Dissertations / Theses on the topic 'Continuous or discrete homogenization'
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1
Rizzi, Gianluca. "Strain-gradient effects in the discrete/continuum transition via homogenization." Doctoral thesis, Università degli studi di Trento, 2019. https://hdl.handle.net/11572/369095.
Abstract:
A second-gradient elastic material has been identified as the equivalent homogeneous material of an hexagonal lattice made up of three different orders of linear elastic bars (hinged at each junction). In particular, the material equivalent to the lattice exhibits: (i.) non-locality, (ii.) non-centrosymmetry, and (iii.) anisotropy (even if the hexagonal geometry leads to isotropy at first-order). A Cauchy elastic equivalent solid is only recovered in the limit of vanishing length of the lattice’s bars. The identification of the second-gradient elastic material is complemented by analyses of positive definiteness and symmetry of the constitutive operators. Solutions of specific mechanical problems in which the lattice response is compared to the corresponding response of an equivalent boundary value problem for the homogeneous second-gradient elastic material are presented. These comparisons show the efficacy of the proposed identification procedure.
2
Rizzi, Gianluca. "Strain-gradient effects in the discrete/continuum transition via homogenization." Doctoral thesis, University of Trento, 2019. http://eprints-phd.biblio.unitn.it/3552/1/Rizzi_Gianluca_PhD_thesis.pdf.
Abstract:
A second-gradient elastic material has been identified as the equivalent homogeneous material of an hexagonal lattice made up of three different orders of linear elastic bars (hinged at each junction). In particular, the material equivalent to the lattice exhibits: (i.) non-locality, (ii.) non-centrosymmetry, and (iii.) anisotropy (even if the hexagonal geometry leads to isotropy at first-order). A Cauchy elastic equivalent solid is only recovered in the limit of vanishing length of the lattice’s bars. The identification of the second-gradient elastic material is complemented by analyses of positive definiteness and symmetry of the constitutive operators. Solutions of specific mechanical problems in which the lattice response is compared to the corresponding response of an equivalent boundary value problem for the homogeneous second-gradient elastic material are presented. These comparisons show the efficacy of the proposed identification procedure.
3
Lauerbach, Laura [Verfasser], Anja [Gutachter] Schlömerkemper, and Martin [Gutachter] Kruzik. "Stochastic Homogenization in the Passage from Discrete to Continuous Systems - Fracture in Composite Materials / Laura Lauerbach ; Gutachter: Anja Schlömerkemper, Martin Kruzik." Würzburg : Universität Würzburg, 2020. http://d-nb.info/1220634239/34.
4
Ruf, Matthias [Verfasser], Marco [Akademischer Betreuer] [Gutachter] Cicalese, Antoine [Gutachter] Gloria, and Andrea [Gutachter] Braides. "Discrete-to-continuum limits and stochastic homogenization of ferromagnetic surface energies / Matthias Ruf ; Gutachter: Antoine Gloria, Marco Cicalese, Andrea Braides ; Betreuer: Marco Cicalese." München : Universitätsbibliothek der TU München, 2017. http://d-nb.info/1137323493/34.
5
Alavi, Seyed Ehsan. "Homogénéisation de milieux architecturés périodiques et quasi-périodiques vers des milieux continus généralisés." Electronic Thesis or Diss., Université de Lorraine, 2021. http://www.theses.fr/2021LORR0305.
Abstract:
Cette thèse vise à revisiter les schémas d'homogénéisation d'ordre supérieur vers des continuums d'ordre ou de gradient supérieurs, successivement pour les matériaux et composites architecturés périodiques et quasi-périodiques, en se basant sur des principes variationnels et une extension de la condition de macrohomogénéité de Hill. Les méthodes d'homogénéisation continue sont exposées dans la première partie pour les milieux micropolaires et micromorphes, suivies par une présentation de l’homogénéisation discrète, alternative de l’homogénéisation continue.Nous avons étendu ces développements théoriques à la situation des matériaux quasi-périodiques, de microstructure régulière, qui peut être transformée en une configuration périodique de référence. L'idée commune aux méthodes d'homogénéisation périodique proposées (de nature continue ou discrète) est de décomposer le déplacement microscopique en une partie homogène représentative de la cinématique du milieu continu effectif adopté, et une fluctuation évaluée à partir d'un principe variationnel. En substance, les développements théoriques permettent l'élaboration de continuums enrichis (milieux continus généralisés) de type micromorphe, et des variantes qui en découlent en utilisant des conditions de dégénérescence appropriées. Des applications numériques ont été réalisées pour des matériaux architecturés et des composites à renforts de type inclusion sujets à de tels effets d'ordre supérieur en raison de leur architecture interne. Sur le plan théorique, les développements réalisés remédient à de nombreuses limitations des schémas d'homogénéisation d'ordre supérieur existants.Dans la partie II, les propriétés mécaniques effectives classiques et d'ordre supérieur des matériaux architecturés ont été évaluées sur la base de schémas d'homogénéisation discrets. En suivant l'idée d'une approche phénoménologique, des modèles consistants de type couple de contraintes de réseaux de poutres répétitifs ont été élaborés. Des milieux de Cosserat enrichis ont été élaborés dans l'esprit de la micromécanique, en adoptant des modèles de poutre de Timoshenko à un niveau microscopique, et en appliquant une méthode de continualisation vers un milieu de substitution effectif de Cosserat. La méthode de continualisation proposée s'avère précise et efficace en termes de calcul par rapport aux schémas d'homogénéisation continus et aux simulations par éléments finis réalisés sur la microstructure initiale. Un résultat essentiel des analyses effectuées est la quantification des effets de bord.Le contexte théorique qui sous-tend l'homogénéisation asymptotique quasi-périodique dans le cadre de l'élasticité anisotrope linéarisée est abordé dans la troisième partie. Différentes méthodologies d'évaluation des propriétés effectives quasi-périodiques ont été élaborées, conduisant à l'émergence de milieux effectifs à gradient de déformation. Les transformations conformes définissent une classe spécifique de transformations géométriques permettant de concevoir des matériaux architecturés générant un gradient de porosité interne, ce qui en fait de bons candidats pour des biosubstituts en biomécanique osseuseThis thesis aims to revisit higher-order homogenization schemes towards higher-order or higher gradient continua, successively for periodic and quasi-periodic architected materials and composites, based on variational principles and an extension of Hill macrohomogeneity condition. Continuous homogenization methods are exposed in Part I for micropolar and micromorphic media, followed by an exposition of the alternative discrete homogenization method.We have extended these theoretical developments to the situation of quasi-periodic materials, which still have a regular microstructure. The common idea to the proposed periodic homogenization methods of continuous or discrete nature is to split the microscopic displacement into a homogeneous part representative of the kinematics of the adopted effective continuum and a fluctuation evaluated from a variational principle. In substance, the theoretical developments allow the elaboration of enriched continua (generalized continua) of micromorphic type and all sub continua obtained using suitable degeneration conditions. Numerical applications have been made for architected materials and inclusion-based composites prone to higher-order effects due to their inner architecture. On the theoretical framework, the performed developments remedy many existing limitations of existing higher-order homogenization schemes.In Part II, repetitive lattice materials' effective classical and higher-order mechanical properties have been evaluated based on discrete homogenization schemes. Following the idea of a phenomenological approach, consistent couple stress models of repetitive beam lattices have been elaborated. Enriched Cosserat media have been derived in the spirit of micromechanics, adopting Timoshenko beam models at a microlevel, and applying a continualization method towards a Cosserat effective substitution medium. The proposed continualization method proves to be accurate and computationally efficient compared to continuous homogenization schemes and fully resolved finite element simulations. One key outcome of the performed analyses is the quantification of edge effects in the response of lattice structures, relying on the surface formulation of the extended Hill macrohomogeneity condition.The theoretical background underlying quasi-periodic asymptotic homogenization in the framework of linearized anisotropic elasticity deserves the development of Part III. Different methodologies for evaluating the effective quasi-periodic properties have been elaborated, leading to the emergence of strain gradient effective media. Conformal transformations define a specific class of geometrical mappings, allowing for designing compatible architected materials with inner porosity gradient, making them suitable bone biomechanics candidates
6
Baird, Graham. "Mixed discrete-continuous fragmentation equations." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:311da0da-6801-4120-9129-d95786a153b6.
