340 research outputs found
Velocity fluctuations of noisy reaction fronts propagating into a metastable state: testing theory in stochastic simulations
The position of a reaction front, propagating into a metastable state,
fluctuates because of the shot noise of reactions and diffusion. A recent
theory [B. Meerson, P.V. Sasorov, and Y. Kaplan, Phys. Rev. E 84, 011147
(2011)] gave a closed analytic expression for the front diffusion coefficient
in the weak noise limit. Here we test this theory in stochastic simulations
involving reacting and diffusing particles on a one-dimensional lattice. We
also investigate a small noise-induced systematic shift of the front velocity
compared to the prediction from the spatially continuous deterministic
reaction-diffusion equation.Comment: 5 pages, 5 figure
Reducing multiphoton ionization in a linearly polarized microwave field by local control
We present a control procedure to reduce the stochastic ionization of
hydrogen atom in a strong microwave field by adding to the original Hamiltonian
a comparatively small control term which might consist of an additional set of
microwave fields. This modification restores select invariant tori in the
dynamics and prevents ionization. We demonstrate the procedure on the
one-dimensional model of microwave ionization.Comment: 8 page
Formation and evolution of density singularities in hydrodynamics of inelastic gases
We use ideal hydrodynamics to investigate clustering in a gas of
inelastically colliding spheres. The hydrodynamic equations exhibit a new type
of finite-time density blowup, where the gas pressure remains finite. The
density blowups signal formation of close-packed clusters. The blowup dynamics
are universal and describable by exact analytic solutions continuable beyond
the blowup time. These solutions show that dilute hydrodynamic equations yield
a powerful effective description of a granular gas flow with close-packed
clusters, described as finite-mass point-like singularities of the density.
This description is similar in spirit to the description of shocks in ordinary
ideal gas dynamics.Comment: 4 pages, 3 figures, final versio
Stochastic ionization through noble tori: Renormalization results
We find that chaos in the stochastic ionization problem develops through the
break-up of a sequence of noble tori. In addition to being very accurate, our
method of choice, the renormalization map, is ideally suited for analyzing
properties at criticality. Our computations of chaos thresholds agree closely
with the widely used empirical Chirikov criterion
Normal scaling in globally conserved interface-controlled coarsening of fractal clusters
Globally conserved interface-controlled coarsening of fractal clusters
exhibits dynamic scale invariance and normal scaling. This is demonstrated by a
numerical solution of the Ginzburg-Landau equation with a global conservation
law. The sharp-interface limit of this equation is volume preserving motion by
mean curvature. The scaled form of the correlation function has a power-law
tail accommodating the fractal initial condition. The coarsening length
exhibits normal scaling with time. Finally, shrinking of the fractal clusters
with time is observed. The difference between global and local conservation is
discussed.Comment: 4 pages, 3 eps figure
Large Fluctuations and Fixation in Evolutionary Games
We study large fluctuations in evolutionary games belonging to the
coordination and anti-coordination classes. The dynamics of these games,
modeling cooperation dilemmas, is characterized by a coexistence fixed point
separating two absorbing states. We are particularly interested in the problem
of fixation that refers to the possibility that a few mutants take over the
entire population. Here, the fixation phenomenon is induced by large
fluctuations and is investigated by a semi-classical WKB
(Wentzel-Kramers-Brillouin) theory generalized to treat stochastic systems
possessing multiple absorbing states. Importantly, this method allows us to
analyze the combined influence of selection and random fluctuations on the
evolutionary dynamics \textit{beyond} the weak selection limit often considered
in previous works. We accurately compute, including pre-exponential factors,
the probability distribution function in the long-lived coexistence state and
the mean fixation time necessary for a few mutants to take over the entire
population in anti-coordination games, and also the fixation probability in the
coordination class. Our analytical results compare excellently with extensive
numerical simulations. Furthermore, we demonstrate that our treatment is
superior to the Fokker-Planck approximation when the selection intensity is
finite.Comment: 17 pages, 10 figures, to appear in JSTA
Counter-propagating radiative shock experiments on the Orion laser and the formation of radiative precursors
We present results from new experiments to study the dynamics of radiative
shocks, reverse shocks and radiative precursors. Laser ablation of a solid
piston by the Orion high-power laser at AWE Aldermaston UK was used to drive
radiative shocks into a gas cell initially pressurised between and $1.0 \
bar with different noble gases. Shocks propagated at {80 \pm 10 \ km/s} and
experienced strong radiative cooling resulting in post-shock compressions of {
\times 25 \pm 2}. A combination of X-ray backlighting, optical self-emission
streak imaging and interferometry (multi-frame and streak imaging) were used to
simultaneously study both the shock front and the radiative precursor. These
