146 research outputs found
Anisotropic Scaling in Threshold Critical Dynamics of Driven Directed Lines
The dynamical critical behavior of a single directed line driven in a random
medium near the depinning threshold is studied both analytically (by
renormalization group) and numerically, in the context of a Flux Line in a
Type-II superconductor with a bulk current . In the absence of
transverse fluctuations, the system reduces to recently studied models of
interface depinning. In most cases, the presence of transverse fluctuations are
found not to influence the critical exponents that describe longitudinal
correlations. For a manifold with internal dimensions,
longitudinal fluctuations in an isotropic medium are described by a roughness
exponent to all orders in , and a
dynamical exponent . Transverse
fluctuations have a distinct and smaller roughness exponent
for an isotropic medium. Furthermore, their
relaxation is much slower, characterized by a dynamical exponent
, where is the
correlation length exponent. The predicted exponents agree well with numerical
results for a flux line in three dimensions. As in the case of interface
depinning models, anisotropy leads to additional universality classes. A
nonzero Hall angle, which has no analogue in the interface models, also affects
the critical behavior.Comment: 26 pages, 8 Postscript figures packed together with RevTeX 3.0
manuscript using uufiles, uses multicol.sty and epsf.sty, e-mail
[email protected] in case of problem
Finite Temperature Depinning of a Flux Line from a Nonuniform Columnar Defect
A flux line in a Type-II superconductor with a single nonuniform columnar
defect is studied by a perturbative diagrammatic expansion around an annealed
approximation. The system undergoes a finite temperature depinning transition
for the (rather unphysical) on-the-average repulsive columnar defect, provided
that the fluctuations along the axis are sufficiently large to cause some
portions of the column to become attractive. The perturbative expansion is
convergent throughout the weak pinning regime and becomes exact as the
depinning transition is approached, providing an exact determination of the
depinning temperature and the divergence of the localization length.Comment: RevTeX, 4 pages, 3 EPS figures embedded with epsf.st
Onset of Propagation of Planar Cracks in Heterogeneous Media
The dynamics of planar crack fronts in hetergeneous media near the critical
load for onset of crack motion are investigated both analytically and by
numerical simulations. Elasticity of the solid leads to long range stress
transfer along the crack front which is non-monotonic in time due to the
elastic waves in the medium. In the quasistatic limit with instantaneous stress
transfer, the crack front exhibits dynamic critical phenomenon, with a second
order like transition from a pinned to a moving phase as the applied load is
increased through a critical value. At criticality, the crack-front is
self-affine, with a roughness exponent . The dynamic
exponent is found to be equal to and the correlation length
exponent . These results are in good agreement with those
obtained from an epsilon expansion. Sound-travel time delays in the stress
transfer do not change the static exponents but the dynamic exponent
becomes exactly one. Real elastic waves, however, lead to overshoots in the
stresses above their eventual static value when one part of the crack front
moves forward. Simplified models of these stress overshoots are used to show
that overshoots are relevant at the depinning transition leading to a decrease
in the critical load and an apparent jump in the velocity of the crack front
directly to a non-zero value. In finite systems, the velocity also shows
hysteretic behaviour as a function of the loading. These results suggest a
first order like transition. Possible implications for real tensile cracks are
discussed.Comment: 51 pages + 20 figur
Strong Phase Separation in a Model of Sedimenting Lattices
We study the steady state resulting from instabilities in crystals driven
through a dissipative medium, for instance, a colloidal crystal which is
steadily sedimenting through a viscous fluid. The problem involves two coupled
fields, the density and the tilt; the latter describes the orientation of the
mass tensor with respect to the driving field. We map the problem to a 1-d
lattice model with two coupled species of spins evolving through conserved
dynamics. In the steady state of this model each of the two species shows
macroscopic phase separation. This phase separation is robust and survives at
all temperatures or noise levels--- hence the term Strong Phase Separation.
This sort of phase separation can be understood in terms of barriers to
remixing which grow with system size and result in a logarithmically slow
approach to the steady state. In a particular symmetric limit, it is shown that
the condition of detailed balance holds with a Hamiltonian which has
infinite-ranged interactions, even though the initial model has only local
dynamics. The long-ranged character of the interactions is responsible for
phase separation, and for the fact that it persists at all temperatures.
