Search results for " singularity"
showing 10 items of 203 documents
Harmonic maps and singularities of period mappings
2015
We use simple methods from harmonic maps to investigate singularities of period mappings at infinity. More precisely, we derive a harmonic map version of Schmid’s nilpotent orbit theorem. MSC Classification 14M27, 58E20
Geometric Singular Perturbation Theory Beyond Normal Hyperbolicity
2001
Geometric Singular Perturbation theory has traditionally dealt only with perturbation problems near normally hyperbolic manifolds of singularities. In this paper we want to show how blow up techniques can permit enlarging the applicability to non-normally hyperbolic points. We will present the method on well chosen examples in the plane and in 3-space.
Collision Orbits in the Isosceles Rectilinear Restricted Problem
1995
In the study of the Collinear Three-Body Problem, McGehee (1974) introduced a new set of coordinates which had the effect of blowing up the triple collision singularity. Subsequently, his method has been used to analyze some other collision or singularities. Recently, Wang (1986) introduced another transformation which differs from the McGehee’s coordinates in the fact that the blowing-up factor is now the potential function, U, instead of the moment of inertia, I. Meyer and Wang (1993) have applied this method to the Restricted Isosceles Three-body Problem with positive energy and Cors and Llibre (1994) to the hyperbolic restricted three-body problem. In this paper we study the singulariti…
Response functions in multicomponent Luttinger liquids
2012
We derive an analytic expression for the zero temperature Fourier transform of the density-density correlation function of a multicomponent Luttinger liquid with different velocities. By employing Schwinger identity and a generalized Feynman identity exact integral expressions are derived, and approximate analytical forms are given for frequencies close to each component singularity. We find power-like singularities and compute the corresponding exponents. Numerical results are shown for the case of three components.
Integrable Hamiltonian systems with swallowtails
2010
International audience; We consider two-degree-of-freedom integrable Hamiltonian systems with bifurcation diagrams containing swallowtail structures. The global properties of the action coordinates in such systems together with the parallel transport of the period lattice and corresponding quantum cells in the joint spectrum are described in detail. The relation to the concept of bidromy which was introduced in Sadovski´ı and Zhilinski´ı (2007 Ann. Phys. 322 164–200) is discussed.
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.