214,093 research outputs found
Dynamic criticality far-from-equilibrium: one-loop flow of Burgers-Kardar-Parisi-Zhang systems with broken Galilean invariance
Burgers-Kardar-Parisi-Zhang (KPZ) scaling has recently (re-) surfaced in a
variety of physical contexts, ranging from anharmonic chains to quantum systems
such as open superfluids, in which a variety of random forces may be
encountered and/or engineered. Motivated by these developments, we here provide
a generalization of the KPZ universality class to situations with long-ranged
temporal correlations in the noise, which purposefully break the Galilean
invariance that is central to the conventional KPZ solution. We compute the
phase diagram and critical exponents of the KPZ equation with -noise
(KPZ) in spatial dimensions using the dynamic
renormalization group with a frequency cutoff technique in a one-loop
truncation. Distinct features of KPZ are: (i) a generically
scale-invariant, rough phase at high noise levels that violates
fluctuation-dissipation relations and exhibits hyperthermal statistics {\it
even in d=1}, (ii) a fine-tuned roughening transition at which the flow
fulfills an emergent thermal-like fluctuation-dissipation relation, that
separates the rough phase from (iii) a {\it massive phase} in (in
the interface is always rough). We point out potential connections to
nonlinear hydrodynamics with a reduced set of conservation laws and noisy
quantum liquids.Comment: 29 pages, 11 figures, 1 table, 54 references, v2 as publishe
Two-dimensional droplet spreading over random topographical substrates
We examine theoretically the effects of random topographical substrates on
the motion of two-dimensional droplets via appropriate statistical approaches.
Different random substrate families are represented as stationary random
functions. The variance of the droplet shift at both early times and in the
long-time limit is deduced and the droplet footprint is found to be a normal
random variable at all times. It is shown that substrate roughness decreases
droplet wetting, illustrating also the tendency of the droplet to slide without
spreading as equilibrium is approached. Our theoretical predictions are
verified by numerical experiments.Comment: 12 pages, 5 figure
Accurate estimators of power spectra in N-body simulations
abridged] A method to rapidly estimate the Fourier power spectrum of a point
distribution is presented. This method relies on a Taylor expansion of the
trigonometric functions. It yields the Fourier modes from a number of FFTs,
which is controlled by the order N of the expansion and by the dimension D of
the system. In three dimensions, for the practical value N=3, the number of
FFTs required is 20. We apply the method to the measurement of the power
spectrum of a periodic point distribution that is a local Poisson realization
of an underlying stationary field. We derive explicit analytic expression for
the spectrum, which allows us to quantify--and correct for--the biases induced
by discreteness and by the truncation of the Taylor expansion, and to bound the
unknown effects of aliasing of the power spectrum. We show that these aliasing
effects decrease rapidly with the order N. The only remaining significant
source of errors is reduced to the unavoidable cosmic/sample variance due to
the finite size of the sample. The analytical calculations are successfully
checked against a cosmological N-body experiment. We also consider the initial
conditions of this simulation, which correspond to a perturbed grid. This
allows us to test a case where the local Poisson assumption is incorrect. Even
in that extreme situation, the third-order Fourier-Taylor estimator behaves
well. We also show how to reach arbitrarily large dynamic range in Fourier
space (i.e., high wavenumber), while keeping statistical errors in control, by
appropriately "folding" the particle distribution.Comment: 18 Pages, 9 Figures. Accepted for publication in MNRAS. The
Fourier-Taylor module as well as the associated power spectrum estimator tool
we propose is available as an F90 package, POWMES, at
http://www.projet-horizon.fr or on request from the author
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