Downloads & Free Reading Options - Results

Mathematical Modeling with Differential Equations and the SAGE Program; by David Joyner. Used for MP520 Computer Systems in Medicine for Radiological Technologies University, South Bend, Indiana Campus. Uploaded by Gerard Arthus and released into the Public Domain under the Creative Commons License Non-Attribute.

Mathematical Modeling with Differential Equations and the SAGE Program; by David Joyner. Used for MP520 Computer Systems in Medicine for Radiological Technologies University, South Bend, Indiana Campus. Uploaded by Gerard Arthus and released into the Public Domain under the Creative Commons License Non-Attribute.

Mathematical Modeling with Differential Equations and the SAGE Program; by David Joyner. Used for MP520 Computer Systems in Medicine for Radiological Technologies University, South Bend, Indiana Campus. Uploaded by Gerard Arthus and released into the Public Domain under the Creative Commons License Non-Attribute.

The Javelin antitank weapon system will replace the Dragon m Infantry and Combat Engineer battalions on a one for one basis. The tactics and techniques for Javelin employment will closely mirror those used for Dragon and TOW missile systems. This thesis examines the effectiveness of Javelin versus Dragon and examines a different employment method. The thesis goals are: • To investigate the suitability of Janus(A) to model the employment of various weapon systems. • To compare Javelin against Dragon, using measures of effectiveness and performance outlined in the Test and Evaluation Plan (TEP). • To examine how changes in the composition and tactical employment of anti-armor weapon systems influence their lethality and survivability, potentially suggesting a more effective employment method. The data generated from the simulated force-on-force scenarios is analyzed using graphical, statistical, and mathematical modeling techniques. The results could benefit the Army's Training and Doctrine Command in their combat development and combat effectiveness analysis.

The Javelin antitank weapon system will replace the Dragon m Infantry and Combat Engineer battalions on a one for one basis. The tactics and techniques for Javelin employment will closely mirror those used for Dragon and TOW missile systems. This thesis examines the effectiveness of Javelin versus Dragon and examines a different employment method. The thesis goals are: • To investigate the suitability of Janus(A) to model the employment of various weapon systems. • To compare Javelin against Dragon, using measures of effectiveness and performance outlined in the Test and Evaluation Plan (TEP). • To examine how changes in the composition and tactical employment of anti-armor weapon systems influence their lethality and survivability, potentially suggesting a more effective employment method. The data generated from the simulated force-on-force scenarios is analyzed using graphical, statistical, and mathematical modeling techniques. The results could benefit the Army's Training and Doctrine Command in their combat development and combat effectiveness analysis.

Adama Science and Technology University Lencha Tamiru Abdisa. (2019). Mathematical Modeling of the Interaction between Langerhans Cells and the Spread of HIV Infection. International Journal on Orange Technologies, 1(2), 1-18. Retrieved from https://journals.researchparks.org/index.php/IJOT/article/view/356 Pdf Url : https://journals.researchparks.org/index.php/IJOT/article/view/356/345 Paper Url : https://journals.researchparks.org/index.php/IJOT/article/view/356

The classical decision tree algorithm in the data mining algorithm is analyzed and studied, the generation principle and steps of the decision tree algorithm are described, and the advantages and disadvantages of the commonly used decision tree algorithms ID3, C4.5 and C5.0 algorithms are analyzed. The strategy of deep integration of information technology in higher vocational mathematics teaching is explored. Deep integration of information technology and mathematical modeling in higher vocational mathematics teaching, optimizing teaching content and teaching mode, constructing perfect curriculum resources, improving teaching efficiency, and stimulating learning interest.

This article is from BMC Genomics , volume 13 . Abstract Background: About 6 million Americans suffer from heart failure and 70% of heart failure cases are caused by myocardial infarction (MI). Following myocardial infarction, increased cytokines induce two major types of macrophages: classically activated macrophages which contribute to extracellular matrix destruction and alternatively activated macrophages which contribute to extracellular matrix construction. Though experimental results have shown the transitions between these two types of macrophages, little is known about the dynamic progression of macrophages activation. Therefore, the objective of this study is to analyze macrophage activation patterns post-MI. Results: We have collected experimental data from adult C57 mice and built a framework to represent the regulatory relationships among cytokines and macrophages. A set of differential equations were established to characterize the regulatory relationships for macrophage activation in the left ventricle post-MI based on the physical chemistry laws. We further validated the mathematical model by comparing our computational results with experimental results reported in the literature. By applying Lyaponuv stability analysis, the established mathematical model demonstrated global stability in homeostasis situation and bounded response to myocardial infarction. Conclusions: We have established and validated a mathematical model for macrophage activation post-MI. The stability analysis provided a possible strategy to intervene the balance of classically and alternatively activated macrophages in this study. The results will lay a strong foundation to understand the mechanisms of left ventricular remodelling post-MI.

