High-Frequency Asymptotic Behavior of the Wave Motion of the Jew-bones, Due to the Vibration Plate, Lying on the Surface of the Liquid

2015 ◽  
pp. 74-79
Author(s):  
Eduard Nikolaevich Potetyunko ◽  
Keyword(s):  
Asymptotic Behavior ◽  
High Frequency ◽  
Wave Motion

ИССЛЕДОВАНИЯ АКУСТИЧЕСКИХ ХАРАКТЕРИСТИК ВЕРХНЕГО СЛОЯ МОРЯ МЕТОДОМ МНОГОЧАСТОТНОГО АКУСТИЧЕСКОГО ЗОНДИРОВАНИЯ

2020 ◽  
Author(s):  
V.A. Bulanov ◽  
I.V. Korskov ◽  
A.V. Storozhenko ◽  
S.N. Sosedko
Keyword(s):  
High Frequency ◽  
Wave Motion ◽  
High Spatial Resolution ◽  
Wind Waves ◽  
Acoustic Parameter ◽  
Sea Surface ◽  
Near Surface ◽  
Acoustical Properties ◽  
Acoustic Spectroscopy ◽  
Sea Bottom

Описано применение акустического зондирования для исследования акустических характеристик верхнего слоя моря с использованием широкополосных остронаправленных инвертированных излучателей,устанавливаемых на дно. В основу метода положен принцип регистрации обратного рассеяния и отраженияот поверхности моря акустических импульсов с различной частотой, позволяющий одновременно измерятьрассеяние и поглощение звука и нелинейный акустический параметр морской воды. Многочастотное зондирование позволяет реализовать акустическую спектроскопию пузырьков в приповерхностных слоях моря,проводить оценку газосодержания и получать данные о спектре поверхностного волнения при различных состояниях моря вплоть до штормовых. Применение остронаправленных высокочастотных пучков ультразвукапозволяет разделить информацию о планктоне и пузырьках и определить с высоким пространственным разрешением структуру пузырьковых облаков, образующихся при обрушении ветровых волн, и структуру планктонных сообществ. Участие планктона в волновом движении в толще морской воды позволяет определитьпараметры внутренних волн спектр и распределение по амплитудам в различное время.This paper represents the application of acoustic probingfor the investigation of acoustical properties of the upperlayer of the sea using broadband narrow-beam invertedtransducers that are mounted on the sea bottom. Thismethod is based on the principle of the recording of thebackscattering and reflections of acoustic pulses of differentfrequencies from the sea surface. That simultaneouslyallows measuring scattering and absorption of the soundand non-linear acoustic parameter of seawater. Multifrequencyprobing allows performing acoustic spectroscopy ofbubbles in the near-surface layer of the sea, estimating gascontent, and obtaining data on the spectrum of the surfacewaves in various states of the sea up to a storm. Utilizationof the high-frequency narrow ultrasound beams allows us toseparate the information about plankton and bubbles and todetermine the structure of bubble clouds, created during thebreaking of wind waves, along with the structure of planktoncommunities with high spatial resolution. The participationof plankton in the wave motion in the seawater columnallows determining parameters of internal waves, such asspectrum and distribution of amplitudes at different times.

scholarly journals Limit Theory for High Frequency Sampled MCARMA Models

2014 ◽  
Vol 46 (3) ◽  
pp. 846-877 ◽  
Author(s):  
Vicky Fasen
Keyword(s):  
Asymptotic Behavior ◽  
High Frequency ◽  
Lévy Process ◽  
Asymptotic Properties ◽  
Domain Of Attraction ◽  
Levy Process ◽  
Sample Variance ◽  
Limit Theory ◽  
Second Moments ◽  
Time Grid

We consider a multivariate continuous-time ARMA (MCARMA) process sampled at a high-frequency time grid {hn, 2hn,…, nhn}, where hn ↓ 0 and nhn → ∞ as n → ∞, or at a constant time grid where hn = h. For this model, we present the asymptotic behavior of the properly normalized partial sum to a multivariate stable or a multivariate normal random vector depending on the domain of attraction of the driving Lévy process. Furthermore, we derive the asymptotic behavior of the sample variance. In the case of finite second moments of the driving Lévy process the sample variance is a consistent estimator. Moreover, we embed the MCARMA process in a cointegrated model. For this model, we propose a parameter estimator and derive its asymptotic behavior. The results are given for more general processes than MCARMA processes and contain some asymptotic properties of stochastic integrals.

High Frequency Vibrations in a Stiff Problem

1997 ◽  
Vol 07 (02) ◽  
pp. 291-311 ◽  
Author(s):  
Miguel Lobo ◽  
Eugenia Pérez
Keyword(s):  
Asymptotic Behavior ◽  
Spectral Problem ◽  
Continuous Spectrum ◽  
High Frequency ◽  
The Other ◽  
Stiff Problem ◽  
Eigenvalues And Eigenfunctions ◽  
High Frequencies ◽  
Stiffness Constant ◽  
High Frequency Vibrations

The stiff problem here considered models the vibrations of a body consisting of two materials, one of them very stiff with respect to the other. We study the asymptotic behavior of the eigenvalues and eigenfunctions of the corresponding spectral problem, when the stiffness constant of only one of the materials tends to 0. We show that the associated operator has a discrete spectrum "converging", in a certain sense, towards a continuous spectrum in [0,∞) corresponding to an operator. We also provide information on the structure of the eigenfunctions associated with the high frequencies.

