Dissertations / Theses on the topic 'Molecular dynamics Mathematical models'
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Shepherd, Tricia D. "Models for chemical processes : activated dynamics across stochastic potentials." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/27062.
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Scholz, Timothy Theodore. "Density matrix theory of diatomic molecules." Title page, contents and summary only, 1989. http://web4.library.adelaide.edu.au/theses/09SM/09sms368.pdf.
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區逸賢 and Yat-yin Au. "Ab initio calculations: an extension of Sankey's method." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1999. http://hub.hku.hk/bib/B31222195.
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Oguz, Cihan. "Control-oriented modeling of discrete configuration molecular scale processes applications in polymer synthesis and thin film growth /." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19867.
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Thesis (Ph.D)--Chemical Engineering, Georgia Institute of Technology, 2008.Committee Chair: Gallivan, Martha A.; Committee Member: Hess, Dennis; Committee Member: Lee, Jay H.; Committee Member: Li, Mo; Committee Member: Ludovice, Pete.
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Quo, Chang Feng. "Reverse engineering homeostasis in molecular biological systems." Thesis, Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/49144.
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This dissertation is an initial study of how modern engineering control may be applied to reverse engineer homeostasis in metabolic pathways using high-throughput biological data. This attempt to reconcile differences between engineering control and biological homeostasis from an interdisciplinary perspective is motivated not only by the observation that robust behavior in metabolic pathways resembles stabilized dynamics in controlled systems, but also by the challenges forewarned in achieving a true meeting of minds between engineers and biologists. To do this, a comparator model is developed and applied to model the effect of single-gene (SPT) overexpression on C16:0 sphingolipid de novo biosynthesis in vitro, specifically to simulate and predict potential homeostatic pathway interactions between the sphingolipid metabolites. Sphingolipid de novo biosynthesis is highly regulated because its pathway intermediates are highly bioactive. Alterations in sphingolipid synthesis, storage, and metabolism are implicated in human diseases. In addition, when variation in structure is considered, sphingolipids are one of the most diverse and complex families of biomolecules. To complete the modeling paradigm, wild type cells are defi ned as the reference that exhibits the "desired" pathway dynamics that the treated cells approach. Key model results show that the proposed modern engineering control approach using a comparator to reverse engineer homeostasis in metabolic systems is: (a) eff ective in capturing observed pathway dynamics from experimental data, with no signifi cant di fference in precision from existing models, (b) robust to potential errors in estimating state-space parameters as a result of sparse data, (c) generalizable to model other metabolic systems, as demonstrated by testing on a separate independent dataset, and (d) biologically relevant in terms of predicting steady-state feedback as a result of homeostasis that is verifi ed in literature and with additional independent data from drug dosage experiments.
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Moore, Matthew Richard. "New mathematical models for splash dynamics." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:c94ff7f2-296a-4f13-b04b-e9696eda9047.
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In this thesis, we derive, extend and generalise various aspects of impact theory and splash dynamics. Our methods throughout will involve isolating small parameters in our models, which we can utilise using the language of matched asymptotics. In Chapter 1 we briefly motivate the field of impact theory and outline the structure of the thesis. In Chapter 2, we give a detailed review of classical small-deadrise water entry, Wagner theory, in both two and three dimensions, highlighting the key results that we will use in our extensions of the theory. We study oblique water entry in Chapter 3, in which we use a novel transformation to relate an oblique impact with its normal-impact counterpart. This allows us to derive a wide range of solutions to both two- and three-dimensional oblique impacts, as well as discuss the limitations and breakdown of Wagner theory. We return to vertical water-entry in Chapter 4, but introduce the air layer trapped between the impacting body and the liquid it is entering. We extend the classical theory to include this air layer and in the limit in which the density ratio between the air and liquid is sufficiently small, we derive the first-order correction to the Wagner solution due to the presence of the surrounding air. The model is presented in both two dimensions and axisymmetric geometries. In Chapter 5 we move away from Wagner theory and systematically derive a series of splash jet models in order to find possible mechanisms for phenomena seen in droplet impact and droplet spreading experiments. Our canonical model is a thin jet of liquid shot over a substrate with a thin air layer trapped between the jet and the substrate. We consider a variety of parameter regimes and investigate the stability of the jet in each regime. We then use this model as part of a growing-jet problem, in which we attempt to include effects due to the jet tip. In the final chapter we summarise the main results of the thesis and outline directions for future work.
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David, Laurent. "Modelisation des interactions electrostatiques des biomolecules en solution." Université Joseph Fourier (Grenoble), 1996. http://www.theses.fr/1996GRE10159.
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Les interactions electrostatiques jouent un role crucial dans la modelisation d'une macromolecule biologique, et particulierement dans la comprehension de l'effet du solvant sur le systeme considere. La resolution de l'equation lineaire de poisson-boltzmann (lpb) permet d'obtenir une representation de ces interactions. Plusieurs methodes resolvant cette equation (ou une approximation de cette equation) sont developpees dans le but d'etre utilisees en dynamique moleculaire. La premiere etude utilise la methode des differences finies pour discretiser le systeme et differents algorithmes mathematiques pour resoudre le systeme d'equations lineaires obtenu. Le temps de calcul reste superieur a celui d'une modelisation du solvant de facon explicite. Dans le but d'optimiser ce temps de calcul, une methode de resolution des equations aux derivees partielles, basee sur la fonctionnelle de l'energie et les fonctions de bases, est adaptee a la resolution de l'equation lpb. L'avantage majeur de cette methode est l'expression analytique du potentiel electrostatique, et par consequent de l'energie et des forces electrostatiques. L'effet du solvant peut aussi etre modelise en considerant les atomes comme des cavites dielectriques, et en exprimant le potentiel electrostatique a l'aide des multipoles. Les resultats obtenus sont tres interessants puisque le temps de calcul est nettement plus faible que pour la resolution de l'equation lpb. Cette methode est donc couplee a la dynamique moleculaire. Les methodes de representation du solvant, decrites precedemment, sont appliquees aux calculs de l'etat de protonation des residus ionisables des proteines. Les resultats obtenus sont en bon accord avec les donnees experimentales. Par ailleurs, trois dynamiques moleculaires sont realisees sur le complexe represseur 434/operateur or1 avec deux representations differentes du solvant et sur le complexe represseur 434/operateur or3 avec une representation implicite du solvant. Cette etude permet de mieux comprendre la specificite des interactions proteines/adn, ainsi que la qualite des differents modeles electrostatiques du solvant
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Stanek, Lucas James. "Deformation of a Graphene Sheet Driven by Lattice Mismatch with a Supporting Substrate." University of Akron / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=akron1493999094753307.
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Stekel, Dov Joseph. "Mathematical models of immune system and virus dynamics." Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.364143.
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Werner, Benjamin [Verfasser]. "Mathematical models of cell population dynamics / Benjamin Werner." Lübeck : Zentrale Hochschulbibliothek Lübeck, 2014. http://d-nb.info/1052328598/34.
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Peskett, Jonathan Paul. "The development of unsteady aerodynamic mathematical models." Thesis, University of Bristol, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299504.
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Daukšte, Liene. "Mathematical Modelling of Cancer Cell Population Dynamics." Thesis, University of Canterbury. Mathematics and Statistics, 2012. http://hdl.handle.net/10092/9356.
