9,653 research outputs found
On the number of metastable states in spin glasses
In this letter, we show that the formulae of Bray and Moore for the average
logarithm of the number of metastable states in spin glasses can be obtained by
calculating the partition function with coupled replicas with the symmetry
among these explicitly broken according to a generalization of the `two-group'
ansatz. This equivalence allows us to find solutions of the BM equations where
the lower `band-edge' free energy equals the standard static free energy. We
present these results for the Sherrington-Kirkpatrick model, but we expect them
to apply to all mean-field spin glasses.Comment: 6 pages, LaTeX, no figures. Postscript directly available
http://chimera.roma1.infn.it/index_papers_complex.htm
Dynamics of swimming bacteria at complex interfaces
Flagellated bacteria exploiting helical propulsion are known to swim along
circular trajectories near surfaces. Fluid dynamics predicts this circular
motion to be clockwise (CW) above a rigid surface (when viewed from inside the
fluid) and counter-clockwise (CCW) below a free surface. Recent experimental
investigations showed that complex physicochemical processes at the nearby
surface could lead to a change in the direction of rotation, both at solid
surfaces absorbing slip-inducing polymers and interfaces covered with
surfactants. Motivated by these results, we use a far-field hydrodynamic model
to predict the kinematics of swimming near three types of interfaces: clean
fluid-fluid interface, slipping rigid wall, and a fluid interface covered by
incompressible surfactants. Representing the helical swimmer by a superposition
of hydrodynamic singularities, we first show that in all cases the surfaces
reorient the swimmer parallel to the surface and attract it, both of which are
a consequence of the Stokes dipole component of the swimmer flow field. We then
show that circular motion is induced by a higher-order singularity, namely a
rotlet dipole, and that its rotation direction (CW vs. CCW) is strongly
affected by the boundary conditions at the interface and the bacteria shape.
Our results suggest thus that the hydrodynamics of complex interfaces provide a
mechanism to selectively stir bacteria
Phase Ordering Dynamics of the O(n) Model - Exact Predictions and Numerical Results
We consider the pair correlation functions of both the order parameter field
and its square for phase ordering in the model with nonconserved order
parameter, in spatial dimension and spin dimension .
We calculate, in the scaling limit, the exact short-distance singularities of
these correlation functions and compare these predictions to numerical
simulations. Our results suggest that the scaling hypothesis does not hold for
the model. Figures (23) are available on request - email
[email protected]: 23 pages, Plain LaTeX, M/C.TH.93/2
Spin-resolved electron-impact ionization of lithium
Electron-impact ionization of lithium is studied using the convergent
close-coupling (CCC) method at 25.4 and 54.4 eV. Particular attention is paid
to the spin-dependence of the ionization cross sections. Convergence is found
to be more rapid for the spin asymmetries, which are in good agreement with
experiment, than for the underlying cross sections. Comparison with the recent
measured and DS3C-calculated data of Streun et al (1999) is most intriguing.
Excellent agreement is found with the measured and calculated spin asymmetries,
yet the discrepancy between the CCC and DS3C cross sections is very large
Global Persistence Exponent for Critical Dynamics
A `persistence exponent' is defined for nonequilibrium critical
phenomena. It describes the probability, , that the
global order parameter has not changed sign in the time interval following
a quench to the critical point from a disordered state. This exponent is
calculated in mean-field theory, in the limit of the model,
to first order in , and for the 1-d Ising model. Numerical
results are obtained for the 2-d Ising model. We argue that is a new
independent exponent.Comment: 4 pages, revtex, one figur
Corrections to Scaling in Phase-Ordering Kinetics
The leading correction to scaling associated with departures of the initial
condition from the scaling morphology is determined for some soluble models of
phase-ordering kinetics. The result for the pair correlation function has the
form C(r,t) = f_0(r/L) + L^{-\omega} f_1(r/L) + ..., where L is a
characteristic length scale extracted from the energy. The
correction-to-scaling exponent \omega has the value \omega=4 for the d=1
Glauber model, the n-vector model with n=\infty, and the approximate theory of
Ohta, Jasnow and Kawasaki. For the approximate Mazenko theory, however, \omega
has a non-trivial value: omega = 3.8836... for d=2, and \omega = 3.9030... for
d=3. The correction-to-scaling functions f_1(x) are also calculated.Comment: REVTEX, 7 pages, two figures, needs epsf.sty and multicol.st
The effect of shear on persistence in coarsening systems
We analytically study the effect of a uniform shear flow on the persistence
properties of coarsening systems. The study is carried out within the
anisotropic Ohta-Jasnow-Kawasaki (OJK) approximation for a system with
nonconserved scalar order parameter. We find that the persistence exponent
theta has a non-trivial value: theta = 0.5034... in space dimension d=3, and
theta = 0.2406... for d=2, the latter being exactly twice the value found for
the unsheared system in d=1. We also find that the autocorrelation exponent
lambda is affected by shear in d=3 but not in d=2.Comment: 6 page
Persistence of Manifolds in Nonequilibrium Critical Dynamics
We study the persistence P(t) of the magnetization of a d' dimensional
manifold (i.e., the probability that the manifold magnetization does not flip
up to time t, starting from a random initial condition) in a d-dimensional spin
system at its critical point. We show analytically that there are three
distinct late time decay forms for P(t) : exponential, stretched exponential
and power law, depending on a single parameter \zeta=(D-2+\eta)/z where D=d-d'
and \eta, z are standard critical exponents. In particular, our theory predicts
that the persistence of a line magnetization decays as a power law in the d=2
Ising model at its critical point. For the d=3 critical Ising model, the
persistence of the plane magnetization decays as a power law, while that of a
line magnetization decays as a stretched exponential. Numerical results are
consistent with these analytical predictions.Comment: 4 pages revtex, 1 eps figure include
Evidence for existence of many pure ground states in 3d Spin Glasses
Ground states of 3d EA Ising spin glasses are calculated for sizes up to
using a combination of genetic algorithms and cluster-exact
approximation . The distribution of overlaps is calculated. For
increasing size the width of converges to a nonzero value, indicating
that many pure ground states exist for short range Ising spin glasses.Comment: 4 pages, 3 figures, 2 tables, 16 reference
Corrections to Scaling in the Phase-Ordering Dynamics of a Vector Order Parameter
Corrections to scaling, associated with deviations of the order parameter
from the scaling morphology in the initial state, are studied for systems with
O(n) symmetry at zero temperature in phase-ordering kinetics. Including
corrections to scaling, the equal-time pair correlation function has the form
C(r,t) = f_0(r/L) + L^{-omega} f_1(r/L) + ..., where L is the coarsening length
scale. The correction-to-scaling exponent, omega, and the correction-to-scaling
function, f_1(x), are calculated for both nonconserved and conserved order
parameter systems using the approximate Gaussian closure theory of Mazenko. In
general, omega is a non-trivial exponent which depends on both the
dimensionality, d, of the system and the number of components, n, of the order
parameter. Corrections to scaling are also calculated for the nonconserved 1-d
XY model, where an exact solution is possible.Comment: REVTeX, 20 pages, 2 figure
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