MELiSSA (Micro Ecological Life Support System Alternative) és el sistema desenvolupat per l'Agència Espacial Europea (ESA) i el consorci MELiSSA en el camp del suport de vida durant missions de llarga durada a l'espai. Basat en un ecosistema aquàtic, MELiSSA va ser concebut com una eina per desenvolupar la tecnologia necessària per a un sistema de suport de vida biològic que en un futur ha de permetre la producció d'aliment, aigua i oxigen a partir dels residus orgànics generats per una tripulació. Per assolir aquest objectiu, el concepte MELiSSA compta amb l'activitat combinada de cinc compartiments colonitzats per diferents microorganismes i plantes superiors, interconnectats entre ells. Aquesta tesi es centra en el tercer compartiment del bucle MELiSSA, en el qual l'amoni és convertit a nitrat, que és la font de nitrogen més adequada per al creixement dels cianobacteris i plantes superiors que colonitzen els compartiments fotosintètics. L'oxidació biològica d'amoni a nitrat té lloc en dues etapes successives que porten a terme dos tipus de soques bacterianes. En el projecte MELiSSA aquest procés es porta a terme en una columna de llit fix mitjançant Nitrosomonas europaea i Nitrobacter winogradkyi immobilitzats sobre un suport polimèric, i amb aportació d'aire en el mateix sentit de circulació que el medi líquid. El reactor pilot del tercer compartiment ha estat operant a la planta pilot del projecte MELiSSA durant períodes prolongats de temps abans de l'inici del treball realitzat en aquesta tesi. La principal aportació d'aquesta tesi es troba en l'obtenció de nova informació sobre el funcionament del reactor a través d'un estudi detallat de la biopel·lícula i també mitjançant el desenvolupament d'un model matemàtic que ens permetrà estudiar els efectes de diferents paràmetres d'operació sobre el procés i l'estructura de la biopel·lícula. S'implementaran també els aparells de mesura necessaris per millorar la qualitat de la monitorització de les diferents espècies de nitrogen a la fase líquida. Els coneixements adquirits en la realització d'aquest treball seran utilitzats per portar a terme el re-disseny del reactor per tal de millorar-ne el funcionament dins de la planta pilot del projecte MELiSSA. / MELiSSA (Micro Ecological Life Support System Alternative) is the system developed by the European Space Agency (ESA) and the MELiSSA consortium in the field of life support for long term manned missions in Space. Based on the principle of an aquatic ecosystem, MELiSSA was conceived as a tool to develop the required technology for a future biological life support system. Its final aim is the production of food, fresh water and oxygen from the organic wastes of a crew. To achieve this goal, the MELiSSA concept is based on the use of five interconnected compartments colonised by several microorganisms and higher plants. This thesis is focused on the third compartment of the MELiSSA loop, in which ammonium is converted to nitrate, the most suitable nitrogen source for the growth of the bacteria and higher plants colonising the photosynthetic compartment. The biological oxidation of ammonium to nitrate, which consists of two successive reactions carried out by two different bacterial strains, takes place in a packed bed biofilm reactor. Nitrosomonas europaea and Nitrobacter winogradskyi are immobilised on a polymeric support, with air flowing cocurrently with the feed medium. The pilot-scale reactor of compartment III (CIII) had been in operation in the MELiSSA pilot plant for several years before the start of the present work. The main contributions of this thesis are in increasing the understanding of the reactor performance by studying the nitrifying biofilm in depth, and by developing a mathematical model that allows the effects of different operational parameters on the process and on the biofilm structure, to be studied. Moreover, continuous monitoring of the nitrifying efficiency will be improved by installing the necessary on-line equipment to experimentally measure the concentrations of all the nitrogen species in the liquid phase. The additional knowledge achieved on the reactor performance via this work will finally lead to re-design the reactor hardware for optimal performance in the MELiSSA pilot plant. The knowledge acquired in this thesis was finally used to define the main features of the re-design of the pilot reactor of the MELiSSA compartment III.

