The acoustic field excited by flexural vibrations of an elastic plate with a circular inclusion

The acoustic field excited by flexural vibrations of a thin elastic plate and the perturbations of this field caused by a homogeneous circular inclusion with other elastic properties are considered. Because the density of air widely differs from that of a metal, this problem can be solved with fair accuracy in two steps: first, by considering the vibrations of the plate in a free space, and, then, by calculating the acoustic field excited by the field of plate’s vertical deflections. The main results of this work are the asymptotic expressions for the far acoustic field excited by each of the Fourier components F _m (r)cosmφ of the flexural wave scattered by the inclusion.     

Quasi-normal Modes of Rerssner-Nordström Black Hole

The minimum interval of event horizon area of Rerssner-Nordström black hole was calculated via using the loop quantum gravity theory. Based on the first law of black hole thermodynamics, the real part of quasi-normal modes frequency of the black hole was calculated. The expression of asymptotically quasi-normal mode frequency of Rerssner-Nordström black hole was deduced strictly. By analyzing the value of the minimum spin j _{m i n} , the two families of quasi-normal mode spectra of the charged black hole were obtained for j _{m i n} = 1/2 and j _{m i n} = 1 respectively. Our conclusion is in complete agreement with the analytical results of Hod. Our results provide the theoretical basis for the source of the real part of the quasi-normal mode frequency of the black hole.     

Calculation of magnetic field in the region of the superconducting winding of window frame dipole for particle accelerators

The necessity of simulations in design of superconducting dipole magnets is due to the following circumstances. First, the critical current as a function of the magnetic field I _c(B) for the multicore superconducting cable which drops strongly requires the knowledge of the value of maximum magnetic field “felt” by its coils for estimation of the working current of the magnet. Second, for choosing the optimal number of coils of the winding (1 or 2) and the working current of the magnet, the ratio of B _max for the inner and outer layers of the dipole magnet winding should be known. Since usually the length of the dipole magnet exceeds many times its transverse size, in this work all calculations of B(x, y) are performed in the transverse plane crossing the center of the magnet. The field at the central point is chosen to be B(0, 0) = 2 T (this is the characteristic working value close to the maximum value in the dipole magnet of this type). In this work, the results of calculation of B(x, y) for single-and double-layered windings with 8 and 16 coils from circular hollow cable are presented.     

Neutral Particle Motion around a Schwarzschild Black Hole in Modified Gravity

We investigate circular motion of neutral test particles on equatorial plane near a black hole in scalar-tensor-vector gravity. We consider three cases (i) α < G/G_N (ii) α = G/G_N and (iii) α > G/G_N to find the regions where motion can exist. The corresponding effective potential, energy, angular momentum and center of mass energy are evaluated. Further, we define four different cases for α > G/G_N and identify stable and unstable regions of circular orbits. It is found that circular orbits having zero angular momentum exist at r = αGNM due to repulsive gravity effects. We conclude that the structure of stable regions for α < G/G_N as well as α = G/G_N case is completely different from that of α > G/G_N.     

Distribution of the amplitude of the magnetic potential of diffractive beams generated in a ferrite slab by a surface spin wave incident on a slit in an opaque screen

The total magnetic potential generated in the far field of a ferrite slab as a result of a plane noncollinear surface spin wave incident on a slit in an opaque screen is investigated. The dependence of the potential amplitude from the polar angle in the plane of a ferrite slab is calculated for different orientations of the screen with relative to an external magnetic field magnetizing the slab. It is found that two diffractive beams are generated in the slab as a result of spin diffraction on the slit. The angular width of each beam depends largely on the slit’s orientation and can be greater or smaller than value λ _n /D (where D is the slit’s width and λ _n is the length of the spin wave corresponding to each beam).     