Abstract:
The work contained in this thesis concerns the development, and the mathematical and numerical analysis, of a new class of hybrid discrete-continuous fragmentation model. The framework is introduced as a potential answer to the occurrence of 'shattering' mass loss, commonly observed in purely continuous fragmentation models. Initially, the study begins by introducing the model, which takes the form of an integro-differential equation, coupled with a system of ordinary differential equations. Once the model has been established, it is subjected to a rigorous mathematical analysis, using the theory and methods of operator semigroups and their generators. Most notably, by applying the theory relating to the Kato-Voigt perturbation theorem, honest substochastic semigroups and operator matrices, the existence of a unique, differentiable solution to the model is established. This solution is also shown to preserve non-negativity and conserve mass. Having determined the existence of a solution, the work continues with the development of a numerical scheme for the approximate solution of the modelling equations. Considering a truncated version of the equations, rewritten in an alternative conservative form, the scheme is built around a finite volume discretisation. Using a standard weak compactness argument, the approximations generated by the numerical scheme are shown to converge (weakly) to a weak solution of the truncated equations. By relating this weak solution to the strong solutions provided by the earlier semigroup analysis, the weak solution is found to be unique and as a consequence, differentiable, non-negative and mass-conserving. The theoretical study is completed with an examination of the effect of varying the truncation point. In particular, establishing that as the length of the truncated interval is increased, in the limit, the original solution to the full model is obtained. Finally, the thesis is completed with a numerical investigation, seeking to experimentally confirm the assertions of the earlier theoretical work and assess the performance of the numerical scheme for a suite of test models.
7
Silva, Pedro André Arroyo. "Modelo matemático com parâmetros que dependem da discretização: aplicação ao estudo de fenômenos de propagação discreta em meios excitáveis." Universidade Federal de Juiz de Fora (UFJF), 2018. https://repositorio.ufjf.br/jspui/handle/ufjf/7194.
Abstract:
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A formação de padrões espaço-temporais são observados em processos químicos e bio-lógicos. Apesar dos sistemas bioquímicos serem altamente heterogêneos, aproximações homogenizadas contínuas formadas por equações diferenciais parciais são utilizadas fre-quentemente. Estas aproximações são usualmente justificadas pela diferença de escalas entre as heterogeneidades e o tamanho da característica espacial dos padrões. Em certas condições do meio, por exemplo, quando há um acoplamento fraco entre as células car-díacas, os modelos homogenizados discretos são mais adequados. Entretanto, os modelos discretos são menos manejáveis, por exemplo, na geração de malha para 2D e 3D, se comparado com os modelos contínuos. Aqui estudamos um modelo matemático homoge-nizado contínuo que se aproxima do modelo homogenizado. Este modelo é dado a partir de equações diferencias parciais com um parâmetro que depende da discretização da ma-lha. Dessa maneira nos referimos a este por um modelo matemático com parâmetros que dependem da discretização. Validamos nossa aproximação em um meio excitável genérico que simula três fenômenos em 1D: a propagação do potencial de ação transmembrânico no tecido cardíaco, a propagação do potencial de ação em filamentos de axônios cobertos por bainhas de mielina e a propagação do ativador e inibidor em microemulsões químicas. Para o caso 2D desenvolvemos uma versão da nossa aproximação que reproduz ondas espirais em um meio com acoplamento fraco.
The spatio-temporal patterns formations are observed in chemical and biological pro-cesses. Although biochemical systems are highly heterogeneous, homogenized continuum approaches formed by partial differential equations have been employed frequently. These approaches are usually justified by the difference scales between the characteristic spatial size of the patterns. Under some conditions of the medium, for instance, under weak coupling between cardiac cells, discrete models are more adequate. On the other hand discrete models may be less manageable, for instance, in terms of mesh generation, com-pared to the continuum models. Here we study a mathematical model to approach the discreteness which permits the computer implementation on non-uniform meshes. The model is cast as a partial differential equation but with a parameter that depends on the discretization mesh. Therefore we refer to it as a mathematical model with parameters dependent of discretization. We validate the approach in a generic excitable media that simulates three different phenomena in 1D: the propagation of action potential in car-diac tissue, the propation of the action potentialin filaments of axons wrapped by myelin sheaths, and the propagation of the activator/inhibitor in chemical microemulsions. For the 2D case we develop a version to this approach in microemulsions where it was possible to reproduce spiral waves with weak coupling of the medium.
8
ElNady, Khaled. "Modèles de comportement non linéaire des matériaux architecturés par des méthodes d'homogénéisation discrètes en grandes déformations. Application à des biomembranes et des textiles." Thesis, Université de Lorraine, 2015. http://www.theses.fr/2015LORR0032/document.
Abstract:
Ce travail porte sur le développement de modèles micromécaniques pour le calcul de la réponse homogénéisée de matériaux architecturés, en particulier des matériaux se présentant sous forme de treillis répétitifs. Les matériaux architecturés et micro-architecturés couvrent un domaine très large de de propriétés mécaniques, selon la connectivité nodale, la disposition géométrique des éléments structuraux, leurs propriétés mécaniques, et l'existence d'une possible hiérarchie structurale. L'objectif principal de la thèse est la prise en compte des nonlinéarités géométriques résultant des évolutions importantes de la géométrie initiale du treillis, causée par une rigidité de flexion des éléments structuraux faible en regard de leur rigidité en extension. La méthode dite d'homogénéisation discrète est développée pour prendre en compte les non linéarités géométriques pour des treillis quais périodiques; des schémas incrémentaux sont construits qui reposent sur la résolution incrémentale et séquentielle des problèmes de localisation - homogénéisation posés sur une cellule de base identifiée, soumise à un chargement contrôlé en déformation. Le milieu continu effectif obtenu est en général un milieu micropolaire anisotrope, dont les propriétés effectives reflètent la disposition des éléments structuraux et leurs propriétés mécaniques. La réponse non affine des treillis conduit à des effets de taille qui sont pris en compte soit par un enrichissement de la cinématique par des variables de microrotation ou par la prise en compte des seconds gradients du déplacement. La construction de milieux effectifs du second gradient est faite dans un formalisme de petites perturbations. Il est montré que ces deux types de milieu effectif sont complémentaires en raison de l'analogie existant lors de la construction théorique des réponses homogénéisées, et par le fait qu'ils fournissent des longueurs internes en extension, flexion et torsion. Des applications à des structures tissées et des membranes biologiques décrites comme des réseaux de filaments quais-périodiques ont été faites. Les réponses homogénéisées obtenues sont validées par des comparaisons avec des simulations par éléments finis réalisées sur un volume élémentaire représentatif de la structure. Les schémas d'homogénéisation ont été implémentés dans un code de calcul dédié, alimenté par un fichier de données d'entrée de la géométrie du treillis et de ses propriétés mécaniques. Les modèles micromécaniques développés laissent envisager du fait de leur caractère prédictif la conception de nouveaux matériaux architecturés permettant d'élargir les frontières de l'espace 'matériaux-propriétés'The present thesis deals with the development of micromechanical schemes for the computation of the homogenized response of architectured materials, focusing on periodical lattice materials. Architectured and micro-architectured materials cover a wide range of mechanical properties according to the nodal connectivity, geometrical arrangement of the structural elements, their moduli, and a possible structural hierarchy. The principal objective of the thesis is the consideration of geometrical nonlinearities accounting for the large changes of the initial lattice geometry, due to the small bending stiffness of the structural elements, in comparison to their tensile rigidity. The so-called discrete homogenization method is extended to the geometrically nonlinear setting for periodical lattices; incremental schemes are constructed based on a staggered localization-homogenization computation of the lattice response over a repetitive unit cell submitted to a controlled deformation loading. The obtained effective medium is a micropolar anisotropic continuum, the effective properties of which accounting for the geometrical arrangement of the structural elements within the lattice and their mechanical properties. The non affine response of the lattice leads to possible size effects which can be captured by an enrichment of the classical Cauchy continuum either by adding rotational degrees of freedom as for the micropolar effective continuum, or by considering second order gradients of the displacement field. Both strategies are followed in this work, the construction of second order grade continua by discrete homogenization being done in a small perturbations framework. We show that both strategies for the enrichment of the effective continuum are complementary due to the existing analogy in the construction of the micropolar and second order grade continua by homogenization. The combination of both schemes further delivers tension, bending and torsion internal lengths, which reflect the lattice topology and the mechanical properties of its structural elements. Applications to textiles and biological membranes described as quasi periodical networks of filaments are considered. The computed effective response is validated by comparison with FE simulations performed over a representative unit cell of the lattice. The homogenization schemes have been implemented in a dedicated code written in combined symbolic and numerical language, and using as an input the lattice geometry and microstructural mechanical properties. The developed predictive micromechanical schemes offer a design tool to conceive new architectured materials to expand the boundaries of the 'material-property' space
9
Schlömerkemper, Anja. "Magnetic forces in discrete and continuous systems." Doctoral thesis, Universitätsbibliothek Leipzig, 2004. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-37349.
