6,238 research outputs found
Asymptotic Scaling of the Diffusion Coefficient of Fluctuating "Pulled" Fronts
We present a (heuristic) theoretical derivation for the scaling of the
diffusion coefficient for fluctuating ``pulled'' fronts. In agreement
with earlier numerical simulations, we find that as ,
approaches zero as , where is the average number of particles per
correlation volume in the stable phase of the front. This behaviour of
stems from the shape fluctuations at the very tip of the front, and is
independent of the microscopic model.Comment: Some minor algebra corrected, to appear in Rapid Comm., Phys. Rev.
Fluctuating "Pulled" Fronts: the Origin and the Effects of a Finite Particle Cutoff
Recently it has been shown that when an equation that allows so-called pulled
fronts in the mean-field limit is modelled with a stochastic model with a
finite number of particles per correlation volume, the convergence to the
speed for is extremely slow -- going only as .
In this paper, we study the front propagation in a simple stochastic lattice
model. A detailed analysis of the microscopic picture of the front dynamics
shows that for the description of the far tip of the front, one has to abandon
the idea of a uniformly translating front solution. The lattice and finite
particle effects lead to a ``stop-and-go'' type dynamics at the far tip of the
front, while the average front behind it ``crosses over'' to a uniformly
translating solution. In this formulation, the effect of stochasticity on the
asymptotic front speed is coded in the probability distribution of the times
required for the advancement of the ``foremost bin''. We derive expressions of
these probability distributions by matching the solution of the far tip with
the uniformly translating solution behind. This matching includes various
correlation effects in a mean-field type approximation. Our results for the
probability distributions compare well to the results of stochastic numerical
simulations. This approach also allows us to deal with much smaller values of
than it is required to have the asymptotics to be valid.Comment: 26 pages, 11 figures, to appear in Phys. rev.
Duality in interacting particle systems and boson representation
In the context of Markov processes, we show a new scheme to derive dual
processes and a duality function based on a boson representation. This scheme
is applicable to a case in which a generator is expressed by boson creation and
annihilation operators. For some stochastic processes, duality relations have
been known, which connect continuous time Markov processes with discrete state
space and those with continuous state space. We clarify that using a generating
function approach and the Doi-Peliti method, a birth-death process (or discrete
random walk model) is naturally connected to a differential equation with
continuous variables, which would be interpreted as a dual Markov process. The
key point in the derivation is to use bosonic coherent states as a bra state,
instead of a conventional projection state. As examples, we apply the scheme to
a simple birth-coagulation process and a Brownian momentum process. The
generator of the Brownian momentum process is written by elements of the
SU(1,1) algebra, and using a boson realization of SU(1,1) we show that the same
scheme is available.Comment: 13 page
Correlation Functions for an Elastic String in a Random Potential: Instanton Approach
We develop an instanton technique for calculations of correlation functions
characterizing statistical behavior of the elastic string in disordered media
and apply the proposed approach to correlations of string free energies
corresponding to different low-lying metastable positions. We find high-energy
tails of correlation functions for the case of long-range disorder (the
disorder correlation length well exceeds the characteristic distance between
the sequential string positions) and short-range disorder with the correlation
length much smaller then the characteristic string displacements. The former
case refers to energy distributions and correlations on the distances below the
Larkin correlation length, while the latter describes correlations on the large
spatial scales relevant for the creep dynamics.Comment: 5 pages; 1 .eps figure include
The urban economy as a scale-free network
We present empirical evidence that land values are scale-free and introduce a
network model that reproduces the observations. The network approach to urban
modelling is based on the assumption that the market dynamics that generates
land values can be represented as a growing scale-free network. Our results
suggest that the network properties of trade between specialized activities
causes land values, and likely also other observables such as population, to be
power law distributed. In addition to being an attractive avenue for further
analytical inquiry, the network representation is also applicable to empirical
data and is thereby attractive for predictive modelling.Comment: Submitted to Phys. Rev. E. 7 pages, 3 figures. (Minor typos and
details fixed
Quasi-stationary regime of a branching random walk in presence of an absorbing wall
A branching random walk in presence of an absorbing wall moving at a constant
velocity undergoes a phase transition as the velocity of the wall
varies. Below the critical velocity , the population has a non-zero
survival probability and when the population survives its size grows
exponentially. We investigate the histories of the population conditioned on
having a single survivor at some final time . We study the quasi-stationary
regime for when is large. To do so, one can construct a modified
stochastic process which is equivalent to the original process conditioned on
having a single survivor at final time . We then use this construction to
show that the properties of the quasi-stationary regime are universal when
. We also solve exactly a simple version of the problem, the
exponential model, for which the study of the quasi-stationary regime can be
reduced to the analysis of a single one-dimensional map.Comment: 2 figures, minor corrections, one reference adde
The VLT-FLAMES Tarantula Survey XXI. Stellar spin rates of O-type spectroscopic binaries
The initial distribution of spin rates of massive stars is a fingerprint of
their elusive formation process. It also sets a key initial condition for
stellar evolution and is thus an important ingredient in stellar population
synthesis. So far, most studies have focused on single stars. Most O stars are
however found in multiple systems. By establishing the spin-rate distribution
of a sizeable sample of O-type spectroscopic binaries and by comparing the
distributions of binary sub-populations with one another as well as with that
of presumed single stars in the same region, we aim to constrain the initial
spin distribution of O stars in binaries, and to identify signatures of the
physical mechanisms that affect the evolution of the massive stars spin rates.
