9,201 research outputs found
Effect of exchange interaction on superparamagnetic relaxation
We use Langer's approach to calculate the reaction rate of a system of two
(classical) spins interacting via the exchange coupling in a magnetic field
, with uniaxial anisotropy of constant .
We find a particular value of the exchange coupling, that is , where , which separates two regimes
corresponding to a two-stage and one-stage switching.
For the N\'eel-Brown result for the one-spin problem is recovered.Comment: 7 pages, 2 eps figures, fig.1 of better quality can be provided upon
reques
Five-Torsion in the Homology of the Matching Complex on 14 Vertices
J. L. Andersen proved that there is 5-torsion in the bottom nonvanishing
homology group of the simplicial complex of graphs of degree at most two on
seven vertices. We use this result to demonstrate that there is 5-torsion also
in the bottom nonvanishing homology group of the matching complex on
14 vertices. Combining our observation with results due to Bouc and to
Shareshian and Wachs, we conclude that the case is exceptional; for all
other , the torsion subgroup of the bottom nonvanishing homology group has
exponent three or is zero. The possibility remains that there is other torsion
than 3-torsion in higher-degree homology groups of when and .Comment: 11 page
Corrections for gravitational lensing of supernovae: better than average?
We investigate the possibility of correcting for the magnification due to
gravitational lensing of standard candle sources, such as Type Ia supernovae.
Our method uses the observed properties of the foreground galaxies along the
lines-of-sight to each source and the accuracy of the lensing correction
depends on the quality and depth of these observations as well as the
uncertainties in translating the observed luminosities to the matter
distribution in the lensing galaxies. The current work is limited to cases
where the matter density is dominated by the individual galaxy halos. However,
it is straightforward to generalize the method to include also gravitational
lensing from cluster scale halos. We show that the dispersion due to lensing
for a standard candle source at z=1.5 can be reduced from about 7% to ~< 3%,
i.e. the magnification correction is useful in reducing the scatter in the Type
Ia Hubble diagram, especially at high redshifts where the required long
exposure times makes it hard to reach large statistics and the dispersion due
to lensing becomes comparable to the intrinsic Type Ia scatter.Comment: Matches accepted version, includes clarifications and additional
issues. 28 pages, 7 figures, accepted for publication in Ap
A streamwise-constant model of turbulent pipe flow
A streamwise-constant model is presented to investigate the basic mechanisms
responsible for the change in mean flow occuring during pipe flow transition.
Using a single forced momentum balance equation, we show that the shape of the
velocity profile is robust to changes in the forcing profile and that both
linear non-normal and nonlinear effects are required to capture the change in
mean flow associated with transition to turbulence. The particularly simple
form of the model allows for the study of the momentum transfer directly by
inspection of the equations. The distribution of the high- and low-speed
streaks over the cross-section of the pipe produced by our model is remarkably
similar to one observed in the velocity field near the trailing edge of the
puff structures present in pipe flow transition. Under stochastic forcing, the
model exhibits a quasi-periodic self-sustaining cycle characterized by the
creation and subsequent decay of "streamwise-constant puffs", so-called due to
the good agreement between the temporal evolution of their velocity field and
the projection of the velocity field associated with three-dimensional puffs in
a frame of reference moving at the bulk velocity. We establish that the flow
dynamics are relatively insensitive to the regeneration mechanisms invoked to
produce near-wall streamwise vortices and that using small, unstructured
background disturbances to regenerate the streamwise vortices is sufficient to
capture the formation of the high- and low-speed streaks and their segregation
leading to the blunting of the velocity profile characteristic of turbulent
pipe flow
Lensing magnification of supernovae in the GOODS-fields
Gravitational lensing of high-redshift supernovae is potentially an important
source of uncertainty when deriving cosmological parameters from the measured
brightness of Type Ia supernovae, especially in deep surveys with scarce
statistics. Photometric and spectroscopic measurements of foreground galaxies
along the lines-of-sight of 33 supernovae discovered with the Hubble Space
Telescope, both core-collapse and Type Ia, are used to model the magnification
probability distributions of the sources. Modelling galaxy halos with SIS or
NFW-profiles and using M/L scaling laws provided by the Faber-Jackson and
Tully-Fisher relations, we find clear evidence for supernovae with lensing
(de)magnification. However, the magnification distribution of the Type Ia