Squeezing of Relative and Center-of-Orbit Coordinates of a Charged Particle by Step-Wise Variations of a Uniform Magnetic Field with an Arbitrary Linear Vector Potential

We consider a quantum charged particle moving in the xy plane under the action of a time-dependent magnetic field described by means of the linear vector potential A = H(t) [?y(1 + β), x(1 ? β)] /2 with a fixed parameter β. The systems with different values of β are not equivalent for nonstationary magnetic fields due to different structures of induced electric fields, whose lines of force are ellipses for |β| < 1 and hyperbolas for |β| > 1. Using the approximation of the stepwise variation of the magnetic field H(t), we obtain explicit formulas describing the evolution of the principal squeezing in two pairs of noncommuting observables: the coordinates of the center of orbit and relative coordinates with respect to this center. Analysis of these formulas shows that no squeezing can arise for the circular gauge (β = 0). On the other hand, for any nonzero value of β, one can find the regimes of excitations resulting in some degree of squeezing in the both pairs. The maximum degree of squeezing can be obtained for the Landau gauge (|β| = 1) if the magnetic field is switched off and returns to the initial value after some time T, in the limit T → ∞.     

A hydrogen atom in a superstrong magnetic field and the Zeldovich effect

We consider the problem of a hydrogen atom in a superstrong magnetic field, B? B _a =2.35×10⁹ G. The analytical formulas that describe the energy spectrum of this atom are derived for states with various quantum numbers n_ρ and m. A comparison with available calculations shows their high accuracy for B?B _a . We note that the derived formulas point to a manifestation of the Zeldovich effect, i.e., a rearrangement of the atomic spectrum under the influence of strong short-range Coulomb potential distortion. We discuss the relativistic corrections to level energies, which increase in importance with magnetic field and become significant for B?10¹⁴ G. We suggest the parameters in terms of which the Zeldovich effect has the simplest form. Analysis of our precision numerical calculations of the energy spectrum for a hydrogen atom in a constant magnetic field indicates that the Zeldovich effect is observed in the spectrum of atomic levels for superstrong fields, B?5×10¹¹ G. Magnetic fields of such strength exist in neutron stars and, possibly, in magnetic white dwarfs. We set lower limits for the fields B_min required for the manifestation of this effect. We discuss some of the properties of atomic states in a superstrong magnetic field, including their mean radii and quadrupole moments. We calculated the probabilities of electric dipole transitions between odd atomic levels and a deep ground level.     

Lattice dynamics of BiFeO<Subscript>3</Subscript> under hydrostatic pressure

The vibrational frequencies of the BiFeO₃ crystal lattice in the cubic phase (Pm3m) and the rhombohedral paraelectric phase (R3c) are calculated in terms of the ab initio model of an ionic crystal with the inclusion of the dipole and quadrupole polarizabilities. In the ferroelectric phase with the symmetry R3c, the calculated spontaneous polarization of 136 μC cm^?2 agrees well with the experimental data. The dependences of the unit cell volume, the elastic modulus, and the vibrational frequencies on the pressure are calculated. It is found that the frequency of an unstable ferroelectric mode in both the cubic (Pm3m) and rhombohedral (R3c) phases are almost independent of the applied pressure, in contrast to classical ferroelectrics with a perovskite structure, where the ferroelectric instability is very sensitive to a variation in the pressure.     

Holographic Superconductor of Regular Phantom Black Hole

Holographic superconductors containing a non-minimal derivative coupling for the scalar field in a regular phantom plane symmetric black hole have been considered. We show that the parameter of the regular black hole b as well as the non-minimal derivative coupling parameter η affect the formation of the condensate as well as the conductivity in the superconductor. Moreover, b has a critical value in which the critical temperature T_c increases without a bound.     

Analysis of tokamak plasma confinement modes using the fast Fourier transformation

The Fourier analysis is a satisfactory technique for detecting plasma confinement modes in tokamaks. The confinement mode of tokamak plasma was analysed using the fast Fourier transformation (FFT). For this purpose, we used the data of Mirnov coils that is one of the identifying tools in the IR-T1 tokamak, with and without external field (electric biasing), and then compared it with each other. After the Fourier analysis of Mirnov coil data, the diagram of power spectrum density was depicted in different angles of Mirnov coils in the ‘presence of external field’ as well as in the ‘absence of external field’. The power spectrum density (PSD) interprets the manner of power distribution of a signal with frequency. In this article, the number of plasma modes and the safety factor q were obtained by using the mode number of q = m /n (m is the mode number). The maximum MHD activity was obtained in 30–35 kHz frequency, using the density of the energy spectrum. In addition, the number of different modes across 0–35 ms time was compared with each other in the presence and absence of the external field.     

