Tesis: "Differentiable simulation"

1

Collins, Jack T. "Simulation to reality and back: A robot's guide to crossing the reality gap". Thesis, Queensland University of Technology, 2022. https://eprints.qut.edu.au/230537/1/Jack_Collins_Thesis.pdf.

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Simulation is an indispensable technology within robotics; however, the reality gap prevents many simulated solutions from transferring perfectly to reality. This thesis investigates the reality gap within the context of robotic manipulation. We present studies that first quantify and then benchmark the reality gap when comparing popular robotic simulators to a real-world ground truth collected using motion capture. We then present a promising new method for overcoming the reality gap that employs an online sim-to-real approach that utilises differentiable physics to iteratively narrow the gap and improve the simulation environment using data collected from the real system.

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2

Yu, Boyang. "High-quality recovery of garment models and sewing patterns from 3D clothed human data". Electronic Thesis or Diss., Strasbourg, 2024. http://www.theses.fr/2024STRAD056.

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3D peut améliorer l’interprétation des vêtements réels et leur reproduction numérique, avec des applications en RV et essayages virtuels. Cette thèse aborde la reconstruction de vêtements en estimant une réplique animable et son patron 2D. Basée sur un simulateur différentiable, notre approche optimise la forme simulée pour qu’elle corresponde à la cible, tout en préservant des propriétés clés comme la symétrie. Notre pipeline s’aligne sur les standards de l’industrie, ajustant patrons et matériaux pour affiner la géométrie et permettre la réanimation. Nous introduisons également une optimisation par déformation pour raffiner davantage la géométrie du maillage afin de capturer des détails fins, améliorant l’ajustement et facilitant l’enregistrement non rigide. Nos expériences sur données réelles et synthétiques montrent que nos méthodes surpassent l’état de l’art en term de précision
Recovering high-quality garment models from 3D clothed human shapes can enhance the interpretability of real garments and their digital reproduction, benefiting applications like VR and virtual try-ons. This thesis tackles the challenge of reconstructing garment geometry by estimating an animatable replica and its 2D pattern. Using a differentiable cloth simulator, we optimize the simulated garment to match the target shape while preserving key properties like symmetry. Our inverse garment design pipeline aligns with industry-standard modeling and simulation processes, adjusting 2D patterns and material properties to refine geometry and enable reanimation. Additionally, we introduce a deformation-based optimization method that refines mesh geometry to capture fine-grained details, improving fit and supporting non-rigid registration. Experiments on real and synthetic data demonstrate that our methods surpass state-of-the-art techniques in garment model quality and pattern accuracy

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3

Carli, Henrique. "Sistemas complexos, séries temporais e previsibilidade". Universidade do Estado do Rio de Janeiro, 2011. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=3296.

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Para qualquer sistema observado, físico ou qualquer outro, geralmente se deseja fazer predições para sua evolução futura. Algumas vezes, muito pouco é conhecido sobre o sistema. Se uma série temporal é a única fonte de informação no sistema, predições de valores futuros da série requer uma modelagem da lei da dinâmica do sistema, talvez não linear. Um interesse em particular são as capacidades de previsão do modelo global para análises de séries temporais. Isso pode ser um procedimento muito complexo e computacionalmente muito alto. Nesta dissertação, nos concetraremos em um determinado caso: Em algumas situações, a única informação que se tem sobre o sistema é uma série sequencial de dados (ou série temporal). Supondo que, por detrás de tais dados, exista uma dinâmica de baixa dimensionalidade, existem técnicas para a reconstrução desta dinâmica.O que se busca é desenvolver novas técnicas para poder melhorar o poder de previsão das técnicas já existentes, através da programação computacional em Maple e C/C++.

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4

Xu, Lina. "Simulation methods for stochastic differential equations in finance". Thesis, Queensland University of Technology, 2019. https://eprints.qut.edu.au/134388/1/Lina_Xu_Thesis.pdf.

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This thesis resolves a number of econometric problems relating to the use of stochastic differential equations based on computer-intensive simulation methods. Stochastic differential equations play an important role in modern finance. They have been used to model the trajectories of key variables such as short-term interest rates and the volatility of financial assets. The central theme of the thesis is the use of Hermite polynomials to approximate the transitional probability distribution functions of stochastic differential equations. Based on these approximations, a new method is proposed for simulating solutions to these equations and new testing procedures are developed to examine the fit of the equations to observed data.

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5

Chalmers, Graeme D. "Implicit numerical simulation of stochastic differential equations with jumps". Thesis, University of Strathclyde, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.501657.

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Implicit numerical methods such as the stochastic theta-method offer a practical way to approximate solutions of stochastic differential equations. The method involves a parameter, θ, which is freely chosen. In this thesis, we investigate strong convergence and linear stability, both mean-square and asymptotic, arising from the implementation of the theta-method when applied to ordinary stochastic differential equations incoroporating jumps. Such models are used in several disciplines; in particular, we note their use as models for various financial quantities such as asset prices, interest rates and volatility.

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6

See, Chong Wee Simon. "Numerical methods for the simulation of dynamic discontinuous systems". Thesis, University of Salford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358276.

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7

Bächle, Simone. "Numerical solution of differential-algebraic systems arising in circuit simulation". [S.l.] : [s.n.], 2007. http://opus.kobv.de/tuberlin/volltexte/2007/1524.

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8

Elerian, Ola. "Simulation estimation of continuous-time models with applications to finance". Thesis, University of Oxford, 1999. https://ora.ox.ac.uk/objects/uuid:9538382d-5524-416a-8a95-1b820dd795e1.

