366 research outputs found
Aspects of the Noisy Burgers Equation
The noisy Burgers equation describing for example the growth of an interface
subject to noise is one of the simplest model governing an intrinsically
nonequilibrium problem. In one dimension this equation is analyzed by means of
the Martin-Siggia-Rose technique. In a canonical formulation the morphology and
scaling behavior are accessed by a principle of least action in the weak noise
limit. The growth morphology is characterized by a dilute gas of nonlinear
soliton modes with gapless dispersion law with exponent z=3/2 and a superposed
gas of diffusive modes with a gap. The scaling exponents and a heuristic
expression for the scaling function follow from a spectral representation.Comment: 23 pages,LAMUPHYS LaTeX-file (Springer), 13 figures, and 1 table, to
appear in the Proceedings of the XI Max Born Symposium on "Anomalous
Diffusion: From Basics to Applications", May 20-24, 1998, Ladek Zdroj, Polan
Domain wall mobility in nanowires: transverse versus vortex walls
The motion of domain walls in ferromagnetic, cylindrical nanowires is
investigated numerically by solving the Landau-Lifshitz-Gilbert equation for a
classical spin model in which energy contributions from exchange, crystalline
anisotropy, dipole-dipole interaction, and a driving magnetic field are
considered. Depending on the diameter, either transverse domain walls or vortex
walls are found. The transverse domain wall is observed for diameters smaller
than the exchange length of the given material. Here, the system behaves
effectively one-dimensional and the domain wall mobility agrees with a result
derived for a one-dimensional wall by Slonczewski. For low damping the domain
wall mobility decreases with decreasing damping constant. With increasing
diameter, a crossover to a vortex wall sets in which enhances the domain wall
mobility drastically. For a vortex wall the domain wall mobility is described
by the Walker-formula, with a domain wall width depending on the diameter of
the wire. The main difference is the dependence on damping: for a vortex wall
the domain wall mobility can be drastically increased for small values of the
damping constant up to a factor of .Comment: 5 pages, 6 figure
Marginal Pinning of Quenched Random Polymers
An elastic string embedded in 3D space and subject to a short-range
correlated random potential exhibits marginal pinning at high temperatures,
with the pinning length becoming exponentially sensitive to
temperature. Using a functional renormalization group (FRG) approach we find
, with the
depinning temperature. A slow decay of disorder correlations as it appears in
the problem of flux line pinning in superconductors modifies this result, .Comment: 4 pages, RevTeX, 1 figure inserte
Solitons in the noisy Burgers equation
We investigate numerically the coupled diffusion-advective type field
equations originating from the canonical phase space approach to the noisy
Burgers equation or the equivalent Kardar-Parisi-Zhang equation in one spatial
dimension. The equations support stable right hand and left hand solitons and
in the low viscosity limit a long-lived soliton pair excitation. We find that
two identical pair excitations scatter transparently subject to a size
dependent phase shift and that identical solitons scatter on a static soliton
transparently without a phase shift. The soliton pair excitation and the
scattering configurations are interpreted in terms of growing step and
nucleation events in the interface growth profile. In the asymmetrical case the
soliton scattering modes are unstable presumably toward multi soliton
production and extended diffusive modes, signalling the general
non-integrability of the coupled field equations. Finally, we have shown that
growing steps perform anomalous random walk with dynamic exponent z=3/2 and
that the nucleation of a tip is stochastically suppressed with respect to
plateau formation.Comment: 11 pages Revtex file, including 15 postscript-figure
How strongly do word reading times and lexical decision times correlate? Combining data from eye movement corpora and megastudies
We assess the amount of shared variance between three measures of visual word recognition latencies: eye movement latencies, lexical decision times and naming times. After partialling out the effects of word frequency and word length, two well-documented predictors of word recognition latencies, we see that 7-44% of the variance is uniquely shared between lexical decision times and naming times, depending on the frequency range of the words used. A similar analysis of eye movement latencies shows that the percentage of variance they uniquely share either with lexical decision times or with naming times is much lower. It is 5 – 17% for gaze durations and lexical decision times in studies with target words presented in neutral sentences, but drops to .2% for corpus studies in which eye movements to all words are analysed. Correlations between gaze durations and naming latencies are lower still. These findings suggest that processing times in isolated word processing and continuous text reading are affected by specific task demands and presentation format, and that lexical decision times and naming times are not very informative in predicting eye movement latencies in text reading once the effect of word frequency and word length are taken into account. The difference between controlled experiments and natural reading suggests that reading strategies and stimulus materials may determine the degree to which the immediacy-of-processing assumption and the eye-mind assumption apply. Fixation times are more likely to exclusively reflect the lexical processing of the currently fixated word in controlled studies with unpredictable target words rather than in natural reading of sentences or texts
Update statistics in conservative parallel discrete event simulations of asynchronous systems
We model the performance of an ideal closed chain of L processing elements
that work in parallel in an asynchronous manner. Their state updates follow a
generic conservative algorithm. The conservative update rule determines the
growth of a virtual time surface. The physics of this growth is reflected in
the utilization (the fraction of working processors) and in the interface
width. We show that it is possible to nake an explicit connection between the
utilization and the macroscopic structure of the virtual time interface. We
exploit this connection to derive the theoretical probability distribution of
updates in the system within an approximate model. It follows that the
theoretical lower bound for the computational speed-up is s=(L+1)/4 for L>3.