Polymer electrolyte membrane (PEM) fuel cells are a promising zero-emission power source for transportation applications. An important tool for advancing PEM fuel cell technology is mathematical modeling. Mathematical models can be used to provide insight on the physical phenomena occurring within a fuel cell, as well as aid in the design of fuel cells by simulating the effect of changes in design or operating conditions on performance. A comprehensive, consistent and systematic general formulation for a mathematical PEM fuel cell model is presented in this thesis. The formulation is developed by considering the fuel cell to be composed of several, co-existing phases. The conservation of mass, momentum, species, and energy are applied to each phase in the fuel cell. The interactions between the phases are modeled by applying a volume-averaging procedure to the conservation equations in each phase. The solution of the governing equations for the general formulation are beyond the scope of this thesis research. Instead, simplifying assumptions are applied to the general formulation in order to reduce the number of governing equations. The cell is assumed to be two-dimensional, steady state and isothermal. As well, the polymer electrolyte is assumed to be impervious to the gas phase and liquid water is assumed to exist only in the gas phase or polymer electrolyte. The numerical solution of the simplified formulation is implemented using the computer language of C++ and the finite volume method. The numerical solution provides details of the transport phenomena within the anode and cathode gas flow channels, electrode backing layers, and catalyst layers, as well as the polymer electrolyte membrane layer. These details include the bulk velocity of the gas phase; the concentrations of the species within the gas phase; the potential and current density in the solid phase and polymer electrolyte; the water content in the polymer electrolyte; and the distribution of reaction rate within the catalyst layers.

Polymer electrolyte membrane (PEM) fuel cells are a promising zero-emission power source for transportation applications. An important tool for advancing PEM fuel cell technology is mathematical modeling. Mathematical models can be used to provide insight on the physical phenomena occurring within a fuel cell, as well as aid in the design of fuel cells by simulating the effect of changes in design or operating conditions on performance. A comprehensive, consistent and systematic general formulation for a mathematical PEM fuel cell model is presented in this thesis. The formulation is developed by considering the fuel cell to be composed of several, co-existing phases. The conservation of mass, momentum, species, and energy are applied to each phase in the fuel cell. The interactions between the phases are modeled by applying a volume-averaging procedure to the conservation equations in each phase. The solution of the governing equations for the general formulation are beyond the scope of this thesis research. Instead, simplifying assumptions are applied to the general formulation in order to reduce the number of governing equations. The cell is assumed to be two-dimensional, steady state and isothermal. As well, the polymer electrolyte is assumed to be impervious to the gas phase and liquid water is assumed to exist only in the gas phase or polymer electrolyte. The numerical solution of the simplified formulation is implemented using the computer language of C++ and the finite volume method. The numerical solution provides details of the transport phenomena within the anode and cathode gas flow channels, electrode backing layers, and catalyst layers, as well as the polymer electrolyte membrane layer. These details include the bulk velocity of the gas phase; the concentrations of the species within the gas phase; the potential and current density in the solid phase and polymer electrolyte; the water content in the polymer electrolyte; and the distribution of reaction rate within the catalyst layers.

Gait study plays an important role in the walking robot, because it is the foundation of walking robots. The robot must first determine the walking pattern and rules, thus we can evolve further design, control, analysis or study. This research focus on hexapod and quadruped walking robots, and establishes a mathematical model which can fully describe natural and artificial gaits, and systematically plan and express them. Another point of this research is planning walk trajectory of robot. Here we purpose a new concept of foot trajectory planning, and establish S-V-A-J models for feet motion. We try to make robots move forward with constant velocity, as a goal, by using piecewise function of cam design theory. Therefore robot can walk with constant velocity and maintain the continuity of acceleration.

Although the physics of interstitial fluid balance is relatively well understood, clinical options for the treatment of edema, the accumulation of fluid in the interstitium, are limited. Two related reasons for this failure can be identified. First, the processes involved in the transfer of fluid and proteins into the interstitium from the microvasculature, and their transfer out of the interstitium via the lymphatic system, are governed by complex equations that are not amenable to manipulation by physiologists. Second, the fundamental processes involved include complex anatomical structures that are not amenable to characterization by engineers. The dual tools of the batwing model and simplified mathematical modeling can be used to address the main objective: to integrate microvascular, interstitial, and lymphatic function to determine the effect of their interaction on interstitial fluid volume. In order to address this objective and the limitations of the current state of knowledge of the field, three specific aims were achieved. 1) Develop a simple, transparent, and general algebraic approach that predicts interstitial fluid pressure, volume and protein concentration resulting from the interaction of microvascular, interstitial and lymphatic function. These algebraic solutions provide a novel characterization of interstitial fluid pressure as a balance point between the two processes that determine interstitial inflow and outflow. 2) Develop a simple, algebraic formulation of Edemagenic Gain (the change in interstitial fluid volume resulting from changes in effective microvascular driving pressure) in terms of microvascular, interstitial and lymphatic structural parameters. By separating the structural parameters from functional variables, this novel approach indicates how these critical parameters interact to determine the tendency to form edema. 3) To expand the list of known interactions of microvascular, interstitial, and lymphatic functions to include the direct interaction of venular and lymphatic function. Venomotion was found not only to extrinsically pump lymph but also to mechanically trigger intrinsic lymphatic contractions. These three advances together represent a new direction in the field of interstitial fluid balance, and could only be possible by taking an interdisciplinary approach integrating physiology and engineering.