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Over recent years, we have witnessed a rapid development in the body of economic theory with applications to finance. It has had great success in finding theoretical explanations to economic phenomena. Typically, theories are employed that are defined by mathematical models. Finance in particular has drawn upon and developed the theory of stochastic differential equations. These produce elegant and tractable frameworks which help us to better understand the world. To directly apply such theories, the models must be assessed and their parameters estimated. Implementation requires the estimation of the model's elements using statistical techniques. These fit the model to the observed data. Unfortunately, existing statistical methods do not work satisfactorily when applied to many financial models. These methods, when applied to complex models often yield inaccurate results. Consequently, simpler analytical models are often preferred, but these are typically unrealistic representations of the underlying process, given the stylised facts reported in the literature. In practical applications, data is observed at discrete intervals and a discretisation is typically used to approximate the continuous-time model. This can lead to biased estimates, since the true underlying model is assumed continuous. This thesis develops new methods to estimate these types of models, with the objective of obtaining more accurate estimates of the underlying parameters present. The methods are applicable to general models. As the solution to the true continuous process is rarely known for these applications, the methods developed rely on building an Euler-Maruyama approximate model and using simulation techniques to obtain the distribution of the unknown quantities of interest. We propose to simulate the missing paths between the observed data points to reduce the bias from the approximate model. Alternatively, one could use a more sophisticated scheme to discretise the process. Unfortunately, their implementation with simulation methods require us to simulate from the density and evaluate the density at any given point. This has until now only been possible for the Euler-Maruyama scheme. One contribution of the thesis is to show the existence of a closed form solution from use of the higher order Milstein scheme. The likelihood based method is implemented within the Bayesian paradigm, as in the context of these models, Bayesian methods are often analytically easier. Concerning the estimation methodology, emphasis is placed on simulation efficiency; design and implementation of the method directly affects the accuracy and stability of the results. In conjunction with estimation, it is important to provide inference and diagnostic procedures. Meaningful information from simulation results must be extracted and summarised. This necessitates developing techniques to evaluate the plausibility and hence the fit of a particular model for a given dataset. An important aspect of model evaluation concerns the ability to compare model fit across a range of possible alternatives. The advantage with the Bayesian framework is that it allows comparison across non-nested models. The aim of the thesis is thus to provide an efficient estimation method for these continuous-time models, that can be used to conduct meaningful inference, with their performance being assessed through the use of diagnostic tools.

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9

Schwarzenberger, Michael. "Affine Processes and Pseudo-Differential Operators with Unbounded Coefficients". Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-211510.

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The concept of pseudo-differential operators allows one to study stochastic processes through their symbol. This approach has generated many new insights in recent years. However, most results are based on the assumption of bounded coefficients. In this thesis, we study Levy-type processes with unbounded coefficients and, especially, affine processes. In particular, we establish a connection between pseudo-differential operators and affine processes which are well-known from mathematical finance. Affine processes are an interesting example in this field since they have linearly growing and hence unbounded coefficients. New techniques and tools are developed to handle the affine case and then expanded to general Levy-type processes. In this way, the convergence of a simulation scheme based on a Markov chain approximation, results on path properties, and necessary conditions for the symmetry of operators were proven.

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10

Geurts, Kevin Richard. "Stochastic simulation of non-Newtonian flow fields /". Thesis, Connect to this title online; UW restricted, 1995. http://hdl.handle.net/1773/9821.

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11

Estévez, Schwarz Diana. "Consistent initialization for index-2 differential algebraic equations and its application to circuit simulation". [S.l. : s.n.], 2000. http://deposit.ddb.de/cgi-bin/dokserv?idn=960337202.

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12

Koppe, Jason. "Differential virtualization for large-scale system modeling /". Online version of thesis, 2008. http://hdl.handle.net/1850/7543.

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13

Compere, Marc Damon. "Simulation of engineering systems described by high-index DAE and discontinuous ODE using single step methods". Thesis, Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3025206.

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14

Intep, Somkid. "Stochastic differential equations with switching and numerical simulation for gene regulation networks". Thesis, University of Strathclyde, 2010. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=14354.

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15

Gaines, Jessica Gabrielle. "Topics in the numerical simulation of pathwise solutions to stochastic differential equations". Thesis, University of Edinburgh, 1995. http://hdl.handle.net/1842/13867.

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This work contains several developments in the area of numerical solution of pathwise solutions to stochastic differential equations (SDE's). In the first chapter we define and motivate pathwise solutions and give a brief survey of numerical methods for approximating them. The main key to enlarging the scope of numerical methods for SDE's is a good representation of Brownian paths. A binary tree structure is an essential tool in Chapter Two, which presents a general method for solution of SDE's using variable time steps. In the case of a general SDE, improvement of the order of convergence compared with standard methods, demands generation of the Lévy area integrals. Chapter Three presents a method of random generation of the Lévy area for a Brownian path in IR². The method is based on Marsaglia's rectangle-wedge-tail method for fast generation of normally distributed deviates. Since the solution of an SDE generally depends on an infinite sequence of iterated integrals of the driving noise, it makes sense to examine these integrals and the algebraic relations between them. In Chapter Four, it is shown how known facts about shuffle algebras can be used to get a better understanding of stochastic iterated integrals of Ito and Stratonovich type and obtain practical algebraic bases for these two sets. We use the algebra to calculate moments of stochastic integrals, needed when calculating moments of error during numerical solutions of SDE's. The work on the generation of area integrals, described in Chapter Three, gives rise to general questions about the generation of random deviates, some of which are addressed in the last two chapters. In Chapter Five, we present a polynomial-time algorithm for finding the partition, into rectangles or triangles, of certain types of region in IR², that has the lowest entropy.

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16

Kwong, Gordon Houng. "Approximations for Nonlinear Differential Algebraic Equations to Increase Real-time Simulation Efficiency". Thesis, Virginia Tech, 2010. http://hdl.handle.net/10919/42753.

