Rayleigh wave dispersion and attenuation on a statistically rough free surface of a hexagonal crystal

Dispersion and attenuation of Rayleigh surface acoustic waves on a statistically rough free surface of a Z-cut hexagonal crystal were analytically studied using a modified mean-field method within the perturbation theory. Numerical calculations were carried out in the frequency range accessible for the perturbation theory using expressions for the real and imaginary parts of the complex frequency shift of Rayleigh waves caused by a slight surface roughness. The Rayleigh wave dispersion and attenuation in the Z-cut hexagonal crystal were shown to coincide qualitatively with those in an isotropic medium, differing only quantitatively. In the long-wavelength limit λ?a, where a is the lateral roughness correlation length, explicit analytical expressions for the relative change in the phase velocity and the inverse damping depth of Rayleigh waves were derived and used in numerical calculations.     

Nonequilibrium energy of Rayleigh waves in half-limited crystals with hot electrons close to the defect surface

Nonequilibrium energies of surface (Rayleigh) lattice oscillations in half-limited crystals with static defects and a two-dimensional layer of hot Fermi and Boltzmann electrons close to the stress free surface were calculated. Substances with electrons heated by an external field retaining their intrinsic temperature for a certain time, T _e ? T, where T is the temperature of the lattice, were considered. As shown earlier, the thermodynamic characteristics of thin films can then be determined by nonequilibrium energy of Rayleigh waves (R-phonons) caused by their interaction with hot electrons. This energy decreases as the widths of the energy spectrum of R-phonons increase. In this work, the earlier calculated spectrum widths are used. These widths are caused by the scattering of R-phonons by electrons and static defects close to the surface (point and extended surface defects, edge dislocations perpendicular to the surface and emerging to it, and random lattice grooves in the lattice plane). In all the calculations, the Keldysh diagram technique transformed for half-limited media was used.     

Attenuation of a Stoneley wave and higher Lamb modes due to the scattering by two-dimensional irregularities of the walls of a fluid-filled borehole

Attenuation of Stoneley waves and higher Lamb modes propagating along an irregular surface of a fluid-filled borehole is investigated. This problem generalizes the problem on the attenuation of Rayleigh waves by an irregular surface of an empty borehole [10]. The technique used to evaluate the attenuation coefficient is based on the perturbation method (surface irregularity heights are considered to be small in comparison with the wavelength) and the mean field method. As a result, an expression is obtained for the partial coefficients of the eigenmode attenuation due to the scattering of eigenmodes by the irregularities of the borehole walls into the same or other eigenmodes, as well as into the bulk longitudinal and transverse waves. The frequency-dependent behavior of the partial attenuation coefficients of both Stoneley waves and higher modes is analyzed against the ratio between the irregularity correlation length and the borehole radius for different correlation functions of irregularities.     

Characteristics of surface acoustic waves in (11$$\bar 2$$ 0)ZnO film/ R-sapphire substrate structures

(11\(\bar 2\)0)ZnO film/R-sapphire substrate structure is promising for high frequency acoustic wave devices. The propagation characteristics of SAWs, including the Rayleigh waves along [0001] direction and Love waves along [1ī00] direction, are investigated by using 3 dimensional finite element method (3D-FEM). The phase velocity (v _p), electromechanical coupling coefficient (k ²), temperature coefficient of frequency (TCF) and reflection coefficient (r) of Rayleigh wave and Love wave devices are theoretically analyzed. Furthermore, the influences of ZnO films with different crystal orientation on SAW properties are also investigated. The results show that the 1st Rayleigh wave has an exceedingly large k ² of 4.95% in (90°, 90°, 0°) (11\(\bar 2\)0)ZnO film/R-sapphire substrate associated with a phase velocity of 5300 m/s; and the 0th Love wave in (0°, 90°, 0°) (11\(\bar 2\)0)ZnO film/R-sapphire substrate has a maximum k ² of 3.86% associated with a phase velocity of 3400 m/s. And (11\(\bar 2\)0)ZnO film/R-sapphire substrate structures can be used to design temperature-compensated and wide-band SAW devices. All of the results indicate that the performances of SAW devices can be optimized by suitably selecting ZnO films with different thickness and crystal orientations deposited on R-sapphire substrates.     

