Isotropic Density Research Articles

Acoustic cloaking using layered pentamode materials

While receiving less attention in the literature than electromagnetic cloaking, theoretical efforts to define and create acoustic cloaks based upon mimicking coordinate transformations through use of metamaterials is of interest. The present work extends recent analysis of Norris [Proc. R. Soc. London, Ser. A 464, 2411-2434 (2008)] by considering a range of cloaks, from those comprised of fluid layers which are isotropic in bulk moduli with anisotropic density to those having anisotropic bulk moduli and isotropic density. In all but pure inertial varieties, fluid layers comprising the cloaks are pentamode materials governed by a special scalar acoustic equation for pseudopressure derived by Norris. In most cases presented, material properties of the fluid/pentamode layers are based upon target values specified by continuously varying properties resulting from theoretical coordinate transformations geared to minimize scattered pressure limited by realistic goals. The present work analyzes such cloaks for the specific case of plane wave scattering from an acoustically hard sphere. An initial exploration of the parameter space defining such cloaks (for example, material properties of its constituent layers, and operating frequency) is undertaken with a view toward "optimal" design.

Acoustic scattering from layered pentamode materials.

While receiving less attention in the literature than in the field of electromagnetic scattering, theoretical efforts to define and create acoustic skins capable of reducing scattered energy from obstacles by way of mimicking coordinate transformations through use of meta-materials have begun. The present work extends recent analysis of Norris by considering a variety of acoustic skins, from those comprised of fluid layers which are isotropic in bulk moduli with anisotropic density to those having anisotropic bulk moduli and isotropic density. In all but pure inertial types, fluid layers comprising the skins are pentamode materials governed by a special scalar acoustic equation for pseudo-pressure derived by Norris. In most cases presented, material properties of the fluid/pentamode layers are based upon target values specified by continuously varying properties resulting from theoretical coordinate transformations geared to minimize scattered pressure limited by realistic goals. The present work analyzes acoustic skins for the specific case of plane wave scattering from an acoustically hard sphere. An initial exploration of the parameter space defining such skins (for example, material properties of its constituent layers and operating frequency) is undertaken with a view toward “optimal” design. [Work supported by the NAVSEA Newport In-House Laboratory Individual Research (ILIR) Program.]

Development of isotropic compatible HDPE/PP blends for structural applications

AbstractIn an attempt to provide superior products for the structural applications, this study aimed at preparing isotropic compatible high density polyethylene (HDPE)/ polypropylene (PP) blends without the use of the expensive compatibilization technique. Morphological and structural characterizations of the homopolymers and blends were carried out. In addition, some of the structurally important mechanical and thermal properties were characterized. Such characterizations were performed to investigate whether or not the blends are compatible and therefore acceptable for the structural applications. Scanning electron microscope (SEM) micrographs of the blend samples indicate that the interfacial adhesion between HDPE and PP phases is intimate in the 5/95 HDPE‐PP, good in the 85/15 HDPE‐PP and 95/5 HDPE‐PP, fair in the 30/70 HDPE‐PP and very poor in the 50/50 HDPE‐PP. Similarly, mechanical and thermal responses of the first three blends are remarkable. The 30/70 HDPE‐PP blend displays a fairly good performance. Whereas, the properties of the 50/50 HDPE‐PP blend are very poor. This decides that the first three blends are compatible and, therefore, structurally attractive materials. The fourth is partially compatible and, as a consequence, can be rather acceptable for the structural applications. However, the fifth is incompatible and, of course, is not acceptable for such applications. On the other hand, SEM micrographs and differential scanning calorimetry results indicate that the crystalline structures of individual polymers are appreciably affected by blending. Additionally, the study reveals that the end use performance of blends is strongly dependent on the crystalline structure changes occurring in each component due to blending as well as the compatibility between the blend components. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010

Relaxation Theorem and Lower-Dimensional Models in Micropolar Elasticity

In this paper we prove the relaxation theorem in micropolar elasticity and use it, together with the semicontinuity theorem, to justify lower-dimensional models of rods (and plates) by means of Γ-convergence starting from general energy functionals. The internal energy density is assumed to be continuous and satisfies some growth and coercivity conditions. In particular, we apply these results to derive a rod model starting from quadratic isotropic energy density function of a cylindrical three-dimensional micropolar body.

Cloaking bending waves propagating in thin elastic plates

We introduce a cylindrical cloak to control the bending waves propagating in thin plates. This is achieved through radially dependent isotropic mass density and radially dependent and orthotropic flexural rigidity deduced from a coordinate transformation for the biharmonic propagation equation in the spirit of the paper of Pendry et al. [Science 312, 1780 (2006)]. We analyze the response of the cloak surrounding a clamped obstacle in the presence of a cylindrical excitation. We note that whereas the studied bending waves are of different physical and mathematical nature, they are cloaked in many ways as their electromagnetic and acoustic counterparts; e.g., when the source lies inside the coating, it seems to radiate from a shifted location (mirage effect).

