A Computational Procedure to Detect a New Type of High Dimensional Chaotic Saddle and its Application to the 3-D Hill's Problem

A computational procedure that allows the detection of a new type of high-dimensional chaotic saddle in Hamiltonian systems with three degrees of freedom is presented. The chaotic saddle is associated with a so-called normally hyperbolic invariant manifold (NHIM). The procedure allows to compute appropriate homoclinic orbits to the NHIM from which we can infer the existence a chaotic saddle. NHIMs control the phase space transport across an equilibrium point of saddle-centre-...-centre stability type, which is a fundamental mechanism for chemical reactions, capture and escape, scattering, and, more generally, ``transformation'' in many different areas of physics. Consequently, the presented methods and results are of broad interest. The procedure is illustrated for the spatial Hill's problem which is a well known model in celestial mechanics and which gained much interest e.g. in the study of the formation of binaries in the Kuiper belt.Comment: 12 pages, 6 figures, pdflatex, submitted to JPhys

Pulse-coupled resonate-and-fire models

We analyze two pulse-coupled resonate-and-fire neurons. Numerical simulation reveals that an anti-phase state is an attractor of this model. We can analytically explain the stability of anti-phase states by means of a return map of firing times, which we propose in this paper. The resultant stability condition turns out to be quite simple. The phase diagram based on our theory shows that there are two types of anti-phase states. One of these cannot be seen in coupled integrate-and-fire models and is peculiar to resonate-and-fire models. The results of our theory coincide with those of numerical simulations.Comment: 15 pages, 8 figure

Direct transition to high-dimensional chaos through a global bifurcation

In the present work we report on a genuine route by which a high-dimensional (with d>4) chaotic attractor is created directly, i.e., without a low-dimensional chaotic attractor as an intermediate step. The high-dimensional chaotic set is created in a heteroclinic global bifurcation that yields an infinite number of unstable tori.The mechanism is illustrated using a system constructed by coupling three Lorenz oscillators. So, the route presented here can be considered a prototype for high-dimensional chaotic behavior just as the Lorenz model is for low-dimensional chaos.Comment: 7 page

Preoperative brain imaging using functional near-infrared spectroscopy helps predict cochlear implant outcome in deaf adults

Currently it is not possible to accurately predict how well a deaf individual will be able to understand speech when hearing is (re)introduced via a cochlear implant. Differences in brain organisation following deafness are thought to contribute to variability in speech understanding with a cochlear implant and may offer unique insights that could help to more reliably predict outcomes. An emerging optical neuroimaging technique, functional near-infrared spectroscopy (fNIRS), was used to determine whether a preoperative measure of brain activation could explain variability in CI outcomes and offer additional prognostic value above that provided by known clinical characteristics. Cross-modal activation to visual speech was measured in bilateral superior temporal cortex of profoundly deaf adults before cochlear implantation. Behavioural measures of auditory speech understanding were obtained in the same individuals following six months of cochlear-implant use. The results showed that stronger preoperative cross-modal activation of auditory brain regions by visual speech was predictive of poorer auditory speech understanding after implantation. Further investigation suggested that this relationship may have been driven primarily by group differences between pre- and post-lingually deaf individuals. Nonetheless, preoperative cortical imaging provided additional prognostic value above that of influential clinical characteristics, including the age-at-onset and duration of auditory deprivation, suggesting that objectively assessing the physiological status of the brain using fNIRS imaging preoperatively may support more accurate prediction of individual CI outcomes. Whilst activation of auditory brain regions by visual speech prior to implantation was related to the CI user’s clinical history of deafness, activation to visual speech did not relate to the future ability of these brain regions to respond to auditory speech stimulation with a CI. Greater preoperative activation of left superior temporal cortex by visual speech was associated with enhanced speechreading abilities, suggesting that visual-speech processing may help to maintain left temporal-lobe specialisation for language processing during periods of profound deafness

Mechanism of delayed double ionization in a strong laser field

When intense laser pulses release correlated electrons, the time delay between the ionizations may last more than one laser cycle. We show that this "Recollision-Excitation with Subsequent Ionization" pathway originates from the inner electron being promoted to a sticky region by a recollision where it is trapped for a long time before ionizing. We identify the mechanism which regulates this region, and predict oscillations in the double ionization yield with laser intensity

