A two-dimensional Cauchy Poisson problem for water with a porous bottom generated by an axisymmetric initial surface disturbance is investigated here. The problem is formulated as an initial value problem for the velocity potential describing the motion in the fluid. The Laplace and Hankel transform techniques have been used in the mathematical analysis to obtain the form of the free surface in terms of a multiple infinite integral. This integral is then evaluated asymptotically by the method of stationary phase. The asymptotic form of the free surface is depicted graphically in a number of figures for different values of the porosity parameter and for different types of initial disturbances.
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A series of glasses in the system xPbOź(100 - x)B2O3 (x = 45, 55, 65 mol %) were prepared using analytical grade PbO consisting of a mixture of orthorhombic and tetragonal phases (ca. 1:1, w/w) and H3BO3 melted in silica beaker in the temperature range of 575-900 oC for 30 min under normal atmosphere. Only the 55PbOź45B2O3 glass prepared at 575 (L2), 650 (L3) and 700 oC (L4) showed several optical absorption bands in the visible region. However, all the bands disappeared either when a 1.7 mol % equivalent PbO from Pb3O4 was added in the batch or the melting temperature was increased to more than 800 oC. L2 glass showed a broad absorption band at ca. 485 nm which was thought to be due to combined effect of nanometallic lead (Pb0) and Pb+. The formation of hexagonal nano-Pb0 particles of 7-13 nm size in 55PbOź45B2O3 glass melted at 575-700 oC was confirmed by TEM and Pb+ was identified by a broad EPR signal with g-value at ca. 2.00. Optical absorption at ca. 485 nm and 565 nm (broad shoulder) was observed in L3 glass whereas a new peak at ca. 525 nm appeared in L4 which was identified due to Pb3+ by EPR signal with g-value ca. 2.176 and A-tensor, ca. 6340×10-4 cm-1. A mechanism for the formation of Pb0, Pb+ and Pb3+ has been proposed.
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