Polarization-Resolved Ultrafast Polarizability Relaxation in Polar Aromatic Liquids

The isotropic part of the polarizability relaxation of three polar aromatic liquids has been measured as a function of temperature using a diffractive optic based heterodyne detection method. The isotropic spectral density, which contains only interaction induced components of the liquid's collective polarizability, is contrasted with the anisotropic response to unravel the interaction induced and molecular contributions to the latter. Very similar behavior was observed for the three different aromatic liquids. The fast damping of the isotropic response in the time domain confirms the assignment of the prominent slow exponential relaxation in the anisotropic response to diffusive molecular orientational relaxation. The isotropic response in the frequency domain is found to be asymmetric and peaked at low frequency but extended to higher frequencies, thus contributing over a rather wide frequency range. The relatively low mean frequency of the isotropic spectral density supports the assignment of the highest frequency part of the anisotropic response to molecular librational motion. Finally, a number of affinities are noted between the interaction-induced (isotropic) response and the low frequency shoulder in the anisotropic spectral density, which is so characteristic of the dynamics of aromatic liquids. These data are discussed in relation to some existing molecular dynamics simulations.

Secondary Post-Traumatic Enophthalmos: High-Resolution Magnetic Resonance Imaging Compared With Multislice Computed Tomography in Postoperative Orbital Volume Measurement

Multislice computed tomography (MSCT) was the modality of choice for orbital volume measurement. This first prospective study compares MSCT with high-resolution magnetic resonance imaging (MRI) combined with micro (MRImc) and headcoil (MRIhc) in volumetric evaluation of the postsurgical enophthalmic orbit. Morphologic and dimensional changes of the orbit, eyebulb, and fat content were investigated 3 to 4 months after reconstruction of complex orbital fractures in 36 patients. Image analysis and volumetric assessment from 2-dimensional and 3-dimensional-MRImc and MRIhc were compared with MSCT. The volume segmentation algorithm operated on multispectral, 3-dimensional MR data acquired at isotropic proton density weighted acquisitions. CT and MRI volume data correlated significantly (P < .01). Enlargement of the posterior segment often resulted in orbital geometry change from conical to convex. Even cases of correct orbital reconstruction presented significant volume enlargement compared to the contralateral side (P < .01). The retro bulbar fat showed itself fragmented and was dislocated in the medial posterior region mostly. We found reduced sagittal eye projection, increased width of the orbital rim, and dislocation of the posteromedial orbital floor (P < .01). High correlation was detected between orbital volume increment and degree of enophthalmos (0.93 mm per 1 cm3 orbital volume enlargement diameter) (P < .01). As MRI orbital volume measurement permitted prediction of postsurgical enophthalmos, which is related to possible failure in orbital volume correction and reduction of the posterior medial bulge and not to fat content changes, it is suited for planning secondary correction.

Radiation characteristics of a coaxial waveguide with eccentric inner conductor for application in hyperthermia and microwave reflex therapy

Abstract. This paper examines the radiation characteristics of a contact emitter conceived for application in hyperthermia and microwave reflex therapy. It is important to analyse the distribution of power density in the near field area, as the radiator's therapeutic sphere of activity is localized here. The contact emitter is a coaxial radiator with an eccentric course of the inner conductor. According to Huygens principle, a theoretical view of the near field radiation characteristics is made by determining the equivalent current densities in the emitter aperture. It is shown that by an eccentric shift of the inner conductor, an almost isotropic near field radiation pattern and power density can be achieved. For this, the electromagnetic field in the emitter aperture is determined by using a Bipolar coordinate system. This calculation considers only the fundamental TEM mode of the contact emitter. Besides the theoretical results near and far fields are simulated using the programme system Ansoft HFSS.

Butterfly patterns in crystalline polymers under uniaxial stretch

We investigate the density fluctuations in crystalline polymers under uniaxial stretch in the order of submicrons to microns with two-dimensional ultrasmall-angle x-ray scattering. Before uniaxial stretch, we found isotropic density fluctuations obeying the mass fractal with the fractal dimension 2.6. After uniaxial stretch, the isotropic scattering pattern was transformed into the butterfly pattern. The butterfly pattern is caused by the stress-induced density fluctuations and the heterogeneous deformation associating with the spatial heterogeneity of stress field due to the distribution of crystalline and amorphous regions.

