3,078 research outputs found
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
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