Search results for "singularity."

Lenses on very curved zones of a singular foliation of C2

2018

Abstract We renormalize, using suitable lenses, small domains of a singular holomorphic foliation of C 2 where the curvature is concentrated. At a proper scale, the leaves are almost translates of a graph that we will call profile. When the leaves of the foliations are levels f = λ , where f is a polynomial in 2 variables, this graph is polynomial. Finally we will indicate how our methods may be adapted to study levels of polynomials and 1-forms in C 3 .

Resolution of singularities for multi-loop integrals

2007

We report on a program for the numerical evaluation of divergent multi-loop integrals. The program is based on iterated sector decomposition. We improve the original algorithm of Binoth and Heinrich such that the program is guaranteed to terminate. The program can be used to compute numerically the Laurent expansion of divergent multi-loop integrals regulated by dimensional regularisation. The symbolic and the numerical steps of the algorithm are combined into one program.

Continuity of the radon transform and its inverse on Euclidean space

1983

The Bruce–Roberts Number of A Function on A Hypersurface with Isolated Singularity

2020

AbstractLet $(X,0)$ be an isolated hypersurface singularity defined by $\phi \colon ({\mathbb{C}}^n,0)\to ({\mathbb{C}},0)$ and $f\colon ({\mathbb{C}}^n,0)\to{\mathbb{C}}$ such that the Bruce–Roberts number $\mu _{BR}(f,X)$ is finite. We first prove that $\mu _{BR}(f,X)=\mu (f)+\mu (\phi ,f)+\mu (X,0)-\tau (X,0)$, where $\mu $ and $\tau $ are the Milnor and Tjurina numbers respectively of a function or an isolated complete intersection singularity. Second, we show that the logarithmic characteristic variety $LC(X,0)$ is Cohen–Macaulay. Both theorems generalize the results of a previous paper by some of the authors, in which the hypersurface $(X,0)$ was assumed to be weighted homogeneous.

Invariant varieties of discontinuous vector fields

2004

We study the geometric qualitative behaviour of a class of discontinuous vector fields in four dimensions around typical singularities. We are mainly interested in giving the conditions under which there exist one-parameter families of periodic orbits (a result that can be seen as one analogous to the Lyapunov centre theorem). The focus is on certain discontinuous systems having some symmetric properties. We also present an algorithm which detects and computes periodic orbits.

Large negative magnetoresistance effects in Co2Cr0.6Fe0.4Al

2003

Abstract Materials, which display large changes in resistivity in response to an applied magnetic field (magnetoresistance) are currently of great interest due to their potential for applications in magnetic sensors, magnetic random access memories, and spintronics. Guided by striking features in the electronic structure of several magnetic compounds, we prepared the Heusler compound Co2Cr0.6Fe0.4Al. Based on our band structure calculations, we have chosen this composition in order to obtain a half-metallic ferromagnet with a van Hove singularity in the vicinity of the Fermi energy in the majority spin channel and a gap in the minority spin channel. We find a magnetoresistive effect of 30% …

Three dimensional reconstruction to visualize atrial fibrillation activation patterns on curved atrial geometry

2021

BackgroundThe rotational activation created by spiral waves may be a mechanism for atrial fibrillation (AF), yet it is unclear how activation patterns obtained from endocardial baskets are influenced by the 3D geometric curvature of the atrium or ‘unfolding’ into 2D maps. We develop algorithms that can visualize spiral waves and their tip locations on curved atrial geometries. We use these algorithms to quantify differences in AF maps and spiral tip locations between 3D basket reconstructions, projection onto 3D anatomical shells and unfolded 2D surfaces.MethodsWe tested our algorithms in N = 20 patients in whom AF was recorded from 64-pole baskets (Abbott, CA). Phase maps were generated by…

Magnetic Heusler Compounds

2013

Abstract Heusler compounds are a remarkable class of intermetallic materials with 1:1:1 (often called Half-Heusler) or 2:1:1 composition comprising more than 1500 members. New properties and potential fields of applications emerge constantly; the prediction of topological insulators is the most recent example. Surprisingly, the properties of many Heusler compounds can easily be predicted by the valence electron count or within a rigid band approach. The wide range of the multifunctional properties of Heusler compounds is reflected in extraordinary magnetooptical, magnetoelectronic, and magnetocaloric properties. Co 2 -Heusler compounds are predicted and proven half-metallic ferromagnets sho…

Disorder-induced vibrational anomalies from crystalline to amorphous solids

2021

The origin of boson peak -- an excess of density of states over Debye's model in glassy solids -- is still under intense debate, among which some theories and experiments suggest that boson peak is related to van-Hove singularity. Here we show that boson peak and van-Hove singularity are well separated identities, by measuring the vibrational density of states of a two-dimensional granular system, where packings are tuned gradually from a crystalline, to polycrystals, and to an amorphous material. We observe a coexistence of well separated boson peak and van-Hove singularities in polycrystals, in which the van-Hove singularities gradually shift to higher frequency values while broadening th…

Understanding the microscopic processes that govern the charge-induced deformation of carbon nanotubes

2009

While carbon nanotubes have technological potential as actuators, the underlying actuation mechanisms remain poorly understood. We calculate charge-induced stresses and strains for electrochemical actuation of carbon nanotubes with different chiralities and defects, using density-functional theory and various tight-binding models. For a given deformation mode the concept of bonding and antibonding orbitals can be redefined depending on the sign of a differential band-structure stress. We use this theoretical framework to analyze orbital contributions to the actuation. These show charge asymmetric behavior which is due to next-nearest-neighbor hopping while Coulombic contributions account fo…