Search results for "GRAVITATION"
showing 10 items of 743 documents
ON THE INDEX OF VECTOR FIELDS TANGENT TO HYPERSURFACES WITH NON-ISOLATED SINGULARITIES
2002
Let $F$ be a germ of a holomorphic function at $0$ in ${\bb C}^{n+1}$ , having $0$ as a critical point not necessarily isolated, and let $\tilde{X}:= \sum^n_{j=0} X^j(\partial/\partial z_j)$ be a germ of a holomorphic vector field at $0$ in ${\bb C}^{n+1}$ with an isolated zero at $0$ , and tangent to $V := F^{-1}(0)$ . Consider the ${\cal O}_{V,0}$ -complex obtained by contracting the germs of Kahler differential forms of $V$ at $0$ \renewcommand{\theequation}{0.\arabic{equation}} \begin{equation} \Omega^i_{V,0}:=\frac{\Omega^i_{{\bb C}^{n+1},0}}{F\Omega^i_{{\bb C}^{n+1},0}+dF\wedge{\Omega^{i-1}}_{{\bb C}^{n+1}},0} \end{equation} with the vector field $X:=\tilde{X}|_V$ on $V$ : \begin{equa…
SELF-ENERGIES AND VERTEX CORRECTIONS WITH TWO FACTORIZING LOOPS
1999
A complete set of factorizing two-loop self-energies and vertex corrections is calculated analytically for arbitrary masses and momenta — including the case of collinear singularities — within the ℛ-functions approach.
About Compactness of Faddeev Integral Equations for Three Charged Particles
1999
Momentum space three-body integral equations of the Faddeev type can not be used for Coulomb-like potentials, for energies above the breakup threshold. The reason is the occurrence of singularities in their kernels which destroy the compactness properties known to exist for purely short-range interactions. Using the rigorously equivalent formulation in terms of an effective-two- body theory, we prove that the nondiagonal kernels occurring therein possess on and off the energy shell only integrable singularities, provided all three particles have charges of the same sign (ie., only repulsive Coulomb interactions). In contrast, if some of the charges have opposite signs the nondiagonal kernel…
Singularity formation for Prandtl’s equations
2009
Abstract We consider Prandtl’s equations for an impulsively started disk and follow the process of the formation of the singularity in the complex plane using the singularity tracking method. We classify Van Dommelen and Shen’s singularity as a cubic root singularity. We introduce a class of initial data, uniformly bounded in H 1 , which have a dipole singularity in the complex plane. These data lead to a solution blow-up whose time can be made arbitrarily short within the class. This is numerical evidence of the ill-posedness of the Prandtl equations in H 1 . The presence of a small viscosity in the streamwise direction changes the behavior of the singularities. They stabilize at a distanc…
Complex singularities in KdV solutions
2016
In the small dispersion regime, the KdV solution exhibits rapid oscillations in its spatio-temporal dependence. We show that these oscillations are caused by the presence of complex singularities that approach the real axis. We give a numerical estimate of the asymptotic dynamics of the poles.
Vereinfachte Rekursionen zur Richardson-Extrapolation in Spezialf�llen
1975
Recursions are given for Richardson-extrapolation based on generalized asymptotic expansions for the solution of a finite algorithm depending upon a parameterh>0. In particular, these expansions may contain terms likeh ?·log(h), (?>0). Simplified formulae are established in special cases. They are applicable to numerical integration of functions with algebraic or logarithmic endpoint singularities and provide a Romberg-type quadrature.
Uniqueness of solutions for some elliptic equations with a quadratic gradient term
2008
We study a comparison principle and uniqueness of positive solutions for the homogeneous Dirichlet boundary value problem associated to quasi-linear elliptic equations with lower order terms. A model example is given by −Δu + λ |∇u| 2 u r = f (x) ,λ , r >0. The main feature of these equations consists in having a quadratic gradient term in which singularities are allowed. The arguments employed here also work to deal with equations having lack of ellipticity or some dependence on u in the right hand side. Furthermore, they could be applied to obtain uniqueness results for nonlinear equations having the p-Laplacian operator as the principal part. Our results improve those already known, even…
The scientific payload on-board the HERMES-TP and HERMES-SP CubeSat missions
2021
HERMES (High Energy Rapid Modular Ensemble of Satellites) Technological and Scientific pathfinder is a space borne mission based on a LEO constellation of nano-satellites. The 3U CubeSat buses host new miniaturized detectors to probe the temporal emission of bright high-energy transients such as Gamma-Ray Bursts (GRBs). Fast transient localization, in a field of view of several steradians and with arcmin-level accuracy, is gained by comparing time delays among the same event detection epochs occurred on at least 3 nano-satellites. With a launch date in 2022, HERMES transient monitoring represents a keystone capability to complement the next generation of gravitational wave experiments. In t…
Understanding Hawking Radiation from Simple Models of Atomic Bose-Einstein Condensates
2013
This chapter is an introduction to the Bogoliubov theory of dilute Bose condensates as applied to the study of the spontaneous emission of phonons in a stationary condensate flowing at supersonic speeds. This emission process is a condensed-matter analog of Hawking radiation from astrophysical black holes but is derived here from a microscopic quantum theory of the condensate without any use of the analogy with gravitational systems. To facilitate physical understanding of the basic concepts, a simple one-dimensional geometry with a stepwise homogenous flow is considered which allows for a fully analytical treatment.
Combination of searches for heavy resonances decaying into bosonic and leptonic final states using 36 fb−1 of proton-proton collision data at s=13 …
2018
Searches for new heavy resonances decaying into different pairings of W, Z, or Higgs bosons, as well as dirffiffiffiectly into leptons, are presented using a data sample corresponding to 36.1 fb(-1 ...