Dissertations / Theses on the topic 'Dynamical'
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Cox, Sander. "Dynamical modelling." Thesis, Uppsala universitet, Tillämpad matematik och statistik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-262477.
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Root, Stephen Thomassy. "Comparison of Kane's dynamical equations to traditional dynamical techniques." Thesis, Massachusetts Institute of Technology, 1991. http://hdl.handle.net/1721.1/105588.
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Ozaki, Junichi. "Dynamical quantum effects in cluster dynamics of Fermi systems." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/199083.
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Rieger, Marc Oliver. "Nonconvex Dynamical Problems." Doctoral thesis, Universitätsbibliothek Leipzig, 2004. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-37269.
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Many problems in continuum mechanics, especially in the theory of elastic materials, lead to nonlinear partial differential equations. The nonconvexity of their underlying energy potential is a challenge for mathematical analysis, since convexity plays an important role in the classical theories of existence and regularity. In the last years one main point of interest was to develop techniques to circumvent these difficulties. One approach was to use different notions of convexity like quasi-- or polyconvexity, but most of the work was done only for static (time independent) equations. In this thesis we want to make some contributions concerning existence, regularity and numerical approximation of nonconvex dynamical problems.
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Haydn, Nicolai Theodorus Antonius. "On dynamical systems." Thesis, University of Warwick, 1986. http://wrap.warwick.ac.uk/55813/.
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Part A. We prove existence of smooth invariant circles for area preserving twist maps close enough to integrable using renormalisation. The smoothness depends upon that of the map and the Liouville exponent of the rotation number. Part B. Ruelle and Capocaccia gave a new definition of Gibbs states on Smale spaces. Equilibrium states of suitable function there on are known to be Gibbs states. The converse in discussed in this paper, where the problem is reduced to shift spaces and there solved by constructing suitable conjugating homeomorphisms in order to verify the conditions for Gibbs states which Bowen gave for shift spaces, where the equivalence to equilibrium states is known. Part C. On subshifts which are derived from Markov partitions exists an equivalence relation which idendifies points that lie on the boundary set of the partition. In this paper we restrict to symbolic dynamics. We express the quotient space in terms of a non-transitive subshift of finite type, give a necessary and sufficient condition for the existence of a local product structure and evaluate the Zeta function of the quotient space. Finally we give an example where the quotient space is again a subshift of finite type.
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Miles, Richard Craig. "Arithmetic dynamical systems." Thesis, University of East Anglia, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.323222.
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Hillman, Chris. "Sturmian dynamical systems /." Thesis, Connect to this title online; UW restricted, 1998. http://hdl.handle.net/1773/5806.
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Che, Dzul-Kifli Syahida. "Chaotic dynamical systems." Thesis, University of Birmingham, 2012. http://etheses.bham.ac.uk//id/eprint/3410/.
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In this work, we look at the dynamics of four different spaces, the interval, the unit circle, subshifts of finite type and compact countable sets. We put our emphasis on chaotic dynamical system and exhibit sufficient conditions for the system on the interval, the unit circle and subshifts of finite type to be chaotic in three different types of chaos. On the interval, we reveal two weak conditions’s role as a fast track to chaotic behavior. We also explain how a strong dense periodicity property influences chaotic behavior of dynamics on the interval, the unit circle and subshifts of finite type. Finally we show how dynamics property of compact countable sets effecting the structure of the sets.
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Leyendecker, Sigrid. "Mechanical integrators for constrained dynamical systems in flexible multibody dynamics." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980411912.
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Sardanyés, i. Cayuela Josep. "Dynamics, evolution and information in nonlinear dynamical systems of replicators." Doctoral thesis, Universitat Pompeu Fabra, 2009. http://hdl.handle.net/10803/7182.
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En aquesta tesi he investigat diversos camps de la biologia que podrien englobar-se en la disciplina general dels sistemes no lineals de replicadors. Els treballs presentats en aquesta tesis investiguen diversos fenomens dinàmics i processos evolutius per virus de RNA, pels anomenats hipercicles i per models generals de replicadors antagonistes. Específicament he investigat les anomenades quasiespècies, utilitzades per a modelitzar poblacions de RNA. Els treballs sobre hipercicles exploren diversos fenomens previs a l'origen de la vida i a l'aparició de la primera cèl.lula vivent. Mitjançant models ecològics com també utilitzant diferents eines computacionals he estudiat l'anomenada hipòtesi de la Reina Roja per entitats replicadores simples amb mutació. Aquests estudis tenen un interès en el contexte de l'evolució prebiòtica i l'ecologia teòrica.In this thesis I have investigated several fields of biology that can be classified in the general subject of replicator nonlinear systems. The works presented in the thesis investigate several dynamical phenomena and evolutionary processes for RNA viruses, for hypercycles and for general models on antagonistic replicator dynamics. I have specifically investigated the dynamics of so-called quasispecies, used for the modelization of RNA populations. The works on hypercycles explore several phenomena related to previous events to the origin of life and to the appearance of the first living cell. By means of some ecologically-based mathematical models as well as of some computational models we also investigate the so-called Red Queen hypothesis for small, replicating-mutating entities. These studies are of interest in the context of prebiotic evolution and theoretical ecology.
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Sardanyés, Cayuela Josep. "Dynamics, evolution and information in nonlinear dynamical systems of replicators." Doctoral thesis, Universitat Pompeu Fabra, 2009. http://hdl.handle.net/10803/7182.
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En aquesta tesi he investigat diversos camps de la biologia que podrien englobar-se en la disciplina general dels sistemes no lineals de replicadors. Els treballs presentats en aquesta tesis investiguen diversos fenomens dinàmics i processos evolutius per virus de RNA, pels anomenats hipercicles i per models generals de replicadors antagonistes. Específicament he investigat les anomenades quasiespècies, utilitzades per a modelitzar poblacions de RNA. Els treballs sobre hipercicles exploren diversos fenomens previs a l'origen de la vida i a l'aparició de la primera cèl.lula vivent. Mitjançant models ecològics com també utilitzant diferents eines computacionals he estudiat l'anomenada hipòtesi de la Reina Roja per entitats replicadores simples amb mutació. Aquests estudis tenen un interès en el contexte de l'evolució prebiòtica i l'ecologia teòrica.In this thesis I have investigated several fields of biology that can be classified in the general subject of replicator nonlinear systems. The works presented in the thesis investigate several dynamical phenomena and evolutionary processes for RNA viruses, for hypercycles and for general models on antagonistic replicator dynamics. I have specifically investigated the dynamics of so-called quasispecies, used for the modelization of RNA populations. The works on hypercycles explore several phenomena related to previous events to the origin of life and to the appearance of the first living cell. By means of some ecologically-based mathematical models as well as of some computational models we also investigate the so-called Red Queen hypothesis for small, replicating-mutating entities. These studies are of interest in the context of prebiotic evolution and theoretical ecology.
