From particle segregation to the granular clock

Recently several authors studied the segregation of particles for a system composed of mono-dispersed inelastic spheres contained in a box divided by a wall in the middle. The system exhibited a symmetry breaking leading to an overpopulation of particles in one side of the box. Here we study the segregation of a mixture of particles composed of inelastic hard spheres and fluidized by a vibrating wall. Our numerical simulations show a rich phenomenology: horizontal segregation and periodic behavior. We also propose an empirical system of ODEs representing the proportion of each type of particles and the segregation flux of particles. These equations reproduce the major features observed by the simulations.Comment: 10 page

Comment on ``Scaling Laws for a System with Long-Range Interactions within Tsallis Statistics''

In their recent Letter [Phys. Rev. Lett. 83, 4233 (1999)], Salazar and Toral (ST) study numerically a finite Ising chain with non-integrable interactions decaying like 1/r^(d+sigma) where -d <= sigma <= 0 (like ST, we discuss general dimensionality d). In particular, they explore a presumed connection between non-integrable interactions and Tsallis's non-extensive statistics. We point out that (i) non-integrable interactions provide no more motivation for Tsallis statistics than do integrable interactions, i.e., Gibbs statistics remain meaningful for the non-integrable case, and in fact provide a {\em complete and exact treatment}; and (ii) there are undesirable features of the method ST use to regulate the non-integrable interactions.Comment: Accepted for publication in Phys. Rev. Let

Improved bounds for the crossing numbers of K_m,n and K_n

It has been long--conjectured that the crossing number cr(K_m,n) of the complete bipartite graph K_m,n equals the Zarankiewicz Number Z(m,n):= floor((m-1)/2) floor(m/2) floor((n-1)/2) floor(n/2). Another long--standing conjecture states that the crossing number cr(K_n) of the complete graph K_n equals Z(n):= floor(n/2) floor((n-1)/2) floor((n-2)/2) floor((n-3)/2)/4. In this paper we show the following improved bounds on the asymptotic ratios of these crossing numbers and their conjectured values: (i) for each fixed m >= 9, lim_{n->infty} cr(K_m,n)/Z(m,n) >= 0.83m/(m-1); (ii) lim_{n->infty} cr(K_n,n)/Z(n,n) >= 0.83; and (iii) lim_{n->infty} cr(K_n)/Z(n) >= 0.83. The previous best known lower bounds were 0.8m/(m-1), 0.8, and 0.8, respectively. These improved bounds are obtained as a consequence of the new bound cr(K_{7,n}) >= 2.1796n^2 - 4.5n. To obtain this improved lower bound for cr(K_{7,n}), we use some elementary topological facts on drawings of K_{2,7} to set up a quadratic program on 6! variables whose minimum p satisfies cr(K_{7,n}) >= (p/2)n^2 - 4.5n, and then use state--of--the--art quadratic optimization techniques combined with a bit of invariant theory of permutation groups to show that p >= 4.3593.Comment: LaTeX, 18 pages, 2 figure

Phase transition in a super superspin glass

We here confirm the occurrence of spin glass phase transition and extract estimates of associated critical exponents of a highly monodisperse and densely compacted system of bare maghemite nanoparticles. This system has earlier been found to behave like an archetypal spin glass, with e.g. a sharp transition from paramagnetic to non-equilibrium behavior, suggesting that this system undergoes a spin-glass phase transition at a relatively high temperature, $T_g$ $\sim$ 140 K.Comment: 4 pages, 3 figure

Liderazgo e instituciones factores endógenos del desarrollo de la economía regional

This paper proposes that a virtuous circle for the sustainable development of a city or region is achieved through a process whereby proactive and strong leadership and effective institutions enhance the capacity and capability of a place to better use its resource endowments and gain an improved market fit in becoming competitive and being entrepreneurial. It is proposed that the performance of a city or region at a point in time and the path of its economic development over time may be represented by its position in a Regional Competitiveness Performance Cube. The paper proposes a new model framework whereby a city or region’s economic development and performance is an outcome dependent on how its resource endowments and market fit as quasi-independent variables are mediated by the interaction between leadership, institutions, and entrepreneurship as intervening variables. The experiences of a number of case study cities from a variety of settings in the US, Europe, Asia and Australia are explored within that framework.Este artículo propone que un círculo virtuoso para el desarrollo sostenible de una ciudad o región se logra a través de un proceso por el que el liderazgo proactivo y fuerte y las instituciones efectivas refuerzan la capacidad y aptitud de un lugar para hacer un mejor uso de sus dotaciones de recursos y lograr un mercado mejorado que consiga ser competitivo y emprendedor. Se propone que el funcionamiento de una ciudad o región en un punto en el tiempo y la trayectoria de su desarrollo económico a lo largo del tiempo puede representarse por su posición en un Cubo de resultados de Competitividad Regional. El artículo propone una nueva estructura de modelo donde el desarrollo económico y funcionamiento de una ciudad o región sea un resultado dependiente de cómo sus dotaciones de recursos y mercado ajustadas como variables cuasi-independientes son mediadas por la interacción entre el liderazgo, instituciones y espíritu empresarial como variables intervinientes. Las experiencias de un cierto número de casos de estudio de ciudades dentro de una variedad de lugares en EE.UU., Europa, Asia y Australia se exploran dentro de esa estructura

The Effects Of Adaptation, Commitment And Trust In Cross-Cultural Marketing Relationships

The spread of global business presents distinct challenges for those wishing to develop marketing relationships. Key elements of successful marketing relationships have been explored in the literature and are well understood (Morgan and Hunt, 1994; Walters, Peters, and Dess, 1994; Anderson and Narus, 1990).&nbsp; &nbsp;This paper expands the understanding of cross-cultural marketing relationships in three ways.&nbsp; It does so first by empirically testing a model of commitment and trust in an international context. Then the paper presents findings that suggest that cultural adaptation by the focal firm has a significant effect on commitment. &nbsp;&nbsp;We hypothesize that a firm's adaptation to its partner&rsquo;s culture significantly effects cooperation in cross?cultural marketing relationships and test the hypotheses by taking a structural equations approach. &nbsp;This paper finds that efforts made by the firm to adapt to the partner's culture improve relationship performance and that higher levels of Trust lead to higher levels of Commitment and that higher levels of both Trust and Commitment lead to greater Cooperation