We present a new method to approximate the Neumann spectrum of a Laplacian on a fractal K in the plane as a renormalized limit of the Neumann spectra of the standard Laplacian on a sequence of domains that approximate K from the outside. The method allows a numerical approximation of eigenvalues and eigenfunctions for lower portions of the spectrum. We present experimental evidence that the met...

sound power is considered as an excellent measure for evaluating the efficiency of noise controls as well as for comparing noise sources in workrooms. this parameter can be determined by sound pressure or intensity based methods in real conditions of workrooms. this paper aims empirically to compare these in situ methods in relation to a typical industrial machine located in workroom in terms o...

Horizontal distribution of the copepod Neocalanus cristatus was shown to be fractal on the scale between tens of meters and over 100 km. The fractal dimensions ranged between 1.68–1.89, significantly higher than those of oceanic turbulence and phytoplankton distribution. 1. Introduction Heterogeneity in the horizontal distribution of zooplankton has been recognized for many years (e.g. Hardy, 1...

We give the first example of a connected 4-regular graph whose Laplace operator’s spectrum is a Cantor set, as well as several other computations of spectra following a common “finite approximation” method. These spectra are simple transforms of the Julia sets associated to some quadratic maps. The graphs involved are Schreier graphs of fractal groups of intermediate growth, and are also “subst...

Computational experiments with a simple algorithm show that it is possible to fill any spatial region with a random fractalization of any shape, with a continuous range of pre-specified fractal dimensions D. The algorithm is presented here in 1, 2, or 3 physical dimensions. The size powerlaw exponent c or the fractal dimension D can be specified ab initio over a substantial range. The method cr...

Frequency analysis is a method of measuring the spatial frequency component in images. We attempted to analyze and assess frequency analyses of images of various contrast medium injection timings using a normalized integral power spectrum. In magnetic resonance imaging, the k-space order was linear and sequential. During the twenty-second scanning time, we injected contrast medium at 3 ml/s and...

In a systematic study, we compare the density statistics in high-resolution numerical experiments of supersonic isothermal turbulence, driven by the usually adopted solenoidal (divergence-free) forcing and by compressive (curl-free) forcing. We find that for the same rms Mach number, compressive forcing produces much stronger density enhancements and larger voids compared to solenoidal forcing....

In a systematic study, we compare the density statistics in high resolution numerical experiments of supersonic isothermal turbulence, driven by the usually adopted solenoidal (divergence-free) forcing and by compressive (curl-free) forcing. We find that for the same rms Mach number, compressive forcing produces much stronger density enhancements and larger voids compared to solenoidal forcing....

The branching systems in our body (vascular and bronchial trees) and those in the environment (plant trees and river systems) are characterized by a fractal nature: the self-similarity in the bifurcation pattern. They increase their branch density toward terminals according to a power function with the exponent called fractal dimension (D). From a stochastic model based-on this feature, we form...

We present a method to characterize lysozyme pre-crystalline aggregates using a forward-lightscattering technique, which is highly sensitive to protein aggregates. The static light scattering properties at small angles of crystallizing lysozyme aggregates are discussed, and related to the crystallization conditions based on the concentration of added precipitant NaCl. Lysozyme solutions that st...