Influence of Magnetic Confinement on the Yellow Excitons in Cuprous Oxide Subject to an Electric Field

We study the spectrum of the yellow exciton series in crossed electric and magnetic fields. The electric field, applied along the optical axis, tilts the Coulomb potential between electron and hole, so that at sufficiently high fields exciton dissociation becomes possible, roughly when the electric dipole interaction energy exceeds the binding energy of an exciton state with principal quantum number n. For an applied voltage of U = 20 V all excitons above n = 6 are dissociated. Additional application of a magnetic field normal to the optical axis introduces magnetic confinement, due to which above a threshold field strength around B = 2.5 T the exciton lines re-emerge. The complex dispersion with increasing fields suggests quantum chaotic behavior in this crossed field configuration, so that the search for exceptional points may be promising.     

Adiabatische Inversion von Zustandsbesetzungen im elektrischen Feld

It is shown that the inversion of electric dipole states in electric fields by the adiabatic passage method is possible in a way analogue to the inversion of magnetic dipole states in magnetic fields. A method developed byDaniels is used to derive the conditions for the minimum amplitude and the frequency of the r.f. field for the inversion (J,m _J ) 1,0?1, ±1 and 2,0?2, ±1, whereJ is the rotational quantum number. Rotational inversions are also considered. Experiments with a molecular beam resonance apparatus have shown that more than 90% of a beam of TIF and CsF molecules could be transferred from the state (J, m _J ) 1,0?1, ±1.     

The shape of the giant dipole resonance for light nuclei

A complete spectrum of the giant dipole resonance is calculated taking into account the finite depth of the single particle potential. The mixing of the one particle-one hole excitations because of residual interactions is treated in the time-dependent Hartree-Fock approximation. If the interaction is approximated by a separable potential a general formula can be derived, which gives the total dipole excitation cross section σ(E) in terms of the simple shell-model cross section σ₀(E). Numerical results are given for O¹⁶ and C¹² by evaluating σ₀(E) in a square well potential.     

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.     

Substituent Dependent Optical Properties of <Emphasis Type="Italic">p</Emphasis>-phenyl Substituted ethenyl-<Emphasis Type="Italic">E</Emphasis>-thiophenes

Various electron donor and acceptor substituted (NO₂, CN, Cl, H, OCH₃, NH₂) p-phenyl ethenyl-E- thiophenes (1–6) were synthesized and substituent dependent optical properties (dipole moment, transition dipole moment, oscillator strength, optical band gap, hyperpolarizability) were studied using Solvatochromism and Density functional theory. It is shown that thiophene acts as a weak electron donor in presence of an electron withdrawing p-phenyl substituent (NO₂, CN, Cl), whereas thiophene acts as a weak electron acceptor in presence of an electron donating p-phenyl substituent (OCH₃, NH₂). In comparison to ethenyl thiophene 4, the HOMO-LUMO energy band gap is decreased upon increasing the electron donating or electron withdrawing capacity of p-phenyl substituent. From the excited state dipole moment calculation, it is shown that the excited state is highly dipolar for nitro and amino compounds 1 and 6, whereas compounds 2–5 show a non-polar excited state. As compared to the ethenyl thiophene 4, the first hyperpolarizability (β) increases upon substitution either with a strong electron withdrawing or strong electron donating p-phenyl substituent. A large β value is found for p-nitro phenyl ethenyl-E-thiophene and p-amino phenyl ethenyl-E- thiophene. Overall, these studies provide useful information in understanding the optical properties of phenyl and heterocyclic based ethenyl systems.     

