Magnetic phase diagram of diluted spinel Zn1−xCuxCr2Se4 system

By using mean field theory, we have evaluated the nearest-neighbour and the next-neighbour super-exchange J₁(x) and J₂(x), respectively, for Zn_1−xCu_xCr₂Se₄ in the range 0?x?1. The intraplanar and the interplanar interactions are deduced. High-temperature series expansions are derived for the magnetic susceptibility and two-spin correlation functions for a Heisenberg ferromagnetic model on the B-spinel lattice. The calculations are developed in the framework of the random phase approximation. The magnetic phase diagram is deduced. A spin glass phase is predicted for intermediate range of concentration. The results are comparable with those obtained by magnetic measurements. The critical exponents associated with the magnetic susceptibility (γ) and the correlation lengths (ν) have been deduced. The values are comparable to those of the 3D Heisenberg model, and are insensitive to the dilution x.     

Equations for the description of wave scattering by multi-valued random surfaces

We consider a scattering theory for multi-valued rough surfaces which cannot be described by the conventional equation of the type z = ζ(x,y). Both Dirichlet and Neumann problems are analyzed. Starting with Green's theorem we obtain a representation of the scattered field, the surface integral equation, and the extinction theorem for such surfaces. In contrast to conventional theory, these equations contain three random functions x = x(u ₁,u ₂), y = y(u ₁,u ₂), and z = z(u ₁,u ₂), where u ₁ and u ₂ are the parameters describing the surface. We introduce two scattering amplitudes S _± for describing the scattered wave above and below the surface. The extinction theorem, if formulated in terms of S _?, allows us to determine S _? for an arbitrary multi-valued surface and after this it becomes possible to derive a simple integral equation for surface sources. Knowledge of the surface sources allows us to find S ₊ by integration.     

Dynamic behaviours of 2∞ attractor and q-phase transitions at bifurcations in logistic map

Dynamic behaviours of the 2^∞ attractor at the accumulation of period doubling in the logistic map are studied by the sum of the local expansion rates S_n(x₁) of nearby orbits. The variance 〈[S_n(x)]²〉 and algebraic exponent ß_n(x₁) = S_n(x₁)/ln(n) exhibits self-similar structures. The critical bifurcations such as intermittency, band merging and crisis-sudden widening of the chaotic attractor are studied in terms of a q-weighted average Λ(q), (− ∞ < q < ∞) of the coarse-grained local expansion rates Λ of nearby orbitals.     

High order asymptotic expansions of the four kernel functions for line formation with the Voigt profile

Analytical expressions are given for the coefficients, as a function of the Voigt parameter a, in the asymptotic expansions of the kernel functions K₁(π), K₂(π), M₁(π), and M₂(π) that describe the transfer of radiation scattered with complete redistribution over a Voigt profile.     

Low-Temperature Transport Properties of Lanthanum Hexaboride La<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>Ce<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>B<Subscript>6</Subscript> Single Crystals

Resistivity (ρ), thermal conductivity (k) and Seebeck coefficient (S) of La_1–xCe_xB₆ single crystals with various concentrations of cerium Ce ions was measured in a wide temperature range 3?300 K. The obtained data were analyzed in the framework of the Coqblin–Shrieffer model. The contributions of scattering of carriers on magnetic ions Ce for all transport parameters ρ(T), k(T), S(T) are revealed. Strong dependence of the magnetic scattering on concentration of the cerium ions are identified. The anomalous behavior of the transport parameters ρ(T), k(T), S(T) in the region near 30 K is attributed to the Δ ~ 30 K splitting of Г₈ level.     

