Search results for " harmonics"
showing 10 items of 73 documents
Non-symmetrized Hyperspherical Harmonics Method for Non-equal Mass Three-Body Systems
2018
The non-symmetrized hyperspherical harmonics method for a three-body system, composed by two particles having equal masses, but different from the mass of the third particle, is reviewed and applied to the $^3$H, $^3$He nuclei and $^3_{\Lambda}$H hyper-nucleus, seen respectively as $nnp$, $ppn$ and $NN\Lambda$ three-body systems. The convergence of the method is first tested in order to estimate its accuracy. Then, the difference of binding energy between $^3$H and $^3$He due to the difference of the proton and the neutron masses is studied using several central spin-independent and spin-dependent potentials. Finally, the $^3_{\Lambda}$H hypernucleus binding energy is calculated using diffe…
ANALYSIS OF A SPHERICAL HARMONICS EXPANSION MODEL OF PLASMA PHYSICS
2004
A spherical harmonics expansion model arising in plasma and semiconductor physics is analyzed. The model describes the distribution of particles in the position-energy space subject to a (given) electric potential and consists of a parabolic degenerate equation. The existence and uniqueness of global-in-time solutions is shown by semigroup theory if the particles are moving in a one-dimensional interval with Dirichlet boundary conditions. The degeneracy allows to show that there is no transport of particles across the boundary corresponding to zero energy. Furthermore, under certain conditions on the potential, it is proved that the solution converges in the long-time limit exponentially f…
Figures of equilibrium in close binary systems
1992
The equilibrium configurations of close binary systems are analyzed. The autogravitational, centrifugal and tidal potentials are expanded in Clairaut's coordinates. From the set of the total potential angular terms an integral equations system is derived. The reduction of them to ordinary differential equations and the determination of the boundary conditions allow a formulation of the problem in terms of a single variable.
Multiple expansions for energy and momenta carried by gravitational waves
2007
We present expressions for the energy, linear momentum and angular momentum carried away from an isolated system by gravitational radiation based on spin-weighted spherical harmonics decomposition of the Weyl scalar $\Psi_4$. We also show that the expressions derived are equivalent to the common expressions obtained when using a framework based on perturbations of a Schwazschild background. The main idea is to collect together all the different expressions in a uniform and consistent way. The formulae presented here are directly applicable to the calculation of the radiated energy, linear momentum and angular momentum starting from the gravitational waveforms which are typically extracted f…
An ab initio potential energy surface for the C2H2-N2 system
2012
International audience; An ab initio potential energy surface determined at the CCSD(T) level of theory is presented for the van der Waals complex C2H2-N2. Additional calculations performed with the HF- and DFT-SAPT methods compare well with the CCSD(T) results and allow a better understanding of the main features of this interaction potential surface. An expansion of this surface over spherical harmonics has also been performed. The global energy minimum of the complex is obtained for the linear conformation. The T conformations are the least attractive. Such characteristics mainly arise because of the variation, in sign and in absolute value of the electrostatic energy between all these c…
Fundamental solutions for general anisotropic multi-field materials based on spherical harmonics expansions
2016
Abstract A unified method to evaluate the fundamental solutions for generally anisotropic multi-field materials is presented. Based on the relation between the Rayleigh expansion and the three-dimensional Fourier representation of a homogenous partial differential operator, the proposed technique allows to obtain the fundamental solutions and their derivatives up to the desired order as convergent series of spherical harmonics. For a given material, the coefficients of the series are computed only once, and the derivatives of the fundamental solutions are obtained without any term-by-term differentiation, making the proposed approach attractive for boundary integral formulations and efficie…
Implementation of local chiral interactions in the hyperspherical harmonics formalism
2021
With the goal of using chiral interactions at various orders to explore properties of the few-body nuclear systems, we write the recently developed local chiral interactions as spherical irreducible tensors and implement them in the hyperspherical harmonics expansion method. We devote particular attention to three-body forces at next-to-next-to leading order, which play an important role in reproducing experimental data. We check our implementation by benchmarking the ground-state properties of $^3$H, $^3$He and $^4$He against the available Monte Carlo calculations. We then confirm their order-by-order truncation error estimates and further investigate uncertainties in the charge radii obta…
Searches for Large-Scale Anisotropy in the Arrival Directions of Cosmic Rays Detected above Energy of $10^{19}$ eV at the Pierre Auger Observatory an…
2014
Spherical harmonic moments are well-suited for capturing anisotropy at any scale in the flux of cosmic rays. An unambiguous measurement of the full set of spherical harmonic coefficients requires full-sky coverage. This can be achieved by combining data from observatories located in both the northern and southern hemispheres. To this end, a joint analysis using data recorded at the Telescope Array and the Pierre Auger Observatory above 1019 eV is presented in this work. The resulting multipolar expansion of the flux of cosmic rays allows us to perform a series of anisotropy searches, and in particular to report on the angular power spectrum of cosmic rays above 1019 eV. No significant devia…
A code to evaluate prolate and oblate spheroidal harmonics
1998
Abstract We present a code to evaluate prolate ( P n m ( x ), Q n m ( x ); n ≥ m , x > 1) and oblate ( P n m ( ix ), Q n m ( ix ); n ≥ m , x > 0) spheroidal harmonics, that is, spherical harmonics ( n and m integers) for real arguments larger than one and for purely imaginary arguments. We start from the known values (in closed form) of P m m and P m +1 m and we apply the forward recurrence relation over n up to a given degree n = N Max . The Wronskian relating P 's and Q 's, together with the evaluation of the continued fraction for Q m+N staggeredMax m / Q m+N staggeredMax -1 m , allows the calculation of Q m+N staggeredMax m and Q m+N staggeredMax -1 m . Backward recurrence is then appli…
Enhanced Mathematical Modelling of Interior Permanent Magnet Synchronous Machine Considering Saturation, Cross-Coupling and Spatial Harmonics effects
2020
The Interior Permanent Magnet Synchronous machine (IPMSM) conventional mathematical model is generally employed to investigate and simulate the IPMSM control and drive system behaviour. However, magnetic nonlinearities and spatial harmonics have a substantial influence on the IPMSM electromagnetic behaviour and performances. In order to simulate the IPMSM real electromagnetic behaviour, this paper describes an enhanced mathematical model that takes into account the saturation, cross-coupling and spatial harmonics effects. This model has been implemented in Matlab®/Simulink environment where the electric and magnetic parameters are derived from FEA investigations and implemented by the use o…