Confinement and diffusion time-scales of CR hadrons in AGN-inflated bubbles

While rich clusters are powerful sources of X-rays, gamma-ray emission from these large cosmic structures has not been detected yet. X-ray radiative energy losses in the central regions of relaxed galaxy clusters are so strong that one needs to consider special sources of energy, likely AGN feedback, to suppress catastrophic cooling of the gas. We consider a model of AGN feedback that postulates that the AGN supplies the energy to the gas by inflating bubbles of relativistic plasma, whose energy content is dominated by cosmic-ray (CR) hadrons. If most of these hadrons can quickly escape the bubbles, then collisions of CRs with thermal protons in the intracluster medium (ICM) should lead to strong gamma-ray emission, unless fast diffusion of CRs removes them from the cluster. Therefore, the lack of detections with modern gamma-ray telescopes sets limits on the confinement time of CR hadrons in bubbles and CR diffusive propagation in the ICM.Comment: 8 pages, 2 figures, accepted for publication in MNRA

An Equivalence Between Adaptive Dynamic Programming With a Critic and Backpropagation Through Time

We consider the adaptive dynamic programming technique called Dual Heuristic Programming (DHP), which is designed to learn a critic function, when using learned model functions of the environment. DHP is designed for optimizing control problems in large and continuous state spaces. We extend DHP into a new algorithm that we call Value-Gradient Learning, VGL(λ), and prove equivalence of an instance of the new algorithm to Backpropagation Through Time for Control with a greedy policy. Not only does this equivalence provide a link between these two different approaches, but it also enables our variant of DHP to have guaranteed convergence, under certain smoothness conditions and a greedy policy, when using a general smooth nonlinear function approximator for the critic. We consider several experimental scenarios including some that prove divergence of DHP under a greedy policy, which contrasts against our proven-convergent algorithm

Clipping in Neurocontrol by Adaptive Dynamic Programming

In adaptive dynamic programming, neurocontrol, and reinforcement learning, the objective is for an agent to learn to choose actions so as to minimize a total cost function. In this paper, we show that when discretized time is used to model the motion of the agent, it can be very important to do clipping on the motion of the agent in the final time step of the trajectory. By clipping, we mean that the final time step of the trajectory is to be truncated such that the agent stops exactly at the first terminal state reached, and no distance further. We demonstrate that when clipping is omitted, learning performance can fail to reach the optimum, and when clipping is done properly, learning performance can improve significantly. The clipping problem we describe affects algorithms that use explicit derivatives of the model functions of the environment to calculate a learning gradient. These include backpropagation through time for control and methods based on dual heuristic programming. However, the clipping problem does not significantly affect methods based on heuristic dynamic programming, temporal differences learning, or policy-gradient learning algorithms

ROSAT X-ray sources and exponential field decay in isolated neutron stars

In this paper we semianalyticaly evaluate influence of the exponential decay of magnetic field on the fate of isolated neutron stars. The fact of ROSAT observations of several X-ray sources, which can be accreting old isolated neutron stars gives us an opportunity to put some limits on the parameters of the exponential decay. We argue, that, if most part of neutron stars have approximately the same decay and initial parameters, then the combinations of the bottom magnetic momentum, $\mu_b$, in the range $\sim 10^{28}-10^{29.5} {\rm G} {\rm cm}^3$ and characteristic time scale, $t_d$, in the range $\sim 10^7-10^8 {\rm yrs}$ for standard initial magnetic momentum, $\mu_0=10^{30} {\rm G} {\rm cm}^3$, can be excluded, because for that sets of parameters neutron stars never come to the stage when accretion of the interstellar medium on their surfaces is possible even for low velocity of neutron stars and relatively high density of the interstellar medium. The region of excluded parameters increases with $\mu_0$ decreasing.Comment: 5 pages, 4 PostScript figures (uses A&A style

Constrains on parameters of magnetic field decay for accreting isolated neutron stars

The influence of exponential magnetic field decay (MFD) on the spin evolution of isolated neutron stars is studied. The ROSAT observations of several X-ray sources, which can be accreting old isolated neutron stars, are used to constrain the exponential and power-law decay parameters. We show that for the exponential decay the ranges of minimum value of magnetic moment, $\mu_b$, and the characteristic decay time, $t_d$, $\sim 10^{29.5}\ge \mu_b \ge 10^{28} {\rm G} {\rm cm}^3$, $\sim 10^8\ge t_d \ge 10^7 {\rm yrs}$ are excluded assuming the standard initial magnetic moment, $\mu_0=10^{30} {\rm G} {\rm cm}^3$. For these parameters, neutron stars would never reach the stage of accretion from the interstellar medium even for a low space velocity of the stars and a high density of the ambient plasma. The range of excluded parameters increases for lower values of $\mu_0$. We also show, that, contrary to exponential MFD, no significant restrictions can be made for the parameters of power-law decay from the statistics of isolated neutron star candidates in ROSAT observations. Isolated neutron stars with constant magnetic fields and initial values of them less than $\mu_0 \sim 10^{29} {\rm G} {\rm cm}^3$ never come to the stage of accretion. We briefly discuss the fate of old magnetars with and without MFD, and describe parameters of old accreting magnetars.Comment: 18 pages, 6 PostScript figures, to be published in the Proceedings of the XXVIII ITEP Winter Schoo

Uncertainty relations in curved spaces

Uncertainty relations for particle motion in curved spaces are discussed. The relations are shown to be topologically invariant. New coordinate system on a sphere appropriate to the problem is proposed. The case of a sphere is considered in details. The investigation can be of interest for string and brane theory, solid state physics (quantum wires) and quantum optics.Comment: published version; phase space structure discussion adde

Evolution of isolated neutron stars in globular clusters: number of Accretors

With a simple model from the point of view of population synthesis we try to verify an interesting suggestion made by Pfahl & Rappaport (2001) that dim sources in globular clusters (GCs) can be isolated accreting neutron stars (NSs). Simple estimates show, that we can expect about 0.5-1 accreting isolated NS per typical GC with $M=10^5 M_{\odot}$ in correspondence with observations. Properties of old accreting isolated NSs in GCs are briefly discussed. We suggest that accreting NSs in GCs experienced significant magnetic field decay.Comment: 6 pages, no figures. Submitted to Astronomical and Astrophysical Transactions (style included

Detecting synchronization of self-sustained oscillators by external driving with varying frequency

We propose a method for detecting the presence of synchronization of self-sustained oscillator by external driving with linearly varying frequency. The method is based on a continuous wavelet transform of the signals of self-sustained oscillator and external force and allows one to distinguish the case of true synchronization from the case of spurious synchronization caused by linear mixing of the signals. We apply the method to driven van der Pol oscillator and to experimental data of human heart rate variability and respiration.Comment: 9 pages, 7 figure