Search results for "Circular symmetry"
showing 10 items of 38 documents
Spherical symmetric parabolic dust collapse: ${\cal C}^{1}$ matching metric with zero intrinsic energy
2016
The collapse of marginally bound, inhomogeneous, pressureless (dust) matter, in spherical symmetry, is considered. The starting point is not, in this case, the integration of the Einstein equations from some suitable initial conditions. Instead, starting from the corresponding general exact solution of these equations, depending on two arbitrary functions of the radial coordinate, the fulfillment of the Lichnerowicz matching conditions of the interior collapsing metric and the exterior Schwarzschild one is tentatively assumed (the continuity of the metric and its first derivatives on the time-like hypersurface describing the evolution of the spherical 2-surface boundary of the collapsing cl…
Deformations of quasi-two-dimensional electron gas clusters
1998
Shell effects and Jahn-Teller deformations of quasi-two-dimensional jellium droplets are studied. Utilizing the ultimate jellium assumption, previously successfully used for three-dimensional systems, we calculate unrestricted shape relaxations and binding energies of the ground-state and the lowest isomers, using the methods of density-functional theory in the local spin-density approximation. Strong variations with particle number are found in the shape of the droplets. In particular, for certain magic electron numbers the shapes show triangular or circular symmetry, while for other electron numbers, more complicated symmetries are found. We finally show that from a more simple ``billiard…
Approximate Modeling of Spherical Membrane
2010
Spherical symmetry is ubiquitous in nature. It's therefore unfortunate that spherical system simulations are so hard, and require complete spheres with millions of interacting particles. Here we introduce an approach to model spherical systems, using revised periodic boundary conditions adapted to spherical symmetry. Method reduces computational costs by orders of magnitude, and is applicable for both solid and liquid membranes, provided the curvature is sufficiently small. We demonstrate the method by calculating the bending and Gaussian curvature moduli of single- and multi-layer graphene. Method works with any interaction (ab initio, classical interactions), with any approach (molecular …
Ellipsoidal deformation of vertical quantum dots
1999
Addition energy spectra at 0 T of circular and ellipsoidally deformed few-electron vertical quantum dots are measured and compared to results of model calculations within spin-density functional theory. Because of the rotational symmetry of the lateral harmonic confining potential, circular dots show a pronounced shell structure. With the lifting of the single- particle level degeneracies, even a small deformation is found to radically alter the shell structure leading to significant modifications in the addition energy spectra. Breaking the circular symmetry with deformation also induces changes in the total spin. This "piezo-magnetic" behavior of quantum dots is discussed, and the additio…
Hyperbolic character of the angular moment equations of radiative transfer and numerical methods
2000
We study the mathematical character of the angular moment equations of radiative transfer in spherical symmetry and conclude that the system is hyperbolic for general forms of the closure relation found in the literature. Hyperbolicity and causality preservation lead to mathematical conditions allowing to establish a useful characterization of the closure relations. We apply numerical methods specifically designed to solve hyperbolic systems of conservation laws (the so-called Godunov-type methods), to calculate numerical solutions of the radiation transport equations in a static background. The feasibility of the method in any kind of regime, from diffusion to free-streaming, is demonstrat…
Tools for incorporating a D-wave contribution in Skyrme energy density functionals
2015
International audience; The possibility of adding a D-wave term to the standard Skyrme effective interaction has been widely considered in the past. Such a term has been shown to appear in the next-to-next-to-leading order of the Skyrme pseudo-potential. The aim of the present article is to provide the necessary tools to incorporate this term in a fitting procedure: first, a mean-field equation written in spherical symmetry in order to describe spherical nuclei and second, the response function to detect unphysical instabilities. With these tools it will be possible to build a new fitting procedure to determine the coupling constants of the new functional.
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…
Explosion and Final State of an Unstable Reissner-Nordström Black Hole
2016
A Reissner-Nordstr\"om black hole (BH) is superradiantly unstable against spherical perturbations of a charged scalar field, enclosed in a cavity, with frequency lower than a critical value. We use numerical relativity techniques to follow the development of this unstable system -- dubbed a charged BH bomb -- into the non-linear regime, solving the full Einstein--Maxwell--Klein-Gordon equations, in spherical symmetry. We show that: $i)$ the process stops before all the charge is extracted from the BH; $ii)$ the system settles down into a hairy BH: a charged horizon in equilibrium with a scalar field condensate, whose phase is oscillating at the (final) critical frequency. For low scalar fie…
Solution of self-consistent equations for the N3LO nuclear energy density functional in spherical symmetry. The program hosphe (v1.02)
2010
Abstract We present solution of self-consistent equations for the N 3 LO nuclear energy density functional. We derive general expressions for the mean fields expressed as differential operators depending on densities and for the densities expressed in terms of derivatives of wave functions. These expressions are then specified to the case of spherical symmetry. We also present the computer program hosphe (v1.02), which solves the self-consistent equations by using the expansion of single-particle wave functions on the spherical harmonic oscillator basis. Program summary Program title: HOSPHE (v1.02) Catalogue identifier: AEGK_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEGK_…
RPA in wavefunction representation
1992
The RPA is formulated in subspaces of coordinate-like and momentum-like I ph operators. This allows to embed a large class of approximative schemes into a generalized RPA treatment. We give a detailed formulation in terms of wavefunctions in coordinate space which is ideally suited to practical programming. In particular, we work out the reduction to spherical tensors in the case of spherical symmetry which is most often the starting point in finite Fermion systems.