Showing papers on "Isotropy published in 1981"
01 Sep 1981
TL;DR: In this article, the results of simulations for irrotational strain (plane and axisymmetric), shear, rotation, and relaxation toward isotropy in an incompressible fluid subjected to uniform deformation or rotation are compared with linear theory and experimental data.
Abstract: The direct simulation methods developed by Orszag and Patternson (1972) for isotropic turbulence were extended to homogeneous turbulence in an incompressible fluid subjected to uniform deformation or rotation. The results of simulations for irrotational strain (plane and axisymmetric), shear, rotation, and relaxation toward isotropy following axisymmetric strain are compared with linear theory and experimental data. Emphasis is placed on the shear flow because of its importance and because of the availability of accurate and detailed experimental data. The computed results are used to assess the accuracy of two popular models used in the closure of the Reynolds-stress equations. Data from a variety of the computed fields and the details of the numerical methods used in the simulation are also presented.
993 citations
TL;DR: A review of wave propagation in anisotropic media can be found in this paper, where the authors present consistent theoretical formulations for the numerical solution of a number of propagation problems, including body and surface wave polarizations.
771 citations
TL;DR: In this paper, a molecular theory for the dynamics of rod-like polymers in concentrated solutions is presented, which describes the rotational motion of rods in both the isotropic phase and the liquid crystalline phase.
Abstract: A molecular theory is presented for the dynamics of rodlike polymers in concentrated solutions. The theory describes the rotational motion of rods in both the isotropic phase and the liquid crystalline phase. Combined with the molecular expression of the stress tensor, it also gives a unified rheological constitutive equation which predicts the nonlinear viscoelasticity in both phases. As an illustrative example, the steady-state viscosity η at zero-shear-rate is calculated. The predicted dependence of η on molecular weight and concentration agrees fairly well with experiments.
624 citations
TL;DR: In this paper, a spectral equation derived from two-point closures applied to three-dimensional isotropic turbulence is studied from the subgrid-scale modeling point of view, with a cutoff wenumber kc located in the inertial range of turbulence.
Abstract: A spectral equation derived from two-point closures applied to three-dimensional isotropic turbulence is studied from the subgrid-scale modeling point of view, with a cutoff wavenumber kc located in the inertial range of turbulence. Ideas of Kraichnan concerning eddy viscosities are then used to evaluate the parameterized subgrid-scale transfer. This, together with a suitable boundary condition at kc, allows us to predict statistically the large scales (k kc). A k−5/3 energy spectrum extending to kc is recovered without any artificial dissipation range in the neighborhood of kc. This procedure is valid both for forced stationary turbulence and for freely decaying turbulence. The same eddy-viscosity is then introduced in a direct numerical simulation of three-dimensional homogeneous isotropic turbulence without external forcing. Again, the energy spectrum, evaluated by averaging on a spherical shell of radius k, follows the Kolmogorov law u...
364 citations
TL;DR: In this article, a finite element program for the analysis of anisotropic optical waveguides is described and the appearance of spurious numerical modes, due to the fact that the functional is non-positive definite, is discussed and a possible solution to the problem is presented.
Abstract: A finite element program for the analysis of anisotropic optical waveguides is described. The appearance of spurious numerical modes, due to the fact that the functional is nonpositive definite is discussed and a possible solution to the problem is presented. For isotropic waveguides it is shown that both EH- and HE-type modes can be very accurately approximated by two different scalar finite element programs. Finally, a method for calculating the attenuation of leaky modes in a single material integrated optic waveguide using this scalar finite element method is proposed.
192 citations
TL;DR: Using a pulse transmission ultrasound method, the elastic properties of bone samples taken from along the length and around the periphery of a bovine femur are determined using nine of the orthotropic elastic constants.
Abstract: Using a pulse transmission ultrasound method, we have determined the elastic properties of bone samples taken from along the length and around the periphery of a bovine femur. Twenty specimens, in the form of 5-mm cubes, were tested. All nine of the orthotropic elastic constants were determined for each specimen. Analysis of our data indicate that there are statistically significant variations from the usual assumption of transverse isotropy.
