Mathematical Wave Functions and 3D Finite Element Modelling of the Electron and Positron

The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.

Laboratory Research on Effective Test Area of Short-Crested Waves Generated by Two-Sided Segmented Wavemakers

The size and shape of the effective test area are crucial to consider when short-crested waves are created by segmented wavemakers. The range of the effective test area of short-crested waves simulated by two-sided segmented wavemakers is analyzed in this paper. The experimental investigation on the wave field distribution of short-crested waves generated by two-sided segmented wavemakers is conducted by using an array of wave gauges. Wave spectra and directional spreading function are analyzed and the results show that when the main direction is at a certain angle with the normal line of wave generators, the wave field of 3D short-crested waves generated by two-sided segmented wavemakers has good spatial uniformity within the model test area. The effective test area can provide good wave environments for seakeeping model tests of various ocean engineering structures in the deep ocean engineering basin.

Electrostatic Attraction and Repulsion Explained and Modelled Mathematically Using Classical Physics—A Detailed Mechanism Based on Particle Wave Functions

The phenomenon of electrical attraction and repulsion between charged particles is well known, and described mathematically by Coulomb’s Law, yet until now there has been no explanation for why this occurs. There has been no mechanistic explanation that reveals what causes the charged particles to accelerate, either towards or away from each other. This paper gives a detailed explanation of the phenomena of electrical attraction and repulsion based on my previous work that determined the exact wave-function solutions for both the Electron and the Positron. It is revealed that the effects are caused by wave interactions between the wave functions that result in Electromagnetic reflections of parts of the particle’s wave functions, causing a change in their momenta.

Earthquake relocation and 3-dimensional crustal structure of P-wave velocity in cen-tral-western China

采用中国中西部地区(2l°～36°N，98°～112°E)193个地震台在1992～1999年间记录到的9988次地震的Pg和Sg震相走时的读数资料，用Roecker的SPHYPIT90程序，反演了该地区三维地壳P波速度结构，并用SPHREL3D90程序进行了地震的重新定位．反演结果揭示了中国中西部地区地震P波速度结构明显的横向不均匀性，这些不同深度上波速的横向变化多以该地区的活动断裂为分界线．可以看出活动断裂两侧存在明显的速度反差．通过重新定位，得到了6459次地震的震源参数，这些精确定位的地震震中明显沿该区活动断裂呈现条带状分布，其范围和尺度清晰地表示了这一地区地震活动与活动断裂的紧密关系．其中，82％重新精确定位的事件的震源深度在20km以内．这一结果与笔者用双差地震定位法得到的重新定位的震源深度分布相一致．

Digital Light Processing 3D-Printed Ceramic Metamaterials for Electromagnetic Wave Absorption

Combining 3D printing with precursor-derived ceramic for fabricating electromagnetic(EM) wave-absorbing metamaterials has attracted great attention. This study presents a novel ultraviolet-curable polysiloxane precursor for digital light processing(DLP) 3D printing to fabricate ceramic parts with complex geometry, no cracks and linear shrinkage. Guiding with the principles of impedance matching, attenuation, and effective-medium theory, we design a crosshelix-array metamaterial model based on the complex permittivity constant of precursor-derived ceramics. The corresponding ceramic metamaterials can be successfully prepared by DLP printing and subsequent pyrolysis process, achieving a low reflection coefficient and a wide effective absorption bandwidth in the X-band even under high temperature. This is a general method that can be extended to other bands, which can be realized by merely adjusting the unit structure of meta-materials. This strategy provides a novel and effective avenue to achieve “target-design-fabricating” ceramic metamaterials, and it exposes the downstream applications of highly efficient and broad EM wave-absorbing materials and structures with great potential applications.

3D elastic waveform modeling with an optimized equivalent staggered-grid finite-difference method

Equivalent staggered-grid(ESG) as a new family of schemes has been utilized in seismic modeling,imaging,and inversion.Traditionally,the Taylor series expansion is often applied to calculate finite-difference(FD) coefficients on spatial derivatives,but the simulation results suffer serious numerical dispersion on a large frequency zone.We develop an optimized equivalent staggered-grid(OESG) FD method that can simultaneously suppress temporal and spatial dispersion for solving the second-order system of the 3 D elastic wave equation.On the one hand,we consider the coupling relations between wave speeds and spatial derivatives in the elastic wave equation and give three sets of FD coefficients with respect to the P-wave,S-wave,and converted-wave(C-wave) terms.On the other hand,a novel plane wave solution for the 3 D elastic wave equation is derived from the matrix decomposition method to construct the time-space dispersion relations.FD coefficients of the OESG method can be acquired by solving the new dispersion equations based on the Newton iteration method.Finally,we construct a new objective function to analyze P-wave,S-wave,and C-wave dispersion concerning frequencies.The dispersion analyses show that the presented method produces less modeling errors than the traditional ESG method.The synthetic examples demonstrate the effectiveness and superiority of the presented method.

