A computational tool that uses an automated and reliable procedure for systematic generation of global phase equilibrium diagram (GPED) is developed for binary system using equation of state and its extension to the ternary system is discussed. The proposed algorithm can handle solid phase and also can predict all major six types of phase diagrams. The procedure enables automatic generation of GPED which incorporates calculations of all important landmarks such as critical endpoints, quadruple point (if any), critical line, liquid-liquid-vapor line (if any), solid-liquid-liquid line (if any) and solid-liquid-vapor line. The method is also capable of locating all azeotropic phenomena such as azeotropic endpoint, critical azeotrope, pure azeotropic point and azeotropic lines. Although, we demonstrated the methodology for cubic equation of state, the proposed strategy is completely general that doesn't require any knowledge about the type of phase diagram and can be applied to any pressure explicit equation of state model. Newton homotopy based global method has been applied for phase stability test and critical point calculations to ensure reliability. Having computed the binary phase diagrams, the methodology to generate global phase diagrams for ternary system is discussed that can locate all important thermodynamic landmarks such as tricritical point, quadruple critical endpoint, quadruple azeotropic endpoint, quintuple point and critical azeotropic endpoint. The procedure to trace ternary phenomena having two degree of freedom such as critical surface, solid-liquid-vapor surface and liquid-liquid-vapor surface has been discussed. Finally, applications of reliable global methods to solve the fluid-fluid phase equilibrium problem using SAFT equation for binary system and the solid-fluid phase equilibrium problem for binary and ternary systems have been demonstrated through representative computations.

Predictive models for diffusion-controlled particle dissolution are important for designing advanced and efficient solid products for controlled release applications. A computer-aided modeling framework was developed to derive the effective dissolution rates of multiple particles as the solid surface material eroded gradually into the surrounding liquid phase. The mathematical models were solved with numerical methods using the computational software MATLAB. Results from the models were imported into COMSOL Script to create three-dimensional plots of the particle size data as a function of time. The release model found for the monodispersed particles was manipulated to incorporate polydisperse solids, as these are found more frequently in chemical processes. The program was further developed to calculate the particle size as a function of time for particles encapsulated for use in controlled release. The parameters, such as radius size, coating material and encapsulation thickness, can be altered in the computer models to aid in the design of particles for different desired applications. Simulations produced conversion profiles and three-dimensional visualizations for the dissolution processes. Experiments for the dissolution of citric acid in water were performed using a reaction microcalorimeter to verify results found from the computer models.

Modern-day management of infectious diseases is critically linked to the use of mathematical models to understand and predict dynamics at many levels, from the mechanisms of pathogenesis to the patterns of population-wide transmission and evolution. This thesis describes the development and application of mathematical techniques for HIV infection and dynamics on social networks. Treatment of HIV infection has improved dramatically in the past few decades but is still limited by the development of drug resistance and the inability of current therapies to completely eradicate the virus from an individual. We begin with a synthesis of the important evolutionary principles governing the HIV epidemic, emphasizing the role of modeling. We then describe a modeling framework to study the emergence of drug-resistant HIV within a patient. Our model integrates laboratory data and patient behavior, with the goal of predicting outcomes of clinical trials. Current results demonstrate how pharmacologic properties of antiretroviral drugs affect selection for drug resistance, and can explain drug-class-specific resistance risks. Thirdly, we describe models for a new class of drugs that aim to eliminate cells with latent viral infection. We provide estimates for the required efficacy of these drugs and describe the potential challenges of future clinical trials. Finally, models and mechanisms for understanding viral dynamics are increasingly finding applications outside traditional virology. They can be used to study the dynamics of behaviors, to help predict and intervene in their spread. We describe techniques for applying infectious disease models to social contagion, drawing on techniques for network epidemiology. We use this framework to interpret data on the interpersonal spread of health-related behaviors.

A cell's ability to sense and respond to mechanical signals highlights the significance of physical forces in biology; however, to date most biomedical research has focused on genetics and biochemical signaling. We sought to further understand the physical mechanisms that guide the cellular migrations that occur in a number of biological processes, such as tissue development and regeneration, bacterial infections and cancer metastasis. We investigated the migration of single cells and determined whether the biomechanics of these cells could be used to elucidate multi-cellular mechanisms. We first studied Borrelia burgdorferi (Bb), the bacterium that causes Lyme disease. We created a mathematical model based on the mechanical interactions between the flagella and cell body that explained the rotation and undulation of the cell body that occurs as the bacterium swims. This model further predicts how the swimming dynamics could be affected by alterations in flagellar or cell wall stiffnesses. Fitting the model to experimental data allowed us to calculate the flagellar torque and drag for Bb, and showed that Treponema pallidum (Tp), the syphilis pathogen, is biomechanically similar to Bb. Next, we used experimentally-determined parameters of Bb's motility to develop a population-level model that accounts for the morphology and spreading of the "bulls-eye" rash that is typically the first indicator of Lyme disease. This work supported clinical findings on the efficacy of antibiotic treatment regimes. Finally, we investigated the dynamics of epithelial monolayers. We found that intracellular contractile stress is the primary driving force behind collective dynamics in epithelial layers, a result previously predicted from a biophysical model. Taken together, these findings identify the relevance of physics in cellular migration and a role of mechanical signaling in biomedical science.

