The decay of 24 min ¹⁴⁶Pr has been studied with Ge(Li), pure Ge, NaI(Tl) and plastic detectors in singles and coincidence modes. Sources were prepared by the chemical separation, called a rapid paper electrophoresis, from the fission products of ²³⁵U. A total of 104 γ-ray transitions, 64 of them not reported before, have been observed and 88 transitions of them are incorporated into a level scheme comprising 32 excited states of ¹⁴⁶Nd. Observed Q_β value was 4.15±0.15 MeV. Gamma-gamma directional angular correlation measurements in ¹⁴⁶Nd have been performed with 12 cascades each including 453.9 keV 2⁺→0⁺ ground state transition. Spin assignments of 13 levels in ¹⁴⁶Nd were deduced. The low lying-states in ¹⁴⁶Nd are discussed in terms of the quasi band.

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Angular distributions for elastic scattering of deuterons by ⁹Be and inelastic scattering to the 1.68 MeV state and to the 2.43 MeV state were measured at energies 12.35 MeV and 14.06 MeV. Excitation functions were measured in the energy range of 12.17 MeV to 14.43 MeV. The elastic scattering data were analyzed in terms of the optical model. The increase of the real central potential depth with the increase of the incident energy is found. The angular distribution for (d, d₂)(2.43 MeV) together with d₀ distribution was reproduced satisfactorily by coupled-channel calculations. The quadrupole deformation parameter of β₂=1.4 was obtained, which is close to the value derived from (e, e′) and (p, p′). The angular distribution for (d, d₁)(1.68 MeV) was qualitatively reproduced by assuming the excitation of ⁹Be as ⁸Be(0⁺)+n(1p_3⁄2)→⁸Be(0⁺)+n(2s_1⁄2).

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Electromagnetic transitions for low-lying states in ⁶⁷Ge were examined by measuring gamma rays and internal conversion electrons following the ^natZn(α, n) ⁶⁷Ge reaction. The 734-keV gamma ray was found to be the single-quasi-neutron (1g_9⁄2→1f_5⁄2) M2 transition. The halflife is (102±10) ns. The reduced M2 matrix element is (2.32±0.24) (eh/2Mc)² fm². This gives the renormalization factor g^eff(M2Me)⁄g^free(M2)=0.25±0.03. A systematic survey was made of the single-quasi-particle M2(1g_9⁄2→1f_5⁄2), the single quasi-particle E3 (1g_9⁄2→2p_3⁄2) and the l-forbidden M1 (1f_5⁄2→2p_3⁄2) transitions in the fp-shell nuclei. The renormalization factors for these transitions were analyzed in terms of the core polarizations associated with those transition modes.

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In connection with freezing, dynamical behaviour of (metastable) liquids is studied based on the nonlinear diffusion equation (ND eq.) derived in a previous paper. From the ND eq., an H-theorem for the free-energy functional (Remark: Graphics omitted.) of Brout is derived in the form (Remark: Graphics omitted.). This shows that the ND eq. gives a dynamic extention of the mean field equation of freezing studied by Kirkwood-Monroe, Brout and others. While two-mode analysis of the ND eq. essentially reproduces the previous results obtained with a reductive perturbation method, N-mode analysis (N>2) shows that a crystalline state bifurcates from a uniform one before the system reaches at the metastability limit. Thermodynamic arguments follow the bifurcation analysis to determine a transition (freezing) point.

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The concept of “stirrable” and “unstirrable” that has been introduced and investigated in a previous paper [J. Phys. Soc. Japan 42 (1977) 424] relates to the change from full uncondensation to condensation enforced on one member by the other members of a compound system of soft modes. In the present paper, the change from full uncondensation to condensation is generalized to the change from one style of condensation to another style of condensation, and hereby a new convenient concept of “stirrable” and “unstirrable” is arrived at. A thermodynamic and a group-theoretical investigation are carried out with simple examples. Also, several general theorems are put forward.

