By showing that the L₂ norm of the error (or residual) term in the Boltzmann equation is nonvanishing, it is proven that no exact solution should exist in the bimodal form for the structure of an infinitely strong shock wave. In addition, the most proper nondimensional form of the “error” norm is described.

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We consider a volume phase transition of gels which are allowed to swell or shrink in only one or two directions. In gels, elastic anisotropy can strongly affect critical properties, two-phase coexistence, domain structures, etc. We predict strongly anisotropic scattering amplitudes.

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The electronic structures of Sb impurities in Cs have been calculated using the self-consistent semirelativistic APW method within the superlattice model. We have investigated the lattice relaxation effects on the band structure and the excess resistivity. Taking the lattice relaxation into account, we have succeeded in explaining the excess resistivity due to Sb impurities in Cs.

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Revised result for the band properties of black phosphorus based on the self-consistent band calculation with the norm-conserving pseudopotential given in a previous paper are presented. The results are in good agreement with experiments in XPS and optical reflectance for linearly polarized light.

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The static magnetic susceptibility of YBa₂(Cu_1−xCo_x)₃O_y in the normal state was measured for both superconducting (slowly cooled) and semiconductor-like (quenched) samples. The susceptibility was composed of a Curie-Weiss term and a temperature-independent paramagnetic term, χ₀, for both samples. The Curie constant and χ₀ increased with increasing cobalt concentrations. No anomaly showing magnetic ordering was observed. The contribution of the impurity phases such as Y₂CuBaO₅ to the magnetic susceptibility was found to be negligibly small in our samples by means of ESR technique.

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Two-dimensional random Josephson networks consisting of small Sn particles with light oxidation on the surface were prepared by repeating vacuum evaporation and oxidation. The size of the particles was about three hundred angstrom in diameter, and the strength of the Josephson coupling was controlled by changing the degree of oxidation. With decreasing temperature below T_c, the samples with normal sheet resistance larger than about 4 kohm showed insulating behavior, while those with less than 4 kohm behaved as usual superconducting thin films. This resistance is close to h/4e², of which the physical importance is currently discussed.

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EPR measurements of Gd³⁺ were performed in the superconducting and non-superconducting GdBa₂Cu₃O_x. There is no distinct difference between the EPR behaviors of the two samples. The results show that even in the superconducting sample, the Gd ions behave as paramagnetic local moments with a mutual exchange interaction of 0.1 K.

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The properties of the ground state in chain-like systems, including the competition between ferromagnetic and antiferromagnetic exchange interactions, are discussed. It is, in particular, pointed out that the characteristic singlet state expressed by the combinations of RVB distributed uniformly to spin lattice points is given as the exact solution on some condition of the competition. Besides analytical discussion, the numerical calculation for the spin number N≤16 is also made so as to make clear the behavior of a multiple degeneracy for the ground state and of low-lying excitation levels.

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The transverse dielectric constant of Rb_0.49(NH₄)_0.51H₂AsO₄, mixed crystals has been measured at temperatures ranging from room temperature to 17 K. ε₁₁′ was observed to follow the Curie-Weiss law down to T_c^*=87.5 K, where the dielectric constant has a rounded peak. The reciprocal of ε₁₁′ gives a Curie temperature of T₀=−36 K, which may be indicative of a diffuse antiferroelectric phase transition rather than proton-glass freezing.

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Single crystals of K₂CoCl₄ grown from a melt by the Bridgman method undergo phase transitions at −131°C and 181°C, respectively, and show ferroelectricity along the a-axis in the phases below 181°C.

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It is shown that systems of the Kadomtsev-Petviashvili equation and the two-dimensional Toda equations admit solutions with two-directional Wronskian structures. It is found that the boundary conditions on the Toda equations change these structures substantially.

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Yang-Baxter operator is shown to be a fundamental object which relates theory of solvable models to theory of knots and links. First, general properties of Yang-Baxter operators are investigated. Second, a method to construct composite Yang-Baxter operators is explicitly shown. Lastly, from Yang-Baxter operators with crossing symmetry, braid-monoid algebras are derived. It is emphasized that the factorized S-matrices and their graphical illustrations link two approaches, algebraic and combinatorial, in the knot theory.

