Non Degeneration of Fibonacci Series, Pascal’s Elements and Hex Series

Generally Fibonacci series and Lucas series are the same, they converge to golden ratio. After I read Fibonacci series, I thought, is there or are there any series which converges to golden ratio. Because of that I explored the inter relations of Fibonacci series when I was intent on Fibonacci series in my difference parallelogram. In which, I found there is no degeneration on Fibonacci series. In my thought, Pascal triangle seemed like a lower triangular matrix, so I tried to find the inverse for that. In inverse form, there is no change against original form of Pascal elements matrix. One day I played with ring magnets, which forms hexagonal shapes. Number of rings which forms Hexagonal shape gives Hex series. In this paper, I give the general formula for generating various types of Fibonacci series and its non-degeneration, how Pascal elements maintain its identities and which shapes formed by hex numbers by difference and matrices.

On the radiogenic heat production of igneous rocks

Radiogenic heat production is a physical parameter crucial to properly estimating lithospheric temperatures and properly understanding processes related to the thermal evolution of the Earth. Yet heat production is, in general, poorly constrained by direct observation because the key radiogenic elements exist in trace amounts making them difficulty image geophysically. In this study, we advance our knowledge of heat production throughout the lithosphere by analyzing chemical analyses of 108,103 igneous rocks provided by a number of geochemical databases. We produce global estimates of the average and natural range for igneous rocks using common chemical classification systems. Heat production increases as a function of increasing felsic and alkali content with similar values for analogous plutonic and volcanic rocks. The logarithm of median heat production is negatively correlated(r^2=0.98)to compositionally-based estimates of seismic velocities between 6.0 and 7.4 km s^(-1), consistent with the vast majority of igneous rock compositions. Compositional variations for continent-wide models are also well-described by a log-linear correlation between heat production and seismic velocity. However, there are differences between the log-linear models for North America and Australia, that are consistent with interpretations from previous studies that suggest above average heat production across much of Australia. Similar log-linear models also perform well within individual geological provinces with^1000 samples. This correlation raises the prospect that this empirical method can be used to estimate average heat production and natural variance both laterally and vertically throughout the lithosphere. This correlative relationship occurs despite a direct causal relationship between these two parameters but probably arises from the process of differentiation through melting and crystallization.

Second Generation Wavelet Finite Element and Rotor Cracks Quantitative Identification Method

The presence of cracks in the rotor is one of the most dangerous and critical defects for rotating machinery. Defect of fatigue cracks may lead to long out-of-service periods, heavy damages of machines and severe economic consequences. With the method of finite element, vibration behavior of cracked rotors and crack detection was received considerable attention in the academic and engineering field. Various researchers studied the response of a cracked rotor and most of them are focused on the crack detection based on vibration behavior of cracked rotors. But it is often difficult to identify the crack parameters quantitatively. Second generation wavelets （SGW） finite element has good ability in modal analysis for singularity problems like a cracked rotor. Based on the fact that the feature of SGW could be designed depending on applications, a multiresolution finite element method is presented. The new model of SGW beam element is constructed. The first three natural frequencies of the rotor with different crack location and size were solved with SGW beam elements, and the database for crack diagnosis is obtained. The first three metrical natural frequencies are employed as inputs of the database and the intersection of the three frequencies contour lines predicted the normalized crack location and size. With the Bently RK4 rotor test rig, rotors with different crack location and size are tested and diagnosed. The experimental results denote the cracks quantitative identification method has higher identification precision. With SGW finite element method, a novel method is presented that has higher precision and faster computing speed to identify the crack location and size.

METHOD FOR ADAPTIVE MESH GENERATION BASED ON GEOMETRICAL FEATURES OF 3D SOLID

In order to provide a guidance to specify the element size dynamically during adaptive finite element mesh generation, adaptive criteria are firstly defined according to the relationships between the geometrical features and the elements of 3D solid. Various modes based on different datum geometrical elements, such as vertex, curve, surface, and so on, are then designed for generating local refined mesh. With the guidance of the defmed criteria, different modes are automatically selected to apply on the appropriate datum objects to program the element size in the local special areas. As a result, the control information of element size is successfully programmed covering the entire domain based on the geometrical features of 3D solid. A new algorithm based on Delatmay triangulation is then developed for generating 3D adaptive finite element mesh, in which the element size is dynamically specified to catch the geometrical features and suitable tetrahedron facets are selected to locate interior nodes continuously. As a result, adaptive mesh with good-quality elements is generated. Examples show that the proposed method can be successfully applied to adaptive finite element mesh automatic generation based on the geometrical features of 3D solid.

