Дисертації з теми "Differentiable model"
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1
Cowan, John D. "A billiard model for a gas of particles with rotation /." Thesis, Connect to Dissertations & Theses @ Tufts University, 2004.
Анотація:
Thesis (Ph.D.)--Tufts University, 2004.Adviser: Boris Hasselblatt. Submitted to the Dept. of Mathematics. Includes bibliographical references (leaves 61-62). Access restricted to members of the Tufts University community. Also available via the World Wide Web;
2
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.
Анотація:
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.
3
Ogden, Richard R. "Differential rotation and the geodynamo." Thesis, University of Glasgow, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.264156.
4
Nagloo, Joel Chris Ronnie. "Model theory, algebra and differential equations." Thesis, University of Leeds, 2014. http://etheses.whiterose.ac.uk/6813/.
Анотація:
In this thesis, we applied ideas and techniques from model theory, to study the structure of the sets of solutions XII - XV I , in a differentially closed field, of the Painlevé equations. First we show that the generic XII - XV I , that is those with parameters in general positions, are strongly minimal and geometrically trivial. Then, we prove that the generic XII , XIV and XV are strictly disintegrated and that the generic XIII and XV I are ω-categorical. These results, already known for XI , are the culmination of the work started by P. Painlevé (over 100 years ago), the Japanese school and many others on transcendence and the Painlevé equations. We also look at the non generic second Painlevé equations and show that all the strongly minimal ones are geometrically trivial.
5
Bjørneng, Bjørn. "How to increase the understanding of differentials by using the Casio-calculator model 9860 G I/II to solve differential equations." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79468.
Анотація:
The major aims of this paper are to present how we can improve the students understanding and involvement in mathematics by using a programming/graphic calculator. I will use differentials as examples such as differentiation ,integrals and differential equations, creating lines of slopes for differential equation of the type y’= f(x,y) . Find the solution of some differential equations by using regression and create the graph connected to the differential equation. As we have different approaches to solving a problem, it is a hope the students interest in mathematics will improve. The tools used will be programming, graphic commands as plot, f-line, etc. One goal is also to show how we can create small programs solving problems in mathematics. For many students this will be a stepping stone for further work with programming. The programs used can be copied using the program FA 124 that can be downloaded from Casios homepages. On request I can send you the programs.
6
Kriwet, Gregor [Verfasser]. "Methods for Model Calibration and Design of Optimal Experiments for Partial Differential Equation Models / Gregor Kriwet." Aachen : Shaker, 2016. http://d-nb.info/1118258258/34.
7
Baldi, Guillaume. "Contributions à la modélisation procédurale de structures cellulaires stochastoques 2D et à leur génération par l'exemple." Electronic Thesis or Diss., Strasbourg, 2024. http://www.theses.fr/2024STRAD001.
Анотація:
La création de matériaux et de textures procéduraux demande une grande expertise et constitue un travail long, fastidieux et coûteux, c’est pourquoi on cherche à développer des outils permettant leur génération automatique à partir d’exemples en entrée fournis sous la forme d’images : on parle de modélisation procédurale inverse.Dans cette thèse, nous proposons un modèle procédural appelé Cellular Point Process Texture Basis Function (C-PPTBF) permettant de représenter des structures cellulaires stochastiques 2D, impliquant des fonctions différentiables par rapport à la plupart de leurs paramètres, ce qui rend possible l’estimation de ces paramètres à partir d’exemples sans recourir entièrement à des réseaux de neurones profonds. Nous avons mis en place une chaîne de traitement permettant d’estimer les paramètres de notre modèle à partir d’exemples de structures fournis sous la forme d’images binaires, combinant une estimation réalisée à l’aide d’un réseau de neurones convolutif entraîné sur des images produites avec notre modèle de C-PPTBF et une phase d’estimation par descente de gradient directement sur les paramètres du modèle procéduralThe creation of procedural materials and textures requires considerable expertise, and is time-consuming, tedious and costly. We are therefore looking to develop tools for the automatic generation of procedural textures and materials from input exemplars provided in the form of images: This is known as inverse procedural modeling.In this thesis, we propose a procedural model called Cellular Point Process Texture Basis Function (C-PPTBF) for representing 2D stochastic cellular structures, involving functions that are differentiable with respect to most of their parameters, making it possible to estimate these parameters from examples without resorting entirely to deep neural networks. We have set up a processing pipeline to estimate the parameters of our model from structural examples provided in the form of binary images, combining an estimation performed using a convolutional neural network trained on images produced with our C-PPTBF model and an estimation phase using gradient descent directly on the parameters of the procedural model
8
Francia, Giulio. "Differential display application to a Melanoma model." Thesis, King's College London (University of London), 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.300029.
9
Hanig, Marco. "Differential gaming models of oligopoly." Thesis, Massachusetts Institute of Technology, 1986. http://hdl.handle.net/1721.1/14869.
Анотація:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Economics, 1987.Title as it appeared in the Massachusetts Institute of Technology Graduate List, June 1987: Differential game models of oligopoly.
Bibliography: leaves 242-249.
by Marco Hanig.
Ph.D.
10
Cruz, Jorge Carlos Ferreira Rodrigues da. "Constraint reasoning for differential models." Doctoral thesis, FCT - UNL, 2003. http://hdl.handle.net/10362/1061.
