6,922 research outputs found
Fluctuating hydrodynamics for a discrete Gross-Pitaevskii equation: mapping to Kardar-Parisi-Zhang universality class
We show that several aspects of the low-temperature hydrodynamics of a
discrete Gross-Pitaevskii equation (GPE) can be understood by mapping it to a
nonlinear version of fluctuating hydrodynamics. This is achieved by first
writing the GPE in a hydrodynamic form of a continuity and an Euler equation.
Respecting conservation laws, dissipation and noise due to the system's chaos
are added, thus giving us a nonlinear stochastic field theory in general and
the Kardar-Parisi-Zhang (KPZ) equation in our particular case. This mapping to
KPZ is benchmarked against exact Hamiltonian numerics on discrete GPE by
investigating the non-zero temperature dynamical structure factor and its
scaling form and exponent. Given the ubiquity of the Gross-Pitaevskii equation
(a.k.a. nonlinear Schrodinger equation), ranging from nonlinear optics to cold
gases, we expect this remarkable mapping to the KPZ equation to be of paramount
importance and far reaching consequences.Comment: 6 pages, 2 figure
Diffusive Boundary Layers in the Free-Surface Excitable Medium Spiral
Spiral waves are a ubiquitous feature of the nonequilibrium dynamics of a
great variety of excitable systems. In the limit of a large separation in
timescale between fast excitation and slow recovery, one can reduce the spiral
problem to one involving the motion of a free surface separating the excited
and quiescent phases. In this work, we study the free surface problem in the
limit of small diffusivity for the slow field variable. Specifically, we show
that a previously found spiral solution in the diffusionless limit can be
extended to finite diffusivity, without significant alteration. This extension
involves the creation of a variety of boundary layers which cure all the
undesirable singularities of the aforementioned solution. The implications of
our results for the study of spiral stability are briefly discussed.Comment: 6 pages, submitted to PRE Rapid Com
Fluctuation Induced Instabilities in Front Propagation up a Co-Moving Reaction Gradient in Two Dimensions
We study 2D fronts propagating up a co-moving reaction rate gradient in
finite number reaction-diffusion systems. We show that in a 2D rectangular
channel, planar solutions to the deterministic mean-field equation are stable
with respect to deviations from planarity. We argue that planar fronts in the
corresponding stochastic system, on the other hand, are unstable if the channel
width exceeds a critical value. Furthermore, the velocity of the stochastic
fronts is shown to depend on the channel width in a simple and interesting way,
in contrast to fronts in the deterministic MFE. Thus, fluctuations alter the
behavior of these fronts in an essential way. These affects are shown to be
partially captured by introducing a density cutoff in the reaction rate. Some
of the predictions of the cutoff mean-field approach are shown to be in
quantitative accord with the stochastic results
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