Analysis of the production of Higgs boson pairs at the one-loop level in the minimal supersymmetric standard model

Within theminimal supersymmetric standardmodel, the amplitudes and total cross sections for the processes e ⁺ e ^? → hh, e ⁺ e ^? → hH, e ⁺ e ^? → HH, and e ⁺ e ^? → AA are calculated in the first order of perturbation theory with allowance for a complete set of one-loop diagrams in the m _e → 0 approximation. Analytic expressions are obtained for the quantities under consideration; numerical results are presented in a graphical form. It is shown that the cross section for the process e ⁺ e ^? → hh is larger than those for the other processes (and is on the same order of magnitude as the cross section for the corresponding processes in the Standard Model). In the case of the collision energy equal to √s = 500 GeV, an integrated luminosity in the region ∫ ? ≥ 500 fb^?1, and a longitudinal polarization of the e ⁺ e ? beams used, 520, 320, and 300 production events are possible in the processes e ⁺ e ^? → hh (at M _h = 115 GeV), e ⁺ e ^? → HH, and e ⁺ e ^? → AA (at M _H,A = 120 GeV), respectively. Even at M _H,A ≈ 500 GeV and √s = 1.5 TeV, not less than 200 events for each of the processes can be accumulated. The cross section for the process e ⁺ e ^? → hH is small (about 10^?2 fb), which complicates the detection of the sought signal significantly.     

Decay channels of the standard Higgs boson

In this paper, we review the results of studies on the decay channels of the standard Higgs boson: H → f + f?, H → Z + f + f?, H → W + f + f?′, H → γ + γ, H → γ + Z and H → g + g. Here ff? or ff?′are the fundamental fermions pair (leptons, quarks). Within the framework of the Standard Model analytical expressions for the partial widths of the indicated decays were obtained and their dependence on the mass of the Higgs boson was studied.     

Electron excitation of nucleon resonances: Structure functions and transition form factors

The electron excitation of nucleon resonances is discussed both from the theoretical and from the experimental point of view. This discussion is based on a phenomenological approach that employs the conservation of the electromagnetic and vector-meson hadronic currents and the requirements of limiting chiral invariance. For the electron excitation of J^π=1/2^±,3/2^±,5/2^±,... nucleon resonances, the structure functions are defined in terms of Sachs transition form factors. The resulting resonance structure functions for l+N → l+R processes are used in parametrizing smooth (background) structure functions for l+N → l+X inelastic scattering.     

Weak radiative hyperon decays in the quark model

Weak radiative hyperon decays are considered on the basis of the quark model including one-quark transitions associated with the effective sdγ vertex and two-quark processes s + u → u + d + γ induced by W-boson exchange. The phenomenological model proposed in this study gives values that describe experimental data well and makes predictions for the asymmetry of the decays Λ → n + γ and ξ^? → Σ^? + γ.     

Sound attenuation in a random waveguide when using a radiating system with different patterns of directivity

Using numerical simulations of sound propagation on Russia’s shallow Arctic shelf, low frequency sound attenuation is analyzed for acoustic sources with different patterns of directivity, i.e., vertical discrete radiating arrays of different length. It is shown that sound attenuation depends largely on the parameters of patterns of directivity and the intensity of surface waves even at short ranges r from a source (r < 250H, where H is the waveguide depth).     

Electrophysical properties of six-component ZTS-based ferrosoft ceramic

The properties of six-component ZTS-based ferrosoft ceramic are studied. The ceramic is found to exhibit properties of a ferroelectric relaxor. The R3c → R3m rhombohedral phase transition is observed in the ferroelectric phase of this composite. Polarization of samples with a constant electric field upon cooling through the Curie point enlarges the temperature range of the R3m phase’s existence, compared to roomtemperature polarization.     

Dispersion and attenuation of Rayleigh waves at a one-dimensional random roughness of the free surface of a hexagonal crystal

Analytical expressions are derived for dispersion and attenuation of Rayleigh waves propagating along the statistically rough free surface of a hexagonal crystal (Z cut). The roughness under consideration is one-dimensional (the profile function of the roughness depends on one coordinate) and has the form of hollows of a random lattice. The results obtained earlier in the solution of an analogous problem for a two-dimensional roughness are used in the one-dimensional case. The relationships derived for the dispersion and attenuation of Rayleigh waves are treated analytically and numerically over the entire range of frequencies acceptable in the framework of the perturbation theory. It is shown that the dispersion and attenuation of Rayleigh waves are qualitatively similar to those observed in an isotropic medium.     

