Site-bond representation and self-duality for totalistic probabilistic cellular automata

We study the one-dimensional two-state totalistic probabilistic cellular automata (TPCA) having an absorbing state with long-range interactions, which can be considered as a natural extension of the Domany-Kinzel model. We establish the conditions for existence of a site-bond representation and self-dual property. Moreover we present an expression of a set-to-set connectedness between two sets, a matrix expression for a condition of the self-duality, and a convergence theorem for the TPCA.Comment: 11 pages, minor corrections, journal reference adde

Weak limits for quantum random walks

We formulate and prove a general weak limit theorem for quantum random walks in one and more dimensions. With $X_n$ denoting position at time $n$, we show that $X_n/n$ converges weakly as $n \to \infty$ to a certain distribution which is absolutely continuous and of bounded support. The proof is rigorous and makes use of Fourier transform methods. This approach simplifies and extends certain preceding derivations valid in one dimension that make use of combinatorial and path integral methods

Wigner formula of rotation matrices and quantum walks

Quantization of a random-walk model is performed by giving a qudit (a multi-component wave function) to a walker at site and by introducing a quantum coin, which is a matrix representation of a unitary transformation. In quantum walks, the qudit of walker is mixed according to the quantum coin at each time step, when the walker hops to other sites. As special cases of the quantum walks driven by high-dimensional quantum coins generally studied by Brun, Carteret, and Ambainis, we study the models obtained by choosing rotation as the unitary transformation, whose matrix representations determine quantum coins. We show that Wigner's $(2j+1)$-dimensional unitary representations of rotations with half-integers $j$'s are useful to analyze the probability laws of quantum walks. For any value of half-integer $j$, convergence of all moments of walker's pseudovelocity in the long-time limit is proved. It is generally shown for the present models that, if $(2j+1)$ is even, the probability measure of limit distribution is given by a superposition of $(2j+1)/2$ terms of scaled Konno's density functions, and if $(2j+1)$ is odd, it is a superposition of $j$ terms of scaled Konno's density functions and a Dirac's delta function at the origin. For the two-, three-, and four-component models, the probability densities of limit distributions are explicitly calculated and their dependence on the parameters of quantum coins and on the initial qudit of walker is completely determined. Comparison with computer simulation results is also shown.Comment: v2: REVTeX4, 15 pages, 4 figure

Workshop on Observations of Recent Comets (1990)

Potential interpretations are presented for observations of four comets: Brorsen-Metcalf (1989o), Okazaki-Levy-Rudenko (1989r), Aarseth-Brewington (1989a1), and Austin (1989o1). The relationship of minor species with each other and possible parents as well as with dust are being pursued in a number of investigations. Of particular interest are the abundance ratios of CH4 to CO and NH3 to N2. The need for closer collaboration betwen observing teams and modelers is examined. The need for dust size distribution as a function of cometocentric distance to be analyzed in closer collaboration between observers and modelers is discussed

Modeling the coma of 2060 Chiron

Observations of comet-like activity and a resolved coma have established that 2060 Chiron is a comet. Determinations of its radius range from 65 to 200 km. This unusually large size for a comet suggests that the atmosphere of Chiron is intermediate to the tightly bound, thin atmospheres typical of planets and satellite and the greatly extended atmospheres in free expansion typical of cometary comae. Under certain conditions it may gravitationally bind an atmosphere that is thick compared to its size, while a significant amount of gas escapes to an extensive exosphere. These attributes coupled with reports of sporadic outbursts at large heliocentric distances and the identification of CN in the coma make Chiron a challenging object to model. Simple models of gas production and the dusty coma were recently presented but a general concensus on many basic features has not emerged. Development was begun on a more complete coma model of Chiron. The objectives are to report progress on this model and give the preliminary results for understanding Chiron

A preliminary model of the coma of 2060 Chiron

We have included gravity in our fluid dynamic model with chemical kinetics of dusty comet comae and applied it with two dust sizes to 2060 Chiron. A progress report on the model and preliminary results concerning gas/dust dynamics and chemistry is given

Innermost stable circular orbits around magnetized rotating massive stars

In 1998, Shibata and Sasaki [Phys. Rev. D 58, 104011 (1998)] presented an approximate analytical formula for the radius of the innermost stable circular orbit (ISCO) of a neutral test particle around a massive, rotating and deformed source. In the present paper, we generalize their expression by including the magnetic dipole moment. We show that our approximate analytical formulas are accurate enough by comparing them with the six-parametric exact solution calculated by Pach\'on et. al. [Phys. Rev. D 73, 104038 (2006)] along with the numerical data presented by Berti and Stergioulas [MNRAS 350, 1416 (2004)] for realistic neutron stars. As a main result, we find that in general, the radius at ISCO exhibits a decreasing behavior with increasing magnetic field. However, for magnetic fields below 100GT the variation of the radius at ISCO is negligible and hence the non-magnetized approximate expression can be used. In addition, we derive approximate analytical formulas for angular velocity, energy and angular momentum of the test particle at ISCO.Comment: 8 pages, 3 figure

Invariant Measures and Decay of Correlations for a Class of Ergodic Probabilistic Cellular Automata

We give new sufficient ergodicity conditions for two-state probabilistic cellular automata (PCA) of any dimension and any radius. The proof of this result is based on an extended version of the duality concept. Under these assumptions, in the one dimensional case, we study some properties of the unique invariant measure and show that it is shift-mixing. Also, the decay of correlation is studied in detail. In this sense, the extended concept of duality gives exponential decay of correlation and allows to compute explicitily all the constants involved

Design of a 3 DOFs parallel actuated mechanism for a biped hip joint

Proceedings of the 2002 IEEE International Conference on Robotics & Automation, Washington, DC, May 200

Flat rotation curves in Chern-Simons modified gravity

We investigate the spacetime of a slowly rotating black hole in the Chern-Simons modified gravity. The long range feature of frame-dragging effect under the Chern-Simon gravity well explains the flat rotation curves of galaxies which is a central evidence of dark matter. Our solution provides a different scenario of rotating space from Goedel's solution.Comment: 4 pages, Accepted for publication in Phys. Rev.