Spherical Isotropy Research Articles

Thermoelastic Analysis of Pressurized Hollow Spherical Vessels with Arbitrary Radial Non-Homogeneity

In this study, a general analysis of one dimensional steady-state thermal stresses of a functionally graded hollow spherical vessel with spherical isotropy and spherically transversely isotropy is presented with material properties of arbitrary radial non-homogeneity. The material properties may arbitrarily vary as continuous or piecewise functions. The boundary value problem associated with a thermo-elastic problem is converted to an integral equation. Radial and tangential thermal stress components distribution can be determined numerically by solving the resulting equation. The influence of the gradient variation of the material properties on the thermal stresses is investigated and the numerical results are presented graphically.

SMSIR: Spherical Measure Based Spherical Image Representation.

This paper presents a spherical measure based spherical image representation(SMSIR) and sphere-based resampling methods for generating our representation. On this basis, a spherical wavelet transform is also proposed. We first propose a formal recursive definition of the spherical triangle elements of SMSIR and a dyadic index scheme. The index scheme, which supports global random access and needs not to be pre-computed and stored, can efficiently index the elements of SMSIR like planar images. Two resampling methods to generate SMSIR from the most commonly used ERP(Equirectangular Projection) representation are presented. Notably, the spherical measure based resampling, which exploits the mapping between the spherical and the parameter domain, achieves higher computational efficiency than the spherical RBF(Radial Basis Function) based resampling. Finally, we design high-pass and low-pass filters with lifting schemes based on the dyadic index to further verify the efficiency of our index and deal with the spherical isotropy. It provides novel Multi-Resolution Analysis(MRA) for spherical images. Experiments on continuous synthetic spherical images indicate that our representation can recover the original image signals with higher accuracy than the ERP and CMP(Cubemap) representations at the same sampling rate. Besides, the resampling experiments on natural spherical images show that our resampling methods outperform the bilinear and bicubic interpolations concerning the subjective and objective quality. Particularly, as high as 2dB gain in terms of S-PSNR is achieved. Experiments also show that our spherical image transform can capture more geometric features of spherical images than traditional wavelet transform.

Three-dimensional vibrations of multilayered hollow spheres submerged in a complex fluid

Fluid–structure interaction is fundamental to the characteristics of the induced flows due to the motion of structures in fluids and also is crucial to the performance of submerged structures. This paper presents a three-dimensional analytical study of the intrinsic free vibration of an elastic multilayered hollow sphere interacting with an exterior non-Newtonian fluid medium. The fluid is assumed to be characterized by a compressible linear viscoelastic model accounting for both the shear and compressional relaxation processes. For small-amplitude vibrations, the equations governing the viscoelastic fluid can be linearized, which are then solved by introducing appropriate potential functions. The solid is assumed to exhibit a particular material anisotropy, i.e. spherical isotropy, which includes material isotropy as a special case. The equations governing the anisotropic solid are solved in spherical coordinates using the state-space formalism, which finally establishes two separate transfer relations correlating the state vectors at the innermost surface with those at the outermost surface of the multilayered hollow sphere. By imposing the continuity conditions at the fluid–solid interface, two separate analytical characteristic equations are derived, which characterize two independent classes of vibration. Numerical examples are finally conducted to validate the theoretical derivation as well as to investigate the effects of various factors, including fluid viscosity and compressibility, fluid viscoelasticity, solid anisotropy and surface effect, as well as solid intrinsic damping, on the vibration characteristics of the submerged hollow sphere. Particularly, our theoretically predicted vibration frequencies and quality factors of gold nanospheres with intrinsic damping immersed in water agree exceptionally well with the available experimentally measured results. The reported analytical solution is truly and fully three-dimensional, covering from the purely radial breathing mode to the torsional mode to any general spheroidal mode as well as being applicable to various simpler situations, and hence can be a broad-spectrum benchmark in the study of fluid–structure interaction.

