Spectral series of the Schrödinger operator in a thin waveguide with a periodic structure. 2. Closed three-dimensional waveguide in a magnetic field

In the paper, which is the second part of the paper by J. Brüning, S. Dobrokhotov, S. Sekerzh-Zenkovich, T. Tudorovskiy, “Spectral series of the Schrödinger operator in thin waveguides with a periodic structure. 1,” Russ. J. Math. Phys. 13 (4), 401–420 (2006), using the adiabatic approximation, diverse quantum states of the stationary Schrödinger equation for a particle in a thin waveguide in a magnetic field are constructed. The problems of “destruction” of the adiabatic approximation as the value of energy increases and of replacing this approximation by the approximation of V. P. Maslov’s theory of complex germ (the complex WKB method) are studied.     

Anomalies of the electrical properties and the stability of the double layer at a metal-electrolyte boundary. Characteristics of the capacitance of a double layer with relaxing “plates∝

An electromechanical model of the electric double layer, whose plates are displaced on charging, is proposed; it is shown for the example of this model that the differential capacitance can diverge and become negative. The reasons why these anomalies were not predicted in the well-known models of the double layer are examined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 9–15, November 1987.     

Dissipative solitons compounds in a fiber laser. Analogy with the states of the matter

We investigate experimentally ordered and disordered pattern formation of solitons in a double-clad fiber laser. We point out an analogy between the different states of matter and the states of a set of dissipative solitons. In particular, we have identified a gas, a supersonic gas flow, a liquid, a polycrystal and a crystal of solitons. The different states are obtained only by adjustment of the intracavity phase plates.     

The additivity of the η-invariant. The case of a singular tangential operator

We prove the decomposition formula for the -invariant of the compatible Dirac operator on a closed manifoldM which is a sum of two submanifolds with common boundary.Research partially supported by NSF     

Origin of the E.S.R. hyperfine anisotropy and the cos2 θ rule of the β-fluorine couplings

The origin of the hyperfine couplings of β-fluorine nuclei in free radicals has been studied using the hyperfine tensors determined for and in single crystals. The direction of the maximum principal element of the β-fluorine coupling tensor in was found to be very close to the direction of the maximum overlap of the fluorine 2p π orbital with the half-filled carbon 2p π orbital. This means that the spin density in the fluorine 2p π orbital is mainly due to the direct overlap with the carbon 2p π orbital and the contributions from the hyperconjugation and the spin polarization mechanisms are less important. The cos²θ rule, B ₀ + B cos²θ, for the β-fluorine coupling tensor was also derived from the conformational dependence of the overlap integral. Using the ratio of B/B ₀ calculated from the overlap integral together with the observed hyperfine tensor for , the absolute values of B ₂ and B were determined and results were applied to the β-fluorine coupling tensor of the rotating CF₃ group in . The calculated tensor is in very good agreement with the one observed.     

Remarks on a recent article of Ch. Obcemea and E. Brändas on the theory of subdynamics

In a recent paper on the theory of subdynamics, Ch. Obcemea and E. Brändas (Ann. Phys (N.Y.)151 (1983), 383–430) claimed to correct a recently published result (M. Courbage, J. Math. Phys.23 (1982), 646, 652). It is shown that this criticism is unfounded. Some additional remarks are made.     

Towards a Post-Keplerian social science: Comments by P. Érdi on the Visioneer white papers by D. Helbing and S. Balietti

This article comments on the Visioneer (Envisioning a Socio Economic Knowledge Collider) Project as described in the following white papers [1–3].     

Comment on “On the threshold characteristics of the flexoelectric domains arising in a homogeneous electric field: The case of anisotropic elasticity” by Y.G. Marinov and H.P. Hinov

It is demonstrated that the key findings of the paper by Y.G. Marinov and H.P. Hinov, Eur. Phys. J. E 31, 179–189 (2010), are in direct conflict with the general physical background of flexoelectric domains. This is caused by a methodological error in the theoretical analysis of the paper.     

