7,550 research outputs found
Regression with strongly correlated data
This paper discusses linear regression of strongly correlated data that
arises, for example, in magnetohydrodynamic equilibrium reconstructions. We
have proved that, generically, the covariance matrix of the estimated
regression parameters for fixed sample size goes to zero as the correlations
become unity. That is, in this limit the estimated parameters are known with
perfect accuracy. Simple examples are shown to illustrate this effect and the
nature of the exceptional cases in which the estimate covariance does not go to
zero
Integrable boundary conditions for multi-species ASEP
The first result of the present paper is to provide classes of explicit
solutions for integrable boundary matrices for the multi-species ASEP with an
arbitrary number of species.
All the solutions we have obtained can be seen as representations of a new
algebra that contains the boundary Hecke algebra. The boundary Hecke algebra is
not sufficient to build these solutions. This is the second result of our
paper.Comment: 20 page
Mathematical and computational studies of equilibrium capillary free surfaces
The results of several independent studies are presented. The general question is considered of whether a wetting liquid always rises higher in a small capillary tube than in a larger one, when both are dipped vertically into an infinite reservoir. An analytical investigation is initiated to determine the qualitative behavior of the family of solutions of the equilibrium capillary free-surface equation that correspond to rotationally symmetric pendent liquid drops and the relationship of these solutions to the singular solution, which corresponds to an infinite spike of liquid extending downward to infinity. The block successive overrelaxation-Newton method and the generalized conjugate gradient method are investigated for solving the capillary equation on a uniform square mesh in a square domain, including the case for which the solution is unbounded at the corners. Capillary surfaces are calculated on the ellipse, on a circle with reentrant notches, and on other irregularly shaped domains using JASON, a general purpose program for solving nonlinear elliptic equations on a nonuniform quadrilaterial mesh. Analytical estimates for the nonexistence of solutions of the equilibrium capillary free-surface equation on the ellipse in zero gravity are evaluated
Optimizing Pulsar Timing Arrays to Maximize Gravitational Wave Single Source Detection: a First Cut
Pulsar Timing Arrays (PTAs) use high accuracy timing of a collection of low
timing noise pulsars to search for gravitational waves in the microhertz to
nanohertz frequency band. The sensitivity of such a PTA depends on (a) the
direction of the gravitational wave source, (b) the timing accuracy of the
pulsars in the array and (c) how the available observing time is allocated
among those pulsars. Here, we present a simple way to calculate the sensitivity
of the PTA as a function of direction of a single GW source, based only on the
location and root-mean-square residual of the pulsars in the array. We use this
calculation to suggest future strategies for the current North American
Nanohertz Observatory for Gravitational Waves (NANOGrav) PTA in its goal of
detecting single GW sources. We also investigate the affects of an additional
pulsar on the array sensitivity, with the goal of suggesting where PTA pulsar
searches might be best directed. We demonstrate that, in the case of single GW
sources, if we are interested in maximizing the volume of space to which PTAs
are sensitive, there exists a slight advantage to finding a new pulsar near
where the array is already most sensitive. Further, the study suggests that
more observing time should be dedicated to the already low noise pulsars in
order to have the greatest positive effect on the PTA sensitivity. We have made
a web-based sensitivity mapping tool available at http://gwastro.psu.edu/ptasm.Comment: 14 pages, 3 figures, accepted by Ap
On recurrence and ergodicity for geodesic flows on noncompact periodic polygonal surfaces
We study the recurrence and ergodicity for the billiard on noncompact
polygonal surfaces with a free, cocompact action of or . In the
-periodic case, we establish criteria for recurrence. In the more difficult
-periodic case, we establish some general results. For a particular
family of -periodic polygonal surfaces, known in the physics literature
as the wind-tree model, assuming certain restrictions of geometric nature, we
obtain the ergodic decomposition of directional billiard dynamics for a dense,
countable set of directions. This is a consequence of our results on the
ergodicity of \ZZ-valued cocycles over irrational rotations.Comment: 48 pages, 12 figure
Behavior of Piles in Liquefiable Soils During Earthquakes: Analysis and Design Issues
A general picture of the current state of the art and the emerging technology for dealing effectively with the seismic design and analysis of pile foundations in liquefiable soils is presented. Two distinct design cases are considered and illustrated by case histories. One is the static response of pile foundations to the pressures and displacements caused by lateral spreading of liquefied ground. The other is the seismic response of piles to strong shaking accompanied by the development of high pore water pressures or liquefaction. Design for lateral spreading is examined in the context of developments in design practice and the findings from shake table and centrifuge tests. Response of piles to earthquake shaking in liquefiable soils is examined in the context of 1.5m cast in place reinforced concrete piles supporting a 14 storey apartment building
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