Anisotropic Inclusions Research Articles

Implementing radial anisotropy with self-similar structures

Radial anisotropy in small objects has been linked to exotic optical properties. It can be implemented with a spherical inclusion that manifests self-similarity. We show that, when a self-similar, onion-like structure with alternating layers is homogenized by using an effective material approximation, the homogenized material becomes uniaxially anisotropic with the axis of anisotropy pointed radially outward from the center of the inclusion. This radial anisotropy becomes exact in the limit of a dense set of layers. The exact equivalence of the layered self-similar inclusion and the radially anisotropic inclusion manifests itself both in the effective permittivities of the two inclusions---when homogenized over the entire volumes---and in the internal potentials. Because the layered sphere and the radially anisotropic sphere are analogous, it is possible to study some of the interesting scattering features of radially anisotropic spheres in a realistic configuration. In particular, we show that the outcome of homogenizing the self-similar inclusion, and consequently the electric response, depends on what the core material at the center of the inclusion is and that a continuous transition between the two homogenization models is possible. The findings suggest intriguing applications in nanophotonics.

Plume deformation, mixing, and reaction kinetics: An analysis of interacting helical flows in three-dimensional porous media.

Heterogeneity and macroscopic anisotropy of porous media play an important role for dilution and reaction enhancement of conservative and reactive plumes. In this study, we perform numerical simulations to investigate steady-state flow and transport in three-dimensional heterogeneous porous media. We consider two macroscopic anisotropic inclusions resulting in helical flows with twisting streamlines in a three-dimensional flow-through domain. The inclusions are obtained by alternating two layers of angled slices of coarse and fine porous media with different hydraulic conductivity. We investigate flow and transport scenarios considering different geometry and relative position of the two anisotropic inclusions yielding helical flow fields with different extent of interaction. We use metrics of stretching and folding to characterize the flow field and entropy-based metrics for the analysis of the conservative and reactive transport problems. The outcomes show that the two helices result in different patterns of twisting streamlines, which cause distinct deformation of the plumes. However, mixing and reaction enhancement could not be directly related to the extent of the flow field deformation: Configurations with strong deformation can result in only moderate mixing enhancement, whereas configurations with limited deformation of the flow field can lead to significant mixing of the solute plume. Finally, we explore the impact of different degradation rates on reactive transport and the role of reaction kinetics on the entropy balance for a reactant undergoing transport and mixing-controlled degradation in the twisting flow fields. The results show that strong mixing enhancement due to helical flow increases the importance of the reaction kinetics that becomes the rate-limiting process for solute reactive transport.

Effective Parameters for 1D Photonic Crystals with Isotropic and Anisotropic Magnetic Inclusions: Coherent Wave Homogenization Theory.

A homogenization theory that can go beyond the regime of long wavelengths is proposed, namely, a theory that is still valid for vectors of waves near the edge of the first zone of Brillouin. In this paper, we consider that the displacement vector and the magnetic induction fields have averages in the volume of the cell associated with the values of the electric and magnetic fields in the edges of the cell, so they satisfy Maxwell’s equations. Applying Fourier formalism, explicit expressions were obtained for the case of a photonic crystal with arbitrary periodicity. In the case of one-dimensional (1D) photonic crystals, the expressions for the tensor of the effective bianisotropic response (effective permittivity, permeability and crossed magneto-electric tensors) are remarkably simplified. Specifically, the effective permittivity and permeability tensors are calculated for the case of 1D photonic crystals with isotropic and anisotropic magnetic inclusions. Through a numerical calculation, the dependence of these effective tensors upon the filling fraction of the magnetic inclusion is shown and analyzed. Our results show good correspondence with the approach solution of Rytov’s effective medium. The derived formulas can be very useful for the design of anisotropic systems with specific optical properties that exhibit metamaterial behavior.

Two-Dimensional Stress Analysis of an Infinite Plate with Anisotropic Inclusions by BFM

Based on the principle of a Body Force Method (BFM), any inclusion problem can besolved only by using a Kelvin solution which corresponds to a stress field caused by a point forceacting in a homogeneous infinite plate, regardless of the mechanical properties of the inclusion. Thischaracteristic is true even for an anisotropic inclusion in which the number of independent elasticconstants are larger than that of a homogeneous material. In the present study, some problems among anisotropic inclusions were analyzed numerically to demonstrate the validity.

Plasmonic Metamaterial Gels with Spatially Patterned Orientational Order via 3D Printing.

