Sampling rare fluctuations of height in the Oslo ricepile model

We have studied large deviations of the height of the pile from its mean value in the Oslo ricepile model. We sampled these very rare events with probabilities of order $10^{-100}$ by Monte Carlo simulations using importance sampling. These simulations check our qualitative arguement [Phys. Rev. E, {\bf 73}, 021303, 2006] that in steady state of the Oslo ricepile model, the probability of large negative height fluctuations $\Delta h=-\alpha L$ about the mean varies as $\exp(-\kappa {\alpha}^4 L^3)$ as $L \to \infty$ with $\alpha$ held fixed, and $\kappa > 0$.Comment: 7 pages, 8 figure

Pairs of inner projections and two applications

Orthogonal projections onto closed subspaces of $H^2(\mathbb{D}^n)$ of the form $\varphi H^2(\mathbb{D}^n)$ for inner functions $\varphi$ on $\mathbb{D}^n$ are referred to as inner projections, where $H^2(\mathbb{D}^n)$ denotes the Hardy space over the open unit polydisc $\mathbb{D}^n$. In this paper, we classify pairs of commuting inner projections. We also present two seemingly independent applications: the first is an answer to a question posed by R. G. Douglas, and the second is a complete classification of partially isometric truncated Toeplitz operators with inner symbols on the polydisc.Comment: 18 page

Probability distribution of residence times of grains in models of ricepiles

We study the probability distribution of residence time of a grain at a site, and its total residence time inside a pile, in different ricepile models. The tails of these distributions are dominated by the grains that get deeply buried in the pile. We show that, for a pile of size $L$, the probabilities that the residence time at a site or the total residence time is greater than $t$, both decay as $1/t(\ln t)^x$ for $L^{\omega} \ll t \ll \exp(L^{\gamma})$ where $\gamma$ is an exponent $\ge 1$, and values of $x$ and $\omega$ in the two cases are different. In the Oslo ricepile model we find that the probability that the residence time $T_i$ at a site $i$ being greater than or equal to $t$, is a non-monotonic function of $L$ for a fixed $t$ and does not obey simple scaling. For model in $d$ dimensions, we show that the probability of minimum slope configuration in the steady state, for large $L$, varies as $\exp(-\kappa L^{d+2})$ where $\kappa$ is a constant, and hence $\gamma = d+2$.Comment: 13 pages, 23 figures, Submitted to Phys. Rev.

Close Circuit Security System Using At89c51

The purpose of this project is to provide a field that’s depending on less manual operations because everyone is interested in automated systems. To face new challenges in the present day situation automated systems are more accurate, flexible and reliable. Due to these reasons every field prefers automated control systems. Especially in electronics automated systems are doing better job. The ideal system to protect your property is CCTV (Closed Circuit Television) Not only does it act a visual deterrent but the video or digital recording provides an invaluable method of recording crime, violence or anti-social behaviour. CCTV systems offer such a wide area of applications and benefits 24-hours a day. Systems can aid the monitoring of stock, personnel, visitors, access control and prevent health and safety incidences

Probability distribution of residence-times of grains in sandpile models

We show that the probability distribution of the residence-times of sand grains in sandpile models, in the scaling limit, can be expressed in terms of the survival probability of a single diffusing particle in a medium with absorbing boundaries and space-dependent jump rates. The scaling function for the probability distribution of residence times is non-universal, and depends on the probability distribution according to which grains are added at different sites. We determine this function exactly for the 1-dimensional sandpile when grains are added randomly only at the ends. For sandpiles with grains are added everywhere with equal probability, in any dimension and of arbitrary shape, we prove that, in the scaling limit, the probability that the residence time greater than t is exp(-t/M), where M is the average mass of the pile in the steady state. We also study finite-size corrections to this function.Comment: 8 pages, 5 figures, extra file delete