CONVERGENCE OF SIMPLIFIED AND STABILIZED MIXED ELEMENT FORMATS BASED ON BUBBLE FUNCTION FOR THE STOKES PROBLEM

Two simplifled and stabilized mixed element formats for the Stokes problem are derived by bubble function, and their convergence, i.e., error analysis, are proved. These formats can save more freedom degrees than other usual formats.

Reduced-order proper orthogonal decomposition extrapolating finite volume element format for two-dimensional hyperbolic equations

This paper is concerned with establishing a reduced-order extrapolating fi- nite volume element （FVE） format based on proper orthogonal decomposition （POD） for two-dimensional （2D） hyperbolic equations. For this purpose, a semi discrete variational format relative time and a fully discrete FVE format for the 2D hyperbolic equations are built, and a set of snapshots from the very few FVE solutions are extracted on the first very short time interval. Then, the POD basis from the snapshots is formulated, and the reduced-order POD extrapolating FVE format containing very few degrees of freedom but holding sufficiently high accuracy is built. Next, the error estimates of the reduced-order solutions and the algorithm procedure for solving the reduced-order for- mat are furnished. Finally, a numerical example is shown to confirm the correctness of theoretical conclusions. This means that the format is efficient and feasible to solve the 2D hyperbolic equations.

Preliminary Study of Chemical Elements Distribution in Petroleum Source Rocks Donga and Yogou Formations of the Termit Sedimentary Basin (Est-Niger)

XRF and EDX analyses were carried out on 18 batches of representative raw samples to determine the distribution of major chemical elements in the petroleum source rocks of Donga and Yogou formations of Termit sedimentary basin. The chemical composition of these formations is dominated by silicon (Si), aluminum (Al) and iron (Fe). This is consistent with the oxide composition, which is also dominated by silicon oxide (SiO2), aluminum oxide (Al2O3) and iron monoxide (FeO). No less important chemical elements are calcium (Ca), potassium (K), sulfur (S), titanium (Ti), magnesium (Mg), manganese (Mn) and barium (Ba), as well as some of their oxides. All these major chemical elements are carried by silicate detrital minerals associated with pyrite and goethite and/or clay minerals such as kaolinite and interstratified illite, smectite and chlorite. This trend is illustrated by the values of the Si/Al and SiO2/Al2O3 ratios.

Calculating standard captured γ spectra of formation elements

Multi-element gamma-ray spectrum logging requires standard spectra of individual elements for its interpretation.Since the standard element spectra are usually derived using Monte Carlo simulation of either a pure element or its oxide,we synthesized the standard neutron captured γ spectra（as would be observed using a NaI（Tl） detector） of elements H,Si,Ca and Fe from each element and its oxide.To compare the standard spectra from the elements and oxides,we operated three simulations of sandstone,limestone and mixed formation of sandstone and limestone each with ten different porosities,and used the two kinds of standard spectra to analyze the mixed spectra modeled from sandstone and limestone formations.The results show that the standard element spectra from oxides have more prominent energy peaks than the standard spectra from pure elements.The calculated formation element contents are close to the theoretical values when the standard element spectra from oxides are used to analyze the formation mixed spectra.Therefore,the formation element standard spectra should be calculated from oxide models in the analysis of neutron captured γ spectra by logging tools.

FINITE ELEMENT ANALYSIS FOR CHIP FORMATION IN HIGH SPEED TURNING OPERATIONS BY ARBITRARY LAGRANGIAN EULERIAN METHOD

A two-dimensional finite element （FE） model for the high speed turning operations when orthogonally machining AISI H13 tool steel at 49HRC using poly crystalline cubic boron nitride （PCBN） is described. An arbitrary Lagrangian Eulerian （ALE） method has been adopted which does not need any chip separation criteria as opposed to the traditional Lagrangian approach. Through FE simulations temperature and stresses distributions are presented that could be helpful in predicting tool life and improving process parameters. The results show that high temperatures are generated along the tool rake face as compared to the shear zone temperatures due to high thermal conductivity of PCBN tools.

Monte Carlo simulation of scintillation crystal detector for formation element logging

Formation elements logging is a neutron gamma spectroscopy logging technique used to acquire the content of elements and minerals by recording the gamma ray produced by the reaction of neutron and elemental nucleus in the formation. It has a wide usage in discriminating complex lithology and evaluating unconventional reservoir. The Monte Carlo simulation model of formation elements logging tool is established in this paper, with which the effects of tool parameters including the material and length of the scintillation crystal and source spacing on logging responses are modeled. The results show that the energy response of LaBr_3: Ce crystal is better than others, and the detection efficiency increases with the crystal length but decrease with source spacing. The above results may be used as a reference for optimizing the tool structure design.

