On the dynamics of the Szekeres system

The gravitational Szekeres differential system is completely integrable with two rational first integrals and an additional analytical first integral. We describe the dynamics of the Szekeres system when one of these two rational first integrals is negative, showing that all the orbits come from the infinity of ${\mathbb{R}}^4$ and go to infinity.     

Features of the optical absorption of crystals of the fullerene C60 in the region of the orientational phase transition

The absorption coefficient of perfect single crystals of the fullerene C₆₀ is measured in the energy range 1.6–2.1 eV at temperatures from 4.2 to 300 K. An absorption fine structure is discovered in the and is assigned to electronic and vibronic transitions with the production of free excitons and excitons localized on structural defects. It is shown that in the region of the structural phase transition from a face-centered cubic structure to a simple cubic structure the absorption coefficient undergoes a jump, which is associated with an energy shift of the free exciton line toward lower energies. It is discovered that spatial inhomogeneity, which is associated with the growth of the new phase from a finite number of nuclei, appears in the crystal at the time of this transition. Zh. éksp. Teor. Fiz. 114, 2211–2224 (December 1998)     

Analysis of the Topology of the Kerr Metric

The equations of motion of a test particle are integrated for the field of a rotating Kerr black hole (BH) (in accordance with [1]). Due to the lack of analytical transformations for the Carter–Penrose diagrams (CPDs) for the Kerr metric, the topology of the Kerr BH is studied by analytical investigation of the equations of motion. Transformations for the CPDs for the Reisner–Nordström metric are analyzed. The problem of boundary conditions for the Reisner–Nordström topology is analyzed. A solution to this problem of boundary conditions is proposed. It is proved that, in the Reisner–Nordström topology, only one way to go to another universe is possible. For the Kerr topology, the possibility of the existence of an alternative transition to another universe that does not coincide with the universe for the ordinary transition is found. This alternative transition is performed through a surface with a zero radial coordinate (zero radius). Initial conditions for the falling particle are found that correspond to an alternative transition to another universe. The tidal forces acting on a falling body in the Kerr metric are estimated, and the possibility of the transition of the body to other universes without being destroyed by tidal forces is proved.     

Dynamics of the thermocline in the equatorial region of the Pacific ocean

This paper is devoted to the subsurface current dynamics in equatorial regions, where the hallmark of a strong stratification is a sharp interface (thermocline), separating two layers of different density, and whose depth is dependent upon the strength of the winds above the ocean's surface. We give here a few monotonicity results concerning the dynamics of the thermocline in the equatorial region. The most important one asserts that the level of the thermocline decreases as the strength of the wind at ten meters above the ocean surface, denoted |U_w|, increases. Moreover, the strength of the current at the thermocline decreases as |U_w| increases.     

On the geometry of the space-time and motion of the spinning bodies

In this paper an alternative theory about space-time is given. First some preliminaries about 3-dimensional time and the reasons for its introduction are presented. Alongside the 3-dimensional space (S) the 3-dimensional space of spatial rotations (SR) is considered independently from the 3-dimensional space. Then it is given a model of the universe, based on the Lie groups of real and complex orthogonal 3 × 3 matrices in this 3+3+3-dimensional space. Special attention is dedicated for introduction and study of the space S × SR, which appears to be isomorphic to SO(3,?) × SO(3,?) or S ³ × S ³. The influence of the gravitational acceleration to the spinning bodies is considered. Some important applications of these results about spinning bodies are given, which naturally lead to violation of Newton’s third law in its classical formulation. The precession of the spinning axis is also considered.     

On the spectrum of the Heisenberg Hamiltonian

The quantum, antiferromagnetic, spin-1/2 Heisenberg Hamiltonian on thed-dimensional cubic lattice ^d is considered for any dimensiond. First the anisotropic case is considered for small transversal coupling and a convergent expansion is given for a family of eigenprojections which is complete in all finite-volume truncations. Then the general case is considered, for which an upper bound to the ground-state energy is given which is optimal for strong enough anisotropy. This bound is expressed through a functional involving the statistical expectation value at finite temperature of a certain correlation function of an Ising model defined on the lattice ^d itself.     

Effect of the dimension of the phonon spectrum on the stability of condensed media states

The effect of dimension index d _f of the phonon spectrum, which is a structural characteristic in continual models, on the stability of states of condensed media is considered in the Einstein and Debye approximations. The estimate of the phase state stability is based on the Lindemann criterion generalized to arbitrary values of 0 ≤ d _f ≤ ∞. The problem of variation of physical characteristic of a substance by controlling the structure of its phonon spectrum is considered by analyzing the possibility of obtaining molecular hydrogen in the superfluid state. The Einstein and Debye models as applied to the problem on the dynamics of atomic oscillations are compared, and the divergence of the latter model for fractal dimensions d _f < 2 of the phonon spectrum is demonstrated, as well as the incompatibility of the Debye model at high temperatures and the model of a classical oscillator for all dimensions except d _f → ∞.     