Анотація:
The basic motivation of this work was the integration of biophysical models within the interval constraints framework for decision support. Comparing the major features of biophysical models with the expressive power of the existing interval constraints framework, it was clear that the most important inadequacy was related with the representation of differential equations. System dynamics is often modelled through differential equations but there was no way of expressing a differential equation as a constraint and integrate it within the constraints framework. Consequently, the goal of this work is focussed on the integration of ordinary differential equations within the interval constraints framework, which for this purpose is extended with the new formalism of Constraint Satisfaction Differential Problems. Such framework allows the specification of ordinary differential equations, together with related information, by means of constraints, and provides efficient propagation techniques for pruning the domains of their variables. This enabled the integration of all such information in a single constraint whose variables may subsequently be used in other constraints of the model. The specific method used for pruning its variable domains can then be combined with the pruning methods associated with the other constraints in an overall propagation algorithm for reducing the bounds of all model variables. The application of the constraint propagation algorithm for pruning the variable domains, that is, the enforcement of local-consistency, turned out to be insufficient to support decision in practical problems that include differential equations. The domain pruning achieved is not, in general, sufficient to allow safe decisions and the main reason derives from the non-linearity of the differential equations. Consequently, a complementary goal of this work proposes a new strong consistency criterion, Global Hull-consistency, particularly suited to decision support with differential models, by presenting an adequate trade-of between domain pruning and computational effort. Several alternative algorithms are proposed for enforcing Global Hull-consistency and, due to their complexity, an effort was made to provide implementations able to supply any-time pruning results. Since the consistency criterion is dependent on the existence of canonical solutions, it is proposed a local search approach that can be integrated with constraint propagation in continuous domains and, in particular, with the enforcing algorithms for anticipating the finding of canonical solutions. The last goal of this work is the validation of the approach as an important contribution for the integration of biophysical models within decision support. Consequently, a prototype application that integrated all the proposed extensions to the interval constraints framework is developed and used for solving problems in different biophysical domains.
11
Bailey, Fred Washington. "Models for differential age acceleration." Thesis, This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-12052009-020133/.
12
JUNQUEIRA, DANIEL HAANWINCKEL. "A COMPENSATING DIFFERENTIALS MODEL OF INFORMAL LABOR MARKETS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2013. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=25494@1.
Анотація:
PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
FUNDAÇÃO DE APOIO À PESQUISA DO ESTADO DO RIO DE JANEIRO
PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO
Este trabalho desenvolve um modelo de busca por emprego com trabalhadores e firmas heterogêneos, salário mínimo e benefícios trabalhistas. Em equilíbrio, as firmas informais são menores, menos produtivas e empregam menos trabalhadores qualificados devido a um efeito de seleção. Trabalhadores informais geralmente recebem salários maiores para compensar a falta de benefícios trabalhistas, mas uma simples comparação de salários médios entre setores mostra um prêmio salarial para a formalidade devido a um efeito de composição. Além disto, o salário mínimo pode quebrar a relação de diferenciais compensatórios, de forma que haja um prêmio de formalidade para trabalhadores pouco qualificados mesmo após controlar para produtividade individual. O modelo é calibrado usando dados do Brasil e utilizado para explicar a evolução do mercado de trabalho neste país de 2003 até 2012. Os resultados sugerem que o aumento da escolaridade média foi o fator mais importante por trás da reversão da tendência de informalidade no Brasil, que ainda é um fato não plenamente explicado na literatura acadêmica. Também mostra-se que, no modelo calibrado, impostos progressivos sobre folha salarial poderiam levar a uma redução tanto do desemprego quanto da informalidade sem comprometer as receitas do governo.
This work develops a search and matching model of informality with heterogeneous workers and firms, minimum wages, and mandated benefits. In equilibrium, informal firms are smaller, less productive and employ fewer skilled workers as a result of self-selection. Informal workers are generally compensated for the lack of mandated benefits by receiving higher wages, but a simple comparison of average earnings between sectors shows a formality wage premium because of compositional effects. In addition, a binding minimum wage can break the equalizing differentials relation, so that there might be a formality wage premium among low wage workers even after controlling for individual productivity. The model is calibrated using Brazilian data and used to explain the evolution of labor market outcomes in that country from 2003 to 2012. The results suggest that rising schooling was the most important factor behind the reversal of the informality trend in Brazil, which remains a puzzle in the current literature. It is also shown that, for the calibrated model, a progressive payroll tax would lead to a decrease in both unemployment and informality without compromising tax revenues.
13
Fernandes, Lourenço Affonso Marcelo. "A decision support model for differential sticking avoidance." Thesis, Curtin University, 2012. http://hdl.handle.net/20.500.11937/700.
Анотація:
An innovative theoretical model to quantify the risk of differential sticking is presented. The proposed risk assessment is based on the concept of likelihood versus consequence. The likelihood of the problem’s occurrence in a given wellbore segment (case) is evaluated from a knowledge-based model and translated by a similarity measure of relevant operational conditions between the target case and historical cases with known outcomes. The stand alone module performed satisfactorily and predicts the likelihood of occurrence by more than a chance probability, demonstrated by a rate of sixty eight percent (68%) correct predictions against field data from forty four wells drilled by different operators in several fields.The consequence assessment is performed through an unidimensional mechanistic model that predicts the downhole overpull (differential sticking force) and performed well while estimating reported overpulls from known field instances of the problem. Together, the models serve as a risk assessment tool able to correctly describe risk operational trends while designing or drilling wells, with critical situations being defined as high likelihood plus high potential overpulls. Both models utilizes unique experimental data about mechanical properties of drilling fluids filtercakes (hardness, torque resistance and adhesion-cohesion strength) under simulated downhole conditions, raised through the HTHP Mudcake Characterization Equipment developed during the course of this research work. Moreover, the study contributes towards the development of modern predictive models aiming at combining large amount of available operational drilling data (LWD, PWD, mudlogging, survey, drilling reports, etc), expert’s knowledge, laboratory data and phenomenological models in order to optimize drilling operations.
14
Fontana, Gaia. "Traffic waves and delay differential equations." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21211/.
Анотація:
Questo elaborato si pone l'obiettivo di studiare il problema del traffico, concentrandosi su un modello semplificato in cui i veicoli sono confinati su una circonferenza e la cui velocità è determinata dal modello optimal velocity.
Il discorso si sviluppa su tre capitoli: nel primo viene presentato il modello optimal velocity per il flusso del traffico e si procede a uno studio della stabilità lineare attorno al punto di equilibrio stazionario.
Nel secondo capitolo lo stesso modello viene studiato nel limite termodinamico per un numero infinito di veicoli. Si ricava una soluzione costituita da un'onda di traffico che si propaga in verso opposto al moto delle auto.