Practical Techniques for Restoration of Architectural Formation Elements in Historical Buildings

Restoration of architectural formation elements is basically trying in estimating the optimization method which places it old architectural artist in his work. The article aims at rooting the methodology of restoration of the architectural formation elements. It is essentially intellectual effort by the restorer in assessing the best way the artist and the old architect in his work. In order to reach the purpose behind this works and analyze the original available techniques in the creation period, the restoration process can be completed as fully as possible. The research is concerned with re-confidence in the classical methods in the restoration of buildings as consolidation and reconstruction. The classical method is a real way to restore the building to its original form especially in the availability of all technological tools to achieve reporting and documentation. It is not necessary to extension in using unapplied materials and technique. In this regard, the research was able to provide solutions, ideas and techniques that helped preserve and restore elements of architectural formation. The research also pointed to the importance of linking the physical and plastic aspects of the archaeological element.

Rare Earths, Trace Element Characteristics of High-Mg Volcanic Rocks of Yixian Formation in Sihetun West Liaoning Province and Its Apocalypse

The high-Mg volcanic rocks of the Yixian Formation in the Sihetun area have the obvious characteristics of mantie-derived lava in rare earth, trace element characteristics with high Mg # （62 - 70） and high content of compatible elements. In the meantime, the volcanic rocks also have the obvious characteristics of Crust-source material in rare earth, trace element characteristics with high ∑ REE （ 158.78 × 10^-6 - 359.66 × 10^-6 ）, high （La/Yb） N （ 14.61 - 29.60）, high La/Nb（2.37 - 7.52） and high Ba/Nb （67.58- 205.96）, obvious positive anomaly of Pb and negative anomaly of Nb, Ta in trace element spider-gram. In Sr-Nd-Pb isotope the （^87Sr/^86Sr）i ratio is higher than 0.706 and the εNd（ t ） ratio is from - 3.4 to - 13, both reflect enriched Mantle characteristics. The characteristics above of the volcanic rocks combined with the content of Sr, Ba, Y, Yb and the ratio of Sr/Y show that the volcanic rocks have the property of the Sanukite rocks in Setouchi Japan beside subduction zone, and illuminate that the Sanukite rocks can be formed not only in island-arc near subduction zone but also in intro-plate. The analysis indicates that the high-Mg volcanic rocks in the Sihetun area result from the collective function of mantle-derived lava and crust-source materials. The result illuminates that the West Liaoning region is very special in tectonic geochemical background in Cretaceous in East China, and is an ideal region for us to further study the characteristics of magmatic activity as well as the process of Crust-Mantle interaction in Eastern China.

The Aghajari (Upper Fars) Formation in the Folded Zagros Zone, Iran: Insights to Identify Facies, Architectural Elements, Fluvial Systems, Petrography and Provenance

The Aghajari Formation, called also the Upper Fars, develops throughout the Folded Zagros Zone and its thickness in the type section in southwest of Iran is 2966 meters. To analyze the sedimentary basin of this Formation, lithofacies, architectural elements and petrofacies of the related deposits in a section in southeast of Sarvestan in Fars Province of Iran with a thickness of 2221.45 meters were examined. Microscopically studying thin sections, the petrography and the occurrence of the deposits were determined. In this section, 16 lithofacies, 10 architectural elements and 2 sandstone petrofacies were identified. The lithofacies were divided into two major and minor groups, in which the major lithofacies consist of coarse-grained （Gh, Gp, Gt and Gm）, medium-grained （Sh, Sp, St, Sl, Sm, Sr and Ss and fine-grained ones （Fm, Fl and Fsm）, and the minor lithofacies were evaporative and mixed silisiclastic-carbonate. The identified architectural elements are CH, SB, GB, LA, DA, CR, CS, LV, LS, CH （FF） and FF. By combining evidences from facies analysis and architectural elements together, the Aghajari Formation was divided into three parts in which the related sedimentation environments, from top to bottom, are gravel, gravel-sand and fine-grained meandering river respectively. There have also been playas and shoreface in the lower part. Based on petrography, the sandstones of this formation were classified into two groups： litharenite and sublitharenite. The origin of these deposits （sandstones） was appointed to the recycled orogeny and the source of quartz is low and medium to high metamorphic rank. Using the field evidences, the paleocurrent direction was achieved indicating the direction of the paleocurrent from northwest to southeast at the time of deposition. It is hoped that these data can be used in the interpretation of the basin and reconstruction of the paleogeography in the local and regional scales.

