Camassa-Holm equation: transformation to deformed sinh-Gordon equations, cuspon and soliton solutions

In this paper a relation between the Camassa-Holm equation and the non-local deformations of the sinh-Gordon equation is used to study some properties of the former equation. We will show that cuspon and soliton solutions can be obtained from soliton solutions of the deformed sinh-Gordon equation.

Casimir energy in a small volume multiply connected static hyperbolic preinflationary universe

A few years ago, Cornish, Spergel and Starkman (CSS) suggested that a multiply connected small universe could allow for classical chaotic mixing as a preinflationary homogenization process. The smaller the volume, the more important the process. Also, a smaller universe has a greater probability of being spontaneously created. Previously DeWitt, Hart and Isham (DHI) calculated the Casimir energy for static multiply connected fat space-times. Because of the interest in small volume hyperbolic universes (e.g., CSS), we generalize the DHI calculation by making a numerical investigation of the Casimir energy for a conformally coupled, massive scalar field in a static universe, whose spatial sections are the Weeks manifold, the smallest universe of negative curvature known. In spite of being a numerical calculation, our result is in fact exact. It is shown that there is spontaneous vacuum excitation of low multipolar components.

Conformal coupling and Foldy-Wouthuysen transformation

The propagation of a free scalar field phi with mass m in a curved background is generally described by the equation (g(munu) delmudelnu + m(2) + xiR)phi = 0. There exist some arguments in the literature that seem to favor the conformal coupling to the detriment of the minimal one. However, the majority of these claims axe inconclusive. Here we show that the exact Foldy Wouthuysen transformation for spin-0 particle coupled to a wide class of static spacetime metrics exists independently of the value of. Nevertheless, if the coupling is of the conformal type, the gravitational Darwin-like term has an uncomplicated structure and it is proportional to the corresponding term in the fermionic case. In addition, an independent computation of this term, which has its origin in the zitterbewegung fluctuation of the boson's position with the mean square <(deltar)(2)> approximate to 1/m(2), gives a result that coincides with that obtained using the aforementioned exact transformation with xi = 1/6.

Casimir energy density in closed hyperbolic universes

The original Casimir effect results from the difference in the vacuum energies of the electromagnetic field, between that in a region of space with boundary conditions and that in the same region without boundary conditions. In this paper we develop the theory of a similar situation, involving a scalar field in spacetimes with closed spatial sections of negative curvature.

Modified Korteweg-de Vries hierarchy with hodograph transformation: Camassa-Holm and Harry-Dym hierarchies

In this paper, we present relations between Camassa-Holm (CH), Harry-Dym (HD) and modified Korteweg-de Vries (mKdV) hierarchies, which are given by the hodograph type transformation. (C) 2001 IMACS. Published by Elsevier B.V. B.V. All rights reserved.

On the birth of a closed hyperbolic universe

We clarify and develop the results of a previous paper on the birth of a closed universe of negative spatial curvature and multiply connected topology. In particular we discuss the initial instanton and the second topology change in more detail, This is followed by a short discussion of the results.

Casimir energy in multiply connected static hyperbolic universes

We generalize a previously obtained result for the case of a few other static hyperbolic universes with manifolds of nontrivial topology as spatial sections.

The impossibility of a universal relativistic temperature transformation

The non-existence of a relativistic temperature transformation is due to the fact that an observer moving in a heat reservoir cannot detect a blackbody spectrum. (C) 2004 Published by Elsevier B.V.

Permutability of Backlund transformation for N=1 supersymmetric sinh-Gordon

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Algebraic properties of Rogers-Szego functions: I. Applications in quantum optics

By means of a well-established algebraic framework, Rogers-Szego functions associated with a circular geometry in the complex plane are introduced in the context of q-special functions, and their properties are discussed in detail. The eigenfunctions related to the coherent and phase states emerge from this formalism as infinite expansions of Rogers-Szego functions, the coefficients being determined through proper eigenvalue equations in each situation. Furthermore, a complementary study on the Robertson-Schrodinger and symmetrical uncertainty relations for the cosine, sine and nondeformed number operators is also conducted, corroborating, in this way, certain features of q-deformed coherent states.

A note about the appearance of non-hyperbolic solutions in a mechanical pendulum system

The investigation of the behavior of a nonlinear system consists in the analysis of different stages of its motion, where the complexity varies with the proximity of a resonance region. Near this region the stability domain of the system undergoes sudden changes due basically to competition and interaction between periodic and saddle solutions inside the phase portrait, leading to the occurrence of the most different phenomena. Depending of the domain of the chosen control parameter, these events can reveal interesting geometric features of the system so that the phase portrait is not capable to express all them, since the projection of these solutions on the two-dimensional surface can hide some aspects of these events. In this work we will investigate the numerical solutions of a particular pendulum system close to a secondary resonance region, where we vary the control parameter in a restrict domain in order to draw a preliminary identification about what happens with this system. This domain includes the appearance of non-hyperbolic solutions where the basin of attraction in the center of the phase portrait diminishes considerably, almost disappearing, and afterwards its size increases with the direction of motion inverted. This phenomenon delimits a boundary between low and high frequency of the external excitation.

Effect of Ag additions on the reverse martensitic transformation in the Cu-10 mass% Al alloy

The effect of Ag additions on the reverse martensitic transformation in the Cu-10 mass% Al alloy was studied using differential thermal analysis (DTA), optical (OM) and scanning electron microscopies (SEM) and X-ray diffractometry. The results indicated that Ag additions to the Cu-10 mass% Al alloy shift the equilibrium concentration to higher Al contents, allow to obtain both beta(1)' and beta' martensitic phases in equilibrium and that Ag precipitation is a process associated with the perlitic phase formation.

Thermal stability of the martensitic transformation of Cu-Al-Ni-Mn-Ti

The development of new shape memory alloys with high martensitic transformation temperature increases the potential for applications. The development and use of these new alloys depends on the stability of the structure during cycling at high temperatures. If it is possible to guarantee that on alloys keeps the structure during cycling, then the alloy can be used because of the shape memory properties. The aim of this work is to obtain a kinetic model of the forward and backward martensitic transformation of two Cu-Al-Ni-Mn-Ti alloys. Differential scanning calorimetry has been performed in order to establish the kinetic stability of the martensite and the beta transformation. (c) 2006 Elsevier B.V. All rights reserved.

Reverse martensitic transformation in the Cu-10 wt% Al-6 wt%Ag alloy

The reverse martensitic transformation in the Cu-10 wt%Al-6 wt%Ag alloy was studied by classical differential thermal analysis (IDTA), scanning electron microscopy (SEM), energy dispersive X-ray analysis (EDX) and X-ray diffractometry (XRD). The results indicated that the presence of Ag in the Cu-10%Al alloy is responsible for the separation of the competitive reactions that occur during the reverse martensitic transformation and is also associated to an increase in the disordering degree at high temperatures, when compared with alloys without Ag addition. (c) 2005 Springer Science + Business Media, Inc.

Order-disorder transformation in the Ni-4.49 at.% Al alloy

The order-disorder transformation in the Ni-4.49 at.% Al alloy was studied using electrical resistivity measurements, microhardness measurements, differential scanning calorimetry (DSC) and transmission electron microscopy (TEM). The results confirmed the ordering behavior expected for Ni-Al dilute alloys and the suggested relation between resistivity changes and microhardness changes with antiferromagnetic spin ordering. The higher value obtained for the activation energy of vacancy migration was associated with a decrease in the Al concentration gradient near solute-depleted regions. (c) 2005 Elsevier B.V. All rights reserved.