Solid state NMR spectroscopy as a probe of structure and bonding in the carbides Sc 3TC 4 (T = Co, Ni, Ru, Rh, Os, Ir)

Scandium transition metal carbides having the formula Sc 3TC 4 (T = Co, Ni, Ru, Rh, Os, Ir) have been structurally characterized by solid state 13C and 45Sc nuclear magnetic resonance spectroscopy. In all the compounds investigated, well-resolved signals are observed for crystallographically distinct carbon and scandium sites, confirming the formation of superstructures in the Rh and Ir compounds at ambient temperature. 45Sc NMR spectra are dominated by anisotropic broadening due to second-order quadrupolar perturbations. The nuclear electric quadrupolar coupling parameters (the coupling constant C Q and the asymmetry parameter η) are generally found in good agreement with values calculated theoretically from the crystal structure using the WIEN2k program. Furthermore, the spectra reveal large isotropic resonance shift differences between inequivalent Sc sites in a given compound and between sites of the same type for different compounds. Altogether the results illustrate that 45Sc NMR is a sensitive method for detecting isotropic and anisotropic local electron density variations in the Sc 3TC 4 family.

Contrasting Mechanical Anisotropies of the SuperfluidHe3Phases in Aerogel

There has been much recent interest in how impurity scattering may affect the phases of the p-wave superfluid 3He. Impurities may be added to the otherwise absolutely pure superfluid by immersing it in aerogel. Some predictions suggest that impurity scattering may destroy orientational order and force all of the superfluid phases to have an isotropic superfluid density. In contrast to this, we present experimental data showing that the response of the A-like phase to superfluid flow is highly anisotropic, revealing a texture that is easily modified by flow.

On measuring the covariance matrix of the non-linear power spectrum from simulations

We show how to estimate the covariance of the power spectrum of a statistically homogeneous and isotropic density field from a single periodic simulation, by applying a set of weightings to the density field, and by measuring the scatter in power spectra between different weightings. We recommend a specific set of 52 weightings containing only combinations of fundamental modes, constructed to yield a minimum variance estimate of the covariance of power. Numerical tests reveal that at non-linear scales the variance of power estimated by the weightings method substantially exceeds that estimated from a simple ensemble method. We argue that the discrepancy is caused by beat-coupling, in which products of closely spaced Fourier modes couple by non-linear gravitational growth to the beat mode between them. Beat-coupling appears whenever non-linear power is measured from Fourier modes with a finite spread of wavevector, and is therefore present in the weightings method but not in the ensemble method. Beat-coupling inevitably affects real galaxy surveys, whose Fourier modes have finite width. Surprisingly, the beat-coupling contribution dominates the covariance of power at non-linear scales, so that, counter-intuitively, it is expected that the covariance of non-linear power in galaxy surveys is dominated not by small-scale structure, but rather by beat-coupling to the largest scales of the survey.

Electronic spin transitions and the seismic properties of ferrous iron‐bearing MgSiO3 post‐perovskite

The elastic constants of post‐perovskite of chemical composition Mg0.9375Fe0.0625SiO3 and Mg0.8750Fe0.1250SiO3 have been calculated at 0 K and 136 GPa using ab initio methods. For both compositions studied, iron remains in a high‐spin state below 180 GPa at 0 K. The effect of spin state on elastic properties is small. Logarithmic derivations of isotropic wave velocities and density with respect to ferrous iron content are similar to those predicted from pure end‐members.

Quantum back reactions in slow-roll cosmologies

We summarize the results of a calculation (B. Losic and W.G. Unruh. Phys. Rev. D, 72, 123510 (2005).) of cosmological back reactions about a slowly rolling background space-time. In particular, we evaluate the effect of the superhorizon second-order corrections on the (superhorizon) inhomogeneous modes of the linearized fluctuations. Their physical significance is quantified by studying their effective equation of state, where the isotropic pressure and energy density at second order are defined in terms of the averaged eigenvalues associated with timelike (spacelike) eigenvectors of a total stress energy for the metric and matter fluctuations. Given a well-defined gauge fixing at second order, we find that the higher order corrections may dominate those of the linear terms and, furthermore, that this result holds for other reasonable gauge-fixing procedures. Our work suggests that for many parameters of slow-roll inflation, the second-order effects may dominate over the first-order effects for the super-Hubble evolution. We also find that the contribution to the equation of state due to the back reactions is that of a negative cosmological constant in this coordinate gauge, confirming earlier work.PACS Nos.: 31.15.Pf, 31.30.Jv, 32.10.Hq

1408 自・公転型研磨工具の提案(S80-1 特殊加工プロセス(1),S80 特殊加工プロセス)

A rotation/revolution type polishing tool has been proposed for surface roughness improvement and for polishing rate stability. Pipe-shaped tool is driven to rotation and revolution, simultaneously. When the rotation axis is inclined in a plane to the revolution axis normal to work surface, the end surface of the pipe-shaped tool would be formed through work polishing and tool wearing from cone to sphere. Then, the spherical contact between tool surface and work surface is expected to result an ideal tool locus condition that is an isotropic and homogenous tool locus density over the contact area.

