Brownian motion in a rotating flow

The Langevin equations for a particle of an arbitrary shape and the correlation functions for the fluctuating forces, torques, or force-torque acting on the particle in a rotating flow are derived from the semimicroscopic level of coarse graining by using fluctuating hydrodynamics. In order to obtain the solution of the Navier-Stokes Langevin equation valid over the entire flow region, use is made of the method of matched asymptotic expansions in ( _f a²/v)^1/2 1. The cases of slow and rapid rotation are analyzed. It is shown that the fluctuation-dissipation theorems hold up to the order of ( _f a²/v)^1/2 in both slow and rapid rotation, and that the diffusivity tensor depends on the angular velocity of the fluid and becomes anisotropic.     

Theory of ferromagnetic resonance in metallic and insulator films

Simple intuitive explanations of the frequencies and intensitiesI of magnetostatic modes (with negligible exchange energy) and exchange modes (negligible microwave-field demagnetization energy) are given. The effects of explicit boundary conditions on the transverse, time-varying componentm of the magnetization (i.e., the amount of pinning) and the effects of inhomogeneities in the internal fieldH _i and saturation magnetizationM _s are discussed. A bulk inhomogeneity inM _s changes the effective exchange constant, while a bulk inhomogeneity inH _i lowers the fields for resonance of all high-order exchange modes by the same amount. The pinning conditions affect the values of andI of the exchange modes and the mixed exchange-magnetostatic modes, but have little effect on the magnetostatic modes. A surface-imperfection source of pinning and of the inhomogeneities inH _i andM _s is discussed.Part of this work was performed while the author was atNorth American Rockwell Science Center, Thousand Oaks, California.     

Dynamics of atoms in the high-temperature superconductor YBa2Cu3O7−δ

In order to obtain insight into the role played by the phonons in the superconducting phase transition, we have performed infrared reflectivity and inelastic neutron scattering experiments on single phase YBa₂Cu₃O_7–(0.1,T _c =94 K, T _10–90=1 K). These experimental results, together with published Raman scattering and specific heat data are used to determine the parameters of a rigid-ion model; the model is able to reproduce qualitatively the experimental data. On the basis of our model we derive and discuss the phonon density of states and the pattern of atomic displacements of some important vibrational modes. In particular, the model reveals the existence of high-frequency oxygen breathing modes and of low-frequency copper dimerization modes in both the CuO₃-chains and the CuO₂-planes. Furthermore, Jahn-Teller like oxygen modes exist in the chains. The possible role of these modes with respect to the pairing mechanism is discussed. In addition there exist low-frequency chain-degrading modes which favour jumps of oxygen atoms out of the CuO₃-chains into neighbouring vacant sites in the basal plane.     

Limiting angular velocity of realistic relativistic neutron star models

The Keplerian velocity as well as those frequencies at which instability against gravitational radiation-reaction sets in are calculated for rotating neutron star models of gravitational mass 1.5M . The investigation is based on four different, realistic neutron star matter equations of state. Our results indicate that the gravitational radiation instability sets in wellbelow (i.e., 63–71% of) the Keplerian frequency, and thatyoung neutron stars are limited to rotational periods greater than about 1 ms. In young and therefore hot (T10¹⁰ K) neutron stars them=5(±1) modes and in old stars after being spun up and reheated by mass accretion, them=4 and/orm=3 modes may set the limit on stable rotation.Dedicated to Prof. Dr. H.J. Mang on the occasion of his 60th birthday.     

Light source and geometrical requirements for the optimization of optical anemometry signals

