2,247 research outputs found
Gowdy waves as a test-bed for constraint-preserving boundary conditions
Gowdy waves, one of the standard 'apples with apples' tests, is proposed as a
test-bed for constraint-preserving boundary conditions in the non-linear
regime. As an illustration, energy-constraint preservation is separately tested
in the Z4 framework. Both algebraic conditions, derived from energy estimates,
and derivative conditions, deduced from the constraint-propagation system, are
considered. The numerical errors at the boundary are of the same order than
those at the interior points.Comment: 5 pages, 1 figure. Contribution to the Spanish Relativity Meeting
200
Interpretación de las reacciones de oxidación-reducción por los estudiantes. Primeros resultados
Geometric optics and instability for semi-classical Schrodinger equations
We prove some instability phenomena for semi-classical (linear or) nonlinear
Schrodinger equations. For some perturbations of the data, we show that for
very small times, we can neglect the Laplacian, and the mechanism is the same
as for the corresponding ordinary differential equation. Our approach allows
smaller perturbations of the data, where the instability occurs for times such
that the problem cannot be reduced to the study of an o.d.e.Comment: 22 pages. Corollary 1.7 adde
Topological Classification of Quadratic Polynomial Differential Systems with a Finite Semi-Elemental Triple Saddle
Agraïments: the second author is is partially supported by CNPq grant "Projeto Universal" 472796/2013-5, by CAPES CSF-PVE-88881.030454/2013-01, by Projeto Temático FAPESP number 2014/00304-2. The third author is supported by CNPq-PDE 232336/2014-8.The study of planar quadratic differential systems is very important not only because they appear in many areas of applied mathematics but due to their richness in structure, stability and questions concerning limit cycles, for example. Even though many papers have been written on this class of systems, a complete understanding of this family is still missing. Classical problems, and in particular Hilbert's 16th problem [Hilbert, 1900, 1902], are still open for this family. In this article, we make a global study of the family QTS of all real quadratic polynomial differential systems which have a finite semi-elemental triple saddle (triple saddle with exactly one zero eigenvalue). This family modulo the action of the affine group and time homotheties is three-dimensional and we give its bifurcation diagram with respect to a normal form, in the three-dimensional real space of the parameters of this normal form. This bifur- cation diagram yields 27 phase portraits for systems in QTS counting phase portraits with and without limit cycles. Algebraic invariants are used to construct the bifurcation set and we present the phase portraits on the Poincar ́e disk. The bifurcation set is not just algebraic due to the presence of a surface found numerically, whose points correspond to connections of separatrices
Robustness of the Blandford-Znajek mechanism
The Blandford-Znajek mechanism has long been regarded as a key ingredient in
models attempting to explain powerful jets in AGNs, quasars, blazzars etc. In
such mechanism, energy is extracted from a rotating black hole and dissipated
at a load at far distances. In the current work we examine the behaviour of the
BZ mechanism with respect to different boundary conditions, revealing the
mechanism robustness upon variation of these conditions. Consequently, this
work closes a gap in our understanding of this important scenario.Comment: 7 pages, accepted in CQ
Nonlinear coherent states and Ehrenfest time for Schrodinger equation
We consider the propagation of wave packets for the nonlinear Schrodinger
equation, in the semi-classical limit. We establish the existence of a critical
size for the initial data, in terms of the Planck constant: if the initial data
are too small, the nonlinearity is negligible up to the Ehrenfest time. If the
initial data have the critical size, then at leading order the wave function
propagates like a coherent state whose envelope is given by a nonlinear
equation, up to a time of the same order as the Ehrenfest time. We also prove a
nonlinear superposition principle for these nonlinear wave packets.Comment: 27 page
Invariants of solvable rigid Lie algebras up to dimension 8
The invariants of all complex solvable rigid Lie algebras up to dimension
eight are computed. Moreover we show, for rank one solvable algebras, some
criteria to deduce to non-existence of non-trivial invariants or the existence
of fundamental sets of invariants formed by rational functions of the Casimir
invariants of the associated nilradical.Comment: 16 pages, 7 table
Multipartite Continuous Variable Solution for the Byzantine Agreement Problem
We demonstrate that the Byzantine Agreement (detectable broadcast) is also
solvable in the continuous-variable scenario with multipartite entangled
Gaussian states and Gaussian operations (homodyne detection). Within this
scheme we find that Byzantine Agreement requires a minimum amount of
entanglement in the multipartite states used in order to achieve a solution. We
discuss realistic implementations of the protocol, which consider the
possibility of having inefficient homodyne detectors, not perfectly correlated
outcomes, and noise in the preparation of the resource states. The proposed
protocol is proven to be robust and efficiently applicable under such non-ideal
conditions.Comment: This paper supersedes and extends arXiv:quant-ph/0507249, title
changed to match the published version, 11 pages, 3 figures, published
versio
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