283 resultados para Mehler-Heine type formulas

em Chinese Academy of Sciences Institutional Repositories Grid Portal


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Formulas for decomposing of complex crystals to a sum of binary crystals are described and applied to the study of bond covalency in La1-xSrxFeO3 (0.0 less than or equal to x less than or equal to 0.9) and Ca1-xSrxMnO3 (0.0 less than or equal to x less than or equal to 0.5). The bond valence is treated by bond-valence sums scheme. The results indicate that, for both compounds, with the increasing doping level, the bond covalency and bond valence show the same trend, namely, larger bond covalency corresponds to higher bond valence. For La1-xSrxFeO3, with the increase of doping level, the bond covalency of La-O, Ca-O decreases in the orthorhombic (0.0 less than or equal to x less than or equal to 0.2) and rhombohedral (0.4 less than or equal to x less than or equal to 0.7) systems, then increases slightly for the cubic (0.8 less than or equal to x less than or equal to 0.9) system, but that of Fe-O increases for all crystal systems. A sharp decrease in bond covalency was observed where the crystal changes from orthorhombic to rhombohedral, while a smooth trend was seen for the rhombohedral-to-cubic transition. On the other hand, for orthorhombic Ca1-xSrxMnO3, the bond covalency of Ca-O, Sr-O, and Mn-O (4-coordinate site) decreases with the increasing doping level, that of Mn-O (2-coordinate site) increases.

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The algebraic formulas of 1.5 and 2.5 rank are given for four space groups P2(1), Pn, Pna2(1), P2(1)2(1)2(1). It is better that the results of applying them to estimating general type of phases for four correspondent crystal structures. And a method of transforming algebraic formulas from 1.5(2.5) rank is proposed.

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The algebraic formulas of 1.5 and 2.5 rank which can be applied to estimating +/- pi/2 type of phases for P2(1)2(1)2(1) space group were derived using the method of structure factor algebra. Both types of the formulas are satisfactory for two known crystal structures in estimating their +/- pi/2 type of phases.

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Fractional energy losses of waves due to wave breaking when passing over a submerged bar are studied systematically using a modified numerical code that is based on the high-order Boussinesq-type equations. The model is first tested by the additional experimental data, and the model's capability of simulating the wave transformation over both gentle slope and steep slope is demonstrated. Then, the model's breaking index is replaced and tested. The new breaking index, which is optimized from the several breaking indices, is not sensitive to the spatial grid length and includes the bottom slopes. Numerical tests show that the modified model with the new breaking index is more stable and efficient for the shallow-water wave breaking. Finally, the modified model is used to study the fractional energy losses for the regular waves propagating and breaking over a submerged bar. Our results have revealed that how the nonlinearity and the dispersion of the incident waves as well as the dimensionless bar height (normalized by water depth) dominate the fractional energy losses. It is also found that the bar slope (limited to gentle slopes that less than 1:10) and the dimensionless bar length (normalized by incident wave length) have negligible effects on the fractional energy losses.

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Numerical study of three-dimensional evolution of wake-type flow and vortex dislocations is performed by using a compact finite diffenence-Fourier spectral method to solve 3-D incompressible Navier-Stokes equations. A local spanwise nonuniformity in momentum defect is imposed on the incoming wake-type flow. The present numerical results have shown that the flow instability leads to three-dimensional vortex streets, whose frequency, phase as well as the strength vary with the span caused by the local nonuniformity. The vortex dislocations are generated in the nonuniform region and the large-scale chain-like vortex linkage structures in the dislocations are shown. The generation and the characteristics of the vortex dislocations are described in detail.

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In addition to the layer thickness and effective Young’s modulus, the impact of the kinematic assumptions, interfacial condition, in-plane force, boundary conditions, and structure dimensions on the curvature of a film/substrate bilayer is examined. Different models for the analysis of the bilayer curvature are compared. It is demonstrated in our model that the assumption of a uniform curvature is valid only if there is no in-plane force. The effects of boundary conditions and structure dimensions, which are not-fully-included in previous models are shown to be significant. Three different approaches for deriving the curvature of a film/substrate bilayer are presented, compared, and analyzed. A more comprehensive study of the conditions regarding the applicability of Stoney’s formula and modified formulas is presented.

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Structure and dynamical processes of vortex dislocations in a kind of wake-type flow are described clearly by vortex lines, which are directly constructed from data of three-dimensional direct numerical simulations of the flow evolution.