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Hartree-Fock calculations for nearly commensurate spin-density-waves (SDW) are presented. The effect of harmonics in the sinusoidal SDW (SSDW) with wave number Q∼0 is studied both by analytic calculations in the limit of Q→0 and by numerical calculations for finite Q with a one-dimensional model of electrons having short range interaction. The odd harmonic SDW’s, bringing about the energy gain by exchange interaction, grow as Q decreases and, as this result, the energy of the SSDW is connected continuously with that of the ferromagnetic state. The even harmonic charge-density-waves, bringing about the energy loss by Coulomb interaction, are important for finite Q but vanishes for Q→0. The relative stability between the SSDW and helical SDW is studied. Finally, the effect of harmonics in the SSDW with Q∼K⁄2 (K being a reciprocal lattice vector) is discussed for the sake of comparison.

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A phase transition in an incommensurate structure induced by a soft mode with the wave vector k near the Brillouin zone boundary k_c is investigated. The soft mode belongs to the lower branch of two split phonon branches degenerate at k_c. It is shown that this general feature of the phonon spectrum leads with decreasing temperature to the shift of k toward k_c and finally to the lock-in transition into a commensurate phase. The present model is appropriate for ammonium fluoroberyllate, for example, and differs qualitatively from those recently suggested for potassium selenate and metal chalcogenides.

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The average number of site exchanges made by a particular atom-vacancy pair has been calculated. It is found that the number of exchanges is equal to the number of visits to the origin of a random walker; for an infinite fcc lattice the number of exchanges is about 1.345, including the first exchange. This result seems invalidate the assumption of an infinite number of exchanges, which is usually made in the derivation of the correlation factor in diffusion via the vacancy mechanism. A modified derivation of the correlation factor, which takes into account the number of exchanges explicitly, is presented.

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The possibility of the superconductive state with the aid of the plasmon in two- and three-dimensional single-carrier systems is investigated by numerical solutions of the gap equation in the weak-coupling theory of superconductivity, in which the effective interactions are calculated in the plasmon-pole approximation. The superconductivity does appear in rather low carrier concentrations and the highest attainable transition temperature is of the order of m^*⁄κ² degrees Kelvin, where the effective mass, m^*, is in the unit of the mass of a free electron and κ is the dielectric constant. Compared with a three-dimensional system, a two-dimensional one is more favorable for the plasmon mechanism of superconductivity, which stems from the difference in the dispersion relation of the plasmon.

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The angular correlation of two γ-rays from positrons annihilating in KCl has been measured at 4.2 K. Obtained data clearly show a narrow component which was not evident in a previous measurement at liquid N₂ temperature. This narrow component is a direct evidence for delocalized positronium formation in KCl. Comparison of the data with the theoretical angular correlation curve calculated by Nieminen and with the results of magnetic quenching experiments indicates that more localized positronium-like states also exist.

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In the S=1⁄2 ferromagnetic Ising-like linear chain, it is expected that the two-magnon bound states are excited thermally together with the single magnons. A new mechanism of the nuclear spin-lattice relaxation in this system is studied. It is associated with the scattering of a spin wave and a two-magnon bound state accompanied by the nuclear-spin flip. The relaxation rate is derived under the assumption that the two-magnon bound state behaves like a boson. It proves that the second-order exchange-scattered process makes a significant contribution to the total relaxation rate. The calculated relaxation times for proton and ³⁵Cl in one-dimensional Ising-like system; [(CH₃)₃NH]CoCl₃·2H₂O agree well with the zero-field experimental data in the order of magnitude as well as in the qualitative nature of the temperature dependence.

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In KCoF₃ magnon-phonon interaction is expected to be strong owing to the residual orbital moments of the Co²⁺ ions, and it plays an important role in the nuclear spin-lattice relaxation. A new mechanism of the nuclear spin-lattice relaxation of the fluorine nuclear spins in KCoF₃ is presented. Second-order relaxation processes involving magnon-phonon interaction are derived by treating as perturbation the magnon-phonon interaction and the hyperfine interaction between fluorine nuclear spins and cobaltous ions. The second-order one-magnon-one-phonon process proves to make a dominant contribution to the nuclear spin-lattice relaxation.

