Hollow-Cathode Low-Pressure Arc Discharges and Their Application in Plasma Generators and Charged-Particle Sources

This paper presents the results of a study of hollow-cathode arc discharges which generate gas-discharge plasmas of densities 10¹⁰–10¹² cm^–3 in large volumes (1 m³) at low pressures (10^–2–1 Pa) and at discharge currents of up to 200 A. Consideration is given to the design and peculiarities of hot-cathode and cold-cathode discharge systems. The parameters of plasma generators and charged-particle sources where use is made of arc discharges are cited and the problems of the most efficient application of such systems in technological processes of solid surface modification are discussed.     

The Charge–Mass–Spin Relation of Clifford Polyparticles, Kerr–Newman Black Holes and the Fine Structure Constant

A Clifford-algebraic interpretation is proposed of the charge, mass, spin relationship found recently by Cooperstock and Faraoini, which was based on the Kerr–Newman metric solutions of the Einstein–Maxwell equations. The components of the polymomentum associated with a Clifford polyparticle in four dimensions provide for such a charge, mass, spin relationship without the problems encountered in Kaluza–Klein compactifications which furnish an unphysically large value for the electron charge. A physical reasoning behind such charge, mass, spin relationship is provided, followed by a discussion on the geometrical derivation of the fine structure constant by Wyler, Smith, Gonzalez-Martin and Smilga. To finalize, the renormalization of electric charge is discussed and some remarks are made pertaining the modifications of the charge–scale relationship, when the spin of the polyparticle changes with scale, that may cast some light into the alleged Astrophysical variations of the fine structure constant.     

New exact solutions of the Dirac equation. V

Four types of external electromagnetic fields allowing an exact solution of the Dirac and Klein — Gordon equations are considered. The motion of the electron in such fields is of a specific character; however, from the mathematical point of view some of the problems reduce to cases already studied in earlier papers [1–4].Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 106–112, September, 1975.     

Correlation between P chemical shift tensor and local structure in lithium cyclohexaphosphates Li6P6O18·3H2O and Li6P6O18

To understand the surprising behavior between the variations of the P′–P–P″ angles and the correlated variations of the O′–P–O″ ones, two lithium cyclohexaphosphate compounds Li₆P₆O₁₈·3H₂O and Li₆P₆O₁₈ are studied by solid state nuclear magnetic resonance (NMR) spectroscopy. The two compounds exhibit the same [P₆O₁₈]⁶⁻ ring anions but with 3m or internal symmetry, respectively. Such symmetries induce local distortions that are exhibited by NMR spectroscopy. One-dimensional (1D) NMR gives information on structural sites of ⁷Li and ³¹P ions and the crystallographic non-equivalencies are observed. Nevertheless, in the anhydrous compound, X-ray diffraction and NMR results do not completely agree and some discrepancy exists between the number of sites observed with the first technique and the number of lines exhibited in the NMR spectra either for ⁷Li or ³¹P nuclei. This problem is elucidated by using 2D double quantum NMR spectroscopy coupled with theoretical considerations. We find that the ³¹P chemical shift tensor is dependent on the deviations of the O–P–O angles from those in the regular tetrahedron. Within the same empirical model, we suggest that the surprising behavior between the variations of the P′–P–P″ and the ones of the O′–P–O″ is related to the overall charge on the PO₄ group. We also find the positions of the isotropic lines for ⁷Li essentially depend on the site co-ordination of this nuclei.     

Decoherence and Bare Mass Induced by Nonconformal Metric Fluctuations

The effects, upon the Klein–Gordon field, of nonconformal stochastic metric fluctuations, are analyzed. It will be shown that these fluctuations allow us to consider an effective mass, i.e., the mass detected in a laboratory is not the parameter appearing in the Klein–Gordon equation, but a function of this parameter and of the fluctuations of the metric. In other words, in analogy to the case of a nonrelativistic electron in interaction with a quantized electromagnetic field, we may speak of a bare mass, where the observed mass shows a dependence upon the stochastic terms included in the metric. Afterwards, we prove, resorting to the influence functional, that the energy–momentum tensor of the Klein–Gordon field inherites this stochastic behavior, and that this feature provokes decoherence upon a particle immersed in the region where this tensor is present.     

Semi-insulating GaAs

Conclusion In a short review on SI-GaAs it is not possible to exhaust all problems related to this important material. We have reviewed the present stage of knowledge about the main defects in SI-GaAs which are responsible for semi-insulating properties of this material and we pointed out some problems concerning the determination of carrier densities and mobilities in SI-GaAs in the dark and at low electric fields. Special problems arise when this material is investigated under illumination or at high electric fields due to the generation of nonequilibrium carriers and various trapping and recombination processes.Invited talk at the International Conference on Radiative Recombination and Related Phenomena in III–V Compound Semiconductors, Prague, 4–7 October, 1983.     

