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Isotropic
Terms modified by Isotropic Selected AbstractsRelativistic and electron-correlation effects on magnetizabilities investigated by the Douglas-Kroll-Hess method and the second-order Mřller-Plesset perturbation theoryJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 15 2009Terutaka Yoshizawa Abstract Isotropic and anisotropic magnetizabilities for noble gas atoms and a series of singlet and triplet molecules were calculated using the second-order Douglas-Kroll-Hess (DKH2) Hamiltonian containing the vector potential A and in part using second-order generalized unrestricted Mřller-Plesset (GUMP2) theory. The DKH2 Hamiltonian was resolved into three parts (spin-free terms, spin-dependent terms, and magnetic perturbation terms), and the magnetizabilities were decomposed into diamagnetic and paramagnetic terms to investigate the relativistic and electron-correlation effects in detail. For Ne, Kr, and Xe, the calculated magnetizabilities approached the experimental values, once relativistic and electron-correlation effects were included. For the IF molecule, the magnetizability was strongly affected by the spin-orbit interaction, and the total relativistic contribution amounted to 22%. For group 17, 16, 15, and 14 hydrides, the calculated relativistic effects were small (less than 3%), and trends were observed in relativistic and electron-correlation effects across groups and periods. The magnetizability anisotropies of triplet molecules were generally larger than those of similar singlet molecules. The so-called relativistic-correlation interference for the magnetizabilities computed using the relativistic GUMP2 method can be neglected for the molecules evaluated, with exception of triplet SbH. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009 [source] Swelling Behaviour of Isotropic Poly(n -butyl acrylate) Networks in Isotropic and Anisotropic SolventsMACROMOLECULAR SYMPOSIA, Issue 1 2008Boumédične Dali Youcef Abstract Summary: The swelling properties of photochemically crosslinked poly(n -butyl acrylate) (PABu) networks in isotropic and anisotropic solvents were investigated experimentally. The purpose of this study was to examine the swelling kinetics of PABu networks in isotropic solvents and to compare the results obtained which those observed in the case of the low molecular weight liquid crystal 4-cyano-4,- n -pentyl-biphenyl known as 5CB. The phase diagrams were established in terms of composition and temperature for isotropic solvents, as toluene, acetone, cyclohexane, and methanol, and 5CB, using the plateau values corresponding to equilibrium states of swelling. The polymer networks were prepared via free radical polymerization/crosslinking processes by ultraviolet (UV) radiation of initial mixtures made up from a monomer, a crosslinker, and a photoinitiator. PABu networks with several crosslinking densities were formed using different quantities of difunctional monomer hexanedioldiacrylate (HDDA). Immersion of these networks in excess solvent allows measuring the solvent uptake by determination of the weight in isotropic solvents and diameter in an anisotropic solvent (5CB). Swelling data were rationalized by calculating weight and diameter ratios considering swollen to dry network states of the samples. [source] Three-dimensional diffusion tensor microscopy of fixed mouse heartsMAGNETIC RESONANCE IN MEDICINE, Issue 3 2004Yi Jiang Abstract The relative utility of 3D, microscopic resolution assessments of fixed mouse myocardial structure via diffusion tensor imaging is demonstrated in this study. Isotropic 100-,m resolution fiber orientation mapping within 5.5° accuracy was achieved in 9.1 hr scan time. Preliminary characterization of the diffusion tensor primary eigenvector reveals a smooth and largely linear angular rotation across the left ventricular wall. Moreover, a higher level of structural hierarchy is evident from the organized secondary and tertiary eigenvector fields. These findings are consistent with the known myocardial fiber and laminar structures reported in the literature and suggest an essential role of diffusion tensor microscopy in developing quantitative atlases for studying the structure,function relationships of mouse hearts. Magn Reson Med 52:453,460, 2004. © 2004 Wiley-Liss, Inc. [source] Thermodynamic Modelling of Defect Migration in Ferroelectric MaterialsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009Oliver Goy Motivated by the phenomenon of electric fatigue, point defects and their interaction in ferroelectric material are studied with a focus on the tendency of clustering. The underlying continuum model takes into account the full anisotropic electromechanical material properties. Isotropic and anisotropic defect descriptions and their influence on defect interaction will be compared. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Introducing dimensionless parameters into the correlation of NMR relaxation time to transport properties of porous mediaCONCEPTS IN MAGNETIC RESONANCE, Issue 3 2007Manolis M. Tomadakis Abstract Dimensionless parameters representing the viscous permeability (k) and NMR relaxation time (T1) of particle beds, while accounting also for the particle size, are shown to improve drastically the accuracy of k-T1 correlations in the slow diffusion regime, in the absence of bulk relaxation effects. The finding is based on a regression analysis of numerical results for k and T1 in both random and ordered isotropic and anisotropic beds of fibers. Use of the formation factor (F) improves further the accuracy of the correlations only for the strongly anisotropic unidirectional arrays of fibers. A survey of related literature reveals an extensive effort in recent years in upgrading k-T1 correlations, driven primarily by applications in petroleum and gas field exploration and recovery. © 2007 Wiley Periodicals, Inc. Concepts Magn Reson Part A 30A: 154,164, 2007. [source] Bi-Stable Adhesion of a Surface with a DimpleADVANCED ENGINEERING MATERIALS, Issue 5 2010Robert M. McMeeking In this paper, we propose a new adhesive system of dimpled surfaces. The principle is derived from a contact mechanics model. The material is assumed to be linear elastic and isotropic, and attraction between the surfaces of the half-spaces is modeled via the concept of a specific adhesion energy. It is found that large and small detachments are unstable and will either grow or shrink spontaneously when their sizes are perturbed. It is shown that this phenomenon can lead to a new bi-stable adhesive system in which weak adhesion can be converted to strong adhesion by the application of pressure. [source] Simulation of water flow and solute transport in free-drainage lysimeters and field soils with heterogeneous structuresEUROPEAN JOURNAL OF SOIL SCIENCE, Issue 2 2004H. M. Abdou Summary Lysimeters are valuable for studying the fate and transport of chemicals in soil. Large-scale field lysimeters are used to assess pesticide behaviour and radionuclide transport, and are assumed to represent natural field conditions better than laboratory columns. Field lysimeters are usually characterized by a free-draining lower boundary. As a result, the hydraulic gradient is disrupted, and leachate cannot be collected until the bottom of the lysimeter becomes saturated. We compared heterogeneously structured, free-drainage lysimeters and field soils with respect to water flow and solute transport. Numerical simulations were carried out in a two-dimensional heterogeneous sandy soil under unsaturated water flow conditions with the CHAIN_2D code. Three different soil structures (isotropic, horizontal, and vertical) were generated, and Miller,Miller similitude was used to scale the hydraulic properties of the soil. The results showed that ponding occurs at the bottom of the lysimeter for the three soil structures and that it occurred faster and was more pronounced with the vertical structure (preferential flow effect). Breakthrough curves of a conservative solute (bromide) showed that solutes are moving faster in the field than in the lysimeters. Fewer differences between lysimeters and field soils were found with the horizontal soil structure than with the isotropic and vertical structures. [source] A laboratory method for measuring the isotropic character of soil swellingEUROPEAN JOURNAL OF SOIL SCIENCE, Issue 4 2000J. -C. Summary Although the swelling of clays has been thoroughly studied, the mechanism by which this occurs in clay soils is not so fully understood. We have developed a technique to study the swelling and three-dimensional deformation of a soil sample during wetting by adapting a triaxial apparatus. This equipment applies a controlled, confined and isotropic pressure to the periphery of the samples. A constant flow of solution is injected into the base of the sample while the lateral and axial deformations are simultaneously controlled. The development of the interstitial pressure, positive or negative, is measured. When the soil is thoroughly wetted, the equipment measures the saturated hydraulic conductivity. The swelling of the soil is not necessarily isotropic, and practically all the possibilities of lateral, isotropic and vertical swelling can be encountered. Furthermore, the swelling can be preceded by significant lateral shrinkage, caused by fissures. The results show the importance of confinement pressure when measuring the swelling of the samples. The adaptation of a triaxial apparatus to the study of the permeability and swelling of soils appears to be promising as it also allows the geometric development of the samples to be traced as well as the changes in the chemical composition of the percolating solutions. [source] Effects of toroidal HVDC ground electrode on earth-return circuitsEUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 5 2002W. Machczy This paper presents a method of evaluation of currents and potentials, excited by conductive effects of high-voltage direct-current (HVDC) transmission system, along two parallel earth-return circuits such as pipelines and cables buried in the vicinity of a toroidal ground electrode. It is assumed that the system considered is linear and that the earth is an isotropic, homogeneous medium of finite conductivity. Conductive coupling between earth-return circuits is taken into account, whereas the reaction of the conductors' currents on the electrode current is disregarded. The transmission line model of the conductor with earth-return, a segmental linear approximation of the curve of the primary earth potential distribution along the conductor and the concept of superposition have been used in the method. It should be pointed out, that the method does not require the time consuming numerical integration. The technical applications of the method are illustrated by examples. [source] The Optimal Grain Sized Nanocrystalline