Element-Assemblage Zoning Features of Gold Deposits in the Cambrian Silicalite Formation,Western Qinling

The gold deposits, occurring in the south subzone of western Qinling, are the onlytypical and important strata-bound gold deposits, which are associated with submarine exhala-tive sedimentation. The god deposits include the La, erma ore deposit, the Qiongmo ore de-posit and the Yaxiang ore occurrence. They are hosted in the Cambrian silicalite formationcomposed of black chert and slate. The presence of typical chert offers important evidence to e-valuate the Possib1e submarine exhalative system and its role in the formation of the gold de-posits, which are closely associated with percolation and diffusion in the horizontal, vertical andaxial directions. Element-assemblage zonation is clearly seen due to differences in element con-centrations in different directions. Such a zonation makes gold, selenium, uranium, copper,stibium, molybdenum, mercury, etc. precipitate in the form of simple 0r composite orebodies.The establishment of the element-assemblage zonation is highly helpful for evaluating directlythe metallogenesis of gold deposits.

Determination of the Minimum Testing Time for Wireline Formation Testing with the Finite Element Method

The wireline formation tester （WFT） is an important tool for formation evaluation, such as calculating the formation pressure and permeability, identifying the fluid type, and determining the interface between oil and water. However, in a low porosity and low permeability formation, the supercharge pressure effect exists, since the mudcake has a poor sealing ability. The mudcake cannot isolate the hydrostatic pressure of the formation around the borehole and the mud seeps into the formations, leading to inaccurate formation pressure measurement. At the same time, the tool can be easily stuck in the low porosity/low permeability formation due to the long waiting and testing time. We present a method for determining the minimum testing time for the wireline formation tester. The pressure distribution of the mudcake and the formation were respectively calculated with the finite element method （FEM）. The radius of the influence of mud pressure was also computed, and the minimum testing time in low porosity/low permeability formations was determined within a range of values for different formation permeabilities. The determination of the minimum testing time ensures an accurate formation pressure measurement and minimizes possible accidents due to long waiting and testing time.

Interrelation of Chemical Elements Content in Plants underConditions of Primary Soil Formation

It is presented the results of a long-term and intensive experiment, which models the processes of primary soil formation under controlled agro-ecosystems. The influence of mineral substrate transformation is analyzed on the content of chemical elements in plants tomato, and wheat. For the first time have been established dynamic synergistic and antagonistic interrelations between the chemical elements in a various bodies of the plant (roots, reproductive bodies, stems, and leaves). Using methods of the theory of information was revealed dynamics of collective state of chemical elements in the plants. It is shown that the collective states of the chemical elements which defined by the information function is strictly differentiated for different plant bodies, and have hierarchic order. We analyzed the following chemical elements Si, Al, Fe, Mg, Ca, K, P, S, Cl, Na, Mn, Zn.

Structure,Orientation and Finite Element Analysis of the Tail Club of Mamenchisaurus hochuanensis

The structure and orientation of the posterior extremity （tail club） of the caudal vertebrae of Mamenchisaurus hochuanensis Young and Chao, 1972 from the Upper Jurassic Shangshaximiao Formation has been analyzed to determine the tail club function using Finite Element Analysis. Of the four caudal vertebrae composing the tail club, the second largest （C＂1＂） was probably the most proximal, and is fixed with the preceding sequence of the caudal vertebrae, whereas the smallest （C＂4＂） is free and forms the termination of the tail club. Our analysis also suggests that the tail club is more efficient in lateral swinging rather than up-and-down motion, and that the best region for the tail club to impact is at the spine of the largest of the four caudals （C＂2＂）, with a maximum load for impact at about 450 N. The tail club of Mamenchisaurus hochuanensis probably also had limitations as a defense weapon and was more possibly a sensory organ to improve nerve conduction velocity to enhance the capacity for sensory perception of its surroundings.