The derivative nonlinear Schrödinger equation on the half-line

We analyze the derivative nonlinear Schrödinger equation on the half-line using the Fokas method. Assuming that the solution q(x,t) exists, we show that it can be represented in terms of the solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter ζ. The jump matrix has explicit x,t dependence and is given in terms of the spectral functions a(ζ), b(ζ) (obtained from the initial data q₀(x)=q(x,0)) as well as A(ζ), B(ζ) (obtained from the boundary values g₀(t)=q(0,t) and g₁(t)=q_x(0,t)). The spectral functions are not independent, but related by a compatibility condition, the so-called global relation. Given initial and boundary values {q₀(x),g₀(t),g₁(t)} such that there exist spectral functions satisfying the global relation, we show that the function q(x,t) defined by the above Riemann-Hilbert problem exists globally and solves the derivative nonlinear Schrödinger equation with the prescribed initial and boundary values.     

The generalized exponential-integral V(x,y)=∫1∞ exp(−xt)ln(t+y)dtt and computer algorithms for y = 0, 1

The generalized exponential-integral function V(x, y) defined here includes as special cases the function E⁽²⁾₁(x) = V(x, 0) introduced by van de Hulst and functions M₀(x) = V(x, 1) and N₀(x) = V(x, -1) introduced by Kourganoff in connection with integrals of the form ∫ E_n)t)E_m(t±x), which play an important role in the theory of monochromatic radiative transfer. Series and asymptotic expressions are derived and, for the most important special cases, y = 0 and y = 1, Chebyshev expansions and rational approximations are obtained that permit the function to be evaluated to at least 10 sf on 0<x<∞ using 16 sf arithmetic.     

Higher order field equations II; Limit properties of green's functions

In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions G^M_R(x) and G^M_A(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for |M| → ∞ the Green's functions G^M_R(x) and G^M_A(x) approach the Green's functions Δ_R(x) and Δ_A(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of G^M_A(x) and G^M_A(x) is the same as of Δ_R(x) and Δ_A(x) - and also the same as for D_R(x) and D_A(x) for t→ ± ∞, where D_R and D_A are the Green n's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense.     

Operators in a translation invariant two-dimensional bag model

Operator matrix elements are studied in a translation invariant version of the bag model in two-dimensional space time. In particular we calculate the matrix elements of quark fields Q(x), currents J_μ(x), and bilocal currents Q(x)γ_μλ^aQ(0) whose Taylor expansion yields the twist two operators of leptoproduction. The structure functions of this model are related to those of a naive cavity approximation by a particularly simple transformation.     

An analysis of the Lorenz equations: Stable exact solutions

We prove the existence of stable solutions (x(t), y(t), z(t)) to the Lorenz system, t being the time variable. These solutions are valid for b = 2σ and r > 1, b, r and σ being positive parameters, and fall into two classes C_i and C_d depending on whether (x(t), z(t)) are both monotonically increasing or decreasing functions of t. The analytic structure of the solutions is also discussed.     

Study of magnetic properties of Mn1−xCuxCr2S4 by: High-temperature series expansions

The high-temperature series expansions method applied in the systems Mn_1−xCu_xCr₂S₄ in the range 0?x?1. The exchange interactions and the magnetic exchange energies are calculated by using the probability law. The high-temperature series expansions have been applied in the spinel Mn_1−xCu_xCr₂S₄ systems, combined with the Padé approximants method, to determine the magnetic phase diagram, i.e. T_C versus dilution x. The critical exponent associated with the magnetic susceptibility (γ) is deduced. The obtained value of γ is insensitive to the dilution ratio x and may be compared with other theoretical results based on 3D Heisenberg model.     

Superconductivity and thermal properties of sulphur doped FeTe with effect of oxygen post annealing

