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This paper investigates the motion response of a floating body in time domain under the influence of small amplitude regular waves. The governing equations of motion describing the balance of wave-exciting force with the inertial, damping, and restoring forces are transformed into frequency domain by applying Laplace transform technique. Assuming the floating body is initially at rest and the waves act perpendicular to the vessel of lateral symmetry, hydrodynamic coefficients were obtained in terms of integrated sectional addedmass, damping, and restoring coefficients, derived from Frank's close-fit curve. A numerical experiment on a vessel of 19190 ton displaced mass was carried out for three different wave frequencies, namely, 0.56 rad/s, 0.74 rad/s, and 1.24 rad/s. The damping parameters (ς i ) reveal the system stability criteria, derived from the quartic analysis, corresponding to the undamped frequencies (β i ). It is observed that the sway and yaw motions become maximum for frequency 0.56 rad/s, whereas roll motion is maximum for frequency 0.74 rad/s. All three motions show harmonic behavior and attain dynamic equilibrium for time t > 100 seconds. The mathematical approach presented here will be useful to determine seaworthiness characteristics of any vessel when wave amplitudes are small and also to validate complex numerical models.2000 Mathematics Subject Classification: 34C15, 70K42, 70K25.

We study the low temperature multisubband electron mobility in a structurally asymmetric GaAs/AlxGa1-xAs delta doped double quantum well. We calculate the subband energy levels and wave functions through selfconsistent solution of the coupled Schrodinger equation and Poisson's equation. We consider ionized impurity scattering, interface roughness scattering, and alloy disorder scattering to calculate the electron mobility. The screening of the scattering potentials is obtained by using static dielectric response function formalism within the random phase approximation. We analyze, for the first time, the effect of asymmetric structure parameters on the enhancement of multisubband electron mobility through intersubband interactions. We show that the asymmetric variation of well width, doping concentration, and spacer width considerably influences the interplay of scattering mechanisms on mobility. Our results of asymmetry induced enhancement of electron mobility can be utilized for low temperature device applications.

We analyse the effect of asymmetry in the structure parameters on low-temperature multisubband electron mobility m in a barrier delta-doped GaAs/AlGaAs double quantum well structure. We obtain the subband energy levels and wave functions through self-consistent solution of Schrodinger and Poisson's equations. We show that m is enhanced through asymmetry in well widths and spacer widths as a function of doping concentration, mediated by intersubband effects. We analyse the interplay of different scattering mechanisms on m and show that the nonlinear enhancement of m arises due to interface roughness (ir-) scattering even though the mobility is mostly limited by ionized impurity (imp-) scattering. We further show that the range of m up to which the ir-scattering dominates depends on the occupation of subbands. Our results can be utilized for low-temperature devices.