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Saripalli, Manjeera. "Mathematical Modeling and Simulation of Colorectal Cancer." OpenSIUC, 2011. https://opensiuc.lib.siu.edu/theses/698.
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Understanding the cancer pathology and develop effective treatment strategies play significant roles in improving cancer survival rates. In this thesis, evaluations of mathematical modeling and simulation were studied and presented. Colorectal system was investigated from gene and cell levels. The Hardware Descriptive Language (HDL) package and codes were developed to simulate the cancer models. Representative codes and figures were illustrated. Results suggest that the HDL is an effective method to conduct the modeling and simulation of cancers. It is essential to develop advanced technology such as HDL modeling and simulation to improve our understandings to fight cancer and save lives.
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Haddon, Antoine. "Mathematical Modeling and Optimization for Biogas Production." Thesis, Montpellier, 2019. http://www.theses.fr/2019MONTS047.
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La digestion anaérobique est un processus biologique au cours duquel des micro-organismes décomposent de la matière organique pour produire du biogaz (dioxyde de carbone et methane) qui peut être utilisé comme source d'énergie renouvelable. Cette thèse porte sur l'élaboration de stratégies de contrôle et la conception de bioréacteurs qui maximisent la production de biogaz.La première partie se concentre sur le problème de contrôle optimal de la maximisation de la production de biogaz dans un chemostat avec un modèle à une réaction, en contrôlant le taux de dilution. Pour le problème à horizon fini, nous étudions des commandes type feedback, similaires à ceux utilisés en pratique et consistant à conduire le réacteur vers un niveau de substrat donné et à le maintenir à ce niveau. Notre approche repose sur une estimation de la fonction de valeur inconnue en considérant différentes fonctions de coût pour lesquelles la solution optimale admet un feedback optimal explicite et autonome. En particulier, cette technique fournit une estimation de la sous-optimalité des régulateurs étudiés pour une large classe de fonctions de croissance dépendant du substrat et de la biomasse. À l'aide de simulations numériques, on montre que le choix du meilleur feedback dépend de l'horizon de temps et de la condition initiale.Ensuite, nous examinons le problème sur un horizon infini, pour les coûts moyen et actualisé. On montre que lorsque le taux d'actualisation tends vers à 0, la fonction de valeur du problème actualisé converge vers la fonction de valeur pour le coût moyen. On identifie un ensemble de solutions optimales pour le problème de limite et avec coût moyen comme étant les contrôles qui conduisent le système vers un état qui maximise le débit de biogaz sur un ensemble invariant.Nous revenons ensuite au problème sur à horizon fini fixe et avec le Principe du Maximum de Pontryagin, on montre que le contrôle optimal à une structure bang arc singulier. On construit une famille de contrôles extremal qui dépendent de la valeur constante du Hamiltonien. En utilisant l'équation de Hamilton-Jacobi-Bellman, on identifie le contrôle optimal comme étant celui associé à la valeur du Hamiltonien qui satisfait une équation de point fixe. On propose ensuite un algorithme pour calculer la commande optimale en résolvant cette équation de point fixe. On illustre enfin cette méthode avec les deux principales types de fonctions de croissance de Monod et Haldane.Dans la deuxième partie, on modélise et on étudie l'impact de l'hétérogénéité du milieu réactionnel sur la production de biogaz. Pour cela, on introduit un modèle de bioréacteur pilote qui décrit les caractéristiques spatiales. Ce modèle tire parti de la géométrie du réacteur pour réduire la dimension spatiale de la section contenant un lit fixe et, dans les autres sections, on considère les équations 3D de Navier-Stokes en régime permanent pour la dynamique des fluides. Pour représenter l'activité biologique, on utilise un modèle à deux réactions et pour les substrats, des équations advection-diffusion-réaction. On considère seulement les biomasses qui sont attachées au lit fixe et on modélise leur croissance avec une fonction densité dépendante. On montre que ce modèle peut reproduire le gradient spatial de données expérimentales et permet de mieux comprendre la dynamique interne du réacteur. En particulier, les simulations numériques indiquent qu'en mélangeant moins, le réacteur est plus efficace, élimine plus de matières organiques et produit plus de biogazAnaerobic digestion is a biological process in which organic compounds are degraded by different microbial populations into biogas (carbon dioxyde and methane), which can be used as a renewable energy source. This thesis works towards developing control strategies and bioreactor designs that maximize biogas production.The first part focuses on the optimal control problem of maximizing biogas production in a chemostat in several directions. We consider the single reaction model and the dilution rate is the controlled variable.For the finite horizon problem, we study feedback controllers similar to those used in practice and consisting in driving the reactor towards a given substrate level and maintaining it there. Our approach relies on establishing bounds of the unknown value function by considering different rewards for which the optimal solution has an explicit optimal feedback that is time-independent. In particular, this technique provides explicit bounds on the sub-optimality of the studied controllers for a broad class of substrate and biomass dependent growth rate functions. With numerical simulations, we show that the choice of the best feedback depends on the time horizon and initial condition.Next, we consider the problem over an infinite horizon, for averaged and discounted rewards. We show that, when the discount rate goes to 0, the value function of the discounted problem converges and that the limit is equal to the value function for the averaged reward. We identify a set of optimal solutions for the limit and averaged problems as the controls that drive the system towards a state that maximizes the biogas flow rate on an special invariant set.We then return to the problem over a fixed finite horizon and with the Pontryagin Maximum Principle, we show that the optimal control has a bang singular arc structure. We construct a one parameter family of extremal controls that depend on the constant value of the Hamiltonian. Using the Hamilton-Jacobi-Bellman equation, we identify the optimal control as the extremal associated with the value of the Hamiltonian which satisfies a fixed point equation. We then propose a numerical algorithm to compute the optimal control by solving this fixed point equation. We illustrate this method with the two major types of growth functions of Monod and Haldane.In the second part, we investigate the impact of mixing the reacting medium on biogas production. For this we introduce a model of a pilot scale upflow fixed bed bioreactor that offers a representation of spatial features. This model takes advantage of reactor geometry to reduce the spatial dimension of the section containing the fixed bed and in other sections, we consider the 3D steady-state Navier-Stokes equations for the fluid dynamics. To represent the biological activity, we use a 2 step model and for the substrates, advection-diffusion-reaction equations. We only consider the biomasses that are attached in the fixed bed section and we model their growth with a density dependent function. We show that this model can reproduce the spatial gradient of experimental data and helps to better understand the internal dynamics of the reactor. In particular, numerical simulations indicate that with less mixing, the reactor is more efficient, removing more organic matter and producing more biogas
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SAENZ, JUAN SERGIO ROMERO. "MATHEMATICAL MODELING AND SIMULATION OF A HYDROCYCLONE MODEL." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1997. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=19769@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOREste trabalho apresenta um modelo matemático completo e a implementação de um sistema computacional para a simulação do escoamento em um hidrociclone, que leva em conta o núcleo de ar como uma superfície livre, caracterizando esta interface livre formada como do tipo Young-Laplace. Pelas características do escoamento foi considerada a difusão turbulenta, que foi necessário acrescentar para poder ajustar bem o modelo aos dados experimentais. São aproximados os campos de velocidades e pressões, assim como a forma e localização da interface, esta através de um método lagrangeano. Neste método utiliza-se uma malha lagrangeana para caracterizar a interface livre e uma malha euleriana para calcular os campos de velocidades e pressões no escoamento através do método dos volumes finitos. O ajuste da interface é feita através de um processo iterativo. São feitas simulações numéricas e são mostradas comparações das previsões teóricas com dados experimentais que validam o modelo.
The present work is realted to the mathematical modeling and computacional simulation of flow through hydrocyclons. The present model assumes the air core being a free surface of Young-Laplace type. As the characterisctic of the flow suggests, the model considers a turbuleny diffusion, this fact is essential to have a good agreement with experimental data. The velocity and pressure with the shape and localization of the interface are approzximated. For the above approximation a langrangian grid is used to characterize the free interface, and an eulerian grid for calculating the velocity and pressure fields thorough a finite-volume method. The approximation of the interface is achieved using an iterative procedure. An extensive comparison of model predictions against experimental data is presented together with some numerical results.
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LETA, FABIANA RODRIGUES. "MATHEMATICAL MODELING AND GRAPHICAL SIMULATION OF FACIAL AGING." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1998. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=19814@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIORCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
O objetivo da presente tese é a modelagem matemática e a simulação gráfica do processo de envelhecimento facial humano. Para modelar este processo foram realizadas as seguintes etapas: estudo dos principais aspectos envolvidos no envelhecimento facial, observação do efeitos visíveis do envelhecimento sobre a face, definição das principais regiões faciais relacionadas com o processo de envelhecimento, medição das variações destas regiões ao longo do tempo em um grupo de pessoas, elaboração de um modelo de envelhecimento comum a todo o grupo e criação de curvas de envelhecimento facial. A partir destas curvas características, utilizando-se técnicas de Processamento de Imagens, foi elaborado um programa de simulação gráfica do envelhecimento facial (Warping de Envelhecimento Facial). Um vez que a quantificação do envelhecimento foi obtida, tornou-se, deste modo, possível visualizá-lo com base científica. A modelagem de um fenômeno biológico e mecânico que ocorre com todos, contribui com as diversas áreas envolvidas no campo da Bio-Engenharia. Conhecendo-se o processo de envelhecimento torna-se possível: propor novas técnicas para retardar ou atenuar tais efeitos, servir de base para pesquisas que permitem avaliar os esforços mecânicos que a pele é submetida ao longo do tempo, apoiar a decisão sobre a idade ideal de intervenção cirúrgica e possivelmente auxiliar no reconhecimento de pessoas que encontram-se por muito tempo desaparecidas.
