3,105 research outputs found
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
Discontinuous percolation transitions in real physical systems
We study discontinuous percolation transitions (PT) in the diffusion-limited
cluster aggregation model of the sol-gel transition as an example of real
physical systems, in which the number of aggregation events is regarded as the
number of bonds occupied in the system. When particles are Brownian, in which
cluster velocity depends on cluster size as with
, a larger cluster has less probability to collide with other
clusters because of its smaller mobility. Thus, the cluster is effectively more
suppressed in growth of its size. Then the giant cluster size increases
drastically by merging those suppressed clusters near the percolation
threshold, exhibiting a discontinuous PT. We also study the tricritical
behavior by controlling the parameter , and the tricritical point is
determined by introducing an asymmetric Smoluchowski equation.Comment: 5 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
Reciprocity relations between ordinary temperature and the Frieden-Soffer's Fisher-temperature
Frieden and Soffer conjectured some years ago the existence of a ``Fisher
temperature" T_F that would play, with regards to Fisher's information measure
I, the same role that the ordinary temperature T plays vis-a-vis Shannon's
logarithmic measure. Here we exhibit the existence of reciprocity relations
between T_F and T and provide an interpretation with reference to the meaning
of T_F for the canonical ensemble.Comment: 3 pages, no figure
Phase transition from quark-meson coupling hyperonic matter to deconfined quark matter
We investigate the possibility and consequences of phase transitions from an
equation of state (EOS) describing nucleons and hyperons interacting via mean
fields of sigma, omega, and rho mesons in the recently improved quark-meson
coupling (QMC) model to an EOS describing a Fermi gas of quarks in an MIT bag.
The transition to a mixed phase of baryons and deconfined quarks, and
subsequently to a pure deconfined quark phase, is described using the method of
Glendenning. The overall EOS for the three phases is calculated for various
scenarios and used to calculate stellar solutions using the
Tolman-Oppenheimer-Volkoff equations. The results are compared with recent
experimental data, and the validity of each case is discussed with consequences
for determining the species content of the interior of neutron stars.Comment: 12 pages, 14 figures; minor typos correcte
New Geometric Algorithms for Fully Connected Staged Self-Assembly
We consider staged self-assembly systems, in which square-shaped tiles can be
added to bins in several stages. Within these bins, the tiles may connect to
each other, depending on the glue types of their edges. Previous work by
Demaine et al. showed that a relatively small number of tile types suffices to
produce arbitrary shapes in this model. However, these constructions were only
based on a spanning tree of the geometric shape, so they did not produce full
connectivity of the underlying grid graph in the case of shapes with holes;
designing fully connected assemblies with a polylogarithmic number of stages
was left as a major open problem. We resolve this challenge by presenting new
systems for staged assembly that produce fully connected polyominoes in O(log^2
n) stages, for various scale factors and temperature {\tau} = 2 as well as
{\tau} = 1. Our constructions work even for shapes with holes and uses only a
constant number of glues and tiles. Moreover, the underlying approach is more
geometric in nature, implying that it promised to be more feasible for shapes
with compact geometric description.Comment: 21 pages, 14 figures; full version of conference paper in DNA2
Arbitrary Steady-State Solutions with the K-epsilon Model
Widely-used forms of the K-epsilon turbulence model are shown to yield arbitrary steady-state converged solutions that are highly dependent on numerical considerations such as initial conditions and solution procedure. These solutions contain pseudo-laminar regions of varying size. By applying a nullcline analysis to the equation set, it is possible to clearly demonstrate the reasons for the anomalous behavior. In summary, the degenerate solution acts as a stable fixed point under certain conditions, causing the numerical method to converge there. The analysis also suggests a methodology for preventing the anomalous behavior in steady-state computations
Nonzero orbital angular momentum superfluidity in ultracold Fermi gases
We analyze the evolution of superfluidity for nonzero orbital angular
momentum channels from the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein
condensation (BEC) limit in three dimensions. First, we analyze the low energy
scattering properties of finite range interactions for all possible angular
momentum channels. Second, we discuss ground state () superfluid
properties including the order parameter, chemical potential, quasiparticle
excitation spectrum, momentum distribution, atomic compressibility, ground
state energy and low energy collective excitations. We show that a quantum
phase transition occurs for nonzero angular momentum pairing, unlike the s-wave
case where the BCS to BEC evolution is just a crossover. Third, we present a
gaussian fluctuation theory near the critical temperature (),
and we analyze the number of bound, scattering and unbound fermions as well as
the chemical potential. Finally, we derive the time-dependent Ginzburg-Landau
functional near , and compare the Ginzburg-Landau coherence length
with the zero temperature average Cooper pair size.Comment: 28 pages and 24 figure
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