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.

Simulation of subcritical flow pattern in 180° uniform and convergent open-channel bends using SSIIM 3-D model

In meandering rivers, the flow pattern is highly complex, with specific characteristics at bends that are not observed along straight paths. A numerical model can be effectively used to predict such flow fields. Since river bends are not uniform-some are divergent and others convergent-in this study, after the SSIIM 3-D model was calibrated using the result of measurements along a uniform 180° bend with a width of 0.6 m, a similar but convergent 180v bend, 0.6 m to 0.45 m wide, was simulated using the SSI1M 3-D numerical model. Flow characteristics of the convergent 180° bend, including lengthwise and vertical velocity profiles, primary and secondary flows, lengthwise and widtbwise slopes of the water surface, and the helical flow strength, were compared with those of the uniform 180° bend. The verification results of the model show that the numerical model can effectively simulate the flow field in the uniform bend. In addition, this research indicates that, in a convergent channel, the maximum velocity path at a plane near the water surface crosses the channel＇s centerline at about a 30° to 40° cross-section, while in the uniform bend, this occurs at about the 50° cross-section. The varying range of the water surface elevation is wider in the convergent channel than in the uniform one, and the strength of the helical flow is generally greater in the uniform channel than in the convergent one. Also, unlike the uniform bend, the convergent bend exhibits no rotational cell against the main direction of secondary flow rotation at the 135° cross-section.

3-D Geological Modeling-Concept,Methods and Key Techniques

3-D geological modeling plays an increasingly important role in Petroleum Geology, Mining Geology and Engineering Geology. The complexity of geological conditions requires different modeling methods in different situations. This paper summarizes the general concept of geological modeling; compares the characteristics of borehole-based modeling, cross-section based modeling and multi- source interactive modeling; analyses key techniques in 3-D geological modeling; and highlights the main difficulties and directions of future studies.

Application of 3-D Geoscience Modeling Technology for the Estimation of Solid Mineral Reserves

Applying new approaches, methods, and technologies for the estimation of reserves can effectively improve the efficiency and accuracy of assessments of solid mineral resources. After analyzing the development of 3-D geoscience modeling technology （3-D GMT）, this paper discusses the application of 3-D GMT for the estimation of solid mineral reserves, emphatically introducing its workflow and two key technologies, 3-D orebody surface modeling, and property modeling. Moreover, the paper analyzes the limitations of traditional methods, such as the section method and geological block method, and points out the advantages of 3-D GMT： building more accurate 3-D orebody models, expressing the internal inhomogeneous attributes of an orebody, reducing the potential for errors in the estimation of reserves, and implementing dynamic estimations of reserves.

A Higher-Efficient Non-Hydrostatic Finite Volume Model for Strong Three-Dimensional Free Surface Flows and Sediment Transport

In order to accurately simulate strong three-dimensional （3-D） free surface flows and sediment transport, the fully 3- D non-hydrostatic pressure models are developed based on the incompressible Navier-Stokes equations and convection-diffusion equation of sediment concentration with the mixing triangle and quadrilateral grids. The governing equations are discretized with the unstructured finite volume method in order to provide conservation properties of mass and momentum, and flexibility with practical application. It is shown that it is first-order accurate on nonuniform plane two-dimensional （2-D） grids and second-order accurate on uniform plane grids. A third-order approximation of the vertical velocity at the top-layer is applied. In such a way, free surface zero stress boundary condition is satisfied maturely, and very few vertical layers are needed to give an accurate solution even for complex discontinuous flow and short wave simulation. The model is applied to four examples to simulate strong 3-D free surface flows and sediment transport where non-hydrostatic pressures have a considerable effect on the velocity field. The newly developed model is verified against analytical solutions with an excellent agreement.

Numerical study on residual current and its impact on mass transport in the Hangzhou Bay and the Changjiang Estuary I. A3-D joint model of the Hangzhou Bay and the Changjiang Estuary

A 3-D numerical model is set up in a large domain covering the Hangzhou Bay and the Changjiang Estuary based on the ECOM model in orthogonal curvilinear coordinates.The numerical schemes for baroclinic pressure gradient (BPG)terms and convective terms are improved in the paper according to the characteristics of velocity field and mass transport in the area.The model is validated by the simulations of residual current and salinity transport in the Hangzhou Bay and the Changjiang Estuary.

Building 3-D Human Data Based on Handed Measurement and CNN

3-dimension(3-D)printing technology is growing strongly with many applications,one of which is the garment industry.The application of human body models to the garment industry is necessary to respond to the increasing personalization demand and still guarantee aesthetics.This paper proposes amethod to construct 3-D human models by applying deep learning.We calculate the location of the main slices of the human body,including the neck,chest,belly,buttocks,and the rings of the extremities,using pre-existing information.Then,on the positioning frame,we find the key points(fixed and unaltered)of these key slices and update these points tomatch the current parameters.To add points to a star slice,we use a deep learning model tomimic the form of the human body at that slice position.We use interpolation to produce sub-slices of different body sections based on the main slices to create complete body parts morphologically.We combine all slices to construct a full 3-D representation of the human body.

