X-ray photoelectron spectroscopy study of the electronic structure of La<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>Ca<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>MnO<Subscript>3+δ</Subscript> solid solutions

The electronic structure of La_1–x Ga _x MnO_3+δ. solid solutions is studied by X-ray photoelectron spectroscopy (XPS). The valence state of the manganese is estimated by various methods: by analyzing the difference in the binding energies of the Mn2p_3/2 and O1s electronic levels, analyzing exchange splitting in the spectrum of Mn3s, and from the dependence of the binding energy of the XPS spectrum of Mn2p_3/2 on the calcium concentration. The state of oxidation of the manganese in the compositions containing calcium lies between Mn³⁺ and Mn⁴⁺. The efficacies of these methods are compared. A correlation is found between the type of crystalline structure of La_1–x Ga _x MnO_3+δ. (0 ≤ x < 1) and the binding energy of the Mn2p_3/2 peak. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 3, pp. 419–427, May–June, 2009.     

Lagrangian instanton for the Kraichnan model

We consider high-order correlation functions of the passive scalar in the Kraichnan model. Using the instanton formalism, we find the scaling exponents ζ_n of the structure functions S _n for n≫1 under the additional condition dζ₂≫1 (where d is the dimensionality of space).At n<n _c (where n _c =dζ₂/[2(2−ζ₂)]) the exponents are ζ_n=(ζ ₂/4)(2n−n ²/n _c ), while at n>n _c they are n-independent: ζ _n=ζ₂ n _c /4. We also estimate the n-dependent factors in S _n . Pis’ma Zh. éksp. Teor. Fiz. 68, No. 7, 588–593 (10 October 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Third-order elastic moduli of single-layer graphene

In the framework of the Keating model with allowance made for the anharmonic constant of the central interaction between the nearest neighbors μ, analytical expressions have been obtained for three third-order independent elastic constants c _ijk (μ, ζ) of single-layer graphene, where ζ = (2α − β)/(4α + β) is the Kleinman internal displacement parameter and α and β are the harmonic constants of the central interaction between the nearest neighbors and the noncentral interaction between the next-nearest neighbors, respectively. The dependences of the second-order elastic constants on the pressure p have been determined. It has been shown that the moduli c ₁₁ and c ₂₂ differently respond to the pressure. Therefore, graphene is isotropic in the harmonic approximation, whereas the inclusion of anharmonicity leads to the appearance of the anisotropy.     

Ferromagnetism of the electron gas

The ground-state energy of the ferromagnetic electron gas is calculated for the relative polarizationζ=0−1 and the interelectron separationr _s =5−12. The method consists in describing the electron gas approximately by a quadratic boson Hamiltonian, and contains the random-phase approximation as a special case. Numerical studies show that in both the random-phase and the present approximations the paramagnetic state has the lowest energy: the energy increases withζ for all values ofr _s considered. In the present approximation instabilities are found to occur forr _s above a critical value, due to exchange processes of finite momentum transfers. Forζ=0 this critical value ofr _s is 9.4; it decreases with increasingζ. However, the fully-polarized state (ζ=1), which lies above the rest, is always stable. The conclusions are as follows: (1) Forr _s <9.4 the electron gas is paramagnetic. (2) Atr _s =9.4 it goes over to the fully-polarized ferromagnetic state. (3) This phase transition requires an energy absorption of 0.03 rydberg per electron. (4) The fully-polarized state is not obtainable as the limitζ→1.     

Internal magnetic field gradients as information source about porous media characteristics

The geometry of particles is analyzed by the example of a model porous system (filling of glass spheres and glass cylinders) studied by nuclear magnetic resonance. The experimental approach is based on the registration of the <G _int> (ζ) dependences, where <G _int> is the effective (average) internal magnetic field gradient and ζ=<r ²>^1/2<R> is the ratio of the root-mean-square displacement of molecules to the average particle size <R>. It is shown that the dependence <G _int> (ζ) can be approximated by the power law <G _int>(ζ) ∝ ζ^α, where the power index α does not depend on the particle size but is sensitive to its geometry.     

