Estimation of scattering from a moist rough surface with spheroidal dust particles

The scattering from moisture rough surface with spheroidal dust particles having surface with spheroidal dust particles has recently received much attention. In part due to the recent prediction and observation of the spheroidal dust particles in rough surfaces under elastic wave by the Kirchhoff scattering model and scalar approximation with slope. Our analysis shows that the scattering depends on the moisture (2–4·5%) with spheroidal dust particles. At slightly moisture rough surface the dielectric properties increase with change in field amplitude in a rough surface with spheroidal dust particles.     

Multistep induction heating regimes for thixoforming 7075 aluminium alloy

Abstract

Thixoforming involves processing alloys with a spheroidal microstructure in the semisolid state. Commercially it is applied to conventional casting alloys, and one of the scientific challenges is to extend its application to high performance aluminium alloys such as 7075. Aluminium alloy 7075 is readily available in extruded form, and one route to a spheroidal microstructure is to reheat extruded material into the semisolid state to obtain recrystallisation, with the liquid penetrating the recrystallised boundaries. Here this route has been followed, but it has been found that the presence of pinning particles in the microstructure inhibits recrystallisation. To overcome this, a multistep induction heating regime has been developed consisting of a 1 min hold at 475-500 °C, a 1 min hold at 575-600 °C and a shorter 20 s hold for the final step at 620 °C.     

Expansion of an arbitrarily oriented, located, and shaped beam in spheroidal coordinates

Within the framework of the generalized Lorenz-Mie theory (GLMT), the incident shaped beam of an arbitrary orientation and location is expanded in terms of the spheroidal vector wave functions in given spheroidal coordinates. The beam shape coefficients (BSCs) in spheroidal coordinates are computed by the quadrature method. The classical localization approximation method for BSC evaluation is found to be inapplicable when the Cartesian coordinates of the beam and the particle are not parallel to each other. Once they are parallel, all the symmetry relationships existing for the BSCs in spherical coordinates (spherical BSCs) [J. Opt. Soc. Am. A11, 1812 (1994)] still pertain to the BSCs in spheroidal coordinates (spheroidal BSCs). In addition, the spheroidal BSCs computed by our method are verified by comparing them with those evaluated by Asano and Yamamoto for plane wave incidence [Appl. Opt.14, 29 (1975)]. Furthermore, formulas are given for field reconstruction from the spheroidal BSCs, and consistency is found between the original incident fields and the reconstructed ones.     

Scattering of a point generated field by a multilayered spheroid

Summary The point source excitation acoustic scattering problem by a multilayer isotropic and homogeneous spheroidal body is presented. The multilayer spheroidal body is reached by an acoustic wave emanated by an external point source. The core spheroidal region is inpenetrable and rigid. The exterior interface and the interfaces separating the interior layers are penetrable. The scattered field is determined given the geometrical and physical characteristics of the spheroidal body, the location of the point source and the form of the incident field. The approach is not limited in a certain region of frequencies.     

A generalized self-consistent method for solids containing randomly oriented spheroidal inclusions

Summary In this paper, a generalized self-consistent method is proposed to predict the effective moduli of a material containing single-phase and randomly oriented spheroidal inclusions, with same aspect ratios. This is achieved by using an energy equivalence framework, associated with a generalization of the classical three phase model to spheroidal inclusions. The localization problem (spheroidal duplex inclusion problem) is formulated with the Papkovitch-Neuber approach; this requires expansion formulae for the spheroidal potentials, which are derived in the Appendix. Finally, the determination of the effective moduli is equivalent to solving a system of nonlinear equations. Effective moduli are presented for various types of inclusions, and comparisons are made with the estimations obtained from the self-consistent and Mori-Tanaka methods. Moreover, the effects of inclusion geometry and spatial distribution of inclusions on the effective moduli are investigated and compared to each other.     

Recrystallisation in the semi-solid state in 7075 aluminium alloy

There is a strong drive to near net shape process 7000 series aluminium alloys, which are currently machined from the wrought state with much waste. Semi-solid processing is one potential near net shaping route. It relies on the thixotropic behaviour of alloys with non-dendritic, spheroidal microstructures in the semi-solid state. If such alloys are sheared they thin and flow to fill the die. One route to spheroidal semi-solid microstructure is by reheating worked material into the semi-solid state. During the reheating, recrystallisation occurs and as liquid forms it penetrates the recrystallised boundaries to form spheroids. Here we examine the formation of spheroids in as-supplied 7075 aluminium alloy. It is generally known that 7075 is very resistant to recrystallisation in the solid state due to the presence of dispersoid particles pinning grain boundaries. In this work, we have reheated 7075 in the extruded and T6 condition into the semi-solid state. As the temperature rises into the semi-solid regime there is a sudden increase in the appearance of spheroidal grains. The occurrence of recrystallised grains is closely associated with the location of the first liquid to form above the solidus. Fully spheroidal microstructures are obtained on reheating as-supplied material to temperatures in the region of 580 °C, although the fractions of liquid at that temperature are still low at around 5%. Conventionally there is extra cost involved in obtaining spheroidal microstructure feedstock for semi-solid processing because additional steps are introduced into the process route. The advantage here is that as-supplied material can be directly thixoformed once appropriate liquid fractions are attained.     