Analytical and numerical study of coupled atomistic-continuum methods for fluids

The stability and convergence rate of coupled atomistic-continuum methods are studied analytically and numerically. These methods couple a continuum model with molecular dynamics through the exchange of boundary conditions in the continuum-particle overlapping region. Different coupling schemes, including velocity–velocity, flux–velocity, velocity–flux and flux–flux, are studied. It is found that the velocity–velocity and flux–velocity schemes are stable. The flux–flux scheme is weakly unstable. The stability of the velocity–flux scheme depends on the parameter T_c which is the length of the time interval between successive exchange of boundary conditions. It is stable when T_c is small and unstable when T_c is large. For steady-state problems, the flux–velocity scheme converges faster than the other coupling schemes.     

Computation of multiphase systems with phase field models

Phase field models offer a systematic physical approach for investigating complex multiphase systems behaviors such as near-critical interfacial phenomena, phase separation under shear, and microstructure evolution during solidification. However, because interfaces are replaced by thin transition regions (diffuse interfaces), phase field simulations require resolution of very thin layers to capture the physics of the problems studied. This demands robust numerical methods that can efficiently achieve high resolution and accuracy, especially in three dimensions. We present here an accurate and efficient numerical method to solve the coupled Cahn–Hilliard/Navier–Stokes system, known as Model H, that constitutes a phase field model for density-matched binary fluids with variable mobility and viscosity. The numerical method is a time-split scheme that combines a novel semi-implicit discretization for the convective Cahn–Hilliard equation with an innovative application of high-resolution schemes employed for direct numerical simulations of turbulence. This new semi-implicit discretization is simple but effective since it removes the stability constraint due to the nonlinearity of the Cahn–Hilliard equation at the same cost as that of an explicit scheme. It is derived from a discretization used for diffusive problems that we further enhance to efficiently solve flow problems with variable mobility and viscosity. Moreover, we solve the Navier–Stokes equations with a robust time-discretization of the projection method that guarantees better stability properties than those for Crank–Nicolson-based projection methods. For channel geometries, the method uses a spectral discretization in the streamwise and spanwise directions and a combination of spectral and high order compact finite difference discretizations in the wall normal direction. The capabilities of the method are demonstrated with several examples including phase separation with, and without, shear in two and three dimensions. The method effectively resolves interfacial layers of as few as three mesh points. The numerical examples show agreement with analytical solutions and scaling laws, where available, and the 3D simulations, in the presence of shear, reveal rich and complex structures, including strings.     

High-order compact exponential finite difference methods for convection–diffusion type problems

A class of high-order compact (HOC) exponential finite difference (FD) methods is proposed for solving one- and two-dimensional steady-state convection–diffusion problems. The newly proposed HOC exponential FD schemes have nonoscillation property and yield high accuracy approximation solution as well as are suitable for convection-dominated problems. The O(h⁴) compact exponential FD schemes developed for the one-dimensional (1D) problems produce diagonally dominant tri-diagonal system of equations which can be solved by applying the tridiagonal Thomas algorithm. For the two-dimensional (2D) problems, O(h⁴ + k⁴) compact exponential FD schemes are formulated on the nine-point 2D stencil and the line iterative approach with alternating direction implicit (ADI) procedure enables us to deal with diagonally dominant tridiagonal matrix equations which can be solved by application of the one-dimensional tridiagonal Thomas algorithm with a considerable saving in computing time. To validate the present HOC exponential FD methods, three linear and nonlinear problems, mostly with boundary or internal layers where sharp gradients may appear due to high Peclet or Reynolds numbers, are numerically solved. Comparisons are made between analytical solutions and numerical results for the currently proposed HOC exponential FD methods and some previously published HOC methods. The present HOC exponential FD methods produce excellent results for all test problems. It is shown that, besides including the excellent performances in computational accuracy, efficiency and stability, the present method has the advantage of better scale resolution. The method developed in this article is easy to implement and has been applied to obtain the numerical solutions of the lid driven cavity flow problem governed by the 2D incompressible Navier–Stokes equations using the stream function-vorticity formulation.     

R-Matrices for Leibniz Algebras

Leibniz agebras are a generalization of Lie algebras, where no symmetry properties of the bracket are required. In this Letter we introduce a notion of R-matrices for this structure and the related Yang–Baxter equations, and discuss some of their basic properties.     

Hawking radiation and Dirac quasinormal modes of 3D EMDλ black holes

Some properties of the Hawking radiation emitted by the family of black holes of the Einstein–Maxwell–Dilaton with cosmologicalconstant theory in three dimensions found by Chan and Mann are studiedusing the complex paths method and the Damour–Ruffini method. Theexact values of the quasinormal frequencies of the massless Diracfield propagating on a particular black hole of this family arecalculated. Taking as a basis the results obtained for the values ofthe quasinormal frequencies the instability of some modes isdiscussed. The extension of these results to the black holes of theEinstein–Maxwell–Dilaton theory in four dimensions is studied in theappendix.     

