474 research outputs found
Avalanche Dynamics in Evolution, Growth, and Depinning Models
The dynamics of complex systems in nature often occurs in terms of
punctuations, or avalanches, rather than following a smooth, gradual path. A
comprehensive theory of avalanche dynamics in models of growth, interface
depinning, and evolution is presented. Specifically, we include the Bak-Sneppen
evolution model, the Sneppen interface depinning model, the Zaitsev flux creep
model, invasion percolation, and several other depinning models into a unified
treatment encompassing a large class of far from equilibrium processes. The
formation of fractal structures, the appearance of noise, diffusion with
anomalous Hurst exponents, Levy flights, and punctuated equilibria can all be
related to the same underlying avalanche dynamics. This dynamics can be
represented as a fractal in spatial plus one temporal dimension. We develop
a scaling theory that relates many of the critical exponents in this broad
category of extremal models, representing different universality classes, to
two basic exponents characterizing the fractal attractor. The exact equations
and the derived set of scaling relations are consistent with numerical
simulations of the above mentioned models.Comment: 27 pages in revtex, no figures included. Figures or hard copy of the
manuscript supplied on reques
Revisiting soliton contributions to perturbative amplitudes
Open Access funded by SCOAP3. CP is
a Royal Society Research Fellow and partly supported by the U.S. Department of Energy
under grants DOE-SC0010008, DOE-ARRA-SC0003883 and DOE-DE-SC0007897. ABR
is supported by the Mitchell Family Foundation. We would like to thank the Mitchell
Institute at Texas A&M and the NHETC at Rutgers University respectively for hospitality
during the course of this work. We would also like to acknowledge the Aspen Center for
Physics and NSF grant 1066293 for a stimulating research environment
Avalanches and Correlations in Driven Interface Depinning
We study the critical behavior of a driven interface in a medium with random
pinning forces by analyzing spatial and temporal correlations in a lattice
model recently proposed by Sneppen [Phys. Rev. Lett. {\bf 69}, 3539 (1992)].
The static and dynamic behavior of the model is related to the properties of
directed percolation. We show that, due to the interplay of local and global
growth rules, the usual method of dynamical scaling has to be modified. We
separate the local from the global part of the dynamics by defining a train of
causal growth events, or "avalanche", which can be ascribed a well-defined
dynamical exponent where is the
roughness exponent of the interface. We observe that the avalanche size
distribution obeys a power-law decay with an exponent .Comment: 7 pages, (5 figures available upon request), REVTeX, RUB-TP3-93-0
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
Force fluctuation in a driven elastic chain
We study the dynamics of an elastic chain driven on a disordered substrate
and analyze numerically the statistics of force fluctuations at the depinning
transition. The probability distribution function of the amplitude of the slip
events for small velocities is a power law with an exponent
depending on the driving velocity. This result is in qualitative agreement with
experimental measurements performed on sliding elastic surfaces with
macroscopic asperities. We explore the properties of the depinning transition
as a function of the driving mode (i.e. constant force or constant velocity)
and compute the force-velocity diagram using finite size scaling methods. The
scaling exponents are in excellent agreement with the values expected in
interface models and, contrary to previous studies, we found no difference in
the exponents for periodic and disordered chains.Comment: 8 page
Static and Dynamic Properties of Inhomogeneous Elastic Media on Disordered Substrate
The pinning of an inhomogeneous elastic medium by a disordered substrate is
studied analytically and numerically. The static and dynamic properties of a
-dimensional system are shown to be equivalent to those of the well known
problem of a -dimensional random manifold embedded in -dimensions.
