Vibration parameter measurement using the temporal digital hologram sequence and windowed Fourier transform

Real time digital recording and numerical reconstruction of a temporal digital hologram sequence have become feasible in recent years.They provide a new measurement method which enjoys the valuable advantages of being full-field,noncontact and high precision.In this paper,a combined method of temporal digital hologram sequence and windowed Fourier transform is proposed to measure the kinematic parameters of random vibration.A series of holograms are recorded by CCD camera and the original phase can be reconstructed by Fresnel reconstruction algorithm.The three-dimensional windowed Fourier transform is used to filter noise in phase and extract the instantaneous kinematic parameters of the specimen,such as the displacement,velocity and acceleration.An experiment is conducted on a chloroprene rubber latex membrane.Results demonstrate that the proposed method determines the vibration parameters precisely and enjoys many merits.

A generic approach to the dynamical interpretation of ocean-atmosphere processes

This paper summarizes the recent development of a portable self-contained system to unravel the intricate multiscale dynamical processes from real oceanic flows, which are in nature highly nonlinear and intermittent in space and time. Of particular focus are the interactions among largescale, mesoscale, and submesoscale processes.We firsu introduce the concept of scale window, and an orthogonal subspace decomposition technigue called multiscale window transform (MWT). Established on MWT is a rigorous formalism of multiscale transport, perfect transfer, and multiscale conversion, which makes a new methodology, multiscale energy and vorticity analysis (MS-EVA). A direct application of the MS-EVA is the development of a novel localized instability analysis, generalizing the classical notion of hydrodynamic instability to finite amplitude processes on irregularly variable domains. The theory is consistent with the analytical solutions of Eady's model and Kuo's model, the benchmark models of baroclinic instability and barotropic instability; it is further validated with a vortex shedding control problem. We have put it to application with a variety of complicated real ocean problems, which would be otherwise very difficult, if not impossible, to tackle. Briefly shown in this paper include the dynamical studies of a highly variable open ocean front, and a complex coastal ocean circulation. In the former, it is found that underlying the frontal meandering is a convective instability followed by an absolute instability, and correspondingly a rapid spatially amplifying mode locked into a temporally growing mode; in the latter, we see a real ocean example of how upwelling can be driven by winds through nonlinear instability, and how winds may excite the ocean via an avenue which is distinctly different from the classical paradigms. This system is mathematically rigorous, physically robust, and practically straightforward.

Drastic change in dynamics as Typhoon Lekima experiences an eyewall replacement cycle

Why does the 1909 typhoon,Lekima,become so destructive after making landfall in China?Using a newly developed mathematical apparatus,the multiscale window transform(MWT),and the MWT-based localized mutliscale energetics analysis and theory of canonical transfer,this study is intended to give a partial answer from a dynamical point of view.The ECMWF reanalysis fields are first reconstructed onto the background window,the TC-scale window,and the convection-scale window.A localized energetics analysis is then performed,which reveals to us distinctly different scenarios before and after August 8–9,2019,when an eyewall replacement cycle takes place.Before that,the energy supply in the upper layer is mainly via a strong upper layer-limited baroclinic instability;the available potential energy thus-gained is then converted into the TC-scale kinetic energy,with a portion to fuel Lekima’s upper part,another portion carried downward via pressure work flux to maintain the cyclone’s lower part.After the eyewall replacement cycle,a drastic change in dynamics occurs.First,the pressure work is greatly increased in magnitude.A positive baroclinic transfer almost spreads throughout the troposphere,and so does barotropic transfer;in other words,the whole air column is now both barotropically and baroclinically unstable.These newly occurred instabilities help compensate the increasing consumption of the TC-scale kinetic energy,and hence help counteract the dissipation of Lekima after making landfalls.

High-precision time domain reactive power measurement in the presence of interharmonics

When interharmonics exist in power system signals,large errors emerge in traditional time domain reactive power measurement.In this paper,we present a novel time domain integral method with good effect of restraining interharmonics,synchronization error,and white noise,as well as the principle of the selection of the sampling periods when employing this approach.The current signal and phase-shifted voltage signal are reconstructed after the harmonic components of signals are extracted,so that the interharmonics are filtered.The influence of the synchronization error on the measurement is reduced through removing the weight coefficients of the reactive components.In the simulation,we apply several cosine windows to the proposed method and analyze signals containing both harmonics and interharmonics.The results show that,in the presence of interharmonics,synchronization error,and white noise (with a fundamental signal-to-noise ratio of 40 dB) all together,the relative errors are within the magnitude of 10 4,which perfectly satisfies the practical requirement.

Reproducing Spaces and Localization Operators

This paper, by using of windowed Fourier transform (WFT), gives a family of embedding operators , s.t. are reproducing subspaces (n = 0, Bargmann Space); and gives a reproducing kernel and an orthonormal basis (ONB) of T n L 2(R). Furthermore, it shows the orthogonal spaces decomposition of . Finally, by using the preceding results, it shows the eigenvalues and eigenfunctions of a class of localization operators associated with WFT, which extends the result of Daubechies in [1] and [6].

Composite Coherent States Approximation for One-Dimensional Multi-Phased Wave Functions

The coherent states approximation for one-dimensional multi-phased wave functions is considered in this paper.The wave functions are assumed to oscillate on a characteristic wave length O(∈)withǫ≪1.A parameter recovery algorithm is first developed for single-phased wave function based on a moment asymptotic analysis.This algorithm is then extended to multi-phased wave functions.If cross points or caustics exist,the coherent states approximation algorithm based on the parameter recovery will fail in some local regions.In this case,we resort to the windowed Fourier transform technique,and propose a composite coherent states approximation method.Numerical experiments show that the number of coherent states derived by the proposedmethod is much less than that by the directwindowed Fourier transform technique.