Low-temperature reaction of magnesium with fluorobenzene

The low-temperature reaction of magnesium with fluorobenzene has been investigated. Joint condensation of magnesium and fluorobenzene vapours at low temperatures quantitatively gave phenylmagnesium fluoride in one stage.     

On the Point-Particle (Newtonian) Limit¶of the Non-Linear Hartree Equation

We consider the nonlinear Hartree equation describing the dynamics of weakly interacting non-relativistic Bosons. We show that a nonlinear M?ller wave operator describing the scattering of a soliton and a wave can be defined. We also consider the dynamics of a soliton in a slowly varying background potential W(ɛx). We prove that the soliton decomposes into a soliton plus a scattering wave (radiation) up to times of order ɛ⁻¹. To leading order, the center of the soliton follows the trajectory of a classical particle in the potential W(ɛx). Received: 30 June 2000 / Accepted: 25 June 2001     

Deuterium NMR studies of inositol liquid crystals [1]

Deuterium NMR investigations are presented on members of two new mesogenic series derived from the naturally occurring stereoisomers myo- and scW/o-inositol. Tetraethers of these two series exhibit thermotropic columnar phases in which the columns are apparently formed by stacked hydrogen bonded dimers of these molecules which chemically are vicinal diols. Deuterium NMR measurements were performed on the tetraoctyl homologues 2e (a cis diol) and 3e (a trans diol) of these series. We have investigated mixtures of these diols with small amounts of benzene-d₆ as probe molecules as well as samples of the neat diol compounds deuteriated at their hydroxyl groups. The results obtained show that the mesophases of both compounds are uniaxial and align partially in a magnetic field upon slow cooling from their isotropic liquids. The alignment is with the director parallel to the field direction indicating that the anisotropic magnetic susceptibility of this mesophase is positive. The deuterium quadrupole splitting of the benzene-d₆ probe in both systems is temperature dependent and in the trans diol 3e it even changes sign. This is interpreted in terms of a model in which the benzene-d₆ probe equilibrates rapidly between two (or more) solvation sites with quadrupole splittings of opposite signs The deuterium spectra of the neat deuterium labelled cis diol 2e exhibit two different signals due to the two deuterons which are located at the axial and equatorial hydroxyl groups. This indicates that there is no fast intra- or intermolecular exchange of the hydroxyl hydrogens. The overall quadrupole splittings of the hydroxyl deuterons in this compound are highly reduced compared to their static values and this is interpreted in terms of motional modes involving both reorientation of the hydroxyl deuterons about their C-O axis and overall reorientation of the molecules (or pairs of molecules) around the columnar axes. The corresponding spectra of the neat deuteriated trans diol 3e exhibit a single spectrum indicating that both hydroxyl deuterons in this compound are equivalent, or very nearly so. Within the mesophase region the spectrum undergoes gradual changes due to the increase in the molecular mobility, but the overall motional narrowing is less than in the cis isomer 2e. Apparently due to stronger hydrogen bonding in the trans isomer 3e the precession of the hydroxyl groups is hindered and a fast molecular reorientation is only possible at high temperatures.     

Dynamics of a pair of coupled nonlinear oscillators

A pair of coupled classical oscillators with a general potential and general form of coupling is investigated. For general potentials, the single-frequency solution is shown to be stable for small excitations. For special potentials, such system remains stable for an arbitrary excitation. In both cases, the stability does not depend on the form of coupling. Transition to the instability regime follows from the way how nonlinear potential entrains the energy transfer between the oscillators. Relation between the existence of multi-frequency quasi-periodic or periodic solutions and the instability of single-frequency ones is discussed.     

