Direct 3D observation and unravelling of electroconvection phenomena during concentration polarization at ion-exchange membranes

A decade ago, two-dimensional microscopic flow visualization proved the theoretically predicted existence of electroconvection roles as well as their decisive role in destabilizing the concentration polarization layer at ion-selective fluid/membrane interfaces. Electroconvection induces chaotic flow vortices injecting volume having bulk concentration into the ion-depleted diffusion layer at the interface. Experimental quantification of these important flow patterns have so far only been carried out in 2D. Numerical direct simulations suggest 3D features, yet experimental proof is lacking. 3D simulations are also limited in covering extended spacial and temporal scales.This study presents a new comprehensive experimental method for the time-resolved recording of the 3D electroconvective velocity field near a cation-exchange membrane. For the first time, the spatio-temporal velocity field can be visualized in 3D at multiples of the overlimiting current density. In contrast to today’s simulations, these experiments cover length and time scales typical for actual electrodialytic membrane processes.We visualize coherent vortex structures and reveal the changes in the velocity field and its statistics during the transition from vortex rolls to vortex rings with increasing current density. The transition is characterized by changes in the rotational direction, mean square velocity, and temporal energy spectrum with only little influence on the spatial spectrum. These findings indicate a more significant impact of EC’s structural change on the mean square velocities and temporal spectra than on the spatial spectra. This knowledge is a prerequisite for engineering ion-selective surfaces that will enable the operation of electrically driven processes beyond the diffusion-limited Nernst regime.

OPERATOR METHOD IN THE PROBLEM OF THE H-POLARIZED WAVE DIFFRACTION BY TWO SEMI-INFINITE GRATINGS PLACED IN THE SAME PLANE

Purpose: Problem of the H-polarized plane wave diffraction by the structure, which consists of two semi-infinite strip gratings, is considered. The gratings are placed in the same plane. The gap between the gratings is arbitrary. The purpose of the paper is to develop the operator method to the structures, which scattered fields have both discrete and continuous spatial spectra. Design/methodology/approach: In the spectral domain, in the domain of the Fourier transform, the scattered field is expressed in terms of the unknown Fourier amplitude. The field reflected by the considered structure is represented as a sum of two fields of currents on the strips of semi-infinite gratings. The operator equations are obtained for the Fourier amplitudes. These equations use the operators of reflection of semi-infinite gratings, which are supposed to be known. The field scattered by a semi-infinite grating can be represented as a sum of plane and cylindrical waves. The reflection operator of a semi-infinite grating has singularities at the points, which correspond to the propagation constants of plane waves. Consequently, the unknown Fourier amplitudes of the fi eld scattered by the considered structure also have singularities. To eliminate these latter, the regularization procedure has been carried out. As a result of this procedure, the operator equations are reduced to the system of integral equations containing the integrals, which should be understood as the Cauchy principal value and Hadamar finite part integrals. The discretization has been carried out. As a result, the system of linear equations is obtained, which is solved with the use of the iterative procedure. Findings: The operator equations with respect to the Fourier amplitudes of the field scattered by the structure, which consists of two semi-infinite gratings, are obtained. The computational investigation of convergence has been made. The near and far scattered fields are investigated for different values of the grating parameters. Conclusions: The effective algorithm to study the fields scattered by the strip grating, which has both discrete and continuous spatial spectra, is proposed. The developed approach can be an effective instrument in solving a series of problems of antennas and microwave electronics. Key words: semi-infinite grating, operator method, singular integral, hypersingular integral, regularization procedure

Bootstrap Empirical Mode Decomposition with Application to CIELAB Color Images

This paper proposes an alternative optimization-based EMD based on the notions of: 1. <i>local mean points </i>that impose mode symmetry via a Tikhonov regularized least-square (RLS) problem, and 2. efficient <i>bootstrap sifting</i> that guarantees asymptotic convergence of the mean envelope to the local mean points, regardless of regularization. Mathematical proof of convergence and a straightforward extension to the 2D-multivariate setting and CIELAB color image sare presented. Performance is demonstrated with a univariate signal and two images. Spectral analysis confirms coordinated feature extraction among image components, and separation of spatial spectra among the intrinsic mode functions.

Bootstrap Empirical Mode Decomposition with Application to CIELAB Color Images

This paper proposes an alternative optimization-based EMD based on the notions of: 1. <i>local mean points </i>that impose mode symmetry via a Tikhonov regularized least-square (RLS) problem, and 2. efficient <i>bootstrap sifting</i> that guarantees asymptotic convergence of the mean envelope to the local mean points, regardless of regularization. Mathematical proof of convergence and a straightforward extension to the 2D-multivariate setting and CIELAB color image sare presented. Performance is demonstrated with a univariate signal and two images. Spectral analysis confirms coordinated feature extraction among image components, and separation of spatial spectra among the intrinsic mode functions.

Estimating the Parameters of Wind Turbulence from Spectra of Radial Velocity Measured by a Pulsed Doppler Lidar

The strategy providing an estimation of both the mean velocity and the temporal and spatial spectra of radial velocity from data of the same pulse coherent Doppler lidar is proposed. Theoretical relations taking into account the averaging over the probing volume while estimating the spectra of fluctuations of the radial velocity measured by lidar are presented. The method of estimation of the turbulent energy dissipation rate and the variance of the vertical component of wind velocity vector from the spectra of radial velocity is carried out. The results of the comparative experiments are discussed and used in further studies of wind turbulence in the atmospheric boundary layer during the formation of low-level jets and propagation of internal gravity waves.

Arbitrary Pulse Shaping using Nonuniform Spacetime Modulation

This paper introduces and demonstrates a pulse shaping technique based on nonuniform spacetime modulation. This technique allows arbitrary pulse shaping and is in this regard unique, to the knowledge of the authors. Although we restrict here our attention to a 1+1D (1 dimension of time + 1 dimension of space) system, this idea can be extended to 1+2D (and 1+3D) systems, which will feature richer scattering phenomenology given the simultaneous transformations of the temporal vectorial spatial spectra of pulses.

Underwater Ambiguity Elimination Method Based on Co-Prime Sensor Array

Recently, the direction of arrival estimation with co-prime arrays has gradually been applied in underwater scenarios because of its significant advantages over traditional uniform linear arrays. Despite the advantages of co-prime arrays, the spatial spectra obtained directly from conventional beamforming can be degraded by grating lobes due to the sparse spatial sampling in passive sensing applications, which will seriously deteriorate the estimation performance. In this paper, capon beamforming is applied to a co-prime sensor array as a pretreatment before high-resolution direction of arrival (DOA) estimation methods. The amplitudes extracted from the beam-domain outputs of two subarrays and the phases extracted from the cross-spectrum of the spatial spectrum are exploited to suppress the spurious peaks in beam patterns and eliminate ambiguities. Consequently, interference can be further mitigated, and the performance of high-resolution DOA methods will be guaranteed. Simulations show that the method proposed can improve the reliability and accuracy of DOA estimation with great value in practice.