67 research outputs found
Systems with Multiplicative Noise: Critical Behavior from KPZ Equation and Numerics
We show that certain critical exponents of systems with multiplicative noise
can be obtained from exponents of the KPZ equation. Numerical simulations in 1d
confirm this prediction, and yield other exponents of the multiplicative noise
problem. The numerics also verify an earlier prediction of the divergence of
the susceptibility over an entire range of control parameter values, and show
that the exponent governing the divergence in this range varies continuously
with control parameter.Comment: Four pages (In Revtex format) with 4 figures (in Postcript
Finite size scaling in the solar wind magnetic field energy density as seen by WIND
Statistical properties of the interplanetary magnetic field fluctuations can provide an important insight into the solar wind turbulent cascade. Recently, analysis of the Probability Density Functions (PDF) of the velocity and magnetic field fluctuations has shown that these exhibit non-Gaussian properties on small time scales while large scale features appear to be uncorrelated. Here we apply the finite size scaling technique to explore the scaling of the magnetic field energy density fluctuations as seen by WIND. We find a single scaling sufficient to collapse the curves over the entire investigated range. The rescaled PDF follow a non Gaussian distribution with asymptotic behavior well described by the Gamma distribution arising from a finite range Lévy walk. Such mono scaling suggests that a Fokker-Planck approach can be applied to study the PDF dynamics. These results strongly suggest the existence of a common, nonlinear process on the time scale up to 26 hours
Period Stabilization in the Busse-Heikes Model of the Kuppers-Lortz Instability
The Busse-Heikes dynamical model is described in terms of relaxational and
nonrelaxational dynamics. Within this dynamical picture a diverging alternating
period is calculated in a reduced dynamics given by a time-dependent
Hamiltonian with decreasing energy. A mean period is calculated which results
from noise stabilization of a mean energy. The consideration of
spatial-dependent amplitudes leads to vertex formation. The competition of
front motion around the vertices and the Kuppers-Lortz instability in
determining an alternating period is discussed.Comment: 28 pages, 11 figure
Real-time DNA microarray analysis
We present a quantification method for affinity-based
DNA microarrays which is based on the
real-time measurements of hybridization kinetics.
This method, i.e. real-time DNA microarrays,
enhances the detection dynamic range of conventional
systems by being impervious to probe
saturation in the capturing spots, washing
artifacts, microarray spot-to-spot variations, and
other signal amplitude-affecting non-idealities. We
demonstrate in both theory and practice that the
time-constant of target capturing in microarrays,
similar to all affinity-based biosensors, is inversely
proportional to the concentration of the target
analyte, which we subsequently use as the fundamental
parameter to estimate the concentration
of the analytes. Furthermore, to empirically
validate the capabilities of this method in practical
applications, we present a FRET-based assay which
enables the real-time detection in gene expression
DNA microarrays
Noise induced transition from an absorbing phase to a regime of stochastic spatiotemporal intermittency
We introduce a stochastic partial differential equation capable of
reproducing the main features of spatiotemporal intermittency (STI).
Additionally the model displays a noise induced transition from laminarity to
the STI regime. We show by numerical simulations and a mean-field analysis that
for high noise intensities the system globally evolves to a uniform absorbing
phase, while for noise intensities below a critical value spatiotemporal
intermittence dominates. A quantitative computation of the loci of this
transition in the relevant parameter space is presented.Comment: 4 pages, 6 eps figures. Submitted to Phys. Rev. Lett. See for
additional information http://imedea.uib.es
Noise Filtering Strategies of Adaptive Signaling Networks: The Case of E. Coli Chemotaxis
Two distinct mechanisms for filtering noise in an input signal are identified
in a class of adaptive sensory networks. We find that the high frequency noise
is filtered by the output degradation process through time-averaging; while the
low frequency noise is damped by adaptation through negative feedback. Both
filtering processes themselves introduce intrinsic noises, which are found to
be unfiltered and can thus amount to a significant internal noise floor even
without signaling. These results are applied to E. coli chemotaxis. We show
unambiguously that the molecular mechanism for the Berg-Purcell time-averaging
scheme is the dephosphorylation of the response regulator CheY-P, not the
receptor adaptation process as previously suggested. The high frequency noise
due to the stochastic ligand binding-unbinding events and the random ligand
molecule diffusion is averaged by the CheY-P dephosphorylation process to a
negligible level in E.coli. We identify a previously unstudied noise source
caused by the random motion of the cell in a ligand gradient. We show that this
random walk induced signal noise has a divergent low frequency component, which
is only rendered finite by the receptor adaptation process. For gradients
within the E. coli sensing range, this dominant external noise can be
comparable to the significant intrinsic noise in the system. The dependence of
the response and its fluctuations on the key time scales of the system are
studied systematically. We show that the chemotaxis pathway may have evolved to
optimize gradient sensing, strong response, and noise control in different time
scalesComment: 15 pages, 4 figure
On the nature of different types of absorbing states
We present a comparison of three different types of Langevin equation
exhibiting absorbing states: the Langevin equation defining the Reggeon field
theory, one with multiplicative noise, and a third type in which the noise is
complex. Each one is found to describe a different underlying physical
mechanism; in particular, the nature of the different absorbing states depends
on the type of noise considered.