Ni with High Strength and Good Ductility Fabricated by a Direct Current Electrodeposition,ADVANCED ENGINEERING MATERIALS, Issue 6 2008X. Shen In this work, six pure Ni specimen which mean grain sizes spans a broad range from ultra-fine to nanometer were fabricated by direct current electrodeposition and a coarse grain Ni was obtained by annealing. A gradual transition of the crystallographic preferred orientation of the deposited Ni from (200) texture to isotropic or random orientation with decreasing the mean grain size was revealed by XRD. [source] Influence of Deformation on Recrystallization of an Yttrium Oxide Dispersion-Strengthened Iron Alloy (PM2000),ADVANCED ENGINEERING MATERIALS, Issue 4 2003C. Capdevila Montes A two-fold effect of non-uniform deformation of the yttria-strengthened Fe alloy PM2000 has been revealed by analysis of the microstructure: Firstly, recrystallization temperature decreases, in accordance with the hypothesis that anything that makes the original microstructure more heterogeneous will encourage recrystallization; and secondly, the increase in number and density of recrystallization nuclei leads to fine grain structures which are more 3D isotropic. [source] Towards Efficient Dispersion of Carbon Nanotubes in Thermotropic Liquid CrystalsADVANCED FUNCTIONAL MATERIALS, Issue 19 2010Stefan Schymura Abstract Motivated by numerous recent reports indicating attractive properties of composite materials of carbon nanotubes (CNTs) and liquid crystals (LCs) and a lack of research aimed at optimizing such composites, the process of dispersing CNTs in thermotropic LCs is systematically studied. LC hosts can perform comparably or even better than the best known organic solvents for CNTs such as N -methyl pyrrolidone (NMP), provided that the dispersion process and choice of LC material are optimized. The chemical structure of the molecules in the LC is very important; variations in core as well as in terminal alkyl chain influence the result. Several observations moreover indicate that the anisotropic nematic phase, aligning the nanotubes in the matrix, per se stabilizes the dispersion compared to a host that is isotropic and thus yields random tube orientation. The chemical and physical phenomena governing the preparation of the dispersion and its stability are identified, taking into account enthalpic, entropic, as well as kinetic factors. This allows a guideline on how to best design and prepare CNT,LC composites to be sketched, following which tailored development of new LCs may take the advanced functional material that CNT,LC composites comprise to the stage of commercial application. [source] Inverse determination of the elastoplastic and damage parameters on small punch testsFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 11 2009I. PEŃUELAS ABSTRACT The small punch test (SPT) is very useful in those situations where it is necessary to use small volumes of material. The aim of this paper is to create and validate a methodology for the determination of the mechanical and damage properties of steels from the load-displacement curve obtained by means of SPTs. This methodology is based on the inverse method, the design of experiments, the polynomial curve adjustment and the evolutionary multi-objective optimization, and also allows simulating the SPTs. In order to validate the proposed methodology, the numerical results have been compared with experimental results obtained by means of normalized tests. Two dimensional axisymmetric and three-dimensional simulations have been performed in order to allow the analysis of isotropic and anisotropic materials, respectively. [source] Cleavage fracture of RPV steel following warm pre-stressing: micromechanical analysis and interpretation through a new modelFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 9-10 2006S. R. BORDET ABSTRACT In this paper, the warm pre-stress (WPS) effect on the cleavage fracture of an 18MND5 (A533B) RPV steel is investigated. This effect, which describes the effective enhancement of the cleavage fracture toughness at low temperature following a prior loading at high temperature, has received great interest in light of its significance in the integrity assessment of structures, such as nuclear pressure vessels, subjected to thermal transients. Several loading cycles between room temperature (RT) and ,150 °C are considered: Load-Unload-Cool-Fracture (LUCF), Load-Cool-Fracture (LCF) and Load-Cool with Increasing K-Fracture (LCIKF). All experiments complied with the conservative principle, which states that no fracture will occur if the applied stress intensity factor (SIF) decreases (or is held constant) while the temperature at the crack-tip decreases, even if the fracture toughness of the virgin material is exceeded. The experimental results indicate that an effective WPS effect is present even at small pre-load (Kwps= 40 MPa,m), and that a minimum critical slope (,,K/,T) in the LCIKF cycle has to be exceeded to induce cleavage fracture between RT and ,150 °C. Numerical modelling was performed using mixed isotropic and kinematic hardening laws identified on notched tensile (NT) specimens, tested in tension to large strains (up to 40%), followed by large compressive strains. Detailed microstructural investigations on compact tensile (CT) and NT fracture test specimens were performed so as to determine the nature of the cleavage initiation sites, as well as the local mechanical conditions