Malaria is an infectious disease, transmitted between humans through mosquito bites, that kills about two million people a year. We derive and analyze a mathematical model to better understand the transmission and spread of this disease. Our main goal is to use this model to compare intervention strategies for malaria control for two representative areas of high and low transmission. We model malaria using ordinary differential equations. We analyze the existence and stability of disease-free and endemic (malaria persisting in the population) equilibria. Key to our analysis is the definition of a reproductive number, R₀ (the number of new infections caused by one individual in an otherwise fully susceptible population through the duration of the infectious period). We prove the loss of stability of the disease-free equilibrium as R0 increases through R₀ = 1. Using global bifurcation theory developed by Rabinowitz, we show the bifurcation of endemic equilibria at R₀ = 1. This bifurcation can be either supercritical (leading to stable endemic equilibria for R₀ > 1) or subcritical (leading to stable endemic equilibria for R₀ < 1 in the presence of hysteresis). We compile two reasonable sets of values for the parameters in the model: for areas of high and low transmission. We compute sensitivity indices of R₀ and the endemic equilibrium to the parameters around the baseline values. R₀ is most sensitive to the mosquito biting rate in both high and low transmission areas. The fraction of infectious humans at the endemic equilibrium is most sensitive to the mosquito biting rate in low transmission areas, and to the human recovery rate in high transmission areas. This sensitivity analysis allows us to compare the effectiveness of different control strategies. According to our model, the most effective methods for malaria control are the use of insecticide-treated bed nets and the prompt diagnosis and treatment of infected individuals.

Pagrindinė šio darbo užduotis yra statybos investicijų efektyvumo analizė taikant matematinio modeliavimo metodus. Darbą sudaro trys pagrindiniai skyriai. Apžvalginiame skyriuje atlikta įvairių pasaulio šalių mokslininkų investicijų efektyvumo nustatymo modelių analizė. Pateikti vieni naujausių mokslinėje literatūroje aptinkamų metodų, taikomų investicijoms skaičiuoti. Apžvelgti finansinių (klasikinių) investicijų efektyvumo vertinimo metodų trūkumai. Apibrėžtos pagrindinės matematinio modeliavimo sąvokos, taikymo sritys bei pagrindiniai matematinių modelių sudarymo principai. Antrasis skyrius skirtas investicinių projektų sudėties ir jų vertinimo principų apžvalgai. Apibrė��ta bendroji bei investicijų statyboje koncepcija, statybos investicinių projektų klasifikacija. Pateikta uždavinių, padedančių nustatyti statybos investicijų efektyvumą, klasifikacija bei statybos investicijų efektyvumo nustatymo etapai. Toliau gilinamasi į bendruosius investicinio projekto vertinimo principus, pateikiama schema, apibrėžianti investicinių projektų vertinimo eigą. Trečiojoje dalyje, pereinant prie statybos investicinių procesų analizės, pateikiama rinkos ir statistinių duomenų apžvalga, kadangi būtent šių duomenų pagrindu sudaromas matematinis modelis, nuo jų tikslumo priklauso galutiniai skaičiavimų rezultatai. Statistinių duomenų apdorojimo programa MINITABTM, regresinės analizės metodu, sudaromas matematinis modelis, nustatantis statybos investicinio proceso efektyvumą. Remiantis... [to full text] / The main task of this project is the analysis of the construction investment efficiency, by applying of mathematical modeling methods. The model is created in order to define the effectiveness of the construction investment process. According to the model, it was calculated the yield of the process and the risk zones.

