Showing papers on "Isotropy published in 2009"

Achieving control of in-plane elastic waves

Abstract: We derive the elastic properties of a cylindrical cloak for in-plane coupled shear and pressure waves. The cloak is characterized by a rank 4 elasticity tensor with spatially varying entries, which are deduced from a geometric transform. Remarkably, the Navier equations retain their form under this transform, which is generally untrue [G. W. Milton et al., N. J. Phys. 8, 248 (2006)]. The validity of our approach is confirmed by comparison of the analytic Green’s function in homogeneous isotropic elastic space against full-wave finite element computations in a heterogeneous anisotropic elastic region surrounded by perfectly matched layers.

Biomimetic isotropic nanostructures for structural coloration

Abstract: We describe the self-assembly of biomimetic isotropic films which display structural color amenable to potential applications in coatings. Isotropic structures can produce color if there is a pronounced characteristic length-scale comparable to the wavelength of visible light and wavelength-independent scattering is suppressed.

An anisotropic rotary diffusion model for fiber orientation in short- and long-fiber thermoplastics

Abstract: The Folgar–Tucker model, which is widely-used to predict fiber orientation in injection-molded composites, accounts for fiber–fiber interactions using isotropic rotary diffusion. However, this model does not match all aspects of experimental fiber orientation data, especially for composites with long discontinuous fibers. This paper develops a fiber orientation model that incorporates anisotropic rotary diffusion. From kinetic theory we derive the evolution equation for the second-order orientation tensor, correcting some errors in earlier treatments. The diffusivity is assumed to depend on a second-order space tensor, which is taken to be a function of the orientation state and the rate of deformation. Model parameters are selected by matching the experimental steady-state orientation in simple shear flow, and by requiring stable steady states and physically realizable solutions. Also, concentrated fiber suspensions align more slowly with respect to strain than models based on Jeffery's equation, and we incorporate this behavior in an objective way. The final model is suitable for use in mold filling and other flow simulations, and it gives improved predictions of fiber orientation for injection molded long-fiber composites.

Generalized hooke's law for isotropic second gradient materials

Abstract: In the spirit of Germain the most general objective stored elastic energy for a second gradient material is deduced using a literature result of Fortune ´ & Vallee. Linear isotropic constitutive relations for stress and hyperstress in terms of strain and strain- gradient are then obtained proving that these materials are characterized by seven elastic moduli and generalizing previous studies by Toupin, Mindlin and Sokolowski. Using a suitable decomposition of the strain-gradient, it is found a necessary and sufficient condition, to be verified by the elastic moduli, assuring positive definiteness of the stored elastic energy. The problem of warping in linear torsion of a prismatic second gradient cylinder is formulated, thus obtaining a possible measurement procedure for one of the second gradient elastic moduli.

Reverse time migration in tilted transversely isotropic (TTI) media

Abstract: Reverse time migration (RTM) exhibits great advantages over other imaging methods because it is based on computing numerical solutions to a two-way wave equation. It does not suffer from dip limitation like one-way downward continuation techniques do, thus enabling overturned reflections to be imaged. As well as correctly handling multipathing, RTM has the potential to image internal multiples when the boundaries responsible for generating the multiples are present in the model. In isotropic media, one can use a scalar acoustic wave equation for RTM of pressure data. In anisotropic media, P- and SV-waves are coupled together so, formally, elastic wave equations must be used for RTM. A new wave equation for P-waves is proposed in tilted transversely isotropic (TTI) media that can be solved as part of an acoustic anisotropic RTM algorithm, using standard explicit finite differencing. If the shear velocity along the axis of symmetry is set to zero, stable numerical solutions can be computed for media with a ...

Power asymmetry in cosmic microwave background fluctuations from full sky to sub-degree scales: Is the universe isotropic?