at fracture. Based on this local information, a new cleavage model was calibrated and applied to predict the probability of cleavage fracture after WPS: it is shown that the predictions are in good agreement with the experimental results. [source] Influence of anisotropy on a limit load of weld strength overmatched middle cracked tension specimensFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 5 2003S. ALEXANDROV ABSTRACT A plane-strain upper bound limit load solution for weld strength overmatched middle cracked tension specimens (M(T) specimens), is found. It is assumed that the weld material is isotropic, but the base material is orthotropic and its axes of orthotropy are straight and parallel to the axes of symmetry of the specimen. A quadratic orthotropic yield criterion is adopted. The solution is based on a simple discontinuous kinematically admissible velocity field and is an extension of the corresponding solution for the specimen made of isotropic materials. These two solutions are compared to demonstrate the influence of anisotropy on the magnitude of the limit load. [source] Self-Assembled, Molecularly Aligned Conjugated Polymer Nanowires via DewettingADVANCED FUNCTIONAL MATERIALS, Issue 18 2010Shion Seng Chang High aspect-ratio poly(9,9,-dioctylfluorene) (F8) nanowires are fabricated on top of silicon/amorphous Teflon substrates, by dewetting of F8 thin-films. The conjugated nature of the polymers enables the self-assembly of continuous molecularly-aligned nanowires of several micrometers in length and tens of nanometers width, without using a template. The sizescale of the dewetted morphology can be controlled by varying the thickness of the F8 and amorphous Teflon layers. As predicted by van der Waals theory the characteristic sizescale of the dewetted morphology increases with F8 film thickness. However, the dependence of the characteristic sizescale on amorphous Teflon thickness is not accounted for, even qualitatively, by standard spinodal theory with van der Waals forces as the de-stabilizing force across the F8 film. The Rayleigh instability is strongly suppressed in the F8 nanowires in the late stages of dewetting, compared to isotropic, amorphous polymers. Polarized Raman measurements show a systematic increase in molecular alignment along the axis of the nanowires as their width is reduced below the typical liquid-crystalline domain size in polyfluorene films. Thus the dewetting process aligns the polymers, and the aligned polymers suppress the Rayleigh instability and enable the formation of high aspect-ratio continuous nanowires. [source] Photoswitchable Gas Permeation Membranes Based on Liquid CrystalsADVANCED FUNCTIONAL MATERIALS, Issue 17 2010Eric G, owacki Abstract We have fabricated switchable gas permeation membranes in which a photoswitchable low-molecular-weight liquid crystalline (LC) material acts as the active element. Liquid crystal mixtures are doped with mesogenic azo dyes and infused into commercially available track-etched membranes with regular cylindrical pores (0.40 to 10.0 ,m). Tunability of mass transfer can be achieved through a combination of (1) LC/mesogenic dye composition, (2) surface-induced alignment, and (3) reversible photoinduced LC-isotropic transitions. Photo-induced isothermal phase changes in the imbibed material afford large and fully reversible changes in the permeability of the membrane to nitrogen. Both the LC and photogenerated isotropic states demonstrate a linear permeability/pressure relationship, but they show significant differences in their permeability coefficients. Liquid crystal compositions can be chosen such that the LC phase is more permeable than the isotropic,or vice versa , and can be further tuned by surface alignment. Permeability switching response times are 5 s, with alternating UV and >420-nm radiation at an intensity of 2 mW/cm2 being sufficient for complete and reversible switching. Thermal and kinetic properties of the confined LC materials are evaluated and correlated with the observed permeation properties. We demonstrate for the first time reversible permeation control of a membrane with light irradiation. [source] Planar Alignment of Columnar Discotic Liquid Crystals by Isotropic Phase Dewetting on Chemically Patterned SurfacesADVANCED FUNCTIONAL MATERIALS, Issue 6 2010Jonathan P. Bramble Abstract A novel method of creating planar aligned columnar discotic liquid crystals (cDLCs) on surfaces, which also gives control over the azimuthal angle, is presented. Surfaces are chemically patterned with stripes via microcontact printing of organothiol self-assembled monolayers (SAMs) on gold, or via deep UV patterning of organosilane SAMs on silicon. These are then used to isolate long droplets of cDLCs by dewetting in the isotropic phase. Upon cooling from the isotropic into the hexagonal columnar phase, polarizing microscopy reveals that the cDLC aligns in a planar orientation. Results for three triphenylene derivatives (HAT-6, HHTT, H7T) and for a phthalocyanine derivative (8H2Pc) are presented. H7T and HAT-6 are found to align with the director perpendicular to the stripe direction, but HHTT and 8H2Pc align parallel to the stripe direction. This relatively simple new method for creating planar aligned columnar phases of DLCs gives control over the azimuthal angle: a condition required for organic field-effect transistor applications of cDLCs. [source] Controlling Light Emission in Luminescent Solar