We provide a mathematical analysis of and a numerical framework for full-field optical coherence elastography, which has unique features including micron-scale resolution, real-time processing, and non-invasive imaging. We develop a novel algorithm for transforming volumetric optical images before and after the mechanical solicitation of a sample with sub-cellular resolution into quantitative shear modulus distributions. This has the potential to improve sensitivities and specificities in the biological and clinical applications of optical coherence tomography.

Development of new material models for describing the high temperature constitutive behavior of real materials represents an important area of research in engineering disciplines. Derivation of mathematical expressions (constitutive equations) which describe this high temperature material behavior can be quite time consuming, involved and error prone; thus intelligent application of symbolic systems to facilitate this tedious process can be of significant benefit. A computerized procedure (SDICE) capable of efficiently deriving potential based constitutive models, in analytical form is presented. This package, running under MACSYMA, has the following features: partial differentiation, tensor computations, automatic grouping and labeling of common factors, expression substitution and simplification, back substitution of invariant and tensorial relations and a relational data base. Also limited aspects of invariant theory were incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). Finally not only calculation of flow and/or evolutionary laws were accomplished but also the determination of history independent nonphysical coefficients in terms of physically measurable parameters, e.g., Young's modulus, was achieved. The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet predefined order and simplify expressions so as to limit expression growth. Results are displayed when applicable utilizing index notation.

Each of the DSN 70-m antennas uses 16 bent-axis hydraulic piston motors as part of the antenna drive system. On each of the two antenna axes, four motors are used to drive the antenna and four motors provide counter torque to remove the backlash in the antenna drive train. This article presents a mathematical model for bent-axis hydraulic piston motors. The model was developed to understand the influence of the hydraulic motors on the performance of the DSN 70-m antennas' servo control system.

The objective of the present work was to explore and identify mathematical analysis techniques, and in particular, the use of linear programming. This topic was then applied to the Tracking and Data Relay Satellite System (TDRSS) in order to understand the space network better. Finally, a small scale version of the system was modeled, variables were identified, data was gathered, and comparisons were made between actual and theoretical data.

We describe a mathematical modeling of the digestion in the small intestine. The main interest of our work is to consider, at the same time, different aspects of the digestion i.e. the transport of the bolus all along the intestine, feedstuffs degradation according to the enzymes and local physical conditions, and nutrients absorption. A system of coupled ordinary differential equations is used to model these phenomena. The major unknowns of this system are the position of the bolus and its composition. This system of equations is solved numerically. We present different numerical computations for the degradation, absorption and transport of the bolus with acceptable accuracy with experimental data. The main feature and interest of this model are its generality. Even if we are at an early stage of development, our approach can be adapted to treat any kind of feedstuffs in any non-ruminant animal to predict the composition and velocity of bolus in the small intestine.

In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the elastic displacements and the dynamic liquid pressure is developed. The discrete scheme is based on the method of discrete singularities. A code to perform the numerical analysis is developed. Comprehensive benchmarking of the obtained results against other methods is done and good agreement is observed. The convergence of the proposed numerical method is demonstrated. One of the advantages of this new model is that the initial 3D problem is analytically reduced to a 1D integral equation. Moreover, it can handle the behaviour of the pressure in the vicinity of the nodes explicitly and the computational technique used has a quick convergence requiring a negligible amount of CPU time.

In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the elastic displacements and the dynamic liquid pressure is developed. The discrete scheme is based on the method of discrete singularities. A code to perform the numerical analysis is developed. Comprehensive benchmarking of the obtained results against other methods is done and good agreement is observed. The convergence of the proposed numerical method is demonstrated. One of the advantages of this new model is that the initial 3D problem is analytically reduced to a 1D integral equation. Moreover, it can handle the behaviour of the pressure in the vicinity of the nodes explicitly and the computational technique used has a quick convergence requiring a negligible amount of CPU time.

