922,981 research outputs found
Oceanic rings and jets as statistical equilibrium states
Equilibrium statistical mechanics of two-dimensional flows provides an
explanation and a prediction for the self-organization of large scale coherent
structures. This theory is applied in this paper to the description of oceanic
rings and jets, in the framework of a 1.5 layer quasi-geostrophic model. The
theory predicts the spontaneous formation of regions where the potential
vorticity is homogenized, with strong and localized jets at their interface.
Mesoscale rings are shown to be close to a statistical equilibrium: the theory
accounts for their shape, their drift, and their ubiquity in the ocean,
independently of the underlying generation mechanism. At basin scale, inertial
states presenting mid basin eastward jets (and then different from the
classical Fofonoff solution) are described as marginally unstable states. These
states are shown to be marginally unstable for the equilibrium statistical
theory. In that case, considering a purely inertial limit is a first step
toward more comprehensive out of equilibrium studies that would take into
account other essential aspects, such as wind forcing.Comment: 15 pages, submitted to Journal of Physical Oceanograph
Shape theory via polar decomposition
This work proposes a new model in the context of statistical theory of shape,
based on the polar decomposition. The non isotropic noncentral elliptical shape
distributions via polar decomposition is derived in the context of zonal
polynomials, avoiding the invariant polynomials and the open problems for their
computation. The new polar shape distributions are easily computable and then
the inference procedure can be studied under exact densities. As an example of
the technique, a classical application in Biology is studied under three
models, the usual Gaussian and two non normal Kotz models; the best model is
selected by a modified BIC criterion, then a test for equality in polar shapes
is performed.Comment: 14 page
Models for Metal Hydride Particle Shape, Packing, and Heat Transfer
A multiphysics modeling approach for heat conduction in metal hydride powders
is presented, including particle shape distribution, size distribution,
granular packing structure, and effective thermal conductivity. A statistical
geometric model is presented that replicates features of particle size and
shape distributions observed experimentally that result from cyclic hydride
decreptitation. The quasi-static dense packing of a sample set of these
particles is simulated via energy-based structural optimization methods. These
particles jam (i.e., solidify) at a density (solid volume fraction) of
0.665+/-0.015 - higher than prior experimental estimates. Effective thermal
conductivity of the jammed system is simulated and found to follow the behavior
predicted by granular effective medium theory. Finally, a theory is presented
that links the properties of bi-porous cohesive powders to the present systems
based on recent experimental observations of jammed packings of fine powder.
This theory produces quantitative experimental agreement with metal hydride
powders of various compositions.Comment: 12 pages, 12 figures, 2 table
Thermodynamic limit of random partitions and dispersionless Toda hierarchy
We study the thermodynamic limit of random partition models for the instanton
sum of 4D and 5D supersymmetric U(1) gauge theories deformed by some physical
observables. The physical observables correspond to external potentials in the
statistical model. The partition function is reformulated in terms of the
density function of Maya diagrams. The thermodynamic limit is governed by a
limit shape of Young diagrams associated with dominant terms in the partition
function. The limit shape is characterized by a variational problem, which is
further converted to a scalar-valued Riemann-Hilbert problem. This
Riemann-Hilbert problem is solved with the aid of a complex curve, which may be
thought of as the Seiberg-Witten curve of the deformed U(1) gauge theory. This
solution of the Riemann-Hilbert problem is identified with a special solution
of the dispersionless Toda hierarchy that satisfies a pair of generalized
string equations. The generalized string equations for the 5D gauge theory are
shown to be related to hidden symmetries of the statistical model. The
prepotential and the Seiberg-Witten differential are also considered.Comment: latex2e using amsmath,amssymb,amsthm packages, 55 pages, no figure;
(v2) typos correcte
Photovoltaic and Rectification Currents in Quantum Dots
We investigate theoretically and experimentally the statistical properties of
dc current through an open quantum dot subject to ac excitation of a
shape-defining gate. The symmetries of rectification current and photovoltaic
current with respect to applied magnetic field are examined. Theory and
experiment are found to be in good agreement throughout a broad range of
frequency and ac power, ranging from adiabatic to nonadiabatic regimes.Comment: 4 pages, 3 figures; related articles at http://marcuslab.harvard.ed
Robust nonparametric detection of objects in noisy images
We propose a novel statistical hypothesis testing method for detection of
objects in noisy images. The method uses results from percolation theory and
random graph theory. We present an algorithm that allows to detect objects of
unknown shapes in the presence of nonparametric noise of unknown level and of
unknown distribution. No boundary shape constraints are imposed on the object,
only a weak bulk condition for the object's interior is required. The algorithm
has linear complexity and exponential accuracy and is appropriate for real-time
systems. In this paper, we develop further the mathematical formalism of our
method and explore important connections to the mathematical theory of
percolation and statistical physics. We prove results on consistency and
algorithmic complexity of our testing procedure. In addition, we address not
only an asymptotic behavior of the method, but also a finite sample performance
of our test.Comment: This paper initially appeared in 2010 as EURANDOM Report 2010-049.
Link to the abstract at EURANDOM repository:
http://www.eurandom.tue.nl/reports/2010/049-abstract.pdf Link to the paper at
EURANDOM repository: http://www.eurandom.tue.nl/reports/2010/049-report.pd
- …