By studying the stationary single-site effective potential, we analyze the
impossibility of finding a reaction-diffusion model in the multiplicative noise
universality class. We also discuss some theoretical questions related to the
nature of complex noise, as for example, whether it is necessary or not to
consider a complex equation in order to describe processes as the annihilation
reaction, .Comment: 7 figures, Latex fil
Recent results on multiplicative noise
Recent developments in the analysis of Langevin equations with multiplicative
noise (MN) are reported. In particular, we:
(i) present numerical simulations in three dimensions showing that the MN
equation exhibits, like the Kardar-Parisi-Zhang (KPZ) equation both a weak
coupling fixed point and a strong coupling phase, supporting the proposed
relation between MN and KPZ;
(ii) present dimensional, and mean field analysis of the MN equation to
compute critical exponents;
(iii) show that the phenomenon of the noise induced ordering transition
associated with the MN equation appears only in the Stratonovich representation
and not in the Ito one, and
(iv) report the presence of a new first-order like phase transition at zero
spatial coupling, supporting the fact that this is the minimum model for noise
induced ordering transitions.Comment: Some improvements respect to the first versio
Nonequilibrium wetting
When a nonequilibrium growing interface in the presence of a wall is
considered a nonequilibrium wetting transition may take place. This transition
can be studied trough Langevin equations or discrete growth models. In the
first case, the Kardar-Parisi-Zhang equation, which defines a very robust
universality class for nonequilibrium moving interfaces, with a soft-wall
potential is considered. While in the second, microscopic models, in the
corresponding universality class, with evaporation and deposition of particles
in the presence of hard-wall are studied. Equilibrium wetting is related to a
particular case of the problem, it corresponds to the Edwards-Wilkinson
equation with a potential in the continuum approach or to the fulfillment of
detailed balance in the microscopic models. In this review we present the
analytical and numerical methods used to investigate the problem and the very
rich behavior that is observed with them.Comment: Review, 36 pages, 16 figure
Effects of Fluctuations on Propagating Fronts
Propagating fronts are seen in varieties of non-equilibrium pattern forming
systems in Physics, Chemistry and Biology. In the last two decades, many
researchers have contributed to the understanding of the underlying dynamics of
the propagating fronts. Of these, the deterministic and mean-field dynamics of
the fronts were mostly understood in late 1980s and 1990s. On the other hand,
although the earliest work on the effect of fluctuations on propagating fronts
dates back to early 1980s, the subject of fluctuating fronts did not reach its
adolescence until the mid 1990s. From there onwards the last few years
witnessed a surge in activities in the effect of fluctuations on propagating
fronts. Scores of papers have been written on this subject since then,
contributing to a significant maturity of our understanding, and only recently
a full picture of fluctuating fronts has started to emerge. This review is an
attempt to collect all the works on fluctuating (propagating) fronts in a
coherent and cogent manner in proper perspective. It is based on the idea of
making our knowledge in this field available to a broader audience, and it is
also expected to help to collect bits and pieces of loose thread-ends together
for possible further investigation.Comment: Review article, minor changes, references updated, 114 pages, 37
figures, to appear in Physics Report
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