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Mizuno, Hideyuki. "Molecular Dynamics Simulation Studies of Dynamical Properties of Supercooled Liquids." 京都大学 (Kyoto University), 2012. http://hdl.handle.net/2433/157540.
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Kuhlman, Christopher James. "Generalizations of Threshold Graph Dynamical Systems." Thesis, Virginia Tech, 2013. http://hdl.handle.net/10919/76765.
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Dynamics of social processes in populations, such as the spread of emotions, influence, language, mass movements, and warfare (often referred to individually and collectively as contagions), are increasingly studied because of their social, political, and economic impacts. Discrete dynamical systems (discrete in time and discrete in agent states) are often used to quantify contagion propagation in populations that are cast as graphs, where vertices represent agents and edges represent agent interactions. We refer to such formulations as graph dynamical systems. For social applications, threshold models are used extensively for agent state transition rules (i.e., for vertex functions). In its simplest form, each agent can be in one of two states (state 0 (1) means that an agent does not (does) possess a contagion), and an agent contracts a contagion if at least a threshold number of its distance-1 neighbors already possess it. The transition to state 0 is not permitted. In this study, we extend threshold models in three ways. First, we allow transitions to states 0 and 1, and we study the long-term dynamics of these bithreshold systems, wherein there are two distinct thresholds for each vertex; one governing each of the transitions to states 0 and 1. Second, we extend the model from a binary vertex state set to an arbitrary number r of states, and allow transitions between every pair of states. Third, we analyze a recent hierarchical model from the literature where inputs to vertex functions take into account subgraphs induced on the distance-1 neighbors of a vertex. We state, prove, and analyze conditions characterizing long-term dynamics of all of these models.Master of Science
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Chapman, Craig K. "Coarsening dynamical systems : dynamic scaling, universality and mean-field theories." Thesis, University of Glasgow, 2012. http://theses.gla.ac.uk/3255/.
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We study three distinct coarsening dynamical systems (CDS) and probe the underlying scaling laws and universal scaling functions. We employ a variety of computational methods to discover and analyse these intrinsic statistical objects. We consider mean-field type models, similar in nature to those used in the seminal work of Lifshitz, Slyozov and Wagner (LSW theory), and statistical information is then derived from these models. We first consider a simple particle model where each particle possesses a continuous positive parameter, called mass, which itself determines the particle’s velocity through a prescribed law of motion. The varying speeds of particles, caused by their differing masses, causes collisions to take place, in which the colliding particles then merge into a single particle while conserving mass. We computationally discover the presence of scaling laws of the characteristic scale (mean mass) and universal scaling functions for the distribution of particle mass for a family of power-law motion rules. We show that in the limit as the power-law exponent approaches infinity, this family of models approaches a probabilistic min-driven model. This min-driven model is then analysed through a mean-field type model, which yields a prediction of the universal scaling function. We also consider the conserved Kuramoto-Sivashinsky (CKS) equation and provide, in particular, a critique of the effective dynamics derived by Politi and ben-Avraham. We consider several different numerical methods for solving the CKS equation, both on fixed and adaptive grids, before settling on an implicit-explicit hybrid scheme. We then show, through a series of detailed numerical simulations of both the CKS equation and the proposed dynamics, that their particular reduction to a length-based CDS does not capture the effective dynamics of the CKS equation. Finally, we consider a faceted CDS derived from a one-dimensional geometric partial differential equation. Unusually, an obvious one-point mean-field theory for this CDS is not present. As a result, we consider the two-point distribution of facet lengths. We derive a mean-field evolution equation governing the two-point distribution, which serves as a two-dimensional generalisation of the LSW theory. Through consideration of the two-point theory, we subsequently derive a non-trivial one-point sub-model which we analytically solve. Our predicted one-point distribution bears a significant resemblance to the LSW distribution and stands in reasonable agreement with the underlying faceted CDS.
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Alam, Tauhidul. "A Dynamical System Approach for Resource-Constrained Mobile Robotics." FIU Digital Commons, 2018. https://digitalcommons.fiu.edu/etd/3825.
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The revolution of autonomous vehicles has led to the development of robots with abundant sensors, actuators with many degrees of freedom, high-performance computing capabilities, and high-speed communication devices. These robots use a large volume of information from sensors to solve diverse problems. However, this usually leads to a significant modeling burden as well as excessive cost and computational requirements. Furthermore, in some scenarios, sophisticated sensors may not work precisely, the real-time processing power of a robot may be inadequate, the communication among robots may be impeded by natural or adversarial conditions, or the actuation control in a robot may be insubstantial. In these cases, we have to rely on simple robots with limited sensing and actuation, minimal onboard processing, moderate communication, and insufficient memory capacity. This reality motivates us to model simple robots such as bouncing and underactuated robots making use of the dynamical system techniques. In this dissertation, we propose a four-pronged approach for solving tasks in resource-constrained scenarios: 1) Combinatorial filters for bouncing robot localization; 2) Bouncing robot navigation and coverage; 3) Stochastic multi-robot patrolling; and 4) Deployment and planning of underactuated aquatic robots.
First, we present a global localization method for a bouncing robot equipped with only a clock and contact sensors. Space-efficient and finite automata-based combinatorial filters are synthesized to solve the localization task by determining the robot’s pose (position and orientation) in its environment.
Second, we propose a solution for navigation and coverage tasks using single or multiple bouncing robots. The proposed solution finds a navigation plan for a single bouncing robot from the robot’s initial pose to its goal pose with limited sensing. Probabilistic paths from several policies of the robot are combined artfully so that the actual coverage distribution can become as close as possible to a target coverage distribution. A joint trajectory for multiple bouncing robots to visit all the locations of an environment is incrementally generated.
Third, a scalable method is proposed to find stochastic strategies for multi-robot patrolling under an adversarial and communication-constrained environment. Then, we evaluate the vulnerability of our patrolling policies by finding the probability of capturing an adversary for a location in our proposed patrolling scenarios.
Finally, a data-driven deployment and planning approach is presented for the underactuated aquatic robots called drifters that creates the generalized flow pattern of the water, develops a Markov-chain based motion model, and studies the long- term behavior of a marine environment from a flow point-of-view.
In a broad summary, our dynamical system approach is a unique solution to typical robotic tasks and opens a new paradigm for the modeling of simple robotics systems
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Crockett, Victoria Jane. "Orbit space reduction for symmetric dynamical systems with an application to laser dynamics." Thesis, University of Exeter, 2010. http://hdl.handle.net/10036/3310.
