Robust Delaunay Tetrahedronal Meshing Coupled with Advancing Front Method

A full automatic tetrahedronal mesh generation method for arbitrary 3D domains is described. First, the classic Delaunay method is coupled with simplified advancing front technique (AFT) to obtain the boundary mesh. Then, advancing front high quality point placement is used to generate internal points with optimal positions and a Delaunay method is used to insert them efficiently. Finally, optimization procedures are used for mesh quality improvements. Several application examples are presented to demonstrate the robustness and efficiency of the proposed meshing scheme.

The QCD Ground State Chiral Tetrahedron Symmetry

We propose that the exotic meson tetraquark ud~dũintroduced in previous papers, may be a pseudo-Goldstone boson having a tetrahedron geometry and symmetry. The transition from the neutral pion superposition of two free mesons, dd~ and uũ, to the tetrahedron geometry with optional two chiral states may be the symmetry breaking of the QCD ground state. The ud~dũtetrahedron mass may be calculated by measuring the β decay rate variability. We assume that electrons and positrons are composite particle exotic tetraquarks, dũdd~ for the electrons and ud~dd~ for the positrons and confined by the strong force. We propose that the QCD tetrahedrons play a central role in electron pairing mechanism in both chemical bond forming and superconductor Cooper pairs. We propose a hypothesis where the QCD ground state tetrahedrons play a central role in low energy physics where quark exchange reactions between particles and the QCD tetrahedrons via gluon junctions transfer all the forces. The QCD ground state ud~dũtetrahedrons hypothesis provides a symmetry breaking and a mass gap may be created by the ground state QCD tetrahedrons Bose-Einstein condensate.

Three-dimensional hydrodynamic model of concrete tetrahedral frame revetments

Revetments of concrete frame tetrahedrons are being used more and more in river engineering in China. Due to their complex geometry, it is difficult to measure the velocity fields inside them using traditional measurement methods. This limits understanding of their mechanics, potentially leading to suboptimal solutions. A 3-D hydrodynamic model based on the commercial computational fluid dynamics （CFD） code, Fluent, was developed to predict velocity fields and drags. The realizable k-e model was adopted for turbulent closure of the Reynolds averaged Navier Stokes （RANS） equations. The study demonstrates that the numerical model can effectively supplement experimental studies in understanding the complex flow fields and mechanics of concrete frame tetrahedron revetments. Graphs showing the drag coefficient CD versus Reynolds number Re and lift coefficient CL versus Reynolds number Re were produced.

Structure and Pozzolanic Activity of Calcined Coal Gangue during the Process of Mechanical Activation

On the basis of analyzing coal gangue＇s chemical and mineral compositions, the structure change of coal gangue during the mechanical activation was investigated by XRD, FTIR, NMR, and the mechanical strength of the cement doped coal gangue with various specific surface area was tested. The experimental results indicate that, the lattice structure of metakaolin in coal gangue samples calcined at 700 ℃ disorganizes gradually and becomes disordered, and the lattice structure of α-quartz is distorted slightly. The pozzolanic activity of the coal gangue increases obviously with its structural disorganization.

Crystal Structure and Antitumor Activity of Tri[2- [N-(4'-methyl-benzylsulfonyl)amino]ethyl]-amine

The crystal structure of the title compound (C27H38N4O7S3, Mr = 626.79) has been determined by single-crystal X-ray diffraction. The crystal is of triclinic, space group Pīwith a = 9.411(1), b = 11.645(2), c = 14.672(2) , a = 91.80(1), b = 95.36(1), g =104.56(1)o, V = 1547.0 3, Z = 2, Dc = 1.346 g/cm3, l = 0.71073 , m(MoKa) = 0.289 mm-1 and F(000) = 664. The structure was refined to R = 0.0406 and wR = 0.1177 for 4103 observed reflections with I > 2s(I). X-ray diffraction analysis reveals that the title compound is a practically distorted tetrahedron and each molecule contains one lattice H2O by hydrogen bond. The antitumor activity of the title compound against HL-60 human leukemia cells has also been studied by MTT method.

