In various industries, specialized filters with activated carbon are used for adsorbing mercury from air-flows. MRT has eight such Activated CarbonFilters (ACFs) in one of their devices. The main purpose of research is tostudy the flow in the ACF filter and suggest a mathematical model for the complete system through which an improved design can be found.Simulation of a single ACF illustrates how the current system’s air flow does not cover the whole filter leaving part of the carbon bed unused forthe adsorption. This is validated by experimental data. A theoretical studybased on a mathematical model is made and the improved air flow pattern of a re-designed ACF is presented. An additional improvement is that byswitching inlet and outlet the usable time of the filters is prolonged.

The operating principles of complex regulatory networks are more easily understood with mathematical modelling than by intuitive reasoning. In this thesis, I study the dynamics of the mitotic exit control system in budding yeast. I present a comprehensive mathematical model, which provides a system’s-level understanding of the mitotic exit process. This model captures the dynamics of classic experimental situations reported in the literature, and overcomes a number of limitations present in previous models. Analysis of the model led to a number of breakthroughs in the understanding of mitotic exit control. Firstly, numerical analysis of the model quantified the dependence of mitotic exit on the proteolytic and non-proteolytic functions of separase. It was shown that the requirement for the non-proteolytic function of separase depends on cyclin-dependent kinase activity. Secondly, APC/Cdc20 is a critical node that controls the phosphatase (Cdc14) branch and both cyclin (Clb2 and Clb5) branches of the cell cycle regulatory network. Thirdly, the model proved to be a useful tool for the systematic analysis of the recently discovered phenomenon of Cdc14 endocycles. Most proteins belonging to the cell cycle control network are regulated at the level of synthesis, degradation and activity. Presumably, these multiple layers of regulation facilitate robust cell cycle behaviour in the face of genetic and environmental perturbations. To falsify this hypothesis, I subjected the model to global parameter perturbations and tested viability against pre-defined criteria. According to these analyses, the regulated transcription and degradation of proteins make different contributions to cell cycle control. Regulated degradation confers cell cycle oscillations with robustness against perturbations, while regulated transcription plays a major role in controlling the period of these oscillations. Both regulated transcription and degradation are part of important feedback loops, that combined promote robust behaviour in the face of parametric variations.

Recent events have thrown the spotlight on infectious disease outbreak response. We developed a data-driven method, EpiGro, which can be applied to cumulative case reports to estimate the order of magnitude of the duration, peak and ultimate size of an ongoing outbreak. It is based on a surprisingly simple mathematical property of many epidemiological data sets, does not require knowledge or estimation of disease transmission parameters, is robust to noise and to small data sets, and runs quickly due to its mathematical simplicity. Using data from historic and ongoing epidemics, we present the model. We also provide modeling considerations that justify this approach and discuss its limitations. In the absence of other information or in conjunction with other models, EpiGro may be useful to public health responders. (C) 2016 The Authors. Published by Elsevier B.V.

The ability to predict the dispersion of substances in the Great Salt Lake is a requisite towards making responsible management decisions relating to uses of the lake. The lake is a complex terminal body of water and will require a fairly sophisticated mathematical model to properly simulate the dispersion process in the lake. This finite element convection-dispersion model is a first step towards developing a comprehensive model. The model provides a finite element solution to the two-dimensional convection-dispersion equation and is capable of simulating steady or unsteady-state situations. It utilizes a known velocity field, dispersion coefficients, an introduced substance concentration, substance decay rates, and the region geometry to produce a solution to a given convection-dispersion problem. At the present time, a quantitative verification of the model has not been done, but qualitative use of the model indicates that it yields reasonable solutions satisfying continuity to convection-dispersion problems. Problems tested utilize a uniform flow field and various methods of introducing a substance, such as internal injections, established concentration gradients, and diffusers. This model affords the options in the approximating techniques of linear or quadratic interpolation functions, the Galerkin or "upwinding" methods of weigh ted residuals, and a linearly or quadratically varying velocity field. The model must use a continuous flow field to produce a credible solution. The model does need improvement in its ability to conserve mass in unsteady-state problems when introducing a substance into the modeled region and allowing dispersive transport at the boundaries. Proper nodal spacing (mesh size) is also important because a relatively coarse mesh size can result in poor approximations in some areas of the region modeled.

