579 research outputs found
Energy spectra of gamma-rays, electrons and neutrinos produced at interactions of relativistic protons with low energy radiation
We derived simple analytical parametrizations for energy distributions of
photons, electrons, and neutrinos produced in interactions of relativistic
protons with an isotropic monochromatic radiation field. The results on
photomeson processes are obtained using numerical simulations of proton-photon
interactions based on the public available Monte-Carlo code SOPHIA. For
calculations of energy spectra of electrons and positrons from the pair
production (Bethe-Heitler) process we suggest a simple formalism based on the
well-known differential cross-section of the process in the rest frame of the
proton. The analytical presentations of energy distributions of photons and
leptons provide a simple but accurate approach for calculations of broad-band
energy spectra of gamma-rays and neutrinos in cosmic proton accelerators
located in radiation dominated environments.Comment: 17 pages, 21 figures, published in Phys.Rev.D. We have corrected two
misprints in the text. We note that the correct expressions were used for
calculations in the previous versions of the paper, thus the misprints did
not have an impact on the figure
On the spectral shape of radiation due to Inverse Compton Scattering close to the maximum cut-off
The spectral shape of radiation due to Inverse Compton Scattering is
analyzed, in the Thomson and the Klein-Nishina regime, for electron
distributions with exponential cut-off. We derive analytical, asymptotic
expressions for the spectrum close to the maximum cut-off region. We consider
monoenergetic, Planckian and Synchrotron photons as target photon fields. These
approximations provide a direct link between the distribution of parent
electrons and the up-scattered spectrum at the cut-off region.Comment: 27 pages, 15 figures, accepted for publication in Ap
Almost Optimal Streaming Algorithms for Coverage Problems
Maximum coverage and minimum set cover problems --collectively called
coverage problems-- have been studied extensively in streaming models. However,
previous research not only achieve sub-optimal approximation factors and space
complexities, but also study a restricted set arrival model which makes an
explicit or implicit assumption on oracle access to the sets, ignoring the
complexity of reading and storing the whole set at once. In this paper, we
address the above shortcomings, and present algorithms with improved
approximation factor and improved space complexity, and prove that our results
are almost tight. Moreover, unlike most of previous work, our results hold on a
more general edge arrival model. More specifically, we present (almost) optimal
approximation algorithms for maximum coverage and minimum set cover problems in
the streaming model with an (almost) optimal space complexity of
, i.e., the space is {\em independent of the size of the sets or
the size of the ground set of elements}. These results not only improve over
the best known algorithms for the set arrival model, but also are the first
such algorithms for the more powerful {\em edge arrival} model. In order to
achieve the above results, we introduce a new general sketching technique for
coverage functions: This sketching scheme can be applied to convert an
-approximation algorithm for a coverage problem to a
(1-\eps)\alpha-approximation algorithm for the same problem in streaming, or
RAM models. We show the significance of our sketching technique by ruling out
the possibility of solving coverage problems via accessing (as a black box) a
(1 \pm \eps)-approximate oracle (e.g., a sketch function) that estimates the
coverage function on any subfamily of the sets
Synchro-curvature radiation of charged particles in the strong curved magnetic fields
It is generally believed that the radiation of relativistic particles in a
curved magnetic field proceeds in either the synchrotron or the curvature
radiation modes. In this paper we show that in strong curved magnetic fields a
significant fraction of the energy of relativistic electrons can be radiated
away in the intermediate, the so-called synchro-curvature regime. Because of
the persistent change of the trajectory curvature, the radiation varies with
the frequency of particle gyration. While this effect can be ignored in the
synchrotron and curvature regimes, the variability plays a key role in the
formation of the synchro-curvature radiation. Using the Hamiltonian formalism,
we find that the particle trajectory has the form of a helix wound around the
drift trajectory. This allows us to calculate analytically the intensity and
energy distribution of prompt radiation in the general case of magnetic
bremsstrahlung in the curved magnetic field. We show that the transition to the
limit of the synchrotron and curvature radiation regimes is determined by the
relation between the drift velocity and the component of the particle velocity
perpendicular to the drift trajectory. The detailed numerical calculations,
which take into account the energy losses of particles, confirm the principal
conclusions based on the simplified analytical treatment of the problem, and
allow us to analyze quantitatively the transition between different radiation
regimes for a broad range of initial pitch angles. We argue that in the case of
realization of specific configurations of the electric and magnetic fields, the
gamma-ray emission of the pulsar magnetospheres can be dominated by the
component radiated in the synchro-curvature regime.Comment: this article supersedes arXiv:1207.6903 and arXiv:1305.078
On transition of propagation of relativistic particles from the ballistic to the diffusion regime
A stationary distribution function that describes the entire processes of
propagation of relativistic particles, including the transition between the
ballistic and diffusion regimes, is obtained. The spacial component of the
constructed function satisfies to the first two moments of the Boltzmann
equation. The angular part of the distribution provides accurate values for the
angular moments derived from the Boltzmann equation, and gives a correct
expression in the limit of small-angle approximation. Using the derived
function, we studied the gamma-ray images produced through the interaction
of relativistic particles with gas clouds in the proximity of the accelerator.
In general, the morphology and the energy spectra of gamma-rays significantly
deviate from the "standard" results corresponding to the propagation of
relativistic particles strictly in the diffusion regime
Mechanics and kinetics in the Friedmann-Lemaitre-Robertson-Walker space-times
Using the standard canonical formalism, the equations of mechanics and
kinetics in the Friedmann-Lemaitre-Robertson-Walker (FLRW) space-times in
Cartesian coordinates have been obtained. The transformation law of the
generalized momentum under the shift of the origin of the coordinate system has
been found, and the form invariance of the Hamiltonian function relative to the
shift transformation has been proved. The general solution of the collisionless
Boltzmann equation has been found. In the case of the homogeneous distribution
the solutions of the kinetic equation for several simple, but important for
applications, cases have been obtained
Point Charge Self-Energy in the General Relativity
Singularities in the metric of the classical solutions to the Einstein
equations (Schwarzschild, Kerr, Reissner -- Nordstr\"om and Kerr -- Newman
solutions) lead to appearance of generalized functions in the Einstein tensor
that are not usually taken into consideration. The generalized functions can be
of a more complex nature than the Dirac \d-function. To study them, a
technique has been used based on a limiting solution sequence. The solutions
are shown to satisfy the Einstein equations everywhere, if the energy-momentum
tensor has a relevant singular addition of non-electromagnetic origin. When the
addition is included, the total energy proves finite and equal to , while
for the Kerr and Kerr--Newman solutions the angular momentum is .
As the Reissner--Nordstr\"om and Kerr--Newman solutions correspond to the point
charge in the classical electrodynamics, the result obtained allows us to view
the point charge self-energy divergence problem in a new fashion.Comment: VI Fridmann Seminar, France, Corsica, Corgeze, 2004, LaTeX, 6 pages,
2 fige
Angular, spectral, and time distributions of highest energy protons and associated secondary gamma-rays and neutrinos propagating through extragalactic magnetic and radiation fields
The angular, spectral and temporal features of the highest energy protons and
accompanying them secondary neutrinos and synchrotron gamma-rays propagating
through the intergalactic magnetic and radiation fields are studied using the
analytical solutions of the Boltzmann transport equation obtained in the limit
of the small-angle and continuous-energy-loss approximation.Comment: 21 pages, 13 figure
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