Multipartite Entanglement of a Tetrahedron Lattice

Three-dimensional Heisenberg model in the form of a tetrahedron lattice is investigated. The concurrence and multipartite entanglement are calculated through 2-concurrence C and 4-concurrence C4. The concurrence C and multipartite entanglement G4 depend on different coupling strengths Ji and are decreased when the temperature T is increased. For a symmetric tetrahedron lattice, the concurrence C is symmetric about J1 when J~ is negative while the multipartite entanglement G4 is symmetric about J1 when J2 〈 2. For a regular tetrahedron lattice, the concurrence G of ground state is 1/3 for ferromagnetic case while G = 0 for antiferromagnetic ca.se. However, there is no multipartitc entanglement since C4=0 in a regular tetrahedron lattice. The external magnetic field 13 can increase the maximum value of the concurrence GB and induce two or three peaks in Cn. There is a peak in the multipartite entanglement G4 B when G4B is varied as a function of the temperature T. This peak is mainly induced by the magnetic field B.

The Optical Resolution of Chiral Tetrahedrone-type Clusters Contai- ning SCoFeM (M=Mo or W) Using High Performance Liquid Chromatography Chiral Stationary Phase

Amylose tris (phenylcarbamate) chiral stationary phase (ATPC-CSP) was prepared and used for optical resolution of clusters 1 and 2. n-Hexane/2-propanol ( 99/1; v/v) were found to be the most suitable mobile phase on ATPC-CSP.

Kinematics Analysis of Motion Simulation Subsystem for Unmanned Vehicle

Unmanned vehicle has attracted wide attention and interests throughout the world since it first deputed in the 1960s. However, the experimental methods for unmanned vehicle＇s intelligent behavior, such as semi-physical simulation and motion subsystem, have not been widely explored. First, the requirements of the motion subsystem in unmanned vehicle semi-physical facility are analyzed, and a six DOF parallel manipulator is selected to reproduce the pose of the vehicle. The link lengths of the motion subsystem are worked out under the given rotational angles of the vehicle. According to the geometric properties of tetrahedron, three joint positions of the top platform are determined, and the rest are obtained from the first three position vectors. Six constraint equations are set up based on the vertices on the top platform and the link lengths. In order to solve the six angle variables, a numerical algorithm built on the Newton-Raphson iterative method is presented, which is based on Taylor series expansion of six constraint equations. The pose of the top platform is ultimately calculated. The eigenvalues of the top platform are solved to obtain the natural frequencies of the motion subsystem. The coordinates of six joint centers on the top platform and six constraint equations can be realized by simple algebraic manipulation, which allows significant abbreviation in the formulation and provides a systematic way of obtaining the kinematic solution of the parallel manipulator. A numerical example is given and its efficacy is demonstrated by the inverse kinematics. The computation strategy based on tetrahedron method and Newton-Raphson iterative method provide a simple and cost-effective method for solving forward kinematics of six DOF parallel manipulators, and this method sheds light on other parallel manipulators.

Discrete Differential Geometry of <i>n</i>-Simplices and Protein Structure Analysis

This paper proposes a novel discrete differential geometry of n-simplices. It was originally developed for protein structure analysis. Unlike previous works, we consider connection between space-filling n-simplices. Using cones of an integer lattice, we introduce tangent bundle-like structure on a collection of n-simplices naturally. We have applied the mathematical framework to analysis of protein structures. In this paper, we propose a simple encoding method which translates the conformation of a protein backbone into a 16-valued sequence.