Doctor of Philosophy / Collective actions of large animal groups result in elaborate behaviour, whose nature can be breathtaking in their complexity. Social organisation is the key to the origin of this behaviour and the mechanisms by which this organisation occurs are of particular interest. In this thesis, these mechanisms of social interactions and their consequences for group-level behaviour are explored. Social interactions amongst individuals are based on simple rules of attraction, alignment and orientation amongst neighbouring individuals. As part of this study, we will be interested in data that takes the form of a set of directions in space. In Chapter 2, we discuss relevant statistical measure and theory which will allow us to analyse directional data. These statistical tools will be employed on the results of the simulations of the mathematical models formulated in the course of the thesis. The first mathematical model for collective group behaviour is a Lagrangian self-organising model, which is formulated in Chapter 3. This model is based on basic social interactions between group members. Resulting collective behaviours and other related issues are examined during this chapter. Once we have an understanding of the model in Chapter 3, we use this model in Chapter 4 to investigate the idea of guidance of large groups by a select number of individuals. These individuals are privy to information regarding the location of a specific goal. This is used to explore a mechanism proposed for honeybee (Apis mellifera) swarm migrations. The spherical theory introduced in Chapter 2 will prove to be particularly useful in analysing the results of the modelling. In Chapter 5, we introduce a second mathematical model for aggregative behaviour. The model uses ideas from electromagnetic forces and particle physics, reinterpreting them in the context of social forces. While attraction and repulsion terms have been included in similar models in past literature, we introduce an orientation force to our model and show the requirement of a dissipative force to prevent individuals from escaping from the confines of the group.

Graduation date: 1995

A crucial step in eukaryotic cell proliferation is the initiation of DNA replication, a tightly regulated process mediated by a multitude of protein factors. In Saccharomyces cerevisiae, this occurs as a result of the concerted action of an assembly of proteins acting at origins of replication, known as the pre-replicative complex (pre-RC). While many of the mechanisms pertaining to the functions of these proteins and the associations amongst them have been explored experimentally, mathematical models are needed to effectively explore the network’s dynamic behaviour. An ordinary differential equation (ODE)-based model of the protein-protein interaction network describing DNA replication initiation was constructed. The model was validated against quantified levels of protein factors determined in vivo and from the literature over a range of cell cycle timepoints. The model behaviour conforms to perturbation trials previously reported in the literature and accurately predicts the results of knockdown experiments performed herein. Furthermore, the DNA replication model was successfully incorporated into an established model of the entire yeast cell cycle, thus providing a comprehensive description of these processes. A screen for novel DNA damage response proteins was investigated using a unique proteomics approach that uses chromatin fractionation samples to enrich for factors bound to the DNA. This form of sub-cellular fractionation was combined with differential-in-gel-electrophoresis (DIGE) to detect and quantify low abundance chromatin proteins in the budding yeast proteome. The method was applied to analyze the effect of the DNA damaging agent methyl methanesulfonate (MMS) on levels of chromatin-associated proteins. Up-regulation of several previously characterized DNA damage checkpoint-regulated proteins, such as Rnr4, Rpa1 and Rpa2, was observed. In addition, several novel DNA damage responsive proteins were identified and assessed for genotoxic sensitivity. A strain in which the expression of the Ran-GTPase binding protein Yrb1 was reduced was found to be hypersensitive to genotoxic stress, pointing to a role for this nuclear import-associated protein in DNA damage response. The model presented in this thesis provides a tool for exploring the biochemical network of DNA replication. This is germane to the exploration of new cancer therapeutics considering the link between this disease (and others) and errors in proper cell cycle regulation. The high functional conservation between cell cycle mechanisms in humans and yeast allows predictive analyses of the model to be extrapolated towards understanding aberrant human cell proliferation. Importantly, the model is useful in identifying potential targets for cancer treatment and provides insights into developing highly specific anti-cancer drugs. Finally, the characterization of factors in the proteomic screen opens the door to further investigation of the roles of potential DNA damage response proteins.

