Interplay Between Finite Resources and a Local Defect in an Asymmetric Simple Exclusion Process

When particle flux is regulated by multiple factors such as particle supply and varying transport rate, it is important to identify the respective dominant regimes. We extend the well-studied totally asymmetric simple exclusion model to investigate the interplay between a controlled entrance and a local defect site. The model mimics cellular transport phenomena where there is typically a finite particle pool and nonuniform moving rates due to biochemical kinetics. Our simulations reveal regions where, despite an increasing particle supply, the current remains constant while particles redistribute in the system. Exploiting a domain wall approach with mean-field approximation, we provide a theoretical ground for our findings. The results in steady-state current and density profiles provide quantitative insights into the regulation of the transcription and translation process in bacterial protein synthesis.

Mass Transport Perspective on an Accelerated Exclusion Process: Analysis of Augmented Current and Unit-Velocity Phases

In an accelerated exclusion process (AEP), each particle can "hop" to its adjacent site if empty as well as "kick" the frontmost particle when joining a cluster of size ℓ⩽ℓ_{max}. With various choices of the interaction range, ℓ_{max}, we find that the steady state of AEP can be found in a homogeneous phase with augmented currents (AC) or a segregated phase with holes moving at unit velocity (UV). Here we present a detailed study on the emergence of the novel phases, from two perspectives: the AEP and a mass transport process (MTP). In the latter picture, the system in the UV phase is composed of a condensate in coexistence with a fluid, while the transition from AC to UV can be regarded as condensation. Using Monte Carlo simulations, exact results for special cases, and analytic methods in a mean field approach (within the MTP), we focus on steady state currents and cluster sizes. Excellent agreement between data and theory is found, providing an insightful picture for understanding this model system.

A General Approach Towards the Synthesis of Amido-Functionalized Biodegradable Polyesters

The thesis presented here describes methodologies to produce pendant group functionalized polyesters from amido-functionalized α-hydroxy acids. The synthetic methods used to produce the functionalized α-hydroxy acids are compatible with a wide array of functional groups, making this technique highly versatile. The synthesis of functionalized polyesters was investigated to develop polymers with properties that may improve the capabilities of existing biodegradable polyesters for applications in controlled release pharmaceuticals. Chemically modified a-hydroxy acids were synthesized by reacting glyoxylic acid with a primary or secondary amide. To demonstrate the utility of this reaction, fourstructurally dissimilar amide substituents were examined including 2-pyrrolidione, benzamide, acetamide and acrylamide. The reaction is synthetically simple, provides high yields and is uniquely flexible, functionalized monomer. The compatibility of this procedure with the collection of functional groups mentioned circumvents the need for syntheses. The amido-functionalized monomers were polymerized by two different techniques: melt polycondensation and solution polymerization. Melt polycondensation was conducted by heating the monomer past its melting temperature under reduced pressure. Oligomeric functionalized polyesters (= 800 g/mol) with low PDIs (= 1.05) were obtained by melt polycondensation. Melt polycondensation was not compatible with all of the synthesized monomers. Two of the monomers (containing benzamide and acrylamide functionalities) degraded before the polycondensation reaction occurred. Thermal gravimetric analysis confirmed that a process other than polyesterification was occurring, indicating that some amido-functionalized α-hydroxy acids cannot be synthesized in the melt.Solution polymerization was conducted to polymerize functionalized α-hydroxy acids that were incompatible with melt polycondensation. Several modified Steglich polyesterifications were tested including p-toluenesulfonic acid mediated and scandium (III) triflate catalyzed. Only oligomeric functionalized polyesters were formed bythis method. A number of possible side reactions including the formation of an N-acylurea and a cyclic polymer ring were possible. The utility of this procedure appears to be limited due to the complexity of the reaction and its inability to produce high molecular weight polymer.