Modeling of Geometric Variations Within Three-Dimensional Tolerance Zones

A tolerance modeling method of geometric variations within three-dimensional(3D) tolerance domain is proposed.According to the classification method of feature variations and classes of invariance or symmetry in the new generation Geometrical Product Specifications(GPS) system,the proposed method is based on the Small Displacement Torsor(SDT) concept,and SDT is used to represent the geometric deviations between the nominal feature and the fitting feature. Furthermore,the variation zones of several kinds complex or irregular geometric features are constructed,and the corresponding tolerance modeling methods are discussed respectively. Finally,an example is presented to verify the efficiency of the presented method for modeling 3D dimensional and geometrical tolerances.The proposed modeling method based on the complete mathematical foundation conforms with the design philosophy and principle of the new generation GPS standards system.

Oxygen tension modulates cell function in an in vitro three-dimensional glioblastoma tumor model

Hypoxia is a typical feature of the tumor microenvironment,one of the most critical factors affecting cell behavior and tumor progression.However,the lack of tumor models able to precisely emulate natural brain tumor tissue has impeded the study of the effects of hypoxia on the progression and growth of tumor cells.This study reports a three-dimensional(3D)brain tumor model obtained by encapsulating U87MG(U87)cells in a hydrogel containing type I collagen.It also documents the effect of various oxygen concentrations(1%,7%,and 21%)in the culture environment on U87 cell morphology,proliferation,viability,cell cycle,apoptosis rate,and migration.Finally,it compares two-dimensional(2D)and 3D cultures.For comparison purposes,cells cultured in flat culture dishes were used as the control(2D model).Cells cultured in the 3D model proliferated more slowly but had a higher apoptosis rate and proportion of cells in the resting phase(G0 phase)/gap I phase(G1 phase)than those cultured in the 2D model.Besides,the two models yielded significantly different cell morphologies.Finally,hypoxia(e.g.,1%O2)affected cell morphology,slowed cell growth,reduced cell viability,and increased the apoptosis rate in the 3D model.These results indicate that the constructed 3D model is effective for investigating the effects of biological and chemical factors on cell morphology and function,and can be more representative of the tumor microenvironment than 2D culture systems.The developed 3D glioblastoma tumor model is equally applicable to other studies in pharmacology and pathology.

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.

Quantum geometric tensor and the topological characterization of the extended Su-Schrieffer-Heeger model

We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger(SSH)model with long-range hopping terms.By computing the quantum geometry tensor,we derive exact expressions for the quantum metric and Berry curvature of the energy band electrons,and we obtain the phase diagram of the model marked by the first Chern number.Furthermore,we also obtain the topological Euler number of the energy band based on the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone.However,some regions where the Berry curvature is identically zero in the first Brillouin zone result in the degeneracy of the quantum metric,which leads to ill-defined non-integer topological Euler numbers.Nevertheless,the non-integer"Euler number"provides valuable insights and an upper bound for the absolute values of the Chern numbers.

Three-dimensional structural models,evolution and petroleum geological significances of transtensional faults in the Ziyang area,central Sichuan Basin,SW China

With drilling and seismic data of Transtensional(strike-slip)Fault System in the Ziyang area of the central Sichuan Basin,SW China plane-section integrated structural interpretation,3-D fault framework model building,fault throw analyzing,and balanced profile restoration,it is pointed out that the transtensional fault system in the Ziyang 3-D seismic survey consists of the northeast-trending F_(I)19 and F_(I)20 fault zones dominated by extensional deformation,as well as 3 sets of northwest-trending en echelon normal faults experienced dextral shear deformation.Among them,the F_(I)19 and F_(I)20 fault zones cut through the Neoproterozoic to Lower Triassic Jialingjiang Formation,presenting a 3-D structure of an“S”-shaped ribbon.And before Permian and during the Early Triassic,the F_(I)19 and F_(I)20 fault zones underwent at least two periods of structural superimposition.Besides,the 3 sets of northwest-trending en echelon normal faults are composed of small normal faults arranged in pairs,with opposite dip directions and partially left-stepped arrangement.And before Permian,they had formed almost,restricting the eastward growth and propagation of the F_(I)19 fault zone.The F_(I)19 and F_(I)20 fault zones communicate multiple sets of source rocks and reservoirs from deep to shallow,and the timing of fault activity matches well with oil and gas generation peaks.If there were favorable Cambrian-Triassic sedimentary facies and reservoirs developing on the local anticlinal belts of both sides of the F_(I)19 and F_(I)20 fault zones,the major reservoirs in this area are expected to achieve breakthroughs in oil and gas exploration.