Nel terzo e ultimo capitolo il modello viene studiato tramite teoria perturbativa nell'intorno del punto critico, introducendo un potenziale termodinamico e seguendo la teoria di Landau delle transizioni di fase. Vengono infine ricavate le medesime condizioni di stabilità del sistema trovate nel primo capitolo.
15
Yung, Tamara. "Traffic Modelling Using Parabolic Differential Equations." Thesis, Linköpings universitet, Kommunikations- och transportsystem, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-102745.
Анотація:
The need of a working infrastructure in a city also requires an understanding of how the traffic flows. It is known that increasing number of drivers prolong the travel time and has an environmental effect in larger cities. It also makes it more difficult for commuters and delivery firms to estimate their travel time. To estimate the traffic flow the traffic department can arrange cameras along popular roads and redirect the traffic, but this is a costly method and difficult to implement. Another approach is to apply theories from physics wave theory and mathematics to model the traffic flow; in this way it is less costly and possible to predict the traffic flow as well. This report studies the application of wave theory and expresses the traffic flow as a modified linear differential equation. First is an analytical solution derived to find a feasible solution. Then a numerical approach is done with Taylor expansions and Crank-Nicolson’s method. All is performed in Matlab and compared against measured values of speed and flow retrieved from Swedish traffic department over a 24 hours traffic day. The analysis is performed on a highway stretch outside Stockholm with no entries, exits or curves. By dividing the interval of the highway into shorter equal distances the modified linear traffic model is expressed in a system of equations. The comparison between actual values and calculated values of the traffic density is done with a nominal average difference. The results reveal that the numbers of intervals don’t improve the average difference. As for the small constant that is applied to make the linear model stable is higher than initially considered.
16
Zeris, E. A. "Investigations of certain implicit finite difference schemes for integration of the long wave equations." Thesis, University of Strathclyde, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.381538.
17
Aslanyan, Vahagn. "Ax-Schanuel type inequalities in differentially closed fields." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:bced8c2d-22df-4a21-9a1f-5e4204b6c85d.
Анотація:
In this thesis we study Ax-Schanuel type inequalities for abstract differential equations. A motivating example is the exponential differential equation. The Ax-Schanuel theorem states positivity of a predimension defined on its solutions. The notion of a predimension was introduced by Hrushovski in his work from the 1990s where he uses an amalgamation-with-predimension technique to refute Zilber's Trichotomy Conjecture. In the differential setting one can carry out a similar construction with the predimension given by Ax-Schanuel. In this way one constructs a limit structure whose theory turns out to be precisely the first-order theory of the exponential differential equation (this analysis is due to Kirby (for semiabelian varieties) and Crampin, and it is based on Zilber's work on pseudo-exponentiation). One says in this case that the inequality is adequate. Thus, by an Ax-Schanuel type inequality we mean a predimension inequality for a differential equation. Our main question is to understand for which differential equations one can find an adequate predimension inequality. We show that this can be done for linear differential equations with constant coefficients by generalising the Ax-Schanuel theorem. Further, the question turns out to be closely related to the problem of recovering the differential structure in reducts of differentially closed fields where we keep the field structure (which is quite an interesting problem in its own right). So we explore that question and establish some criteria for recovering the derivation of the field. We also show (under some assumptions) that when the derivation is definable in a reduct then the latter cannot satisfy a non-trivial adequate predimension inequality. Another example of a predimension inequality is the analogue of Ax-Schanuel for the differential equation of the modular j-function due to Pila and Tsimerman. We carry out a Hrushovski construction with that predimension and give an axiomatisation of the first-order theory of the strong Fraïssé limit. It will be the theory of the differential equation of j under the assumption of adequacy of the predimension. We also show that if a similar predimension inequality (not necessarily adequate) is known for a differential equation then the fibres of the latter have interesting model theoretic properties such as strong minimality and geometric triviality. This, in particular, gives a new proof for a theorem of Freitag and Scanlon stating that the differential equation of j defines a trivial strongly minimal set.
18
Baisden, Andrew Carson. "Generalized Terminal Modeling of Electro-Magnetic Interference." Diss., Virginia Tech, 2009. http://hdl.handle.net/10919/29810.
Анотація:
Terminal models have been used for various power electronic applications. In this work a two- and three-terminal black box model is proposed for electro-magnetic interference (EMI) characterization. The modeling procedure starts with a time-variant system at a particular operating condition, which can be a converter, set of converters, sub-system or collection of components. A unique, linear equivalent circuit is created for applications in the frequency domain. Impedances and current / voltage sources define the noise throughout the entire EMI frequency spectrum. All parameters needed to create the model are clearly defined to ensure convergence and maximize accuracy.
The model is then used to predict the attenuation caused by a filter with increased accuracy over small signal insertion gain measurements performed with network analyzers. Knowledge of EMI filters interactions with the converter allows for advanced techniques and design constraints to optimize the filter for size, weight, and cost. Additionally, the model is also demonstrated when the operating point of the system does not remain constant, as with AC power systems. Modeling of a varying operating point requires information of all the operating conditions for a complete and accurate model. However, the data collection and processing quickly become unmanageable due to the large amounts of data needed. Therefore, simplification techniques are used to reduce the complexity of the model while maintaining accuracy throughout the frequency spectrum.
The modeling approach is verified for linear and power electronic networks including: a dc-dc boost converter, phase-leg module, and a simulated dc-ac inverter. The accuracy of the model is confirmed up to 100 MHz in simulation and at least 50 MHz for experimental validation.Ph. D.
19
Sun, Bingyao. "EMI Terminal Behavioral Modeling of SiC-based Power Converters." Thesis, Virginia Tech, 2015. http://hdl.handle.net/10919/78154.
Анотація:
With GaN and SiC switching devices becoming more commercially available, higher switching frequency is being applied to achieve higher efficiency and power density in power converters. However, electro-magnetic interference (EMI) becomes a more severe problem as a result. In this thesis, the switching frequency effect on conducted EMI noise is assessed.
