Extreme fluctuations and the finite lifetime of the turbulent state

We argue that the transition to turbulence is controlled by large amplitude events that follow extreme distribution theory. The theory suggests an explanation for recent observations of the turbulent state lifetime which exhibit super-exponential scaling behaviour with Reynolds number.Comment: Change log: Universality of c2/c1 argument has been removed, scaling with size of puff added. To appear in Phys. Rev. E Rapid Communications

Global fluctuations and Gumbel statistics

We explain how the statistics of global observables in correlated systems can be related to extreme value problems and to Gumbel statistics. This relationship then naturally leads to the emergence of the generalized Gumbel distribution G_a(x), with a real index a, in the study of global fluctuations. To illustrate these findings, we introduce an exactly solvable nonequilibrium model describing an energy flux on a lattice, with local dissipation, in which the fluctuations of the global energy are precisely described by the generalized Gumbel distribution.Comment: 4 pages, 3 figures; final version with minor change

Distribution of extremes in the fluctuations of two-dimensional equilibrium interfaces

We investigate the statistics of the maximal fluctuation of two-dimensional Gaussian interfaces. Its relation to the entropic repulsion between rigid walls and a confined interface is used to derive the average maximal fluctuation $\sim \sqrt{2/(\pi K)} \ln N$ and the asymptotic behavior of the whole distribution $P(m) \sim N^2 e^{-{\rm (const)} N^2 e^{-\sqrt{2\pi K} m} - \sqrt{2\pi K} m}$ for $m$ finite with $N^2$ and $K$ the interface size and tension, respectively. The standardized form of $P(m)$ does not depend on $N$ or $K$, but shows a good agreement with Gumbel's first asymptote distribution with a particular non-integer parameter. The effects of the correlations among individual fluctuations on the extreme value statistics are discussed in our findings.Comment: 4 pages, 4 figures, final version in PR

1989 Commencement Address: Bryant Gumbel

Bryant Gumbel, host of NBC\u27s Today Show, will receive an honorary degree, Doctor of Public Service, from the College of the Holy Cross and address this year’s graduates during the College’s Commencement ceremonies on Friday, May 26, at 10:30 a.m. on the campus. Gumbel, the Today program host since January 1982, has anchored NBC news, sports and entertainment broadcasts from around the globe and across the country, including NBC\u27s coverage of the 1988 Summer Olympics in Seoul, Korea. Gumbel has received numerous awards for broadcasting and journalism, including the Edward R. Murrow Award for Outstanding Foreign Affairs Work, the Edward Weintal Prize for diplomatic reporting, 1986 Broadcaster of the Year, the Graham McNamee Award, and the 1988 NAACP Image Award. Following graduation from Bates College, Gumbel was a sportswriter for Black Sports magazine. He entered broadcasting as a sportscaster for KNBC-TV in Los Angeles in 1972, where he remained until 1980. During that period, Gumbel also worked for NBC sports, co-hosting the National Footbal League pre-game show, major league baseball, NCAA basketball and NFL games.https://crossworks.holycross.edu/commence_address/1013/thumbnail.jp

The Federal Prosecution of Al Capone and Its Impact on the Evidentiary Evolution of Forensic Accounting

In the prohibition-era, Alphonse ‘Al’ Capone’s notoriety in Chicago was at its height, and a conglomerate investigation composed of multiple Federal departments launched to take down the impenetrable mobster. Capone’s sound completion of crimes and the threat of retaliation towards key-witnesses inhibited the success of the investigation for the Federal government. Therefore, the Treasury Department’s special investigative unit took charge, seeking to unveil the vast income that Capone failed to report on tax filings. Their efforts led to the successful prosecution of the seemingly untouchable man. An examination of the legal structures in place that allowed for the utilization of tax evasion as a means of conviction are examined through the review of statutes and superseding tax evasion court rulings. In order to determine the role of forensic accounting in the Treasury Department’s approach, the efforts to acquire key evidence and the examination of those documents is reviewed. Furthermore, multiple landmark court cases are referenced in a legal chronology. Their citation of the Capone ruling as precedent is analyzed to determine their influence on the acceptance of tax evasion and forensic accounting as a legitimate practice in criminal investigations. This research investigation determined forensic accounting’s increased presence in criminal investigations and its influence on increasing the prevalence of tax evasion in union with the legal approach of pretextual prosecution

Investigations of potential mechanisms underlying spinal cord injury-induced polyuria.