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Mn+ irons were implanted to n-type Ge(1 1 1) single crystal at room temperature with an energy of 100 keV and a dose of 3 x 10(16) cm(-2). Subsequently annealing was performed at 400degreesC for 1 h under flowing nitrogen gas. X-ray diffraction measurements show that as-implanted sample is amorphous and the structure of crystal is restored after annealing. Polycrystalline germanium is formed in annealed sample. There are no new phases found except germanium. The samples surface morphologies indicate that annealed sample has island-like feature while there is no such kind of characteristic in as-implanted sample. The elemental composition of annealed sample was analyzed by Auger electron spectroscopy. It shows that manganese ions are deeply implanted into germanium substrate and the highest manganese atomic concentration is 8% at the depth of 120 nm. The magnetic properties of samples were investigated by an alternating gradient magnetometer. The annealed sample shows ferromagnetic behavior at room temperature.

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Low-dimensional systems are constructed to investigate dynamics of vortex dislocations in a wake-type shear flow. High-resolution direct numerical simulations are employed to obtain flow snapshots from which the most energetic modes are extracted using proper orthogonal decomposition (POD). The first 10 modes are classified into two groups. One represents the general characteristics of two-dimensional wake-type shear flow, and the other is related to the three-dimensional properties or non-uniform characteristics along the span. Vortex dislocations are generated by these two kinds of coherent structures. The results from the first 20 three-dimensional POD modes show that the low- dimensional systems have captured the basic properties of the wake-type shear flow with vortex dislocation, such as two incommensurable frequencies and their beat frequency.

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Mn+ ions were implanted into n-type Ge(111) single crystal at room temperature at an energy of 100 keV with a dose of 3 x 1016 cm-2. Subsequent annealing was performed on the samples at 400 °C and 600 °C in a flowing nitrogen atmosphere. The magnetic properties of the samples have been investigated by alternating gradient magnetometer at room temperature. The compositional properties of the annealed samples were studied by Auger electron spectroscopy and the structural properties were analyzed by X-ray diffraction measurements. Magnetization measurements reveal room-temperature ferromagnetism for the annealed samples. The magnetic analysis supported by compositional and structural properties indicates that forming the diluted magnetic semiconductor (DMS) MnxGe1-x after annealing may account for the ferromagnetic behavior in the annealed samples.

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Cell adhesion is crucial to many biological processes, such as inflammatory responses, tumor metastasis and thrombosis formation. Recently a commercial surface plasmon resonance (SPR)-based BIAcore biosensor has been extended to determine cell binding mediated by surface-bound biomolecular interactions. How such cell binding is quantitatively governed by kinetic rates and regulating factors, however, has been poorly understood. Here we developed a novel assay to determine the binding kinetics of surface-bound biomolecular interactions using a commercial BIAcore 3000 biosensor. Human red blood cells (RBCs) presenting blood group B antigen and CM5 chip bearing immobilized anti-B monoclonal antibody (mAb) were used to obtain the time courses of response unit, or sensorgrams, when flowing RBCs over the chip surface. A cellular kinetic model was proposed to correlate the sensorgrams with kinetic rates. Impacts of regulating factors, such as cell concentration, flow duration and rate, antibody-presenting level, as well as pH value and osmotic pressure of suspending medium were tested systematically, which imparted the confidence that the approach can be applied to kinetic measurements of cell adhesion mediated by surface-bound biomolecular interactions. These results provided a new insight into quantifying cell binding using a commercial SPR-based BIAcore biosensor.

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Concrete is usually described as a three-phase material, where matrix, aggregate and interface zones are distinguished. The beam lattice model has been applied widely by many investigators to simulate fracture processes in concrete. Due to the extremely large computational effort, however, the beam lattice model faces practical difficulties. In our investigation, a new lattice called generalized beam (GB) lattice is developed to reduce computational effort. Numerical experiments conducted on a panel subjected to uniaxial tension show that the GB lattice model can reproduce the load-displacement curves and crack patterns in agreement to what are observed in tests. Moreover, the effects of the particle overlay on the fracture process are discussed in detail. (C) 2007 Elsevier Ltd. All rights reserved.

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In the present paper, by use of the boundary integral equation method and the techniques of Green fundamental solution and singularity analysis, the dynamic infinite plane crack problem is investigated. For the first time, the problem is reduced to solving a system of mixed-typed integral equations in Laplace transform domain. The equations consist of ordinary boundary integral equations along the outer boundary and Cauchy singular integral equations along the crack line. The equations obtained are strictly proved to be equivalent with the dual integral equations obtained by Sih in the special case of dynamic Griffith crack problem. The mixed-type integral equations can be solved by combining the numerical method of singular integral equation with the ordinary boundary element method. Further use the numerical method for Laplace transform, several typical examples are calculated and their dynamic stress intensity factors are obtained. The results show that the method proposed is successful and can be used to solve more complicated problems.