1,048 research outputs found
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
B-splines, Pólya curves, and duality
AbstractLocal duality between B-splines and Pólya curves is examined, mostly from the viewpoint of computer-aided geometric design. Certain known results for the two curve types are shown to be related. A few new results for Pólya curves and a curve scheme related to B-splines also follow from these investigations
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
Functions preserving nonnegativity of matrices
The main goal of this work is to determine which entire functions preserve
nonnegativity of matrices of a fixed order -- i.e., to characterize entire
functions with the property that is entrywise nonnegative for every
entrywise nonnegative matrix of size . Towards this goal, we
present a complete characterization of functions preserving nonnegativity of
(block) upper-triangular matrices and those preserving nonnegativity of
circulant matrices. We also derive necessary conditions and sufficient
conditions for entire functions that preserve nonnegativity of symmetric
matrices. We also show that some of these latter conditions characterize the
even or odd functions that preserve nonnegativity of symmetric matrices.Comment: 20 pages; expanded and corrected to reflect referees' remarks; to
appear in SIAM J. Matrix Anal. App
Coordinate Space HFB Calculations for the Zirconium Isotope Chain up to the Two-Neutron Dripline
We solve the Hartree-Fock-Bogoliubov (HFB) equations for deformed, axially
symmetric even-even nuclei in coordinate space on a 2-D lattice utilizing the
Basis-Spline expansion method. Results are presented for the neutron-rich
zirconium isotopes up to the two-neutron dripline. In particular, we calculate
binding energies, two-neutron separation energies, normal densities and pairing
densities, mean square radii, quadrupole moments, and pairing gaps. Very large
prolate quadrupole deformations (beta2=0.42,0.43,0.47) are found for the
(102,104,112)Zr isotopes, in agreement with recent experimental data. We
compare 2-D Basis-Spline lattice results with the results from a 2-D HFB code
which uses a transformed harmonic oscillator basis.Comment: 9 pages, 9 figure
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B-spline neural networks based PID controller for Hammerstein systems
A new PID tuning and controller approach is introduced for Hammerstein systems based on input/output data. A B-spline neural network is used to model the nonlinear static function in the Hammerstein system. The control signal is composed of a PID controller together with a correction term. In order to update the control signal, the multi-step ahead predictions of the Hammerstein system based on the B-spline neural networks and the associated Jacobians matrix are calculated using the De Boor algorithms including both the functional and derivative recursions. A numerical example is utilized to demonstrate the efficacy of the proposed approaches
Lower bounds for the approximation with variation-diminishing splines
We prove lower bounds for the approximation error of the variation-diminishing Schoenberg operator on the interval [0, 1] in terms of classical moduli of smoothness depending on the degree of the spline basis. For this purpose we use a functional analysis framework in order to characterize the spectrum of the Schoenberg operator and investigate the asymptotic behavior of its iterates
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
Bivariate spline interpolation with optimal approximation order
Let be a triangulation of some polygonal domain f c R2 and let S9 (A) denote the space of all bivariate polynomial splines of smoothness r and degree q with respect to A. We develop the first Hermite-type interpolation scheme for S9 (A), q >_ 3r + 2, whose approximation error is bounded above by Kh4+i, where h is the maximal diameter of the triangles in A, and the constant K only depends on the smallest angle of the triangulation and is independent of near-degenerate edges and nearsingular vertices. Moreover, the fundamental functions of our scheme are minimally supported and form a locally linearly independent basis for a superspline subspace of Sr, (A). This shows that the optimal approximation order can be achieved by using minimally supported splines. Our method of proof is completely different from the quasi-interpolation techniques for the study of the approximation power of bivariate splines developed in [71 and [181
Lattice QCD study of a five-quark hadronic molecule
We compute the ground-state energies of a heavy-light K-Lambda like system as
a function of the relative distance r of the hadrons. The heavy quarks, one in
each hadron, are treated as static. Then, the energies give rise to an
adiabatic potential Va(r) which we use to study the structure of the five-quark
system. The simulation is based on an anisotropic and asymmetric lattice with
Wilson fermions. Energies are extracted from spectral density functions
obtained with the maximum entropy method. Our results are meant to give
qualitative insight: Using the resulting adiabatic potential in a Schroedinger
equation produces bound state wave functions which indicate that the ground
state of the five-quark system resembles a hadronic molecule, whereas the first
excited state, having a very small rms radius, is probably better described as
a five-quark cluster, or a pentaquark. We hypothesize that an all light-quark
pentaquark may not exist, but in the heavy-quark sector it might, albeit only
as an excited state.Comment: 11 pages, 15 figures, 4 table
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