On conversion of plastic work to heat during plastic deformation of tin-lead alloy and mild steel

The temperature rise caused by plastic deformation during the quick upsetting of tin-lead alloy and mild steel was investigated via experiments and numerical simulations aiming at a better understanding of the heat generation mechanism in friction welding. The results show that the compression amount and deformation temperature influence significantly the temperature rise during the upsetting of tin-lead alloy. The temperature rise increases with increasing the compression but decreases with increasing the deformation temperature. The simulation results are in good agreement with the experimental inspection for Sn63A alloy. The simulation results of mild steel present a similar tendency with tin-lead alloy. Moreover, the temperature rise of mild steel at elevated temperatures is comparable to that of tin-lead alloy at low temperatures.

Measurements of Pulsed 532 nm Laser Breakdown Spectroscopy of Synthesized Magnetite Nanoferrofluid

We describe the results of 532 nm pulse laser-induced breakdown spectroscopy (LIBS) of two samples of magnetite nanoparticles (SPIONs) nanoferrofluid synthesized at room (S1) and elevated temperatures (S2) and at three different laser energy levels and pulse frequency. The size of magnetite nanoparticles, size distribution, magnetic crystalline phase and magnetization were analyzed and measured using transmission electron microscopy (TEM), X-ray diffraction spectroscopy (XRD) and vibrating sample magnetometry (VSM). The SPIONs showed a distribution between 4 - 22 nm with a peak about 12 nm and saturation magnetization of about 65 emu/g. The Saha-Boltzmann analysis of spectra for medium energy level (1050 mJ) yields plasma temperatures of (3881 ± 200) K and (26,047 ± 200) K for Fe I and OV as the lowest and highest temperatures respectively. A range of corresponding electron density (Ne-) of (0.47 - 6.80) × 1020, (0.58 - 8.30) × 1020 and (0.69 - 9.96) × 1020 cm-3?were determined at 860, 1050 and 1260 mJ respectively using the estimated CCD pictures. The results confirmed a higher elements ratio for S1 than S2 and the signal intensity indicated a non-linear behaviour as a function of pulse frequency with the maximum ratio value at 3 Hz. At higher frequency of 6 Hz no such turning point was observed. The highest and lowest temperatures corresponded to Fe I and OV respectively. The LIBS technique can be utilized to study, characterize and determine the elements ratio required in most applications involving the synthesizing process.

A Modified Paving Approach and Automatic Mesh Grading Method to Quadrilateral Mesh Generation

A modified paving technique for automatic generation of all-quadrilateral mesh fromarbitrary 2-D geometry is presented. The generated mesh elementS are nearly square andperpendicular to boundaries. Aner the nodes and elementS formation is completed. a fully automaticgrading method is applied to increase the accuracy and reliability of engineering analysis. In thispaper, we mainly describe the theory of mathematical algorithm and present some examples ofautomatically generated mesh.

密云水库上游不同造林树种叶片-凋落物-土壤生态化学计量特征

平原生态林作为北京人工林生态系统的重要组成部分,探究其生态化学计量特征是揭示平原造林后森林生态系统物质周转和养分循环等生态功能的关键。本研究以北京市密云水库上游平原生态林区域的刺槐、侧柏、臭椿和白榆4种林分为对象,采用野外取样和室内实验分析相结合的方法,研究4种造林树种叶片-凋落物-土壤的碳(C)、氮(N)和磷(P)生态化学计量特征及其相关性。结果显示:4种树种叶片、凋落物和土壤中C、N和P的含量呈现显著差异,其中白榆的C含量在叶片、凋落物和土壤最高,4种树种鲜叶和凋落叶C︰N︰P化学计量比存在显著差异。4种树种鲜叶C︰N与C︰P均表现为白榆>刺槐>臭椿>侧柏。4种树种凋落叶N︰P表现为刺槐>臭椿>侧柏>白榆,且三者之间存在显著差异性。土壤C︰N,C︰P、 N︰P与SOC和TN含量有非常显著的相关性(P<0.01),说明植物体内的养分需求与土壤的SOC和TN养分供应有一定的关联。该区域刺槐、臭椿、白榆叶片N/P为16~19,说明这3种树种生长可能受P的限制。研究结果表明,在未来北京平原生态林养护管理中,可以通过开展合适的树种混交和提高树种多样性来有效改善养分限制,提高林分养分循环能力,维持林分长期生产力。

“五音”的数理体系与解乐模式

“五音”之序的调整与确定,基于“五音”的“数5-10-12”模式的调试与形成,既使得“五音”的数理体系得以确立,亦是早期中国音乐知识扩容的过程。三分损益法的先益后损、先损后益,分别得出了宫音居中、宫音居首的五音音高之序。将五音设定音数数值,以数值大小排列,皆以宫音为首。以宫为中心,月令系统中形成了“数5-10-12”模式,其模式既在数理上构成了等分结构,也在义理上构成了平衡效果,由此奠定了早期中国“算数事物”的基础。