Here, we report the synthesis and characterization of sulphur-substituted iron telluride i.e. FeTe_1?xS_x; (x = 0–30 %) system and study the impact of low temperature oxygen (O₂) annealing as well. Rietveld analysis of room temperature X-ray diffraction (XRD) patterns shows that all the compounds are crystallized in a tetragonal structure (space group P4/nmm) and no secondary phases are observed. Lattice constants are decreased with increasing S concentration. The parent compound of the system i.e. FeTe does not exhibit superconductivity but shows an anomaly in the resistivity measurement at around 78 K, which corresponds to a structural phase transition. Heat capacity C_p(T) measurement also confirms the structural phase transition of FeTe compound. Superconductivity appears by S substitution; the onset of superconducting transition temperature is about 8 K for FeTe_0.75S_0.25 sample. Thermoelectric power measurements S(T) also shows the superconducting transition at around 7 K for FeTe_0.75S_0.25 sample. The upper critical fields H_c2(10%), H_c2(50%) and H_c2(90%) are estimated to be 400, 650 and 900 kOe respectively at 0 K by applying Ginzburg Landau (GL) equation. Interestingly, superconducting volume fraction is increased with low temperature (200 °C) O₂ annealing at normal pressure. Detailed investigations related to structural (XRD), transport [S(T), R(T)H], magnetization (AC and DC susceptibility) and thermal [C_p(T)] measurements for FeTe_1?xS:O₂ system are presented and discussed.     

Chiral-odd transversity spin structure function h1(x) of the nucleon in a constituent quark model

We study the chiral-odd transversity spin-dependent quark distribution function h₁(x) of the nucleon in a constituent quark model. The twist-2 structure functions, f₁(x), g₁(x) and h₁(x) are calculated within the diquark spectator approximation. Whereas an inequality f₁(x) > h₁(x) > g₁(x) holds with the interaction between quark and diquark being scalar, the axial-vector effective quark-diquark interaction, which contributes to the d-quark distribution, does not lead to such a simple relation. We find that h₁(x) for the d-quark becomes somewhat smaller than g₁^d(x), when we fix the model parameter to reproduce known other structure functions. We also include corrections due to the non-trivial structure of the constituent quark, which is modeled by the Goldstone boson dressing. This improves agreements of f₁(x) and g₁(x) with experiments, and brings further reduction of h₁^d(x) distribution. Consequences for semi-inclusive experiments are also discussed.     

Functional integral representations of partition function without limiting procedure. Techniques of calculation of moments

A definition of the Feynman path integral which does not rest on a limiting procedure based on time-slicing has been given by DeWitt-Morette. We present in this paper a discussion of real Gaussian measures and formulate expressions for the quantum statistical partition function directly in terms of measures of integration on the topological vector space ø₀ of continuous functions defined on the time intervalT = (t _a ,t _b ), such thatx(t _a ,t _b )=0 for allx ? ø₀. We give a definition of a measure for the space ø₀ equivalent to the path integral based on the Uhlenbeck-Ornstein probability distribution. We give expressions for the partition function using the Wiener-Feynman measure and the Uhlenbeck-Ornstein measure. As an exercise in the use of the new techniques, we present calculations of moments of potential functions. The techniques will enable one to solve in a rigorous manner practical problems in quantum statistical mechanics.     

Global properties of radial wave functions in Schwarzschild's space-time

The radial factorR(x, x _s ) of a scalar field in Schwarzschild's space-time satisfies a second order ordinary differential equation with two regular singular points atx=0 andx=x _s and one irregular singular point atx=∞. The analytical properties of four solutions ?₁, ?₂, ?₃, and ?₄ (defined by their power series expansions aboutx=0 andx=x _s ) with respect tox _s are studied. An analytical continuation is given for each solution outside its circle of convergence. Relations to the flat-space solutions are established. Finally the coefficients relating linearly any three of these solutions are determined and studied as functions of the parameterx _s .     

Qualitative calorimetry of some sulphur rich glasses

By DS calorimetry of Ge₃₀S₇₀(a), Ge₂₀S₈₀(b), Ge₂₀Sb_2.5S_77.5(c) and Ge₂₀Bi₅S₇₅(d) crystalline sulphur was identified in (b), (c) and (d) glasses, respectively. It means that these compositions are heterogeneous. Thus the application of the Phillips topological model for estimation of the “ideal” glassy composition in Ge_xS_1?x system seems to be open.     

