One-Dimensional Directed Sandpile Models and the Area under a Brownian Curve

We derive the steady state properties of a general directed ``sandpile'' model in one dimension. Using a central limit theorem for dependent random variables we find the precise conditions for the model to belong to the universality class of the Totally Asymmetric Oslo model, thereby identifying a large universality class of directed sandpiles. We map the avalanche size to the area under a Brownian curve with an absorbing boundary at the origin, motivating us to solve this Brownian curve problem. Thus, we are able to determine the moment generating function for the avalanche-size probability in this universality class, explicitly calculating amplitudes of the leading order terms.Comment: 24 pages, 5 figure

Analytical approximation to the multidimensional Fokker--Planck equation with steady state

The Fokker--Planck equation is a key ingredient of many models in physics, and related subjects, and arises in a diverse array of settings. Analytical solutions are limited to special cases, and resorting to numerical simulation is often the only route available; in high dimensions, or for parametric studies, this can become unwieldy. Using asymptotic techniques, that draw upon the known Ornstein--Uhlenbeck (OU) case, we consider a mean-reverting system and obtain its representation as a product of terms, representing short-term, long-term, and medium-term behaviour. A further reduction yields a simple explicit formula, both intuitive in terms of its physical origin and fast to evaluate. We illustrate a breadth of cases, some of which are `far' from the OU model, such as double-well potentials, and even then, perhaps surprisingly, the approximation still gives very good results when compared with numerical simulations. Both one- and two-dimensional examples are considered.Comment: Updated version as publishe

Distribution of the time at which the deviation of a Brownian motion is maximum before its first-passage time

We calculate analytically the probability density $P(t_m)$ of the time $t_m$ at which a continuous-time Brownian motion (with and without drift) attains its maximum before passing through the origin for the first time. We also compute the joint probability density $P(M,t_m)$ of the maximum $M$ and $t_m$. In the driftless case, we find that $P(t_m)$ has power-law tails: $P(t_m)\sim t_m^{-3/2}$ for large $t_m$ and $P(t_m)\sim t_m^{-1/2}$ for small $t_m$. In presence of a drift towards the origin, $P(t_m)$ decays exponentially for large $t_m$. The results from numerical simulations are in excellent agreement with our analytical predictions.Comment: 13 pages, 5 figures. Published in Journal of Statistical Mechanics: Theory and Experiment (J. Stat. Mech. (2007) P10008, doi:10.1088/1742-5468/2007/10/P10008

Wave function-dependent mobility and suppression of interface roughness scattering in a strained SiGe p-channel field-effect structure

The 4 K Hall mobility has been measured in a top-gated, inverted, modulation-doped Si/Si0.8Ge0.2 structure having a Si:B doping layer beneath the alloy. From comparisons with theoretical calculations, we argue that, unlike an ordinary enhancement-mode SiGe p-channel metal–oxide–semiconductor structure, this configuration leads to a decrease of interface roughness scattering with increasing sheet carrier density. We also speculate on the nature of the interface charge observed in these structures at low temperature

A study of multiplex data bus techniques for the space shuttle

A comprehensive technology base for the design of a multiplexed data bus subsystem is provided. Extensive analyses, both analytical and empirical, were performed. Subjects covered are classified under the following headings: requirements identification and analysis; transmission media studies; signal design and detection studies; synchronization, timing, and control studies; user-subsystem interface studies; operational reliability analyses; design of candidate data bus configurations; and evaluation of candidate data bus designs

The Impact of the Level of Feed-On-Offer Available to Merino Ewes During Winter-Spring on the Wool Production of Their Progeny as Adults

New opportunities for developing optimum ewe management systems, based on achieving liveweight and body condition score (CS) targets at critical stages of the reproductive cycle, have emerged from the acceptance that nutrition during pregnancy can have substantial impacts on the lifetime wool performance of the progeny (Kelly et al,. 1996). However, most studies of the impacts of nutrition on foetal growth and development tended to focus on late pregnancy and have also only considered extreme nutritional regimes often outside the boundaries of commercial reality. Hence, the Lifetime Wool team (Thompson & Oldham, 2004) conducted dose-response experiments to determine the levels of feed-on-offer (FOO; kg dry matter/ha; Hyder et al., 2004) needed at different stages of the reproductive cycle to optimise both wool and meat production per ha in the short term and the lifetime performance of the progeny in the long term. This paper reports the response in the first two years of the experiment of clean fleece weight (CFW) and fibre diameter (FD) of the progeny as adults to the level of FOO available to their mother in late pregnancy and lactation