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Small Displacements (small + displacement)
Selected AbstractsTheoretical studies of the spin Hamiltonian parameters and the local structure for the orthorhombic V4+ in CaYAlO4PHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 6 2008Chuan-Ji Fu Abstract The spin Hamiltonian parameters (g -factors and the hyperfine structure constants) and the local structure for the orthorhombic V4+ in CaYAlO4 are theoretically studied from the perturbation formulas of these parameters for a 3d1 ion in orthorhombically distorted octahedra. Based on the present studies, this center is explicitly assigned to V4+ occupying the Al3+ site, associated with one next-nearest-neighbor Mg2+ replacing the host Al3+ (i.e. MgAl) in the ab -plane due to the charge compensation. Since the effective charge of the compensator is negative (,e), the ligand O2, intervening in the impurity V4+ and the MgAl would undergo a small displacement (,0.08 Å) towards the central ion because of the electrostatic repulsion. The local structure of this center can be described as elongation of the oxygen octahedron along the c- axis and the slight orthorhombic distortion in the perpendicular direction. The theoretical spin Hamiltonian parameters and the optical transitions based on the above local structure show reasonable agreement with the experimental data. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Impulsive Dirac-delta forces in the rocking motionEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 7 2004F. Prieto Abstract In this work the classical theory of one block rocking motion is revisited. A Dirac-delta type interaction as impact mechanism is found to be an alternative for the traditional model. Numerical computations with this new formulation have shown that the agreement with the classical theory is excellent for the case of slender blocks and small displacements. Good agreement with experimental data has also been found for the case of arbitrary angles and slenderness. The approach presented in this paper opens new lines for further theoretical developments and computational applications. Copyright © 2004 John Wiley & Sons, Ltd. [source] Introduction to Hydromechanical Well Tests in Fractured Rock AquifersGROUND WATER, Issue 1 2009Todd Schweisinger This article introduces hydromechanical well tests as a viable field method for characterizing fractured rock aquifers. These tests involve measuring and analyzing small displacements along with pressure transients. Recent developments in equipment and analyses have simplified hydromechanical well tests, and this article describes initial field results and interpretations during slug and constant-rate pumping tests conducted at a site underlain by fractured biotite gneiss in South Carolina. The field data are characterized by displacements of 0.3 ,m to more than 10 ,m during head changes up to 10 m. Displacements are a hysteretic function of hydraulic head in the wellbore, with displacements late in a well test always exceeding those at similar wellbore pressures early in the test. Displacement measurements show that hydraulic aperture changes during well tests, and both scaling analyses and field data suggest that T changed by a few percent per meter of drawdown during slug and pumping tests at our field site. Preliminary analyses suggest that displacement data can be used to improve estimates of storativity and to reduce nonuniqueness during hydraulic well tests involving single wells. [source] Homogenizing the acoustic properties of a porous matrix containing an incompressible inviscid fluidMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 10 2003J. L. Ferrin We undertake a rigorous derivation of the Biot's law for a porous elastic solid containing an inviscid fluid. We consider small displacements of a linear elastic solid being itself a connected periodic skeleton containing a pore structure of the characteristic size ,. It is completely saturated by an incompressible inviscid fluid. The model is described by the equations of the linear elasticity coupled with the linearized incompressible Euler system. We study the homogenization limit when the pore size ,tends to zero. The main difficulty is obtaining an a priori estimate for the gradient of the fluid velocity in the pore structure. Under the assumption that the solid part is connected and using results on the first order elliptic systems, we obtain the required estimate. It allows us to apply appropriate results from the 2-scale convergence. Then it is proved that the microscopic displacements and the fluid pressure converge in 2-scales towards a linear hyperbolic system for an effective displacement and an effective pressure field. Using correctors, we also give a strong convergence result. The obtained system is then compared with the Biot's law. It is found that there is a constitutive relation linking the effective pressure with the divergences of the effective fluid and solid displacements. Then we prove that the homogenized model coincides with the Biot's equations but with the added mass ,a being a matrix, which is calculated through an auxiliary problem in the periodic cell for the tortuosity. Furthermore, we get formulas for the matricial coefficients in the Biot's effective stress,strain relations. Finally, we consider the degenerate case when the fluid part is not connected and obtain Biot's model with the relative fluid displacement equal to zero. Copyright © 2003 John Wiley & Sons, Ltd. [source] X-ray powder diffraction and electron diffraction studies of the thortveitite-related L phase, (Zn,Mn)2V2O7ACTA CRYSTALLOGRAPHICA SECTION B, Issue 2 2009Kevin M. Knowles The phase designated ,-Zn3(VO4)2 reported as a minor second phase in zinc oxide-based varistor materials doped with vanadium oxide and manganese oxide is shown to be the L phase, (Zn1,,,xMnx)2V2O7 (0.188 < x < 0.538), in the pseudo-binary Mn2V2O7,Zn2V2O7 system. Analysis of X-ray powder diffraction patterns and electron diffraction patterns of this phase shows that the previously published a, c and , values for this thortveitite-related phase are incorrect. Instead, Rietveld refinement of the X-ray powder pattern of the L phase shows that it has a monoclinic C lattice with Z = 6, with a = 10.3791,(1), b = 8.5557,(1), c = 9.3539,(1),Å and , = 98.467,(1)°. Although prior convergent-beam electron diffraction work of `,-Zn3(VO4)2' confirmed the C Bravais lattice, the space group was found to be Cm rather than C2/m, the difference perhaps arising from the inability of the X-rays to detect small displacements of oxygen. Attempts to refine the structure in Cm did not produce improved R factors. The relationship between the crystal structure of the L phase and the high-temperature C2/m,,-Zn2V2O7 thortveitite-type solid solution is discussed. [source] | ||||||||||