On wave and rheidity properties of the Earth’s crust

The properties of the Earth’s solid crust have been studied on the assumption that this crust has a block structure. According to the rotation model, the motion of such a medium (geomedium) follows the angular momentum conservation law and can be described in the scope of the classical elasticity theory with a symmetric stress tensor. A geomedium motion is characterized by two types of rotation waves with shortand long-range actions. The first type includes slow solitons with velocities of 0 ≤ V_sol ≤ c0, max = 1–10 cm s^–1; the second type, fast excitons with V₀ ≤ V_ex ≤ V_S–V_P. The exciton minimal velocity (V₀ = 0) depends on the energy of the collective excitation of all seismically active belt blocks proportional to the Earth’s pole vibration frequency (the Chandler vibration frequency). The exciton maximal velocity depends on the velocities of S (V_S ≈ 4 km s^–1) and/or P (V_P ≈ 8 km s^–1) seismic (acoustic) waves. According to the rotation model, a geomedium is characterized by the property physically close to the corpuscular–wave interaction between blocks that compose this medium. The possible collective wave motion of geomedium blocks can be responsible for the geomedium rheidity property, i.e., a superplastic volume flow. A superplastic motion of a quantum fluid can be the physical analog of the geomedium rheid motion.     

RETRACTED ARTICLE: Density,viscosity and speed of sound of benzaldehyde with benzene at 303.15, 308.15, and 313.15 K

The values of density, viscosity and speed of sound for the binary liquid mixture of Benzaldehyde with Benzene were measured over the entire range of composition at 303.15, 308.15, and 313.15 K. These values are used to calculate the excess molar volume (V ^E), deviation in viscosity (Δη), deviation in speed of sound (ΔU), deviation in isentropic compressibility (Δβ _s ), excess internal pressure (Δπ), excess intermolecular free length (ΔL _f ), excess free volume (V _E ^f ) and excess acoustic impedance (ΔZ). McAllister’s three-body interaction model is used for correlating Kinematic Viscosity of binary mixtures. The excess values were correlated using the Redlich–Kister polynomial equation to obtain their coefficients and standard deviations. The thermophysical properties (density, viscosity, and speed of sound) under the study were fit to the Jouyban–Acree model.     

Antiferromagnetic Resonance in GdB<Subscript>6</Subscript>

The electron spin resonance has been measured for the first time both in the paramagnetic phase of the metallic GdB₆ antiferromagnet (T_N = 15.5K) and in the antiferromagnetic state (T < T_N). In the paramagnetic phase below T* ~ 70 K, the material is found to exhibit a pronounced increase in the resonance linewidth and a shift in the g-factor, which is proportional to the linewidth Δg(T) ~ ΔH(T). Such behavior is not characteristic of antiferromagnetic metals and seems to be due to the effects related to displacements of Gd³⁺ ions from the centrosymmetric positions in the boron cage. The transition to the antiferromagnetic phase is accompanied by an abrupt change in the position of resonance (from μ₀H₀ ≈ 1.9 T to μ₀H₀ ≈ 3.9 T at ν = 60 GHz), after which a smooth evolution of the spectrum occurs, resulting eventually in the formation of the spectrum consisting of four resonance lines. The magnetic field dependence of the frequency of the resonant modes ω₀(H₀) obtained in the range of 28–69 GHz is well interpreted within the model of ESR in an antiferromagnet with the easy anisotropy axis ω/γ = (H ₀ ² +2H_AH_E)^1/2, where H_E is the exchange field and H_A is the anisotropy field. This provides an estimate for the anisotropy field, H_A ≈ 800 Oe. This value can result from the dipole?dipole interaction related to the mutual displacement of Gd³⁺ ions, which occurs at the antiferromagnetic transition.     

