668 research outputs found
Ising Dynamics with Damping
We show for the Ising model that is possible construct a discrete time
stochastic model analogous to the Langevin equation that incorporates an
arbitrary amount of damping. It is shown to give the correct equilibrium
statistics and is then used to investigate nonequilibrium phenomena, in
particular, magnetic avalanches. The value of damping can greatly alter the
shape of hysteresis loops, and for small damping and high disorder, the
morphology of large avalanches can be drastically effected. Small damping also
alters the size distribution of avalanches at criticality.Comment: 8 pages, 8 figures, 2 colum
Bending crystals: Emergence of fractal dislocation structures
We provide a minimal continuum model for mesoscale plasticity, explaining the
cellular dislocation structures observed in deformed crystals. Our dislocation
density tensor evolves from random, smooth initial conditions to form
self-similar structures strikingly similar to those seen experimentally -
reproducing both the fractal morphologies and some features of the scaling of
cell sizes and misorientations analyzed experimentally. Our model provides a
framework for understanding emergent dislocation structures on the mesoscale, a
bridge across a computationally demanding mesoscale gap in the multiscale
modeling program, and a new example of self-similar structure formation in
non-equilibrium systems.Comment: 4 pages, 4 figures, 5 movies (They can be found at
http://www.lassp.cornell.edu/sethna/Plasticity/SelfSimilarity.html .) In
press at Phys. Rev. Let
Nucleation at the DNA supercoiling transition
Twisting DNA under a constant applied force reveals a thermally activated
transition into a state with a supercoiled structure known as a plectoneme.
Using transition state theory, we predict the rate of this plectoneme
nucleation to be of order 10^4 Hz. We reconcile this with experiments that have
measured hopping rates of order 10 Hz by noting that the viscosity of the bead
used to manipulate the DNA limits the measured rate. We find that the intrinsic
bending caused by disorder in the base-pair sequence is important for
understanding the free energy barrier that governs the transition. Both
analytic and numerical methods are used in the calculations. We provide
extensive details on the numerical methods for simulating the elastic rod model
with and without disorder.Comment: 18 pages, 15 figure
Universal Pulse Shape Scaling Function and Exponents: A Critical Test for Avalanche Models applied to Barkhausen Noise
In order to test if the universal aspects of Barkhausen noise in magnetic
materials can be predicted from recent variants of the non-equilibrium zero
temperature Random Field Ising Model (RFIM), we perform a quantitative study of
the universal scaling function derived from the
Barkhausen pulse shape in simulations and experiment. Through data collapses
and scaling relations we determine the critical exponents and
in both simulation and experiment. Although we find agreement
in the critical exponents, we find differences between theoretical and
experimental pulse shape scaling functions as well as between different
experiments.Comment: 19 pages (in preprint format), 5 figures, 1 tabl
Spectral responses in granular compaction
The slow compaction of a gently tapped granular packing is reminiscent of the
low-temperature dynamics of structural and spin glasses. Here, I probe the
dynamical spectrum of granular compaction by measuring a complex
(frequency-dependent) volumetric susceptibility . While the
packing density displays glass-like slow relaxations (aging) and
history-dependence (memory) at low tapping amplitudes, the susceptibility
displays very weak aging effects, and its spectrum shows no
sign of a rapidly growing timescale. These features place in
sharp contrast to its dielectric and magnetic counterparts in structural and
spin glasses; instead, bears close similarities to the complex
specific heat of spin glasses. This, I suggest, indicates the glass-like
dynamics in granular compaction are governed by statistically rare relaxation
processes that become increasingly separated in timescale from the typical
relaxations of the system. Finally, I examine the effect of finite system size
on the spectrum of compaction dynamics. Starting from the ansatz that low
frequency processes correspond to large scale particle rearrangements, I
suggest the observed finite size effects are consistent with the suppression of
large-scale collective rearrangements in small systems.Comment: 18 pages, 17 figures. Submitted to PR
Analysis of wasp-waisted hysteresis loops in magnetic rocks
The random-field Ising model of hysteresis is generalized to dilute magnets
and solved on a Bethe lattice. Exact expressions for the major and minor
hysteresis loops are obtained. In the strongly dilute limit the model provides
a simple and useful understanding of the shapes of hysteresis loops in magnetic
rock samples.Comment: 11 pages, 4 figure
Barkhausen Noise and Critical Scaling in the Demagnetization Curve
The demagnetization curve, or initial magnetization curve, is studied by
examining the embedded Barkhausen noise using the non-equilibrium, zero
temperature random-field Ising model. The demagnetization curve is found to
reflect the critical point seen as the system's disorder is changed. Critical
scaling is found for avalanche sizes and the size and number of spanning
avalanches. The critical exponents are derived from those related to the
saturation loop and subloops. Finally, the behavior in the presence of long
range demagnetizing fields is discussed. Results are presented for simulations
of up to one million spins.Comment: 4 pages, 4 figures, submitted to Physical Review Letter
Critical Hysteresis in Random Field XY and Heisenberg Models
We study zero-temperature hysteresis in random-field XY and Heisenberg models
in the zero-frequency limit of a cyclic driving field. We consider three
distributions of the random field and present exact solutions in the mean field
limit. The results show a strong effect of the form of disorder on critical
hysteresis as well as the shape of hysteresis loops. A discrepancy with an
earlier study based on the renormalization group is resolved.Comment: 10 pages, 6 figures; this is published version (added some text and
references
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