Abstract: We repeat and extend the analysis of Eriksen et al. and Hansen et al., testing the isotropy of the cosmic microwave background fluctuations. We find that the hemispherical power asymmetry previously reported for the largest scales l = 2-40 extends to much smaller scales. In fact, for the full multipole range l = 2-600, significantly more power is found in the hemisphere centered at (θ = 107° ± 10°, ∅ = 226° ± 10°) in galactic co-latitude and longitude than in the opposite hemisphere, consistent with the previously detected direction of asymmetry for l = 2-40. We adopt a model selection test where the direction and amplitude of asymmetry, as well as the multipole range, are free parameters. A model with an asymmetric distribution of power for l = 2-600 is found to be preferred over the isotropic model at the 0.4% significance level, taking into account the additional parameters required to describe it. A similar direction of asymmetry is found independently in all six subranges of 100 multipoles between l = 2-600. None of our 9800 isotropic simulated maps show a similarly consistent direction of asymmetry over such a large multipole range. No known systematic effects or foregrounds are found to be able to explain the asymmetry.

Equilibrium and travelling-wave solutions of plane Couette flow

Abstract: We present 10 new equilibrium solutions to plane Couette flow in small periodic cells at low Reynolds number Re and two new travelling-wave solutions. The solutions are continued under changes of Re and spanwise period. We provide a partial classification of the isotropy groups of plane Couette flow and show which kinds of solutions are allowed by each isotropy group. We find two complementary visualizations particularly revealing. Suitably chosen sections of their three-dimensional physical space velocity fields are helpful in developing physical intuition about coherent structures observed in low-Re turbulence. Projections of these solutions and their unstable manifolds from their ∞-dimensional state space on to suitably chosen two- or three-dimensional subspaces reveal their interrelations and the role they play in organizing turbulence in wall-bounded shear flows.

Laboratory test of the isotropy of light propagation at the 10(-17) level.

Abstract: We report on the results of a strongly improved test of local Lorentz invariance, consisting of a search for an anisotropy of the resonance frequencies of electromagnetic cavities. The apparatus comprises two orthogonal standing-wave optical cavities interrogated by a laser, which were rotated approximately 175 000 times over the duration of 13 months. The measurements are interpreted as a search for an anisotropy of the speed of light, within the Robertson-Mansouri-Sexl (RMS) and the standard model extension (SME) photon sector test theories. We find no evidence for an isotropy violation at a 1sigma uncertainty level of 0.6 parts in 10{sup 17} (RMS) and 2 parts in 10{sup 17} for seven of eight coefficients of the SME.

Light propagation in statistically homogeneous and isotropic dust universes

Abstract: We derive the redshift and the angular diameter distance in rotationless dust universes which are statistically homogeneous and isotropic, but have otherwise arbitrary geometry. The calculation from first principles shows that the Dyer-Roeder approximation does not correctly describe the effect of clumping. Instead, the redshift and the distance are determined by the average expansion rate, the matter density today and the null geodesic shear. In particular, the position of the CMB peaks is consistent with significant spatial curvature provided the expansion history is sufficiently close to the spatially flat ΛCDM model.

Overdetermined anisotropic elliptic problems

Abstract: A symmetry result is established for solutions to overdetermined anisotropic elliptic problems in variational form, which extends Serrin’s theorem dealing with the isotropic radial case. The involved anisotropy arises from replacing the Euclidean norm of the gradient with an arbitrary norm in the associated variational integrals. The resulting symmetry of the solutions is that of the so-called Wulff shape.

Zero thermal expansion in a pure-form antiperovskite manganese nitride

Abstract: A zero thermal expansion material in a pure form is fabricated using an antiperovskite manganese nitride. The isotropic zero thermal expansion is achieved by optimizing the heat treatment and the chemical composition. The present study suggests that the heat treatment affects the thermal expansion mainly via the nitrogen content of the material. The obtained materials exhibit a low expansion of |α|<0.5×10−6 K−1 (α is the coefficient of linear thermal expansion) over a broad temperature range, which includes room temperature. They are desirable for many fields of industry as reliable, mechanically hard, and low-cost zero thermal expansion materials.