The energetic evaluations of graphite-to-diamond transition by electron irradiation are performed. The heat conduction problem is solved for the diamond synthesis when a pulse-periodic source of energy is located within a graphite cylinder; time dependences of temperature and pressure are found. It is shown, that the temperatures and pressures implemented in graphite are sufficient for graphite-to-diamond transition under electron bombardment.

In this paper, we propose a mathematical model to describe the functioning of a bioreactor landfill, that is a waste management facility in which biodegradable waste is used to generate methane. The simulation of a bioreactor landfill is a very complex multiphysics problem in which bacteria catalyze a chemical reaction that starting from organic carbon leads to the production of methane, carbon dioxide and water. The resulting model features a heat equation coupled with a non-linear reaction equation describing the chemical phenomena under analysis and several advection and advection-diffusion equations modeling multiphase flows inside a porous environment representing the biodegradable waste. A framework for the approximation of the model is implemented using Feel++, a C++ open-source library to solve Partial Differential Equations. Some heuristic considerations on the quantitative values of the parameters in the model are discussed and preliminary numerical simulations are presented.

This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and findings from mathematics education. Teacher beliefs about mathematics, learning and self-efficacy were expected to have a major impact on their classroom practices. We therefore assessed teacher beliefs about the usefulness of mathematics, learning (constructivist and socio-constructivist beliefs) and teacher self-efficacy when teaching modeling (teacher or class level variable). The student level variables assessed were modeling competence and other individual factors, such as basic mathematical skills and cognitive abilities. The effectiveness of the intervention was measured in a pre-post control group design using multilevel structural equation modeling. The results showed no direct effect of the intervention on student modeling competence. However, they did reveal that the intervention had a significant effect on teacher beliefs about learning (constructivist and socio-constructivist view) and an effect of these teacher beliefs about learning on student modeling competence. Further, the results showed that students' gains in modeling competence is not only mediated by teacher beliefs, but also influenced by individual factors. Implications for teaching as well as limitations of the study are discussed.

Sponsored search mechanisms have drawn much attention from both academic community and industry in recent years since the seminal papers of [13] and [14]. However, most of the existing literature concentrates on the mechanism design and analysis within the scope of only one search engine in the market. In this paper we propose a mathematical framework for modeling the interaction of publishers, advertisers and end users in a competitive market. We first consider the monopoly market model and provide optimal solutions for both ex ante and ex post cases, which represents the long-term and short-term revenues of search engines respectively. We then analyze the strategic behaviors of end users and advertisers under duopoly and prove the existence of equilibrium for both search engines to co-exist from ex-post perspective. To show the more general ex ante results, we carry out extensive simulations under different parameter settings. Our analysis and observation in this work can provide useful insight in regulating the sponsored search market and protecting the interests of advertisers and end users.

An equivalence relation in the set of all square binary matrices is described in this work. It is discussed a combinatoric problem about finding the cardinal number and the elements of the factor set according to this relation. We examine the possibility to get some special elements of this factor set. We propose an algorithm, which solves these problems. The results we have received are used to describe the topology of the different weaving structures.

This study explores a continuous spatio-temporal mathematical model to illustrate the dynamics of Monkeypox virus spread across various regions, considering both human and animal hosts. We propose a comprehensive strategy that includes awareness campaigns, security measures, and health interventions in areas where the virus is prevalent. The goal is to reduce transmission between humans and animals, thereby decreasing human infections and eradicating the virus in animal populations. Our model, which integrates spatial variables, accurately reflects the geographical spread of the virus and the impact of interventions, followed by the implementation and analysis of an applicable optimal control problem. Optimal control theory methods are applied in this work to demonstrate the existence of optimal control and the necessary conditions for optimality. We conduct numerical simulations using MATLAB with the forward-backward sweep method, revealing the efficiency of strategies focused on protecting vulnerable populations, preventing contact with infected individuals and animals, and promoting the use of quarantine facilities as the most effective means to control the spread of the Monkeypox virus. Additionally, the study examines the socio-economic impacts of the virus and the benefits of timely intervention. This approach provides valuable insights for policymakers and public health officials in managing and controlling the spread of Monkeypox.

