8,214 research outputs found
Persistence exponents for fluctuating interfaces
Numerical and analytic results for the exponent \theta describing the decay
of the first return probability of an interface to its initial height are
obtained for a large class of linear Langevin equations. The models are
parametrized by the dynamic roughness exponent \beta, with 0 < \beta < 1; for
\beta = 1/2 the time evolution is Markovian. Using simulations of
solid-on-solid models, of the discretized continuum equations as well as of the
associated zero-dimensional stationary Gaussian process, we address two
problems: The return of an initially flat interface, and the return to an
initial state with fully developed steady state roughness. The two problems are
shown to be governed by different exponents. For the steady state case we point
out the equivalence to fractional Brownian motion, which has a return exponent
\theta_S = 1 - \beta. The exponent \theta_0 for the flat initial condition
appears to be nontrivial. We prove that \theta_0 \to \infty for \beta \to 0,
\theta_0 \geq \theta_S for \beta
1/2, and calculate \theta_{0,S} perturbatively to first order in an expansion
around the Markovian case \beta = 1/2. Using the exact result \theta_S = 1 -
\beta, accurate upper and lower bounds on \theta_0 can be derived which show,
in particular, that \theta_0 \geq (1 - \beta)^2/\beta for small \beta.Comment: 12 pages, REVTEX, 6 Postscript figures, needs multicol.sty and
epsf.st
The Reaction-Diffusion Front for in One Dimension
We study theoretically and numerically the steady state diffusion controlled
reaction , where currents of and particles
are applied at opposite boundaries. For a reaction rate , and equal
diffusion constants , we find that when the
reaction front is well described by mean field theory. However, for , the front acquires a Gaussian profile - a result of
noise induced wandering of the reaction front center. We make a theoretical
prediction for this profile which is in good agreement with simulation.
Finally, we investigate the intrinsic (non-wandering) front width and find
results consistent with scaling and field theoretic predictions.Comment: 11 pages, revtex, 4 separate PostScript figure
Analysis of the decay
In this paper we study the angular distribution of the rare B decay , which is expected to be observed soon. We use the
standard effective Hamiltonian approach, and use the form factors that have
already been estimated for the corresponding radiative decay . The additional form factors that come into play for the dileptonic
channel are estimated using the large energy effective theory (LEET), which
enables one to relate the additional form factors to the form factors for the
radiative mode. Our results provide, just like in the case of the
resonance, an opportunity for a straightforward comparison of the basic theory
with experimental results which may be expected in the near future for this
channel.Comment: 14 pages, 5 figures; as accepted for Phys. Rev.
Refined Simulations of the Reaction Front for Diffusion-Limited Two-Species Annihilation in One Dimension
Extensive simulations are performed of the diffusion-limited reaction
AB in one dimension, with initially separated reagents. The reaction
rate profile, and the probability distributions of the separation and midpoint
of the nearest-neighbour pair of A and B particles, are all shown to exhibit
dynamic scaling, independently of the presence of fluctuations in the initial
state and of an exclusion principle in the model. The data is consistent with
all lengthscales behaving as as . Evidence of
multiscaling, found by other authors, is discussed in the light of these
findings.Comment: Resubmitted as TeX rather than Postscript file. RevTeX version 3.0,
10 pages with 16 Encapsulated Postscript figures (need epsf). University of
Geneva preprint UGVA/DPT 1994/10-85
Persistence in systems with conserved order parameter
We consider the low-temperature coarsening dynamics of a one-dimensional
Ising ferromagnet with conserved Kawasaki-like dynamics in the domain
representation. Domains diffuse with size-dependent diffusion constant, with . We generalize this model to arbitrary
, and derive an expression for the domain density, with , using a scaling argument. We also
investigate numerically the persistence exponent characterizing the
power-law decay of the number, , of persistent (unflipped) spins at
time , and find where depends on
. We show how the results for and are related to
similar calculations in diffusion-limited cluster-cluster aggregation (DLCA)
where clusters with size-dependent diffusion constant diffuse through an
immobile `empty' phase and aggregate irreversibly on impact. Simulations show
that, while is the same in both models, is different except for
. We also investigate models that interpolate between symmetric
domain diffusion and DLCA.Comment: 9 pages, minor revision
Scaling laws for the movement of people between locations in a large city
Large scale simulations of the movements of people in a ``virtual'' city and