Resonances of a submerged fluid-filled spherically isotropic microsphere with partial-slip interface condition

Motivated by the numerous applications of spherical shell models in micro and nano scales (such as microbubbles, bacterial cells, and viral capsids), we have considered the axisymmetric free vibrations of a spherically isotropic fluid-filled thick microspherical shell suspended in another unbounded fluid. A partial-slip condition is considered at the solid-fluid interface(s). Three-dimensional linear elasticity equations for the spherically isotropic shell dynamics and linearized Navier-Stokes equations for the two compressible viscous fluids are used in the analysis. The eigenvalue problem is discretized and solved to find the resonances and quality factors. A perfectly matched layer technique is used to separate the solid driven spectrum from the boundary reflecting spectrum. An example of air filled polymer shell suspended in water is presented. The added mass effect and partial-slip condition from water (air) on the frequencies and quality factors are found to be significant (negligible). Spherical isotropy is found to have major influence on the low frequency and large meridional wave number region of the resonance spectrum. High quality eigenmodes are observed due to very small viscous penetration depth compared to the shell size. In the thin-shell limit, the eigenvalue problem can have only two modes of vibration for any meridional wave number greater than or equal to two. This explains the reason for the second resonance frequency found for the quadrupole shape oscillations of various bacterium cells in the earlier work. The partial-slip condition is found to have very small influence on the first few modes of vibration. Surface tension is found to have significant influence only on the lowest frequency trend of the eigenspectrum. Perfectly matched layer technique used in the present analysis is found to be very effective in handling the boundary truncated problems.

Convective Drying Analysis of a Single Wheat Kernel Based on an Irreversible Thermodynamics Model

The application of irreversible thermodynamics offers a formal treatment for drying analysis that allows the evaluation of intra-particle or intra-medium temperature and moisture profiles, and enthalpy, liquid, and vapor fluxes. However, researchers have claimed that its implementation is complex. This work presents a simple methodology for modeling, solving, and validating the drying equations, as applied to wheat kernels, and for obtaining the inherent and usually unavailable transport coefficients. To clarify and simplify the ensuing physical analysis, a spherical shape and isotropy were assumed. Additionally, solutions obtained with both Dirichlet and convective boundary conditions were analyzed and compared against experimental data. The thermal and hydro-stresses depend heavily on internal vapor and liquid fluxes and on the respective drying evaporation fronts, all of which were evaluated and compared.

Differentiation between low-grade and high-grade glioma using combined diffusion tensor imaging metrics

ObjectiveTo ascertain whether diffusion tensor imaging (DTI) metrics including tensor shape measures such as planar and spherical isotropy coefficients (CP and CS) can be used to distinguish high-grade from low-grade gliomas. MethodsTwenty-five patients with histologically proved brain gliomas (10 low-grade and 15 high-grade) were included in this study. Contrast-enhanced T1-weighted images, non-diffusion weighted b=0 (b0) images, fractional anisotropy (FA), apparent diffusion coefficient (ADC), CS and CP maps were co-registered and each lesion was divided into two regions of interest (ROI): enhancing and immediate peritumoral edema (edema adjacent to tumor). Univariate and multivariate logistic regression analyses were applied to determine the best classification model. ResultsThere was a statistically significant difference in the multivariate logistic regression analysis. The best logistic regression model for classification combined three parameters (CS, FA and CP) from the immediate peritumoral part (p=0.02), resulting in 86% sensitivity, 80% specificity and area under the curve of 0.81. ConclusionOur study revealed that combined DTI metrics can function in effect as a non-invasive measure to distinguish between low-grade and high-grade gliomas.

The scattering of P-waves by a piezoelectric particle with FGPM interfacial layers in a polymer matrix

Propagation of P-wave in an unbounded elastic polymer medium which contains a set of nested concentric spherical piezoelectric inhomogeneities is formulated. The polymer matrix is made of Epoxy and is isotropic; each phase of the inhomogeneity is made of a different piezoelectric material and is radially polarized and has spherical isotropy. Note that the individual phases are homogeneous, and all interfaces are perfectly bonded. The scattered displacement and electric potentials in the matrix are expressed in terms of spherical wave vector functions and Legendre functions, respectively. The transmitted displacement and electric potentials within each phase of the piezoelectric particle are expressed in terms of Legendre functions. The equations of motion and electrostatics in each phase of the piezoelectric inhomogeneity lead to a system of coupled second order differential equations, which is solved using the generalized Frobenius series. The present theory is extended to the case where the core of the inhomogeneity is made of PZT-4 and its coating is made of functionally graded piezoelectric material (FGPM) whose microstructural composition varies smoothly from PZT-4 at the core–coating interface to Epoxy at the coating–matrix interface. The effects of different types of variation in the electro-mechanical properties of FGPM on scattering cross-section and other electro-mechanical fields are addressed. The present theory is valid for arbitrary coating thickness, and arbitrary frequencies.