Concentrators Through Use of Dye Molecules Aligned in a Planar Manner by Liquid CrystalsADVANCED FUNCTIONAL MATERIALS, Issue 17 2009Paul P. C. Verbunt Abstract A luminescent solar concentrator (LSC) is a potential low-cost enhancement of the standard large-area silicon photovoltaic panels for the generation of electricity from sunlight. In this work, guest,host systems are investigated using anisotropic fluorescent dyes and liquid crystal mesogens to control the direction of emitted light in the LSC. It is determined that up to 30% more light is emitted from the edge of an LSC waveguide with planar dye alignment parallel to the alignment direction than from any edge of an LSC with no alignment (isotropic). The aligned samples continue to show dichroic performance after additions of both edge mirrors and rear scattering layer. [source] An Anisotropic Model for Spatial ProcessesGEOGRAPHICAL ANALYSIS, Issue 1 2008Minfeng Deng One of the key assumptions in spatial econometric modeling is that the spatial process is isotropic, which means that direction is irrelevant in the specification of the spatial structure. On the one hand, this assumption largely reduces the complexity of the spatial models and facilitates estimation and interpretation; on the other hand, it appears rather restrictive and hard to justify in many empirical applications. In this article a very general anisotropic spatial model, which allows for a high level of flexibility in the spatial structure, is proposed. This new model can be estimated using maximum likelihood and its asymptotic properties are derived at length. When the model is applied to the well-known 1970 Boston housing prices data, it significantly outperforms the isotropic spatial lag model. It also provides interesting additional insights into the price determination process in the properties market. Finally, a Monte Carlo simulation study is used to confirm the optimal properties of the model. [source] Surface deformation due to loading of a layered elastic half-space: a rapid numerical kernel based on a circular loading elementGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2007E. Pan SUMMARY This study is motivated by a desire to develop a fast numerical algorithm for computing the surface deformation field induced by surface pressure loading on a layered, isotropic, elastic half-space. The approach that we pursue here is based on a circular loading element. That is, an arbitrary surface pressure field applied within a finite surface domain will be represented by a large number of circular loading elements, all with the same radius, in which the applied downwards pressure (normal stress) is piecewise uniform: that is, the load within each individual circle is laterally uniform. The key practical requirement associated with this approach is that we need to be able to solve for the displacement field due to a single circular load, at very large numbers of points (or ,stations'), at very low computational cost. This elemental problem is axisymmetric, and so the displacement vector field consists of radial and vertical components both of which are functions only of the radial coordinate r. We achieve high computational speeds using a novel two-stage approach that we call the sparse evaluation and massive interpolation (SEMI) method. First, we use a high accuracy but computationally expensive method to compute the displacement vectors at a limited number of r values (called control points or knots), and then we use a variety of fast interpolation methods to determine the displacements at much larger numbers of intervening points. The accurate solutions achieved at the control points are framed in terms of cylindrical vector functions, Hankel transforms and propagator matrices. Adaptive Gauss quadrature is used to handle the oscillatory nature of the integrands in an optimal manner. To extend these exact solutions via interpolation we divide the r -axis into three zones, and employ a different interpolation algorithm in each zone. The magnitude of the errors associated with the interpolation is controlled by the number, M, of control points. For M= 54, the maximum RMS relative error associated with the SEMI method is less than 0.2 per cent, and it is possible to evaluate the displacement field at 100 000 stations about 1200 times faster than if the direct (exact) solution was evaluated at each station; for M= 99 which corresponds to a maximum RMS relative error less than 0.03 per cent, the SEMI method is about 700 times faster than the direct solution. [source] The lowermost mantle beneath northern Asia,II.GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2002Evidence for lower-mantle anisotropy Summary We have analysed prediffracted S -waves with turning points beneath northern Siberia in a study of anisotropy in the lowermost mantle. Deep-focus earthquakes beneath the Marianas, Izu Bonin and the Sea of Japan recorded at stations in western Europe are used. A correction for upper-mantle anisotropy is applied to the data. Comparisons of the data with synthetic data for models with and without a high velocity D, layer suggest that there is a velocity discontinuity at the top of the D, region and that the style of anisotropy is transversely isotropic in this region. Time separations between S -waves on the radial and transverse component show a weak trend where the separation increases with epicentral distance. A normalization of this separation with the