Amplitude Distribution Function Research Articles

Analysis of the Grid Quantization for the Microwave Radar Coincidence Imaging Based on Basic Correlation Algorithm

In Microwave Radar Coincidence Imaging (MRCI), the imaging region is typically discretized into a fine grid. In other words, it assumes that the equivalent scatterers of the target are precisely located at the centers of these pre-discretized grids. However, this approach usually encounters the off-grid problem, which can significantly degrade the imaging performance. In this paper, to establish a criterion for grid quantization, the performance of the MRCI system related to the grid size and the distribution of imaging points is investigated. First, the discretization of the imaging scene is regarded as a random sampling problem, and the off-grid imaging model for MRCI is established. Then, the probability distribution function (PDF) of the imaging amplitude for a single point target is analyzed, and the mean first-order imaging error (MFE) for multiple point targets is derived based on the Basic Correlation Algorithm (BCA). Finally, the relationship between the grid quantization of the imaging area and the performance of the MRCI system is analyzed, providing a theoretical guidance for enhancing the performance of MRCI. The validity of the analyses is verified through simulation experiments.

RCS measurement and ISAR imaging radar in VHF/UHF radio channels

ABSTRACT The Radar Cross Section (RCS) plays a crucial role in radar systems, serving to detect and characterize radar targets. Moreover, the need to penetrate foliage and capture images of man-made structures like roads and buildings has driven the development of very high frequency/ultra high frequency (VHF/UHF)-based radar systems. In this context, we propose a novel polyphase-coded spread spectrum (PCSS) radar system designed for RCS measurements and ISAR imaging over VHF/UHF radio channels in open environments. To provide a comprehensive understanding, we examined the open range, considering factors such as amplitude distribution function, root mean square (RMS) delay, and coherence bandwidth, followed by a link budget analysis. We also conducted a comparative study of RCS measurements to evaluate the performance of the proposed radar system, demonstrating its effectiveness through theoretical calculations. Furthermore, we assessed the radar imaging capabilities by applying the CLEAN algorithm to improve the quality of the generated images.

Effect of inter-electrode gap on surface characteristics in conventional electrochemical machining

Conventional electrochemical machining (CECM) is an established toolroom process for the machining of conductive workpiece (W/P) substrates. In CECM, the material removal takes place through an electrochemical reaction between the cathode and anode. Significant studies have reported process parametric optimization of CECM with input parameters like voltage, feed rate, type of electrolyte and electrolyte concentration, etc., and their effect on the material removal rate (MRR), and surface roughness (Ra). But hitherto little has been reported on the effect of inter-electrode gap (IEG) and other CECM parameters in combination with a different tool and work materials. This study outlines the experimental investigations on CECM with a different tool and work materials based on Taguchi L18 orthogonal array (OA) on surface characteristics of machined surface for tool room applications in line with sustainable development goal (SDG) (with a special target on the industry, innovation, and infrastructure). The results suggest that for Ra, IEG is the most significant factor at a 95% confidence level. The results have been supported by scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), and Ra analysis (with amplitude distribution function (ADF), and peak count (PC).

Evolution and Statistical Analysis of Internal Random Wave Fields within the Benjamin–Ono Equation

This study investigates the numerical evolution of an initially internal random wave field characterized by a Gaussian spectrum shape using the Benjamin–Ono (BO) equation. The research focuses on analyzing various properties associated with the random wave field, including the transition to a steady state of the spectra, statistical moments, and the distribution functions of wave amplitudes. Numerical simulations are conducted across different Ursell parameters, revealing intriguing findings. Notably, it is observed that the spectra of the wave field converge to a stationary state in a statistical sense, while exhibiting statistical characteristics that deviate from a Gaussian distribution. Moreover, as the Ursell parameter increases, the positive skewness of the wave field intensifies, and the kurtosis increases. The investigation also involves the computation of the probability of rogue wave formation, revealing deviations from the Rayleigh distribution. Notably, the study uncovers distinct types of internal rogue waves, specifically referred to as the “two sisters” and “three sisters” phenomena.