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Mathematical models, that depict the dynamics of a cancer cell population growing out of the human body (in vitro) in unconstrained microenvironment conditions, are considered in this thesis. Cancer cells in vitro grow and divide much faster than cancer cells in the human body, therefore, the effects of various cancer treatments applied to them can be identified much faster. These cell populations, when not exposed to any cancer treatment, exhibit exponential growth that we refer to as the balanced exponential growth (BEG) state. This observation has led to several effective methods of estimating parameters that thereafter are not required to be determined experimentally. We present derivation of the age-structured model and its theoretical analysis of the existence of the solution. Furthermore, we have obtained the condition for BEG existence using the Perron- Frobenius theorem. Amathematical description of the cell-cycle control is shown for one-compartment and two-compartment populations, where a compartment refers to a cell population consisting of cells that exhibit similar kinetic properties. We have incorporated into our mathematical model the required growing/aging times in each phase of the cell cycle for the biological viability. Moreover, we have derived analytical formulae for vital parameters in cancer research, such as population doubling time, the average cell-cycle age, and the average removal age from all phases, which we argue is the average cell-cycle time of the population. An estimate of the average cell-cycle time is of a particular interest for biologists and clinicians, and for patient survival prognoses as it is considered that short cell-cycle times correlate with poor survival prognoses for patients. Applications of our mathematical model to experimental data have been shown. First, we have derived algebraic expressions to determine the population doubling time from single experimental observation as an alternative to empirically constructed growth curve. This result is applicable to various types of cancer cell lines. One option to extend this model would be to derive the cellcycle time from a single experimental measurement. Second, we have applied our mathematical model to interpret and derive dynamic-depicting parameters of five melanoma cell lines exposed to radiotherapy. The mathematical result suggests there are shortcomings in the experimental methods and provides an insight into the cancer cell population dynamics during post radiotherapy. Finally, a mathematical model depicting a theoretical cancer cell population that comprises two sub-populations with different kinetic properties is presented to describe the transition of a primary culture to a cell line cell population.
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Edman, Lars. "Single molecule dynamics /." Stockholm, 2000. http://diss.kib.ki.se/2000/91-628-4025-8/.
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Stefanovic, Jelena. "On the mathematics of molecular dynamics." Thesis, Imperial College London, 2000. http://hdl.handle.net/10044/1/8076.
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Yu, Albert Chun-ming. "The dynamics of capital structure choice." Thesis, University of British Columbia, 1985. http://hdl.handle.net/2429/24408.
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This thesis employs two-period state-contingent model based upon the "tax shield plus bankruptcy costs" approach to examine the dynamic capital structure decision. By allowing recapitalization at the end of period one, we can analyse the dynamics of the firm's capital structure choice. Also, the effect of a call provision on bonds can be examined.
Simulated results show that the firm will recapitalize at the end of period one only if the gain in firm value, with- or ex-dividend, resulting from recapitalization exceeds the after-tax flotation costs. There exists a tolerable recapitalization boundary within which the firm will not recapitalize. This implies that the empirically observed capital structure is not necessarily at the acme of the firm value function, as most empirical studies assume.
Another important result is that a call provision on bonds may be wealth reducing; the call provision may reduce the wealth of shareholders by inducing recapitalization in states which is suboptimal if there is no call provision, and incurs flotation costs which could have been avoided. The gain in firm value resulting from recapitalization may be too small to justify the extra flotation costs and thus reduces the overall firm value.Business, Sauder School of
Graduate
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Cinquin, O. "Clocks, gradients, and molecular networks : mathematical models for morphogenesis." Thesis, University College London (University of London), 2005. http://discovery.ucl.ac.uk/1445367/.
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The acquisition of a spatial structure during embryo development involves the differentiation of cells, often according to positional information. The complexity of the molecular networks regulating differentiation and of the mechanisms generating positional information makes it necessary to study them by means of mathematical modeling. Vertebrate embryos also acquire a segmented structure during somitogenesis this requires spatial and temporal variations in gene expression, which mathematical modeling can also help understand. A molecular mechanism for the somitogenesis clock is proposed, which accounts for inter-cellular synchronisation, and is based on positive feedback, even though it is compatible with all experimental data interpreted as showing that the clock is based on negative feedback. Experiments proposed to test this model involve real-time clock reporters, as well as inducible systems to induce spatially-controlled perturbations. Theoretical and experimental results have led to conflicting ideas as to how useful positional information can be established. In particular, it has been pointed out that some models of extracellular diffusion of morphogen exhibit inadequate traveling waves of receptor saturation. Two alternative (but not mutually exclusive) models are proposed, which are based on recent experimental results highlighting the roles of extracellular glycoproteins and morphogen oligomerization. The readout of positional information is translated to a discrete set of gene expression patterns. Intriguingly, it has been observed in numerous contexts that genes regulating differentiation are initially co-expressed in progenitors despite their antagonism. We characterise conditions under which three classes of generic "master regulatory networks" can behave as a "multi-switch", directing differentiation in an all-or-none fashion to a specific cell-type chosen among more than two possible outcomes. bHLH dimerisation networks can readily display coexistence of many antagonistic factors when competition is low. Decision-making can be forced by a transient increase in competition, which could correspond to some unexplained experimental observations related to Id proteins.
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Burmenko, Irina. "Brownian dynamics simulations of fine-scale molecular models." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/32330.
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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2005.Includes bibliographical references (leaves 105-111).
One of the biggest challenges in non-Newtonian fluid mechanics is calculating the polymer contribution to the stress tensor, which is needed to calculate velocity and pressure fields as well as other quantities of interest. In the case of a Newtonian fluid, the stress tensor is linearly proportional to the velocity gradient and is given by the Newton's law of viscosity, but no such unique constitutive equation exists for non-Newtonian fluids. In order to predict accurately a polymer's rheological properties, it is important to have a good understanding of the molecular configurations in various flow situations. To obtain this information about molecular configurations and orientations, a micromechanical representation of a polymer molecule must be proposed. A micromechanical model may be fine scale, such as the Kramers chain model, which accurately predicts a real polymer's heological properties, but at the same time possesses too many degrees of freedom to be used in complex flow simulations, or it may be a coarse-grained model, such as the Hookean or the FENE dumbbell models, which can be used in complex flow analysis, but have too few degrees of freedom to adequately describe the rheology. The Adaptive Length Scale (ALS) model proposed by Ghosh et al. is only marginally more complicated than the FENE dumbbell model, yet it is able to capture the rapid stress growth in the start-up of uniaxial elongational flow, which is not predicted correctly by the simple dumbbell models. The ALS model is optimized in order to have its simulation time as close as possible to that of the FENE dumbbell.
