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Showing 1 to 20 of 258 for “"exponents"”.
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Lyapunov Exponents, Entropy and Dimension
We consider diffeomorphisms of a compact Riemann Surface. A development of Oseledec's Multiplicative Ergodic Theorem is given, along with a development of measure theoretic entropy and dimension. The main result, due to L.S. Young, is that for certain diffeomorphisms of a surface, there is a …
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Local complex singularity exponents for isolated singularities
… the stability of local complex'singularity exponents (lcse) for holomorphic functions whose zero sets have only isolated singularities. For a given holomorphic function f defined on a neighborhood of the origin in C[to the power of]n, the lcse c[sub]0(f) is defined as the supremum of all …
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Quantifying Dynamic Stability of Musculoskeletal Systems using Lyapunov Exponents
Increased attention has been paid in recent years to the means in which the body maintains stability and the subtleties of the neurocontroller. Variability of kinematic data has been used as a measure of stability but these analyses are not appropriate for quantifying stability of dynamic systems. …
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Computation of Lyapunov Exponents and Control of a Hyperchaotic System
<p>This paper presents algorithms developed in MATLAB to simulate the hyperchaotic Chen system and also estimates the largest Lyapunov characteristic exponent (LCE) and provides a method to compute the entire Lyapunov spectrum of the dynamical system. The computation of the Lyapunov spectrum relies …
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Error exponents for multipath fading channels : a strong coding theorem
… lower bounds on the probability of error (the exponents of which are the error exponents) with "peaky" signaling -- the signaling strategy that achieves the capacity of the multipath fading channel under an average power constraint in the limit of infinite bandwidth. These bounds constitute a …
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Statistical properties and scaling of the Lyapunov exponents in stochastic systems
Die vorliegende Arbeit umfaßt drei Abhandlungen, welche allgemein mit einer stochastischen Theorie für die Lyapunov-Exponenten befaßt sind. Mit Hilfe dieser Theorie werden universelle Skalengesetze untersucht, die in gekoppelten chaotischen und ungeordneten Systemen auftreten. Zunächst werden zwei …
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Biodynamic Analysis of Human Torso Stability using Finite Time Lyapunov Exponents
Low back pain is a common medical problem around the world afflicting 80% of the population some time in their life. Low back injury can result from a loss of torso stability causing excessive strain in soft tissue. This investigation seeks to apply existing methods to new applications and to …
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Application of Lyapunov Exponents to Strange Attractors and Intact & Damaged Ship Stability
… This research presents the use of Lyapunov exponents, a quantity that measures the rate of trajectory separation in phase space, to predict capsize events for both intact and damaged stability cases. The algorithm searches backwards in ship motion time histories to gather neighboring points …
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Lyapunov Exponents and Invariant Manifold for Random Dynamical Systems in a Banach Space
<p>We study the Lyapunov exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space, which are generated by, for example, stochastic or random partial differential equations. We prove a multiplicative ergodic theorem. Then, we use this …
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John McLeod Campbell and Thomas Erskine: Scottish Exponents of Righteousness, Faith, and the Atonement
<p>This thesis focuses upon the reaffirmation and clarification by two independent 19th-century theologians of certain New Testament and Reformation emphases which had become largely obscured amid the rigidities of later Calvinism. These emphases, when employed by Campbell and Erskine in their …
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Topics in Lattice Statistics: I. Systematics of Multilayer Adsorption Phenomena on Attractive Substrates. Ii. Dynamical Critical Exponents for the Kinetic Ising Model: A Finite-Size Hamiltonian Calculation
This thesis consists of two parts. The first and major part is contained in Chapter I and deals with multilayer adsorption and wetting phenomena on attractive substrates. The second part, contained in Chapter II, is devoted to the study of kinetic Ising models, using finite-size Hamiltonian methods.
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Topics in Lattice Statistics: I. Systematics of Multilayer Adsorption Phenomena on Attractive Substrates II. Dynamical Critical Exponents for the Kinetic Ising Model: A Finite-Size Hamiltonian Calculation
Submitted by Carolyn Rauber (crauber2@illinois.edu) on 2011-06-02T17:26:09Z No. of bitstreams: 1 1982_pandit.pdf: 5769733 bytes, checksum: 3cf1cd189904f2a0b5ccbc3238ccdebc (MD5)
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Eine hybride Methode zur Berechnung von Liapunow-Exponenten
… method for computing some or all Lyapunov exponents of a discrete dynamical system. It is called hybrid because it combines the classical QR method with more recent methods that use spatial integration with respect to an invariant ergodic measure. We also investigate error expansions for …
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Nonequilibrium Relaxation and Aging Scaling Properties of the Coulomb Glass and Bose Glass
… by a full-aging scaling analysis. The scaling exponents depend on both temperature and filling fraction, and are thus non-universal. We look at the trends of these exponents and found that as either the temperature decreases or the filling fraction deviates more from half-filling, the exponents …
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Thermal stability criteria embedded in avanced control systems for batch process intensification
… based on the divergence criterion. Lyapunov exponents are an alternative method to predict thermal runaway behaviour. Embedding thermal stability criteria within Model Predictive Control (MPC) frameworks results in advanced control systems capable of intensifying batch processes safely, hence …
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Characterisation of local properties and prediction in chaotic dynamical systems
… This is done using two kinds of local exponents as well as ensemble studies. In conservative systems with trapping, the distribution of finite-time Lyapunov exponents (FTLE) has multiple maxima. These can be attributed to pieces of the trajectory that stay in the vicinity of islands of …
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Linear and bilinear restriction estimates for the Fourier transform
… a bilinear estimate for the light cone when the exponents are on a critical line. This extends results proven by Wolff, Tao and Lee-Vargas. The second result is a linear restriction estimate for surfaces with positive Gaussian curvature that improves over estimates proven by Bourgain and Guth, …
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Percolation behavior of diffusionally evolved two-phase systems simulated using phase field methods
… the percolation threshold and critical scaling exponents of randomly assembled composites. However many materials are non-random as a result of correlations that are introduced during processing. This work seeks to address this case by studying the percolation behavior of diffusionally evolved …
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Determination of Three Dimensional Time Varying Flow Structures
… these flow structures is finite time Lyapunov exponents (FTLEs). These exponents can reveal regions in the fluid, referred to as Lagragnian coherent structures (LCSs), where fluid elements diverge or attract. Better knowledge of how these time varying structures behave can greatly impact a wide …
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