Heat transfer enhancement—a review of techniques and their possible impact on energy efficiency in the U.K.

There are many techniques for enhancing heat transfer. These may be usefully categorized as active or passive in nature. Approximately 20 enhancement methods are reviewed in this paper, and their status in the United Kingdom discussed. An attempt is made to predict the effect more widespread use of enhancement would have on energy cost savings due to heat recovery. The use of enhancement in other unit operations is briefly discussed. Recent U.S. patents on enhancement methods are reviewed.     

E.S.R. spectra of the radicals produced in γ-irradiated diborane in the solid state

The hopping and Coulomb repulsion integrals of the Hubbard model, as applied to the NMP-TCNQ charge-transfer crystal, are found by an INDO calculation of the neutral and charged monomer and dimer of TCNQ. The ratio of these integrals is in satisfactory agreement with experiment, although the calculated integrals themselves are very different from the effective ones for electronic transport, due to renormalization, caused largely by counter-ion polarizability.     

The Neumann solution of the multiple scattering problem in a plane-parallel medium—IIc. The specific intensity in a semi-infinite space

Using a new formulation of the resolvent function [Rutily and Bergeat JQSRT 38, 61 (1987)], we solve the Milne integral equation for the mean intensity in a semi-infinite plane-parallel atmosphere. The specific intensity is then derived at any optical depth. By expanding the intensity in power series in the albedo, we derive the corresponding intensities of a n-times scattered radiation field propagating in a half-space (n ⩾/ 1).     

N.M.R. spectra of the XnAA′ Xn′ type

The method described previously for the calculation of the X spectrum for spin systems of of the X_nAA′X_n′ type is extended by means of magnetic equivalence factoring to cases in which the long-range coupling constant J_x is non-zero. This coupling is treated as a first-order perturbation to the energy levels obtained when J_x =0, and it is found that J_x may be measured directly from the separations between easily identified lines in the spectrum. A detailed account of the X ₃ AA′X ₃′ system is given, and the N.M.R. spectrum of fluoro-N,N′-dimethyl-1,3,2,4-diazadiphosphetidine is analysed. The spectral parameters obtained are discussed. A computer programme which calculates the spectra of systems involving magnetic equivalence is used to examine the validity of the approximations in the method.     

Erratum to “Lower bounds for the eigenvalues of the basic Dirac operator on a Riemannian foliation” [J. Geom. Phys. 51 (2004) 166–182]

We correct some statements in the paper mentioned in the title.     

Poloidal–toroidal decomposition in a finite cylinder. I: Influence matrices for the magnetohydrodynamic equations

The Navier–Stokes equations and magnetohydrodynamics equations are written in terms of poloidal and toroidal potentials in a finite cylinder. This formulation insures that the velocity and magnetic fields are divergence-free by construction, but leads to systems of partial differential equations of higher order, whose boundary conditions are coupled. The influence matrix technique is used to transform these systems into decoupled parabolic and elliptic problems. The magnetic field in the induction equation is matched to that in an exterior vacuum by means of the Dirichlet-to-Neumann mapping, thus eliminating the need to discretize the exterior. The influence matrix is scaled in order to attain an acceptable condition number.     

Soliton of Bose–Einstein condensate in a trap with rapidly oscillating walls: II. Analysis of the soliton behavior upon a decrease in the wall oscillation frequency