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Anelastic behavior in a single crystal of Mn ferrite (Mn_0.82Fe_2.18O₄) was studied at temperatures between 280 and 730 K by longitudinal vibrations of 125 kHz. The acoustic loss curve showed three kinds of internal friction peaks.
One of them appeared very near to the Curie temperature and was very sensitive to applied magnetic field and strain amplitudes of vibrations. This peak was explained by magneto-mechanical coupling factor and the loss tangent of magnetic permeability.
Another peak was observed at 500 K by longitudinal vibrations along the [110] and [111] directions but not along [100]. This was independent of strain amplitudes of vibrations and external magnetic field. The activation energy of this peak was estimated as 0.78 eV and explained by mutual exchange between cations and their vacancies on the octahedral sites in the spinel lattice.
The last one was at 300 K and independent of strain amplitudes of the vibrations and magnetic field. This peak was much smaller than the above two peaks.

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Kondo effect on the de Haas-van Alphen effect was observed in MgMn dilute alloys. The s-d exchange interaction J was estimated as −0.41 eV from measurements of temperature dependence of the Dingle temperature.

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Measurements of a half-field transition in the EPR spectrum are reported in the one-dimensional Heisenberg magnet (CH₃)₄NMnCl₃ (TMMC), and compared with a theory developed here. The theory accounts in a satisfactory way for the observed anisotropic feature. The results reveal that the appearance of the subsidiary resonance provides a direct evidence of the long-time tail of spin correlation functions in low-dimensional systems.

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The influence of atomic order for a Fe–Al (25 at%)–C alloy on the magnetic permeability disaccommodation occuring at the temperature range from 260 to 400 K was investigated. The sample was aged at 873 K, that is at temperature higher than the temperature of order-disorder phase transition for the DO₃ structure. The obtained results were discussed on the background of an atomic model of individual elementary relaxations.

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Anomalous population increase of the first excited state of Dy³⁺ in Dy₃Al₅O₁₂ in a pulsed magnetic field of a few ms duration is observed optically at 4.2 K. From experiments of the field and time dependences of the population increase, it is concluded that this phenomenon is due to the adiabatic magnetization of an effective-spin system with a large initial splitting. In deriving this conclusion, it is assumed that, during the pulsed field being applied, the spin system is thermally isolated from the heat reservoir but the spin system is in thermal equilibrium because of a fast effective spin-spin relaxation time. The anomalous population increase is also observed in DyAlO₃, Er₃Ga₅O₁₂, Ho₃Al₅O₁₂, HoAlO₃, but not in TmAlO₃.

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MnSb, which is a ferromagnet with NiAs type crystal structure, is investigated by using the polarized neutron diffraction technique. Precise measurements of the magnetic structure factors give the following results: (i) The magnetic form factor of Mn on high angle reflections, which is sensitive to the asphericity of 3d-wave function, gives the unpaired electron population to be (0.89, 1.61, 1.22) for (ψ_xo, ψ_x±, ψ_u±) orbitals, respectively. These facts indicate that MnSb should be understood with a well overlapped 3d-subbands model proposed in the band calculation on NiS rather than the broadened 3d-level model proposed for MnAs(P) system. (ii) 3d-electron number of Mn is found to be four in MnSb on the basis of the asphericity of the magnetic form factor in conformity with the band calculation. (iii) Sb is magnetically polarized with moment of about 0.2 μ_B antiparallel to the total magnetization.

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The Onodera model of electron-hole exchange coupling at an L_II,III X-ray edge is extended (i) giving a lineshape formula expressed in terms of experimentally accessible quantities, and (ii) providing a means of accounting approximately for the energy dependences of both the absorption spectrum above threshold and the exchange interaction. The experimental implications are discussed.

