4,978 research outputs found
A Wiener-Laguerre model of VIV forces given recent cylinder velocities
Slender structures immersed in a cross flow can experience vibrations induced
by vortex shedding (VIV), which cause fatigue damage and other problems. VIV
models in engineering use today tend to operate in the frequency domain. A time
domain model would allow to capture the chaotic nature of VIV and to model
interactions with other loads and non-linearities. Such a model was developed
in the present work: for each cross section, recent velocity history is
compressed using Laguerre polynomials. The compressed information is used to
enter an interpolation function to predict the instantaneous force, allowing to
step the dynamic analysis. An offshore riser was modeled in this way: Some
analyses provided an unusually fine level of realism, while in other analyses,
the riser fell into an unphysical pattern of vibration. It is concluded that
the concept is promissing, yet that more work is needed to understand orbit
stability and related issues, in order to further progress towards an
engineering tool
Semi-classical Laguerre polynomials and a third order discrete integrable equation
A semi-discrete Lax pair formed from the differential system and recurrence
relation for semi-classical orthogonal polynomials, leads to a discrete
integrable equation for a specific semi-classical orthogonal polynomial weight.
The main example we use is a semi-classical Laguerre weight to derive a third
order difference equation with a corresponding Lax pair.Comment: 11 page
Fourth Moment Theorems for Markov Diffusion Generators
Inspired by the insightful article arXiv:1210.7587, we revisit the
Nualart-Peccati-criterion arXiv:math/0503598 (now known as the Fourth Moment
Theorem) from the point of view of spectral theory of general Markov diffusion
generators. We are not only able to drastically simplify all of its previous
proofs, but also to provide new settings of diffusive generators (Laguerre,
Jacobi) where such a criterion holds. Convergence towards gamma and beta
distributions under moment conditions is also discussed.Comment: 15 page
Design of interpolative sigma delta modulators via a semi- infinite programming approach
This paper considers the design of interpolative sigma delta modulators (SDMs). The design problem is formulated as two different optimization problems. The first optimization problem is to determine the denominator coefficients. The objective of the optimization problem is to minimize the energy of the error function in the passband of the loop filter in which the error function reflects the noise output transfer function and the ripple of the input output transfer function. The constraint of the optimization problem refers to the specification of the error function defined in the frequency domain. The second optimization problem is to determine the numerator coefficients in which the cost function is to minimize the stopband ripple energy of the loop filter subject to the stability condition of the noise output and input output transfer functions. These two optimization problems are actually quadratic semi-infinite programming (SIP) problems. By employing our recently proposed dual parameterization method for solving the problems, global optimal solutions that satisfy the corresponding continuous constraint are guaranteed if the solutions exist. The advantages of this formulation are the guarantee of the stability of the noise output and input output transfer functions, applicability to design rational IIR filters without imposing specific filter structures such as Laguerre filter and Butterworth filter structures, and the avoidance of the iterative design of numerator and the denominator coefficients because the convergence of the iterative design is not guaranteed. Our simulation results show that this proposed design yields a significant improvement in the signal-to-noise ratio (SNR) compared to the existing designs
Notions of optimal transport theory and how to implement them on a computer
This article gives an introduction to optimal transport, a mathematical
theory that makes it possible to measure distances between functions (or
distances between more general objects), to interpolate between objects or to
enforce mass/volume conservation in certain computational physics simulations.
Optimal transport is a rich scientific domain, with active research
communities, both on its theoretical aspects and on more applicative
considerations, such as geometry processing and machine learning. This article
aims at explaining the main principles behind the theory of optimal transport,
introduce the different involved notions, and more importantly, how they
relate, to let the reader grasp an intuition of the elegant theory that
structures them. Then we will consider a specific setting, called
semi-discrete, where a continuous function is transported to a discrete sum of
Dirac masses. Studying this specific setting naturally leads to an efficient
computational algorithm, that uses classical notions of computational geometry,
such as a generalization of Voronoi diagrams called Laguerre diagrams.Comment: 32 pages, 17 figure
Bose-Einstein condensation in dark power-law laser traps
We investigate theoretically an original route to achieve Bose-Einstein
condensation using dark power-law laser traps. We propose to create such traps
with two crossing blue-detuned Laguerre-Gaussian optical beams. Controlling
their azimuthal order allows for the exploration of a multitude of
power-law trapping situations in one, two and three dimensions, ranging from
the usual harmonic trap to an almost square-well potential, in which a
quasi-homogeneous Bose gas can be formed. The usual cigar-shaped and
disk-shaped Bose-Einstein condensates obtained in a 1D or 2D harmonic trap take
the generic form of a "finger" or of a "hockey puck" in such Laguerre-Gaussian
traps. In addition, for a fixed atom number, higher transition temperatures are
obtained in such configurations when compared with a harmonic trap of same
volume. This effect, which results in a substantial acceleration of the
condensation dynamics, requires a better but still reasonable focusing of the
Laguerre-Gaussian beams
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