Search results for "Cartesian coordinate"
showing 10 items of 42 documents
Comparison of cartesian and lobe function Gaussian basis sets
1970
The lobe function and cartesian (spherical harmonic) gaussian are compared with reference to calculations for second-row atoms. Single and grouped gaussian basis sets which have been reported for cartesian functions are taken over directly to construct corresponding lobe function bases with identical sets of exponents and with lobe separations chosen by a scaling procedure. Total and orbital energies and SCF coefficients resulting from calculations on the second-row atoms using the two types of functions for both primitive and grouped gaussian basis sets are seen to be in excellent agreement, thereby emphasizing the essential equivalence of lobe functions and cartesian gaussians, at the ver…
Flux expressions and NEMD perturbations for models of semi-flexible molecules
2001
We derive energy and momentum flux expressions, for systems composed of a general class of semi-flexible molecules, in the Ciccotti-Ferrario-Ryckaert linear constraint formalism. According to this formalism, the whole set of Cartesian coordinates is divided into basic (independent) and secondary (dependent) subsets. It is found that energy and momentum flux vectors have a simple and general expression using both basic and secondary coordinates. In the case of non-equilibrium molecular dynamics, we give general and simple heat and shear flow algorithms, deriving the dissipative fluxes in the space of all Cartesian coordinates. In comparison with previous derivations for some models of flexib…
Nonlocal energy density functionals for low-energy nuclear structure
2014
We introduce a finite-range pseudopotential built as an expansion in derivatives up to next-to-next-to-next-to-leading order (N$^3$LO) and we calculate the corresponding nonlocal energy density functional (EDF). The coupling constants of the nonlocal EDF, for both finite nuclei and infinite nuclear matter, are expressed through the parameters of the pseudopotential. All central, spin-orbit, and tensor terms of the pseudopotential are derived both in the spherical-tensor and Cartesian representation. At next-to-leading order (NLO), we also derive relations between the nonlocal EDF expressed in the spherical-tensor and Cartesian formalism. Finally, a simplified version of the finite-range pse…
Fully Covariant and Conformal Formulation of the Z4 System Compared to the BSSN Formulation in Spherical Symmetry
2014
We have generalized a covariant and conformal version of the Z4 system of the Einstein equations by adopting a reference metric approach, that we denote as fCCZ4, well suited for curvilinear as well as Cartesian coordinates. We implement this formalism in spherical polar coordinates under the assumption of spherical symmetry using a partially-implicit Runge-Kutta (PIRK) method, without using any regularization scheme, and show that our code can evolve both vacuum and non-vacuum spacetimes without encountering instabilities. We have performed several tests and compared the Hamiltonian constraint violations of the fCCZ4 system, for different choices of certain free parameters, with these of B…
Fully covariant and conformal formulation of the Z4 system in a reference-metric approach: Comparison with the BSSN formulation in spherical symmetry
2014
We adopt a reference-metric approach to generalize a covariant and conformal version of the Z4 system of the Einstein equations. We refer to the resulting system as ``fully covariant and conformal", or fCCZ4 for short, since it is well suited for curvilinear as well as Cartesian coordinates. We implement this fCCZ4 formalism in spherical polar coordinates under the assumption of spherical symmetry using a partially-implicit Runge-Kutta (PIRK) method and show that our code can evolve both vacuum and non-vacuum spacetimes without encountering instabilities. Our method does not require regularization of the equations to handle coordinate singularities, nor does it depend on constraint-preservi…
Monte Carlo calculation of dose rate distributions around the Walstam CDC.K-type137Cs sources
2001
Basic dosimetric data for the Walstam CDC.K-type low dose rate 137Cs sources in water have been calculated using Monte Carlo techniques. These sources, CDC.K1 -K3 and CDC.K4, are widely used in a range of applicators and moulds for the treatment of intracavitary and superficial cancers. Our purpose is to improve existing data about these sources using the Monte Carlo simulation code GEANT3. Absolute dose rate distributions in water have been calculated around these sources and are presented as conventional 2D Cartesian look-up tables. Also the AAPM Task Group 43 formalism for dose calculation has been applied. The calculated dose rate constant for the CDC.K1-K3 source is A = 1.106 +/- 0.001…
Maximal slicings in spherical symmetry: Local existence and construction
2011
We show that any spherically symmetric spacetime locally admits a maximal spacelike slicing and we give a procedure allowing its construction. The construction procedure that we have designed is based on purely geometrical arguments and, in practice, leads to solve a decoupled system of first order quasi-linear partial differential equations. We have explicitly built up maximal foliations in Minkowski and Friedmann spacetimes. Our approach admits further generalizations and efficient computational implementation. As by product, we suggest some applications of our work in the task of calibrating Numerical Relativity complex codes, usually written in Cartesian coordinates.
Monte Carlo dosimetry of the Buchler high dose rate 192Ir source.
2001
In this study a complete set of dosimetric data is presented for the high dose rate (HDR) source from Amersham used in the Buchler remote afterloading HDR unit. These data have been calculated by means of the Monte Carlo simulation code GEANT taking into account the detailed geometry of the source. Absolute dose rate distributions in water were calculated around this source and are presented as conventional 2D Cartesian look-up tables. All dosimetric quantities recommended by the AAPM Task Group 43 report have been calculated. Quantities determined are: dose rate constant, radial dose function, anisotropy function, anisotropy factor and anisotropy constant. The dose rate distributions of th…
Grid-based Methods in Relativistic Hydrodynamics and Magnetohydrodynamics
2015
An overview of grid-based numerical methods used in relativistic hydrodynamics (RHD) and magnetohydrodynamics (RMHD) is presented. Special emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods. Results of a set of demanding test bench simulations obtained with different numerical methods are compared in an attempt to assess the present capabilities and limits of the various numerical strategies. Applications to three astrophysical phenomena are briefly discussed to motivate the need for and to demonstrate the success of RHD and RMHD simulations in their understanding. The review further provides FORTRAN programs to compute the exact solution…
A local picture associated with a triply degenerate vibrational mode: vibrational and rovibrational local states
1998
International audience; Abstract: A symmetrized basis adapted to the study of some vibrational excited states of spherical top molecules is proposed. This basis, consistent with the Cartesian picture associated with a three-dimensional mode, is then tested numerically through various XY6 and XY4 molecules. In addition, some simulations, made with 238UF6 and a simplified version of an effective Hamiltonian, clearly show that the method can be further extended through the construction of a symmetrized local rovibrational basis.