Directed percolation with incubation times

We introduce a model for directed percolation with a long-range temporal diffusion, while the spatial diffusion is kept short ranged. In an interpretation of directed percolation as an epidemic process, this non-Markovian modification can be understood as incubation times, which are distributed accordingly to a Levy distribution. We argue that the best approach to find the effective action for this problem is through a generalization of the Cardy-Sugar method, adding the non-Markovian features into the geometrical properties of the lattice. We formulate a field theory for this problem and renormalize it up to one loop in a perturbative expansion. We solve the various technical difficulties that the integrations possess by means of an asymptotic analysis of the divergences. We show the absence of field renormalization at one-loop order, and we argue that this would be the case to all orders in perturbation theory. Consequently, in addition to the characteristic scaling relations of directed percolation, we find a scaling relation valid for the critical exponents of this theory. In this universality class, the critical exponents vary continuously with the Levy parameter.Comment: 17 pages, 7 figures. v.2: minor correction

Crystallization and gelation in colloidal systems with short-ranged attractive interactions

We systematically study the relationship between equilibrium and non-equilibrium phase diagrams of a system of short-ranged attractive colloids. Using Monte Carlo and Brownian dynamics simulations we find a window of enhanced crystallization that is limited at high interaction strength by a slowing down of the dynamics and at low interaction strength by the high nucleation barrier. We find that the crystallization is enhanced by the metastable gas-liquid binodal by means of a two-stage crystallization process. First, the formation of a dense liquid is observed and second the crystal nucleates within the dense fluid. In addition, we find at low colloid packing fractions a fluid of clusters, and at higher colloid packing fractions a percolating network due to an arrested gas-liquid phase separation that we identify with gelation. We find that this arrest is due to crystallization at low interaction energy and it is caused by a slowing down of the dynamics at high interaction strength. Likewise, we observe that the clusters which are formed at low colloid packing fractions are crystalline at low interaction energy, but glassy at high interaction energy. The clusters coalesce upon encounter.Comment: 8 pages, 8 figure

Stellar Dynamics at the Galactic Center with an Extremely Large Telescope

We discuss experiments achievable via monitoring of stellar dynamics near the massive black hole at the Galactic center with a next generation, extremely large telescope (ELT). Given the likely observational capabilities of an ELT and current knowledge of the stellar environment at the Galactic center, we synthesize plausible samples of stellar orbits around the black hole. We use the Markov Chain Monte Carlo method to evaluate the constraints that orbital monitoring places on the matter content near the black hole. Results are expressed as functions of the number N of stars with detectable orbital motions and the astrometric precision dtheta and spectroscopic precision dv at which stellar proper motions and radial velocities are monitored. For N = 100, dtheta = 0.5 mas, and dv = 10 km/s -- a conservative estimate of the capabilities of a 30 meter telescope -- the extended matter distribution enclosed by the orbits will produce measurable deviations from Keplerian motion if >1000 Msun is enclosed within 0.01 pc. The black hole mass and distance to the Galactic center will be measured to better than ~0.1%. Lowest-order relativistic effects, such as the prograde precession, will be detectable if dtheta < 0.5 mas. Higher-order effects, including frame dragging due to black hole spin, requires dtheta < 0.05 mas, or the favorable discovery of a compact, highly eccentric orbit. Finally, we calculate the rate at which monitored stars undergo detectable nearby encounters with background stars. Such encounters probe the mass function of stellar remnants that accumulate near the black hole. We find that ~30 encounters will be detected over a 10 yr baseline for dtheta = 0.5 mas.Comment: 14 pages, 5 figures; discussion no longer aperture-specific (TMT -> ELT), matches ApJ versio

A glimpse at the flat-spacetime limit of quantum gravity using the Bekenstein argument in reverse