Blood is a complex mixture of formed cellular elements, proteins, and ions dissolved in a solution. It is a difficult fluid to model because it is a shear-thinning, viscoelastic fluid that stress- relaxes. In this study, a new mathematical model for whole blood is developed from a general equation for a fluid with a shear dependent viscosity. The model is then used as a backdrop for 28 different biochemical factors interacting to form a clot. The full intrinsic and extrinsic pathways are both used in the simulation; the inclusion of the full intrinsic pathway is something that had not been done prior to this work. The model is executed in one spatial direction in an infinite domain as well as within a rigid walled cylinder using a finite volume scheme. The rigid wall, similar to the new mathematical equation for blood, is an oversimplification of actual in-vitro conditions. The results of both simulations show the formation and dissolution of the clot. Sensitivity analysis is then performed in the finite domain model by adjusting the initial levels of factors Va and Xa. The results show that by increasing the initial level of one or both of these factors leads to the quicker formation of a clot.

The objective of this thesis is to provide the systematic design procedure for a high-speed PM motor with portable sizes, along with the detailed mathematical model developments and the thorough operational analysis. The entire scheme is realized by first following an available design reference to estimate the desired machine physical structures. Then, based on the related field theory, recoil line characteristics of permanent magnets, and the magnetic equivalent circuit method, the system mathematical model can be devised. Finally, the system operational behaviors can be investigated by the devised analytical models, and their accuracies will also be confirmed by the reference design tool. It is believed that the proposed design and verification scheme can provide a valuable and reasonable guidance for the related industry application.

We study algorithms and models for several economics-related problems from the perspective of linear programming. In network bargaining games, stable and balanced outcomes have been investigated in previous work. However, existence of such outcomes requires that the linear program relaxation of a certain maximum matching problem has integral optimal solution. We propose an alternative model for network bargaining games in which each edge acts as a player, who proposes how to split the weight of the edge among the two incident nodes. We show that the distributed protocol by Kanoria et. al can be modified to be run by the edge players such that the configuration of proposals will converge to a pure Nash Equilibrium, without the linear program integrality gap assumption. Moreover, ambiguous choices can be resolved in a way such that there exists a Nash Equilibrium that will not hurt the social welfare too much. In the oblivious matching problem, an algorithm aims to find a maximum matching while it can only makes (random) decisions that are essentially oblivious to the input graph. Any greedy algorithm can achieve performance ratio 0:5, which is the expected number of matched nodes to the number of nodes in a maximum matching. We revisit the Ranking algorithm using the linear programming framework, where the constraints of the linear program are given by the structural properties of Ranking. We use continuous linear program relaxation to analyze the limiting behavior as the finite linear program grows. Of particular interest are new duality and complementary slackness characterizations that can handle monotone constraints and mixed evolving and boundary constraints in continuous linear program, which enable us to achieve a theoretical ratio of 0:523 on arbitrary graphs. The J-choice K-best secretary problem, also known as the (J;K)-secretary problem, is a generalization of the classical secretary problem. An algorithm for the (J;K)-secretary problem is allowed to make J choices and the payoff to be maximized is the expected number of items chosen among the K best items. We use primal-dual continuous linear program techniques to analyze a class of infinite algorithms, which are general enough to capture the asymptotic behavior of the finite model with large number of items. Our techniques allow us to prove that the optimal solution can be achieved by a (J;K)-threshold algorithm, which has a nice \rational description" for the case K = 1. / published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy