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Full-motion driving simulators require efficient real-time high fidelity vehicle models in order to provide a more realistic vehicle response. Typically, multi-body models are used to represent the vehicle dynamics, but these have the unfortunate drawback of requiring the solution of a set of coupled differential algebraic equations (DAE). DAE's are not conducive to real-time implementation such as in a driving simulator, without a very expensive processing capability. The primary objective of this thesis is to show that multi-body models constructed from DAE's can be reasonably approximated with linear models using suspension elements that have nonlinear constitutive relationships. Three models were compared in this research, an experimental quarter-car test rig, a multi-body dynamics differential algebraic equation model, and a linear model with nonlinear suspension elements. Models constructed from differential algebraic equations are computationally expensive to compute and are difficult to realize for real-time simulations. Instead, a linear model with nonlinear elements was proposed for a more computationally efficient solution that would retain the nonlinearities of the suspension. Simplifications were made to the linear model with nonlinear elements to further reduce computation time for real-time simulation. The development process of each model is fully described in this thesis. Each model was excited with the same input and their outputs were compared. It was found that the linear model with nonlinear elements provides a reasonably good approximation of actual model with the differential algebraic equations.
Master of Science

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17

Wensch, Jörg. "Beiträge zur geometrischen Integration und Anwendungen in der numerischen Simulation". [S.l.] : [s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=974103195.

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18

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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19

Sickenberger, Thorsten. "Efficient transient noise analysis in circuit simulation". Berlin Logos-Verl, 2008. http://d-nb.info/989242609/04.

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20

Bilbao, Héctor Uhalte. "DAB Transmission System Simulation". Thesis, Linköping University, Department of Electrical Engineering, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-2595.

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DAB (Digital Audio Broadcasting) is the radio digital system developed as an european standard by the ETSI, EN 300 400, based on the Eureka-147 group works, to improve the performance of the analogue radio systems (AM and FM). The system is based on the OFDM technology which allows DAB to exploit the spectrum frequencies in a better way with a higher quality of sound for mobile receivers specially. The main part of the OFDM system is based on the FFT algorithms to spread the data flow over different orthogonal carriers. The simulation has been developed in Simulink^TMand Matlab^TMand the layout designed follows faithfully the standard for the transmission system. The simulation can be reloaded by the user with the information presented in this thesis. Thus, this work can be continued to complete the DAB whole system simulation. The results obtained running this simulation show the main DAB system characteristics.

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21

Knorr, stephanie. "Wavelet-based simulation of multirate partial differential-algebraic systems in radio frequency applications /". Düsseldorf : VDI, 2007. http://opac.nebis.ch/cgi-bin/showAbstract.pl?u20=9783183408207.

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22

McCall, Daryl Lynn. "Investigation through simulation techniques of the application of differential GPS to civil aviation". Ohio : Ohio University, 1985. http://www.ohiolink.edu/etd/view.cgi?ohiou1184013759.

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23

Shen, Wensheng. "Computer Simulation and Modeling of Physical and Biological Processes using Partial Differential Equations". UKnowledge, 2007. http://uknowledge.uky.edu/gradschool_diss/501.

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Scientific research in areas of physics, chemistry, and biology traditionally depends purely on experimental and theoretical methods. Recently numerical simulation is emerging as the third way of science discovery beyond the experimental and theoretical approaches. This work describes some general procedures in numerical computation, and presents several applications of numerical modeling in bioheat transfer and biomechanics, jet diffusion flame, and bio-molecular interactions of proteins in blood circulation. A three-dimensional (3D) multilayer model based on the skin physical structure is developed to investigate the transient thermal response of human skin subject to external heating. The temperature distribution of the skin is modeled by a bioheat transfer equation. Different from existing models, the current model includes water evaporation and diffusion, where the rate of water evaporation is determined based on the theory of laminar boundary layer. The time-dependent equation is discretized using the Crank-Nicolson scheme. The large sparse linear system resulted from discretizing the governing partial differential equation is solved by GMRES solver. The jet diffusion flame is simulated by fluid flow and chemical reaction. The second-order backward Euler scheme is applied for the time dependent Navier-Stokes equation. Central difference is used for diffusion terms to achieve better accuracy, and a monotonicity-preserving upwind difference is used for convective ones. The coupled nonlinear system is solved via the damped Newton's method. The Newton Jacobian matrix is formed numerically, and resulting linear system is ill-conditioned and is solved by Bi-CGSTAB with the Gauss-Seidel preconditioner. A novel convection-diffusion-reaction model is introduced to simulate fibroblast growth factor (FGF-2) binding to cell surface molecules of receptor and heparan sulfate proteoglycan and MAP kinase signaling under flow condition. The model includes three parts: the flow of media using compressible Navier-Stokes equation, the transport of FGF-2 using convection-diffusion transport equation, and the local binding and signaling by chemical kinetics. The whole model consists of a set of coupled nonlinear partial differential equations (PDEs) and a set of coupled nonlinear ordinary differential equations (ODEs). To solve the time-dependent PDE system we use second order implicit Euler method by finite volume discretization. The ODE system is stiff and is solved by an ODE solver VODE using backward differencing formulation (BDF). Findings from this study have implications with regard to regulation of heparin-binding growth factors in circulation.

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24

Mašlan, Stanislav. "Diferenční zesilovače s bipolárními a unipolárními tranzistory". Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2009. http://www.nusl.cz/ntk/nusl-217743.

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25

Thorslund, Gustaf. "Simulating Partial Differential Equations using the Explicit Parallelism of ParModelica". Thesis, Linköpings universitet, Programvara och system, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-120079.

