Showing papers on "Isotropy published in 2006"

Bounds on the basic physical parameters for anisotropic compact general relativistic objects

Abstract: We derive the upper and lower limits for the basic physical parameters (mass-radius ratio, anisotropy, redshift and total energy) for arbitrary anisotropic general relativistic matter distributions in the presence of a cosmological constant. The values of these quantities are strongly dependent on the value of the anisotropy parameter (the difference between the tangential and radial pressure) at the surface of the star. In the presence of the cosmological constant, a minimum mass configuration with a given anisotropy does exist. Anisotropic compact stellar-type objects can be much more compact than the isotropic ones, and their radii may be close to their corresponding Schwarzschild radii. Upper bounds for the anisotropy parameter are also obtained from the analysis of the curvature invariants. General restrictions for the redshift and the total energy (including the gravitational contribution) for anisotropic stars are obtained in terms of the anisotropy parameter. Values of the surface redshift parameter greater than two could be the main observational signature for anisotropic stellar-type objects. © 2006 IOP Publishing Ltd.

A general interface model for a three-dimensional curved thin anisotropic interphase between two anisotropic media

Abstract: An arbitrarily curved three-dimensional anisotropic thin interphase between two anisotropic solids is considered. The purpose of this study is to model this interphase as a surface between its two neighbouring media by means of appropriately devised interface conditions on it. The analysis is carried out in the setting of unsteady heat conduction and dynamic elasticity, and makes use of the simple idea of a Taylor expansion of the relevant fields in thin regions. It consists of a generalization of a previous study by Bovik [1994. On the modelling of thin interface layers in elastic and acoustic scattering problems. Q. J. Mech. Appl. Math. 47, 17–42] which was confined to the isotropic setting. The remarkable feature of the presently derived anisotropic interface model is that formally it has a more compact form than that of Bovik's isotropic version. This is achieved by a judicious choice of surface differential operators which have been used in the derivation, and makes possible to show that several previously known classical interface models are recovered as special cases of the one obtained in this study, once suitable assumptions are made on the magnitude of the conductivity and elasticity tensors of the interphase.

Analysis and reduction of the spurious current in a class of multiphase lattice Boltzmann models.

Abstract: We show that the spurious current present near a curved interface in a class of multiphase lattice Boltzmann (LB) models is due to the insufficient isotropy of the discrete gradient operator. A method of obtaining highly isotropic gradient operators on a lattice is given. Numerical simulations show that both the magnitude and the spatial extent of the spurious current are significantly reduced as gradient operators of increasingly higher order of isotropy is adopted in multiphase LB models.