A 1D–3D mixed method for the numerical simulation of blast waves in confined geometries

Blast wave generated by a high detonating spherical charge and propagating in confined domains is modeled using the Euler equations. The problem is split into two parts. The first calculation part relies on spherical isotropy to solve the problem in the radial component. Overpressure distribution is presented and shows a very good agreement with experimental and numerical data. The one-dimensional data need to be made three-dimensional mesh-compatible thanks to an appropriate remapping technique. To this end, a remapping technique is presented and its effectiveness, accuracy and efficiency are demonstrated. The second calculation part consists of a three-dimensional computation fed with the remapped data. The effectiveness of this mixed approach is demonstrated through three-dimensional applications in confined domains.

Diffusion tensor anisotropy magnetic resonance imaging: a new tool to assess synovial inflammation

Diffusion tensor imaging (DTI) has been used to study the structure of ordered biological tissue. DTI-derived metrics correlate with inflammatory cytokines and adhesion molecules, expressed in the brain abscess. We aimed to study the role of DTI-derived metrics in delineating the synovitis and their correlation with inflammatory proteins expressed in the SF of chronic inflammatory arthritis patients. DTI was performed on 18 patients and 6 healthy controls. A follow-up DTI at 6 months was performed in 10 patients. Quantification of inflammatory cytokines (TNF-alpha, IL-1beta) and soluble intercellular adhesion molecule-1 (sICAM-1) in SF and their correlation with DTI-derived metrics was performed. DTI-derived metrics, fractional anisotropy (FA), cylindrical isotropy (CL), planar anisotropy (CP) and spherical isotropy (CS), were significantly altered in the inflamed synovium of the patients as compared to the healthy controls. Significant correlation between FA and TNF-alpha (r = 0.68, P = 0.002) and IL-1beta (r = 0.48, P < 0.05) and inverse correlations between mean diffusivity (MD) and TNF-alpha (r = -0.54, P < 0.05) and CS and TNF-alpha (r = -0.53, P < 0.05) and CP and IL-1beta and sICAM (r = 0.48, P < 0.05 and r = 0.49, P < 0.05, respectively) were observed. A significant correlation between post-contrast signal intensity (PCI) and IL-1beta and sICAM-1 (r = 0.61, P = 0.01 and r = 0.46, P = 0.05) and volume and sICAM-1 (r = 0.45, P = 0.05) was observed, respectively. Results of this pilot study suggest that the DTI-derived metrics have the potential to delineate synovial inflammation; however, it is not superior to conventional MRI for its detection and assessment of therapeutic response.

Measurement of cytotoxic and interstitial components of cerebral edema in acute hepatic failure by diffusion tensor imaging

To use diffusion tensor imaging (DTI) metrics for measuring cytotoxic and interstitial components of cerebral edema (CE) in acute hepatic failure (AHF) patients. CE is a major complication in patients with AHF. DTI was performed in 20 patients with AHF and 15 controls. Ten patients underwent repeat imaging after recovery from encephalopathy. Various regions of interest (ROIs) were drawn in the white and deep gray matter of the brain for the quantitation of fractional anisotropy (FA), mean diffusivity (MD), spherical isotropy (CS), linear anisotropy (CL), and planar anisotropy (CP) values. Significantly decreased MD values were observed in most brain ROIs in patients compared to controls. Significantly decreased FA, CL with increased CS values was also observed. In survivors with normal clinical profile after 3 weeks, a significant increase in MD and FA values were associated with decreased CS values in some regions compared to baseline study; however, it was still significantly changed compared to controls. Decreased MD and increased CS associated with decreased FA represent cytotoxic and interstitial components of CE, respectively. Incomplete normalization of these metrics in survivors after 3 weeks clinical recovery may be due to incomplete metabolic recovery.

