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The classical planar Richtmyer–Meshkov instability (RMI) at a fluid interface supported by a constant pressure is investigated by a formal perturbation expansion up to the third order, and then according to definition of nonlinear saturation amplitude (NSA) in Rayleigh–Taylor instability (RTI), the NSA in planar RMI is obtained explicitly. It is found that the NSA in planar RMI is affected by the initial perturbation wavelength and the initial amplitude of the interface, while the effect of the initial amplitude of the interface on the NSA is less than that of the initial perturbation wavelength. Without marginal influence of the initial amplitude, the NSA increases linearly with wavelength. The NSA normalized by the wavelength in planar RMI is about 0.11, larger than that corresponding to RTI.

We present first-principles studies on the transport properties of small silicon and aluminium clusters: Al2, Si2, Al4 and AlSi sandwiched between two Al (100) electrodes. The variation of the equilibrium conductance as a function of contact distance for these two-probe systems is probed. Our results show that the transport properties are dependent on both the specific nanostructure and the separation distance between the central molecule and the electrodes. For equilibrium transport properties, the clusters with the similar structure show similar transmission spectra at large distances, the small difference can be explained by the electron filling. For current-voltage characteristics, all the clusters show the metallic behaviour at lower bias, however very different non-linear behaviour can be observed at higher bias. For AlSi and Al2, when the distance between the central cluster and the electrodes is 3.5 A, large negative differential resistance (NDR) can be found in the bias range 0.8 V~1.4 V.

Based on dividing the profile into a number of absolute phase intervals, the phase-resolved spectra (PHRS) are derived from published time-aligned average profiles at radio frequencies over two decades for the classic conal-double pulsar B1133+16. The relative spectral index, defined as the difference between the spectral indices of a reference and the given arbitrary phase interval, is obtained by power-law fit at each phase interval. The derived phase-resolved spectra show an ``M-like'' shape, of which the leading part and trailing part are approximately symmetrical. The basic feature of the PHRS is that the spectrum first flattens then steepens as the pulse phase sweeps from the profile center to the profile edges. The PHRS provide a coherent explanation of the major features of profile evolution of B1133+16, namely, the pulse width shrinkage with increasing frequency and the frequency evolution of the relative intensity between the leading and trailing conal components, and the bridge emission. The PHRS may be an indicator for emission spectral variation across the pulsar magnetosphere. Possible mapping from PHRS to emission-location-dependent spectral variation is presented, and some intrinsic mechanisms are discussed.

The classical Rayleigh–Taylor instability (RTI) at the interface between two variable density fluids in the cylindrical geometry is explicitly investigated by the formal perturbation method up to the second order. Two styles of RTI, convergent (i.e., gravity pointing inward) and divergent (i.e., gravity pointing outwards) configurations, compared with RTI in Cartesian geometry, are taken into account. Our explicit results show that the interface function in the cylindrical geometry consists of two parts: oscillatory part similar to the result of the Cartesian geometry, and non-oscillatory one contributing nothing to the result of the Cartesian geometry. The velocity resulting only from the non-oscillatory term is followed with interest in this paper. It is found that both the convergent and the divergent configurations have the same zeroth-order velocity, whose magnitude increases with the Atwood number, while decreases with the initial radius of the interface or mode number. The occurrence of non-oscillation terms is an essential character of the RTI in the cylindrical geometry different from Cartesian one.