On a Periodic Soliton Cellular Automaton

We propose a box and ball system with a periodic boundary condition (pBBS). The time evolution rule of the pBBS is represented as a Boolean recurrence formula, an inverse ultradiscretization of which is shown to be equivalent with the algorithm of the calculus for the 2Nth root. The relations to the pBBS of the combinatorial R matrix of ${U'}_q(A_N^{(1)})$ are also discussed.Comment: 17 pages, 5 figure

Detection of extrasolar planets by the large deployable reflector

The best wavelength for observing Jupiter-size planetary companions to stars other than the Sun is one at which a planet's thermal emission is strongest; typically this would occur in the far-infrared region. It is assumed that the orbiting infrared telescope used is diffraction-limited so that the resolution of the planet from the central star is accomplished in the wings of the star's Airy pattern. Proxima Centauri, Barnard's Star, Wolf 359, and Epsilon Eridani are just a few of the many nearest main-sequence stars that could be studied with the large deployable relfector (LDR). The detectability of a planet improves for warmer planets and less luminous stars; therefore, planets around white dwarfs and those young planets which have sufficient internal gravitational energy release so as to cause a significant increase in their temperatures are considered. If white dwarfs are as old as they are usually assumed to be (5-10 billion yr), then only the nearest white dwarf (Sirius B) is within the range of LDR. The Ursa Major cluster and Perseu cluster are within LDR's detection range mainly because of their proximity and young age, respectively

Exploring Vacuum Structure around Identity-Based Solutions

We explore the vacuum structure in bosonic open string field theory expanded around an identity-based solution parameterized by $a(>=-1/2)$. Analyzing the expanded theory using level truncation approximation up to level 20, we find that the theory has the tachyon vacuum solution for $a>-1/2$. We also find that, at $a=-1/2$, there exists an unstable vacuum solution in the expanded theory and the solution is expected to be the perturbative open string vacuum. These results reasonably support the expectation that the identity-based solution is a trivial pure gauge configuration for $a>-1/2$, but it can be regarded as the tachyon vacuum solution at $a=-1/2$.Comment: 12 pages, 5 figures; new numerical data up to level (20,60) included; Contribution to the proceedings of "Second International Conference on String Field Theory and Related Aspects" (Steklov Mathematical Institute, Moscow, Russia, April 12-19, 2009

Modified Spin Wave Analysis of Low Temperature Properties of Spin-1/2 Frustrated Ferromagnetic Ladder

Low temperature properties of the spin-1/2 frustrated ladder with ferromagnetic rungs and legs, and two different antiferromagnetic next nearest neighbor interaction are investigated using the modified spin wave approximation in the region with ferromagnetic ground state. The temperature dependence of the magnetic susceptibility and magnetic structure factors is calculated. The results are consistent with the numerical exact diagonalization results in the intermediate temperature range. Below this temperature range, the finite size effect is significant in the numerical diagonalization results, while the modified spin wave approximation gives more reliable results. The low temperature properties near the limit of the stability of the ferromagnetic ground state are also discussed.Comment: 9 pages, 8 figure

Separation of colour degree of freedom from dynamics in a soliton cellular automaton

We present an algorithm to reduce the coloured box-ball system, a one dimensional integrable cellular automaton described by motions of several colour (kind) of balls, into a simpler monochrome system. This algorithm extracts the colour degree of freedom of the automaton as a word which turns out to be a conserved quantity of this dynamical system. It is based on the theory of crystal basis and in particular on the tensor products of sl_n crystals of symmetric and anti-symmetric tensor representations.Comment: 19 page

Max-Plus Algebra for Complex Variables and Its Application to Discrete Fourier Transformation

A generalization of the max-plus transformation, which is known as a method to derive cellular automata from integrable equations, is proposed for complex numbers. Operation rules for this transformation is also studied for general number of complex variables. As an application, the max-plus transformation is applied to the discrete Fourier transformation. Stretched coordinates are introduced to obtain the max-plus transformation whose imaginary part coinsides with a phase of the discrete Fourier transformation

Monte Carlo Simulations of Globular Cluster Evolution - II. Mass Spectra, Stellar Evolution and Lifetimes in the Galaxy

We study the dynamical evolution of globular clusters using our new 2-D Monte Carlo code, and we calculate the lifetimes of clusters in the Galactic environment. We include the effects of a mass spectrum, mass loss in the Galactic tidal field, and stellar evolution. We consider initial King models containing N = 10^5 - 3x10^5 stars, and follow the evolution up to core collapse, or disruption, whichever occurs first. We find that the lifetimes of our models are significantly longer than those obtained using 1-D Fokker-Planck (F-P) methods. We also find that our results are in very good agreement with recent 2-D F-P calculations, for a wide range of initial conditions. Our results show that the direct mass loss due to stellar evolution can significantly accelerate the mass loss through the tidal boundary, causing most clusters with a low initial central concentration (Wo <~ 3) to disrupt quickly in the Galactic tidal field. Only clusters born with high initial central concentrations (Wo >~ 7) or steep initial mass functions are likely to survive to the present and undergo core collapse. We also study the orbital characteristics of escaping stars, and find that the velocity distribution of escaping stars in collapsing clusters looks significantly different from the distribution in disrupting clusters. We calculate the lifetime of a cluster on an eccentric orbit in the Galaxy, such that it fills its Roche lobe only at perigalacticon. We find that such an orbit can extend the lifetime by at most a factor of a few compared to a circular orbit in which the cluster fills its Roche lobe at all times.Comment: 32 pages, including 10 figures, to appear in ApJ, minor corrections onl

Entropy production by Q-ball decay for diluting long-lived charged particles

The cosmic abundance of a long-lived charged particle such as a stau is tightly constrained by the catalyzed big bang nucleosynthesis. One of the ways to evade the constraints is to dilute those particles by a huge entropy production. We evaluate the dilution factor in a case that non-relativistic matter dominates the energy density of the universe and decays with large entropy production. We find that large Q balls can do the job, which is naturally produced in the gauge-mediated supersymmetry breaking scenario.Comment: 8 pages, 1 figur

Factorization, reduction and embedding in integrable cellular automata

Factorized dynamics in soliton cellular automata with quantum group symmetry is identified with a motion of particles and anti-particles exhibiting pair creation and annihilation. An embedding scheme is presented showing that the D^{(1)}_n-automaton contains, as certain subsectors, the box-ball systems and all the other automata associated with the crystal bases of non-exceptional affine Lie algebras. The results extend the earlier ones to higher representations by a certain reduction and to a wider class of boundary conditions.Comment: LaTeX2e, 20 page

Fundamental Cycle of a Periodic Box-Ball System

We investigate a soliton cellular automaton (Box-Ball system) with periodic boundary conditions. Since the cellular automaton is a deterministic dynamical system that takes only a finite number of states, it will exhibit periodic motion. We determine its fundamental cycle for a given initial state.Comment: 28 pages, 6 figure