As EMI noise increases, the EMI filter plays a more important role in a power converter. As a result, an effective EMI modeling technique of the power converter system is required in order to find an optimized size and effective EMI filter.
The frequency-domain model is verified to be an efficient and easy model to explore the EMI noise generation and propagation in the system. Of the various models, the unterminated behavioral model can simultaneously predict CM input and output noise of an inverter, and the prediction falls in line with the measurement around 10 MHz or higher. The DM terminated behavioral model can predict the DM input or output noise of the motor drive higher than 20 MHz. These two models are easy to extract and have high prediction capabilities; this is verified on a 10 kHz-switching-frequency Si motor drive. It is worthwhile to explore the prediction capability of the two models when they are applied to a SiC-based power inverter with switching frequency ranges from 20 kHz to 70 kHz.
In this thesis, the CM unterminated behavioral model is first applied to the SiC power inverter, and results show that the model prediction capability is limited by the noise floor of the oscilloscope measurement. The proposed segmented-frequency-range measurement is developed and verified to be a good solution to the noise floor. With the improved impedance fixtures, the prediction from CM model matches the measurement to 30 MHz.
To predict the DM input and output noise of the SiC inverter, the DM terminated behavioral model can be used under the condition that the CM and DM noise are decoupled. With the system noise analysis, the DM output side is verified to be independent of the CM noise and input side. The DM terminated behavioral model is extracted at the inverter output and predicts the DM output noise up to 30 MHz after solving the noise floor and DM choke saturation problem.
At the DM input side, the CM and DM are seen to be coupled with each other. It is found experimentally that the mixture of the CM and DM noise results from the asymmetric impedance of the system. The mixed mode terminated behavioral model is proposed to predict the DM noise when a mixed CM effect exists. The model can capture the DM noise up to to 30 MHz when the impedance between the inverter to CM ground is not balanced. The issue often happens in extraction of the model impedance and is solved by the curving-fitting optimization described in the thesis.
This thesis ends with a summary of contributions, limitations, and some future research directions.Master of Science
20
Björnberg, Jakob Erik. "Graphical representations of Ising and Potts models : Stochastic geometry of the quantum Ising model and the space-time Potts model." Doctoral thesis, KTH, Matematik (Inst.), 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-11267.
Анотація:
HTML clipboard Statistical physics seeks to explain macroscopic properties of matter in terms of microscopic interactions. Of particular interest is the phenomenon of phase transition: the sudden changes in macroscopic properties as external conditions are varied. Two models in particular are of great interest to mathematicians, namely the Ising model of a magnet and the percolation model of a porous solid. These models in turn are part of the unifying framework of the random-cluster representation, a model for random graphs which was first studied by Fortuin and Kasteleyn in the 1970’s. The random-cluster representation has proved extremely useful in proving important facts about the Ising model and similar models. In this work we study the corresponding graphical framework for two related models. The first model is the transverse field quantum Ising model, an extension of the original Ising model which was introduced by Lieb, Schultz and Mattis in the 1960’s. The second model is the space–time percolation process, which is closely related to the contact model for the spread of disease. In Chapter 2 we define the appropriate space–time random-cluster model and explore a range of useful probabilistic techniques for studying it. The space– time Potts model emerges as a natural generalization of the quantum Ising model. The basic properties of the phase transitions in these models are treated in this chapter, such as the fact that there is at most one unbounded fk-cluster, and the resulting lower bound on the critical value in 
. In Chapter 3 we develop an alternative graphical representation of the quantum Ising model, called the random-parity representation. This representation is based on the random-current representation of the classical Ising model, and allows us to study in much greater detail the phase transition and critical behaviour. A major aim of this chapter is to prove sharpness of the phase transition in the quantum Ising model—a central issue in the theory— and to establish bounds on some critical exponents. We address these issues by using the random-parity representation to establish certain differential inequalities, integration of which gives the results. In Chapter 4 we explore some consequences and possible extensions of the results established in Chapters 2 and 3. For example, we determine the critical point for the quantum Ising model in and in ‘star-like’ geometries.HTML clipboard Statistisk fysik syftar till att förklara ett materials makroskopiska egenskaper i termer av dess mikroskopiska struktur. En särskilt intressant egenskap är är fenomenet fasövergång, det vill säga en plötslig förändring i de makroskopiska egenskaperna när externa förutsättningar varieras. Två modeller är särskilt intressanta för en matematiker, nämligen Ising-modellen av en magnet och perkolationsmodellen av ett poröst material. Dessa två modeller sammanförs av den så-kallade fk-modellen, en slumpgrafsmodell som först studerades av Fortuin och Kasteleyn på 1970-talet. fk-modellen har sedermera visat sig vara extremt användbar för att bevisa viktiga resultat om Ising-modellen och liknande modeller. I den här avhandlingen studeras den motsvarande grafiska strukturen hos två näraliggande modeller. Den första av dessa är den kvantteoretiska Isingmodellen med transverst fält, vilken är en utveckling av den klassiska Isingmodellen och först studerades av Lieb, Schultz och Mattis på 1960-talet. Den andra modellen är rumtid-perkolation, som är nära besläktad med kontaktmodellen av infektionsspridning. I Kapitel 2 definieras rumtid-fk-modellen, och flera probabilistiska verktyg utforskas för att studera dess grundläggande egenskaper. Vi möter rumtid-Potts-modellen, som uppenbarar sig som en naturlig generalisering av den kvantteoretiska Ising-modellen. De viktigaste egenskaperna hos fasövergången i dessa modeller behandlas i detta kapitel, exempelvis det faktum att det i fk-modellen finns högst en obegränsad komponent, samt den undre gräns för det kritiska värdet som detta innebär. I Kapitel 3 utvecklas en alternativ grafisk framställning av den kvantteoretiska Ising-modellen, den så-kallade slumpparitetsframställningen. Denna är baserad på slumpflödesframställningen av den klassiska Ising-modellen, och är ett verktyg som låter oss studera fasövergången och gränsbeteendet mycket närmare. Huvudsyftet med detta kapitel är att bevisa att fasövergången är skarp—en central egenskap—samt att fastslå olikheter för vissa kritiska exponenter. Metoden består i att använda slumpparitetsframställningen för att härleda vissa differentialolikheter, vilka sedan kan integreras för att lägga fast att gränsen är skarp. I Kapitel 4 utforskas några konsekvenser, samt möjliga vidareutvecklingar, av resultaten i de tidigare kapitlen. Exempelvis bestäms det kritiska värdet hos den kvantteoretiska Ising-modellen på
, samt i ‘stjärnliknankde’ geometrier.QC 20100705
21
Bruynooghe, Daniel. "Differential cumulants, hierarchical models and monomial ideals." Thesis, London School of Economics and Political Science (University of London), 2011. http://etheses.lse.ac.uk/441/.
