Numerical analysis of the master equation

Applied to the master equation, the usual numerical integration methods, such as Runge-Kutta, become inefficient when the rates associated with various transitions differ by several orders of magnitude. We introduce an integration scheme that remains stable with much larger time increments than can be used in standard methods. When only the stationary distribution is required, a direct iteration method is even more rapid; this method may be extended to construct the quasi-stationary distribution of a process with an absorbing state. Applications to birth-and-death processes reveal gains in efficiency of two or more orders of magnitude.Comment: 7 pages 3 figure

Garnet: a middleware architecture for distributing data streams originating in wireless sensor networks

We present an architectural framework, Garnet, which provides a data stream centric abstraction to encourage the manipulation and exploitation of data generated in sensor networks. By providing middleware services to allow mutually-unaware applications to manipulate sensor behaviour, a scalable, extensible platform is provided. We focus on sensor networks with transmit and receive capabilities as this combination poses greater challenges for managing and distributing sensed data. Our approach allows simple and sophisticated sensors to coexist, and allows data consumers to be mutually unaware of each other This also promotes the use of middleware services to mediate among consumers with potentially conflicting demands for shared data. Garnet has been implemented in Java, and we report on our progress to date and outline some likely scenarios where the use of our distributed architecture and accompanying middleware support enhances the task of sharing data in sensor network environments

Asymptotic behavior of the order parameter in a stochastic sandpile

We derive the first four terms in a series for the order paramater (the stationary activity density rho) in the supercritical regime of a one-dimensional stochastic sandpile; in the two-dimensional case the first three terms are reported. We reorganize the pertubation theory for the model, recently derived using a path-integral formalism [R. Dickman e R. Vidigal, J. Phys. A 35, 7269 (2002)], to obtain an expansion for stationary properties. Since the process has a strictly conserved particle density p, the Fourier mode N^{-1} psi_{k=0} -> p, when the number of sites N -> infinity, and so is not a random variable. Isolating this mode, we obtain a new effective action leading to an expansion for rho in the parameter kappa = 1/(1+4p). This requires enumeration and numerical evaluation of more than 200 000 diagrams, for which task we develop a computational algorithm. Predictions derived from this series are in good accord with simulation results. We also discuss the nature of correlation functions and one-site reduced densities in the small-kappa (large-p) limit.Comment: 18 pages, 5 figure

Variable-rate data sampling for low-power microsystems using modified Adams methods

A method for variable-rate data sampling is proposed for the purpose of low-power data acquisition in a small footprint microsystem. The procedure enables energy saving by utilizing dynamic power management techniques and is based on the Adams-Bashforth and Adams-Moulton multistep predictor-corrector methods for ordinary differential equations. Newton-Gregory backward difference interpolation formulae and past value substitution are used to facilitate sample rate changes. It is necessary to store only 2m+1 equispaced past values of t and the corresponding values of y, where y=g(t), and m is the number of steps in the Adams methods. For the purposes of demonstrating the technique, fourth-order methods are used, but it is possible to use higher orders to improve accuracy if required

Path-integral representation for a stochastic sandpile

We introduce an operator description for a stochastic sandpile model with a conserved particle density, and develop a path-integral representation for its evolution. The resulting (exact) expression for the effective action highlights certain interesting features of the model, for example, that it is nominally massless, and that the dynamics is via cooperative diffusion. Using the path-integral formalism, we construct a diagrammatic perturbation theory, yielding a series expansion for the activity density in powers of the time.Comment: 22 pages, 6 figure

Greater Confinement Disposal Test at the Nevada Test Site, Final Technology Report

The Greater Confinement Disposal Test (GCDT) was conducted at the Nevada Test Site to demonstrate an alternative method for management of high-specific-activity (HSA) low-level waste (LLW). The GCDT was initially conceived as a method for managing small volumes of highly concentrated tritium wastes, which, due to their environmental mobiilty, are considered unsuitable for routine shallow land disposal. Later, the scope of the GCDT was increased to address a variety of other "problem" HSA wastes including isotope sources and thermal generating wastes. The basic design for the GCDT evolved from a series of studies and assessments. Operational design objectives were to (1) emplace the wastes at a depth sufficient to minimize or eliminate routine environmental transport mechanisms and instrusion scenarios and (2) provide sufficient protection for operations personnel in the handling of HSA sources. To achieve both objectives, a large diameter borehole was selected. The GCDT consisted of a borehole 3 meters (10 feet) in diameter and 36 meters (120 feet) deep, surrounded by nine monitoring holes at varying radii. The GCDT was instrumented for the measurement of temperature, moisture, and soil-gas content. Over one million curies of HSA LLW were emplaced in GCDT. This report reviews the development of the GCDT project and presents analyses of data collected

Maximum entropy approach to power-law distributions in coupled dynamic-stochastic systems

Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a power-law statistics are investigated. It is demonstrated that, from a quite general point of view, the power-law dependencies may appear as a consequence of "global" constraints restricting both the dynamic phase space and the stochastic fluctuations. As a result, at sufficiently long observation times the dynamic counterpart is driven into a non-equilibrium steady state whose deviation from the usual exponential statistics is given by the distance from the conventional equilibrium