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.

Conformal mapping of ultrasonic crystals: confining ultrasound and cochlear-like wave guiding

Conformal mapping of a slab of a two-dimensional ultrasonic crystal generate a closed geometrical arrangement of ultrasonic scatterers with appealing acoustic properties. This acoustic shell is able to confine ultrasonic modes. Some of these internal resonances can be induced from an external wave source. The mapping of a linear defect produces a wave-guide that exhibits a spatial-frequency selection analogous to that characteristic of a synthetic "cochlea". Both, experimental and theoretical results are reported here.Comment: 4 pages, 4 figure

Influence of self-gravity on the runaway instability of black hole-torus systems

Results from the first fully general relativistic numerical simulations in axisymmetry of a system formed by a black hole surrounded by a self-gravitating torus in equilibrium are presented, aiming to assess the influence of the torus self-gravity on the onset of the runaway instability. We consider several models with varying torus-to-black hole mass ratio and angular momentum distribution orbiting in equilibrium around a non-rotating black hole. The tori are perturbed to induce the mass transfer towards the black hole. Our numerical simulations show that all models exhibit a persistent phase of axisymmetric oscillations around their equilibria for several dynamical timescales without the appearance of the runaway instability, indicating that the self-gravity of the torus does not play a critical role favoring the onset of the instability, at least during the first few dynamical timescales.Comment: To appear on Phys.Rev.Let

Parrondo-like behavior in continuous-time random walks with memory

The Continuous-Time Random Walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this article we will show how the random combination of two different unbiased CTRWs can give raise to a process with clear drift, if one of them is a CTRW with memory. If one identifies the other one as noise, the effect can be thought as a kind of stochastic resonance. The ultimate origin of this phenomenon is the same of the Parrondo's paradox in game theoryComment: 8 pages, 3 figures, revtex; enlarged and revised versio

Gravitational waves from the Papaloizou-Pringle instability in black hole-torus systems

Black hole (BH)--torus systems are promising candidates for the central engine of gamma-ray bursts (GRBs), and also possible outcomes of the collapse of supermassive stars to supermassive black holes (SMBHs). By three-dimensional general relativistic numerical simulations, we show that an $m=1$ nonaxisymmetric instability grows for a wide range of self-gravitating tori orbiting BHs. The resulting nonaxisymmetric structure persists for a timescale much longer than the dynamical one, becoming a strong emitter of large amplitude, quasiperiodic gravitational waves. Our results indicate that both, the central engine of GRBs and newly formed SMBHs, can be strong gravitational wave sources observable by forthcoming ground-based and spacecraft detectors.Comment: 4 pages, 4 figure, to be published in PR

Management of Virtual Machines on Globus Grids Using GridWay

Virtual machines are a promising technology to over-come some of the problems found in current Grid infras-tructures, like heterogeneity, performance partitioning or application isolation. In this work, we present an straight-forward deployment of virtual machines in Globus Grids. This solution is based on standard services and does not re-quire additional middleware to be installed. Also, we assess the suitability of this deployment in the execution of a high throughput scientific application, the XMM-Newton Scien-tific Analysis System

Forward-backward equations for nonlinear propagation in axially-invariant optical systems

We present a novel general framework to deal with forward and backward components of the electromagnetic field in axially-invariant nonlinear optical systems, which include those having any type of linear or nonlinear transverse inhomogeneities. With a minimum amount of approximations, we obtain a system of two first-order equations for forward and backward components explicitly showing the nonlinear couplings among them. The modal approach used allows for an effective reduction of the dimensionality of the original problem from 3+1 (three spatial dimensions plus one time dimension) to 1+1 (one spatial dimension plus one frequency dimension). The new equations can be written in a spinor Dirac-like form, out of which conserved quantities can be calculated in an elegant manner. Finally, these new equations inherently incorporate spatio-temporal couplings, so that they can be easily particularized to deal with purely temporal or purely spatial effects. Nonlinear forward pulse propagation and non-paraxial evolution of spatial structures are analyzed as examples.Comment: 11 page

How to reduce the number of rating scale items without predictability loss?

Rating scales are used to elicit data about qualitative entities (e.g., research collaboration). This study presents an innovative method for reducing the number of rating scale items without the predictability loss. The "area under the receiver operator curve method" (AUC ROC) is used. The presented method has reduced the number of rating scale items (variables) to 28.57\% (from 21 to 6) making over 70\% of collected data unnecessary. Results have been verified by two methods of analysis: Graded Response Model (GRM) and Confirmatory Factor Analysis (CFA). GRM revealed that the new method differentiates observations of high and middle scores. CFA proved that the reliability of the rating scale has not deteriorated by the scale item reduction. Both statistical analysis evidenced usefulness of the AUC ROC reduction method.Comment: 14 pages, 5 figure

Multiple-Time Higher-Order Perturbation Analysis of the Regularized Long-Wavelength Equation

By considering the long-wave limit of the regularized long wave (RLW) equation, we study its multiple-time higher-order evolution equations. As a first result, the equations of the Korteweg-de Vries hierarchy are shown to play a crucial role in providing a secularity-free perturbation theory in the specific case of a solitary-wave solution. Then, as a consequence, we show that the related perturbative series can be summed and gives exactly the solitary-wave solution of the RLW equation. Finally, some comments and considerations are made on the N-soliton solution, as well as on the limitations of applicability of the multiple scale method in obtaining uniform perturbative series.Comment: 15 pages, RevTex, no figures (to appear in Phys. Rev. E