Perfectly diffuse sound fields play an important role in architectural acoustics and there are established theoretical characterizations of perfect diffuseness. Although sound fields in real rooms are diffuse to some extent, they are not perfectly diffuse, and therefore theories are required to describe pseudo-perfectly diffuse sound fields. Here, we aim to spatially characterize pseudo-perfect diffuseness via directional characterization of that, finite-degree spherical harmonic diffuseness. Our results show that finite-degree diffuse sound fields yield local spatial diffuseness, suggesting that spatial pseudo-perfect diffuseness is characterized using the effective radius of diffuseness.
Isotropy is a fundamental property of a diffuse sound field. Although several studies have proposed an isotropy indicator to quantify the extent of the isotropy of a sound field, what is not yet very clear is how to interpret the quantified isotropy using these indicators. This study aims to contribute to the understanding of the isotropy by (i) modifying an existing isotropy indicator based on the spherical harmonic expansion and (ii) presenting isotropic sound field model composed of a finite number of plane waves. Theoretical and numerical investigations show that a limited-degree isotropy can be established by using the isotropy indicator and the isotropic sound field model.
The function "SphQuadrat.m" returns efficient quadrature rules on the sphere in a 3-dimensional space. The quadrature rules consist of the coordinates of the samling points and the (positive) weights of each point. Cartesian and spherical coordinate systems are available; please note that the notation of elevation angles θ in the spsherical coordinate systems differs from that in MATLAB. That is, the function returns vertical angles θ maesured from the z-axis. Available exactitude degrees of the quadratures are 0,2,4,...,100. MAT files containing the points and the weights of the quadratures are named as "xxx-yyyyy.mat", where "xxx" denotes the degree of exactitude and "yyyyy" denotes the number of points. By default, the weights are normalized as sum(weight)=1, while the function also provides 4pi-normalization sum(weight)=4*pi and the-number-of-points-normalization sum(weight)=numel(weight). Reference: Manuel Gräf, Efficient Algorithms for the Computation of Optimal Quadrature Points on Riemannian Manifolds, Ph.D. thesis, Technische Universität Chemnitz, (2013)
Superconductive-assisted machining (SUAM) is a polishing method that employs a magnetic levitation tool, which is based on a superconductive phenomenon called the pinning effect. Since the tool magnetically levitates, the issue of tool interference is eliminated. In this study, in order to set up the polishing conditions of the magnetic levitation tool, we evaluated the relation between the flux density distribution relative to the tool position and the holding force acting on the magnetic levitation tool to maintain its initial position, set by field cooling by the superconducting bulk. For the holding force, we measured the attractive, repulsive, restoring, and driving forces. We found that the greater the holding force, the smaller the initial distance between the superconducting bulk and the magnetic levitation tool. The attractive force was found to peak when the levitated tool was displaced 6 mm from an initial position of 9 mm from the bulk, and it became only the self-weight of the magnetic levitation tool at displacements of 30 mm and above, where the pinning effect broke down. We then evaluated the polishing characteristics for SUS304 and A1100P at a tool displacement that results in the maximum attractive force. In the polishing experiment, we employed a water-based diamond slurry because the temperature of the workpiece was close to room temperature. We found that it was possible to polish SUS304 and A1100P while avoiding the effects of magnetization due to the polishing pressure or induced currents that accompany the rotation of the metal plate. The arithmetic average roughness, Ra , of A1100P was relatively high due to the effect of scratches, while that of SUS304 improved from 92 nm before polishing to 55 nm after polishing when polished with grains with a diameter of 1 μm.
The function "SphQuadrat.m" returns efficient quadrature rules on the sphere in a 3-dimensional space. The quadrature rules consist of the coordinates of the samling points and the (positive) weights of each point. Cartesian and spherical coordinate systems are available; please note that the notation of elevation angles θ in the spsherical coordinate systems differs from that in MATLAB. That is, the function returns vertical angles θ maesured from the z-axis. Available exactitude degrees of the quadratures are 0,2,4,...,100. MAT files containing the points and the weights of the quadratures are named as "xxx-yyyyy.mat", where "xxx" denotes the degree of exactitude and "yyyyy" denotes the number of points. By default, the weights are normalized as sum(weight)=1, while the function also provides 4pi-normalization sum(weight)=4*pi and the-number-of-points-normalization sum(weight)=numel(weight). Reference: Manuel Gräf, Efficient Algorithms for the Computation of Optimal Quadrature Points on Riemannian Manifolds, Ph.D. thesis, Technische Universität Chemnitz, (2013)
Sound field diffuseness plays a key role in room acoustics. Although several attempts have been made to characterize diffuseness quantitatively, how to quantify the extent of diffuseness has yet to be understood. This paper considers a directional diffuseness of a sound field from a viewpoint of statistics. Using an existing approach to the evaluation of diffuseness that employs a covariance of electric acoustic signals in the spherical-harmonics domain, a limited-degree directional diffuseness is formulated. In addition, a spherical design is used to model the diffuse sound field composed of finite number of plane waves. The formulation and the model can contribute to a better understanding of the evaluation of the diffuseness. Results also suggest that Gaussianity of a sound field in the spherical-harmonics domain can be interpreted as Gaussianity of plane waves in the diffuse field model.
