7,945 research outputs found
Transport of Single Molecules Along the Periodic Parallel Lattices with Coupling
General discrete one-dimensional stochastic models to describe the transport
of single molecules along coupled parallel lattices with period are
developed. Theoretical analysis that allows to calculate explicitly the
steady-state dynamic properties of single molecules, such as mean velocity
and dispersion , is presented for N=1 and N=2 models. For the systems with
exact analytic expressions for the large-time dynamic properties are
obtained in the limit of strong coupling between the lattices that leads to
dynamic equilibrium between two parallel kinetic pathways.Comment: Submitted to J. Chem. Phy
No many-scallop theorem: Collective locomotion of reciprocal swimmers
To achieve propulsion at low Reynolds number, a swimmer must deform in a way
that is not invariant under time-reversal symmetry; this result is known as the
scallop theorem. We show here that there is no many-scallop theorem. We
demonstrate that two active particles undergoing reciprocal deformations can
swim collectively; moreover, polar particles also experience effective
long-range interactions. These results are derived for a minimal dimers model,
and generalized to more complex geometries on the basis of symmetry and scaling
arguments. We explain how such cooperative locomotion can be realized
experimentally by shaking a collection of soft particles with a homogeneous
external field
Zero Temperature Dynamics of the Weakly Disordered Ising Model
The Glauber dynamics of the pure and weakly disordered random-bond 2d Ising
model is studied at zero-temperature. A single characteristic length scale,
, is extracted from the equal time correlation function. In the pure
case, the persistence probability decreases algebraically with the coarsening
length scale. In the disordered case, three distinct regimes are identified: a
short time regime where the behaviour is pure-like; an intermediate regime
where the persistence probability decays non-algebraically with time; and a
long time regime where the domains freeze and there is a cessation of growth.
In the intermediate regime, we find that , where
. The value of is consistent with that
found for the pure 2d Ising model at zero-temperature. Our results in the
intermediate regime are consistent with a logarithmic decay of the persistence
probability with time, , where .Comment: references updated, very minor amendment to abstract and the
labelling of figures. To be published in Phys Rev E (Rapid Communications), 1
March 199
Non-equilibrium Phase-Ordering with a Global Conservation Law
In all dimensions, infinite-range Kawasaki spin exchange in a quenched Ising
model leads to an asymptotic length-scale
at because the kinetic coefficient is renormalized by the broken-bond
density, . For , activated kinetics recovers the
standard asymptotic growth-law, . However, at all temperatures,
infinite-range energy-transport is allowed by the spin-exchange dynamics. A
better implementation of global conservation, the microcanonical Creutz
algorithm, is well behaved and exhibits the standard non-conserved growth law,
, at all temperatures.Comment: 2 pages and 2 figures, uses epsf.st
Critical properties of the unconventional spin-Peierls system TiOBr
We have performed detailed x-ray scattering measurements on single crystals
of the spin-Peierls compound TiOBr in order to study the critical properties of
the transition between the incommensurate spin-Peierls state and the
paramagnetic state at Tc2 ~ 48 K. We have determined a value of the critical
exponent beta which is consistent with the conventional 3D universality
classes, in contrast with earlier results reported for TiOBr and TiOCl. Using a
simple power law fit function we demonstrate that the asymptotic critical
regime in TiOBr is quite narrow, and obtain a value of beta_{asy} = 0.32 +/-
0.03 in the asymptotic limit. A power law fit function which includes the first
order correction-to-scaling confluent singularity term can be used to account
for data outside the asymptotic regime, yielding a more robust value of
beta_{avg} = 0.39 +/- 0.05. We observe no evidence of commensurate fluctuations
above Tc1 in TiOBr, unlike its isostructural sister compound TiOCl. In
addition, we find that the incommensurate structure between Tc1 and Tc2 is
shifted in Q-space relative to the commensurate structure below Tc1.Comment: 12 pages, 8 figures. Submitted to Physical Review
Persistence in systems with algebraic interaction
Persistence in coarsening 1D spin systems with a power law interaction
is considered. Numerical studies indicate that for sufficiently
large values of the interaction exponent ( in our
simulations), persistence decays as an algebraic function of the length scale
, . The Persistence exponent is found to be
independent on the force exponent and close to its value for the
extremal () model, . For smaller
values of the force exponent (), finite size effects prevent the
system from reaching the asymptotic regime. Scaling arguments suggest that in
order to avoid significant boundary effects for small , the system size
should grow as .Comment: 4 pages 4 figure
Approach to Asymptotic Behaviour in the Dynamics of the Trapping Reaction
We consider the trapping reaction A + B -> B in space dimension d=1, where
the A and B particles have diffusion constants D_A, D_B respectively. We
calculate the probability, Q(t), that a given A particle has not yet reacted at
time t. Exploiting a recent formulation in which the B particles are eliminated
from the problem we find, for t -> \infty, , where
is the density of B particles and for .Comment: 8 pages, 2 figures; minor change
Evidence for the droplet/scaling picture of spin glasses
We have studied the Parisi overlap distribution for the three dimensional
Ising spin glass in the Migdal-Kadanoff approximation. For temperatures T
around 0.7Tc and system sizes upto L=32, we found a P(q) as expected for the
full Parisi replica symmetry breaking, just as was also observed in recent
Monte Carlo simulations on a cubic lattice. However, for lower temperatures our
data agree with predictions from the droplet or scaling picture. The failure to
see droplet model behaviour in Monte Carlo simulations is due to the fact that
all existing simulations have been done at temperatures too close to the
transition temperature so that sytem sizes larger than the correlation length
have not been achieved.Comment: 4 pages, 6 figure
Velocity Distribution of Topological Defects in Phase-Ordering Systems
The distribution of interface (domain-wall) velocities in a
phase-ordering system is considered. Heuristic scaling arguments based on the
disappearance of small domains lead to a power-law tail,
for large v, in the distribution of . The exponent p is
given by , where d is the space dimension and 1/z is the growth
exponent, i.e. z=2 for nonconserved (model A) dynamics and z=3 for the
conserved case (model B). The nonconserved result is exemplified by an
approximate calculation of the full distribution using a gaussian closure
scheme. The heuristic arguments are readily generalized to conserved case
(model B). The nonconserved result is exemplified by an approximate calculation
of the full distribution using a gaussian closure scheme. The heuristic
arguments are readily generalized to systems described by a vector order
parameter.Comment: 5 pages, Revtex, no figures, minor revisions and updates, to appear
in Physical Review E (May 1, 1997
Hydrodynamic synchronisation of non-linear oscillators at low Reynolds number
We introduce a generic model of weakly non-linear self-sustained oscillator
as a simplified tool to study synchronisation in a fluid at low Reynolds
number. By averaging over the fast degrees of freedom, we examine the effect of
hydrodynamic interactions on the slow dynamics of two oscillators and show that
they can lead to synchronisation. Furthermore, we find that synchronisation is
strongly enhanced when the oscillators are non-isochronous, which on the limit
cycle means the oscillations have an amplitude-dependent frequency.
Non-isochronity is determined by a nonlinear coupling being non-zero.
We find that its () sign determines if they synchronise in- or
anti-phase. We then study an infinite array of oscillators in the long
wavelength limit, in presence of noise. For , hydrodynamic
interactions can lead to a homogeneous synchronised state. Numerical
simulations for a finite number of oscillators confirm this and, when , show the propagation of waves, reminiscent of metachronal coordination.Comment: 4 pages, 2 figure
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