First- and second-order Coriolis interactions in symmetric top molecules: Application to the microwave spectrum of cyclopentadienyl thallium

Matrix elements are derived for both first- and second-order Coriolis interactions between A₁ and E₁ vibrational modes in symmetric tops, with particular reference to sign. The results are applied to the observed microwave transitions J → J + 1 for A₁ and E₁ states of the C_5ν molecule cyclopentadienyl thallium in various excited vibrational states. The microwave transitions in the excited A₁ states v₄ = 1, 2, 3, the excited E′ state v′₀ = 1 and the combination state v₄ = 1, v′₀ = 1 have yielded constants which are anomalous in several respects (1). Coriolis interactions between the ν₄ and ν₁₀ vibrations are shown to account for the observed anomalies.     

Proximity effect in the finite and incommensurate ferromagnet/superconductor systems

The original theory of a proximity effect is proposed for the bi- and tri-layered system ferromagnetic metal/superconductor (F/S) in dirty limit. The F₁/S/F₂ trilayer is examined more closely. The distinctions in materials, in thicknesses of F layers (d_f1 and d_f2), in parameters interfaces, and in local environments of layers are considered among the causes of incommensurability of trilayer. The peculiar T_c(d_f1, d_f2) interference pattern is predicted for the F₁/S/F₂ systems. The reentrant superconductivity and possibility of the better observability of the spin-valve regime are discussed.     

Two-dimensional wigner crystal under magnetic field

Dispersion relations of phonons are obtained in the harmonic approximation for the two-dimensional Wigner crystal under the magnetic field. For small wave vector, the eigen-energies of two modes are ω₊ = ω_c = eH/mc and ω_? → ω_lω_t/ω_c, where ω_l and ω_t are frequencies of longitudinal and transverse phonons in the absence of the field.     

High-resolution infrared study of Coriolis resonances in the ν9 and ν10 bands of allene-d4

The infrared perpendicular bands ν₉ and ν₁₀ in allene-d₄, which are located at 824 and 666 cm^?1, respectively, have been studied at a resolution near to 0.010 cm^?1. The bands were analyzed by taking into account the z-Coriolis resonance between these bands and the (x,y)-Coriolis resonance between ν₁₀ and ν₄(B₁), which is only Raman active. Upper-state parameters and interaction constants are derived from this analysis. Additional Coriolis interactions between ν₉ and ν₃(A₁) as well as between ν₁₀ and 2ν₁₁²(B₁,B₂) are also discussed. Special attention is paid to the study of l-type doublings. Doublets due to q^(?) doubling were resolved both in ν₉ and in ν₁₀. l-type doubling constants including their signs are also obtained.     

Scaling models of thermodynamic properties on the coexistence curve: Problems and some solutions

Models consistent with the scaling theory of critical phenomena and capable of describing the thermodynamic properties F of substances on the coexistence curve, such as the density of the liquid ρ _l , density of the gas ρ _g , order parameter f _s , mean coexistence curve diameter f _d , and saturation pressure P _s are discussed. The models are presented in the form of equations F = (τ, D, C), where τ = (T _c ? T)/T _c , and D = (α, β, T _c , ρ _c , P _c , ...) are the critical characteristics, such as T _c , ρ _c , and P _c (temperature, density, and pressure, respectively), α and β are the scaling exponents, and C are adjustable coefficients. The authors developed combined models f(τ, D, C) for describing the indicated properties of a number of compounds (CH₄, NH₃, SF₆, water, methanol, ethanol, diethyl ether, and freons R134a, R143a, and R236ea). The coefficients C were determined based on experimental data over a wide temperature range, including the critical point. The equations derived are used to perform practical calculations, including estimates of the first and second derivatives of the saturation pressure with respect to the temperature in the critical region.     

3-Band theory of Fe pnictide superconductors

For the Fe pnictide superconductors, band features important for superconductivity (SC) in the neighborhood of ε_F are mimicked by tight-binding bands with bases of Fe d_xz, d_yz and d_xy orbitals. In terms of this 3-band model, effective pair transfer processes originating from Coulombic integrals are shown to be largely enhanced due to the nesting between electron and hole pockets by explicitly summing up ladder diagrams. Obtained coupled gap equations lead to s^±-type SC. This framework are argued to provide a scheme for discussing important elements working for the high T_c SC, although its validity is restricted to the case where Dirac cones are away from ε_F. Experimental results on Fe pnictides are discussed in terms of the present results. The pair transfer process explicitly due to the exchange-like integral is suggested to be considerably important for the high T_c in MFeAsO_1−xF_x to occur.     