178 citations
TL;DR: In this paper, the spin-spin coupling tensors for one-bond coupling between main group elements are calculated using a sum-over-states of relativistically parameterized extended Huckel (REX) wavefunctions and the relativistic analogue of Ramsey's theory.
Abstract: Spin-spin coupling tensors for one-bond coupling between main group elements are calculated using a sum-over-states of relativistically parameterized extended Huckel (REX) wavefunctions and the relativistic analogue of Ramsey's theory. All parameters, including the tabulated magnetic hyperfine integrals, come from relativistic (or non-relativistic) atomic Hartree-Fock calculations, affording a systematic comparison of these two cases. The results reconfirm the strong relativistic increase of K(XH) in XH4, X = C-Pb, and the role of the new, isotropic term K ps . The relativistic increase of the relative anisotropy R = (K ‖-K ⊥)/K is found to be a rather general phenomenon. Its origin is traced to the s-tp 1/2 contribution and, ultimately, to a phase factor for p 1/2 orbitals. Thus, for example, the R(PbC) in Pb(CH3)4 is predicted to be larger than the corresponding R(SnC) in Sn(CH3)4. For molecules having lone pairs, both the increase of Z along a column and the relativistic effects diminish the 1 K, makin...
140 citations
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TL;DR: In this paper, a review of the effects of magic angle spinning on a variety of interactions and materials are given, including magnetic dipolar interactions, the chemical shift interaction, pseudo-dipolar interactions and electric quadrupolar interactions.
Abstract: Rapid specimen rotation about an axis inclined at the magic angle of 54° 44′ to the direction of the applied magnetic field can remove many sources of broadening from the NMR spectrum of a solid and enable finer features to be revealed. The review commences with a discussion of the basic principles of magic angle spinning and an examination of the effects on magnetic dipolar interactions, the chemical shift interaction, pseudo-dipolar interactions and electric quadrupolar interactions. The anisotropic parts of these interactions are removed from the central spectrum and appear as spinning sidebands. The interactions that remain are the isotropic shifts and J couplings as in isotropic fluids; however some essential differences between solids and fluids remain. Examples of the effects of magic angle spinning on a variety of interactions and materials are given. When applied to metals the anisotropy of Knight shift is removed, isotropic Knight shifts may be measured with precision, and the Ruderman-...
135 citations
TL;DR: TEMTY as mentioned in this paper is a code for large-eddy simulation of a passive scalar in isotropic turbulence, where the role of each term in the scalar equation is examined.
Abstract: TEMTY, a code for large-eddy simulation of a passive scalar in isotropic turbulence, is developed and proved by successful simulation of experiment. The role of each term in the scalar equation and the concept of prefiltering the scalar equation is examined. The ratio of the exponents in the decay of velocity and temperature intensities is found to parametrize with the ratio Λu/Λ0, where Λu, Λ0, are the velocity and temperature Taylor microscales respectively.
124 citations
TL;DR: In this paper, a method for the second-order analysis of point processes, and, basing on it, for their orientation analysis, is presented, which has some advantages in comparison to RIPLEY's estimator.
Abstract: The paper presents a method for the second-order analysis of point processes, and, basing on it, for their orientation analysis. For the reduced second moment measure of stationary and of stationary and isotropic point processes a new estimator is given, which has some advantages in comparison to RIPLEY's estimator. Three examples illustrate the use of the statistical techniques.
124 citations
TL;DR: In this paper, a computer program generated 3000 interpenetrating spheres in a cubic container and used a relaxation technique to reduce overlaps, which resulted in an isotropic and homogeneous packing with a density of 0.6366.
TL;DR: In this article, the creep and recovery behavior of ultra high modulus polyethylene has been studied over the temperature range 20 −70°C and four types of material were examined; low molecular weight and intermediate molecular weight homopolymer, an ethylene hexene-1 copolymer, and a sample prepared by γ-irradiation of isotropic low molecular-weight polymer prior to drawing.
