3,685 research outputs found
The Densest Hemisphere Problem
Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / DAAB-07-72-C-0259National Science Foundation / MC76-1732
Robust Algorithm to Generate a Diverse Class of Dense Disordered and Ordered Sphere Packings via Linear Programming
We have formulated the problem of generating periodic dense paritcle packings
as an optimization problem called the Adaptive Shrinking Cell (ASC) formulation
[S. Torquato and Y. Jiao, Phys. Rev. E {\bf 80}, 041104 (2009)]. Because the
objective function and impenetrability constraints can be exactly linearized
for sphere packings with a size distribution in -dimensional Euclidean space
, it is most suitable and natural to solve the corresponding ASC
optimization problem using sequential linear programming (SLP) techniques. We
implement an SLP solution to produce robustly a wide spectrum of jammed sphere
packings in for and with a diversity of disorder
and densities up to the maximally densities. This deterministic algorithm can
produce a broad range of inherent structures besides the usual disordered ones
with very small computational cost by tuning the radius of the {\it influence
sphere}. In three dimensions, we show that it can produce with high probability
a variety of strictly jammed packings with a packing density anywhere in the
wide range . We also apply the algorithm to generate various
disordered packings as well as the maximally dense packings for
and 6. Compared to the LS procedure, our SLP protocol is able to ensure that
the final packings are truly jammed, produces disordered jammed packings with
anomalously low densities, and is appreciably more robust and computationally
faster at generating maximally dense packings, especially as the space
dimension increases.Comment: 34 pages, 6 figure
Rigidity of spherical codes
A packing of spherical caps on the surface of a sphere (that is, a spherical
code) is called rigid or jammed if it is isolated within the space of packings.
In other words, aside from applying a global isometry, the packing cannot be
deformed. In this paper, we systematically study the rigidity of spherical
codes, particularly kissing configurations. One surprise is that the kissing
configuration of the Coxeter-Todd lattice is not jammed, despite being locally
jammed (each individual cap is held in place if its neighbors are fixed); in
this respect, the Coxeter-Todd lattice is analogous to the face-centered cubic
lattice in three dimensions. By contrast, we find that many other packings have
jammed kissing configurations, including the Barnes-Wall lattice and all of the
best kissing configurations known in four through twelve dimensions. Jamming
seems to become much less common for large kissing configurations in higher
dimensions, and in particular it fails for the best kissing configurations
known in 25 through 31 dimensions. Motivated by this phenomenon, we find new
kissing configurations in these dimensions, which improve on the records set in
1982 by the laminated lattices.Comment: 39 pages, 8 figure
Monte Carlo Neutrino Transport Through Remnant Disks from Neutron Star Mergers
We present Sedonu, a new open source, steady-state, special relativistic
Monte Carlo (MC) neutrino transport code, available at
bitbucket.org/srichers/sedonu. The code calculates the energy- and
angle-dependent neutrino distribution function on fluid backgrounds of any
number of spatial dimensions, calculates the rates of change of fluid internal
energy and electron fraction, and solves for the equilibrium fluid temperature
and electron fraction. We apply this method to snapshots from two-dimensional
simulations of accretion disks left behind by binary neutron star mergers,
varying the input physics and comparing to the results obtained with a leakage
scheme for the case of a central black hole and a central hypermassive neutron
star. Neutrinos are guided away from the densest regions of the disk and escape
preferentially around 45 degrees from the equatorial plane. Neutrino heating is
strengthened by MC transport a few scale heights above the disk midplane near
the innermost stable circular orbit, potentially leading to a stronger
neutrino-driven wind. Neutrino cooling in the dense midplane of the disk is
stronger when using MC transport, leading to a globally higher cooling rate by
a factor of a few and a larger leptonization rate by an order of magnitude. We
calculate neutrino pair annihilation rates and estimate that an energy of
2.8e46 erg is deposited within 45 degrees of the symmetry axis over 300 ms when
a central BH is present. Similarly, 1.9e48 erg is deposited over 3 s when an
HMNS sits at the center, but neither estimate is likely to be sufficient to
drive a GRB jet.Comment: 23 pages, 16 figures, Accepted to The Astrophysical Journa
- …