A nonlinear Schr\"odinger equation for water waves on finite depth with constant vorticity

A nonlinear Schr\"odinger equation for the envelope of two dimensional surface water waves on finite depth with non zero constant vorticity is derived, and the influence of this constant vorticity on the well known stability properties of weakly nonlinear wave packets is studied. It is demonstrated that vorticity modifies significantly the modulational instability properties of weakly nonlinear plane waves, namely the growth rate and bandwidth. At third order we have shown the importance of the coupling between the mean flow induced by the modulation and the vorticity. Furthermore, it is shown that these plane wave solutions may be linearly stable to modulational instability for an opposite shear current independently of the dimensionless parameter kh, where k and h are the carrier wavenumber and depth respectively

Dyadic existential rules

In the field of ontology-based query answering, existential rules (a.k.a. tuple-generating dependencies) form an expressive Datalog-based language to specify implicit knowledge. The presence of existential quantification in rule-heads, however, makes the main reasoning tasks undecidable. To overcome this limitation, in the last two decades, a number of classes of existential rules guaranteeing the decidability of query answering have been proposed. Unfortunately, such classes are typically based on different syntactic conditions imposing the development of different ad hoc reasoners. This paper introduces a novel general condition that allows to define, systematically, from any decidable class C of existential rules, a new class called Dyadic-C that enjoys the following properties: (i) it is decidable; (ii) it generalizes C; (iii) it keeps the same data complexity as C; and (iv) it can exploit any reasoner for query answering over C. Additionally, the paper proposes a simple and elegant syntactic condition that gives rise to the class Ward+ generalizing the well-known decidable classes Shy and Ward, and being included in Dyadic-Shy

Single-mode tuneable laser operation of hybrid microcavities based on CdSe/CdS core/shell colloidal nanorods on silica microspheres

Colloidal core/shell semiconductor nanonorystals have generated a great deal of interest as gain media in recent years due to a number of salient properties originating from their small size and the associated quantum confinement [1]. These include low-threshold and temperature-insensitive lasing, reduced trapping of excited carriers, and the possibility to alleviate non-radiative Auger recombination by engineering the wavefunction distributions of the electrons, and holes within their volume. Here, single-mode, tuneable operation of fiber-coupled hybrid lasers based on colloidal CdSe/CdS core/shell nanorods on silica microspheres is reported

Boussinesq Solitary-Wave as a Multiple-Time Solution of the Korteweg-de Vries Hierarchy

We study the Boussinesq equation from the point of view of a multiple-time reductive perturbation method. As a consequence of the elimination of the secular producing terms through the use of the Korteweg--de Vries hierarchy, we show that the solitary--wave of the Boussinesq equation is a solitary--wave satisfying simultaneously all equations of the Korteweg--de Vries hierarchy, each one in an appropriate slow time variable.Comment: 12 pages, RevTex (to appear in J. Math Phys.

Dynamics of bootstrap percolation

Bootstrap percolation transition may be first order or second order, or it may have a mixed character where a first order drop in the order parameter is preceded by critical fluctuations. Recent studies have indicated that the mixed transition is characterized by power law avalanches, while the continuous transition is characterized by truncated avalanches in a related sequential bootstrap process. We explain this behavior on the basis of a through analytical and numerical study of the avalanche distributions on a Bethe lattice.Comment: Proceedings of the International Workshop and Conference on Statistical Physics Approaches to Multidisciplinary Problems, IIT Guwahati, India, 7-13 January 200

Chaos in Sandpile Models

We have investigated the "weak chaos" exponent to see if it can be considered as a classification parameter of different sandpile models. Simulation results show that "weak chaos" exponent may be one of the characteristic exponents of the attractor of \textit{deterministic} models. We have shown that the (abelian) BTW sandpile model and the (non abelian) Zhang model posses different "weak chaos" exponents, so they may belong to different universality classes. We have also shown that \textit{stochasticity} destroys "weak chaos" exponents' effectiveness so it slows down the divergence of nearby configurations. Finally we show that getting off the critical point destroys this behavior of deterministic models.Comment: 5 pages, 6 figure

Sandpile Model with Activity Inhibition

A new sandpile model is studied in which bonds of the system are inhibited for activity after a certain number of transmission of grains. This condition impels an unstable sand column to distribute grains only to those neighbours which have toppled less than m times. In this non-Abelian model grains effectively move faster than the ordinary diffusion (super-diffusion). A novel system size dependent cross-over from Abelian sandpile behaviour to a new critical behaviour is observed for all values of the parameter m.Comment: 11 pages, RevTex, 5 Postscript figure

Order Parameter and Scaling Fields in Self-Organized Criticality

We present a unified dynamical mean-field theory for stochastic self-organized critical models. We use a single site approximation and we include the details of different models by using effective parameters and constraints. We identify the order parameter and the relevant scaling fields in order to describe the critical behavior in terms of usual concepts of non equilibrium lattice models with steady-states. We point out the inconsistencies of previous mean-field approaches, which lead to different predictions. Numerical simulations confirm the validity of our results beyond mean-field theory.Comment: 4 RevTex pages and 2 postscript figure