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Showing 1 to 17 of 17 for “"Hyperbolicity"”.
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Tautness and Kobayashi hyperbolicity
The main objects studied in this work are hyperbolicity, tautness, and completeness for domains in C n. In the first chapter we introduce necessary notions and facts. In particular, in §1.1 we give some properties related to the Minkowski functions. In §1.3 and §1.4 we recall Royden's criterion for …
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Mega-bimodules of topological polynomials: sub-hyperbolicity and Thurston obstructions
… to topological polynomials. We prove sub- hyperbolicity in the simplest non-trivial case and apply these mega-bimodules to holomorphic dynamics to prove a partial converse to the Berstein-Levy Theorem proved in 1985.
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Analysis of interfacial forces on the physics of two-phase flow and hyperbolicity of the two-fluid model
… ill-posedness, showing how it is related to non-hyperbolicity and giving a measurement that I call the numerical hyperbolicity. As a cure to this important issue, we will propose a combination of physical and mathematical solutions. The physical forces that we will focus on are two interfacial …
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Gromov boundaries of complexes associated to surfaces
… proved a stronger result which was the uniform hyperbolicity of the curve graph, and they also gave the first proof of the uniform hyperbolicity of the arc graph using unicorn arcs. For closed surfaces, their proof is indirect, but Przytycki and Sisto gave a more direct proof of hyperbolicity in …
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One-dimensional modelling of rock-ice avalanches: mathematical features, numerical solutions, and strategies to enlarge the hyperbolic range
… Results show that the proposed approach loses hyperbolicity for specific ranges of the flow variables. Due to this feature, numerical modelling is performed by maintaining the numerical solutions in the hyperbolic domain of the flow variables. In this way, we consider the uniformly accelerated …
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Shadowing and numerical analysis of set-valued dynamical systems
… dynamical systems. In particular, a notion of hyperbolicity is proposed and the corresponding shadowing and inverse shadowing theorems are proved. Explicit error estimates for the Viability Kernel Algorithm are given for systems which possess the shadowing property.
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Hyperbolic Property of Earthquake Networks
… property of metric spaces. Gromov delta-hyperbolicity quantifies the curvature of a metric space via four point condition, which is a computationally convenient analog of the famous slim triangle property. We estimate the delta-hyperbolicity for observed events from several different …
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Discontinuous Galerkin solutions of the Boltzmann equation: spectral collocation and moment methods
… of different moment closures that preserve hyperbolicity and model accuracy. The approaches studied in this thesis, the globally hyperbolic moment methods, restore hyperbolicity by introducing a term that cannot be written in conservative form. The equations are typically solved with …
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Spatiotemporal Chaos in Large Systems Driven Far-From-Equilibrium: Connecting Theory with Experiment
… of perturbation growth and decay. The degree of hyperbolicity can also be quantified by the covariant Lyapunov vectors. To know whether a dynamical system is hyperbolic is important for the development of a theoretical understanding. In this thesis, the degree of hyperbolicity is calculated for …
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An Approximation for the Twenty-One-Moment Maximum-Entropy Model of Rarefied Gas Dynamics
… model also has realizable states for which hyperbolicity is lost. Unfortunately, the velocity distribution function associated with the twenty-one moment model is an exponential of a fourth-order polynomial. Such a function cannot be integrated in closed form, resulting in closing fluxes …
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Holomorphic flexibility properties of complements and mapping spaces.
… Oka property can be thought of as a sort of anti-hyperbolicity; the notion of Kobayashi hyperbolicity expresses a type of holomorphic rigidity, and conversely, Oka manifolds are those that enjoy a high degree of holomorphic flexibility. Other flexibility properties enjoyed by Oka manifolds include …
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Investigating Hamiltonian dynamics by the method of covariant Lyapunov vectors
… motion, an observation which is related to the hyperbolicity of the system. Additionally, we investigate the dynamics of bubbles (i.e. thermal openings between base pairs) in homogeneous DNA sequences using the Peyrard-Bishop-Dauxois lattice model of DNA. For the purpose of studying short-lived …
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Causality and the initial value problem in Modified Gravity
… when the background fields are large, even weak hyperbolicity may fail. Hence, we consider the weak field regime, in which these equations can be considered as small perturbations of the Einstein equations. We prove that both Lovelock and Horndeski theories are weakly hyperbolic in a generic weak …
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Detecting topological properties of boundaries of hyperbolic groups
… a negative curvature property, such as Gromov hyperbolicity. Such groups are surprisingly common: there is a sense in which a random group admits such an action, as do some groups of classical interest, such as fundamental groups of closed Riemannian manifolds with negative sectional curvature. …
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Tensorial spacetime geometries carrying predictive, interpretable and quantizable matter dynamics
… it is again the three geometric conditions of hyperbolicity, time-orientability and energy-distinguishability that allow the quantization of general linear electrodynamics on an area metric spacetime and the quantization of massive point particles obeying any admissible dispersion relation. We …
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Linear and non-linear collisionless many-particle systems
… black hole region. The proof exploits the normal hyperbolicity of the null geodesic flow in a neighborhood of the trapped set to show quantitative decay estimates for the stress energy momentum tensor of matter. In particular, we prove exponential decay for the stress energy momentum tensor in a …