Derivative Geometric Modeling of Basic Rotational Solids on CATIA

Hybrid models derived from rotational solids like cylinders, cones and spheres were implemented on CATIA software. Firstly, make the isosceles triangular prism, cuboid, cylinder, cone, sphere, and the prism with tangent conic and curved triangle ends, the cuboid with tangent cylindrical and curved rectangle ends, the cylinder with tangent spherical and curved circular ends as the basic Boolean deference units to the primary cylinders, cones and spheres on symmetrical and some critical geometric conditions, forming a series of variant solid models. Secondly, make the deference units above as the basic union units to the main cylinders, cones, and spheres accordingly, forming another set of solid models. Thirdly, make the tangent ends of union units into oblique conic, cylindrical, or with revolved triangular pyramid, quarterly cylinder and annulus ends on sketch based features to the main cylinders, cones, and spheres repeatedly, thus forming still another set of solid models. It is expected that these derivative models be beneficial both in the structure design, hybrid modeling, and finite element analysis of engineering components and in comprehensive training of spatial configuration of engineering graphics.

Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model

Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.

Geometric modeling of Holocene large-river delta growth patterns,as constrained by environmental settings

Topographic/bathymetric conditions of the continental shelf can significantly influence the long-term growth of river deltas.In particular,these conditions constrain the accommodation space for sedimentation in the deltaic areas.In this study,we use a conceptual geometric model to evaluate the role played by this factor,on the basis of the principle of mass conservation.The Ganges-Brahmaputra,Mekong and Nile deltas are examined as three typical examples,in terms of their different original seabed morphologies.The control variate method is applied to eliminate the effect of the difference in model input variables.The results show that,assuming a constant sediment load,the delta growth rate will decrease with time;a higher value of the original seabed slope leads to a lower shoreline progradation rate for the subaerial delta and a higher growth rate for the subaqueous delta.Thus,the original seabed morphology represented by slope is a critical factor affecting the evolution of Holocene large-river deltas.These results explain the interrelationships between sediment load,deltaic plain area,and the original seabed slopes for the 27 large-river deltas worldwide,located in the middle/low latitudes,with different tectonic backgrounds.In the future,the conceptual geometric model may be combined with sediment dynamic modeling to identify more details of the evolution of these deltas.

Geometric modeling of underground ferromagnetic pipelines for magnetic dipole reconstruction-based magnetic anomaly detection

To aid the magnetic anomaly detection(MAD)of underground ferromagnetic pipelines,this paper proposes a geometric modeling method based on the magnetic dipole reconstruction method(MDRM).First,the numerical modeling of basic pipe components such as straight sections,bends and elbows,and tee joints are discussed and the relevant mathematical formulations for these components are derived.Next,after analyzing the function of MDRM and various element division strategies,the sectional division and blocked division methods are introduced and applied to the appropriate pipeline components to determine the volume and center coordinates of each element,establishing the general models for the three typical pipeline components considered.The resulting volume and center coordinates of each component are the fundamental parameters for determining the MAD forwarding of underground ferromagnetic pipelines using the MDRM.Finally,based on the combination and transformation of the basic pipeline components considered,the visualized geometric models of typical pipeline layouts including parallel pipelines,pipelines with elbows,and a pipeline with a tee joint are constructed.The results demonstrate the feasibility of the proposed method of geometric modeling for the MDRM,which can be further applied to the finite element modeling of these and other components when analyzing MAD data.Furthermore,the models with output parameters proposed in this paper establish a foundation for the inversion of MAD.

Geometrical Modeling by NURBS Surface and RCS Computing by Visualization for Complex Targets

A novel approach to compute the high frequency radar cross-section (RCS) of complex targets is described in this paper.From the three views or the sectional views of the target, target is geometrically modeled by non-uniform rational B-spline (NURBS) parametric surfaces using the software CNFEOV developed by oneself which constructs NURBS representation of complex target from engineering orthographic views. RCS is obtained through PO, PTD, MEC and IBC techniques. When calculating RCS of the target, it is necessary to get the unit normal vector to surface illumi- nated by radar and the value Z which is the distance from the point on the surface to radar. ln this novel approach, the unit normal vector to the surface can be obtained either by the Phong rendering model, in which the color components (RGB) of every pixel on the image are equal to the coordinate components of the normal, or by the NURBS expressions. The value Z can be achieved by software or hardware Z-buffer. The effects of the size of image on the RCS of target are discussed and the correct method is recommended. The RCS of the perfect conducting sphere, cylinder and dihedral as well as the coated cylinder, as some examples, are computed. The accuracy of the method is verified by comparing the numerical results with those obtained by using other methods.

