Three-dimensional Modeling of Ore-forming Elements and Mineralization Prognosis for the Yechangping Mo Deposit,Henan Province,China

Three-dimensional geochemical modeling of ore-forming elements is crucial for predicting deep mineralization.This approach provides key information for the quantitative prediction of deep mineral localization,three-dimensional fine interpolation,analysis of spatial distribution patterns,and extraction of quantitative mineral-seeking markers.The Yechangping molybdenum(Mo)deposit is a significant and extensive porphyry-skarn deposit in the East Qinling-Dabie Mo polymetallic metallogenic belt at the southern margin of the North China Block.Abundant borehole data on oreforming elements underpin deep geochemical predictions.The methodology includes the following steps:(1)Threedimensional geological modeling of the deposit was established.(2)Correlation,cluster,and factor analyses post delineation of mineralization stages and determination of mineral generation sequence to identify(Cu,Pb,Zn,Ag)and(Mo,W,mfe)assemblages.(3)A three-dimensional geochemical block model was constructed for Mo,W,mfe,Cu,Zn,Pb,and Ag using the ordinary kriging method,and the variational function was developed.(4)Spatial distribution and enrichment characteristics analysis of ore-forming elements are performed to extract geological information,employing the variogram and w(Cu+Pb+Zn+Ag)/w(Mo+W)as predictive indicators.(5)Identifying the western,northwestern,and southwestern areas of the mine with limited mineralization potential,contrasted by the northeastern and southeastern areas favorable for mineral exploration.

Numerical three-dimensional modeling of earthen dam piping failure

A physically-based numerical three-dimensional earthen dam piping failure model is developed for homogeneous and zoned soil dams.This model is an erosion model,coupled with force/moment equilibrium analyses.Orifice flow and two-dimensional(2D)shallow water equations(SWE)are solved to simulate dam break flows at different breaching stages.Erosion rates of different soils with different construction compaction efforts are calculated using corresponding erosion formulae.The dam's real shape,soil properties,and surrounding area are programmed.Large outer 2D-SWE grids are used to control upstream and downstream hydraulic conditions and control the boundary conditions of orifice flow,and inner 2D-SWE flow is used to scour soil and perform force/moment equilibrium analyses.This model is validated using the European Commission IMPACT(Investigation of Extreme Flood Processes and Uncertainty)Test#5 in Norway,Teton Dam failure in Idaho,USA,and Quail Creek Dike failure in Utah,USA.All calculated peak outflows are within 10%errors of observed values.Simulation results show that,for a V-shaped dam like Teton Dam,a piping breach location at the abutment tends to result in a smaller peak breach outflow than the piping breach location at the dam's center;and if Teton Dam had broken from its center for internal erosion,a peak outflow of 117851 m'/s,which is 81%larger than the peak outflow of 65120 m3/s released from its right abutment,would have been released from Teton Dam.A lower piping inlet elevation tends to cause a faster/earlier piping breach than a higher piping inlet elevation.

Three-dimensional forward modeling of DC resistivity using the aggregation-based algebraic multigrid method

To speed up three-dimensional （3D） DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method （AGMG）. We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner （AGMG-CG） to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling （3DDCXH）. In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.

Research on the Three-dimensional Modeling and Optimization of a Virtual Tower Crane Based on 3DS Max, Solidworks and EON Professional

Three-dimensional modeling of virtual hoisting machinery is the critical works to structure the system of virtual construction, and the foundation to realize intelligent and interactive virtual hoisting. Aimed at enhancing the requests of image quality and stability of the virtual construction scene, taking a tower crane for example. We studied the technology of three-dimensional modeling and optimization of a virtual tower crane, and a method named two-stage model optimization was put forward. This depended on the modeling stage using Solidworks and 3DS Max and the performance optimization stage in EON. The practice of software development indicates that the proposed methods of three-dimensional modeling and optimization could satisfy the performance request of virtual construction system and be popularized to other virtual system.

Three-dimensional acoustic wave equation modeling based on the optimal finite-difference scheme

Generally, FD coefficients can be obtained by using Taylor series expansion （TE） or optimization methods to minimize the dispersion error. However, the TE-based FD method only achieves high modeling precision over a limited range of wavenumbers, and produces large numerical dispersion beyond this range. The optimal FD scheme based on least squares （LS） can guarantee high precision over a larger range of wavenumbers and obtain the best optimization solution at small computational cost. We extend the LS-based optimal FD scheme from two-dimensional （2D） forward modeling to three-dimensional （3D） and develop a 3D acoustic optimal FD method with high efficiency, wide range of high accuracy and adaptability to parallel computing. Dispersion analysis and forward modeling demonstrate that the developed FD method suppresses numerical dispersion. Finally, we use the developed FD method to source wavefield extrapolation and receiver wavefield extrapolation in 3D RTM. To decrease the computation time and storage requirements, the 3D RTM is implemented by combining the efficient boundary storage with checkpointing strategies on GPU. 3D RTM imaging results suggest that the 3D optimal FD method has higher precision than conventional methods.