22
Vasu, Aishwarya. "MODEL-BASED CONTROL OF DIFFERENTIALLY DRIVEN TWO-WHEELED MOBILE ROBOT." OpenSIUC, 2010. https://opensiuc.lib.siu.edu/theses/360.
Анотація:
The objective is to model a two wheeled nonholonomic mobile robot for the parking problem and stabilize it using piecewise continuous static feedback control. The nonholonomic robots cannot be stabilized using continuous static feedback controls. In this thesis, the kinematic model of the robot is transformed into a feasible coordinate system. A stabilizing kinematic controller is designed for the stabilization problem in the new coordinate system. The robot has two inputs, viz., v, linear velocity and ω, angular velocity. Two DC motors are used for the left and the right wheels to implement the computed linear and angular velocities. This is included to realize the robot driven by electric motors. The two DC motors are controlled using PID controllers. The practical implementation for a two wheeled robot is also discussed. Pololu 3PI robot is used for the implementation. Line tracking and Line tracking algorithm with PID is also discussed. Possible enhancements include the implementation of the algorithm in dsPIC family of microcontrollers. CMX scheduler for dsPIC family of products can also be ported on dsPIC and the same environment can be simulated in real time. This can be extended to multiple agents who are controlled by a single master, thus forming a single master multi slave network.
23
Solanki, Nikesh. "Uniform companions for expansions of large differential fields." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/uniform-companions-for-expansions-of-large-differential-fields(a565a0d0-24b5-40a6-a414-5ead1631bc8d).html.
24
Liu, Yang, and 劉洋. "Optimization and differential geometry for geometric modeling." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40988077.
25
Zararsiz, Zarife. "On an epidemic model given by a stochastic differential equation." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-5747.
26
Cinar, Selahittin. "Analysis of a Partial Differential Equation Model of Surface Electromigration." TopSCHOLAR®, 2014. https://digitalcommons.wku.edu/theses/1368.
Анотація:
A Partial Differential Equation (PDE) based model combining surface electromigration and wetting is developed for the analysis of the morphological instability of mono-crystalline metal films in a high temperature environment typical to operational conditions of microelectronic interconnects. The atomic mobility and surface energy of such films are anisotropic, and the model accounts for these material properties. The goal of modeling is to describe and understand the time-evolution of the shape of film surface. I will present the formulation of a nonlinear parabolic PDE problem for the height function h(x,t) of the film in the horizontal electric field, followed by the results of the linear stability analyses and computations of fully nonlinear evolution equation.
27
Dray, Alyssa W. "A Multistage Incidence Estimation Model for Diseases with Differential Mortality." Scholarship @ Claremont, 2010. https://scholarship.claremont.edu/hmc_theses/21.
Анотація:
According to theWorld Health Organization, surgically removable cataract remains the leading cause of blindness worldwide. In sub-Saharan Africa, cataract surgical rate targets should ideally be set based on cataract incidence (the number of new cataracts developed each year). Unfortunately, the longitudinal studies necessary to measure incidence have not yet been feasible in these areas. Our research instead proposes a method for estimating incidence based on available cataract prevalence data. We extend a method proposed by Podgor and Leske (1986) to estimate age-specific incidence from age-specific prevalence in single diseases with differential mortality. A two-stage disease extension is created in order to differentiate between unilateral cataract and bilateral cataract. The new model, along with a numerical simulation method to generate confidence intervals, is implemented in the statistical programming language R. The model is then applied to Rapid Assessment of Avoidable Blindness survey data from parts of Eritrea, The Gambia, Kenya (two regions), Mali, Rwanda and Tanzania. Our results suggest significant geographic variations in cataract incidence, a hypothesis to be further investigated as the RAAB survey expands and improves. We also show how the model can be further extended to model any n-stage progressive disease with differential mortality. to model any n-stage progressive disease with differential mortality.
28
Birch, S. "The demand for health : Extensions to the human capital model." Thesis, University of York, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.378059.
29
Cartwright, Madeleine Clare. "Collective coordinates approach for travelling waves in stochastic partial differential equations." Thesis, The University of Sydney, 2021. https://hdl.handle.net/2123/25942.
Анотація:
We propose a formal framework based on collective coordinates to reduce infinite-dimensional stochastic partial differential equations (SPDEs) with symmetry to a set of finite-dimensional stochastic differential equations which describe the shape of the solution and the dynamics along the symmetry group. We study dissipative and non-dissipative SPDEs that support travelling wave solutions. We find that the collective coordinate approach provides a remarkably good quantitative description of the shape and the position of the travelling wave. We corroborate our analytical results with numerical simulations of the full SPDEs.
30
Schelp, Richard Charles. "The standard model and beyond in noncommutative geometry /." Digital version accessible at:, 2000. http://wwwlib.umi.com/cr/utexas/main.
31
Yereniuk, Michael A. "Global Approximations of Agent-Based Model State Changes." Digital WPI, 2020. https://digitalcommons.wpi.edu/etd-dissertations/614.