Numerical Simulation of the Protective Effect of Complex Boundaries Toward Shock Waves in a 3D Explosive Field

A numerical method is presented that simulates 3D explosive field problems. A code MMIC3D using this method can be used to simulate the propagation and reflected effects of all kinds of rigid boundaries to shock waves produced by an explosive source. These numerical results indicate that the code MMIC3D has the ability in computing cases such as 3D shock waves produced by air explosion, vortex region of the shock wave, the Mach wave, and reflected waves behind rigid boundaries.

An explicit method for numerical simulation of wave equations: 3D wave motion

In this paper, an explicit method is generalized from 1D and 2D models to a 3D model for numerical simulation of wave motion, and the corresponding recursion formulas are developed for 3D irregular grids. For uniform cubic grids, the approach used to establish stable formulas with 2M-order accuracy is discussed in detail, with M being a positive integer, and is illustrated by establishing second order （M=1） recursion formulas. The theoretical results presented in this paper are demonstrated through numerical testing.

Earthquake relocation and 3-dimensional crustal structure of P-wave velocity in central-western China

A simultaneous inversion of earthquake relocation and three-dimensional crustal structure of P-wave velocity in central-western China (21癗~36癗, 98癊~112癊) were performed in this paper. The crustal P-wave velocity model and earthquake relocation for this region are obtained using Pg and Sg phase readings of 9 988 earthquakes from 1992 to 1999 recorded at 193 seismic stations within central-western China by SPHYPIT90 and SPHREL3D90 programs. A lateral inhomogeneous structure of P-wave velocity in this region was obtained. Ob-vious contrast of P-wave velocities was revealed on both sides of active fault zones. Relocated epicenters of 6 459 events show clear lineation along active faults, which indicated a close correlation between seismicity and the active faults in this region. Focal depths of 82% relocated events ranged from 0 to 20 km, which is in good agreement with that from double-difference earthquake location algorithm.

A LiDAR Point Clouds Dataset of Ships in a Maritime Environment

For the first time, this article introduces a LiDAR Point Clouds Dataset of Ships composed of both collected and simulated data to address the scarcity of LiDAR data in maritime applications. The collected data are acquired using specialized maritime LiDAR sensors in both inland waterways and wide-open ocean environments. The simulated data is generated by placing a ship in the LiDAR coordinate system and scanning it with a redeveloped Blensor that emulates the operation of a LiDAR sensor equipped with various laser beams. Furthermore,we also render point clouds for foggy and rainy weather conditions. To describe a realistic shipping environment, a dynamic tail wave is modeled by iterating the wave elevation of each point in a time series. Finally, networks serving small objects are migrated to ship applications by feeding our dataset. The positive effect of simulated data is described in object detection experiments, and the negative impact of tail waves as noise is verified in single-object tracking experiments. The Dataset is available at https://github.com/zqy411470859/ship_dataset.

Efficient solution of large-scale matrix of acoustic wave equations in 3D frequency domain

In 3D frequency domain seismic forward and inversion calculation,the huge amount of calculation and storage is one of the main factors that restrict the processing speed and calculation efficiency.The frequency domain finite-difference forward simulation algorithm based on the acoustic wave equation establishes a large bandwidth complex matrix according to the discretized acoustic wave equation,and then the frequency domain wave field value is obtained by solving the matrix equation.In this study,the predecessor's optimized five-point method is extended to a 3D seven-point finite-difference scheme,and then a perfectly matched layer absorbing boundary condition(PML)is added to establish the corresponding matrix equation.In order to solve the complex matrix,we transform it to the equivalent real number domain to expand the solvable range of the matrix,and establish two objective functions to transform the matrix solving problem into an optimization problem that can be solved using gradient methods,and then use conjugate gradient algorithm to solve the problem.Previous studies have shown that in the conjugate gradient algorithm,the product of the matrix and the vector is the main factor that affects the calculation efficiency.Therefore,this study proposes a method that transform bandwidth matrix and vector product problem into some equivalent vector and vector product algorithm,thereby reducing the amount of calculation and storage.

Defects Recognition of 3D Braided Composite Based on Dual-Tree Complex Wavelet Packet Transform

Textile-reinforced composites,due to their excellent highstrength-to-low-mass ratio, provide promising alternatives to conventional structural materials in many high-tech sectors. 3D braided composites are a kind of advanced composites reinforced with 3D braided fabrics; the complex nature of 3D braided composites makes the evaluation of the quality of the product very difficult. In this investigation,a defect recognition platform for 3D braided composites evaluation was constructed based on dual-tree complex wavelet packet transform( DT-CWPT) and backpropagation( BP) neural networks. The defects in 3D braided composite materials were probed and detected by an ultrasonic sensing system. DT-CWPT method was used to analyze the ultrasonic scanning pulse signals,and the feature vectors of these signals were extracted into the BP neural networks as samples. The type of defects was identified and recognized with the characteristic ultrasonic wave spectra. The position of defects for the test samples can be determined at the same time. This method would have great potential to evaluate the quality of 3D braided composites.