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This work considers the effect of symmetries on analysing bifurcations in dynamical systems. We consider an example of a laser with strong optical feedback which is modelled using coupled non-linear differential equations. A stationary point can be found in space, which can then be continued in parameter space using software such as AUTO. This software will then detect and continue bifurcations which indicate change in dynamics as parameters are varied. Due to symmetries in the equations, using AUTO may require the system of equations to be reduced in order to study periodic orbits of the original system as (relative) equilibria of the reduced system. Reasons for this are explored as well as considering how the equations can be changed or reduced to remove the symmetry. Invariant and Equivariant theory provide the tools for reducing the system of equations to the orbit space, allowing further analysis of the lasers dynamics.
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Marzi, Tommaso. "Dynamical models for pedestrian dynamics using data from pedestrian flow sensors." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21219/.
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The purpose of this thesis is to give a contribution in a wider project regarding the development of new tools for the governance of tourist flows in Venice. Because of the virus COVID-19, this topic has increased in interest, since it can be used both to look for possible solutions to make public places safer and to study the spread of the virus itself.
Once the testing of the sensors that provide the data on mobility is carried out, a macroscopic approach to the pedestrian dynamics based on the Fundamental Diagram is proposed: scenarios with different geometries as streets, crossroads or bridges are compared, focusing in particular on representative parameters of the model.
In the last part, a microscopic approach to pedestrian mobility is presented: a simulation model is calibrated on the basis of the available data, in order to define whether it can actually reproduce the behaviour of a crowd.
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Quer, Jannes [Verfasser]. "Importance sampling for metastable dynamical systems in molecular dynamics / Jannes Quer." Berlin : Freie Universität Berlin, 2018. http://d-nb.info/1176632485/34.
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Giboudot, Yoel. "Study of beam dynamics in NS-FFAG EMMA with dynamical map." Thesis, Brunel University, 2011. http://bura.brunel.ac.uk/handle/2438/5947.
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Dynamical maps for magnetic components are fundamental to studies of beam dynamics in accelerators. However, it is usually not possible to write down maps in closed form for anything other than simplified models of standard accelerator magnets. In the work presented here, the magnetic field is expressed in analytical form obtained from fitting Fourier series to a 3D numerical solution of Maxwell’s equations. Dynamical maps are computed for a particle moving through this field by applying a second order (with the paraxial approximation) explicit symplectic integrator. These techniques are used to study the beam dynamics in the first non-scaling FFAG ever built, EMMA, especially challenging regarding the validity of the paraxial approximation for the large excursion of particle trajectories. The EMMA lattice has four degrees of freedom (strength and transverse position of each of the two quadrupoles in each periodic cell). Dynamical maps, computed for a set of lattice configurations, may be efficiently used to predict the dynamics in any lattice configuration. We interpolate the coefficients of the generating function for the given configuration, ensuring the symplecticity of the solution. An optimisation routine uses this tool to look for a lattice defined by four constraints on the time of flight at different beam energies. This provides a way to determine the tuning of the lattice required to produce a desired variation of time of flight with energy, which is one of the key characteristics for beam acceleration in EMMA. These tools are then benchmarked against data from the recent EMMA commissioning.
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Homer, Martin Edward. "Bifurcations and dynamics of piecewise smooth dynamical systems of arbitrary dimension." Thesis, University of Bristol, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299271.
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Ruiter, Julia. "Practical Chaos: Using Dynamical Systems to Encrypt Audio and Visual Data." Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/scripps_theses/1389.
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Although dynamical systems have a multitude of classical uses in physics and applied mathematics, new research in theoretical computer science shows that dynamical systems can also be used as a highly secure method of encrypting data. Properties of Lorenz and similar systems of equations yield chaotic outputs that are good at masking the underlying data both physically and mathematically. This paper aims to show how Lorenz systems may be used to encrypt text and image data, as well as provide a framework for how physical mechanisms may be built using these properties to transmit encrypted wave signals.
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Uthushagen, Kristian Siegel. "Entropy in Dynamical Networks." Thesis, Norges Teknisk-Naturvitenskaplige Universitet, 2013. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-20918.
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This thesis presents a new type of dynamical entropy, defined by the movement of particles beetween the nodes in a network. The entropy is intended to have similar properties as the well-known thermodynamic entropy. Simulations are run on different versions of known networks, and exhibits expected behaviour. A few applications of the variable have also been suggested, in which topographical properties, centrality and node distance is decided in relative terms for spesific networks. In addition, a historical recap is the science of thermodynamics and networks is given, and also an explanation to how these fields have come together over the recent years, culminating in this effort to further connect them.
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Behrisch, Mike, Sebastian Kerkhoff, Reinhard Pöschel, Friedrich Martin Schneider, and Stefan Siegmund. "Dynamical Systems in Categories." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-129909.
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In this article we establish a bridge between dynamical systems, including topological and measurable dynamical systems as well as continuous skew product flows and nonautonomous dynamical systems; and coalgebras in categories having all finite products. We introduce a straightforward unifying definition of abstract dynamical system on finite product categories. Furthermore, we prove that such systems are in a unique correspondence with monadic algebras whose signature functor takes products with the time space. We substantiate that the categories of topological spaces, metrisable and uniformisable spaces have exponential objects w.r.t. locally compact Hausdorff, σ-compact or arbitrary time spaces as exponents, respectively. Exploiting the adjunction between taking products and exponential objects, we demonstrate a one-to-one correspondence between monadic algebras (given by dynamical systems) for the left-adjoint functor and comonadic coalgebras for the other. This, finally, provides a new, alternative perspective on dynamical systems.
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Aznar, Siguan Gabriela. "White dwarf dynamical interactions." Doctoral thesis, Universitat Politècnica de Catalunya, 2015. http://hdl.handle.net/10803/290737.
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Merging white dwarfs is a promising channel to trigger Type Ia supernovae, known as the double degenerate scenario. Supernovae are stellar explosions that radiate as much energy as any ordinary star is expected to emit over its entire life span, outshining briefly the whole hosting galaxy. They enrich the interstellar medium with higher mass elements and trigger the formation of new stars by the produced expanding shock. Additionally, Type Ia supernovae have been used as standard candles and have allowed the discovery that the universe was expanding at an accelerating rate. Despite the important role that Type Ia supernovae play in Astrophysics, we still do not know what stellar systems give rise to them. There are approximately a few hundred million double white dwarf systems in the Milky Way alone and their study would help to establish whether one can produce sufficient Type Ia explosions via this route. Nevertheless, even if a white dwarf merger does not succeed in exploding as a Type Ia supernova, other interesting phenomena might result. R Coronae Borealis, magnetars and high-field magnetic white dwarfs, or at least some of them, could be the product of some white dwarf mergers.