A three-dimensional numerical study on the effect of geometric asymmetry on arcjet thruster performance

In an arcjet thruster,the cathode and constrictor degrade with time,and the electrical arc discharge may become unsymmetrical.In this work,a three-dimensional numerical model of a hydrogen plasma arcjet is developed and validated to study the effect of unsymmetrical electric arc discharge on thruster performance.The unsymmetrical arc discharge is realized by introducing a radial shift of the cathode so that the cathode tip offset is 80μm(25%of the constrictor radius).Simulations are conducted for both axially centered cathode(coaxial)and off-centered cathode(non-coaxial)configurations with identical propellant flow rates and input current.Simulations show asymmetrical arc discharge in the non-coaxial cathode configuration,resulting in azimuthally asymmetric Joule heating,species concentrations,and velocity field.This asymmetry continues as the plasma expands in the divergent section of the nozzle.Temperature,species concentrations,and axial velocity exhibit asymmetric radial distribution at the nozzle exit.The computed Joule heating was found to reduce with cathode shift,and consequently,the thrust and specific impulse of the thruster was decreased by about 6.6%.In the case of the non-coaxial cathode,geometric asymmetry also induces a small side thrust.

Permeability differences based on three-dimensional geometrical information of void spaces

In this study,the permeabilities of Berea and Otway sandstones were measured under different confining pressures,and porosity was investigated through mercury intrusion porosimetry(MIP).The total porosities of the Berea and Otway sandstones were approximately 17.4%and 25%,respectively.Pore size distributions of each sandstone were almost the same,but the pores in the Otway sandstone were slightly narrower.However,the permeability of the Otway sandstone was smaller than that of the Berea sandstone by one order of magnitude.Three-dimensional(3D)void geometry and geometrical properties of the void spaces relevant to flow were compared to obtain the relation between the permeability differences and porosities of the two sandstones.The 3D geometrical analysis using microfocus X-ray computed tomography(CT)was performed,and the pore geometries of both sandstones were compared using the 3D medial axis(3DMA)method.Pore and throat radii,pore coordination number,tortuosity,number of connecting paths,connecting path volume,and other factors were determined using 3DMA.The Otway sandstone was characterized by a small effective throat/pore radius ratio.Based on the fluid flow mechanism,the lower effective throat/pore radius ratio results in a lower permeability induced by the fluid energy loss,which means that the 3D geometrical shape of void spaces affects the permeability value.

Geometric Modeling of Rape (Brassica napus L.) during Seedling Stage

[Objective] The paper was to study the geometric modeling of rape（Brassica napus L.） during seedling stage.[Method] Based on the analysis and observation of morphological structure and growth process of rape during seedling stage,a characteristic parameters-based three-dimensional mathematical model of rape and its visible method was proposed.The individual control parameters were extracted according to the morphological structures of various organs of rape.Different sizes of leaf and petiole model were constructed by using cubic Bézier surface.The cylinder with different upper and lower bottom area was adopted as the main stem model.Finally,three-dimensional reconstruction of whole Rape plant during seedling stage was achieved through the operations of rotation,scaling and splicing.[Result] This method had certain controllability,which was also easy and convenient,and could quickly use to build the geometric model of rape during seedling stage.[Conclusion] The results provided reference for study on structural model of rape.

Evaluation of the effect of geometrical parameters on stope probability of failure in the open stoping method using numerical modeling

Stress-induced failure is among the most common causes of instability in Canadian deep underground mines.Open stoping is the most widely practiced underground excavation method in these mines,and creates large stopes which are subjected to stress-induced failure.The probability of failure(POF)depends on many factors,of which the geometry of an open stope is especially important.In this study,a methodology is proposed to assess the effect of stope geometrical parameters on the POF,using numerical modelling.Different ranges for each input parameter are defined according to previous surveys on open stope geometry in a number of Canadian underground mines.A Monte-Carlo simulation technique is combined with the finite difference code FLAC3D,to generate model realizations containing stopes with different geometrical features.The probability of failure(POF)for different categories of stope geometry,is calculated by considering two modes of failure;relaxation-related gravity driven(tensile)failure and rock mass brittle failure.The individual and interactive effects of stope geometrical parameters on the POF,are analyzed using a general multi-level factorial design.Finally,mathematical optimization techniques are employed to estimate the most stable stope conditions,by determining the optimal ranges for each stope’s geometrical parameter.