This thesis describes a mathermatical model and graphical simulation for human being facial ageing phenomenon. The modelling procedure was defined as follows: study about the main characteristics of the facial ageing, the definition and measurement of the main affected áreas by the ageing; the generation of na ageing pattern based on the variation of the measured areas and the definition of ageing curves. The graphical simulation was based on the use of image processing techniques. A graphical software was developed using waríng procedures which promotes on facial images based on the mentioned ageing curves. Once the ageing phenomenon was mathematically modelled it is possible its scientific visualization. The main applications of the implemented software are in the Bioengineering área. The proposed model na help the understandig of the ageing which can be used in the development of new techniques to control its effects. The software also can be used as a decision support system in surgical área allowing the proposition of the ideal age for plastic surgery. Besides these scientific applications, social one is the assistance in the edentification of disappeared people.
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Jourdana, Clément. "Mathematical modeling and numerical simulation of innovative electronic nanostructures." Toulouse 3, 2011. http://www.theses.fr/2011TOU30200.
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Dans cette thèse, nous nous intéressons à la modélisation et la simulation de dispositifs nanoélectroniques innovants. Premièrement, nous dérivons formellement un modèle avec masse effective pour décrire le transport quantique des électrons dans des nanostructures très fortement confinées. Des simulations numériques illustrent l'intérêt du modèle obtenu pour un dispositif simplifié mais déjà significatif. La deuxième partie est consacrée à l'étude du transport non ballistique dans ces mêmes structures confinées. Nous analysons rigoureusement un modèle de drift-diffusion et puis nous décrivons et implémentons une approche de couplage spatial classique-quantique. Enfin, nous modélisons et simulons un nanodispositif de spintronique. Plus précisement, nous étudions le renversement d'aimantation dans un matériau ferromagnétique multi-couches sous l'effet d'un courant de spinIn this PhD thesis, we are interested in the modeling and the simulation of innovative electronic nanodevices. First, we formally derive an effective mass model describing the quantum motion of electrons in ultra-scaled confined nanostructures. Numerical simulations aim at testing the relevance of the obtained model for a simplified (but already significant) device. The second part is devoted to non-ballistic transport in these confined nanostructures. We rigorously analyse a drift-diffusion model and afterwards we describe and implement a classical-quantum spatial coupling approach. In the last part, we model and simulate a spintronic nanodevice. More precisely, we study the magnetization switching of a ferromagnetic material driven by a spin-current
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Wang, Shihu. "Computer Simulation and Mathematical Modeling of Reversibly Associated Polymers." Case Western Reserve University School of Graduate Studies / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=case1275488088.
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LAWOT, NIWAS. "MATHEMATICAL MODELING OF SMALLPOX WITHOPTIMAL INTERVENTION POLICY." Master's thesis, University of Central Florida, 2006. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3397.
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In this work, two differential equation models for smallpox are numerically solved to find the optimal intervention policy. In each model we look for the range of values of the parameters that give rise to the worst case scenarios. Since the scale of an epidemic is determined by the number of people infected, and eventually dead, as a result of infection, we attempt to quantify the scale of the epidemic and recommend the optimum intervention policy. In the first case study, we mimic a densely populated city with comparatively big tourist population, and heavily used mass transportation system. A mathematical model for the transmission of smallpox is formulated, and numerically solved. In the second case study, we incorporate five different stages of infection: (1) susceptible (2) infected but asymptomatic, non infectious, and vaccine-sensitive; (3) infected but asymptomatic, noninfectious, and vaccine-in-sensitive; (4) infected but asymptomatic, and infectious; and (5) symptomatic and isolated. Exponential probability distribution is used for modeling this case. We compare outcomes of mass vaccination and trace vaccination on the final size of the epidemic.M.S.
Department of Mathematics
Sciences
Mathematics
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Stredie, Valentin Gabriel Hou Thomas Y. Wu Theodore Y. T. "Mathematical modeling and simulation of aquatic and aerial animal locomotion /." Diss., Pasadena, Calif. : California Institute of Technology, 2004. http://resolver.caltech.edu/CaltechETD:etd-05272005-004852.
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Numfor, Eric Shu. "Mathematical Modeling, Simulation, and Time Series Analysis of Seasonal Epidemics." Digital Commons @ East Tennessee State University, 2010. https://dc.etsu.edu/etd/1745.
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Seasonal and non-seasonal Susceptible-Exposed-Infective-Recovered-Susceptible (SEIRS) models are formulated and analyzed. It is proved that the disease-free steady state of the non-seasonal model is locally asymptotically stable if Rv < 1, and disease invades if Rv > 1. For the seasonal SEIRS model, it is shown that the disease-free periodic solution is locally asymptotically stable when R̅v < 1, and I(t) is persistent with sustained oscillations when R̅v > 1. Numerical simulations indicate that the orbit representing I(t) decays when R̅v < 1 < Rv. The seasonal SEIRS model with routine and pulse vaccination is simulated, and results depict an unsustained decrease in the maximum of prevalence of infectives upon the introduction of routine vaccination and a sustained decrease as pulse vaccination is introduced in the population.
Mortality data of pneumonia and influenza is collected and analyzed. A decomposition of the data is analyzed, trend and seasonality effects ascertained, and a forecasting strategy proposed.
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Weens, William. "Mathematical modeling of liver tumor." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2012. http://tel.archives-ouvertes.fr/tel-00779177.
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Comme démontre récemment pour la régénération du foie après un dommage cause par intoxication, l'organisation et les processus de croissance peuvent être systématiquement analyses par un protocole d'expériences, d'analyse d'images et de modélisation [43]. Les auteurs de [43] ont quantitativement caractérise l'architecture des lobules du foie, l'unité fonctionnelle fondamentale qui constitue le foie, et en ont conçu un modèle mathématique capable de prévoir un mécanisme jusqu'alors inconnu de division ordonnée des cellules. La prédiction du modèle fut ensuite validée expérimentalement. Dans ce travail, nous étendons ce modèle a l'échelle de plusieurs lobules sur la base de résultats expérimentaux sur la carcinogène dans le foie [15]. Nous explorons les scénarios possibles pouvant expliquer les différents phénotypes de tumeurs observés dans la souris. Notre modèle représente les hépatocytes, principal type de cellule dans le foie, comme des unités individuels avec un modèle a base d'agents centré sur les cellules et le système vasculaire est représenté comme un réseau d'objets extensibles. L'équation de Langevin qui modélise le mouvement des objets est calculée par une discrétisation explicite. Les interactions mécaniques entre cellules sont modélisées avec la force de Hertz ou de JKR. Le modèle est paramètre avec des valeurs mesurables a l'échelle de la cellule ou du tissue et ses résultats sont directement comparés avec les résultats expérimentaux. Dans une première étape fondamentale, nous étudions si les voies de transduction du signal de Wnt et Ras peuvent expliquer les observations de [15] où une prolifération instantanée dans les souris mutées est observée seulement si 70% des hépatocytes sont dépourvues d'APC. Dans une deuxième étape, nous présentons une analyse de sensibilité du modèle sur la rigidité de la vasculature et nous la mettons en relation avec un phénotype de tumeur (observe expérimentalement) où les cellules tumorales sont bien différentiées. Nous intégrons ensuite dans une troisième 'étape la destruction de la vasculature par les cellules tumorales et nous la mettons en relation avec un autre phénotype observe expérimentalement caractérise par l'absence de vaisseaux sanguins. Enfin, dans la dernière étape de notre étude nous montrons que des effets qui sont détectables dans les petits nodules tumoraux et qui reflètent les propriétés des cellules tumorales, ne sont plus présents dans la forme ou dans le phénotype des tumeurs d'une taille excédant la moitié de celle d'un lobule.
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Sadeghi, Mohsen. "Modeling and Simulation Phenomena in Paper Drying." Thesis, McGill University, 2003. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=55196.
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A comprehensive microscale model of transport phenomena in paper drying was developed. The model includes five species (free water, sorbed water, air, water vapor, fibers) in three phases: humid air, liquid, solid. AlI relevant transport mechanisms were treated: capillary transport of free water, diffusion of sorbed water, convective-diffusive transport of water vapor. Effects on drying from the hygroscopic nature of paper were included: the reduced vapor pressure and extra evaporation energy for bound water and the changes in porosity and thickness because of sorbed water removal.Un modèle détaillé des phénomènes de transport à petite échelle a été développé pour le séchage du papier. Le modèle inclut cinq espèces (eau libre, eau sorbée, air, vapeur d'eau et fibres) et trois phases: air humide, liquide et solide. Tous les mécanismes de transport pertinents du séchage ont été traités: le transport par capillarité de l'eau libre, la diffusion de l'eau sorbée ainsi que le transport de la vapeur d'eau par convectiondiffusion. Plusieurs effets sur le séchage de la nature hygroscopique du papier ont été inclus: l'énergie supplémentaire nécessaire à l'évaporation de l'eau liée, la réduction de la pression de vapeur de l'eau liée et les changements de porosité et d'épaisseur provenant de l'enlèvement de l'eau sorbée. fr
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Reinecke, Isabel [Verfasser]. "Mathematical modeling and simulation of the female menstrual cycle / Isabel Reinecke." Berlin : Freie Universität Berlin, 2009. http://d-nb.info/102366514X/34.
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Hesse, Marc Andre. "Mathematical modeling and multiscale simulation of CO₂ storage in saline aquifers /." May be available electronically:, 2008. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.
