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.

Interaction of Hawking radiation with static sources in de Sitter and Schwarzschild-de Sitter spacetimes

We study and look for similarities between the response rates R-dS(a(0),Lambda) and R-SdS(a(0),Lambda,M) of a static scalar source with constant proper acceleration a(0) interacting with a massless, conformally coupled Klein-Gordon field (i) in de Sitter spacetime, in the Euclidean vacuum, which describes a thermal flux of radiation emanating from the de Sitter cosmological horizon and (ii) in Schwarzschild-de Sitter spacetime, in the Gibbons-Hawking vacuum, which describes thermal fluxes of radiation emanating from both the hole and the cosmological horizons, respectively, where Lambda is the cosmological constant and M is the black hole mass. After performing the field quantization in each of the above spacetimes, we obtain the response rates at the tree level in terms of an infinite sum of zero-energy field modes possessing all possible angular momentum quantum numbers. In the case of de Sitter spacetime, this formula is worked out and a closed, analytical form is obtained. In the case of Schwarzschild-de Sitter spacetime such a closed formula could not be obtained, and a numerical analysis is performed. We conclude, in particular, that R-dS(a(0),Lambda) and R-SdS(a(0),Lambda,M) do not coincide in general, but tend to each other when Lambda-->0 or a(0)-->infinity. Our results are also contrasted and shown to agree (in the proper limits) with related ones in the literature.

Is the equivalence for the response of static scalar sources in the Schwarzschild and Rindler spacetimes valid only in four dimensions?

It was shown recently that in four dimensions scalar sources with fixed proper acceleration minimally coupled to a massless Klein-Gordon field lead to the same responses when they are (i) uniformly accelerated in Minkowski spacetime (in the inertial vacuum) and (ii) static in the Schwarzschild spacetime (in the Unruh vacuum). Here we show that this equivalence is broken if the spacetime dimension is more than four.

Exact static soliton solutions of (3+1)-dimensional integrable theory with nonzero Hopf numbers

In this paper, we explicitly construct an infinite number of Hopfions (static, soliton solutions with nonzero Hopf topological charges) within the recently proposed (3 + 1)-dimensional, integrable, and relativistically invariant field theory. Two integers label the family of Hopfions we have found. Their product is equal to the Hopf charge which provides a lower bound to the soliton's finite energy. The Hopfions are explicitly constructed in terms of the toroidal coordinates and shown to have a form of linked closed vortices.

Stabilization of a light bullet in a layered Kerr medium with sign-changing nonlinearity

Using the numerical solution of the nonlinear Schrodinger equation and a variational method, it is shown that (3+1)-dimensional spatiotemporal optical solitons, known as light bullets, can be stabilized in a layered Kerr medium with sign-changing nonlinearity along the propagation direction.

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.

Effective potential of two coupled binary matter wave bright solitons with spatially modulated nonlinearity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Evolutions of matter-wave bright soliton with spatially modulated nonlinearity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the dynamical properties of an elliptical-oval billiard with static boundary

Some dynamical properties for a classical particle confined inside a closed region with an elliptical-oval-like shape are studied. The dynamics of the model is made by using a two-dimensional nonlinear mapping. The phase space of the system is of mixed kind and we have found the condition that breaks the invariant spanning curves in the phase space. We have discussed also some statistical properties of the phase space and obtained the behaviour of the positive Lyapunov exponent. (C) 2009 Elsevier B.V. All rights reserved.

Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. (C) 2007 Elsevier Ltd. All rights reserved.

Recurrence of particles in static and time varying oval billiards

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Ultrafast nonlinearity of antimony polyphosphate glasses

We report on the ultrafast nonlinearity of antimony polyphosphate glasses measured using the Kerr shutter technique. The nonlinear refractive index, n(2), was (1.1+/-0.2)x10(-14) cm(2)/W at 800 nm, and enhancement of n(2) by approximate to80% was observed by adding 10% of lead oxide in the glass composition. The full width at half-maximum of the third-order correlation signal was 150 fs, which implies a fast response of the samples (less than or equal to100 fs). Nonlinear absorption was negligible in the range of intensities used. (C) 2003 American Institute of Physics.

Static potential in scalar QED(3) with non-minimal coupling

Here we compute the static potential in scalar QED(3) at leading order in 1/Nf. We show that the addition of a non-minimal coupling of Pauli-type (is an element of(mu nu alpha)j(mu)partial derivative(nu)A(alpha)), although it breaks parity, it does not change the analytic structure of the photon propagator and consequently the static potential remains logarithmic ( confining) at large distances. The non-minimal coupling modifies the potential, however, at small charge separations giving rise to a repulsive force of short range between opposite sign charges, which is relevant for the existence of bound states. This effect is in agreement with a previous calculation based on Moller scattering, but differently from such calculation we show here that the repulsion appears independently of the presence of a tree level Chern-Simons term which rather affects the large distance behaviour of the potential turning it into a constant.

Electromyographic study in Erector spinae, Rectus abdominis, Glutaeous maximus and Rectus femuris muscles, in standing and static posture with load on hands

Observe the loads associates application with in position of body, in the static or dynamic postures. Methods: the electromyographic study in erector spinae, rectus abdominis, glutaeous maximus and rectus femoris muscles was accomplished in female volunteers from 18 have 27 years old, previously selected. The muscles electric activities was gotten with surface electrodes, in standing and static posture, with the parallels and horizontal upper limbs with load on their hands. Conclusion: In this study it was clearly observed influence of the load and distance there is over studied musculature associated with standing erect posture.

Analysis of heuristic algorithms for the transportation model in static and multistage planning in network expansion systems

The usefulness of the application of heuristic algorithms in the transportation model, first proposed by Garver, is analysed in relation to planning for the expansion of transmission systems. The formulation of the mathematical model and the solution techniques proposed in the specialised literature are analysed in detail. Starting with the constructive heuristic algorithm proposed by Garver, an extension is made to the problem of multistage planning for transmission systems. The quality of the solutions found by heuristic algorithms for the transportation model is analysed, as are applications in problems of planning transmission systems.