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A non-linear mechanical model for the martensitic transformation is proposed. The formation process of the nucleus of the martensitic phase is described as the results of the evolution of the transverse lattice waves in a non-linear dispersive lattice of the parent phase. A significant role of the dispersion relationship in the martensitic transformation is found; it is the dispersion relationship of the transverse lattice waves in the parent phase that governs the structure of the martensitic nucleus. However, the presence of such strong anomaly in the dispersion relationship as accompanied by a soft phonon is not required for the nucleation of the martensitic phase.

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de Haas-van Alphen oscillations in cobalt are studied for various crystallographic directions by using a pulsed field method. The oscillation with a frequency of about 1 MG is observed for the [0001] direction, and the frequency is nearly constant in the (1\bar210) plane, while the frequency increases with increasing θ (angle between the magnetic field direction and the [0001] direction) in the (10\bar10) plane. The effective mass is also obtained based upon the measurements of the temperature dependence of the amplitude for the oscillation in the temperature range from 4.2 K to 1.3 K. The angular dependence of the effective mass is consistent with that of the frequency. The angular dependence of the frequency can be qualitatively explained by assuming a set of oblate-ellipsoidal shaped surfaces for the Fermi surface located near the L-point of the Brillouin zone.

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Applications of the discrete variational (DV) Xα molecular orbital method based on the self-consistent Hartree-Fock-Slater model to metal clusters are presented. Numerical basis functions are utilized in the present calculations. Variations of orbital energies and populations with exchange scaling parameter α are investigated. It is proved that the self-consistent-charge (SCC) approximation to the SCF method gives accurate orbital energies. The numerical basis SCC–DV–Xα method is shown to be very efficient for studies of rather large metal clusters such as Ni₁₃.

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Various optical spectra such as time-resolved luminescence spectra are studied for excitonic molecules in CuCl under two-photon resonance excitation by using picosecond and nanosecond frequency-tunable laser pulses. Two sharp emission lines observed under resonance excitation are ascribed to the radiative decay of “cold” excitonic molecules created directly at k∼2k₀, while the broad emission band on the low energy side of the sharp line to the luminescence of “hot” molecules created through single excitons. The stimulated emission process gives a considerable influence on both the sharp luminescence lines and the hot molecule band, and further on two-photon resonant excitonic Raman lines as well. Discussions are made on the Bose condensation of the excitonic molecules and also on whether the emission under just-resonance excitation is due to Raman scattering or luminescence.

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The surface-state energy band structures of the MgO (100) and (110) surfaces have been investigated using both the Green’s function formalism and LCAO method. We have studied the band structures of both Shockley and Tamn surface states in some detail. Numerical identity of energies for surface states, one from a semi-infinite system and the other from a thin film, is established.

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Transverse spin relaxation processes of the F_A(Li) centers in KCl and KBr at LHeT have been studied by the following three methods; cw microwave saturation of steady-state ESR intensity and that of steady-state ENDOR intensity, and the saturation recovery of transient ESR signal. Most of analyses are carried out by modifying the Clough and Scott form which includes two sorts of relaxation processes via spin-packets specified by half widths of (2⁄T₂^L) and (2⁄T₂′), respectively. T₂^L- and T₂′-packets are caused by static and fluctuating motions of the Li⁺ ion, respectively. T₂^L are short of 10⁻⁸∼10⁻⁹ sec for both crystals. In KBr, T₂^L<<T₂′\simeq10⁻⁶ sec, so that a hole-burning of the T₂′-packet facilitates the ENDOR observation even at 1.8 K. In KCl, T₂^L\simeqT₂′, the T₂′-packet is too wide to burn a hole: this leads to disappearance of the ENDOR at LHeT.

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Absorption spectra of excitonic region in GaSe were measured at 2 K and 77 K, using a pulsed dye laser. Disappearance of an exciton line was observed. This phenomenon is attributed to a transition from an excitonic state to an electron-hole plasma state. This transition is possibly caused by a collision process between two excitons.

