26,385 research outputs found
Stress Propagation through Frictionless Granular Material
We examine the network of forces to be expected in a static assembly of hard,
frictionless spherical beads of random sizes, such as a colloidal glass. Such
an assembly is minimally connected: the ratio of constraint equations to
contact forces approaches unity for a large assembly. However, the bead
positions in a finite subregion of the assembly are underdetermined. Thus to
maintain equilibrium, half of the exterior contact forces are determined by the
other half. We argue that the transmission of force may be regarded as
unidirectional, in contrast to the transmission of force in an elastic
material. Specializing to sequentially deposited beads, we show that forces on
a given buried bead can be uniquely specified in terms of forces involving more
recently added beads. We derive equations for the transmission of stress
averaged over scales much larger than a single bead. This derivation requires
the Ansatz that statistical fluctuations of the forces are independent of
fluctuations of the contact geometry. Under this Ansatz, the
-component stress field can be expressed in terms of a d-component
vector field. The procedure may be generalized to non-sequential packings. In
two dimensions, the stress propagates according to a wave equation, as
postulated in recent work elsewhere. We demonstrate similar wave-like
propagation in higher dimensions, assuming that the packing geometry has
uniaxial symmetry. In macroscopic granular materials we argue that our approach
may be useful even though grains have friction and are not packed
sequentially.=17Comment: 15 pages, 4 figures, revised vertion for Phys. Rev.
Sliced rotated sphere packing designs
Space-filling designs are popular choices for computer experiments. A sliced
design is a design that can be partitioned into several subdesigns. We propose
a new type of sliced space-filling design called sliced rotated sphere packing
designs. Their full designs and subdesigns are rotated sphere packing designs.
They are constructed by rescaling, rotating, translating and extracting the
points from a sliced lattice. We provide two fast algorithms to generate such
designs. Furthermore, we propose a strategy to use sliced rotated sphere
packing designs adaptively. Under this strategy, initial runs are uniformly
distributed in the design space, follow-up runs are added by incorporating
information gained from initial runs, and the combined design is space-filling
for any local region. Examples are given to illustrate its potential
application
Stress in frictionless granular material: Adaptive Network Simulations
We present a minimalistic approach to simulations of force transmission
through granular systems. We start from a configuration containing cohesive
(tensile) contact forces and use an adaptive procedure to find the stable
configuration with no tensile contact forces. The procedure works by
sequentially removing and adding individual contacts between adjacent beads,
while the bead positions are not modified. In a series of two-dimensional
realizations, the resulting force networks are shown to satisfy a linear
constraint among the three components of average stress, as anticipated by
recent theories. The coefficients in the linear constraint remain nearly
constant for a range of shear loadings up to about .6 of the normal loading.
The spatial distribution of contact forces shows strong concentration along
``force chains". The probability of contact forces of magnitude f shows an
exponential falloff with f. The response to a local perturbing force is
concentrated along two characteristic rays directed downward and laterally.Comment: 8 pages, 8 figure
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Zero-one IP problems: Polyhedral descriptions & cutting plane procedures
A systematic way for tightening an IP formulation is by employing classes of linear inequalities that define facets of the convex hull of the feasible integer points of the respective problems. Describing as well as identifying these inequalities will help in the efficiency of the LP-based cutting plane methods. In this report, we review classes of inequalities that partially described zero-one poly topes such as the 0-1 knapsack polytope, the set packing polytope and the travelling salesman polytope. Facets or valid inequalities derived from the 0-1 knapsack and the set packing polytopes are algorithmically identifie
Nearly Linear-Work Algorithms for Mixed Packing/Covering and Facility-Location Linear Programs
We describe the first nearly linear-time approximation algorithms for
explicitly given mixed packing/covering linear programs, and for (non-metric)
fractional facility location. We also describe the first parallel algorithms
requiring only near-linear total work and finishing in polylog time. The
algorithms compute -approximate solutions in time (and work)
, where is the number of non-zeros in the constraint
matrix. For facility location, is the number of eligible client/facility
pairs
Importance of chirality and reduced flexibility of protein side chains: A study with square and tetrahedral lattice models
In simple models side chains are often represented implicitly (e.g., by
spin-states) or simplified as one atom. We study side chain effects using
square lattice and tetrahedral lattice models, with explicitly side chains of
two atoms. We distinguish effects due to chirality and effects due to side
chain flexibilities, since residues in proteins are L-residues, and their side
chains adopt different rotameric states. Short chains are enumerated
exhaustively. For long chains, we sample effectively rare events (eg, compact
conformations) and obtain complete pictures of ensemble properties of these
models at all compactness region. We find that both chirality and reduced side
chain flexibility lower the folding entropy significantly for globally compact
conformations, suggesting that they are important properties of residues to
ensure fast folding and stable native structure. This corresponds well with our
finding that natural amino acid residues have reduced effective flexibility, as
evidenced by analysis of rotamer libraries and side chain rotatable bonds. We
further develop a method calculating the exact side-chain entropy for a given
back bone structure. We show that simple rotamer counting often underestimates
side chain entropy significantly, and side chain entropy does not always
correlate well with main chain packing. Among compact backbones with maximum
side chain entropy, helical structures emerges as the dominating
configurations. Our results suggest that side chain entropy may be an important
factor contributing to the formation of alpha helices for compact
conformations.Comment: 16 pages, 15 figures, 2 tables. Accepted by J. Chem. Phy
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Computer-aided programming for multiprocessing systems
As both the number of processors and the complexity of problems to be solved increase, programming multiprocessing systems becomes more difficult and error-prone. This report discusses parallel models of computation and tools for computer-aided programming (CAP). Program development tools are necessary since programmers are not able to develop complex parallel programs efficiently. In particular, a CAP tool, named Hypertool, is described here. It performs scheduling and handles the communication primitive insertion automatically so that many errors are eliminated. It also generates the performance estimates and other program quality measures to help programmers in improving their algorithms and programs. Experiments have shown that up to a 300% performance improvement can be achieved by computer-aided programming
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