4,674 research outputs found
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 amortized time per
edge insertion or deletion, and 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 is the average batch size of all deletions, our
algorithm achieves expected amortized work per
edge insertion and deletion and depth w.h.p. Our algorithm
answers a batch of connectivity queries in expected
work and 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
Least Squares Approximation of Bezier Coefficients provides Best Degree Reduction in the L 2-Norm
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 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
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