Characterization and functional evaluation of surface texture of micro eccentric shaft based on multi-index

Micro eccentric shaft has important application in many high-tech fields because of its small specific gravity, material, and energy saving. The machined surface texture has an indispensable influence on the surface integrity and the final functional capability. However, due to the micro scale and weak rigidity, it is difficult to characterize the surface texture and evaluate the functionality by traditional quantitative parameters. In order to comprehensively realize the surface texture characterization and functional analysis, a mathematical model is established to simulate the surface texture machined with different cutting tools. Then the surface microscopic profile and functional performance of the surface texture are analyzed by amplitude distribution function (ADF) and bearing area curve (BAC), and the surface texture is also evaluated by fractal dimension, which can avoid the negative effects of scale and resolution. Furthermore, power spectrum density (PSD) is utilized to analyze the relationship between the process dynamic state and geometrical specification of the surface texture. The validity of experimental results shown that the microscopic height distribution of surface machined by flat end milling cutter tends to be more random and there are more microscopic geometric features than that of the ball end milling cutter. The machined surface obtained by the flat end milling cutter has better load bearing, wear resistance, and liquid retention capability.

Характеристическая функция самоподобного случайного процесса

A stochastic differential equation is proposed for a characteristic function whose inverse function describes a self-similar random process with a power-law behavior of power spectra in a wide frequency range and a power-law amplitude distribution function. Gaussian “tails” for the characteristic distribution make it possible to evaluate its stability according to the formulas of classical statistics using the maximum of the Gibbs-Shannon entropy and, therefore, the stability of a random process given by an inverse function.

Characteristic function of a self-similar random process

A stochastic differential equation is proposed for a characteristic function whose inverse function describes a self-similar random process with a power-law behavior of power spectra in a wide frequency range and a power-law amplitude distribution function. Gaussian "tails" for the characteristic distribution make it possible to evaluate its stability according to the formulas of classical statistics using the maximum of the Gibbs-Shannon entropy and, therefore, the stability of a random process given by an inverse function. Keywords: self-similar random processes, stochastic equations, power spectrum, 1/f-noise, maximum entropy.

Biotribology in Arthroplasty: Worn Surfaces Investigation on Ceramic Hip Femoral Heads Considering Wettability

Ceramic-on-ceramic bearings for total hip replacement are considered the best choice to avoid problems such as osteolysis and wear, mainly related to soft bearings. The aim of this work was to investigate in a comparative way different kinds of ceramic femoral heads for total hip replacements from a biotribological point of view, discussing the results obtained in terms of topographies, presence of metal transfer (MT) phenomena, and wettability on their worn surfaces in a tribological framework. Different ceramic femoral heads derived from in vitro wear tests, retrieved form patients, and brand new total hip replacements were investigated. The patients group had an average age of 60 years (ranging from 27 to 83). In most cases, the cause of failure was aseptic loosening of the acetabular component. Roughness analyses were performed to measure the tribological surface evolution of the material; an SEM and EDS investigation on the explanted heads proves and quantified MT, while the wettability was measured through a novel optical laboratory set-up with the aim to furnish useful data in the framework of synovial lubrication phenomena acting in the tribosystem. For the average roughness measurements on explanted specimens were considered three parameters (Ra = the average area between the roughness profile and its mean line; Rt = the vertical distance from the deepest valley to the highest peak of the roughness profile; and Rsk = it is the skewness and it is a measure of the asymmetry of the amplitude distribution function. In other words, the skewness indicates whether a surface is dominated by peaks or by valleys) and their values were: Ra 0.22 ± 0.12 μm, Rt 34.5 ± 13.5 μm and Rsk −0.01 ± 11.3; on the new specimens we measured Ra 0.01 ± 0.001 μm, Rt 0.12 ± 0.09 μm, and Rsk = 5.67 ± 8.7; for the in vitro specimens they were Ra 0.05 ± 0.12 μm, Rt 0.71 ± 1.4 μm and Rsk 7.73 ± 20.6. The wettability angle measurements showed hydrophilic surfaces for all femoral heads considered in this study with small differences between the three investigated categories, allowing to discuss their effects on the biobearings’ lubrication phenomena.