Abstract:
The topic of this thesis is a mathematically rigorous derivation of formulae for the magnetic force which is exerted on a part of a bounded magnetized body by its surrounding. Firstly, the magnetic force is considered within a continuous system based on macroscopic magnetostatics. The force formula in this setting is called Brown's force formula referring to W. F. Brown, who gave a mainly physically motivated discussion of it. This formula contains a surface integral which shows a nonlinear dependence on the normal. Brown assumes the existence of an additional term in the surface force which cancels the nonlinearity to allow an application of Cauchy's theorem in continuum mechanics to a magnetoelastic material. The proof of Brown's formula which is given in this work involves a suitable regularization of a hypersingular kernel and uses singular integral methods. Secondly, we consider a discrete, periodic setting of magnetic dipoles and formulate the force between a part of a bounded set and its surrounding. In order to pass to the continuum limit we start from the usual force formula for interacting magnetic dipoles. It turns out that the limit of the discrete force is different from Brown's force formula. One obtains an additional nonlinear surface term which allows one to regard Brown's assumption on the surface force as a consequence of the atomistic approach. Due to short range effects one obtains moreover an additional linear surface term in the continuum limit of the discrete force. This term contains a certain lattice sum which depends on a hypersingular kernel and the underlying lattice structureDas Thema dieser Arbeit ist eine mathematisch strenge Herleitung von Formeln für die magnetische Kraft, die auf einen Teil eines beschränkten, magnetischen Körpers durch seine Umgebung ausgeübt wird. Zunächst wird die magnetische Kraft in einem kontinuierlichen System auf Grundlage der makroskopischen Magnetostatik betrachtet. Mit Bezug auf W. F. Brown, der eine vor allem physikalisch motivierte Herleitung der Kraftformel gegeben hat, wird diese auch Brownsche Kraftformel genannt. Das Oberflächenintegral in dieser Formel zeigt eine nichtlineare Abhängigkeit von der Normalen. Um Cauchys Theorem aus der Kontinuumsmechanik in einem magnetoelastischen Material anwenden zu können, nimmt Brown an, dass die Oberflächenkraft einen zusäatzlichen Term enthält, der den nichtlinearen Ausdruck aufhebt. Der Beweis der Brownschen Kraftformel in dieser Arbeit beruht auf einer geeigneten Regularisierung eines hypersingulären Kerns und benutzt Methoden für singuläre Integrale. Danach gehen wir von einem diskreten, periodischen System von magnetischen Dipolen aus und betrachten die Kraft zwischen einem Teil einer beschränkten Menge und der Umgebung. Um zum Kontinuumslimes überzugehen, starten wir von der üblichen Kraftformel für wechselwirkende magnetische Dipole. Es zeigt sich, dass sich der Limes der diskreten Kraft von der Brownschen Kraftformel unterscheidet. Man erhält einen zusätzlichen nichtlinearen Oberflächenterm, der es ermöglicht, Browns Annahme als Konsequenz des atomistischen Zugangs zu sehen. Kurzreichweitige Effekte führen zudem zu einem linearen Oberflächenterm im Kontinuumlimes der diskreten Kraft. Dieser Zusatzterm enthält eine gewisse Gittersumme, die von einem hypersingulären Kern und der Struktur des zugrundeliegenden Gitters abhängt
10
Kimia, Behjoo. "Deblurring Gaussian blur : continuous and discrete approaches." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=65339.
11
Lee, Wai Ha. "Continuous and discrete properties of stochastic processes." Thesis, University of Nottingham, 2010. http://eprints.nottingham.ac.uk/11194/.
Abstract:
This thesis considers the interplay between the continuous and discrete properties of random stochastic processes. It is shown that the special cases of the one-sided Lévy-stable distributions can be connected to the class of discrete-stable distributions through a doubly-stochastic Poisson transform. This facilitates the creation of a one-sided stable process for which the N-fold statistics can be factorised explicitly. The evolution of the probability density functions is found through a Fokker-Planck style equation which is of the integro-differential type and contains non-local effects which are different for those postulated for a symmetric-stable process, or indeed the Gaussian process. Using the same Poisson transform interrelationship, an exact method for generating discrete-stable variates is found. It has already been shown that discrete-stable distributions occur in the crossing statistics of continuous processes whose autocorrelation exhibits fractal properties. The statistical properties of a nonlinear filter analogue of a phase-screen model are calculated, and the level crossings of the intensity analysed. It is found that rather than being Poisson, the distribution of the number of crossings over a long integration time is either binomial or negative binomial, depending solely on the Fano factor. The asymptotic properties of the inter-event density of the process are found to be accurately approximated by a function of the Fano factor and the mean of the crossings alone.
12
Sherman, Benjamin (Benjamin Marc). "Making discrete decisions based on continuous values." Thesis, Massachusetts Institute of Technology, 2017. http://hdl.handle.net/1721.1/112004.
Abstract:
Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2017.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 99-102).
Many safety-critical software systems are cyber-physical systems that compute with continuous values; confirming their safety requires guaranteeing the accuracy of their computations. It is impossible for these systems to compute (total and deterministic) discrete computations (e.g., decisions) based on connected input spaces such as R. We propose a programming language based on constructive topology, whose types are spaces and programs are executable continuous maps, that facilitates making formal guarantees of accuracy of computed results. We demonstrate that discrete decisions can be made based on continuous values by permitting nondeterminism. This thesis describes variants of the programming language allowing nondeterminism and/or partiality, and introduces two tools for creating nondeterministic programs on spaces. Overlapping pattern matching is a generalization of pattern matching in functional programming, where patterns need not represent decidable predicates and also may overlap, allowing potentially nondeterministic behavior in overlapping regions. Binary covers, which are pairs of predicates such that at least one of them holds, yield a formal logic for constructing approximate decision procedures.
by Benjamin Sherman.
S.M.
13
Janiszewski, Szymon Pawel. "Optimization problems in discrete and continuous time." Thesis, University of Hull, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.396087.
14
Zhu, Qingxin Carleton University Dissertation Computer Science. "Optimal search in discrete and continuous spaces." Ottawa, 1996.
15
Houben, Dirk. "Return Smoothing in Discrete and Continuous Time." Thesis, The University of Sydney, 2020. https://hdl.handle.net/2123/24564.
Abstract:
In this thesis we propose four novel continuous-time return smoothing models. Borrowing from the
private commercial real estate literature, we start with a benchmark model for return smoothing
in discrete time. The benchmark model is translated into continuous time, taking us from an
autoregressive moving average (ARMA) specification for the smoothed holding period return to
an Ornstein-Uhlenbeck (OU) specification for the instantaneous continuously compounding rate
of return on the smoothed asset price. The model is then extended to allow for the possibility of
predictability in the underlying “true” return.
In a second line of investigation, we propose an alternative continuous-time return smoothing
model in which we keep the OU smoothing mechanism, but replace the instantaneous smoothed
return with the smoothed detrended log price. This model leads to unrealistic autocorrelations
in the smoothed return, and we address this with an extension that introduces a higher-order
smoothing equation described by a continuous-time autoregressive moving average (CARMA)
process—the continuous-time analogue of the ARMA process.
We show that each of our four models belongs to a general framework for linear return smoothing
in continuous time in which a CARMA process governing the underlying “true” asset price is
overlaid with a CARMA-type smoothing equation that summarises the market mechanism whereby
the “true” price is transformed into a market-observed, smoothed price. In each model, as with
the general framework, the noise in the “true” price is represented by a Lévy process, allowing for
non-normality and sample path discontinuities.
To quantify the effect the smoothing models have on holding period returns, we develop a common set of smoothing metrics. These metrics are then computed for each of the models (including the discrete-time benchmark model), and form a basis on which the models can be compared. We also rely on the autocorrelation function in appraising the impact of return smoothing. We comment on the ability of the continuous-time smoothing models to reproduce stylised statistical properties commonly associated with smoothed returns, such as a reduction in return variance and an increase in return autocorrelation. Additionally, we develop the theory needed to operationalise
the smoothing metrics for the smoothing framework in general.
16
Westhead, Martin D. "Continuous automata : bridging the gap between discrete and continuous time system models." Thesis, University of Edinburgh, 1998. http://hdl.handle.net/1842/27642.