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A direct proof of the, N-soliton solution of the Benjamin-Ono (BO) equation is presented within the framework of the theory of determinants. It is shown that the bilinear equation for the BO N-soliton solution is reduced to Jacobi’s formula and hence it has a very simple structure. At the same time, various novel formulas for determinants are derived as a by-product of the present theory.

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From the eigenvalue equation H_λ|Ψ_n(λ)⟩=E_n(λ)|Ψ_n(λ)⟩ where H_λ≡H₀+λV, one can derive an autonomous system of first-order differential equations for the eigenvalues E_n(λ) and the matrix elements V_mn(λ):=⟨Ψ_m(λ)|V|Ψ_n(λ)⟩ where λ is the independent variable. To solve the dynamical system we need the initial values E_n(λ=0) and |Ψ_n(λ=0)⟩. Thus one finds the motion of the energy levels E_n(λ). We derive the dependence of the survival probability as well as some thermodynamic quantities (free energy, entropy, specific heat) on λ. Then we derive the equations of motions for the extended case H_λ=H₀+λV₁+λ²V₂ and give an application to a supersymmetric Hamiltonian.

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Thermodynamic properties of spin 1/2 antiferromagnetic Heisenberg model are investigated by a quantum Monte Carlo method. Fluctuation of the order parameter, namely the square of staggered magnetization, shows large enhancement at low temperatures. Size dependence of the order parameter in the ground state is investigated and it is fitted by a form with a power law dependence on the size which means that the long range order does not exist although the fluctuation diverges. Staggered susceptibility, namely the canonical (Kubo’s) correlation of staggered magnetization, is also investigated and is found to be largely suppressed by quantum fluctuation compared with the square of staggered magnetization. Susceptibility for the uniform field is found to have a broad peak.

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The 34.2 keV isomeric state (4⁺) with T_1⁄2=52 min was produced via ⁹³Nb(α, n)^96mTc reaction at a beam energy of 15 MeV. The K-conversion coefficient, α_K of the 34.2 keV, M3 transition (4⁺→7⁺) was determined for the first time using the XPG technique. The value of α_K was found to be, 1880±145, which is in agreement with the theoretical value of 1735 due to Hager and Seltzer for a pure M3 transition.

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Total electron scattering cross sections (σ_t) for Ar, N₂, H₂O and D₂O are determined in the energy range between 7 and 500 eV using a linear electron transmission device. The thermal transpiration effect is considered. Results for Ar and N₂ are in good agreement with those of previous experiments. The present results for H₂O agree well with those of Brüche, Szmytkowski, Szmytkowski et al. and Zecca et al. However, some difference still remains among the recent results in the energy region below 15 eV. The σ_t for D₂O is much the same as for H₂O within the experimental uncertainty.

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In order to show that the transition from bubble flow to slug flow observed in a vertical riser is due to the instability of a voidage wave, an analysis and a calculation are performed on the basis of a dilute bubbly liquid model. The result demonstrates such a possibility, together with expressions for propagation velocities, growth rate and coefficient of negative diffusion. Comparison is made with the previous experimental result.

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The effect of rotational excitation of O₂, N₂, and NO by free electrons in partially ionized nonequilibrium flows of air is investigated in this paper. Terms representing the average electron energy loss rates are included in the electron energy equation. An exact expression for the average electron energy loss rate by excitation of rotational states of a polar molecule such as NO is obtained. The effect on the electron temperature is studied for nozzle flow and for flow behind a normal shock wave. In the nozzle flow, the electron temperature decreases and approaches the heavy gas temperature due to this effect. It originates mainly from the rotational excitation of N₂, because of the overwhelming concentration of this species. In the flow behind a shock wave, this effect causes an increase in the electron temperature, but only in the region near the shock front.

