On the Perturbation of Self-Adjoint Operators with Absolutely Continuous Spectrum

The perturbation of the linear self-adjoint operator with absolutely continuous spectrum is studied and the inverse problem on finding the perturbation by the given spectrum is solved.Изучен случай возмущения линейного самосопряженного оператора с абсолютно непрерывным спектром, а также решена обратная задача нахождения возмущения по заданному спектру

Cosmic ray photodisintegration and the knee of the spectrum

We explore in some detail the scenario proposed to explain the observed knee of the cosmic ray (CR) spectrum as due to the effects of photodisintegration of the CR nuclei by interactions with optical and soft UV photons in the source region. We show that the photon column densities needed to explain the experimental data are significantly lower than those obtained in previous estimations which neglected multinucleon emission in the photodisintegration process. We also treat more accurately the photodisintegration thresholds, we discuss the effects of photopion production processes and the neutron escape mechanism, identifying the physical processes responsible for the qualitative features of the results. This scenario would require the CR nuclei to traverse column densities of $\sim 5 \times 10^{27}- 2 \times 10^{28}$ eV/cm$^2$ after being accelerated in order to reproduce the observed knee, and predicts that the CR composition should become lighter above $\sim 10^{16}$ eV.Comment: 17 pp. Comments and references added. To appear in Astroparticle Physic

Turbulent diffusion and drift in galactic magnetic fields and the explanation of the knee in the cosmic ray spectrum

We reconsider the scenario in which the knee in the cosmic ray spectrum is explained as due to a change in the escape mechanism of cosmic rays from the Galaxy from one dominated by transverse diffusion to one dominated by drifts. We solve the diffusion equations adopting realistic galactic field models and using diffusion coefficients appropriate for strong turbulence (with a Kolmogorov spectrum of fluctuations) and consistent with the assumed magnetic fields. We show that properly taking into account these effects leads to a natural explanation of the knee in the spectrum, and a transition towards a heavier composition above the knee is predicted.Comment: 17 pp., 6 figures; revised version with minor changes. To appear in JHE

Quiet Sun coronal heating: statistical model

Recent observations of Krucker & Benz (1998) give strong support to Parker's hypothesis (Parker 1988) that small scale dissipative events make the main contribution to quiet Sun coronal heating. They also showed that these small scale events are associated not only with the magnetic network, but also with the cell interiors (Benz & Krucker, 1998). Taking into account in addition the results of the analysis performed by Priest with co-authors (Priest et al. 2000) who demonstrated that the heating is quasi-homogeneous along the arcs we come to the conclusion that the sources driving these dissipative events are also small scale sources. Typically they are of the order of or smaller than the linear scale of the events observed, that is smaller than 2000 km. To describe statistical properties of quiet Sun corona heating by microflares, nanoflares, and even smaller events, we consider a cellular automata model subject to uniform small scale driving and dissipation. The model consists of two elements, the magnetic field source supposed to be associated with the small scale hydrodynamic turbulence convected from the photosphere and local dissipation of small scale currents. The dissipation is assumed to be provided by either anomalous resistivity, when the current density exceeds a certain threshold value, or by the magnetic reconnection. The main problem considered is how the statistical characteristics of dissipated energy flow depend upon characteristics of the magnetic field source and on physical mechanism responsible for the magnetic field dissipation. As the threshold value of current is increased, we observe the transition from Gaussian statistics to power-law type. In addition, we find that the dissipation provided by reconnection results in stronger deviations from Gaussian distribution.Comment: 14 pages, 12 figures, submitted to A&

A possible Universal Origin of Hadronic Cosmic Rays from Ultrarelativistic Ejecta of Bipolar Supernovae

Based on the ``cannonball model'' for gamma-ray bursts of Dar and De Rujula it is proposed that masses of baryonic plasma (``cannonballs''), ejected in bipolar supernova explosions in our Galaxy are the sources of hadronic Galactic cosmic rays (CRs) at all energies. The propagation of the cannonballs in the Galactic disk and halo is studied. Two mechanisms for the acceleration of the observed CRs are proposed. The first is based on ultrarelativistic shocks in the interstellar medium and could accelerate the bulk of CRs up to the ``knee'' energy of 4 x 10(15) eV. The second operates with second-order Fermi acceleration within the cannonball. If the total initial energy of the ejected plasmoids in a SN explosion is 10(53) ergs or higher this second mechanism may explain the CR spectrum above the knee up to the highest observed energies. It is shown that together with plausible assumptions about CR propagation in the Galactic confinement volume the observed spectral indices of the CR spectrum can be theoretically understood to first order. The model allows a natural understanding of various basic CR observations like the absence of the Greisen-Zatsepin cutoff, the anisotropy of arrival directions as function of energy and the small Galactocentric gradient of the CR density.Comment: various corrections, see http://rplaga.tripod.com/CosmicRay/na7_317/referees.html for controversial disussions about this pape

