Inverse problems of symbolic dynamics

This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval exchange transformation. Rauzy graphs language can express many important combinatorial and some dynamical properties. In this case combinatorial properties are considered as being generated by substitutional system, and dynamical properties are considered as criteria of superword being generated by interval exchange transformation. As a consequence, one can get a morphic word appearing in interval exchange transformation such that frequencies of letters are algebraic numbers of an arbitrary degree. Concerning multydimensional systems, our main result is the following. Let P(n) be a polynomial, having an irrational coefficient of the highest degree. A word $w$ (w=(w_n), n\in \nit) consists of a sequence of first binary numbers of $\{P(n)\}$ i.e. $w_n=[2\{P(n)\}]$. Denote the number of different subwords of $w$ of length $k$ by $T(k)$ . \medskip {\bf Theorem.} {\it There exists a polynomial $Q(k)$, depending only on the power of the polynomial $P$, such that $T(k)=Q(k)$ for sufficiently great $k$.

Electrodynamics of Magnetars: Implications for the Persistent X-ray Emission and Spindown of the Soft Gamma Repeaters and Anomalous X-ray Pulsars

(ABBREVIATED) We consider the structure of neutron star magnetospheres threaded by large-scale electrical currents, and the effect of resonant Compton scattering by the charge carriers (both electrons and ions) on the emergent X-ray spectra and pulse profiles. In the magnetar model for the SGRs and AXPs, these currents are maintained by magnetic stresses acting deep inside the star. We construct self-similar, force-free equilibria of the current-carrying magnetosphere with a power-law dependence of magnetic field on radius, B ~ r^(-2-p), and show that a large-scale twist softens the radial dependence to p < 1. The spindown torque acting on the star is thereby increased in comparison with a vacuum dipole. We comment on the strength of the surface magnetic field in the SGR and AXP sources, and the implications of this model for the narrow measured distribution of spin periods. A magnetosphere with a strong twist, B_\phi/B_\theta = O(1) at the equator, has an optical depth ~ 1 to resonant cyclotron scattering, independent of frequency (radius), surface magnetic field strength, or charge/mass ratio of the scattering charge. When electrons and ions supply the current, the stellar surface is also heated by the impacting charges at a rate comparable to the observed X-ray output of the SGR and AXP sources, if B_{dipole} ~ 10^{14} G. Redistribution of the emerging X-ray flux at the ion and electron cyclotron resonances will significantly modify the emerging pulse profile and, through the Doppler effect, generate a non-thermal tail to the X-ray spectrum. The sudden change in the pulse profile of SGR 1900+14 after the 27 August 1998 giant flare is related to an enhanced optical depth to electron cyclotron scattering, resulting from a sudden twist imparted to the external magnetic field.Comment: 31 January 2002, minor revisions, new section 5.4.

Gamma Ray Bursts from the Evolved Galactic Nuclei

A new cosmological scenario for the origin of gamma ray bursts (GRBs) is proposed. In our scenario, a highly evolved central core in the dense galactic nucleus is formed containing a subsystem of compact stellar remnants (CSRs), such as neutron stars and black holes. Those subsystems result from the dynamical evolution of dense central stellar clusters in the galactic nuclei through merging of stars, thereby forming (as has been realized by many authors) the short-living massive stars and then CSRs. We estimate the rate of random CSR collisions in the evolved galactic nuclei by taking into account, similar to Quinlan & Shapiro (1987), the dissipative encounters of CSRs, mainly due to radiative losses of gravitational waves, which results in the formation of intermediate short-living binaries, with further coalescence of the companions to produce GRBs. We also consider how the possible presence of a central supermassive black hole, formed in a highly evolved galactic nucleus, influences the CSR binary formation. This scenario does not postulate ad hoc a required number of tight binary neutron stars in the galaxies. Instead, it gives, for the most realistic parameters of the evolved nuclei, the expected rate of GRBs consistent with the observed one, thereby explaining the GRB appearance in a natural way of the dynamical evolution of galactic nuclei. In addition, this scenario provides an opportunity for a cosmological GRB recurrence, previously considered to be a distinctive feature of GRBs of a local origin only. We also discuss some other observational tests of the proposed scenario.Comment: 25 pages, LATEX, uses aasms4.sty, accepted by Ap

Properties of Neutral Charmed Mesons in Proton--Nucleus Interactions at 70 GeV

The results of treatment of data obtained in the SERP-E-184experiment "Investigation of mechanisms of the production of charmed particles in proton-nucleus interactions at 70 GeV and their decays" by irradiating the active target of the SVD-2 facility consisting of carbon, silicon, and lead plates, are presented. After separating a signal from the two-particle decay of neutral charmed mesons and estimating the cross section for charm production at a threshold energy {\sigma}(c\v{c})=7.1 \pm 2.4(stat.) \pm 1.4(syst.) \mub/nucleon, some properties of D mesons are investigated. These include the dependence of the cross section on the target mass number (its A dependence); the behavior of the differential cross sections d{\sigma}/dpt2 and d{\sigma}/dxF; and the dependence of the parameter {\alpha} on the kinematical variables xF, pt2, and plab. The experimental results in question are compared with predictions obtained on the basis of the FRITIOF7.02 code.Comment: 9 pages, 9 figures,3 table

Observation of narrow baryon resonance decaying into pKs0pK^0_s in pA-interactions at 70GeV/c70 GeV/c with SVD-2 setup

SVD-2 experiment data have been analyzed to search for an exotic baryon state, the $\Theta^+$-baryon, in a $pK^0_s$ decay mode at $70 GeV/c$ on IHEP accelerator. The reaction $pA \to pK^0_s+X$ with a limited multiplicity was used in the analysis. The $pK^0_s$ invariant mass spectrum shows a resonant structure with $M=1526\pm3(stat.)\pm 3(syst.) MeV/c^2$ and $\Gamma < 24 MeV/c^2$. The statistical significance of this peak was estimated to be of $5.6 \sigma$. The mass and width of the resonance is compatible with the recently reported $\Theta^+$- baryon with positive strangeness which was predicted as an exotic pentaquark ($uudd\bar{s}$) baryon state. The total cross section for $\Theta^+$ production in pN-interactions for $X_F\ge 0$ was estimated to be $(30\div120) \mu b$ and no essential deviation from A-dependence for inelastic events $(\sim A^{0.7})$ was found.Comment: 8 pages, 7 figures, To be submitted to Yadernaya Fizika. v3-v5 - Some references added, minor typos correcte

Search for Gravitational Wave Bursts from Soft Gamma Repeaters

We present the results of a LIGO search for short-duration gravitational waves (GWs) associated with Soft Gamma Repeater (SGR) bursts. This is the first search sensitive to neutron star f-modes, usually considered the most efficient GW emitting modes. We find no evidence of GWs associated with any SGR burst in a sample consisting of the 27 Dec. 2004 giant flare from SGR 1806-20 and 190 lesser events from SGR 1806-20 and SGR 1900+14 which occurred during the first year of LIGO's fifth science run. GW strain upper limits and model-dependent GW emission energy upper limits are estimated for individual bursts using a variety of simulated waveforms. The unprecedented sensitivity of the detectors allows us to set the most stringent limits on transient GW amplitudes published to date. We find upper limit estimates on the model-dependent isotropic GW emission energies (at a nominal distance of 10 kpc) between 3x10^45 and 9x10^52 erg depending on waveform type, detector antenna factors and noise characteristics at the time of the burst. These upper limits are within the theoretically predicted range of some SGR models.Comment: 6 pages, 1 Postscript figur