430 research outputs found
Pattern Formation Induced by Time-Dependent Advection
We study pattern-forming instabilities in reaction-advection-diffusion
systems. We develop an approach based on Lyapunov-Bloch exponents to figure out
the impact of a spatially periodic mixing flow on the stability of a spatially
homogeneous state. We deal with the flows periodic in space that may have
arbitrary time dependence. We propose a discrete in time model, where reaction,
advection, and diffusion act as successive operators, and show that a mixing
advection can lead to a pattern-forming instability in a two-component system
where only one of the species is advected. Physically, this can be explained as
crossing a threshold of Turing instability due to effective increase of one of
the diffusion constants
Heating of Micro-protrusions in Accelerating Structures
The thermal and field emission of electrons from protrusions on metal
surfaces is a possible limiting factor on the performance and operation of
high-gradient room temperature accelerator structures. We present here the
results of extensive numerical simulations of electrical and thermal behavior
of protrusions. We unify the thermal and field emission in the same numerical
framework, describe bounds for the emission current and geometric enhancement,
then we calculate the Nottingham and Joule heating terms and solve the heat
equation to characterize the thermal evolution of emitters under RF electric
field. Our findings suggest that, heating is entirely due to the Nottingham
effect, that thermal runaway scenarios are not likely, and that high RF
frequency causes smaller swings in temperature and cooler tips. We build a
phenomenological model to account for the effect of space charge and show that
space charge eliminates the possibility of tip melting, although near melting
temperatures reached.Comment: 8 pages, 10 figure
The effect of short ray trajectories on the scattering statistics of wave chaotic systems
In many situations, the statistical properties of wave systems with chaotic
classical limits are well-described by random matrix theory. However,
applications of random matrix theory to scattering problems require
introduction of system specific information into the statistical model, such as
the introduction of the average scattering matrix in the Poisson kernel. Here
it is shown that the average impedance matrix, which also characterizes the
system-specific properties, can be expressed in terms of classical trajectories
that travel between ports and thus can be calculated semiclassically.
Theoretical results are compared with numerical solutions for a model
wave-chaotic system
Scattering a pulse from a chaotic cavity: Transitioning from algebraic to exponential decay
The ensemble averaged power scattered in and out of lossless chaotic cavities
decays as a power law in time for large times. In the case of a pulse with a
finite duration, the power scattered from a single realization of a cavity
closely tracks the power law ensemble decay initially, but eventually
transitions to an exponential decay. In this paper, we explore the nature of
this transition in the case of coupling to a single port. We find that for a
given pulse shape, the properties of the transition are universal if time is
properly normalized. We define the crossover time to be the time at which the
deviations from the mean of the reflected power in individual realizations
become comparable to the mean reflected power. We demonstrate numerically that,
for randomly chosen cavity realizations and given pulse shapes, the probability
distribution function of reflected power depends only on time, normalized to
this crossover time.Comment: 23 pages, 5 figure
Scalar Decay in Chaotic Mixing
I review the local theory of mixing, which focuses on infinitesimal blobs of
scalar being advected and stretched by a random velocity field. An advantage of
this theory is that it provides elegant analytical results. A disadvantage is
that it is highly idealised. Nevertheless, it provides insight into the
mechanism of chaotic mixing and the effect of random fluctuations on the rate
of decay of the concentration field of a passive scalar.Comment: 35 pages, 15 figures. Springer-Verlag conference style svmult.cls
(included). Published in "Transport in Geophysical Flows: Ten Years After,"
Proceedings of the Grand Combin Summer School, 14-24 June 2004, Valle
d'Aosta, Italy. Fixed some typo
Dynamics and Pattern Formation in Large Systems of Spatially-Coupled Oscillators with Finite Response Times
We consider systems of many spatially distributed phase oscillators that
interact with their neighbors. Each oscillator is allowed to have a different
natural frequency, as well as a different response time to the signals it
receives from other oscillators in its neighborhood. Using the ansatz of Ott
and Antonsen (Ref. \cite{OA1}) and adopting a strategy similar to that employed
in the recent work of Laing (Ref. \cite{Laing2}), we reduce the microscopic
dynamics of these systems to a macroscopic partial-differential-equation
description. Using this macroscopic formulation, we numerically find that
finite oscillator response time leads to interesting spatio-temporal dynamical
behaviors including propagating fronts, spots, target patterns, chimerae,
spiral waves, etc., and we study interactions and evolutionary behaviors of
these spatio-temporal patterns
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