Possible experimental tests of the phenomenon are discussed.Comment: To appear in Phys Rev E (1 January 2000), 16 pages, RevTex, uses
epsf, three ps figure
A Ball in a Groove
We study the static equilibrium of an elastic sphere held in a rigid groove
by gravity and frictional contacts, as determined by contact mechanics. As a
function of the opening angle of the groove and the tilt of the groove with
respect to the vertical, we identify two regimes of static equilibrium for the
ball. In the first of these, at large opening angle or low tilt, the ball rolls
at both contacts as it is loaded. This is an analog of the "elastic" regime in
the mechanics of granular media. At smaller opening angles or larger tilts, the
ball rolls at one contact and slides at the other as it is loaded, analogously
with the "plastic" regime in the mechanics of granular media. In the elastic
regime, the stress indeterminacy is resolved by the underlying kinetics of the
ball response to loading.Comment: RevTeX 3.0, 4 pages, 2 eps figures included with eps
Dynamics and Instabilities of Planar Tensile Cracks in Heterogeneous Media
The dynamics of tensile crack fronts restricted to advance in a plane are
studied. In an ideal linear elastic medium, a propagating mode along the crack
front with a velocity slightly less than the Rayleigh wave velocity, is found
to exist. But the dependence of the effective fracture toughness on
the crack velocity is shown to destabilize the crack front if
. Short wavelength radiation due to weak random
heterogeneities leads to this instability at low velocities. The implications
of these results for the crack dynamics are discussed.Comment: 12 page
Roughness at the depinning threshold for a long-range elastic string
In this paper, we compute the roughness exponent zeta of a long-range elastic
string, at the depinning threshold, in a random medium with high precision,
using a numerical method which exploits the analytic structure of the problem
(`no-passing' theorem), but avoids direct simulation of the evolution
equations. This roughness exponent has recently been studied by simulations,
functional renormalization group calculations, and by experiments (fracture of
solids, liquid meniscus in 4He). Our result zeta = 0.390 +/- 0.002 is
significantly larger than what was stated in previous simulations, which were
consistent with a one-loop renormalization group calculation. The data are
furthermore incompatible with the experimental results for crack propagation in
solids and for a 4He contact line on a rough substrate. This implies that the
experiments cannot be described by pure harmonic long-range elasticity in the
quasi-static limit.Comment: 4 pages, 3 figure
On the Fibonacci universality classes in nonlinear fluctuating hydrodynamics
We present a lattice gas model that without fine tuning of parameters is
expected to exhibit the so far elusive modified Kardar-Parisi-Zhang (KPZ)
universality class. To this end, we review briefly how non-linear fluctuating
hydrodynamics in one dimension predicts that all dynamical universality classes
in its range of applicability belong to an infinite discrete family which we
call Fibonacci family since their dynamical exponents are the Kepler ratios
of neighbouring Fibonacci numbers , including
diffusion (), KPZ (), and the limiting ratio which is the
golden mean . Then we revisit the case of two
conservation laws to which the modified KPZ model belongs. We also derive
criteria on the macroscopic currents to lead to other non-KPZ universality
classes.Comment: 17 page
Lateral Separation of Macromolecules and Polyelectrolytes in Microlithographic Arrays
A new approach to separation of a variety of microscopic and mesoscopic
objects in dilute solution is presented. The approach takes advantage of unique
properties of a specially designed separation device (sieve), which can be
readily built using already developed microlithographic techniques. Due to the
broken reflection symmetry in its design, the direction of motion of an object
in the sieve varies as a function of its self-diffusion constant, causing
separation transverse to its direction of motion. This gives the device some
significant and unique advantages over existing fractionation methods based on
centrifugation and electrophoresis.Comment: 4 pages with 3 eps figures, needs RevTeX 3.0 and epsf, also available
in postscript form http://cmtw.harvard.edu/~deniz
Randomly Charged Polymers, Random Walks, and Their Extremal Properties
Motivated by an investigation of ground state properties of randomly charged
polymers, we discuss the size distribution of the largest Q-segments (segments
with total charge Q) in such N-mers. Upon mapping the charge sequence to
one--dimensional random walks (RWs), this corresponds to finding the
probability for the largest segment with total displacement Q in an N-step RW
to have length L. Using analytical, exact enumeration, and Monte Carlo methods,
we reveal the complex structure of the probability distribution in the large N
limit. In particular, the size of the longest neutral segment has a
distribution with a square-root singularity at l=L/N=1, an essential
singularity at l=0, and a discontinuous derivative at l=1/2. The behavior near
l=1 is related to a another interesting RW problem which we call the "staircase
problem". We also discuss the generalized problem for d-dimensional RWs.Comment: 33 pages, 19 Postscript figures, RevTe
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