TL;DR: In this paper, a method to calculate homogeneous anisotropic turbulent fields associated with a constant mean velocity gradient is described, and the equations governing the Fourier transform of the triple velocity correlations are closed by using an extended eddy-damped quasi-normal approximation.
Abstract: The paper describes a method to calculate homogeneous anisotropic turbulent fields associated with a constant mean velocity gradient. The equations governing the Fourier transform of the triple velocity correlations are closed by using an extended eddy-damped quasi-normal approximation. An angular parametrization of the second-order spectral tensor is introduced in order to integrate analytically all the directional terms over a spherical shell. Numerical solutions of the model are presented for typical homogeneous anisotropic flows.
TL;DR: In this article, the zeroth, first, and second moments of the solution phase infrared, isotropic Raman, and anisotropic Raman bands of a totally symmetric mode are calculated.
Abstract: The zeroth, first, and second moments of the solution phase infrared, isotropic Raman, and anisotropic Raman bands of a totally symmetric mode are calculated. The existence of a strong orientationally dependent intermolecular potential is shown to lead to concentration dependent peak frequencies and bandwidths, as well as possible deviations from Beer’s law. Assumining a dominant transition dipole–transition dipole interaction, expressions for the explicit concentration dependence of the infrared, isotropic Raman, and anisotropic Raman first moments are derived and applied to the interpretation of the observed Raman spectra of polar molecules in the solution phase.
TL;DR: A new two-layer cylindrical model is proposed to describe the nonlinear properties of carotid arteries and the agreement between experimental and theoretical curves lies within 2% accuracy which cannot be achieved with single-layer models.
TL;DR: In this paper, the authors used ion exchange resin beads of various diameters in a bubble column to determine the liquid-solid mass transfer coefficients (k s) of a mixture of glycol, glucose, and polyethylene glycol.
TL;DR: In this paper, the authors extend the theory of isotropic tensors to cover the general case of turbulence with a pseudovector-preferred direction, without assuming mirror-reflection invariance.
Abstract: We extend the theory of isotropic tensors, developed by Robertson, Batchelor, and Chandrasekhar, to cover the general case of turbulence with a pseudovector-preferred direction, without assuming mirror-reflection invariance. Attention is focused on two-point-correlation functions, and it is shown that the form of the decomposition into proper and pseudotensor contributions is restricted by the homogeneity requirement. We present the somewhat unexpected result that the vector- and pseudovector-preferred-direction cases yield different results: A pseudovector-preferred direction allows the correlation matrix one more functional degree of freedom than does the "proper" vector case. We present an explicit form of the two-point-correlation tensor in the presence of a uniform mean magnetic field which may be appropriate for use in analysis of magnetic fluctuations in plasma containment devices or the interplanetary medium. A procedure for determining the magnetic helicity from experimental data is presented.
TL;DR: Particle interactions in small particle samples were investigated by measuring their influences on the surface plasmon polariton absorption of the single particle, and comparing with (a) various effective medium theories and (b) a theory for direct dipole coupling in particle clusters as discussed by the authors.
TL;DR: In this article, two and three-dimensional finite strips are developed for the analysis of thin and thick sectorial plates, which can be isotropic or orthotropic, of constant or variable thickness, and can have different combinations of boundary conditions.
TL;DR: In this article, a general phenomenological theory of capillary excess or surface viscosities is developed from considerations of momentum balance in the neighbourhood of a fluid phase boundary, where a coordinate system may be erected in the interfacial region for which the constitutive equations are anisotropic in the normal direction but tangentially isotropic.
Abstract: A general phenomenological theory of capillary excess or surface viscosities is developed from considerations of momentum balance in the neighbourhood of a fluid phase boundary. It is assumed that a coordinate system may be erected in the interfacial region for which the constitutive equations are anisotropic in the normal direction but tangentially isotropic. This anisotropy together with certain assumptions regarding the continuity of the velocity vector and its derivatives leads to the identification for incompressible fluids of four surface viscosity coefficients $\kappa$, $\eta$, $\kappa\_N$ and $\eta\_N$. The first two have been recognized since the time of Boussinesq, and experimental data regarding them are accumulating. The second two appear to be new, and experiments to measure them are only in a preliminary stage. In all cases, the surface viscosity coefficients are formally identified as integrals taken through the interfacial region from one bulk phase to the next. The theory is limited to interfacial regions whose curvatures are small with respect to the reciprocal thickness of the transition zone and of greater than ultra-low surface tension.
