On the Problem of the Amenability of the Gauge Group

Let G be one of the local gauge groups C(X, U(n)),C (X, U(n)), C(X, SU(n)) or C (X, SU(n)) where X is a compact Riemannian manifold. We observe that G has a nontrivial group topology, coarser than its natural topology, w.r.t. which it is amenable, viz. the relative weak topology of C(X, M(n)). This topology seems more useful than other known amenable topologies for G. We construct a simple fermionic model containing an action of G, continuous w.r.t. this amenable topology.     

Effect of the configuration of the discharge chamber of the plasma focus on the neutron yield

Preliminary probe experiments on the Filippov-type plasma focus with the energy E = 70 kJ and a current of about 1 MA show significant stray currents flowing near the insulator. To suppress them and optimize the discharge circuit, the main discharge chamber elements, i.e., the insulator, anode and cathode liner, were changed. As a result, a 30-fold increase in the setup neutron yield to Y _n = 5· 10¹⁰ neutrons per pulse was detected.     

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.     

On the asymptotic behavior of the solutions of the Caldirola-Kanai equation

We study in this Letter the asymptotic behavior, as t+, of the solutions of the one-dimensional Caldirola-Kanai equation for a large class of potentials satisfying the condition V(x)+ as |x|. We show, first of all, that if I is a closed interval containing no critical points of V, then the probability P _t (t) of finding the particle inside I tends to zero as t+. On the other hand, when I contains critical points of V in its interior, we prove that P _t (t) does not oscillate indefinitely, but tends to a limit as t+. In particular, when the potential has only isolated critical points x ₁, ..., x _N our results imply that the probability density of the particle tends to in the sense of distributions.Supported by Fulbright-MEC grant 85-07391.     

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.     

Calculation of the dependence of the centrifugal constants of the molecule H2O on the quantum number v2 on the basis of the Morse oscillator

An explanation is given in this paper for the anomalous dependence of the centrifugal distortion in flexible molecules of the type H₂O on the bending quantum number v₂ on the basis of the Morse oscillator. A computation of the dependence of the rapidly varying rotational, quartic, sextic constants of the molecule H₂O on v₂ describes the experimental behavior of these constants well.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 93–96, August, 1982.     

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.     

Determination of the optical constants of the SiSiO2 system by the method of the angular modulation of reflectance

The sensitivity of the method of the angular modulation of reflectance, recently developed by the authors, in the determination of the optical constants of the SiSiO₂ system is analyzed. This system, which can be approximated to a TFAS system in the visible region, is considered in the limit of small relative thicknesses $\text{d}{}_{\mathrm{<mtext>ox</mtext>}}\text{λ}$. The method proved sufficiently accurate to give the refractive index of the substrate n_s as well as the parameters of the oxide n_ox and d_ox with an accuracy of 2 % down to $\text{d}{}_{\mathrm{<mtext>ox</mtext>}}\text{= 200}\text{A}\text{?}$. The overall accuracy increases at larger oxide thicknesses.     

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.     

On the variability of the transmission coefficient of the atmospheric optical window

Summary We use experimental data to show that the amplitudeA of the oscillations impressed upon upper atmospheric electrons by the electric field vectors of incident solar radiation increases with the solar energy wavelength λ over the visible spectrum. Calculations based upon experimental data show that the transmission coefficientT of the upper atmosphere for incident solar energy (say at intensityI ₀) also increases with λ over the visible spectrum, implying thatT increases withA over the latter range. Finally we show thatI ₀ ^1/2 λ² bears a positive linear relationship withT over the visible solar spectrum. The latter conclusion, which confirms theoretical results contained in a recent paper, is then used to show that the 100 000 year eccentricity cycle effectively causes a maximum change in the total solar energy reaching the lower atmosphere of approximately 4.5% which is enough to trigger an ice age.     

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 → ∞.     

On the limitations of the equation of state based on the Lennard-Jones potential

It is emphasized that any equation of state (EOS) based on the generalized Lennard-Jones potential or the Mie potential, suffers from two main shortcomings as pointed out by Stacey and Davis [2]. One of the shortcomings viz. the problem related to imaginary numbers for the exponents in the potential function, has been removed recently by Jiuxun [11] by using a relationship between the exponents. However, the modified EOS obtained by Jiuxun suffers from the second shortcoming viz. it gives lower values for −B ₀ B″₀, an important equation of state parameter related to the second pressure derivative of the bulk modulus. Values of B ₀ B″₀ obtained by Jiuxun are not consistent with those reported by Stacey and Davis.      