Abstract:
The principal use of models in design and maintenance of a system is fundamental to the engineering methodology. As the complexity and sophistication of systems increase so do the demands on the system models required to design them. In particular, the design of agent systems situated in the real world, such as robots, will require design models capable of expressing discrete and continuous changes of system parameters. Such systems are referred to as mode-switching, or hybrid systems. This thesis investigates ways in which time is represented in automata system models with discrete and continuously changing parameters. Existing automata approaches to hybrid modelling rely on describing continuous change at a sequence of points in time. In such approaches the time that elapses between each point is chosen nondeterministically in order to ensure that the model does not over step a discrete change. In contrast, the new approach this thesis proposes describes continuous change by a continuum of points which can naturally and deterministically capture such change. The main contribution of this work is the derivation of a limiting process which provides a theoretical foundation for this new approach. It not only provides a link between discrete and continuous time representations, but also provides a basis for deciding which continuous time representations are theoretically sound. The resulting formalism, the Continuous I/O machine, is demonstrated to be comparable to Hybrid Automata in expressibility. The conclusion of this work is that it is possible to define an automata model that describes a continuum of events and that this can be effectively used to model mode-switching physical systems. An investigation of potential theoretical benefits lies outside the scope of this thesis, however I argue that it provides a more natural, and elegant way to describe such systems than existing models.
17
Liao, Tianjun. "Population-based heuristic algorithms for continuous and mixed discrete-continuous optimization problems." Doctoral thesis, Universite Libre de Bruxelles, 2013. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209439.
Abstract:
Continuous optimization problems are optimization problems where all variableshave a domain that typically is a subset of the real numbers; mixed discrete-continuous
optimization problems have additionally other types of variables, so
that some variables are continuous and others are on an ordinal or categorical
scale. Continuous and mixed discrete-continuous problems have a wide range
of applications in disciplines such as computer science, mechanical or electrical
engineering, economics and bioinformatics. These problems are also often hard to
solve due to their inherent difficulties such as a large number of variables, many
local optima or other factors making problems hard. Therefore, in this thesis our
focus is on the design, engineering and configuration of high-performing heuristic
optimization algorithms.
We tackle continuous and mixed discrete-continuous optimization problems
with two classes of population-based heuristic algorithms, ant colony optimization
(ACO) algorithms and evolution strategies. In a nutshell, the main contributions
of this thesis are that (i) we advance the design and engineering of ACO algorithms to algorithms that are competitive or superior to recent state-of-the-art
algorithms for continuous and mixed discrete-continuous optimization problems,
(ii) we improve upon a specific state-of-the-art evolution strategy, the covariance
matrix adaptation evolution strategy (CMA-ES), and (iii) we extend CMA-ES to
tackle mixed discrete-continuous optimization problems.
More in detail, we propose a unified ant colony optimization (ACO) framework
for continuous optimization (UACOR). This framework synthesizes algorithmic
components of two ACO algorithms that have been proposed in the literature
and an incremental ACO algorithm with local search for continuous optimization,
which we have proposed during my doctoral research. The design of UACOR
allows the usage of automatic algorithm configuration techniques to automatically
derive new, high-performing ACO algorithms for continuous optimization. We also
propose iCMAES-ILS, a hybrid algorithm that loosely couples IPOP-CMA-ES, a
CMA-ES variant that uses a restart schema coupled with an increasing population
size, and a new iterated local search (ILS) algorithm for continuous optimization.
The hybrid algorithm consists of an initial competition phase, in which IPOP-CMA-ES and the ILS algorithm compete for further deployment during a second
phase. A cooperative aspect of the hybrid algorithm is implemented in the form
of some limited information exchange from IPOP-CMA-ES to the ILS algorithm
during the initial phase. Experimental studies on recent benchmark functions
suites show that UACOR and iCMAES-ILS are competitive or superior to other
state-of-the-art algorithms.
To tackle mixed discrete-continuous optimization problems, we extend ACOMV
and propose CESMV, an ant colony optimization algorithm and a covariance matrix adaptation evolution strategy, respectively. In ACOMV and CESMV ,the decision variables of an optimization problem can be declared as continuous, ordinal, or categorical, which allows the algorithm to treat them adequately. ACOMV and
CESMV include three solution generation mechanisms: a continuous optimization
mechanism, a continuous relaxation mechanism for ordinal variables, and a categorical optimization mechanism for categorical variables. Together, these mechanisms allow ACOMV and CESMV to tackle mixed variable optimization problems.
We also propose a set of artificial, mixed-variable benchmark functions, which can
simulate discrete variables as ordered or categorical. We use them to automatically tune ACOMV and CESMV's parameters and benchmark their performance.
Finally we test ACOMV and CESMV on various real-world continuous and mixed-variable engineering optimization problems. Comparisons with results from the
literature demonstrate the effectiveness and robustness of ACOMV and CESMV
on mixed-variable optimization problems.
Apart from these main contributions, during my doctoral research I have accomplished a number of additional contributions, which concern (i) a note on the
bound constraints handling for the CEC'05 benchmark set, (ii) computational results for an automatically tuned IPOP-CMA-ES on the CEC'05 benchmark set and
(iii) a study of artificial bee colonies for continuous optimization. These additional
contributions are to be found in the appendix to this thesis.
Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished
18
Maza, Sabido Susanna. "Discrete and continuous symetries in planar vector fields." Doctoral thesis, Universitat de Lleida, 2008. http://hdl.handle.net/10803/81314.
Abstract:
Aquesta tesi es situa en el marc de la teoriaqualitativadelssistemesd’equacionsdiferencials en el pla. Cada capítol conté un aspectediferent, però en totsells es tractenproblemes, la soluciódelsqualsestà basada en el rol que hi juguen les simetriesdiscretes i continues (reversibilitat o simetries de Lie) de campsvectorialsplans. A la introducció, es dóna un resumdelsresultatsmésconeguts i s’hiintrodueix la notació que es fa servir al llarg de la tesi.
En el segon i tercer capítol, s’aborda el problema de trobarl’expressió explícita del canvilinealitzant o orbitalmentlinealitzantd#un camp vectorial suau a partir del coneixementd’uncommutador, en el cas de la linealització, o una simetria de Lie, en el cas de la linealització orbital. Cada capítol finalitzaambexemplesil.lustratius del procedimentconstructiudelscanvis.
Al Capítol 5 s’apliquenelsresultatsdelscapítolsanteriors, combinatsamblinealitzacionsDarbouxianes. Concretament, es considera un sistema quadràtictipusLotka-Volterra i es caracteritzen les selles linealitzables i orbitalmentlinealitzablesmitjançant la troballadelscanvislinealitzants o orbitalmentlinealitzants.
En el sisè capítol, s’utilitzal’existènciad’unàlgebra de simetriespuntuals de Lie per donar informació sobre l’existència i localitzaciód’òrbitesperiòdiques. En particular, quanl’àlgebra de simetriespuntuals de Lie d’unaequació diferencial escalar de segónordreautònoma i suau té dimensiómajor o igual a dos, definim les anomenadesfuncionsfonamentals que enspermeten estudiar les òrbitesperiòdiques al pla de fases. En el cas particular d’equacionspolinomials de Liénard, mostrem la no existència de cicles límit en tot el pla de fases.
Finalment, al Capítol 7 es relacionen elssistemes reversibles amb el problema del centre aixícomamb el problema de la integrabilitat analítica. Consideremsistemesd’equacionsdiferencialsanalíticsamb centres degenerats i mostrem que poden transformar-se, després d’un reescalat del temps, en un sistema lineal i reversible. El coneixement de integralsprimeresens proporciona un procediment per caracteritzar, en alguns casos, la condició de reversibilitat del centre degenerat. D’altra banda, relacioneml’existència de integralsprimeresanalítiquesamb la reversibilitat orbital analítica en el cas de singularitatsdèbils no degenerades.
19
Maza, Sabido Susana. "Discrete and continuous symetries in planar vector fields." Doctoral thesis, Universitat de Lleida, 2008. http://hdl.handle.net/10803/81314.
Abstract:
Aquesta tesi es situa en el marc de la teoriaqualitativadelssistemesd’equacionsdiferencials en el pla. Cada capítol conté un aspectediferent, però en totsells es tractenproblemes, la soluciódelsqualsestà basada en el rol que hi juguen les simetriesdiscretes i continues (reversibilitat o simetries de Lie) de campsvectorialsplans. A la introducció, es dóna un resumdelsresultatsmésconeguts i s’hiintrodueix la notació que es fa servir al llarg de la tesi.
En el segon i tercer capítol, s’aborda el problema de trobarl’expressió explícita del canvilinealitzant o orbitalmentlinealitzantd#un camp vectorial suau a partir del coneixementd’uncommutador, en el cas de la linealització, o una simetria de Lie, en el cas de la linealització orbital. Cada capítol finalitzaambexemplesil.lustratius del procedimentconstructiudelscanvis.