3-D Fracture Network Modelling in Hydropower Engineering Based on Optimal Monte Carlo Simulation

Effectively and accurately modelling the spatial relation of fracture surfaces is crucial in the design and construction of large hydropower dams having a complex underlying geology. However, fracture surfaces are randomly formed and vary greatly with respect to their spatial distribution, which makes the construction of accurate 3-D models challenging. In this study, we use an optimal Monte Carlo simulation and dynamic conditioning to construct a fracture network model. We found the optimal Monte Carlo simulation to effectively reduce the error associated with the Monte Carlo method and use dynamic conditioning to ensure the consistency of the model with the actual distribution of fractures on the excavation faces and outcrops. We applied this novel approach to a hydropower station on the Jinshajiang River, China. The simulation results matched the real sampled values well, confirming that the model is capable of effectively and accurately simulating the spatial relations in a fracture network.

Conical Sonic-Supersonic Solutions for the 3-D Steady Full Euler Equations

This paper concerns the sonic-supersonic structures of the transonic crossflow generated by the steady supersonic flow past an infinite cone of arbitrary cross section.Under the conical assumption,the three-dimensional(3-D)steady Euler equations can be projected onto the unit sphere and the state of fluid can be characterized by the polar and azimuthal angles.Given a segment smooth curve as a conical-sonic line in the polar-azimuthal angle plane,we construct a classical conical-supersonic solution near the curve under some reasonable assumptions.To overcome the difficulty caused by the parabolic degeneracy,we apply the characteristic decomposition technique to transform the Euler equations into a new degenerate hyperbolic system in a partial hodograph plane.The singular terms are isolated from the highly nonlinear complicated system and then can be handled successfully.We establish a smooth local solution to the new system in a suitable weighted metric space and then express the solution in terms of the original variables.

3-D modeling of rock burst in pillar No. 19 of Fetr6 chromite mine

Fetr6 is an underground mine in which chromite is extracted using stope and pillar mining method. Despite of all improving works such as roof supporting and replacing of ore pillars with concrete pillars, pillar No. 19 failed and other pillars failed progressively as a domino effect and 4000 m2 of mine collapsed within a few minutes, consequently. For detail investigation, two 3-D numerical models were developed by 3Dec. The first, a base model, was used for estimation of stress on pillars just before failure and the other for investigation of rock burst in pillar No. 19. The results show that discontinuity parameters such as friction angle and shear stiffness is critical parameters in this pillar failure. In addition, it indicates that W/H ratio equal 0.3, the lack of ore extraction strategy and inadequate roof support are the major reasons for this failure. In this paper, the procedure of study was described.

Modeling of the Changes in Flow Velocity on Seawalls under Different Conditions Using FLOW-3D Software

Seawalls are among protective structures that are constructed for decreasing the level of wave force and/or protecting from other structures. In this regard, more accurate investigation of these structures takes great importance from different perspectives. This research investigates the change of the velocity on seawall crown by considering the obstacles in different layouts and slopes. FLOW-3D has been used in this research for modeling. The results of the modeling show that the existence of obstacles has a determinative role in decreasing flow rate in the crown of seawalls. Also, as it was expected, the slope factor on upstream seawalls is very determinative in decreasing this rate such that the lowest velocity on the wall occurs in D-state layout and the slope of 45°.

NUMERICAL SIMULATION OF 3-D TURBULENT FLOWS OVER DREDGED TRENCHES

A 3- D free surface flow in open channels based on the Reynolds equations with the k-ε turbulence closure model is presented in this paper. Insted of the 'rigid lid' approximation, the solution of the free surface equation is implemented in the velocity-pressure iterative procedure on the basis of the conventional SIMPLE method. This model was used to compute the flow in rectangular channels with trenches dredged across the bottom. The velocity, eddy viscosity coefficient, turbulent shear stress, turbulent kinetic energy and elevation of the free surface can be obtained. The computed results are in good agreement with previous experimental data.

3-D crustal-scale gravity model of the San Rafael Block and Payenia volcanic province in Mendoza,Argentina

The San Rafael Block(SRB)is part of one of the main retroarc volcanic provinces in southern Central Andes in Mendoza,Argentina.This block is located in the Andean foothills between the orogenic front and foreland basement uplifts of late Miocene age.In order to analyze the geochronological evolution of the Quaternary volcanism in the region,several geologic and geophysical studies have been conducted.Nevertheless,the crust,where the SRB is located,has not been well characterized yet.Based on gravimetric and magnetic data,together with isostatic and elastic thickness analyses,we modeled the crustal structure of the area.Information obtained has allowed us to understand the crust where the SRB and the Payenia volcanic province are located.Bouguer anomalies indicate that the SRB presents higher densities to the North of Cerro Nevado and Moho calculations suggest depths for this block between 40 and 50 km.Determinations of elastic thickness would indicate that the crust supporting the San Rafael Block presents values of approximately 10 km,being enough to support the block loading.However,in the Payenia region,elastic thickness values are close to zero due to the regional temperature increase.

