170 research outputs found
Topological constraints on spiral wave dynamics in spherical geometries with inhomogeneous excitability
We analyze the way topological constraints and inhomogeneity in the
excitability influence the dynamics of spiral waves on spheres and punctured
spheres of excitable media. We generalize the definition of an index such that
it characterizes not only each spiral but also each hole in punctured,
oriented, compact, two-dimensional differentiable manifolds and show that the
sum of the indices is conserved and zero. We also show that heterogeneity and
geometry are responsible for the formation of various spiral wave attractors,
in particular, pairs of spirals in which one spiral acts as a source and a
second as a sink -- the latter similar to an antispiral. The results provide a
basis for the analysis of the propagation of waves in heterogeneous excitable
media in physical and biological systems.Comment: 5 pages, 6 Figures, major revisions, accepted for publication in
Phys. Rev.
Wide-pulse electrical stimulation to an intrinsic foot muscle induces acute functional changes in forefoot-rearfoot coupling behaviour during walking.
Interventions for strengthening intrinsic foot muscles may be beneficial for rehabilitation from overuse injuries. In this study the acute effects of high-frequency, low-intensity wide-pulse electrical stimulation (WPS) over an intrinsic muscle on subsequent foot function during walking was assessed in healthy participants. WPS was delivered to the m. abductor hallucis (m.AH) of the non-dominant foot during relaxed standing. 3-dimensional forefoot (FF)--rearfoot (RF) coordination was quantified with a vector coding technique within separate periods of the stance phase to study WPS functional effects on foot motion. 4 types of coordinative strategies between the FF and RF were interpreted and compared PRE-to-POST-WPS for both the experimental and control feet. Bilateral electromyography (EMG) from m.AH was analysed during the intervention period for evidence of acute neuromuscular adaptation. The results showed that WPS significantly modulated FF-RF coordination during mid-stance, indicative of a more stable foot. Specifically, a statistically significant increase in FF eversion with concomitant RF inversion in the frontal plane and RF-dominated adduction in the transverse plane was observed. Subject-specific increases in post-stimulus m.AH EMG activation were observed but this was not reflected in an overall group effect. It is concluded that the structural integrity of the foot during walking is enhanced following an acute session of WPS and that this mechanical effect is most likely due to stimulation induced post-tetanic potentiation of synaptic transmission
Topological effects in the thermal properties of knotted polymer rings
The topological effects on the thermal properties of several knot
configurations are investigated using Monte Carlo simulations. In order to
check if the topology of the knots is preserved during the thermal fluctuations
we propose a method that allows very fast calculations and can be easily
applied to arbitrarily complex knots. As an application, the specific energy
and heat capacity of the trefoil, the figure-eight and the knots are
calculated at different temperatures and for different lengths. Short-range
repulsive interactions between the monomers are assumed. The knots
configurations are generated on a three-dimensional cubic lattice and sampled
by means of the Wang-Landau algorithm and of the pivot method. The obtained
results show that the topological effects play a key role for short-length
polymers. Three temperature regimes of the growth rate of the internal energy
of the system are distinguished.Comment: 7 pages, 12 figures, LaTeX + RevTeX. With respect to the first
version, in the second version the text has been improved and all figures are
now in black and whit
On the Dominance of Trivial Knots among SAPs on a Cubic Lattice
The knotting probability is defined by the probability with which an -step
self-avoiding polygon (SAP) with a fixed type of knot appears in the
configuration space. We evaluate these probabilities for some knot types on a
simple cubic lattice. For the trivial knot, we find that the knotting
probability decays much slower for the SAP on the cubic lattice than for
continuum models of the SAP as a function of . In particular the
characteristic length of the trivial knot that corresponds to a `half-life' of
the knotting probability is estimated to be on the cubic
lattice.Comment: LaTeX2e, 21 pages, 8 figur
Knot localization in adsorbing polymer rings
We study by Monte Carlo simulations a model of knotted polymer ring adsorbing
onto an impenetrable, attractive wall. The polymer is described by a
self-avoiding polygon (SAP) on the cubic lattice. We find that the adsorption
transition temperature, the crossover exponent and the metric exponent
, are the same as in the model where the topology of the ring is
unrestricted. By measuring the average length of the knotted portion of the
ring we are able to show that adsorbed knots are localized. This knot
localization transition is triggered by the adsorption transition but is
accompanied by a less sharp variation of the exponent related to the degree of
localization. Indeed, for a whole interval below the adsorption transition, one
can not exclude a contiuous variation with temperature of this exponent. Deep
into the adsorbed phase we are able to verify that knot localization is strong
and well described in terms of the flat knot model.Comment: 27 pages, 10 figures. Submitter to Phys. Rev.