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Magnetic circular dichroism in the E₁ region is measured for InSb, Ge, GaAs, and Si to investigate Zeeman splittings of energy bands at Λ critical points involved in the E₁ transitions. The results are well explained within the band theory in contrast to the previous experiments on Landau levels, and it is found that a “linear k_t term” plays an important role in determining the Zeeman splittings.

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Fine details of ferroelectric domain structure in guanidinium aluminum sulfate hexahydrate have been revealed by an improved powder pattern technique. Within large positive or negative segments which correspond to growth pyramids, striation-type domains and small circular domains have been clearly resolved. Two types of the preferential wall orientation are characterized; one is parallel to the crystallographic symmetry planes, and the other is perpendicular to them. Spontaneous switching of many small domains has been found at low temperature (about 1.2×10⁵ cm⁻² at −100°C); they change in shape with lowering temperature from circle to hexagon with edges parallel to the symmetry planes. From an application of the Zhirnov-type continuum theory, the wall energy density is obtained as 0.3 erg/cm², and is shown to be almost independent of wall orientation.

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The adiabatic elastic compliances, s_ii^S (i=1, 2, 3), of NaNO₂ were measured near T_N(165.3°C) and T_c(164.0°C) by a composite-oscillator method. The isothermal compliances, s_ii^T, were calculated from s_ii^S and the data on specific heat at constant pressure, C_p, and thermal expansion coefficients, β_i. The isothermal compliances tend to diverge toward T_N, while the adiabatic compliances exhibit only small cusps at this temperature. It was found that the Pippard equations hold among s_ii^T, β_i and C_p, and the anomalous part of s_ii^S is proportional to −T⁄C_p. From a thermodynamic relation between elastic compliances and specific heat, it is expected that, incontrast to a large λ-like anomaly of C_p, the specific heat at constant volume shows only a small cusp-like anomaly at T_N. This means that the growth of the long-range and short-range order is dramatically suppressed if the free thermal expansion of the crystal is inhibited.

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Nucleation and growth of tin films deposited onto sodium chloride single crystal substrate were studied by transmission electron microscope by scanning the growth of the film from 10 Å to 1500 Å thickness range. The substrate temperature was also varied from 30°C to 125°C to study the effect of substrate temperature on the orientation in these films. It was observed that highly oriented films could be obtained by depositing films onto a heated substrate (nearly equal to 2/3 of melting point) at a relatively low deposition rate (∼6 Å/sec.).

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The formation of F and H centers under the double excitation by a pulsed electron beam and a Q-switched ruby laser has been observed in KCl crystals between 5 K and 16.5 K. The efficiency of the F center formation due to the conversion of the self trapped exciton (STE) from the ³Σ_u⁺(σ_u, 1sσ_g) state to a higher state, possibly to the ³Π_g(σ_u, 2pπ_u) state, is as high as 0.35∼0.50 in this temperature range, and the efficiency of the back conversion ³Π_g→³Σ_u⁺ is very small. This small efficiency suggests a process faster than the ³Π_g→³Σ_u⁺ transition, supporting fast formation time of F centers (11±9 ps) in KCl. Rest of the STE, i.e. 65%∼50% of them, appear to go down to the ground ¹Σ_g⁺ state nonradiatively. A possible formation process of F and H centers is discussed.

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Absorption, emission and excitation spectra of two water-free LiI crystals prepared from different origins were observed at liquid nitrogen temperature. Emission band with a peak at 3.40 eV is excited above the energy of the fundamental absorption edge, and excitation spectra of this band for both crystals are same with each other. Excitation spectrum of this band shows not only a sharp dip reflecting an exciton absorption band, but also a phonon side-band of the exciton.