(cont.) Subsequently, the ALS model is simulated in the start-up of the uniaxial elongational and shear flows as well as in steady extensional and shear flows, and the results are compared to those obtained with other competing rheological models such as the Kramers chain, FENE chain, and FENE dumbbell. While a 5-spring FENE chain predicts results that are in very good agreement with the Kramers chain, the required simulation time clearly makes it impossible to use this model in complex flow simulations. The ALS model agrees better with the Kramers chain than does the FENE dumbbell in the start-up of shear and elongational flows. However, the ALS model takes too long to achieve steady state, which is something that needs to be explored further before the model is used in complex flow calculations. Understanding of this phenomena may explain why the stress-birefringence hysteresis loop predicted by the ALS model is unexpectedly small. In general, if polymer stress is to be calculated using Brownian dynamics simulations, a large number of stochastic trajectories must be simulated in order to predict accurately the macroscopic quantities of interest, which makes the problem computationally expensive. However, recent technological advances as well as a new simulation algorithm called Brownian configuration fields make such problems much more tractable. The operation count in order to assess the feasibility of using the ALS model in complex flow situations yields very promising results if parallel computing is used to calculate polymer contribution to stress. In an attempt to capture polydispersity of real polymer solutions, the use of multi-mode models is explored.
(cont.) The model is fit to the linear viscoelastic spectrum to obtain relaxation times and individual modes' contributions to polymer viscosity. Then, data-fitting to the dimensionless extensional viscosity in the startup of the uniaxial elongational flow is performed for the ALS and the FENE dumbbell models to obtain the molecule's contour length, bmax. It is found that the results from the single-mode and the four-mode ALS models agree much better with the experimental data than do the corresponding single-mode and four-mode FENE dumbbell models. However, all four models resulted in a poor fit to the steady shear data, which may be explained by the fact that the zero-shear-rate viscosity obtained via a fit to the dynamic data by Rothstein and McKinley and used in present simulations, tends to be somewhat lower than the steady-state shear viscosity at very low shear rates, which may have caused a mismatch between the value of ... used in the simulation and the true ... of the polymer solution. As a motivation for using the ALS model in complex flow calculations, the results by Phillips, who simulated the closed-form version of the model in the benchmark 4:1:4 contraction- expansion problem are presented and compared to the experimental results by Rothstein and McKinley [49]. While the experimental observations show that there exists a large extra pres- sure drop, which increases monotonically with increasing De above the value observed for a Newtonian fluid subjected to the same flow conditions, the simulation results with a closed-form version of the FENE dumbbell model, called FENE-CR, exhibit the opposite trend.
(cont.) The ALS-C model, on the other hand, is able to predict the trend correctly. The use of the ALS-C model in another benchmark problem, namely the flow around an array of cylinders confined between two parallel plates, also shows very promising results, which are in much better agreement with experimental data by Liu as compared to the Oldroyd-B model. The simulation results for the ALS-C and the Oldroyd-B models are due to Joo, et al. [28] and Smith et al. [50], respectively. Overall, it is concluded that the ALS model is superior to the commonly used FENE dumb- bell model, although more work is needed to understand why it takes significantly longer than the FENE dumbbell to achieve steady state in uniaxial elongational flows, and why the stress birefringence hysteresis loop predicted by the ALS model is much smaller than that of the other rheological models.
by Irina Burmenko.
S.M.
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趙崇諾 and Sung-nok Chiu. "Stochastic models of molecular mechanisms in biology." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1992. http://hub.hku.hk/bib/B31210752.
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Uribe, Guillermo. "On the relationship between continuous and discrete models for size-structured population dynamics." Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186197.
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We address the problem of the consistency between discrete and continuous models for density-dependent size-structured populations. Some earlier works have discussed the consistency of density independent age and size-structured models. Although the issue of consistency between these models has raised interest in recent years, it has not been discussed in depth, perhaps because of the non-linear nature of the equations involved. We construct a numerical scheme of the continuous model and show that the transition matrix of this scheme has the form of the standard discrete model. The construction is based on the theory of Upwind Numerical Schemes for non-Linear Hyperbolic Conservation Laws with one important difference, that we do have a non-linear source at the boundary; interestingly, this case has not been explored in depth from the purely mathematical point of view. We prove the consistency, non-linear stability and hence convergence of the numerical scheme which guarantee that both models yield results that are completely consistent with each other. Several examples are worked out: a simple linear age-structured problem, a density-independent size-structured problem and a non-linear size-structured problem. These examples confirm the convergence just proven theoretically. An ample revision of relevant biological and computational literature is also presented and used to establish realistic restrictions on the objects under consideration and to prepare significant examples to illustrate our points.
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Lloyd, Alun Lewis. "Mathematical models for spatial heterogeneity in population dynamics and epidemiology." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.337603.
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Danbaba, Ahmed. "Mathematical models and analysis for the transmission dynamics of malaria." Diss., University of Pretoria, 2015. http://hdl.handle.net/2263/53483.
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Malaria is one of the most widespread and complex parasitic diseases in the world.
According to the World Health Organization's records for the year 2013, there
were 207 million malaria cases with 627,000 deaths in 2012 globally. Although its
control and prevention has been pursued for a long time, however, because the
parasite developed resistance to many of the standard treatments, it is becoming
more di cult for researchers to stay ahead of the disease. In this dissertation, two
deterministic models for the transmission dynamics of malaria are presented. First
we comprehensively studied the dynamical interaction of sporozoites with humans,
production of merozoites, and the invasion of red blood cells during erythrocytic
stage of malaria infection. Then we construct a model, which takes the form of
an autonomous deterministic system of non-linear di erential equations with standard
incidence, consisting of seven mutually-exclusive compartments representing
the human and vector dynamics. The model is then extended to incorporate additional
compartment of vaccinated individuals. Rigorous analysis of the two models (with and without vaccine) shows that, both the non-vaccinated and vaccinated
models have a locally asymptotically stable disease-free equilibrium (DFE) whenever
their respective threshold parameters, known as the basic reproduction number
and the vaccinated reproduction number are respectively less than unity, and the
DFE is unstable when they are greater than unity. In addition, the models exhibit
the phenomenon of backward bifurcation, where the stable disease-free equilibrium
coexists with a stable endemic equilibrium when the associated reproduction numbers
are less than unity. Furthermore, it was shown that, the backward bifurcation
phenomenon can be removed by substituting the associated standard incidence
function with the mass action incidence, this is achieved using Lyapunov functions
in conjunction with LaSalle invariance principle. We further presented numerical
simulations using parameter values for both low and high malaria incidence regions.Dissertation (MSc)--University of Pretoria, 2015.
Mathematics and Applied Mathematics
MSc
Unrestricted
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Carracedo, Rodriguez Andrea. "Mathematical Models of Hepatitis B Virus Dynamics during Antiviral Therapy." Thesis, Virginia Tech, 2016. http://hdl.handle.net/10919/70759.
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Antiviral therapy for patients infected with hepatitis B virus is only partially efficient. The field is in high demand for understanding the connections between the virus, immune responses, short-term and long-term drug efficacy and the overall health of the liver. A mathematical model was introduced in 2009 to help elucidate the host-virus dynamics after the start of therapy. The model allows the study of complicated viral patterns observed in HBV patients. In our research, we will analyze this model to determine the biological markers (e.g. liver proliferation, immune responses, and drug efficacy) that determine the different decay patterns. We will also investigate how such markers affect the length of therapy and the amount of liver damage.Master of Science
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Danbaba, Usman Ahmed. "Mathematical models and analysis for the transmission dynamics of malaria." Diss., University of Pretoria, 2015. http://hdl.handle.net/2263/53483.
Full textAbstract:
Malaria is one of the most widespread and complex parasitic diseases in the world.