DEVELOPMENT OF A HYBRID MODEL FOR THREE-DIMENSIONAL GIS

This paper presents a hybrid model for three-dimensional Geographical Information Systems which is an integration of surface- and volume-based models. The Triangulated Irregular Network (TIN) and octree models are integrated in this hybrid models. The TIN model works as a surface-based model which mainly serves for surface presentation and visualization. On the other hand, the octree encoding supports volumetric analysis. The designed data structure brings a major advantage in the three-dimensional selective retrieval. This technique increases the efficiency of three-dimensional data operation.

A three-dimensional semi-implicit unstructured grid finite volume ocean model

A new three-dimensional semi-implicit finite-volume ocean model has been developed for simulating the coastal ocean circulation, which is based on the staggered C-unstructured non-orthogonal grid in the hor- izontal direction and z-level grid in the vertical direction. The three-dimensional model is discretized by the semi-implicit finite-volume method, in that the free-surface and the vertical diffusion are semi-implicit, thereby removing stability limitations associated with the surface gravity wave and vertical diffusion terms. The remaining terms in the momentum equations are discretized explicitly by an integral method. The partial cell method is used for resolving topography, which enables the model to better represent irregular topography. The model has been tested against analytical cases for wind and tidal oscillation circulation, and is applied to simulating the tidal flow in the Bohal Sea. The results are in good agreement both with the analytical solutions and measurement results.

Three-dimensional numerical modeling of gravity anomalies based on Poisson equation in spacewavenumber mixed domain

In gravity-anomaly-based prospecting, the computational and memory requirements for practical numerical modeling are potentially enormous. Achieving an efficient and precise inversion for gravity anomaly imaging over large-scale and complex terrain requires additional methods. To this end, we have proposed a new topography-capable By performing a two-dimensional Fourier transform in the horizontal directions, threedimensional partial differential equations in the spatial domain were transformed into a group of independent, one-dimensional differential equations engaged with different wave numbers. These independent differential equations are highly parallel across different wave numbers. differential equations with different wave numbers, and the efficiency of solving fixedbandwidth linear equations was further improved by a chasing method. In a synthetic test, a prism model was used to verify the accuracy and reliability of the proposed algorithm by comparing the numerical solution with the analytical solution. We studied the computational precision and efficiency with and without topography using different Fourier transform methods. The results showed that the Guass-FFT method has higher numerical precision, while the standard FFT method is superior, in terms of computation time, for inversion and quantitative interpretation under complicated terrain.

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.

Three-dimensional cell culture systems as an in vitro platform for cancer and stem cell modeling

Three-dimensional(3D)culture systems are becoming increasingly popular due to their ability to mimic tissue-like structures more effectively than the monolayer cultures.In cancer and stem cell research,the natural cell characteristics and architectures are closely mimicked by the 3D cell models.Thus,the 3D cell cultures are promising and suitable systems for various proposes,ranging from disease modeling to drug target identification as well as potential therapeutic substances that may transform our lives.This review provides a comprehensive compendium of recent advancements in culturing cells,in particular cancer and stem cells,using 3D culture techniques.The major approaches highlighted here include cell spheroids,hydrogel embedding,bioreactors,scaffolds,and bioprinting.In addition,the progress of employing 3D cell culture systems as a platform for cancer and stem cell research was addressed,and the prominent studies of 3D cell culture systems were discussed.

Three-Dimensional Tidal Model and Its Application to Numerical Simulation of Water Quality in Coastal Waters

The turbulence mechanism plays an important part in the mixing process and momentum transfer of turbulence. A three-dimensional Prandtl mixing length tidal model has been developed to simulate tidal flows and water quality. The eddy viscosities and diffusivities are computed from the Prandtl mixing length model. In order to model the water quality of an estuary or coastal area many interdependent processes need to be simulated. These may be conveniently separated into three main groups: transport and mixing processes, biochemical interaction of water quality variables and the utilization and re-cycling of nutrients by living matter. The model simulates full oxygen and nutrient balance, primary productivity and the transport, reaction mechanism and fate of pollutants over tidal time-scales. The model is applied to numerical simulation of tidal flows and water quality in Dalian Bay. The model has been calibrated against a limited data set of historical water quality observations and in general demonstrates excellent agreement with all available data.