Анотація:
How can we model global phenomenon based on local interactions? Agent-Based (AB) models are local rule-based discrete method that can be used to simulate complex interactions of many agents. Unfortunately, the relative ease of implementing the computational model is often counter-balanced by the difficulty of performing rigorous analysis to determine emergent behaviors. Calculating existence of fixed points and their stability is not tractable from an analytical perspective and can become computationally expensive, involving potentially millions of simulations. To construct meaningful analysis, we need to create a framework to approximate the emergent, global behavior. Our research has been devoted to developing a framework for approximating AB models that move via random walks and undergo state transitions. First, we developed a general method to estimate the density of agents in each state for AB models whose state transitions are caused by neighborhood interactions between agents. Second, we extended previous random walk models of instantaneous state changes by adding a cumulative memory effect. In this way, our research seeks to answer how memory properties can also be incorporated into continuum models, especially when the memory properties effect state changes on the agents. The state transitions in this type of AB model is primarily from the agents’ interaction with their environment. These modeling frameworks will be generally applicable to many areas and can be easily extended.
32
Guo, Xu. "Fractional differential equations for modelling financial processes with jumps." HKBU Institutional Repository, 2015. https://repository.hkbu.edu.hk/etd_oa/192.
Анотація:
The standard Black-Scholes model is under the assumption of geometric Brownian motion, and the log-returns for Black-Scholes model are independent and Gaussian. However, most of the recent literature on the statistical properties of the log-returns makes this hypothesis not always consistent. One of the ongoing research topics is to nd a better nancial pricing model instead of the Black-Scholes model. In the present work, we concentrate on two typical 1-D option pricing models under the general exponential L evy processes, namely the nite moment log-stable (FMLS) model and the the Carr-Geman-Madan-Yor-eta (CGMYe) model, and we also propose a multivariate CGMYe model. Both the frameworks, and the numerical estimations and simulations are studied in this thesis. In the future work, we shall continue to study the fractional partial di erential equations (FPDEs) of the nancial models, and seek for the e cient numerical algorithms of the American pricing problems. Keywords: fractional partial di erential equation; option pricing models; exponential L evy process; approximate solution.
33
Whitaker, Gavin Andrew. "Bayesian inference for stochastic differential mixed-effects models." Thesis, University of Newcastle upon Tyne, 2016. http://hdl.handle.net/10443/3398.
Анотація:
Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units, SDE driven mixed- effects models allow the quantification of both between and within individual variation. Performing Bayesian inference for such models, using discrete-time data that may be incomplete and subject to measurement error, is a challenging problem and is the focus of this thesis. Since, in general, no closed form expression exists for the transition densities of the SDE of interest, a widely adopted solution works with the Euler-Maruyama approximation, by replacing the intractable transition densities with Gaussian approximations. These approximations can be made arbitrarily accurate by introducing intermediate time-points between observations. Integrating over the uncertainty associated with the process at these time-points necessitates the use of computationally intensive algorithms such as Markov chain Monte Carlo (MCMC). We extend a recently proposed MCMC scheme to include the SDE driven mixed-effects framework. Key to the development of an e fficient inference scheme is the ability to generate discrete-time realisations of the latent process between observation times. Such realisations are typically termed diffusion bridges. By partitioning the SDE into two parts, one that accounts for nonlinear dynamics in a deterministic way, and another as a residual stochastic process, we develop a class of novel constructs that bridge the residual process via a linear approximation. In addition, we adapt a recently proposed construct to a partial and noisy observation regime. We compare the performance of each new construct with a number of existing approaches, using three applications: a simple birth-death process, a Lotka-Volterra model and a model for aphid growth. We incorporate the best performing bridge construct within an MCMC scheme to determine the posterior distribution of the model parameters. This methodology is then applied to synthetic data generated from a simple SDE model of orange tree growth, and real data consisting of observations on aphid numbers recorded under a variety of different treatment regimes. Finally, we provide a systematic comparison of our approach with an inference scheme based on a tractable approximation of the SDE, that is, the linear noise approximation.
34
Medlock, Jan P. "Integro-differential-equation models in ecology and epidemiology /." Thesis, Connect to this title online; UW restricted, 2004. http://hdl.handle.net/1773/6790.
35
Sinclair, Peter. "Differential outcomes of various models of work experience." Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 1995. https://ro.ecu.edu.au/theses/1159.
Анотація:
In Western Australia an increasing number of secondary school students participate in work experience programs. Different models of work experience are becoming more common. The Ministry of. Education promotes the use of four such models. The purpose of this study was to examine the outcomes of work experience, as perceived by secondary school students in selected Government Schools, to see if there were any differences according to the model of work experience used. These perceptions were further examined to see if there was a significant difference in perceived outcomes according to other independent variables of student gender, year level, geographic location, duration of work experience or recency of work experience. Data were collected by means of a questionnaire. Students completing work experience in the survey period in responding government secondary schools with appointed Youth Education Officers were asked to complete the questionnaire using a Likert Scale of attitude response. The results of the questionnaire were analyzed using multiple analysis of variance. This gave an objective measure of the extent of achievement, as well as indicating any significant differences according to the independent variable examined. The study concluded that work experience produces positive outcomes in areas related to the employability, career choice, educational attitude and social development of students.
36
Church, Kevin. "Applications of Impulsive Differential Equations to the Control of Malaria Outbreaks and Introduction to Impulse Extension Equations: a General Framework to Study the Validity of Ordinary Differential Equation Models with Discontinuities in State." Thesis, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/31874.
Анотація:
Impulsive differential equations are often used in mathematical modelling to simplify
complicated hybrid models. We propose an inverse framework inspired by impulsive
differential equations, called impulse extension equations, which can be used as a tool to determine when these impulsive models are accurate. The linear theory is the
primary focus, for which theorems analoguous to ordinary and impulsive differential
equations are derived. Results explicitly connecting the stability of impulsive differential equations to related impulse extension equations are proven in what we call time scale consistency theorems. Opportunities for future research in this direction are discussed.
Following the work of Smith? and Hove-Musekwa on malaria vector control by
impulsive insecticide spraying, we propose a novel autonomous vector control scheme based on human disease incidence. Existence and stability of periodic orbits is established. We compare the implementation cost of the incidence-based control to a fixed-time spraying schedule. Hybrid control strategies are discussed.