Multiport beam-splitter controlled transformations with postselection of superposition single-photon states

Two components of superposition single-photon state are entering into two different ports of multiport interferometer. Interference effects in which the inputs into the interferometer are controlling the outputs are studied. In particular we study a multiport beam-splitter (BS) configuration, in which eight input operators a₀, a₁, a₂…a₇ are mixed by 12 BS's to produce the output operators b₀, b₁, b₂…b₇. Multiport beam-splitter transformations of superposition single-photon states are analyzed with a possible use of postselection effects.     

Hall and transverse even effects in the vicinity of a quantum critical point in Tm1 ? x Yb x B12

The angular, temperature, and magnetic field dependences of the resistance recorded in the Hall effect geometry are studied for the rare-earth dodecaboride Tm_{1 ? x} Yb _x B₁₂ solid solutions where the metal-insulator and antiferromagnetic-paramagnetic phase transitions are observed in the vicinity of the quantum critical point x _c ?? 0.3. The measurements performed on high-quality single crystals in the temperature range 1.9?C300 K for the first time have revealed the appearance of the second harmonic contribution, a transverse even effect in these fcc compounds near the quantum critical point. This contribution a is found to increase drastically both under the Tm-to-ytterbium substitution in the range x > x _c and with an increase in the external magnetic field. Moreover, as the Yb concentration x increases, a negative peak of a significant amplitude appears on the temperature dependences of the Hall coefficient R _H(T) for the Tm^{1 ? x} Yb _x B₁₂ compounds, in contrast to the invariable behavior R _H(T) ?? const found for TmB₁₂. The complicated activation-type behavior of the Hall coefficient is observed at intermediate temperatures for x ?? 0.5 with activation energies E _g /k _B ?? 200 K and E _a/k _B = 55?C75 K, and the sign inversion of R _H(T) is detected at liquid-helium temperatures in the coherent regime. Renormalization effects in the electron density of states induced by variation of the Yb concentration are analyzed. The anomalies of the charge transport in Tm_{1 ? x} Yb _x B₁₂ solid solutions in various regimes (charge gap formation, intra-gap many-body resonance, and coherent regime) are discussed in detail and the results are interpreted in terms of the electron phase separation effects in combination with the formation of nanosize clusters of rare earth ions in the cage-glass state of the studied dodecaborides. The data obtained allow concluding that the emergence of Yb-Yb dimers in the Tm_{1 ? x} Yb _x B₁₂ cage-glass matrix is the origin of the metal-insulator transition observed in the achetypal strongly correlated electron system of YbB₁₂.     

Effect of polymers doping on flux pinning behavior of MgB2

The effects of polymers doping on irreversibility field (H_irr) and critical current density (J_c) of MgB₂ have been investigated in this work. It is found that both J_c, and H_irr, are improved by doping at relative lower temperature region. The J_c−B curves of all samples studied in this work are well fitted using J_c(B) formula in percolation model. The values of upper critical field anisotropy (γ) are obtained from the fitting result at various temperatures. It is observed that values of γ for polymers doping samples are reduced at these temperatures. This is considered to be responsible for the enhancement of values of J_c for doped samples. Moreover, the percolation threshold, p_c, is found to be enhanced with increasing temperature. It is believed that the grain boundary pinning is still dominating in MgB₂, while the deviation of experimental data from the theoretical values is due to the percolation of suppercurrent in polycrystalline MgB₂.     

Neutron diffraction study of the layered compounds MnPSe3 and FePSe3

In the insulating compounds MnPSe₃ (1) and FePSe₃ (2) the divalent transition metal ions form planar honeycomb lattices. A neutron diffraction study revealed a collinear antiferromagnetic order below T_N = 74 ± 2 K (1) and T_N = 119 ± 1 K (2) with the corresponding wavevectors k = [000] (1) and $\text{k = [}\text{1}\text{2}\text{0}\text{1}\text{2}\text{]}$ (2). In MnPSe₃ the magnetic moments (m₀ = 4.74 μ_B) lie within the basal plane and in FePSe₃ (m₀ = 4.9 μ_B) they are pointing along the c-axis. The collinear structures are determined by the dominating intralayer interactions between first (J₁), second (J₂) and third neighbours (J₃) which in MnPSe₃ are all antiferromagnetic whereas in FePSe₃J₁ is ferromagnetic and J₂ and J₃ are antiferromagnetic.     