Al Capítol 5 s’apliquenelsresultatsdelscapítolsanteriors, combinatsamblinealitzacionsDarbouxianes. Concretament, es considera un sistema quadràtictipusLotka-Volterra i es caracteritzen les selles linealitzables i orbitalmentlinealitzablesmitjançant la troballadelscanvislinealitzants o orbitalmentlinealitzants.
En el sisè capítol, s’utilitzal’existènciad’unàlgebra de simetriespuntuals de Lie per donar informació sobre l’existència i localitzaciód’òrbitesperiòdiques. En particular, quanl’àlgebra de simetriespuntuals de Lie d’unaequació diferencial escalar de segónordreautònoma i suau té dimensiómajor o igual a dos, definim les anomenadesfuncionsfonamentals que enspermeten estudiar les òrbitesperiòdiques al pla de fases. En el cas particular d’equacionspolinomials de Liénard, mostrem la no existència de cicles límit en tot el pla de fases.
Finalment, al Capítol 7 es relacionen elssistemes reversibles amb el problema del centre aixícomamb el problema de la integrabilitat analítica. Consideremsistemesd’equacionsdiferencialsanalíticsamb centres degenerats i mostrem que poden transformar-se, després d’un reescalat del temps, en un sistema lineal i reversible. El coneixement de integralsprimeresens proporciona un procediment per caracteritzar, en alguns casos, la condició de reversibilitat del centre degenerat. D’altra banda, relacioneml’existència de integralsprimeresanalítiquesamb la reversibilitat orbital analítica en el cas de singularitatsdèbils no degenerades.
20
Dasci, Abdullah. "Discrete and continuous models for production-distribution systems." Thesis, McGill University, 2001. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=37625.
Abstract:
This thesis presents a series of integrated models for simultaneous optimization of location, capacity, product range, and production technology decisions in production-distribution systems. The interactions between these decisions can be significant. This thesis draws its motivation from these interactions. In order to benefit from the capital and/or employment subsidies, preferential tax rates, and free trade zones provided by governments, firms need to take the interdependencies between their location, capacity and technology decisions into account. These decisions could be further complicated due to varying scale and scope economies inherent in different production technologies.The models proposed in this thesis are based on two fundamentally different but equally central approaches. The first approach builds on traditionally popular integer programming formulation in facility location theory, in which two such models presented in this thesis. The first one assumes that there are a number of dedicated production technologies for each product whereas, the second one assumes that a set of flexible technologies is also present. Analytical properties of the models are described, which lead to the development of exact and heuristic solution procedures. Results of several sets of computational experiments are also reported. The second approach is based on continuous approximation (also known as continuum mechanics), which has not been used to its potential in the literature. The third model in this thesis is proposed for a system with single product. It is based on the use of continuous functions in representing spatial distribution of cost parameters and decision variables. In this model, the focus is to compute the service regions leaving the precise plant locations to a subsequent analysis. This model lends itself to closed form solutions and allows derivation of a number of insights on the impact of several cost factors on facility design decisions. Then, it is utilized in an analytical framework to analyze several plant focus decisions of firms in a multi-product environment. The closed form solution is used to analyze several product and market focus strategies, which have provided several insights into more sophisticated plant focus decisions and into the impact of different production technologies on these decisions.
21
Smith, Jason Marko. "Discrete properties of continuous, non-Gaussian random processes." Thesis, University of Nottingham, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.438330.
22
Webster, Helen Nicola. "On the continuous and discrete third Painleve equations." Thesis, University of Kent, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.267390.
23
Parra, Rojas César. "Intrinsic fluctuations in discrete and continuous time models." Thesis, University of Manchester, 2017. https://www.research.manchester.ac.uk/portal/en/theses/intrinsic-fluctuations-in-discrete-and-continuous-time-models(d7006a2b-1496-44f2-8423-1f2fa72be1a5).html.
Abstract:
This thesis explores the stochastic features of models of ecological systems in discrete and in continuous time. Our interest lies in models formulated at the microscale, from which a mesoscopic description can be derived. The stochasticity present in the models, constructed in this way, is intrinsic to the systems under consideration and stems from their finite size. We start by exploring a susceptible-infectious-recovered model for epidemic spread on a network. We are interested in the case where the connectivity, or degree, of the individuals is characterised by a very broad, or heterogeneous, distribution, and in the effects of stochasticity on the dynamics, which may depart wildly from that of a homogeneous population. The model at the mesoscale corresponds to a system of stochastic differential equations with a very large number of degrees of freedom which can be reduced to a two-dimensional model in its deterministic limit. We show how this reduction can be carried over to the stochastic case by exploiting a time-scale separation in the deterministic system and carrying out a fast-variable elimination. We use simulations to show that the temporal behaviour of the epidemic obtained from the reduced stochastic model yields reasonably good agreement with the microscopic model under the condition that the maximum allowed degree that individuals can have is not too close to the population size. This is illustrated using time series, phase diagrams and the distribution of epidemic sizes. The general mesoscopic theory used in continuous-time models has only very recently been developed for discrete-time systems in one variable. Here, we explore this one-dimensional theory and find that, in contrast to the continuous-time case, large jumps can occur between successive iterates of the process, and this translates at the mesoscale into the need for specifying `boundary' conditions everywhere outside of the system. We discuss these and how to implement them in the stochastic difference equation in order to obtain results which are consistent with the microscopic model. We then extend the theoretical framework to make it applicable to systems containing an arbitrary number of degrees of freedom. In addition, we extend a number of analytical results from the one-dimensional stochastic difference equation to arbitrary dimension, for the distribution of fluctuations around fixed points, cycles and quasi-periodic attractors of the corresponding deterministic map. We also derive new expressions, describing the autocorrelation functions of the fluctuations, as well as their power spectrum. From the latter, we characterise the appearance of noise-induced oscillations in systems of dimension greater than one, which have been previously observed in continuous-time systems and are known as quasi-cycles. Finally, we explore the ability of intrinsic noise to induce chaotic behaviour in the system for parameter values for which the deterministic map presents a non-chaotic attractor; we find that this is possible for periodic, but not for quasi-periodic, states.
24
Vanel, Alice. "Asymptotic analysis of discrete and continuous periodic media." Thesis, Imperial College London, 2018. http://hdl.handle.net/10044/1/64911.
Abstract:
Mechanical mass-spring networks have long acted to motivate, and gain qualitative intuition, in solid-state physics, continuous media containing periodic arrays of inclu- sions such as phononic crystals, and more recently in metamaterials. While in some cases an exact or approximate analogy between the continuous model and its discrete representation can be systematically drawn, more often such analogies are introduced heuristically to aid interpretation with the lumped parameters estimated and accepted as qualitative. This thesis builds towards making the analogy exact; we first look at the discrete masses and springs lattices and apply multiple-scales methods directly to Green’s function integrals to extract the behaviour near critical frequencies. The features we uncover, and the asymptotics, are generic for many lattice structures. We then identify and study a new class of materials, two- and three- dimensional phononic crystals formed by closely spaced rigid cylinders or interconnected perforated boxes, respectively, and show that such materials constitute a versatile and tuneable family of subwavelength metamaterials. Intuitively, the voids and narrow gaps that characterise the crystals form an interconnected network of Helmholtz-like resonators. We use this intuition to argue that these continuous phononic crystals are in fact asymptotically equivalent, at low frequencies, to discrete mass-spring networks whose lumped param- eters we derive explicitly. The crystals are tantamount to metamaterials as their entire acoustic branch is squeezed into a subwavelength regime where the ratio of wavelength to period scales like the ratio of period to gap width raised to the power 1/4 in two dimensions and 1/2 in three dimensions; at yet larger wavelengths we accordingly find a comparably large effective refractive index. The fully analytical dispersion relations predicted by the discrete models yield dispersion curves that agree with those from finite-element simulations of the continuous crystals.
25
Schimmer, Lukas Wolfgang. "Spectral inequalities for discrete and continuous differential operators." Thesis, Imperial College London, 2014. http://hdl.handle.net/10044/1/29337.