Simulation of large-scale numerical substructure in real-time dynamic hybrid testing

A solution scheme is proposed in this paper for an existing RTDHT system to simulate large-scale finite element （FE） numerical substructures. The analysis of the FE numerical substructure is split into response analysis and signal generation tasks, and executed in two different target computers in real-time. One target computer implements the response analysis task, wherein a large time-step is used to solve the FE substructure, and another target computer implements the signal generation task, wherein an interpolation program is used to generate control signals in a small time-step to meet the input demand of the controller. By using this strategy, the scale of the FE numerical substructure simulation may be increased significantly. The proposed scheme is initially verified by two FE numerical substructure models with 98 and 1240 degrees of freedom （DOFs）. Thereafter, RTDHTs of a single frame-foundation structure are implemented where the foundation, considered as the numerical substructure, is simulated by the FE model with 1240 DOFs. Good agreements between the results of the RTDHT and those from the FE analysis in ABAQUS are obtained.

Finite element simulation of inertia friction welding of superalloy bars

A thermo-mechanical coupling.finite element model was built to investigate the inertia friction welding of GH4169 bars. The remeshing and map solution techniques were adopted. Ttle whole welding process was investigated by adopting an innovative heat generation model and the flywheel rotational speed measured via the experiment. The simulated evolution of axial shortening shows a good agreement with the experiment. In addition, extensive .strain concentration presents in the interface and flash, and the largest ,strain exists near the flash root. Moreover, an intere.sting thermal reflux phenomenon during the cooling stage was found.

APPLICATION OF PENALTY FUNCTION METHOD IN ISOPARANIETRIC HYBRID FINITE ELEMENT ANALYSIS

By the aid of the penalty function method, the equilibrium restriction conditions were introduced to the isoparametric hybrid finite element analysis, and the concrete application course of the penalty function method in three-dimensional isoparametdc hybrid finite element was discussed. The separated penalty parameters method and the optimal hybrid element model with penalty balance were also presented. The penalty balance method can effectively refrain the parasitical stress on the premise of no additional degrees of freedom. The numeric experiment shows that the presented element not only is effective in improving greatly the numeric calculation precision of distorted grids but also has the universality.

3D UNSTRUCTURED GRID GENERATION TECH-NOLOGY & EULER SOLUTION FOR WING/FUSELAGE COMBINATION

Finite element method is based on element matrix, so regardless of whetherthe mesh is structured or unstructured, it Possesses an unified fashion of treatment. Finiteelement method in conjunction with unstructured grid will improve the ability of numericalsimulation for complicated now field. In this paper, a 3D unstructured grid generationtechno1ogy is developed and the Euler equation on the unstructured mesh for real compli-cated aircraft configurations is solved by the finite e1ement method. Numerical results in-dicate that the method presented is reliable end efficient.

Analysis of Electromagnetic Performance of Modulated Coaxial Magnetic Gears Used in Semi-Direct Drive Wind Turbines

Wind turbine is a key device to realize the utilization of wind energy,and it has been highly valued by all countries.But the mechanical gear transmission of the existing wind power device has the disadvantages of high vibration and noise,high failure rate,and short service time.Magneticfield modulation electromagnetic gear transmission is a new non-contact transmission method.However,the conventional modulation magnetic gear has low torque density and torque defects with largefluctuations.In order to overcome the gear transmis-sion problems of the existing semi-direct drive wind power generation machinery and improve the electromag-netic performance of the traditional magnetic gear transmission,this paper proposes a new transmission scheme of a non-contact semi-direct drive wind generator with a surface mount Halbach array modulated mag-netic gear method,and considers the electromagnetic properties of the semi-direct drive modulation magnetic gear of the wind turbine.Thefinite element software is used to construct the model of the surface-mounted Halbach array magnetic gear and the conventional gear,analyzed the distribution of magneticfield lines of the two magnetic gears,calculated the air gap magneticflux density of the inner and outer air gap,and obtained the main harmonics of the inner and outer air gap magnetic density;calculated the static torque and steady-state operating torque of the inner and outer rotors in the model,compared the air gapflux density,harmonics and torque of the magnetic gears.The simulation results show that the magneticfield modulation type mag-netic gear of the surface mount Halbach array magnetic gear method improves the magnetic induction wave-form of the inner and outer air gap,reduces the pulse torquefluctuation,and has a 60%higher static torque.Applying it to semi-direct drive wind power generation equipment not only overcomes the shortcomings of mechanical gears,but also has higher electromagnetic performance.Therefore,the surface-mounted Halbach array modulated magnetic gear can be used to replace the mechanical gearbox in the semi-direct drive wind power generation equipment.