A Novel Strategy for the Identification of Radiation Force Models

2014 ◽  
Author(s):  
Roman M. Janssen ◽  
Henk Jansen ◽  
Jan-Willem van Wingerden
Keyword(s):  
Asymptotic Behavior ◽  
Frequency Domain ◽  
High Frequency ◽  
State Of The Art ◽  
Radiation Force ◽  
The State ◽  
Test Cases ◽  
Subspace Identification ◽  
Domain Identification

A novel frequency domain identification (FDI) strategy for the identification of radiation force models from frequency domain hydrodynamic data is proposed. First, a subspace identification method is augmented with a convex constraint that guarantees a stable solution. Then, in a second convex optimization problem, constraints on low- and high frequency asymptotic behavior and passivity are enforced. This novel method, constrained frequency domain subspace identification (CFDSI), is validated by comparing both SISO and MIMO CFDSI results with the state-of-the-art FDI toolbox, which is part of the Marine Systems Simulator MATLAB toolbox. In two test cases, it is shown that the novel algorithm can successfully identify a model with either a SISO or MIMO structure, where stability, passivity and the desired low- and high-frequency asymptotic behavior are guaranteed. For the two test cases presented, the quality of the CFDSI models matches the quality of the state-of-the-art FDI models.

A Comparison of the Roughness Regimes in Hydrodynamic Lubrication

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
John Fabricius ◽  
Afonso Tsandzana ◽  
Francesc Perez-Rafols ◽  
Peter Wall
Keyword(s):  
Asymptotic Behavior ◽  
Stokes Flow ◽  
High Frequency ◽  
Reynolds Equation ◽  
Pressure Field ◽  
Hydrodynamic Lubrication ◽  
Narrow Gap ◽  
Surface Textures ◽  
Lubrication Regimes ◽  
Generalized Reynolds Equation

This work relates to previous studies concerning the asymptotic behavior of Stokes flow in a narrow gap between two surfaces in relative motion. It is assumed that one of the surfaces is rough, with small roughness wavelength μ, so that the film thickness h becomes rapidly oscillating. Depending on the limit of the ratio h/μ, denoted as λ, three different lubrication regimes exist: Reynolds roughness (λ = 0), Stokes roughness (0 < λ < ∞), and high-frequency roughness (λ = ∞). In each regime, the pressure field is governed by a generalized Reynolds equation, whose coefficients (so-called flow factors) depend on λ. To investigate the accuracy and applicability of the limit regimes, we compute the Stokes flow factors for various roughness patterns by varying the parameter λ. The results show that there are realistic surface textures for which the Reynolds roughness is not accurate and the Stokes roughness must be used instead.

scholarly journals Transition from Discrete to Continuous Media: The Impact of Symmetry Changes on Asymptotic Behavior of Waves

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1008
Author(s):  
Igor Andrianov ◽  
Steve Koblik ◽  
Galina Starushenko
Keyword(s):  
Asymptotic Behavior ◽  
Analytical Solution ◽  
Wave Motion ◽  
Initial Value ◽  
Phase And Group Velocities ◽  
The Impact ◽  
Group Velocities ◽  
Continuous Approximations ◽  
Initial Motion ◽  
Discrete Medium

This paper is devoted to comparing the asymptotics of a solution, describing the wave motion of a discrete lattice and its continuous approximations. The transition from a discrete medium to a continuous one changes the symmetry of the system. The influence of this change on the asymptotic behavior of waves is of great interest. For the discrete case, Schrödinger’s analytical solution of the initial-value problem for the Lagrange lattice is used. Various continuous approximations are proposed to approximate the lattice. They are based on Debye’s concept of quasicontinuum. The asymptotics of the initial motion and the behavior of the systems in the vicinity of the quasifront and at large times are compared. The approximations of phase and group velocities is analyzed. The merits and limitations of the described approaches are discussed.

ON VIBRATING MEMBRANES WITH VERY HEAVY THIN INCLUSIONS

2004 ◽  
Vol 14 (07) ◽  
pp. 987-1034 ◽  
Author(s):  
YU. D. GOLOVATY ◽  
D. GÓMEZ ◽  
M. LOBO ◽  
E. PÉREZ
Keyword(s):  
Asymptotic Behavior ◽  
High Frequency ◽  
Concentrated Mass ◽  
High Frequency Vibrations

We consider the vibrations of a membrane that contains a very thin and heavy inclusion around a curve γ. We assume that the membrane occupies a domain Ω of ℝ2. The inclusion occupies a layer-like domain ωε of width 2ε and it has a density of order O(ε-m). The density is of order O(1) outside this inclusion ωε, the concentrated mass around the curve γ. ε and m are positive parameters, ε∈(0,1) and m>2. We set m=3 and show that low, middle and high frequency vibrations are necessary in order to describe the asymptotic behavior of the vibrations of the whole membrane. We study the asymptotic behavior, as ε→0, of these frequencies and of the corresponding eigenfunctions.

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