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The electron distribution function in a plasma with the steep temperature gradient is obtained from the Fokker-Planck equation by the Green’s function method, extending the previous differential formula [J. Phys. Soc. Jpn. 52 (1983) 3389]. The formula describes the nonlocal effects on the thermal transport over the range of λ_e⁄L\lesssim0.1 (λ_e: electron mean free path, L: temperature scale length). The formula includes the self-consistent electrostatic potential and exactly recovers the Spitzer-Härm thermal conductivity in the long scale length limit, λ_e⁄L→0. As an example, the heat wave propagation is numerically analyzed by employing the integral formula and the nonlocal properties of the heat flux, which is obtained in the Fokker-Planck simulation, are well reproduced.

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Effects of irradiation nonuniformities on target implosion and ignition conditions for inertial-confinement fusion with ion beams are studied by using a 2-dimensional code. The following results are obtained. When the beam energy is 5 MJ which is 1.6 times the threshold beam energy (=3.2 MJ) in the spherical symmetric case, ignition occurs if the peak-to-valley nonuniformity rate is smaller than 0.05. On the other hand, this value rises up to 0.1 when the beam energy is 7 MJ, i.e., it is 2.2 times the threshold beam energy in the spherical symmetric case. Furthermore, the ignition condition is the severest for the nonuniformity with the largest spatial scale.

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Vacuum magnetic fields in helical configurations are analyzed by using the scalar potential which satisfies Laplace equation. By adding the axisymmetric toroidal and vertical magnetic fields to the helical field, the nested magnetic surfaces are constructed. The rotational transform, aspect ratio, specific volume and helical ripple ratio are calculated for the l=2 stellarator/heliotron/torsatron configurations (l; multipolarity of the field) for various values of m (m; toroidal pitch number). The magnetic surface is optimized in regard to the rotational transform and the area surrounded by the outermost magnetic surface. The generation of the magnetic well and the increment of the confinement region by the vertical field are also discussed. Finally, the m=2 low aspect ratio system is discussed.

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A new formulation of renormalized theory for fluid-type turbulence to obtain wavenumber spectrum and turbulent diffusivity is presented. An application to the resistive interchange mode turbulence is discussed. The turbulent diffusivity using the reduced MHD equations agrees with evaluations based on the mixing length argument or the scale invariance except a coefficient of about four. An extended model based on finite Larmor radius magnetohydrodynamics (FLR–MHD) including coupling between the resistive drift wave and the resistive interchange mode is analyzed by the renormalized theory. The diffusivity depends on the phase difference and the relative magnitude between the density fluctuation and the potential fluctuation, and role of density gradient becomes more significant than the reduced MHD result. However, the wavenumber spectrum does not change much by the extended model.

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A white line was observed across the 002 X-ray thermal diffuse spot of a pentaerythritol crystal. Cause of the line was attributed to the Bragg reflection of thermally scattered X-rays. The contrast and the width of the line obtained by means of photographic method in the Bragg case as well as in the Laue case were compared successfully with those calculated on the basis of the theory given by Bushuev et al.: Sov. Phys.-Solid State 25 (1983) 228. The application limit of the theory is discussed. In the analysis, a correction of the contrast and the width of the line for the source size and collimator system was introduced. This gives a new interpretation about the fact that the line becomes clear as the film stands at a long distance from the specimen.

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Electric polarization of magnetite, induced by rotating magnetic field in the triclinic bc plane, was measured along the triclinic a axis below 60 K where magnetite is ferrimagnetic as well as ferroelectric. The magnetoelectric polarization was influenced by the way of application of mechanical stress onto the single crystal. Mechanism of this phenomenon was discussed on the basis of the formation of twins including new types. Point group of the crystallographic symmetry of the magnetoelectric single phase was analyzed. It was shown that the present experiment was not inconsistent with the fact that among three crystalline angles, in addition to the ac, at least the bc is not right-angle. Thus magnetite in the temperature range, 4.2 K to 35 K, is of triclinic 1, irrespective of the magnitude of the angle ab.

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Phase diagram of chiral smectic C liquid crystal in a magnetic field is studied. Temperature dependences of soliton lattices, especially magnitude and wave number, are analyzed numerically near a Lifshitz point, in correspondence with the asymptotic results derived theoretically by Michelson.