Spinal cord injury (SCI) results in neurological impairments including motor, sensory, and autonomic dysfunction. These neurological deficits result in a litany of complications apart from muscular paralysis, including bladder, bowel, cardiovascular, and sexual function. SCI-induced polyuria (the overproduction/passage of urine) remains understudied, and therefore mechanisms behind it are largely unknown and require extensive investigation for potential targeted therapies to improve quality of life. The objective of this dissertation was to investigate potential mechanisms of SCI-induced polyuria and explore potential therapies to improve quality of life in the SCI population. Metabolic cages, Western blot, enzyme-linked immunoassay, and immunostaining were first used to determine the timing of fluctuations in biomarkers associated with SCI-induced polyuria, including arginine vasopressin (AVP), atrial natriuretic peptide (ANP), vasopressin 2 receptor (V2R), natriuretic peptide receptor A (NPRA), and epithelial sodium channel (ENaC). Next, to identify which neural substrates induce polyuria with a T9-level SCI, a higher level (T3) contusion above the local sympathetic supply to the kidneys were also examined. Lastly, the effect of anantin (NPRA antagonist) on SCI-induced polyuria was explored, in addition to utilizing an established treadmill activity-based recovery training (ABRT) program. There were significant alterations of multiple biomarkers after SCI, beginning at 7 days post injury (dpi), in addition to a lower number of AVP-labeled neurons in the hypothalamus. By 7 dpi, continuing through 6 weeks post-SCI, T3 contused rats showed a significant increase in 24-hour void volume as well as significant changes in ANP and AVP like the T9 injury. There was also a significant decrease in AVP-labelled cells in the suprachiasmatic nucleus post-T9 and T3 contusion relative to controls. A reduction in void volume was found for rats having ABRT but not anantin treatment. A significant decrease in mean arterial pressure was measured in all animal groups lasting chronically, and there was a significant increase in serum potassium at 14 dpi in addition to a significant decrease in serum sodium at the chronic time point. Together, these studies provide a detailed account of systemic responses to SCI that are associated with SCI-induced polyuria and fluid homeostasis

The capacitated transshipment location problem with stochastic handling utilities at the facilities

The problem consists in finding a transshipment facilities location that maximizes the total net utility when the handling utilities at the facilities are stochastic variables, under supply, demand, and lower and upper capacity constraints. The total net utility is given by the expected total shipping utility minus the total fixed cost of the located facilities. Shipping utilities are given by a deterministic utility for shipping freight from origins to destinations via transshipment facilities plus a stochastic handling utility at the facilities, whose probability distribution is unknown. After giving the stochastic model, by means of some results of the extreme values theory, the probability distribution of the maximum stochastic utilities is derived and the expected value of the optimum of the stochastic model is found. An efficient heuristics for solving real-life instances is also given. Computational results show a very good performance of the proposed methods both in terms of accuracy and efficienc

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.

Classical diffusion of N interacting particles in one dimension: General results and asymptotic laws

I consider the coupled one-dimensional diffusion of a cluster of N classical particles with contact repulsion. General expressions are given for the probability distributions, allowing to obtain the transport coefficients. In the limit of large N, and within a gaussian approximation, the diffusion constant is found to behave as N^{-1} for the central particle and as (\ln N)^{-1} for the edge ones. Absolute correlations between the edge particles increase as (\ln N)^{2}. The asymptotic one-body distribution is obtained and discussed in relation of the statistics of extreme events.Comment: 6 pages, 2 eps figure