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 $k$.

Particle Physics Probes Of Extra Spacetime Dimensions

The possibility that spacetime is extended beyond the familiar 3+1-dimensions has intrigued physicists for a century. Indeed, the consequences of a dimensionally richer spacetime would be profound. Recently, new theories with higher dimensional spacetimes have been developed to resolve the hierarchy problem in particle physics. These scenarios make distinct predictions which allow for experiment to probe the existence of extra dimensions in new ways. We review the conceptual framework of these scenarios, their implications in collider and short-range gravity experiments, their astrophysical and cosmological effects, as well as the constraints placed on these models from present data.Comment: Submitted to Annual Review of Nuclear and Particle Science, 29 page

Average Emissivity Curve of BATSE Gamma-Ray Bursts with Different Intensities

Six intensity groups with ~150 BATSE gamma-ray bursts each are compared using average emissivity curves. Time-stretch factors for each of the dimmer groups are estimated with respect to the brightest group, which serves as the reference, taking into account the systematics of counts-produced noise effects and choice statistics. A stretching/intensity anti-correlation is found with good statistical significance during the average back slopes of bursts. A stretch factor ~2 is found between the 150 dimmest bursts, with peak flux 4.1 ph cm^{-2} s^{-1}. On the other hand, while a trend of increasing stretching factor may exist for rise fronts for burst with decreasing peak flux from >4.1 ph cm^{-2} s^{-1} down to 0.7 ph cm^{-2} s^{-1}, the magnitude of the stretching factor is less than ~ 1.4 and is therefore inconsistent with stretching factor of back slope.Comment: 21 pages, 3 figures. Accepted to Ap

Fast Ray Tracing of Lunar Digital Elevation Models

Ray-tracing (RT) of Lunar Digital Elevation Models (DEM)'s is performed to virtually derive the degree of radiation incident to terrain as a function of time, orbital and ephemeris constraints [I- 4]. This process is an integral modeling process in lunar polar research and exploration due to the present paucity of terrain information at the poles and mission planning activities for the anticipated spring 2009 launch of the Lunar Reconnaissance Orbiter (LRO). As part of the Lunar Exploration Neutron Detector (LEND) and Lunar Crater Observation and Sensing Satellite (LCROSS) preparations RI methods are used to estimate the critical conditions presented by the combined effects of high latitude, terrain and the moons low obliquity [5-7]. These factors yield low incident solar illumination and subsequently extreme thermal, and radiation conditions. The presented research uses RT methods both for radiation transport modeling in space and regolith related research as well as to derive permanently shadowed regions (PSR)'s in high latitude topographic minima, e.g craters. These regions are of scientific and human exploration interest due to the near constant low temperatures in PSRs, inferred to be < 100 K. Hydrogen is thought to have accumulated in PSR's through the combined effects of periodic cometary bombardment and/or solar wind processes, and the extreme cold which minimizes hydrogen sublimation [8-9]. RT methods are also of use in surface position optimization for future illumination dependent on surface resources e.g. power and communications equipment

Comparison of Image Restoration Methods for Lunar Epithermal Neutron Emission Mapping

Orbital measurements of neutrons by the Lunar Exploring Neutron Detector (LEND) onboard the Lunar Reconnaissance Orbiter are being used to quantify the spatial distribution of near surface hydrogen (H). Inferred H concentration maps have low signal-to-noise (SN) and image restoration (IR) techniques are being studied to enhance results. A single-blind. two-phase study is described in which four teams of researchers independently developed image restoration techniques optimized for LEND data. Synthetic lunar epithermal neutron emission maps were derived from LEND simulations. These data were used as ground truth to determine the relative quantitative performance of the IR methods vs. a default denoising (smoothing) technique. We review and used factors influencing orbital remote sensing of neutrons emitted from the lunar surface to develop a database of synthetic "true" maps for performance evaluation. A prior independent training phase was implemented for each technique to assure methods were optimized before the blind trial. Method performance was determined using several regional root-mean-square error metrics specific to epithermal signals of interest. Results indicate unbiased IR methods realize only small signal gains in most of the tested metrics. This suggests other physically based modeling assumptions are required to produce appreciable signal gains in similar low SN IR applications

Interaction of electric and acoustic vibrations in combustion

The results of experimental studies of the interaction of electrical discharges in the acoustic oscillations in the combustion of isobutane are presented in the article. Electric discharges were created using a pulsed high voltage source at specified intervals. The purpose of the study was to determine the feasibility of using electrical pulse action to control combustion. The study was conducted on the specifically designed pattern of the combustion chamber with a swirl burner in the frequency range from 100 Hz to 1400 Hz. The study found that the method of periodic pulsed electrical influences can be used to control the combustion in the combustion chamber model. There is a steady increase in the amplitude of the oscillations in the combustion chamber model. Effects due to the mechanism of interaction of acoustic waves and oscillations heat release from the combustion zone. Estimated physical mechanism is a periodic change in the concentration of ions in the interaction of the combustion zone with the electric field of high potential. The proposed control method is advantageous in terms of energy costs