travel distance within D, (300 km thick in this region) suggests that the anisotropy is uniformly distributed within this layer and has an average value of 0.5 per cent. A combination of different studies which investigate the structure of the lowermost mantle beneath Europe and northern Siberia reveals a complicated picture. Tomographic models from this area and evidence of D, anisotropy, lower mantle scatterers, reflections from a D, discontinuity and ultra-low-velocity zones suggest two distinct regions. One exhibits high velocities, D, anisotropy, a D, discontinuity and no evidence of scatterers or ultra-low-velocity zones. These features are likely associated with the palaeosubduction of the Izanagi plate well into the lowermost mantle. The other region has a lower overall velocity and shows evidence of scatterers and ultra-low-velocity zones, perhaps suggesting the presence of partial melt. These results suggest dramatic lateral variations in the nature of the lowermost mantle beneath northern Asia over a length scale of roughly 30 degrees. [source] A Maslov-propagator seismogram for weakly anisotropic mediaGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2002Georg Rümpker Summary We introduce a formalism to calculate shear-wave seismograms for weakly-anisotropic and inhomogeneous media. The method is based on the combination of the forward-propagator method, which accounts for shear-wave interaction along a single reference ray, and the Maslov ray-summation, which incorporates amplitude and phase information from neighbouring rays to account for waveform and diffraction effects at caustics and in shadow regions. The approach is based on the assumption that the multiply split shear waves, on the way to a given receiver, travel along a common ray path that can by obtained from ray tracing in an isotropic reference medium (i.e. the common-ray approximation). The forward propagator and the Maslov amplitude are expressed with respect to radial and transverse coordinates (perpendicular to the ray propagation direction) that are defined uniquely by the initial conditions. Local polarizations and slownesses of the fast and slow shear-waves in the direction of propagation are obtained from the eikonal equation. The Maslov-propagator phase is given by the average shear-wave traveltime along the reference ray. Phase advances and delays of individual shear wave components are accounted for by the propagator. The geometrical-spreading information required for the Maslov integration is supplied by dynamic ray tracing in the isotropic reference medium. In the high-frequency limit effective phase functions are defined to assess the validity of the Maslov propagator phase information. For a homogeneous isotropic reference medium, we find good agreement with exact Maslov phase functions for anisotropic perturbations of up to 20 per cent. As a numerical application we consider effects of inhomogeneous anisotropy in a shear-wave cross-hole survey. The variations of the transversely-isotropic medium require 2-D slowness integrals. The method can handle discontinuities of the fast polarization along the ray path and also for neighbouring rays which is important for the slowness integration. Smooth transitions between isotropic and anisotropic regions along the ray path can be accounted for without the need to switch between numerical formulations. [source] Sequential integrated inversion of refraction and wide-angle reflection traveltimes and gravity data for two-dimensional velocity structuresGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2000Rosaria Tondi A new algorithm is presented for the integrated 2-D inversion of seismic traveltime and gravity data. The algorithm adopts the ,maximum likelihood' regularization scheme. We construct a ,probability density function' which includes three kinds of information: information derived from gravity measurements; information derived from the seismic traveltime inversion procedure applied to the model; and information on the physical correlation among the density and the velocity parameters. We assume a linear relation between density and velocity, which can be node-dependent; that is, we can choose different relationships for different parts of the velocity,density grid. In addition, our procedure allows us to consider a covariance matrix related to the error propagation in linking density to velocity. We use seismic data to estimate starting velocity values and the position of boundary nodes. Subsequently, the sequential integrated inversion (SII) optimizes the layer velocities and densities for our models. The procedure is applicable, as an additional step, to any type of seismic tomographic inversion. We illustrate the method by comparing the velocity models recovered from a standard seismic traveltime inversion with those retrieved using our algorithm. The inversion of synthetic data calculated for a 2-D isotropic, laterally inhomogeneous model shows the stability and accuracy of this procedure, demonstrates the improvements to the recovery of true velocity anomalies, and proves that this technique can efficiently overcome some of the limitations of both gravity and seismic traveltime inversions, when they are used independently. An interpretation of field data from the 1994 Vesuvius test experiment is also presented. At depths down to 4.5 km, the model retrieved after a SII shows a more detailed structure than the model obtained from an interpretation