ihrer Hilfe einige physikalische Eigenschaften realer geladener Systeme (Kolloide und Elektrolyte) einfangen können. / One of the rules-of-thumb of colloid and surface physics is that most surfaces are charged when in contact with a solvent, usually water. This is the case, for instance, in charge-stabilized colloidal suspensions, where the surface of the colloidal particles are charged (usually with a charge of hundreds to thousands of e, the elementary charge), monolayers of ionic surfactants sitting at an air-water interface (where the water-loving head groups become charged by releasing counterions), or bilayers containing charged phospholipids (as cell membranes). In this work, we look at some model-systems that, although being a simplified version of reality, are expected to capture some of the physical properties of real charged systems (colloids and electrolytes).<br /> <br /> We initially study the simple double layer, composed by a charged wall in the presence of its counterions. The charges at the wall are smeared out and the dielectric constant is the same everywhere. The Poisson-Boltzmann (PB) approach gives asymptotically exact counterion density profiles around charged objects in the weak-coupling limit of systems with low-valent counterions, surfaces with low charge density and high temperature (or small Bjerrum length). Using Monte Carlo simulations, we obtain the profiles around the charged wall and compare it with both Poisson-Boltzmann (in the low coupling limit) and the novel strong coupling (SC) theory in the opposite limit of high couplings. In the latter limit, the simulations show that the SC leads in fact to asymptotically correct density profiles. We also compare the Monte Carlo data with previously calculated corrections to the Poisson-Boltzmann theory. We also discuss in detail the methods used to perform the computer simulations.<br /> <br /> After studying the simple double layer in detail, we introduce a dielectric jump at the charged wall and investigate its effect on the counterion density distribution. As we will show, the Poisson-Boltzmann description of the double layer remains a good approximation at low coupling values, while the strong coupling theory is shown to lead to the correct density profiles close to the wall (and at all couplings). For very large couplings, only systems where the difference between the dielectric constants of the wall and of the solvent is small are shown to be well described by SC.<br /> <br /> Another experimentally relevant modification to the simple double layer is to make the charges at the plane discrete.<br /> The counterions are still assumed to be point-like, but we constraint the distance of approach between ions in the plane and counterions to a minimum distance D. The ratio between D and the distance between neighboring ions in the plane is, as we will see, one of the important quantities in determining the influence of the discrete nature of the charges at the wall over the density profiles. Another parameter that plays an important role, as in the previous case, is the coupling as we will demonstrate, systems with higher coupling are more subject to discretization effects than systems with low coupling parameter.<br /> <br /> After studying the isolated double layer, we look at the interaction between two double layers. The system is composed by two equally charged walls at distance d, with the counterions confined between them. The charge at the walls is smeared out and the dielectric constant is the same everywhere. Using Monte-Carlo simulations we obtain the inter-plate pressure in the global parameter space, and the pressure is shown to be negative (attraction) at certain conditions. The simulations also show that the equilibrium plate separation (where the pressure changes from attractive to repulsive) exhibits a novel unbinding transition. We compare the Monte Carlo results with the strong-coupling theory, which is shown to describe well the bound states of systems with moderate and high couplings. The regime where the two walls are very close to each other is also shown to be well described by the SC theory.<br /> <br /> Finally, Using a field-theoretic approach, we derive the exact low-density ("virial") expansion of a binary mixture of positively and negatively charged hard spheres (two-component hard-core plasma, TCPHC). The free energy obtained is valid for systems where the diameters d_+ and d_- and the charge valences q_+ and q_- of positive and negative ions are unconstrained, i.e., the same expression can be used to treat dilute salt solutions (where typically d_+ ~ d_- and q_+ ~ q_-) as well as colloidal suspensions (where the difference in size and valence between macroions and counterions can be very large). We also discuss some applications of our results.

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