According to the World Health Organization's records for the year 2013, there
were 207 million malaria cases with 627,000 deaths in 2012 globally. Although its
control and prevention has been pursued for a long time, however, because the
parasite developed resistance to many of the standard treatments, it is becoming
more di cult for researchers to stay ahead of the disease. In this dissertation, two
deterministic models for the transmission dynamics of malaria are presented. First
we comprehensively studied the dynamical interaction of sporozoites with humans,
production of merozoites, and the invasion of red blood cells during erythrocytic
stage of malaria infection. Then we construct a model, which takes the form of
an autonomous deterministic system of non-linear di erential equations with standard
incidence, consisting of seven mutually-exclusive compartments representing
the human and vector dynamics. The model is then extended to incorporate additional
compartment of vaccinated individuals. Rigorous analysis of the two models (with and without vaccine) shows that, both the non-vaccinated and vaccinated
models have a locally asymptotically stable disease-free equilibrium (DFE) whenever
their respective threshold parameters, known as the basic reproduction number
and the vaccinated reproduction number are respectively less than unity, and the
DFE is unstable when they are greater than unity. In addition, the models exhibit
the phenomenon of backward bifurcation, where the stable disease-free equilibrium
coexists with a stable endemic equilibrium when the associated reproduction numbers
are less than unity. Furthermore, it was shown that, the backward bifurcation
phenomenon can be removed by substituting the associated standard incidence
function with the mass action incidence, this is achieved using Lyapunov functions
in conjunction with LaSalle invariance principle. We further presented numerical
simulations using parameter values for both low and high malaria incidence regions.Dissertation (MSc)--University of Pretoria, 2015.
Mathematics and Applied Mathematics
MSc
Unrestricted
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Borges, Rutz Ricardo. "Mathematical models of physiologically structured cell populations." Doctoral thesis, Universitat Autònoma de Barcelona, 2012. http://hdl.handle.net/10803/96187.
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En aquesta tesi es té en compte un model no lineal de creixement de població de cèl·lules que s'estructuren pel seu contingut de ciclina i cinases depenents de ciclina (CDK). Aquest model condueix a un sistema no lineal d'equacions en derivades parcials de primer ordre amb termes no locals. Per estudiar aquest sistema utilitzem la teoria de semigrups lineals positius i la formulació semilineal, que són eines molt poderoses per fer front a l'anàlisi d'aquest tipus de models, tant des del punt de vista del problema de valor inicial, com de l'existència i l'estabilitat d'estats estacionaris.
El model que es considera a la tesi descriu la següent situació biològica: les cèl·lules s'estructuren en relació amb el contingut d'un determinat grup de proteïnes anomenades ciclines i CDK i es divideixen en dos tipus: proliferants i quiescents. Les cèl·lules proliferants creixen i es divideixen, donant a lloc al final del cicle cel·lular a noves cèl·lules, o bé van cap al compartiment de les quiescents, mentre que les cèl·lules quiescents no envelleixen ni es divideixen, ni canvien el seu contingut de ciclina, però o tornen cap al compartiment de proliferació o bé romanen en l’estat de repòs. D'altra banda, tant les cèl·lules proliferants com les quiescents poden experimentar l'apoptosi, la mort cel·lular programada. L'únic terme no lineal en el model és un terme de reclutament de cèl·lules quiescents cap a la fase de proliferació.
En aquest treball demostrem l'existència global, unicitat i positivitat de les solucions del problema de valor inicial. Reescrivint el nostre sistema en una forma abstracta podem demostrar que un cert operador lineal és el generador infinitesimal d'un semigrup positiu fortament continu. D'altra banda s'utilitza la formulació semilineal estàndard per a l’equació no lineal abstracta i obtenim una única solució global positiva per a qualsevol condició inicial positiva a L1.
També es prova l'existència i unicitat d'un estat estacionari no trivial del nostre sistema sota hipòtesis adequades. Com es fa sovint en situacions similars, el problema és relacionat amb provar l'existència (i unicitat) d'un vector propi positiu normalitzat. Això correspon als vectors propis del valor propi dominant d'un determinat operador lineal positiu parametritzat pel valor de la variable de feedback. L'existència tant del valor propi dominant i de (l’únic) vector propi positiu està donat per una versió del teorema de Perron- Frobenius en dimensió infinita.
També s’inclouen simulacions numèriques basades en la integració al llarg de les línies característiques. Amb l'ajuda d'aquestes simulacions numèriques trobem inestabilitat de l'estat estacionari per a valors de paràmetres compatibles amb els que donen inestabilitat en el model de dimensió finita. També s'inclou la demostració de l'existència de solucions independents del contingut de ciclina per a una elecció molt particular dels valors dels paràmetres i funcions que defineixen el model.
Finalment s'utilitza la formulació anomenada cumulativa (o en retard) de la dinàmica de poblacións estructurades. En particular s'ha considerat una versió diferent del model estudiat abans, on es suposa que el pas de proliferants a quiescents només pot ocórrer una sola vegada, enfocament oposat al primer model on aquestes transicions poden ocórrer infinites vegades. A més a més, també suposem que hi ha un valor particular x del contingut de ciclina que separa les cèl·lules que encara no es poden dividir de les altres que sí que poden dividir-se. L'equació del model resulta ser una equació amb retard que relaciona els valors actuals d'aquestes variables amb la seva història (el seu valor en el passat). Fent servir aquest enfocament, es pot provar l'existència i unicitat de solucions del problema de valor inicial, i el principi d'estabilitat lineal a través d'una formulació semilineal en el marc dels semigrups duals.In this thesis we consider a nonlinear cell population model where cells are structured with respect to the content of cyclin and cyclin dependent kinases (CDK). This model leads to a first order nonlinear partial differential equations system with non local terms. To study this system we use the theory of positive linear semigroups and the semilinear formulation, which are very powerful tools to deal with the analysis of this kind of models, both from the point of view of the initial value problem as well as the existence and stability of steady states. The model considered in the thesis describes the following biological situation: cells are structured with respect to the content of a certain group of proteins called cyclin and CDK and are distributed into two types: proliferating and quiescent cells. The proliferating cells grow and divide, giving birth at the end of the cell cycle to new cells, or else transit to the quiescent compartment, whereas quiescent cells do not age nor divide nor change their cyclin content but either transit back to the proliferating compartment or else stay in the quiescent compartment. Moreover, both proliferating and quiescent cells may experiment apoptosis, i.e. programmed cell death. The only nonlinear term is a recruitment term of quiescent cells going back to the proliferating phase. In this work we start proving global existence, uniqueness and positiveness of the solutions of the initial value problem. We rewrite our system in an abstract form and show that some linear operator is the infinitesimal generator of a positive strongly continuous semigroup. On the other hand we use the standard semilinear formulation for the nonlinear (abstract) equation and obtain a unique global positive solution for any positive initial condition in L1. We also prove the existence and uniqueness of a nontrivial steady state of our system under suitable hypotheses. As it is often done in similar situations, the problem is related to proving the existence (and uniqueness) of a positive normalized eigenvector. This eigenvector corresponds to the dominant eigenvalue of a certain positive linear operator parameterized by the value of the (one dimensional) feedback variable G. The existence of both dominant eigenvalue and (unique) positive eigenvector is given by a version of the infinite dimensional Perron-Frobenius theorem. We include numerical simulations based on the integration along characteristic lines. With the help of these numerical simulations we find instability of the steady state for parameter values compatible with the ones which give instability in the finite dimensional model. We also include a computation showing the existence of cyclin-independent solutions for a very particular choice of the parameter values and functions defining the model. Finally we use the so-called cumulative or delayed formulation of the structured population dynamics. In particular we have considered a different version of the model studied before, where one assumes that proliferating cells can become quiescent only once opposed to the other approach where these transitions can occur infinitely many times and moreover, we also assume that there is a particular value x of the cyclin content that separates cells which still cannot divide from the others which are able to divide. The model equation turns out to be a delay equation relating the current values of these variables with their history (their value in the past). Using this approach, one can prove existence and uniqueness of solutions of the initial value problem, and the linear stability principle by means of a semi-linear formulation in the framework of dual semigroups.