An insightful argument for a linear relation between the entropy and the area of a black hole was given by Bekenstein using only the energy-momentum dispersion relation, the uncertainty principle, and some properties of classical black holes. Recent analyses within String Theory and Loop Quantum Gravity describe black-hole entropy in terms of a dominant contribution, which indeed depends linearly on the area, and a leading log-area correction. We argue that, by reversing the Bekenstein argument, the log-area correction can provide insight on the energy-momentum dispersion relation and the uncertainty principle of a quantum-gravity theory. As examples we consider the energy-momentum dispersion relations that recently emerged in the Loop Quantum Gravity literature and the Generalized Uncertainty Principle that is expected to hold in String Theory.Comment: 7 pages, LaTex; this essay received an "honorable mention" in the 2004 Essay Competition of the Gravity Research Foundation; submitted to IJMPD on 23 June 2004; published as Int.J.Mod.Phys.D13:2337-2343,200

Chameleonic dilaton, nonequivalent frames, and the cosmological constant problem in quantum string theory

The chameleonic behaviour of the String theory dilaton is suggested. Some of the possible consequences of the chameleonic string dilaton are analyzed in detail. In particular, (1) we suggest a new stringy solution to the cosmological constant problem and (2) we point out the non-equivalence of different conformal frames at the quantum level. In order to obtain these results, we start taking into account the (strong coupling) string loop expansion in the string frame (S-frame), therefore the so-called form factors are present in the effective action. The correct Dark Energy scale is recovered in the Einstein frame (E-frame) without unnatural fine-tunings and this result is robust against all quantum corrections, granted that we assume a proper structure of the S-frame form factors in the strong coupling regime. At this stage, the possibility still exists that a certain amount of fine-tuning may be required to satisfy some phenomenological constraints. Moreover in the E-frame, in our proposal, all the interactions are switched off on cosmological length scales (i.e. the theory is IR-free), while higher derivative gravitational terms might be present locally (on short distances) and it remains to be seen whether these facts clash with phenomenology. A detailed phenomenological analysis is definitely necessary to clarify these points

Dynamics and delocalisation transition for an interface driven by a uniform shear flow

We study the effect of a uniform shear flow on an interface separating the two broken-symmetry ordered phases of a two-dimensional system with nonconserved scalar order parameter. The interface, initially flat and perpendicular to the flow, is distorted by the shear flow. We show that there is a critical shear rate, \gamma_c, proportional to 1/L^2, (where L is the system width perpendicular to the flow) below which the interface can sustain the shear. In this regime the countermotion of the interface under its curvature balances the shear flow, and the stretched interface stabilizes into a time-independent shape whose form we determine analytically. For \gamma > \gamma_c, the interface acquires a non-zero velocity, whose profile is shown to reach a time-independent limit which we determine exactly. The analytical results are checked by numerical integration of the equations of motion.Comment: 5 page

On the nonextensive character of some magnetic systems

During the past few years, nonextensive statistics has been successfully applied to explain many different kinds of systems. Through these studies some interpretations of the entropic parameter q, which has major role in this statistics, in terms of physical quantities have been obtained. The aim of the present work is to yield an overview of the applications of nonextensive statistics to complex problems such as inhomogeneous magnetic systems.Comment: to appear in the Proceedings of the conference CTNEXT07, Complexity, Metastability and Nonextensivity, Catania, Italy, 1-5 July 2007, Eds. S. Abe, H.J. Herrmann, P. Quarati, A. Rapisarda and C. Tsallis (American Institute of Physics, 2007) in pres

Towards wave extraction in numerical relativity: the quasi-Kinnersley frame

The Newman-Penrose formalism may be used in numerical relativity to extract coordinate-invariant information about gravitational radiation emitted in strong-field dynamical scenarios. The main challenge in doing so is to identify a null tetrad appropriately adapted to the simulated geometry such that Newman-Penrose quantities computed relative to it have an invariant physical meaning. In black hole perturbation theory, the Teukolsky formalism uses such adapted tetrads, those which differ only perturbatively from the background Kinnersley tetrad. At late times, numerical simulations of astrophysical processes producing isolated black holes ought to admit descriptions in the Teukolsky formalism. However, adapted tetrads in this context must be identified using only the numerically computed metric, since no background Kerr geometry is known a priori. To do this, this paper introduces the notion of a quasi-Kinnersley frame. This frame, when space-time is perturbatively close to Kerr, approximates the background Kinnersley frame. However, it remains calculable much more generally, in space-times non-perturbatively different from Kerr. We give an explicit solution for the tetrad transformation which is required in order to find this frame in a general space-time.Comment: 13 pages, 3 figure