Abstract:
In this thesis spectral inequalities and trace formulae for discrete and continuous differential operators are discussed. We first investigate spectral inequalities for Jacobi operators with matrix-valued potentials and present a new, direct proof of a sharp inequality corresponding to a Lieb-Thirring inequality for the power 3/2 using the commutation method. For the special case of a discrete Schrödinger operator we also prove new inequalities for higher powers of the eigenvalues and the potential and compare our results to previously established bounds. We then approximate a Schrödinger operator on L²(R) by Jacobi operators on ℓ²(Z) and use the established inequalities to provide new proofs of sharp Lieb-Thirring inequalities for the powers γ = 1/2 and γ = 3/2. By means of interpolation we derive spectral inequalities for Jacobi operators that yield (non-sharp) Lieb-Thirring constants on the real line for powers 1/2 < γ < 3/2. We then consider Schrödinger operators on a finite interval [0,b] with matrix-valued potentials and establish trace formulae of the Buslaev-Faddeev-Zakharov type. The results link sums of powers of the negative eigenvalues to terms dependent on the potential and scattering functions. Finally, we discuss the Berezin inequality, which is well-known on sets of finite measure and find an analogous inequality for the magnetic operator with constant magnetic field on a set whose complement has finite measure. We obtain a similar bound for the Heisenberg sub-Laplacian.
26
Kim, Sunha. "A Comparison of Discrete and Continuous Survival Analysis." Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/47933.
Abstract:
There has been confusion in choosing a proper survival model between two popular survival models of discrete and continuous survival analysis. This study aimed to provide empirical outcomes of two survival models in educational contexts and suggest a guideline for researchers who should adopt a suitable survival model. For the model specification, the study paid attention to three factors of time metrics, censoring proportions, and sample sizes. To arrive at comprehensive understanding of the three factors, the study investigated the separate and combined effect of these factors. Furthermore, to understand the interaction mechanism of those factors, this study examined the role of the factors to determine hazard rates which have been known to cause the discrepancies between discrete and continuous survival models. To provide empirical evidence from different combinations of the factors in the use of survival analysis, this study built a series of discrete and continuous survival models using secondary data and simulated data. In the first study, using empirical data from the National Longitudinal Survey of Youth 1997 (NLSY97), this study compared analyses results from the two models having different sizes of time metrics. In the second study, by having various specifications with combination of two other factors of censoring proportions and sample sizes, this study simulated datasets to build two models and compared the analysis results. The major finding of the study is that discrete models are recommended in the conditions of large units of time metrics, low censoring proportion, or small sample sizes. Particularly, discrete model produced better outcomes for conditions with low censoring proportion (20%) and small number (i.e., four) of large time metrics (i.e., year) regardless of sample sizes. Close examination of those conditions of time metrics, censoring proportion, and sample sizes showed that the conditions resulted into high hazards (i.e., 0.20). In conclusion, to determine a proper model, it is recommended to examine hazards of each of the time units with the specific factors of time metrics, censoring proportion and sample sizes.Ph. D.
27
Kilian, Stephanie L. "Coordination of Continuous and Discrete Components of Action." Cleveland State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=csu1403047071.
28
Desmarais, Bruce A. Carsey Thomas M. "Discrete measurement, continuous time and event history modeling." Chapel Hill, N.C. : University of North Carolina at Chapel Hill, 2008. http://dc.lib.unc.edu/u?/etd,1900.
Abstract:
Thesis (M.A.)--University of North Carolina at Chapel Hill, 2008.Title from electronic title page (viewed Dec. 11, 2008). "... in partial fulfillment of the requirements for the degree of Master of Political Science in the Department of Political Science." Discipline: Political Science; Department/School: Political Science.
29
Mayeli, Azita. "Discrete and continuous wavelet transformations on the Heisenberg group." [S.l.] : [s.n.], 2006. http://mediatum2.ub.tum.de/doc/602044/document.pdf.
30
Barton, Paul Inigo. "The modelling and simulation of combined discrete/continuous processes." Thesis, Imperial College London, 1992. http://hdl.handle.net/10044/1/8478.
31
Perrin, Nicolas. "Footstep planning for humanoid robots: discrete and continuous approaches." Phd thesis, Institut National Polytechnique de Toulouse - INPT, 2011. http://tel.archives-ouvertes.fr/tel-00647469.
Abstract:
Dans cette thèse nous nous intéressons à deux types d'approches pour la planification de pas pour robots humanoïdes : d'une part les approches discrètes où le robot n'a qu'un nombre fini de pas possibles, et d'autre part les approches où le robot se base sur des zones de faisabilité continues. Nous étudions ces problèmes à la fois du point de vue théorique et pratique. En particulier nous décrivons deux méthodes originales, cohérentes et efficaces pour la planification de pas, l'une dans le cas discret (chapitre 5) et l'autre dans le cas continu (chapitre 6). Nous validons ces méthodes en simulation ainsi qu'avec plusieurs expériences sur le robot HRP-2.
32
Koshkouei, Ali Jafari. "Continuous and discrete-time sliding mode control design techniques." Thesis, University of Sheffield, 1997. http://etheses.whiterose.ac.uk/15037/.
Abstract:
Sliding mode control is a well-known approach to the problem of the control of uncertain systems, since it is invariant to a class of parameter variations. Well-established investigations have shown that the sliding mode controller/ observer is a good approach from the point of view of robustness, implementation, numerical stability, applicability, ease of design tuning and overall evaluation. In the sliding mode control approach, the controller and/ or observer is designed so that the state trajectory converges to a surface named the sliding surface. It is desired to design the sliding surface so that the system stability is achieved. Many new methods and design techniques for the sliding controller/ observer are presented in this thesis. LQ frequency shaping sliding mode is a way of designing the sliding surface and control. By using this method, corresponding to the weighting functions in conventional quadratic performance, a compensator can be designed. The intention of observer design is to find an estimate for the state and, if the input is unknown, estimate a suitable input. Using the sliding control input form, a suitable estimated input can be obtained. The significance of the observer design method in this thesis is that a discontinuous observer for full order systems, including disturbance inputs, is designed. The system may not be ideally in the sliding mode and the uncertainty may not satisfy the matching condition. In discrete-time systems instead of having a hyperplane as in the continuous case, there is a countable set of points comprising a so-called lattice; and the surface on which these sliding points lie is named the latticewise hyperplane. Control and observer design using the discrete-time sliding mode, the robust stability of the sliding mode dynamics and the problem of stabilization of discrete-time systems are also studied. The sliding mode control of time-delay systems is also considered. Time-delay sliding system stability is studied for the cases of full information about the delay and also lack of information. The sliding surface is delay-independent as for the traditional sliding surface, and the reaching condition is achieved by applying conventional discontinuous control. A well-known method of control design is to specify eigenvalues in a region in the left-hand half-plane, and to design the gain feedback matrix to yield these eigenvalues. This method can also be used to design the sliding gain matrix. The regions considered in this thesis are, a sector, an infinite vertical strip, a disc, a hyperbola and the intersection ii of two sectors. Previous erroneous results are rectified and new theory developed. The complex Riccati equation, positivity of a complex matrix and the control of complex systems are significant problems which arise in many control theory problems and are discussed in this thesis.
33
Poufinas, Thomas. "Discrete-Time and Continuous-Time Option Pricing with Fees /." The Ohio State University, 1996. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487934589977028.
34
Rasolonjanahary, Manan'Iarivo. "Scaling of morphogenetic patterns in continuous and discrete models." Thesis, University of Liverpool, 2013. http://livrepository.liverpool.ac.uk/17293/.
Abstract:
In biological systems, individuals which belong to the same species can have different sizes. However, the ratios between the different parts of their bodies remain the same for individuals of different sizes. For example, for fully developed organism with segmented structure (i.e. insects), the number of segment across the size range of the individuals does not change. This morphological scaling plays a major role in the development of the organism and it has been the object of biological studies (Cooke 1981, Day and Lawrence 2000, Parker 2011) and mathematical modelling (Othmer and Pate 1980, Gregor, Tank et al. 2007, Kerszberg and Wolpert 2007) for many decades. Such scaling involves adjusting intrinsic scale of spatial patterns of gene expression that are set up during the development to the size of the system (Umulis and Othmer 2013). On the biological side, the evidence of scaling has been demonstrated experimentally on various objects including embryos. (Spemann 1938, Gregor, Bialek et al. 2005). For example, a Xenopus embryo was physically cut into dorsal and ventral halves in experimental conditions. The dorsal half which contains the “Spemann organizer” developed into a small embryo with normal proportion (Spemann 1938). Similar experiments carried out for the case of the sea urchin embryo lead to a smaller size of individuals (Khaner 1993). Also for flies of different species, the number of stripes on their embryos during their development remains the same although they are of different sizes. These stripes, which are visible at an earlier stage of the embryonic development, correspond to the spatial pattern of gene expressions and are the origin of the segmented body of the flies (Jaeger, Surkova et al. 2004, Gregor, Bialek et al. 2005, Arias 2008). On the mathematical side, Turing introduced the term “morphogens” for protein which is a key factor for pattern formation and he derived a model involving morphogens in which spatial patterns arise under certain conditions. Since then, various mathematical models of pattern formations have been developed. For the diffusion-based models, the spatial patterns do not scale with size. For models using reaction-diffusion equations, (combination of diffusion and biochemical reactions) a characteristic length scale is determined by the diffusion constant and reaction rate. Thus, when the size of the embryo changes, the spacing of the patterning remains fixed. This means that solutions of mathematical models based on reaction-diffusion do not show scaling (Tomlin and Axelrod 2007). The motivation of this work is to introduce possible mechanisms of scaling in biological systems and demonstrate those using mathematical models. After a discussion on how the scaling is considered in a few continuous models, we introduce our definition of scaling. We apply our definition of scaling to analyse properties of concentration profiles arising in various continuous models. Upon analysis of these profiles, we introduce modifications of mathematical models, in particular, two famous continuous models (Turing and Fitzhugh-Nagumo) to achieve scaling of their solutions. Following a presentation of continuous models, a discrete model of pattern formation based on a chain of logical elements (cellular automata) is also presented. This is more appropriate to represent the discreteness of biological systems with respect to their scaling properties: for a number of problems the issue of scaling doesn’t appear in the discrete formulation. This model has been developed to take account of local interactions between cells resulting into stationary pattern formation. We conclude this thesis by comparing our results with results obtained on other models and with experimental data particularly related to the different stages of the development of the fly embryo.