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Commensurate-incommensurate (C–IC) phase transition of Rb₂ZnCl₄ is studied by low temperature transmission electron microscopy. Nucleation and disappearance of pairs of “dislocations” composed of six discommensurations (DCs) and their motions along the c plane play an important role in the transition prcccess. During the motions rearrangements of “dislocations” due to interactions with neighbouring DCs are observed. On heating from the C to the IC phases, small displacements of the DCs along the direction perpendicular to the DCs produce rather uniform distribution of the DCs in the IC phase. On the other hand on cooling, large displacements of the DCs do not take plase in the C phase. In the C phase specimens are divided into two regions, one with a low DC density and the other with a high DC density. Pinning of the DCs and “dislocations” at defects is also observed.

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The thermal diffusivity in polyethylene has been measured by the laser-flash method at temperatures between 2 K and 300 K. Heavily oriented specimens were prepared by an extrusion method, and the diffusivities in the specimens in the directions perpendicular and parallel to the oriented molecular chains, D_⊥ and D_⁄⁄, and also the diffusivity in unextruded specimen, D₀, were measured. A large anisotropy was shown in the thermal diffusivity, namely, D_⊥<D₀<D_⁄⁄ at all temperatures, and the dependences of the diffusivities D_⊥, D₀, and D_⁄⁄ on temperature were found to be different. The experimental results could well be explained by considering that three-dimensional Debye phonons conducted both in crystalline and amorphous parts, and one-dimensional phonons could conduct along the long molecular chains; and that the Umklapp and the boundary scattering were dominant for the crystalline three-dimensional phonons, the one-dimensional phonons were scattered by scatterers on the chains, and the conducting phonons in the amorphous parts might be scattered by low-energy localized excitations.

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The ground state of a Quantum Lattice Model (QLM) in which all atoms are quantum-mechanically migrating from site to site on the lattice points is given in the crudest approximation. From the QLM the energy spectrum of roton-like excitation is derived on the basis of a simple picture, where the roton excitation is regarded as the motion of an atom which does not undergo the quantum migration. According to Matsuda and Matsubara, by setting two parameters, the effective mass of QLM m=(1⁄7)m₀ (m₀ is the mass of ⁴He atom), and the lattice spacing d=3.1 Å, the density dependence of Δ and m^* in roton spectrum are calculated. The obtained results are somewhat higher than the experiments. However the tendencies of density dependence of these parameters are in an excellent agreement with the experiments.

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Si/Ge/Si monolayer heterostructures grown on Si(100) by molecular beam epitaxy (MBE) have been studied by a surface sensitive EXAFS technique. It is shown that the heterointerfaces at several tens of angstrom below the surface can be probed by monitoring fluorescence yield with a high energy resolution detector in a total reflection geometry. The formation of ordered Si/Ge/Si heterointerface is evidenced by a Fourier transform analysis of the Ge K–EXAFS. In the Si/Ge/Si heterostructure, the determined Ge–Si distance suggests a large contribution of bond length relaxation.

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Hall voltage of a ferromagnet, Fe₃O₄, was measured on a single crystal platelet as a function of the direction of the external magnetic field. The data was successfully analysed and divided into two terms, those proportional to M_x and to B_x. Here, M is the magnetization and B is the magnetic flux density and the x axis is perpendicular to the platelet. Thus, ordinary and extraordinary Hall coefficients are separated at each field strength. The result of this separation is much different from that of a conventional method, by linear dependence of the Hall voltage on the external field strength. The difference suggests that higher order terms, those proportional to cubic and higher power of M and B, cannot be ignored in Fe₃O₄. Without knowledge of higher order effect, ordinary Hall coefficient cannot be determined since it is small compared with other terms. The validity of discussion on the character of charge carriers must be reexamined, if it is based on the ordinary Hall effect determined conventionally.

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Electronic surface states are calculated in the pseudopotential scheme for the Si(111) surface with a series of adatoms at the same model chemisorption site. The results are analyzed from a common point of view. The change in the electronic structure due to the increase of adatom electron number is understood in some case only by the “rigid shift” of the Fermi level, but a drastic change in the electronic structure is found in other case.