Structural Variation between the Western and Eastern Kuqa Fold-and-thrust Belt,China:Insights from Seismic Interpretation and Analog Modeling

The Kuqa fold-and-thrust belt exhibits apparent structural variation in the western and eastern zone.Two salt layer act as effective decollements and influence the varied deformation.In this study,detailed seismic interpretations and analog modeling are presented to construct the suprasalt and subsalt structures in the transfer zone of the middle Kuqa and investigate the influence of the two salt layers.The results reveal that the relationship of the two salt layers changes from separated to connected,and then overlapped toward the foreland in the transfer zone.Different structural models are formed in the suprasalt and subsalt units due to the interaction of the two salt layers.The imbricate thrust faults form two broom-like fault systems in the subsalt units.The suprasalt units develop detached folds terminating toward the east in the region near the orogenic belt.Whereas,two offset anticlines with different trends develop at the frontal edge of the lower salt layer and the trailing edge of the upper salt layer,respectively.According to exploration results in this region,the relationship between suprasalt and subsalt structures has an influence on hydrocarbon accumulation.We believe that the connected deformation contains high-risk plays while the decoupled deformation contains well-preserved plays.

Software development for modeling irregular fine protrusions formed by sputter etching

Irregular fine protrusions formed on the surface of a mechanical part through biomimetic technology can enhance the part’s properties,including tribology,self-cleaning,and light absorption.However,underlying principles for the formation of fine protrusions according to the requirements of their shapes,sizes,and material distributions have not been studied sufficiently.This paper presents the software development for modeling irregular fine protrusions,which is essential for the simulation,experimentation,and analysis of fine protrusions formed by sputter etching.

REVERSE MODELING FOR CONIC BLENDING FEATURE

A novel method to extract conic blending feature in reverse engineering is presented. Different from the methods to recover constant and variable radius blends from unorganized points, it contains not only novel segmentation and feature recognition techniques, but also bias corrected technique to capture more reliable distribution of feature parameters along the spine curve. The segmentation depending on point classification separates the points in the conic blend region from the input point cloud. The available feature parameters of the cross-sectional curves are extracted with the processes of slicing point clouds with planes, conic curve fitting, and parameters estimation and compensation, The extracted parameters and its distribution laws are refined according to statistic theory such as regression analysis and hypothesis test. The proposed method can accurately capture the original design intentions and conveniently guide the reverse modeling process. Application examples are presented to verify the high precision and stability of the proposed method.

Prediction on the viscosity of multi-component melts with a new geometric model

A geometric model for calculating the viscosity of multi-component melt fromrelated binary physicochemistry properties was derived based on Chou's thermodynamic geometricmodel. The model derived was employed to predict the viscosity of Au-Ag-Cu alloys. The results showthat the calculated viscosity for Au-Ag-Cu alloys meet the experimental data very well. In addition,the viscosity of Bi-Sn-In systems was also predicted with this model.

Mathematical Model and Geometrical Model of Double Pitch ZN-type Worm Gear Set Based on Generation Mechanism

The current researches on the tooth surface mathematical equations and the theory of gearing mainly pay attention to the ordinary type worm gear set（e.g., ZN, ZA, or ZK）. The research of forming mechanism and three-dimensional modeling method for the double pitch worm gear set is not enough. So there are some difficulties in mathematical model deducing and geometry modeling of double pitch ZN-type worm gear set based on generation mechanism. In order to establish the mathematical model and the precise geometric model of double pitch ZN-type worm gear set, the structural characteristics and generation mechanism of the double pitch ZN-type worm gear set are investigated. Mathematical model of the ZN-type worm gear set is derived based on its generation mechanism and the theory of gearing. According to the mathematical model of the worm gear set which has been developed, a geometry modeling method of the double pitch ZN-type worm and worm gear is presented. Furthermore, a geometrical precision calculate method is proposed to evaluate the geometrical quality of the double pitch worm gear set. As a result, the maximum error is less than 6′10–4 mm in magnitude, thus the model of the double pitch ZN-type worm gear set is available to meet the requirements of finite element analysis and engineering application. The derived mathematical model and the proposed geometrical modeling method are helpful to guiding the design, manufacture and contact analysis of the worm gear set.

