Superposition Of Wavelets Research Articles

Simulation of a Multifractal Turbulent Electromagnetic Field in Cosmic Plasma

A two-dimensional model of a multifractal turbulent electromagnetic field is proposed that allows flexibly varying the width of the multifractal spectrum and the level of intermittency. The electromagnetic field is modeled using a superposition of wavelets that are distributed uniformly throughout the computational domain. By means of a special distribution of amplitudes, we ensure that the resulting field is multifractal and intermittent. This model was used to study the effect of multifractality and intermittency on the acceleration of charged particles in a turbulent field in the Earth’s magnetotail. It was shown that, in the case of a multifractal field, individual particles are able to achieve higher energy values in comparison with monofractal turbulence.

Dipole-Based Wavelet Superposition for Accurate Design and Analysis of Metasurface

Design and analysis of metasurface-based devices mainly rely on the ideal ray theory and full-wave simulation technique. However, for near-field and low-frequency applications, these idealized design and time-consuming full-wave simulation methods often suffer from inaccuracy and inefficiency, which hinders the rapid prototyping and further evolution of metasurface-based devices. Here, dipole-based wavelet superposition (DWS) is proposed and formulated to accurately and efficiently design the metasurface and analyze its diffraction field, by treating unit cell on the metasurface and every wavefront representing the target field as Hertzian dipole. We further define quantitatively an effective zone, within which the proposed DWS offers sufficiently accurate results comparable to the full-wave simulation. A series of numerical experiments on design and analysis of metasurface are then carried out to validate our DWS method. Excellent and more superior consistence with the full-wave analysis and theoretical results confirms that the DWS method provides an advanced closed-loop design and analysis tool with significantly improved accuracy and efficiency for metasurface-based devices.

Finite Gaussian wavelet superposition and Fresnel diffraction integral for calculating the propagation of truncated, non-diffracting and accelerating beams

We demonstrate that the propagation of truncated, non-diffracting and accelerating beams can be accurately calculated by using a method that represents these beams by a finite superposition of Gaussian wavelets to be in turn propagated by means of the Fresnel diffraction integral. We support our proposal by demonstrating analytically that the Fresnel diffraction integral describes properly the non-diffracting and accelerating characteristics of non-truncated beams under propagation. We present numerical results of the propagation of this type of truncated beams and we propose analytical equations of a truncated accelerating beam with improved performance.

Automatic detection of multiple oscillations by wavelet analysis

This paper proposes an automatic method based on wavelet analysis to detect multiple oscillations in control loops. Continuous wavelet transform provides a way to represent the signal as a superposition of wavelets. The redundancy of the representation can be exploited to precisely indicate the location of oscillatory behaviors in the time-frequency plane. Oscillatory components are separated by the adaptive design of filter bank. It uncovers all the zero-crossings in the frequency bands which possibly include oscillations to be confirmed by Auto-covariance Function (ACF). The method is applicable to non-stationary and noisy data due to the multi-resolution analysis of orthonormal wavelet bases. This paper ends with demonstrating the effectiveness of the proposed method with benchmark industrial data.

Wavelet-based protocols for ion channel electrophysiology

BackgroundFluctuation-induced phenomena caused by both random and deterministic stimuli have been previously studied in a variety of contexts. They are based on the interplay between the spectro-temporal patterns of the signal and the kinetics of the system it is applied to. The aim of this study was to develop a method for designing fluctuating inputs into nonlinear system which would elicit the most desired system output and to implement the method to studies of ion channels.ResultsWe describe an algorithm based on constructing the input as a superposition of wavelets and optimizing it according to a selected cost functional. The algorithm is applied to ion channel electrophysiology where the input is the fluctuating voltage delivered through a patch-clamp experimental apparatus and the output is the whole-cell ionic current. The algorithm is optimized to aid selection of Markov models of the gating kinetics of the voltage-gated Shaker K+ channel and tested by comparison of numerically obtained ionic currents predicted by different models with experimental data obtained from the Shaker K+ channels. Other applications and optimization criteria are also suggested.ConclusionThe method described in this paper can be useful in development and testing of models of ion channel gating kinetics, developing voltage inputs that optimize certain nonequilibrium phenomena in ion channels, such as the kinetic focusing, and potentially has applications to other fields.

