For unmagnetized dusty plasma with many different dust grain species containing both hot isothermal electrons and ions, both the linear dispersion relation and the Kadomtsev–Petviashvili equation for small, but finite amplitude dust acoustic waves are obtained. The linear dispersion relation is investigated numerically. Furthermore, the variations of amplitude, width, and propagation velocity of the nonlinear solitary wave with an arbitrary dust size distribution function are studied as well. Moreover, both the power law distribution and the Gaussian distribution are approximately simulated by using appropriate arbitrary dust size distribution functions.

A Zakharov–Kuznetsov (ZK) equation, a modified ZK (mZK) equation, and a coupled ZK (cZK) equation for small but finite amplitude dust acoustic waves in a magnetized two-ion-temperature dusty plasma with dust size distribution have been investigated in this paper. The variations of the linear dispersion relation and group velocity, nonlinear solitary wave amplitude, and width with an arbitrary dust size distribution function are studied numerically. We conclude that they all increase as the total number density of dust grains increases, and they are greater for unusual dusty plasma (the number density of larger dust grains is greater than that of smaller dust grains) than that of usual dusty plasma (the number density of smaller dust grains is greater than that of larger dust grains). It is noted that the frequency of the linear wave increases as the wave number along the magnetic direction increases. Furthermore, the width of the nonlinear waves increases but its amplitude decreases as the wave number along the magnetic direction increases.

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The vacuum degree is the key parameter reflecting the quality and performance of vacuum glass. This investigation proposed a novel method, based on digital holography, to detect the vacuum degree of vacuum glass. The detection system was composed of an optical pressure sensor, a Mach–Zehnder interferometer and software. The results showed that the deformation of monocrystalline silicon film in an optical pressure sensor could respond to the attenuation of the vacuum degree of vacuum glass. Using 239 groups of experimental data, pressure differences were shown to have a good linear relationship with the optical pressure sensor’s deformations; pressure differences were linearly fitted to obtain the numerical relationship between pressure difference and deformation and to calculate the vacuum degree of the vacuum glass. Measuring the vacuum degree of vacuum glass under three different conditions proved that the digital holographic detection system could measure the vacuum degree of vacuum glass quickly and accurately. The optical pressure sensor’s deformation measuring range was less than 4.5 μm, the measuring range of the corresponding pressure difference was less than 2600 pa, and the measuring accuracy’s order of magnitude was 10 pa. This method has potential market applications.

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