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Rinaldi, Stephanie. "Experiments on the dynamics of cantilevered pipes subjected to internal andor external axial flow." Thesis, McGill University, 2009. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=111615.
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The main objective of this thesis is to study and investigate the dynamics and stability of cantilevered structures subjected to internal, external, or simultaneous internal and external axial flows. This was accomplished, in some cases, by deriving the linear equations of motion using a Newtonian approach and, in other cases, by making the necessary modifications to existing theoretical models. The continuous cantilevered systems were then discretized using the Galerkin method in order to determine their complex eigenfrequencies. Moreover, numerous experiments were performed to compare and validate, or otherwise, the theoretical models proposed. More specifically, the four cantilevered systems studied were the following: (i) a pipe conveying fluid that is fitted with a stabilizing end-piece, which suppresses flutter by blocking the straight-through exit of flow at the downstream end; (ii) a pipe aspirating fluid, which flutters at low flow velocities in its first mode; (iii) a free-clamped cylinder (i.e. with the upstream end free and the downstream end clamped) in confined axial flow, which also flutters at low flow velocities in its first mode and eventually develops a buckling instability; and (iv) a pipe subjected to internal flow, which after exiting the pipe is transformed to a confined counter-current annular flow, that becomes unstable by flutter too.
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Sher, Anna. "Modelling local calcium dynamics and the sodium/calcium exchanger in ventricular myocytes." Thesis, University of Oxford, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.670114.
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Cheung, On-pong, and 張安邦. "Computational fluid dynamics simulations on the natural ventilation bahaviour within a building cluster." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B45590084.
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Akinlotan, Deborah Morenikeji. "Modelling the dynamics of HIV related malignancies." Thesis, Stellenbosch : Stellenbosch University, 2014. http://hdl.handle.net/10019.1/86573.
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Thesis (MSc)--Stellenbosch University, 2014.ENGLISH ABSTRACT: In recent years, HIV-associated cancers have proven to be the bane of our time, since HIV is decimating humanity across the globe, even in the twilight of the last century. Cancer rates continue to rise in developing countries, where 95% of the world’s HIV-infected population lives, yet less than 1% have access to antiretroviral therapy. HIV-infected individuals have a higher proclivity to develop cancers, mainly from immunosuppression. An understanding of the immunopathogenesis of HIV-related cancers (HRC) is therefore a major prerequisite for rationally developing and/or improving therapeutic strategies, developing immunotherapeutics and proplylatic vaccines. In this study, we explore the pathology of HIV-related cancer malignancies, taking into account the pathogenic mechanisms and their potential for improving the treatment of management of these malignancies especially in developing countries. We mathematically model the dynamics of malignant tumors in an HIV-free environment, investigate the impact of cancer malignancies on HIV-positive patients and explore the benefits of various therapeutic intervention strategies in the management of HIV-related cancers. We present two deterministic models of infectious diseases to implement these, and they were analysed. We use HIV-related lymphomas in the Western Cape of South Africa as a case study. We validated the proposed models using lymphoma incidence data from the Tygerberg Lymphoma Study Group (TLSG), Tygerberg Hospital, Western Cape, South Africa. We show that the increasing prevalence of HIV increases lymphoma cases, and thus, other HIV-related cancers. Our models also suggests that an increase in the roll-out of the HAART program can reduce the number of lymphoma cases in the nearest future, while it averts many deaths. Furthermore, the results indicate that a highly crucial factor to consider in the prognosis of the incidence of lymphoma (and other cancer types) in HIV-infected patients is their CD4 cell count, irrespective of whether the patient has developed an HRC or not.
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Barker, D. R. "Frozen electron gas models for molecular dynamics of liquids." Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.596361.
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Methods for improving the size of accurate Kohn-Sham (KS) DFT calculations have often focused on embedding the KS calculation within a region of fixed electronic density. This thesis examines the potential for a similar type of approach within Car-Parrinello, ab-initio, Molecular Dynamics (CPMD). A frozen electron density (FED) model is incorporated into a KS-DFT based simulations of liquid water. Interactions between FED and KS species are determined using total energy expressions taken from the study of embedded systems. The initial step during this development was a study of the FED electron gas model proposed by Gordon and Kim for rare gas systems, using a modified version of the DL_POLY MD code. The adapted code was applied to investigate various options for extending this scheme to inter-molecular interactions in liquid water, including assessment of the suitability of a number of kinetic energy (KE) functionals. The optimisation of electron density for a FED model of water was explored semi-empirically, based on adaptation of the fixed molecular electron density to the condensed phase environment. Consistent with experience from force field methods, enhancement of the molecular dipole moment proved to be necessary to reproduce the properties of the liquid. Using the TF, PW01 and LLP KE functionals, models giving good agreement with experimental results were obtained. These each carried a dipole moment of 2.95 D, the same as has been observed by recent ab-initio MD studies based on fully self-consistent KS methods. Finally the CPMD code was adapted to incorporate these models into mixed KS/FED simulations, in which both molecular types occupied the same simulation cell. All MD runs showed energetic stability and good overall structure. However, more acceptable reproduction of the inter-molecular interactions of a fully KS-DFT calculation were obtained with the PW91 and LLP based models, than with that based on the TF functional. This is in agreement with similar calculations reported for the gas phase dimer.
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Vekstein, Daniel. "Dynamics of organizational growth in the international automobile industry." Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186248.
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The phenomenon of organizational growth has traditionally been assumed to be indeterminate largely due to chance or accidents found in organizational worlds. This research takes up the causal processes underlying the growth (and decline) of virtually all world-class manufacturers in the international automobile industry from 1946 to 1989. Two models are developed as alternative explanations for the long-term trends observed in growth rates and their differences across firms. The models are estimated with a nonlinear method and tested through various empirical implications. The model that seems most consistent with the data shows unambiguously that they were not generated by a random or chance process but by underlying processes of collective learning, innovation, and outnovation in technologies and organizational routines. Firms that had generated different rates in these processes differed as hypothesized in their long-term growth performance. The dynamics of collective learning processes, as measured by the parameters of the model, largely explain the dynamics of organizational growth in the world automobile industry, hence, the dynamics of interorganizational competition. The results from tests of ecological hypotheses suggest that organizational ecology might benefit from the application of matrices of collective learning rates generated from interorganizational learning curves, particularly where ecology seeks to explain patterns of competition by organizational size. As shown, this research strategy is general and gauges directly interactions among organizations over long periods. It is also flexible in dealing with various levels of analysis in longitudinal and cross-sectional dimensions. As also shown, the collective learning theory, its model, and the ecology of interorganizational learning curves derived from them can help in evaluating empirically the competitive potential of firms by indicators of innovation and outnovation relative to other firms, patterns of competition (gauged by relative learning rates) among firms, and any changes of those patterns over time. Thus, the research strategy used here provides potentially useful causal analyses as well as meaningful measures on which different organizations can be compared, with each other and with themselves. These measures may also provide important benchmarks and diagnostics for strategic management.