Estimation of the effect of non-isotropic distributed energy on the apparent arrival time in correlations

Abstract: Correlations of random seismic noise are now widely used to retrieve the Green’s function between two points. Whereas this technique provides useful results in tomography and monitoring studies, it is mainly limited by an uneven distribution of noise sources. In that case, theoretical requirements are not completely fulfilled and we may wonder how reliable the reconstructed signals are, in particular for the purpose of estimating traveltime from correlations. This study finds a way to quantify effects of a nonisotropic noise field by estimating the arrival-time error resulting from a particular nonisotropic distribution of recorded wave intensity. Our study is based on a theoretical prediction of this bias and we successfully test the theory by comparing the theoretical expectation to real measurements from seismic-prospecting data. In particular, we distinguish between the effects of source distribution and the effects of medium heterogeneity between the sources and the region of receivers. We find relat...

Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth.

Abstract: The authors introduce a general mechanism, based on electrostatic and magnetostatic considerations, for designing three-dimensional isotropic metamaterials that possess an enhanced refractive index over an extremely large frequency range. The mechanism allows nearly independent control of effective electric permittivity and magnetic permeability without the use of resonant elements.

Linear and Circular Array Optimization: a Study Using Particle Swarm Intelligence

Abstract: Linear and circular arrays are optimized using the particle swarm optimization (PSO) method. Also, arrays of isotropic and cylindrical dipole elements are considered. The parameters of isotropic arrays are elements excitation amplitude, excitation phase and locations, while for dipole array the optimized parameters are elements excitation amplitude, excitation phase, location, and length. PSO is a high-performance stochastic evolutionary algorithm used to solve N-dimensional problems. The method of PSO is used to determine a set of parameters of antenna elements that provide the goal radiation pattern. The efiectiveness of PSO for the design of antenna arrays is shown by means of numerical results. Comparison with other methods is made whenever possible. The results reveal that design of antenna arrays using the PSO method provides considerable enhancements compared with the uniform array and the synthesis obtained from other optimization techniques.

One-way diffraction effects in photonic crystal gratings made of isotropic materials

Abstract: The anomalous diffraction effects arising in the intrinsically isotropic photonic crystal gratings with different periods of the front-side and back-side interfaces are studied with the emphasis put on wideband one-way transmission. It is demonstrated that more than 80 percent of the incident-wave energy can be transmitted unidirectionally, i.e., with zero transmission in the opposite direction, by changing side of illumination only, while polarization always remains linear. Most but not all of the related diffraction effects can be predicted using isofrequency contours (IFCs) and wave-vector diagrams, which take into account the IFC-shape-dependent additional transmission channels that can appear due to corrugations. Three main regimes, i.e., isolation and bidirectional and unidirectional translation, can be distinguished, depending on whether the front-side corrugations affect the far field in the half space bounded by the back-side interface, and whether transmission is vanishing only at illumination from the side of one of the interfaces. The conditions providing the existence of these regimes are given and discussed in terms of the features of wave-vector diagrams. In some cases, similar regimes can appear being in contradiction with these conditions. Variation in the angle of incidence and the angle between the characteristic directions of photonic crystal and the interfaces of the corresponding noncorrugated structure allows one extending variety of situations, in which unidirectional transmission can be realized. The general condition of unidirectionality is that the zero diffraction order is not coupled to a Floquet-Bloch wave.

Spherical cloaking with homogeneous isotropic multilayered structures.

Abstract: We propose a practical realization of electromagnetic spherical cloaking by layered structure of homogeneous isotropic materials. By mimicking the classic anisotropic cloak by many alternating thin layers of isotropic dielectrics, the permittivity and permeability in each isotropic layer can be properly determined by effective medium theory in order to achieve invisibility. The model greatly facilitates modeling by Mie theory and realization by multilayer coating of dielectrics. Eigenmode analysis is also presented to provide insights of the discretization in multilayers.