A New Kind of Conjugate-nested Central Configurations in Consisted of One Regular Tetrahedron and One Regular Octahedron

A new case configuration in R^3, the conjugate-nest consisted of one regular tetrahedron and one regular octahedron is discussed. If the configuration is a central configuration, then all masses of outside layer are equivalent, the masses of inside layer are also equivalent. At the same time the following relation between ρ（r =√3/3ρ is the radius ratio of the sizes） and mass ratio τ=~↑m/m must be satisfied τ=~↑m/m=ρ（ρ＋3）（3＋2ρ＋ρ^2）^-3/2＋ρ（-ρ＋3）（3-2ρ＋ρ^2）^-3/2-4.2^-3/2ρ^-2-^-1ρ^-2/2（1＋ρ）（3＋2ρ＋ρ^2）^-3/2＋2（ρ-1）（3-2ρ＋ρ^2）^-3/2-4（2√2）^-3ρ, and for any mass ratio τ, when mass ratio r is in the open interval （0, 0.03871633950 ... ）, there exist three central configuration solutions（the initial configuration conditions who imply hamagraphic solutions） corresponding radius ratios are r1, r2, and r3, two of them in the interval （2.639300779… , ＋∞） and one is in the interval （0.7379549890…, 1.490942703… ）. when mass ratio τ is in the open interval （130.8164950… , ＋∞）, in the same way there have three corresponding radius ratios, two of them in the interval （0, 0.4211584789... ） and one is in the interval （0.7379549890…, 1.490942703…）. When mass ratio τ is in the open interval （0.03871633950…, 130.8164950…）, there has only one solution r in the interval （0.7379549890…, 1.490942703… ）.

Un-thorough Delaunay Approach for Tetrahedral Mesh Generation

An integrated tetrahedrization algorithm in 3D domain which combines the Delaunay tetrahedral method with un-Delaunay tetrahedral method is described. The algorithm was developed by constructing Delaunay Tetrahedrons from a scattered point set, recovering boundaries using Delaunay and un-Delaunay method, inserting additional nodes in unsuitable tetrahedrons, optimizing tetrahedrons and smoothing the tetrahedral mesh with the 2D-3D Laplacian method. The algorithm has been applied to the injection molding CAE preprocessing.

Tetrahedral DNA Nanostructure-modified Gold Nanorod-based Anticancer Nanomaterials for Combined Photothermal Therapy and Chemotherapy

Objective To develop an effective treatment strategy to simultaneously avoid fatal adverse effects in the treatment of oral cancer,combination therapy has been explored because of its multiple functions.This work aims to develop a novel type of gold-nanorod-based nanomaterials decorated with tetrahedral DNA nanostructures(TDN)carrying antitumor drugs,namely,GNR@TDN-DOX nanocomposites.Methods In the designed structure,TDN,with a three-dimensional geometry composed of DNA strands,can provide GC base pairs for binding with the anticancer drug doxorubicin(DOX).The photothermal heating properties,biocompatibility properties,and antitumor performance of obtained GNR@TDN-DOX nanocomposites were investigated to assess their application potential in tumor treatment.Results Systematic studies have shown that the obtained GNR@TDN-DOX nanocomposites have high photothermal conversion under the illumination of an 808-nm infrared laser,leading to effective antitumor applications.In addition,the cell viability study shows that GNR@TDN-DOX nanocomposites have good biocompatibility.In vitro studies based on A375 cells show that the GNR@TDN-DOX nanocomposites can effectively eliminate cancer cells because of the combination of photothermal therapy induced by GNRS and chemotherapy induced by TDN-carrying DOX.The result shows that the obtained GNR@TDN-DOX nanocomposites have efficient cellular uptake and lysosome escape ability,together with their nuclear uptake behavior,which results in a significant antitumor effect.Conclusion This work has demonstrated a potential nanoplatform for anticancer applications.

Synthesis and Crystal Structure of a Novel Tetravanadate Modified by Chiral Racemoid Zirconium Complex

