Search results for "Coordinate system"
showing 10 items of 118 documents
Removal of Resonances
2001
From the perturbative procedure in the last chapter we have learned that in the proximity of resonances of the unperturbed system, resonant denominators appear in the expression for the adiabatic invariants. We now wish to begin to locally remove such resonances by trying, with the help of a canonical transformation, to go to a coordinate system which rotates with the resonant frequency.
Estimating the angular resolution of tracks in neutrino telescopes based on a likelihood analysis
2004
A semianalytic method to estimate the angular resolution of tracks, that have been reconstructed by a likelihood approach, is presented. The optimal choice of coordinate systems and resolution parameters, as well as tests of the method are discussed based on an application for a neutrino telescope.
Diagnosing the Horizontal Propagation of Rossby Wave Packets along the Midlatitude Waveguide
2017
AbstractIt has been suggested that upper-tropospheric Rossby wave packets propagating along the midlatitude waveguide may play a role for triggering severe weather. This motivates the search for robust methods to detect and track Rossby wave packets and to diagnose their properties. In the framework of several observed cases, this paper compares different methods that have been proposed for these tasks, with an emphasis on horizontal propagation and on a particular formulation of a wave activity flux previously suggested by Takaya and Nakamura. The utility of this flux is compromised by the semigeostrophic nature of upper-tropospheric Rossby waves, but this problem can partly be overcome by…
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…
Simulations with Smoothed Particles Confirm Stationary Shocks in Accretion Flows onto Black Holes
1994
We present the results of time dependent numerical simulations of the accretion of gas onto Schartzschild black holes. We find that stable shocks are a common feature for flows of inviscid gas accreting with small angular momentum per unit mass. We used the Smoothed Particles Hydrodynamics tecnique, expressed into cylindrical coordinates to exploit the axial symmetry of the problem. For the case of 1-Dimensional axis-symmetric simulations we find that the shock location is exactly at the position predicted by the stationary analysis developed by Chakrabarti. We solve also the ambiguity related to the two possible shock positions: only the outer shock is stable. The case of 2-Dimensional axi…
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…
Potential and energy of some spheroidal charge distributions with azimuthal symmetry
1989
Abstract The Poisson equation is solved for three types of spheroidal charge distributions with azimuthal symmetry, namely, those depending on one cartesian coordinate, on the radial cylindrical coordinate and on the radial spherical coordinate. The energy of such distributions is found for the case of power functions of these coordinates and it has been normalized, computed and plotted for some low values of the exponent.
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…
A "horizon adapted" approach to the study of relativistic accretion flows onto rotating black holes
1998
We present a new geometrical approach to the study of accretion flows onto rotating (Kerr) black holes. Instead of Boyer-Lindquist coordinates, the standard choice in all existing numerical simulations in the literature, we employ the simplest example of a horizon adapted coordinate system, the Kerr-Schild coordinates. This choice eliminates boundary ambiguities and unphysical divergent behavior at the event horizon. Computations of Bondi-Hoyle accretion onto extreme Kerr black holes, performed here for the first time, demonstrate the key advantages of this procedure. We argue it offers the best approach to the numerical study of the, observationally, increasingly more accesible relativisti…