Stability of High-Order Staggered-Grid Schemes for 3D Elastic Wave Equation in Heterogeneous Media

In this paper, we firstly derive the stability conditions of high-order staggered-grid schemes for the three-dimensional (3D) elastic wave equation in heterogeneous media based on the energy method. Moreover, the plane wave analysis yields a sufficient and necessary stability condition by the von Neumann criterion in homogeneous case. Numerical computations for 3D wave simulation with point source excitation are given.

3-D Scattering of Obliquely Incident Plane P Waves by Alluvial Valley Embedded in Layered Half-Space

The indirect boundary element method(IBEM) was established to solve the problem of 3-D seismic responses of 2-D topographies,by calculating the free-field responses with the direct-stiffness method and simulating the scattering wave fields with the dynamic Green's functions of moving distributed loads.The proposed method yields accurate results,because the 3-D dynamic stiffness matrixes used are exact and the fictitious moving distributed loads can be acted directly on the interface between the alluvial valley and the layered half-space without singularity.The comparison with the published methods verifies the validity of the proposed method.And the numerical analyses are performed to give some beneficial conclusions.The study shows that 3-D scattering by an alluvial valley is essentially different from the 2-D case,and that the presence of soil layer affects not only the amplitude value of surface displacements but also the distribution of surface displacements.

High-Frequency Guided Wave Scattering by a Partly Through-Thickness Hole Based on 3D Theory

We present a theoretical investigation of the scattering of high frequency S0 Lamb mode from a circular blind hole defect in a plate based on the 3D theory. The SO wave is incident at the frequency above the A1 mode cut-off frequency, in which the popular approximate plate theories are inapplicable. Due to the non-symmetric blind hole defect, the scattered fields will contain higher order converted modes in addition to the fundamental SO and AO modes. The far-field scattering amplitudes of various propagating Lamb modes for different hole sizes are inspected. The results are compared with those of lower frequencies and some different phenomena are found. Two-dimensional Fourier transform （2DFT） results of transient scattered Lamb and SH wave signals agree well with the analytical dispersion curves, which check the validity of the solutions from another point of view.

Three-dimensional P-wave velocity structure of the crust beneath Hainan Island and its adjacent regions,China

Using over 3 500 first P arrival times recorded by nine digital seismic stations from Hainan Digital Seismic Net-work during 1999～2005,a 3-D P-wave velocity model of the crust under Hainan Island and adjacent regions has been determined. The results show that the pattern of velocity anomalies in the shallower upper crust is somewhat associated with the surface geological tectonics in the region. A relative low-velocity anomaly appears north of the Wangwu-Wenjiao fault zone and a relative high-velocity anomaly appears south of the Wangwu-Wenjiao fault zone,corresponding to the depressed areas in north Hainan Island,where many volcanoes are frequently active and geothermal values are relatively higher,and the uplifted and stable regions in central and south of the Hainan Is-land. In the middle and lower crust velocities are relatively lower in east Hainan than those in west Hainan,possi-bly suggesting the existence of the upwelling of hot materials from the mantle in east Hainan. The pattern of veloc-ity anomalies also indicates that NW faults,i.e.,the Puqian-Qinglan fault,may be shallower,while the E-W Wangwu-Wenjiao fault may be deeper,which perhaps extends down to Moho depth or deeper.

地下圆形衬砌洞室对SH波的散射(Ⅰ):3-D级数解

针对地下圆形衬砌洞室对入射平面SH波的散射问题,采用波函数展开法,研究了不同频率入射波作用下,圆形衬砌洞室散射的三维级数解.结果表明:当入射波所在平面与圆形衬砌洞室Z轴互相垂直时,该级数解退化为半无限二维空间中的结果.级数解为定量研究圆形衬砌洞室对不同入射角度和入射波长下的SH波的散射引起的地震动的影响提供了理论依据.

2—D与3—D横向各向同性介质中地震波动方程的解耦

在2-D横向各向同性介质中,似P波与似SV波耦合;3-D介质中,似P波与似SV波及似SH波均耦合于偏微分波动方程组中,为便于2-D与3-D横向各向同性介质中震波激发以及地震记录合成研究,本文首先对波动方程组本身进行了讨论,进而分别研究了二维与三维横向各向同性介质中波动方程组的解耦问题,得到了解耦后的关于位移分量偏微分方程。

基于3-D打印技术的新型微波/毫米波无源波导器件

综述了近年来基于多种3-D打印工艺的微波直至太赫兹频段无源波导器件的发展研究现状,并介绍了作者所在小组研制的多个基于立体光刻3-D打印工艺的滤波器(包括基于新型高Q值单模和双模球形腔体谐振器的X频段带通滤波器以及基于裂缝波导和紧凑片上结构的W频段带通滤波器).这些滤波器射频性能的测量与仿真结果吻合良好.与相同形状的铜制器件相比,采用非金属材料的3-D打印器件的重量减轻了80%以上,并保持了优良的射频性能.