Renal autoregulation is unique and critically important in maintaining homeostasis in the body via control of renal blood flow and filtration. The myogenic reflex responds directly to pressure variation and is present throughout the vasculature in varying degrees, while the tubuloglomerular feedback (TGF) mechanism adjusts microvascular resistance and glomerular filtration rate (GFR) to maintain distal tubular NaCl delivery. No simple models are available which allow the independent contributions of the myogenic and TGF responses to be compared and which include control over multiple metabolic and physiological parameters. Independently developed mathematical models of myogenic autoregulation and TGF control of GFR have been combined to produce a comprehensive model for the rat kidney which is responsive to multiple small step changes in mean arterial pressure. The system encompasses every level of the renal vasculature and the tubular system of the nephrons while simultaneously incorporating the modulatory effects of changes in viscosity and shear stress-induced nitric oxide (NO) production. The vasculature of the rat kidney has previously been divided via a Strahler ordering scheme using morphological data derived from micro-CT imaging. This data, combined with an extensive literature review of the relevant experimental data, led to the development of order-specific parameter sets for each of the eleven vascular levels. The model of the myogenic response depends primarily on circumferential wall tension, corresponding to a distally dominant resistance distribution with the highest contributions localized to the afferent arterioles and interlobular arteries. The constrictive response is tempered by the vasodilatory influence of flow-induced NO. Experimental comparison with data from groups that inhibited the TGF mechanism showed that the model was able to accurately reproduce the characteristics of renal myogenic autoregulation. This myogenic model was coupled with a system of equations that represented both spatial and temporal changes in concentration of the filtrate in the tubular system of the nephrons and the corresponding resistance changes of the afferent arteriole via the TGF mechanism. Computer simulation results of the system response to pressure perturbations were examined, as well as the interaction between mechanisms and the modulatory influences of metabolic and hemodynamic factors on the steady state and transient characteristics of whole-organ renal autoregulation. The responses of the model were consistent with experimental observations and showed that the frequency of the myogenic reflex was approximately 0.4 Hz while that of TGF was 0.06 Hz, corresponding to a 2-3 sec response time for myogenic contraction and 16.7 sec for TGF. Within the autoregulatory range step increases in pressure induced damped oscillations in tubular flow, macula densa NaCl concentration, arteriolar diameter, and renal blood flow. The model demonstrated that these oscillations were triggered by TGF and confined to vessels less than 100 micrometer in diameter. The pressure response in larger vessels remained important in characterizing total autoregulatory efficacy. Examination of the steady-state and transient characteristics of the model results demonstrates the necessity of considering the whole organ response in studies of renal autoregulation. A comprehensive model of autoregulation also allows for the examination of pathological states, such as the altered NO production in hypertension or the excess tubular reabsorption of water seen in diabetes. The model was able to reproduce experimental results when simulating diseased states, enabling the analysis of impaired autoregulation as well as the identification of key factors affecting the autoregulatory response.

Finding a common language in describing and interpreting multivariate data associated with rehabilitation and disturbance ecology, has became a major challenge. The main objective of this study is to find and evaluate mathematical models to describe ecosystem change based on selected indicators of change. Existing data from a previous rehabilitation project on Hendrina Power Station (Mpumalanga, South Africa) was used as a database for this study and this study aims to report on the development of models concentrating on radar graphs and a model based on matrix mathematics. The main groups of organisms selected for the construction of models, were vegetation, soil mesofauna and ant species. The datasets were limited to some indicative species and their mean abundances were determined. The grids that were used were randomly chosen and the models were constructed. Radar graphs were constructed to model the suite of species identified, through a sensitivity analysis, to indicate possible rehabilitation success over time and was applied to the different rehabilitation ages. The surface areas under the radar graphs were determined and compared for the different rehabilitation ages in the same year of survey. Correlation graphs were drawn between the surface area and the rehabilitation ages. These graphs did not indicate much relevance in indicating rehabilitation success, but the radar graphs proved to be good indicators of change in abundance of the selected species over time. iv The vegetation species, Eragrostis curvula, was the only species that showed a strong significant positive relationship with rehabilitation age and could be considered a good rehabilitation species and indicator of rehabilitation success. After the evaluation of this model, Eragrostis curvula, and two additional ant species, Tetramorium setigerum and Lepisiota laevis, were added. These species that were added, showed an increase in abundance over time, as found in a previous study. These radar graphs also did not indicate much relevance and it can be concluded that the radar graphs can only be used for a visual representation of the changes in abundance of the relevant species over time. This study also refers to a matrix model. This model focused on the interactions between the different variables selected. The percentage carbon in the soil were also added to the list of species. Model fitting graphs were constructed and correlations were drawn between the species that had significant values in the interaction table. This model could be useful for future studies, but more data and replication is necessary, over a longer period of time. This will serve to eliminate possible shortcomings of the model. / Thesis (M. Environmental Science (Biodiversity and Conservation Biology))--North-West University, Potchefstroom Campus, 2007.