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Vantzos, Orestis. "Mathematical Modeling of Charged Liquid Droplets: Numerical Simulation and Stability Analysis." Thesis, University of North Texas, 2006. https://digital.library.unt.edu/ark:/67531/metadc5240/.
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The goal of this thesis is to study of the evolution of 3D electrically charged liquid droplets of fluid evolving under the influence of surface tension and electrostatic forces. In the first part of the thesis, an appropriate mathematical model of the problem is introduced and the linear stability analysis is developed by perturbing a sphere with spherical harmonics. In the second part, the numerical solution of the problem is described with the use of the boundary elements method (BEM) on an adaptive mesh of triangular elements. The numerical method is validated by comparison with exact solutions. Finally, various numerical results are presented. These include neck formation in droplets, the evolution of surfaces with holes, singularity formation on droplets with various symmetries and numerical evidence that oblate spheroids are unstable.
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Li, Ping, and 李平. "Numerical methodologies for electromagnetic parasitic system modeling and simulation." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/202361.
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In this thesis, to efficiently and accurately model the electromagnetic radiations from electronic and antenna systems, and to analyze the hybrid electromagnetic (EM)-circuit system and the interactions between EM waves and multi-physics systems, a plethora of full-wave approaches are developed. Specifically, a set of frequency-domain methods are proposed in the first part of this thesis to characterize the electromagnetic radiations from device under test (DUT) based on the sampled near-field data. For the first approach, the dyadic Green function (DGF) in the presence of perfectly conducting sphere is expanded by spherical vector wave functions, which is mathematically rigorous. Based on this DGF and the reciprocity theorem, the radiation outside the spherical sampling surface can be accurately predicted with only the tangential components of the electric near-field over this sampling surface.
Sometimes for situations where electronic devices are placed in good conductive shielding enclosures with apertures or ventilation slots, only partially planar electric near-field sampling over the apertures or the slots is sufficient according to Schelkunoff’s principle. Due to the unavailability of analytical DGF and the prohibitively computational cost for the numerical DGF, a novel two-step process approach by considering the radiation problem as a scattering issue with incident waves from the equivalent magnetic currents derived from the sampled electric near-field is proposed.
However, the very near-field radiation inside the sampling surface cannot be retrieved with the above two approaches. To overcome this limitation, the equivalent source reconstruction based methods are introduced by replacing the radiators with equivalent current sources that are capable of reproducing the original radiation. Due to the difficulty of acquiring the phase information of the near-field data, a fully new iterative phaseless source reconstruction method (SRM) which only needs the amplitude of the electric field is developed. To reduce the computational cost of traditional SRM for broadband radiators, a wideband SRM based on a Stoer-Bulirsh (SB) recursive tabular algorithm is proposed. Enhanced by an adaptive frequency sampling strategy, only a very small number of frequency samples are required.
With the purpose to capture the nonlinear response of EM-circuit systems, transient scattering from penetrable objects, surface plasmon polarization (SPP) of grapheme below the terahertz range, and the impacts of random parameters on the physical behavior of stochastic systems, various novel discontinuous Galerkin time-domain (DGTD) based methods and their extensions are developed. For a practical electronic system, apart from the EM part, the presence of lumped elements must be considered. Therefore, a hybrid EM-circuit solver is indispensable. For the EM subsystem governed by Maxwell’s equations, it is solved by DGTD with an explicit time-marching scheme. For the lumped subsystem, circuit equations are constructed based on either the modified nodal analysis (MNA) derived from Kirchoff’s current law or the basic I-V relations. By introducing a port voltage and current, the EM and circuit solvers are synchronized in the temporal sequence at the lumped port. This synchronized EM-circuit solver is free of instabilities even though nonlinear circuit elements are involved.
For open-region scattering problem analysis, a novel approach by integrating the time-domain boundary integral (TDBI) algorithm with DGTD is developed. At the truncation boundary, the fields required for the incoming flux in DGTD is calculated using the TDBI from the equivalent currents over a Huygens’ surface enclosing the scatterer. The hybrid DGTD-BI ensures that the radiation condition is mathematically exact and the resulting computation domain is as small as possible since the truncation boundary conforms to scatterer’s shape.
By considering the one atom-thick graphene as an infinitesimally thin conductive sheet, a surface impedance boundary condition (SIBC) augmented DGTD algorithm is developed to model the graphene. With this SIBC, straightforward volumetric discretization is avoided, thus significantly reducing the memory cost and meanwhile alleviating the restriction on the minimum time marching size. Due to the complex relation between the surface conductivity σg (comprising contributions from both intraband and interband) and the angular frequency ω, direct mapping the numerical flux from the frequency to the time-domain via inverse Fourier transform is not available. To address this issue, a fast-relaxing vector-fitting (FRVF) technique is used to approximate the σg by rational functions in the Laplace-domain. Via inverse Laplace transform, the time-domain matrix equations are obtained in integral forms of time t. Resorting to finite integral technique (FIT), a fully-discrete matrix system can be achieved.
Finally, to consider the impact of random parameters on realistic electronic systems, a stochastic solver based on DGTD and sparse-grid collocation method is developed. To reduce the number of supporting, an adaptive strategy is utilized by using the local hierarchical surplus as error indicator. To improve the flexibility of the proposed algorithm, both piecewise linear and Lagrange polynomial basis functions are employed to handle different stochastic systems. Particularly, the piecewise linear basis function is more efficient for non-smoothly observables while Lagrange polynomials are more suitable for smoothly observables. With these strategies, the singularities and quick variations can be efficiently captured but with very small number of collocation points.
The above proposed algorithms are demonstrated by various examples, the accuracy, efficiency, and robustness of these algorithms are clearly observed.published_or_final_version
Electrical and Electronic Engineering
Doctoral
Doctor of Philosophy
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Beaver, Joseph Edward. "Paleolithic Ungulate Hunting: Simulation and Mathematical Modeling for Archaeological Inference and Explanation." Diss., The University of Arizona, 2007. http://hdl.handle.net/10150/194175.
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Formal models, those which explicitly specify the postulates on which they are based, the development of their 'predictions' from those postulates, and the boundary conditions under which they apply, have the potential to be useful tools in archaeological inference and explanation. Detailed examination of one such model, the mathematical model commonly referred to as the diet breadth or prey choice model, shows that its archaeological application is severely complicated by two factors that are difficult or impossible to specify for prehistoric cases: 1) limits on the amount of meat consumable by a food-sharing group before spoilage or loss to scavengers and 2) hunting failure rates. The former introduce significant uncertainties into the food yield or energetic return term of resource rankings, while the latter affect both resource rankings and the resouce encounter rates leading to prey inclusion or exclusion from the diet. Together, these factors make rigorous diet breadth / prey choice model-based inferences from ungulate archaeofaunas impractical, especially in Paleolithic cases. Following success in recent years in making diet breadth model-based inferences about Paleolithic demography from small game analyses that involved computer simulation modeling of prey species' resilience to hunting pressure, the development and employment of a similar model applied to ungulate species reveals that, in general, the differences in the abilty of populations of different ungulate species to sustain harvest rates are not sufficient to allow the relative representation of ungulate remains in archaeological sites to be a viable basis for human demographic inferences. However, in cases where ungulate remains allow the determination of both prey age structure and sex ratio, it is possible to distinguish low exploitation rates, high exploitation rates, and overhunting. In some cases, the sex ratio data may also alter relative hunting resilience levels in such a way that it may be possible to infer that one species was capable of supporting a larger human population than another.
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Mahmoud, Haydar. "MODELING AND SIMULATION OF THE MATHEMATICAL MODEL OF THE HUMAN RENAL SYSTEM." OpenSIUC, 2011. https://opensiuc.lib.siu.edu/theses/754.
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The purpose of this study is to present a functional approach to develop a computer program using Verilog programming language. This software is used to test and validate the overall mathematical model of the renal/body fluid system developed by Uttamsingh et al (1985). This approach can be used to develop advanced algorithms to simulate a wide range of biological systems that need to be investigated without the risk of using humans as experiment subjects; also it can be used to model physiological mechanisms related to medical disorders such as diabetic, cardiac disorders and many others. The Simulation results indicated that the model and the developed software system are in agreement with the responses presented in the literature of the real physiological system within adequate confines; therefore it's valid and suitable for hypothesis testing.
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Nemaranzhe, Lutendo. "A mathematical modeling of optimal vaccination strategies in epidemiology." University of the Western Cape, 2010. http://hdl.handle.net/11394/3065.
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Magister Scientiae - MScWe review a number of compartmental models in epidemiology which leads to a nonlinear system of ordinary differential equations. We focus an SIR, SEIR and SIS epidemic models with and without vaccination. A threshold parameter R0 is identified which governs the spread of diseases, and this parameter is known as the basic reproductive number. The models have at least two equilibria, an endemic equilibrium and the disease-free equilibrium. We demonstrate that the disease will die out, if the basic reproductive number R0 < 1. This is the case of a disease-free state, with no infection in the population. Otherwise the disease may become endemic if the basic reproductive number R0 is bigger than unity. Furthermore, stability analysis for both endemic and disease-free steady states are investigated and we also give some numerical simulations. The second part of this dissertation deals with optimal vaccination strategy in epidemiology. We use optimal control technique on vaccination to minimize the impact of the disease. Hereby we mean minimizing the spread of the disease in the population, while also minimizing the effort on vaccination roll-out. We do this optimization for the cases of SIR and SEIR models, and show how optimal strategies can be obtained which minimize the damage caused by the infectious disease. Finally, we describe the numerical simulations using the fourth-order Runge-Kutta method. These are the most useful references: [G. Zaman, Y.H Kang, II. H. Jung. BioSystems 93, (2008), 240 − 249], [K. Hattaf, N. Yousfi. The Journal of Advanced Studies in Biology, Vol. 1(8), (2008), 383 − 390.], [Lenhart, J.T. Workman. Optimal Control and Applied to Biological Models. Chapman and Hall/CRC, (2007).], [P. Van den Driessche, J. Watmough. Math. Biosci., 7, (2005)], and [J. Wu, G. R¨ost. Mathematical Biosciences and Engineering, Vol 5(2), (2008), 389 − 391].