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The Modelica language is a modelling and programming language for modelling cyber-physical systems using equations and algorithms. In this thesis two suggested extensions of the Modelica language are covered. Those are Partial Differential Equations (PDE) and explicit parallelism in algorithmic code. While PDEs are not yet supported by the Modelica language, this thesis presents a framework for solving PDEs using the algorithmic part of the Modelica language, including parallel extensions. Different numerical solvers have been implemented using the explicit parallel constructs suggested for Modelica by the ParModelica language extensions, and implemented as part of OpenModelica. The solvers have been evaluated using different models, and it can be seen how bigger models are suitable for a parallel solver. The intention has been to write a framework suitable for modelling and parallel simulation of PDEs. This work can, however, also be seen as a case study of how to write a custom solver using parallel algorithmic Modelica and how to evaluate the performance of a parallel solver.

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26

Colakovic, Sabina y Viktor Ågren. "Multilevel Monte Carlo Simulation for American Option Pricing". Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-54356.

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In this thesis, we center our research around the analytical approximation of American put options with the Multilevel Monte Carlo simulation approach. The focus lies on reducing the computational complexity of estimating an expected value arising from a stochastic differential equation. Numerical results showcase that the simulations are consistent with the theoretical order of convergence of Monte Carlo simulations. The approximations are accurate and considerately more computationally efficient than the standard Monte Carlo simulation method.

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27

Gao, Zhenlan. "Transition to chaos of natural convection between two vertical differentially heated plates". Paris 6, 2013. http://www.theses.fr/2013PA066544.

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La transition vers le chaos de la convection naturelle d’air entre deux plaques infinies verticales différentiellement chauffées est étudiée. La première instabilité est une bifurcation de fourche conduisant à des rouleaux 2D. L’équation de Ginzburg-Landau est dérivée pour cette première bifurcation et comparée aux résultats de la DNS. La DNS 2D montre que les rouleaux sont instables via une bifurcation de Hopf. L’écoulement devient ensuite quasipériodique puis chaotique. A plus haut Rayleigh (Ra), l’écoulement redevient stationnaire. La DNS dans une configuration 3D comprenant quatre rouleaux verticaux, mais de petite dimension transverse, montre que les rouleaux 2D deviennent 3D par une bifurcation de fourche. Puis l’écoulement devient oscillant via une bifurcation de Hopf. On observe une cascade de doublement de période des motifs 3D, dominée par un mécanisme de modulation du nombre des rouleaux. Lorsqu’un seul rouleau est considéré, le scénario sousharmonique devient persistant et conduit au chaos. A plus grand Ra, on oberve une intermittence de crise, correspondant au déplacement du rouleau d’une demi-hauteur. L’analyse de stabilité linéaire des rouleaux est effectuée avec la méthode d’Arnoldi. Les résultats sont comparés avec la simulation nonlinéaire dans un domaine de grande dimension transverse. Les rouleaux 2D bifurquent vers un état 3D composé de rouleaux ondulés, qui devienent ensuite des rouleaux brisés. L’écoulement devient oscillant via une bifurcation de Hopf. A plus haut Rayleigh une bifurcation sous-harmonique est observée, qui conduit au chaos temporel
The transition to chaos of the natural convection of air between two infinite differentially heated vertical plates is studied. The first instability is a pitchfork bifurcation leading to steady 2D rolls. A Ginzburg-Landau equation is derived analytically for the flow around the first bifurcation and compared with DNS results. 2D DNS shows that rolls become unstable via a Hopf bifurcation. At higher Rayleigh numbers, the flow becomes quasiperiodic then chaotic. At still higher Rayleigh numbers the flow becomes steady again. DNS in a 3D configuration with a small transverse extent shows that 2D rolls undergo another pitchfork bifurcation to a 3D pattern, which consists of deformed rolls connected by counter-rotating vortices. The flow then becomes oscillatory via a Hopf bifurcation. Chaotic behavior subsequently occurs through a sequence of period-doubling bifurcations, which gives way to a spatial modulation pattern. When only one roll is allowed in the domain, the cascade of period-doubling bifurcations becomes persistent, leading the flow to temporal chaos. At higher Ra, a crisis-induced intermittency is observed, as the flow structures shift vertically by half a vertical wavelength. We use the Arnoldi method to determine the unstable transverse wavenumbers. 3D DNS in a domain of large extent shos that the 2D rolls bifurcate to a steady 3D pattern consisting of pinched rolls, which gives way to broken rolls. Then the flow becomes oscillatory via a Hopf bifurcation. Subsequently, a period-doubling bifurcation is observed, and eventually the flow becomes temporally chaotic

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28

Elson, J. Scott. "Simulation and performance analysis of Cellular Digital Packet Data". Thesis, Virginia Tech, 1996. http://hdl.handle.net/10919/45069.

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As the wireless telecommunications industry becomes more widely accepted, the need for mobile data communication has followed the rise in mobile voice communication. Cellular Digital Packet Data (CDPD) offers an unobtrusive data service that overlays the existing Advanced Mobile Phone Service (AMPS) in a cost effective manner that will be attractive to most service providers. Using idle time between voice traffic, CDPD uses Gaussian Minimum Shift Keying (GMSK) to send bursts of Reed-Solomon encoded information while channel hopping to avoid interfering with voice transmissions.

This thesis assesses the performance of CDPD for different channel environments through simulation. Specifically, Gaussian noise, Rayleigh fading, co-channel interference models are incorporated to identify the performance of the system.

Master of Science

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29

Qiao, Zhonghua. "Numerical solution for nonlinear Poisson-Boltzmann equations and numerical simulations for spike dynamics". HKBU Institutional Repository, 2006. http://repository.hkbu.edu.hk/etd_ra/727.

