156 research outputs found
Large time existence for 3D water-waves and asymptotics
We rigorously justify in 3D the main asymptotic models used in coastal
oceanography, including: shallow-water equations, Boussinesq systems,
Kadomtsev-Petviashvili (KP) approximation, Green-Naghdi equations, Serre
approximation and full-dispersion model. We first introduce a ``variable''
nondimensionalized version of the water-waves equations which vary from shallow
to deep water, and which involves four dimensionless parameters. Using a
nonlocal energy adapted to the equations, we can prove a well-posedness
theorem, uniformly with respect to all the parameters. Its validity ranges
therefore from shallow to deep-water, from small to large surface and bottom
variations, and from fully to weakly transverse waves. The physical regimes
corresponding to the aforementioned models can therefore be studied as
particular cases; it turns out that the existence time and the energy bounds
given by the theorem are always those needed to justify the asymptotic models.
We can therefore derive and justify them in a systematic way.Comment: Revised version of arXiv:math.AP/0702015 (notations simplified and
remarks added) To appear in Inventione
Power, Composition, and Decision Making: The Behavioral Consequences of Institutional Reform on Brazil's Supremo Tribunal Federal
How does a court's policy-making authority shape the nature of judicial behavior? We argue that judicial systems that limit policy-making authority also discourage the politicization of courts, encouraging judges to think narrowly about the interests of litigating parties. In contrast, granting a court high policy-making authority—affecting potentially thousands of cases and other branches of government—naturally encourages judges to consider broader ideological principles. Typically, unraveling cause and effect would be difficult, as judicial behavior and institutions are usually stable and endogenous. But an especially stark sequence of political and institutional changes in Brazil affords analytic leverage to explore these questions. A series of judicial reforms greatly expanded the Brazilian Supreme Court's authority, and our analysis of judicial decisions shows the emergence of a political cleavage on the court after these reforms. (JEL C140, K39, K49
Large time wellposdness to the 3-D Capillary-Gravity Waves in the long wave regime
In the regime of weakly transverse long waves, given long-wave initial data,
we prove that the nondimensionalized water wave system in an infinite strip
under influence of gravity and surface tension on the upper free interface has
a unique solution on [0,{T}/\eps] for some \eps independent of constant
We shall prove in the subsequent paper \cite{MZZ2} that on the same time
interval, these solutions can be accurately approximated by sums of solutions
of two decoupled Kadomtsev-Petviashvili (KP) equations.Comment: Split the original paper(The long wave approximation to the 3-D
capillary-gravity waves) into two parts, this is the first on
Normalizers of tori
We determine the groups which can appear as the normalizer of a maximal torus
in a connected 2-compact group. The technique depends on using ideas of Tits to
give a novel description of the normalizer of the torus in a connected compact
Lie group, and then showing that this description can be extended to the
2-compact case.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol9/paper31.abs.htm
Global well-posedness of the 3-D full water wave problem
We consider the problem of global in time existence and uniqueness of
solutions of the 3-D infinite depth full water wave problem. We show that the
nature of the nonlinearity of the water wave equation is essentially of cubic
and higher orders. For any initial interface that is sufficiently small in its
steepness and velocity, we show that there exists a unique smooth solution of
the full water wave problem for all time, and the solution decays at the rate
.Comment: 60 page
Asymptotic models for the generation of internal waves by a moving ship, and the dead-water phenomenon
This paper deals with the dead-water phenomenon, which occurs when a ship
sails in a stratified fluid, and experiences an important drag due to waves
below the surface. More generally, we study the generation of internal waves by
a disturbance moving at constant speed on top of two layers of fluids of
different densities. Starting from the full Euler equations, we present several
nonlinear asymptotic models, in the long wave regime. These models are
rigorously justified by consistency or convergence results. A careful
theoretical and numerical analysis is then provided, in order to predict the
behavior of the flow and in which situations the dead-water effect appears.Comment: To appear in Nonlinearit
A multiple-beam CLEAN for imaging intra-day variable radio sources
The CLEAN algorithm, widely used in radio interferometry for the
deconvolution of radio images, performs well only if the raw radio image (dirty
image) is, to good approximation, a simple convolution between the instrumental
point-spread function (dirty beam) and the true distribution of emission across
the sky. An important case in which this approximation breaks down is during
frequency synthesis if the observing bandwidth is wide enough for variations in
the spectrum of the sky to become significant. The convolution assumption also
breaks down, in any situation but snapshot observations, if sources in the
field vary significantly in flux density over the duration of the observation.
Such time-variation can even be instrumental in nature, for example due to
jitter or rotation of the primary beam pattern on the sky during an
observation. An algorithm already exists for dealing with the spectral
variation encountered in wide-band frequency synthesis interferometry. This
algorithm is an extension of CLEAN in which, at each iteration, a set of N
`dirty beams' are fitted and subtracted in parallel, instead of just a single
dirty beam as in standard CLEAN. In the wide-band algorithm the beams are
obtained by expanding a nominal source spectrum in a Taylor series, each term
of the series generating one of the beams. In the present paper this algorithm
is extended to images which contain sources which vary over both frequency and
time. Different expansion schemes (or bases) on the time and frequency axes are
compared, and issues such as Gibbs ringing and non-orthogonality are discussed.
It is shown that practical considerations make it often desirable to
orthogonalize the set of beams before commencing the cleaning. This is easily
accomplished via a Gram-Schmidt technique.Comment: 9 pages, 7 figures. Accepted for publication in A&
WKB analysis for nonlinear Schr\"{o}dinger equations with potential
We justify the WKB analysis for the semiclassical nonlinear Schr\"{o}dinger
equation with a subquadratic potential. This concerns subcritical, critical,
and supercritical cases as far as the geometrical optics method is concerned.
In the supercritical case, this extends a previous result by E. Grenier; we
also have to restrict to nonlinearities which are defocusing and cubic at the
origin, but besides subquadratic potentials, we consider initial phases which
may be unbounded. For this, we construct solutions for some compressible Euler
equations with unbounded source term and unbounded initial velocity.Comment: 25 pages, 11pt, a4. Appendix withdrawn, due to some inconsistencie
An analytical study of PPP-RTK corrections: precision, correlation and user-impact
PPP-RTK extends the PPP concept by providing single-receiver users, next to orbits and clocks, also information about the satellite phase and code biases, thus enabling single-receiver ambiguity resolution. It is the goal of the present contribution to provide an analytical study of the quality of the PPP-RTK corrections as well as of their impact on the user ambiguity resolution performance. We consider the geometry-free and the geometry-based network derived corrections, as well as the impact of network ambiguity resolution on these corrections. Next to the insight that is provided by the analytical solutions, the closed form expressions of the variance matrices also demonstrate how the corrections depend on network parameters such as number of epochs, number of stations, number of satellites, and number of frequencies. As a result we are able to describe in a qualitative sense how the user ambiguity resolution performance is driven by the data from the different network scenarios
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