Search results for "singular"
showing 10 items of 589 documents
Singularities for Prandtl's equations.
2006
We used a mixed spectral/finite-difference numerical method to investigate the possibility of a finite time blow-up of the solutions of Prandtl's equations for the case of the impulsively started cylinder. Our toll is the complex singularity tracking method. We show that a cubic root singularity seems to develop, in a time that can be made arbitrarily short, from a class of data uniformely bounded in H^1.
Comparison of parallel implementation of some multi-level Schwarz methods for singularly perturbed parabolic problems
1999
Abstract Parallel multi-level algorithms combining a time discretization and an overlapping domain decomposition technique are applied to the numerical solution of singularly perturbed parabolic problems. Two methods based on the Schwarz alternating procedure are considered: a two-level method with auxiliary “correcting” subproblems as well as a three-level method with auxiliary “predicting” and “correcting” subproblems. Moreover, modifications of the methods using time extrapolation on subdomain interfaces are investigated. The emphasis is given to the description of the algorithms as well as their computer realization on a distributed memory multiprocessor computer. Numerical experiments …
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…
La singularité de O’Grady
2006
Let M 2 v M_{2v} be the moduli space of semistable sheaves with Mukai vector 2 v 2v on an abelian or K 3 K3 surface where v v is primitive such that ⟨ v , v ⟩ = 2 \langle v,v \rangle =2 . We show that the blow-up of the reduced singular locus of M 2 v M_{2v} provides a symplectic resolution of singularities. This provides a direct description of O’Grady’s resolutions of M K 3 ( 2 , 0 , 4 ) M_{K3}(2,0,4) and M A b ( 2 , 0 , 2 ) M_{Ab}(2,0,2) . Résumé. Soit M 2 v M_{2v} l’espace de modules des faisceaux semi-stables de vecteur de Mukai 2 v 2v sur une surface K 3 K3 ou abélienne où v v est primitif tel que ⟨ v , v ⟩ = 2 \langle v,v \rangle =2 . Nous montrons que l’éclatement de M 2 v M_{2v} le…
Existence and almost uniqueness for p -harmonic Green functions on bounded domains in metric spaces
2020
We study ($p$-harmonic) singular functions, defined by means of upper gradients, in bounded domains in metric measure spaces. It is shown that singular functions exist if and only if the complement of the domain has positive capacity, and that they satisfy very precise capacitary identities for superlevel sets. Suitably normalized singular functions are called Green functions. Uniqueness of Green functions is largely an open problem beyond unweighted $\mathbf{R}^n$, but we show that all Green functions (in a given domain and with the same singularity) are comparable. As a consequence, for $p$-harmonic functions with a given pole we obtain a similar comparison result near the pole. Various c…
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.
Iterative construction of Dupin cyclides characteristic circles using non-stationary Iterated Function Systems (IFS)
2012
International audience; A Dupin cyclide can be defined, in two different ways, as the envelope of an one-parameter family of oriented spheres. Each family of spheres can be seen as a conic in the space of spheres. In this paper, we propose an algorithm to compute a characteristic circle of a Dupin cyclide from a point and the tangent at this point in the space of spheres. Then, we propose iterative algorithms (in the space of spheres) to compute (in 3D space) some characteristic circles of a Dupin cyclide which blends two particular canal surfaces. As a singular point of a Dupin cyclide is a point at infinity in the space of spheres, we use the massic points defined by J.C. Fiorot. As we su…