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30

Templeton, Anne Mills. "Physical crowds and psychological crowds : applying self-categorization theory to computer simulation of collective behaviour". Thesis, University of Sussex, 2017. http://sro.sussex.ac.uk/id/eprint/70452/.

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Computer models are used to simulate pedestrian behaviour for safety at mass events. Previous research has indicated differences between physical crowds of co-present individuals, and psychological crowds who mobilise collective behaviour through a shared social identity. This thesis aimed to examine the assumptions models use about crowds, conduct two studies of crowd movement to ascertain the behavioural signatures of psychological crowds, and implement these into a theoretically-driven model of crowd behaviour. A systematic review of crowd modelling literature is presented which explores the assumptions about crowd behaviour being used in current models. This review demonstrates that models portray the crowd as either an identical mass with no inter-personal connections, unique individuals with no connections to others, or as small groups within a crowd. Thus, no models have incorporated the role of self-categorisation theory needed to simulate collective behaviour. The empirical research in this thesis aimed to determine the behavioural effects of self-categorisation on pedestrian movement. Findings from a first study illustrate that, in comparison to a physical crowd, perception of shared social identities in the psychological crowd motivated participants to maintain close proximity with ingroup members through regulation of their speed and distance walked. A second study showed that collective self-organisation seemed to be increased by the presence of an outgroup, causing ingroup members to tighten formation to avoid splitting up. Finally, a computer model is presented which implements the quantified behavioural effects of self-categorisation found in the behavioural studies. A self-categorisation parameter is introduced to simulate ingroup members self-organising to remain together. This is compared to a physical crowd simulation with group identities absent. The results demonstrate that the self-categorisation parameter provides more accurate simulation of psychological crowd behaviour. Thus, it is argued that models should implement self-categorisation into simulations of psychological crowds to increase safety at mass events.

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31

Steinbrecher, Andreas. "Numerical solution of quasi-linear differential-Algebraic equations and industrial simulation of multibody systems". [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980015936.

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32

Schwarz, Diana Estévez. "Consistent initialization for index-2 differential algebraic equations and its application to circuit simulation". Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2000. http://dx.doi.org/10.18452/14512.

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Zur numerischen L\"osung von Algebro-Differentialgleichungen (ADGln) m\"ussen konsistente Anfangswerte berechnet werden. Diese Arbeit befasst sich mit einem Ansatz zur Behandlung dieses Problems f\"ur Index-2 DAEs unter Verwendung von Projektoren auf die zur DAE zugeh\"origen Unterr\"aume. Die Arbeit hat zwei Schwerpunkte.\\ Zum einen werden neue Struktureigenschaften aus schwachen Voraussetzungen hergeleitet. Anschlie{\ss}end wird eine Vorgehensweise zur Auswahl von geeigneten Gleichungen einer Index-2 ADGln vorgeschlagen, deren Differentiation zu einer Indexreduktion f\"uhrt. Diese Indexreduktion liefert neue Existenz- und Eindeutigkeitsergebnisse f\"ur L\"osungen von Index-2 ADGln. Die Ergebnisse umfassen eine allgemeinere Aufgabenklasse als die bisherigen Resultate. Beruhend auf dieser Vorgehensweise wird ein stufenweiser Ansatz zur Berechnung konsistenter Anfangswerte hergeleitet. Auf diese Weise werden neue Einsichten hinsichtlich der Ausnutzung von Struktureigenschaften von Index-2 ADGln gewonnen. Insbesondere stellt sich heraus, dass im Vergleich zu Index-1 ADGln der zus\"atzliche Schritt oft in der L\"osung eines linearen Systems besteht. Die sich hieraus ergebenden numerischen Folgen werden f\"ur zwei in der Schaltungssimulation h\"aufig verwendete Verfahren, das implizite Eulerverfahren und die Trapezregel, erl\"autert. \\ Zum anderen wird die Anwendung der erhaltenen Ergebnisse auf die Gleichungen, die bei der Schaltungssimulation mittels modifizierter Knotenanalyse entstehen, ausgearbeitet. Abschlie{\ss}end wird eine kurze \"Ubersicht der durchgef\"uhrten Umsetzung gegeben.\\
For solving DAEs numerically, consistent initial values have to be calculated. This thesis deals with an approach for handling this problem for index-2 DAEs by considering projectors onto the spaces related to the DAE. There are two major aspects in this work.\\ On the one hand, new structural properties are deduced from weak assumptions. Subsequently, a method is proposed to choose suitable equations of an index-2 DAE, whose differentiation leads to an index reduction. This index reduction yields new theoretical results for the existence and uniqueness of solutions of index-2 DAEs which apply to a wider class of applications than previous results. Based on this method, a step-by-step approach to compute consistent initial values is developed. In this way, we gain new insights about how to deal with structural properties of index-2 DAEs. In particular, it turns out that, in comparison to index-1 DAEs, the additional step that has to be undertaken in practice often consists in solving a linear system. The numerical consequences of this fact are exemplified for two methods commonly used in circuit simulation, the implicit Euler method and the trapezoidal rule.\\ On the other hand, the application of the obtained results to the equations arising in circuit simulation by means of the modified nodal analysis (MNA) is worked out. Finally, a short overview of the specifics of their realization is given.

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33

Vijapurapu, Vamsi Krishna. "Differential relay model development and validation using real time digital simulator". Master's thesis, Mississippi State : Mississippi State University, 2008. http://library.msstate.edu/etd/show.asp?etd=etd-09222008-143941.

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34

Poon, Chun-Kin. "Numerical simulation of coupled long wave-short wave system with a mismatch in group velocities". Click to view the E-thesis via HKUTO, 2005. http://sunzi.lib.hku.hk/hkuto/record/B35381334.