Density Scaling and Anisotropy in Supersonic Magnetohydrodynamic Turbulence

We study the statistics of density for supersonic turbulence in a medium with magnetic pressure larger than the gaseous pressure. Our simulations exhibit clumpy density structures, with the contrast increasing with the Mach number. At Mach 10, the densities of some clumps are 3 orders of magnitude higher than the mean density. These clumps give rise to a flat and approximately isotropic density spectrum corresponding to the random distribution of clumps in space. We claim that the clumps originate from our random, isotropic turbulence driving. When the contribution from those clumps is suppressed by studying the logarithm of density, the density statistics exhibit scale-dependent anisotropy consistent with the models in which density structures arise from shearing by Alfven waves. It is noteworthy that originally such models were advocated for the case of low-Mach, nearly incompressible turbulence.

On the multidimensional extension of the quincunx subsampling matrix

The dilation matrix associated with the three-dimensional (3-D) face-centered cubic (FCC) sublattice is often considered to be the natural 3-D extension of the two-dimensional (2-D) quincunx dilation matrix. However, we demonstrate that both dilation matrices are of different nature: while the 2-D quincunx matrix is a similarity transform, the 3-D FCC matrix is not. More generally, we show that is impossible to obtain a dilation matrix that is a similarity transform and performs downsampling of the Cartesian lattice by a factor of two in more than two dimensions. Furthermore, we observe that the popular 3-D FCC subsampling scheme alternates between three different lattices: Cartesian, FCC, and quincunx. The latter one provides a less isotropic sampling density, a property that should be taken into account to properly orient 3-D data before processing using such a subsampling matrix.

Critical Evaluation of C−H···X Hydrogen Bonding in the Crystalline State

Contacts of the type C−H···X where X = F, Cl, Br, I, O, S, or N were analyzed statistically using structures available in the Cambridge Structural Database. For this analysis, the cone correction method was extended to an isotropic density correction. This method corrects for both angular and distance effects by normalizing isotropic contact densities from the experimental distributions. It was possible to show the widespread occurrence of C−H···X interactions in the crystalline state using this method. Distances of highest incidence, at which the largest number of contacts were sampled after normalization of isotropic distribution, were determined for each interaction type. These distances were compared to the classically accepted van der Waals cutoff radii, often used to distinguish between hydrogen-bonded interactions and van der Waals contacts. Generally, distances of highest incidence did not occur at the sum of van der Waals cutoff radii but occurred either below or above that distance depending on the specific interaction analyzed. This methodology, while of course not yielding quantitative data on hydrogen bond strength, allowed for a qualitative ordering of the interactions studied, in terms of expected interaction strengths.

A space–time in toroidal coordinates

We present an exact solution of Einstein’s field equations in toroidal coordinates. The solution has three regions: an interior with a string equation of state; an Israel boundary layer; and an exterior with constant isotropic pressure and constant density, locally isometric to anti–de Sitter space–time. The exterior can be a cosmological vacuum with negative cosmological constant. The size and mass of the toroidal loop depend on the size of Λ.

Micromechanical modeling of the elasto-viscoplastic behavior of semi-crystalline polymers

A micromechanically based constitutive model for the elasto-viscoplastic deformation and texture evolution of semi-crystalline polymers is developed. The model idealizes the microstructure to consist of an aggregate of two-phase layered composite inclusions. A new framework for the composite inclusion model is formulated to facilitate the use of finite deformation elasto-viscoplastic constitutive models for each constituent phase. The crystalline lamellae are modeled as anisotropic elastic with plastic flow occurring via crystallographic slip. The amorphous phase is modeled as isotropic elastic with plastic flow being a rate-dependent process with strain hardening resulting from molecular orientation. The volume-averaged deformation and stress within the inclusions are related to the macroscopic fields by a hybrid interaction model. The uniaxial compression of initially isotropic high density polyethylene (HDPE) is taken as a case study. The ability of the model to capture the elasto-plastic stress–strain behavior of HDPE during monotonic and cyclic loading, the evolution of anisotropy, and the effect of crystallinity on initial modulus, yield stress, post-yield behavior and unloading–reloading cycles are presented.