Isomerization dynamics of a buckled nanobeam

We analyze the dynamics of a model of a nanobeam under compression. The model is a two mode truncation of the Euler-Bernoulli beam equation subject to compressive stress. We consider parameter regimes where the first mode is unstable and the second mode can be either stable or unstable, and the remaining modes (neglected) are always stable. Material parameters used correspond to silicon. The two mode model Hamiltonian is the sum of a (diagonal) kinetic energy term and a potential energy term. The form of the potential energy function suggests an analogy with isomerisation reactions in chemistry. We therefore study the dynamics of the buckled beam using the conceptual framework established for the theory of isomerisation reactions. When the second mode is stable the potential energy surface has an index one saddle and when the second mode is unstable the potential energy surface has an index two saddle and two index one saddles. Symmetry of the system allows us to construct a phase space dividing surface between the two "isomers" (buckled states). The energy range is sufficiently wide that we can treat the effects of the index one and index two saddles in a unified fashion. We have computed reactive fluxes, mean gap times and reactant phase space volumes for three stress values at several different energies. In all cases the phase space volume swept out by isomerizing trajectories is considerably less than the reactant density of states, proving that the dynamics is highly nonergodic. The associated gap time distributions consist of one or more `pulses' of trajectories. Computation of the reactive flux correlation function shows no sign of a plateau region; rather, the flux exhibits oscillatory decay, indicating that, for the 2-mode model in the physical regime considered, a rate constant for isomerization does not exist.Comment: 42 pages, 6 figure

A generalized theory of semiflexible polymers

DNA bending on length scales shorter than a persistence length plays an integral role in the translation of genetic information from DNA to cellular function. Quantitative experimental studies of these biological systems have led to a renewed interest in the polymer mechanics relevant for describing the conformational free energy of DNA bending induced by protein-DNA complexes. Recent experimental results from DNA cyclization studies have cast doubt on the applicability of the canonical semiflexible polymer theory, the wormlike chain (WLC) model, to DNA bending on biological length scales. This paper develops a theory of the chain statistics of a class of generalized semiflexible polymer models. Our focus is on the theoretical development of these models and the calculation of experimental observables. To illustrate our methods, we focus on a specific toy model of DNA bending. We show that the WLC model generically describes the long-length-scale chain statistics of semiflexible polymers, as predicted by the Renormalization Group. In particular, we show that either the WLC or our new model adequate describes force-extension, solution scattering, and long-contour-length cyclization experiments, regardless of the details of DNA bend elasticity. In contrast, experiments sensitive to short-length-scale chain behavior can in principle reveal dramatic departures from the linear elastic behavior assumed in the WLC model. We demonstrate this explicitly by showing that our toy model can reproduce the anomalously large short-contour-length cyclization J factors observed by Cloutier and Widom. Finally, we discuss the applicability of these models to DNA chain statistics in the context of future experiments

The Interpersonal Style and Complementarity Between Crisis Negotiators and Forensic Inpatients

Previous negotiation research has explored the interaction and communication between crisis negotiators and perpetrators. A crisis negotiator attempts to resolve a critical incident through negotiation with an individual, or group of persons in crisis. The purpose of this study was to establish the interpersonal style of crisis negotiators and complementarity of the interpersonal interaction between them and forensic inpatients. Crisis negotiators, clinical workers and students (n = 90) used the Check List of Interpersonal Transactions-Revised (CLOIT-R) to identify interpersonal style, along with eight vignettes detailing interpersonal styles. Crisis negotiators were most likely to have a friendly interpersonal style compared to the other non-trained groups. Complementarity theory was not exclusively supported as submissive individuals did not show optimistic judgments in working with dominant forensic inpatients and vice versa. Exploratory analysis revealed that dominant crisis negotiators were optimistic in working with forensic inpatients with a dominant interpersonal style. This study provides insight into the area of interpersonal complementarity of crisis negotiators and forensic inpatients. Whilst further research is required, a potential new finding was established, with significant ‘similarity’ found when dominant crisis negotiators are asked to work with dominant forensic inpatients

Imperfect identity

Questions of identity over time are often hard to answer. A long tradition has it that such questions are somehow soft: they have no unique, determinate answer, and disagreements about them are merely verbal. I argue that this claim is not the truism it is taken to be. Depending on how it is understood, it turns out either to be false or to presuppose a highly contentious metaphysical claim