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A feasibility study of a polarized proton filter for slow neutrons was successfully carried out. Ethylene glycol containing a few percents of Cr^V ions was used as filter material in which protons were dynamically polarized. Polarization of protons was varied between 20 and 72%. The maximum polarizability of 0.84±0.01 (flipping ratio of 11.5±0.5) was obtained for neutrons of 80 meV. This value corresponds to the polarization cross section of 27±1.4 b.
The idea will open a way for the polarization of intense neutron beams of white spectra. In addition, this method does not impose serious restriction on the angular divergence of the incoming neutron beam.

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The successive phase transitions in K₂PbCu(NO₂)₆ have been studied by precise X-ray and neutron measurements. In phase II, we have observed the satellite reflections at (H±0.416, K±0.430, 0) around each fundamental Bragg reflection. In phase III, we have observed the superlattice reflections, instead of the satellite reflections of phase II, at (Remark: Graphics omitted.). This fact indicates that the crystal undergoes the successive phase transitions as normal→incommensurate→commensurate phase. The mode analysis of the Jahn-Teller active phonon mode was carried out and the experimental intensity distribution of satellite and super lattice reflections were analysed from the standpoint of the condensation of the phonon mode. The displacements in phase II is explained as the condensation of the transverse acoustic mode as well as the optical mode compatible with local Jahn-Teller active mode with the wave vector k₀=(0.42, 0.43, 0), while these in phase III is explained as the condensation of the same modes with k₀=(1/2, 1/2, 1/2).

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The temperature dependence of the excitation energy transfer rate is expressed in terms of the resonance transfer with phonon emission and absorption. By the use of this theory and of the kinetic parameters obtained from the data of picosecond fluorescence of the photosynthetic pigment systems (by Yu et al.), both the mean excitation transfer distance between light-harvesting pigments and the mean distance between the two reaction centeral chlorophyll molecules were evaluated. The present numerical results for the temperature dependence of the excitation transfer rate show that the excitation transfer in photosynthetic pigment system is very efficient around the temperature on the earth.

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Ion-Polar molecule collisions are studied in the Perturbed Rotational State approach. The basic idea is that the molecular rotation is nearly adiabatically deformed during the collision. The semiclassical, impact-parameter method is adopted. This formulation of the collision problem gives an easy way to calculate the rotational excitation cross sections. Numerical examples are given for the low-energy collision between a proton and a CN molecule. A scaling law is derived so that the numerical results obtained can be used also for many other collision systems.

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A statistical theory applicable to crystals of helical-chain molecules is developed in terms of the mean-field approximation; interchain potential energy which contains terms relevant to the screw displacements along the chain axis is taken into account. Simultaneous equations of complex variables describing states of the system are obtained; they are solved in several limited cases. Successive phase transitions observed in polytetrafluoroethylene crystals with increasing temperature at atmospheric pressure can be explained from the results.

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Ion acoustic turbulence is excited by the current-driven ion acoustic instability in a dc discharge plasma. By measuring the dispersion relation of test waves in the plasma with the ion acoustic turbulence, we find that the wave energy transfers from high frequencies to low frequencies and the phase velocity of the ion acoustic wave becomes smaller than the ion acoustic velocity in low frequencies near the peak of the turbulence spectrum. These experimental results can be interpreted theoretically.

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Nonlinear evolution of collisional drift wave instability is studied numerically. The model equations of quasilinear type are used which describe the modification of background density and the amplitude of unstable drift wave. Their solutions are classified according to the value of a parameter η which is proportional to the ratio of ion viscous damping to linear growth rate γ_L. In the vicinity of marginal stability the unstable drift waves are shown to be saturated by flattening of the background density. As η decreases further we first obtain periodic and latter aperiodic solutions. The wave associated diffusion coefficient is obtained numerically as a function of η and found to be much less than the usual estimate γ_L⁄k_⊥².