Three-dimensional land FD-CSEM forward modeling using edge finite-element method

A modeling tool for simulating three-dimensional land frequency-domain controlled-source electromagnetic surveys,based on a finite-element discretization of the Helmholtz equation for the electric fields,has been developed.The main difference between our modeling method and those previous works is edge finite-element approach applied to solving the three-dimensional land frequency-domain electromagnetic responses generated by horizontal electric dipole source.Firstly,the edge finite-element equation is formulated through the Galerkin method based on Helmholtz equation of the electric fields.Secondly,in order to check the validity of the modeling code,the numerical results are compared with the analytical solutions for a homogeneous half-space model.Finally,other three models are simulated with three-dimensional electromagnetic responses.The results indicate that the method can be applied for solving three-dimensional electromagnetic responses.The algorithm has been demonstrated,which can be effective to modeling the complex geo-electrical structures.This efficient algorithm will help to study the distribution laws of3-D land frequency-domain controlled-source electromagnetic responses and to setup basis for research of three-dimensional inversion.

The study on three-dimensional numerical model and fronts of the Jiulong Estuary and the Xiamen Bay

Applying the methods of on-site observation and dynamic model, the research on the fronts at the Jiulong Estuary has been carried out, during which spatial and temporal distribution, dynamic characteristics and formation mechanism of salinity fronts are analyzed and discussed. The research shows that the estuarine fronts mainly lie in the area from the Jiyu Islet to the Haimen Island, outside of Yuweizai to Hulishan cross-section, the near coast of Yuweizai and the south of the Songyu-Gulangyu Channel. The fronts in the former two regions are formed directly by plume, while the one near the coast of Yuweizai is a tidal intrusion front caused by flood current and the one at the south of the Songyu-Gulangyu Channel is the result of current shear transformation. Under normal circumstances, fresh water of the Jiulong River mainly influences the inside of the Xiamen Bay, and when it is in typhoon seasons, plume front can affect the Taiwan Strait and has an effect on the biogeochemical Drocesses in the strait.

Failure Impact,Availability and Cost Analysis of PONs Based on a Network Geometric Model

Passive Optical Networks(PONs)are considered as the preferred solution for broadband fibre-based access networks.This is because PONs present low cost deployment,low energy consumption and also meet high bandwidth demands from end users.In addition,end users expect a high availability for access networks,while operators are more concerned about reducing the failure impact(number of clients affected by failures).Moreover,operators are also interested in reducing the cost of the access network.This paper provides a deep insight into the consequences that the physical topology and design decisions cause on the availability,the failure impact and the cost of a PON.In order to do that,the physical layout of the PON deployment area is approximated by a network geometric model.A PON deployed according to the geometric model is then assessed in terms of failure impact,availability and cost.This way,the effects of different design decisions and the physical layout on these three parameters are evaluated.In addition,the tradeoffs between availability,failure impact and cost caused by planning decisions and the physical topology are identified and pinpointed.

Microstructure modeling and virtual test of asphalt mixture based on three-dimensional discrete element method

The objective of this work is to model the microstructure of asphalt mixture and build virtual test for asphalt mixture by using Particle Flow Code in three dimensions(PFC^(3D))based on three-dimensional discrete element method.A randomly generating algorithm was proposed to capture the three-dimensional irregular shape of coarse aggregate.And then,modeling algorithm and method for graded aggregates were built.Based on the combination of modeling of coarse aggregates,asphalt mastic and air voids,three-dimensional virtual sample of asphalt mixture was modeled by using PFC^(3D).Virtual tests for penetration test of aggregate and uniaxial creep test of asphalt mixture were built and conducted by using PFC^(3D).By comparison of the testing results between virtual tests and actual laboratory tests,the validity of the microstructure modeling and virtual test built in this study was verified.Additionally,compared with laboratory test,the virtual test is easier to conduct and has less variability.It is proved that microstructure modeling and virtual test based on three-dimensional discrete element method is a promising way to conduct research of asphalt mixture.

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.