Collision of Polymers in a Vacuum

In a number of experimental situations, single polymer molecules can be suspended in a vacuum. Here collisions between such molecules are considered. The limit of high collision velocity is investigated numerically for a variety of conditions. The distribution of contact times, scattering angles, and final velocities are analyzed. In this limit, self avoiding chains are found to become highly stretched as they collide with each other, and have a distribution of scattering times that depends on the scattering angle. The velocity of the molecules after the collisions is similar to predictions of a model assuming thermal equilibration of molecules during the collision. The most important difference is a significant subset of molecules that inelastically scatter but do not substantially change direction.Comment: 7 pages, 6 figure

Parallel Batch-Dynamic Graph Connectivity

In this paper, we study batch parallel algorithms for the dynamic connectivity problem, a fundamental problem that has received considerable attention in the sequential setting. The most well known sequential algorithm for dynamic connectivity is the elegant level-set algorithm of Holm, de Lichtenberg and Thorup (HDT), which achieves $O(\log^2 n)$ amortized time per edge insertion or deletion, and $O(\log n / \log\log n)$ time per query. We design a parallel batch-dynamic connectivity algorithm that is work-efficient with respect to the HDT algorithm for small batch sizes, and is asymptotically faster when the average batch size is sufficiently large. Given a sequence of batched updates, where $\Delta$ is the average batch size of all deletions, our algorithm achieves $O(\log n \log(1 + n / \Delta))$ expected amortized work per edge insertion and deletion and $O(\log^3 n)$ depth w.h.p. Our algorithm answers a batch of $k$ connectivity queries in $O(k \log(1 + n/k))$ expected work and $O(\log n)$ depth w.h.p. To the best of our knowledge, our algorithm is the first parallel batch-dynamic algorithm for connectivity.Comment: This is the full version of the paper appearing in the ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 201

Simulations of collision times in gravity driven granular flow

We use simulations to investigate collision time distributions as one approaches the static limit of steady-state flow of dry granular matter. The collision times fall in a power-law distribution with an exponent dictated by whether the grains are ordered or disordered. Remarkably, the exponents have almost no dependence on dimension. We are also able to resolve a disagreement between simulation and experiments on the exponent of the collision time power-law distribution.Comment: 7 pages, 5 figure

A Characterization of (Locally) Uniformly Convex Spaces in Terms of Relative Openness of Quotient Maps on the Unit Ball

AbstractRelative openness of quotient maps on the closed unit ball U of a normed linear space X is studied quantitatively. Particularly, it follows from the results that the quotient maps on X associated with the closed linear subspaces of X are equally relatively open on U if and only if X is locally uniformly convex. Also, X is locally uniformly convex if and only if for any family of linear maps defined on X, equal relative openness on X implies equal relative openness on U. Similarly, uniformly convex spaces can be characterized in terms of equal uniform relative openness of quotient maps on U

Electron-phonon coupling and longitudinal mechanical-mode cooling in a metallic nanowire

We investigate electron-phonon coupling in a narrow suspended metallic wire, in which the phonon modes are restricted to one dimension but the electrons behave three-dimensionally. Explicit theoretical results related to the known bulk properties are derived. We find out that longitudinal vibration modes can be cooled by electronic tunnel refrigeration far below the bath temperature provided the mechanical quality factors of the modes are sufficiently high. The obtained results apply to feasible experimental configurations.Comment: 4+ pages, 3 figure

A Model for Phase Transition based on Statistical Disassembly of Nuclei at Intermediate Energies

Consider a model of particles (nucleons) which has a two-body interaction which leads to bound composites with saturation properties. These properties are : all composites have the same density and the ground state energies of composites with k nucleons are given by -kW+\sigma k^{2/3} where W and \sigma are positive constants. W represents a volume term and \sigma a surface tension term. These values are taken from nuclear physics. We show that in the large N limit where N is the number of particles such an assembly in a large enclosure at finite temperature shows properties of liquid-gas phase transition. We do not use the two-body interaction but the gross properties of the composites only. We show that (a) the p-\rho isotherms show a region where pressure does not change as $\rho$ changes just as in Maxwell construction of a Van der Waals gas, (b) in this region the chemical potential does not change and (c) the model obeys the celebrated Clausius-Clapeyron relations. A scaling law for the yields of composites emerges. For a finite number of particles N (upto some thousands) the problem can be easily solved on a computer. This allows us to study finite particle number effects which modify phase transition effects. The model is calculationally simple. Monte-Carlo simulations are not needed.Comment: RevTex file, 21 pages, 5 figure

Collective pinning of imperfect vortex lattices by material line defects in extreme type-II superconductors

The critical current density shown by a superconductor at the extreme type-II limit is predicted to follow an inverse square-root power law with external magnetic field if the vortex lattice is weakly pinned by material line defects. It acquires an additional inverse dependence with thickness along the line direction once pinning of the interstitial vortex lines by material point defects is included. Moderate quantitative agreement with the critical current density shown by second-generation wires of high-temperature superconductors in kG magnetic fields is achieved at liquid-nitrogen temperature.Comment: 10 pages, 3 figures, 2 tables. To appear in Physical Review