TL;DR: In this paper, the authors considered the problem of a uniaxial type-II superconductor near the upper critical field in the framework of the Ginzburg-Landau equations with a phenomenological mass tensor.
Abstract: The problem of a uniaxial type-II superconductor near the upper critical field is considered in the framework of the Ginzburg-Landau equations with a phenomenological mass tensor. The currents are shown to flow in planes which are in general no longer orthogonal to the direction of the vortex axes as in the isotropic case; the inclination angle is obtained in terms of anisotropic masses. The magnetic field has a component normal to the vortex axes; equations are derived which relate the transverse and axial fields. The average value of the transverse field (the transverse induction) vanishes. The constitutive relation between the induction and the magnetization is obtained. The components of the magnetization normal and parallel to the vortex direction are simply related in terms of the effective masses.
TL;DR: In this article, the effect of model anisotropy on the critical temperature, critical field, and high-temperature specific heat from an exact solution of the anisotropic Eliashberg equations was investigated.
Abstract: The thermodynamics of several elemental superconductors is computed from isotropic Eliashberg theory formulated on the imaginary frequency axis. A symmary of the available experimental literature is presented and a comparison with theory is given. The small disagreements that are found are all in the direction expected from anisotropy effects. We calculate the effect of a small amount of model anisotropy on the critical temperature, critical field, and high-temperature specific heat from an exact solution of the anisotropic Eliashberg equations. These are the first such results below the critical temperature; unlike previous analytical work, we include retardation, anisotropy in the mass enhancement, and the effect of the Coulomb repulsion in enhancing anisotropy, all of which are significant. We derive a new formula independent of any model anisotropy for the rate of decrease with impurity lifetime of the critical temperature. Finally we demonstrate how the commonly used formulas of Markowitz and Kadanoff and of Clem may give entirely misleading estimates of the gap anisotropy when used to interpret certain experiments.
TL;DR: In this paper, the authors investigated the body force equivalents for a seismic dislocation occurring in an anisotropic source medium and study radiation patterns of seismic body waves resulting from them.
Abstract: We investigate body force equivalents for a seismic dislocation occurring in an anisotropic source medium and study radiation patterns of seismic body waves resulting from them. The point source representation of the equivalent body forces is obtained following a result of Kosevich (1962, 1965). Green9s tensor for an anisotropic medium is calculated using a far-field approximate method by Kosevich and Natsik (1964). Radiation patterns of seismic body waves are obtained by a straightforward convolution operation on the equivalent forces with the approximate Green9s tensor. The seismic dislocation occurring in an anisotropic source medium is equivalent in general to the sum of three orthogonal dipole forces with different magnitudes, for which the seismic moment tensor has a nonzero trace. Because of the third dipole force which never appears for an isotropic medium, a significant distortion of the radiation patterns occurs in a direction near the null vector. Nodal lines of P -wave radiation patterns are separated into isolated loops and/or secondary nodal lines appear. In directions where group velocity differs from the corresponding phase velocity, the effect of the medium transfer response on the polarities of body waves seems to be larger than that in other directions. The combination of the effects of source forces and medium transfer response distorts the radiation pattern.
TL;DR: In this paper, the authors adapted the Eishelby model of the strain field of a coherent inclusion in an infinite matrix to describe the strain fields associated with a circular plate of ellipsoidal cross-section transformed martensitically.
TL;DR: In this article, a rigorous semi-analytical formulation is presented to study the static and dynamic response of rigid strip footings supported on the surface of a horizontally layered soil deposit, each layer is modelled as a homogeneous cross-anisotropic medium with a vertical axis of material symmetry while the loading consists of harmonically time-varying horizontal or vertical forces and moments.