Spontaneous magnetization of the vacuum and the strength of the magnetic field in the hot Universe

Intergalactic magnetic fields are assumed to have been spontaneously generated at the reheating stage of the early Universe, due to vacuum polarization of non-Abelian gauge fields at high temperature. The fact that the screening mass of this type of fields has zero value was discovered recently. A procedure to estimate their field strengths, B(T), at different temperatures is here developed, and the value B(T _ew)∼10¹⁴ G at the electroweak phase transition temperature is derived by taking into consideration the present value of the intergalactic magnetic field strength, B ₀∼10⁻¹⁵ G, coherent on the ∼1 Mpc scale. As a particular case, the standard model is considered and the field scale at high temperature is estimated in this case. Model-dependent properties of the phenomena under investigation are briefly discussed, too.     

Evaluation of the single ionisation transition amplitude using the CDW-EIS model within the framework of the impact-parameter method

The continuum distorted-wave model with an eikonal initial state for ionisation is discussed within the framework of the impact-parameter method. Particular attention is paid to the surface term, which describes the transition by a distorting potential, and which has been omitted in all of the previous calculations performed using the model. However, this term is included in the transition amplitude in a recent application of the model based upon a quantum-mechanical treatment. The present study, in which the surface term is evaluated within the impact-parameter method, shows that this term does not contribute to the transition amplitude. In describing the electron-ejection mechanism for a p^±–H collision, the cross-sections evaluated using the impact-parameter model show numerical agreement with those determined in the quantum-mechanical version. This agreement indicates that the contribution of the surface term calculated in the wave treatment is negligible over the region in which the impact-parameter model is valid.     

From the Solution of the Tsarev System to the Solution of the Whitham Equations

We study the Cauchy problem for the Whitham modulation equations for increasing smooth initial data. The Whitham equations are a collection of one-dimensional quasi-linear hyperbolic systems. This collection of systems is enumerated by the genus g=0,1,2, ... of the corresponding hyperelliptic Riemann surface. Each of these systems can be integrated by the so-called hodograph transformation introduced by Tsarev. A key step in the integration process is the solution of the Tsarev linear overdetermined system. For each g>0, we construct the unique solution of the Tsarev system, which matches the genus g+1 and g–1 solutions on the transition boundaries.     

Calculation of the vibronic transition moment when the geometries of the combining states of the molecules are significantly different

The concept of the adiabatic approximation is introduced from a few new standpoints, and the conditions are refined under which we can assume that the total energy of an electronic-vibrational (vibronic) state is the sum of the energies of the “electronic” and the “nuclear” problems and the wave function is represented as the product of the corresponding functions. An expression exactly corresponding to such an approximation is considered for the optical transition matrix element, and its individual terms are analyzed for any change in the geometric structure of the molecule upon optical excitation. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 3, pp. 290–293, May–June, 2006.     

222Rn concentrations of water in the Balaton Highland and in the southern part of Hungary,and the assessment of the resulting dose

In this study the ²²²Rn concentration of mains water in 120 settlements in Hungary (Southern Hungary, the Balaton Highland region) was measured. The average ²²²Rn concentration was 5.56 $(0–24.3)\mathrm{Bq}{\mathrm{l}}^{-1}$. On the basis of the ²²²Rn concentration of mains water inspected in the Southern Great Plain region, it can be stated that the ²²²Rn concentration of mains water here is, as an average, half of the ²²²Rn concentration of fountains in the same region. This decrease in radon probably happens during the water management and storage of mains drinking water. The ²²²Rn concentration of spring-water examined in the region of the Balaton Highland exceeds the average ²²²Rn concentration of drinking water (average $27.1\mathrm{Bq}{\mathrm{l}}^{-1}$).The radiation dose originating from the consumption of mains drinking water in case of adults does not reach the value of $0.1\mathrm{mSv}{\mathrm{year}}^{-1}$, even as a conservative assessment ($1\mathrm{l}{\mathrm{day}}^{-1}$ water consumption and ${10}^{-8}\mathrm{Sv}{\mathrm{Bq}}^{-1}$ dose conversion factor).     