experiments present a new configuration to produce counter-propagating
radiative shocks, allowing for the study of reverse shocks and providing a
unique platform for numerical validation. In addition, the radiative shocks
were able to expand freely into a large gas volume without being confined by
the walls of the gas cell. This allows for 3-D effects of the shocks to be
studied which, in principle, could lead to a more direct comparison to
astrophysical phenomena. By maintaining a constant mass density between
different gas fills the shocks evolved with similar hydrodynamics but the
radiative precursor was found to extend significantly further in higher atomic
number gases (\sim4$ times further in xenon than neon). Finally, 1-D and 2-D
radiative-hydrodynamic simulations are presented showing good agreement with
the experimental data.Comment: HEDLA 2016 conference proceeding
Conditioned stochastic particle systems and integrable quantum spin systems
We consider from a microscopic perspective large deviation properties of
several stochastic interacting particle systems, using their mapping to
integrable quantum spin systems. A brief review of recent work is given and
several new results are presented: (i) For the general disordered symmectric
exclusion process (SEP) on some finite lattice conditioned on no jumps into
some absorbing sublattice and with initial Bernoulli product measure with
density we prove that the probability of no absorption event
up to microscopic time can be expressed in terms of the generating function
for the particle number of a SEP with particle injection and empty initial
lattice. Specifically, for the symmetric simple exclusion process on conditioned on no jumps into the origin we obtain the explicit first and
second order expansion in of and also to first order in
the optimal microscopic density profile under this conditioning. For the
disordered ASEP on the finite torus conditioned on a very large current we show
that the effective dynamics that optimally realizes this rare event does not
depend on the disorder, except for the time scale. For annihilating and
coalescing random walkers we obtain the generating function of the number of
annihilated particles up to time , which turns out to exhibit some universal
features.Comment: 25 page
The effect of parallel static and microwave electric fields on excited hydrogen atoms
Motivated by recent experiments we analyse the classical dynamics of a
hydrogen atom in parallel static and microwave electric fields. Using an
appropriate representation and averaging approximations we show that resonant
ionisation is controlled by a separatrix, and provide necessary conditions for
a dynamical resonance to affect the ionisation probability.
The position of the dynamical resonance is computed using a high-order
perturbation series, and estimate its radius of convergence. We show that the
position of the dynamical resonance does not coincide precisely with the
ionisation maxima, and that the field switch-on time can dramatically affect
the ionisation signal which, for long switch times, reflects the shape of an
incipient homoclinic. Similarly, the resonance ionisation time can reflect the
time-scale of the separatrix motion, which is therefore longer than
conventional static field Stark ionisation. We explain why these effects should
be observed in the quantum dynamics.
PACs: 32.80.Rm, 33.40.+f, 34.10.+x, 05.45.Ac, 05.45.MtComment: 47 pages, 20 figure
Interstellar MHD Turbulence and Star Formation
This chapter reviews the nature of turbulence in the Galactic interstellar
medium (ISM) and its connections to the star formation (SF) process. The ISM is
turbulent, magnetized, self-gravitating, and is subject to heating and cooling
processes that control its thermodynamic behavior. The turbulence in the warm
and hot ionized components of the ISM appears to be trans- or subsonic, and
thus to behave nearly incompressibly. However, the neutral warm and cold
components are highly compressible, as a consequence of both thermal
instability in the atomic gas and of moderately-to-strongly supersonic motions
in the roughly isothermal cold atomic and molecular components. Within this
context, we discuss: i) the production and statistical distribution of
turbulent density fluctuations in both isothermal and polytropic media; ii) the
nature of the clumps produced by thermal instability, noting that, contrary to
classical ideas, they in general accrete mass from their environment; iii) the
density-magnetic field correlation (or lack thereof) in turbulent density
fluctuations, as a consequence of the superposition of the different wave modes
in the turbulent flow; iv) the evolution of the mass-to-magnetic flux ratio
(MFR) in density fluctuations as they are built up by dynamic compressions; v)
the formation of cold, dense clouds aided by thermal instability; vi) the
expectation that star-forming molecular clouds are likely to be undergoing
global gravitational contraction, rather than being near equilibrium, and vii)
the regulation of the star formation rate (SFR) in such gravitationally
contracting clouds by stellar feedback which, rather than keeping the clouds
from collapsing, evaporates and diperses them while they collapse.Comment: 43 pages. Invited chapter for the book "Magnetic Fields in Diffuse
Media", edited by Elisabete de Gouveia dal Pino and Alex Lazarian. Revised as
per referee's recommendation
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