509 research outputs found
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
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
On dissipationless shock waves in a discrete nonlinear Schr\"odinger equation
It is shown that the generalized discrete nonlinear Schr\"odinger equation
can be reduced in a small amplitude approximation to the KdV, mKdV, KdV(2) or
the fifth-order KdV equations, depending on values of the parameters. In
dispersionless limit these equations lead to wave breaking phenomenon for
general enough initial conditions, and, after taking into account small
dispersion effects, result in formation of dissipationless shock waves. The
Whitham theory of modulations of nonlinear waves is used for analytical
description of such waves.Comment: 15 pages, 9 figure
On the mechanism for breaks in the cosmic ray spectrum
The proof of cosmic ray (CR) origin in supernova remnants (SNR) must hinge on
full consistency of the CR acceleration theory with the observations; direct
proof is impossible because of the orbit stochasticity of CR particles. Recent
observations of a number of galactic SNR strongly support the SNR-CR connection
in general and the Fermi mechanism of CR acceleration, in particular. However,
many SNR expand into weakly ionized dense gases, and so a significant revision
of the mechanism is required to fit the data. We argue that strong ion-neutral
collisions in the remnant surrounding lead to the steepening of the energy
spectrum of accelerated particles by \emph{exactly one power}. The spectral
break is caused by a partial evanescence of Alfven waves that confine particles
to the accelerator. The gamma-ray spectrum generated in collisions of the
accelerated protons with the ambient gas is also calculated. Using the recent
Fermi spacecraft observation of the SNR W44 as an example, we demonstrate that
the parent proton spectrum is a classical test particle power law , steepening to at .Comment: APS talk to appear in PoP, 4 figure
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
Cluster magnetic fields from large-scale-structure and galaxy-cluster shocks
The origin of the micro-Gauss magnetic fields in galaxy clusters is one of
the outstanding problem of modern cosmology. We have performed
three-dimensional particle-in-cell simulations of the nonrelativistic Weibel
instability in an electron-proton plasma, in conditions typical of cosmological
shocks. These simulations indicate that cluster fields could have been produced
by shocks propagating through the intergalactic medium during the formation of
large-scale structure or by shocks within the cluster. The strengths of the
shock-generated fields range from tens of nano-Gauss in the intercluster medium
to a few micro-Gauss inside galaxy clusters.Comment: 4 pages, 2 color figure
Analytic model for a frictional shallow-water undular bore
We use the integrable Kaup-Boussinesq shallow water system, modified by a
small viscous term, to model the formation of an undular bore with a steady
profile. The description is made in terms of the corresponding integrable
Whitham system, also appropriately modified by friction. This is derived in
Riemann variables using a modified finite-gap integration technique for the
AKNS scheme. The Whitham system is then reduced to a simple first-order
differential equation which is integrated numerically to obtain an asymptotic
profile of the undular bore, with the local oscillatory structure described by
the periodic solution of the unperturbed Kaup-Boussinesq system. This solution
of the Whitham equations is shown to be consistent with certain jump conditions
following directly from conservation laws for the original system. A comparison
is made with the recently studied dissipationless case for the same system,
where the undular bore is unsteady.Comment: 24 page
Canonical description of ideal magnetohydrodynamic flows and integrals of motion
In the framework of the variational principle the canonical variables
describing ideal magnetohydrodynamic (MHD) flows of general type (i.e., with
spatially varying entropy and nonzero values of all topological invariants) are
introduced. The corresponding complete velocity representation enables us not
only to describe the general type flows in terms of single-valued functions,
but also to solve the intriguing problem of the ``missing'' MHD integrals of
motion. The set of hitherto known MHD local invariants and integrals of motion
appears to be incomplete: for the vanishing magnetic field it does not reduce
to the set of the conventional hydrodynamic invariants. And if the MHD analogs
of the vorticity and helicity were discussed earlier for the particular cases,
the analog of Ertel invariant has been so far unknown. It is found that on the
basis of the new invariants introduced a wide set of high-order invariants can
be constructed. The new invariants are relevant both for the deeper insight
into the problem of the topological structure of the MHD flows as a whole and
for the examination of the stability problems. The additional advantage of the
proposed approach is that it enables one to deal with discontinuous flows,
including all types of possible breaks.Comment: 16 page
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
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