Anomalies of the electronic properties of alloys in the presence of variation of the local magnetic moments

The concentration dependences of the electronic properties (residual electrical resistivity, diffusion thermoelectric power, normal Hall effect, and low-temperature specific heat) and the magnetic characteristics (magnetization and paramagnetic susceptibility) of quasibinary (Pd_xPt_1−x )₃Fe, Pt₃Mn_xFe_1−x , (Pd_xAu_1−x )₃Fe, and Sc_xTi_1−x Fe₂ alloys are investigated. A relationship is established between the anomalous behavior of the kinetic properties and the variation of the local magnetic moments. The absence of corresponding anomalies in the concentration dependence of the specific heat indicates that the density of states at the Fermi level does not change significantly and, therefore, that the conventional Mott two-band model cannot be used to describe the anomalies in the properties of the alloys in question. A single interpretation of the sum-total of the experimental results is given on the basis of the theory of local fluctuations of the electron spin density in metal magnets. Fiz. Tverd. Tela (St. Petersburg) 39, 1257–1262 (July 1997)     

Effect of the neutrino magnetic moment on the properties of the muon

The effect of the neutrino dipole magnetic moment on the properties of the muon is investigated within the standard model of electroweak interactions and a model based on the SU(2) _L × SU(2) _R × U(1) _B-L gauge group (left-right model). In the case of the Dirac neutrino, muon decay through the channel µ^? → e ^?γ is studied with allowance for the neutrino dipole magnetic moment. It is shown that, both in the standard model supplemented with an SU(2) _L right-handed neutrino singlet and in the standard model featuring two doublets of Higgs fields, radiative muon decay is unobservable. In the left-right model, the contributions of diagrams associated with the neutrino dipole magnetic moment become significant only in the case of a mutual compensation of the contributions of diagrams involving the electromagnetic vertices of charged gauge bosons and singly charged Higgs bosons. At specific values of the parameters of the left-right model, one can then obtain an experimental upper limit on the branching fraction of this reaction. The contributions of the neutrino dipole magnetic moment to the muon anomalous magnetic moment are found for the Dirac and the Majorana neutrino. It is established that, both in the standard model and in the left-right model, values of the neutrino anomalous magnetic moment that are required for explaining the (g ? 2)_µ anomaly are in excess of the theoretical predictions for this moment.     

Statistical estimates of the influence of the source divergence angle on the characteristics of acoustic radiation transmitted through the atmosphere

The method of statistical simulation (Monte Carlo) is used for the first time to study the influence of the angular source divergence on the characteristics of transmitted acoustic radiation with allowance for the multiple scattering contribution. Results of calculations for a point source of unit power with divergence angles φ = 5, 10, 15, 20, and 25° at frequencies F = 1, 2, 3, and 4 kHz are presented for the outer scale of turbulence L ₀ = 10, 15, 20, 40, 60, and 80 m. It is established that for F = 2 kHz the multiple scattering contribution to the transmitted radiation intensity increases with the outer scale of turbulence from ∼10% (for L ₀ = 10 m) to 90% (for L ₀ = 60 m); for L ₀ = 80 m, the transmitted radiation intensity is virtually completely determined by the contribution of multiple scattering. When the width of the source directivity pattern (2φ) increases from 10 to 50°, the intensity of transmitted acoustic radiation decreases by 96%. Based on the results of statistical simulation, analytical dependences of the transmitted radiation intensity on the sound source divergence angle are suggested for typical sodar frequencies.     

Effect of the Global Rotation of the Universe on the Formation of Galaxies

The effect of the global rotation of the universe on the formation of galaxies is investigated. It is found that the global rotation provides a natural origin for the rotation of galaxies, and the morphology of the objects formed from gravitational instability in a rotating and expanding universe depends on the amplitude of the density fluctuation, different values of the amplitude of the fluctuation lead to the formation of elliptical galaxies, spiral galaxies, and walls. The global rotation gives a natural explanation of the empirical relation between the angular momentum and mass of galaxies: J M^5/3. The present angular velocity of the universe is estimated at 10^-13rad yr^-1.     

About the Stability of the Dodecatoplet

A new investigation is done of the possibility of binding the “dodecatoplet”, a system of six top quarks and six top antiquarks, (t ⁶ t̄ ⁶), using the Yukawa potential mediated by Higgs exchange. A simple variational method gives a upper bound close to that recently estimated in a mean-field calculation. It is supplemented by a lower bound provided by identities among the Hamiltonians describing the system and its subsystems.     

Behavior of the excitation cross sections of the perturbed series of the xenon atom

Behavior of the excitation cross sections of the perturbed 6s[3/2]_n°?np[1/2]₀ spectral series of the xenon atom is experimentally studied. By using the methods of extended electron beam and optical spectroscopy, the cross sections are measured and the optical excitation functions are recorded for the transitions of this series with n=6–13. A deviation of the dependence Q=f(n) from a power-law function is revealed, as well as changes in the form of optical excitation functions and in the nature of the branching caused by perturbation of the 7p[1/2]₀ level by levels of the 5p ⁵(² P _1/2°)6p configuration.     

The influence of the transformation of waves on the threshold currents of the beam instability

In a hot anisotropic plasma with an inhomogeneity across the magnetic field, eigenmodes are a superposition of long waves of cold plasma and the short-wave Bernstein modes. As a consequence of the fact that the Bernstein modes with non-zero wave numbers are damped more intensively than the waves of cold plasma, the threshold currents of the beam instability increase correspondingly compared with the case of homogeneous plasma. For frequencies between the first and second harmonics of the electron cyclotron frequency the threshold current is from ₀/ _T to ( ₀/ _T )³ times greater, where ₀ is the beam velocity and _T is the thermal velocity of plasma electrons.It is the author's pleasant duty to express his thanks to the theorists of the Institute of Plasma Physics, especially to ing. K. Jungwirth CSc, for valuable discussions he has had with them.