1,027 research outputs found
A connection between the Camassa-Holm equations and turbulent flows in channels and pipes
In this paper we discuss recent progress in using the Camassa-Holm equations
to model turbulent flows. The Camassa-Holm equations, given their special
geometric and physical properties, appear particularly well suited for studying
turbulent flows. We identify the steady solution of the Camassa-Holm equation
with the mean flow of the Reynolds equation and compare the results with
empirical data for turbulent flows in channels and pipes. The data suggests
that the constant version of the Camassa-Holm equations, derived under
the assumptions that the fluctuation statistics are isotropic and homogeneous,
holds to order distance from the boundaries. Near a boundary, these
assumptions are no longer valid and the length scale is seen to depend
on the distance to the nearest wall. Thus, a turbulent flow is divided into two
regions: the constant region away from boundaries, and the near wall
region. In the near wall region, Reynolds number scaling conditions imply that
decreases as Reynolds number increases. Away from boundaries, these
scaling conditions imply is independent of Reynolds number. Given the
agreement with empirical and numerical data, our current work indicates that
the Camassa-Holm equations provide a promising theoretical framework from which
to understand some turbulent flows.Comment: tex file, 29 pages, 4 figures, Physics of Fluids (in press
Determination of the tunneling flight time as the reflected phase time
Using the time parameter in the time-dependent Schrödinger equation, we study the time of flight for a particle tunneling through a square barrier potential. Comparing the mean and variance of the energy and the flight time for transmitted and reflected particles, using both density and flux distributions, we find that, when accounting for momentum filtering, the suitably normalized transmitted and reflected distributions are identical in both the density and flux cases. In contrast to previous studies, we demonstrate that these results do not imply a vanishing tunneling time, but rather that the time it takes to tunnel through a square barrier is precisely given by the reflected phase time. For wide barriers, this becomes independent of the barrier width, as predicted independently by MacColl and Hartman. We show that these conclusions can be reached using a variety of arguments, including purely quantum mechanical ones. Analysis of the shapes of the distributions under consideration reveals that wave-packet reshaping is not an explanation for the MacColl-Hartman effect. The results presented here have direct implications for understanding recent experimental results in the study of the barrier crossing of rubidium atoms. The finite width of an incident wave packet significantly “masks” the tunneling time, and induces substantial asymmetry between the flight times of transmitted and reflected atoms
The relativistic tunneling flight time may be superluminal, but it does not imply superluminal signaling
Wavepacket tunneling, in the relativistic limit, is studied via solutions to the Dirac equation for a square barrier potential. Specifically, the arrival time distribution (the time-dependent flux) is computed for wavepackets initiated far away from the barrier, and whose momentum is well below the threshold for above-barrier transmission. The resulting distributions exhibit peaks at shorter times than those of photons with the same initial wavepacket transmitting through a vacuum. However, this apparent superluminality in time is accompanied by very low transmission probabilities. We discuss these observations, and related observations by other authors, in the context of published objections to the notion that tunneling can be superluminal in time. We find that many of these objections are not consistent with our observations, and conclude that post-selected (for transmission) distributions of arrival times can be superluminal. However, the low probability of tunneling means a photon will most likely be seen first and therefore the superluminality does not imply superluminal signaling
Optimal Schedules for Parallelizing Anytime Algorithms: The Case of Shared Resources
The performance of anytime algorithms can be improved by simultaneously
solving several instances of algorithm-problem pairs. These pairs may include
different instances of a problem (such as starting from a different initial
state), different algorithms (if several alternatives exist), or several runs
of the same algorithm (for non-deterministic algorithms). In this paper we
present a methodology for designing an optimal scheduling policy based on the
statistical characteristics of the algorithms involved. We formally analyze the
case where the processes share resources (a single-processor model), and
provide an algorithm for optimal scheduling. We analyze, theoretically and
empirically, the behavior of our scheduling algorithm for various distribution
types. Finally, we present empirical results of applying our scheduling
algorithm to the Latin Square problem
Prevention of suicidal behaviour in prisons: an overview of initiatives based on a systematic review of research on near-lethal suicide attempts
Background: Worldwide, prisoners are at high risk of suicide. Research on near-lethal suicide attempts can provide important insights into risk and protective factors, and inform suicide prevention initiatives in prison. Aims: To synthesize findings of research on near-lethal attempts in prisons, and consider their implications for suicide prevention policies and practice, in the context of other research in custody and other settings. Method: We searched two bibliographic indexes for studies in any language on near-lethal and severe self-harm in prisoners, supplemented by targeted searches over the period 2000–2014. We extracted information on risk factors descriptively. Data were not meta-analyzed owing to heterogeneity of samples and methods. Results: We identified eight studies reporting associations between prisoner near-lethal attempts and specific factors. The latter included historical, prison-related, and clinical factors, including psychiatric morbidity and comorbidity, trauma, social isolation, and bullying. These factors were also identified as important in prisoners' own accounts of what may have contributed to their attempts (presented in four studies). Conclusion: Factors associated with prisoners' severe suicide attempts include a range of potentially modifiable clinical, psychosocial, and environmental factors. We make recommendations to address these factors in order to improve detection, management, and prevention of suicide risk in prisoners
Toughening and asymmetry in peeling of heterogeneous adhesives
The effective adhesive properties of heterogeneous thin films are
characterized through a combined experimental and theoretical investigation. By
bridging scales, we show how variations of elastic or adhesive properties at
the microscale can significantly affect the effective peeling behavior of the
adhesive at the macroscale. Our study reveals three elementary mechanisms in
heterogeneous systems involving front propagation: (i) patterning the elastic
bending stiffness of the film produces fluctuations of the driving force
resulting in dramatically enhanced resistance to peeling; (ii) optimized
arrangements of pinning sites with large adhesion energy are shown to control
the effective system resistance, allowing the design of highly anisotropic and
asymmetric adhesives; (iii) heterogeneities of both types result in front
motion instabilities producing sudden energy releases that increase the overall
adhesion energy. These findings open potentially new avenues for the design of
thin films with improved adhesion properties, and motivate new investigation of
other phenomena involving front propagation.Comment: Physical Review Letters (2012)
- …