A numerical study of the spectrum and eigenfunctions on a tubular arc

The Hamiltonian for a particle constrained to move on the surface of a curved nanotube is derived using the methods of differential forms. A two-dimensional Gram-Schmidt orthonormalization procedure is employed to calculate basis functions for determining the eigenvalues and eigenstates of a tubular arc (a nanotube in the shape of a hyperbolic cosine) with several hundred scattering centers. The curvature of the tube is shown to induce bound states that are dependent on the curvature parameters and bend location of the tube.Comment: 14 pages, 5 tables, 6 figure

Granular Impact: A Grain-scale Approach

This work summarizes a series of studies on two-dimensional granular impact, where an intruding object strikes a granular material at high speed. Many previous studies on granular impact have used a macroscopic force law, which is dominated by an inertial drag term proportional to the intruder velocity squared. The primary focus here is on the microscopic force response of the granular material, and how the grain-scale effects give rise to this inertial drag term. We show that the inertial drag arises from intermittent collisions with force-chain-like structures. We construct a simple collisional model to explain the inertial drag, as well as off-axis instability and rotations. Finally, we show how the granular response changes when the intruder speed approaches $d/t_c$, leading to a failure of the inertial drag description in this regime. Here, $d$ is the mean particle diameter and $t_c$ the characteristic momentum-transfer time between two grains.Comment: This is draft version of a book chapter appearing in "Rapid Penetration into Granular Media" (eds. Iskander et al.

Curvature induced toroidal bound states

Curvature induced bound state (E < 0) eigenvalues and eigenfunctions for a particle constrained to move on the surface of a torus are calculated. A limit on the number of bound states a torus with minor radius a and major radius R can support is obtained. A condition for mapping constrained particle wave functions on the torus into free particle wave functions is established.Comment: 6 pages, no figures, Late

Dynamical Adaptation in Photoreceptors

Adaptation is at the heart of sensation and nowhere is it more salient than in early visual processing. Light adaptation in photoreceptors is doubly dynamical: it depends upon the temporal structure of the input and it affects the temporal structure of the response. We introduce a non-linear dynamical adaptation model of photoreceptors. It is simple enough that it can be solved exactly and simulated with ease; analytical and numerical approaches combined provide both intuition on the behavior of dynamical adaptation and quantitative results to be compared with data. Yet the model is rich enough to capture intricate phenomenology. First, we show that it reproduces the known phenomenology of light response and short-term adaptation. Second, we present new recordings and demonstrate that the model reproduces cone response with great precision. Third, we derive a number of predictions on the response of photoreceptors to sophisticated stimuli such as periodic inputs, various forms of flickering inputs, and natural inputs. In particular, we demonstrate that photoreceptors undergo rapid adaptation of response gain and time scale, over ∼ 300 ms—i. e., over the time scale of the response itself—and we confirm this prediction with data. For natural inputs, this fast adaptation can modulate the response gain more than tenfold and is hence physiologically relevant

Run, Jump, Throw and Catch: How proficient are children attending English schools at the Fundamental Motor Skills identified as key within the school curriculum?

This study examined proficiency levels in fundamental motor skills (FMS) in children within Key Stage 1 and 2 of the English school system. Four hundred and ninety-two children aged 6–9 Years old (245 boys, 247 girls) from school Years Two (n = 130), Three (n = 154) and Four (n = 208) participated in this study. FMS for the run, jump, throw and catch were assessed using the Test of Gross Motor Development – 2. The proportion of children who achieved mastery or near mastery of the skills was determined. For the whole sample, 18.5% (n = 91) did not achieve mastery in any of the four skills. A similar proportion (18.7%, n = 92) achieved mastery in all four of the FMS examined in this study. The proportion of children achieving mastery of all four skills was lower for Year Two children (0%) compared to children in years Three (24%) and Four (25%). More boys (25.7%) achieved mastery in all four of the FMS compared to girls (11.7%). Individual behavioural components in skill performance were also examined. The results of the present study highlight that less than one-fifth of children aged 6–9 years old have mastered the four key FMS identified by the physical education (PE) curriculum despite having the developmental potential to become fundamentally competent by six years of age. Fostering positive trajectories of FMS development presents a challenge for PE specialists given the association between FMS mastery in childhood and physical activity, weight status and health.N/

