115 research outputs found
Simple digital quantum algorithm for symmetric first order linear hyperbolic systems
This paper is devoted to the derivation of a digital quantum algorithm for
the Cauchy problem for symmetric first order linear hyperbolic systems, thanks
to the reservoir technique. The reservoir technique is a method designed to
avoid artificial diffusion generated by first order finite volume methods
approximating hyperbolic systems of conservation laws. For some class of
hyperbolic systems, namely those with constant matrices in several dimensions,
we show that the combination of i) the reservoir method and ii) the alternate
direction iteration operator splitting approximation, allows for the derivation
of algorithms only based on simple unitary transformations, thus perfectly
suitable for an implementation on a quantum computer. The same approach can
also be adapted to scalar one-dimensional systems with non-constant velocity by
combining with a non-uniform mesh. The asymptotic computational complexity for
the time evolution is determined and it is demonstrated that the quantum
algorithm is more efficient than the classical version. However, in the quantum
case, the solution is encoded in probability amplitudes of the quantum
register. As a consequence, as with other similar quantum algorithms, a
post-processing mechanism has to be used to obtain general properties of the
solution because a direct reading cannot be performed as efficiently as the
time evolution.Comment: 28 pages, 12 figures, major rewriting of the section describing the
numerical method, simplified the presentation and notation, reorganized the
sections, comments are welcome
Estimating mean dynamic topography in the tropical Pacific Ocean from gravity and altimetry satellites
SIGLEAvailable from Bibliothek des Instituts fuer Weltwirtschaft, ZBW, Duesternbrook Weg 120, D-24105 Kiel W 1190 (59) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman
Estimating mean dynamic topography in the tropical Pacific Ocean from gravity and altimetry satellites
International audienceA new geoid model, combining the CHAMP satellite gravity data and an accurate altimetric mean sea surface, was used to investigate the 1993â1999 mean dynamic topography in the tropical Pacific Ocean. The mean dynamic topography, represented by a spherical harmonic expansion to degree 60 appear to be consistent with our knowledge of the tropical circulation, notably the South Equatorial Counter Current which is clearly visible in the western Pacific. This satellite solution, validated with inâsitu data, is independent from any climatology and has a resolution similar to other classical mean dynamic topographies. Altimetry combined with geodesy can thus provide an absolute sea level which will be useful for data assimilation and tropical oceanography
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