of seismic traveltime only, and yields additional information for a further study of the area. [source] Vertically fractured transversely isotropic media: dimensionality and deconstructionGEOPHYSICAL PROSPECTING, Issue 2 2009Michael A. Schoenberg ABSTRACT A vertically fractured transversely isotropic (VFTI) elastic medium is one in which any number of sets of vertical aligned fractures (each set has its normal lying in the horizontal x1, x2 -plane) pervade the medium and the sets of aligned fractures are the only features of the medium disturbing the axi-symmetry about the x3 -axis implying that in the absence of fractures, the background medium is transversely isotropic (TI). Under the assumptions of long wavelength equivalent medium theory, the compliance matrix of a fractured medium is the sum of the background medium's compliance matrix and a fracture compliance matrix. For sets of parallel rotationally symmetric fractures (on average), the fracture compliance matrix is dependent on 3 parameters , its normal and tangential compliance and its strike direction. When one fracture set is present, the medium is orthorhombic and the analysis is straightforward. When two (non-orthogonal) or more sets are present, the overall medium is in general elastically monoclinic; its compliance tensor components are subject to two equalities yielding an 11 parameter monoclinic medium. Constructing a monoclinic VFTI medium with n embedded vertical fracture sets, requires 5 TI parameters plus 3×n fracture set parameters. A deconstruction of such an 11 parameter monoclinic medium involves using its compliance tensor to find a background transversely isotropic medium and several sets of vertical fractures which, in the long wavelength limit, will behave exactly as the original 11 parameter monoclinic medium. A minimal deconstruction, would be to determine, from the 11 independent components, the transversely isotropic background (5 parameters) and two fracture sets (specified by 2 × 3 = 6 parameters). Two of the background TI medium's compliance matrix components are known immediately by inspection, leaving nine monoclinic components to be used in the minimal deconstruction of the VFTI medium. The use of the properties of a TI medium, which are linear relations on its compliance components, allows the deconstruction to be reduced to solving a pair of non-linear equations on the orientations of two fracture sets. A single root yielding a physically meaningful minimum deconstruction yields a unique minimal representation of the monoclinic medium as a VFTI medium. When no such root exists, deconstruction requires an additional fracture set and uniqueness is lost. The boundary between those monoclinic media that have a unique minimal representation and those that do not is yet to be determined. [source] The effect of the electrical anisotropy on the response of helicopter-borne frequency-domain electromagnetic systemsGEOPHYSICAL PROSPECTING, Issue 5 2004Changchun Yin ABSTRACT Helicopter electromagnetic (HEM) systems are commonly used for conductivity mapping and the data are often interpreted using an isotropic horizontally layered earth model. However, in regions with distinct dipping stratification, it is useful to extend the model to a layered earth with general anisotropy by assigning each layer a symmetrical 3 × 3 resistivity tensor. The electromagnetic (EM) field is represented by two scalar potentials, which describe the poloidal and toroidal parts of the magnetic field. Via a 2D Fourier transform, we obtain two coupled ordinary differential equations in the vertical coordinate. To stabilize the numerical calculation, the wavenumber domain is divided into two parts associated with small and large wavenumbers. The EM field for small wavenumbers is continued from layer to layer with the continuity conditions. For large wavenumbers, the EM field behaves like a DC field and therefore cannot be sensed by airborne EM systems. Thus, the contribution from the large wavenumbers is simply ignored. The magnetic fields are calculated for the vertical coaxial (VCX), horizontal coplanar (HCP) and vertical coplanar (VCP) coil configurations for a helicopter EM system. The apparent resistivities defined from the VCX, VCP and HCP coil responses, when plotted in polar coordinates, clearly identify the principal anisotropic axes of an anisotropic earth. The field example from the Edwards Aquifer recharge area in Texas confirms that the polar plots of the apparent resistivities identify the principal anisotropic axes that coincide well with the direction of the underground structures. [source] Traveltime computation with the linearized eikonal equation for anisotropic mediaGEOPHYSICAL PROSPECTING, Issue 4 2002Tariq Alkhalifah A linearized eikonal equation is developed for transversely isotropic (TI) media with a vertical symmetry axis (VTI). It is linear with respect to perturbations in the horizontal velocity or the anisotropy parameter ,. An iterative linearization of the eikonal equation is used as the basis for an algorithm of finite-difference traveltime computations. A practical implementation of this iterative technique is to start with a background model that consists of an elliptically anisotropic, inhomogeneous medium, since traveltimes for this type of medium can be calculated efficiently using eikonal solvers, such as the fast marching method. This constrains the perturbation to changes in the anisotropy