Summary of the Superconducting RF Linac for Muon Collider and Neutrino Factory

Project-X is a proposed project to be built at Fermi National Accelerator Laboratory with several potential missions. A primary part of the Project-X accelerator chain is a Superconducting linac, and In October 2009 a workshop was held to concentrate on the linac parameters. The charge of the workshop was to "..focus only on the SRF linac approaches and how it can be used...". The focus of Working Group 2 of this workshop was to evaluate how the different linac options being considered impact the potential realization of Muon Collider (MC) and Neutrino Factory (NF) applications. In particular the working group charge was, "to investigate the use of a multi-megawatt proton linac to target, phase rotate and collect muons to support a muon collider and neutrino factory". To focus the working group discussion, three primary questions were identified early on, to serve as a reference: 1) What are the proton source requirements for muon colliders and neutrino factories? 2) What are the issues with respect to realizing the required muon collider and neutrino factory proton sources? a. General considerations b. Considerations specific to the two linac configurations identified by Project-X. 3) What things need to be done before we can be reasonably confident that ICD1/ICD2 can be upgraded to provide the neutrino factory / muon collider needs? A number of presentations were given, and are available at the workshop web-site. This paper does not summarize the individual presentations, but rather addresses overall findings as related to the three guiding questions listed above.Comment: 6 pp. Workshop on Applications of High Intensity Proton Accelerators 19-21 Oct 2009: Batavia, Illinoi

Universal Statistics of the Critical Depinning Force of Elastic Systems in Random Media

We study the rescaled probability distribution of the critical depinning force of an elastic system in a random medium. We put in evidence the underlying connection between the critical properties of the depinning transition and the extreme value statistics of correlated variables. The distribution is Gaussian for all periodic systems, while in the case of random manifolds there exists a family of universal functions ranging from the Gaussian to the Gumbel distribution. Both of these scenarios are a priori experimentally accessible in finite, macroscopic, disordered elastic systems.Comment: 4 pages, 4 figure

Probabilistic analysis of algorithms for dual bin packing problems

In the dual bin packing problem, the objective is to assign items of given size to the largest possible number of bins, subject to the constraint that the total size of the items assigned to any bin is at least equal to 1. We carry out a probabilistic analysis of this problem under the assumption that the items are drawn independently from the uniform distribution on [0, 1] and reveal the connection between this problem and the classical bin packing problem as well as to renewal theory.

Progressive Probabilistic Hough Transform for line detection

We present a novel Hough Transform algorithm referred to as Progressive Probabilistic Hough Transform (PPHT). Unlike the Probabilistic HT where Standard HT is performed on a pre-selected fraction of input points, PPHT minimises the amount of computation needed to detect lines by exploiting the difference an the fraction of votes needed to detect reliably lines with different numbers of supporting points. The fraction of points used for voting need not be specified ad hoc or using a priori knowledge, as in the probabilistic HT; it is a function of the inherent complexity of the input data. The algorithm is ideally suited for real-time applications with a fixed amount of available processing time, since voting and line detection is interleaved. The most salient features are likely to be detected first. Experiments show that in many circumstances PPHT has advantages over the Standard HT

Probing the tails of the ground state energy distribution for the directed polymer in a random medium of dimension d=1,2,3d=1,2,3 via a Monte-Carlo procedure in the disorder

In order to probe with high precision the tails of the ground-state energy distribution of disordered spin systems, K\"orner, Katzgraber and Hartmann \cite{Ko_Ka_Ha} have recently proposed an importance-sampling Monte-Carlo Markov chain in the disorder. In this paper, we combine their Monte-Carlo procedure in the disorder with exact transfer matrix calculations in each sample to measure the negative tail of ground state energy distribution $P_d(E_0)$ for the directed polymer in a random medium of dimension $d=1,2,3$. In $d=1$, we check the validity of the algorithm by a direct comparison with the exact result, namely the Tracy-Widom distribution. In dimensions $d=2$ and $d=3$, we measure the negative tail up to ten standard deviations, which correspond to probabilities of order $P_d(E_0) \sim 10^{-22}$. Our results are in agreement with Zhang's argument, stating that the negative tail exponent $\eta(d)$ of the asymptotic behavior $\ln P_d (E_0) \sim - | E_0 |^{\eta(d)}$ as $E_0 \to -\infty$ is directly related to the fluctuation exponent $\theta(d)$ (which governs the fluctuations $\Delta E_0(L) \sim L^{\theta(d)}$ of the ground state energy $E_0$ for polymers of length $L$) via the simple formula $\eta(d)=1/(1-\theta(d))$. Along the paper, we comment on the similarities and differences with spin-glasses.Comment: 13 pages, 16 figure

Fluctuating Fronts as Correlated Extreme Value Problems: An Example of Gaussian Statistics

In this paper, we view fluctuating fronts made of particles on a one-dimensional lattice as an extreme value problem. The idea is to denote the configuration for a single front realization at time $t$ by the set of co-ordinates $\{k_i(t)\}\equiv[k_1(t),k_2(t),...,k_{N(t)}(t)]$ of the constituent particles, where $N(t)$ is the total number of particles in that realization at time $t$. When $\{k_i(t)\}$ are arranged in the ascending order of magnitudes, the instantaneous front position can be denoted by the location of the rightmost particle, i.e., by the extremal value $k_f(t)=\text{max}[k_1(t),k_2(t),...,k_{N(t)}(t)]$. Due to interparticle interactions, $\{k_i(t)\}$ at two different times for a single front realization are naturally not independent of each other, and thus the probability distribution $P_{k_f}(t)$ [based on an ensemble of such front realizations] describes extreme value statistics for a set of correlated random variables. In view of the fact that exact results for correlated extreme value statistics are rather rare, here we show that for a fermionic front model in a reaction-diffusion system, $P_{k_f}(t)$ is Gaussian. In a bosonic front model however, we observe small deviations from the Gaussian.Comment: 6 pages, 3 figures, miniscule changes on the previous version, to appear in Phys. Rev.

Contest based on a directed polymer in a random medium

We introduce a simple one-parameter game derived from a model describing the properties of a directed polymer in a random medium. At his turn, each of the two players picks a move among two alternatives in order to maximize his final score, and minimize opponent's return. For a game of length $n$, we find that the probability distribution of the final score $S_n$ develops a traveling wave form, ${\rm Prob}(S_n=m)=f(m-v n)$, with the wave profile $f(z)$ unusually decaying as a double exponential for large positive and negative $z$. In addition, as the only parameter in the game is varied, we find a transition where one player is able to get his maximum theoretical score. By extending this model, we suggest that the front velocity $v$ is selected by the nonlinear marginal stability mechanism arising in some traveling wave problems for which the profile decays exponentially, and for which standard traveling wave theory applies

Universal distribution of threshold forces at the depinning transition

We study the distribution of threshold forces at the depinning transition for an elastic system of finite size, driven by an external force in a disordered medium at zero temperature. Using the functional renormalization group (FRG) technique, we compute the distribution of pinning forces in the quasi-static limit. This distribution is universal up to two parameters, the average critical force, and its width. We discuss possible definitions for threshold forces in finite-size samples. We show how our results compare to the distribution of the latter computed recently within a numerical simulation of the so-called critical configuration.Comment: 12 pages, 7 figures, revtex