The criteria for the design of optical arrangements for laser anemometry are formulated for reference-beam, two-beam and single-beam modes of operation. The dependence of useful light intensity upon optical path-length difference and number of axial laser modes is calculated. Laser power requirements are evaluated and the dependence upon band-pass filtering is quantitatively assessed. A new two-channel integrated-optical unit, with light-path compensation, and embodying the proposed design criteria, is described.Nomenclature c velocity of light - D _1/e diameter of laser beam at 1/e-point - d half distance separating the beams leaving the lens - d _m effective diameter of measuring control volume - d _ph diameter of aperture in front of photo-multiplier - d _r waist diameter of focused reference beam - d _s waist diameter of scattering light beam - d _l waist diameter of fucused light beam - F f-number of lens - scattering function introduced in Mie's theory - f signal frequency - f bandwidth of filter - f _D Doppler line width of laser radiation - f _G effective bandwidth of gain envelope of a laser - f _M frequency difference between two adjacent axial modes - h Planck constant (6.6256×10^–34J sec) - K 2/ wave number - L cavity length of laser - l _m length of measuring control volume - m total number of axial modes of laser - M magnification (a/b) - N _fr number of fringes in crossing region of the two light beams - N _ph number of fringes seen by photomultiplier - N _s number of photons scattered per particle passage - N _e number of electrons leaving photo cathode per unit time - P _l total light power emitted by laser - P _s total light power scattered by particle - Q _scat scattering coefficient - R distance from particle centre to point on plane of observation - r _p radius of scattering particle - u velocity component perpendicular to fringe pattern - _fr distance between fringes inside measuring control volume - _c efficiency of light collecting system - _q overall quantum efficiency of photodetector - g _q coordinate measuring angle from the optical axis - half angle between wave fronts - wave length of light - frequency of incident light wave - _e standard deviation of electron flux - transit time of scattering particle - solid angle - d solid angle element This paper was presented at the Conference on Electro-optic Systems in Flow Measurement, Southampton, September 1972.     

Equal-phase-velocity propagation for the TE and TM modes of planar metal-clad optical waveguides

An asymmetrical four-layered metal-clad dielectric optical waveguide can support the TE_N and TM_N modes forN0 with the same phase-velocity if the core thickness,t ₃, and the buffer layer thickness,t ₂, are suitably chosen. Only metals that have a negative real part ₁ of their complex permittivity at optical frequencies are considered as the cladding material. It is shown that the application of a lossless approximation which set ₁=0 enables the development of a real expression which may be solved directly for the values oft ₂ andt ₃ that are required to achieve the equal-phase-velocity characteristic. Parametric plots for the guide dimensions are presented for representative waveguides and it is shown that an appropriate choice oft ₂ andt ₃ will reduce the absorption losses of the TE and TM modes to negligible levels. This property of the waveguide will find application in thin film optical devices such as polarization rotation modulators that require the simultaneous propagation of TE and TM polarized waves.     

C*-dynamical systems that are asymptotically highly anticommutative

It is shown that with probability 1 on , resp. ongx the irrational rotation algebra with respect to the CAT map and the generalized Price-Powers shiftA _X are asymptotically highly anticommutative.     

Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice Boltzmann BGK model

In this paper we analytically solve the velocity of the lattice Boltzmann BGK equation (LBGK) for several simple flows. The analysis provides a framework to theoretically analyze various boundary conditions. In particular, the analysis is used to derive the slip velocities generated by various schemes for the nonslip boundary condition. We find that the slip velocity is zero as long as fe=0 at boundaries, no matter what combination of distributions is chosen. The schemes proposed by Nobleet al. and by Inamuroet al. yield the correct zeroslip velocity, while some other schemes, such as the bounce-back scheme and the equilibrium distribution scheme, would inevitably generate a nonzero slip velocity. The bounce-back scheme with the wall located halfway between a flow node and a bounce-back node is also studied for the simple flows considered and is shown to produce results of second-order accuracy. The momentum exchange at boundaries seems to be highly related to the slip velocity at boundaries. To be specific, the slip velocity is zero only when the momentum dissipated by boundaries is equal to the stress provided by fluids.     

Planar ferromagnets: Low-velocity kink dynamics near to the easy plane and static solitary spin structures bifurcating from the azimuthal kink

Ferromagnetic spin chains with planar single ion anisotropy, exchange anisotropy and with an external fieldb applied in the easy plane are considered in classical continuum approximation. It is pointed out that in the static case the sine-Gordon approximation is only accidentally exact: it breaks down in the neighborhood of the easy plane already for infinitesimal kink velocities, unlessb0. It is also shown that at certain valuesb _n ,n=0, 1, 2, 3, ... of the applied field there bifurcate from the static in-plane kink (azimuthal kink) other static out-of-plane kink solutions. The azimuthal kink is linearly stable below the critical strengthb ₀ of the applied field. For increasingb, there occurs at each of the bifurcation fieldsb ₁<b ₂<b ₃... an instability with respect to an additional mode. In the undamped system the instabilities atb _2k ,k=0, 1, 2, ... are associated with the recently discovered soft-velocity change mechanism of the critical slowing-down, whereas atb _2k+1 , soft localized dynamic modes occur. If phenomenological spin damping is included, soft relaxation modes occur in the neighborhood of all the bifurcation fields.Work supported by the Swiss National Science Foundation     