This study explores a continuous spatio-temporal mathematical model to illustrate the dynamics of Monkeypox virus spread across various regions, considering both human and animal hosts. We propose a comprehensive strategy that includes awareness campaigns, security measures, and health interventions in areas where the virus is prevalent. The goal is to reduce transmission between humans and animals, thereby decreasing human infections and eradicating the virus in animal populations. Our model, which integrates spatial variables, accurately reflects the geographical spread of the virus and the impact of interventions, followed by the implementation and analysis of an applicable optimal control problem. Optimal control theory methods are applied in this work to demonstrate the existence of optimal control and the necessary conditions for optimality. We conduct numerical simulations using MATLAB with the forward-backward sweep method, revealing the efficiency of strategies focused on protecting vulnerable populations, preventing contact with infected individuals and animals, and promoting the use of quarantine facilities as the most effective means to control the spread of the Monkeypox virus. Additionally, the study examines the socio-economic impacts of the virus and the benefits of timely intervention. This approach provides valuable insights for policymakers and public health officials in managing and controlling the spread of Monkeypox.

The modeling of communication receivers is described at both the circuit detail level and at the block level. The largest effort was devoted to developing new models at the block modeling level. The available effort did not permit full development of all of the block modeling concepts envisioned, but idealized blocks were developed for signal sources, a variety of filters, limiters, amplifiers, mixers, and demodulators. These blocks were organized into an operational computer simulation of communications receiver circuits identified as the frequency and time circuit analysis technique (FATCAT). The simulation operates in both the time and frequency domains, and permits output plots or listings of either frequency spectra or time waveforms from any model block. Transfer between domains is handled with a fast Fourier transform algorithm.

A methodology is described for automatic mathematical modeling and generating simulation models. The major objective was to create a user friendly environment for engineers to design, maintain, and verify their models; to automatically convert the mathematical models into conventional code for computation; and finally, to document the model automatically.

A mathematical model for a general multibody flexible spacecraft is obtained. The generic spacecraft considered consists of a flexible central body to which a number of flexible multibody structures are attached. The coordinate systems used in the derivation allow effective decoupling of the translational motion of the entire spacecraft from its rotational motion about its center of mass. The derivation assumes that the deformations in the bodies are only due to elastic motions. The dynamic model derived is a closed-form vector-matrix differential equation. The model developed can be used for analysis and simulation of many realistic spacecraft configurations.

The Coastal Modeling System (CMS) is an integrated numerical modeling system for simulating nearshore waves, currents, water levels, salinity and sediment transport, and morphology change. The CMS was designed and developed for coastal inlets and navigation applications, including channel performance and sediment exchange between inlets and adjacent beaches. The present report provides an updated description of the mathematical formulations and numerical methods of hydrodynamic, salinity and sediment transport, and morphology change model CMS-Flow. The CMS-Flow uses the Finite Volume Method on Cartesian grids and has both fully explicit and fully implicit time stepping schemes. A detailed description of the explicit time stepping scheme was provided in Militello et al. (2004) and Buttolph et al. (2006). The present report focuses on the recent changes in the mathematical formulations, and the implicit time stepping schemes. The CMS-Wave and CMS-Flow models are tightly coupled within a single inline code. The CMS-Wave and CMS-Flow grids may be the same or have different spatial extents and resolutions. The hydrodynamic model includes physical processes such as advection, turbulent mixing, combined wave-current bottom friction; wave mass flux; wind, atmospheric pressure, wave, river, and tidal forcing; Coriolis force; and the influence of coastal structures. The implicit hydrodynamic model is coupled to a nonequilibrium transport model of multiple-sized total-load sediments. The model includes physical processes such as hiding and exposure, bed sorting and gradation, bed slope effects, nonerodible surfaces, and avalanching.

The goal is the development of a time-domain acoustical method for investigating the spatial and temporal stochastic variations in fish density within fish schools, and thereby to study the statistical fluctuations in the scattering of sound from these objects.

Some theoretical questions involved in the mathematical modeling of the kinetics of complex chemical process are discussed. The analysis is carried out for the homogeneous oxidation of ethylbenzene in the liquid phase. Particular attention is given to the determination of the general characteristics of chemical systems from an analysis of mathematical models developed on the basis of linear algebra.

A study is performed under NASA contract to evaluate data from an AN/FPS-16 radar installed for support of flight programs at Dryden Flight Research Facility of NASA Ames Research Center. The purpose of this study is to provide information necessary for improving post-flight data reduction and knowledge of accuracy of derived radar quantities. Tracking data from six flights are analyzed. Noise and bias errors in raw tracking data are determined for each of the flights. A discussion of an altitude bias error during all of the tracking missions is included. This bias error is defined by utilizing pressure altitude measurements made during survey flights. Four separate filtering methods, representative of the most widely used optimal estimation techniques for enhancement of radar tracking data, are analyzed for suitability in processing both real-time and post-mission data. Additional information regarding the radar and its measurements, including typical noise and bias errors in the range and angle measurements, is also presented. This report is in two parts. This is part 2, a discussion of the modeling of propagation path errors.