Effects of Cr doping in bilayered manganite LaSr2Mn2O7: Resistivity, thermoelectric power, and thermal conductivity

Systematic studies of resistivity, thermoelectric power, and thermal conductivity have been performed on polycrystalline bilayered manganites LaSr₂Mn_2−xCr_xO₇ (0≤x≤0.2). It is found that the temperature dependence of both Seebeck coefficient S(T) and resistivity ρ(T) in the high temperature region follows the small polaron transport mechanism for all the samples. But in the low temperature region, variable-range-hopping (VRH) model matches the experimental data better. In addition, the maximum of absolute S(T) at low temperatures is gradually suppressed for the sample with Cr-doping level of x>0.04, implying that a new FM order probably arises. With decreasing the temperatures further, S(T) has a sign change and becomes positive for the sample with Cr-doping level of x>0.04, indicating that there may occur a variation of the type of charge carrier. As to thermal conduction κ(T), the low-temperature peak is suppressed due to Cr-doping. The variation of κ(T) is analyzed based on the combined effect due to the suppression of local Mn³⁺O₆ Jahn-Teller (JT) lattice distortion because of the substitution of Cr³⁺ ions for Mn³⁺ ions, which results in the increase in thermal conduction, and the introduction of the disorder due to Cr-doping, which contributes to the decrease in thermal conduction.     

Selective wet-etching of amorphous/crystallized Ag–As–S and Ag–As–S–Se chalcogenide thin films

The paper is focused on the possibilities of selective wet etching of optically and thermally crystallized/amorphous Ag-doped chalcogenide thin films, namely Ag_x(As_0.33S_0.67)_100−x and Ag_x(As_0.33S_0.335Se_0.335)_100−x. The selective etching of optically(thermally) crystallized Ag_x(As_0.33S_0.67)_100−x and thermally crystallized Ag_x(As_0.33S_0.335Se_0.335)_100−x thin films in water solution of NaCN is presented. The good surface quality is an important and crucial parameter for optical elements fabrication (e.g. grids, waveguides, etc.) especially in nanometer dimensions. The selective etching of undoped and Ag optically doped region was also carried out to observe surface roughness of doped region before and after selective etching. Characterization of the structure and surface of studied films by Raman spectroscopy, X-ray diffraction, AFM and SEM methods has been done and potential application suggested.     

Bandgap engineering of Cd1−xSrxO

Structural, electronic and optical properties of Cd_1−xSr_xO (0≤x≤1) are calculated for the first time using density functional theory. Our results show that these properties are strongly dependent on x. The bond between Cd and O is partially covalent and the covalent nature of the bond decreases as the concentration of Sr increases from 0% to 100%. It is found that Cd_1−xSr_xO is an indirect bandgap compound for the entire range of x and the bandgap of the alloy increases from 0.85 to 6.00 eV with the increase in Sr concentration. Frequency dependent dielectric functions ε₁(ω), ε₂(ω), refractive index n(ω) and absorption coefficient α(ω) are also calculated and discussed in detail. The peak value of refractive indices shifts to higher energy regions with the increase in Sr. The striking feature of these alloys is that Cd_0.5Sr_0.5O is an anisotropic material. The larger value of the extraordinary refractive index confirms that the material is positive birefringence crystal. The present comprehensive theoretical study of the optoelectronic properties of the material predicts that it can be effectively used in optoelectronic applications in the wide range of spectrum; IR, visible and UV.     

Generalized Voigt functions and their derivatives

This paper deals with a special class of functions called generalized Voigt functions H⁽ⁿ⁾(x,a) and G⁽ⁿ⁾(x,a) and their partial derivatives, which are useful in the theory of polarized spectral line formation in stochastic media. For n=0 they reduce to the usual Voigt and Faraday-Voigt functions H(x,a) and G(x,a). A detailed study is made of these new functions. Simple recurrence relations are established and employed for the calculation of the functions themselves and of their partial derivatives. Asymptotic expansions are given for large values of x and a. They are used to examine the range of applicability of the recurrence relations and to construct a numerical algorithm for the calculation of the generalized Voigt functions and of their derivatives valid in a large (x,a) domain. It is also shown that the partial derivatives of the usual H(x,a) and G(x,a) can be expressed in terms of H⁽ⁿ⁾(x,a) and G⁽ⁿ⁾(x,a).