South Africa
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Grose, Daniel J. "Mathematical modelling and simulation of irrigation sprinklers." Thesis, Cranfield University, 1999. http://dspace.lib.cranfield.ac.uk/handle/1826/9603.
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A set of equations suitable for describing the dynamics of a liquid droplet - gas mixture (spray) have been developed. The equations are arrived at by considering the spray as a multiphase continuum within which the gas and droplets of different sizes constitute individual phases. By ignoring droplet-droplet interactions and considering the gas phase as an inviscid fluid a simplified form of the equations of motion has been arrived at. The equations are considered in one dimension and used to describe the dynamics of the interior of spray produced by a large or medium scale irrigation sprinkler. When combined with data representing the distribution of droplet diameters within the spray this model can be used to predict the water application produced by a sprinkler operating in windy conditions. Such simulations have been undertaken to predict the water application from static sprinklers and the results validated by comparison with data obtained experimentally. A simulation methodology is used to determine the uniformity of water application produced by a travelling sprinkler. By considering the results of large number of simulations produced using meteorological data spanning several years the manner in which the simulation can be used for determining optimum irrigation practice is demonstrated. A simple model has been developed for predicting the water application from a travelling sprinkler operating in still air. The model can be used for obtaining first approximations to optimum operating conditions and provides a means for easily quantifying the performance of a given sprinkler. Further use of the model may be made for aiding in the design and control of irrigation sprinklers.
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Osman, Mohamad Hussein. "Mathematical modelling and simulation of biofuel cells." Thesis, University of Southampton, 2013. https://eprints.soton.ac.uk/363762/.
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Bio-fuel cells are driven by diverse and abundant bio-fuels and biological catalysts. The production/consumption cycle of bio-fuels is considered to be carbon neutral and, in principle, more sustainable than that of conventional fuel cells. The cost benefits over traditional precious-metal catalysts, and the mild operating conditions represent further advantages. It is important that mathematical models are developed to reduce the burden on laboratory based testing and accelerate the development of practical systems. In this study, recent key developments in bio-fuel cell technology are reviewed and two different approaches to modelling biofuel cells are presented, a detailed physics-based approach, and a data-driven regression model. The current scientific and engineering challenges involved in developing practical bio-fuel cell systems are described, particularly in relation to a fundamental understanding of the reaction environment, the performance and stability requirements, modularity and scalability. New materials and methods for the immobilization of enzymes and mediators on electrodes are examined, in relation to performance characteristics and stability. Fuels, mediators and enzymes used (anode and cathode), as well as the cell configurations employed are discussed. New developments in microbial fuel cell technologies are reviewed in the context of fuel sources, electron transfer mechanisms, anode materials and enhanced O2 reduction. Multi-dimensional steady-state and dynamic models of two enzymatic glucose/air fuel cells are presented. Detailed mass and charge balances are combined with a model for the reaction mechanism in the electrodes. The models are validated against experimental results. The dynamic performance under different cell voltages is simulated and the evolution of the system is described. Parametric studies are performed to investigate the effect of various operating conditions. A data-driven model, based on a reduced-basis form of Gaussian process regression, is also presented and tested. The improved computational efficiency of data-driven models makes them better candidates for modelling large complex systems.
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Venkatachalam, Sangeeta. "Modeling Infectious Disease Spread Using Global Stochastic Field Simulation." Thesis, University of North Texas, 2006. https://digital.library.unt.edu/ark:/67531/metadc5335/.
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Susceptibles-infectives-removals (SIR) and its derivatives are the classic mathematical models for the study of infectious diseases in epidemiology. In order to model and simulate epidemics of an infectious disease, a global stochastic field simulation paradigm (GSFS) is proposed, which incorporates geographic and demographic based interactions. The interaction measure between regions is a function of population density and geographical distance, and has been extended to include demographic and migratory constraints. The progression of diseases using GSFS is analyzed, and similar behavior to the SIR model is exhibited by GSFS, using the geographic information systems (GIS) gravity model for interactions. The limitations of the SIR and similar models of homogeneous population with uniform mixing are addressed by the GSFS model. The GSFS model is oriented to heterogeneous population, and can incorporate interactions based on geography, demography, environment and migration patterns. The progression of diseases can be modeled at higher levels of fidelity using the GSFS model, and facilitates optimal deployment of public health resources for prevention, control and surveillance of infectious diseases.
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Gao, Wenzhong. "New methodology for power system modeling and its application in machine modeling and simulation." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/14732.
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Harutyunyan, Mané [Verfasser], and Bernd [Akademischer Betreuer] Simeon. "Mathematical Modeling and Numerical Simulation of Magnetoelastic Coupling / Mané Harutyunyan ; Betreuer: Bernd Simeon." Kaiserslautern : Technische Universität Kaiserslautern, 2019. http://d-nb.info/1179776887/34.
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Tari, Hafez. "Robust and Efficient Mathematical Techniques for Modeling and Simulation of Smart Material Systems." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1408371296.
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Olsén, Jörgen. "Stochastic Modeling and Simulation of the TCP protocol." Doctoral thesis, Uppsala University, Mathematical Statistics, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3534.
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The success of the current Internet relies to a large extent on a cooperation between the users and the network. The network signals its current state to the users by marking or dropping packets. The users then strive to maximize the sending rate without causing network congestion. To achieve this, the users implement a flow-control algorithm that controls the rate at which data packets are sent into the Internet. More specifically, the Transmission Control Protocol (TCP) is used by the users to adjust the sending rate in response to changing network conditions. TCP uses the observation of packet loss events and estimates of the round trip time (RTT) to adjust its sending rate.
In this thesis we investigate and propose stochastic models for TCP. The models are used to estimate network performance like throughput, link utilization, and packet loss rate. The first part of the thesis introduces the TCP protocol and contains an extensive TCP modeling survey that summarizes the most important TCP modeling work. Reviewed models are categorized as renewal theory models, fixed-point methods, fluid models, processor sharing models or control theoretic models. The merits of respective category is discussed and guidelines for which framework to use for future TCP modeling is given.
The second part of the thesis contains six papers on TCP modeling. Within the renewal theory framework we propose single source TCP-Tahoe and TCP-NewReno models. We investigate the performance of these protocols in both a DropTail and a RED queuing environment. The aspects of TCP performance that are inherently depending on the actual implementation of the flow-control algorithm are singled out from what depends on the queuing environment.
Using the fixed-point framework, we propose models that estimate packet loss rate and link utilization for a network with multiple TCP-Vegas, TCP-SACK and TCP-Reno on/off sources. The TCP-Vegas model is novel and is the first model capable of estimating the network's operating point for TCP-Vegas sources sending on/off traffic. All TCP and network models in the contributed research papers are validated via simulations with the network simulator ns-2.
This thesis serves both as an introduction to TCP and as an extensive orientation about state of the art stochastic TCP models.
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Ding, Ding. "Modeling and simulation of highway traffic using a cellular automaton approach." Thesis, Uppsala universitet, Matematisk statistik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-167359.
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Vedovoto, João Marcelo. "Mathematical and numerical modeling of turbulent reactive flows using a hybrid LES/PDF methodology." Chasseneuil-du-Poitou, Ecole nationale supérieure de mécanique et d'aérotechnique, 2011. http://www.theses.fr/2011ESMA0015.