This work is a continuation of our study [1], in which a two-scale analytical approach to the investigation of a soliton oscillon in a trap with rapidly oscillating walls has been developed. In terms of this approach, the solution to the equation of motion of the soliton center is sought as a series expansion in powers of a small parameter, which is a ratio of the intrinsic frequency of slow soliton oscillations to the frequency of fast trap wall oscillations. In [1], we have examined the case ε ? 1, in which, to describe the motion of the soliton, it is sufficient to restrict the consideration to the zero approximation of the sought solution. However, when the frequency of wall oscillations begins to decrease, while the parameter begins to increase, it is necessary to take into account corrections to the zero approximation. In this work, we have calculated corrections of the first and second orders in to this approximation. We have shown that, with an increase in, the role played by the corrections related to fast oscillations of the trap walls increases, which results in a complex shape of the envelope of oscillations of the soliton center. It follows from our calculations that, if the difference between the amplitudes of wall oscillations is not too large, the analytical solution of the equation of motion of the soliton center will coincide very well with the numerical solution. However, with an increase in this difference, as well as with a decrease in the wall oscillation frequency, the discrepancy between the numerical and analytical solutions generally begins to increase. Regimes of irregular oscillations of the soliton center arise. With a decrease in the frequency of wall oscillations, the instability boundary shows a tendency toward a smaller difference between the wall oscillation amplitudes. In general, this leads to enlargement of the range of irregular regimes. However, at the same time, stability windows can arise in this range in which the analytical and numerical solutions correlate rather well with each other. Our comparative analysis of the analytical and numerical solutions has allowed us not only to study their properties in detail, but also to draw conclusions on the limits of applicability of the analytical approach.     

Nobel Prizes in the “light” of Vavilov–Cherenkov radiation. To the 125th anniversary of the birth of S.I. Vavilov

The objective of this paper is not a detailed review or an analysis of the studies in the field of high-energy physics initiated by the discovery of Vavilov–Cherenkov radiation, occurred more than 80 years ago at the Lebedev Physical Institute, and awarded Nobel Prizes. The paper is written to emphasize the historical significance of the discovery of the effect and its key role in further studies in high-energy physics, commended by the high award of the Nobel committee. In 1958, 24 years after the first publication about the new phenomenon, i.e., emission of electrons moving in matter with the superlight speed, discovered by P.A. Cherenkov under the supervision by S.I. Vavilov, the Nobel Prize was awarded to a group of scientists of the Lebedev Physical Institute, P.A. Cherenkov, I.M. Frank, and I.E. Tamm “for the discovery and explanation of the Cherenkov effect”. Since then, practical application of Vavilov–Cherenkov radiation is widely spread.     

Reply to the Comment by A.W. Thomas et al. on “The role of the orbital angular momentum in the proton spin”

The orbital angular momenta L^u and L^d of up- and down-quarks in the proton are estimated as functions of the energy scale as model independently as possible on the basis of Ji's angular-momentum sum rule. This analysis indicates that L ^u - L ^d is large and negative even at the low energy scale of nonperturbative QCD, in contrast to Thomas' similar analysis based on the refined cloudy bag model. We pursuit the origin of this apparent discrepancy and suggest that it may have a connection with the fundamental question of how to define quark orbital angular momenta in QCD.     

Curing One Discontinuity With Another: Comment on S. K. Ghosal Et Al., “On the Anisotropy of the Speed of Light on a Rotating Platform”

No Heading A recent paper by Ghosal, Raychaudhuri, Chowdhury, and Sarker (GRCS in the following) discussed a seven-years old argument in relativity concerning the speed of light as measured by an observer on board a rotating disk. The argument, put forward by the present author, contains the theoretical proof of an anisotropy in the speed of light in a reference frame comoving with the edge of a rotating disk even in the limit of zero acceleration. This conclusion challenges the internal consistency of the relativistic theories and undermines the basic tenet of the conventionality thesis of relativistic simultaneity. GRCS believe to be able to resolve the issue by recasting the original argument in the Galilean world and thereby exposing the weak points of the reasonings leading to the fallacy. We will defend the original argument and show that the treatment proposed by GRCS is as bad as the illness it asserts to cure.     

On the occurrence of b.c.c.–h.c.p. structural phase transition in Mo under pressure

Abstract

To resolve the controversy on the occurrence of a b.c.c.–h.c.p. transition in shock as well as static measurements in Mo, we have done more accurate total energy electronic structure calculations. Our results show that this phasetransition should occur at much higher pressures than suggested by earlier calculations.