[Zr（phen）4（H2O）4O2（V4O12）]（phen）2 1 （phen = 1,10-phenanthroline） was synthesized under hydrothermal condition. The crystal of 1 belongs to triclinic, space group P1^- with a = 10.6334（8）, b = 11.9201（8）, c = 14.6505（10） A, α = 69.9980（10）, β = 84.9240（10）, γ = 84-1300（10）°, V = 1733.0（2） A^3, Z = 1, Mr = 1672.27, Dc = 1.602 g/cm^3, C72H56N12O18V4Zr, F（000） = 848, μ（MoKa） = 0.747 mm^-1, S = 0.957, R = 0.0504 and wR = 0.1173 for 4011 observed reflections （1 〉 20（I））. The crystal structure of 1 could be discussed in terms of {Zr（phen）2（H2O）2O2}, un-coordinated 1,10-phenanthroline molecules and { V4O12 } unit. In { Zr（phen）2（H2O）2O2 }, the coordination geometry of zirconium is a dodecahedron, but {V4O12} unit is constructed from four apex-sharing {VO4} tetrahedra. Furthermore, {V4O12} links with two {Zr（phen）2（H2O）2O2} units via two bridging oxygen atoms. Interestingly, the two {Zr（phen）2（H2O）2O2} units display D- and L-enantiomers, respectively, upon which the whole molecule represents a racemoid configuration.

Eight-body central configuration for conjugate-nested regular tetrahedrons

The sufficient and necessary conditions, the existence and uniqueness of a new class of central configuration in R^3, for the conjugate-nest consisting of two regular tetrahedrons, are proved. If the configuration is a central configuration, then all masses of outside layer are equivalent, and the masses of inside layer are also equivalent. At the same time p （the ratio of the sizes） and mass ratio τ=m^/m must be satisfied by some formulas. For any radius ratios ρ∈（0, 0.152996 918 2） or （0.715 223 148 7, 1.398 165 037）, there is only one central configuration. Otherwise, for any given mass ratio τ, there may exist more than one central configuration.

STUDY ON MAXIMUM HYDROGEN CAPACITY FOR Zr-Ni AMORPHOUS ALLOY

To design the amorphous hydrogen storage alloy efficiently, the maximum hydrogen capacities for Zr - Ni amorphous alloy were calculated. Based on the Rhomb Unit Structure Model(RUSM) for amorphous alloy and the experimental result that hydrogen atoms exist in 3Zr1Ni and 4Zr tetrahedron interstices in Zr-Ni amolphous alloy, the numbers of 3Zr-1Ni and 4Zr tetrahedron interstices in a RUSM were calculated which correspond to the hydrogen capacity. The two extremum Zr distribution states were calculated, such as highly heterogeneous Zr distribution and homogeneous Zr distribution. The calculated curves of hydrogen capacity with different Zr contents at two states indicate that the hydrogen capacity increases with increasing Zr content and reaches its maximum when Zr is 75%. The theoretical maximum hydrogen capacity for Zr - Ni amorphous alloy is 2.0 (H/M). Meanwhile, the hydrogen capacity of heterogenous Zr distribution alloy is higher than that of homogenous one at the same Zr content. The experimental results prove the calculated results reasonable, and accordingly, the experimental results that the distribution of Zr atom in amorphous alloy occur heterogeneous after a few hydrogen absorption desorption cycles can be explained.

Examples of Cable-Bar Modular Structures Based on the Class-Theta Tensegrity Systems

The relationship between forms and forces is one of the main topics of structural morphology. This harmonious coexisting link is very strong for systems in tensegrity state, commonly called ＂tensegrity systems＂. It is currently apparent that, among the tensegrity systems, there also exist cable-bar cells with a discontinuous network of cables. It is possible to design a separate set of cables inside the cable-bar elementary cell and to establish a self-stress state of equilibrium. In this connection, the author of this paper suggested to assume a new Class-Theta tensegrity systems. Each of the basic tensegrity systems termed Class-Theta possesses an external and internal set of tension components. The shape of Greek capital letter 69 （Theta） reflects two sets of such components （two sets of tendons, cables, etc.）. This notation corresponds to Skelton＇s Class-k tensegrity structure. As shown in this paper, the Class-Theta tensegrity cell can exemplify a geometrically and practically useful form for the lightweight and long-span modular structures, mainly but not only in view of civil engineering and architecture.