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Ce travail de thèse est consacré au développement d'une approche numérique permettant de conduire des simulations "low Mach number" d'écoulements réactifs. L'algorithme d'intégration retenu pour procéder à la résolution des équations de transport repose sur une méthode implicite de prédiction-correction (méthode de projection). Une contrainte physique est retenue pour garantir que le champ de vitesse est résolue correctement. Le code de calcul est soumis à plusieurs séries de vérifications préliminaires basées sur l'emploi de la méthode solution manufacturées pour des conditions incompressibles d'abord puis à masse volumique variable qui permettent de statuer quant à la bonne implémentation des schémas numériques retenus. Les performances de l'outil numérique en terme de stabilité et de robustesse sont elles-aussi analysées dans des situations simples : couche de mélange à densité variable en développement spatial et temporel. Le modèle numérique final repose sur l'emploi d'une méthode hybride LES/PDF. Pour ce qui concerne la représentation de la turbulence, deux fermetures sont implémentées pour représenter l'effet des fluctuations de vitesse non résolues. Il s'agit du modèle de Smagorinsky dans sa version dynamique ou non. La spécification de conditions aux limites turbulentes réalistes est elle-aussi analysée en détail et trois approches différentes sont considérées. Pour ce qui concerne la combustion, l'influence des fluctuations de composition aux échelles non résolues est pris en compte par le biais d'une résolution de la PDF scalaire de sous maille. Le modèle de PDF correspondant repose sur l'emploi d'une méthode de Monte Carlo. Des équations différentielles stochastiques, équivalentes aux équations de Fokker-Planck, sont résolues pour la variable de progrès de la réaction chimique. L'objectif final est aussi de pouvoir procéder, à moyen terme, à des simulations LES en géométries complexes et l'emploi du calcul distribué est essentiel. De ce point de vue, la méthode de décomposition de domaine retenue dans ce travail montre des niveau de performances relativement satisfaisants. Les capacités du modèle numérique résultant de ces développements sont illustrées sur deux configurations expérimentales. La première géométrie correspond à un écoulement très fortement turbulent de réactifs pré-mélangés dans un canal bidimensionnel. La seconde correspond à un jet rapide et non confiné de réactifs pré-mélangésThe present work is devoted to the development and implementation of a computational framework to perform numerical simulations of low Mach number turbulent reactive flows. The numerical algorithm designed for solving the transport equations relies on a fully implicit predictor-corrector integration scheme. A physically consistent constraint is retained to ensure that the velocity field is solved correctly, and the numerical solver is extensively verified using the Method of Manufactured Solutions (MMS) in both incompressible and variable-density situations. The final computational model relies on a hybrid Large Eddy Simulation / transported Probability Density Function (LES-PDF) framework. Two different turbulence closures are implemented to represent the residual stresses: the classical and the dynamic Smagorinsky models. The specification of realistic turbulent inflow boundary conditions is also addressed in details, and three distinct methodologies are implemented. The crucial importance of this issue with respect to both inert and reactive high fidelity numerical simulations is unambiguously assessed. The influence of residual sub-grid scale scalar fluctuations on the filtered chemical reaction rate is taken into account within the Lagrangian PDF framework. The corresponding PDF model makes use of a Monte Carlo technique: Stochastic Differential Equations (SDE) equivalent to the Fokker-Planck equations are solved for the progress variable of chemical reactions. With the objective of performing LES of turbulent reactive flows in complex geometries, the use of distributed computing is mandatory, and the retained domain decomposition algorithm displays very satisfactory levels of speed-up and efficiency. Finally, the capabilities of the resulting computational model are illustrated on two distinct experimental test cases: the first is a two-dimensional highly turbulent premixed flame established between two streams of fresh reactants and hot burnt gases which is stabilized in a square cross section channel flow. The second is an unconfined high velocity turbulent jet of premixed reactants stabilized by a large co-flowing stream of burned products
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Sanjari, Pirmahaleh Seyedeh Azin. "Examining Mathematical Modeling of Fifth Grade Students Using InteractiveSimulations." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1563290145665376.
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Alhassani, Maha. "Mathematical Modeling of Immuno-radioprotector Delivery System Using a Monoclonal Antibody." Thesis, Université d'Ottawa / University of Ottawa, 2015. http://hdl.handle.net/10393/32533.
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Amifostine (WR-2721, delivered as Ethyol) is a radioprotector agent that reduces
the likelihood of early and/or late biological effects by eliminating free radical particles
during ionizing radiation fraction (radiotherapy). It activates in under normal tissues
conditions to reduce mutation and fraction in DNA. Among 4000 prodrug compounds,
amifostine is the only agent has been approved from the US Food and Drug
Administration in clinical purposes. The main effective mechanisms of amifostine are
based on scavenging for free radical, improving for DNA repair step and indication of
cellular hypoxia. In the same time, this drug is not widely used around the world for
different reasons mainly its high cost and toxicity level (lethal dose). Conjugating a
monoclonal antibody with amifostine by a suitable linker is a process of Antibody Drug
Conjugate producing immuno-radioprotector molecule hypothesis. Administrated
molecule is an approach of targeted delivery therapy that increases the dosage uptake into
particular area of treatment to minimize the dose distribution in non-targeted area in the
body.
In the present work, we proposed a three-compartment system model to simulate
the two-pore theory pathway of an immuno-radioprotector molecule when it is crossing
the physiological barriers. The model investigated its distribution and elimination in
porous media (with both large and small pores) within a pharmacokinetics
compartmented model approach.
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Boyaval, Sébastien. "Mathematical modelling and numerical simulation in materials science." Phd thesis, Université Paris-Est, 2009. http://tel.archives-ouvertes.fr/tel-00499254.
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In a first part, we study numerical schemes using the finite-element method to discretize the Oldroyd-B system of equations, modelling a viscoelastic fluid under no flow boundary condition in a 2- or 3- dimensional bounded domain. The goal is to get schemes which are stable in the sense that they dissipate a free-energy, mimicking that way thermodynamical properties of dissipation similar to those actually identified for smooth solutions of the continuous model. This study adds to numerous previous ones about the instabilities observed in the numerical simulations of viscoelastic fluids (in particular those known as High Weissenberg Number Problems). To our knowledge, this is the first study that rigorously considers the numerical stability in the sense of an energy dissipation for Galerkin discretizations. In a second part, we adapt and use ideas of a numerical method initially developped in the works of Y. Maday, A.T. Patera et al., the reduced-basis method, in order to efficiently simulate some multiscale models. The principle is to numerically approximate each element of a parametrized family of complicate objects in a Hilbert space through the closest linear combination within the best linear subspace spanned by a few elementswell chosen inside the same parametrized family. We apply this principle to numerical problems linked : to the numerical homogenization of second-order elliptic equations, with two-scale oscillating diffusion coefficients, then ; to the propagation of uncertainty (computations of the mean and the variance) in an elliptic problem with stochastic coefficients (a bounded stochastic field in a boundary condition of third type), last ; to the Monte-Carlo computation of the expectations of numerous parametrized random variables, in particular functionals of parametrized Itô stochastic processes close to what is encountered in micro-macro models of polymeric fluids, with a control variate to reduce its variance. In each application, the goal of the reduced-basis approach is to speed up the computations without any loss of precision
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Wang, Yu. "Large scale agent interactions : mathematical modelling and simulation." Thesis, Imperial College London, 2006. http://hdl.handle.net/10044/1/11286.
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Deville, Manon. "Mathematical Modeling of enhanced drug delivery by mean of Electroporation or Enzymatic treatment." Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0755/document.
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Cette thèse présente des travaux concernant la modélisation mathématique de deux méthodes physiques existantes pour surmonter les barrières biologiques s’opposant à l’administration efficace de médicaments. Dans la première partie, plusieurs manières de modéliser l’électroporation sont exposées, aux échelles tissulaire et cellulaire. Des modèles phénoménologiques existants d’électroporation tissulaire sont présentés et comparés numériquement. Puis un modèle macroscopique d’électroporation est déduit d’un modèle d’électroporation cellulaire bien établi en utilisant des techniques d’homogénéisation. Dans la seconde partie, un nouveau modèle poroélastique est introduit pour décrire les écoulements dans un tissu biologique. Celui-ci prend en compte la dégradation tissulaire consécutive à un traitement par enzyme. Pour finir, un algorithme d’optimisation est proposé dans le but de déterminer un protocole optimal pour effectuer un traitement enzymatiqueThis PhD thesis is devoted to the mathematical modeling and simulation of two existing physical methods to overcome the biological barriers to drug delivery. In the first part, several ways to model electroporation are considered, from the cell scale to the tissue scale. Existing phenomenological models of tissue electroporation are presented and numerically compared. Then a macroscopic model of electroporation is derived from a well-established model of cell elecroporation using homogenization techniques. In the second part, a new poroelastic model for the flows in biological tissues is presented to account for tissue degradation after an enzymatic treatment. To finish, an optimization algorithm is suggested in attempt to determine an optimal protocol when considering enzyme based therapies
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Chakravarthy, Veerathu Kalyana. "Stochastic subgrid modeling of turbulent premixed flames." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/12934.
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Sreeranganathan, Arun. "Realistic micromechanical modeling and simulation of two-phase heterogeneous materials." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24607.
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Thesis (Ph.D.)--Materials Science and Engineering, Georgia Institute of Technology, 2008.Committee Chair: Gokhale, Arun; Committee Member: Gall, Kenneth; Committee Member: Garmestani, Hamid; Committee Member: Kurtis, Kimberly; Committee Member: Thadhani, Naresh
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Audebert, Chloé. "Mathematical liver modeling : hemodynamics and function in hepatectomy." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066077/document.