An optical method and neural network for surface roughness measurement

The measurement of surface roughness using stylus equipment has several disadvantages. A non-contact optical method is needed for measuring the surface roughness of engineering metals with improved accuracy. One candidate for an optical method is the use of a laser source, where the laser light intensity reflected from the surface represents the surface roughness of the illuminated area. A relation can be developed between the reflected laser beam intensity and the surface roughness of the metal. The present study examines the measurement of the surface roughness of the stainless steel samples using a He-Ne laser beam. In the measurement a Gaussian curve parameter of a Gaussian function approximating the peak of the reflected intensity is measured with a fast response photodetector. In order to achieve this, an experimental setup is designed and built. In the experimental apparatus, fiber-optic cables are used to collect the reflected beam from the surface. The output of the fiber-optic system is fed to a back-propagation neural network to classify the resulting surface profile and predict the surface roughness value. The results obtained from the present study are then compared with the stylus measurement results. It is found that the resolution of the surface texture improves considerably in the case of optical method and the neural network developed for this purpose can classify the surface texture according to the control charts developed mathematically.     

Diffusion-limited annihilation in inhomogeneous environments

We study diffusion-limited (on-site) pair annihilation A + A → 0 and (on-site) fusion A + A → A which we show to be equivalent for arbitrary space-dependent diffusion and reaction rates. For one-dimensional lattices with nearest neighbour hopping we find that in the limit of infinite reaction rate the time-dependent n-point density correlations for many-particle initial states are determined by the correlation functions of a dual diffusion-limited annihilation process with at most 2n particles initially. Furthermore, by reformulating general properties of annihilating random walks in one dimension in terms of fermionic anticommutation relations we derive an exact representation for these correlation functions in terms of conditional probabilities for a single particle performing a random walk with dual hopping rates. This allows for the exact and explicit calculation of a wide range of universal and non-universal types of behaviour for the decay of the density and density correlations.     

Theory of Non-Equilibrium Stationary States as a Theory of Resonances

We study a small quantum system (e.g., a simplified model for an atom or molecule) interacting with two bosonic or fermionic reservoirs (say, photon or phonon fields). We show that the combined system has a family of stationary states parametrized by two numbers, T ₁ and T ₂ (‘reservoir temperatures’). If T ₁ ≠ T ₂, then these states are non-equilibrium stationary states (NESS). In the latter case we show that they have nonvanishing heat fluxes and positive entropy production and are dynamically asymptotically stable. The latter means that the evolution with an initial condition, normal with respect to any state where the reservoirs are in equilibria at temperatures T ₁ and T ₂, converges to the corresponding NESS. Our results are valid for the temperatures satisfying the bound min (T ₁,T ₂) > g ^{2 + α}, where g is the coupling constant and 0 < α < 1 is a power related to the infra-red behaviour of the coupling functions. Submitted: March 20, 2006. Revised: March 19, 2007. Accepted: May 11, 2007. Marco Merkli: Partly supported by an NSERC PDF, the Institute of Theoretical Physics of ETH Zürich, Switzerland, the Departments of Mathematics of McGill University and the University of Toronto, Canada. Matthias Mück: Supported by DAAD under grant HSP III. Israel Michael Sigal: Supported by NSERC under grant NA7901.     

Effect of γ-ray irradiation on the magnetic properties of NdFeB and Fe–Cr–Co permanent magnets

The effect of γ-ray irradiation on the magnetic properties of NdFeB and Fe–Cr–Co permanent magnets has been investigated. The magnetic flux loss of two kinds of magnets before and after irradiation was measured. Results show that the effect of γ-ray irradiation on the magnetic properties of sintered NdFeB is not so obvious as that on Fe–Cr–Co magnet. Irradiation-induced damage from γ-ray for the Fe–Cr–Co magnets was characterized for the first time. The decline of permanent magnetic properties of Fe–Cr–Co magnet induced by γ-ray irradiation is reversible except for the maximum energy product (BH)_max. The difference of coercivity mechanism between these two kinds of permanent magnets is responsible for the different dependence of magnetic properties loss induced by γ-ray irradiation.     

Characteristics of soft magnetic composite material under rotating magnetic fluxes

This paper reports the measurement of magnetic properties of the soft magnetic composite material SOMALOY^TM 500 in a square sample under different patterns of flux density with 2D magnetic excitations. The test system, principle of measurement, magnetic power loss calculation, and methods of correction for misalignment of H surface sensing coils are presented. The experimental results show that although nominally isotropic, the SOMALOY^TM 500 sample exhibits some anisotropy. The results are useful in the design and performance analysis of rotating electrical machines.