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Three intense Raman bands were observed at 158, 180 and 2142 cm⁻¹ after the exposure of the silver film to about 0.5 L of carbon monoxide (CO) at 80 K. We found that oxygen coadsorbed with CO induces an upward peak shift of the C–O stretching Raman band to a frequency above that of a gas phase CO. The re-enforcement of the bond between CO and the substrate by the presence of the coadsorbed oxygen was confirmed by the observation of the upward peak shifts of the low frequency bands. Discussion on the change in the adsorption state of CO due to the coadsorption is given in relation to an electronegativity of the coadsorbate. The proposed scheme consistently explains not only the peak shift of the C–O stretching band but also the change in the bond strength between CO and the substrate.

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We study the effective pairing interaction mediated by the vibration of the O-ions in the insulating layers in the high-T_c oxide superconductors, and find that the on-site attractive interaction may become strong enough to dominate the on-site repulsion. Such strong electron-phonon coupling is due to the poor screening effects by the conduction electrons in the CuO₂-conducting layers. Using this effective pairing interaction together with the realistic values of the parameters, we calculate T_c for various types of anisotropic pairing states as functions of the average number of the conduction electrons. The results suggest that the S-like pairing state containing the anisotropic component may be the most favorable. We also study the isotope effect and find that it is appreciably suppressed when the Fermi level stays near the Van Hove singularity.

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Magnetization measurement, ⁵⁵Mn NMR and ¹H NMR measurements were performed in hydrides of pseudobinary intermetallics Y(Mn_1−xT_x)₂ (T=Al, Co and Ni); x=0∼0.15). The magnetization measurement indicates that Y(Mn_1−xT_x)₂H_y with y≤3.5 exhibit ferromagnetism with Mn moments ranging from 0.07 to 0.32 μ_B and more charged Y(Mn_1−xT_x)₂H_4.0 exhibit paramagnetic behaviours. From the x dependence of the mean Mn moment In Y(Mn_1−xAl_x)₂H_3.0, It was found that an appearance of the Mn moment is considerably sensitive to the Mn concentration. ⁵⁵Mn NMR signals are discussed based on the transferred hyperfine field from the neighbouring Mn moments. ¹H NMR signals are discussed in terms of a dipole interaction between the ¹H nuclei and the neighbouring Mn moments on the assumption that hydrogen atoms almost occupy only the g-sites which composed by two Y and two Mn atoms.

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Neutron elastic and inelastic scattering experiments have been performed on Fe₂P single crystals in the temperature range from 8 K to 800 K. Fe₂P is of the hexagonal C-22 type structure and exhibits c-axis ferromagnetism below 130 K. In the intermediate range between 130 K and 217 K, the canted ferromagnetism with a uniform component along the c-axis M₀ and a staggered component in the c-plane M_Q appears, and the first order transition takes place at T_c=217 K from the canted ferromagnetism to paramagnetism. The most interesting behaviour is the existence of giant short range order up to T=3T_c. It originates in the small stiffness constants D and leads to the strong deviation of susceptibility from the Curie-Weiss law. The amplitude of the spin fluctuation observed In Fe₂P In the pararnagnetic phase is understood by the simple model with parameters deduced from the spin wave dispersion at low temperature, the magnetization and uniform susceptibility.

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A new organic ion-radical salt, [3,3′-dimethyl-2,2′-thiazolinocyanine]₂-[TCNQ]₃ which is simply written by [DMTzNc]₂-[TCNQ]₃, is synthesized and the crystallographic and magnetic properties are investigated. This salt forms triclinic crystal in the space group P\bar1 with a=9.976(3), b=16.129(5), c=8.371(2) Å, α=101.80(3), β=106.02(3), γ=77.02(3)° and Z=2. The planar TCNQ molecules are stacked face-to-face to form a column parallel to the a-axis with two unpaired electrons per three TCNQ molecules. The magnetic susceptibility and ESR are measured. The unpaired electrons on the TCNQ column form the spin-pair state with the exchange energy of 500 K below about 200 K. The localized spin-pair decouples with increasing temperature and the one-dimensional spin correlation appears on the TCNQ column accompanying with the increases in the magnetic susceptibility and the electrical conductivity.