35
Ingerman, David V. "Discrete and continuous inverse boundary problems on a disc /." Thesis, Connect to this title online; UW restricted, 1997. http://hdl.handle.net/1773/5756.
36
Rivera, G. Angel J. "Reasoning about co-evolving discrete, continuous and hybrid states." Related electronic resource: Current Research at SU : database of SU dissertations, recent titles available full text, 2008. http://wwwlib.umi.com/cr/syr/main.
37
Sivaramakrishnan, Kamakshi. "Universal schemes for denoising discrete-time continuous-amplitude signals /." May be available electronically:, 2008. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.
38
Liu, Qing. "Elliptic Asymptotic Behaviours of Continuous and Discrete Painlevé Equations." Thesis, The University of Sydney, 2018. http://hdl.handle.net/2123/18883.
Abstract:
This thesis investigates the asymptotic behaviours of both continuous and discrete Painlevé equations as their independent variables approach complex infinity. We focus on the third to the fifth Painlevé equations and three discrete Painlevé equations referred to as d-PI, q-PI and q-PIII in the literature. In each case, the generic asymptotic behaviours are found to be given by elliptic functions. We deduce the properties of the respective elliptic functions in terms of energy-like parameters which are Hamiltonians and invariants of the corresponding autonomous continuous and discrete Painlevé equations. By using the method of averaging, we show that the Hamiltonians and invariants vary slowly across a local period parallelogram of the leading-order behaviour. For the continuous Painlevé equations we show the surprising result that all the equations PI-PV share the same modulation to the first two orders. We also show that the Hamiltonians are bounded on a path to infinity at any fixed angle. The Picard-Fuchs equations are derived for the related elliptic integrals. We solve the Picard-Fuchs equation at its regular singular points to find expansions of the approximate-periods at their degenerate points. The method of averaging is extended to discrete Painlevé equations to show that the invariants are also slowly varying. We also find the singular points of the invariant curves. The Picard-Fuchs equation is derived for q-PIII for its periods. The expansion of the periods at their degenerate points are also given. The main new results of this thesis are summarised in Theorems 1 and 2.1-2.3.
39
Nutaro, James Joseph. "Parallel discrete event simulation with application to continuous systems." Diss., The University of Arizona, 2003. http://hdl.handle.net/10150/280490.
Abstract:
Recent advances in discrete event modeling of continuous systems have emphasized the need for high performance simulation engines. This need is particularly acute when discrete event methods are applied to the numerical solution of partial differential equations. Accurate approximations can require thousands, or even millions, of cells. The corresponding requirements for memory and computing power can readily exceed what is available on a single processor computer. Discrete event simulations are characterized by asynchronous and irregular, random, or data dependent behavior. This makes parallel algorithm design particularly challenging. Known parallel discrete event simulation algorithms have been developed in terms of event and process oriented world views. In contrast to this, the Discrete Event System Specification (DEVS) forms the foundation of research into discrete event approximations of continuous systems. While event and process oriented models can be expressed in terms of the DEVS modeling formalism, there are DEVS models that do not seem to have an equivalent representation in the event or process oriented world views. This leaves open the question of how existing parallel discrete event simulation algorithms must be adapted in order to simulate DEVS models. In this dissertation, discrete simulation algorithms are built up from the basic definition of a discrete event system. The parallel algorithms that are developed through this approach are shown to operate correctly. To conclude this study, these algorithms are applied to producing numerical solutions of a hyperbolic conservation law (Sod's shock tube problem) and the wave equation.
40
Hu, Siyi S. M. Massachusetts Institute of Technology. "Discrete-continuous optimization for robot perception via semidefinite relaxation." Thesis, Massachusetts Institute of Technology, 2019. https://hdl.handle.net/1721.1/122515.
Abstract:
Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2019Cataloged from PDF version of thesis.
Includes bibliographical references (pages 85-90).
In this thesis, we propose polynomial-time algorithms based on semidefinite programming (SDP) relaxation to find approximate solutions to nonconvex problems arising in two fields of robot perception, semantic segmentation and robust pose graph optimization. Compared with other inference techniques, SDP relaxation have shown to provide accurate estimate with provable sub-optimality guarantees without relying on an initial guess for optimization. On the downside, general SDP solvers scale poorly in terms of time and memory with the problem size. However, for problems admitting low-rank solutions, low-rank solvers and smooth Riemannian optimization can speed up computation significantly. Along this direction, the first contribution is two fast and scalable techniques for inference in Markov Random Fields (MRFs). MRFs are a popular model for several pattern recognition and reconstruction problems in robotics and computer vision, but are intractable to solve in general. The first technique, named Dual Ascent Riemannian Staircase (DARS), is able to solve large problem instances in seconds. The second technique, named Fast Unconstrained SEmidefinite Solver (FUSES), utilizes a novel SDP relaxation and is able to solve similar problems in milliseconds. We benchmark both techniques in multi-class image segmentation problems against state-of-the-art MRF solvers and show that both techniques achieves comparable accuracy with the best existing solver while FUSES is much faster. Building on top of MRF models, our second contribution is a Discrete-Continuous Graphical Model (DC-GM) that combines discrete binary labeling with standard least-square pose graph optimization to identify and reject spurious measurements for Simultaneous Localization and Mapping (SLAM). We then perform inference in the DC-GM via semidefinite relaxation. Experiment results on synthetic and real benchmarking datasets show that the proposed approach compares favorably with state-of-the-art methods.
by Siyi Hu.
S.M.
S.M. Massachusetts Institute of Technology, Department of Aeronautics and Astronautics
41
Goda, Ibrahim. "Micromechanical models of network materials presenting internal length scales : applications to trabecular bone under stable and evolutive conditions." Thesis, Université de Lorraine, 2015. http://www.theses.fr/2015LORR0055/document.
Abstract:
Des méthodes micromécaniques spécifiques ont été développées pour la détermination du comportement effectif de matériaux cellulaires dotés d’une architecture discrète à l’échelle microscopique. La méthode d’homogénéisation discrète a été appliquée à des structures tissées monocouches ainsi qu’à l’os trabéculaire. La topologie discrète initiale de ces milieux est remplacée à l’échelle mésoscopique par un milieu effectif anisotrope micropolaire, qui rend compte des effets d’échelles observés. Ces méthodes d’homogénéisation permettent d’accéder à des propriétés classiques et non classiques dont la mesure expérimentale est souvent difficile. Des modèles 3D ont été développé afin de décrire la rupture fragile et ductile de l’os trabéculaire, incorporant des effets de taille des surfaces d’écoulement plastique. Nous avons construit par des analyses éléments finis de la microstructure de l’os trabéculaire un milieu de substitution 3D homogène, orthotrope de type couple de contraintes, sur la base d’une équivalence en énergie. Les tissus osseux ont la capacité d’adapter leur densité locale et leur taille et forme aux stimuli mécaniques. Nous avons développé des modèles de remodelage interne et externe dans le cadre de la thermodynamique des processus irréversibles, aux échelles cellulaire et macroscopique. Finalement, le remodelage interne anisotrope a été couplé à l’endommagement de fatigue, dans le cadre de la théorie continue de l’endommagementA methodology based on micromechanics has been developed to determine the effective behavior of network materials endowed with a discrete architecture at the microscopic level. It relies on the discrete homogenization method, which has been applied to textile monolayers and trabecular bones. The initially discrete topology of the considered network materials results after homogenization at the mesoscopic level in anisotropic micropolar effective continuum, which proves able to capture the observed internal scale effects. Such micromechanical methods are useful to remedy the difficulty to measure the effective mechanical properties at the intermediate mesoscopic level scale. The bending and torsion responses of vertebral trabecular bone beam specimens are formulated in both static and dynamic situations, based on the Cosserat theory. 3D models have been developed for describing the multiaxial yield and brittle fracture behavior of trabecular bone, including the analysis of size-dependent non-classical plastic yield. We have constructed by FE analyses a homogeneous, orthotropic couple-stress continuum model as a substitute of the 3D periodic heterogeneous cellular solid model of vertebral trabecular bone, based on the equivalent strain energy approach. Bone tissues are able to adapt their local density and load bearing capacities as well as their size and shape to mechanical stimuli. We have developed models for combined internal and external bone remodeling in the framework of the thermodynamics of irreversible processes, at both the cellular and macroscopic levels. We lastly combined anisotropic internal remodeling with fatigue continuum damage
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Xu, Kun. "Static hedging of barrier options in discrete and continuous time." Thesis, Uppsala University, Department of Mathematics, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-120232.