This investigation is motivated by the need to study the cyclic plasticity response of standard aerospace fasteners within the context of finite element analysis. The available literature on mathematical models of plasticity along with their implementation in finite element procedures was reviewed. The investigation was limited to models of rate-independent plasticity based on the existence of a yield surface and the incremental (rate-type) theory of plasticity. Section II of the report introduces certain definitions and basic concepts including a discussion of the typical response of metals to cyclic loading. The mathematical models of the plastic behavior of metals are reviewed in Section III. Section IV covers the finite element implementation of certain models. A summary and some recommendations for future investigations are presented in Section V. (Author)

This project examines and assesses the extent to which U.S. military policy has effectively interpreted and responded to the military implications of Soviet weapons innovations. It focuses on the contributions of Soviet weapons innovations to military mission performance, and also examines the ability of the Soviet weapons innovation process to offer a militarily significant breakout option. Three related lines of inquiry were pursued. First, we examined the Soviet approach to weapons innovation as it is portrayed in their force planning and weapons evaluation literature. Next we analyzed the Soviet approach to measuring the relative contributions of weapons innovation efforts towards improving mission capabilities; and third, we assessed the degree to which the Soviets have the capacity for 'breakout' -- significantly improving their military capabilities in a short period of time -- through weapons innovation. Part I addressed one aspect of the second task. In part II we take a closer look at Soviet mathematical modeling related to notions of strategic technology innovation and strategic force development from their efforts to measure the nuclear balance. Keywords: Mathematical models; Weapon system effectiveness; Mission profiles; Innovations; Foreign technology.

A mathematical model for the quantitative analysis of cancer immune interaction, considering the role of antibodies has been proposed in this paper. The model is based on the clinical evidence, which states that antibodies can directly kill cancerous cells [1]. The existence of transcritical and saddle-node bifurcation, which has been proved using Sotomayor theorem, provides strong biological implications. Through numerical simulations, it has been illustrated that under certain therapy (like monoclonal antibody therapy), which is capable of altering the parameters of the system, cancer-free state can be obtained.

Motivated by the desire to bridge the gap between the microscopic description of price formation (agent-based modeling) and the stochastic differential equations approach used classically to describe price evolution at macroscopic time scales, we present a mathematical study of the order book as a multidimensional continuous-time Markov chain and derive several mathematical results in the case of independent Poissonian arrival times. In particular, we show that the cancellation structure is an important factor ensuring the existence of a stationary distribution and the exponential convergence towards it. We also prove, by means of the functional central limit theorem (FCLT), that the rescaled-centered price process converges to a Brownian motion. We illustrate the analysis with numerical simulation and comparison against market data.

This document is a final report of the research sponsored by AFOSR under contract No. F49620-91-C-0048-P0002 with Stanford University. This research effort focused on the mathematical modeling and numerical simulation of the dynamics of flexible structures undergoing large overall motions. The results reported below fall within the following areas: (i) Enhanced numerical models for shell intersections, (ii) Asymptotic methods for nonlinear shells, and (iii) Conserving time-stepping algorithms for nonlinear dynamics. (AN)

This article addresses the logistics of implementing projects in an undergraduate mathematics class and is intended both for new instructors and for instructors who have had negative experiences implementing projects in the past. Project implementation is given for both lower and upper division mathematics courses with an emphasis on mathematical modeling and data collection. Projects provide tangible connections to course content which can motivate students to learn at a deeper level. Logistical pitfalls and insights are highlighted as well as descriptions of several key implementation resources. Effective assessment tools, which allowed me to smoothly adjust to student feedback, are demonstrated for a sample class. As I smoothed the transition into each project and guided students through the use of the technology, their negative feedback on projects decreased and more students noted how the projects had enhanced their understanding of the course topics. Best practices learned over the years are given along with project summaries and sample topics. These projects were implemented at a small liberal arts university, but advice is given to extend them to larger classes for broader use.