The effect of high pressure on the structure and on the magnetic and electronic properties of nickel monoxide

A diamond anvil cell is used to investigate the effect of high pressure (up to 37.5 GPa) on the optical absorption spectra of a single crystal of nickel oxide (NiO). In addition, strain-gage measurements are used to experimentally investigate the V(P) equation of state at a hydrostatic pressure of up to 8.5 GPa in a high-pressure chamber of the “toroid” type. Measurements are performed at room temperature. Absorption bands are observed, which correspond to optical d-d transitions of Ni²⁺ ion in the crystal field of ligands ³A_2g → ³T_2g, ³A_2g → {au1}E_1g, ³A_2g → ³T_1g(F), and ³A_2g → ¹T_2g. The values of energy of these transitions increase linearly with pressure, and their pressure coefficients are 7.3 ± 0.2, 2.87 ± 0.9, 9.7 ± 0.5, and 8.9 ± 0.3 meV/GPa, respectively. The pressure derivative of the crystal field parameter 10Dq corresponding to the ³A_2g → ³T_2g transition gives the pressure dependence of the magnitude of exchange integral J in the Anderson hybridization model. It is found that, in the pressure range from zero to 37.5 GPa, the behavior of the exchange integral J is largely defined by the hybridization parameter b = (10Dq/3). At the same time, the Coulomb interaction parameter U_eff is independent of pressure and, therefore, has no effect on the variation of J. The Coulomb interaction U_eff ≈ 7.47 ± 0.005 eV is determined. The experimental data on the equation of state are used to derive the \(J \propto V^\varepsilon \) correlation, where ε = ?2.99 ± 0.15, which is in good agreement with the predictions of Bloch’s theory (ε = ?10/3).     

Transformation of dielectric properties and appearance of relaxation behavior in Pb<Subscript>5</Subscript>(Ge<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Si<Subscript>x</Subscript>)<Subscript>3</Subscript>O<Subscript>11</Subscript> crystals

The special features of the dielectric properties and conduction of ferroelectric crystals of Pb₅(Ge_1?xSi_x)₃O₁₁ (0 ≤ x ≤ 0.67) solid solutions were studied. Permittivity anomalies close to the temperatures T₁ ≈ 260 K and T₂ ≈ 130 K, the appearance of relaxator behavior at x > 0.35, and critical behavior of the concentration dependences of dielectric and pyroelectric characteristics at x₁ = 0.35 and x₂ = 0.60 were observed and studied. These phenomena were found to be related to the dynamics of charge localization on defects with activation energies of U_a1 ≈ 0.6 eV and U_a2 ≈ 0.23 eV. Relaxator behavior appears when the Curie point lies in the temperature region of thermal charge localization. The concentration dependence features at x₁ and x₂ are explained by the coincidence of the Curie point and the centers of the temperature regions of charge localization on the U_a1 and U_a2 defect levels, respectively.     

Isotopically invariant dunham parameters and the potential function of the HCl molecule

The isotopically invariant Dunham parameters U _mj , Δ _mj ^H and Δ _mj ^Cl were determined by simultaneously fitting the line centers of vibration-rotation transitions of six isotopic HCl forms in the ground electronic state. Fitting included relations between U _mj values. The parameters of the isotopically invariant potential of HCl were determined using independent U _m0 and U _m1 values. The contributions to the vibrational terms of H³⁵Cl caused by violation of the Born-Oppenheimer approximation were calculated.     

Selective Reflection of Potassium Vapor Nanolayers in a Magnetic Field

The selective reflection of laser radiation from the interface between a dielectric window and the atomic vapors confined in a nanocell of thickness L ≈ 350 nm is used to develop effective Doppler-broadening- free spectroscopy of potassium atoms. A small atomic line width and a relation between the signal intensity and the transition probability allowed us to resolve four lines of atomic transitions responsible for the D1 lines of the ³⁹K and ⁴¹K isotopes. Two groups containing four atomic transitions form in an applied magnetic field upon pumping by radiation with circular polarization σ⁺ or σ^–. Different intensities (probabilities) of transitions for the σ⁺ and σ^– excitations are detected in magnetic field B₀ ≈ A _hfs /μ_B ≈ 165 G (A _hfs is the magnetic dipole constant for the ground state and μ_B is the Bohr magneton). A substantially different situation is observed at B ? B₀, since high symmetry appears for the two groups formed by radiation with circular polarization σ⁺ or σ^–. Each group is the mirror image of the other group with respect to the frequency of the 4²S_1/2–4²P_1/2 transition, which additionally proves the occurrence of the complete Paschen–Back regime of the hyperfine structure at B ≈ 2.5 kG. A developed theoretical model well reproduces the experimental results. Possible practical applications are described. The results obtained can also be applied to the D₁ lines of ⁸⁷Rb and ²³Na.     

