8,496 research outputs found
Fast QMC matrix-vector multiplication
Quasi-Monte Carlo (QMC) rules
can be used to approximate integrals of the form , where is a matrix and
is row vector. This type of integral arises for example from
the simulation of a normal distribution with a general covariance matrix, from
the approximation of the expectation value of solutions of PDEs with random
coefficients, or from applications from statistics. In this paper we design QMC
quadrature points
such that for the matrix whose rows are the quadrature points, one can
use the fast Fourier transform to compute the matrix-vector product , , in operations and at most extra additions. The proposed method can be
applied to lattice rules, polynomial lattice rules and a certain type of
Korobov -set.
The approach is illustrated computationally by three numerical experiments.
The first test considers the generation of points with normal distribution and
general covariance matrix, the second test applies QMC to high-dimensional,
affine-parametric, elliptic partial differential equations with uniformly
distributed random coefficients, and the third test addresses Finite-Element
discretizations of elliptic partial differential equations with
high-dimensional, log-normal random input data. All numerical tests show a
significant speed-up of the computation times of the fast QMC matrix method
compared to a conventional implementation as the dimension becomes large
Marginally stable solutions
In previous work constant magnetic field strength solutions for SU(2) gauge
theory on a torus were found, which somewhat surprisingly turned out to be
classically stable. This was called marginal stability, as moving along one of
its zero-modes, two of the stable modes turn unstable. Here we investigate the
stability under quantum fluctuations in the domain where the solutions possess
the marginal stability at the classical level.Comment: 4p with 2 figs, as one uuencoded PostScript.gz file, presented at
Lattice'95, Melbourne, 11-15 July, 199
Momentum-resolved evolution of the Kondo lattice into 'hidden-order' in URu2Si2
We study, using high-resolution angle-resolved photoemission spectroscopy,
the evolution of the electronic structure in URu2Si2 at the Gamma, Z and X
high-symmetry points from the high-temperature Kondo-screened regime to the
low-temperature `hidden-order' (HO) state. At all temperatures and symmetry
points, we find structures resulting from the interaction between heavy and
light bands, related to the Kondo lattice formation. At the X point, we
directly measure a hybridization gap of 11 meV already open at temperatures
above the ordered phase. Strikingly, we find that while the HO induces
pronounced changes at Gamma and Z, the hybridization gap at X does not change,
indicating that the hidden-order parameter is anisotropic. Furthermore, at the
Gamma and Z points, we observe the opening of a gap in momentum in the HO
state, and show that the associated electronic structure results from the
hybridization of a light electron band with the Kondo-lattice bands
characterizing the paramagnetic state.Comment: Updated published version. Mansucript + Supplemental Material (8
pages, 9 figures). Submitted 16 September 201
Andreev Tunneling in Strongly Interacting Quantum Dots
We review recent work on resonant Andreev tunneling through a strongly
interacting quantum dot connected to a normal and to a superconducting lead. We
derive a general expression for the current flowing in the structure and
discuss the linear and non-linear transport in the nonperturbative regime. New
effects associated to the Kondo resonance combined with the two-particle
tunneling arise. The Kondo anomaly in the characteristics depends on the
relative size of the gap energy and the Kondo temperature.Comment: 8 pages, 4 figures; submitted to Superlattices and Microstructure
The Proteus Navier-Stokes code
An effort is currently underway at NASA Lewis to develop two- and three-dimensional Navier-Stokes codes, called Proteus, for aerospace propulsion applications. The emphasis in the development of Proteus is not algorithm development or research on numerical methods, but rather the development of the code itself. The objective is to develop codes that are user-oriented, easily-modified, and well-documented. Well-proven, state-of-the-art solution algorithms are being used. Code readability, documentation (both internal and external), and validation are being emphasized. This paper is a status report on the Proteus development effort. The analysis and solution procedure are described briefly, and the various features in the code are summarized. The results from some of the validation cases that have been run are presented for both the two- and three-dimensional codes
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