Search results for "singularity"

Mixed mode energy release rates for bonded composite joints

2011

Abstract: Analytical formulae developed by Luo and Tong (2009) to determine the mixed mode strain energy release rates of laminated and co-cured composite structures and joints are reviewed. The effects of varying loading conditions and geometries on the mode mixity found analytically are investigated via a parametric study. A critical evaluation of the analytical formulae indicates that the formulae are robust in calculating the total strain energy release rate, but may underestimate the mode II component compared with the finite element analysis and experimental results. Possible reasons for this discrepancy are discussed, including the effect of stress concentrations and singularities at…

Metal–Metal Distances, Electron Counts, and Superconducting TC's in AM2B2C

2001

Abstract We present first principles band structure calculations on representative boron carbides belonging to the class of superconducting compounds with the general formula AM 2 B 2 C with A =Lu, La, or Th and M =Ni or Pd. The compounds are analyzed within the framework of the so-called van Hove scenario, where superconductivity is linked to certain kinds of instabilities in the band structure. We attempt to determine why the addition of the extra electron on replacing the rare earth with Th does not make a significant difference to the superconducting properties, and why the compound LaNi 2 B 2 C is not superconducting.

Ni-based superconductor: Heusler compoundZrNi2Ga

2008

This work reports on the novel Heusler superconductor ZrNi2Ga. Compared to other nickel-based superconductors with Heusler structure, ZrNi2Ga exhibits a relatively high superconducting transition temperature of Tc=2.9 K and an upper critical field of 1.5 T. Electronic structure calculations show that this relatively high transition temperature is caused by a van Hove singularity, which leads to an enhanced density of states at the Fermi energy. The van Hove singularity originates from a higher order valence instability at the L-point in the electronic structure. The enhanced density of states at the Fermi level was confirmed by specific heat and susceptibility measurements. Although many He…

Inflection points and topology of surfaces in 4-space

2000

We consider asymptotic line fields on generic surfaces in 4-space and show that they are globally defined on locally convex surfaces, and their singularities are the inflection points of the surface. As a consequence of the generalized Poincare-Hopf formula, we obtain some relations between the number of inflection points in a generic surface and its Euler number. In particular, it follows that any 2-sphere, generically embedded as a locally convex surface in 4-space, has at least 4 inflection points.

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…

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…