Theoretical investigation on heat transfer to burning char of spheroidal particles

The combustion of biomass fuel provides efficient and inexpensive utilization of solid biomass. Biomass particles generally exhibit non-spherical shapes, which affect the heat and mass transfer and further the char surface reactions. The prolate and oblate spheroidal particles are considered presently. The energy balance is employed for the gas phase near the particle in spheroidal coordinate system. A theoretical study is conducted on the char combustion of the spheroidal particles under either static conditions or forced convection. The expressions for the Nusselt numbers of both prolate and oblate spheroids are obtained. The char combustion rates for the spheroidal particles are affected by the Nusselt number and the particle surface area.     

Elevated temperature thermal conductivities of some as-cast and austempered cast irons

The aim of this study was to provide insight on thermal conductivity of three cast iron groups, namely lamellar, compacted and spheroidal graphite irons at elevated temperatures up to 673?K (400°C) in as-cast and austempered states. Austempering treatments increased mechanical properties of all the studied materials while decreasing thermal conductivity across the line. The effects of austempering on conductivity were lower for grey and compacted graphite iron than for spheroidal graphite irons. The results indicate that heat treating can be a viable option in increasing cast iron performance in thermally stressed applications. One ferritic low-silicon spheroidal graphite iron surpassed lamellar graphite iron in conductivity at elevated temperatures, while high-silicon spheroidal graphite irons exhibited low conductivities.     

Scattering of electromagnetic waves by spheroidal particles: a novel approach exploiting the T matrix computed in spheroidal coordinates

A method other than the extended-boundary-condition method (EBCM) to compute the T matrix for electromagnetic scattering is presented. The separation-of-variables method (SVM) is used to solve the electromagnetic scattering problem for a spheroidal particle and to derive its T matrix in spheroidal coordinates. A transformation is developed for transforming the T matrix in spheroidal coordinates into the corresponding T matrix in spherical coordinates. The T matrix so obtained can be used for analytical calculation of the optical properties of ensembles of randomly oriented spheroids of arbitrary shape by use of an existing method to average over orientational angles. The optical properties obtained with the SVM and the EBCM are compared for different test cases. For mildly aspherical particles the two methods yield indistinguishable results. Small differences appear for highly aspherical particles. The new approach can be used to compute optical properties for arbitrary values of the aspect ratio. To test the accuracy of the expansion coefficients of the spheroidal functions for arbitrary arguments, a new testing method based on the completeness relation of the spheroidal functions is developed.     

Stress analysis of a penny-shaped crack locted between two oblate spheroidal cavities in an infinite solid

The problem of a penny-shaped crack located between two oblate spheroidal cavities in an infinite solid subjected to uniaxial loads is considered. Using transformations between harmonic functions in cylindrical coordinates and those in oblate spheroidal ones, the problem is reduced to non-homogeneous linear equations. The obtained equations are solved numerically and the stress intensity factors at the penny-shaped crack tip under the influence of the two oblate spheroidal cavities are shown graphically.     

Scattering of a spheroidal particle illuminated by a gaussian beam

An approach to expanding a Gaussian beam in terms of the spheroidal wave functions in spheroidal coordinates is presented. The beam-shape coefficients of the Gaussian beam in spheroidal coordinates can be computed conveniently by use of the known expression for beam-shape coefficients, g(n), in spherical coordinates. The unknown expansion coefficients of scattered and internal electromagnetic fields are determined by a system of equations derived from the boundary conditions for continuity of the tangential components of the electric and magnetic vectors across the surface of the spheroid. A solution to the problem of scattering of a Gaussian beam by a homogeneous prolate (or oblate) spheroidal particle is obtained. The numerical values of the expansion coefficients and the scattered intensity distribution for incidence of an on-axis Gaussian beam are given.     

Theoretical and experimental investigation of steady-state voltammetry for quasi-reversible heterogeneous electron transfer on a mercury oblate spheroidal microelectrode.

A mercury microelectrode formed by electroreduction of mercury on an inlaid gold microdisk is experimentally shown to be well modeled by oblate spheroidal geometry when the ratio of the semiminor axis to the semimajor axis of the protruding drop is less than 1. The validity of the geometry is established by comparison of the experimentally determined coefficient in the steady-state diffusion current equation with the theoretical value for oblate spheroidal geometry. Spherical cap geometry is also shown to be an equally valid geometric model; however, theoretical treatment for this system is more difficult. The theory of a quasi-reversible electrode process is developed and applied to the determination of the electrode parameters of the RuIII(NH3)6/RuII(NH3)6 electrode reaction on a mercury oblate spheroidal microelectrode. Results agree well with others found in the literature for the same process on a mercury electrode.     