37
Csémi, András. "Nápravový samosvorný diferenciál." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2020. http://www.nusl.cz/ntk/nusl-433532.
Анотація:
The topic of this master‘s thesis is the axle Limited-slip Differential. The first part is devoted to the description of types of differentials open, locked or self-locking. The next part describes the procedure of creating a mathematical model for the simulation of vehicle movement based on input parameters and subsequent comparison of vehicle behavior with open and locked differential. The final part of the work based on data obtained from the model with a Limited-slip Differential is devoted to the design of a differential for a vehicle with one driven axle.
38
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.
39
Romijn, Reinout Carel [Verfasser]. "Empirical Model Reduction of Differential-Algebraic Equation Systems / Reinout Carel Romijn." Aachen : Shaker, 2016. http://d-nb.info/1084536692/34.
40
Ma, Zhiwen. "A combined differential and integral model for high temperature fuel cells." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/15831.
41
Olien, Leonard. "Analysis of a delay differential equation model of a neural network." Thesis, McGill University, 1995. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=23927.
Анотація:
In this thesis I examine a delay differential equation model for an artificial neural network with two neurons. Linear stability analysis is used to determine the stability region of the stationary solutions. They can lose stability through either a pitchfork or a supercritical Hopf bifurcation. It is shown that, for appropriate parameter values, an interaction takes place between the pitchfork and Hopf bifurcations. Conditions are found under which the set of initial conditions that converge to a stable stationary solution is open and dense in the function space. Analytic results are illustrated with numerical simulations.
42
Pereira, Lo Bernardino. "Parameter estimation for a stochastic differential equation model of polymer rheology." Thesis, Imperial College London, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.441346.
43
Romijn, Reinout [Verfasser]. "Empirical Model Reduction of Differential-Algebraic Equation Systems / Reinout Carel Romijn." Aachen : Shaker, 2016. http://nbn-resolving.de/urn:nbn:de:101:1-201602282397.
44
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.
45
Pade, Jonas. "Analysis and waveform relaxation for a differential-algebraic electrical circuit model." Doctoral thesis, Humboldt-Universität zu Berlin, 2021. http://dx.doi.org/10.18452/23044.
Анотація:
Die Hauptthemen dieser Arbeit sind einerseits eine tiefgehende Analyse von nichtlinearen differential-algebraischen Gleichungen (DAEs) vom Index 2, die aus der modifizierten Knotenanalyse (MNA) von elektrischen Schaltkreisen hervorgehen, und andererseits die Entwicklung von Konvergenzkriterien für Waveform Relaxationsmethoden zum Lösen gekoppelter Probleme. Ein Schwerpunkt in beiden genannten Themen ist die Beziehung zwischen der Topologie eines Schaltkreises und mathematischen Eigenschaften der zugehörigen DAE.
Der Analyse-Teil umfasst eine detaillierte Beschreibung einer Normalform für Schaltkreis DAEs vom Index 2 und Abschätzungen, die für die Sensitivität des Schaltkreises bezüglich seiner Input-Quellen folgen. Es wird gezeigt, wie diese Abschätzungen wesentlich von der topologischen Position der Input-Quellen im Schaltkreis abhängen.
Die zunehmend komplexen Schaltkreise in technologischen Geräten erfordern oftmals eine Modellierung als gekoppeltes System. Waveform relaxation (WR) empfiehlt sich zur Lösung solch gekoppelter Probleme, da sie auf die Subprobleme angepasste Lösungsmethoden und Schrittweiten ermöglicht. Es ist bekannt, dass WR zwar bei Anwendung auf gewöhnliche Differentialgleichungen konvergiert, falls diese eine Lipschitz-Bedingung erfüllen, selbiges jedoch bei DAEs nicht ohne Hinzunahme eines Kontraktivitätskriteriums sichergestellt werden kann. Wir beschreiben allgemeine Konvergenzkriterien für WR auf DAEs vom Index 2. Für den Fall von Schaltkreisen, die entweder mit anderen Schaltkreisen oder mit elektromagnetischen Feldern verkoppelt sind, leiten wir außerdem hinreichende topologische Konvergenzkriterien her, die anhand von Beispielen veranschaulicht werden. Weiterhin werden die Konvergenzraten des Jacobi WR Verfahrens und des Gauss-Seidel WR Verfahrens verglichen. Simulationen von einfachen Beispielsystemen zeigen drastische Unterschiede des WR-Konvergenzverhaltens, abhängig davon, ob die Konvergenzbedingungen erfüllt sind oder nicht.The main topics of this thesis are firstly a thorough analysis of nonlinear differential-algebraic equations (DAEs) of index 2 which arise from the modified nodal analysis (MNA) for electrical circuits and secondly the derivation of convergence criteria for waveform relaxation (WR) methods on coupled problems. In both topics, a particular focus is put on the relations between a circuit's topology and the mathematical properties of the corresponding DAE. The analysis encompasses a detailed description of a normal form for circuit DAEs of index 2 and consequences for the sensitivity of the circuit with respect to its input source terms. More precisely, we provide bounds which describe how strongly changes in the input sources of the circuit affect its behaviour. Crucial constants in these bounds are determined in terms of the topological position of the input sources in the circuit. The increasingly complex electrical circuits in technological devices often call for coupled systems modelling. Allowing for each subsystem to be solved by dedicated numerical solvers and time scales, WR is an adequate method in this setting. It is well-known that while WR converges on ordinary differential equations if a Lipschitz condition is satisfied, an additional convergence criterion is required to guarantee convergence on DAEs. We present general convergence criteria for WR on higher index DAEs. Furthermore, based on our results of the analysis part, we derive topological convergence criteria for coupled circuit/circuit problems and field/circuit problems. Examples illustrate how to practically check if the criteria are satisfied. If a sufficient convergence criterion holds, we specify at which rate of convergence the Jacobi and Gauss-Seidel WR methods converge. Simulations of simple benchmark systems illustrate the drastically different convergence behaviour of WR depending on whether or not the circuit topological convergence conditions are satisfied.
