1,310 research outputs found
Divided Differences
Starting with a novel definition of divided differences, this essay derives
and discusses the basic properties of, and facts about, (univariate) divided
differences.Comment: 24 page
The Stability of One-Step Schemes for First-Order Two-Point Boundary Value Problems
The stability of a finite difference scheme is related explicitly to the stability of the continuous problem being solved. At times, this gives materially better estimates for the stability constant than those obtained by the standard process of appealing to the stability of the numerical scheme for the associated initial value problem
Universal resonant ultracold molecular scattering
The elastic scattering amplitudes of indistinguishable, bosonic,
strongly-polar molecules possess universal properties at the coldest
temperatures due to wave propagation in the long-range dipole-dipole field.
Universal scattering cross sections and anisotropic threshold angular
distributions, independent of molecular species, result from careful tuning of
the dipole moment with an applied electric field. Three distinct families of
threshold resonances also occur for specific field strengths, and can be both
qualitatively and quantitatively predicted using elementary adiabatic and
semi-classical techniques. The temperatures and densities of heteronuclear
molecular gases required to observe these univeral characteristics are
predicted. PACS numbers: 34.50.Cx, 31.15.ap, 33.15.-e, 34.20.-bComment: 4 pages, 5 figure
Smoothing under Diffeomorphic Constraints with Homeomorphic Splines
In this paper we introduce a new class of diffeomorphic smoothers based on general spline smoothing techniques and on the use of some tools that have been recently developed in the context of image warping to compute smooth diffeomorphisms. This diffeomorphic spline is defined as the solution of an ordinary differential equation governed by an appropriate time-dependent vector field. This solution has a closed form expression which can be computed using classical unconstrained spline smoothing techniques. This method does not require the use of quadratic or linear programming under inequality constraints and has therefore a low computational cost. In a one dimensional setting incorporating diffeomorphic constraints is equivalent to impose monotonicity. Thus, as an illustration, it is shown that such a monotone spline can be used to monotonize any unconstrained estimator of a regression function, and that this monotone smoother inherits the convergence properties of the unconstrained estimator. Some numerical experiments are proposed to illustrate its finite sample performances, and to compare them with another monotone estimator. We also provide a two-dimensional application on the computation of diffeomorphisms for landmark and image matching
Theoretical description of two ultracold atoms in finite 3D optical lattices using realistic interatomic interaction potentials
A theoretical approach is described for an exact numerical treatment of a
pair of ultracold atoms interacting via a central potential that are trapped in
a finite three-dimensional optical lattice. The coupling of center-of-mass and
relative-motion coordinates is treated using an exact diagonalization
(configuration-interaction) approach. The orthorhombic symmetry of an optical
lattice with three different but orthogonal lattice vectors is explicitly
considered as is the Fermionic or Bosonic symmetry in the case of
indistinguishable particles.Comment: 19 pages, 5 figure
A numerical study of two-photon ionization of helium using the Pyprop framework
Few-photon induced breakup of helium is studied using a newly developed ab
initio numerical framework for solving the six-dimensional time-dependent
Schroedinger equation. We present details of the method and calculate
(generalized) cross sections for the process of two-photon nonsequential
(direct) double ionization at photon energies ranging from 39.4 to 54.4 eV, a
process that has been very much debated in recent years and is not yet fully
understood. In particular, we have studied the convergence property of the
total cross section in the vicinity of the upper threshold (54.4 eV), versus
the pulse duration of the applied laser field. We find that the cross section
exhibits an increasing trend near the threshold, as has also been observed by
others, and show that this rise cannot solely be attributed to an unintended
inclusion of the sequential two-photon double ionization process, caused by the
bandwidth of the applied field.Comment: 7 pages, 3 figure
Single Image Super-Resolution Using Multi-Scale Convolutional Neural Network
Methods based on convolutional neural network (CNN) have demonstrated
tremendous improvements on single image super-resolution. However, the previous
methods mainly restore images from one single area in the low resolution (LR)
input, which limits the flexibility of models to infer various scales of
details for high resolution (HR) output. Moreover, most of them train a
specific model for each up-scale factor. In this paper, we propose a
multi-scale super resolution (MSSR) network. Our network consists of
multi-scale paths to make the HR inference, which can learn to synthesize
features from different scales. This property helps reconstruct various kinds
of regions in HR images. In addition, only one single model is needed for
multiple up-scale factors, which is more efficient without loss of restoration
quality. Experiments on four public datasets demonstrate that the proposed
method achieved state-of-the-art performance with fast speed
Adaptive grid methods for Q-tensor theory of liquid crystals : a one-dimensional feasibility study
This paper illustrates the use of moving mesh methods for solving partial differential equation (PDE) problems in Q-tensor theory of liquid crystals. We present the results of an initial study using a simple one-dimensional test problem which illustrates the feasibility of applying adaptive grid techniques in such situations. We describe how the grids are computed using an equidistribution principle, and investigate the comparative accuracy of adaptive and uniform grid strategies, both theoretically and via numerical examples
Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants
We present two new adaptive quadrature routines. Both routines differ from
previously published algorithms in many aspects, most significantly in how they
represent the integrand, how they treat non-numerical values of the integrand,
how they deal with improper divergent integrals and how they estimate the
integration error. The main focus of these improvements is to increase the
reliability of the algorithms without significantly impacting their efficiency.
Both algorithms are implemented in Matlab and tested using both the "families"
suggested by Lyness and Kaganove and the battery test used by Gander and
Gautschi and Kahaner. They are shown to be more reliable, albeit in some cases
less efficient, than other commonly-used adaptive integrators.Comment: 32 pages, submitted to ACM Transactions on Mathematical Softwar
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