Predictions for the weak leptonic baryon form factors from the hybrid groupSU 3⊗SU 3⊗U 1

Relations between the form factors of the weak leptonic baryon interaction are obtained from invariance under the groupSU ₃?SU ₃?U ₁. The weak interaction operatorV _μ ?A _μ is assumed to behave like the corresponding components of representations35 ofSU ₆ with different parities. One gets the result that the well-known predictions of the staticSU ₆ theory, viz., pureF-coupling for the vector- and 3D+2F-coupling for the axial-vector part, are only valid in the limit of vanishing momentum transfer. In the same limit the resultC _A /C _V =?\(\tfrac{5}{3}\) is obtained if one further assumes thatV ₀ and\(\vec A\) belong to thesame representation35 ofSU ₆.     

Effect of bias voltage polarity of a substrate on the texture,microstructure, and magnetic properties of Ni films prepared by magnetron sputtering

The influence of the bias voltage polarity U_s on microstructure, crystallographic texture and magnetic properties has been investigated for Ni films with a thickness of ≈15–420 nm, which are obtained via magnetron sputtering at a working gas pressure P corresponding to the collision-deficient flight mode of atoms of the sputtered target between the target and the substrate. The Ni(111)-textured films have been shown to form at U_s ≈–100 V, whose microstructure and magnetic parameters are almost unchanged with a thickness. In contrast, the Ni(200) films are formed at U_s ≈ +100 V, whose magnetic properties and micro-structure depend significantly on the thickness d that manifests in a critical thickness d* ≈ 150 nm, when the structure of the film becomes inhomogeneous in the thickness, the remagnetization loops are changed from rectangular to supercritical with the formation of the band domain structure.     

Standard leptons and the next lepton in the byuon theory

A physical picture of the origin of lepton mass is presented on the basis of the byuon theory (BT). The BT is the theory of the life of special unobservable discrete objects: byuons, from which the world surrounding us are formed (physical space; fundamental constants h, e, c; the mass of elementary particles; the four fundamental interactions; the predicted new force in nature, and so on). A key difference between this theory and current models of the classical and quantum field theories is that the potentials of physical fields acquire precise fixable, measurable values. The definition of byuon contains a new fundamental vector constant: the cosmological vector potential (A_g ≈ 1.95 × 10¹¹ G cm). The BT contains only three constants: \(\tilde x_0 \) ≈ 2.78 × 10^–33 cm, τ₀ ≈ 0.927 × 10^–43 s, and a modulus of A_g that allows us to obtain the masses of all known leptons and predict the mass of the next lepton (80.4 GeV).     

Cohesive energy of zincblende (A<Superscript>III</Superscript>B<Superscript>V</Superscript> and A<Superscript>II</Superscript>B<Superscript>VI</Superscript>) structured solids

In this paper we present an expression relating the cohesive energy (E _coh in kcal/mol) of A^IIIB^V and A^IIB^VI semiconductors with the product of ionic charges (Z ₁ Z ₂) and nearest-neighbour distance d (Å). The cohesive energy values of these solids exhibit a linear relationship when plotted on a log-log scale against the nearest-neighbour distance d (Å), but fall on different straight lines according to the ionic charge product of the solids. A good agreement has been found between the experimental and calculated values of the cohesive energy of A^IIIB^V and A^IIB^VI semiconductors.     

