Representing Structural Information of Helical Charge Distributions in Cylindrical Coordinates

Structural information in the local electric field produced by helical charge distributions, such as dissolved DNA, is revealed in a straightforward manner employing cylindrical coordinates. Comparison of structure factors derived in terms of cylindrical and helical coordinates is made. A simple coordinate transformation serves to relate the Green function in cylindrical and helical coordinates. We also compare the electric field on the central axis of a single helix as calculated in both systems.Comment: 11 pages in plain LaTex, no figures. Accepted for publication in PRE March, 199

False discovery rate: setting the probability of false claim of detection

When testing multiple hypothesis in a survey --e.g. many different source locations, template waveforms, and so on-- the final result consists in a set of confidence intervals, each one at a desired confidence level. But the probability that at least one of these intervals does not cover the true value increases with the number of trials. With a sufficiently large array of confidence intervals, one can be sure that at least one is missing the true value. In particular, the probability of false claim of detection becomes not negligible. In order to compensate for this, one should increase the confidence level, at the price of a reduced detection power. False discovery rate control is a relatively new statistical procedure that bounds the number of mistakes made when performing multiple hypothesis tests. We shall review this method, discussing exercise applications to the field of gravitational wave surveys.Comment: 7 pages, 3 table, 3 figures. Prepared for the Proceedings of GWDAW 9 (http://lappc-in39.in2p3.fr/GWDAW9) A new section was added with a numerical example, along with two tables and a figure related to the new section. Many smaller revisions to improve readibilit

Effective Potential of a Black Hole in Thermal Equilibrium with Quantum Fields

Expectation values of one-loop renormalized thermal equilibrium stress-energy tensors of free conformal scalars, spin-${1 \over 2}$ fermions and U(1) gauge fields on a Schwarzschild black hole background are used as sources in the semi-classical Einstein equation. The back-reaction and new equilibrium metric are solved for at $O({\hbar})$ for each spin field. The nature of the modified black hole spacetime is revealed through calculations of the effective potential for null and timelike orbits. Significant novel features affecting the motions of both massive and massless test particles show up at lowest order in $\epsilon= (M_{Pl}/M)^2 < 1$, where $M$ is the renormalized black hole mass, and $M_{Pl}$ is the Planck mass. Specifically, we find the tendency for \underline{stable} circular photon orbits, an increase in the black hole capture cross sections, and the existence of a gravitationally repulsive region associated with the black hole which is generated from the U(1) back-reaction. We also consider the back-reaction arising from multiple fields, which will be useful for treating a black hole in thermal equilibrium with field ensembles belonging to gauge theories.Comment: 25 pages (not including seven figures), VAND-TH-93-6. Typed in Latex, uses RevTex macro

Energy Density of Non-Minimally Coupled Scalar Field Cosmologies

Scalar fields coupled to gravity via $\xi R {\Phi}^2$ in arbitrary Friedmann-Robertson-Walker backgrounds can be represented by an effective flat space field theory. We derive an expression for the scalar energy density where the effective scalar mass becomes an explicit function of $\xi$ and the scale factor. The scalar quartic self-coupling gets shifted and can vanish for a particular choice of $\xi$. Gravitationally induced symmetry breaking and de-stabilization are possible in this theory.Comment: 18 pages in standard Late

Heat kernel regularization of the effective action for stochastic reaction-diffusion equations

The presence of fluctuations and non-linear interactions can lead to scale dependence in the parameters appearing in stochastic differential equations. Stochastic dynamics can be formulated in terms of functional integrals. In this paper we apply the heat kernel method to study the short distance renormalizability of a stochastic (polynomial) reaction-diffusion equation with real additive noise. We calculate the one-loop {\emph{effective action}} and its ultraviolet scale dependent divergences. We show that for white noise a polynomial reaction-diffusion equation is one-loop {\emph{finite}} in $d=0$ and $d=1$, and is one-loop renormalizable in $d=2$ and $d=3$ space dimensions. We obtain the one-loop renormalization group equations and find they run with scale only in $d=2$.Comment: 21 pages, uses ReV-TeX 3.

Vacuum decay via Lorentzian wormholes

We speculate about the spacetime description due to the presence of Lorentzian wormholes (handles in spacetime joining two distant regions or other universes) in quantum gravity. The semiclassical rate of production of these Lorentzian wormholes in Reissner-Nordstr\"om spacetimes is calculated as a result of the spontaneous decay of vacuum due to a real tunneling configuration. In the magnetic case it only depends on the field theoretical fine structure constant. We predict that the quantum probability corresponding to the nucleation of such geodesically complete spacetimes should be actually negligible in our physical Universe

Cylindrical thin-shell wormholes

A general formalism for the dynamics of non rotating cylindrical thin-shell wormholes is developed. The time evolution of the throat is explicitly obtained for thin-shell wormholes whose metric has the form associated to local cosmic strings. It is found that the throat collapses to zero radius, remains static or expands forever, depending only on the sign of its initial velocity.Comment: 10 page

A Liquid Model Analogue for Black Hole Thermodynamics

We are able to characterize a 2--dimensional classical fluid sharing some of the same thermodynamic state functions as the Schwarzschild black hole. This phenomenological correspondence between black holes and fluids is established by means of the model liquid's pair-correlation function and the two-body atomic interaction potential. These latter two functions are calculated exactly in terms of the black hole internal (quasilocal) energy and the isothermal compressibility. We find the existence of a ``screening" like effect for the components of the liquid.Comment: 20 pages and 6 Encapsulated PostScript figure

Brans-Dicke wormholes in the Jordan and Einstein frames

We examine the possibility of static wormhole solutions in the vacuum Brans-Dicke theory both in the original (Jordan) frame and in the conformally rescaled (Einstein) frame. It turns out that, in the former frame, wormholes exist only in a very narrow interval of the coupling parameter, viz., -3/2<omega<-4/3. It is shown that these wormholes are not traversable in practice. In the latter frame, wormhole solutions do not exist at all unless energy conditions are violated by hand.Comment: Minor errors corrected, uploaded for the benefit of the researcher