Expanding Domain Limit for Incompressible Fluids in the Plane

The general class of problems we consider is the following: Let Ω ₁ be a bounded domain in \({\mathbb{R}^d}\) for d ≥ 2 and let u ⁰ be a velocity field on all of \({\mathbb{R}^d}\) . Suppose that for all R ≥ 1 we have an operator \({\mathcal{T}_R}\) that projects u ⁰ restricted to RΩ ₁ (Ω ₁ scaled by R) into a function space on RΩ ₁ for which the solution to some initial value problem is well-posed with \({\mathcal{T}_{R}u^0}\) as the initial velocity. Can we show that as R → ∞ the solution to the initial value problem on RΩ ₁ converges to a solution in the whole space? We answer this question when d  =  2 for weak solutions to the Navier-Stokes and Euler equations. For the Navier-Stokes equations we assume the lowest regularity of u ⁰ for which one can obtain adequate control on the pressure. For the Euler equations we assume the lowest feasible regularity of u ⁰ for which uniqueness of solutions to the Euler equations is known (thus, we allow “slightly unbounded” vorticity). In both cases, we obtain strong convergence of the velocity and the vorticity as R → ∞ and, for the Euler equations, the flow. Our approach yields, in principle, a bound on the rates of convergence.     

Using a chiral anomaly to determine the number of colors

The N_c dependence of PPPγ vertices, where P is a pseudoscalar meson and N_c is the number of colors, is analyzed with allowance for the N_c dependence of the quark charges. It is shown that the reactions Kγ → Kπ and π^±γ → π^±η and the decay η → π⁺π^?γ are the best processes for determining N_c. The cross section σ(π^?γ → π^?η) as measured by using the VES facility at IHEP agrees with the value of N_c=3.     

Radiation of electromagnetic waves by a dipole in an external uniform electrostatic field

Exact solution for the electromagnetic field densities E and H of a dipole of uniformly accelerated point-charges with identical masses is discussed. It is shown that, for any fixed time t and a large distance R between the center of the dipole and the fieldpoint, |E| ~ R ^?4, |H| ~ R ^?5, while for large c|t| ~ R, |E| ~ |H| ~1/R as in spherical electromagnetic waves. Nevertheless, any irreversible radiation of electromagnetic waves is absent since the wave zone does not exist.     

Proton-proton interaction with high multiplicity at energy of 70 GeV (proposal)

The goal of the proposed experiment is to investigate the collective behavior of particles in the process of multiple hadron production in pp interaction pp → n _π π + 2N at the beam energy E_lab = 70 GeV. The domain of high multiplicity n _π = 30–40, or z = n/\(\bar n\) = 4–6, will be studied. Near the threshold of reaction n _π → 69, z → z_th = 8.2, all particles acquire small relative momentum Δq < 1/R, where R is the dimension of the particle production region. As a consequence of multiboson interference, a number of collective effects may show up: (a) a drastic increase in the partial cross section σ(n) of production of n identical particles is expected, compared with commonly accepted extrapolation; (b) the formation of jets consisting of identical particles may occur as a result of the multiboson Bose-Einstein correlation (BEC) effect; (c) a large fluctuation of charged n(π⁺,π^?) and neutral n(π⁰) components and onset of centauros or chiral condensate effects are anticipated; (d) an increase in the rate of direct γ as a result of the bremsstrahlung in the partonic cascade and annihilation of π⁺π^? → nγ in dense and cold pionic gas or condensate is expected. In the domain of high multiplicity z ≥ 5, a major part of the c.m. energy \(\sqrt s = 11.6\) GeV is materialized, leading to a high-density thermalized hadronic system. Under this condition, a phase transition to cold quark-gluon plasma (QGP) may occur. The search for QGP signatures like large intermittency in the phase-space particle distribution and an enhanced rate of direct photons will be performed. The experimental setup is designed for detection of rare high-multiplicity events. The experiment is to be carried out at the extracted proton beam of the IHEP U-70 accelerator. The required beam intensity is ～10⁷ s^?1. Under the assumption that the partial cross section σ(n _π = 35) = 10-1 nb, the anticipated counting rate is 10-1 events/h. The multiboson BEC enhancement may drastically increase the counting rate.     

