Kinetic theory of high-n (n: toroidal mode number) electromagnetic ballooning mode is presented with consistent inclusion of plasma β-value, ion gyroradius, kinetic parallel conductivity, ∇B drift and magnetic shear effects. A new unstable branch of nonlocal eixenmodes in a collisionless toroidal plasma is found. The growth rate of kinetic high-n ballooning mode is of order of drift frequency.

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In order to investigate the nonlinear characteristics of ionization waves (moving-striations) in the positive column of glow discharge, a nonlinear modulation of ionization waves in the region of the Pupp critical current is analysed by means of the reductive perturbation method. The modulation of ionization waves is described by a nonlinear Schrödinger type equation. The coefficients of the equation are evaluated using the data of the low pressure Argon-discharge, and the simple solutions (plane wave and envelope soliton type solutions) are presented. Under a certain condition an envelope soliton is propagated through the positive column.

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Nernst effect is taken into account in the analysis of the magnetic field generating thermal instability. Instability condition and the growth rate γ are obtained. The Nernst effect as well as the hydrodynamic effect induces the instability in the region of ∇n₀·∇T₀<0 and it increases the magnitude of the magnetic field especially in the overdense region.

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A theoretical investigation is made on the linear, spatial stability of the developing flow in a two-dimensional channel. The velocity profile of the developing flow region is obtained using Bodoia and Osterle’s finite difference method and its stability is investigated assuming that the flow is approximately parallel at each axial position. Among the four methods used for dealing with the einenvalue problem, it is found that the integration of the momentum and continuity equations separately while applying selectively the Gram-Schmidt orthonormalization procedure provides the most efficient and accurate method.
The critical Reynolds number, frequency, and wavenumber decrease with increasing axial distance from the entrance and approach asymptotically the corresponding values for the fully developed flow. The present results give considerably lower critical Reynolds numbers than those for the Sparrow profile in the near entrance region but agree well with the latter in the farther downstream region.

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A new method is proposed for the purpose of analysing the system of weakly nonlinear integral equations. The essence of this method consists in expanding the integral operator in powers of ε:
(Remark: Graphics omitted.),
where N is a positive integer, ε is a small parameter specifying the multiple scales, and I_n are algebraic functions of operators defined in the text.
The practical application of the method is made to a nonlinear Volterra and a nonlinear Fredholm integral equation.

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A phase diagram for two weakly coupled Belousov-Zhabotinsky systems was experimentally obtained as a function of coupling strength and the difference between the natural frequency of the constituent cells. The results indicate existence of six phases. To find out a universal features for the weak coupling, kinetic equations for phase and radius of limit cycle were derived from ordinary reaction diffusion equations in a two component system. Simple models of the coupling states from the simple equations of phase and radius explained qualitative features of the experimental results.

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The problem of the onset of instability driven by surface tension gradients (the Marangoni effect) in an isothermal gas-liquid reaction process is investigated by using a linear theory. Including a deformation of free surface, effects of capillary and gravity waves are considered. These effects are important for the disturbance of small wave-numbers. It is shown that there exist two distinct mechanisms of instability, either with the essential effects of surface deformation or without them. For the former, the critical Marangoni number linearly depends on the ratio of the Weber number to the Crispation number and on the reaction parameter, on the other hand, for the latter, it depends on the reaction parameter and the diffusivity ratio. By considering different conditions at lower surface, two cases are treated in a similar manner and it is examined how these affect on instability.

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Theoretical investigation is made on the unsteady radiative heat transfer through an absorbing and emitting gray medium which occupies a semi-infinite space bounded by a semitransparent gray plate. The system is initially in a uniform state. At an instance the temperature of the plate is changed to a constant value in addition to the impose of a beam radiation through the plate. They are main-tained hereafter. It is found that the problem has two stages of time evolution: the initial stage and the large time stage, whose time scales as well as spatial scales are different each other. At first, the temperature rises rapidly in the radiation layer. The solution is solved in a form of time series expansion. In the large time stage, the temperature rises gradually in the asymptotic region. The solution is solved by the matched asymptotic expansions.

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A new set of analytical soliton solutions of the cylindrical KdV equation u_t+6uu_x+u_xxx+u⁄2t=0 is obtained. In contrast to other solutions, these new solutions agree with numerical simulation of Maxon and Viecelli and the experiment by Hershkowitz and Romesser. We present here derivation of these soliton solutions up to N=3 (three-soliton) by Hirota bilinear method (direct method).

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