Quantification of cerebral edema on diffusion tensor imaging in acute‐on‐chronic liver failure

Cerebral edema is a major complication of acute liver failure but may also be seen in other forms of liver failure such as acute-on-chronic liver failure (ACLF) and chronic liver failure (CLF). ACLF develops in patients with previously well-compensated chronic liver disease following acute hepatitis A or E superimposed on underlying liver cirrhosis. The aim of this study was to detect the occurrence, and determine the nature, of cerebral edema in patients with the defined subset of ACLF using diffusion tensor imaging (DTI) metrics. Twenty-three patients with ACLF were studied and compared with 15 healthy controls and 15 patients with CLF. DTI metrics including fractional anisotropy (FA), mean diffusivity (MD), linear anisotropy (CL), planar anisotropy (CP), and spherical isotropy (CS) were calculated by selecting regions of interest in the white matter and deep grey matter of the brain. Significantly decreased FA and increased CS were observed in the anterior limb (ALIC) and posterior limb (PLIC) of the internal capsule and frontal white matter (P<0.05) in patients with different grades (1-4) of ACLF when compared with healthy controls. No significant changes in MD and CP were seen in any brain region. However, significantly decreased CL was observed in the PLIC, caudate nuclei and putamen. In patients with CLF, significantly decreased FA with increased CS in the ALIC and PLIC along with significantly increased MD in the ALIC and caudate nuclei were observed. The presence of significantly decreased FA and CL and increased CS along with no significant change in MD and CP suggests the presence of both intracellular and extracellular components of cerebral edema in patients with ACLF.

The scattering of electro-elastic waves by a spherical piezoelectric particle in a polymer matrix

This paper is devoted to the study of scattering of plane harmonic waves by a piezoelectric sphere with spherical isotropy embedded in an unbounded isotropic polymer matrix. The scattered displacement field and the electric potential in the matrix are expressed in terms of spherical vector wave functions and spherical harmonic functions, respectively. For the field points inside the inhomogeneity, new displacement functions are introduced. Expansion of the new displacement functions and the electric potential in terms of spherical harmonic functions, the equations of motion and electrostatic lead to four second order ordinary differential equations (odes), where three of them are coupled. The coupled system of odes is solved by the generalized Frobenius series. This approach is readily used to handle low and high frequencies. Three different types of piezoelectric inhomogeneities, PZT-4, PZT-5H, and BaTiO 3 are considered and the associated piezoelectric effects on the electro-mechanical fields, differential and total scattering cross-sections are addressed.

Acoustic vector-sensor correlations in ambient noise

Most array-processing methods require knowledge of the correlation structure of the noise. While such information may sometimes be obtained from measurements made when no sources are present, this may not always be possible. Furthermore, measurements made in-situ can hardly be used to analyze system performance before deployment. The development of models of the correlation structure under various environmental assumptions is therefore very important. In this paper, we obtain integral and closed form expressions for the auto- and cross-correlations between the components of an acoustic vector sensor (AVS) for a wideband-noise field, under the following assumptions concerning its spatial distribution: 1) azimuthal independence; 2) azimuthal independence and elevational symmetry; and 3) spherical isotropy. We also derive expressions for the cross-covariances between all components of two spatially displaced AVSs in a narrowband-noise field under the same assumptions. These results can be used to determine the noise-covariance matrix of an array of acoustic vector sensors in ambient noise. We apply them to a uniform linear AVS array to asses its beamforming capabilities and localization accuracy, via the Cramer-Rao bound, in isotropic and anisotropic noise.

A State-Space-Based Stress Analysis of a Multilayered Spherical Shell With Spherical Isotropy

This paper presents an exact static stress analysis of a multilayered elastic spherical shell (hollow sphere) completely based on three-dimensional elasticity for spherical isotropy. Two independent state equations are derived after introducing three displacement functions and two stress functions. In particular, a variable substitution technique is used to derive the state equations with constant coefficients. Matrix theory is then employed to obtain the relationships between the state variables at the upper and lower surfaces of each lamina. By virtue of the continuity conditions between two adjacent layers, a second-order linear algebraic equation and a fourth-order one about the boundary variables at the inner and outer surfaces of a multilayered spherical shell are obtained. Numerical examples are presented to show the effectiveness of the present method.

