Hanbury Brown and Twiss Correlations of Anderson Localized Waves

When light waves propagate through disordered photonic lattices, they can eventually become localized due to multiple scattering effects. Here we show experimentally that while the evolution and localization of the photon density distribution is similar in the two cases of diagonal and off-diagonal disorder, the density-density correlation carries a distinct signature of the type of disorder. We show that these differences reflect a symmetry in the spectrum and eigenmodes that exists in off-diagonally disordered lattices but is absent in lattices with diagonal disorder.Comment: 4 pages, 3 figures, comments welcom

Relativistic Photon Mediated Shocks

A system of equations governing the structure of a steady, relativistic radiation dominated shock is derived, starting from the general form of the transfer equation obeyed by the photon distribution function. Closure is obtained by truncating the system of moment equations at some order. The anisotropy of the photon distribution function inside the shock is shown to increase with increasing shock velocity, approaching nearly perfect beaming at upstream Lorentz factors $\Gamma_{-}>>1$. Solutions of the shock equations are presented for some range of upstream conditions. These solutions are shown to converge as the truncation order is increased.Comment: 5 pages, a shorter version will appear in PR

Thermal collapse of a granular gas under gravity

Free cooling of a gas of inelastically colliding hard spheres represents a central paradigm of kinetic theory of granular gases. At zero gravity the temperature of a freely cooling homogeneous granular gas follows a power law in time. How does gravity, which brings inhomogeneity, affect the cooling? We combine molecular dynamics simulations, a numerical solution of hydrodynamic equations and an analytic theory to show that a granular gas cooling under gravity undergoes thermal collapse: it cools down to zero temperature and condenses on the bottom of the container in a finite time.Comment: 4 pages, 12 eps figures, to appear in PR

Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas

We employ Navier-Stokes granular hydrodynamics to investigate the long-time behavior of clustering instability in a freely cooling dilute granular gas in two dimensions. We find that, in circular containers, the homogeneous cooling state (HCS) of the gas loses its stability via a sub-critical pitchfork bifurcation. There are no time-independent solutions for the gas density in the supercritical region, and we present analytical and numerical evidence that the gas develops thermal collapse unarrested by heat diffusion. To get more insight, we switch to a simpler geometry of a narrow-sector-shaped container. Here the HCS loses its stability via a transcritical bifurcation. For some initial conditions a time-independent inhomogeneous density profile sets in, qualitatively similar to that previously found in a narrow-channel geometry. For other initial conditions, however, the dilute gas develops thermal collapse unarrested by heat diffusion. We determine the dynamic scalings of the flow close to collapse analytically and verify them in hydrodynamic simulations. The results of this work imply that, in dimension higher than one, Navier-Stokes hydrodynamics of a dilute granular gas is prone to finite-time density blowups. This provides a natural explanation to the formation of densely packed clusters of particles in a variety of initially dilute granular flows.Comment: 18 pages, 19 figure

Discrete charging of metallic grains: Statistics of addition spectra

We analyze the statistics of electrostatic energies (and their differences) for a quantum dot system composed of a finite number $K$ of electron islands (metallic grains) with random capacitance-inductance matrix $C$, for which the total charge is discrete, $Q=Ne$ (where $e$ is the charge of an electron and $N$ is an integer). The analysis is based on a generalized charging model, where the electrons are distributed among the grains such that the electrostatic energy E(N) is minimal. Its second difference (inverse compressibility) $\chi_{N}=E(N+1)-2 E(N)+E(N-1)$ represents the spacing between adjacent Coulomb blockade peaks appearing when the conductance of the quantum dot is plotted against gate voltage. The statistics of this quantity has been the focus of experimental and theoretical investigations during the last two decades. We provide an algorithm for calculating the distribution function corresponding to $\chi_{N}$ and show that this function is piecewise polynomial.Comment: 21 pages, no figures, mathematical nomenclature (except for Abstract and Introduction

Layered connectors: revisiting the formal basis of architectural connection for complex distributed systems

The complex distributed systems of nowadays require the dynamic composition of multiple components, which are autonomous and so complex that they can be considered as systems in themselves. These components often use different application protocols and are implemented on top of heterogeneous middleware, which hamper their successful interaction. The explicit and rigorous description and analysis of components interaction is essential in order to enable the dynamic composition of these components. In this paper, we propose a formal approach to represent and reason about interactions between components using layered connectors. Layered connectors describe components interaction at both the application and middleware layers and make explicit the role of middleware in the realisation of this interaction. We provide formal semantics of layered connectors and present an approach for the synthesis of layered connectors in order to enable the dynamic composition of highly heterogeneous components. We validate our approach through a case study in the area of collaborative emergency management

A nonlinear theory of non-stationary low Mach number channel flows of freely cooling nearly elastic granular gases

We use hydrodynamics to investigate non-stationary channel flows of freely cooling dilute granular gases. We focus on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity. Eliminating the acoustic modes, we reduce the hydrodynamic equations to a single nonlinear and nonlocal equation of a reaction-diffusion type in Lagrangian coordinates. This equation describes a broad class of channel flows and, in particular, can follow the development of the clustering instability from a weakly perturbed homogeneous cooling state to strongly nonlinear states. If the heat diffusion is neglected, the reduced equation is exactly soluble, and the solution develops a finite-time density blowup. The heat diffusion, however, becomes important near the attempted singularity. It arrests the density blowup and brings about novel inhomogeneous cooling states (ICSs) of the gas, where the pressure continues to decay with time, while the density profile becomes time-independent. Both the density profile of an ICS, and the characteristic relaxation time towards it are determined by a single dimensionless parameter that describes the relative role of the inelastic energy loss and heat diffusion. At large values of this parameter, the intermediate cooling dynamics proceeds as a competition between low-density regions of the gas. This competition resembles Ostwald ripening: only one hole survives at the end.Comment: 20 pages, 15 figures, final versio

A unifying perspective on protocol mediation: interoperability in the Future Internet

Given the highly dynamic and extremely heterogeneous software systems composing the Future Internet, automatically achieving interoperability between software components —without modifying them— is more than simply desirable, it is quickly becoming a necessity. Although much work has been carried out on interoperability, existing solutions have not fully succeeded in keeping pace with the increasing complexity and heterogeneity of modern software, and meeting the demands of runtime support. On the one hand, solutions at the application layer target higher automation and loose coupling through the synthesis of intermediary entities, mediators, to compensate for the differences between the interfaces of components and coordinate their behaviours, while assuming the use of the same middleware solution. On the other hand, solutions to interoperability across heterogeneous middleware technologies do not reconcile the differences between components at the application layer. In this paper we propose a unified approach for achieving interoperability between heterogeneous software components with compatible functionalities across the application and middleware layers. First, we provide a solution to automatically generate cross-layer parsers and composers that abstract network messages into a uniform representation independent of the middleware used. Second, these generated parsers and composers are integrated within a mediation framework to support the deployment of the mediators synthesised at the application layer. More specifically, the generated parser analyses the network messages received from one component and transforms them into a representation that can be understood by the application-level mediator. Then, the application-level mediator performs the necessary data conversion and behavioural coordination. Finally, the composer transforms the representation produced by the application-level mediator into network messages that can be sent to the other component. The resulting unified mediation framework reconciles the differences between software components from the application down to the middleware layers. We validate our approach through a case study in the area of conference management