Effective actions of a Gauss-Bonnet brane world with brane curvature terms

We consider a warped brane world scenario with two branes, Gauss-Bonnet gravity in the bulk, and brane localised curvature terms. When matter is present on both branes, we investigate the linear equations of motion and distinguish three regimes. At very high energy and for an observer on the positive tension brane, gravity is four dimensional and coupled to the brane bending mode in a Brans-Dicke fashion. The coupling to matter and brane bending on the negative tension brane is exponentially suppressed. In an intermediate regime, gravity appears to be five dimensional while the brane bending mode remains four dimensional. At low energy, matter on both branes couple to gravity for an observer on the positive tension brane, with a Brans-Dicke description similar to the 2--brane Randall-Sundrum setup. We also consider the zero mode truncation at low energy and show that the moduli approximation fails to reproduce the low energy action.Comment: 14 page

Evolution of a Bose-condensed gas under variations of the confining potential

We discuss the dynamic properties of a trapped Bose-condensed gas under variations of the confining field and find analytical scaling solutions for the evolving coherent state (condensate). We further discuss the characteristic features and the depletion of this coherent state.Comment: 4 pages, no postscript figure

Analysis of solitary wave impulses in granular chains using ultrasonic excitation

The propagation of broad bandwidth solitary wave impulses, generated within granular chains by narrow bandwidth ultrasonic excitation, is studied in detail. Theoretical predictions are compared to experimental results. It is demonstrated that the observed effects result from a sum of a solitary wave traveling out from the source with a wave that reflects from the far end of the chain. It is shown that this combination, when used with an excitation in the form of a long-duration tone burst, encourages the generation of multiple impulses with a characteristic periodicity. This study shows that the properties of the chain structure and the excitation can be adjusted so as to generate ultrasonic solitary wave impulses with a high amplitude and known frequency content, which are of interest in applications such as biomedical ultrasound

The dynamic excitation of a granular chain for biomedical ultrasound applications: contact mechanics finite element analysis and validation

There has been recent interest in the transmission of acoustic signals along granular chains of spherical beads to produce waveforms of relevance to biomedical ultrasound applications. Hertzian contact between adjacent beads can introduce different harmonic content into the signal as it propagates. This transduction mechanism has the potential to be of use in both diagnostic and therapeutic ultrasound applications, and is the object of the study presented here. Although discrete dynamics models of this behaviour exist, a more comprehensive solution must be sought if changes in shape and deformation of individual beads are to be considered. Thus, the finite element method was used to investigate the dynamics of a granular chain of six, 1 mm diameter chrome steel spherical beads excited at one end using a sinusoidal displacement signal at 73 kHz. Output from this model was compared with the solution provided by the discrete dynamics model, and good overall agreement obtained. In addition, it was able to resolve the complex dynamics of the granular chain, including the multiple collisions which occur. It was demonstrated that under dynamic excitation conditions, the inability of discrete mechanics models to account for elastic deformation of the beads when these lose contact, could lead to discrepancies with experimental observations

Ultrasonic propagation in finite-length granular chains

A narrowband ultrasound source has been used to generate solitary wave impulses in finite-length chains of spheres. Once the input signal is of sufficient amplitude, both harmonics and sub-harmonics of the input frequency can be generated as non-linear normal modes of the system, allowing a train of impulses to be established from a sinusoidal input. The characteristics of the response have been studied as a function of the physical properties of the chain, the input waveform and the level of static pre-compression. The results agree with the predictions of a theoretical model, based on a set of discrete dynamic equations for the spheres for finite-length chains. Impulses are only created for very small pre-compression forces of the order of 0.01 N, where strongly non-linear behaviour is expected

Simplicial cohomology of orbifolds

For any orbifold M, we explicitly construct a simplicial complex S(M) from a given triangulation of the ‘coarse ’ underlying space together with the local isotropy groups of M. We prove that, for any local system on M, this complex S(M) has the same cohomology as M. The use of S(M) in explicit calculations is illustrated in the example of the ‘teardrop ’ orbifold. Introduction. Orbifolds or V-manifolds were first introduced by Satake [9], and arise naturally in many ways. For example, the orbit space of any proper action by a (discrete) group on a manifold has the structure of an orbifold; this applies in particular to moduli spaces. Furthermore, the orbit space of any almost free action by

Condensate fraction and critical temperature of a trapped interacting Bose gas

By using a mean field approach, based on the Popov approximation, we calculate the temperature dependence of the condensate fraction of an interacting Bose gas confined in an anisotropic harmonic trap. For systems interacting with repulsive forces we find a significant decrease of the condensate fraction and of the critical temperature with respect to the predictions of the non-interacting model. These effects go in the opposite direction compared to the case of a homogeneous gas. An analytic result for the shift of the critical temperature holding to first order in the scattering length is also derived.Comment: 8 pages, REVTEX, 2 figures, also available at http://anubis.science.unitn.it/~oss/bec/BEC.htm