Two-Dimensional Simulation of Nonlinear Acoustic Wave Propagation Using Constrained Interpolation Profile Method

Abstract

The high-pressure behaviour of LiGdF 4 scheelite (I 4 1 /a, Z = 4) was studied by measuring its angle-dispersive x-ray powder diffraction patterns as a function of pressure and temperature in a diamond anvil cell and a large-volume Paris-Edinburgh cell using a synchrotron radiation source. Upon compression to about 11 GPa at room temperature, the stable structure is of the scheelite type. At higher pressures and T = 298 K, new reflections occur that cannot be explained with the fergusonite structural model previously observed for LiYF 4 . Associated with this is the growth of an amorphous component. All the transformations are largely irreversible upon decompression. Annealing of the sample at 13.1 GPa led to a nucleation of a solid solution series Li y Gd 1−y F 3−2y (P6 3 /mmc, Z = 2) and traces of LiF. The new material Li y Gd 1−y F 3−2y (P6 3 /mmc, Z = 2) was recovered to ambient conditions but back-transformed to a YF 3 -type phase (Pnma, Z = 4) after regrinding at room temperature for several hours. These observations are discussed in relation to the high-pressure high-temperature systematics of the AMX 4 -type compounds.

Numerical simulation of sound wave propagation using multimoment method of characteristics with general Hermite interpolation

“…The constrained interpolation profile (CIP) method [9][10][11][12][13][14]] is a novel low-dispersion numerical scheme. It is a method of characteristics (MOCs) [15].…”

“…This scheme is an example of a multimoment scheme. By such treatment of fields, the CIP method gives the numerical phase velocity with high accuracy for very wide frequency bands [10][11][12]. This is an advantage of the method.…”

Numerical simulation of sound wave propagation using hybrid technique combining FDTD method and CIP method

“…The constrained interpolation profile/cubic-interpolated pseudoparticle (CIP) method [9][10][11][12][13][14][15] is known as a novel numerical scheme, which is a method of characteristics (MOC) [16]. It is a numerical scheme with high accuracy that hardly causes numerical dispersion error [13][14][15].…”

“…It is a numerical scheme with high accuracy that hardly causes numerical dispersion error [13][14][15]. The remarkable future of this method is that it uses not only the values of the acoustic field but also their spatial derivatives at the grid point, to solve the problem of sound wave propagation.…”

A novel method for numerical simulation of sound wave propagation using Heptic interpolation profile method

“…The Constrained Interpolation Profile (CIP) method [9][10][11][12][13][14][15]is a novel low-dispersive numerical scheme. It is a method of characteristics (MOC) [16].…”