Elasticity of transversely isotropic materials

Abstract: Preface Chapter 1 BASIC EQUATIONS OF ANISOTROPIC ELASTICITY: 1.1 Transformation of Strains and Stresses 1.2 Basic Equations 1.2.1 Geometric equations 1.2.2 Equations of motion 1.2.3 Constitutive equations 1.3 Boundary and Initial Conditions 1.3.1 Boundary conditions 1.3.2 Initial conditions 1.4 Thermoelasticity. Chapter 2 GENERAL SOLUTION FOR TRANSVERSELY ISOTROPIC PROBLEMS: 2.1 Governing Equations 2.1.1 Methods of solution 2.1.2 Governing equations for the displacement method 2.1.3 Equations for a mixed method - the state-space method 2.2 Displacement Method 2.2.1 General solution in Cartesian coordinates 2.2.2 General solution in cylindrical coordinates 2.3 Stress Method for Axisymmetric Problems 2.4 Displacement Method for Spherically Isotropic Bodies 2.4.1 General solution 2.4.2 Relationship between transversely isotropic and spherically isotropic solutions. Chapter 3 PROBLEMS FOR INFINITE SOLIDS: 3.1 The Unified Point Force Solution 3.1.1 A point force perpendicular to the isotropic plane 3.1.2 A point force within the isotropic plane 3.2 The Point Force Solution for an Infinite Solid Composed of two Half-Spaces 3.2. 1 A point force perpendicular to the isotropic plane 3.2.2 A point force within the isotropic plane 3.2.3 Some remarks 3.3 An Infinite Transversely Isotropic Space with an Inclusions 3.4 Spherically Isotropic Materials 3.4.1 An infinite space subjected to a point force 3.4.2 Stress concentration in neighbourhood of a spherical cavity. Chapter 4 HALF-SPACE AND LAYERED MEDIA: 4.1 Unified Solution for a Half-Space Subjected to a Surface Point Force 4.1.1 A point force normal to the half-space surface 4.1.2 A point force tangential to the half-space surface 4.2 A Half-Space Subjected to an Interior Point Force 4.2. 1 A point force normal to the half-space surface 4.2.2 A point force tangential to the half-spacesurface 4.3 General Solution by Fourier Transform 4.4 Point Force Solution of an Elastic Layer 4.5 Layered Elastic Media. Chapter 5 EQUILIBRIUM OF BODIES OF REVOLUTION: 5.1 Some Harmonic Functions 5.1.1 Harmonic polynomials 5.1.2 Harmonic functions containing ln(r I ij ) 5.1.3 Harmonic functions containing R 5.2 An Annular (Circular) Plate Subjected to Axial Tension and Radial Compression 5.3 An Annular (Circular) Plate Subjected to Pure Bending 5.4 A Simply-Supported Annular (Circular) Plate Under Uniform Transverse Loading 5.5 A Uniformly Rotating Annular (Circular) Plate 5.6 Transversely Isotropic Cones 5.6.1 Compression of a cone under an axial force 5.6.2 Bending of a cone under a transverse force 5.7 Spherically Isotropic Cones 5.7.1. Equilibrium and boundary conditions 5.7.2. A cone under tip forces 5.7.3. A cone under concentrated moments at its apex 5.7.4. Conical shells. Chapter 6 THERMAL STRESSES: 6.1 Transversely Isotropic Materials 6.2 A Different General Solution for Transversely Isotropic Thermoelasticity 6.2. 1 General solution for dynamic problems 6.2.2 General solution for static problems 6.3 Spherically Isotropic Materials. Chapter 7 FRICTIONAL CONTACT: 7.1 Two Elastic Bodies in Contact 7.1.1 Mathematical description of a contact system 7.1.2 Deformation of transversely isotropic bodies under frictionless contact 7.1.3 A half-space under point forces 7.2 Contact of a Sphere with a Half-Space 7.2.1 Contact with normal loading 7.2.2 Contact with tangential loading 7.3 Contact of a Cylindrical Punch with a Half-Space 7.3.1 Contact with normal loading 7.3.2 Contact with tangential loading 7.4 Indentation by a Cone 7.4.1 Contact with normal loading 7.4.2 Contact with tangential loading 7.5 Inclined Contact of a Cylindrical Punch with a Half-Space 7.5.1 Contact with normal loading 7.5.2 Contact with tangential loading 7.6 Discussions on Solu

Bounds on the basic physical parameters for anisotropic compact general relativistic objects

Abstract: We derive upper and lower limits for the basic physical parameters (mass-radius ratio, anisotropy, redshift and total energy) for arbitrary anisotropic general relativistic matter distributions in the presence of a cosmological constant. The values of these quantities are strongly dependent on the value of the anisotropy parameter (the difference between the tangential and radial pressure) at the surface of the star. In the presence of the cosmological constant, a minimum mass configuration with given anisotropy does exist. Anisotropic compact stellar type objects can be much more compact than the isotropic ones, and their radii may be close to their corresponding Schwarzschild radii. Upper bounds for the anisotropy parameter are also obtained from the analysis of the curvature invariants. General restrictions for the redshift and the total energy (including the gravitational contribution) for anisotropic stars are obtained in terms of the anisotropy parameter. Values of the surface redshift parameter greater than two could be the main observational signature for anisotropic stellar type objects.

Unitary gas in an isotropic harmonic trap: Symmetry properties and applications

Abstract: We consider $N$ atoms trapped in an isotropic harmonic potential, with $s$-wave interactions of infinite scattering length. In the zero-range limit, we obtain several exact analytical results: mapping between the trapped problem and the free-space zero-energy problem, separability in hyperspherical coordinates, SO(2,1) hidden symmetry, existence of a decoupled bosonic degree of freedom, and relations between the moments of the trapping potential energy and the moments of the total energy.

Nonlinear Electroelastic Deformations

Abstract: Electro-sensitive (ES) elastomers form a class of smart materials whose mechanical properties can be changed rapidly by the application of an electric field. These materials have attracted considerable interest recently because of their potential for providing relatively cheap and light replacements for mechanical devices, such as actuators, and also for the development of artificial muscles. In this paper we are concerned with a theoretical framework for the analysis of boundary-value problems that underpin the applications of the associated electromechanical interactions. We confine attention to the static situation and first summarize the governing equations for a solid material capable of large electroelastic deformations. The general constitutive laws for the Cauchy stress tensor and the electric field vectors for an isotropic electroelastic material are developed in a compact form following recent work by the authors. The equations are then applied, in the case of an incompressible material, to the solution of a number of representative boundary-value problems. Specifically, we consider the influence of a radial electric field on the azimuthal shear response of a thick-walled circular cylindrical tube, the extension and inflation characteristics of the same tube under either a radial or an axial electric field (or both fields combined), and the effect of a radial field on the deformation of an internally pressurized spherical shell.

