A minimal model for kinetic arrest

To elucidate slow dynamics in glassy materials, we introduce the {\it Figure-8 model} in which $N$ hard blocks undergo Brownian motion around a circuit in the shape of a figure-8. This system undergoes kinetic arrest at a critical packing fraction $\phi=\phi_g < 1$, and for $\phi\approx\phi_g$ long-time diffusion is controlled by rare, cooperative `junction-crossing' particle rearrangements. We find that the average time between junction crossings $\tau_{JC}$, and hence the structural relaxation time, does not simply scale with the configurational volume \OmegaLow of transition states, because $\tau_{JC}$ also depends on the time to complete a junction crossing. The importance of these results in understanding cage-breaking dynamics in glassy systems is discussed.Comment: 4 pages, 4 figure

Impaired aerobic exercise adaptation in children and adolescents with craniopharyngioma is associated with hypothalamic involvement

OBJECTIVE: Many patients treated for craniopharyngioma (CP) complain of a relative incapacity for physical activity. Whether this is due to an objective decrease in adaptation to exercise is unclear. We assessed exercise tolerance in children with surgically treated CP and appropriate pituitary hormone replacement therapy compared with healthy controls and we examined the potential relationships with hypothalamic involvement, GH replacement, and the catecholamine deficiency frequently observed in these subjects. DESIGN AND METHODS: Seventeen subjects (12 males and five females) with CP and 22 healthy controls (14 males and eight females) aged 15.3+/-2.5 years (7.3-18 years) underwent a standardized cycle ergometer test. Maximum aerobic capacity was expressed as the ratio of VO(2max) to fat-free mass (VO(2max)/FFM), a measure independent of age and fat mass in children. RESULTS: VO(2max)/FFM was 20% lower in children with CP compared with controls (P&lt;0.05), even after adjustment for gender. Children with hypothalamic involvement (n=10) had a higher percentage of fat mass (P&lt;0.05) than those without hypothalamic involvement (n=7) and lower VO(2max)/FFM (P&lt;0.05), whereas children without hypothalamic involvement had VO(2max)/FFM close to that of controls (P&gt;0.05). GH treatment was associated with a significant positive effect on aerobic capacity (P&lt;0.05) only in the absence of hypothalamic involvement. No relationship was found between exercise capacity parameters and daily urine epinephrine excretion or epinephrine peak response to insulin-induced hypoglycemia. CONCLUSIONS: Children with CP have a decrease in aerobic capacity mainly related to hypothalamic involvement. The hypothalamic factors altering aerobic capacity remain to be determined

Selective nanomanipulation using optical forces

We present a detailed theoretical study of the recent proposal for selective nanomanipulation of nanometric particles above a substrate using near-field optical forces [Chaumet {\it et al.} Phys. Rev. Lett. {\bf 88}, 123601 (2002)]. Evanescent light scattering at the apex of an apertureless near-field probe is used to create an optical trap. The position of the trap is controlled on a nanometric scale via the probe and small objects can be selectively trapped and manipulated. We discuss the influence of the geometry of the particles and the probe on the efficiency of the trap. We also consider the influence of multiple scattering among the particles on the substrate and its effect on the robustness of the trap.Comment: 12 pages, 17 figure

Statistical Properties of Functionals of the Paths of a Particle Diffusing in a One-Dimensional Random Potential

We present a formalism for obtaining the statistical properties of functionals and inverse functionals of the paths of a particle diffusing in a one-dimensional quenched random potential. We demonstrate the implementation of the formalism in two specific examples: (1) where the functional corresponds to the local time spent by the particle around the origin and (2) where the functional corresponds to the occupation time spent by the particle on the positive side of the origin, within an observation time window of size $t$. We compute the disorder average distributions of the local time, the inverse local time, the occupation time and the inverse occupation time, and show that in many cases disorder modifies the behavior drastically.Comment: Revtex two column 27 pages, 10 figures, 3 table

Invariants and separating morphisms for algebraic group actions

The first part of this paper is a refinement of Winkelmann’s work on invariant rings and quotients of algebraic group actions on affine varieties, where we take a more geometric point of view. We show that the (algebraic) quotient X//G given by the possibly not finitely generated ring of invariants is “almost” an algebraic variety, and that the quotient morphism π: X → X//G has a number of nice properties. One of the main difficulties comes from the fact that the quotient morphism is not necessarily surjective. These general results are then refined for actions of the additive group Ga, where we can say much more. We get a rather explicit description of the so-called plinth variety and of the separating variety, which measures how much orbits are separated by invariants. The most complete results are obtained for representations. We also give a complete and detailed analysis of Roberts’ famous example of a an action of Ga on 7-dimensional affine space with a non-finitely generated ring of invariants

Force Distribution in a Granular Medium

We report on systematic measurements of the distribution of normal forces exerted by granular material under uniaxial compression onto the interior surfaces of a confining vessel. Our experiments on three-dimensional, random packings of monodisperse glass beads show that this distribution is nearly uniform for forces below the mean force and decays exponentially for forces greater than the mean. The shape of the distribution and the value of the exponential decay constant are unaffected by changes in the system preparation history or in the boundary conditions. An empirical functional form for the distribution is proposed that provides an excellent fit over the whole force range measured and is also consistent with recent computer simulation data.Comment: 6 pages. For more information, see http://mrsec.uchicago.edu/granula