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35

Gritsis, Dimitrios. "The dynamic simulation and optimal control of systems described by index two differential-algebraic equations". Thesis, Imperial College London, 1990. http://hdl.handle.net/10044/1/8535.

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36

Pietschmann, Jan-Frederik. "On some partial differential equation models in socio-economic contexts : analysis and numerical simulations". Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/241495.

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This thesis deals with the analysis and numerical simulation of different partial differential equation models arising in socioeconomic sciences. It is divided into two parts: The first part deals with a mean-field price formation model introduced by Lasry andLions in 2007. This model describes the dynamic behaviour of the price of a good being traded between a group of buyers and a group of vendors. Existence (locally in time) of smooth solutions is established, and obstructions to proving a global existence result are examined. Also, properties of a regularised version of the model are explored and numerical examples are shown. Furthermore, the possibility of reconstructing the initial datum given a number of observations, regarding the price and the transaction rate, is considered. Using a variational approach, the problem can be expressed as a non-linear constrained minimization problem. We show that the initial datum is uniquely determined by the price (identifiability). Furthermore, a numerical scheme is implemented and a variety of examples are presented. The second part of this thesis treats two different models describing the motion of (large) human crowds. For the first model, introduced by R.L. Hughes in 2002, several regularised versions are considered. Existence and uniqueness of entropy solutions are proven using the technique of vanishing viscosity. In one space dimension, the dynamic behaviour of solutions of the original model is explored for some special cases. These results are compared to numerical simulations. Moreover, we consider a discrete cellular automaton model introduced by A. Kirchner and A. Schadschneider in 2002.By (formally) passing to the continuum limit, we obtain a system of partial differential equations. Some analytical properties, such as linear stability of stationary states, areexamined and extensive numerical simulations show capabilities and limitations of the model in both the discrete and continuous setting.

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37

Yannios, Nicholas y mikewood@deakin edu au. "Computational aspects of the numerical solution of SDEs". Deakin University. School of Computing and Mathematics, 2001. http://tux.lib.deakin.edu.au./adt-VDU/public/adt-VDU20060817.123449.

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In the last 30 to 40 years, many researchers have combined to build the knowledge base of theory and solution techniques that can be applied to the case of differential equations which include the effects of noise. This class of ``noisy'' differential equations is now known as stochastic differential equations (SDEs). Markov diffusion processes are included within the field of SDEs through the drift and diffusion components of the Itô form of an SDE. When these drift and diffusion components are moderately smooth functions, then the processes' transition probability densities satisfy the Fokker-Planck-Kolmogorov (FPK) equation -- an ordinary partial differential equation (PDE). Thus there is a mathematical inter-relationship that allows solutions of SDEs to be determined from the solution of a noise free differential equation which has been extensively studied since the 1920s. The main numerical solution technique employed to solve the FPK equation is the classical Finite Element Method (FEM). The FEM is of particular importance to engineers when used to solve FPK systems that describe noisy oscillators. The FEM is a powerful tool but is limited in that it is cumbersome when applied to multidimensional systems and can lead to large and complex matrix systems with their inherent solution and storage problems. I show in this thesis that the stochastic Taylor series (TS) based time discretisation approach to the solution of SDEs is an efficient and accurate technique that provides transition and steady state solutions to the associated FPK equation. The TS approach to the solution of SDEs has certain advantages over the classical techniques. These advantages include their ability to effectively tackle stiff systems, their simplicity of derivation and their ease of implementation and re-use. Unlike the FEM approach, which is difficult to apply in even only two dimensions, the simplicity of the TS approach is independant of the dimension of the system under investigation. Their main disadvantage, that of requiring a large number of simulations and the associated CPU requirements, is countered by their underlying structure which makes them perfectly suited for use on the now prevalent parallel or distributed processing systems. In summary, l will compare the TS solution of SDEs to the solution of the associated FPK equations using the classical FEM technique. One, two and three dimensional FPK systems that describe noisy oscillators have been chosen for the analysis. As higher dimensional FPK systems are rarely mentioned in the literature, the TS approach will be extended to essentially infinite dimensional systems through the solution of stochastic PDEs. In making these comparisons, the advantages of modern computing tools such as computer algebra systems and simulation software, when used as an adjunct to the solution of SDEs or their associated FPK equations, are demonstrated.

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38

Paiement, Richard V. "The study of differential 8-PSK trellis-coded modulation in indoor wireless communications through computer simulation". Thesis, University of Ottawa (Canada), 1991. http://hdl.handle.net/10393/7641.

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This thesis work studies the use of 4- and 8-state trellis-coded modulation with phase-shift keying and non-coherent, differential signaling for digital indoor wireless communications, at an operating frequency of 1.5 GHz and a transmission rate of 10 Mbits/s. Many other modulation schemes have been considered for the indoor wireless channel in other studies, and trellis-coded modulation has been considered for the satellite and mobile channel. This study presents new BER performance results, obtained through computer simulations, that suggest a performance gain with TCM relative to DQPSK, for certain ranges of SNR and rms delay spread. Equalization is also considered, and it is shown that it can provide considerable performance gain.

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39

Shu, Chang. "Generalized differential-integral quadrature and application to the simulation of incompressible viscous flows including parallel computation". Thesis, University of Glasgow, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.361006.

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40

Skjellum, Anthony Morari Manfred. "Concurrent dynamic simulation : multicomputer algorithms research applied to ordinary differential-algebraic process systems in chemical engineering /". Diss., Pasadena, Calif. : California Institute of Technology, 1990. http://resolver.caltech.edu/CaltechETD:etd-11132007-090727.

