Magnetic Reversal in Nanoscopic Ferromagnetic Rings

We present a theory of magnetization reversal due to thermal fluctuations in thin submicron-scale rings composed of soft magnetic materials. The magnetization in such geometries is more stable against reversal than that in thin needles and other geometries, where sharp ends or edges can initiate nucleation of a reversed state. The 2D ring geometry also allows us to evaluate the effects of nonlocal magnetostatic forces. We find a `phase transition', which should be experimentally observable, between an Arrhenius and a non-Arrhenius activation regime as magnetic field is varied in a ring of fixed size.Comment: RevTeX, 23 pages, 7 figures, to appear in Phys. Rev.

Noisy Classical Field Theories with Two Coupled Fields: Dependence of Escape Rates on Relative Field Stiffnesses

Exit times for stochastic Ginzburg-Landau classical field theories with two or more coupled classical fields depend on the interval length on which the fields are defined, the potential in which the fields deterministically evolve, and the relative stiffness of the fields themselves. The latter is of particular importance in that physical applications will generally require different relative stiffnesses, but the effect of varying field stiffnesses has not heretofore been studied. In this paper, we explore the complete phase diagram of escape times as they depend on the various problem parameters. In addition to finding a transition in escape rates as the relative stiffness varies, we also observe a critical slowing down of the string method algorithm as criticality is approached.Comment: 16 pages, 10 figure

An \u3cem\u3ein vitro\u3c/em\u3e Study on the Influence of Residual Sugars on Aerobic Changes in Grass Silages

How do residual sugars in high dry matter grass silages influence microbial metabolism? To answer this question a simple laboratory method was developed using pH as main indicator for aerobic changes

No elliptic islands for the universal area-preserving map

A renormalization approach has been used in \cite{EKW1} and \cite{EKW2} to prove the existence of a \textit{universal area-preserving map}, a map with hyperbolic orbits of all binary periods. The existence of a horseshoe, with positive Hausdorff dimension, in its domain was demonstrated in \cite{GJ1}. In this paper the coexistence problem is studied, and a computer-aided proof is given that no elliptic islands with period less than 20 exist in the domain. It is also shown that less than 1.5% of the measure of the domain consists of elliptic islands. This is proven by showing that the measure of initial conditions that escape to infinity is at least 98.5% of the measure of the domain, and we conjecture that the escaping set has full measure. This is highly unexpected, since generically it is believed that for conservative systems hyperbolicity and ellipticity coexist

On the Hyperbolicity of Lorenz Renormalization

We consider infinitely renormalizable Lorenz maps with real critical exponent $\alpha>1$ and combinatorial type which is monotone and satisfies a long return condition. For these combinatorial types we prove the existence of periodic points of the renormalization operator, and that each map in the limit set of renormalization has an associated unstable manifold. An unstable manifold defines a family of Lorenz maps and we prove that each infinitely renormalizable combinatorial type (satisfying the above conditions) has a unique representative within such a family. We also prove that each infinitely renormalizable map has no wandering intervals and that the closure of the forward orbits of its critical values is a Cantor attractor of measure zero.Comment: 63 pages; 10 figure

The Order of Phase Transitions in Barrier Crossing

A spatially extended classical system with metastable states subject to weak spatiotemporal noise can exhibit a transition in its activation behavior when one or more external parameters are varied. Depending on the potential, the transition can be first or second-order, but there exists no systematic theory of the relation between the order of the transition and the shape of the potential barrier. In this paper, we address that question in detail for a general class of systems whose order parameter is describable by a classical field that can vary both in space and time, and whose zero-noise dynamics are governed by a smooth polynomial potential. We show that a quartic potential barrier can only have second-order transitions, confirming an earlier conjecture [1]. We then derive, through a combination of analytical and numerical arguments, both necessary conditions and sufficient conditions to have a first-order vs. a second-order transition in noise-induced activation behavior, for a large class of systems with smooth polynomial potentials of arbitrary order. We find in particular that the order of the transition is especially sensitive to the potential behavior near the top of the barrier.Comment: 8 pages, 6 figures with extended introduction and discussion; version accepted for publication by Phys. Rev.

Distracting the Mind Improves Performance: An ERP Study

When a second target (T2) is presented in close succession of a first target (T1), people often fail to identify T2, a phenomenon known as the attentional blink (AB). However, the AB can be reduced substantially when participants are distracted during the task, for instance by a concurrent task, without a cost for T1 performance. The goal of the current study was to investigate the electrophysiological correlates of this paradoxical effect.Participants successively performed three tasks, while EEG was recorded. The first task (standard AB) consisted of identifying two target letters in a sequential stream of distractor digits. The second task (grey dots task) was similar to the first task with the addition of an irrelevant grey dot moving in the periphery, concurrent with the central stimulus stream. The third task (red dot task) was similar to the second task, except that detection of an occasional brief color change in the moving grey dot was required. AB magnitude in the latter task was significantly smaller, whereas behavioral performance in the standard and grey dots tasks did not differ. Using mixed effects models, electrophysiological activity was compared during trials in the grey dots and red dot tasks that differed in task instruction but not in perceptual input. In the red dot task, both target-related parietal brain activity associated with working memory updating (P3) as well as distractor-related occipital activity was significantly reduced.The results support the idea that the AB might (at least partly) arise from an overinvestment of attentional resources or an overexertion of attentional control, which is reduced when a distracting secondary task is carried out. The present findings bring us a step closer in understanding why and how an AB occurs, and how these temporal restrictions in selective attention can be overcome

Statistical properties of energy levels of chaotic systems: Wigner or non-Wigner

For systems whose classical dynamics is chaotic, it is generally believed that the local statistical properties of the quantum energy levels are well described by Random Matrix Theory. We present here two counterexamples - the hydrogen atom in a magnetic field and the quartic oscillator - which display nearest neighbor statistics strongly different from the usual Wigner distribution. We interpret the results with a simple model using a set of regular states coupled to a set of chaotic states modeled by a random matrix.Comment: 10 pages, Revtex 3.0 + 4 .ps figures tar-compressed using uufiles package, use csh to unpack (on Unix machine), to be published in Phys. Rev. Let

Maximal Accuracy and Minimal Disturbance in the Arthurs-Kelly Simultaneous Measurement Process

The accuracy of the Arthurs-Kelly model of a simultaneous measurement of position and momentum is analysed using concepts developed by Braginsky and Khalili in the context of measurements of a single quantum observable. A distinction is made between the errors of retrodiction and prediction. It is shown that the distribution of measured values coincides with the initial state Husimi function when the retrodictive accuracy is maximised, and that it is related to the final state anti-Husimi function (the P representation of quantum optics) when the predictive accuracy is maximised. The disturbance of the system by the measurement is also discussed. A class of minimally disturbing measurements is characterised. It is shown that the distribution of measured values then coincides with one of the smoothed Wigner functions described by Cartwright.Comment: 12 pages, 0 figures. AMS-Latex. Earlier version replaced with final published versio