supernovae used to determine cosmological distances matches very well the
expectations for an unbiased sample, i.e.their mean magnification factor is
consistent with unity. Our results show that the lensing distortions of the
supernova brightness can be well understood for the GOODS sample and that
correcting for this effect has a negligible impact on the derived cosmological
parameters.Comment: 22 pages, 9 figures, accepted for publication by Ap
Force generation in small ensembles of Brownian motors
The motility of certain gram-negative bacteria is mediated by retraction of
type IV pili surface filaments, which are essential for infectivity. The
retraction is powered by a strong molecular motor protein, PilT, producing very
high forces that can exceed 150 pN. The molecular details of the motor
mechanism are still largely unknown, while other features have been identified,
such as the ring-shaped protein structure of the PilT motor. The surprisingly
high forces generated by the PilT system motivate a model investigation of the
generation of large forces in molecular motors. We propose a simple model,
involving a small ensemble of motor subunits interacting through the
deformations on a circular backbone with finite stiffness. The model describes
the motor subunits in terms of diffusing particles in an asymmetric,
time-dependent binding potential (flashing ratchet potential), roughly
corresponding to the ATP hydrolysis cycle. We compute force-velocity relations
in a subset of the parameter space and explore how the maximum force (stall
force) is determined by stiffness, binding strength, ensemble size, and degree
of asymmetry. We identify two qualitatively different regimes of operation
depending on the relation between ensemble size and asymmetry. In the
transition between these two regimes, the stall force depends nonlinearly on
the number of motor subunits. Compared to its constituents without
interactions, we find higher efficiency and qualitatively different
force-velocity relations. The model captures several of the qualitative
features obtained in experiments on pilus retraction forces, such as roughly
constant velocity at low applied forces and insensitivity in the stall force to
changes in the ATP concentration.Comment: RevTex 9 pages, 4 figures. Revised version, new subsections in Sec.
III, removed typo
Extrinsic Curvature Embedding Diagrams
Embedding diagrams have been used extensively to visualize the properties of
curved space in Relativity. We introduce a new kind of embedding diagram based
on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an
extrinsic curvature embedding diagram, when used together with the usual kind
of intrinsic curvature embedding diagram, carries the information of how a
surface is {\it embedded} in the higher dimensional curved space. Simple
examples are given to illustrate the idea.Comment: 22 pages, 4 figure
Effect of non-zero constant vorticity on the nonlinear resonances of capillary water waves
The influence of an underlying current on 3-wave interactions of capillary
water waves is studied. The fact that in irrotational flow resonant 3-wave
interactions are not possible can be invalidated by the presence of an
underlying current of constant non-zero vorticity. We show that: 1) wave trains
in flows with constant non-zero vorticity are possible only for two-dimensional
flows; 2) only positive constant vorticities can trigger the appearance of
three-wave resonances; 3) the number of positive constant vorticities which do
trigger a resonance is countable; 4) the magnitude of a positive constant
vorticity triggering a resonance can not be too small.Comment: 6 pages, submitte
Memory and superposition in a spin glass
Non-equilibrium dynamics in a Ag(Mn) spin glass are investigated by
measurements of the temperature dependence of the remanent magnetisation. Using
specific cooling protocols before recording the thermo- or isothermal remanent
magnetisations on re-heating, it is found that the measured curves effectively
disclose non-equilibrium spin glass characteristics such as ageing and memory
phenomena as well as an extended validity of the superposition principle for
the relaxation. The usefulness of this "simple" dc-method is discussed, as well
as its applicability to other disordered magnetic systems.Comment: REVTeX style; 8 pages, 4 figure
Magnetic-field dependence of dynamical vortex response in two-dimensional Josephson junction arrays and superconducting films
The dynamical vortex response of a two-dimensional array of the resistively
shunted Josephson junctions in a perpendicular magnetic field is inferred from
simulations. It is found that, as the magnetic field is increased at a fixed
temperature, the response crosses over from normal to anomalous, and that this
crossover can be characterized by a single dimensionless parameter. It is
described how this crossover should be reflected in measurements of the complex
impedance for Josephson junction arrays and superconducting films.Comment: 4 pages including 5 figures in two columns, final versio
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