Physica D: Nonlinear Phenomena 

About: Physica D: Nonlinear Phenomena is an academic journal. The journal publishes majorly in the area(s): Nonlinear system & Attractor. It has an ISSN identifier of 0378-4371. Over the lifetime, 14058 publication(s) have been published receiving 500833 citation(s).

Nonlinear total variation based noise removal algorithms

Abstract: A constrained optimization type of numerical algorithm for removing noise from images is presented. The total variation of the image is minimized subject to constraints involving the statistics of the noise. The constraints are imposed using Lagrange multipliers. The solution is obtained using the gradient-projection method. This amounts to solving a time dependent partial differential equation on a manifold determined by the constraints. As t---~ 0o the solution converges to a steady state which is the denoised image. The numerical algorithm is simple and relatively fast. The results appear to be state-of-the-art for very noisy images. The method is noninvasive, yielding sharp edges in the image. The technique could be interpreted as a first step of moving each level set of the image normal to itself with velocity equal to the curvature of the level set divided by the magnitude of the gradient of the image, and a second step which projects the image back onto the constraint set.

Determining Lyapunov exponents from a time series

Abstract: We present the first algorithms that allow the estimation of non-negative Lyapunov exponents from an experimental time series. Lyapunov exponents, which provide a qualitative and quantitative characterization of dynamical behavior, are related to the exponentially fast divergence or convergence of nearby orbits in phase space. A system with one or more positive Lyapunov exponents is defined to be chaotic. Our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems: we monitor the long-term growth rate of small volume elements in an attractor. The method is tested on model systems with known Lyapunov spectra, and applied to data for the Belousov-Zhabotinskii reaction and Couette-Taylor flow.

Brownian motion in a field of force and the diffusion model of chemical reactions

Abstract: A particle which is caught in a potential hole and which, through the shuttling action of Brownian motion, can escape over a potential barrier yields a suitable model for elucidating the applicability of the transition state method for calculating the rate of chemical reactions.

Über die Zuordnung von Wellenfunktionen und Eigenwerten zu den Einzelnen Elektronen Eines Atoms

Abstract: Zusammenfassung Die von Fock im Rahmen seiner Naherungsmethode zur Behandlung des quantenmechanischen Mehrelektronenproblems aufgestellten Gleichungen werden auf etwas allgemeinerer Grundlage diskutiert. Es wird angegeben, wie man in eindeutiger Weise den einzelnen Elektronen bestimmte Wellenfunktionen und Eigenwerte zuordnen kann. Diese Eigenfunktionen genugen einer Gleichung, die in einem etwas anderen Zusammenhang von Fock abgeleitet wurde. Die Eigenwerte sind bis auf kleinen Korrektionen den Ablosungsarbeiten der einzelnen Elektronen entgegengesetzt gleich. Das erreichte Ergebnis hat nur Bedeutung in denjenigen Fallen, wo der Ansatz einer einzigen Slaterschen Determinante fur die Wellenfunktion sinnvoll ist.

Measuring the Strangeness of Strange Attractors

Abstract: We study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise. The exponent v is closely related to the fractal dimension and the information dimension, but its computation is considerably easier. Its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed. Algorithms for extracting v from the time series of a single variable are proposed. The relations between the various measures of strange attractors and between them and the Lyapunov exponents are discussed. It is shown that the conjecture of Kaplan and Yorke for the dimension gives an upper bound for v. Various examples of finite and infinite dimensional systems are treated, both numerically and analytically.