Electromagnetic processes in silver isotopes

Peculiarities of electromagnetic interactions in silver isotopes are considered. Excited states of Ag isotopes are studied as a function of the mass number A = 95–117. Low-lying excited states reveal clear features that are specific for rotational spectra for the energies E < 4–5 MeV. In the energy domain above the nucleon separation threshold of 5–10 MeV, single-particle excited states overlap and produce a continuous spectrum. For energies E = 10–35 MeV, excitation of giant dipole resonance plays the most important role in Ag isotopes. Experimental data on the cross sections of photonuclear reactions in Ag isotopes are analyzed.     

On the hole scattering anisotropy in the PbSb<Subscript>2</Subscript>Te<Subscript>4</Subscript> layered compound from data on the Nernst-Ettingshausen coefficient

Three independent components of the Nernst-Ettingshausen coefficient tensor Q _ikl are experimentally measured for an anisotropic single crystal of the p-PbSb₂Te₄ layered compound. The components Q ₁₂₃ and Q ₁₃₂ are found to be negative, whereas the component Q ₃₂₁ is positive. The experimental data on the anisotropy of the Nernst-Ettingshausen coefficient are discussed together with the available data on the thermopower, the Hall effect, and the electrical conductivity. The analysis demonstrates that the experimental data on the transport effects in p-PbSb₂Te₄ can be explained within a one-band model of the band spectrum and a mixed mechanism of hole scattering under the assumption that scattering from acoustic phonons and scattering from impurity ions are dominant in the cleavage plane and along the c ₃ trigonal axis, respectively.     

On the influence of disjoining pressure on nonlinear oscillations of a water layer on the surface of a charged melting hailstone

The influence of a disjoining pressure on the nonlinear oscillations of a thin charged liquid layer on the surface of a spherical solid core is investigated by means of second-order asymptotic calculations. With the initial deformation governed by a kth mode in the spectrum of modes excited via nonlinear interaction, the disjoining pressure causes the frequencies of modes with numbers smaller than k to decrease and the frequencies of modes with numbers larger than k to increase. In the presence of the disjoining pressure, the amplitudes of all nonlinearly excited modes grow compared with the respective amplitudes without the pressure.     

Waves in a superlattice with arbitrary interlayer boundary thickness

The transmittance D(ω), reflectance R(ω), and dispersion ω(k) are investigated for waves of various nature propagating through a one-dimensional superlattice (multilayer structure) with arbitrary thickness of the interlayer boundary. The dependences of the band gap widths δω_m and their positions in the wave spectrum of the superlattice on the interlayer boundary thickness d and the band number m are calculated. Calculations are performed in terms of the modified coupled-mode theory (MCMT) using the frequency dependence of R(ω), as well as in the framework of perturbation theory using the function ω (k), which made it possible to estimate the accuracy of the MCMT method; the MCMT method is found to have a high accuracy in calculating the band gap widths and a much lower accuracy in determining the gap positions. It is shown that the m dependence of δω _m for electromagnetic (or elastic) waves is different from that for spin waves. Furthermore, the widths of the band gaps with m=1 and 2 are practically independent of d, whereas the widths of all gaps for m>2 depend strongly on d. Experimental measurements of these dependences allow one to determine the superlattice interface thicknesses by using spectral methods.     

Retardation of the relaxation over quantum-well energy levels in CdSe/ZnS quantum dots with increasing number of excited carriers

The differential transmission spectra of CdSe/ZnS quantum dots are investigated. It is revealed that the differential transmission spectra measured upon resonant excitation of electrons into the first excited state 1P(e) exhibit a number of specific features, such as a decrease in transmission at the pump frequency, bleaching in the course of the pump pulse at frequencies corresponding to the fundamental optical transition 1S _3/2(h)-1S(e) and transitions between excited hole states and the 1S(e) electron ground state, and retardation of this process with an increase in the energy of the pump pulse. The observed specific features can be explained by the following factors: (i) the absence of a “phonon bottleneck” for electrons due to the energy transfer from hot electrons to rapidly relaxing holes, (ii) relaxation through intermediate quantum-well energy levels of holes, and (iii) retardation of relaxation with increasing number of excited charge carriers in a quantum dot.