Electronic structure and energies of interatomic bonds in the TiSi<Subscript>2</Subscript> compound with a <Emphasis Type="Italic">C</Emphasis>49 crystal structure

Full-electron calculations of the electronic structure of the TiSi₂ compound in the structural modification C49 are performed using the augmented-plane-wave method. The total energy, the electronic band structure, and the density of states are calculated for an extended translational unit cell Ti₄Si₈, which is formed during the growth of a silicon nanowire on a p-Si substrate. Calculations are also carried out for two orthorhombic unit cells of the nonstoichiometric compositions Ti₃Si₉ and Ti₅Si₇. The energies of the interatomic bonds are determined to be E _Si-Si = 1.8 eV, E _Ti-Ti = 2.29 eV, and E _Ti-Si = 4.47 eV. The dependence of the total energy of the unit cell E _tot(V) on the unit cell volume V is obtained by optimizing the unit cell volume. The bulk modulus B ₀ = 132 GPa is determined from the Murnaghan equation of state for solids and the dependence E _tot (V). This value of the bulk modulus is used to estimate the activation energy for interstitial diffusion of silicon atoms Q _i(Si) ≈ 0.8 eV.     

Über die mathematische Struktur und eine Klasse strenger Lösungen der Jordanschen erweiterten Gravitationstheorie

Theβ-α. angular correlationW(Θ)=1+a cosΘ+cos² Θ of the decay of Li⁸ was measured for average electron energies ofE _β ≈5 MeV, 11 MeV and 12 MeV. The experiment yields an anisotropyA=(0·0036±0·0011)·E _β (MeV)^?1. This result is in good agreement with the results of the other groups. The measurements were performed in a counting chamber separated from the activation room simultaneously for two sealer positionsΘ=90° and 180°. The result is discussed in terms of the CVC-theory, taking into account the second forbidden Fermi-matrixelements (‖M1‖) and (‖E2‖).     

Self-similar magnetic structures and magnetic flux “Giant” creep

The penetration of a magnetic flux into a type-II high-T _c superconductor occupying the half-space x > 0 is considered. At the superconductor surface, the magnetic field amplitude increases in accordance with the law b(0, t) = b ₀(1 + t)^m (in dimensionless coordinates), where m > 0. The velocity of penetration of vortices is determined in the regime of thermally activated magnetic flux flow: v = v ₀exp?ub;?(U _0/T )(1-b?b/?x)?ub;, where U ₀ is the effective pinning energy and T is the thermal energy of excited vortex filaments (or their bundles). magnetic flux “Giant” creep (for which U ₀/T? 1) is considered. The model Navier-Stokes equation is derived with nonlinear “viscosity” v ∝ U ₀/T and convection velocity v _f ∝ (1 ? U ₀/T). It is shown that motion of vortices is of the diffusion type for j → 0 (j is the current density). For finite current densities 0 < j < j _c, magnetic flux convection takes place, leading to an increase in the amplitude and depth of penetration of the magnetic field into the superconductor. It is shown that the solution to the model equation is finite at each instant (i.e., the magnetic flux penetrates to a finite depth). The penetration depth x _eff ^A (t) ∝ (1 + t)^{(1 + m/2)/2} of the magnetic field in the superconductor and the velocity of the wavefront, which increases linearly in exponent m, exponentially in temperature T, and decreases upon an increase in the effective pinning barrier, are determined. A distinguishing feature of the solutions is their self-similarity; i.e., dissipative magnetic structures emerging in the case of giant creep are invariant to transformations b(x, t) = β^m b(t/β, x/β^{(1 + m/2)/2}), where β > 0.     

Measurement of polarization angular coefficients in <Emphasis Type="Italic">Z</Emphasis> boson leptonic decays with ATLAS at the LHC

This paper presents the complete set of polarization angular coefficients A _0?7 describing lepton angular distributions in Z boson decay, which were measured at the ATLAS experiment in proton–proton collisions with the energy √s = 8 TeV. Theoretical values for the difference A ₀ ? A ₂ calculated in the fixed-order QCD perturbation theory O(α _s ² ), demonstrate significant deviation from the measured data, which indicates the necessity of taking into account higher order corrections. The evidence of nonzero coefficients A _5,6,7 was obtained for the first time, in accordance with theoretical calculations in O(α _s ² ) approximation. Measurement of the polarization angular coefficients A _i is important for subsequent precision measurement of parameters of the electroweak model at the LHC, such as the sine of Weinberg electroweak mixing angle sin² θ _W and the W boson mass.     

