422 research outputs found
Super-Arrhenius dynamics for sub-critical crack growth in disordered brittle media
Taking into account stress fluctuations due to thermal noise, we study
thermally activated irreversible crack growth in disordered media. The
influence of material disorder on sub-critical growth of a single crack in
two-dimensional brittle elastic material is described through the introduction
of a rupture threshold distribution. We derive analytical predictions for crack
growth velocity and material lifetime in agreement with direct numerical
calculations. It is claimed that crack growth process is inhibited by disorder:
velocity decreases and lifetime increases with disorder. More precisely,
lifetime is shown to follow a super-Arrhenius law, with an effective
temperature theta - theta_d, where theta is related to the thermodynamical
temperature and theta_d to the disorder variance.Comment: Submitted to Europhysics Letter
Transition between Two Oscillation Modes
A model for the symmetric coupling of two self-oscillators is presented. The
nonlinearities cause the system to vibrate in two modes of different
symmetries. The transition between these two regimes of oscillation can occur
by two different scenarios. This might model the release of vortices behind
circular cylinders with a possible transition from a symmetric to an
antisymmetric Benard-von Karman vortex street.Comment: 12 pages, 0 figure
Dissipative flow and vortex shedding in the Painlev\'e boundary layer of a Bose Einstein condensate
Raman et al. have found experimental evidence for a critical velocity under
which there is no dissipation when a detuned laser beam is moved in a
Bose-Einstein condensate. We analyze the origin of this critical velocity in
the low density region close to the boundary layer of the cloud. In the frame
of the laser beam, we do a blow up on this low density region which can be
described by a Painlev\'e equation and write the approximate equation satisfied
by the wave function in this region. We find that there is always a drag around
the laser beam. Though the beam passes through the surface of the cloud and the
sound velocity is small in the Painlev\'e boundary layer, the shedding of
vortices starts only when a threshold velocity is reached. This critical
velocity is lower than the critical velocity computed for the corresponding 2D
problem at the center of the cloud. At low velocity, there is a stationary
solution without vortex and the drag is small. At the onset of vortex shedding,
that is above the critical velocity, there is a drastic increase in drag.Comment: 4 pages, 4 figures (with 9 ps files
Subcritical crack growth in fibrous materials
We present experiments on the slow growth of a single crack in a fax paper
sheet submitted to a constant force . We find that statistically averaged
crack growth curves can be described by only two parameters : the mean rupture
time and a characteristic growth length . We propose a model
based on a thermally activated rupture process that takes into account the
microstructure of cellulose fibers. The model is able to reproduce the shape of
the growth curve, the dependence of on as well as the effect of
temperature on the rupture time . We find that the length scale at which
rupture occurs in this model is consistently close to the diameter of cellulose
microfibrils
Onset of Wave Drag due to Generation of Capillary-Gravity Waves by a Moving Object as a Critical Phenomenon
The onset of the {\em wave resistance}, via generation of capillary gravity
waves, of a small object moving with velocity , is investigated
experimentally. Due to the existence of a minimum phase velocity for
surface waves, the problem is similar to the generation of rotons in superfluid
helium near their minimum. In both cases waves or rotons are produced at
due to {\em Cherenkov radiation}. We find that the transition to the
wave drag state is continuous: in the vicinity of the bifurcation the wave
resistance force is proportional to for various fluids.Comment: 4 pages, 7 figure
Energy Transport in an Ising Disordered Model
We introduce a new microcanonical dynamics for a large class of Ising systems
isolated or maintained out of equilibrium by contact with thermostats at
different temperatures. Such a dynamics is very general and can be used in a
wide range of situations, including disordered and topologically inhomogenous
systems. Focusing on the two-dimensional ferromagnetic case, we show that the
equilibrium temperature is naturally defined, and it can be consistently
extended as a local temperature when far from equilibrium. This holds for
homogeneous as well as for disordered systems. In particular, we will consider
a system characterized by ferromagnetic random couplings . We show that the dynamics relaxes to steady states,
and that heat transport can be described on the average by means of a Fourier
equation. The presence of disorder reduces the conductivity, the effect being
especially appreciable for low temperatures. We finally discuss a possible
singular behaviour arising for small disorder, i.e. in the limit .Comment: 14 pages, 8 figure
Weakly nonlinear theory of grain boundary motion in patterns with crystalline symmetry
We study the motion of a grain boundary separating two otherwise stationary
domains of hexagonal symmetry. Starting from an order parameter equation
appropriate for hexagonal patterns, a multiple scale analysis leads to an
analytical equation of motion for the boundary that shares many properties with
that of a crystalline solid. We find that defect motion is generically opposed
by a pinning force that arises from non-adiabatic corrections to the standard
amplitude equation. The magnitude of this force depends sharply on the
mis-orientation angle between adjacent domains so that the most easily pinned
grain boundaries are those with an angle between four and eight degrees.
Although pinning effects may be small, they do not vanish asymptotically near
the onset of this subcritical bifurcation, and can be orders of magnitude
larger than those present in smectic phases that bifurcate supercritically
Rayleigh-Benard Convection in Large-Aspect-Ratio Domains
The coarsening and wavenumber selection of striped states growing from random
initial conditions are studied in a non-relaxational, spatially extended, and
far-from-equilibrium system by performing large-scale numerical simulations of
Rayleigh-B\'{e}nard convection in a large-aspect-ratio cylindrical domain with
experimentally realistic boundaries. We find evidence that various measures of
the coarsening dynamics scale in time with different power-law exponents,
indicating that multiple length scales are required in describing the time
dependent pattern evolution. The translational correlation length scales with
time as , the orientational correlation length scales as ,
and the density of defects scale as . The final pattern evolves
toward the wavenumber where isolated dislocations become motionless, suggesting
a possible wavenumber selection mechanism for large-aspect-ratio convection.Comment: 5 pages, 6 figure
A simulation study of energy transport in the Hamiltonian XY-model
The transport properties of the planar rotator model on a square lattice are
analyzed by means of microcanonical and non--equilibrium simulations. Well
below the Kosterlitz--Thouless--Berezinskii transition temperature, both
approaches consistently indicate that the energy current autocorrelation
displays a long--time tail decaying as t^{-1}. This yields a thermal
conductivity coefficient which diverges logarithmically with the lattice size.
Conversely, conductivity is found to be finite in the high--temperature
disordered phase. Simulations close to the transition temperature are insted
limited by slow convergence that is presumably due to the slow kinetics of
vortex pairs.Comment: Submitted to Journal of Statistical Mechanics: theory and experimen
Limitations on the smooth confinement of an unstretchable manifold
We prove that an m-dimensional unit ball D^m in the Euclidean space {\mathbb
R}^m cannot be isometrically embedded into a higher-dimensional Euclidean ball
B_r^d \subset {\mathbb R}^d of radius r < 1/2 unless one of two conditions is
met -- (1)The embedding manifold has dimension d >= 2m. (2) The embedding is
not smooth. The proof uses differential geometry to show that if d<2m and the
embedding is smooth and isometric, we can construct a line from the center of
D^m to the boundary that is geodesic in both D^m and in the embedding manifold
{\mathbb R}^d. Since such a line has length 1, the diameter of the embedding
ball must exceed 1.Comment: 20 Pages, 3 Figure
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