Search results for "singular"

ASYMPTOTIC CURVES ON SURFACES IN ℝ5

2008

We study asymptotic curves on generically immersed surfaces in ℝ5. We characterize asymptotic directions via the contact of the surface with flat objects (k-planes, k = 1 - 4), give the equation of the asymptotic curves in terms of the coefficients of the second fundamental form and study their generic local configurations.

Appendix: Diophantine Approximation on Hyperbolic Surfaces

2002

In this (independent) appendix, we study the Diophantine approximation properties for the particular case of the cusped hyperbolic surfaces, in the spirit of Sect. 2 (or [11]), and the many still open questions that arise for them. We refer to [9], [10]for fundamental results and further developments. We study in particular the distance to a cusp of closed geodesics on a hyperbolic surface.

On the number of singularities of a generic surface with boundary in a 3-manifold

1998

Surface order in body-centered cubic alloys

1993

Free (100)-surfaces of body-centered cubic binary alloys are studied in a parameter range where the bulk turns from the ordered B2-phase to the disordered A2-phase. A model is chosen that describes iron-aluminium alloys in a fairly realistic way. Mean field treatments and Monte Carlo investigations both show that under certain circumstances the surface remains ordered far above the bulk disordering temperatureT c, though the surface order parameter and the surface susceptibility exhibit a singularity atT c with critical exponents characteristic for the ordinary transition. One finds, that if the surface is nonstoechiometric and different layers are not equivalent with respect to perfect bul…

Limit Periodic Sets

1998

As explained at the end of the previous chapter, the most difficult problem in the study of bifurcations in a family of vector fields on a surface of genus 0 is the control of the periodic orbits. In fact, in generic smooth families the periodic orbits will be isolated for each value of the parameter. For analytic families we have two possibilities for each orbit: it may be isolated or belong to a whole annulus of periodic orbits. In this last case and for the parameter values for which the system has infinitely many periodic orbits, the vector field has a local analytic first integral and the nearby vector fields in the family may be studied by the perturbation theory introduced in Chapter…

Convergent transformations into a normal form in analytic Hamiltonian systems with two degrees of freedom on the zero energy surface near degenerate …

2004

We study an analytic Hamiltonian system with two degrees of freedom, having the origin as an elliptic singularity. We assume that the full Birkhoff normal form exists and is divisible by its quadratic part, being indefinite. We show that under the Bruno condition and under the restriction to the zero energy surface, a real analytic transformation into a normal form exists. Such a normal form coincides with the restriction of the Birkhoff normal form to the zero energy surface up to an order as large as we want.

On stability of generic subriemannian caustic in the three-space

2000

Abstract The singularities of exponential mappings in subriemannian geometry are interesting objects, that are already non-trivial at the local level, contrarily to their Riemannian analogs. The simplest case is the three-dimensional contact case. Here we show that the corresponding generic caustics have moduli at the origin, and the first module that occurs has a simple geometric interpretation. On the contrary, we prove a stability result of the “big wave front”, that is, of the graph of the multivalued arclength function, reparametrized in a certain way. This object is a three-dimensional surface, which has also the natural structure of a wave front. The projection on the three-dimension…

Tree Singularities: Limits, Series and Stability

2013

A tree singularity is a surface singularity that consists of smooth components, glued along smooth curves in the pattern of a tree. Such singularities naturally occur as degenerations of certain rational surface singularities. To be more precise, they can be considered as limits of certain series of rational surface singularities with reduced fundamental cycle. We introduce a general class of limits, construct series deformations for them and prove a stability theorem stating that under the condition of finite dimensionality of T 2 the base space of a semi-universal deformation for members high in the series coincides up to smooth factor with the “base space of the limit”. The simplest tree…

A symmetric Galerkin BEM for plate bending analysis

2009

Abstract The Symmetric Galerkin Boundary Element Method is employed in thin plate bending analysis in accordance with the Love–Kirchhoff kinematical assumption. The equations are obtained through the stationary conditions of the total potential energy, written for a plate whose boundary is discretized in boundary elements. Since the matrix coefficients are made up as double integrals with high order singularities, a strategy is shown to compute these coefficients in closed form. Furthermore, in order to model the kinematical discontinuities and to weight the mechanical quantities along the boundary elements, the Lagrangian quadratic shape functions, rather than C 1 type (spline, Hermitian),…

Robust three-dimensional best-path phase-unwrapping algorithm that avoids singularity loops.

2009

In this paper we propose a novel hybrid three-dimensional phase-unwrapping algorithm, which we refer to here as the three-dimensional best-path avoiding singularity loops (3DBPASL) algorithm. This algorithm combines the advantages and avoids the drawbacks of two well-known 3D phase-unwrapping algorithms, namely, the 3D phase-unwrapping noise-immune technique and the 3D phase-unwrapping best-path technique. The hybrid technique presented here is more robust than its predecessors since it not only follows a discrete unwrapping path depending on a 3D quality map, but it also avoids any singularity loops that may occur in the unwrapping path. Simulation and experimental results have shown that …