Heat capacity anomaly in the vicinity of the tricritical and upper critical points

The anomalous behavior of the isochoric heat capacity of a mixture of methane, pentane and heptane is studied experimentally in the vicinity of the liquid-vapor critical point in the cases when (a) the critical temperature T _c approaches the tricritical point T _TCP and (b) the critical temperature approaches the upper critical end point T _U . It is shown that in all cases, the singular part of the heat capacity of the mixture has the form C_sing=A¦τ¦^?α, where τ=(T ? T _c )/T _c and α≈0.11. When T _c →T _U , amplitude A of the heat capacity anomaly is found to be approximately constant. At the same time, the amplitude of the anomaly tends to zero in the vicinity of the tricritical point: A∝¦τ_c¦^ε, where τ_c=(T _c ? T _TCP )/T _TCP and ε=1.6?1.7. The inevitable vanishing of this mode of the heat capacity anomaly leads to a negative value of the critical index \(\tilde \alpha\) characterizing the heat capacity anomaly at the tricritical point, while the tricritical point theory and the isomorphism hypothesis predict \(\tilde \alpha = 0.5\).     

Extremal Theory for Spectrum of Random Discrete Schrödinger Operator. II. Distributions with Heavy Tails

We study the asymptotic structure of the first K largest eigenvalues λ _k,V and the corresponding eigenfunctions ψ(?;λ _k,V ) of a finite-volume Anderson model (discrete Schrödinger operator) \(\mathcal{H}_{V}= \kappa \Delta_{V}+\xi(\cdot)\) on the multidimensional lattice torus V increasing to the whole of lattice ? ^ν , provided the distribution function F(?) of i.i.d. potential ξ(?) satisfies condition ?log(1?F(t))=o(t ³) and some additional regularity conditions as t→∞. For z∈V, denote by λ ⁰(z) the principal eigenvalue of the “single-peak” Hamiltonian κΔ _V +ξ(z)δ _z in l ²(V), and let \(\lambda^{0}_{k,V}\) be the kth largest value of the sample λ ⁰(?) in V. We first show that the eigenvalues λ _k,V are asymptotically close to \(\lambda^{0}_{k,V}\). We then prove extremal type limit theorems (i.e., Poisson statistics) for the normalized eigenvalues (λ _k,V ?B _V )a _V , where the normalizing constants a _V >0 and B _V are chosen the same as in the corresponding limit theorems for \(\lambda^{0}_{k,V}\). The eigenfunction ψ(?;λ _k,V ) is shown to be asymptotically completely localized (as V↑?) at the sites z _k,V ∈V defined by \(\lambda^{0}(z_{k,V})=\lambda^{0}_{k,V}\). Proofs are based on the finite-rank (in particular, rank one) perturbation arguments for discrete Schrödinger operator when potential peaks are sparse.     

Studies of the defect structure from the calculations of optical and electron paramagnetic resonance spectra for Ni<Superscript>2+</Superscript> centre in <Emphasis Type="Italic">α</Emphasis>-LiIO<Subscript>3</Subscript> crystal

By calculating the optical spectrum band positions and EPR parameters (g factors, g‖, g⊥ and zero-field splitting D) by diagonalizing the complete energy matrix of 3d⁸ ions in trigonal symmetry, the defect structure of Ni²⁺ centre in α-LiIO₃ crystal is studied. It is found that to reach the good fits of optical and EPR data between calculation and experiment, the Ni²⁺ ion should shift by Δz ≈ 0.298 Å along C₃-axis and the O^2? ions between the Ni²⁺ ion and Li⁺ vacancy (V _Li) should be displaced away from the V _Li by Δx ≈ 0.097 Å because of the electrostatic interaction. The results are discussed.