Optical properties can be programmed on mesoscopic scales by patterning host materials while ordering their nanoparticle inclusions. While liquid crystals are often used to define the ordering of nanoparticles dispersed within them, this approach is typically limited to liquid crystals confined in classic geometries. In this work, the orientational order that liquid crystalline colloidal hosts impose on anisotropic nanoparticle inclusions is combined with an additive manufacturing method that enables engineered, macroscopic three-dimensional (3D) patterns of co-aligned gold nanorods and cellulose nanocrystals. These gels exhibit polarization-dependent plasmonic properties that emerge from the unique interaction between the host medium’s anisotropic optical properties defined by orientationally ordered cellulose nanocrystals, from the liquid crystal’s gold nanorod inclusions, and from the complexity of spatial patterns accessed with 3D printing. The gels’ optical properties that are defined by the interplay of these effects are tuned by controlling the gels’ order, which is tuned by adjusting the gels’ cellulose nanocrystal concentrations. Lithe optical responsiveness of these composite gels to polarized radiation may enable unique technological applications like polarization-sensitive optical elements.

Elastic geobarometry for anisotropic inclusions in cubic hosts

Mineral inclusions entrapped in other minerals may record the local stresses at the moment of their entrapment in the deep Earth. When rocks are exhumed to the surface of the Earth, residual stresses and strains may still be preserved in the inclusion. If measured and interpreted correctly through elastic geobarometry, they give us invaluable information on the pressures (P) and temperatures (T) of metamorphism. Current estimates of P and T of entrapment rely on simplified models that assumes that the inclusion is spherical and embedded in an infinite host, and that their elastic properties are isotropic. We report a new method for elastic geobarometry for anisotropic inclusions in quasi-isotropic hosts. The change of strain in the inclusion is modelled with the axial equations of state of the host and the inclusion. Their elastic interaction is accounted for by introducing a 4th rank tensor, the relaxation tensor, that can be evaluated numerically for any symmetry of the host and the inclusion and for any geometry of the system. This approach can be used to predict the residual strain/stress state developed in an inclusion after exhumation from known entrapment conditions, or to estimate the entrapment conditions from the residual strain measured in real inclusions. In general, anisotropic strain and stress states are developed in non-cubic mineral inclusions such as quartz and zircon, with deviatoric stresses typically limited to few kbars. For garnet hosts, the effect of the mutual crystallographic orientation between the host and the inclusion on the residual strain and stress is negligible when the inclusion is spherical and isolated. Assuming external hydrostatic conditions, our results suggest that the isotropic and the new anisotropic models give estimations of entrapment conditions within 2%.

Estimates for the Thermoelastic Properties of a Composite with Ellipsoidal Anisotropic Inclusions

A mathematical model describing the thermoelastic characteristics of a composite reinforced by anisotropic ellipsoidal inclusions is proposed. The model is applied to estimating the thermoelastic properties in the case of strengthening the material with single-walled carbon nanotubes. The estimates obtained by the self-consistent method and dual variational formulation of a thermoelasticity problem for an inhomogeneous solid body are compared.

Parallel Volume Integral Equation Method for Two-Dimensional Elastodynamic Analysis

The parallel volume integral equation method (PVIEM) is applied for the analysis of two-dimensional elastic wave scattering problems in an unbounded isotropic solid containing various types of multiple multilayered anisotropic inclusions. It should be noted that the volume integral equation method (VIEM) does not require the use of the Green’s function for the anisotropic inclusion — only the Green’s function for the unbounded isotropic matrix is needed. A detailed analysis of the SH wave scattering problem is presented for various types of multiple multilayered orthotropic inclusions. Numerical results are presented for the elastic fields at the interfaces for square and hexagonal packing arrays of various types of multilayered orthotropic inclusions in a broad frequency range of practical interest. Standard parallel programming was used to speed up computation in the VIEM. The PVIEM enables us to investigate the effects of single/multiple scattering, fiber packing type, fiber volume fraction, single/multiple layer(s), multilayer’s shapes and geometry, isotropy/anisotropy, and softness/hardness of various types of multiple multilayered anisotropic inclusions on displacements and stresses at the interfaces of the inclusions and far-field scattering patterns. Also, powerful capabilities of the PVIEM for the analysis of general two-dimensional multiple scattering problems are investigated.

Determination of stresses in anisotropic plates with elastic inclusions based on singular integral equations

In this paper, the singular integral equations are written for anisotropic plates with elastic anisotropic inclusions in a simple form based on simple dependencies between the Lekhnitskii complex potentials and stress and strain [5]. The numerical method for solving integral equations is developed by the mechanical quadrature formulas. Simplicity, precision of the application and stability of obtained numerical solution is illustrated in stress calculations with controlled accuracy in anisotropic plates: with inclusions of arbitrary shapes; with a system of inclusions, including periodic one; at tension at infinity and concentrated forces applied to inclusions.

