From basis functions to basis fields: vector field approximation from sparse data

1992 ◽  
Vol 67 (6) ◽  
pp. 479-489 ◽  
Author(s):  
Ferdinando A. Mussa-Ivaldi
Keyword(s):  
Vector Field ◽  
Sparse Data ◽  
Field Approximation ◽  
Basis Functions

scholarly journals Vector field approximation using radial basis functions

2013 ◽  
Vol 240 ◽  
pp. 163-173 ◽  
Author(s):  
Daniel A. Cervantes Cabrera ◽  
Pedro González-Casanova ◽  
Christian Gout ◽  
L. Héctor Juárez ◽  
L. Rafael Reséndiz
Keyword(s):  
Vector Field ◽  
Radial Basis Functions ◽  
Field Approximation ◽  
Basis Functions ◽  
Radial Basis

QUANTUM FIELDS WITH MODIFIED DISPERSION RELATIONS IN CURVED SPACES

2011 ◽  
Vol 20 (05) ◽  
pp. 745-756 ◽  
Author(s):  
FRANCISCO DIEGO MAZZITELLI
Keyword(s):  
Vector Field ◽  
General Structure ◽  
Scalar Fields ◽  
Field Approximation ◽  
Weak Field ◽  
Dispersion Relations ◽  
Quantum Fields ◽  
Renormalization Procedure ◽  
Modified Dispersion Relations ◽  
Weak Field Approximation

We discuss the renormalization procedure for quantum scalar fields with modified dispersion relations in curved spacetimes. We consider two different ways of introducing modified dispersion relations: through the interaction with a dynamical temporal vector field, as in the context of the Einstein–Aether theory, and breaking explicitly the covariance of the theory, as in Hǒrava–Lifshitz gravity. Working in the weak field approximation, we show that the general structure of the counterterms depends on the UV behavior of the dispersion relations and on the mechanism chosen to introduce them.

DIV-CURL WEIGHTED MINIMIZING SPLINES

2007 ◽  
Vol 05 (02) ◽  
pp. 95-122 ◽  
Author(s):  
M. N. BENBOURHIM ◽  
A. BOUHAMIDI
Keyword(s):  
Vector Field ◽  
Radial Basis Functions ◽  
Thin Plate ◽  
Approximation Problem ◽  
Scattered Data ◽  
Scalar Function ◽  
Basis Functions ◽  
Thin Plate Splines ◽  
Numerical Examples ◽  
Radial Basis

The paper deals with a div-curl approximation problem by weighted minimizing splines. The weighted minimizing splines are an extension of the well-known thin plate splines and are radial basis functions which allow the approximation or the interpolation of a scalar function from given scattered data. In this paper, we show that the theory of the weighted minimizing splines may also be used for the approximation or for the interpolation of a vector field controlled by the divergence and the curl of the vector field. Numerical examples are given to show the efficiency of this method.

Vector field approximation: a computational paradigm for motor control and learning

1992 ◽  
Vol 67 (6) ◽  
pp. 491-500 ◽  
Author(s):  
Ferdinando A. Mussa-Ivaldi ◽  
Simon F. Giszter
Keyword(s):  
Motor Control ◽  
Vector Field ◽  
Field Approximation ◽  
Computational Paradigm

scholarly journals A comparison of various basis functions based on meshless local Petrov-Galerkin method for linear stability of circular jet

2013 ◽  
Vol 17 (5) ◽  
pp. 1329-1335
Author(s):  
Qing He ◽  
Mingliang Xie
Keyword(s):  
Vector Field ◽  
Linear Stability ◽  
Basis Function ◽  
Degrees Of Freedom ◽  
Basis Functions ◽  
Axial Component ◽  
Continuum Equation ◽  
Perturbation Vector ◽  
Galerkin Spectral Method ◽  
Chebyshev Functions

Various basis functions based on Fourier-Chebyshev Petrov-Galerkin spectral method are described for computation of temporal linear stability of a circular jet. Basis functions presented here are exponentially mapped Chebyshev functions. There is a linear dependence between the components of the perturbation vector field, and there are only two degrees of freedom for the perturbation continuum equation. According to the principle of permutation and combination, the basis function has three basic forms, i. e., the radial, azimuthal or axial component, respectively. The results show that three eigenvalues for various cases are consistent, but there is a preferable basis function for numerical computation.

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