A computer model to predict traffic noise in urban situations under free flow and traffic light conditions

A computer model is presented for predicting traffic noise indices in built-up situations for free flow traffic conditions and for a flow interrupted by a traffic light. The stream of vehicles is simulated by a given time headway distribution, and a transfer function obtained from a 1 : 100 scale model is used to simulate the specific built-up situation. Different time headway distributions result in only very small discrepancies; even the simple “equally spaced” distribution is adequate for predicting noise indices with high accuracy, unless L₉₀ has to be predicted. In eight built-up situations along a road with freely flowing traffic only minor mutual differences are found when L₁ ? L_eq and L₁₀ ? L_eq are compared, but L₅₀ and L₉₀, and consequently TNI and L_np, show discrepancies of the order of 10 dB(A). If a traffic light is introduced the value of L_eq rises compared with the free flow case, and the values of L₁ and L₁₀ increase, especially at higher traffic intensities, while L₅₀ and L₉₀ decrease. If the noise indices are calculated as a function of the distance along the road to the traffic light increases in L₁, L₁₀ and L_eq are found at about 50 m beyond the traffic light. The principal cause for this increase appears to be the differences between the peak levels of an accelerating car and the sound level at the ultimate speed. More in situ measurements are required to test the accuracy of the model, especially for accelerating vehicles.     

The 250 nm absorption spectrum of benzene: Vibronic analysis

The supporting details for assignment of band maxima (see paper I) in the one-photon ${}^1\text{B}{}_{\mathrm{2u}}\text{←}{}^1\text{A}{}_{\mathrm{1g}}$ absorption spectra of benzene vapor are given. By the criteria of band separations and Franck-Condon intensities, maxima are first sorted into ν₁ progressions (Table II). The progressions are then assigned by systematic search for allowed first-, second-, and third-order Herzberg-Teller transitions as set forth in Table II of Paper II. Much attention is given to vibrational angular momentum as it affects band contours and component splittings. Over 90% of the intensity is assigned and a consistent pattern of Herzberg-Teller activity is found. Both the list of modes observed to be active in vibronically inducing the transition (ν₄, ν₅, ν₆, ν₇, ν₉, ν₁₀, ν₁₁, ν₁₆, ν₁₇) and the relative intensities of various types of transitions found in absorption match well that seen in SVL fluorescence. Third-order transitions are comparatively few in number, but are equivalent in intensity to many second-order transitions. Variation in the separation between progression members suggests that small (and unidentified) perturbations of upper state vibronic levels are ubiquitous. Revised or new values of nine fundamentals in the ¹B_2u state and two in the ¹A_1g state are given (Table IV). Some of the excited and ground state anharmonic constants x_i⁰, x_i,i⁰, x_i,j⁰, g_i,i, and g_i,j are deduced for ν₅, ν₆, ν₁₀, ν₁₁, ν₁₆, and ν₁₇ (Table V).     

Semi-simple real subalgebras of non-compact semi-simple real Lie algebras IV

The investigation of the problem of embedding a semi-simple real Lie algebra $\text{L}$′ in a non-compact semi-simple real Lie algebra $\text{L}$ is extended to the case in which at least one of the real Lie algebras has a semi-simple complex extension, which consists of the direct sum of two simple complex Lie algebras. Detailed procedures are given, which together with those given previously, allow the construction of all embeddings of $\text{L}$′ in $\text{L}$ when their complex extensions are A₁, B₁, C₁, D₁ or a direct sum of any two of these. The procedures are illustrated by considering examples corresponding to complex Lie algebra embeddings A₁?(A₂⊕A₂), (A₁⊕A₁)?(A₂⊕A₂), (A₁⊕A₁)?A₃, (A₁⊕A₁)??(A₃⊕A₃) and (A₁⊕A₁)?(A₃⊕A₂). Because of its physical significanc embeddings of SL(2,C) in simple and semi-simple real Lie algebras are studied in detail.     

Relativistic calculation of atomic X-ray transition rates

The fully relativistic transition probabilities in atomic X-ray emission are calculated for a wide range of selected elements of the periodic table, fromZ=21 toZ=93. The treatment includes the effect of the retardation of the radiation field. The atomic model used is the self-consistent relativistic Hartree-Fock, with the Slater approximation for the exchange term. The formulas for EL and ML multipole transition rates are derived, and transition rates are calculated for all transitions to theK-shell,L-subshells, andM-subshells. The contributions of all multipoles, as determined by the angular momentum and parity selection rules, are included in the present work. The calculated values of (Kα ₂/Kα ₁), (Kβ ₁/Kα ₁), (Kβ ₃/Kβ ₁) and (Kβ ₂ Kβ ₁) transition rates are in good agreement with the available experimental data. Rates for the forbidden (M1) 2s _1/2→1s _1/2 transitions are also presented.     

