1,328 research outputs found
Invariant subspaces and invertibility properties for singular systems: The general case
Control Systems;operations research
Exact solutions and their interpretation
This is the account of the workshop Exact solutions and their interpretation
at the 16-th International Conference on General Relativity and Gravitation
held in Durban, July 15-21, 2001. Work reported in 32 oral contributions
spanned a wide variety of topics, ranging from exact radiative spacetimes to
cosmological solutions. Two invited review talks, on the role of exact
solutions in string theory and in cosmology, are also described.Comment: 18 pages. To be published in: Proceedings of the 16th International
Conference on General Relativity and Gravitation, Durban, 15 - 21 July, 2001,
eds. N.T. Bishop and S.D. Maharaj, World Scientifi
Collision of plane gravitational and electromagnetic waves in a Minkowski background: solution of the characteristic initial value problem
We consider the collisions of plane gravitational and electromagnetic waves
with distinct wavefronts and of arbitrary polarizations in a Minkowski
background. We first present a new, completely geometric formulation of the
characteristic initial value problem for solutions in the wave interaction
region for which initial data are those associated with the approaching waves.
We present also a general approach to the solution of this problem which
enables us in principle to construct solutions in terms of the specified
initial data. This is achieved by re-formulating the nonlinear dynamical
equations for waves in terms of an associated linear problem on the spectral
plane. A system of linear integral ``evolution'' equations which solve this
spectral problem for specified initial data is constructed. It is then
demonstrated explicitly how various colliding plane wave space-times can be
constructed from given characteristic initial data.Comment: 33 pages, 3 figures, LaTeX. Accepted for publication in Classical and
Quantum Gravit
Disturbance Decoupling in Nonlinear Impulsive Systems
International audienceThis work deals with the problem of structural disturbance decoupling by state feedback for nonlinear impulsive systems. The dynamical systems addressed exhibit a hybrid behavior characterized by a nonlinear continuous-time state evolution interrupted by abrupt discontinuities at isolated time instants. The problem considered consists in finding a state feedback such that the system output is rendered totally insensitive to the disturbance. Both the case of static state feedback and that of dynamic state feedback are considered. A necessary and sufficient condition for the existence of a static state feedback that solves the problem in the multivariable case is proven by defining suitable tools in the context of the differential geometric approach. The situation concerning solvability by a dynamic state feedback is examined in the framework of the differntial algeraic approach. A necessary and sufficient solvaility condition is conjectured and discussed
The wave equation on singular space-times
We prove local unique solvability of the wave equation for a large class of
weakly singular, locally bounded space-time metrics in a suitable space of
generalised functions.Comment: Latex, 19 pages, 1 figure. Discussion of class of metrics covered by
our results and some examples added. Conclusion more detailed. Version to
appear in Communications in Mathematical Physic
Einstein equations in the null quasi-spherical gauge III: numerical algorithms
We describe numerical techniques used in the construction of our 4th order
evolution for the full Einstein equations, and assess the accuracy of
representative solutions. The code is based on a null gauge with a
quasi-spherical radial coordinate, and simulates the interaction of a single
black hole with gravitational radiation. Techniques used include spherical
harmonic representations, convolution spline interpolation and filtering, and
an RK4 "method of lines" evolution. For sample initial data of "intermediate"
size (gravitational field with 19% of the black hole mass), the code is
accurate to 1 part in 10^5, until null time z=55 when the coordinate condition
breaks down.Comment: Latex, 38 pages, 29 figures (360Kb compressed
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