Critical exponents for random knots
The size of a zero thickness (no excluded volume) polymer ring is shown to
scale with chain length in the same way as the size of the excluded volume
(self-avoiding) linear polymer, as , where . The
consequences of that fact are examined, including sizes of trivial and
non-trivial knots.Comment: 4 pages, 0 figure
Abundance of unknots in various models of polymer loops
A veritable zoo of different knots is seen in the ensemble of looped polymer
chains, whether created computationally or observed in vitro. At short loop
lengths, the spectrum of knots is dominated by the trivial knot (unknot). The
fractional abundance of this topological state in the ensemble of all
conformations of the loop of segments follows a decaying exponential form,
, where marks the crossover from a mostly unknotted
(ie topologically simple) to a mostly knotted (ie topologically complex)
ensemble. In the present work we use computational simulation to look closer
into the variation of for a variety of polymer models. Among models
examined, is smallest (about 240) for the model with all segments of the
same length, it is somewhat larger (305) for Gaussian distributed segments, and
can be very large (up to many thousands) when the segment length distribution
has a fat power law tail.Comment: 13 pages, 6 color figure
IceCube - the next generation neutrino telescope at the South Pole
IceCube is a large neutrino telescope of the next generation to be
constructed in the Antarctic Ice Sheet near the South Pole. We present the
conceptual design and the sensitivity of the IceCube detector to predicted
fluxes of neutrinos, both atmospheric and extra-terrestrial. A complete
simulation of the detector design has been used to study the detector's
capability to search for neutrinos from sources such as active galaxies, and
gamma-ray bursts.Comment: 8 pages, to be published with the proceedings of the XXth
International Conference on Neutrino Physics and Astrophysics, Munich 200
Numerical study of linear and circular model DNA chains confined in a slit: metric and topological properties
Advanced Monte Carlo simulations are used to study the effect of nano-slit
confinement on metric and topological properties of model DNA chains. We
consider both linear and circularised chains with contour lengths in the
1.2--4.8 m range and slits widths spanning continuously the 50--1250nm
range. The metric scaling predicted by de Gennes' blob model is shown to hold
for both linear and circularised DNA up to the strongest levels of confinement.
More notably, the topological properties of the circularised DNA molecules have
two major differences compared to three-dimensional confinement. First, the
overall knotting probability is non-monotonic for increasing confinement and
can be largely enhanced or suppressed compared to the bulk case by simply
varying the slit width. Secondly, the knot population consists of knots that
are far simpler than for three-dimensional confinement. The results suggest
that nano-slits could be used in nano-fluidic setups to produce DNA rings
having simple topologies (including the unknot) or to separate heterogeneous
ensembles of DNA rings by knot type.Comment: 12 pages, 10 figure
Tightness of slip-linked polymer chains
We study the interplay between entropy and topological constraints for a
polymer chain in which sliding rings (slip-links) enforce pair contacts between
monomers. These slip-links divide a closed ring polymer into a number of
sub-loops which can exchange length between each other. In the ideal chain
limit, we find the joint probability density function for the sizes of segments
within such a slip-linked polymer chain (paraknot). A particular segment is
tight (small in size) or loose (of the order of the overall size of the
paraknot) depending on both the number of slip-links it incorporates and its
competition with other segments. When self-avoiding interactions are included,
scaling arguments can be used to predict the statistics of segment sizes for
certain paraknot configurations.Comment: 10 pages, 6 figures, REVTeX
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