Search results for "gravitation"
showing 10 items of 743 documents
Regularity of the solution to a class of weakly singular fredholm integral equations of the second kind
1979
Continuity and differentiability properties of the solution to a class of Fredholm integral equations of the second kind with weakly singular kernel are derived. The equations studied in this paper arise from e.g. potential problems or problems of radiative equilibrium. Under reasonable assumptions it is proved that the solution possesses continuous derivatives in the interior of the interval of integration but may have mild singularities at the end-points.
Complex powers of elliptic pseudodifferential operators
1986
The aim of this paper is the construction of complex powers of elliptic pseudodifferential operators and the study of the analytic properties of the corresponding kernels kS (x,y). For x=y, the case of principal interest, the domain of holomorphy and the singularities of kS (x,x) are shown to depend on the asymptotic expansion of the symbol. For classical symbols, kS (x,x) is known to be meromorphic on ℂ with simple poles in a set of equidistant points on the real axis. In the more general cases considered here, the singularities may be distributed over a half plane and kS (x,x) can not always be extended to337-2. An example is given where kS (x,x) has a vertical line as natural boundary.
Pseudodifferential Analysis on Manifolds with Boundary — a Comparison of b-Calculus and Cone Algebra
2001
We establish a relation between two different approaches to a complete pseudodifferential analysis of totally characteristic or Fuchs type operators on compact manifolds with boundary respectively conical singularities: Melrose’s (overblown) b-calculus and Schulze’s cone algebra. Though quite different in their definition, we show that these two pseudodifferential calculi basically contain the same operators.
Symmetric Surfaces with Many Singularities
2004
Abstract Let G ⊂ SO(4) denote a finite subgroup containing the Heisenberg group. In this paper we classify all such groups, we find the dimension of the spaces of G-invariant polynomials and we give equations for the generators whenever the space has dimension two. Then we complete the study of the corresponding G-invariant pencils of surfaces in ℙ3 which we started in Sarti [Sarti, A. (2000). Pencils of symmetric surfaces in ℙ3(C). J. Algebra 246:429–452]. It turns out that we have five more pencils, two of them containing surfaces with nodes.
Collision de similaritons optiques dans un amplificateur optique fibré Raman
2005
National audience; Nous abordons les aspects théoriques et expérimentaux de la génération et propagation de deux similaritons optiques de fréquences centrales différentes dans un amplificateur optique fibré Raman à dispersion normale. Nous observons les effets intervenant durant la collision des deux similaritons: un battement sinusoïdal apparaît dans la zone de recouvrement temporel des impulsions et des effets de la modulation de phase croisée modifient le spectre des similaritons. Les similaritons retrouvent néanmoins, après collision, leurs caractéristiques paraboliques.
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.
Dynamics of thick discs around Schwarzschild-de Sitter black holes
2003
We consider the effects of a cosmological constant on the dynamics of constant angular momentum discs orbiting Schwarzschild-de Sitter black holes. The motivation behind this study is to investigate whether the presence of a radial force contrasting the black hole's gravitational attraction can influence the occurrence of the runaway instability, a robust feature of the dynamics of constant angular momentum tori in Schwarzschild and Kerr spacetimes. In addition to the inner cusp near the black hole horizon through which matter can accrete onto the black hole, in fact, a positive cosmological constant introduces also an outer cusp through which matter can leave the torus without accreting on…
On the timing properties of SAX J1808.4-3658 during its 2015 outburst
2017
We present a timing analysis of the 2015 outburst of the accreting millisecond X-ray pulsar SAX J1808.4-3658, using non-simultaneous XMM-Newton and NuStar observations. We estimate the pulsar spin frequency and update the system orbital solution. Combining the average spin frequency from the previous observed, we confirm the long-term spin down at an average rate $\dot{\nu}_{\text{SD}}=1.5(2)\times 10^{-15}$ Hz s$^{-1}$. We also discuss possible corrections to the spin down rate accounting for mass accretion onto the compact object when the system is X-ray active. Finally, combining the updated ephemerides with those of the previous outbursts, we find a long-term orbital evolution compatibl…
Relativistic simulations of rotational core collapse : I. Methods, initial models, and code tests
2002
We describe an axisymmetric general relativistic code for rotational core collapse. The code evolves the coupled system of metric and fluid equations using the ADM 3+1 formalism and a conformally flat metric approximation of the Einstein equations. The relativistic hydrodynamics equations are formulated as a first-order flux-conservative hyperbolic system and are integrated using high-resolution shock-capturing schemes based on Riemann solvers. We assess the quality of the conformally flat metric approximation for relativistic core collapse and present a comprehensive set of tests which the code successfully passed. The tests include relativistic shock tubes, the preservation of the rotatio…
The planar two-body problem for spheroids and disks
2021
We outline a new method suggested by Conway (2016) for solving the two-body problem for solid bodies of spheroidal or ellipsoidal shape. The method is based on integrating the gravitational potential of one body over the surface of the other body. When the gravitational potential can be analytically expressed (as for spheroids or ellipsoids), the gravitational force and mutual gravitational potential can be formulated as a surface integral instead of a volume integral, and solved numerically. If the two bodies are infinitely thin disks, the surface integral has an analytical solution. The method is exact as the force and mutual potential appear in closed-form expressions, and does not invol…