The analogy is found to be very robust, applicable to a wide range of elastic
media, including those which are amorphous or nearly-periodic, with local or
nonlocal elasticity. Also demonstrated explicitly is the equivalence between
the dynamic depinning transition obtained at a constant driving force, and the
self-organized, near-critical behavior obtained by a (small) constant velocity
drive.Comment: 20 pages, RevTeX. Related (p)reprints also available at
http://matisse.ucsd.edu/~hwa/pub.htm
On thermodynamics of N=6 superconformal Chern-Simons theory
We study thermodynamics of N=6 superconformal Chern-Simons theory by
computing quantum corrections to the free energy. We find that in weakly
coupled ABJM theory on R(2) x S(1), the leading correction is non-analytic in
the 't Hooft coupling lambda, and is approximately of order lambda^2
log(lambda)^3. The free energy is expressed in terms of the scalar thermal mass
m, which is generated by screening effects. We show that this mass vanishes to
1-loop order. We then go on to 2-loop order where we find a finite and positive
mass squared m^2. We discuss differences in the calculation between Coulomb and
Lorentz gauge. Our results indicate that the free energy is a monotonic
function in lambda which interpolates smoothly to the N^(3/2) behaviour at
strong coupling.Comment: 29 pages. v2: references added. v3: minor changes, references added,
published versio
Disorder-Induced Critical Phenomena in Hysteresis: Numerical Scaling in Three and Higher Dimensions
We present numerical simulations of avalanches and critical phenomena
associated with hysteresis loops, modeled using the zero-temperature
random-field Ising model. We study the transition between smooth hysteresis
loops and loops with a sharp jump in the magnetization, as the disorder in our
model is decreased. In a large region near the critical point, we find scaling
and critical phenomena, which are well described by the results of an epsilon
expansion about six dimensions. We present the results of simulations in 3, 4,
and 5 dimensions, with systems with up to a billion spins (1000^3).Comment: Condensed and updated version of cond-mat/9609072,``Disorder-Induced
Critical Phenomena in Hysteresis: A Numerical Scaling Analysis'
Hysteresis, Avalanches, and Disorder Induced Critical Scaling: A Renormalization Group Approach
We study the zero temperature random field Ising model as a model for noise
and avalanches in hysteretic systems. Tuning the amount of disorder in the
system, we find an ordinary critical point with avalanches on all length
scales. Using a mapping to the pure Ising model, we Borel sum the
expansion to for the correlation length exponent. We sketch a
new method for directly calculating avalanche exponents, which we perform to
. Numerical exponents in 3, 4, and 5 dimensions are in good
agreement with the analytical predictions.Comment: 134 pages in REVTEX, plus 21 figures. The first two figures can be
obtained from the references quoted in their respective figure captions, the
remaining 19 figures are supplied separately in uuencoded forma
Automated ventricular systems segmentation in brain CT images by combining low-level segmentation and high-level template matching
<p>Abstract</p> <p>Background</p> <p>Accurate analysis of CT brain scans is vital for diagnosis and treatment of Traumatic Brain Injuries (TBI). Automatic processing of these CT brain scans could speed up the decision making process, lower the cost of healthcare, and reduce the chance of human error. In this paper, we focus on automatic processing of CT brain images to segment and identify the ventricular systems. The segmentation of ventricles provides quantitative measures on the changes of ventricles in the brain that form vital diagnosis information.</p> <p>Methods</p> <p>First all CT slices are aligned by detecting the ideal midlines in all images. The initial estimation of the ideal midline of the brain is found based on skull symmetry and then the initial estimate is further refined using detected anatomical features. Then a two-step method is used for ventricle segmentation. First a low-level segmentation on each pixel is applied on the CT images. For this step, both Iterated Conditional Mode (ICM) and Maximum A Posteriori Spatial Probability (MASP) are evaluated and compared. The second step applies template matching algorithm to identify objects in the initial low-level segmentation as ventricles. Experiments for ventricle segmentation are conducted using a relatively large CT dataset containing mild and severe TBI cases.</p> <p>Results</p> <p>Experiments show that the acceptable rate of the ideal midline detection is over 95%. Two measurements are defined to evaluate ventricle recognition results. The first measure is a sensitivity-like measure and the second is a false positive-like measure. For the first measurement, the rate is 100% indicating that all ventricles are identified in all slices. The false positives-like measurement is 8.59%. We also point out the similarities and differences between ICM and MASP algorithms through both mathematically relationships and segmentation results on CT images.</p> <p>Conclusion</p> <p>The experiments show the reliability of the proposed algorithms. The novelty of the proposed method lies in its incorporation of anatomical features for ideal midline detection and the two-step ventricle segmentation method. Our method offers the following improvements over existing approaches: accurate detection of the ideal midline and accurate recognition of ventricles using both anatomical features and spatial templates derived from Magnetic Resonance Images.</p
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