Surface alteration implications on potential use of semi-alicyclic polyimide as biomedical materials

A semi-alicyclic polyimide (PI) is tested for hemocompatibility and cell growth purposes. The PI configuration in the presence of the adhesion proteins and interaction energy were computed showing a different stability dictated by the protein structure. PI film surface was altered by roughening with sand paper and the morphology was examined by atomic force microscopy (AFM). The recorded images show a conversion of the initial isotropic peak-to-valley height on the surface of the PI film into an anisotropic one made of microgrooves. This is supported by the amplitude distribution function, which for the pristine sample has a narrow peak (a single morphological entity), while upon surface roughening, it has two peaks, associated with tracks valleys and top of the hills. The shape parameters (skewness and kurtosis) related to the asymmetry of the surface departure and spread of the height distribution are significantly changed after altering of the PI surface. The values of the surface functional indexes and functional volume parameters are increasing upon the PI surface roughening. The changes in random character of the initial PI are also evidenced by autocorrelation cross-section profile. The altered PI film surface determines an anisotropic character of adhesion or spreading of blood and fibroblasts.

Mechanical characterization of FDM filaments with PVDF matrix reinforced with Graphene and Barium Titanate

In past one decade number of studies has been reported on optimization of process parameters of fused deposition modelling (FDM) for in-house developed thermoplastic composite based feed stock filaments. This paper investigates smart polymer-based composites prepared with hybrid feed stock filament (comprising of polyvinylidene fluoride (PVDF) reinforced with graphene (Gr) and barium titanate (BTO) powder). This work started with the Functional prototypes were 3D printed for tensile and flexural characterization using inhouse developed filament (PVDF (78%)+Gr (2%) with BTO (20%)) at optimized settings of FDM. The printed specimens were subjected to destructive testing for mechanical properties (to analyze the process capability indices, Cp and Cpk). For morphological properties, scanning electron microscopy (SEM) images and 3D rendered images of the fractured surfaces of tensile and flexural specimen were used. It has been revealed from the SEM and 3D rendered images that the optimized settings of 3D printing process parameters resulted into uniform morphological features (based upon surface roughness (Ra) and amplitude distribution function (ADF), peak count (PC) and bearing ratio (BR) curve).

Comparison of Cold and Hot Forged EN8 Flats: Spring Back Effect, Surface Hardness and Microstructural Features

This paper reports the comparison of cold and hot forged EN8 flats for spring back effect, surface hardness and microstructural features as a case study of an industrial component ‘U-Fork’ (a subpart of tractor’s three-point hitch’s lift rod). The industrial component/benchmark has been selected as a common agricultural automobile component used under cyclic loading conditions. For this comparative study, surface hardness and surface roughness (Ra) of the material have been analyzed by using micro-Vickers hardness and 3D rendered images, Ra profiles, amplitude distribution function, respectively, whereas microstructure and its features (grain size number, average grain diameter, porosity, etc.) have been characterized using energy-dispersive X-ray spectroscopy and scanning electron microscope. The result of the case study reveals that hot forging has increased the dimensional accuracy by 11.15%, overcoming the spring back effect. Also, a significant reduction in porosity (54.28%) and increment in surface hardness (15.66%) are observed for hot forged EN8 flats in comparison to cold forged components.

3D printed tensile and flexural prototypes of thermoplastic matrix reinforced with multi-materials: A statistical analysis

Fused deposition modelling (FDM) is one of the established low cost 3D printing techniques for preparation of functional/ non functional prototypes from thermoplastic composite matrix (prepared as multi/ hybrid blended material). But hitherto little has been reported on multi material reinforced thermoplastic matrix in successive 3D printed layers from repeatability view point. Since the adaptability of any processing technique is dependent upon repeatability/ reproducibility (for which the process output must be statistically controlled), this work reports the statistical analysis of 3D printed tensile and flexural samples printed on FDM as functional prototypes of poly lactic acid (PLA) matrix reinforced with multi materials (poly vinyl chloride (PVC), wood dust and magnetite (Fe 3 O 4 ) powder) as functionally graded thermoplastic matrix. Further in this work functional prototypes of tensile and flexural sample were 3D printed and tested for their mechanical properties to analyze the process capability index (Cp and Cpk) along with morphological characteristics using optical images of the fractured surfaces. The result of the study suggests that the process was observed to be in statistical control as Cp and Cpk was found to be more than 1 for tensile and flexural properties. Based upon optical photo micrographs it has been ascertained that the optimized 3D printing parameters resulted into uniform morphological features (based upon surface roughness (Ra) and amplitude distribution function (ADF), peak count (PC) and bearing ratio (BR) curve).