Study on relative orbital configuration in satellite formation flying

In this paper, the relative orbital configurations of satellites in formation flying with non-perturbation and J2 perturbation are studied, and an orbital elements method is proposed to obtain the relative orbital configurations of satellites in formation. Firstly, under the condition of non-perturbation, we obtain many shapes of relative orbital configurations when the semi-major axes of satellites are equal. These shapes can be lines, ellipses or distorted closed curves. Secondly, on the basis of the analysis of J2 effect on relative orbital configurations, we find out that J2 effect can induce two kinds of changes of relative orbital configurations. They are distortion and drifting, respectively. In addition, when J2 perturbation is concerned, we also find that the semi-major axes of the leading and following satellites should not be the same exactly in order to decrease the J2 effect. The relationship of relative orbital elements and J2 effect is obtained through simulations. Finally, the minimum relation perturbation conditions are established in order to reduce the influence of the J2 effect. The results show that the minimum relation perturbation conditions can reduce the J2 effect significantly when the orbital element differences are small enough, and they can become rules for the design of satellite formation flying.

Solution set on the natural satellite formation orbits under first-order earth's non-spherical perturbation

Using the reference orbital element approach, the precise governing equations for the relative motion of formation flight are formulated. A number of ideal formations with respect to an elliptic orbit can be designed based on the relative motion analysis from the equations. The features of the oscillating reference orbital elements are studied by using the perturbation theory. The changes in the relative orbit under perturbation are divided into three categories, termed scale enlargement, drift and distortion respectively. By properly choosing the initial mean orbital elements for the leader and follower satellites, the deviations from originally regular formation orbit caused by the perturbation can be suppressed. Thereby the natural formation is set up. It behaves either like non-disturbed or need little control to maintain. The presented reference orbital element approach highlights the kinematics properties of the relative motion and is convenient to incorporate the results of perturbation analysis on orbital elements. This method of formation design has advantages over other methods in seeking natural formation and in initializing formation.

Inverse Transformation of Elliptical Relative State Transition Matrix

A new set of relative orbit elements (ROEs) is used to derive a new elliptical formation flying model in previous work. In-plane and out-of-plane relative motions can be completely decoupled, which benefits elliptical formation design. In order to study the elliptical control strategy and perturbation effects, it is necessary to derive the inverse transformation of the relative state transition matrix based on relative orbit elements. Poisson bracket theory is used to obtain the linear transformations between the two representations: the relative orbit elements and the geocentric orbital frame. In this paper, the details of these transformations are presented.

Three-dimensional discrete element numerical simulation of Paleogene salt structures in the western Kuqa foreland thrust belt

Taking the Paleogene salt strata in the west of Kuqa foreland thrust belt as study object, the deformation features of salt structure in the compression direction and perpendicular to the compression direction were examined to find out the control factors and formation mechanisms of the salt structures. By using the three-dimensional discrete element numerical simulation method, the formation mechanisms of typical salt structures of western Kuqa foreland thrust belt in Keshen and Dabei work areas were comprehensively analyzed. The simulation results show that the salt deformation in Keshen and Dabei work areas is of forward spread type, with deformation concentrated in the piedmont zone;the salt deformation is affected by the early uplift near the compression end, pre-existing basement faults, synsedimentary process and the initial salt depocenter;in the direction perpendicular to the compression direction, salt rocks near the compression end have strong lateral mobility with the velocity component moving towards the middle part, and the closer to the middle, the larger the velocity will be, so that salt rocks will aggregate towards the middle and deform intensely, forming complex folds and separation of salt structures from salt source, and local outcrop with thrust faults. Compared with 2 D simulation, 3 D simulation can analyze salt structures in the principal stress direction and direction perpendicular to the principal stress, give us a full view of the formation mechanisms of salt structures, and guide the exploration of oil and gas reservoirs related to salt structures.

Fracture prediction in the tight-oil reservoirs of the Triassic Yanchang Formation in the Ordos Basin,northern China

It is important to predict the fracture distribution in the tight reservoirs of the Ordos Basin because fracturing is very crucial for the reconstruction of the low-permeability reservoirs. Three-dimensional finite element models are used to predict the fracture orientation and distribution of the Triassic Yanchang Formation in the Longdong area, southern Ordos Basin. The numerical modeling is based on the distribution of sand bodies in the Chang 7a and 72 members, and the different forces that have been exerted along each boundary of the basin in the Late Mesozoic and the Cenozoic. The calculated results demonstrate that the fracture orientations in the Late Mesozoic and the Ceno- zoic are NW-EW and NNE-ENE, respectively. In this paper, the two-factor method is applied to analyze the distribution of fracture density. The distribution maps of predicted fracture density in the Chang 71 and 72 members are obtained, indicating that the tectonic movement in the Late Mesozoic has a greater influence on the fracture development than that in the Cenozoic. The average fracture densities in the Chang 71 and 72 members are similar, but there are differences in their distributions. Compared with other geological elements, the lithology and the layer thickness are the primary factors that control the stress distribution in the study area, which further determine the fracture distribution in the stable Ordos Basin. The predicted fracture density and the two-factor method can be utilized to guide future exploration in the tight-sand reservoirs.