Statistical mechanics of quantum mechanical particles with hard cores

The states of a quantum mechanical system of hard core particles are characterized as a convex weak *compact subset of the states over aC* algebra associated with the canonical (anti-) commutation relations. It is shown that the mean conditional entropy, i.e. entropy minus energy, can be defined as an affine upper semi-continuous function over theG-invariant hard core states whereG is an invariance group containing space translations. An abstract definition of the pressure and equilibrium states is given in terms of the maximum of the conditional entropy and it is shown that the pressureP _S obtained in this way satisfiesPP _S P whereP andP are the thermodynamic pressures obtained from the usual Gibbs formalism with elastic wall, and repulsive wall, boundary conditions respectively. A number of additional results concerning the equilibrium states are also given.     

A Fitting Procedure for Magnetic Multiphase Materials Mössbauer Spectra

In this work a practical method of fitting complex multiphase Mössbauer effect spectra is proposed. The task is simplified imposing specific restrictions to the analysing functions, which are appropriate for cases where the component phases spectra do not change substantially during the process under study. The ME spectra can be analysed using the phases subspectra, by defining only a reduced number of parameters. The constraints are equivalent to assume a Doppler velocity transformation v=(v–_m)B _m0/B _m+_m0 for each phase, where _m and B _m are fitting parameters containing information on the phase mean isomer shift and hyperfine field and _m0 and B _m0 their reference values. In this manner physically meaningful results are easy to obtain. The idea was applied to partially nitrogenated R₂Fe₁₇N _x (R= Sm and Y) and partially hydrogen-decomposed Nd–Fe–B materials.     

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.     

Exact solutions of the SO(3)-invariant nonlinear O-model in the special theory of relativity

Exact solutions for the four-dimensional SO(3)-invariant-model are obtained using the relation between groups of isometric motions in the space-time V₄ and chiral space U_N. A means for separating corresponding solutions in the two-dimensional-model is found. It is shown that the classical instanton and meron solutions correspond to consistent rotation of V₄ and U₂, and a general solution for this case is obtained. Four-dimensional analogs of free fields for two-dimensional-models are considered using a local approach. A non-trivial general solution which diverges logarithmically is given for the SO(N)-invariant-model.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 22–26, October, 1985.In conclusion I would like to thank G. G. Ivanov for his statement of the problem and useful discussions and D. Maison from Munich for delivering study [10].     

Besov spaces and the multifractal hypothesis

Parisi and Frisch proposed some time ago an explanation for multiscaling of turbulent velocity structure functions in terms of a multifractal hypothesis, i.e., they conjecture that the velocity field has local Hölder exponents in a range [h _min,h _max], with exponents <h occurring on a setS(h) with a fractal dimensionD(h). Heuristic reasoning led them to an expression for the scaling exponentz _p ofpth order as the Legendre transform of the codimensiond-D(h). We show here that a part of the multifractal hypothesis is correct under even weaker assumptions: namely, if the velocity field hasL ^p -mean Hölder indexs, i.e., if it lies in the Besov spaceB _p ^s, , then local Hölder regularity is satisfied. Ifs<d/p, then the hypothesis is true in a generalized sense of Hölder space with negative exponents and we discuss the proper definition of local Hölder classes of negative index. Finally, if a certain box-counting dimension exists, then the Legendre transform of its codimension gives the scaling exponentz _p , and, more generally, the maximal Besov index of order,p, ass _p =z _p /p. Our method of proof is derived from a recent paper of S. Jaffard using compactly-supported, orthonormal wavelet bases and gives an extension of his results. We discuss implications of the theorems for ensemble-average scaling and fluid turbulence.     

Modes in weakly guiding elliptical optical fibres

Approximate and much simplified dispersion relations are obtained for the problem of optical wave propagation within weakly guiding elliptical fibres. The refractive index difference between the core and its cladding of weakly guiding optical fibres that are contenders for use as practical optical communication lines is very small; i.e., (n ₁/n₀–1) 1 wheren ₁ is the core index andn ₀ is the cladding index. These greatly simplified dispersion relations are then used to calculate the propagation constants for several higher order modes on an elliptical optical fibre.Supported partly by NELC, San Diego; this paper was presented at 1974 URSI Electromagnetic Waves Conference, London.     