Estimate of the rate of contact melting of metals in the nonstationary-diffusion regime by the methods of the thermodynamics of irreversible processes

On the basis of the thermodynamics of irreversible processes, an equation is derived for the estimation of the average rate ¯v_n of contact melting in conditions of non-steady-state diffusion when the liquid is not drawn away from the contact zone and its thickness increases with time. If follows from the derived equation that ¯v_n 1/t, where t is the melting time. A formula is also obtained for the rate of contact melting in the steady state, v_s; under certain conditions this formula coincides with the equations obtained by other authors.Translated from Izvestiya Vysshikh Uchebnykh Zavadenii, Fizika, No. 12, pp. 66–71, December, 1970.     

Dependence of the Electronic Spectra of the Chlorin Molecule on the Degree of Alternation of the Macrocycle Bond Lengths

The geometric structure of the chlorin molecule (H₂Ch) has been calculated by the restricted and unrestricted Hartree-Fock (RHF and UHF) methods with an AM1 Hamiltonian. Transformations of this molecule into excited electronic states have been calculated by the CNDO/S method. The RHF method without symmetry restrictions gives a plane structure for the chlorin macrocycle with an alternation of the lengths of the bonds along the 18-member azacyclopolyene and a C_1h symmetry for the molecule as a whole. The level of the first excited state Q₁ of this structure is substantially shifted (δ ≅ +4000 cm⁻¹) relative to the Q_x level of porphin (H₂P) toward shorter waves, which is in contradiction with the experimental data, according to which this shift is long-wave and is equal to δ = −400 to −550 cm⁻¹. The optimization of the geometry of H₂Ch by the UHF method has shown that it has a structure with an 18-member azacyclopolyene with bonds of equal lengths and a D_2h symmetry. For this geometry of H₂Ch the calculated shift of the Q_x level, equal to δ = −70 cm⁻¹, is bathochromic and the position of the Q_y level is practically exactly coincident with the experimental one. For the geometry calculated by the RHF method with restrictions on the D_2h symmetry of the 18-member azacyclopolyene δ = +180 cm⁻¹, and for the geometry calculated with restrictions on the highest C_2v symmetry of the H₂Ch molecule δ = +620 cm⁻¹. The latter result shows that the “natural” requirement for the C_2v symmetry of the H₂Ch macrocycle, which is frequently used in various calculations, is inadequate to achieve a quantitative agreement between the calculation and experimental data and, in this case, the lengths of the bonds along the 18-member azacyclopolyene are not equal. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 3, pp. 339–347, May–June, 2005.     

Effect of the carrier temperature and the intensity of the recording beam on the energy of a photomagnetic recording of information

If one takes into account thermally active transitions in the kinetic equations for photoinduced spin-reorientation transitions in the monocrystal Y₃Fe₅O₁₂, it can be shown that the limiting temperature of the photomagnetic recording on which such an effect is based is a function of the intensity of the recording beam. This conclusion is confirmed experimentally.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 66–69, January, 1986.     

Investigation of the chiral structure of the Y/Dy multilayer system by the method of the small-angle scattering of polarized neutrons

The magnetic spiral structure of a Y/Dy sample has been investigated for temperatures from 30 to 190 K by the method of the small-angle scattering of polarized neutrons. The sample is a sequence of layers Y_50nm [Dy_4.3nm /Y_2.8nm ]₃₅₀/Y_234nm /Nd_200nm Al₂O₃ (substrate) that is grown as a single crystal with the [001] axis of the hexagonal lattice, which is perpendicular to the layer plane. The experiments demonstrate the appearance of the magnetic peak below T _N = 165.4 K, which is associated with the helicoidal phase, and the helicoid coherence length is larger than the layer thickness of the Y/Dy layer. The use of polarized neutrons allows the separation of the polarization-independent and polarization-independent components of magnetic scattering. The polarization-independent component of the magnetic neutron cross section is proportional to magnetization squared 〈S _Z 〉², whereas the polarization-dependent component is proportional to the average chirality of the system 〈C〉 = 〈[·S ₁ × S ₂]〉. The critical exponents β_C = 1.02(1) and β = 0.39(1) have been determined for the average chirality and magnetization, respectively. The magnetization critical exponent β for Dy/Y coincides with the exponent obtained for Dy bulk samples. The difference β_C ? 2β = 0.24(2) shows that the chirality can be a component of the order parameter that is independent of magnetization. This experiment corroborates the results that were obtained for the critical chirality in Ho and were reported in Phys. Rev. B 64, 100402(R) (2001).     

Effect of the nonuniformity of the radio-frequency field of the sensor of an NQR detector of explosives on the signal intensity and the possibility of its compensation

The intensities of ¹⁴ N NQR signals have been calculated in relation to the amplitude of the initiating radiofrequency (RF) field of the radiopulse, the pulse duration, and the detuning. It is discussed whether it is possible to compensate the decrease in intensity of signals from some regions of an explosive which is in a nonuniform RF field by varying the detuning and the duration of the initiating pulse.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 105–107, October, 2004.