Geochemistry and Sedimentology of Jhill Limestone of Gaj Formation, in CapeMonze and Adjoining Area, Karachi

Among several lithostratigraphic subdivisions of the Ga Formation of Miocene age,the Jhill limestone is entirely different with respect to its colour, texture and structures. This limestone unit has been evaluated to elaborate its geochemical and sedimentological characteristics. The distribution of various elements in the acid-soluble fraction has been studied in order to determine their mineralogy, sedimentary environment, facies and diagenesis. Mineralogy,recrystallization and other diagenetic changes are the main factors affecting the distribution of trace elements and their mutual relationships in the limestones. Samples of the Jhill limestone show depletion in large-sized ions (Sr, Pb & K) and also in the ions that are not compatible with calcite space group. Elements (Fe, Mn, Zn, Cu & Co) having distribution eoefficient (D) above unity for natural calcites, are more enriched. Microscopic and X-ray studies revealed nearly complete conversion of aragonite into stable low-Mg calcite.An attempt has also been made to verify the reefal conditions for these limestones on the basis of geochemical studies. The plots of Sr and other facies-indicator elements show that the majority of the beds belong to forereef flank facies with some algal banks. Low Mg/Ca and Sr/Ca ratios suggest that a phreatic diagenetic environment prevailed after the deposilion. High concentrations of Cr, Ni, and Co in the Jhill limestone show a positive correlation with a higher amount of insoluble residue, which reflects a relatively high rate of influx of terrigenous material.

Influence of contamination on banded iron formations in the Isua supracrustal belt, West Greenland: Reevaluation of the Eoarchean seawater compositions

Banded Iron Formations（BIFs） are chemical sediments, ubiquitously distributed in the Precambrian supracrustal belts; thus their trace element compositions are helpful for deciphering geochemical evolution on the Earth through time. However, it is necessary to elucidate factors controlling the whole-rock compositions in order to decode the ancient seawater compositions because their compositions are highly variable. We analyzed major and trace element contents of the BIFs in the 3.8-3.7 Ga Isua supracrustal belt（ISB）, southern West Greenland. The BIFs are petrographically classified into four types：Black-,Gray-, Green-and White-types, respectively. The Green-type BIFs contain more amphiboles, and are significantly enriched in Co, Ni, Cu, Zn, Y, heavy rare earth element（HREE） and U contents. However,their bulk compositions are not suitable for estimate of seawater composition because the enrichment was caused by secondary mobility of metamorphic Mg, Ca and Si-rich fluid, involvement of carbonate minerals and silicate minerals of olivine and pyroxene and/or later silicification or contamination of volcanic and clastic materials. The White-type BIFs are predominant in quartz, and have lower transition element and REE contents. The Gray-type BIFs contain both quartz and magnetite. The Black-type BIFs are dominated by magnetite, and contain moderate to high transition element and REE contents. But,positive correlations of V, Ni, Zn and U contents with Zr contents suggest that involvement of detrital,volcanic and exhalative materials influences on their contents. The evidence for significant influence of the materials on the transition element contents such as Ni in the BIFs indicates the transition element contents in the Archean ocean were much lower than previously estimated. We reconstructed secular variations of V,Co, Zn and U contents of BIFs through time, which show Ni and Co contents decreased whereas V, Zn and U contents increased through time. Especially, the Ni and Co contents drastically decreased in the Mesoarchean rather than around the Great Oxidation Event. On the other hand, the V,Zn and U contents progressively increased from the Mesoarchean to the Proterozoic. Stratigraphical trends of the BIFs show increase in Y/Ho ratios and decrease in positive Eu anomaly upwards, respectively. The stratigraphic changes indicate that a ratio of hydrothermal fluid to seawater component gradually decrease through the deposition, and support the Eoarchean plate tectonics, analogous to the their stratigraphic variations of seafloor metalliferous sediments at present and in the Mesoarchean.