their analyses are used to generate new insights into understanding the dynamic
processes that depend on the interactions between people. Models, based on
these interactions, can be used in optimizing traffic flow, slowing the spread
of infectious diseases or predicting the change in cell phone usage in a
disaster. We analyzed cumulative and aggregated data generated from the
simulated movements of 1.6 million individuals in a computer (pseudo
agent-based) model during a typical day in Portland, Oregon. This city is
mapped into a graph with nodes representing physical locations such
as buildings. Connecting edges model individual's flow between nodes. Edge
weights are constructed from the daily traffic of individuals moving between
locations. The number of edges leaving a node (out-degree), the edge weights
(out-traffic), and the edge-weights per location (total out-traffic) are fitted
well by power law distributions. The power law distributions also fit subgraphs
based on work, school, and social/recreational activities. The resulting
weighted graph is a ``small world'' and has scaling laws consistent with an
underlying hierarchical structure. We also explore the time evolution of the
largest connected component and the distribution of the component sizes. We
observe a strong linear correlation between the out-degree and total
out-traffic distributions and significant levels of clustering. We discuss how
these network features can be used to characterize social networks and their
relationship to dynamic processes.Comment: 18 pages, 10 figure
A theory for investment across defences triggered at different stages of a predator-prey encounter
We introduce a general theoretical description of a combination of defences acting sequentially at different stages in the predatory sequence in order to make predictions about how animal prey should best allocate investment across different defensive stages. We predict that defensive investment will often be concentrated at stages early in the interaction between a predator individual and the prey (especially if investment is concentrated in only one defence, then it will be in the first defence). Key to making this prediction is the assumption that there is a cost to a prey when it has a defence tested by an enemy, for example because this incurs costs of deployment or tested costs as a defence is exposed to the enemies; and the assumption that the investment functions are the same among defences. But if investment functions are different across defences (e.g. the investment efficiency in making resources into defences is higher in later defences than in earlier defences), then the contrary could happen. The framework we propose can be applied to other victim-exploiter systems, such as insect herbivores feeding on plant tissues. This leads us to propose a novel explanation for the observation that herbivory damage is often not well explained by variation in concentrations of toxic plant secondary metabolites. We compare our general theoretical structure with related examples in the literature, and conclude that coevolutionary approaches will be profitable in future work
Quasi-normal modes for doubly rotating black holes
Based on the work of Chen, L\"u and Pope, we derive expressions for the
dimensional metric for Kerr-(A)dS black holes with two independent
rotation parameters and all others set equal to zero: . The Klein-Gordon equation is then explicitly separated on this
background. For this separation results in a radial equation coupled
to two generalized spheroidal angular equations. We then develop a full
numerical approach that utilizes the Asymptotic Iteration Method (AIM) to find
radial Quasi-Normal Modes (QNMs) of doubly rotating flat Myers-Perry black
holes for slow rotations. We also develop perturbative expansions for the
angular quantum numbers in powers of the rotation parameters up to second
order.Comment: RevTeX 4-1, various figure
Noise-induced volatility of collective dynamics
"Noise-induced volatility" refers to a phenomenon of increased level of
fluctuations in the collective dynamics of bistable units in the presence of a
rapidly varying external signal, and intermediate noise levels. The
archetypical signature of this phenomenon is that --beyond the increase in the
level of fluctuations-- the response of the system becomes uncorrelated with
the external driving force, making it different from stochastic resonance.
Numerical simulations and an analytical theory of a stochastic dynamical
version of the Ising model on regular and random networks demonstrate the
ubiquity and robustness of this phenomenon, which is argued to be a possible
cause of excess volatility in financial markets, of enhanced effective
temperatures in a variety of out-of-equilibrium systems and of strong selective
responses of immune systems of complex biological organisms. Extensive
numerical simulations are compared with a mean-field theory for different
network topologies
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