3-D MODELLING OF COMPUTER AIDED GARMENT DESIGN

This paper describes a method of the computer aided garment design,and discusses 3-D humanbody,wire frame modelling,approaches of expressing and a shading model of the 3-D garment.

MODELING OF 3-D IMAGES AND SPACE MARKOV CUBIC MESH MODELS

Three-dimensional(3-D)Markov cubic random mesh models are presented andproved in the form of two theorems in details.Its applications to the modeling and description of3-D images are described.The model presented here is a appropriate mathematical tool for thesegmentation,modeling,classification and other processing.Finally,an example is given.

3-D physical model in strong ground motion numerical simulation:A case study of Kunming basin

Seismic hazard assessment based on urban active faults can provide scientific bases for city planning and project construction, while numerical simulation of strong ground motion is an important method for seismic hazard prediction and assessment. A 3-D physical model in conformity with real strata configuration of （mainly） the Quaternary is a prerequisite to ensure the reliability of the simulation results. In this paper, we give a detailed account of the technical scheme and process for creating a 3-D physical model in Kunming basin. The data used are synthe- sized from seismogeological data, borehole data, topographic data, digital elevation mode （DEM） data, seismic exploration results and wave velocity measurements. Strafigraphic division is based mainly on shear wave velocity, with strata sequence taken into consideration. The model construction is finally accomplished with ArcGIS and many relevant programming techniques via layer-by-layer stacking （in depth direction） of the adjacent medium interfaces （meshes）. Meanwhile, a database of 3-D physical models is set up, which provides model data and parameters for strong ground motion simulation. Some processing methods and significant issues are also addressed in the paper in accordance with different types of exploration and experimental data.

EFFECT OF SUBMERGED ENTRY NOZZLE (SEN) PARAMETERS AND SHAPE ON 3-D FLUID FLOW IN MOULD FOR BEAM BLANK CONTINUOUS CASTING

According to turbulent theory and characteristics of beam blank continuous casting, 3-D model to represent the flow of beam blank mould is established. The predicted results indicate that the exit obliquity of up 15°(+15°) should be adopted, which will benefit the floatation of non-metallic inclusion and purification of the molten steel. When the nozzle angle is 120°, the flow pattern is reasonable. Proper nozzle depth can be 200mm. Turbulent kinetic of meniscus can be reduced by adopting the square nozzle and suitable area of side outlet when casting speed increases. The results are consistent with those of water model experiment, so the model is exact and reasonable. The model can provide important information for design of SEN and defining of immersion depth.

A Higher-Efficient Three-Dimensional Numerical Model for Small Amplitude Free Surface Flows

A higher-efficient three-dimensional non-hydrostatic model is developed to simulate small amplitude free surface flows based on a staggered unstructured grid. In this model, a fractional step algorithm is adopted to solve the Navier-Stokes equations in two major steps. A top-layer pressure method is proposed to minimize the number of vertical layers and subsequently the computational cost. Three classical examples of small amplitude free surface flows are used to demonstrate the capability and efficiency of the model. The satisfactory results demonstrated the capability and efficiency of modelling a range of small amplitude free surface flows with only a small number of vertical layers.

Research of the ATR system based on the 3-D models and L-M BP neural network

Automatic target recognition （ATR） is an important issue for military applications, the topic of the ATR system belongs to the field of pattern recognition and classification. In the paper, we present an approach for building an ATR system with improved artificial neural network to recog- nize and classify the typical targets in the battle field. The invariant features of Hu invariant moments and roundness were selected to be the inputs of the neural network because they have the invari- ances of rotation, translation and scaling. The pictures of the targets are generated by the 3-D mod- els to improve the recognition rate because it is necessary to provide enough pictures for training the artificial neural network. The simulations prove that the approach can be implement ed in the ATR system and it has a high recognition rate and can be applied in real time.

Statistical Model of the 3-D Braided Composites Strength

Based on the statistical model for the tensile statistical strength of unidirectional composite materials and the stress analysis of 3-D braided composites, a new method is proposed to calculate the tensile statistical strength of the 3-D braided compos- ites. With this method, the strength of 3-D braided composites can be calculated with very large accuracy, and the statistical parameters of 3-D braided composites can be determined. The numerical result shows that the tensile statistical strength of 3-D braided composites can be predicted using this method.