Stability for Quasi-Periodically Perturbed Hill's Equations

We consider a perturbed Hill's equation of the form +(p₀(t)+ɛp₁(t))ϕ=0, where p₀ is real analytic and periodic, p₁ is real analytic and quasi-periodic and ɛ ∈ℝ is ``small'. Assuming Diophantine conditions on the frequencies of the decoupled system, i.e. the frequencies of the external potentials p₀ and p₁ and the proper frequency of the unperturbed (ɛ=0) Hill's equation, but without making any assumptions on the perturbing potential p₁ other than analyticity, we prove that quasi-periodic solutions of the unperturbed equation can be continued into quasi-periodic solutions if ɛ lies in a Cantor set of relatively large measure in where ɛ₀ is small enough. Our method is based on a resummation procedure of a formal Lindstedt series obtained as a solution of a generalized Riccati equation associated to Hill's problem.     

Threshold and compactification effects in GUTS

We review general results on threshold effects and their implications on GUTs in the context of LEP data. Among the blooming grand-desert models, threshold effects are computed in the presence of a single real scalar ζ (3, 0, 8) with M_ζ≃10¹⁰ GeV leading to experimentally testable predictions on the proton lifetimeτ _p in SU (5) and, in addition, small neutrino masses in SO (10) needed for the solar neutrino flux and the dark matter of the universe. The fine structure constant matching at M_Z is ensured by including threshold effects on the unification coupling. In the minimal SUSY SU (5) such effects at the GUT scale modify the prediction of the supersymmetric mass threshold near the TeV scale and the precision measurments of the Standard Model couplings at M_Z probe into the superheavy mass spectrum. Consequences of theorems proved very useful for threshold, compactification and multiloop effects are discussed. It is noted that in a class of GUTs the highest intermediate scale M_I above which G_224P becomes a good symmetry is not affected by the GUT threshold or compactification effects or multiloop contributions in the range M_I-M_U. But spontaneous compatification effects can decrease the intermediate scale drastically in models where parity and SU(2)_R breakings are decoupled. Low mass W_R-bsosns are permitted in models with decoupled parity and SU (2)_R breakings.     

On Static Shells and the Buchdahl Inequality for the Spherically Symmetric Einstein-Vlasov System

In a previous work [1] matter models such that the energy density ρ ≥ 0, and the radial- and tangential pressures p ≥ 0 and q, satisfy p + q ≤ Ωρ, Ω ≥ 1, were considered in the context of Buchdahl’s inequality. It was proved that static shell solutions of the spherically symmetric Einstein equations obey a Buchdahl type inequality whenever the support of the shell, [R ₀, R ₁], R ₀ > 0, satisfies R ₁/R ₀ < 1/4. Moreover, given a sequence of solutions such that R ₁/R ₀ → 1, then the limit supremum of 2M/R ₁ was shown to be bounded by ((2Ω + 1)² − 1)/(2Ω + 1)². In this paper we show that the hypothesis that R ₁/R ₀ → 1, can be realized for Vlasov matter, by constructing a sequence of static shells of the spherically symmetric Einstein-Vlasov system with this property. We also prove that for this sequence not only the limit supremum of 2M/R ₁ is bounded, but that the limit is ((2Ω + 1)² − 1)/(2Ω + 1)² = 8/9, since Ω = 1 for Vlasov matter. Thus, static shells of Vlasov matter can have 2M/R ₁ arbitrary close to 8/9, which is interesting in view of [3], where numerical evidence is presented that 8/9 is an upper bound of 2M/R ₁ of any static solution of the spherically symmetric Einstein-Vlasov system.     

Phase transitions in solid solutions (1 ? x)BaTiO3-xBaMg1/3B2/3O3 (B = Nb, Ta)

The dielectric properties of ceramic samples of (1 − x)BaTiO₃-xBaMg_1/3Nb_2/3O₃ and (1 − x)BaTio₃-xBaMg_1/3Ta_2/3O₃ solid solutions (x = 0–0.25) are investigated in the frequency range from 10 Hz to 100 kHz at temperatures of 77–450 K. It is shown that the (x−T) phase diagrams of these solid solutions at x = 0.05 have a multiphase point at which the lines of all three phase transitions of BaTiO₃ converge. Original Russian Text ? V.G. Zalesskiĭ, V.V. Lemanov, E.P. Smirnova, A.V. Sotnikov, N. V. Zaĭtseva, 2007, published in Fizika Tverdogo Tela, 2007, Vol. 49, No. 1, pp. 108–112.     

