Poissonian resetting of subdiffusion in a linear potential

Resetting a stochastic process is an important problem describing the evolution of physical, biological and other systems which are continually returned to their some fixed point different from their initial position. We consider the motion of a subdiffusive particle with a constant drift under Poissonian resetting. In this model the stochastic process is Brownian motion subordinated by an inverse infinitely divisible process (subordinator). Although this approach includes a wide class of subdiffusive system with Poissonian resetting by using different subordinators, each of such systems has a stationary state with the asymmetric Laplace distribution in which the scale and asymmetric parameters depend on the Laplace exponent of used subordinators. Moreover, the mean time for the particle to reach a target is finite and has a minimum, optimal with respect to the resetting rate. Features of Levy motion under this resetting and the influence of a linear potential are discussed.Comment: 14 pages, 5 figure

Beam propagation in a Randomly Inhomogeneous Medium

An integro-differential equation describing the angular distribution of beams is analyzed for a medium with random inhomogeneities. Beams are trapped because inhomogeneities give rise to wave localization at random locations and random times. The expressions obtained for the mean square deviation from the initial direction of beam propagation generalize the "3/2 law".Comment: 4 page

Free-free absorption parameters of Cassiopeia A from low-frequency interferometric observations

Context. Cassiopeia A is one of the most extensively studied supernova remnants (SNRs) in our Galaxy. The analysis of its spectral features with the help of low frequency observations plays an important role for understanding the evolution of the radio source through the propagation of synchrotron emission to observers through the SNR environment and the interstellar medium. Aims. In this paper we present measurements of the integrated spectrum of Cas A to characterize the properties of free-free absorption towards this SNR. We also add new measurements to track its slowly evolving and decreasing integrated flux density. Methods. We use the Giant Ukrainian radio telescope (GURT) for measuring the continuum spectrum of Cassiopeia A within the frequency range of 16-72 MHz. The radio flux density of Cassiopeia A relative to the reference source of the radio galaxy Cygnus A has been measured on May-October, 2019 with two subarrays of the GURT, used as a two-element correlation interferometer. Results. We determine magnitudes of emission measure, electron temperature and an average number of charges of the ions for both internal and external absorbing ionized gas towards in Cassiopeia A. Generally, their values are close to the ones suggested by Arias et al. (2018), although for some there are slight differences. In the absence of clumping we find the unshocked ejecta of M = 2.61 solar mass at the electron density of 15.3 cm^-3 has a gas temperature of T=100 K. If the clumping factor is 0.67, then the unshocked ejecta of 0.96 solar mass the electron density of 18.7 cm^-3. Conclusions. The integrated flux density spectrum of Cassiopeia A obtained with the GURT interferometric observations is consistent with the theoretical model within measurement errors and also reasonably consistent with other recent results in the literature.Comment: 9 pages, 9 figures, 2 table

Twist of fractional oscillations

Using the method of the Laplace transform, we consider fractional oscillations. They are obtained by the time-clock randomization of ordinary harmonic vibrations. In contrast to sine and cosine, the functions describing the fractional oscillations exhibit a finite number of damped oscillations with an algebraic decay. Their fractional differential equation is derived.Comment: 12 pages, 2 figure