1,540 research outputs found
Stochastic relativistic shock-surfing acceleration
We study relativistic particles undergoing surfing acceleration at
perpendicular shocks. We assume that particles undergo diffusion in the
component of momentum perpendicular to the shock plane due to moderate
fluctuations in the shock electric and magnetic fields. We show that dN/dE, the
number of surfing-accelerated particles per unit energy, attains a power-law
form, dN/dE \propto E^{-b}. We calculate b analytically in the limit of weak
momentum diffusion, and use Monte Carlo test-particle calculations to evaluate
b in the weak, moderate, and strong momentum-diffusion limits.Comment: 20 pages, 6 figures, accepted by ApJ; this version corrects a few
minor typographical error
The chaotic dynamics of comets and the problems of the Oort cloud
The dynamic properties of comets entering the planetary zone from the Oort cloud are discussed. Even a very slight influence of the large planets can trigger stochastic cometary dynamics. Multiple interactions of comets with the large planets produce diffusion of the parameters of cometary orbits and a mean increase in the semi-major axis of comets. Comets are lifted towards the Oort cloud, where collisions with stars begin to play a substantial role. The transport of comets differs greatly from the customary law of diffusion and noticeably alter cometary distribution
Magnetic and density spikes in cosmic ray shock precursors
In shock precursors populated by accelerated cosmic rays (CR), the CR return
current instability is believed to significantly enhance the pre-shock
perturbations of magnetic field. We have obtained fully-nonlinear exact ideal
MHD solutions supported by the CR return current. The solutions occur as
localized spikes of circularly polarized Alfven envelopes (solitons, or
breathers). As the conventional (undriven) solitons, the obtained magnetic
spikes propagate at a speed proportional to their amplitude,
. The sufficiently strong solitons run thus
ahead of the main shock and stand in the precursor, being supported by the
return current. This property of the nonlinear solutions is strikingly
different from the linear theory that predicts non-propagating (that is,
convected downstream) circularly polarized waves. The nonlinear solutions may
come either in isolated pulses (solitons) or in soliton-trains (cnoidal waves).
The morphological similarity of such quasi-periodic soliton chains with
recently observed X-ray stripes in Tycho supernova remnant (SNR) is briefly
discussed. The magnetic field amplification determined by the suggested
saturation process is obtained as a function of decreasing SNR blast wave
velocity during its evolution from the ejecta-dominated to the Sedov-Taylor
stage.Comment: 21 pages, 4 figure
Non-linear effects in the cyclotron resonance of a massless quasi-particle in graphene
We consider the classical motion of a massless quasi-particle in a magnetic
field and under a weak electromagnetic radiation with the frequency .
Due to the non-parabolic, linear energy dispersion, the particle responds not
only at the frequency but generates a broad frequency spectrum around
it. The linewidth of the cyclotron resonance turns out to be very broad even in
a perfectly pure material which allows one to explain recent experimental data
in graphene. It is concluded that the linear response theory does not work in
graphene in finite magnetic fields.Comment: 5 pages, 4 figure
Pick-up ion dynamics at the structured quasi-perpendicular shock
We study the pickup ion dynamics and mechanism of multiple reflection and
acceleration at the structured quasi-perpendicular supercritical shock. The
motion of the pickup ions in the shock is studied analytically and numerically
using the test particle analysis in the model shock front. The analysis shows
that slow pickup ions may be accelerated at the shock ramp to high energies.
The maximum ion energy is determined by the fine structure of the
electro-magnetic field at the shock ramp and decreases when the angle between
magnetic field and shock normal decreases. Evolution of pickup ion distribution
across the nearly-perpendicular shock and pickup ion spectrum is also studied
by direct numerical analysis.Comment: LaTeX (elsart.cls), packages: times,amsmath,amssymb; 15 pages + 13
figures (GIF). To appear in Planetary and Space Science
On fast radial propagation of parametrically excited geodesic acoustic mode
The spatial and temporal evolution of parametrically excited geodesic
acoustic mode (GAM) initial pulse is investigated both analytically and
numerically. Our results show that the nonlinearly excited GAM propagates at a
group velocity which is, typically, much larger than that due to finite ion
Larmor radius as predicted by the linear theory. The nonlinear dispersion
relation of GAM driven by a finite amplitude drift wave pump is also derived,
showing a nonlinear frequency increment of GAM. Further implications of these
findings for interpreting experimental observations are also discussed
VC-saturated set systems
The well-known Sauer lemma states that a family of VC-dimension at most has size at most
. We obtain both random and explicit constructions to
prove that the corresponding saturation number, i.e., the size of the smallest
maximal family with VC-dimension , is at most , and thus is
independent of
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