102,383 research outputs found
A Model for Force Fluctuations in Bead Packs
We study theoretically the complex network of forces that is responsible for
the static structure and properties of granular materials. We present detailed
calculations for a model in which the fluctuations in the force distribution
arise because of variations in the contact angles and the constraints imposed
by the force balance on each bead of the pile. We compare our results for force
distribution function for this model, including exact results for certain
contact angle probability distributions, with numerical simulations of force
distributions in random sphere packings. This model reproduces many aspects of
the force distribution observed both in experiment and in numerical simulations
of sphere packings
Statistical properties of determinantal point processes in high-dimensional Euclidean spaces
The goal of this paper is to quantitatively describe some statistical
properties of higher-dimensional determinantal point processes with a primary
focus on the nearest-neighbor distribution functions. Toward this end, we
express these functions as determinants of matrices and then
extrapolate to . This formulation allows for a quick and accurate
numerical evaluation of these quantities for point processes in Euclidean
spaces of dimension . We also implement an algorithm due to Hough \emph{et.
al.} \cite{hough2006dpa} for generating configurations of determinantal point
processes in arbitrary Euclidean spaces, and we utilize this algorithm in
conjunction with the aforementioned numerical results to characterize the
statistical properties of what we call the Fermi-sphere point process for to 4. This homogeneous, isotropic determinantal point process, discussed
also in a companion paper \cite{ToScZa08}, is the high-dimensional
generalization of the distribution of eigenvalues on the unit circle of a
random matrix from the circular unitary ensemble (CUE). In addition to the
nearest-neighbor probability distribution, we are able to calculate Voronoi
cells and nearest-neighbor extrema statistics for the Fermi-sphere point
process and discuss these as the dimension is varied. The results in this
paper accompany and complement analytical properties of higher-dimensional
determinantal point processes developed in \cite{ToScZa08}.Comment: 42 pages, 17 figure
A Monte-Carlo study of the AdS/CFT correspondence: an exploration of quantum gravity effects
In this paper we study the AdS/CFT correspondence for N=4 SYM with gauge
group U(N), compactified on S^3 in four dimensions using Monte-Carlo
techniques. The simulation is based on a particular reduction of degrees of
freedom to commuting matrices of constant fields, and in particular, we can
write the wave functions of these degrees of freedom exactly. The square of the
wave function is equivalent to a probability density for a Boltzman gas of
interacting particles in six dimensions. From the simulation we can extract the
density particle distribution for each wave function, and this distribution can
be interpreted as a special geometric locus in the gravitational dual. Studying
the wave functions associated to half-BPS giant gravitons, we are able to show
that the matrix model can measure the Planck scale directly. We also show that
the output of our simulation seems to match various theoretical expectations in
the large N limit and that it captures 1/N effects as statistical fluctuations
of the Boltzman gas with the expected scaling. Our results suggest that this is
a very promising approach to explore quantum corrections and effects in
gravitational physics on AdS spaces.Comment: 40 pages, 7 figures, uses JHEP. v2: references adde
Using Relative Entropy to Find Optimal Approximations: an Application to Simple Fluids
We develop a maximum relative entropy formalism to generate optimal
approximations to probability distributions. The central results consist in (a)
justifying the use of relative entropy as the uniquely natural criterion to
select a preferred approximation from within a family of trial parameterized
distributions, and (b) to obtain the optimal approximation by marginalizing
over parameters using the method of maximum entropy and information geometry.
As an illustration we apply our method to simple fluids. The "exact" canonical
distribution is approximated by that of a fluid of hard spheres. The proposed
method first determines the preferred value of the hard-sphere diameter, and
then obtains an optimal hard-sphere approximation by a suitably weighed average
over different hard-sphere diameters. This leads to a considerable improvement
in accounting for the soft-core nature of the interatomic potential. As a
numerical demonstration, the radial distribution function and the equation of
state for a Lennard-Jones fluid (argon) are compared with results from
molecular dynamics simulations.Comment: 5 figures, accepted for publication in Physica A, 200
Nanoelectromechanics of Piezoresponse Force Microscopy
To achieve quantitative interpretation of Piezoresponse Force Microscopy
(PFM), including resolution limits, tip bias- and strain-induced phenomena and
spectroscopy, analytical representations for tip-induced electroelastic fields
inside the material are derived for the cases of weak and strong indentation.
In the weak indentation case, electrostatic field distribution is calculated
using image charge model. In the strong indentation case, the solution of the
coupled electroelastic problem for piezoelectric indentation is used to obtain
the electric field and strain distribution in the ferroelectric material. This
establishes a complete continuum mechanics description of the PFM contact
mechanics and imaging mechanism. The electroelastic field distribution allows
signal generation volume in PFM to be determined. These rigorous solutions are
compared with the electrostatic point charge and sphere-plane models, and the
applicability limits for asymptotic point charge and point force models are
established. The implications of these results for ferroelectric polarization
switching processes are analyzed.Comment: 81 pages, 19 figures, to be published in Phys. Rev.
Cell size distribution in a random tessellation of space governed by the Kolmogorov-Johnson-Mehl-Avrami model: Grain size distribution in crystallization
The space subdivision in cells resulting from a process of random nucleation
and growth is a subject of interest in many scientific fields. In this paper,
we deduce the expected value and variance of these distributions while assuming
that the space subdivision process is in accordance with the premises of the
Kolmogorov-Johnson-Mehl-Avrami model. We have not imposed restrictions on the
time dependency of nucleation and growth rates. We have also developed an
approximate analytical cell size probability density function. Finally, we have
applied our approach to the distributions resulting from solid phase
crystallization under isochronal heating conditions
The maximally entangled symmetric state in terms of the geometric measure
The geometric measure of entanglement is investigated for permutation
symmetric pure states of multipartite qubit systems, in particular the question
of maximum entanglement. This is done with the help of the Majorana
representation, which maps an n qubit symmetric state to n points on the unit
sphere. It is shown how symmetries of the point distribution can be exploited
to simplify the calculation of entanglement and also help find the maximally
entangled symmetric state. Using a combination of analytical and numerical
results, the most entangled symmetric states for up to 12 qubits are explored
and discussed. The optimization problem on the sphere presented here is then
compared with two classical optimization problems on the S^2 sphere, namely
Toth's problem and Thomson's problem, and it is observed that, in general, they
are different problems.Comment: 18 pages, 15 figures, small corrections and additions to contents and
reference
Harmonic Exponential Families on Manifolds
In a range of fields including the geosciences, molecular biology, robotics
and computer vision, one encounters problems that involve random variables on
manifolds. Currently, there is a lack of flexible probabilistic models on
manifolds that are fast and easy to train. We define an extremely flexible
class of exponential family distributions on manifolds such as the torus,
sphere, and rotation groups, and show that for these distributions the gradient
of the log-likelihood can be computed efficiently using a non-commutative
generalization of the Fast Fourier Transform (FFT). We discuss applications to
Bayesian camera motion estimation (where harmonic exponential families serve as
conjugate priors), and modelling of the spatial distribution of earthquakes on
the surface of the earth. Our experimental results show that harmonic densities
yield a significantly higher likelihood than the best competing method, while
being orders of magnitude faster to train.Comment: fixed typ
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