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Hussaini, Nafiu. "Mathematical modelling and analysis of HIV transmission dynamics." Thesis, Brunel University, 2010. http://bura.brunel.ac.uk/handle/2438/5672.
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This thesis firstly presents a nonlinear extended deterministic Susceptible-Infected (SI) model for assessing the impact of public health education campaign on curtailing the spread of the HIV pandemic in a population. Rigorous qualitative analysis of the model reveals that, in contrast to the model without education, the full model with education exhibits the phenomenon of backward bifurcation (BB), where a stable disease-free equilibrium coexists with a stable endemic equilibrium when a certain threshold quantity, known as the effective reproduction number (Reff ), is less than unity. Furthermore, an explicit threshold value is derived above which such an education campaign could lead to detrimental outcome (increase disease burden), and below which it would have positive population-level impact (reduce disease burden in the community). It is shown that the BB phenomenon is caused by imperfect efficacy of the public health education program. The model is used to assess the potential impact of some targeted public health education campaigns using data from numerous countries. The second problem considered is a Susceptible-Infected-Removed (SIR) model with two types of nonlinear treatment rates: (i) piecewise linear treatment rate with saturation effect, (ii) piecewise constant treatment rate with a jump (Heaviside function). For Case (i), we construct travelling front solutions whose profiles are heteroclinic orbits which connect either the disease-free state to an infected state or two endemic states with each other. For Case (ii), it is shown that the profile has the following properties: the number of susceptible individuals is monotone increasing and the number of infectives approaches zero, while their product converges to a constant. Numerical simulations are shown which confirm these analytical results. Abnormal behavior like travelling waves with non-monotone profile or oscillations are observed.
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Ma, Ou. "Dynamics of serial-type robotic manipulators." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=63771.
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Spyksma, Kyle. "On the dynamics and predictability of moist turbulence." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=103296.
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In this thesis I present a simple, computationally-inexpensive moist turbulence model in order to study the differences between moist and dry turbulence. The model is validated by comparing a moist-bubble simulation with ones presented in Grabowski and Clark (1993) using a more-sophisticated model. We show that the outputs compare well and that our model can easily be extended to higher resolutions due to its simplified equations and uncomplicated implementation. Measurements of liquid water content spectra from the 3843 validation run are shown having shallow slopes, implying that moist processes require high resolution. Consideration is also given to the issue of Gibb's oscillations near sharp gradients, such as at a cloud boundary. It is shown that, due to our high resolutions, the dynamics of our model are not seriously affected if corrections are not made to address them.The model is used to study the small-scale predictability and dynamics of moist and dry shallow convective turbulence. Although moist flows are less predictable than their associated dry flows, we can account for the differences via a simple scaling. Using large-scale (the root-mean-squared vorticity) and small-scale (the dissipation wavenumber, kd) measures, we can reconcile classical predictability statistics from both wet and dry runs, with different lapse rates and relative humidities.
Finally, I present a more thorough investigation of the dynamical differences between wet and dry convective turbulence, and then consider the very small-scale (ℓ ≲ 10 m) variability of liquid water content and compare our high-resolution simulation results to existing in situ cumulus-cloud observations. We find that there is a small decrease in the spatial intermittency of vorticity in wet runs relative to dry ones. This is consistent with the idea that evaporation of the liquid water in the clouds reduces the instabilities that would lead to the most intense vortices. At the same time, the liquid water content spectra show that in these areas of intense mixing and cloud decay, the characteristic scale of variability is shifted to smaller scales compared to a passive scalar. Further integrations in which the convective forcing is removed show that as the amount of liquid water decreases through evaporation, there is delayed decay of the smallest scales of the cloud. These findings may explain the small-scale shallow liquid water content spectra from cumulus-cloud fly-through measurements reported in Davis et al. (1999).
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Kooner, Priya. "Mathematical modelling of tumour invasion : from biochemical networks to tissue dynamics." Thesis, University of Oxford, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.670187.
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Ye, Feng. "Derivation of a two-layer non-hydrostatic shallow water model." Thesis, Water Resources Research Center, University of Hawaii at Manoa, 1995. http://hdl.handle.net/10125/21919.
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A theoretical non-hydrostatic model is developed to describe the dynamics of a two-layer shallow water system in the presence of viscous and Coriolis effects. The Navier-Stokes equations are integrated over the water depth in each layer to obtain the layer-mean equations. To close the resulting equation set, perturbation expansions of the vertical momentum equation are used and the dynamic pressures are solved in terms of wave elevations and horizontal velocities. A preliminary analysis is also carried out and a result for the quasigeostrophic problems is given based on an previous study. Our final model is of the Bousinesq class which is nonlinear and dispersive, and includes the effects of surface wind stress, bottom friction, eddy diffusion and earth rotation. It is shown that our new model can be readily reduced to previous inviscid non-hydrostatic models. Our model can be used in numerical simulations to study real ocean problems such as hurricane generated waves, tidal induced current, and interactions among surface waves, internal waves and variable topographies.Thesis (M. S.)--University of Hawaii at Manoa, 1995.
Includes bibliographical references (leaves 55-59).
UHM: Has both book and microform.
U.S. Geological Survey; project no. 06; grant agreement no. 14-08-0001-G2015
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馮達淸 and Tat-ching Fung. "Steady state solutions of nonlinear dynamic systems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1989. http://hub.hku.hk/bib/B31231809.
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鄭定陽 and Dingyang Zheng. "Vibration and stability analysis of plate-type structures under movingloads by analytical and numercial methods." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1999. http://hub.hku.hk/bib/B31239791.
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Chan, Hing-kai, and 陳慶佳. "Impacts of flexibility in delivery quantity and due date on supply chain dynamics." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B3857651X.
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Mark, Pekka. "Molecular dynamics studies of water and biomolecules /." Stockholm, 2002. http://diss.kib.ki.se/2002/91-7349-251-5.
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Kiss, Andrew Elek. "Dynamics of laboratory models of the wind-driven ocean circulation." View thesis entry in Australian Digital Theses Program, 2000. http://thesis.anu.edu.au/public/adt-ANU20011018.115707/index.html.
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Modarres, Najafabadi Seyed Ali. "Dynamics modelling and analysis of impact in multibody systems." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=115886.
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In this thesis, we discuss a novel approach to the dynamics modelling and analysis of impact in unilaterally constrained multibody systems. This approach is based on an analysis of energy absorption and restitution during impact, using a decomposition technique, which decouples the kinetic energy associated with the spaces of admissible and constrained motions of unilateral contacts. This is done based on the decomposition of the tangent space of the configuration manifold at the pre-impact instant. The decomposition of the kinetic energy can provide a picture of how the energy absorption and dissipation during impact is related to the variation of the generalized velocities and the configuration of multibody systems.Further, based on the above analysis approach, we introduce a new interpretation of the energetic coefficient of restitution, specially applicable to contact involving multibody systems. This interpretation generalizes the concept of the energetic coefficient of restitution and allows for consideration of simultaneous multiple-point contact scenarios. Moreover, based on the concept of the generalized energetic coefficient of restitution, the contact modes and the post-impact state of planar single-point impact are determined. Further, the problem of simultaneous multiple-point impact is considered, where it is shown that our approach can also be advantageous to characterize the dynamics of interaction in such systems.