Two-dimensional finite element mesh generation algorithm for electromagnetic field calculation

Two-dimensional finite element mesh generation algorithm for electromagnetic field calculation is proposed in this paper to improve the efficiency and accuracy of electromagnetic calculation. An image boundary extraction algorithm is developed to map the image on the geometric domain. Identification algorithm for the location of nodes in polygon area is proposed to determine the state of the node. To promote the average quality of the mesh and the efficiency of mesh generation, a novel force-based mesh smoothing algorithm is proposed. One test case and a typical electromagnetic calculation are used to testify the effectiveness and efficiency of the proposed algorithm. The results demonstrate that the proposed algorithm can produce a high-quality mesh with less iteration.

On Restricted Lie Superalgebras with Semisimple Elements

In the present paper, we give some sufficient conditions for the commutativity of restricted Lie superalgebras and characterize some properties of restricted Lie superalgebras with semisimple elements.

Mapping-Based 3D Hexahedral Finite Element Mesh Generation Method

Mapping mesh generation is widely applied in pre-processes of Finite Element Method （FEM）. In this study, the basic 3D mapping equations by Lagrange interpolating function are founded. Based these equations, a mapping pattern library, which maps essential configurations e.g. line, circle, rotary body, sphere etc. to hexahedral FEM mesh, has been built. Then available FEM mesh will be generated by clipping and assembling the mapped essential objects. Study case illustrates that the proposed method is simple and efficient to generate valid FEM mesh for complex 3D engineering structure.

Electricity Generation System with Piezoelectric Element Using Acoustic Radiation Energy

In this study, a circular plate that is installing a piezoelectric element at its center is adopted as energy-harvesting system and is subjected to a harmonic point force. Because this system cannot avoid the influence of its acoustic radiation, the influence is considered theoretically using the equation of plate motion taking into account its radiation impedance and is estimated by the electricity generation efficiency, which is derived from the ratio of the electric power in the electricity generation and the mechanical power supplied to the plate. As a result, the efficiency is suppressed by the acoustic radiation from the plate, so that the efficiencies are so different in whether to take into consideration the radiation impedance or not. Because those results are verified by the electricity generation experiment and radiation acoustic energy has a hopeful prospect for improving the performance of this system, mechanical-acoustic coupling is used to make the most of the acoustic energy. Therefore, a cylinder that has the above plates at both ends is also adopted as the electricity generation system and mechanical-acoustic coupling is caused between the plate vibrations and an internal sound field into the cylindrical enclosure by subjecting one side of each plate to a harmonic point force. Then, the effect of coupling is evaluated by comparing with the efficiencies in the electricity generation system of only plate. Specifically, because the radiation impedance increases with the plate thickness, i.e., with the natural frequency of the plate, it is demonstrated that the effect of coupling becomes remarkable with increasing the thickness on the electricity generation efficiency.

Mechanical Properties of Soil-Rock Mixture Filling in Fault Zone Based on Mesostructure

Soil-rock mixture(SRM)filling in fault zone is an inhomogeneous geomaterial,which is composed of soil and rock block.It controls the deformation and stability of the abutment and dam foundation,and threatens the long-term safety of high arch dams.To study the macroscopic and mesoscopic mechanical properties of SRM,the development of a viable mesoscopic numerical simulation method with a mesoscopic model generation technology,and a reasonable parametric model is crucially desired to overcome the limitations of experimental conditions,specimen dimensions,and experiment fund.To this end,this study presents a mesoscopic numerical method for simulating the mechanical behavior of SRM by proposing mesoscopic model generation technology based on its mesostructure features,and a rock parameter model considering size effect.The validity and rationality of the presented mesoscopic numerical method is experimentally verified by the triaxial compression tests with different rock block contents(RBC).The results indicate that the rock block can increase the strength of SRM,and it is proved that the random generation technique and the rock parameter model considering size effect are validated.Furthermore,there are multiple failure surfaces for inhomogeneous geomaterial of SRM,and the angle of the failure zone is no longer 45◦.The yielding zones of the specimen are more likely to occur in thin sections of soil matrix isolated by blocks with the failure path avoiding the rock block.The proposed numerical method is effective to investigate the meso-damage mechanism of SRM.

Study on Mesh-Control Device for the Mesh Generator Based on Tree Structures

In this paper, a process of the quadtree mesh generation is described, then a mesh control device of the tree based mesh generators is analyzed in detail. Some examples are given to demonstrate that the mesh control device allows for efficient a priori and a posteriori mesh refinements.