The paper presents two new approaches to modeling the interaction of small and medium pricetaking traders with a stock exchange. In the framework of these approaches, the traders can form and manage their portfolios of financial instruments traded on a stock exchange with the use of linear, integer, and mixed programming techniques. Unlike previous authors publications on the subject, besides standard securities, the present publication considers derivative financial instruments such as futures and options contracts.

The paper presents two new approaches to modeling the interaction of small and medium pricetaking traders with a stock exchange. In the framework of these approaches, the traders can form and manage their portfolios of financial instruments traded on a stock exchange with the use of linear, integer, and mixed programming techniques. Unlike previous authors publications on the subject, besides standard securities, the present publication considers derivative financial instruments such as futures and options contracts.

This technical note describes Microwave Landing System (MLS) and Precision Distance Equipment (DME/P) mathematical modeling performed for runway 19L, Andrews Air Force Base (ADW), Camp Springs, Maryland. This study evaluates the effects of scattering and shadowing from selected buildings, hangars, aircraft, and terrain. Results are provided as plots illustrating the predicted multipath levels, separation angles, and the resulting error plots from the worst case contributors. Scenarios were modeled to determine the effects of the multipath sources in the modeled environment. These resulting errors were analyzed and compared to error tolerance (FAA-STD-022d) to determine if the errors are acceptable. The effects of the ADW environment were analyzed and evaluated. It was determined that the proposed site will perform satisfactorily with no changes.

The objectives of the project 'Biological-Mathematical Modeling of Chronic Toxicity' were to study the factors affecting the fate of inhaled vapors in the body and to develop a mathematical model. The main accomplishments are: (1) A general pharmacokinetic model for inhalation administration, based on physiological parameters of the exposed subject and on physical and chemical properties of the inhaled substance, was defined. (2) Information on interspecies differences was extracted from the literature; partition coefficients of eight organic solvents were determined for eight tissues of three species (man, monkey, rat); steady state clearances calculated from pulmonary uptake, and intrinsic clearance determined from vapor distribution in rats were used in the model as elimination rate constants. (3) The models were used to evaluate the effects of the following parameters on uptake, distribution and elimination of inhaled vapors: solubility, metabolism, body build, interspecies differences, physical exertion, exposure duration, exposure repetition, and short-term excursion limit. (4) Nonlinear dependence of pulmonary uptake on exposure concentration was observed in the animal model. (5) Reduced pulmonary uptake and quantitative and qualitative changes in elimination were observed if two vapors were inhaled simultaneously.

A mathematical model has been developed which can be applied to evaluate the least-cost alternatives to meet the projected potable and non-potable water requirements of a US Army Corps-sized operation. It included the adaptation of the model to an existing solution technique, the Out-of-Kilter Algorithm (OKA), a search of the literature to obtain cost data for the various elements within the alternatives, a search of the literature for health and other related factors, a review of existing scenarios, a review of collateral issues pertinent to the production of water in an arid or semi-arid environment, and finally, proposed systems for the re-use of laundry and shower wastewaters. (Author)

Human immunodeficiency virus (HIV-1 or simply HIV) induces a persistent infection, which in the absence of treatment leads to AIDS and death in almost all infected individuals. HIV infection elicits a vigorous immune response starting about 2-3 weeks post infection that can lower the amount of virus in the body, but which cannot eradicate the virus. How HIV establishes a chronic infection in the face of a strong immune response remains poorly understood. It has been shown that HIV is able to rapidly change its proteins via mutation to evade recognition by virus-specific cytotoxic T lymphocytes (CTLs). Typically, an HIV-infected patient will generate 4-12 CTL responses specific for parts of viral proteins called epitopes. Such CTL responses lead to strong selective pressure to change the viral sequences encoding these epitopes so as to avoid CTL recognition. Here we review experimental data on HIV evolution in response to CTL pressure, mathematical models developed to explain this evolution, and highlight problems associated with the data and previous modeling efforts. We show that estimates of the strength of the epitope-specific CTL response depend on the method used to fit models to experimental data and on the assumptions made regarding how mutants are generated during infection. We illustrate that allowing CTL responses to decay over time may improve the fit to experimental data and provides higher estimates of the killing efficacy of HIV-specific CTLs. We also propose a novel method for simultaneously estimating the killing efficacy of multiple CTL populations specific for different epitopes of HIV using stochastic simulations. Lastly, we show that current estimates of the efficacy at which HIV-specific CTLs clear virus-infected cells can be improved by more frequent sampling of viral sequences and by combining data on sequence evolution with experimentally measured CTL dynamics.