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Dimtriadish, Veniamin. "Modelling, safety verification and design of discrete/continuous processing systems." Thesis, Imperial College London, 1997. http://hdl.handle.net/10044/1/7263.
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Kristensson, Per Ola. "Discrete and Continuous Shape Writing for Text Entry and Control." Doctoral thesis, Linköping : Department of Computer and Information Science, Linköping University, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-8877.
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Chaves, Madalena. "Predictive analysis of dynamical systems: combining discrete and continuous formalisms." Habilitation à diriger des recherches, Université Nice Sophia Antipolis, 2013. http://tel.archives-ouvertes.fr/tel-00908927.
Abstract:
The mathematical analysis of dynamical systems covers a wide range of challenging problems related to the time evolution, transient and asymptotic behavior, or regulation and control of physical systems. A large part of my work has been motivated by new mathematical questions arising from biological systems, especially signaling and genetic regulatory networks, where the classical methods usually don't directly apply. Problems include parameter estimation, robustness of the system, model reduction, or model assembly from smaller modules, or control of a system towards a desired state. Although many different formalisms and methodologies can be used to study these problems, in the past decade my work has focused on discrete and hybrid modeling frameworks with the goal of developing intuitive, computationally amenable, and mathematically rigorous, methods of analysis. Discrete (and, in particular, Boolean) models involve a high degree of abstraction and provide a qualitative description of the systems' dynamics. Such models are often suitable to represent the known interactions in gene regulatory networks and their advantage is that a large range of theoretical analysis tools are available using, for instance, graph theoretical concepts. Hybrid (piecewise affine) models have discontinuous vector fields but provide a continuous and more quantitative description of the dynamics. These systems can be analytically studied in each region of an appropriate partition of the state space, and the full solution given as a concatenation of the solutions in each region. Here, I will introduce the two formalisms and then, using several examples, illustrate how a combination of different formalisms permits comparison of results, as well as gaining quantitative knowledge and predictive power on a biological system, through the use of complementary mathematical methods.
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Ouaknine, Joel. "Discrete analysis of continuous behaviour in real-time concurrent systems." Thesis, University of Oxford, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365293.
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Perreira, Das Chagas Thiago. "Stabilization of periodic orbits in discrete and continuous-time systems." Phd thesis, Université Paris Sud - Paris XI, 2013. http://tel.archives-ouvertes.fr/tel-00852424.
Abstract:
The main problem evaluated in this manuscript is the stabilization of periodic orbits of non-linear dynamical systems by use of feedback control. The goal of the control methods proposed in this work is to achieve a stable periodic oscillation. These control methods are applied to systems that present unstable periodic orbits in the state space, and the latter are the orbits to be stabilized.The methods proposed here are such that the resulting stable oscillation is obtained with low control effort, and the control signal is designed to converge to zero when the trajectory tends to the stabilized orbit. Local stability of the periodic orbits is analyzed by studying the stability of some linear time-periodic systems, using the Floquet stability theory. These linear systems are obtained by linearizing the trajectories in the vicinity of the periodic orbits.The control methods used for stabilization of periodic orbits here are the proportional feedback control, the delayed feedback control and the prediction-based feedback control. These methods are applied to discrete and continuous-time systems with the necessary modifications. The main contributions of the thesis are related to these methods, proposing an alternative control gain design, a new control law and related results.
48
Ypma, J. Y. "Dynamic models of continuous and discrete outcomes : methods and applications." Thesis, University College London (University of London), 2013. http://discovery.ucl.ac.uk/1386923/.
Abstract:
This thesis contains three chapters on dynamic models with discrete and continuous outcomes. In the rest chapter, I focus on indirect inference estimation. Indirect inference is used to estimate parameters in models where evaluation of the objective function directly is complicated or infeasible. Indirect inference is typically formulated as an optimization problem nesting one or more other optimization problems. In some cases the solution to the inner optimization problems can be obtained in one step, but when such a solution is not available, indirect inference estimation is computationally demanding. I show how constrained optimization methods can be used to replace the nesting of optimization problems and I provide Monte Carlo evidence showing when this approach is bene cial. The second chapter uses panel data from the United Kingdom to estimate a model of wage dynamics with labour participation where the variance in wages is decomposed in a permanent and a transitory component. Most studies that estimate similar models ignore non-participation; individuals without a wage are simply removed from the analysis. This leads to biased estimates of the parameters if working individuals are di erent in their unobservable characteristics compared to people that do not work. I use a dynamic selection model to include a discrete labour participation choice in a simple model of wage dynamics and compare the results to a version of the model that does not include labour participation. In the third chapter, I show how some of the assumptions on the dynamics of the unobservables in the second chapter can be relaxed. High dimensional integrals have to be approximated to estimate the less restrictive models. I use sparse grids and simulation methods to approximate these integrals and compare their performance on simulated data.
49
Rao, V. A. P. "Markov chain Monte Carlo for continuous-time discrete-state systems." Thesis, University College London (University of London), 2012. http://discovery.ucl.ac.uk/1349490/.
Abstract:
A variety of phenomena are best described using dynamical models which operate on a discrete state space and in continuous time. Examples include Markov (and semi-Markov) jump processes, continuous-time Bayesian networks, renewal processes and other point processes. These continuous-time, discrete-state models are ideal building blocks for Bayesian models in fields such as systems biology, genetics, chemistry, computing networks, human-computer interactions etc. However, a challenge towards their more widespread use is the computational burden of posterior inference; this typically involves approximations like time discretization and can be computationally intensive. In this thesis, we describe a new class of Markov chain Monte Carlo methods that allow efficient computation while still being exact. The core idea is an auxiliary variable Gibbs sampler that alternately resamples a random discretization of time given the state-trajectory of the system, and then samples a new trajectory given this discretization. We introduce this idea by relating it to a classical idea called uniformization, and use it to develop algorithms that outperform the state-of-the-art for models based on the Markov jump process. We then extend the scope of these samplers to a wider class of models such as nonstationary renewal processes, and semi-Markov jump processes. By developing a more general framework beyond uniformization, we remedy various limitations of the original algorithms, allowing us to develop MCMC samplers for systems with infinite state spaces, unbounded rates, as well as systems indexed by more general continuous spaces than time.
50
Chagas, Thiago Pereira das. "Stabilization of periodic orbits in discrete and continuous-time systems." Instituto Tecnológico de Aeronáutica, 2013. http://www.bd.bibl.ita.br/tde_busca/arquivo.php?codArquivo=2770.
Abstract:
The main problem evaluated in this manuscript is the stabilization of periodic orbits of non-linear dynamical systems by use of feedback control. The goal of the control methods proposed in this work is to achieve a stable periodic oscillation. These control methods are applied to systems that present unstable periodic orbits in the state space, and the latter are the orbits to be stabilized. The methods proposed here are such that the resulting stable oscillation is obtained with low control effort, and the control signal is designed to converge to zero when the trajectory tends to the stabilized orbit. Local stability of the periodic orbits is analyzed by studying the stability of some linear time-periodic systems, using the Floquet stability theory. These linear systems are obtained by linearizing the trajectories in the vicinity of the periodic orbits. The control methods used for stabilization of periodic orbits here are the proportional feedback control, the delayed feedback control and the prediction-based feedback control. These methods are applied to discrete and continuous-time systems with the necessary modifications. The main contributions of the thesis are related to these methods, proposing an alternative control gain design, a new control law and related results.