Search results for "Singularity"

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…

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 …

A quantum model of Schwarzschild black hole evaporation

1996

We construct a one-loop effective metric describing the evaporation phase of a Schwarzschild black hole in a spherically symmetric null-dust model. This is achieved by quantising the Vaidya solution and by chosing a time dependent quantum state. This state describes a black hole which is initially in thermal equilibrium and then the equilibrium is switched off, so that the black hole starts to evaporate, shrinking to a zero radius in a finite proper time. The naked singularity appears, and the Hawking flux diverges at the end-point. However, a static metric can be imposed in the future of the end-point. Although this end-state metric cannot be determined within our construction, we show tha…

On C1 robust singular transitive sets for three-dimensional flows

1998

Abstract The main goal of this paper is to study robust invariant transitive sets containing singularities for C 1 flows on three-dimensional compact boundaryless manifolds: they are partially hyperbolic with volume expanding central direction. Moreover, they are either attractors or repellers. Robust here means that this property cannot be destroyed by small C 1 -perturbations of the flow.

Rescaling principle for isolated essential singularities of quasiregular mappings

2012

We establish a rescaling theorem for isolated essential singularities of quasiregular mappings. As a consequence we show that the class of closed manifolds receiving a quasiregular mapping from a punctured unit ball with an essential singularity at the origin is exactly the class of closed quasiregularly elliptic manifolds, that is, closed manifolds receiving a non-constant quasiregular mapping from a Euclidean space.

Structural and magnetic properties of the solid solution series Sr2Fe1–xMxReO6(M = Cr, Zn)

2005

Strong correlations between the electronic, structural and magnetic properties have been found during the study of doped double perovskites Sr2Fe1−xMxReO6 (0 ≤ x ≤ 1, M = Zn, Cr). The interplay between the van Hove singularity and the Fermi level plays a crucial role for the magnetic properties. Cr doping of the parent compound Sr2FeReO6 leads to a non-monotonic behaviour of the saturation magnetization and an enhancement for doping levels up to 10%. The Curie temperatures monotonically increase from 401 to 616 K. In contrast, Zn doping leads to a continuous decrease in the saturation magnetization and the Curie temperatures. Superimposed on the electronic effects is the structural influenc…

Valence instabilities and inhomogeneous mixed valence in some ternary europium compounds

1997

Abstract Photoemission spectra and TB-LMTO-ASA band structure calculations of some mixed valency europium compounds hve been studied. The band structures are compared with the band structures of the isostructural lanthanum and strontium compounds. Surprisingly a 4f density of states in the vicinity of the Fermi level is observed in inhomogenous mixed valency EuPd 3 B, Eu 3 S 4 , and EuPdP. Indeed a van Hove Singularity (vHS) derived from the d states of La and Pd or p states of boron or phosphorous are found in La 3 S 4 , LaPd 3 B and SrPdP. The valence instability in the Eu compounds is thus not necessarily due to Eu 4f states. The results also provide some ground for the assumption that i…

Numerical study of blow-up in solutions to generalized Kadomtsev-Petviashvili equations

2013

We present a numerical study of solutions to the generalized Kadomtsev-Petviashvili equations with critical and supercritical nonlinearity for localized initial data with a single minimum and single maximum. In the cases with blow-up, we use a dynamic rescaling to identify the type of the singularity. We present a discussion of the observed blow-up scenarios.

ON THE BOUSSINESQ HIERARCHY

2002

A new sequence of nonlinear evolution systems satisfying the zero curvature property is constructed, by using the invariant singularity analysis. All these systems are completely integrable and a pseudo-potential (linearization) is explicitly determined for each of them. The second system of the sequence is the Broer-Kaup system, which, as is well known, corresponds to the higher order Boussinesq approximation in describing shallow water waves.

Double point curves for corank 2 map germs from C2 to C3

AbstractWe characterize finite determinacy of map germs f:(C2,0)→(C3,0) in terms of the Milnor number μ(D(f)) of the double point curve D(f) in (C2,0) and we provide an explicit description of the double point scheme in terms of elementary symmetric functions. Also we prove that the Whitney equisingularity of 1-parameter families of map germs ft:(C2,0)→(C3,0) is equivalent to the constancy of both μ(D(ft)) and μ(ft(C2)∩H) with respect to t, where H⊂C3 is a generic plane.