Tension Effects on the Interaction between Anisotropic Inclusions in a Fluid Membrane

The interaction between two inclusions embedded in a fluid membrane is studied analytically. We consider the case that the inclusions of a convex disk can change the curvature of the membrane aroun...

Analysis of the interference problem for anisotropic inclusion and notches by BFM

Analysis of the interference problem for anisotropic inclusion and notches by BFM

Conditions for the Jump of Stresses and Displacements on Thin Anisotropic Interlayers and Inclusions in Continuous Media

For problems of thin anisotropic interlayers, overlays, and inclusions in continuous three-dimensional media, we establish conditions that enable us to represent the action of the indicated heterogeneities by the presence of a surface with certain properties. In particular, in passing through this surface, the components of the vectors of displacements and stresses have discontinuities. In complicated problems of anisotropic heterogeneities in the medium, this enables us to decrease the dimensionality of defects in homogeneous structures, namely, the three-dimensional defects are reduced to two-dimensional defects and two-dimensional defects are reduced to one-dimensional. As a result, the problems are mathematically simplified, which makes it possible to obtain their efficient solutions.

Shaped beam scattering by an object with a uniaxial anisotropic inclusion

The differential scattering characteristics of an object having a uniaxial anisotropic inclusion, for incidence of an arbitrarily shaped beam, are theoretically investigated. The scattering problem is solved in a spherical basis by using the boundary conditions, method of moments technique and Schelkunoff’s equivalence theorem, which leads to a system of linear equations for the expansion coefficients of the scattered and internal fields when the description of the incident shaped beam is known. The theoretical formulation is reviewed, and the numerical problems are discussed. As examples, for a Gaussian beam, zero-order Bessel beam and Hertzian electric dipole radiation striking a spheroid with a uniaxial anisotropic spheroid inclusion and a circular cylinder with a uniaxial anisotropic circular cylinder inclusion, the normalized differential scattering cross sections are calculated, and the scattering properties are analyzed concisely.

Toward a Robust Elastic Geobarometry of Kyanite Inclusions in Eclogitic Diamonds

AbstractHere we report the first results from elastic geobarometry applied to a kyanite inclusion entrapped within an eclogitic diamond (from Voorspoed mine, South Africa) using micro‐Raman and Fourier transform infrared spectroscopy, electron microprobe analysis, ab initio calculations, and finite element modeling. Application of elastic geobarometry to very elastically anisotropic kyanite inclusions is challenging, as current models do not allow for elastic anisotropy. In order to minimize the effects of anisotropy, we have explored the effects of deviatoric stress on Raman modes via ab initio density functional theory. The results allowed us to select the Raman mode (at ca. 638 cm−1) that is the least sensitive to deviatoric stress. The shift of this band in the inclusion while still trapped within the diamond relative to the inclusion in air (once liberated) was used under hydrostatic approximation to determine a residual pressure on the inclusion of 0.184 ± 0.045 GPa and an entrapment pressure of 5.2 ± 0.3 GPa (~160 km depth) for an FTIR N‐aggregation residence temperature of 1119 ± 50 °C. This is the first geothermobarometric determination for a diamond from the Voorspoed kimberlite. It overlaps with P–T estimates obtained by traditional chemical geobarometry for diamonds from other kimberlites from the Kaapvaal craton, suggesting that the hydrostatic approximation does not introduce significant errors in the geobarometric evaluation. Our protocol of Raman peak selection can be used for geobarometry of further kyanite‐bearing diamonds and may provide a guide for more robust geobarometry of other types of mineral inclusions in diamonds, both eclogitic and peridotitic.

ABOUT THE PRE-OUTBURST STATE OF THE COAL AND SANDSTONE AND THE POSSIBLE MECHANISM OF COAL AND GAS OUTBURST PROCESS

The paper aims to examine the suitability of A. S. Balankin brittle fracture criterion in predicting the of large-scale coal and gas outbursts in underground coal mines under compression load. Formation of dissipative structures as cracks and clusters of local microcracking occurs under the influence of the rock pressure. The formation of microdefects in dissipative structures occurs mainly on local anisotropic inclusions. Mechanism of pre-outburst spalling of gas-saturated coal is analyzed. Destruction (primary outburst) occurs when the brittle fracture conditions are met. And also in the case of such a ratio of “coal seam thickness – the size of micro defects aggregations”, which provides reduction in coal strength to a minimum. Further destruction occurs by known scenario.

Scattering of elastic bulk waves by periodic arrays of voids or anisotropic inclusions

A two-scale asymptotic analysis coupled with the spatially periodic fundamental solutions is used for analyzing diffraction of elastic bulk waves propagating in anisotropic media containing periodic inclusions or voids. The explicit equations are derived for the scattering cross sections and velocities of bulk waves propagating in spatially periodic media with arbitrary elastic anisotropy.