In this thesis we study first two different scenarios which involve two interacting white dwarfs. They differ from the classical double degenerate scenario in the mechanism which makes both stars interact. First we consider the core degenerate scenario. In this case the merger of both white dwarfs is triggered by the interaction with a circumbinary disk. This disk is made up of the material that falls back after the ejection of the common envelope, at the final stages of the common envelope phase which precedes the formation of the white dwarf binary system. As the binary system transfers angular momentum to the circumbinary disk, the separation of the pair decreases and the eccentricity of the system increases while the core of the post-AGB star, the proto-white dwarf, is still hot. For massive enough disks the decrease of the orbital separation is enough to drive a merger before the disk is ejected. Then, the merger occurs in an eccentric orbit with a hot binary component, in contrast to the conditions found in the classical double degenerate scenario, which is driven by gravitational radiation. Otherwise, if the disk is not massive enough, the merger is driven by gravitational wave emission and the orbit is nearly circular, while the core of the AGB star is cold.
Secondly, we studied different white dwarf close encounters. These interactions occur in dense and old stellar systems, as globular clusters and galactic nuclei, or in multiple stellar systems, where a white dwarf binary is perturbed by a third star. We perform several simulations of close encounters of white dwarfs with different masses and compositions, and obtain three different outcomes. Either an eccentric binary is formed, or a lateral or a direct collision occur. We compute when detonation conditions are met and when one or both white dwarfs are disrupted. Furthermore, we compute the observational signatures of these interactions. These include the emission of gravitational waves, X-ray luminosities, thermal neutrino emission and bolometric light curves.
Finally, we analyze two possible outcomes of a white dwarf merger. We start studying the formation of a dynamo in the outer layers of the compact merger remnant. Then, we prove that the generated magnetic fields are confined in the outer layers of the remnant and can reach high magnitudes, showing that the remnants of some white dwarf binary mergers can explain some observed high-field magnetic white dwarfs. To conclude, we study if the anomalous X-ray pulsar 4U 0142+61 has observational characteristics which fit the properties of the white dwarf merger remnant composed of the high-field magnetic white dwarf surrounded by a rapidly rotating disk.La coalescència de nanes blanques és un dels possibles escenaris que podrien originar una supernova del tipus Ia, i es conegut com l'escenari doble degenerat. Les supernoves són explosions estel·lars que irradien tanta energia com la que un estel ordinari emet durant tota la seva vida, eclipsant breumente tota la galàxia que habita. Aquestes explosions enriqueixen el mitjà interestel·lar amb elements pesants i afavoreixen la creació de nous estels en produir un xoc en expansió. A , les supernoves del tipus Ia han sigut utilitzades com a candeles estàndard, ajudant a descobrir que l'univers s'està expandint a un ritme accelerat. Malgrat la seva importància, seguim sense saber quins sistemes generen aquest tipus d'explosions. Hi ha aproximadament uns centenars de milions de sistemes binaris de nanes blanques a la Via Làctia, i el seu estudi ajudaria a establir si la seva coalescència pot produir el suficient nombre de supernovae tipus Ia. No obstant això, encara que la coalescència no produexi una explosió de aquest tipus, aquestes interaccions podríen donar lloc a d'altres fenòmens interessants, com ara els estels R Coronae Borealis, els magnetars i les nanes blanques amb camps magnétics elevats. En aquesta tesi estudiem primer dos escenaris diferents que involucren dues nanes blanques que interactuen. Aquests difereixen del clàssic escenari doble degenerat en el mecanisme que provoca la seva interacció. Primer considerem l'escenari anomenat "core degenerate". En aquest, la coalescència es produeix a causa de la interacció posterior a la fase d'embolcall comú del sistema binari. Aquest disc està compost pel material que torna a caure després de l'expulsió de l'embolcall comú que envolta el sistema, en les últimes etapes de la fase que precedeix a la formació del sistema de dues nanes blanques. Com que el sistema binari transfereix moment angular al disc, la separació entre els estels decreix i l'excentricitat de la seva òrbita augmenta, a més el nucli de l'estel post-AGB, la proto-nana blanca, está calent. Quan el disc és massiu, la coalescència del sistema abans de que el disc sigui expulsat. Aleshores, la coalescència es produeix en una òrbita excèntrica amb una component calent, al contrari que en l'escenari doble degenerat clàssic, el qual és desenvolupat degut a l¿emissió d¿ones gravitatòries. Si, pel contrari, el disc es poc massiu, la interacció es produeix per emissió d'ones gravitatòries i la órbita excèntrica i el nucli de l'estel post-AGB es fred. També hem estudiat encontres propers entre nanes blanques. Aquestes interaccions poden succeir en sistemes estel·lars vells i densos, com ara els cúmuls globulars o els nuclis galàctics, o en un sistema estel·lar múltiple, on el sistema binari de nanes blanques és pertorbat per un tercer estel. Hem realitzat vàries simulacions de trobades entre nanes blanques amb òrbites excèntriques i amb diferents masses i composicions, i obtenim tres resultats diferents. O bé es forma un sistema binari excèntric, o bé es produeix una col·lisió lateral o una directa. Els nostres càlculs especifiquen quan s¿arriba a condicions de detonació i quan aquestes resulten en la disrupció d'un o tots dos estels. També calculem l'emissió d'ones gravitatòries, la luminositat de raigs X, les emissions de neutrins tèrmics i les corbes de llum bolométriques. Finalment, analitzem dos possibles fenòmens que poden succeir després de la coalescència. Un d'ells es la formació d'una dinamo en les capes externes del romanent compacte. Demostrem que el camp magnètic generat es queda limitat en aquesta regió i pot assolir magnituds altes. Així, provem que les nanes blanques resultants d'una coalescència poden donar lloc a algunes de les nanes blanques altament magnètiques observades. Per finalitzar, estudiem si el púlsar de raigs X anòmal 4U 0142+61 té característiques que poden ser explicades a partir del romanent obtingut, format per la nana blanca magnètica envoltada per un disc
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Dam, Albert Anton ten. "Unilaterally constrained dynamical systems." [S.l : [Groningen] : s.n.] ; [University Library Groningen] [Host], 1997. http://irs.ub.rug.nl/ppn/159407869.
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George, A. "Five dimensional dynamical triangulations." Thesis, Swansea University, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.637039.
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The dynamical triangulations approach to quantum gravity is investigated in detail for the first time in five dimensions. In this case, the most general action that is linear in components of the f-vector has three terms. It was suspected that the corresponding space of couplings would yield to rich phase structure. This work is primarily motivated by the hope that this new viewpoint will lead to a deeper understanding of dynamical triangulations in general. Ultimately, this research programme may give a better insight into the potential application of dynamical triangulations to quantum gravity. This thesis serves as an exploratory study of this uncharted territory. The five dimensional (k,l) moves used in the Monte Carlo algorithm are proven to be ergodic in the space of combinatorially equivalent simplicial 5-manifolds. A statement is reached regarding the possible existence of an exponential upper bound on the number of combinatorially equivalent triangulations of the 5-sphere. Monte Carlo simulations reveal non-trivial phase structure which is analysed in some detail. Further investigations deal with the geometric and fractal nature of triangulations. This is followed by a characterisation of the weak coupling limit in terms of stacked spheres. Simple graph theory arguments are used to reproduce and generalise a well-known result in combinatorial topology. Finally, a comprehensive study of singular structures in dynamical triangulations is presented. It includes a new understanding of their existence, which appears to be consistent with the non-existence of singular vertices in three dimensions. The thesis is concluded with an overview of results, general discussion and suggestions for future work.
