Search results for "Singularity"
showing 10 items of 352 documents
Instabilities of optical solitons and Hamiltonian singular solutions in a medium of finite extension
2011
International audience; We analyze the role of soliton solutions and Hamiltonian singularities in the dynamics of counterpropagating waves in a medium of finite spatial extension. The soliton solution can become unstable due to the finite extension of the system. We show that the spatiotemporal dynamics then relaxes toward a Hamiltonian singular state of a nature different than that of the soliton state. This phenomenon can be explained through a geometrical analysis of the singularities of the stationary Hamiltonian system.
Theory for the control of dark rays by means of discrete symmetry diffractive elements
2013
We present an analytical theory that describes the disintegration of a highly charged phase singularity by the presence of a thin discrete symmetry diffractive element, i.e., an optical diffractive element possessing rotational symmetry of finite order. The process is described in terms of dark rays, defined as the trajectories where there is no light, i.e., those for which the complex optical field vanishes. We provide explicit analytical expressions for the equations that describe the dark ray trajectories. We show that dark rays follow straight line trajectories asymptotically, like ordinary rays, but with properties which differ in essential features with respect to their bright counter…
Multifractal Properties of Eigenstates in Weakly Disordered Two-Dimensional Systems without Magnetic Field
1992
In order to investigate the electronic states in weakly disordered 2D samples very large (up to 180 000 * 180 000) secular matrices corresponding to the Anderson Hamiltonian are diagonalized. The analysis of the resulting wave functions shows multifractal fluctuations on all length scales in the considered systems. The set of generalized (fractal) dimensions and the singularity spectrum of the fractal measure are determined in order to completely characterize the eigenfunctions.
On Scattering and Bound States for a Singular Potential
1970
To understand the origin of the difficulties in the determination of the physical wavefunc tion for an attractive inverse square potential, we study a model in which the singularity at the origin is substituted by a repulsive core. The structure of the spectrum of energy levels is discussed in some detail. The physical interpretation of the solutions of the Schrodinger equation for a potential of the form - (-h 2 /2m) 11/ r 2 presents difficulties, which occur for 11 larger than (l + 1/2)\ where l is the angular momentum. The difficulties are due to the fact that the condition of square integrability usually imposed on the wavefunction is not sufficient in this case to determine phase shif…
Complex singularities and PDEs
2015
In this paper we give a review on the computational methods used to capture and characterize the complex singularities developed by some relevant PDEs. We begin by reviewing the classical singularity tracking method and give an example of application using the Burgers equation as a case study. This method is based on the analysis of the Fourier spectrum of the solution and it allows to determine and characterize the complex singularity closest to the real domain. We then introduce other methods generally used to detect the hidden singularities. In particular we show some applications of the Padé approximation, of the Kida method, and of Borel-Polya method. We apply these techniques to the s…
Plane foliations with a saddle singularity
2012
Abstract We study the set of planar vector fields with a unique singularity of hyperbolic saddle type. We found conditions to assure that a such vector field is topologically equivalent to a linear saddle. Furthermore, we describe the plane foliations associated to these vector fields. Such a foliation can be split in two subfoliations. One without restriction and another one that is topologically characterized by means of trees.
Real and Complex Singularities
2016
In this paper a Minkowski analogue of the Euclidean medial axis of a closed and smooth plane curve is introduced. Its generic local configurations are studied and the types of shocks that occur on these are also determined.
Analysis of complex singularities in high-Reynolds-number Navier-Stokes solutions
2013
AbstractNumerical solutions of the laminar Prandtl boundary-layer and Navier–Stokes equations are considered for the case of the two-dimensional uniform flow past an impulsively-started circular cylinder. The various viscous–inviscid interactions that occur during the unsteady separation process are investigated by applying complex singularity analysis to the wall shear and streamwise velocity component of the two solutions. This is carried out using two different methodologies, namely a singularity-tracking method and the Padé approximation. It is shown how the van Dommelen and Shen singularity that occurs in solutions of the Prandtl boundary-layer equations evolves in the complex plane be…
Singularity formation and separation phenomena in boundary layer theory
2009
In this paper we review some results concerning the behaviour of the incompressible Navier–Stokes solutions in the zero viscosity limit. Most of the emphasis is put on the phenomena occurring in the boundary layer created when the no-slip condition is imposed. Numerical simulations are used to explore the limits of the theory. We also consider the case of 2D vortex layers, i.e. flows with internal layers in the form of a rapid variation, across a curve, of the tangential velocity.
Incremental forming using KUKA KR210-2 industrial robot - research regarding design rules and process modelling
2021
Incremental sheet forming (ISF) process show a great potential in the manufacturing of small series production or prototype development parts. One of the sheet metal forming process, where the contact between punch and metal sheet is in a single point, is known as single point incremental forming (SPIF). The part is manufacture with a simple tool, known as punch, that performs a series of combined movements on the vertically and horizontally directions. The paper introduces a study regarding the design rules and process modelling of this unconventional process, by means of a KUKA KR210-2 industrial robot as technological equipment able to control the correlated movement of the punch. Supple…