The use and applicability of the approach reported are further investigated by conducting an experimental study on a robotic testbed. The open architecture of the testbed allows us to perform various contact experiments, such as single- and multiple-point impact scenarios, with different pre-impact configurations and velocities. The kinematic and dynamic models of the system have been developed and implemented for real-time analysis. It is shown that impact between multibody systems is considerably affected by not only the local dynamics characteristics of the interacting bodies, but also the (global) configuration of the interacting multibody systems. The reported results suggest that the material presented herein offers a useful means to characterize impact in complex systems.
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Kucharski, Adam. "The dynamics of immunity to seasonal influenza." Thesis, University of Cambridge, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.607908.
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Yin, Xiaopeng 1963. "Endogenous growth, international trade and dynamics." Thesis, McGill University, 2001. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=37914.
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This PhD. dissertation consists of three essays to fill some gaps in the recent research in international trade and endogenous growth theory. The first essay explores the dynamic effect of interaction of research and development (R&D) activities among countries on endogenous economic growth. It attempts to fill the gap between the current endogenous growth research focused on independent R&D activities and decision-making in the international competition and the interdependent R&D competition in reality. This paper finds that the growth rates, welfare, and investment on R&D in the world do differ between independent R&D activity and interdependent R&D activities among countries. The welfare for each country in the open-loop Nash equilibrium is higher than that of the Markov-perfect Nash equilibrium, and both are lower than that in the cooperative game. The model shows that the ability to commit turns out to make every country better off. The interesting results are that when an increase in the number of countries does increase the growth rate in the open-loop Nash equilibrium, it is very possible to have the negative effect on the growth rate in the Markov-perfect equilibrium. Particularly, the model shows that the tendency of free-ride rises with more countries in the competition. The more general models with durable physical capital, and with the endogenous rate of time preference following Uzawa-Epstein tradition, also prove these conclusions.The second essay turns to the Samuelson-Diamond overlapping generation paradigm, a finite-horizon overlapping generations model with education proposed by Michel (1993). The focus is shifted to the effect of trade on growth. It turns out that when trade affects the formation of human capital, endogenous growth is possible even in the simplest economy with a single sector and constant returns to scale technologies, which is opposite from Boldrin's (1992) and Jones and Manuelli's (1992) results.
While the existing theory of trade under oligopolistic competition is mostly static in nature, the third essay fills this gap by modeling international trade under oligopoly in a dynamic setting. This essay adopts the dynamics in the model provided by allowing the demand curve to shift over time as a result of "habit formation". It shows that when the importing country is committing to a policy of voluntary import expansions (VIEs), in the certain condition (i.e. k > 1), VIEs can improve the global welfare, the welfare of the importing country, and the profit of both firms. So, in a sense, voluntary import expansion is truly voluntary.
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Johnson, Quentin Ramon. "An Analysis of Prominent Water Models by Molecular Dynamics Simulations." Digital Archive @ GSU, 2010. http://digitalarchive.gsu.edu/chemistry_theses/30.
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Water is the most common solvent for most biological reactions, therefore it is vital that we fully understand water and all its properties. The complex hydrogen bonding network that water forms can influence protein-protein and protein-substrate interactions and can slow protein conformational shifts. Here, I examine an important property of water known as energetic roughness. The network of interactions between individual water molecules affect the energy landscape of proteins by altering the underlying energetic roughness. I have attributed this roughness to the making and breaking of hydrogen bonds as the network of hydrogen bonds constantly adopts new conformations. Through a novel computational approach I have analyzed five prominent water models and have determined their inherent roughness to be between 0.43 and 0.62 kcal/mol.
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Cho, Eunjung. "Efficient Molecular Dynamics Simulation on Reconfigurable Models with MultiGrid Method." Digital Archive @ GSU, 2008. http://digitalarchive.gsu.edu/cs_diss/32.
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In the field of biology, MD simulations are continuously used to investigate biological studies. A Molecular Dynamics (MD) system is defined by the position and momentum of particles and their interactions. The dynamics of a system can be evaluated by an N-body problem and the simulation is continued until the energy reaches equilibrium. Thus, solving the dynamics numerically and evaluating the interaction is computationally expensive even for a small number of particles in the system. We are focusing on long-ranged interactions, since the calculation time is O(N^2) for an N particle system. In this dissertation, we are proposing two research directions for the MD simulation. First, we design a new variation of Multigrid (MG) algorithm called Multi-level charge assignment (MCA) that requires O(N) time for accurate and efficient calculation of the electrostatic forces. We apply MCA and back interpolation based on the structure of molecules to enhance the accuracy of the simulation. Our second research utilizes reconfigurable models to achieve fast calculation time. We have been working on exploiting two reconfigurable models. We design FPGA-based MD simulator implementing MCA method for Xilinx Virtex-IV. It performs about 10 to 100 times faster than software implementation depending on the simulation accuracy desired. We also design fast and scalable Reconfigurable mesh (R-Mesh) algorithms for MD simulations. This work demonstrates that the large scale biological studies can be simulated in close to real time. The R-Mesh algorithms we design highlight the feasibility of these models to evaluate potentials with faster calculation times. Specifically, we develop R-Mesh algorithms for both Direct method and Multigrid method. The Direct method evaluates exact potentials and forces, but requires O(N^2) calculation time for evaluating electrostatic forces on a general purpose processor. The MG method adopts an interpolation technique to reduce calculation time to O(N) for a given accuracy. However, our R-Mesh algorithms require only O(N) or O(logN) time complexity for the Direct method on N linear R-Mesh and N¡¿N R-Mesh, respectively and O(r)+O(logM) time complexity for the Multigrid method on an X¡¿Y¡¿Z R-Mesh. r is N/M and M = X¡¿Y¡¿Z is the number of finest grid points.
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DITOLLA, ROBERT JOHN. "RANDOM VIBRATION ANALYSIS BY THE POWER SPECTRUM AND RESPONSE SPECTRUM METHODS (WHITE NOISE, FINITE-ELEMENT, VANMARCKE, DENSITY, NASTRAN)." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/183836.
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Determination of the stresses and displacements which occur in response to random excitations cannot be accomplished by traditional deterministic analysis methods. As the specification of the excitation and the response of the structure become more complex, solutions by direct, closed-form methods require extensive computations. Two methods are presented which can be used in the analysis of structures which are subjected to random excitations. The Power Spectrum Method is a procedure which determines the random vibration response of the structure based upon a frequency response analysis of a structural model. The Response Spectrum Method is a method which is based upon specified forces or displacements as a function of time. A derivation of each of the methods is presented and followed by comparisons of the results which were obtained for single and multiple-degree-of-freedom systems. Assumptions and limitations of the methods are discussed as well as their accuracy over ranges of frequency, damping and loading specification. As a direct application and comparison of the two methods, an analysis of the support system for the primary mirror of the Space Infrared Telescope Facility (SIRTF) has been performed. In addition, a method for the evaluation of the critical damping in a single-degree-of-freedom structure is demonstrated.
