Multiplier Sequences for Simple Sets of Polynomials

In this paper we give a new characterization of simple sets of polynomials B with the property that the set of B-multiplier sequences contains all Q-multiplier sequence for every simple set Q. We characterize sequences of real numbers which are multiplier sequences for every simple set Q, and obtain some results toward the partitioning of the set of classical multiplier sequences

Comment on "Finite Size Corrections to the Radiation Reaction Force in Classical Electrodynamics" [arXiv:1005.2617]

In [1, arXiv:1005.2617] effective field theory methods have been employed to compute the equations of motion of a spherically symmetric charged shell of radius R, taking into account the radiation reaction force exerted by the shell's own electromagnetic field up to O(R^2). The authors of Ref. [1] have stated that the known result for the self force of the shell as can be found from Eq. (16.28) of the textbook of Jackson [2] (see also Chap. 4 in the review of Pearle [3]) is incorrect, in that the term linear in R should be absent. We claim that this conclusion of Ref. [1] is incorrect, and that the textbook result, Eq. (1) does hold.Comment: 1 pag

Gravitational waves from binaries on unbound orbits

A generalized true anomaly-type parametrization, convenient to describe both bound and open orbits of a two-body system in general relativity is introduced. A complete description of the time evolution of both the radial and of the angular equations of a binary system taking into account the first order post-newtonian (1PN) is given. The gravitational radiation field emitted by the system is computed in the 1PN approximation including higher multipole moments beyond the standard quadrupole term. The gravitational waveforms in the time domain are explicitly given up to the 1PN order for unbound orbits, but the results are also illustrated on binaries on elliptic orbits with special attention given to the effects of eccentricity.Comment: 27 pages, 10 figures, to appear in Phys. Rev.

Negative radiation pressure exerted on kinks

The interaction of a kink and a monochromatic plane wave in one dimensional scalar field theories is studied. It is shown that in a large class of models the radiation pressure exerted on the kink is negative, i.e. the kink is {\sl pulled} towards the source of the radiation. This effect has been observed by numerical simulations in the $\phi^4$ model, and it is explained by a perturbative calculation assuming that the amplitude of the incoming wave is small. Quite importantly the effect is shown to be robust against small perturbations of the $\phi^4$ model. In the sine-Gordon (sG) model the time averaged radiation pressure acting on the kink turns out to be zero. The results of the perturbative computations in the sG model are shown to be in full agreement with an analytical solution corresponding to the superposition of a sG kink with a cnoidal wave. It is also demonstrated that the acceleration of the kink satisfies Newton's law.Comment: 23 pages, 8 figures, LaTeX/RevTe

Long-term variation in distribution of sunspot groups

We studied the relation between the distribution of sunspot groups and the Gleissberg cycle. As the magnetic field is related to the area of the sunspot groups, we used area-weighted sunspot group data. On the one hand, we confirm the previously reported long-term cyclic behaviour of the sum of the northern and southern sunspot group mean latitudes, although we found a somewhat longer period (P~104 years). We introduced the difference between the ensemble average area of sunspot groups for the two hemispheres, which turns out to show similar behaviour. We also investigated a further aspect of the Gleissberg cycle where while in the 19th century the consecutive Schwabe cycles are sharply separated from each other, one century later the cycles overlap each other more and more.Comment: 4 page

On the Stability of Gravitating Nonabelian Monopoles

The behaviour of magnetic monopole solutions of the Einstein-Yang-Mills-Higgs equations subject to linear spherically symmetric perturbations is studied. Using Jacobi's criterion some of the monopoles are shown to be unstable. Furthermore the numerical results and analytical considerations indicate the existence of a set of stable solutions.Comment: 9 pages, 7 figures, minor change

Static spherically symmetric monopole solutions in the presence of a dilaton field

A numerical study of static spherically symmetric monople solutions of a spontaneously broken SU(2) gauge theory coupled to a dilaton field is presented. Regular solutions seem to exist only up to a maximal value of the dilaton coupling. In addition to the generalization of the 't Hooft-Polyakov monopole a discrete family of regular solutions is found, corresponding to radial excitations, absent in the theory without dilaton.Comment: 9 pages (incl. 14 figures in eps format) Latex. Figures are to be decompressed from figs.uu included here as an uuencoded file. Cause of resubmission:problem with the previously uuencoded fil

Computation of the radiation amplitude of oscillons

The radiation loss of small amplitude oscillons (very long-living, spatially localized, time dependent solutions) in one dimensional scalar field theories is computed in the small-amplitude expansion analytically using matched asymptotic series expansions and Borel summation. The amplitude of the radiation is beyond all orders in perturbation theory and the method used has been developed by Segur and Kruskal in Phys. Rev. Lett. 58, 747 (1987). Our results are in good agreement with those of long time numerical simulations of oscillons.Comment: 22 pages, 9 figure

Some Recent Developments on Kink Collisions and Related Topics

We review recent works on modeling of dynamics of kinks in 1+1 dimensional $\phi^4$ theory and other related models, like sine-Gordon model or $\phi^6$ theory. We discuss how the spectral structure of small perturbations can affect the dynamics of non-perturbative states, such as kinks or oscillons. We describe different mechanisms, which may lead to the occurrence of the resonant structure in the kink-antikink collisions. We explain the origin of the radiation pressure mechanism, in particular, the appearance of the negative radiation pressure in the $\phi^4$ and $\phi^6$ models. We also show that the process of production of the kink-antikink pairs, induced by radiation is chaotic.Comment: 26 pages, 9 figures; invited chapter to "A dynamical perspective on the {\phi}4 model: Past, present and future", Eds. P.G. Kevrekidis and J. Cuevas-Maraver; Springer book class with svmult.cls include

Tidal and rotational effects in the perturbations of hierarchical triple stellar systems. II. Eccentric systems - the case of AS Camelopardalis

We study the perturbations of a relatively close third star on a tidally distorted eccentric eclipsing binary. We consider both the observational consequences of the variations of the orbital elements and the interactions of the stellar rotation with the orbital revolution in the presence of dissipation. We concentrate mainly on the effect of a hypothetical third companion on both the real, and the observed apsidal motion period. We investigate how the observed period derived mainly from some variants of the O-C relates to the real apsidal motion period. We carried out both analytical and numerical investigations and give the time variations of the orbital elements of the binary both in the dynamical and the observational reference frames. We give the direct analytical form of an eclipsing O-C affected simultaneously by the mutual tidal forces and the gravitational interactions with a tertiary. We also integrated numerically simultaneously the orbital and rotational equations for the possible hierarchical triple stellar system AS Camelopardalis. We find that there is a significant domain of the possible hierarchical triple system configurations, where both the dynamical and the observational effects tend to measure longer apsidal advance rate than is expected theoretically. This happens when the mutual inclination of the close and the wide orbits is large, and the orbital plane of the tertiary almost coincides with the plane of the sky. We also obtain new numerical results on the interaction of the orbital evolution and stellar rotation in such triplets. The most important fact is that resonances might occur as the stellar rotational rate varies during the dissipation-driven synchronization process...Comment: 33 pages, 12 figures (reduced quality!), accepted for publication for Astronomy and Astrophysic