88 research outputs found
Equation-Free Dynamic Renormalization: Self-Similarity in Multidimensional Particle System Dynamics
We present an equation-free dynamic renormalization approach to the
computational study of coarse-grained, self-similar dynamic behavior in
multidimensional particle systems. The approach is aimed at problems for which
evolution equations for coarse-scale observables (e.g. particle density) are
not explicitly available. Our illustrative example involves Brownian particles
in a 2D Couette flow; marginal and conditional Inverse Cumulative Distribution
Functions (ICDFs) constitute the macroscopic observables of the evolving
particle distributions.Comment: 7 pages, 5 figure
Macrospin Models of Spin Transfer Dynamics
The current-induced magnetization dynamics of a spin valve are studied using
a macrospin (single domain) approximation and numerical solutions of a
generalized Landau-Lifshitz-Gilbert equation. For the purpose of quantitative
comparison with experiment [Kiselev {\it et al.} Nature {\bf 425}, 380 (2003)],
we calculate the resistance and microwave power as a function of current and
external field including the effects of anisotropies, damping, spin-transfer
torque, thermal fluctuations, spin-pumping, and incomplete absorption of
transverse spin current. While many features of experiment appear in the
simulations, there are two significant discrepancies: the current dependence of
the precession frequency and the presence/absence of a microwave quiet magnetic
phase with a distinct magnetoresistance signature. Comparison is made with
micromagnetic simulations designed to model the same experiment.Comment: 14 pages, 14 figures. Email [email protected] for a
pdf with higher quality figure
Numerical schemes for continuum models of reaction-diffusion systems subject to internal noise
We present new numerical schemes to integrate stochastic partial differential
equations which describe the spatio-temporal dynamics of reaction-diffusion
(RD) problems under the effect of internal fluctuations. The schemes conserve
the nonnegativity of the solutions and incorporate the Poissonian nature of
internal fluctuations at small densities, their performance being limited by
the level of approximation of density fluctuations at small scales. We apply
the new schemes to two different aspects of the Reggeon model namely, the study
of its non-equilibrium phase transition and the dynamics of fluctuating pulled
fronts. In the latter case, our approach allows to reproduce quantitatively for
the first time microscopic properties within the continuum model.Comment: 5 pages, 3 figures, Accepted for publication in Physical Review E as
a Rapid Communicatio
Spectral density in resonance region and analytic confinement
We study the role of finite widths of resonances in a nonlocal version of the
Wick-Cutkosky model. The spectrum of bound states is known analytically in this
model and forms linear Regge tragectories. We compute the widths of resonances,
calculate the spectral density in an extension of the Breit-Wigner {\it ansatz}
and discuss a mechanism for the damping of unphysical exponential growth of
observables at high energy due to finite widths of resonances.Comment: 13 pages, RevTeX, 6 figures. Revised version with typographical
corrections and additional comments in conclusion
Factorizing the hard and soft spectator scattering contributions for the nucleon form factor F_1 at large Q^2
We investigate the soft spectator scattering contribution for the FF .
We focus our attention on factorization of the hard-collinear scale corresponding to transition from SCET-I to SCET-II. We compute the
leading order jet functions and find that the convolution integrals over the
soft fractions are logarithmically divergent. This divergency is the
consequence of the boost invariance and does not depend on the model of the
soft correlation function describing the soft spectator quarks. Using as
example a two-loop diagram we demonstrated that such a divergency corresponds
to the overlap of the soft and collinear regions. As a result one obtains large
rapidity logarithm which must be included in the correct factorization
formalism. We conclude that a consistent description of the factorization for
implies the end-point collinear divergencies in the hard and soft
spectator contributions, i.e. convolution integrals with respect to collinear
fractions are not well-defined. Such scenario can only be realized when the
twist-3 nucleon distribution amplitude has specific end-point behavior which
differs from one expected from the evolution of the nucleon distribution
amplitude. Such behavior leads to the violation of the collinear factorization
for the hard spectator scattering contribution. We suggest that the soft
spectator scattering and chiral symmetry breaking provide the mechanism
responsible for the violation of collinear factorization in case of form factor
.Comment: 25 pages, 6 figures, text is improved, few typos corrected, one
figure added, statement about end-point behavior of the nucleon DA is
formulated more accuratel
Scaling of waves in the Bak-Tang-Wiesenfeld sandpile model
We study probability distributions of waves of topplings in the
Bak-Tang-Wiesenfeld model on hypercubic lattices for dimensions D>=2. Waves
represent relaxation processes which do not contain multiple toppling events.
We investigate bulk and boundary waves by means of their correspondence to
spanning trees, and by extensive numerical simulations. While the scaling
behavior of avalanches is complex and usually not governed by simple scaling
laws, we show that the probability distributions for waves display clear power
law asymptotic behavior in perfect agreement with the analytical predictions.
Critical exponents are obtained for the distributions of radius, area, and
duration, of bulk and boundary waves. Relations between them and fractal
dimensions of waves are derived. We confirm that the upper critical dimension
D_u of the model is 4, and calculate logarithmic corrections to the scaling
behavior of waves in D=4. In addition we present analytical estimates for bulk
avalanches in dimensions D>=4 and simulation data for avalanches in D<=3. For
D=2 they seem not easy to interpret.Comment: 12 pages, 17 figures, submitted to Phys. Rev.
Universality in sandpiles
We perform extensive numerical simulations of different versions of the
sandpile model. We find that previous claims about universality classes are
unfounded, since the method previously employed to analyze the data suffered a
systematic bias. We identify the correct scaling behavior and conclude that
sandpiles with stochastic and deterministic toppling rules belong to the same
universality class.Comment: 4 pages, 4 ps figures; submitted to Phys. Rev.
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