Modeling of isotropic backward-wave materials composed of resonant spheres

Abstract: A possible realization of isotropic artificial backward-wave materials is theoretically analyzed. An improved mixing rule for the effective permittivity of a composite material consisting of two sets of resonant dielectric spheres in a homogeneous background is presented. The equations are validated using the Mie theory and numerical simulations. The effect of a statistical distribution of sphere sizes on the increase of losses in the operating frequency band is discussed and some examples are shown.

A unified bounding surface plasticity model for unsaturated soils

Abstract: A unified constitutive model for unsaturated soils is presented in a critical state framework using the concepts of effective stress and bounding surface plasticity theory. Consideration is given to the effects of unsaturation and particle crushing in the definition of the critical state. A simple isotropic elastic rule is adopted. A loading surface and a bounding surface of the same shape are defined using simple and versatile functions. The bounding surface and elastic rules lead to the existence of a limiting isotropic compression line, towards which the stress trajectories of all isotropic compression load paths approach. A non-associated flow rule of the same general form is assumed for all soil types. Isotropic hardening/softening occurs due to changes in plastic volumetric strains as well as suction for some unsaturated soils, enabling the phenomenon of volumetric collapse upon wetting to be accounted for. The model is used to simulate the stress–strain behaviour observed in unsaturated speswhite kaolin subjected to three triaxial test load paths. The fit between simulation and experiment is improved compared to that of other constitutive models developed using conventional Cam-Clay-based plasticity theory and calibrated using the same set of data. Also, the model is used to simulate to a high degree of accuracy the stress–strain behaviour observed in unsaturated Kurnell sand subjected to two triaxial test load paths and the oedometric compression load path. For oedometric compression theoretical simulations indicate that the suction was not sufficiently large to cause samples to separate from the confining ring. Copyright © 2005 John Wiley & Sons, Ltd.

Plane-wave propagation in attenuative transversely isotropic media

Abstract: Directionally dependent attenuation in transversely isotropic (TI) media can influence significantly the body-wave amplitudes and distort the results of the AVO (amplitude variation with offset) analysis. Here, we develop a consistent analytic treatment of plane-wave properties for TI media with attenuation anisotropy. We use the concept of homogeneous wave propagation, assuming that in weakly attenuative media the real and imaginary parts of the wave vector are parallel to one another. The anisotropic quality factor can be described by matrix elements Qij , defined as the ratios of the real and imaginary parts of the corresponding stiffness coefficients. To characterize TI attenuation, we follow the idea of the Thomsen notation for velocity anisotropy and replace the components Qij by two reference isotropic quantities and

Second harmonic generation from a nanopatterned isotropic nonlinear material

Abstract: Second harmonic generation (SHG) from a nanopatterned isotropic nonlinear material (GaAs) located inside the subwavelength gaps of a metallic coaxial array is demonstrated. The SHG results from the strong electromagnetic fields in the vicinity of the coaxial gaps; the signal strength is comparable to that from z-cut LiNbO3 even though the path length is much shorter (∼100 nm compared to 14 μm). Numerical simulations are in good agreement with the experimental data. The observation of a peak-wavelength blue shift between the SH spectrum and the linear transmission spectrum is explained.

Isotropic−Nematic Phase Transition of Single-Walled Carbon Nanotubes in Strong Acids

Abstract: We present the first quantitative assessment of the maximum amount of nanotubes that can exist in the isotropic phase ( ) of single-walled carbon nanotubes (SWNTs) in Bronsted−Lowry acids. We employ a centrifugation technique in conjunction with UV−vis−nIR spectroscopy to quantify , which is also the critical concentration of the isotropic−nematic transition of SWNTs in strong acids. Centrifugation of biphasic dispersions of SWNTs, that is, acid dispersions consisting of an isotropic phase in equilibrium with an ordered nematic liquid crystalline phase, results in a clear phase separation, where the isotropic phase is supernatant. Dilution of the isotropic phase with a known amount of acid followed by UV−vis−nIR absorbance measurements yields , that is, the maximum concentration of SWNTs that can exist in the isotropic phase in a given acid for a given SWNTs' length distribution. At low SWNT concentration (below 200 ppm) in superacids, light absorbance in the range from 400 to 1400 nm scales linearly with...