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Hardiman, S. C. "Stratosphere-troposphere dynamical coupling." Thesis, University of Cambridge, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603685.
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This thesis is concerned with dynamical coupling between the stratosphere and troposphere. The first part of the thesis examines mechanisms whereby dynamical perturbations to the upper stratosphere can lead to a significant response in the lower stratosphere, looking particularly at how this response is determined by the extra-tropical dynamics. A one dimensional model is used to show that the response is much greater when the external parameters are such that the flow has multiple stable states. The same principle is shown to apply to a fully three dimensional flow and does not depend qualitatively on the representation of the troposphere and tropospheric wave forcing. The dependence of the response on the height of the applied dynamical perturbation, the amplitude of planetary wave forcing, and the relaxation to radiative equilibrium temperatures is considered. In the second part of the thesis we consider the interhemispheric differences in the extratropical seasonal cycle and suggest that resonance of topographically forced waves with free travelling planetary waves could be in part responsible for these differences. The seasonal cycle in mass upwelling in the tropical lower stratosphere is also considered. In particular we look at the differences in this upwelling caused by the strength and location of tropospheric wave driving, the thermal relaxation timescale of the atmosphere, baroclinic instability, and the seasonal cycle in the tropospheric radiative equilibrium temperature field. Finally we consider the interannual variability seen in the tropical mass upwelling. We quantify the different parts of this variability – the part that can be considered forced variability and the part that arises due to internal variability. We suggest that the high forced variability seen in the mass upwelling may be due to it being linked, via extratropical wave driving, to sea surface temperatures.
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Chan, N. "Dynamical systems in cosmology." Thesis, University College London (University of London), 2012. http://discovery.ucl.ac.uk/1348375/.
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In this PhD thesis, the role of dynamical systems in cosmology has been studied. Many systems and processes of cosmological interest can be modelled as dynamical systems. Motivated by the concept of hypothetical dark energy that is believed to be responsible for the recently discovered accelerated expansion of the universe, various dynamical dark energy models coupled to dark matter have been investigated using a dynamical systems approach. The models investigated include quintessence, three-form and phantom fields, interacting with dark matter in different forms. The properties of these models range from mathematically simple ones to those with better physical motivation and justification. It was often encountered that linear stability theory fails to reveal behaviour of the dynamical systems. As part of this PhD programme, other techniques such as application of the centre manifold theory, construction of Lyapunov functions were considered. Applications of these so-called methods of non-linear stability theory were applied to cosmological models. Aforementioned techniques are powerful tools that have direct applications not only in applied mathematics, theoretical physics and engineering, but also in finance, economics, theoretical immunology, neuroscience and many more. One of the main aims of this thesis is to bridge the gap between dynamical systems theory, an area of applied mathematics, and cosmology, an exciting area of physics that studies the universe as a whole.
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Schinkel, Michael. "Nondeterministic hybrid dynamical systems." Thesis, University of Glasgow, 2002. http://theses.gla.ac.uk/1853/.
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This thesis is concerned with the analysis, control and identification of hybrid dynamical systems. The main focus is on a particular class of hybrid systems consisting of linear subsystems. The discrete dynamic, i.e., the change between subsystems, is unknown or nondeterministic and cannot be influenced, i.e. controlled, directly. However changes in the discrete dynamic can be detected immediately, such that the current dynamic (subsystem) is known. In order to motivate the study of hybrid systems and show the merits of hybrid control theory, an example is given. It is shown that real world systems like Anti Locking Brakes (ABS) are naturally modelled by such a class of linear hybrids systems. It is shown that purely continuous feedback is not suitable since it cannot achieve maximum braking performance. A hybrid control strategy, which overcomes this problem, is presented. For this class of linear hybrid system with unknown discrete dynamic, a framework for robust control is established. The analysis methodology developed gives a robustness radius such that the stability under parameter variations can be analysed. The controller synthesis procedure is illustrated in a practical example where the control for an active suspension of a car is designed. Optimal control for this class of hybrid system is introduced. It is shows how a control law is obtained which minimises a quadratic performance index. The synthesis procedure is stated in terms of a convex optimisation problem using linear matrix inequalities (LMI). The solution of the LMI not only returns the controller but also the performance bound. Since the proposed controller structures require knowledge of the continuous state, an observer design is proposed. It is shown that the estimation error converges quadratically while minimising the covariance of the estimation error. This is similar to the Kalman filter for discrete or continuous time systems. Further, we show that the synthesis of the observer can be cast into an LMI, which conveniently solves the synthesis problem.
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Hayden, Kevin. "Modeling of dynamical systems /." abstract and full text PDF (UNR users only), 2007. http://0-gateway.proquest.com.innopac.library.unr.edu/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:1446796.
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Thesis (M.S.)--University of Nevada, Reno, 2007."May, 2007." Includes bibliographical references (leaves 128-129). Library also has microfilm. Ann Arbor, Mich. : ProQuest Information and Learning Company, [2008]. 1 microfilm reel ; 35 mm. Online version available on the World Wide Web.
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Sun, Hongyan. "Coupled nonlinear dynamical systems." Morgantown, W. Va. : [West Virginia University Libraries], 2000. http://etd.wvu.edu/templates/showETD.cfm?recnum=1636.
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Thesis (Ph. D.)--West Virginia University, 2000.Title from document title page. Document formatted into pages; contains xi, 113 p. : ill. (some col.). Includes abstract. Includes bibliographical references.
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Ghan, S. J. (Steven John). "Unstable radiative-dynamical interactions." Thesis, Massachusetts Institute of Technology, 1988. http://hdl.handle.net/1721.1/52897.
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McKee, Andrew. "Multipliers of dynamical systems." Thesis, Queen's University Belfast, 2017. https://pure.qub.ac.uk/portal/en/theses/multipliers-of-dynamical-systems(65b93a06-6e7b-420b-ae75-c28d373f8bdf).html.