Polymer electrolyte membrane (PEM) fuel cells have increasingly become promising green energy sources for automobile and stationary cogeneration applications but its success in commercialization depends on performance optimization and manufacturing cost. The activation losses, expensive platinum catalyst, and water flooding phenomenon are the key factors currently hindering commercialization of PEM fuel cells. These factors are associated with the cathode catalyst layer (CCL), which is about ten micrometers thick. Given the small scale of this layer, it is extremely difficult to study transport phenomena inside the catalyst layer experimentally, either intrusively or non-intrusively. Therefore, mathematical and numerical models become the only means to provide insight on the physical phenomena occurring inside the CCL and to optimize the CCL designs before building a prototype for engineering application. In this thesis research, a comprehensive two-phase mathematical model for the CCL has been derived from the fundamental conservation equations using a volume-averaging method. The model also considers several water transport and physical processes that are involved in the CCL. The processes are: (a) electro-osmotic transport from the membrane to the CCL, (b) back-diffusion of water from the CCL to the membrane, (c) condensation and evaporation of water, and (d) removal of liquid water to the gas flow channel through the gas diffusion layer (GDL). A simple analytical model for the activation overpotential in the CCL has also been developed and an optimization study has been carried out using the analytical activation overpotential formulation. Further, the mathematical model has been simplified for the CCL and an analytical approach has been provided for the liquid water transport in the catalyst layer. The volume-averaged mathematical model of the CCL is finally implemented numerically along with an investigation how the physical structure of a catalyst layer affects fuel cell performance. Since the numerical model requires various effective transport properties, a set of mathematical expressions has been developed for estimating the effective transport properties in the CCL and GDL of a PEM fuel cell. The two-dimensional (2D) numerical model has been compared with the analytical model to validate the numerical results. Subsequently, using this validated model, 2D numerical studies have been carried out to investigate the effect of various physical and wetting properties of CCL and GDL on the performance of a PEM fuel cell. It has been observed that the wetting properties of a CCL control the flooding behavior, and hydrophilic characteristics of the CCL play a significant role on the cell performance. To investigate the effect of concentration variation in the flow channel, a three-dimensional numerical simulation is also presented.

Process control and monitoring is a common problem in high value added chemical manufacturing industries where batch processes are used to produce wide range of products on the same piece of equipment. This results in frequent adjustments on control and monitoring schemes. A chemical toner manufacturing process is representative of an industrial case which is used in this thesis. Process control and monitoring problem of batch processes have been researched, mostly through the simulation, and published in the past . However, the concept of applying the subject to chemical toner manufacturing process or to use a single indicator for multiple pieces of equipment have never been visited previously. In the case study of this research, there are many different factors that may affect the final quality of the products including reactor batch temperature, jacket temperature, impeller speed, rate of the addition of material to the reactor, or process variable associated with the pre-weight tank. One of the challenging tasks for engineers is monitoring of these process variables and to make necessary adjustments during the progression of a batch and change controls strategy of future batches upon completion of an existing batch. Another objective of the proposed research is the establishment of the operational boundaries to monitor the process through the usage of process trajectories of the history of the past successful batches. In this research, process measurements and product quality values of the past successful batches were collected and projected into matrix of data; and preprocessed through time alignment, centering, and scaling. Then the preprocessed data was projected into lower dimensions (latent variables) to produce latent variables and their trajectories during successful batches. Following the identification of latent variables, an empirical model was built through a 4-fold cross validation that can represent the operation of a successful batch. The behavior of two abnormal batches, batch 517 and 629, is then compared to the model by testing its statistical properties. Once the abnormal batches were flagged, their data set were folded back to original dimension to form a localization path for the time of abnormality and process variables that contributed to the abnormality. In each case the process measurement were used to establish operational boundaries on the latent variable space.

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Drug active transport into milk is a major concern for breastfeeding mothers and healthcare providers. Studies from the literature indicated that breast cancer resistance protein (ABCG2) plays an important role in drug transfer into milk. There has been limited study on stereoselective interactions with ABCG2. A mechanistic analysis of flux across cell monolayer model is a critical first step toward extrapolating in vitro results for predicting in vivo disposition (including distribution into milk), drug disposition or drug-drug interactions. The objectives of this thesis were (1) to establish a “Chemical knockout model” in rat for studying drug accumulation into milk, (2) to investigate the impact of stereoselective interaction between ABCG2/Abcg2 and pantoprazole on drug transport in milk, (3) to understand in vitro monolayer flux model using experimental data and a mechanistic mathematical model. Quantitive PCR, Western blotting and immunohistochemistry results indicated that Abcg2 was up-regulated during lactation and localized on apical side of epithelial cells in mammary gland. In vitro and in vivo experiments confirmed that Abcg2 is responsible for nitrofurantoin active transport in rat milk and GF120918 was established as a chemical knockout model. Abcg2 interacts stereoselectively with pantoprazole isomers. A significant different apical flux between two pantoprazole isomers was observed in Abcg2-MDCKII cell line. The milk to serum (M/S) ratio of (-)-pantoprazole was almost 3 times as that of (+)-pantoprazole in lactating rats. Administration GF120918 decreased M/S of (-)-pantoprazole (p<0.001) but not (+)-pantoprazole (p>0.05). A stably transfected ABCG2/Abcg2 overexpressing MDCKII cell line was successfully created and used to explore the theoretical relationships in a monolayer flux model. Based on the profiles of pantoprazole isomer transport, a simple three compartment model for drug transfer into breast milk incorporating the permeability-surface area products for passive diffusion (PSD), paracellular flux (PSPC) and apically efflux ABCG2 (PSA,E) transfection was developed. The mathematical model was developed to more fully understand the interplay of paracellular, passive diffusion, active transport, and flux kinetic parameters (Km, Vmax, IC50 and Ki). This model provided useful insights into the meaning and limitation of parameters obtained from monolayer flux.