A spectral transport equation is derived here that governs the evolution of a random field of surface gravity waves in a two layer fluid model. This equation is used to study the stability of an initially homogeneous Lorentz spectrum under long wave length perturbations. It is observed that the effect of randomness is to reduce the growth rate of instability. An increase in the thickness of the upper fluid results in an increase in the extent of instability. It is also found that the extent of instability becomes less for a smaller density difference of the two fluids.
The electron transfer reaction of L-cysteine (RSH) with pyridinium chlorochromate (PCC) has been studied spectrophotometrically over the range 2.0 ≤ 10^3 [RSH] ≤ 6.0; 0.01 ≤ [H+] ≤ 0.2; 298 ≤ T ≤ 318 K and I = 0.3 mol dm-3 (NaClO4). The electron transfer reaction has also been carried out in the presence of anionic, cationic and neutral micelle. The reaction in acid medium is strongly catalyzed by changing [SDS]T (sodium dodecyl sulfate) up to 3 × 10-2 mol dm-3, beyond this concentration of SDS, the rate is retarded. The cationic and neutral micelle has a small effect on the rate. ΔH≠ (kJ mol-1) and ΔS≠ (JK-1 mol-1) values for the k1 and k2 paths are 30.20 ± 0.25, -159.65 ± 0.83 and 29.60 ± 0.62, -127.09 ± 2.17, respectively. The negative activation entropy is indicative of the ordered transition state for the electron transfer reaction. Formation of 2-amino-3-(2-amino-2-carboxy-ethyl) disulfanyl-propanoic acid as product is strongly supported by IR spectra.
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Fourth order nonlinear evolution equations are derived for a three dimensional surface gravity wave packet in the presence of long wave length an interfacial wave in a two layer fluid domain in which the lower fluid depth is infinite. For derivation of evolution equations, the multiple-scale method is used. Using these evolution equations, stability of uniform stokes wavetrain is investigated for different values of density ratio of the two fluids and for different values of the depth of the lighter fluid.
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