Search results for "rotational symmetry"
showing 10 items of 58 documents
Mixed Probabilistic-Guaranteed Optimal Design
2009
This chapter deals with the mixed probabilistic-guaranteed approach to optimal design of quasi-brittle membrane shells. Special attention is devoted to different problem formulations and analytical methods for their solution. Optimal thickness distributions are presented for various axisymmetric membrane shells. The presentation follows research results of [BRS03b].
Multi-domain spectral approach with Sommerfeld condition for the Maxwell equations
2021
We present a multidomain spectral approach with an exterior compactified domain for the Maxwell equations for monochromatic fields. The Sommerfeld radiation condition is imposed exactly at infinity being a finite point on the numerical grid. As an example, axisymmetric situations in spherical and prolate spheroidal coordinates are discussed.
Eulerian models of the rotating flexible wheelset for high frequency railway dynamics
2019
Abstract In this paper three formulations based on an Eulerian approach are presented to obtain the dynamic response of an elastic solid of revolution, which rotates around its main axis at constant angular velocity. The formulations are especially suitable for the study of the interaction of a solid with a non-rotating structure, such as occurs in the coupled dynamics of a railway wheelset with the track. With respect to previous publications that may adopt similar hypotheses, this paper proposes more compact formulations and eliminates certain numerical problems associated with the presence of second-order derivatives with respect to the spatial coordinates. Three different models are dev…
Discrete-Gauss states and the generation of focussing dark beams
2014
Discrete-Gauss states are a new class of gaussian solutions of the free Schr\"odinger equation owning discrete rotational symmetry. They are obtained by acting with a discrete deformation operator onto Laguerre-Gauss modes. We present a general analytical construction of these states and show the necessary and sufficient condition for them to host embedded dark beams structures. We unveil the intimate connection between discrete rotational symmetry, orbital angular momentum, and the generation of focussing dark beams. The distinguishing features of focussing dark beams are discussed. The potential applications of Discrete-Gauss states in advanced optical trapping and quantum information pro…
Axisymmetric solutions for a chemotaxis model of Multiple Sclerosis
2018
In this paper we study radially symmetric solutions for our recently proposed reaction–diffusion–chemotaxis model of Multiple Sclerosis. Through a weakly nonlinear expansion we classify the bifurcation at the onset and derive the amplitude equations ruling the formation of concentric demyelinating patterns which reproduce the concentric layers observed in Balò sclerosis and in the early phase of Multiple Sclerosis. We present numerical simulations which illustrate and fit the analytical results.
Topological charge selection rule for phase singularities
2009
We present a study of the dynamics and decay pattern of phase singularities due to the action of a system with a discrete rotational symmetry of finite order. A topological charge conservation rule is identified. The role played by the underlying symmetry is emphasized. An effective model describing the short range dynamics of the vortex clusters has been designed. A method to engineer any desired configuration of clusters of phase singularities is proposed. Its flexibility to create and control clusters of vortices is discussed.
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…
Numerical simulations of the jetted tidal disruption event Swift J1644+57
2016
In this work we focus on the technical details of the numerical simulations of the non- thermal transient Swift J1644+57, whose emission is probably produced by a two-component jet powered by a tidal disruption event. In this context we provide details of the coupling between the relativistic hydrodynamic simulations and the radiative transfer code. First, we consider the technical demands of one-dimensional simulations of a fast relativistic jet, and show to what extent (for the same physical parameters of the model) do the computed light curves depend on the numerical parameters of the different codes employed. In the second part we explain the difficulties of computing light curves from …
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…
Stability of an electromagnetically levitated spherical sample in a set of coaxial circular loops
2005
This paper presents a theoretical study of oscillatory and rotational instabilities of a solid spherical body, levitated electromagnetically in axisymmetric coils made of coaxial circular loops. We apply our previous theory to analyze the static and dynamic stability of the sample depending on the ac frequency and the position of the sample in the coils for several simple configurations. We introduce an original analytical approach employing a gauge transformation for the vector potential. First, we calculate the spring constants that define the frequency of small-amplitude oscillations. For static stability, the spring constants must be positive. Dynamic instabilities are characterized by …