Wind-Induced vibration responses of prestressed double-layered spherical latticed shells

This paper focuses on the wind-induced vibration response of prestressed double-layered spherical latticed shell (PDSLS) structures by adopting time-domain analysis method. Welch spectrum analysis method is used to make precision evaluation of power spectrum of fluctuating wind speed time history simulated by weighted amplitude wavelet superposition (WAWS) method and linear filtering method of auto-regression (AR) model. Results show that the two methods produce little precision difference, but AR method is far more efficient than WAWS and is more suitable for wind speed simulation of PDSLSs. The effect of various parameters on the wind-induced vibration response of PDSLS structures are comprehensively investigated, including rise-span ratio, span, shell thickness, elastic constraint stiffness, prestress value, with or without cables and cable layout scheme. Results show that rise-span ratio and span are the major factors that affect wind-induced vibration response of PDSLSs. When cables are set, the wind vibration coefficient of nodal vertical displacement becomes smaller and more equally distributed, which demonstrates that PDSLSs are less sensitive to fluctuating wind effect than common latticed shell structures without cables. Finally, based on the envelopment concept and with the maximum dynamic and average wind-induced displacement responses as control indicators, the calculating method for global wind vibration coefficient (GWVC) of PDSLSs is proposed and the value with usual design parameters is given. Meanwhile, when the structure is made static analysis by means of the equivalent static wind load obtained from GWVC, the obtained internal member force response is relatively accordant with the actual response got from time-history analysis, and is a little safer.

Explanation of the patterns in Mie theory

The far-field scattered light intensity, or the related phase function, for a spherical particle is known to display an overall power-law structure when formulated in terms of the scattering wave vector. Empirically determined patterns in the intensity relating to the particle size and refractive index are known. The cause of the patterns, however, has not been satisfactorily explained. This work applies an exact microphysical model to explain most of the patterns, and specifically, to reveal the physical cause of crossovers from one power-law to another. A unique aspect of this microphysical approach is phasor analysis, which provides a visually based way to examine the angle-dependent wavelet superposition involved in the model. A simple color coding scheme connects the phasors to the interior of the particle, and it is this connection that reveals the meaning of the crossovers.

MULTISCALE ANALYSIS OF WAVE PROPAGATION IN COMPOSITE MATERIALS

The multiscale solution of the Klein‐Gordon equations in the linear theory of (two‐phase) materials with microstructure is defined by using a family of wavelets based on the harmonic wavelets. The connection coefficients are explicitly computed and characterized by a set of differential equations. Thus the propagation is considered as a superposition of wavelets at different scale of approximation, depending both on the physical parameters and on the connection coefficients of each scale. The coarse level concerns with the basic harmonic trend while the small details, arising at more refined levels, describe small oscillations around the harmonic zero‐scale approximation.

CONVERGENCE ORDER OF ONE REGULARIZATION METHOD

The multiscale solution of the Klein‐Gordon equations in the linear theory of (two‐phase) materials with microstructure is defined by using a family of wavelets based on the harmonic wavelets. The connection coefficients are explicitly computed and characterized by a set of differential equations. Thus the propagation is considered as a superposition of wavelets at different scale of approximation, depending both on the physical parameters and on the connection coefficients of each scale. The coarse level concerns with the basic harmonic trend while the small details, arising at more refined levels, describe small oscillations around the harmonic zero‐scale approximation.

A FILTER DESIGN METHOD BASED ON COMBINATION WAVELETS

This paper presents a method to design a filter with combination wavelets. The combination wavelets filter (CWF) is formed by frequency shift and single wavelet superposition. This paper discusses how to select the parameters needed to construct the filters with Gaussian combination wavelets. The low-pass, high-pass, band-pass, band elimination and multiband-pass filters are designed and the examples given. The combination wavelets filter can be designed easily and conveniently by choosing the correct parameters. This method can be used flexibly and widely.

INTERACTION EFFECTS IN MARINE SEISMIC SOURCE ARRAYS*

AbstractPast design of marine source arrays has been based on one or more of the following principles: simultaneous operation of multiple identical sources to increase radiated signal strength by simple addition; superposition of wavelets of different fundamental frequency to achieve a total pulse of desired, front‐loaded form (e.g. mixed volume air‐gun arrays); horizontal spacing of units or groups to achieve spatial filtering effects. The phenomenon of interaction between sources, affecting the loading experienced by each, has usually been ignored, or else avoided by wide spacing of units. However, interactions can significantly affect the efficiency and frequency response, in a way that can be favourable.Calculations are presented for sources emitting continuous or long duration signals, showing the energy efficiency as a function of frequency for arrays in a variety of configurations. Interaction effects are significant for inter‐source spacings smaller than or comparable with the wavelength—not, as is often stated, up to a distance related to the radii of the sources. The results show that potential exists for tailoring the frequency response of a source system, according to the application, by simple spatial rearrangement of units.Similar effects occur with interacting impulsive sources, but it is shown that different criteria apply for the optimum arrangements of units.