GEOMETRIC MODEL AND APPLIED METHOD FOR THE CALCULATION OF GRAIN SIZE DISTRIBUTIONS

Most of the available methods for the calculation of the three dimensional(3D)grain size dis- tribution functions(SDF)are based on the S model and lead a grave systematical error.The origin is the basic supposition of spherical grains in the S model,which does not correspond with the feature of real grains.A new model called A model is developed based on the hypothe- sis of polvhedral grains.The probability functions of the A model and the method to calculate the 3D SDFs using the A model are given in the present paper.The theoretical analyses and experimental tests have demonstrated that the A model reduces the systematical error radical- ly.It is nearly as simple as the so far used S model,but gives much better results in repro- ducing of 3D SDFs from the measured ID or 2D SDFs.

Geometric model of roboticarc welding for automatic programming

Geometric information is important for automatic programming of arc welding robot. Complete geometric models of robotic arc welding are established in this paper. In the geometric model of weld seam, an equation with seam length as its parameter is introduced to represent any weld seam. The method to determine discrete programming points on a weld seam is presented. In the geometric model of weld workpiece, three class primitives and CSG tree are used to describe weld workpiece. Detailed data structure is presented. In pose transformation of torch, world frame, torch frame and active frame are defined, and transformation between frames is presented. Based on these geometric models, an automatic programming software package for robotic arc welding, RAWCAD, is developed. Experiments show that the geometric models are practical and reliable.

Experimental Observation of the Ground-State Geometric Phase of Three-Spin XY Model

The geometric phase has become a fundamental concept in many fields of physics since it was revealed. Recently, the study of the geometric phase has attracted considerable attention in the context of quantum phase transition, where the ground state properties of the system experience a dramatic change induced by a variation of an external parameter. In this work, we experimentally measure the ground-state geometric phase of the three-spin XY model by utilizing the nuclear magnetic resonance technique. The experimental results indicate that the geometric phase could be used as a fingerprint of the ground-state quantum phase transition of many-body systems.

A General Representation of Geometrical Solution Model for Predicting Ternary Thermodynamic Properties

The existing geometrical solution models for predicting ternary thermodynamic properties from relevant binary ones have been analysed,and a general representation was proposed in an integral form on the bases of these models.

Geometric Drawing Model of Shape of Water Sections for the Investigation of Solid Flow Transport in the Basin of Mono River in Republic of Benin

The hydrologic and hydraulic changings on the behavior of Mono river are the result of the stress involved by human activities, on one hand and the construction of the dam of Nangbéto and the exploitation of sand in downstream of the dam by the population, between Athiémé and Agbanankin on other hand. That effect had also affected the shape of the sections of the river in the context of climate variability. It shows consequently that area is also a trapping area of sediments eroded in downstream of the dam and is responsible for the trapping of sediments in the river. The slope and the flow rate are the main factors of the real capacity of transport of a watercourse. They also determine the transport of solid flows from upstream to downstream. This drawing model established by taking into account the bathymetry of a transversal section of the Mono river at Athiémé, is the first step of a global investigation of the solid flow transport in the basin of Mono river and the boundary condition for the characterization of its hydro-sedimentary dynamics study. It aims to take into account sections and the used technique which consist to measure on one located section as the representative section of the river at Athiémé, by moving the boat used for bathymetry.

Sparsity-based efficient simulation of cluster targets electromagnetic scattering

An efficient and real-time simulation method is proposed for the dynamic electromagnetic characteristics of cluster targets to meet the requirements of engineering practical applications.First,the coordinate transformation method is used to establish a geometric model of the observation scene,which is described by the azimuth angles and elevation angles of the radar in the target reference frame and the attitude angles of the target in the radar reference frame.Then,an approach for dynamic electromagnetic scattering simulation is proposed.Finally,a fast-computing method based on sparsity in the time domain,space domain,and frequency domain is proposed.The method analyzes the sparsity-based dynamic scattering characteristic of the typical cluster targets.The error between the sparsity-based method and the benchmark is small,proving the effectiveness of the proposed method.

