scholarly journals Application of B-splines in determining the eigenspectrum of diatomic molecules: robust numerical description of halo-state and Feshbach molecules

2009 ◽  
Vol 87 (1) ◽  
pp. 67-74 ◽  
Author(s):  
A Derevianko ◽  
E Luc-Koenig ◽  
F Masnou-Seeuws
Keyword(s):  
Diatomic Molecules ◽  
Scattering Length ◽  
Bound State ◽  
Basis Set ◽  
Dissociation Limit ◽  
Universal Relation ◽  
B Spline ◽  
B Splines ◽  
Feshbach Molecules ◽  
Spline Basis

The B-spline basis-set method is applied to determining the rovibrational eigenspectrum of diatomic molecules. Particular attention is paid to a challenging numerical task of an accurate and efficient description of the vibrational levels near the dissociation limit (halo-state and Feshbach molecules). Advantages of using B-splines are highlighted by comparing the performance of the method with that of the commonly used discrete-variable representation (DVR) approach. Several model cases, including the Morse potential and realistic potentials with 1/R3 and 1/R6 long-range dependence of the internuclear separation are studied. We find that the B-spline method is superior to the DVR approach and it is robust enough to properly describe the Feshbach molecules. The developed numerical method is applied to studying the universal relation of the energy of the last bound state to the scattering length. We illustrate numerically the validity of the quantum-defect-theoretic formulation of such a relation for a 1/R6 potential.PACS Nos.: 31.15.–p,34.50.Cx

ELECTRONIC STRUCTURE CALCULATIONS OF LOW-DIMENSIONAL SEMICONDUCTOR STRUCTURES USING B-SPLINE BASIS FUNCTIONS

2005 ◽  
Vol 16 (02) ◽  
pp. 237-251
Author(s):  
BORA DIKMEN ◽  
MEHMET TOMAK
Keyword(s):  
Electronic Structure Calculations ◽  
Basis Functions ◽  
Basis Set ◽  
B Spline ◽  
B Splines ◽  
Semiconductor Structures ◽  
Spline Basis ◽  
The Finite Difference Method ◽  
Low Dimensional ◽  
Structure Calculations

An efficient method for the low-dimensional semiconductor structure is investigated. The method is applied to symmetric double rectangular quantum well as an example. A basis set of Cubic B-Splines is used as localized basis functions. The method compares well with analytical solutions and the finite difference method.

Generation and Modification of Non-Uniform B-Spline Surface Approximations to PDE Surfaces Using the Finite Element Method

1990 ◽  
Author(s):  
Joanna M. Brown ◽  
Malcolm I. G. Bloor ◽  
M. Susan Bloor ◽  
Michael J. Wilson
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Spline Approximation ◽  
The Finite Element Method ◽  
B Spline ◽  
B Splines ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Spline Basis ◽  
Element Method

Abstract A PDE surface is generated by solving partial differential equations subject to boundary conditions. To obtain an approximation of the PDE surface in the form of a B-spline surface the finite element method, with the basis formed from B-spline basis functions, can be used to solve the equations. The procedure is simplest when uniform B-splines are used, but it is also feasible, and in some cases desirable, to use non-uniform B-splines. It will also be shown that it is possible, if required, to modify the non-uniform B-spline approximation in a variety of ways, using the properties of B-spline surfaces.

scholarly journals Application of the Hylleraas- B -spline basis set: Nonrelativistic Bethe logarithm of helium

2019 ◽  
Vol 100 (4) ◽  
Author(s):  
San-Jiang Yang ◽  
Yong-Bo Tang ◽  
Yong-Hua Zhao ◽  
Ting-Yun Shi ◽  
Hao-Xue Qiao
Keyword(s):  
Basis Set ◽  
B Spline ◽  
Spline Basis

scholarly journals Numerical Solution of Nonlinear Sine-Gordon Equation by Modified Cubic B-Spline Collocation Method

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
R. C. Mittal ◽  
Rachna Bhatia
Keyword(s):  
Numerical Solution ◽  
Collocation Method ◽  
Gordon Equation ◽  
Spline Collocation ◽  
Sine Gordon Equation ◽  
B Spline ◽  
Spline Collocation Method ◽  
B Splines ◽  
Spline Basis ◽  
The Given

Modified cubic B-spline collocation method is discussed for the numerical solution of one-dimensional nonlinear sine-Gordon equation. The method is based on collocation of modified cubic B-splines over finite elements, so we have continuity of the dependent variable and its first two derivatives throughout the solution range. The given equation is decomposed into a system of equations and modified cubic B-spline basis functions have been used for spatial variable and its derivatives, which gives results in amenable system of ordinary differential equations. The resulting system of equation has subsequently been solved by SSP-RK54 scheme. The efficacy of the proposed approach has been confirmed with numerical experiments, which shows that the results obtained are acceptable and are in good agreement with earlier studies.

Application of Rational B-Splines to the Synthesis of Cam-Follower Motion Programs

1993 ◽  
Vol 115 (3) ◽  
pp. 621-626 ◽  
Author(s):  
D. M. Tsay ◽  
C. O. Huey
Keyword(s):  
Basis Functions ◽  
Spline Functions ◽  
B Spline ◽  
B Splines ◽  
Motion Constraints ◽  
Cam Follower ◽  
Spline Basis

A procedure employing rational B-spline functions for the synthesis of cam-follower motion programs is presented. It differs from earlier techniques that employ spline functions by using rational B-spline basis functions to interpolate motion constraints. These rational B-splines permit greater flexibility in refining motion programs. Examples are provided to illustrate application of the approach.

scholarly journals Image segmentation and preserve the boundary of the image using b-spline basis

2021 ◽  
Vol 5 (2) ◽  
pp. 121-131
Author(s):  
Gajalakshmi N ◽  
Karunanith S
Keyword(s):  
Image Segmentation ◽  
Optimal Solution ◽  
Input Image ◽  
Mean Square ◽  
Knot Insertion ◽  
Spline Collocation ◽  
B Spline ◽  
B Splines ◽  
Number Of Zeros ◽  
Spline Basis

This paper focuses the knot insertion in the B-spline collocation matrix, with nonnegative determinants in all n x n sub-matrices. Further by relating the number of zeros in B-spline basis as well as changes (sign changes) in the sequence of its B-spline coefficients. From this relation, we obtained an accurate characterization when interpolation by B-splines correlates with the changes leads uniqueness and this ensures the optimal solution. Simultaneously we computed the knot insertion matrix and B-spline collocation matrix and its sub-matrices having nonnegative determinants. The totality of the knot insertion matrix and B-spline collocation matrix is demonstrated in the concluding section by using the input image and shows that these concepts are fit to apply and reduce the errors through mean square error and PSNR values

A finite B-spline basis set for accurate diatomic molecule calculations

2003 ◽  
Vol 25 (3) ◽  
pp. 368-374 ◽  
Author(s):  
A. N. Artemyev ◽  
E. V. Ludeña ◽  
V. V. Karasiev ◽  
A. J. Hernández
Keyword(s):  
Diatomic Molecule ◽  
Basis Set ◽  
B Spline ◽  
Spline Basis
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