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We present a stationary k-spectrum of pseudo-three-dimensional electrostatic plasma turbulence in a uniform, loss-less, magnetized plasma based on the model equation of Hasegawa and Mima; ∂⁄∂t(φ−∇²φ)+[∇φ×\hatz·∇]∇²φ=0. The k-spectrum for a potential φ_k is given by ⟨|φ_k|²⟩=(1+k²)⁻¹(α+βk²)⁻¹, where α and β are constants. The existence of the two constants, α and β, in the spectrum is the consequence of the two rugged constants of motion. The spectrum is obtained using three different methods, namely, the method of Gibbs distribution, of Hopf’s equation and of Wiener Hermite expansion. Because of the similarity of the equation, the obtained spectrum should also apply to the hydrodynamic turbulence of geostrophic vortices.

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The presence of a monochromatic ion acoustic wave with a finite amplitude in a plasma leads to a reduction of the electrical conductivity σ. This effect is re-examined on the basis of a simplified Landau collision term employed by Zakharov and Karpman (1962) and the correct result is σ=σ₀{1−0.283(eφ₀⁄T_e)^3⁄2}. Here σ₀, φ₀ and T_e are the classical conductivity, the amplitude of the wave and the electron temperature, respectively.

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On the basis of the variational formulation, a problem of ablation of elastic solid is discussed. A melting elastic rod is insulated at one end and exposed to a prescribed heat input at the other end and at the latter end the ablation occurs. A thermal potential and a dissipation function are introduced as variational invariants, and a variational equation is derived by use of the differential equation of thermoelasticity and the boundary condition of ablation. Using a parabolic formula as a test function, an approximate differential equation of melting line is derived. With the aid of Adams-Bashforth’s method a series solution of the position of the melting line is found.

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Kolmogorov’s −5⁄3 power law is derived by a statistical approach based on turbulent viscosity. A crucial point in this analysis is that no use is made of the response (Green’s) function which may lead to a divergence at lowest wave numbers. An equation is found for the two-time velocity covariance by using turbulent viscosity to be determined as a part of the solution. Convection effect of big eddies upon small ones is uniquely removed from the equation for small time separation. As the result, Kolmogorov’s law are derived with a good estimate of Kolmogorov’s constant.

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Shock wave structures of dusty gases which contain radiating particles are numerically investigated on the basis of the Boltzmann equation for gas-particle mixture and a differential equation for radiative heat flux. Ahead of a shock front, the particles are heated by radiative energy transfer from behind the shock front, and the gas is also heated owing to the energy exchange with those particles. For strong radiation, this preheated layer extends largely, and the temperature difference between the particle and the gas becomes small, and the temperature just ahead of the shock front is close to the downstream equilibrium value. For weak radiation, the temperature rise is not so high, and the preheated layer is thin. Behind the shock front, the gas temperature profile has a peak higher than the case without radiation. This peak becomes sharp with increasing radiation effect.

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A theoretical study is made of the sedimentation of a small sphere in a viscous fluid bounded by horizontal and vertical walls. The analysis is based on the quasi-steady equations of motion, and the first-order wall effect is taken into account. The trajectory of the particle slightly deviates from the vertical line, the magnitude of which is determined by the angular position of the sphere. When the ensemble of spheres with randomly distributed initial positions is considered, the spheres which originally lay at a height h are found most frequently at the distance 0.591 h from the side wall.

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The flow around a circular cylinder performing a rotatory oscillation about its axis in a uniform flow has been investigated experimentally by means of flow visualization methods at Reynolds numbers between 30 and 300 and Strouhal numbers between 0 and 55. It has been found that the dead water region is reduced as the frequency of the oscillation is increased, and that the critical Strouhal number at which the dead water region vanishes is approximately proportional to the reciprocal of the angular amplitude of oscillation, but is independent of the Reynolds number. It has also been found that when the Strouhal number is much higher than the critical Strouhal number the flow past the cylinder is strongly accelerated.

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It is shown that infinite number of conservation laws can be derived for the nonlinear partial difference-difference equations that have the Bäcklund transform in a parallel manner to the continuous case. Explicit conservation laws are derived for discrete sine-Gordon equation and discrete-time Toda lattice equation.

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