Single-particle model for a granular ratchet

A simple model for a granular ratchet corresponding to a single grain bouncing off a vertically vibrating sawtooth-like base is studied. Depending on the vibration strength, the sawtooth roughness and the restitution coefficient, horizontal transport in both the preferred and unfavoured directions is observed. A phase diagram indicating the regions in parameter space where each of the three possible regimes (no current, normal current, and current reversal) occurs is presented.Comment: 7 pages, 3 figures, submitted to Physica

La relación Estados Unidos–América Latina: un reto para Obama

La crisis en la relación de Estados Unidos con América Latina, que surgió con la entrada del nuevo milenio, tocó su punto más bajo en las últimas décadas y se caracterizó por la falta de confianza hacia Estados Unidos, por ser un gran reto para el presidente Barack Obama y por representar también una oportunidad fascinante, según se expresa en el artículo, que indica que las antiguas relaciones interamericanas de dependencia y subordinación enfrentaban la posibilidad de convertirse en una alianza en la cual América Latina y el Caribe asumieran, por primera vez, un papel dominante en la gobernanza global

Stability Conditions for Coupled Oscillators in Linear Arrays

In this paper, we give necessary conditions for stability of flocks in R. We focus on linear arrays with decentralized agents, where each agent interacts with only a few its neighbors. We obtain explicit expressions for necessary conditions for asymptotic stability in the case that the systems consists of a periodic arrangement of two or three different types of agents, i.e. configurations as follows: ...2-1-2-1 or ...3-2-1-3-2-1. Previous literature indicated that the (necessary) condition for stability in the case of a single agent (...1-1-1) held that the first moment of certain coefficients governing the interactions between agents has to be zero. Here, we show that that does not generalize. Instead, the (necessary) condition in the cases considered is that the first momentum \emph{plus a nonlinear correction term} must be zero

Classical stability of U(1)_A domain walls in dense matter QCD

It was recently shown that there exists metastable U(1)_A domain wall configurations in high-density QCD (\mu >> 1 GeV). In the following we will assess the stability of such non-trivial field configurations at intermediate densities (\mu < 1 GeV). The existence of such configurations at intermediate densities could have interesting consequences for the physics of neutron stars with high core density.Comment: 13 pages, 2 Postscript figures, typos correcte

The Projection Method for Reaching Consensus and the Regularized Power Limit of a Stochastic Matrix

In the coordination/consensus problem for multi-agent systems, a well-known condition of achieving consensus is the presence of a spanning arborescence in the communication digraph. The paper deals with the discrete consensus problem in the case where this condition is not satisfied. A characterization of the subspace $T_P$ of initial opinions (where $P$ is the influence matrix) that \emph{ensure} consensus in the DeGroot model is given. We propose a method of coordination that consists of: (1) the transformation of the vector of initial opinions into a vector belonging to $T_P$ by orthogonal projection and (2) subsequent iterations of the transformation $P.$ The properties of this method are studied. It is shown that for any non-periodic stochastic matrix $P,$ the resulting matrix of the orthogonal projection method can be treated as a regularized power limit of $P.$Comment: 19 pages, 2 figure

Coordination in multiagent systems and Laplacian spectra of digraphs

Constructing and studying distributed control systems requires the analysis of the Laplacian spectra and the forest structure of directed graphs. In this paper, we present some basic results of this analysis partially obtained by the present authors. We also discuss the application of these results to decentralized control and touch upon some problems of spectral graph theory.Comment: 15 pages, 2 figures, 40 references. To appear in Automation and Remote Control, Vol.70, No.3, 200

Random Walks on Digraphs

Let V = {1, · · · n} be a vertex set and S a non-negative row-stochastic matrix (i.e. rows sum to 1). V and S define a digraph G = G(V, S) and a directed graph Laplacian L as follows. If (S)ij \u3e 0 (in what follows we will leave out the parentheses) there is a directed edge j → i. Thus the ith row of S identifies the edges coming into vertex i and their weights. This set of vertices are collectively the neighbors of i, and is denoted by Ni . The diagonal elements Sii are chosen such that each row sum equals 1. In particular, if a vertex i has no incoming edges, we choose Sii = 1. For the purposes of this work, we define the Laplacian by..

Equators Have at Most Countable Many Singularities with Bounded Total Angle

For distinct points p and q in a two-dimensional Riemannian manifold, one defines their mediatrix Lpq as the set of equidistant points to p and q. It is known that mediatrices have a cell decomposition consisting of a finite number of branch points connected by Lipschitz curves. In the case of a topological sphere, mediatrices are called equators and it can benoticed that there are no branching points, thus an equator is a topological circle with possibly many Lipschitz singularities. This paper establishes that mediatrices have the radial

On the Uniformity of (3/2)n Modulo 1

It has been conjectured that the sequence (3/2)n modulo 1 is uniformly distributed. The distribution of this sequence is significant in relation to unsolved problems in number theory including the Collatz conjecture. In this paper, we describe an algorithm to compute (3/2)n modulo 1 to n = 108 . We then statistically analyze its distribution. Our results strongly agree with the hypothesis that (3/2)n modulo 1 is uniformly distributed

On the spectra of certain directed paths

AbstractWe describe the eigenpairs of special kinds of tridiagonal matrices related to problems on traffic on a one-lane road. Some numerical examples are provided