A unitary correlation operator method

The short range repulsion between nucleons is treated by a unitary correlation operator which shifts the nucleons away from each other whenever their uncorrelated positions are within the replusive core. By formulating the correlation as a transformation of the relative distance between particle pairs, general analytic expressions for the correlated wave functions and correlated operators are given. The decomposition of correlated operators into irreducible n-body operators is discussed. The one- and two-body-irreducible parts are worked out explicitly and the contribution of three-body correlations is estimated to check convergence. Ground state energies of nuclei up to mass number A=48 are calculated with a spin-isospin-dependent potential and single Slater determinants as uncorrelated states. They show that the deduced energy- and mass-number-independent correlated two-body Hamiltonian reproduces all "exact" many-body calculations surprisingly well.Comment: 43 pages, several postscript figures, uses 'epsfig.cls'. Submitted to Nucl. Phys. A. More information available at http://www.gsi.de/~fm

Chemotaxis When Bacteria Remember: Drift versus Diffusion

{\sl Escherichia coli} ({\sl E. coli}) bacteria govern their trajectories by switching between running and tumbling modes as a function of the nutrient concentration they experienced in the past. At short time one observes a drift of the bacterial population, while at long time one observes accumulation in high-nutrient regions. Recent work has viewed chemotaxis as a compromise between drift toward favorable regions and accumulation in favorable regions. A number of earlier studies assume that a bacterium resets its memory at tumbles -- a fact not borne out by experiment -- and make use of approximate coarse-grained descriptions. Here, we revisit the problem of chemotaxis without resorting to any memory resets. We find that when bacteria respond to the environment in a non-adaptive manner, chemotaxis is generally dominated by diffusion, whereas when bacteria respond in an adaptive manner, chemotaxis is dominated by a bias in the motion. In the adaptive case, favorable drift occurs together with favorable accumulation. We derive our results from detailed simulations and a variety of analytical arguments. In particular, we introduce a new coarse-grained description of chemotaxis as biased diffusion, and we discuss the way it departs from older coarse-grained descriptions.Comment: Revised version, journal reference adde

Local Food Systems: Concepts, Impacts, and Issues

This comprehensive overview of local food systems explores alternative definitions of local food, estimates market size and reach, describes the characteristics of local consumers and producers, and examines early indications of the economic and health impacts of local food systems. There is no consensus on a definition of “local” or “local food systems” in terms of the geographic distance between production and consumption. But defining “local” based on marketing arrangements, such as farmers selling directly to consumers at regional farmers’ markets or to schools, is well recognized. Statistics suggest that local food markets account for a small, but growing, share of U.S. agricultural production. For smaller farms, direct marketing to consumers accounts for a higher percentage of their sales than for larger farms. Findings are mixed on the impact of local food systems on local economic development and better nutrition levels among consumers, and sparse literature is so far inconclusive about whether localization reduces energy use or greenhouse gas emissions.local food systems, farmers’ markets, direct-to-consumer marketing, direct-to-retail/ foodservice marketing, community supported agriculture, farm to school programs, Farmers’ Market Promotion Program, food miles, Community/Rural/Urban Development,

Electron wave functions on T2T^2 in a static magnetic field of arbitrary direction

A basis set expansion is performed to find the eigenvalues and wave functions for an electron on a toroidal surface $T^2$ subject to a constant magnetic field in an arbitrary direction. The evolution of several low-lying states as a function of field strength and field orientation is reported, and a procedure to extend the results to include two-body Coulomb matrix elements on $T^2$ is presented.Comment: 18 pages, 6 figure