Human Performance Assessments in Cadet Populations

This study assessed potential physiological differences between the Ranger Challenge (RC) Competition team and junior year cadets in an Army Reserve Officer Training Corps (ROTC) program. The method included: RC (m = 11, f = 2) and junior year cadets (m = 7, f = 3) were assessed in the following areas: 1) quickness and agility (5-10-5 shuttle run), 2) total-body power (standing broad jump), and 3) grip strength (hand grip dynamometry) assessed. The 5-10-5 shuttle run was performed twice (opening once to the left and once to the right). The standing broad jump required that cadets stand with their toes behind a line, perform a maximum of three preparatory movements, triple extend their knees, hips, and ankles while using their upper body to propel them as far forward as possible. After the jump the distanced reached was measured from the line to the heel of the nearest foot. Hand grip dynamometry was performed once on each hand. The cadet held the dynamometer out to his or her side and squeezed it as they lowered it to their hip. The results were that there were no significant differences between groups for the 5-10-5 shuttle run (p = 0.91), standing broad jump (p = 0.49), or grip strength (p = 0.31). RC did not outperform

Solving the quartic with a pencil

This expository paper presents the general solution of a quartic equation as a jump off point to introduce Lefschetz fibrations. It should be accessible to a broad audience.Comment: final versio

Jump-like unravelings for non-Markovian open quantum systems

Non-Markovian evolution of an open quantum system can be `unraveled' into pure state trajectories generated by a non-Markovian stochastic (diffusive) Schr\"odinger equation, as introduced by Di\'osi, Gisin, and Strunz. Recently we have shown that such equations can be derived using the modal (hidden variable) interpretation of quantum mechanics. In this paper we generalize this theory to treat jump-like unravelings. To illustrate the jump-like behavior we consider a simple system: A classically driven (at Rabi frequency $\Omega$) two-level atom coupled linearly to a three mode optical bath, with a central frequency equal to the frequency of the atom, $\omega_0$, and the two side bands have frequencies $\omega_0\pm\Omega$. In the large $\Omega$ limit we observed that the jump-like behavior is similar to that observed in this system with a Markovian (broad band) bath. This is expected as in the Markovian limit the fluorescence spectrum for a strongly driven two level atom takes the form of a Mollow triplet. However the length of time for which the Markovian-like behaviour persists depends upon {\em which} jump-like unraveling is used.Comment: 11 pages, 5 figure

Super-diffusion around the rigidity transition: Levy and the Lilliputians

By analyzing the displacement statistics of an assembly of horizontally vibrated bidisperse frictional grains in the vicinity of the jamming transition experimentally studied before, we establish that their superdiffusive motion is a genuine Levy flight, but with `jump' size very small compared to the diameter of the grains. The vibration induces a broad distribution of jumps that are random in time, but correlated in space, and that can be interpreted as micro-crack events at all scales. As the volume fraction departs from the critical jamming density, this distribution is truncated at a smaller and smaller jump size, inducing a crossover towards standard diffusive motion at long times. This interpretation contrasts with the idea of temporally persistent, spatially correlated currents and raises new issues regarding the analysis of the dynamics in terms of vibrational modes.Comment: 7 pages, 6 figure

A complete identification of lithium sites in a model of LiPO3_3 glass: effects of the local structure and energy landscape on ionic jump dynamics

We perform molecular dynamics simulations to study lithium dynamics in a model of LiPO$_3$ glass at temperatures below the glass transition. A straightforward analysis of the ionic trajectories shows that lithium diffusion results from jumps between sites that are basically unmodified on the time scale of the lithium ionic relaxation. This allows us a detailed identification and characterization of the sites. The results indicate that the number of lithium sites is only slightly bigger than the number of lithium ions so that the fraction of vacant sites is very limited at every instant. Mapping the ionic trajectories onto series of jumps between the sites provides direct access to lithium jump dynamics. For each site, we determine the mean residence time $\tau_s$ and the probability $p_s^b$ that a jump from this site to another site is followed by a direct backjump. While a broad distribution $G(\lg \tau_s)$ shows that different sites feature diverse lithium dynamics, high values of $p_s^b$ give direct evidence for back-and-forth jumps. We further study how the local glass structure and the local energy landscape affect lithium jump dynamics. We observe substantial effects due to the energy landscape, which are difficult to capture within single-particle approaches.Comment: 10 pages, 8 figure

Large deviations for Markov jump processes with mean-field interaction via the comparison principle for an associated Hamilton-Jacobi equation

We prove the large deviation principle for the trajectory of a broad class of mean field interacting Markov jump processes via a general analytic approach based on viscosity solutions. Examples include generalized Ehrenfest models as well as Curie-Weiss spin flip dynamics with singular jump rates. The main step in the proof of the large deviation principle, which is of independent interest, is the proof of the comparison principle for an associated collection of Hamilton-Jacobi equations. Additionally, we show that the large deviation principle provides a general method to identify a Lyapunov function for the associated McKean-Vlasov equation