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L’ablation partielle du foie est une chirurgie qui intervient dans le traitement des lésions du foie et lors d’une transplantation partielle de foie. Les relations entre l’hémodynamique du foie, son volume et ses fonctions restent à élucider pour mieux comprendre les causes des complications de ces chirurgies. Lors de la chirurgie, l’hémodynamique du foie est altérée suite à l’augmentation de la résistance au flux sanguin de l’organe. La régénération du foie semble dépendante des changements de débit et de pression dans la veine porte. D’autre part, comme le foie reçoit 25% du débit cardiaque, la chirurgie impacte la circulation sanguine globale. Dans ce contexte, le premier objectif est de mieux comprendre, grâce à des modèles mathématiques, l’influence de l’hépatectomie sur l’hémodynamique. Le second objectif est l’analyse de la perfusion et de la fonction du foie. Premièrement, la procédure chirurgicale, les conditions expérimentales ainsi que les mesures obtenues sont détaillées. Ensuite, les valeurs moyennes mesurées lors de douze chirurgies sont reproduites par un modèle de circulation entière, basé sur des équations différentielles ordinaires. Lors des différentes hépatectomies, des changements de forme de courbe sont observés. Un modèle de circulation entière, basée sur des équations 1D et 0D est proposé pour analyser ces changements. Ce travail pourrait permettre une meilleure compréhension des changements d’architecture du foie induits par l’hépatectomie. Puis, le transport dans le sang d’un composé ainsi que son traitement par le foie sont modélisés. Un modèle pharmacocinétique est développé et grâce aux mesures, les paramètres du modèle sont estimésMajor liver resection is being performed to treat liver lesions or for adult-to-adult living donor liver transplantation. Complications of these surgeries are related to a poor liver function. The links between liver hemodynamics, liver volume and liver function remain unclear and are important to better understand these complications. The surgery increases the resistance to blood flow in the organ, therefore it modifies liver hemodynamics. Large modifications of the portal vein hemodynamics have been associated with poor liver regeneration. Moreover the liver receives 25% of the cardiac outflow, therefore liver surgery may impact the whole blood circulation. In this context, the first goal is to investigate with mathematical models the impact of liver surgery on liver hemodynamics. The second goal is to study the liver perfusion and function with mathematical models. The first part describes the experimental conditions and reports the measurements recorded. Then, the second part focuses on the liver hemodynamics during partial hepatectomy. On one hand, the hemodynamics during several surgeries is quantitatively reproduced and explained by a closed-loop model based on ODE. On the other hand, the change of waveforms observed after different levels of liver resection is reproduced with a model of the global circulation, including 0D and 1D equations. This may contribute to a better understanding of the change of liver architecture induced by hepatectomy. Next, the transport in blood of a compound is studied. And a pharmacokinetics model and its parameter identification are developed to quantitatively analyze indocyanine green fluorescence dynamics in the liver tissue
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Moon, Hyun. "Mathematical modeling and simulation analysis of hydraulic fracture propagation in three-layered poro-elastic media." The Ohio State University, 1992. http://rave.ohiolink.edu/etdc/view?acc_num=osu1335201786.
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Ozogur, Sureyya. "Mathematical Modelling Of Enzymatic Reactions, Simulation And Parameter Estimation." Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12605856/index.pdf.
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A deep and analytical understanding of the human metabolism grabbed attention of scientists from biology, medicine and pharmacy. Mathematical models of metabolic pathways offer several advances for this deep and analytical understanding due to their incompensable potential in predicting metabolic processes and anticipating appropriate interventions when required. This thesis concerns mathematical modeling analysis and simulation of metabolic pathways. These pathways include intracellular and extracellular compounds such as enzymes, metabolites, nucleotides and cofactors. Experimental data and available knowledge on metabolic pathways are used in constituting a mathematical model. The models are either in the form of nonlinear ordinary differential equations (ode's) or differential algebraic equations (dae'
s). These equations are composed of kinetic parameters such as kinetic rate constants, initial rates and concentrations of metabolites. The non-linear nature of enzymatic reactions and large number of parameters cause trouble in efficient simulation of those reactions. Metabolic engineering tries to simplify these equations by reducing the number of parameters. In this work, enzymatic system which includes Creatine Kinase, Hexokinase and Glucose 6-Phosphate Dehydrogenase (CK-HK-G6PDH) is modeled in the form of dae'
s, solved numerically and the system parameters are estimated. The numerical results are compared with the results from an existing work in literature. We demonstrated that, our solution method based on direct solution of the CK-HK-G6PDH system significantly from simplified solutions. We also showed that genetic algorithm(GA) for parameter estimation, provides much clear results to the experimental values of the metabolite, especially with NADPH. Keywords: metabolic engineering, kinetic modelling, biochemical reactions, enzymatic reactions, differential algebraic equations, parameter estimation, genetic algorithm.
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Quedeville, Vincent. "Mathematical analysis, modelling and simulation of microbial population dynamics." Thesis, Toulouse, INPT, 2020. http://www.theses.fr/2020INPT0033.
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La physiologie d’organismes unicellulaires est la conséquence d’un métabolisme central dont le bilan entrée-sortie témoigne à la fois de la richesse du milieu de culture des cellules et de leur état propre. Lorsque des bactéries sont cultivées dans un fermenteur biologique alimenté en un point, transportées dans un écoulement turbulent, elles doivent composer avec des gradients de concentration tout au long de leur séjour dans le réacteur. Simuler cette physique dans une démarche de modélisation multi-échelle nécessite de prendre en compte les lois, bien connues, de l’hydrodynamique, mais aussi de la biochimie des cellules, laquelle est encore assez mal comprise à l’heure actuelle. De plus, le coût prohibitif des expériences numériques impose de réduire les modèles afin de limiter la durée des calculs à quelques semaines. Dans ce contexte, l’attention a été portée sur la phase biologique. La dynamique de la population bactérienne est donnée par une équation intégro-différentielle de transport-rupture dans l’espace des propriétés internes des particules. Le choix des variables les plus à-propos est d’une importance capitale pour rendre compte au mieux de l’évolution temporelle de l’état des cellules au cours de leur trajectoire dans le fermenteur, laquelle est assimilable à un processus markovien. La longueur des micro-organismes rend compte de leur morphologie et leur progression dans le cycle cellulaire, et la vitesse d’assimilation du substrat environnant du transfert de matière avec la phase liquide. La résultante en est le calcul des flux d’entrée dans le métabolisme central des organismes dont les sorties sont les vitesses apparentes d’allongement et, en cas de sur-assimilation, mobilisation de réactions périphériques de combustion de l’excès de matière organique. Outre leur histoire propre, les rendus métaboliques des individus peuvent être impactés par la disponibilité du substrat à leur voisinage, laquelle résulte de l’alimentation et de l’état de mélange du réacteur. Les variables d’état sont à support compact, ce qui soulève la question du caractère bien posé du problème mathématique, de même que résoudre une EDP sur un borné est traditionnellement plus difficile que dans ℝ^n, n∈ℕ. Il est montré que la solution de Malthus de l’équation de transport-rupture est de classe C¹ dès que la fragmentation l’emporte sur la croissance des cellules près du bord droit du support de la distribution en taille. Dans l’ensemble, la solution est continue à chaque instant dans l’espace des états. Ces résultats autorisent la mise en place d’algorithmes de résolution (dans ce travail, par méthodes de Monte- Carlo, Volumes Finis et Quadrature de MOMents) du problème bien posé, lesquels sont exploités pour simuler cinq expériences de génie biochimique dont les conclusions sont détaillées dans la littératureThe physiology of unicellular organisms results from a central metabolism which input-output balance accounts for both the cells’ state and their culture medium’s abundance. When bacteria are cultivated in a locally fed fermenter and transported in a turbulent flow, they have to deal with concentration gradients throughout their trajectory in the reactor. Simulating this physics in a multiscale modelling approach requires taking into account not only the well-known laws of hydrodynamics, but also the cells’ biochemistry which is still ill-understood to date. Moreover, the prohibitive cost of the numerics forces to reduce the models to constrain the duration of the experiments to a few weeks. In this context, special consideration has been given to the biological phase. The bacteria population dynamics is given by an integro-differential transport-rupture equation in the space of the particles’ inner coordinates. Picking the most appropriate variables is of paramount importance to best report the time evolution of the cells’ state throughout their history in the fermenter, the latter being comparable to a markovian process. The microorganisms’ length testifies to their morphology and their progress in the cell cycle, whereas the uptake rate of the surrounding resources leads to an evaluation of the material transfer between the liquid and biotic phases. The result is the estimation of the source term in the organisms’ central metabolism which outputs are the apparent rate of anabolism and, if over-uptake, activation of peripheral reactions to combust the surplus in organic compounds. Beyond their own history, the individuals’ metabolic yields can be impacted by the substrate availability at their neighbourhood, which stems from the feeding and the level of mixing in the reactor. The state variables have a compact support, what raises the question of the mathematical problem’s wellposedness, similarly as solving a PDE over a bounded set is traditionally more difficult than over ℝ^n, n∈ℕ. It is shown that the Malthus eigenfunction associated with the transport-rupture equation is C¹ as soon as fragmentation trumps cell growth near the right-hand edge of the size-distribution’s support. All in all, the solution is continuous at each time in the state space. These results allow the implementation of numerical codes to solve (in this work, by Monte-Carlo, Finite Volume, or Quadrature of MOMents methods) the well-posed problem, the algorithms being exploited to simulate five biochemical engineering experiments which conclusions are detailed in the literature
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Patel, Chirag S. "Wireless channel modeling, simulation, and estimation." Diss., Available online, Georgia Institute of Technology, 2006, 2006. http://etd.gatech.edu/theses/available/etd-03282006-200818/.
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Thesis (Ph. D.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2006.Andrew, Alfred, Committee Member ; Durgin, Gregory, Committee Member ; Li, Geoffrey, Committee Member ; Ingram, Mary Ann, Committee Member ; Stuber, Gordon, Committee Chair.
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Ahmed, Ibrahim H. I. "Mathematical modeling of an epidemic under vaccination in two interacting populations." Thesis, University of the Western Cape, 2011. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_8857_1360922452.