Cosmic ray spectrum and anisotropies from the knee to the second knee

We consider the scenario in which the knee in the cosmic ray spectrum is due to a change in the escape mechanism of cosmic rays from the Galaxy from one dominated by transverse diffusion to one dominated by drifts. We show that this scenario explains not only the changes in spectral slope at the knee and at the second knee, but can also account for the main characteristics of the observed energy dependent anisotropy amplitude and phase of first harmonic in the energy range between $10^{15}$ and $10^{18}$ eV. This provides a useful handle to distinguish this diffusion/drift model from other scenarios proposed to explain the knee in the spectrum.Comment: 13 pages, 3 figures; revised version with minor changes. To appear in JCA

Electron acceleration and heating in collisionless magnetic reconnection

We discuss electron acceleration and heating during collisionless magnetic reconnection by using the results of implicit kinetic simulations of Harris current sheets. We consider and compare electron dynamics in plasmas with different \beta values and perform simulations up to the physical mass ratio. We analyze the typical trajectory of electrons passing through the reconnection region, we study the electron velocity, focusing on the out-of-plane velocity, and we discuss the electron heating along the in-plane and out-of-plane directions

Rigidity dependent knee and cosmic ray induced high energy neutrino fluxes

Scenarios in which the knee of the cosmic ray spectrum depends on the particle rigidities usually predict that the cosmic ray composition becomes heavier above the knee and have associated a change in the spectral slope of each individual nuclear component which is steeper than the change ($\Delta\alpha\simeq 0.3$) observed in the total spectrum. We show that this implies that the very high energy ($E_\nu>10^{14}$ eV) diffuse neutrino fluxes produced by cosmic rays hitting the atmosphere or colliding with the interstellar medium in the Galaxy will be significantly suppressed, making their detection harder but also reducing the background for the search of other (more challenging) astrophysical neutrino sources.Comment: 20 pages, 5 figure

Interpretation and Gas Distribution Net Threat Attack Markov models

This paper will focus on mathematical models to reduce the possibility of gas distribution net threat attacks, in order to avoid environmental damage caused by the siphoning off gas. These models are based on Markov models and theory of graphs. The article also shows some forms of attacks on gas distribution net. Environmental damage includes thermal influence caused by gas inflammation, terrain disturbance, biochemical processes. Among siphoning off gas indicators are: Interference in gas meter; Documentation noncompliance; Gas distribution off-the-meter; Power counter range discrepancy; Gas meter failure; Expired recalibration interval; Gas siphoning; Other discrepancies

About Perturbation of Selfadjoint Operators in Case of Multiple Spectrum

Одне з найважливіших завдань теорії збурень полягає у вивченні спектра збуреного оператора й опису спектральних проекторів цього оператора. У роботі вивчено випадки одновимірного і двовимірного збурення лінійного самоспряженого оператора при умові кратного спектра, а також розв’язано зворотню задачу − знай-дено збурення по заданому спектрові. ; ne of major tasks of perturbation theory is to study spectrum of the perturbed operator and to describe spectral projectors of it. A classic result which gives the solution of this task in finite -dimensional case for operators with a simple spectrum is the Lowner theorem. In this case the fact that it is always possible to find such one-dimensional perturbation on two spectrums of original and perturbed operators, that the spectrum of perturbation will have the prescribed values is an unexpected and nontrivial statement. This work devoted to generalization of this non-trivial fact for operators with a multiple spectrum. In the paper perturbation of linear selfadjoint operator under one -dimensional and two-dimensional perturbation in case of multiple spectrum in finite-dimensional Gilbert space is described and the reverse task is solved. Reverse task in the work is the task of finding the perturbation by the given spectrums of original and perturbed operators