446 research outputs found
Chaos from turbulence: stochastic-chaotic equilibrium in turbulent convection at high Rayleigh numbers
It is shown that correlation function of the mean wind velocity generated by
a turbulent thermal convection (Rayleigh number ) exhibits
exponential decay with a very long correlation time, while corresponding
largest Lyapunov exponent is certainly positive. These results together with
the reconstructed phase portrait indicate presence of chaotic component in the
examined mean wind. Telegraph approximation is also used to study relative
contribution of the chaotic and stochastic components to the mean wind
fluctuations and an equilibrium between these components has been studied in
detail
Fermi acceleration in time-dependent rectangular billiards due to multiple passages through resonances
We consider a slowly rotating rectangular billiard with moving boundaries and
use the canonical perturbation theory to describe the dynamics of a billiard
particle. In the process of slow evolution certain resonance conditions can be
satisfied. Correspondingly, phenomena of scattering on a resonance and capture
into a resonance happen in the system. These phenomena lead to destruction of
adiabatic invariance and to unlimited acceleration of the particle.Comment: 20 pages. Presented on School-Conference "Mathematics and Physics of
Billiard-Like Systems" (Ubatuba, 2011). Accepted to Chao
Electron heating in the laser and static electric and magnetic fields
A 2D slab approximation of the interactions of electrons with intense
linearly polarized laser radiation and static electric and magnetic fields is
widely used for both numerical simulations and simplified semi-analytical
models. It is shown that in this case electron dynamics can be conveniently
described in the framework of 3/2 dimensional Hamiltonian approach. The
electron acceleration beyond a standard ponderomotive scaling, caused by the
synergistic effects of the laser and static electro-magnetic fields, is due to
an onset of stochastic electron motion
Synthesis of nitroxyl radical by direct nucleophilic functionalization of a C-H bond in the azadiene systems
Cyclic dinitrones underwent nucleophilic substitution of the hydrogen atom in the reaction with a paramagnetic carbanion, the lithium derivative of 4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazol-1-oxyl 3-oxide, to give polyfunctional nitronyl nitroxyls. © 2012 Springer Science+Business Media New York
Directed current due to broken time-space symmetry
We consider the classical dynamics of a particle in a one-dimensional
space-periodic potential U(X) = U(X+2\pi) under the influence of a
time-periodic space-homogeneous external field E(t)=E(t+T). If E(t) is neither
symmetric function of t nor antisymmetric under time shifts , an ensemble of trajectories with zero current at t=0 yields a nonzero
finite current as . We explain this effect using symmetry
considerations and perturbation theory. Finally we add dissipation (friction)
and demonstrate that the resulting set of attractors keeps the broken symmetry
property in the basins of attraction and leads to directed currents as well.Comment: 2 figure
On chaotic behavior of gravitating stellar shells
Motion of two gravitating spherical stellar shells around a massive central
body is considered. Each shell consists of point particles with the same
specific angular momenta and energies. In the case when one can neglect the
influence of gravitation of one ("light") shell onto another ("heavy") shell
("restricted problem") the structure of the phase space is described. The
scaling laws for the measure of the domain of chaotic motion and for the
minimal energy of the light shell sufficient for its escape to infinity are
obtained.Comment: e.g.: 12 pages, 8 figures, CHAOS 2005 Marc
Nonlinear Mirror and Weibel modes: peculiarities of quasi-linear dynamics
A theory for nonlinear evolution of the mirror modes near
the instability threshold is developed. It is shown that during initial
stage the major instability saturation is provided by the flattening of the
velocity distribution function in the vicinity of small parallel ion
velocities. The relaxation scenario in this case is accompanied by rapid
attenuation of resonant particle interaction which is replaced by a weaker
adiabatic interaction with mirror modes. The saturated plasma state can be
considered as a magnetic counterpart to electrostatic BGK modes. After
quasi-linear saturation a further nonlinear scenario is controlled by the
mode coupling effects and nonlinear variation of the ion Larmor radius. Our
analytical model is verified by relevant numerical simulations. Test
particle and PIC simulations indeed show that it is a modification of
distribution function at small parallel velocities that results in fading
away of free energy driving the mirror mode. The similarity with resonant
Weibel instability is discussed
Electrical excitation of shock and soliton-like waves in two-dimensional electron channels
We study electrical excitation of nonlinear plasma waves in heterostructures
with two-dimensional electron channels and with split gates, and the
propagation of these waves using hydrodynamic equations for electron transport
coupled with two-dimensional Poisson equation for self-consistent electric
potential. The term related to electron collisions with impurities and phonons
as well as the term associated with viscosity are included into the
hydrodynamic equations. We demonstrate the formation of shock and soliton-like
waves as a result of the evolution of strongly nonuniform initial electron
density distribution. It is shown that the shock wave front and the shape of
soliton-like pulses pronouncedly depend on the coefficient of viscosity, the
thickness of the gate layer and the nonuniformity of the donor distribution
along the channel. The electron collisions result in damping of the shock and
soliton-like waves, while they do not markedly affect the thickness of the
shock wave front.Comment: 9 pages, 11 figure
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