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In this dissertation we present the quantitative response of an epidemic of the so-called SIR-type, in a population consisting of a local component and a migrant component. Each component can be divided into three classes, the susceptible individuals, usually denoted by S, who are uninfected but may contract the disease, infected individuals (I) who are infected and can spread the disease to the susceptible individuals and the class (R) of recovered individuals. If a susceptible individual becomes infected, it moves into the infected class. An infected individual, at recovery, moves to the class R. Firstly we develop a model describing two interacting populations with vaccination. Assuming the vaccination rate in both groups or components are constant, we calculate a threshold parameter and we call it a vaccination reproductive number. This invariant determines whether the disease will die out or becomes endemic on the (in particular, local) population. Then we present the stability analysis of equilibrium points and the effect of vaccination. Our primary finding is that the behaviour of the disease free equilibrium depend on the vaccination rates of the combined population. We show that the disease free equilibrium is locally asymptotically stable if the vaccination reproductive number is less than one. Also our stability analysis show that the global stability of the disease free equilibrium depends on the basic reproduction number, not the vaccination reproductive number. If the vaccination reproductive number is greater than one, then the disease free equilibrium is unstable and there exists three endemic equilibrium points in our model. Two of these three endemic equilibria are so-called boundary equilibrium points, which means that the infection is only in one group of the population. The third one which we focus on is the general endemic point for the whole system. We derive a threshold condition that determines whether the endemic equilibria is locally asymptotically stable or not. Secondly, by assuming that the rate of vaccination in the migrant population is constant, we apply optimal control theory to find an optimal vaccination strategy in the local population. Our numerical simulation shows the effectiveness of the control strategy. This model is suitable for modeling the real life situation to control many communicable diseases. Models similar to the model used in the main contribution of our dissertation do exist in the literature. In fact, our model can be regarded as being in-between those of [Jia et al., Theoretical Population Biology 73 (2008) 437-448] and [Piccolo and Billings, Mathematical and Computer Modeling 42 (2005) 291-299]. Nevertheless our stability analysis is original, and furthermore we perform an optimal control study whereas the two cited papers do not. The essence of chapter 5 and 6 of this dissertation is being prepared for publication.
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Calhoon, William Henry Jr. "On subgrid combustion modeling for large-eddy simulations." Diss., Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/12336.
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Zhu, Xiaoxiang Ph D. Massachusetts Institute of Technology. "Mathematical modeling and simulation of intravascular drug delivery from drug-eluting stents with biodegradable PLGA coating." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/98152.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Chemical Engineering, 2014.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 178-190).
Drug-eluting stents (DES) are commonly used in coronary angioplasty procedures. A DES elutes drug compounds from a thin polymeric coating into the surrounding coronary artery tissue to reduce in-stent restenosis (a significant lumen loss due to growth of vascular tissue). Biodurable (non-erodible) polymers are often used in the current DES coatings, which stay permanently in the patients. While promising treatment results were obtained, in-stent restenosis remains an issue and late in-stent thrombosis, which is associated with hypersensitivities to the polymer coatings, is also reported. Increasing interests have been raised towards the design of a more biocompatible coating, in particular a poly(lactic acid-co-glycolic acid) (PLGA) coating, for DES applications to improve the drug delivery and reduce adverse outcomes in patients. This dissertation aims to develop a mathematical model for describing the process of drug release from a biodegradable PLGA stent coating, and subsequent drug transport, pharmacokinetics, and distribution in the arterial wall. A model framework is developed in the first part of the dissertation, where a biodurable stent coating is considered, and the intravascular delivery of a hydrophobic drug from an implanted DES in a coronary artery is mathematically modeled. The model integrates drug diffusion in the coating with drug diffusion and reversible drug binding in the arterial wall. The model was solved by the finite volume method. The drug diffusivities in the coating and in the arterial wall were investigated for the impact on the drug release and arterial drug uptake. In particular, anisotropic vascular drug diffusivities result in slightly different average arterial drug levels but can lead to very different spatial drug distributions, and is likely related to the reported non-uniform restenosis thickness distribution in the artery cross-section. The second part of the dissertation focuses on modeling drug transport in a biodegradable poly(D,L-lactic-co-glycolic acid) (PLGA) coating. A mathematical model for the PLGA degradation, erosion, and coupled drug release from PLGA stent coating is developed and validated. An analytical expression is derived for PLGA mass loss. The drug transport model incorporates simultaneous drug diffusion through both the polymer solid and the liquid-filled pores in the coating, where an effective drug diffusivity model is derived taking into account factors including polymer molecular weight change, stent coating porosity change, and drug partitioning between solid and aqueous phases. The model predicted in vitro sirolimus release from PLGA stent coating, and demonstrated the significance of the developed model by comparing with existing drug transport models. An integrated model for intravascular drug delivery from a PLGA-coated DES is developed in the last part of the dissertation. The integrated model describes the processes of drug release in a PLGA coating and subsequent drug delivery, distribution, and drug pharmacokinetics in the arterial wall. Model simulations first compared a biodegradable PLGA coating with a biodurable coating for stent-based drug delivery. The simulations further investigated drug internalization, interstitial fluid flow in the arterial wall, and stent embedment for impact on the drug release and arterial drug distribution of a PLGA-coated stent. These three factors greatly change the average drug concentrations in the arterial wall. Each factor leads to significant and distinguished alterations in the arterial drug distribution that can potentially influence the treatment outcomes. The developed model here provides the basis of a design tool for evaluating and studying a PLGA coating for stent applications. Simulations using the model helped to provide insights into the potential impacts of various factors that can affect the efficacy of drug delivery. With the developed model, optimization of the model parameters can also be performed for future exploration on the design of PLGA-coated drug-eluting stents.
by Xiaoxiang Zhu.
Ph. D.
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Wargnier, Quentin. "Mathematical modeling and simulation of non-equilibrium plasmas : application to magnetic reconnection in the Sun atmosphere." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLC066.
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La capacité de modéliser, simuler et prédire le phénomène de reconnexion magnétique est un enjeu crucial pour de nombreuses applications (ITER, plasmas astrophysiques) et impacte la prédiction du « temps solaire » et des « orages magnétiques » pouvant perturber les satellites. L’enjeu scientifique fondamental est la description du transfert instationnaire d’énergie magnétique en énergie cinétique et thermique, encore hors d’atteinte des modèles magnéto-hydrodynamique (MHD) actuels. L’objectif premier de la thèse est le développement d’un modèle fluide cohérent de plasma magnétisé hors équilibrethermique et chimique avec une description détaillée des effets dissipatifs basée sur la théorie cinétique des gaz et une bonne structure mathématique. Le second repose sur le développement d’une stratégie numérique innovante, précise et robuste, dans un code de calcul massivement parallèle avec adaptation demaillage permettant de capturer tout le spectre d’échelle en jeu et la raideur numérique en résultant. L’ensemble des coefficients de transport, la thermodynamique et la chimie correspondante seront étudiés et comparés aux données préalablement utilisées dans le domaine. Puis on montrera que le modèle et sa simulation, issus d’un travail transdisciplinaire impliquant ingénierie, physique des plasmas, physique solaire, mathématique, et calcul scientifique et parallèle, est capable de reproduire correctement la physique du phénomène. La validation de l’approche à travers une série de cas test issus de l’application à la dynamique de l’atmosphère solaire en lien avec la NASA et le VKI permettra de disposer d’un outil, ouvert à la communauté, capable de lever plusieurs verrous scientifiques et technologiquesThe ability to model, simulate and predict magnetic reconnection (MR) is a stumbling block in order to predict space weather and geomagnetic storms, which can lead to great perturbation of satellites. Some fundamental aspects of MR are not yet well understood. The scientific issue at stake is the proper description of the unsteady energy transfer from magnetic energy to kinetic and thermal energy, which is still out of reach for the standard Magneto-hydrodynamics (MHD) models. The first objective of the present project is to develop a coherent fluid model for magnetized plasmas out of thermal and chemical equilibrium with a detailed description of the dissipative effects based on kinetic theory of gases, which thus inherits a proper mathematical structure. The second goal is the development of a new numerical strategy, with high accuracy and robustness, based on a massively parallel code with adaptive mesh refinement able to cope with the full spectrum of scales of the model and related stiffness. The whole set of transport coefficients, thermodynamics relations and chemical rates in this magnetized two-temperature setting will be studied and compared to the one in the literature used in the field. Then, we will show that the model and related numerical strategy, obtained from this transdisciplinary work involving engineering, plasma physics, solar physics, mathematics, scientific computing and HPC, is able to properly reproduce the physics of MR. The validation of the approach through a series of test-cases relevant for the application to the dynamics of solar atmosphere in connection with VKI and NASA will provide a tool, open to the community, capable of resolving several critical scientific and technological issues
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Bonhomme, Phillip. "Circuit modeling of spintronic devices: a SPICE implementation." Thesis, Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51818.
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Every engineer that has worked on designing an integrated circuit has to leverage an under- standing of device physics. Understanding device physics is essential when optimizing a design for speed, power, etc. These characteristics affect the bottom line when considering an integrated circuit used in a particular application. In order for there to be an under- standing of device physics, there must be a device model that is developed for a device of interest. The development of a device model often involves utilizing fundamental physical equations in a manner that is solvable by either analytical or numerical means.
This typically begins by simplifying fundamental physical equations, possibly spanning multiple domains, and considering the physical quantities of interest. In order to make simplifications, assumptions about the underlying physics must be made. It is the process of transitioning from known physics laws to simplified mathematical models that a device modeler spans.
This thesis will cover the device modeling aspects of a new classification of computing devices, spintronics. It will begin by stating the physical assumptions necessary for the operation of spintronic devices. Then it will go the process of deriving the underlying physical equations and stating them in a tractable form with the appropriate boundary conditions. Then these equations will be manipulated and mapped into an equivalent circuit. The equivalent circuits will them be validated against analytical solutions provided from other works. It will then finish by providing example devices that can be simulated with the develop device models, and some optimization results are proposed based off a simplified circuit model.
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Yilmaz, Deniz. "Evaluation And Comparison Of Helicopter Simulation Models With Different Fidelities." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12609707/index.pdf.