Compression Mechanical Performance Simulation and Parameter Optimization of Degradable Ureteral Stent Based on ABAQUS

The compression performance of a degradable ureteral stent is analyzed and the parameters are optimized by a finite element modeling method.The degradable ureteral stent explored in this paper is developed from poly(glycolic acid)(PGA)and poly(lactic-co-glycolic acid)(PLGA)degradable materials.Based on the actual measurement of fabric structure parameters,the three-dimensional model of the stent is established with the help of the modeling software.The finite element analysis software is used to simulate the compression process of the degradable ureteral stent.The parameters of materials,interactions and boundary conditions are set according to the compression environment of the stent for modeling and simulation.On this basis,the friction coefficient of yarns,the yarn radius,and the braided angle of the stent are further compared.The comparison test is carried out by a single variable.The experimental results show that the change of yarn friction coefficient has little influence on the compressive stress,while the yarn radius and the braided angle of the stent have a great influence on the compressive stress.

No-Arbitrage in Financial Economics: Solution of the Mystery of Implied Volatility and S&P 500 Volatility Index

We have shown that classic works of Modigliani and Miller, Black and Scholes, Merton, Black and Cox, and Leland making the foundation of the modern asset pricing theory, are wrong due to misinterpretation of no arbitrage as the martingale no-arbitrage principle. This error explains appearance of the geometric Brownian model (GBM) for description of the firm value and other long-term assets considering the firm and its assets as self-financing portfolios with symmetric return distributions. It contradicts the empirical observations that returns on firms, stocks, and bonds are skewed. On the other side, the settings of the asset valuation problems, taking into account the default line and business securing expenses, BSEs, generate skewed return distributions for the firm and its securities. The Extended Merton model (EMM), taking into account BSEs and the default line, shows that the no-arbitrage principle should be understood as the non-martingale no arbitrage, when for sufficiently long periods both the predictable part of returns and the mean of the stochastic part of returns occur negative, and the value of the return deficit depends on time and the states of the firm and market. The EMM findings explain the problems with the S&P 500 VIX, the strange behavior of variance and skewness of stock returns before and after the crisis of 1987, etc.

Homological dimensions of gentle algebras via geometric models

Let A=kQ/I be a finite-dimensional basic algebra over an algebraically closed field k,which is a gentle algebra with the marked ribbon surface(SA,MA,ΓA).It is known that SAcan be divided into some elementary polygons{Δi|1≤i≤d}byΓA,which has exactly one side in the boundary of SA.Let■(Δi)be the number of sides ofΔibelonging toΓAif the unmarked boundary component of SAis not a side ofΔi;otherwise,■(Δi)=∞,and let f-Δbe the set of all the non-co-elementary polygons and FA(resp.f-FA)be the set of all the forbidden threads(resp.of finite length).Then we have(1)the global dimension of A is max1≤i≤d■(Δi)-1=maxΠ∈FAl(Π),where l(Π)is the length ofΠ;(2)the left and right self-injective dimensions of A are 0,if Q is either a point or an oriented cycle with full relations.masΔi∈f-Δ{1,■(Δi)-1}=max n∈f-F_(A)l(П),otherwise,As a consequence,we get that the finiteness of the global dimension of gentle algebras is invariant under AvellaGeiss(AG)-equivalence.In addition,we get that the number of indecomposable non-projective Gorenstein projective modules over gentle algebras is also invariant under AG-equivalence.

Ablation and geometry change study of solid armature in a railgun

Armature plays an important role in the electromagnetic launch process. Due to the skin effect, the current density distribution is neither uniform on the rail, nor on the armature. High current density centralization in one part could lead to a partial high temperature and make the armature material melt down and be ablated, especially at low velocity. In this paper we try to change the geometry of a Cshaped armature to improve the current density distribution and reduce the ablation. Four variants of C-shaped armatures are designed to study the specific features, including a conventional C-shaped armature （CCA）, a rounded leading edge C-shaped armature （LCA）, a rounded trailing edge C-shaped armature （TCA）, and a rounded incorporate edge C-shaped armature （ICA）. A novel low-speed experiment is constructed and tested. The armatures are ablated and recovered to compare the improved effects. Then finite element simulations according to the experimental results are performed to further analyze the experimental results. It is proved that the current density and hence the temperature distribution can be immensely improved by simply changing the armature geometry. LCA and ICA show that the erosion is more uniform on the contact surface due to the rounded leading edge. The curved trailing edge could improve the uniformity of the current on the interface. ICA which combinesthe effects of LCA and TCA is the best option in the four armatures. How much the leading edge and the trailing edge should be curved involves the geometry of CCA and the posture of the interface on the rail. A saddle shape is a good option to improve the current density and temperature distribution in the throat. Erosion mechanism is analyzed finally. The experiments and simulations support the erosion and transition mechanism. A detailed description of the experiments and simulations is also presented in this paper.