2,377 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
Must naive realists be relationalists?
Relationalism maintains that perceptual experience involves, as part of its nature, a distinctive kind of conscious perceptual relation between a subject of experience and an object of experience. Together with the claim that perceptual experience is presentational, relationalism is widely believed to be a core aspect of the naive realist outlook on perception. This is a mistake. I argue that naive realism about perception can be upheld without a commitment to relationalism
Telling time with an intrinsically noisy clock
Intracellular transmission of information via chemical and transcriptional
networks is thwarted by a physical limitation: the finite copy number of the
constituent chemical species introduces unavoidable intrinsic noise. Here we
provide a method for solving for the complete probabilistic description of
intrinsically noisy oscillatory driving. We derive and numerically verify a
number of simple scaling laws. Unlike in the case of measuring a static
quantity, response to an oscillatory driving can exhibit a resonant frequency
which maximizes information transmission. Further, we show that the optimal
regulatory design is dependent on the biophysical constraints (i.e., the
allowed copy number and response time). The resulting phase diagram illustrates
under what conditions threshold regulation outperforms linear regulation.Comment: 10 pages, 5 figure
Recommended from our members
Dynamic Patterns and Self-Knotting of a Driven Hanging Chain
When shaken vertically, a hanging chain displays a startling variety of distinct behaviors. We find experimentally that instabilities occur in tonguelike bands of parameter space, to swinging or rotating pendular motion, or to chaotic states. Mathematically, the dynamics are described by a nonlinear wave equation. A linear stability analysis predicts instabilities within the well-known resonance tongues; their boundaries agree very well with experiment. Full simulations of the 3D dynamics reproduce and elucidate many aspects of the experiment. The chain is also observed to tie knots in itself, some quite complex. This is beyond the reach of the current analysis and simulations
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
Geometrical Models of the Phase Space Structures Governing Reaction Dynamics
Hamiltonian dynamical systems possessing equilibria of stability type display \emph{reaction-type
dynamics} for energies close to the energy of such equilibria; entrance and
exit from certain regions of the phase space is only possible via narrow
\emph{bottlenecks} created by the influence of the equilibrium points. In this
paper we provide a thorough pedagogical description of the phase space
structures that are responsible for controlling transport in these problems. Of
central importance is the existence of a \emph{Normally Hyperbolic Invariant
Manifold (NHIM)}, whose \emph{stable and unstable manifolds} have sufficient
dimensionality to act as separatrices, partitioning energy surfaces into
regions of qualitatively distinct behavior. This NHIM forms the natural
(dynamical) equator of a (spherical) \emph{dividing surface} which locally
divides an energy surface into two components (`reactants' and `products'), one
on either side of the bottleneck. This dividing surface has all the desired
properties sought for in \emph{transition state theory} where reaction rates
are computed from the flux through a dividing surface. In fact, the dividing
surface that we construct is crossed exactly once by reactive trajectories, and
not crossed by nonreactive trajectories, and related to these properties,
minimizes the flux upon variation of the dividing surface.
We discuss three presentations of the energy surface and the phase space
structures contained in it for 2-degree-of-freedom (DoF) systems in the
threedimensional space , and two schematic models which capture many of
the essential features of the dynamics for -DoF systems. In addition, we
elucidate the structure of the NHIM.Comment: 44 pages, 38 figures, PDFLaTe
Gamma-Ray Multiplicities in 6-Li Induced Reactions
This work was supported by National Science Foundation Grants PHY 76-84033A01, PHY 78-22774, and Indiana Universit
The Benefit of Cross-Modal Reorganization on Speech Perception in Pediatric Cochlear Implant Recipients Revealed Using Functional Near-Infrared Spectroscopy
Cochlear implants (CIs) are the most successful treatment for severe-to-profound deafness in children. However, speech outcomes with a CI often lag behind those of normally-hearing children. Some authors have attributed these deficits to the takeover of the auditory temporal cortex by vision following deafness, which has prompted some clinicians to discourage the rehabilitation of pediatric CI recipients using visual speech. We studied this cross-modal activity in the temporal cortex, along with responses to auditory speech and non-speech stimuli, in experienced CI users and normally-hearing controls of school-age, using functional near-infrared spectroscopy. Strikingly, CI users displayed significantly greater cortical responses to visual speech, compared with controls. Importantly, in the same regions, the processing of auditory speech, compared with non-speech stimuli, did not significantly differ between the groups. This suggests that visual and auditory speech are processed synergistically in the temporal cortex of children with CIs, and they should be encouraged, rather than discouraged, to use visual speech
Phase space structures governing reaction dynamics in rotating molecules
Recently the phase space structures governing reaction dynamics in
Hamiltonian systems have been identified and algorithms for their explicit
construction have been developed. These phase space structures are induced by
saddle type equilibrium points which are characteristic for reaction type
dynamics. Their construction is based on a Poincar{\'e}-Birkhoff normal form.
Using tools from the geometric theory of Hamiltonian systems and their
reduction we show in this paper how the construction of these phase space
structures can be generalized to the case of the relative equilibria of a
rotational symmetry reduced -body system. As rotations almost always play an
important role in the reaction dynamics of molecules the approach presented in
this paper is of great relevance for applications.Comment: 28 pages, 7 figures, pdflate
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
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