4,067 research outputs found
Measuring the configurational temperature of a binary disc packing
Jammed packings of granular materials differ from systems normally described
by statistical mechanics in that they are athermal. In recent years a
statistical mechanics of static granular media has emerged where the
thermodynamic temperature is replaced by a configurational temperature X which
describes how the number of mechanically stable configurations depends on the
volume. Four different methods have been suggested to measure X. Three of them
are computed from properties of the Voronoi volume distribution, the fourth
takes into account the contact number and the global volume fraction. This
paper answers two questions using experimental binary disc packings: First we
test if the four methods to measure compactivity provide identical results when
applied to the same dataset. We find that only two of the methods agree
quantitatively. Secondly, we test if X is indeed an intensive variable; this
becomes true only for samples larger than roughly 200 particles. This result is
shown to be due to recently found correlations between the particle volumes
[Zhao et al., Europhys. Lett., 2012, 97, 34004].Comment: Open access under Creative Commons Attribution-NonCommercial 3.0
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Crater formation during raindrop impact on sand
After a raindrop impacts on a granular bed, a crater is formed as both drop
and target deform. After an initial, transient, phase in which the maximum
crater depth is reached, the crater broadens outwards until a final steady
shape is attained. By varying the impact velocity of the drop and the packing
density of the bed, we find that avalanches of grains are important in the
second phase and hence, affect the final crater shape. In a previous paper, we
introduced an estimate of the impact energy going solely into sand deformation
and here we show that both the transient and final crater diameter collapse
with this quantity for various packing densities. The aspect ratio of the
transient crater is however altered by changes in the packing fraction.Comment: 9 pages, 9 figure
Liquid-grain mixing suppresses droplet spreading and splashing during impact
Would a raindrop impacting on a coarse beach behave differently from that
impacting on a desert of fine sand? We study this question by a series of model
experiments, where the packing density of the granular target, the wettability
of individual grains, the grain size, the impacting liquid, and the impact
speed are varied. We find that by increasing the grain size and/or the
wettability of individual grains the maximum droplet spreading undergoes a
transition from a capillary regime towards a viscous regime, and splashing is
suppressed. The liquid-grain mixing is discovered to be the underlying
mechanism. An effective viscosity is defined accordingly to quantitatively
explain the observations
SDPNAL+: A Matlab software for semidefinite programming with bound constraints (version 1.0)
SDPNAL+ is a {\sc Matlab} software package that implements an augmented
Lagrangian based method to solve large scale semidefinite programming problems
with bound constraints. The implementation was initially based on a majorized
semismooth Newton-CG augmented Lagrangian method, here we designed it within an
inexact symmetric Gauss-Seidel based semi-proximal ADMM/ALM (alternating
direction method of multipliers/augmented Lagrangian method) framework for the
purpose of deriving simpler stopping conditions and closing the gap between the
practical implementation of the algorithm and the theoretical algorithm. The
basic code is written in {\sc Matlab}, but some subroutines in C language are
incorporated via Mex files. We also design a convenient interface for users to
input their SDP models into the solver. Numerous problems arising from
combinatorial optimization and binary integer quadratic programming problems
have been tested to evaluate the performance of the solver. Extensive numerical
experiments conducted in [Yang, Sun, and Toh, Mathematical Programming
Computation, 7 (2015), pp. 331--366] show that the proposed method is quite
efficient and robust, in that it is able to solve 98.9\% of the 745 test
instances of SDP problems arising from various applications to the accuracy of
in the relative KKT residual
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