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Craig, Erin Michelle. "Models for Brownian and biomolecular motors /." Connect to title online (Scholars' Bank) Connect to title online (ProQuest), 2008. http://hdl.handle.net/1794/8565.
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Thesis (Ph. D.)--University of Oregon, 2008.Typescript. Includes vita and abstract. Includes bibliographical references (leaves 164-171). Also available online in Scholars' Bank; and in ProQuest, free to University of Oregon users.
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Harvey, Emily Paige. "Analysing mathematical models of intracellular calcium dynamics using geometric singular perturbation techniques." Thesis, University of Auckland, 2011. http://hdl.handle.net/2292/10814.
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Oscillations in free intracellular calcium (Ca2+) concentration are known to act as signals in almost all cell types, transmitting messages which control cellular processes including muscle contraction, cellular secretion and neuronal firing. Due to the universal nature of calcium oscillations, understanding the physiological mechanisms that underlie them is of great importance. A key feature of intracellular calcium dynamics that has been found experimentally is that some physiological processes occur much faster than others. This leads to models with variables evolving on very different time scales. In this thesis we survey a range of representative models of intracellular calcium dynamics, using geometric singular perturbation techniques with the aim of determining the usefulness of these techniques and what their limitations are. We find that the number of distinct time scales and the number of variables evolving on each time scale varies between models, but that in all cases there are at least two time scales, with at least two slower variables. Using geometric singular perturbation techniques we identify parameter regimes in which relaxation oscillations are seen and those where canard induced mixed mode oscillations are present. We find that in some cases these techniques are very useful and explain the observed dynamics well, but that the theory is limited in its ability to explain the dynamics when there are three or more distinct time scales in a model. It has been proposed that a simple experiment, whereby a pulse of inositol (1,4,5)- trisphosphate (IP3) is applied to a cell, can be used to distinguish between two competing mechanisms which lead to calcium oscillations [53]. However, detailed mathematical investigation of models has identified an anomalous delay in the pulse responses of some models, making interpretation of the experimental data difficult [14]. In this thesis we find that the response of models to a pulse of IP3 can be understood in part by using geometric singular perturbation techniques. Using recently developed theory for systems with three or more slow variables, we find that the anomalous delay can be due to the presence of folded nodes and their corresponding canard solutions or due to the presence of a curve of folded saddles. This delay due to a curve of folded saddles is a novel delay mechanism that can occur in systems with three or more slow variables. Importantly, we find that in some models the response to a pulse of IP3 is contrary to predictions for all bifurcation parameter values, which invalidates the proposed experimental protocol.
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Danbaba, Usman Ahmed. "Mathematical analysis of models for the transmission dynamics of mosquito borne diseases." Thesis, University of Pretoria, 2019. http://hdl.handle.net/2263/77885.
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Mosquitoes are long-legged, two winged flies that are responsible for the transmission
of many diseases such as Zika fever, malaria, yellow fever, chikungunya and dengue
hemorrhagic fever. Mosquito borne diseases account for substantial amount of para-
sitic and infectious diseases, they have profound effects on economic growth of many
developing countries. There have been continuous efforts to optimize and improve on
existing mosquito control strategies, as well as to develop new tools aimed at reducing
burden of mosquito borne diseases. Control strategies are either applied alone or in
combination depending on available resources, education, health risk and burden of
the disease.
The main aim of this thesis is to mathematically study three mosquito borne dis-
eases in the presence of control, the diseases are Zika fever (this is because, in addition
to the disease being transmitted vertically, it is the first mosquito borne disease known
to be transmitted sexually), yellow fever (because despite having effective vaccine for
the disease, it has continue to pose sporadic challenges in different regions of the
world), and malaria (because it has the highest global burden among mosquito borne
diseases despite continuous efforts to eradicate it).
Some major highlights of the thesis include: Roles of mosquito vertical transmission
in the transmission dynamics of mosquito borne diseases, and effects of incorporating
human-human transmission are evaluated. Assessment of impact of using different
control measures both in human and mosquito populations, and effects of controlling
population of adult male (non-disease transmitting) mosquitoes through sterilization
are conducted. Implication of incorporating aquatic stage of mosquito development in
models for the transmission of mosquito borne diseases, as well as effect of temperature
variation in the transmission dynamics of malaria are also studied.
In Chapter 1, brief introduction to the epidemiology of mosquito borne diseases
is presented. Basic results and definitions in mathematical epidemiology are also dis-
cussed. In addition, some important mathematical theories and definitions used in
subsequent chapters are also presented. A Zika model that incorporates vectorial ver-
tical transmission, human-human horizontal transmission, as well as human-mosquito
and mosquito-human transmissions is studied in Chapter 2. Another Zika model is
considered in Chapter 3, the model incorporated human-human transmission in the
presence of mosquito sterilization. In Chapter 4, a yellow fever model with vaccina-
tion, use of bed nets and mosquito control at both aquatic and non-aquatic stages
is constructed and analysed. Chapter 5 considered a temperature dependent malaria
model in the presence of control. General conclusion is given in Chapter 6.Thesis (PhD)--University of Pretoria, 2019.
Mathematics and Applied Mathematics
PhD
Unrestricted
50
Konrad, Bernhard Paul. "On the dynamics of HIV and malaria infection : insights from mathematical models." Thesis, University of British Columbia, 2015. http://hdl.handle.net/2429/54829.
Full textAbstract:
We develop and apply mathematical models to obtain insights into the dynamics of HIV and malaria infection. We consider three case studies.
1. The duration of the time between exposure and detectability of HIV infection is difficult to estimate because precise dates of exposure are rarely known. Therefore, the reliability of clinical HIV testing during the first few weeks of infections is unknown, creating anxiety among HIV-exposed individuals and their physicians. We address this knowledge gap by fitting stochastic models of early HIV infection to detailed viral load time-courses, taken shortly after exposure, from 78 plasma donors. Since every plasma donor in our data eventually becomes infected, we condition our model to reflect this bias before fitting to the data. Our model prediction for the mean eclipse period is 8-10 days. We further quantify the reliability of a negative test t days after potential exposure to inform physicians about the value of initial and follow-up testing.
2. The recently launched Get Checked Online (GCO) program aims at increasing the HIV testing rate in the Vancouver men who have sex with men population by facilitating test taking and result delivery. We develop mathematical models and extract parameter values from surveys and interviews to quantify GCO's population-level impact. Our models predict that the epidemic is growing overall, that its severeness is increased by the presence of a high-risk group and that, even at modest effectiveness, GCO might avert 34-66 new infections in the next five years.
3. Metarhizium anisopliae is a naturally occurring fungal pathogen of mosquitoes that has been engineered to act against malaria by effectively blocking onward transmission from the mosquito vector. We develop and analyse two mathematical models to examine the efficacy of this fungal pathogen. We find that, in many plausible scenarios, the best effects are achieved with a reduced or minimal pathogen virulence, even if the likelihood of resistance to the fungus is negligible. The results depend on the interplay between two main effects: the ability of the fungus to reduce the mosquito population, and the ability of fungus-infected mosquitoes to compete for resources with non-fungus-infected mosquitoes.Science, Faculty of
Mathematics, Department of
Graduate