Abstract: A rigorous semi-analytical formulation is presented to study the static and dynamic response of rigid strip footings supported on the surface of a horizontally layered soil deposit. Each layer is modelled as a homogeneous cross-anisotropic medium with a vertical axis of material symmetry while the loading consists of harmonically time-varying horizontal or vertical forces and moments. The solution, based on an experimentally verified relationship among the anisotropic soil parameters that uncouples the wave equations in closedform, is exact in that it properly accounts for the true boundary conditions at the layer interfaces and the surface. Comprehensive parametric studies are presented in the form of normalized displacement-load or rotation-moment ratios as functions of dimensionless geometric and material parameters. Simple and sufficiently accurate formulas ofdirect practical applicability are also given for static displacements and resonant frequency factors. The results clearly demonstrate the significance of soil anisotropy in determining undrained static and dynamic response of foundations; soils with a large ratio of horizontal to vertical Young’s moduli experience smaller static displacements and quite different dynamic response characteristics from equivalent isotropic soil deposits.
TL;DR: In this paper, isotropic compression tests and radial shear stress tests were performed on cubical specimens consisting of glass beads under the condition of independent stress control, and the results showed that the direction of specimen deposition was identical with that of gravity.
01 Nov 1981
TL;DR: In this paper, an improved transverse shear deformation theory for laminated anisotropic plates under bending is presented, which eliminates the need for an arbitrarily chosen shear correction factor.
Abstract: An improved transverse shear deformation theory for laminated anisotropic plates under bending is presented. The theory eliminates the need for an arbitrarily chosen shear correction factor. For a general laminate with coupled bending and stretching, the constitutive equations connecting resultants with average displacements and rotations are derived. Simplified forms of these relations are also obtained for the special case of a symmetric laminate with uncoupled bending. The governing equation for this special case is obtained as a sixth-order equation for the normal displacement requiring prescription of the three physically natural bounday conditions along each edge. For the limiting case of isotropy, the present theory reduces to an improved version of Mindlin's theory. Numerical results are obtained from the present theory for an example of a laminated plate under cylindrical bending. Comparison with results from exact three-dimensional analysis shows that the present theory is more accurate than other theories of equivalent order.
01 Jan 1981
TL;DR: In this article, a finite strain version of the J 2 deformation theory of plasticity is given, where the material model is an isotropic, nonlinearly elastic solid and the range of states is investigated for which the equations governing incremental responses are elliptic.
Abstract: A finite strain version of the J 2 deformation theory of plasticity is given. The material model is an isotropic, nonlinearly elastic solid. The range of states is investigated for which the equations governing incremental responses are elliptic.
TL;DR: In this article, the relationship between drawing rate and drawing stress was studied for amorphous poly(ethylene terephthalate) (PET) under various experimental conditions, and three types of expriments were performed: simple drawing with necking at constant rate, drawing through a conical die, and drawing at constant stress.
Abstract: The relationship between drawing rate and drawing stress was studied for amorphous poly(ethylene terephthalate) (PET) under various experimental conditions. Three types of expriments were performed: simple drawing with necking at constant rate, drawing through a conical die, and drawing at constant stress. Under constant stress conditions a transition between two stable regimes of drawing can be observed. The transition occurs at a critical stress σc at which the rate of neck propagation changes by some orders of magnitude. Such a transition was found both below and above the glass transition of PET. With constant drawing rates instabilities of neck propagation were observed under certain experimental conditions. Such self-oscillations, described by other authors, are not due to heat effects as has been proposed, but are related to the existence of the critical stres σc.
Stress-induced transitions in deformation behavior as in PET were observed for polypropylene and nylon 6 but not for polycarbonate. The results obtained by various methods including morphological studies do not support the assumption that the instabilities are caused by thermal effects due to the dissipation of deformation energy. Rather, a model is proposed which is based on the existence of a “spinodal transition” from the isotropic into the highly oriented state.