On the decay of isotropic turbulence

Abstract: We investigate the decay of freely-evolving, isotropic turbulence whose spectrum takes the form E(k→0)∼Ik4, I being Loitsyansky's integral We report numerical simulations in a periodic domain whose dimensions, lbox, are much larger than the integral scale of the turbulence, l We find that, provided lbox≫l and Re≫1, the turbulence evolves to a state in which Loitsyansky's integral is approximately constant and Kolmogorov's decay law, u2∼t−10/7, holds true The approximate conservation of I in fully-developed turbulence implies that the long-range interactions between remote eddies, as measured by the triple correlations, are very weak

Traveltime approximations for a layered transversely isotropic medium

Abstract: We consider multiple transmitted, reflected, and converted qP-qSV-waves or multiple transmitted and reflected SH-waves in a horizontally layered medium that is transversely isotropic with a vertical symmetry axis (VTI). Traveltime and offset (horizontal distance) between a source and receiver, not necessarily in the same layer, are expressed as functions of horizontal slowness. These functions are given in terms of a Taylor series in slowness in exactly the same form as for a layered isotropic medium. The coefficients depend on the parameters of the anisotropic layers through which the wave has passed, and there is no weak anisotropy assumption. Using classical formulas, the traveltime or traveltime squared can then be expressed as a Taylor series in even powers of offset. These Taylor series give rise to a shifted hyperbola traveltime approximation and a new continued-fraction approximation, described by four parameters that match the Taylor series up to the sixth power in offset. Further approximations give several simplified continued-fraction approximations, all of which depend on three parameters: zero-offset traveltime, NMO velocity, and a heterogeneity coefficient. The approximations break down when there is a cusp in the group velocity for the qSV-wave. Numerical studies indicate that approximations of traveltime squared are generally better than those for traveltime. A new continued-fraction approximation that depends on three parameters is more accurate than the commonly used continued-fraction approximation and the shifted hyperbola.

Local Symmetry Group in the General Theory of Elastic Shells

Abstract: We establish the local symmetry group of the dynamically and kinematically exact theory of elastic shells. The group consists of an ordered triple of tensors which make the shell strain energy density invariant under change of the reference placement. Definitions of the fluid shell, the solid shell, and the membrane shell are introduced in terms of members of the symmetry group. Within solid shells we discuss in more detail the isotropic, hemitropic, and orthotropic shells and corresponding invariant properties of the strain energy density. For the physically linear shells, when the density becomes a quadratic function of the shell strain and bending tensors, reduced representations of the density are established for orthotropic, cubic-symmetric, and isotropic shells. The reduced representations contain much less independent material constants to be found from experiments.

Turbulent channel flow with either transverse or longitudinal roughness elements on one wall

Abstract: Direct numerical simulation results are presented for turbulent channel flows with two-dimensional roughness elements of different shapes. The focus is mainly on a geometry where the separation between consecutive roughness elements is small and for which the rate of change of the roughness function with respect to the separation between consecutive elements is large. Roughness elements are placed either along the flow direction or orthogonally to it. In the latter case, the drag is increased. For the former case, the possibility of drag reduction reflects the different relative contributions from viscous and Reynolds shear stresses. The Reynolds shear stress depends on the shape of the surface more than the viscous stress and is closely related to the near-wall structures. For orthogonal elements, there is no satisfactory correlation between the roughness function and parameters describing the roughness geometry. On the other hand, a satisfactory collapse of the data is achieved when the roughness function is plotted against the root mean square wall-normal velocity averaged over the plane of the roughness crests. Relative to a smooth wall surface, the Reynolds stress tensor near the wall tends to become more isotropic when the elements are orthogonal to the flow and less isotropic when the elements are aligned with the flow. The interdependencies between the departure from isotropy in the wall region, the organization of the wall structures, and the magnitude of the drag are assessed by examining the rotational component of the turbulent kinetic energy production and the probability density function of the helicity density.

The four-spinon dynamical structure factor of the Heisenberg chain

Abstract: We compute the exact four-spinon contribution to the zero-temperature dynamical structure factor of the spin-1/2 Heisenberg isotropic antiferromagnet in zero magnetic field, directly in the thermodynamic limit. We make use of the expressions for matrix elements of local spin operators obtained by Jimbo and Miwa using the quantum affine symmetry of the model, and of their adaptation to the isotropic case by Abada, Bougourzi and Si-Lakhal (correcting some overall factors). The four-spinon contribution to the first frequency moment sum rule at fixed momentum is calculated. This shows, as expected, that most of the remaining correlation weight above the known two-spinon part is carried by four-spinon states. Our results therefore provide an extremely accurate description of the exact structure factor.

A micromechanics-based model for the Mullins effect

Abstract: We propose a model for the stress softening of isotropic, incompressible rubberlike materials. The model is derived from a micromechanical scheme of a polymeric network reinforced with fine filler particles, idealized as rigid, and connected by two different types of chains: elastic and breakable. The fraction of breakable chains, assigned through an appropriate distribution function, is responsible for the network alteration. This prototypical system is then extended to a three-dimensional model with isotropic stress softening. In order to illustrate this model, we discuss two explicit examples: the homogeneous deformation of uniaxial extension and the inhomogeneous deformation of azimuthal shear.