We use ground-based optical spectroscopy obtained in the framework of the
VLT-FLAMES Tarantula Survey (VFTS) to establish the projected equatorial
rotational velocities (\vrot) for components of 114 spectroscopic binaries in
30 Doradus. The \vrot\ values are derived from the full-width at half-maximum
(FWHM) of a set of spectral lines, using a FWHM vs. \vrot\ calibration that we
derive based on previous line analysis methods applied to single O-type stars
in the VFTS sample. The overall \vrot\ distribution of the primary stars
resembles that of single O-type stars in the VFTS, featuring a low-velocity
peak (at \vrot < 200 kms) and a shoulder at intermediate velocities (200 <
\vrot < 300 kms). The distributions of binaries and single stars however
differ in two ways. First, the main peak at \vrot \sim100 kms is broader and
slightly shifted toward higher spin rates in the binary distribution compared
to that of the presumed-single stars. Second, the \vrot distribution of
primaries lacks a significant population of stars spinning faster than 300 kms
while such a population is clearly present in the single star sample.Comment: 16 pages, 16 figures, paper accepted in Astronomy & Astrophysic
Noisy traveling waves: effect of selection on genealogies
For a family of models of evolving population under selection, which can be
described by noisy traveling wave equations, the coalescence times along the
genealogical tree scale like , where is the size of the
population, in contrast with neutral models for which they scale like . An
argument relating this time scale to the diffusion constant of the noisy
traveling wave leads to a prediction for which agrees with our
simulations. An exactly soluble case gives trees with statistics identical to
those predicted for mean-field spin glasses in Parisi's theory.Comment: 4 pages, 2 figures New version includes more numerical simulations
and some rewriting of the text presenting our result
The Weakly Pushed Nature of "Pulled" Fronts with a Cutoff
The concept of pulled fronts with a cutoff has been introduced to
model the effects of discrete nature of the constituent particles on the
asymptotic front speed in models with continuum variables (Pulled fronts are
the fronts which propagate into an unstable state, and have an asymptotic front
speed equal to the linear spreading speed of small linear perturbations
around the unstable state). In this paper, we demonstrate that the introduction
of a cutoff actually makes such pulled fronts weakly pushed. For the nonlinear
diffusion equation with a cutoff, we show that the longest relaxation times
that govern the convergence to the asymptotic front speed and profile,
are given by , for
.Comment: 4 pages, 2 figures, submitted to Brief Reports, Phys. Rev.
Shift in the velocity of a front due to a cut-off
We consider the effect of a small cut-off epsilon on the velocity of a
traveling wave in one dimension. Simulations done over more than ten orders of
magnitude as well as a simple theoretical argument indicate that the effect of
the cut-off epsilon is to select a single velocity which converges when epsilon
tends to 0 to the one predicted by the marginal stability argument. For small
epsilon, the shift in velocity has the form K(log epsilon)^(-2) and our
prediction for the constant K agrees very well with the results of our
simulations. A very similar logarithmic shift appears in more complicated
situations, in particular in finite size effects of some microscopic stochastic
systems. Our theoretical approach can also be extended to give a simple way of
deriving the shift in position due to initial conditions in the
Fisher-Kolmogorov or similar equations.Comment: 12 pages, 3 figure
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