Three-dimensional modeling of effect of surface intermetallic phase on surface defects of Al-Fe-Si aluminum foils during twin-roll casting

Scanning electron microscopy and X-ray energy dispersive spectrum analysis show that the clusters of intermetallic AlFeSi particle are distributed on or near the aluminum foil stock surfaces heterogeneously. 3D finite element modeling shows that these clusters of hard particles induce the fracture of the nano-scale lubricant oil film at first and further lead to severe deformation in the nearby aluminum foil substrate along the rolling direction. Consequently, the optical property in this region differs from that in the surroundings, resulting in surface defects.

Modeling time-dependent mechanical behavior of hard rock considering excavation-induced damage and complex 3D stress states

To investigate the long-term stability of deep rocks,a three-dimensional(3D)time-dependent model that accounts for excavation-induced damage and complex stress state is developed.This model comprises three main components:a 3D viscoplastic isotropic constitutive relation that considers excavation damage and complex stress state,a quantitative relationship between critical irreversible deformation and complex stress state,and evolution characteristics of strength parameters.The proposed model is implemented in a self-developed numerical code,i.e.CASRock.The reliability of the model is validated through experiments.It is indicated that the time-dependent fracturing potential index(xTFPI)at a given time during the attenuation creep stage shows a negative correlation with the extent of excavationinduced damage.The time-dependent fracturing process of rock demonstrates a distinct interval effect of the intermediate principal stress,thereby highlighting the 3D stress-dependent characteristic of the model.Finally,the influence of excavation-induced damage and intermediate principal stress on the time-dependent fracturing characteristics of the surrounding rocks around the tunnel is discussed.

Abundant invariant solutions of extended(3+1)-dimensional KP-Boussinesq equation

Lie group analysis method is applied to the extended(3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation and the corresponding similarity reduction equations are obtained with various infinitesimal generators.By selecting suitable arbitrary functions in the similarity reduction solutions,we obtain abundant invariant solutions,including the trigonometric solution,the kink-lump interaction solution,the interaction solution between lump wave and triangular periodic wave,the two-kink solution,the lump solution,the interaction between a lump and two-kink and the periodic lump solution in different planes.These exact solutions are also given graphically to show the detailed structures of this high dimensional integrable system.

3D Road Network Modeling and Road Structure Recognition in Internet of Vehicles

Internet of Vehicles (IoV) is a new system that enables individual vehicles to connect with nearby vehicles,people, transportation infrastructure, and networks, thereby realizing amore intelligent and efficient transportationsystem. The movement of vehicles and the three-dimensional (3D) nature of the road network cause the topologicalstructure of IoV to have the high space and time complexity.Network modeling and structure recognition for 3Droads can benefit the description of topological changes for IoV. This paper proposes a 3Dgeneral roadmodel basedon discrete points of roads obtained from GIS. First, the constraints imposed by 3D roads on moving vehicles areanalyzed. Then the effects of road curvature radius (Ra), longitudinal slope (Slo), and length (Len) on speed andacceleration are studied. Finally, a general 3D road network model based on road section features is established.This paper also presents intersection and road section recognition methods based on the structural features ofthe 3D road network model and the road features. Real GIS data from a specific region of Beijing is adopted tocreate the simulation scenario, and the simulation results validate the general 3D road network model and therecognitionmethod. Therefore, thiswork makes contributions to the field of intelligent transportation by providinga comprehensive approach tomodeling the 3Droad network and its topological changes in achieving efficient trafficflowand improved road safety.

Multi-scale Modeling and Finite Element Analyses of Thermal Conductivity of 3D C/SiC Composites Fabricating by Flexible-Oriented Woven Process

Thermal conductivity is one of the most significant criterion of three-dimensional carbon fiber-reinforced SiC matrix composites(3D C/SiC).Represent volume element(RVE)models of microscale,void/matrix and mesoscale proposed in this work are used to simulate the thermal conductivity behaviors of the 3D C/SiC composites.An entirely new process is introduced to weave the preform with three-dimensional orthogonal architecture.The 3D steady-state analysis step is created for assessing the thermal conductivity behaviors of the composites by applying periodic temperature boundary conditions.Three RVE models of cuboid,hexagonal and fiber random distribution are respectively developed to comparatively study the influence of fiber package pattern on the thermal conductivities at the microscale.Besides,the effect of void morphology on the thermal conductivity of the matrix is analyzed by the void/matrix models.The prediction results at the mesoscale correspond closely to the experimental values.The effect of the porosities and fiber volume fractions on the thermal conductivities is also taken into consideration.The multi-scale models mentioned in this paper can be used to predict the thermal conductivity behaviors of other composites with complex structures.