Concerning the structural mechanism of oxygen inclusion into the lattice of titanium carbide

Variations in the unit cell occupancy of TiC_xO_y phase are considered in terms of successive oxygen inclusion into the lattice of defect carbides TiC_0.5 ? TiC_0.9. A classification of TiC_xO_y solid solutions formed and the concentration limits of their existence are presented. Three types of cubic ternary solid solutions are shown to occur in the system TiCO: solid solutions of interstitial oxygen inclusion into the initial carbide; solid solutions of oxygen inclusion—carbon and metal exclusion; and solid solutions of oxygen inclusion—oxygen substitution for carbon-carbon and metal exclusion.Specific points (inflection and breaks) on the plots where n_i is the number of atoms per unit cell, n_i = f(y) for TiC_xO_y, are accounted for by both variations in the type of solid solution and the possibility of atomic arrangement in the vicinity of these points. On the basis of the above scheme some experimental peculiarities of Ti carbide phase oxydation are explained.     

Stoichiometry invariants for ternary and quatenary solid solutions with two nearly perfect sublattices

We consider a quatenary semiconductor compound, (A_1?uB_u)_1?y(C_1?vD_v)_y, in which the A and B atoms occupy sites in one sublattice. the C and D atoms occupy sites in a second sublattice, and for which y is always near $\text{1}\text{2}$. A statistical thermodynamic analysis for a specific defect model gives three independent “stoichiometry invariants” for the chemical potentials, e.g. μ_B + μ_D, μ_A ? μ_B, and μ_C ? μ_D, which are independent of approximation for small ratios of defect to site concentration. This result is independent of the specific defects chosen, but is obtained under the assumptions that the distribution of the A and B atoms among themselves and that of C and D atoms among themselves are random. A more general analysis that removes these assumptions still yields the same stoichiometry invariants. These invariants provide simple, model-independent relations among the chemical potentials that are extremely useful and to some extent already employed. They also provide the basis for a check on internal self-consistency when all the chemical potentials are measured. The analogous results for a ternary compound are readily extracted as a special case.     

On the construction of invariant curves of period-two points in two-dimensional maps

We present an equation describing invariant curves associated with periodic points of period two in a wide class of two-dimensional invertible maps. Several branches of the unstable manifolds for the map x_n+1 = 1 - a|x_n| + bz_n, z_n+1 = x_n are constructed in a situation when they are related to a two-piece strange attractor.     

Interphase boundaries and high piezoelectric activity of xPbTiO3-(1−x)Pb(Zn1/3Nb2/3)O3 crystals

Model concepts of the interphase boundaries whose displacements are capable of substantially affecting the piezoelectric properties of xPbTiO₃-(1?x)Pb(Zn_1/3Nb_2/3)O₃ multidomain crystals in the R3m-P4mm morphotropic region are developed. The contributions of the interphase boundaries Δd ₃₃ to the piezoelectric modulus d ₃₃ are determined, and the factors responsible for the large ratios Δd ₃₃/d ₃₃≈0.5–0.9 are analyzed.     

Analysis of the diffraction by the gratings generated in the materials with a nonlinear response

Diffraction by a thick transmission phase grating being illuminated by a plane wave at the first, second and third Bragg angles is analyzed using the rigorous coupled-wave theory for the materials having a nonlinear response to the holographic illumination. It is shown that in the case of nonlinear holographic recording the two-wave approximation can be applied with the use of the effective value of the amplitudes of the refractive index modulation (n_1ef, n_2ef, and n_3ef). The applicability conditions of such approximation are defined. The analytical dependencies of n_1ef, n_2ef, and n_3ef on the amplitudes of the first, second and third harmonics of spatial frequency of the refraction index modulation amplitude n₁, n₂ and n₃ are derived and the criteria of their applicability are established here. The resulting expressions for the diffraction efficiencies are given for readout at three Bragg angles. The results of analytical and numerical methods are compared. The obtained formulas are used for the calculation of n₁, n₂ and n₃ of the holographic gratings generated in the photopolymer material.