Search results for "methods"
showing 10 items of 4526 documents
Ab initioderivation of model energy density functionals
2015
I propose a simple and manageable method that allows for deriving coupling constants of model energy density functionals (EDFs) directly from ab initio calculations performed for finite fermion systems. A proof-of-principle application allows for linking properties of finite nuclei, determined by using the nuclear nonlocal Gogny functional, to the coupling constants of the quasilocal Skyrme functional. The method does not rely on properties of infinite fermion systems but on the ab initio calculations in finite systems. It also allows for quantifying merits of different model EDFs in describing the ab initio results.
Equivalent-Single-Layer discontinuous Galerkin methods for static analysis of multilayered shells
2021
Abstract An original formulation for the elastic analysis of multilayered shells is presented in this work. The key features of the formulation are: the representation of the shell mean surface via a generic system of curvilinear coordinates; the unified treatment of general shell theories via an Equivalent-Single-Layer approach based on the through-the-thickness expansion of the covariant components of the displacement field; and an Interior Penalty discontinuous Galerkin scheme for the solution of the set of governing equations. The combined use of these features enables a high-order solution of the multilayered shell problem. Several numerical tests are presented for isotropic, orthotrop…
The algebra eigenstates method for some systems with spin-like interactions
2006
International audience; An extension of the algebra eigenstates formalism is proposed to solve the eigenvalue equation for a class of problems involving "spin interactions". The method is detailed for the harmonic oscillator, su(2) and su(1, 1) algebras. Special emphasis is given to the resolution of problems in vibronic spectroscopy involving doubly degenerate electronic states.
Achromatic Fresnel diffraction patterns
1993
Abstract A novel method for obtaining a single, but arbitrary, achromatic Fresnel diffraction pattern of any pupil with broadband parallel illumination is presented. The optical device simply consists of an achromatic objective and an on-axis zone plate. A criterion for selecting the system parameters in order to minimize the residual chromatic aberrations is given. The recording of the selected diffraction field is obtained with low chromatic aberrations even for white-light illumination. An experimental verification is shown to illustrate this approach.
Spectral anomalies in focused waves of different Fresnel numbers
2004
Light propagation induces remarkable changes in the spectrum of focused diffracted beams. We show that spectral changes take place in the vicinity of phase singularities in the focal region of spatially coherent, polychromatic spherical waves of different Fresnel numbers. Instead of the Debye formulation, we use the Kirchhoff integral to evaluate the focal field accurately. We find that as a result of a decrease in the Fresnel number, some cylindrical spectral switches are geometrically transformed into conical spectral switches.
White-light Fourier transformer with low chromatic aberration.
1992
A simple Fourier transformation system working with broadband parallel illumination is presented. The proposed setup, consisting of two on-axis zone plates and an achromatic objective, allows us to obtain the achromatic Fourier transform representation of the input at a finite distance with a low chromatic aberration. The discussion of the system, using the Fresnel diffraction theory, leads to an analytical expression to evaluate the transversal and longitudinal chromatic aberrations. It is shown that the resulting chromatic aberrations for typical values of the involved parameters are less than 1% over the entire visible spectrum.
Scale-tunable optical correlation with natural light
2008
We describe two different scale-tunable optical correlators working under totally incoherent light. They behave as spatially incoherent wavelength-independent imaging systems with an achromatic point-spread function (PSF). In both cases it is possible to adapt the scale of the achromatic PSF, i.e., to modify the scaling factor of the PSF and preserve the chromatic compensation, by one's shifting the input along the optical axis. The remarkable properties of these systems allow us to carry out a scale-tunable color pattern-recognition experiment with natural light.
Focal squeeze in axicons
2005
The on-axis irradiance distribution of a truncated conical wavefront is evaluated in terms of the Fresnel number of the focusing geometry. In agreement with geometrical optics, a focal line of increasing intensity is generated for extremely high Fresnel numbers. Otherwise clear deviations may be observed for the position of the maximum irradiance along the optical axis. A remarkable focal squeeze appears and, for decreasing Fresnel numbers, this effect manifests stronger. An analytical formula is provided for the fast evaluation of the focal squeeze.
Debye representation of dispersive focused waves
2006
We report on a matrix-based diffraction integral that evaluates the focal field of any diffraction-limited axisymmetric complex system. This diffraction formula is a generalization of the Debye integral applied to apertured focused beams, which may be accommodated to broadband problems. Longitudinal chromatic aberration may limit the convenience of the Debye formulation and, additionally, spatial boundaries of validity around the focal point are provided. Fresnel number is reformulated in order to guarantee that the focal region is entirely into the region of validity of the Debye approximation when the Fresnel number of the focusing geometry largely exceeds unity. We have applied the matri…
Quasirelativistic transition property calculations by the intermediate Hamiltonian method: Electronic transition dipole moments and radiative lifetim…
2001
We present a quasirelativistic method of ab initio calculations on molecular excited states and electronic transition moments within the relativistic effective potential approximation, based on the construction of intermediate Hamiltonians and spin-free one-particle transition density matrices by means of the many-body multipartitioning perturbation theory. The method is applied to describe the electronic transitions involved in the radiative decay of the ${A0}_{u}^{+},$ ${B0}_{u}^{+},$ and ${B1}_{u}$ states of ${\mathrm{Te}}_{2}.$ Good agreement of the computed transition dipole moment functions with their empirical counterparts is achieved. Theoretical radiative lifetime estimates for sev…