On Schwarzschild's Topology in Brane-Worlds

The topological structure of Schwarzschild's space-time and its maximal analytic extension are investigated in context of brane-worlds. Using the embedding coordinates, these geometries are seen as different states of the evolution of a single brane-world. Comparing the topologies and the embeddings it is shown that this evolution must be followed by a signature change in the bulk.Comment: 6 page

Future dynamics in f(R) theories

The $f(R)$ gravity theories provide an alternative way to explain the current cosmic acceleration without invoking dark energy matter component. However, the freedom in the choice of the functional forms of $f(R)$ gives rise to the problem of how to constrain and break the degeneracy among these gravity theories on theoretical and/or observational grounds. In this paper to proceed further with the investigation on the potentialities, difficulties and limitations of $f(R)$ gravity, we examine the question as to whether the future dynamics can be used to break the degeneracy between $f(R)$ gravity theories by investigating the future dynamics of spatially homogeneous and isotropic dust flat models in two $f(R)$ gravity theories, namely the well known $f(R) = R + \alpha R^{n}$ gravity and another by A. Aviles et al., whose motivation comes from the cosmographic approach to $f(R)$ gravity. To this end we perform a detailed numerical study of the future dynamic of these flat model in these theories taking into account the recent constraints on the cosmological parameters made by the Planck team. We show that besides being powerful for discriminating between $f(R)$ gravity theories, the future dynamics technique can also be used to determine the fate of the Universe in the framework of these $f(R)$ gravity theories. Moreover, there emerges from our numerical analysis that if we do not invoke a dark energy component with equation-of-state parameter $\omega < -1$ one still has dust flat FLRW solution with a big rip, if gravity deviates from general relativity via $f(R) = R + \alpha R^n$. We also show that FLRW dust solutions with $f''<0$ do not necessarily lead to singularity.Comment: 12 pages, 8 figures. V2: Generality and implications of the results are emphasized, connection with the recent literature improved, typos corrected, references adde

Particle Creation by a Moving Boundary with Robin Boundary Condition

We consider a massless scalar field in 1+1 dimensions satisfying a Robin boundary condition (BC) at a non-relativistic moving boundary. We derive a Bogoliubov transformation between input and output bosonic field operators, which allows us to calculate the spectral distribution of created particles. The cases of Dirichlet and Neumann BC may be obtained from our result as limiting cases. These two limits yield the same spectrum, which turns out to be an upper bound for the spectra derived for Robin BC. We show that the particle emission effect can be considerably reduced (with respect to the Dirichlet/Neumann case) by selecting a particular value for the oscillation frequency of the boundary position

Local structure of Liquid-Vapour Interfaces

The structure of a simple liquid may be characterised in terms of ground state clusters of small numbers of atoms of that same liquid. Here we use this sensitive structural probe to consider the effect of a liquid-vapour interface upon the liquid structure. At higher temperatures (above around half the critical temperature) we find that the predominant effect of the interface is to reduce the local density, which significantly suppresses the local cluster populations. At lower temperatures, however, pronounced interfacial layering is found. This appears to be connected with significant orientational ordering of clusters based on 3- and 5-membered rings, with the rings aligning perpendicular and parallel to the interface respectively. At all temperatures, we find that the population of five-fold symmetric structures is suppressed, rather than enhanced, close to the interface.Comment: 10 pages, 8 figures, accepted for publication by Molecular Physic

Compressive Phase Contrast Tomography

When x-rays penetrate soft matter, their phase changes more rapidly than their amplitude. In- terference effects visible with high brightness sources creates higher contrast, edge enhanced images. When the object is piecewise smooth (made of big blocks of a few components), such higher con- trast datasets have a sparse solution. We apply basis pursuit solvers to improve SNR, remove ring artifacts, reduce the number of views and radiation dose from phase contrast datasets collected at the Hard X-Ray Micro Tomography Beamline at the Advanced Light Source. We report a GPU code for the most computationally intensive task, the gridding and inverse gridding algorithm (non uniform sampled Fourier transform).Comment: 5 pages, "Image Reconstruction from Incomplete Data VI" conference 7800, SPIE Optical Engineering + Applications 1-5 August 2010 San Diego, CA United State

Quantum radiation in a plane cavity with moving mirrors

We consider the electromagnetic vacuum field inside a perfect plane cavity with moving mirrors, in the nonrelativistic approximation. We show that low frequency photons are generated in pairs that satisfy simple properties associated to the plane geometry. We calculate the photon generation rates for each polarization as functions of the mechanical frequency by two independent methods: on one hand from the analysis of the boundary conditions for moving mirrors and with the aid of Green functions; and on the other hand by an effective Hamiltonian approach. The angular and frequency spectra are discrete, and emission rates for each allowed angular direction are obtained. We discuss the dependence of the generation rates on the cavity length and show that the effect is enhanced for short cavity lengths. We also compute the dissipative force on the moving mirrors and show that it is related to the total radiated energy as predicted by energy conservation.Comment: 17 pages, 1 figure, published in Physical Review

Diffusive epidemic process: theory and simulation

We study the continuous absorbing-state phase transition in the one-dimensional diffusive epidemic process via mean-field theory and Monte Carlo simulation. In this model, particles of two species (A and B) hop on a lattice and undergo reactions B -> A and A + B -> 2B; the total particle number is conserved. We formulate the model as a continuous-time Markov process described by a master equation. A phase transition between the (absorbing) B-free state and an active state is observed as the parameters (reaction and diffusion rates, and total particle density) are varied. Mean-field theory reveals a surprising, nonmonotonic dependence of the critical recovery rate on the diffusion rate of B particles. A computational realization of the process that is faithful to the transition rates defining the model is devised, allowing for direct comparison with theory. Using the quasi-stationary simulation method we determine the order parameter and the survival time in systems of up to 4000 sites. Due to strong finite-size effects, the results converge only for large system sizes. We find no evidence for a discontinuous transition. Our results are consistent with the existence of three distinct universality classes, depending on whether A particles diffusive more rapidly, less rapidly, or at the same rate as B particles.Comment: 19 pages, 5 figure

Casimir torque between corrugated metallic plates

We consider two parallel corrugated plates and show that a Casimir torque arises when the corrugation directions are not aligned. We follow the scattering approach and calculate the Casimir energy up to second order in the corrugation amplitudes, taking into account nonspecular reflections, polarization mixing and the finite conductivity of the metals. We compare our results with the proximity force approximation, which overestimates the torque by a factor 2 when taking the conditions that optimize the effect. We argue that the Casimir torque could be measured for separation distances as large as 1 $\mu{\rm m}.$Comment: 7 pages, 3 figures, contribution to QFEXT07 proceeding

Dynamical Casimir effect with Dirichlet and Neumann boundary conditions

We derive the radiation pressure force on a non-relativistic moving plate in 1+1 dimensions. We assume that a massless scalar field satisfies either Dirichlet or Neumann boundary conditions (BC) at the instantaneous position of the plate. We show that when the state of the field is invariant under time translations, the results derived for Dirichlet and Neumann BC are equal. We discuss the force for a thermal field state as an example for this case. On the other hand, a coherent state introduces a phase reference, and the two types of BC lead to different results.Comment: 12 page