Tidal modeling based on satellite altimetry observations of TOPEX/ Poseidon, Jason1, Jason2, and Jason3 with high prediction capability: A case study of the Baltic Sea

This research aims to optimize the utilization of long-term sea level data from the TOPEX/Poseidon,Jason1,Jason2,and Jason3 altimetry missions for tidal modeling.We generate a time series of along-track observations and apply a developed method to produce tidal models with specific tidal constituents for each location.Our tidal modeling methodology follows an iterative process:partitioning sea surface height(SSH)observations into analysis/training and prediction/validation parts and ultimately identi-fying the set of tidal constituents that provide the best predictions at each time series location.The study focuses on developing 1256 time series along the altimetry tracks over the Baltic Sea,each with its own set of tidal constituents.Verification of the developed tidal models against the sSH observations within the prediction/validation part reveals mean absolute error(MAE)values ranging from 0.0334 m to 0.1349 m,with an average MAE of 0.089 m.The same validation process is conducted on the FES2014 and EOT20 global tidal models,demonstrating that our tidal model,referred to as BT23(short for Baltic Tide 2023),outperforms both models with an average MAE improvement of 0.0417 m and 0.0346 m,respectively.In addition to providing details on the development of the time series and the tidal modeling procedure,we offer the 1256 along-track time series and their associated tidal models as supplementary materials.We encourage the satellite altimetry community to utilize these resources for further research and applications.

UAV-based transient electromagnetic 3D forward modeling and inversion and analysis of exploration capability

Unmanned aerial vehicle transient electromagnetic(UAV-TEM)is a novel airborne exploration method that offers advantages such as low cost,simple operation,high exploration efficiency and suitability for near-surface exploration in complex terrain areas.To improve the accuracy of data interpretation in this method,the authors conducted a systematic three-dimensional(3D)forward modeling and inversion of the UAV-TEM.This study utilized the finite element method based on unstructured tetrahedral elements and employed the second-order backward Euler method for time discretization.This allowed for accurate 3D modeling and accounted for the effects of complex terrain.Based on these,the influence characteristics of flight altitudes and the sizes,burial depths,and resistivities of anomalies are compared and analyzed to explore the UAV-TEM systems’exploration capability.Lastly,four typical geoelectrical models of landslides are designed,and the inversion method based on the Gauss-Newton optimization method is used to image the landslide models and analyze the imaging effect of the UAV-TEM method on landslide geohazards.Numerical results showed that UAV-TEM could have better exploration resolution and fine imaging of nearsurface structures,providing important technical support for monitoring,early warning,and preventing landslides and other geological hazards.

A 3-DIMENSIONAL DATA MODEL FOR VISUALIZING CLOVERLEAF JUNCTION IN A CITY MODEL

The research work has been seldom done about cloverleaf junction expression in a 3-dimensional city model (3DCM). The main reason is that the cloverleaf junction is often in a complex and enormous construction. Its main body is bestraddle in air,and has aerial intersections between its parts. This complex feature made cloverleaf junction quite different from buildings and terrain, therefore, it is difficult to express this kind of spatial objects in the same way as for buildings and terrain. In this paper,authors analyze spatial characteristics of cloverleaf junction, propose an all-constraint points TIN algorithm to partition cloverleaf junction road surface, and develop a method to visualize cloverleaf junction road surface using TIN. In order to manage cloverleaf junction data efficiently, the authors also analyzed the mechanism of 3DCM data management, extended BLOB type in relational database, and combined R-tree index to manage 3D spatial data. Based on this extension, an appropriate data

Analytical Solutions for Testing of Baroclinic and Wind-Driven Three-Dimensional Hydrodynamic Models

It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analytical solutions. In this paper, exact solutions for the periodic forcing by surface heat flux and wind stress are given by solving the linearized equations of motion neglecting the rotation, advection and horizontal diffusion terms. The temperature at the bottom is set to a prescribed periodic value and a slip condition on flow is enforced at the bottom. The geometry of the quarter annulus, which has been extensively studied for two- and three-dimensional analytical solutions of unstratified water bodies, is used with a general power law variation of the bottom slope in the radial direction and is constant in the azimuthal direction. The analytical solutions are derived in a cylindrical coordinate system, which describes the three-dimensional fluid field in a Cartesian coordinate system. The results presented in this paper should provide a foundation for studying and verifying the baroclinic term over a varied topography in a three-dimensional numerical model.

