Superluminality in DGP

We reconsider the issue of superluminal propagation in the DGP model of infrared modified gravity. Superluminality was argued to exist in certain otherwise physical backgrounds by using a particular, physically relevant scaling limit of the theory. In this paper, we exhibit explicit five-dimensional solutions of the full theory that are stable against small fluctuations and that indeed support superluminal excitations. The scaling limit is neither needed nor invoked in deriving the solutions or in the analysis of its small fluctuations. To be certain that the superluminality found here is physical, we analyze the retarded Green's function of the scalar excitations, finding that it is causal and stable, but has support on a widened light-cone. We propose to use absence of superluminal propagation as a method to constrain the parameters of the DGP model. As a first application of the method, we find that whenever the 4D energy density is a pure cosmological constant and a hierarchy of scales exists between the 4D and 5D Planck masses, superluminal propagation unavoidably occurs.Comment: 23 pages. Minor corrections. Version to appear in JHE

Hill's Equation with Random Forcing Parameters: Determination of Growth Rates through Random Matrices

This paper derives expressions for the growth rates for the random 2 x 2 matrices that result from solutions to the random Hill's equation. The parameters that appear in Hill's equation include the forcing strength and oscillation frequency. The development of the solutions to this periodic differential equation can be described by a discrete map, where the matrix elements are given by the principal solutions for each cycle. Variations in the forcing strength and oscillation frequency lead to matrix elements that vary from cycle to cycle. This paper presents an analysis of the growth rates including cases where all of the cycles are highly unstable, where some cycles are near the stability border, and where the map would be stable in the absence of fluctuations. For all of these regimes, we provide expressions for the growth rates of the matrices that describe the solutions.Comment: 22 pages, 3 figure

Sums over Graphs and Integration over Discrete Groupoids

We show that sums over graphs such as appear in the theory of Feynman diagrams can be seen as integrals over discrete groupoids. From this point of view, basic combinatorial formulas of the theory of Feynman diagrams can be interpreted as pull-back or push-forward formulas for integrals over suitable groupoids.Comment: 27 pages, 4 eps figures; LaTeX2e; uses Xy-Pic. Some ambiguities fixed, and several proofs simplifie

Charm in cosmic rays (The long-flying component of EAS cores)

Experimental data on cosmic ray cascades with enlarged attenuation lengths (Tien-Shan effect) are presented and analyzed in terms of charm hadroproduction. The very first estimates of charm hadroproduction cross sections from experimental data at high energies are confirmed and compared with recent accelerator results.Comment: 12 pages, 8 figures, LATE

Duality properties of indicatrices of knots

The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two invariants, and interpret it in terms of the tangent indicatrix of the knot conformation. Using the concepts of dual and derivative curves of spherical curves as introduced by Arnold, we show that the graph of the bridge map is the union of the binormal indicatrix, its antipodal curve, and some number of great circles. Similarly, we define the inflection map of a knot conformation, interpret it in terms of the binormal indicatrix, and express its graph in terms of the tangent indicatrix. This duality relationship is also studied for another dual pair of curves, the normal and Darboux indicatrices of a knot conformation. The analogous concepts are defined and results are derived for stick knots.Comment: 22 pages, 9 figure

Atom gratings produced by large angle atom beam splitters

An asymptotic theory of atom scattering by large amplitude periodic potentials is developed in the Raman-Nath approximation. The atom grating profile arising after scattering is evaluated in the Fresnel zone for triangular, sinusoidal, magneto-optical, and bichromatic field potentials. It is shown that, owing to the scattering in these potentials, two \QTR{em}{groups} of momentum states are produced rather than two distinct momentum components. The corresponding spatial density profile is calculated and found to differ significantly from a pure sinusoid.Comment: 16 pages, 7 figure

Bumpy black holes from spontaneous Lorentz violation

We consider black holes in Lorentz violating theories of massive gravity. We argue that in these theories black hole solutions are no longer universal and exhibit a large number of hairs. If they exist, these hairs probe the singularity inside the black hole providing a window into quantum gravity. The existence of these hairs can be tested by future gravitational wave observatories. We generically expect that the effects we discuss will be larger for the more massive black holes. In the simplest models the strength of the hairs is controlled by the same parameter that sets the mass of the graviton (tensor modes). Then the upper limit on this mass coming from the inferred gravitational radiation emitted by binary pulsars implies that hairs are likely to be suppressed for almost the entire mass range of the super-massive black holes in the centers of galaxies.Comment: 40 pages, 4 figure

Vanishing Viscous Limits for 3D Navier-Stokes Equations with A Navier-Slip Boundary Condition

In this paper, we investigate the vanishing viscosity limit for solutions to the Navier-Stokes equations with a Navier slip boundary condition on general compact and smooth domains in $\mathbf{R}^3$. We first obtain the higher order regularity estimates for the solutions to Prandtl's equation boundary layers. Furthermore, we prove that the strong solution to Navier-Stokes equations converges to the Eulerian one in $C([0,T];H^1(\Omega))$ and L^\infty((0,T)\times\o), where $T$ is independent of the viscosity, provided that initial velocity is regular enough. Furthermore, rates of convergence are obtained also.Comment: 45page

On operad structures of moduli spaces and string theory

Recent algebraic structures of string theory, including homotopy Lie algebras, gravity algebras and Batalin-Vilkovisky algebras, are deduced from the topology of the moduli spaces of punctured Riemann spheres. The principal reason for these structures to appear is as simple as the following. A conformal field theory is an algebra over the operad of punctured Riemann surfaces, this operad gives rise to certain standard operads governing the three kinds of algebras, and that yields the structures of such algebras on the (physical) state space naturally.Comment: 33 pages (An elaboration of minimal area metrics and new references are added

Determination of the high-twist contribution to the structure function xF3νNxF^{\nu N}_3

We extract the high-twist contribution to the neutrino-nucleon structure function $xF_3^{(\nu+\bar{\nu})N}$ from the analysis of the data collected by the IHEP-JINR Neutrino Detector in the runs with the focused neutrino beams at the IHEP 70 GeV proton synchrotron. The analysis is performed within the infrared renormalon (IRR) model of high twists in order to extract the normalization parameter of the model. From the NLO QCD fit to our data we obtained the value of the IRR model normalization parameter $\Lambda^2_{3}=0.69\pm0.37~({\rm exp})\pm0.16~({\rm theor})~{\rm GeV}^2$. We also obtained $\Lambda^2_{3}=0.36\pm0.22~({\rm exp})\pm0.12~({\rm theor})~{\rm GeV}^2$ from a similar fit to the CCFR data. The average of both results is $\Lambda^2_{3}=0.44\pm0.19~({\rm exp})~{\rm GeV}^2$.Comment: preprint IHEP-01-18, 7 pages, LATEX, 1 figure (EPS