New phenomena in homoepitaxial growth of metals

The growth of Pt(111) by Pt vapour deposition is studied by He diffraction as a function of substrate temperature and deposition rate. At a deposition rate of about 2.5×10^–2 monolayers/second several growth modes are observed: layer-by-layer (2D-) growth at 450 KT _s800 K, multilayer (3D-) growth at 340 KT _s450 K and reentrant layer-by-layer (2D-) growth at T _s340 K. The observed growth modes and in particular the reentrant 2D-growth are shown to be characteristic of growing Pt(111) under clean conditions, i.e. not influenced by contaminants. The influence of the intra- and interlayer mass transport on the growth mode is discussed in the light of experimental and simulation results. The 3D-growth mode is attributed to the existence of an activation barrier which suppresses the descent of adatoms from the top of the growing adatom islands onto the lower terraces. The barrier can be overcome by thermal adatoms at T _s450 K enabling interlayer mass transport which leads to 2D-growth. The reentrant 2D-growth occurs due to a break down of this barrier for small, irregularly shaped islands.     

Analysis of the Electronic Vibrational Spectra of Bisanthene by Calculating Normal Modes

At 4.2 K, the quasiline fluorescence and fluorescence-excitation spectra (in the region of the S ₁ S ₀- and S ₂ S ₀ transitions) of bisanthene in n-hexane have been obtained. Using the MO/M8ST method, the calculation of the A _g normal modes in the S ₀, S ₁, and S ₂ electronic states was carried out for the bisanthene molecule; the relative intensities of the transitions in the corresponding vibronic spectra were also calculated. The analysis of the results of calculations and experiment made it possible to draw conclusions on the form of the modes for a number of normal vibrations which are active in the bisanthene vibronic spectra.     

Far-infrared absorption of the superionic conductor Li3N. temperature and isotope effects

The far-infrared absorption spectrum (20–250cm^–1) of the superionic conductor Li₃N —with⁶Li- and⁷Li-isotopes in the starting material—has been measured for different polarizations and temperatures (4–150 K). TheE c spectrum yields two lines near 80 and 140 cm^–1, which are not observed forE c. From the isotopic frequency ratio ( ₆/ ₇1.07) and from the comparison to lattice dynamics it is concluded that these lines are due to resonant modes, weakly coupled to the lattice. Measurements of the isotope effects on the dielectric properties (10 Hz to 1 MHz) establish that the local diffusive type motion in shallow potentials and the low lying resonant modes originate from the same defect system (including Li-ions in non-regular positions).     

E(transverse optical)-mode properties in the LiTaO3: Nd crystal at room temperature

E(TO)-mode properties in LiTaO₃:Nd crystal were examined by analyzing the Raman spectra measured.E(TO) modes appear in the transverseA ₁ spectrum. Their intensities obviously increase in theE andE+A ₁ mixed-symmetry spectra but decrease in theE spectrum which shows new vibrational modes. In particular, in the transverse-E spectrum of y(xz) geometry, the properties ofE(TO) modes are similar to those of pure LiTaO₃ of the same geometry, whereas in the transverse-E spectrum in x(yz) geometry these modes are turned intoA ₁ (TO) modes. We attribute these properties to both the surface strain produced by mechanical polishing of the sample and the microstructural change of the LiTaO₃ crystal resulting from Nd doping.     

Theory of the diffusive glide of dislocations with narrow kinks

A theory of glide velocity of a dislocation with narrow kinks which encounter spatially periodic, relatively high energy barriers is developed. The thermally activated generation of double kinks is considered as the mechanism of the dislocation movement. It is assumed that the saddle point is determined by the elastic interaction between the two kinks and that diffusion of the kinks is rate controlling. According to this theory velocities of screw dislocations in -iron are calculated in dependence on temperature and the applied stress with 2E _k =0·68 eV andE=0·07 eV (E _k is the energy of an isolated kink,E is the second-order Peierls energy). Relations to three other theories, which may be considsred for calculation of velocities of screw dislocations in b.c.c. metals are discussed and demonstrated by numerical calculations for iron. It appears that there are no serious objections suggested by experiments which might be raised against the screw dislocation velocities in iron calculated according to the presented theory.