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41

Poon, Chun-Kin y 潘俊健. "Numerical simulation of coupled long wave-short wave system with a mismatch in group velocities". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B35381334.

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42

Epple, Alexander. "Methods for increased computational efficiency of multibody simulations". Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26532.

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Thesis (Ph. D.)--Aerospace Engineering, Georgia Institute of Technology, 2009.
Committee Chair: Olivier A. Bauchau; Committee Member: Andrew Makeev; Committee Member: Carlo L. Bottasso; Committee Member: Dewey H. Hodges; Committee Member: Massimo Ruzzene. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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43

Yalman, Hatice. "Change Point Estimation for Stochastic Differential Equations". Thesis, Växjö University, School of Mathematics and Systems Engineering, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-5748.

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A stochastic differential equationdriven by a Brownian motion where the dispersion is determined by a parameter is considered. The parameter undergoes a change at a certain time point. Estimates of the time change point and the parameter, before and after that time, is considered.The estimates were presented in Lacus 2008. Two cases are considered: (1) the drift is known, (2) the drift is unknown and the dispersion space-independent. Applications to Dow-Jones index 1971-1974 and Goldmann-Sachs closings 2005-- May 2009 are given.

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44

Schöön, Jonathan. "Pricing Put Options with Multilevel Monte Carlo Simulation". Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-55404.

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Monte Carlo path simulations are common in mathematical and computational finance as a way of estimating the expected values of a quantity such as a European put option, which is functional to the solution of a stochastic differential equation (SDE). The computational complexity of the standard Monte Carlo (MC) method grows quite large quickly, so in this thesis we focus on the Multilevel Monte Carlo (MLMC) method by Giles, which uses multigrid ideas to reduce the computational complexity. We use a Euler-Maruyama time discretisation for the approximation of the SDE and investigate how the convergence rate of the MLMC method improves the computational times and cost in comparison with the standard MC method. We perform a numerical analysis on the computational times and costs in order to achieve the desired accuracy and present our findings on the performance of the MLMC method on a European put option compared to the standard MC method.

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45

Taylor, Phillip. "Simulating Gaussian random fields and solving stochastic differential equations using bounded Wiener increments". Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/simulating-gaussian-random-fields-and-solving-stochastic-differential-equations-using-bounded-wiener-increments(b77a0fcc-3d86-46b2-8dbf-2a689d9f8f77).html.

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46

Turkedjiev, Plamen. "Numerical methods for backward stochastic differential equations of quadratic and locally Lipschitz type". Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2013. http://dx.doi.org/10.18452/16784.

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Der Fokus dieser Dissertation liegt darauf, effiziente numerische Methode für ungekoppelte lokal Lipschitz-stetige und quadratische stochastische Vorwärts-Rückwärtsdifferenzialgleichungen (BSDE) mit Endbedingungen von schwacher Regularität zu entwickeln. Obwohl BSDE viele Anwendungen in der Theorie der Finanzmathematik, der stochastischen Kontrolle und der partiellen Differenzialgleichungen haben, gibt es bisher nur wenige numerische Methoden. Drei neue auf Monte-Carlo- Simulationen basierende Algorithmen werden entwickelt. Die in der zeitdiskreten Approximation zu lösenden bedingten Erwartungen werden mittels der Methode der kleinsten Quadrate näherungsweise berechnet. Ein Vorteil dieser Algorithmen ist, dass sie als Eingabe nur Simulationen eines Vorwärtsprozesses X und der Brownschen Bewegung benötigen. Da sie auf modellfreien Abschätzungen aufbauen, benötigen die hier vorgestellten Verfahren nur sehr schwache Bedingungen an den Prozess X. Daher können sie auf sehr allgemeinen Wahrscheinlichkeitsräumen angewendet werden. Für die drei numerischen Algorithmen werden explizite maximale Fehlerabschätzungen berechnet. Die Algorithmen werden dann auf Basis dieser maximalen Fehler kalibriert und die Komplexität der Algorithmen wird berechnet. Mithilfe einer zeitlich lokalen Abschneidung des Treibers der BSDE werden quadratische BSDE auf lokal Lipschitz-stetige BSDE zurückgeführt. Es wird gezeigt, dass die Komplexität der Algorithmen im lokal Lipschitz-stetigen Fall vergleichbar zu ihrer Komplexität im global Lipschitz-stetigen Fall ist. Es wird auch gezeigt, dass der Vergleich mit bereits für Lipschitz-stetige BSDE existierenden Methoden für die hier vorgestellten Algorithmen positiv ausfällt.
The focus of the thesis is to develop efficient numerical schemes for quadratic and locally Lipschitz decoupled forward-backward stochastic differential equations (BSDEs). The terminal conditions satisfy weak regularity conditions. Although BSDEs have valuable applications in the theory of financial mathematics, stochastic control and partial differential equations, few efficient numerical schemes are available. Three algorithms based on Monte Carlo simulation are developed. Starting from a discrete time scheme, least-square regression is used to approximate conditional expectation. One benefit of these schemes is that they require as an input only the simulations of an explanatory process X and a Brownian motion W. Due to the use of distribution-free tools, one requires only very weak conditions on the explanatory process X, meaning that these methods can be applied to very general probability spaces. Explicit upper bounds for the error are obtained. The algorithms are then calibrated systematically based on the upper bounds of the error and the complexity is computed. Using a time-local truncation of the BSDE driver, the quadratic BSDE is reduced to a locally Lipschitz BSDE, and it is shown that the complexity of the algorithms for the locally Lipschitz BSDE is the same as that of the algorithm of a uniformly Lipschitz BSDE. It is also shown that these algorithms are competitive compared to other available algorithms for uniformly Lipschitz BSDEs.