Demonstration of lateral resolution enhancement by focusing amplitude modulated radially polarized light in a confocal imaging system

Lateral resolution enhancement is demonstrated in a confocal imaging system with amplitude-modulated radially polarized (RP) light at the wavelength Annular pupil fields and optimized amplitude distribution functions can be realized with a spatial light modulator. By comparing images obtained with full and amplitude modulated apertures of RP illuminations using a high numerical aperture (NA = 0.9), spatial resolution of has been achieved experimentally. This result agrees very well with theoretical simulation results and will be helpful in improving performance of the non-fluorescent imaging systems.

Modeling on Vibration of Sandwich Plate Possessing a Compressible Core and Interacting with Viscous Fluid

The paper proposed a mathematical model for analyzing the dynamic response of a three-layered channel wall with a compressible core. The narrow channel formed by two parallel walls is considered. The bottom channel wall was a simply supported three-layered plate. The upper channel wall was considered to be absolutely rigid. The channel was filled with a viscous incompressible liquid with pulsating pressure due to a given harmonic law of pressure pulsation at the channel edges. Longitudinal and transverse vibrations of the three-layered channel wall were studied. The dynamic response of the three-layered channel wall was determined on the basis of hydroelastic oscillations problem solution. The frequency-dependent distribution functions of longitudinal and transverse elastic displacements amplitudes of the three-layered channel wall were constructed. These functions make it possible to obtain amplitude-frequency characteristics of the three-layered channel wall in fixed channel cross-sections. The study was supported by Russian Foundation for Basic Research (projects № 18-01-00127-a and № 19-01-00014-a).

INFLUENCE OF THE ß SOLAR WIND PARAMETER ON STATISTICAL CHARACTERISTICS OF THE Ap INDEX IN THE SOLAR ACTIVITY CYCLE

We have studied the effect of the β solar wind parameter (equal to the ratio of the plasma pressure to the magnetic pressure) on statistical characteristics of the Ap index reflecting the triggering behavior of the activity of Earth’s magnetosphere. The trigger effect of the dynamics of magnetospheric activity consists in the abrupt transition from the periodic mode to the chaotic mode in the solar activity cycle. It is shown that cumulative amplitude distribution functions and power spectra of the Ap index of both the periodic and chaotic modes are well approximated by power and exponential functions respectively. At the same time, the indices of power functions and the indices characterizing the slope of the Ap index spectrum differ significantly in magnitude for the periodic and chaotic modes. We have found that Ap nonlinearly depends on β for both the modes of magnetospheric dynamics. The maximum of the Ap index amplitude for periodic modes is observed when β>1; and for chaotic ones, when β<1. In almost every cycle of solar activity, the energy of the Ap index fluctuations of chaotic modes is higher than that of periodic ones. The results indicate intermittency and its associated turbulence of magnetospheric activity. The exponential character of the spectral density of the Ap index suggests that the behavior of magnetospheric activity is determined by its internal dynamics, which can be described by a finite number of deterministic equations. The trigger effect of magnetospheric activity is assumed to be due to the angle of inclination of the axis of the solar magnetic dipole to the ecliptic plane, on which the dynamics of the β parameter in the solar activity cycle depends.

Mathematical Model of Oscillations of a Three-Layered Channel Wall Possessing a Compressible Core and Interacting with a Pulsating Viscous Liquid Layer

The paper deals with the formulation of a mathematical model to study a dynamics interaction of a three-layered channel wall with a pulsating viscous fluid layer in a channel. The narrow channel formed by two parallel walls was considered. The lower channel wall was a three-layered plate with a compressible core, and the upper one was absolutely rigid. The face sheets of the three-layered plate satisfied Kirchhoff's hypotheses. The plate core was considered rigid taking into account its compression in the transverse direction. Plate deformations were assumed to be small. The continuity conditions of displacements are satisfied at the layers' boundaries of the three-layered plate. The oscillations of the three-layered channel wall occurred under the action of a given law of pressure pulsation at the channel edges. The dynamics of the viscous incompressible fluid layer within the framework of a creeping motion was considered. The formulated mathematical model consisted of the dynamics equations of the three-layered plate with compressible core, Navier --- Stokes equations, and the continuity equation. The boundary conditions of the model were the conditions at the plate edges, the no-slip conditions at the channel walls and the conditions for pressure at the channel edges. The steady-state harmonic oscillations were investigated and longitudinal displacements and deflections of the plate face sheets were determined. Frequency-dependent distribution functions of amplitudes of plate layers displacements were introduced. These functions allow us to investigate the dynamic response of the channel wall and the fluid pressure change in the channel. The elaborated model can be used for the evolution of non-destructive testing of elastic three-layered elements contacting with a viscous fluid layer and being part of the lubrication, damping or cooling systems of modern instruments and units.