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This thesis concerns the development, evaluation, comparison and testing of a UH-1H helicopter
simulation model with various fidelity levels. In particular, the well known minimum
complexity simulation model is updated with various higher fidelity simulation components,
such as the Peters-He inflow model, horizontal tail contribution, improved tail rotor model,
control mapping, ground eect, fuselage interactions, ground reactions etc. Results are compared
with available flight test data. The dynamic model is integrated into the open source
simulation environment called Flight Gear. Finally, the model is cross-checked through evaluations
using test pilots.
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Helal, A. M. "Mathematical modelling and simulation of multistage flash (MSF) desalination plants." Thesis, University of Leeds, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.356426.
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Meesumrarn, Thiraphat. "Simulation of Dengue Outbreak in Thailand." Thesis, University of North Texas, 2018. https://digital.library.unt.edu/ark:/67531/metadc1248484/.
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The dengue virus has become widespread worldwide in recent decades. It has no specific treatment and affects more than 40% of the entire population in the world. In Thailand, dengue has been a health concern for more than half a century. The highest number of cases in one year was 174,285 in 1987, leading to 1,007 deaths. In the present day, dengue is distributed throughout the entire country. Therefore, dengue has become a major challenge for public health in terms of both prevention and control of outbreaks. Different methodologies and ways of dealing with dengue outbreaks have been put forward by researchers. Computational models and simulations play an important role, as they have the ability to help researchers and officers in public health gain a greater understanding of the virus's epidemic activities.
In this context, this dissertation presents a new framework, Modified Agent-Based Modeling (mABM), a hybrid platform between a mathematical model and a computational model, to simulate a dengue outbreak in human and mosquito populations. This framework improves on the realism of former models by utilizing the reported data from several Thai government organizations, such as the Thai Ministry of Public Health (MoPH), the National Statistical Office, and others. Additionally, its implementation takes into account the geography of Thailand, as well as synthetic mosquito and synthetic human populations. mABM can be used to represent human behavior in a large population across variant distances by specifying demographic factors and assigning mobility patterns for weekdays, weekends, and holidays for the synthetic human population. The mosquito dynamic population model (MDP), which is a component of the mABM framework, is used for representing the synthetic mosquito population dynamic and their ecology by integrating the regional model to capture the effect of dengue outbreak. The two synthetic populations can be linked to each other for the purpose of presenting their interactions, and the Local Stochastic Contact Model for Dengue (LSCM-DEN) is utilized. For validation, the number of cases from the experiment is compared to reported cases from the Thailand Vector Borne Disease Bureau for the selected years.
This framework facilitates model configuration for sensitivity analysis by changing parameters, such as travel routes and seasonal temperatures. The effects of these parameters were studied and analyzed for an improved understanding of dengue outbreak dynamics.
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Kagunda, Joséphine. "Mathematical analysis and dynamical systems : modeling Highland malaria in western Kenya." Thesis, Université de Lorraine, 2012. http://www.theses.fr/2012LORR0271/document.
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L'objectif de cette thèse est de modéliser la transmission du paludisme dans la région montagneuse de l'ouest du Kenya, en se servant des outils de systèmes dynamiques. Nous considérons deux modèles mathématiques. Le premier prend en compte une susceptibilité et une infectivité différentielle dans les métapopulations, et le second un taux de saturation des repas sanguins dans la population des moustiques. Dans le premier modèle, nous considérons plusieurs écosystèmes identifiés comme zones sensibles dans la région montagneuse de l'ouest du Kenya. Dans ce modèle, ces zones sensibles sont considérées comme nos différents patchs. Les populations de chaque patch sont divisées en deux : les enfants et les adultes. Le modèle nous permet d'évaluer le rôle de l'hétérogénéité de l'écosystème et la persistance de l'épidémie dans la région, due à la structuration d'âge. Nous prenons en compte la susceptibilité et l'infectivité différentielle afin d'étendre le modèle d'un patch en un modèle à plusieurs patchs. Après avoir subdivisé la région en n zones sensibles, nous faisons une analyse mathématique du modèle obtenu. Pour effectuer cette analyse, nous utilisons la théorie des systèmes triangulaires, des systèmes dynamiques monotones, des systèmes dynamiques non linéaires anti-monotones et le principe d'invariance de LaSalle. Un des éléments très utilisés dans notre analyse qui est un concept clé en épidémiologie, est le taux de reproduction de base, très souvent noté Ro. Cette quantité, sans dimension, est le nombre moyen de cas secondaires, engendré par un individu infectieux typique durant sa période d'infectiosité, quand il est introduit dans une population constituée entièrement de susceptibles. L'existence et la stabilité du point d'équilibre sans maladie (DFE) sont établies et nous prouvons que le DFE est globalement asymptotiquement stable lorsque Ro<1. Lorsque Ro>1, le modèle admet un point d'équilibre endémique qui est globalement asymptotiquement stable. L'analyse de notre modèle montre que la structuration d'âge réduit l'ampleur de l'infection. En utilisant les données relevées, nous faisons quelques simulations numériques afin de montrer l'impact de la métapopulation et de la structuration d'âge sur le taux de reproduction de base. Dans la seconde partie, nous formulons un modèle de paludisme avec saturation du taux d'alimentation des moustiques qui nous conduit à une incidence non linéaire. Nous démontrons que DFE est globalement asymptotiquement stable si Ro<1. Lorsque Ro>1, il existe un unique point d'équilibre endémique qui est globalement asymptotiquement stable. Des simulations numériques sont faites afin d'illustrer l'impact de la saturation d'alimentation sur le taux de reproduction de baseThe objective of this thesis is to model highland malaria in western Kenya using dynamical systems. Two mathematical models are formulated ; one, on differentiated susceptibility and differentiated infectivity in a metapopulation setting with age structure, the other, a saturated vector feeding rate model with disease induced deaths and varying host and vector populations. In the first model, we consider the different ecosystems identified as malaria hotspots in the western Kenya highlands and consider the ecosystems as different patches. The population in each patch is classified as, either child or, adult. The model will aid in examining the role of ecosystem heterogeneity and age structure to the persistent malaria epidemics in the highlands. We formulate the differentiated susceptibility and infectivity model that extend to multiple patches the well known epidemiological models in one patch. Classifying the hot spots as n patches, we give its mathematical analysis using the theory of triangular system, monotone non-linear dynamical systems, and Lyapunov-Lasalle invariance principle techniques. Key to our analysis is the definition of a reproductive number, Ro, the number of new infections caused by one individual in an otherwise fully susceptible population throughout the duration of the infectious period. The existence and stability of disease-free and endemic equilibrium is established. We prove that the disease free state of the systems is globally asymptotically stable when the basic reproduction number Ro<1, and when Ro>1 an endemic equilibrium is established which is locally and globally asymptotically stable. The model shows that the age structuring reduces the magnitude of infection. Using relevant data we did some simulation, to demonstrate the role played by metapopulation and age structuring on the incidence and Ro. In the second part we formulate a model for malaria with saturation on the vector feeding rates that lead to a nonlinear function in the infection term. The vector feeding rate is assumed, as in the predator prey models, to rise linearly as a function of the host-vector ratio until it reaches a threshold Qv, after which the vector feeds freely at its desired rate. The two populations are variable and drive malaria transmission, such that when the vectors are fewer than hosts, the rate of feeding is determined by the vectors feeding desire, whereas, when the hosts are more than the vectors, the feeding rate is limited by host availability and other feeding sources may have to be sought by the vector. Malaria induced deaths are introduced in the host population, while the vector is assumed to survive with the parasite till its death. We prove that the Disease Free Equilibrium is locally and globally asymptotically stable if Ro<1 and when Ro>1, an endemic equilibrium emerges, which is unique, locally and globally asymptotically stable. The role of the saturated mosquito feeding rate is explored with simulation showing the crucial role it plays especially on the basic reproduction number
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Gebremedhin, Mahder. "Automatic and Explicit Parallelization Approaches for Mathematical Simulation Models." Licentiate thesis, Linköpings universitet, Programvara och system, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-117346.
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The move from single core and processor systems to multi-core and many-processors systemscomes with the requirement of implementing computations in a way that can utilizethese multiple units eciently. This task of writing ecient multi-threaded algorithmswill not be possible with out improving programming languages and compilers to providethe mechanisms to do so. Computer aided mathematical modeling and simulationis one of the most computationally intensive areas of computer science. Even simpli-ed models of physical systems can impose a considerable amount of computational loadon the processors at hand. Being able to take advantage of the potential computationpower provided by multi-core systems is vital in this area of application. This thesis triesto address how we can take advantage of the potential computation power provided bythese modern processors to improve the performance of simulations. The work presentsimprovements for the Modelica modeling language and the OpenModelica compiler. Two approaches of utilizing the computational power provided by modern multi-corearchitectures are presented in this thesis: Automatic and Explicit parallelization. Therst approach presents the process of extracting and utilizing potential parallelism fromequation systems in an automatic way with out any need for extra eort from the modelers/programmers side. The thesis explains improvements made to the OpenModelicacompiler and presents the accompanying task systems library for ecient representation,clustering, scheduling proling and executing complex equation/task systems with heavydependencies. The Explicit parallelization approach explains the process of utilizing parallelismwith the help of the modeler or programmer. New programming constructs havebeen introduced to the Modelica language in order to enable modelers write parallelizedcode. the OpenModelica compiler has been improved accordingly to recognize and utilizethe information from this new algorithmic constructs and generate parallel code toimprove the performance of computations.The series name Linköping Studies in Science and Technology Licentiate Thesis is incorrect. The correct series name is Linköping Studies in Science and Technology Thesis.
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Salem, Ali F. "Advanced numerical simulation modeling for semiconductor devices and it application to metal-semiconductor-metal photodetectors." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/13834.
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