We propose a shallow water model that combines the dispersion relation of water waves and Boussinesq equations, and that extends the Whitham equation to permit bidirectional propagation. We show that its sufficiently small and periodic traveling wave is spectrally unstable to long wavelength perturbations if the wave number is greater than a critical value, like the Benjamin‐Feir instability of a Stokes wave. We verify that the associated linear operator possesses infinitely many collisions of purely imaginary eigenvalues, but they do not contribute to instability to the leading order in the amplitude parameter. We discuss the effects of surface tension. The results agree with those from a formal asymptotic expansion and a numerical computation for the physical problem.
Ultrasonic mist chemical vapour deposition (UM-CVD) system has been developed to prepare ZnO nanopowder. This is a promising method for large area deposition at low temperature inspite of being simple, inexpensive and safe. The particle size, lattice parameters and crystal structure of ZnO nanopowder are characterized by in situ high temperature X-ray diffraction (XRD). Surface morphology of powder was studied using transmission electron microscopy (TEM) and field emission electron microscope (FESEM). The optical properties are observed using UV-visible spectrophotometer. The influence of high temperature vacuum annealing on XRD pattern is systematically studied. Results of high temperature XRD showed prominent 100, 002 and 101 reflections among which 101 is of highest intensity. With increase in temperature, a systematic shift in peak positions towards lower 2θ values has been observed, which may be due to change in lattice parameters. Temperature dependence of lattice constants under vacuum shows linear increase in their values. Diffraction patterns obtained from TEM are also in agreement with the XRD data. The synthesized powder exhibited the estimated direct bandgap (E g ) of 3⋅43 eV. The optical bandgap calculated from Tauc's relation and the bandgap calculated from the particle size inferred from XRD were in agreement with each other.
Abstract. We study the stability and instability of periodic traveling waves in the vicinity of the origin in the spectral plane, for equations of BenjaminBona-Mahony (BBM) and regularized Boussinesq types permitting nonlocal dispersion. We extend recent results for equations of Korteweg-de Vries type and derive modulational instability indices as functions of the wave number of the underlying wave. We show that a sufficiently small, periodic traveling wave of the BBM equation is spectrally unstable to long wavelength perturbations if the wave number is greater than a critical value and a sufficiently small, periodic traveling wave of the regularized Boussinesq equation is stable to square integrable perturbations.
Mixed metal-hexacyanoferrates (MHCF) have shown promising applications for technological development particularly in energy storage technologies, ferromagnetic materials, and electrode materials. However, the challenge of controlling their chemical synthesis, solubility, polycrystallinity and nanogeometry have restricted the practical implementation of MHCF in commercial designs. Further, MHCFs have shown potential as peroxidase mimetics. There is still challenging demand to enhance the catalytic efficiency of such materials to the equivalent of biocatalytic activity thereby allowing the precise control of the mimetic character and ultimately leading to the development of new materials as powerful peroxidases i.e. Horseradish peroxidase (HRP) replacement during enzyme and immuno-sensors development. We report herein a new process that allows the controlled synthesis of biocompatible mixed MHCF nanoparticles with a variety of transition metal ions. The resulting polycrystalline mixed MHCF shows enhanced catalytic efficiency to hydrogen peroxide (H2O2) as compared to that of polycrystalline Prussian blue (PB) made under similar conditions with significant increase in catalytic efficiency as a function of respective hetero-transition metal ion of mixed FeHCF in the order of FeHCF < Mn-FeHCF < Ni-FeHCF < Cu-FeHCF justifying as perfect peroxidase replacement.
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