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Item SPIN COMPLEXES IN FERROMAGNETISM(1988-11) AGBOOLA, A. I.The spin-wave theory in Heisenberg model of ferromagnetism is investigated with the Holstein - Primakoff transformation and with emphasis on the spin wave interactions. The temperature Tₒ below which the concept of magnons is valid is determined. By a special expansion formalism of operator (l-a+a/2S)1/2 which yields 1+(1-(1-1/2S)1/2 )a+a it is shown that quantized spin waves which behave like spin 1 quasiparticles (with dispersion relation ω~ k2 ) called magnons at temperatures T < Tₒ, are Bosons with an effective (negative) electrochemical potential µ that varies as T in the wave-wave interaction approximation. The various coefficients of Tv in the expression of the spontaneous magnetization M(T)/M(o) = l-(C1T3/2+C2T5/2+C3T7/2+C4T4) as well as the specific heat for some ferromagnets are calculated. The results are remarkably close to the experimental values obtained by other investigators. The method used enables one to deal especially with regimes of small spin values S for which µ differs substantially from zero. The influence of the chemical potential on some thermodynamic quantities are found for ferromagnets with Hexagonal-close-packed structures, as well as for cubic crystals, The existence of the spin wave interactions and hence of non-zero effective chemical potential is shown to give rise to a lowering of the thermodynamic internal energy with the implication that spin waves, on the average, form bound states called spin complexes. The kinematical as well as the dynamical interactions on the thermodynamic quantities are also found for some ferromagnets, by subjecting the magnons to intermediate statistics. The influence of the spin-wave-spin-wave-spin-wave interactions on the coefficients of Tv in the expression of the spontaneous magnetization of some ferromagnets are found to be negligible in comparison with wave-wave interactions. An attempt is made to extend the above calculations to spin complexes in antiferromagnetism, a phenomenon which seems to be relevant to high temperature superconductivity.Item INITIAL STAGES AND SOME CHARACTERISTICS OF WEST AFRICAN LINE SQUALLS(1983-03) ADEDOYIN, J. A.A review of West African synoptic weather pattern reveals that the sub-region experiences a special kind of atmospheric disturbance -the line squall - whenever the south-westerlies cover, approximately, the whole of Nigeria. Various methods that have been used to study the squalls (i.e. observational investigations, satellite investigations and modelling) have not been very successful in isolating the trigger mechanism of the phenomenon. It is been proposed that line squalls are initiated through the amplification (with time) of any wave-like perturbation along the surface of discontinuity between the south-westerlies and the north-easterlies. The amplifying perturbations could block the 650 mb. mid-tropospheric jet which further distorts the 'bump' formed by the undulating perturbation. This distortion forces the southwesterlies further up and they could condense. The precipitates fall into the underlying, dry jet and some of them evaporate; the latent heat of evaporation being supplied by the jet. The jet, now cooler, sinks. On sinking, the jet could hit the surface of the earth on which it forms the squall front and crawls; thereby lifting the south-westerlies ahead of it. The cycle of condensation, evaporation and sinking then continunes. A gravity-wave model of this mechanism is presented through the solution of a frequency equation with the aid of a two-layer atmospheric model. The solution is an eigenvalue problem from which many modes of different growth rates and phase velocities could be obtained. Some of these phase velocities will be complex - the real part representing the phase velocity while the imaginary part represents the amplification. Waves with the largest amplifications (i.e. the largest imaginary part) are those that could possibly block the 650 mb. mid-tropospheric jet and trigger off line squalls. Among others, this proposal on the trigger mechanism of line squalls is able to explain: (i) the preference of highlands as places of origin of line squalls, (ii) the close association between the speeds of propagation of line squalls and the mid-tropospheric jet and (iii) the observed overturning of the atmosphere after the passage of line squalls.