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Successive phase transitions in betaine arsenate (BA) have been investigated around its ferroelastic phase transition at 411 K (T₁) and ferroelectric transition at 119 K (T₂). Temperature dependence of elastic compliances s₁₁, s₂₂ and s₃₃ and the frequency dependence of ε_a, were measured around the ferroelectric transition. Clear elastic anomalies at T₂ are observed in s₁₁ and s₃₃ and marked frequency dependence of ε_a is found in the ferroelectric phase. Temperature dependence of the domain pattern and the rotation angle of indicatrix in the ferroelastic phase are observed. Brief discussion on the successive phase transitions of BA is made.

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Monte Carlo (MC) simulation is performed for samples modeled on OH⁻:KCl to show that the electric dipole-dipole interaction (Remark: Graphics omitted.) leads freezing of permanent electric dipoles distributed randomly in dielectrics. Frustration due to (Remark: Graphics omitted.) yields a huge number of metastable states as in spin glasses. Although the result for the dielectric constant shows a rounded maximum in the temperature dependence, no sign can be found in the order parameter q corresponding to the maximum of the dielectric constant. In fact q remains finite up to high temperature. As far as the simulation is limited to 1000 MC steps per moment, the electtic moments seem to freeze gradually with decreasing temperature by growing cluster size. This contrasts sharply with the behavior in the Sherrington-Kirkpatrick spin glass where a considerably clear sign for the phase transition can be found in MC simulation.

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Time evolution of the dielectric constant ε at 100 kHz after a stepwise temperature change has been studied near T_N and T_C of sodium nitrite. In the normal and commensurate phases, ε follows the temperature change without any noticeable time delay. The time evolution of ε in the incommensurate phase consists of a quick response which follows the temperature change immediately and a slow relaxation which proceeds taking a few hundred seconds. The slow relaxation is not of a simple exponential type, its relaxation rate is slowed down as equilibrium is approached. We ascribe the quick process to relaxation of the modulation amplitude of the incommensurate structure and the slow process to that of the modulation period. The quick process has been studied also by measuring the response of ε to an AC temperature change at 1Hz.

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The resonance and the relaxational dielectric dispersions of KH₂PO₄ found in the ferroelectric phase were examined for ordinary and lossy specimens. The magnitudes of these two dispersions decreased markedly with crystal defects as well as with a d.c. bias field. A universal relation between the free dielectric constant ε^X and the elastic stiffness C₆₆^E was found regardless of the specimens and their states examined. The small C₆₆^E and the large ε^X were obtained for the specimens with high densities of domain walls. The mean value and the standard deviation of the energy parameter E in the relaxation time, τ=τ₀ exp {E⁄(T−T₀)}, as well as the Vogel-Fulcher temperature T₀ decreased with the crystal defects. A possible model for the domain freezing is proposed in connection with these two dispersions.

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Optical nonlinearity is studied in a PbI₂ evaporated film under the pump and probe configuration using two tunable nanosecond pulsed lasers. A change of the transmitted probe intensity is observed when the pump frequency is equal to the probe one and is in the exciton region. This Rayleigh-type nonlinearity is neither due to hole burning effect nor thermal grating effect, but due to excitonic population oscillation. The maximum nonlinear absorption amounts to −2×10⁵ cm/MW which corresponds to a third-order nonlinear susceptibility of −10⁻⁴ esu. Such a large nonlinearity can be explained if the nonlinear interaction takes place over many unit cells, which comes from coherent expanse of an exciton in the crystal.

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The decay of the 2.2 eV emission band in KTaO₃ single crystal was measured using an N₂ laser. The decay of the 2.2 eV emission band at low temperature is in good agreement with that of the 2.6 eV emission band. However, the decay of the 2.2 eV emission band differs from that of the 2.6 eV emission band above 70 K. The decay kinetics of the 2.2 eV emission band is explained by the theory of the recombination of holes trapped on two classes of acceptors and electrons trapped on one class of donors.

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