Quantum work of an optical lattice

A classic example of a quantum quench concerns the release of a interacting Bose gas from an optical lattice. The local properties of quenches such as this have been extensively studied however the global properties of these non-equilibrium quantum systems have received far less attention. Here we study several aspects of global non-equilibrium behavior by calculating the amount of work done by the quench as measured through the work distribution function. Using Bethe Ansatz techniques we determine the Loschmidt amplitude and work distribution function of the Lieb-Liniger gas after it is released from an optical lattice. We find the average work and its universal edge exponents from which we determine the long time decay of the Loshcmidt echo and highlight striking differences caused by the the interactions as well as changes in the geometry of the system. We extend our calculation to the attractive regime of the model and show that the system exhibits properties similar to the super Tonks-Girardaeu gas. Finally we examine the prominent role played by bound states in the work distribution and show that, with low probability, they allow for work to be extracted from the quench.

A Non-Data-Aided OSNR Estimation Algorithm for Coherent Optical Fiber Communication Systems Employing Multilevel Constellations

The performance of existing moments-based non-data-aided (NDA) optical signal-to-noise ratio (OSNR) estimation approaches degrades greatly for coherent optical systems employing multilevel constellations. We propose a novel NDA OSNR estimation algorithm, which provides enhanced performance for such systems. The proposed algorithm utilizes the empirical cumulative distribution function of the signal's amplitude to extract the information on the noise variance. Analytical and extensive simulation results show the feasibility and advantages of the algorithm. For the studied systems employing multilevel constellations such as 8-quadrature amplitude modulation (QAM), 16-QAM, 32-QAM, and 64-QAM, the proposed algorithm attains the derived Cramer–Rao lower bound. Furthermore, it achieves a lower mean square error with significantly lower complexity when compared to the conventional moments-based NDA estimation approach. Moreover, the impact of fiber nonlinearity is investigated with a five-channel Nyquist wavelength division multiplexing system, and the proposed algorithm outperforms the moments-based counterpart.

Tapered Antenna Array with Non-identical Triangular MSA Elements for FSLL Reduction

Reduced interference from nearby communication systems is an essential need in all generations of wireless communication systems. In this paper, interference is reduced by reducing the first side lobe level (FSLL) by using the concept of tapering realized with non-identical triangular elements. Resonance frequency of an Equilateral triangular microstrip antenna depends on its patch height. This property has been used effectively to realize isosceles triangular microstrip antenna with equal height, thus resonating at the same frequency. The isosceles triangular elements are designed as non-identical elements, based on its area reduction and hence gain variation, with respect to three different standard amplitude distribution functions. Six such arrays have been designed with two different inset notch feed gaps. An analysis of the non-identical elements’ antenna arrays with varying inset notch feed gaps to realize tapering in the H-plane for FSLL reduction has been presented. To verify the proposed concept, one triangular patch array using eight non-identical equilateral and isosceles triangular elements designed at 6 GHz is fabricated and tested. A reasonably acceptable agreement between the simulated and measured results validates the proposed concept.

Tunable Magnetization Chains Induced With Annular Parabolic Mirrors

Based on the inverse Faraday effect, tunable light-induced magnetization chains are investigated by focusing narrow annular azimuthally polarized vortex beams with a 4 $\pi$ focusing system composed of double annular parabolic mirrors. Using Richards–Wolf vector diffraction theory, approximate analytical expressions of all parameters of the magnetization chains are theoretically calculated, realizing that all parameters are tunable. The calculated results show that the parameters are independent of the amplitude distribution function of the incident beam and the apodization factor of the focusing system. Hence, different kinds of long (about $100\lambda$ ) chains with sub-wavelength lateral size can be achieved by adjusting the central angular position, the angular width, and the phase difference of two counter-propagating incident beams. Compared with lenses, parabolic mirrors can generate multi-needle fields that lenses cannot.