Search results for "singularity."

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…

Stability of Hamiltonian Systems of Two Degrees of Freedom and of Formally Conservative Mappings Near a Singular Point

1985

We restrict ourselves to the stability problems considered in our lecture because the length of this paper is limited. In contrast to the lecture, however, we consider here not only area preserving mappings but a more general class of mappings.

Singularities of rational Bézier curves

2001

We prove that if an nth degree rational Bezier curve has a singular point, then it belongs to the two (n − 1)th degree rational Bezier curves defined in the (n − 1)th step of the de Casteljau algorithm. Moreover, both curves are tangent at the singular point. A procedure to construct Bezier curves with singularities of any order is given.  2001 Elsevier Science B.V. All rights reserved.

Generic properties of singular trajectories

1997

Abstract Let M be a σ-compact C∞ manifold of dimension d ≥ 3. Consider on M a single-input control system : x (t) = F 0 (x(t)) + u(t) F 1 (x(t)) , where F0, F1 are C∞ vector fields on M and the set of admissible controls U is the set of bounded measurable mappings u : [0Tu]↦ R , Tu > 0. A singular trajectory is an output corresponding to a control such that the differential of the input-output mapping is not of maximal rank. In this article we show that for an open dense subset of the set of pairs of vector fields (F0, F1), endowed with the C∞-Whitney topology, all the singular trajectories are with minimal order and the corank of the singularity is one.

Complex powers on noncompact manifolds and manifolds with singularities

1988

A Global View on Generic Geometry

2018

We describe how the study of the singularities of height and distance squared functions on submanifolds of Euclidean space, combined with adequate topological and geometrical tools, shows to be useful to obtain global geometrical properties. We illustrate this with several results concerning closed curves and surfaces immersed in \(\mathbb {R}^n\) for \(n=3,4, 5\).