Search results for "Singularity"
showing 10 items of 352 documents
The polyhedral Hodge number $h^{2,1}$ and vanishing of obstructions
2000
We prove a vanishing theorem for the Hodge number $h^{2,1}$ of projective toric varieties provided by a certain class of polytopes. We explain how this Hodge number also gives information about the deformation theory of the toric Gorenstein singularity derived from the same polytope. In particular, the vanishing theorem for $h^{2,1}$ implies that these deformations are unobstructed.
Cohomologie relative des applications polynomiales
2001
Let F be a polynomial dominating mapping from Cn to Cq with n>q. We study the de Rham cohomology of the fibres of F, and its relative cohomology groups. Let us fix a strictly positive weighted homogeneous degree on C[x1,…,xn]. With the leading terms of the coordinate functions of F, we construct a fibre of F that is said to be “at infinity”. We introduce the cohomology groups of F at infinity. These groups, denoted by Hk(F−1(∞)), enable us to study all the other cohomology groups of F. For instance, if the fibre at infinity has an isolated singularity at the origin, we prove that any quasi-homogeneous basis of Hn−q(F−1(∞)) provides a basis of all groups Hn−q(F−1(y)), as well as a basis of t…
Fourier integral operators and inhomogeneous Gevrey classes
1988
Fourier integral operators with inhomogeneous amplitude and phase junction are studied in the frame of Gevrey classes. Applications are given to propagation of singularities for a pseudodifferential equation.
Closed form coefficients in the Symmetric Boundary Element Approach
2006
Abstract In the area of the structural analysis, the problems connected to the use of the symmetric Galerkin Boundary Element Method (SGBEM) must be investigated especially in the mathematical and computational difficulties that are present in computing the solving system coefficients. Indeed, any coefficient is made by double integrals including often fundamental solutions having a high degree of singularity. Therefore, the related computation proves to be difficult in the solution. This paper suggests a simple computation technique of the coefficients obtained in closed form. Using a particular matrix, called ‘progenitor’ matrix [Panzeca T, Cucco F, Terravecchia S. Symmetric boundary elem…
Regularization of spherical and axisymmetric evolution codes in numerical relativity
2007
Several interesting astrophysical phenomena are symmetric with respect to the rotation axis, like the head-on collision of compact bodies, the collapse and/or accretion of fields with a large variety of geometries, or some forms of gravitational waves. Most current numerical relativity codes, however, can not take advantage of these symmetries due to the fact that singularities in the adapted coordinates, either at the origin or at the axis of symmetry, rapidly cause the simulation to crash. Because of this regularity problem it has become common practice to use full-blown Cartesian three-dimensional codes to simulate axi-symmetric systems. In this work we follow a recent idea idea of Rinne…
Critical end point behaviour in a binary fluid mixture
1997
We consider the liquid-gas phase boundary in a binary fluid mixture near its critical end point. Using general scaling arguments we show that the diameter of the liquid-gas coexistence curve exhibits singular behaviour as the critical end point is approached. This prediction is tested by means of extensive Monte-Carlo simulations of a symmetrical Lennard-Jones binary mixture within the grand canonical ensemble. The simulation results show clear evidence for the proposed singularity, as well as confirming a previously predicted singularity in the coexistence chemical potential [Fisher and Upton, Phys. Rev. Lett. 65, 2402 (1990)]. The results suggest that the observed singularities, particula…
NONSINGULAR BLACK HOLES IN PALATINI EXTENSIONS OF GENERAL RELATIVITY
2015
An introduction to extended theories of gravity formulated in metric-affine (or Palatini) spaces is presented. Focusing on spherically symmetric configurations with electric fields, we will see that in these theories the central singularity present in General Relativity is generically replaced by a wormhole structure. The resulting space-time becomes geodesically complete and, therefore, can be regarded as non-singular. We illustrate these properties considering two different models, namely, a quadratic f(R) theory and a Born-Infeld like gravity theory.
On singularities of discontinuous vector fields
2003
Abstract The subject of this paper concerns the classification of typical singularities of a class of discontinuous vector fields in 4D. The focus is on certain discontinuous systems having some symmetric properties.
Periodic solutions of a class of non-autonomous second order differential equations with discontinuous right-hand side
2012
Abstract The main goal of this paper is to discuss the existence of periodic solutions of the second order equation: y ″ + η sgn ( y ) = α sin ( β t ) with ( η , α , β ) ∈ R 3 η > 0 . We analyze the dynamics of such an equation around the origin which is a typical singularity of non-smooth dynamical systems. The main results consist in exhibiting conditions on the existence of typical periodic solutions that appear generically in such systems. We emphasize that the mechanism employed here is applicable to many more systems. In fact this work fits into a general program for understanding the dynamics of non-autonomous differential equations with discontinuous right-hand sides.
Invariant deformation theory of affine schemes with reductive group action
2015
We develop an invariant deformation theory, in a form accessible to practice, for affine schemes $W$ equipped with an action of a reductive algebraic group $G$. Given the defining equations of a $G$-invariant subscheme $X \subset W$, we device an algorithm to compute the universal deformation of $X$ in terms of generators and relations up to a given order. In many situations, our algorithm even computes an algebraization of the universal deformation. As an application, we determine new families of examples of the invariant Hilbert scheme of Alexeev and Brion, where $G$ is a classical group acting on a classical representation, and describe their singularities.