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Herz–Schur multipliers of a locally compact group have a well developed theory coming from a large literature; they have proved very useful in the study of the reduced C∗-algebra of a locally compact group. There is also a rich connection to Schur multipliers,which have been studied since the early twentieth century, and have a large number of applications. We develop a theory of Herz–Schur multipliers of a C∗-dynamical system, extending the classical Herz–Schur multipliers, making Herz–Schur multiplier techniques available to study a much larger class of C∗-algebras. Furthermore, we will also introduce and study generalised Schur multipliers, and derive links between these two notions which extend the classical results describing Herz–Schur multipliers in terms of Schur multipliers. This theory will be developed in as much generality as possible, with reference to the classical motivation. After introducing all the necessary concepts we begin the investigation by defining generalised Schur multipliers. The main result is a dilation type characterisation of these multipliers; we also show how such multipliers can be represented using HilbertC∗-modules. Next we introduce and study generalised Herz–Schur multipliers, first extending a classical result involving the representation theory of SU(2), before studying how such functions are related to our generalised Schur multipliers. We give a characterisation of generalised Herz–Schur multipliers as a certain class of the generalised Schur multipliers, and obtain a description of precisely which Schur multipliers belong to this class. Finally, we consider some ways in which the generalised multipliers can arise; firstly, from the classical multipliers which provide our motivation, secondly, from the Haagerup tensor product of a C∗-algebra with itself, and finally from positivity considerations. We show that our theory behaves well with respect to positivity and give conditions under which our multipliers are automatically positive in a natural sense.
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Ahmadi, Seyedfarzad. "Dynamical Phase-Change Phenomena." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/99420.
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Matter on earth exists mostly in three different phases of solid, liquid, and gas. With extreme amounts of energy, temperature, or pressure, a matter can be changed between the phases. Six different types of phase-change phenomena are possible: freezing (the substance changes from a liquid to a solid), melting (solid to liquid), condensation (gas to liquid), vaporization (liquid to gas), sublimation (solid to gas), and desublimation (gas to solid). Another form of phase change which will be discussed here is the wetting or dewetting transitions of a superhydrophobic surface, in which the phase residing within the surface structure switches between vapor and liquid. Phase transition phenomena frequently occur in our daily life; examples include: a ``liquid'' to ``solid'' transition when cars decrease their distance at a traffic light, solidification of liquids droplets during winter months, and the dancing of droplets on a non-sticking pan. In this dissertation we will address seven different phase-change problems occurring in nature. We unveil completely new forms of phase-change phenomena that exhibit rich physical behavior. For example, during traffic flow, drivers keep a large distance from the vehicle in front of them to ensure safe driving. When vehicles come to a stop, for example at a red light, drivers voluntarily induce a ``phase transition'' from this ``liquid phase'' to a close-packed ``solid phase''. This phase transition is motivated by the intuition that traveling as far as possible before stopping will minimize the overall travel time. However, we are going to investigate this phase-change process and show that this long standing intuition is wrong. Phase-change of solidification will be discussed for different problems. Moreover, the complex physics of oil as it wicks up sheets of frost and freezing of bubble unveil completely new forms of multiphase flows that exhibit rich physical behavior. Finally, the ``Cassie'' to ``Wenzel'' transition will be investigated for layered nano-textured surfaces. These phenomena will be modeled using thermodynamics and fluid mechanics equations.Doctor of Philosophy
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Krcelic, Khristine M. "Chaos and Dynamical Systems." Youngstown State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1364545282.
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Royals, Robert. "Arithmetic and dynamical systems." Thesis, University of East Anglia, 2015. https://ueaeprints.uea.ac.uk/57191/.
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In this thesis we look at a number of topics in the area of the interaction between dynamical systems and number theory. We look at two diophantine approximation problems in local �fields of positive characteristic, one a generalisation of the Khintchine{Groshev theorem, another a central limit theorem. We also prove a P�olya{Carlson dichotomy result for a large class of adelicly perturbed rational functions. In particular we prove that for a finite set of primes S that the power series f(z) generated by the Fibonacci series with all primes in S removed has a natural boundary.
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Hook, James Louis. "Topics in dynamical systems." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/topics-in-dynamical-systems(427b5d98-197d-4b53-876e-a81142f72375).html.
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In this thesis I explore three new topics in Dynamical Systems. In Chapters 2 and 3 I investigate the dynamics of a family of asynchronous linear systems. These systems are of interest as models for asynchronous processes in economics and computer science and as novel ways to solve linear equations. I find a tight sandwich of bounds relating the Lyapunov exponents of these asynchronous systems to the eigenvalue of their synchronous counterparts. Using ideas from the theory of IFSs I show how the random behavior of these systems can be quickly sampled and go some way to characterizing the associated probability measures. In Chapter 4 I consider another family of random linear dynamical system but this time over the Max-plus semi-ring. These models provide a linear way to model essentially non-linear queueing systems. I show how the topology of the queue network impacts on the dynamics, in particular I relate an eigenvalue of the adjacency matrix to the throughput of the queue. In Chapter 5 I consider non-smooth systems which can be used to model a wide variety of physical systems in engineering as well as systems in control and computer science. I introduce the Moving Average Transformation which allows us to systematically 'smooth' these systems enabling us to apply standard techniques that rely on some smoothness, for example computing Lyapunov exponents from time series data.
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Hua, Xinhou. "Dynamical systems and wavelets." Thesis, University of Ottawa (Canada), 2002. http://hdl.handle.net/10393/6143.
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The first part of this thesis is concerned with Bakers Conjecture (1984) which says that two permutable transcendental entire functions have the same Julia set. To this end, we shall exhibit that two permutable transcendental entire functions of a certain type have the same Julia set. So far, this is the best result to the conjecture. The second part relates to Newton's method to find zeros of functions. We shall look for the locations of the limits of the iterating sequence of the relaxed Newton function on its wandering domains. A relaxed Newton function with corresponding properties is constructed. The third part relates to the dynamics of ordinary differential equations and inverse problems. Given a target solution, we shall construct second-order differential equations with Legendre polynomial basis to approximate the target solution. An algorithm and numerical solutions are provided. Examples show that the approximations we have found are much better than the known results obtained by means of first-order differential equations. We shall also discuss approximation using a wavelet basis. MATLAB is used to compute the numerical results. In the fourth part, we deal with variational problems in signal and image processing. For a given signal or image represented by a function, we shall provide a good approximation to the function, which minimizes a given functional.
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Soklakov, Andrei Nikolaevich. "Measures of dynamical complexity." Thesis, Royal Holloway, University of London, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.271547.
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Kawashima, Hiroaki. "Interval-Based Hybrid Dynamical System for Modeling Dynamic Events and Structures." 京都大学 (Kyoto University), 2007. http://hdl.handle.net/2433/68896.
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Lazaryan, Shushan, Nika LAzaryan, and Nika Lazaryan. "Discrete Nonlinear Planar Systems and Applications to Biological Population Models." VCU Scholars Compass, 2015. http://scholarscompass.vcu.edu/etd/4025.
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We study planar systems of difference equations and applications to biological models of species populations. Central to the analysis of this study is the idea of folding - the method of transforming systems of difference equations into higher order scalar difference equations. Two classes of second order equations are studied: quadratic fractional and exponential.