Millimeter-resolution E-field probe for isotropic measurement in lossy media between 100 MHz and 20 GHz

Currently, most advanced isotropic E-field probes for near-field measurements in lossy dielectric media have a tip diameter of typically 4-6 mm, housing three 2-3 mm long sensors. Although these probes are very well suited for many applications, their general use is constrained by several limitations: (1) upper frequency range of <4 GHz in tissue simulating liquids, (2) spatial resolution of a few millimeters, 3() unsuitable for measurements closer than 3-5 mm from any media boundary (boundary effects); and therefore (4) inapplicable for assessment of the induced field strengths in structures of a few millimeters. On the other hand, many current and future research projects require evaluation of the field distributions for frequencies larger than a few gigahertz, for measurements within small structures (e.g., in in vitro and in vivo experiments), for evaluations of special physical interactions such as strongly nonhomogeneous field distributions or characterization of larger probes, etc. A new probe has been developed which is applicable for frequencies well above 10 GHz in tissue-like media and provides a spatial resolution of at least 1 mm. Although it is a one sensor probe, it has been designed such that the isotropic measurement (spherical isotropy: <0.2 dB) can be obtained simply by taking three measurements each shifted by 1200 rotation around the probe's axis. The probe has been fully characterized and tested in various applications.

Stress distribution in a rotating elastic functionally graded material hollow sphere with spherical isotropy

The stress distribution in a rotating, spherically isotropic, functionally graded material (FGM) spherical shell that has its elastic constants and mass density as functions of the radial coordinate is exactly investigated in the paper. Three displacement functions are employed to simplify the basic equations of equilibrium for a spherically isotropic, radially inhomogeneous elastic medium. By expanding the displacement functions in terms of spherical harmonics, the basic equations are finally turned into an uncoupled second-order ordinary differential equation and a coupled system of two such equations. Exact analysis of a steadily rotating spherical shell with the material constants being power functions of the radial coordinate is carried out and a numerical example is presented.

Free vibration of a fluid-filled hollow sphere of a functionally graded material with spherical isotropy

An exact, three-dimensional method is developed in the paper to analyze the free vibration of a spherically isotropic hollow sphere made of a functionally graded material and filled with a compressible fluid medium. The material is assumed to be inhomogeneous along the radial direction. By introducing three displacement functions and employing the function expansion method, the governing equations are simplified to an uncoupled second-order ordinary differential equation, and a coupled system of two such equations. Solutions to these equations are given when the elastic constants and the mass density are power functions of the radial direction. To investigate the effect of material gradient on the natural frequencies, numerical calculations are finally performed.

Spatial - temporal modeling

Spatial - temporal modeling

Bifurcations at a spherical cavity in a compressible solid with spherical isotropy: K. T. Chau, International Journal for Numerical & Analytical Methods in Geomechanics, 19(6), 1995, pp 381–398

Bifurcations at a spherical cavity in a compressible solid with spherical isotropy: K. T. Chau, International Journal for Numerical & Analytical Methods in Geomechanics, 19(6), 1995, pp 381–398

Bifurcations at a spherical cavity in a compressible solid with spherical isotropy

AbstractThis paper investigates bifurcations, including surface mode and localized mode of deformations, at a spherical cavity in an infinite compressible solid with spherical isotropy. Two types of surface modes are found satisfying the zero traction rate conditions on the surface of the hole: (1) the torsional modes, corresponding to bifurcations with zero radial velocity and zero rate of dilatation; and (2) the spheroidal modes, corresponding to bifurcations with zero rate of spin on the tangential planes. Both of these bifurcations can be written in terms of surface harmonics of degree n. Three‐dimensional pictures of some of the bifurcation modes are devised for both torsional and spheroidal modes, showing both the displaced nodes and nodal lines. Torsional bifurcation occurs only if the ratio of the radial shear modulus to the tangential shear modulus (Gr/Gt) vanishes. Three types of spheroidal modes are possible depending on the combination of the five material parameters; their eigenvalue equations are obtained analytically. As expected, numerical results show that the conditions of bifurcations are independent of the size of the spherical hole. Radial bifurcation modes (n = 0) are always possible at the peak applied stress; and pre‐peak bifurcations are also possible for mode shapes composed of surface harmonics of higher degree (n &gt; 0). Spherically isotropic solids (i.e. Gt/Gr &lt; 1) are more conducive to bifurcations than isotropic solids if n &gt; 2. Surface mode with large degree (n → ∞ ) is not necessarily the lowest possible bifurcation; this finding differs from the conclusion by Bassani et al.1 for incompressible isotropic solids.