parameter , (the parameter most responsible for imaging improvements in anisotropic media). The iterative implementation includes repetitive calculation of , from traveltimes, which is then used to evaluate the perturbation needed for the next round of traveltime calculations using the linearized eikonal equation. Unlike isotropic media, interpolation is needed to estimate , in areas where the traveltime field is independent of ,, such as areas where the wave propagates vertically. Typically, two to three iterations can give sufficient accuracy in traveltimes for imaging applications. The cost of each iteration is slightly less than the cost of a typical eikonal solver. However, this method will ultimately provide traveltime solutions for VTI media. The main limitation of the method is that some smoothness of the medium is required for the iterative implementation to work, especially since we evaluate derivatives of the traveltime field as part of the iterative approach. If a single perturbation is sufficient for the traveltime calculation, which may be the case for weak anisotropy, no smoothness of the medium is necessary. Numerical tests demonstrate the robustness and efficiency of this approach. [source] Out-of-plane geometrical spreading in anisotropic mediaGEOPHYSICAL PROSPECTING, Issue 4 2002Norman Ettrich Two-dimensional seismic processing is successful in media with little structural and velocity variation in the direction perpendicular to the plane defined by the acquisition direction and the vertical axis. If the subsurface is anisotropic, an additional limitation is that this plane is a plane of symmetry. Kinematic ray propagation can be considered as a two-dimensional process in this type of medium. However, two-dimensional processing in a true-amplitude sense requires out-of-plane amplitude corrections in addition to compensation for in-plane amplitude variation. We provide formulae for the out-of-plane geometrical spreading for P- and S-waves in transversely isotropic and orthorhombic media. These are extensions of well-known isotropic formulae. For isotropic and transversely isotropic media, the ray propagation is independent of the azimuthal angle. The azimuthal direction is defined with respect to a possibly tilted axis of symmetry. The out-of-plane spreading correction can then be calculated by integrating quantities which describe in-plane kinematics along in-plane rays. If, in addition, the medium varies only along the vertical direction and has a vertical axis of symmetry, no ray tracing need be carried out. All quantities affecting the out-of-plane geometrical spreading can be derived from traveltime information available at the observation surface. Orthorhombic media possess no rotational symmetry and the out-of-plane geometrical spreading includes parameters which, even in principle, are not invertible from in-plane experiments. The exact and approximate formulae derived for P- and S-waves are nevertheless useful for modelling purposes. [source] Isotropic resolution diffusion tensor imaging with whole brain acquisition in a clinically acceptable timeHUMAN BRAIN MAPPING, Issue 4 2002Derek Kenton Jones Abstract Our objective was to develop a diffusion tensor MR imaging pulse sequence that allows whole brain coverage with isotropic resolution within a clinically acceptable time. A single-shot, cardiac-gated MR pulse sequence, optimized for measuring the diffusion tensor in human brain, was developed to provide whole-brain coverage with isotropic (2.5 × 2.5 × 2.5 mm) spatial resolution, within a total imaging time of approximately 15 min. The diffusion tensor was computed for each voxel in the whole volume and the data processed for visualization in three orthogonal planes. Anisotropy data were further visualized using a maximum-intensity projection algorithm. Finally, reconstruction of fiber-tract trajectories i.e., ,tractography' was performed. Images obtained with this pulse sequence provide clear delineation of individual white matter tracts, from the most superior cortical regions down to the cerebellum and brain stem. Because the data are acquired with isotropic resolution, they can be reformatted in any plane and the sequence can therefore be used, in general, for macroscopic neurological or psychiatric neuroimaging investigations. The 3D visualization afforded by maximum intensity projection imaging and tractography provided easy visualization of individual white matter fasciculi, which may be important sites of neuropathological degeneration or abnormal brain development. This study has shown that it is possible to obtain robust, high quality diffusion tensor MR data at 1.5 Tesla with isotropic resolution (2.5 × 2.5 × 2.5 mm) from the whole brain within a sufficiently short imaging time that it may be incorporated into clinical imaging protocols. Hum. Brain Mapping 15:216,230, 2002. © 2002 Wiley-Liss, Inc. [source] Piezoelectric and Electric-Field-Induced Properties of a Ferroelectric Bent-Core Liquid CrystalADVANCED MATERIALS, Issue 37 2009Antal Jákli A new adamantane bent-core liquid crystal exhibiting a metastable ferroelectric phase with large polarization is synthesized and characterized. The material shows reversible switching between a birefringent (opaque) and an optically isotropic (clear) state. In the clear state, the observed piezoelectric constant is comparable to those of commercial solid-state piezotransducers. [source] | |||||||||||||||||||||||||||||||