Transect-based Three-Dimensional Road Modeling and Visualization

On the basis of the study on road elements and th e existing three-dimensional road data models, this paper puts forward the transe ct-based road modeling, resolves the modeling of the simplest road with two roa d transects, and fulfils the visualization of the road. OpenGL is applied as the tool of visualization. The map texture technology, LOD algorithm and dynamic mu lti-differentiating texture technology are of benefit to the construction of 3D road GIS, and improve the speed of roaming and effective visualization. This pa per also disusses the combination of 2D digitall road map and 3D road scene, and the dynamic response between them. Finally, on the basis of the research on the transect-based road model, this paper develops the three-dimensional road geo graphic information system called virtual road ( VRoad ), which not only suppli es road designers with a set of tool which can turn the designed 2D road data in to 3D road and the high road assistant function area in computer, but also suppl ies the road management with a set of tool which can realize the road real time and interactive roaming, high-efficiency management.

Component-based Topological Data Model for Three-dimensional Geology Modeling

On the study of the basic characteristics of geological objects and the special requirement for computing 3D geological model, this paper gives an object-oriented 3D topologic data model. In this model, the geological objects are divided into four object classes: point, line, area and volume. The volume class is further divided into four subclasses: the composite volume, the complex volume, the simple volume and the component. Twelve kinds of topological relations and the related data structures are designed for the geological objects.

Three-dimensional modeling in complex liver surgery and liver transplantation

Liver resection and transplantation are the most effective therapies for many hepatobiliary tumors and diseases.However,these surgical procedures are challenging due to the anatomic complexity and many anatomical variations of the vascular and biliary structures.Three-dimensional(3D)printing models can clearly locate and describe blood vessels,bile ducts and tumors,calculate both liver and residual liver volumes,and finally predict the functional status of the liver after resection surgery.The 3D printing models may be particularly helpful in the preoperative evaluation and surgical planning of especially complex liver resection and transplantation,allowing to possibly increase resectability rates and reduce postoperative complications.With the continuous developments of imaging techniques,such models are expected to become widely applied in clinical practice.

Applications of Extended Mapping Deformation Method in Two （3＋1）-Dimensional Nonlinear Models

Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solutions include solitary solution, periodic wave solution, rational travelling wave solution, and Jacobian and Weierstrass function solution, etc.

Three-dimensional forward modeling and response characteristics analysis of foundation pit leakage electric-field considering electrokinetic effect

The traditional ground direct current method is not suitable for leakage detection of underground diaphragm walls in foundation pits because of its low accuracy and poor anti-noise ability.Here,we propose a joint surface-borehole observation device for leakage electric fi eld detection to achieve rapid measurement of the electric fi eld distribution characteristics at ground level in the foundation pit,thus enabling rapid localization of leakage points.We first establish the mechanism and basic equation of the leakage electric field response by combining the electric field formed by electrokinetic effect(EK)and the stable electric fi eld formed by conduction current in a combined leakage channel.Then,the fi nite–infi nite element coupling method is used to solve the electric fi eld equation to simulate the responses of a three-dimensional foundation pit leakage model.Furthermore,we conduct numerical simulations of diff erent pit models to investigate the infl uencing factors of the detection device and response characteristics of the change in the properties of the leakage channel.The results demonstrate that the proposed joint surface-borehole observation device can effi ciently reveal anomalous potential caused by leakage,and the amplitude of the electric fi eld generated by EK can eff ectively strengthen the leakage electric fi eld signal at the leakage,thus improving detection accuracy and effi ciency.

Three-dimensional numerical modeling of nearshore circulation

A three-dimensional nearshore circulation model was developed by coupling CH3D, a three-dimensional hydrodynamic model and REF/DIF, a nearshore wave transformation model. The model solves the three-dimensional wave-averaged equations of motion. Wave-induced effects on circulation were introduced in the form of radiation stresses, wave-induced mass transport, wave-induced enhancement of bottom friction and wave-induced turbulent mixing. Effects of breaking waves were considered following Svendsen (1984a and 1984b) and Stive and Wind (1986). The model was successfully tested against the analytical solution of longshore currents by Longuet and Higgins (1970). The model successfully simulated the undertow as observed in a laboratory experiment by Stive and Wind (1982). In addition, the model was applied to a physical model by Mory and Hamm (1997) and successfully reproduced the eddy behind a detached breakwater as well as the longshore current on the open beach and the contiguous eddy in the open area of the wave tank. While the qualitative agreement between model results and experimental observations was very good, the quantitative agreement needs to be further improved. Albeit difficult to explain every discrepancy between the model results and observations, in general, sources of errors are attributed to the lack of understanding and comprehensive description of following processes: (1)the horizontal and vertical distribution of radiation stress, especially for breaking waves;(2)the detailed structure of turbulence;(3)Wave-current interaction (not included at this moment); and (4)the wave-current boundary layer and the resulting bottom shear stress.