46
Cheng, Jie. "An Ordinary Differential Equation Based Model For Clustering And Vector Quantization." Available to subscribers only, 2009. http://proquest.umi.com/pqdweb?did=1878994541&sid=3&Fmt=2&clientId=1509&RQT=309&VName=PQD.
Анотація:
Thesis (Ph. D.)--Southern Illinois University Carbondale, 2009."Department of Electrical and Computer Engineering." Keywords: Clustering, Ordinary differential equations, Real time, Vector quantization. Includes bibliographical references (p. 80-83). Also available online.
47
Comer, Janet Mary 1944. "DEVELOPMENT OF A SEMANTIC DIFFERENTIAL PROFILE FOR THE ANGER THERAPY MODEL." Thesis, The University of Arizona, 1986. http://hdl.handle.net/10150/275548.
48
Swatzel, James Paul. "A partial differential equation to model the Tacoma Narrows Bridge failure." CSUSB ScholarWorks, 2004. https://scholarworks.lib.csusb.edu/etd-project/2631.
Анотація:
The purpose of this thesis was to examine a partial differential equation to model the Tacoma Narrows bridge failure. This thesis will examine the equation developed by Lazer and McKenna to model a suspension bridge in no wind.
49
Zhou, Chao. "Model Uncertainty in Finance and Second Order Backward Stochastic Differential Equations." Palaiseau, Ecole polytechnique, 2012. https://pastel.hal.science/docs/00/77/14/37/PDF/Thesis_ZHOU_Chao_Pastel.pdfcc.
Анотація:
L'objectif principal de cette thèse est d'étudier quelques problèmes de mathématiques financières dans un marché incomplet avec incertitude sur les modèles. Récemment, la théorie des équations différentielles stochastiques rétrogrades du second ordre (2EDSRs) a été développée par Soner, Touzi et Zhang sur ce sujet. Dans cette thèse, nous adoptons leur point de vue. Cette thèse contient quatre parties dans le domain des 2EDSRs. Nous commençons par généraliser la théorie des 2EDSRs initialement introduite dans le cas de générateurs lipschitziens continus à celui de générateurs à croissance quadratique. Cette nouvelle classe des 2EDSRs nous permettra ensuite d'étudier le problème de maximisation d'utilité robuste dans les modèles non-dominés. Dans la deuxième partie, nous étudions ce problème pour trois fonctions d'utilité. Dans chaque cas, nous donnons une caractérisation de la fonction valeur et d'une stratégie d'investissement optimale via la solution d'une 2EDSR. Dans la troisième partie, nous fournissons également une théorie d'existence et unicité pour des EDSRs réfléchies du second ordre avec obstacles inférieurs et générateurs lipschitziens, nous appliquons ensuite ce résultat à l'étude du problème de valorisation des options américaines dans un modèle financier à volatilité incertaine. Dans la quatrième partie, nous étudions des 2EDSRs avec sauts. En particulier, nous prouvons l'existence d'une unique solution dans un espace approprié. Comme application de ces résultats, nous étudions un problème de maximisation d'utilité exponentielle robuste avec incertitude sur les modèles. L'incertitude affecte à la fois le processus de volatilité, mais également la mesure des sautsThe main objective of this PhD thesis is to study some financial mathematics problems in an incomplete market with model uncertainty. In recent years, the theory of second order backward stochastic differential equations (2BSDEs for short) has been developed by Soner, Touzi and Zhang on this topic. In this thesis, we adopt their point of view. This thesis contains of four key parts related to 2BSDEs. In the first part, we generalize the 2BSDEs theory initially introduced in the case of Lipschitz continuous generators to quadratic growth generators. This new class of 2BSDEs will then allow us to consider the robust utility maximization problem in non-dominated models. In the second part, we study this problem for exponential utility, power utility and logarithmic utility. In each case, we give a characterization of the value function and an optimal investment strategy via the solution to a 2BSDE. In the third part, we provide an existence and uniqueness result for second order reflected BSDEs with lower obstacles and Lipschitz generators, and then we apply this result to study the problem of American contingent claims pricing with uncertain volatility. In the fourth part, we define a notion of 2BSDEs with jumps, for which we prove the existence and uniqueness of solutions in appropriate spaces. We can interpret these equations as standard BSDEs with jumps, under both volatility and jump measure uncertainty. As an application of these results, we shall study a robust exponential utility maximization problem under model uncertainty, where the uncertainty affects both the volatility process and the jump measure
50
Zigic, Jovan. "Optimization Methods for Dynamic Mode Decomposition of Nonlinear Partial Differential Equations." Thesis, Virginia Tech, 2021. http://hdl.handle.net/10919/103862.
Анотація:
Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations. Naturally, reduced-order modeling techniques come at the price of either computational accuracy or computation time. Optimization techniques are studied to improve either or both of these objectives and decrease the total computational cost of the problem. This thesis focuses on the dynamic mode decomposition (DMD) applied to nonlinear PDEs with periodic boundary conditions. It provides one study of an existing optimization framework for the DMD method known as the Optimized DMD and provides another study of a newly proposed optimization framework for the DMD method called the Split DMD.Master of Science
The Navier-Stokes (NS) equations are the primary mathematical model for understanding the behavior of fluids. The existence and smoothness of the NS equations is considered to be one of the most important open problems in mathematics, and challenges in their numerical simulation is a barrier to understanding the physical phenomenon of turbulence. Due to the difficulty of studying this problem directly, simpler problems in the form of nonlinear partial differential equations (PDEs) that exhibit similar properties to the NS equations are studied as preliminary steps towards building a wider understanding of the field. Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations. Naturally, reduced-order modeling techniques come at the price of either computational accuracy or computation time. Optimization techniques are studied to improve either or both of these objectives and decrease the total computational cost of the problem. This thesis focuses on the dynamic mode decomposition (DMD) applied to nonlinear PDEs with periodic boundary conditions. It provides one study of an existing optimization framework for the DMD method known as the Optimized DMD and provides another study of a newly proposed optimization framework for the DMD method called the Split DMD.