We investigate the boundedness and persistence of solutions, the global stability of the positive fixed point and the occurrence of periodic solutions of the quadratic rational equations. These results are applied to a class of linear/rational systems that can be transformed into a quadratic fractional equation via folding. These results apply to systems with negative parameters, instances not commonly considered in previous studies. We also identify ranges of parameter values that provide sufficient conditions on existence of chaotic and multiple stable orbits of different periods for the planar system.
We study a second order exponential difference equation with time varying parameters and obtain sufficient conditions for boundedness of solutions and global convergence to zero. For the autonomous case, we show occurrence of multistable periodic and nonperiodic orbits. For the case where parameters are periodic, we show that the nature of the solutions differs qualitatively depending on whether the period of the parameters is even or odd.
The above results are applied to biological models of populations. We investigate a broad class of planar systems that arise in the study of stage-structured single species populations. In biological contexts, these results include conditions on extinction or survival of the species in some balanced form, and possible occurrence of complex and chaotic behavior. Special rational (Beverton-Holt) and exponential (Ricker) cases are considered to explore the role of inter-stage competition, restocking strategies, as well as seasonal fluctuations in the vital rates.
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Izquierdo, Eduardo J. "The dynamics of learning behaviour : a situated, embodied, and dynamical systems approach." Thesis, University of Sussex, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.488595.
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Engel, Maximilian. "Local phenomena in random dynamical systems : bifurcations, synchronisation, and quasi-stationary dynamics." Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/57613.
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We consider several related topics in the bifurcation theory of random dynamical systems: synchronisation by noise, noise-induced chaos, qualitative changes of finite-time behaviour and stability of systems surviving in a bounded domain. Firstly, we study the dynamics of a two-dimensional ordinary differential equation exhibiting a Hopf bifurcation subject to additive white noise. Depending on the deterministic Hopf bifurcation parameter and a phase-amplitude coupling parameter called shear, three dynamical phases can be identified: a random attractor with uniform synchronisation of trajectories, a random attractor with non-uniform synchronisation of trajectories and a random attractor without synchronisation of trajectories. We prove the existence of the first two phases which both exhibit a random equilibrium with negative top Lyapunov exponent but differ in terms of finite-time and uniform stability properties. We provide numerical results in support of the existence of the third phase which is characterised by a so-called random strange attractor with positive top Lyapunov exponent implying chaotic behaviour. Secondly, we reduce the model of the Hopf bifurcation to its linear components and study the dynamics of a stochastically driven limit cycle on the cylinder. In this case, we can prove the existence of a bifurcation from an attractive random equilibrium to a random strange attractor, indicated by a change of sign of the top Lyapunov exponent. By establishing the existence of a random strange attractor for a model with white noise, we extend results by Qiudong Wang and Lai-Sang Young on periodically kicked limit cycles to the stochastic context. Furthermore, we discuss a characterisation of the invariant measures associated with the random strange attractor and deduce positive measure-theoretic entropy for the random system. Finally, we study the bifurcation behaviour of unbounded noise systems in bounded domains, exhibiting the local character of random bifurcations which are usually hidden in the global analysis. The systems are analysed by being conditioned to trajectories which do not hit the boundary of the domain for asymptotically long times. The notion of a stationary distribution is replaced by the concept of a quasi-stationary distribution and the average limiting behaviour can be described by a so-called quasi-ergodic distribution. Based on the well-explored stochastic analysis of such distributions, we develop a dynamical stability theory for stochastic differential equations within this context. Most notably, we define conditioned average Lyapunov exponents and demonstrate that they measure the typical stability behaviour of surviving trajectories. We analyse typical examples of random bifurcation theory within this environment, in particular the Hopf bifurcation with additive noise, with reference to whom we also study (numerically) a spectrum of conditioned Lyapunov exponents. Furthermore, we discuss relations to dynamical systems with holes.
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Boily, Patrick. "Spiral wave dynamics under full Euclidean symmetry-breaking: A dynamical system approach." Thesis, University of Ottawa (Canada), 2006. http://hdl.handle.net/10393/29341.
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Spirals are common in Nature: the snail's shell and the ordering of seeds in the sunflower are amongst the most widely-known occurrences. While these are static, dynamic spirals can also be observed in excitable systems such as heart tissue, retina, certain chemical reactions, slime mold aggregates, flame fronts, etc. The images associated with these spirals are often breathtaking, but spirals have also been linked to cardiac arrhythmias, a potentially fatal heart ailment.
In the literature, very specific models depending on the excitable system of interest are used to explain the observed behaviour of spirals (such as anchoring or drifting). Barkley [5] first noticed that the Euclidean symmetry of these models, and not the model itself, is responsible for the observed behaviour. But in experiments, the physical domain is never Euclidean. The heart, for instance, is finite, anisotropic and littered with inhomogeneities. To capture this loss of symmetry, LeBlanc and Wulff [48,51] introduced forced Euclidean symmetry-breaking (FESB) in the analysis.
To accurately model the physical situation, two basic types of symmetry-breaking perturbations are used: translational symmetry-breaking (TSB) and rotational symmetry-breaking (RSB) terms. LeBlanc and Wulff, [51] and LeBlanc [48] have studied the effects of these individual perturbations, and they have shown that phenomena such as anchoring and quasi-periodic meandering can be explained by FESB. However, these specific perturbations only tell part of the story.
In this thesis, the effects of multiple TSB perturbations, as well as those of combined TSB-RSB perturbations are studied and provide a more complete explanation for two aspects of spiral dynamics: anchoring and boundary drifting. Higher co-dimension phenomena are also considered.
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Capdevilla, Roldan Rodolfo Maia [UNESP]. "Dynamical chiral symmetry breaking: the fermionic gap equation with dynamical gluon mass and confinement." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/92026.
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capdevillaroldan_rm_me_ift.pdf: 1695600 bytes, checksum: 56f8cc2724bbe924e0b430ebe1a3b24e (MD5)Alguns aspectos da quebra de simetria quiral para quarks na representação fundamental são discutidos no contexto das equações de Schwinger-Dyson. Estudamos a equação de gap fermionica incluindo o efeito de uma massa dinêmica para os gluons. Ao estudar esta equação de gap verificamos que a intenção não é forte o suficiente para gerar uma massa dinâmica dos quarks compatível com os dados experimentais. Também discutimos como a introdução de um propagador confinante pode mudar este cenário, exatamente como foi proposto por Cornwall [1] recentemente, desta forma estudamos uma equação de gap completa, composta pela troca de um gluon massivo e por um termo confinante; M('p POT 2') = 'M IND. c('p POT 2') + 'M IND. 1g'('p POT 2'). Encontramos soluções assintótica desta equação de gap nos casos de constante de acoplamento constante e corredora. Este último caso corresponde a um aprimoramento do cálculo com constante de acoplamento constante feito por Doff, Machado e Natale [2]
Some aspects of chiral symmetry breaking for quarks in the fundamental representation are discussed in the framework of the Schwinger-Dyson equations. We study the fermionic gap equation including effects of dynamical gluon mass. Studying the bifurcation equation of this gap equation we verify that the interaction is not strong enough to generate a satisfactory dynamical quark mass. We also discuss how the introduction of a confining propagator may change this scenario as recently pointed out by Cornwall [1], so we study a complete gap equation composed by the one-dressed-gluon exchange term and a confining term: M('p POT 2') = 'M IND. c('p POT 2') + 'M IND. 1g'('p POT 2'). We find asymptotic solutions for this gap equation in the cases of constant coupling and running coupling constant. This last case is an improvement of the constant coupling calculation of Doff, Machado and Natale [2]
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Capdevilla, Roldan Rodolfo Maia. "Dynamical chiral symmetry breaking : the fermionic gap equation with dynamical gluon mass and confinement /." São Paulo, 2013. http://hdl.handle.net/11449/92026.