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47

Sekerci, Yadigar. "Some recent simulation techniques of diffusion bridge". Thesis, Växjö University, School of Mathematics and Systems Engineering, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-5749.

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We apply some recent numerical solutions to diffusion bridges written in Iacus (2008). One is an approximate scheme from Bladt and S{\o}rensen (2007), another one, from Beskos et al (2006), is an algorithm which is exact: no numerical error at given grid points!

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48

Wang, Shuo. "Analysis and Application of Haseltine and Rawlings's Hybrid Stochastic Simulation Algorithm". Diss., Virginia Tech, 2016. http://hdl.handle.net/10919/82717.

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Stochastic effects in cellular systems are usually modeled and simulated with Gillespie's stochastic simulation algorithm (SSA), which follows the same theoretical derivation as the chemical master equation (CME), but the low efficiency of SSA limits its application to large chemical networks. To improve efficiency of stochastic simulations, Haseltine and Rawlings proposed a hybrid of ODE and SSA algorithm, which combines ordinary differential equations (ODEs) for traditional deterministic models and SSA for stochastic models. In this dissertation, accuracy analysis, efficient implementation strategies, and application of of Haseltine and Rawlings's hybrid method (HR) to a budding yeast cell cycle model are discussed. Accuracy of the hybrid method HR is studied based on a linear chain reaction system, motivated from the modeling practice used for the budding yeast cell cycle control mechanism. Mathematical analysis and numerical results both show that the hybrid method HR is accurate if either numbers of molecules of reactants in fast reactions are above certain thresholds, or rate constants of fast reactions are much larger than rate constants of slow reactions. Our analysis also shows that the hybrid method HR allows for a much greater region in system parameter space than those for the slow scale SSA (ssSSA) and the stochastic quasi steady state assumption (SQSSA) method. Implementation of the hybrid method HR requires a stiff ODE solver for numerical integration and an efficient event-handling strategy for slow reaction firings. In this dissertation, an event-handling strategy is developed based on inverse interpolation. Performances of five wildly used stiff ODE solvers are measured in three numerical experiments. Furthermore, inspired by the strategy of the hybrid method HR, a hybrid of ODE and SSA stochastic models for the budding yeast cell cycle is developed, based on a deterministic model in the literature. Simulation results of this hybrid model match very well with biological experimental data, and this model is the first to do so with these recently available experimental data. This study demonstrates that the hybrid method HR has great potential for stochastic modeling and simulation of large biochemical networks.
Ph. D.

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49

Beersing-Vasquez, Kiran. "Suturing in Surgical Simulations". Thesis, KTH, Numerisk analys, NA, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-260254.

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The goal of this project is to develop virtual surgical simulation software in order to simulate the suturing and knot tying processes associated with surgical thread. State equations are formulated using Lagrangian mechanics, which is useful for the conservation of energy. Solver methods are developed with theory based in Differential Algebraic Equations (DAEs) which concern governing Ordinary Differential Equations (ODEs) that are constraint with Algebraic Equations (AE). An implicit integration scheme and Newton's method is used to solve the system in each step. Furthermore, a collision response process based on the Linear Complementarity Problem (LCP) is implemented to handle collisions and measure their forces. Models have been developed to represent the different types of objects. A spline model is used to represent the suture and mass-spring model for the tissue. They were both selected for their efficiency and base on real physical properties. The spline model was also chosen as it is continuous and can be evaluated at any point along the length. Other objects are also defined such as rigid bodies. The Lagrangian multiplier method is used to define the constraints in the model. This allows for the construction of complex models. An important constraint is the suturing constraint, which is created when a sufficient force is applied by the suture tip on to the tissue. This constraint allows only a sliding point along the suture to pass through a specific point on the tissue. This results in a virtual suturing model which can be built on for use in surgical simulations. Further investigations would be interesting to increase performance, accuracy and scope of the simulator.
Det här projektet syftar till att utveckla mjukvara för virtuell simulering av kirurgi som involverar knytande av suturtråd. Lagranges ekvationer används för att härleda energibevarande tillståndsekvationer. Lösningsmetoderna grundar sig i teori från området Differential-Algebraiska Ekvationer (DAEer), som avser att kontrollera Ordinära Differentialekvationer (ODEer) med algebraiska bivillkor. Ett implicit integrationsschema och Newtons metod används för att lösa systemet i varje steg. Utöver det så implementeras en kollisionsrespons-process baserad på det linjära komplementaritetsproblemet (LCP) för att hantera kollisioner och mäta deras krafter. Modeller har utvecklats för att representera olika typer av objekt. En spline-modell används för att representera suturtråden och ett mass-fjäder system för vävnaden. Valet baserades på deras höga prestanda samt starka anknytning till objektens fysiska egenskaper. Spline-modellen valdes också då dess kontinuitet innebär att den går att evaluera för en godtycklig punkt inom dess domän. Andra objekt, såsom stela kroppar, finns också definierade. Lagrangemultiplikator används för att definiera bivillkor i modellen. Detta tillåter konstruktionen av komplexa modeller. Ett viktigt bivillkor är sutur-bivillkoret som uppstår när tillräcklig kraft från spetsen på den kirurgiska nålen appliceras på vävnaden. Detta bivillkor tillåter att endast en glidande punkt längsmed suturen passerar genom en specifik punkt på vävnaden. Detta resulterar i en virtuell modell för stygn som kan byggas vidare på för användning i kirurgiska simulationer. Det vore intressant med ytterligare undersökningar för att förbättra prestandan, precisionen och simulatorns omfattning.

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50

Carter, Nathan T. "APPLICATIONS OF DIFFERENTIAL FUNCTIONING METHODS TO THE GENERALIZED GRADED UNFOLDING MODEL". Bowling Green State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1290885927.

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