A generalization of prolate spheroidal functions with more uniform resolution to the triangle

Prolate spheroidal functions constitute a one-parameter (α) family of orthogonal functions in the interval. For α = 0, they are the Legendre polynomials. For larger α, the prolate spheroidal functions oscillate more uniformly than the Legendre polynomials, and provide more uniform resolution in the interval. The prolate spheroidal functions can be obtained by adding a zeroth-order term to the Sturm–Liouville equation for the Legendre polynomials. Here, the Sturm–Liouville equation for orthogonal polynomials in the triangle is modified in a similar fashion. The modification maintains the self-adjointness and symmetry properties of the original Sturm–Liouville equation, so that the new eigenfunctions are orthogonal and give spectrally accurate approximations of smooth functions with arbitrary boundary conditions in the triangle. The properties of the new eigenfunctions mimic those in the interval. For larger α, the new eigenfunctions provide more uniform resolution in the triangle.     

Dark matter annihilations search in dwarf spheroidal galaxies with fermi

Launched in June 2008, the Fermi Gamma-ray Telescope includes a pair conversion detector designed for the 20 MeV to gamma-ray sky study, the Large Area Telescope (LAT). Operating in all-sky survey mode, its excellent sensitivity and angular resolution will allow either to discover or constrain a signal coming through the annihilation of dark matter particles. Predicted by cold dark matter scenarios as the largest clumps, dwarf spheroidal galaxies are amongst the most attractive targets for indirect search of dark matter by gamma-ray experiments. We present here an overview of the Fermi LAT Dark Matter and New Physics Working Group efforts in the searches of gamma-ray fluxes coming from WIMP pair annihilations in dwarf spheroidal galaxies.     

Application of Mie theory to assess structure of spheroidal scattering in backscattering geometries

Inverse light scattering analysis seeks to associate measured scattering properties with the most probable theoretical scattering distribution. Although Mie theory is a spherical scattering model, it has been used successfully for discerning the geometry of spheroidal scatterers. The goal of this study was an in-depth evaluation of the consequences of analyzing the structure of spheroidal geometries, which are relevant to cell and tissue studies in biology, by employing Mie-theory-based inverse light scattering analysis. As a basis for this study, the scattering from spheroidal geometries was modeled using T-matrix theory and used as test data. In a previous study, we used this technique to investigate the case of spheroidal scatterers aligned with the optical axis. In the present study, we look at a broader scope which includes the effects of aspect ratio, orientation, refractive index, and incident light polarization. Over this wide range of parameters, our results indicate that this method provides a good estimate of spheroidal structure.     

On the stressed state of a transversely isotropic piezoceramic material with arbitrarily oriented spheroidal inhomogeneity

We consider a stressed state problem of a piezoelectric medium containing an arbitrarily oriented spheroidal inclusion under uniform mechanical and electrical loads. The problem has been solved by using a generalized Eshelby method of equivalent inclusion for the case of piezoceramic material. Testing of the approach for the case of a spheroidal cavity (when the cavity rotation axis coincides with the material polarization axis), for which an exact solution of the problem exists, confirms its high efficiency. Numerical investigations have been carried out, and the stress distribution along the surface of an arbitrarily oriented spheroidal cavity has been studied. __________ Translated from Problemy Prochnosti, No. 2, pp. 112–120, March–April, 2008.     

耐磨白口铁中球形碳化物的离子蚀刻研究

用离子蚀刻加扫描电镜观察和微区成分分析的方法研究了耐磨白口铁中球形碳化物的结构。实验结果表明，球形碳化物为多晶体，其形成机制为碳化物结晶时在稀土硫氧化物上非自发形核并长大。     

On the Possibility of Approximation of Irregular Porous Microstructure by Isolated Spheroidal Pores

Calculation of the effective elastic constants of a material with irregularly shaped porous space is discussed. It is shown that isolated pores of irregular shapes may be approximated, with good accuracy, by the spheroidal ones. Procedure of evaluation of the average aspect ratio from the photomicrograph is described. Several commonly used approximate schemes are applied to predict effective Young’s and shear moduli of a material with spheroidal pores. Comparisons of these predictions with the experimentally measured elastic constants for completely sintered hydroxyapatite exhibit reasonably good accuracy. The best agreement is given by self-consistent and effective field methods.     

Information content of the scattering matrix for spheroidal particles

The T-matrix method is shown to be an efficient and accurate procedure for calculating the scattering matrix for randomly oriented nonspherical particles. Calculated scattering matrix elements for spheroidal particles are identical to those obtained by the spheroidal harmonic approach. T-matrix calculations for a randomly oriented finite length cylinder agree well with microwave scattering measurements. Analysis of the information content of the angular variation of the matrix elements for a set of moderately sized absorbing spheroidal particles is presented. It is found that the Fourier spectrum of the phase function and a parameter related to the depolarization ratio contain particle size and shape information, respectively.     

基于奥贝球墨可锻铸铁性能的影响因素

介绍了奥贝球墨可锻铸铁性能影响因素。奥贝球墨可锻铸铁是在球墨可锻铸铁的基础上通过等温淬火处理获得奥贝基体组织,具有类似于奥贝球铁的组织和性能,可放宽原材料对Mn、P元素的含量限制,是一种有前途的新型结构材料。