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Orientador: Adriano Antonio NataleBanca: Adriano Doff Sotta Gomes
Banca: Alex Gomes Dias
Resumo: Alguns aspectos da quebra de simetria quiral para quarks na representação fundamental são discutidos no contexto das equações de Schwinger-Dyson. Estudamos a equação de gap fermionica incluindo o efeito de uma massa dinêmica para os gluons. Ao estudar esta equação de gap verificamos que a intenção não é forte o suficiente para gerar uma massa dinâmica dos quarks compatível com os dados experimentais. Também discutimos como a introdução de um propagador confinante pode mudar este cenário, exatamente como foi proposto por Cornwall [1] recentemente, desta forma estudamos uma equação de gap "completa", composta pela troca de um gluon massivo e por um termo confinante; M('p POT 2') = 'M IND. c('p POT 2') + 'M IND. 1g'('p POT 2'). Encontramos soluções assintótica desta equação de gap nos casos de constante de acoplamento "constante" e "corredora". Este último caso corresponde a um aprimoramento do cálculo com constante de acoplamento "constante" feito por Doff, Machado e Natale [2]
Abstract: Some aspects of chiral symmetry breaking for quarks in the fundamental representation are discussed in the framework of the Schwinger-Dyson equations. We study the fermionic gap equation including effects of dynamical gluon mass. Studying the bifurcation equation of this gap equation we verify that the interaction is not strong enough to generate a satisfactory dynamical quark mass. We also discuss how the introduction of a confining propagator may change this scenario as recently pointed out by Cornwall [1], so we study a "complete" gap equation composed by the one-dressed-gluon exchange term and a confining term: M('p POT 2') = 'M IND. c('p POT 2') + 'M IND. 1g'('p POT 2'). We find asymptotic solutions for this gap equation in the cases of "constant coupling" and "running coupling constant". This last case is an improvement of the constant coupling calculation of Doff, Machado and Natale [2]
Mestre
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Löbner, Clemens. "Integrable Approximations for Dynamical Tunneling." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-178216.
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Generic Hamiltonian systems have a mixed phase space, where classically disjoint regions of regular and chaotic motion coexist. For many applications it is useful to approximate the regular dynamics of such a mixed system H by an integrable approximation Hreg. We present a new, iterative method to construct such integrable approximations. The method is based on the construction of an integrable approximation in action representation which is then improved in phase space by iterative applications of canonical transformations. In contrast to other known approaches, our method remains applicable to strongly non-integrable systems H. We present its application to 2D maps and 2D billiards. Based on the obtained integrable approximations we finally discuss the theoretical description of dynamical tunneling in mixed systemsTypische Hamiltonsche Systeme haben einen gemischten Phasenraum, in dem disjunkte Bereiche klassisch regulärer und chaotischer Dynamik koexistieren. Für viele Anwendungen ist es zweckmäßig, die reguläre Dynamik eines solchen gemischten Systems H durch eine integrable Näherung Hreg zu beschreiben. Wir stellen eine neue, iterative Methode vor, um solche integrablen Näherungen zu konstruieren. Diese Methode basiert auf der Konstruktion einer integrablen Näherung in Winkel-Wirkungs-Variablen, die im Phasenraum durch iterative Anwendungen kanonischer Transformationen verbessert wird. Im Gegensatz zu bisher bekannten Verfahren bleibt unsere Methode auch auf stark nichtintegrable Systeme H anwendbar. Wir demonstrieren sie anhand von 2D-Abbildungen und 2D-Billards. Mit den gewonnenen integrablen Näherungen diskutieren wir schließlich die theoretische Beschreibung von dynamischem Tunneln in gemischten Systemen
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Zhao, Zhenyuan. "Dynamical Grouping in Complex Systems." Scholarly Repository, 2010. http://scholarlyrepository.miami.edu/oa_dissertations/498.
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Quantifying the behavior of complex systems arguably presents the common ¡°hard¡±problem across the physical, biological, social, economic sciences. Individual-based or agent-based models have proved useful in a variety of different real world systems: from the physical, biological, medical domains through to social and even financial domains. There are many different models in each of these fields, each with their own particular assumptions, strengths and weaknesses for particular application areas. However, there is a lack of minimal model analysis in which both numerical and analytic results can be obtained, and hence allowing different application domains to be analyzed on a common footing. This thesis focuses on a few simple, yet highly non-trivial, minimal models of a population of interacting objects (so-called agents) featuring internal dynamical grouping. In addition to analyzing these models, I apply them to a number of distinct real world systems. Both the numerical and analytical results suggest that these simple models could be key factors in explaining the overall collective behavior and emergent properties in a wide range of real world complex systems. In particular, I study variants of a particular model (called the EZ model) in order to explain the attrition time in modern conflicts, and the evolution of contagion phenomena in such a dynamically evolving population. I also study and explain the empirical data obtained for online guilds and offline gangs, leading to a team-based model which captures the common quantitative features of the data. I then move on to develop a resource competition model (i.e. the so-called El Farol model) and apply it to the carbon emissions market, mapping the different market factors into model parameters which enable me to explore the potential market behaviors under a variety of scenarios.
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Badar, Muhammad. "Dynamical Systems Over Finite Groups." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-17948.
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In this thesis, the dynamical system is used as a function on afinite group, to show how states change. We investigate the'numberof cycles' and 'length of cycle' under finite groups. Using grouptheory, fixed point, periodic points and some examples, formulas tofind 'number of cycles' and 'length of cycle' are derived. Theexamples used are on finite cyclic group Z_6 with respectto binary operation '+'. Generalization using finite groups ismade. At the end, I compared the dynamical system over finite cyclic groups with the finite non-cyclic groups and then prove the general formulas to find 'number of cycles' and 'length of cycle' for both cyclic and non-cyclic groups.
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Heidemann, Ralf. "Dynamical phenomena in complex plasmas." Diss., lmu, 2013. http://nbn-resolving.de/urn:nbn:de:bvb:19-152519.
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