Preliminary Discussion on the Refinement Mesh Generation for Adaptive Analysis

In recent years, due to the rapid development of computer hardware and the urgent need of complex engineering problems, great support has been provided in the related fields of unstructured mesh generation. A large number of research results show that the adaptive analysis is an effective way to improve the efficiency and precision of the numerical calculation. The reliable error estimation and the powerful mesh generation are two key problems in the process of adaptive numerical analysis. H-type refinement strategy adding the new nodes in the high error area, gradually refines the mesh to reduce the size of the element to achieve the purpose of mesh adaptation;this strategy is simple, intuitive and easy to program. Although the calculation accuracy of unstructured triangle and tetrahedron elements is not high, these elements are suitable for discretization of any complex problem domain, and have a wider range of application in academic and engineering fields.

Numerical Experiment for Dipole-Dipole Interaction in Electro-Magnetism with Help of a Regular Tetrahedron

Aim of this work is to try to explain, on a Rational basis, some equations of Electro-Magnetism, which are based on Experimental data. Any Electric Field can produce a Field of many small Electric Dipoles, continuously distributed in space. In a region, where the Electric Field is constant, in direction and magnitude, all the small Dipoles are parallel to the Electric Field, and are represented by a single, long, parallel to them, fixed in space, Electric Dipole, which is here called Compass. An Alternating current, in a straight Conductor, is studied, by a simple, short computer program, for step-by-step nonlinear dynamic analysis. It is found that, only an Alternating current, not a direct current, can produce an Electric Dipole, in a straight Conductor. The two above Dipoles (Compass-Conductor) are assumed with equal lengths &#8467;, lying on two skew lines, perpendicular to each other, at a distance &#8467;√2, thus forming, by their four ends, a Regular Tetrahedron, with side length &#8467;. Repulsion, between Like Charges, obeys the simple Coulomb Electro-Static law. Whereas Interaction (Attraction or Repulsion), between Unlike Charges, obeys a more accurate Lennard-Jones law. The analysis of Dipole-Dipole (Compass-Conductor) Interaction is performed by hand calculator. The only out-of-balance forces, in the regular Tetrahedron, acting on the Rigid Conductor, are the so-called magnetic forces. Their direction is found, in a simple Rational way, with help of Regular Tetrahedron, without recoursing to a “right-hand-rule”. The proposed model is applied to 1) The force acting on an Electric Charge moving in a magnetic field. 2) The force acting on a Current carrying straight Conductor, due to a magnetic field. 3) The magnetic fields created around a Current carrying straight Conductor. In these applications, proposed model gives reasonable results. Particularly, in third application, results, obtained by proposed model, are found in satisfactory approximation with corresponding ones, obtained by an empirical formula, based on relevant Experimental observations of H.-C. Oersted and A.-M. Ampère. So, the reliability of proposed model is checked. Position and direction of magnetic field vector coincide with those of a corresponding fixed Compass of a constant Electric Field. Main point of present work is that, without introducing the concept of a magnetic field vector, by combining field of dipoles, produced by an electric field, with dipole of an alternating current carrying conductor, the magnetic forces can be determined.

An Upwind Finite Volume Element Method for Nonlinear Convection Diffusion Problem

A class of upwind finite volume element method based on tetrahedron partition is put forward for a nonlinear convection diffusion problem. Some techniques, such as calculus of variations, commutating operators and the a priori estimate, are adopted. The a priori error estimate in L2-norm and H1-norm is derived to determine the error between the approximate solution and the true solution.

A Research for a Division of Regular Polyhedron by Rhombic Dodecahedron

Abstract：A space-filling polyhedron is a polyhedron which ＇tile＇ space, analogous to the way of certain polygons tiled the plane. The cube is the unique space-filling platonic solid. If we make line connections the center with the vertices in the certain cube, the cube is divided into six pyramids. And if we glued six pyramids to the faces of the cube, we obtain a ＇rhombic dodecahedron＇. Since cubes are packing a space, rhombic dodecahedra are also space-filling polyhedra and a rhombic dodecahedron is divided into two regular tetrahcdra and one regular octahedron. In this study, we present how rhombic dodecahedron can be split into tetrahedra and octahedron. In this process, we can research a variety of divisions of regular polyhedron.