Soldering is the default joining proce0073s in the electronic packaging industry. Solder joints are obtained by interaction of the substrate (mostly copper) with the molten solder. The dissolution kinetics of copper and the growth of intermetallic compound (IMC) during soldering process are concurrent processes. The dissolution of the metal from the substrate components is even more critical due to ever increasing miniaturization of the electronic components.The assessment of base metal lost during the process is another important subject being investigated by the researchers in the last two decades. Extensive experimentation is done to quantify the IMC thickness and metal dissolution for various combinations of substrate metal and solders. As a matter of fact these experiments are time consuming and expensive. Moreover, the experimental results have the application to a limited domain. Various models have been suggested by researchers to quantify the substrate thickness lost and IMC growth during soldering. Most of the existing models to estimate the IMC growth and metal dissolution during the soldering process are heavily based on the experimental data. These models do not depict the actual physics of the process. In the present study a review of the modeling techniques has been done and a model has been proposed which is based on the diffusion of and interface kinetics during soldering process. The proposed one-dimensional model has been solved and compared with the experimental data. The present model has a good potential to be extended in two and possibly three dimensions and incorporation of scalloped IMC in order to capture the complete physics of the process.

Accompanied by 3.5" disc

Accompanied by 3.5" disc

Accompanied by 3.5" disc

The primary focus of this study is to model steady-state performance of a Loop Heat Pipe (LHP). The mathematical model is based on the steady-state energy balance equations at each component of the LHP. The heat exchange between each LHP component and the surrounding is taken into account. Both convection and radiation environments are modeled. The loop operating temperature is calculated as a function of the applied power at a given loop condition. Experimental validation of the model is attempted by using two different LHP designs. The mathematical model is tested at different sink temperatures and at different elevations of the loop. Tbc comparison of the calculations and experimental results showed very good agreement (within 3%). This method proved to be a useful tool in studying steady-state LHP performance characteristics.

Population-centric operations force modern western democratic states to deploy both police and military capacities. Globalization and undergoverned states have transformed traditional security threats; now external security threats are generated by internal factors, and internal security threats are generated by external factors. Military organizations designed to address external security threats are ill-suited to deal with internal security threats. Operations in Kosovo, Afghanistan, and Iraq show the need for police expeditionary capacities to fill in for indigenous institutions following regime overthrow. Modern state organizations do not produce the quality and quantity of deployable police needed in the time required. States have several options for addressing their police expeditionary shortages. This thesis assesses the options for solving this problem with a mathematical model of the dynamics between military and police organizations. The thesis describes a hybrid option with best organizational practices, represented by gendarmerie-type organizations. Comparing their characteristics with the outcomes of the modeled game demonstrates that the hybrid option best captures the characteristics of the Nash point as the hypothetically optimal objective of the arbitration process. It thus represents a suitable and sustainable organizational solution. The outcomes of the modeled game also suggest an arbitration process to consider the hybrid option.

The goal of the conducted research was to find improved mathematical models for the physical processes that occur in radio frequency discharges. Existing models of the plasma sheath have been studied and new ones have been developed for the bounded plasma problem. Numerical algorithms and analytical formulas have been found for solving the equations governing these models, and physical characteristics of the sheath have been obtained.

This paper discusses dimensional manipulation, essentially a problem requiring symbolic techniques, using a numerical method obeys the laws of dimensional arithmetic. This is achieved by specifying an encoding of units of measurement as prime numbers, and manipulating the resulting expressions numerically. The unique factorization theorem is applied to show that this method makes trivial the problems of dimensional simplification and verification of dimensional equivalency, which are central issues in dimensional arithmetic. The solution has immediate application in mathematical modeling system, chiefly in the model validation and model solution phases.

Nitro-aromatics: 2,4,6-trinitrotoluene (TNT), 2,4-dinitrotoluene (DNT) and hexa-hydro-1,3,5-trinitro-triazine (RDX) are the major constituents of wastewaters discharged from propellant and explosive manufacturing units and munitions load, assembly, and pack Operations. More than 1,200 current and former U.S. Department of Defense and U.S. Department of Energy facilities have problems with explosive contamination. The objective of this project was to study the electrochemical degradation of nitro-aromatic compounds under various conditions to enable the formulation of a mathematical model and to design a plug flow reactor for the same. The transformation of DNT and TNT to their corresponding reduced by-products has been shown to occur through purely abiotic mechanisms induced by electric current.