Silicon molecules in space and in the laboratory

Despite the highly non-volatile nature of Si, silicon bearing molecules are a significant trace constituent of the gas associated with late-type stars and star forming regions, representing nearly 10% of the molecular species that have been identified in space. The early astronomical detection of SiO and its remarkable maser emission stimulated laboratory studies of other small silicon species that were crucial to the astronomical identifications. Although the pace of this laboratory work until recently has been slow, the application of Fourier transform microwave spectroscopy to supersonic molecular beams has overcome many experimental difficulties, yielding the detection of more than 20 new silicon chains and rings of astronomical interest during the past three years. Three of these, the rhomboidal ring Sic3 and the isovalent linear molecules SiCN and SiNC, have now been found in space, and with dedicated searches other recently discovered silicon molecules may soon be found. A number of exotic silicon molecules of astronomical and chemical interest should be amenable to laboratory detection with present techniques.     

Axisymmetric isospectral annular plates and membranes

A simpler ‘conditional’ form of the vibrating plateequation for which all the physical parameters may be spatiallyvarying is found when the relationship D(1 – v) = constantis satisfied between flexural rigidity and Poisson's ratio.A method of coordinate inversion is used to find a family ofinhomogeneous clamped annular plates (with axisymmetric spatiallyvarying density, thickness, Young's modulus, and Poisson's ratio)which have the same complete frequency spectrum as a standardhomogeneous clamped annular plate of the same inner and outerradii. In particular, these inhomogeneous plates have inversefourthpower radial dependence of density. General radial power-lawtransformations are also considered, leading to conclusionsfor the axisymmetric vibration spectra. Various results forcircular and annular membranes also emerge from the analysis.