First-principles study of elastic and vibrational properties of Ni<Subscript>2</Subscript>MnIn magnetic shape memory alloys

We present the results of ab initio calculations of lattice dynamics and the second order elastic stiffness constants of nickel-based magnetic shape memory alloy Ni₂MnIn in stoichiometric composition. The plane wave basis sets and pseudopotential method within spin-polarized generalized gradient approximation (σ-GGA) scheme of the density functional theory (DFT) is applied. Elastic constants are calculated by tetragonal and monoclinic isochoric strains on cubic L2₁ structure. The calculated elastic constants agree very well with the recent ultrasonic experimental data. Phonon dispersion spectra are investigated within linear response technique of the density functional perturbation theory (DFPT). A vibrational anomaly is observed in phonon spectra at the transverse acoustic mode (TA₂) in [ζ ζ0] direction at wavevector ζ = 0.3 as an indication of the structural instability of the system to shear deformation. This anomaly is also verified by the low shear modulus and large elastic anisotropy ratio. Phonon dispersion curves are in excellent agreement with the results of recent neutron diffraction experiments.     

Theoretical studies on dielectronic recombination of neonlike gold and its effects on plasma ionization balance and radiation energy

The dielectronic recombination (DR) of neonlike gold ions is investigated employing the flexible atomic code based on the relativistic configuration interaction method, and its influence on the ionization balance and radiation energy in high-temperature plasma is also studied. The total resonance strength for LMM configuration complex is in a good agreement with the experimental measurement and other theoretical works. The DR rate coefficients are calculated and compared with the three-body recombination and radiative recombination rate coefficients. The DR process is the dominant recombination mechanism of Ne-like gold ions for plasma with temperature T_e≥6.5 keV and density n_e≤2×10²² cm^-3, which is close to the condition of X-ray conversion region in the inertial confinement fusion. Moreover, the DR satellite spectra of LMM, LMN and LMO resonances are simulated, and compared with the intensities of the corresponding resonance lines induced by the electron impact excitation. The intensity ratio of the satellite line 3D’ [(2p⁵_3/23d_3/23d_5/2)_J=5/2[(2p^{5}_{3/2}3d_{3/2}3d_{5/2})_{J=5/2}–(2p⁶3d_3/2) _J=3/2](2p^{6}3d_{3/2})_{ J=3/2}] and the resonance line 3D [(2p⁵_3/23d_5/2)_J=1[(2p^{5}_{3/2}3d_{5/2})_{J=1}–(2p⁶)_J=0](2p^{6})_{J=0}] is given, which can be applied for diagnostics of plasma temperature.     

Acidichromism and Ionochromism of Luteolin and Apigenin,the Main Components of the Naturally Occurring Yellow Weld: A Spectrophotometric and Fluorimetric Study

Luteolin and apigenin, extracted from Reseda luteola L., were spectrophotometrically and fluorimetrically studied. The spectra were investigated as a function of pH in methanol/water solutions (1/2, v/v) in the 2–12 pH range. The absorption spectra markedly shifted to the red by increasing the pH. Three acid–base dissociation steps were detected for luteolin (pK _a = 6.9; 8.6; 10.3) and two for apigenin (pK _a = 6.6; 9.3). Fluorescence emission was very weak or undetectable (Φ _F < 10⁻⁴) in acidic solution, but increased in intensity with increasing the pH. Both molecules exhibited a great propensity towards complex formation with metal ions, with association constants on the order of 10⁵–10⁷ for the first complexation step; in the presence of excess Al³⁺ ions, multiple equilibria were detected. A marked fluorescence enhancement was observed upon complexation with Al³⁺ ions (Φ _F ∼ 1 for luteolin and ∼10⁻² for apigenin).     

Bianchi Type V Magnetized String Dust Bulk Viscous Fluid Cosmological Model with Variable Magnetic Permeability

Bianchi Type V magnetized string dust bulk viscous fluid cosmological model with variable magnetic permeability, is investigated. The magnetic field is due to an electric current produced along x-axis. Thus the magnetic fields is in yz-plane and F ₂₃ is the only non-vanishing component of electromagnetic field tensor F _ij . To get the deterministic model in terms of cosmic time t, we have also assumed the condition ζ θ=constant where ζ the coefficient of bulk viscosity and θ the expansion in the model. The behaviour of the model in presence and absence of magnetic field and bulk viscosity and singularities in the model are also discussed.      