Anisotropic micro-sphere-based finite elasticity applied to blood vessel modelling

Abstract: A fully three-dimensional anisotropic elastic model for vascular tissue modelling is here presented. The underlying strain energy density function is assumed to additively decouple into volumetric and deviatoric contributions. A straightforward isotropic neo-Hooke-type law is used to model the deviatoric response of the ground substance, whereas a micro-structurally or rather micro-sphere-based approach will be employed to model the contribution and distribution of fibres within the biological tissue of interest. Anisotropy was introduced by means of the use of von Mises orientation distribution functions. Two different micro-mechanical approaches -- a, say phenomenological, exponential ansatz and a worm-like-chain-based formulation -- are applied to the micro-fibres and illustratively compared. The passage from micro-structural contributions to the macroscopic response is obtained by a computational homogenisation scheme, namely numerical integration over the surface of the individual micro-spheres. The algorithmic treatment of this integration is discussed in detail for the anisotropic problem at hand, so that several cubatures of the micro-sphere are tested in order to optimise the accuracy at reasonable computational cost. Moreover, the introduced material parameters are identified from simple tension tests on human coronary arterial tissue for the two micro-mechanical models investigated. Both approaches are able to recapture the experimental data. Based on the identified sets of parameters, we first discuss a homogeneous deformation in simple shear to evaluate the models' response at the micro-structural level. Later on, an artery-like two-layered tube subjected to internal pressure is simulated by making use of a non-linear finite element setting. This enables to obtain the micro- and macroscopic responses in an inhomogeneous deformation problem, namely a blood-vessel-representative boundary value problem. The effect of residual stresses is additionally included in the model by means of a multiplicative decomposition of the deformation gradient tensor which turns out to crucially affect the simulation results. (Less)

A new paradigm: the linear isotropic Cosserat model with conformally invariant curvature energy.

Abstract: This is an essay on a linear Cosserat model with weakest possible constitutive assumptions on the curvature energy still providing for existence, uniqueness and stability. The assumed curvature energy is the conformally invariant expression L 2 k dev symr axlAk 2 , where axlA is the axial vector of the skewsymmetric microrotation A 2 so(3), dev is the orthogonal projection on the Lie-algebra sl(3) of trace free matrices and sym is the orthogonal projection onto symmetric matrices. It is observed that unphysical singular stiening for small samples is avoided in torsion and bending while size eects are still present. The number of Cosserat parameters is reduced from six to four: in addition to the (size-independent) classical linear elastic Lam e moduli and only one Cosserat coupling constant c > 0 and one length scale parameter Lc > 0 need to be determined. We investigate those deformations not leading to moment stresses for dierent curvature

Inflation from N-Forms and its stability

Abstract: We investigate whether inflation, either isotropic or anisotropic, may be sup- ported by n-forms. Canonical field strengths and their duals are taken into account, and they are allowed to have a potential and also, when necessary for slow-roll, a nonminimal curvature coupling. New isotropic solutions are found for three-forms. It is also shown that some n-form actions are equivalent to f(R) gravity and scalar field models with pos- sible nonminimal couplings. Anisotropic solutions are found for two-forms, generalising vector inflation. However, as the later also the two-form is unstable during inflation due to the nonminimal coupling to curvature. The stability of the isotropic background solutions supported by a triad of vectors is also analysed.

When and how do cracks propagate

Abstract: Crack propagation in an isotropic 2d brittle material is widely viewed as the interplay between two separate criteria. Griffith's cap on the energy release rate along the crack path decides when the crack propagates, while the Principle of Local Symmetry PLS decides how, that is, in which direction, that crack propagates. The PLS , which essentially predicts mode I propagation, cannot possibly hold in an anisotropic setting. Further it disagrees with its competitor, the principle of maximal energy release, according to which the direction of propagation should coincide with that of maximal energy release. Also, continuity of the time propagation is always implicitly assumed. In the spirit of the rapidly growing variational theory of fracture, we revisit crack path in the light of an often used tool in physics, i.e. energetic meta-stability of the current state among suitable competing crack states. In so doing, we do not need to appeal to either isotropy, or continuity in time. Here, we illustrate the impact of meta-stability in a 2d setting. In a 2d isotropic setting, it recovers the PLS for smooth crack paths. In the anisotropic case, it gives rise to a new criterion. But, of more immediate concern to the community, it also demonstrates that 2d crack kinking in an isotropic setting is incompatible with continuity in time of the propagation. Consequently, if viewing time continuity as non-negotiable, our work implies that the classical view of crack kinking along a single crack branch is not correct and that a change in crack direction necessarily involves more subtle geometries or evolutions.