Thermoelastic Characteristics of a Composite with Anisotropic Platelike Inclusions

A mathematical model is constructed describing the thermomechanical action of the elements of a composite structure (platelike inclusion and matrix particles) and isotropic elastic medium with the required thermomechanical characteristics. The model is used at the first stage to obtain the matrix relations by the self-consistent method to find the elastic modulus of the composite. At the second stage, it is used to determine the temperature coefficient of linear expansion. Using the variation approach for the composite considered, the two-way estimates of the volumetric elasticity modulus, shearing modulus, and temperature coefficient of linear expansion are determined. The estimated dependences presented allow forecasting the thermoelastic characteristics of the composite, which is reinforced with the anisotropic platelike inclusions (including in the form of nanostructural elements).

Lipid-protein interaction induced domains: Kinetics and conformational changes in multicomponent vesicles.

The spatio-temporal organization of proteins and the associated morphological changes in membranes are of importance in cell signaling. Several mechanisms that promote the aggregation of proteins at low cell surface concentrations have been investigated in the past. We show, using Monte Carlo simulations, that the affinity of proteins for specific lipids can hasten their aggregation kinetics. The lipid membrane is modeled as a dynamically triangulated surface with the proteins defined as in-plane fields at the vertices. We show that, even at low protein concentrations, strong lipid-protein interactions can result in large protein clusters indicating a route to lipid mediated signal amplification. At high protein concentrations, the domains form buds similar to that seen in lipid-lipid interaction induced phase separation. Protein interaction induced domain budding is suppressed when proteins act as anisotropic inclusions and exhibit nematic orientational order. The kinetics of protein clustering and resulting conformational changes are shown to be significantly different for the isotropic and anisotropic curvature inducing proteins.

Near and far field scattering of SH waves by multiple multilayered anisotropic circular inclusions using parallel volume integral equation method

PurposeThe purpose of this paper is to calculate near field and far field scattering of SH waves by multiple multilayered anisotropic circular inclusions using parallel volume integral equation method (PVIEM) quantitatively.Design/methodology/approachThe PVIEM is applied for the analysis of elastic wave scattering problems in an unbounded solid containing multiple multilayered anisotropic circular inclusions. It should be noted that this numerical method does not require the use of the Green’s function for the inclusion – only the Green’s function for the unbounded isotropic matrix is needed. This method can also be applied to solve general elastodynamic problems involving inhomogeneous and/or anisotropic inclusions whose shape and number are arbitrary.FindingsA detailed analysis of the SH wave scattering problem is presented for multiple multilayered orthotropic circular inclusions. Numerical results are presented for the displacement fields at the interfaces and the far field scattering patterns for square and hexagonal packing arrays of multilayered circular inclusions in a broad frequency range of practical interest.Originality/valueTo the best of the authors’ knowledge, the solution for scattering of SH waves by multiple multilayered anisotropic circular inclusions in an unbounded isotropic matrix is not currently available in the literature. However, in this paper, calculation of displacements on interfaces and far field scattering patterns of multiple multilayered anisotropic circular inclusions using PVIEM as a pioneer of numerical modeling enables us to investigate the effects of single/multiple scattering, fiber packing type, fiber volume fraction, single/multiple layer(s), the multilayer’s geometry, isotropy/anisotropy and softness/hardness.

Effects of strain energy on the recrystallization within narrow metallization

Elastic strain energy within materials due to recrystallization of grains with a specific orientation, or texture, can be calculated through the use of Eshelby inclusions, where a recrystallized grain can be treated as an elastically anisotropic inclusion in an elastically isotropic matrix. The evolution of texture that minimizes elastic strain energy is shown to be dependent on the specific strain state. The interaction strains generated by this elastic incompatibility and corresponding strain energy have been derived for grains with cubic symmetry for general forms of the applied strain tensor. For uniaxial and isotropic, biaxial strain tensors, the interaction strain tensor and corresponding elastic strain energy density are proportional to the orientation parameter, Γ, which relates the Miller indices of the recrystallized grain to the loading direction: either parallel to the uniaxial strain direction or perpendicular to the plane in which isotropic biaxial strain is applied. It is rigorously proven that for elastically isotropic inclusions, corresponding to Γ = 1/5, the interaction strain is zero. Although blanket films often possess an isotropic, biaxial stress state, metallization trenches can exhibit a combination of normal and shear strain components, particularly near the trench corners. It is shown that in cases where shear is present, the resulting elastic strain energy can be lowered by the development of (110) texture despite its higher surface energy, as has been observed in thin films and interconnect trenches. These results suggest that shear strain can play an important role in the evolution of texture in narrow, metallization structures.