Our approach uses simple statistics to count distinct surface configuration
classes consistent with the model growth rule. It enables one to compute
analytically microscopic properties of an interface, which are unavailable by
continuum methods.Comment: 15 pages, 12 figure
Towards a Simple Model of Compressible Alfvenic Turbulence
A simple model collisionless, dissipative, compressible MHD (Alfvenic)
turbulence in a magnetized system is investigated. In contrast to more familiar
paradigms of turbulence, dissipation arises from Landau damping, enters via
nonlinearity, and is distributed over all scales. The theory predicts that two
different regimes or phases of turbulence are possible, depending on the ratio
of steepening to damping coefficient (m_1/m_2). For strong damping
(|m_1/m_2|<1), a regime of smooth, hydrodynamic turbulence is predicted. For
|m_1/m_2|>1, steady state turbulence does not exist in the hydrodynamic limit.
Rather, spikey, small scale structure is predicted.Comment: 6 pages, one figure, REVTeX; this version to be published in PRE. For
related papers, see http://sdphpd.ucsd.edu/~medvedev/papers.htm
Non-Linear Stochastic Equations with Calculable Steady States
We consider generalizations of the Kardar--Parisi--Zhang equation that
accomodate spatial anisotropies and the coupled evolution of several fields,
and focus on their symmetries and non-perturbative properties. In particular,
we derive generalized fluctuation--dissipation conditions on the form of the
(non-linear) equations for the realization of a Gaussian probability density of
the fields in the steady state. For the amorphous growth of a single height
field in one dimension we give a general class of equations with exactly
calculable (Gaussian and more complicated) steady states. In two dimensions, we
show that any anisotropic system evolves on long time and length scales either
to the usual isotropic strong coupling regime or to a linear-like fixed point
associated with a hidden symmetry. Similar results are derived for textural
growth equations that couple the height field with additional order parameters
which fluctuate on the growing surface. In this context, we propose
phenomenological equations for the growth of a crystalline material, where the
height field interacts with lattice distortions, and identify two special cases
that obtain Gaussian steady states. In the first case compression modes
influence growth and are advected by height fluctuations, while in the second
case it is the density of dislocations that couples with the height.Comment: 9 pages, revtex
Shear-induced quench of long-range correlations in a liquid mixture
A static correlation function of concentration fluctuations in a (dilute)
binary liquid mixture subjected to both a concentration gradient and uniform
shear flow is investigated within the framework of fluctuating hydrodynamics.
It is shown that a well-known long-range correlation at
large wave numbers crosses over to a weaker divergent one for wave numbers
satisfying , while an asymptotic shear-controlled
power-law dependence is confirmed at much smaller wave numbers given by , where , , and are the
mass concentration, the rate of the shear, the mass diffusivity and the
kinematic viscosity of the mixture, respectively. The result will provide for
the first time the possibility to observe the shear-induced suppression of a
long-range correlation experimentally by using, for example, a low-angle light
scattering technique.Comment: 8pages, 2figure
Renormalization group study of one-dimensional systems with roughening transitions
A recently introduced real space renormalization group technique, developed
for the analysis of processes in the Kardar-Parisi-Zhang universality class, is
generalized and tested by applying it to a different family of surface growth
processes.
In particular, we consider a growth model exhibiting a rich phenomenology
even in one dimension. It has four different phases and a directed percolation
related roughening transition. The renormalization method reproduces extremely
well all the phase diagram, the roughness exponents in all the phases and the
separatrix among them. This proves the versatility of the method and elucidates
interesting physical mechanisms.Comment: Submitted to Phys. Rev.
- …