Stabilization of Ferromagnetism in BiFeO<Subscript>3</Subscript>:Ho at Hydrostatic Pressure

The isothermal magnetization of the Bi_{1 – x}Ho _x FeO₃ (x = 0?0.2) multiferroic has been studied at a hydrostatic pressure up to 9 GPa in the range of room temperatures. A new anomaly at P_C ≈ 3.81 GPa related to intermediate phases between the structural transition R3c → Pnma has been found against the background of the pressure-induced antiferromagnetic ordering in BiFeO₃ (BFO) at P ≈ 2.59 GPa. It is established that the ferromagnetic behavior under pressure depends on the Ho impurity concentration: P_C decreases at 0.05 ≤ x ≤ 0.1 because of the decrease in R3c bond lengths in the structure, and the stabilization of ferromagnetism is implemented at 0.1 ≤ x ≤ 0.2 probably because of the coexistence of the R3c and Pnma phases. The results of studies indicate that, in Bi_{1 – x}Ho _x FeO₃ with x = 0.2, the transition pressure P_C = 3.7 GPa exceeds the values for BFO doped with other 4f elements (Eu, Y, Sm) in the region R3c → Pnma of the transition.     

Energy and momentum losses of a magnetized plasma via familon emission

Familon emission from a dense magnetized plasma in the processes e^? → e^?φ and e^? → μ^?φ is investigated. The contribution of these processes to the energy losses of a supernova remnant is calculated. It is shown that, at a late stage of the cooling of a supernova remnant, the energy loss of a plasma via familon emission may become commensurate with the loss via neutrino emission. It is found that, because of asymmetry of familon emission in the process e^? → gm^?φ, there arises a force acting on the plasma.     

Electro-optical properties of strontium-barium niobate crystals and their relation to the domain structure of the crystals

The electro-optical coefficients r _ij and half-wave voltage V_λ/2 of strontium-barium niobate crystals poled in the ferroelectric phase are shown to vary along the polar axis. The r _ij (z) and V_λ/2(z) dependences indicate the presence of a residual domain density D(z) and clearly depend on the sign of the polarizing field, with r _ij being minimum (D being maximum) near the negative electrode. This character of the D(z) distribution and, hence, the r _ij (z) and V_λ/2(z) coordinate dependences can be explained by predominant domain nucleation near the negative electrode, which is revealed when the switching processes are studied using 90° (Rayleigh) light scattering from domain walls.     

Multiple exchanges in lepton pair production in high-energy heavy ion collisions

As an archetype reaction for pQCD multigluon hard processes in collisions of ultrarelativistic nuclei, we analyze generic features of lepton pair production via multiphoton processes in peripheral heavy ion scattering. We report explicit results for collisions of two photons from one nucleus with two photons from the other nucleus, 2γ + 2γ → l⁺l^?. The results suggest that the familiar eikonalization of Coulomb distortions breaks down for oppositely moving Coulomb centers. The breaking of eikonalization in QED suggests that multigluon pQCD processes cannot be described in terms of collective nuclear gluon distributions. We discuss a logarithmic enhancement of the contribution from the 2γ + 2γ → l⁺l^? process to production of lepton pairs with large transverse momentum; similar enhancement is absent for the nγ + mγ → l⁺l^? processes with m, n > 2. We comment on the general structure of multiphoton collisions and properties of higher-order terms that cannot be eikonalized.     

Computability of Brolin-Lyubich Measure

Brolin-Lyubich measure λ _R of a rational endomorphism \({R:{\hat{\mathbb {C}}}\to {\hat{\mathbb {C}}}}\) with deg R ≥ 2 is the unique invariant measure of maximal entropy \({h_{\lambda_R}=h_{{\rm top}}(R)=\log d}\) . Its support is the Julia set J(R). We demonstrate that λ _R is always computable by an algorithm which has access to coefficients of R, even when J(R) is not computable. In the case when R is a polynomial, the Brolin-Lyubich measure coincides with the harmonic measure of the basin of infinity. We find a sufficient condition for computability of the harmonic measure of a domain, which holds for the basin of infinity of a polynomial mapping, and show that computability may fail for a general domain.