Critical behavior of a mixed ferrimagnetic ternary alloy on the Bethe lattice

The critical behavior of the mixed Ising model of the type AB _p C_1−p ternary alloy consisting of spins σ = 1/2, S = 1, and m = 3/2 is investigated on the Bethe lattice by using the exact recursion relations. The exact expressions for the magnetizations and magnetic susceptibilities are found, and the thermal behaviors of the magnetizations and susceptibilities are studied. The magnetizations and susceptibilities have also been investigated as functions of the crystal-field interaction or single-ion anisotropy. The phase diagram has been constructed according to which the system always undergoes a second-order phase transition for the coordination number q ≤ 3 and second-and first-order phase transitions for q > 3; hence, the system has a tricritical point. The system also exhibits reentrant behaviors. The text was submitted by the authors in English.     

Non-Topological Multi-Vortex Solutions to the Self-Dual Chern-Simons-Higgs Equation

 In this article, we construct self-dual N-vortex solutions with a large magnetic flux Φ of (2+1)-dimensional relativistic Chern-Simons model, provided that the coupling constant κ is small and the cites of vorticity satisfies

Multiple Instantons Representing Higher-Order Chern–Pontryagin Classes

It has been shown in the work of Chakrabarti, Sherry and Tchrakian that the chiral SO _±(4 p) Yang–Mills theory in the Euclidean 4 p (p≥ 2) dimensions allows an axially symmetric self-dual system of equations similar to Witten's instanton equations in the classical 4-dimensional SU(2)∼SO _±(4) theory and the solutions represent a new class of instantons. However the rigorous existence of these higher-dimensional instanton solutions has remained open except for the solution of unit charge representing a single instanton. In this paper we establish an existence and uniqueness theorem for multi-instantons of arbitrary charges in the case p≥ 2. These solutions are the first known instantons, with the Chern–Pontryagin index greater than one, of the Yang–Mills model in higher dimensions. Our approach is a study of a nonlinear variational equation defined on the Poincaré half plane. Received: 20 May 1996 / Accepted: 30 April 1997     

He diffraction study of the OH(1×1)−Ag(110) phase

Summary The OH(1×1)−Ag(110) phase obtained after H₂O dissociation on the O(2×1)−Ag(110) surface is investigated. Structural and electronic properties are studied by He diffractive scattering and angularly resolved ultraviolet photoemission spectroscopy (ARUPS). Diffractive data are interpreted in terms of the hard corrugated wall (HCW) potential leading to the determination of the corrugation function ζ(R). The shape of ζ(R) indicates that the phase under study is formed of OH rows along where hydroxil groups interact strongly. The interaction between rows instead is weak and essentially republsive. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Quantitative EPR spectroscopy: Comparison between primary standards and application to MgO-MnO and α-Al2O3-Cr2O3 solid solutions

To study their reliability as primary standards in the quantitative EPR spectroscopy, a large series of pure paramagnetic compounds with known spin concentrations, whose spectra vary considerably in intensity, shape, structure and overall width are compared. The paramagnetic species examined as pure solid compounds and solutions, were free radicals (DPPH and TEMPO), vanadyl and Cu²⁺ ions (S = 1/2), Cr³⁺ (S = 3/2) and Mn²⁺ (5 = 5/2) ions. The quantitative EPR findings suggest that all theS = 1/2 paramagnetic compounds investigated and MnSO₄ · H₂O (S = 5/2) are reliable primary standards. By contrast, none of the pure Cr³⁺ compounds proved useful as primary standards because of their large fine-structure terms or high Néel temperature that invalidated the simple Curie law. Application of quantitative EPR in the study of dilute MgO-MnO and α-Al₂O₃-Cr₂O₃ solid solutions, focussing on the circumstances making paramagnetic species undetectable, is reported. In MgO-MnO solid solutions of high surface area, detection problems arising from the variation of local site symmetry can be circumvented and almost all Mn²⁺ are detected only by reducing the surface area. In concentrated α-Al₂O₃-Cr₂O₃ solid solutions, magnetic interactions lead to paramagnetic species being undetectable.     

Stealth scalar field overflying a 2+1 black hole

A nontrivial scalar field configuration of vanishing energy-momentum is reported. These matter configurations have no influence on the metric and therefore they are not be “detected" gravitationally. This phenomenon occurs for a time–dependent nonminimally coupled and self-interacting scalar field on the 2+1 (BTZ) black hole geometry. We conclude that such stealth configurations exist for the static 2+1 black hole for any value of the nonminimal coupling parameter ζ≠0 with a fixed self-interaction potential U _ζ(Φ). For the range 0 < ζ≤1/2 potentials are bounded from below and for the range 0 < ζ < 1/4 the stealth field falls into the black hole and is swallowed by it at an exponential rate, without any consequence for the black hole.