This thesis deals with the development of a mathematical model for an air brake system in the presence of leaks. Brake systems in trucks are crucial for ensuring the safety of vehicles and passengers on the roadways. Most trucks in the US are equipped with S-cam drum brake systems and they are sensitive to maintenance. Brake defects such as leaks are a major cause of accidents involving trucks. Leaks in the air brake systems affect braking performance drastically by decreasing the peak braking pressures attained and also increasing the time required to attain the same, thereby resulting in longer stopping distances. Hence there is a need for detecting leaks in an air brake system. In this thesis, a mathematical model for an air brake system in the presence of leaks is developed with a view towards developing an automatic leak detection system in the near future. The model developed here builds on an earlier research at Texas A&M University in which a "fault free" model of an air brake system is developed, i.e., a mathematical model of an air brake system that predicts how the pressure in the brake chamber evolves as a function of the brake pedal input when there are no leaks in the air brake system.In order to develop a model for an air brake system in the presence of leaks, one must characterize a "leak". A leak may be characterized by the location and its size. Since the pipes are short, the location of the leak does not significantly affect the evolution in the brake pressure as much as its size. For this reason, "effective area" of the leak was chosen as a characteristic of the leak. It was estimated by fitting an empirical relation for leak with leak flow measurement data. The supply pressure and effective area of leak comprised the inputs to the model along with the displacement of the foot pedal (treadle valve plunger). The model was corroborated with the experimental data collected using the setup at Texas A&M University.

A one dimensional mass transfer analysis was performed for convective transport as well as mass transport within a porous media. This analysis was based on the analogous average heat transfer within a duct. Equations were developed to calculate the concentration of gas species at the triple phase boundary sites present at the interface of a porous electrode and a nonporous electrolyte. The mass transport analyzed on the steam side electrode of a solid oxide electrolysis cell was performed for a ternary gas mixture. In this analysis two gas species were actively diffusing in the presence of a third inert carrier gas. Multicomponent diffusion coefficients were determined for each species in the steam side electrode mixture. The mass transport analysis performed on the air side electrode utilized a binary gas mixture, namely air. At less than one percent of the total mixture of air, the combined effects of Argon and Carbon Dioxide were assumed to be negligible. This assumption allowed us to consider air a binary mixture. A comprehensive model was developed to determine cell performance under various operating condition and multiple cell geometries. The output of this model was used to optimize various physical features of the cell. Tests were performed on electrode supported solid oxide electrolysis cells at the Idaho National Laboratory. These cells were subjected to various operating temperatures and inlet steam mole fractions. Voltage vs. current density experimental data were collected and compared to computational data in order to validate the model.

The removal of milk fouling deposits often requires the diffusion of electrolyte solutions such as sodium hydroxide through a gel. Very often more than one single anion and one single cation are involved and thus the modelling of such diffusion requires a multicomponent description. Diffusion of electrolyte solutions through gels can be modelled using the Maxwell-Stefan equation. The driving forces for diffusion are the chemical potential gradients of ionic species and the diffusion potential, i.e., the electrostatic potential induced by diffusion of the ions. A model based on the Maxwell-Stefan equation was applied to electrolyte solutions and electrolyte solutions with a gel. When modelling the diffusion of electrolyte solutions, the resulting equations were found to be a partial differential algebraic equation system with a differentiation index of two. The identification of this characteristic of the system enabled a solution method using the method of lines to be developed. When modelling the diffusion of electrolyte solutions through a gel an explicit expression for diffusion potential was developed and hence the diffusion equations were solved. Numerical solutions were presented for a number of case studies and comparisons were made with solutions from literature and between different electrolyte systems. It was found that the results of diffusion of electrolytes were in good agreement with those of experiments and literature. In the case of diffusion of electrolytes through a gel, swelling of the gel was predicted. The model can be improved by adding thermodynamic factors and can be easily extended to multiple ion systems.