Notes on technique in the laboratory determination of e/m for electrons by the magnetron method

The paper concerns a fairly common basic error in the formulation of the laboratory experiment on the determination of e/m for electrons by the magnetron method, in that a diode is replaced by a tube with several grids connected to the cathode. It is shown that in that case the experimental value for the specific charge as given by the usual formula is dependent on the plate voltage. Above some plate voltage (the critical value), the relationship to the plate voltage becomes linear, so a value exceeding the tabulated value by a substantial factor can be obtained by increasing the plate voltage appropriately. On the other hand, the tabulated value is obtained only for a single plate voltage. However, even this value lies in the range of voltages where the working formula is inapplicable. Therefore, this approach is simply one of adjusting the observed result to the tabulated value.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 79–88, April, 1976.     

Metastability and Convergence to Equilibrium for the Random Field Curie–Weiss Model

We study a dynamics for the magnetization of the random field Curie–Weiss model. A metastable behavior is exhibited and asymptotic estimates on the speed of convergence to equilibrium are given. The results are given almost surely and in law with respect to the realizations of the random magnetic fields.     

Microstructure and surface wear resistance in rapidly quenched Fe–Cr–B alloy spray coatings

Fe–Cr–B alloy coatings were fabricated by thermal spraying and investigated in this research as to its wear-resistance and friction properties. The Fe–Cr–B spray-coated layers exhibited much higher wear resistance and significantly low friction coefficient in comparison with those of Fe–Cr base tool steel. The present paper reports that the presence of amorphous surface film formed during the sliding wear will be the main cause of noticeably improved friction properties and wear resistance. It was also observed that the Fe–Cr solid solution phase with supersaturated B and Si was the phase contributing to the crystalline-to-amorphous transition induced by sliding wear. These results imply the possible application of the present alloy coatings to the lubricant-free sliding systems in which the use of organic lubricants is limited or prohibited.     

A General Deterministic Treatment of Derivatives in Particle Methods

A unified approach to approximating spatial derivatives in particle methods using integral operators is presented. The approach is an extension of particle strength exchange, originally developed for treating the Laplacian in advection–diffusion problems. Kernels of high order of accuracy are constructed that can be used to approximate derivatives of any degree. A new treatment for computing derivatives near the edge of particle coverage is introduced, using “one-sided” integrals that only look for information where it is available. The use of these integral approximations in wave propagation applications is considered and their error is analyzed in this context using Fourier methods. Finally, simple tests are performed to demonstrate the characteristics of the treatment, including an assessment of the effects of particle dispersion, and their results are discussed.     

Padé–Legendre approximants for uncertainty analysis with discontinuous response surfaces

A novel uncertainty propagation method for problems characterized by highly non-linear or discontinuous system responses is presented. The approach is based on a Padé–Legendre (PL) formalism which does not require modifications to existing computational tools (non-intrusive approach) and it is a global method. The paper presents a novel PL method for problems in multiple dimensions, which is non-trivial in the Padé literature. In addition, a filtering procedure is developed in order to minimize the errors introduced in the approximation close to the discontinuities. The numerical examples include fluid dynamic problems characterized by shock waves: a simple dual throat nozzle problem with uncertain initial state, and the turbulent transonic flow over a transonic airfoil where the flight conditions are assumed to be uncertain. Results are presented in terms of statistics of both shock position and strength and are compared to Monte Carlo simulations.     

The Thirring interaction in the two-dimensional axial–current–pseudoscalar derivative coupling model

We reexamine the two-dimensional model of massive fermions interacting with a massless pseudoscalar field via axial-current derivative coupling. The hidden Thirring interaction in the axial-derivative coupling model is exhibited compactly by performing a canonical field transformation on the Bose field algebra and the model is mapped into the Thirring model with an additional vector–current–scalar derivative interaction (Schroer–Thirring model). The Fermi field operator is rewritten in terms of the Mandelstam soliton operator coupled to a free massless scalar field. The charge sectors of the axial-derivative model are mapped into the charge sectors of the massive Thirring model. The complete bosonized version of the model is presented. The bosonized composite operators of the quantum Hamiltonian are obtained as the leading operators in the Wilson short distance expansions.     

Rotational symmetry of solutions of some nonlinear problems in statistical mechanics and in geometry

The method of moving planes is used to establish a weak set of conditions under which the nonlinear equation –u(x)=V(|x|)e ^u(x) ,x² admits only rotationally symmetric solutions. Additional structural invariance properties of the equation then yield another set of conditions which are not originally covered by the moving plane technique. For instance, nonmonotonicV can be accommodated. Results for –u(y)=V(y)e ^u(y) –c, withyS ², are obtained as well. A nontrivial example of broken symmetry is also constructed. These equations arise in the context of extremization problems, but no extremization arguments are employed. This is of some interest in cases where the extremizing problem is neither manifestly convex nor monotone under symmetric decreasing rearrangements. The results answer in part some conjectures raised in the literature. Applications to logarithmically interacting particle systems and geometry are emphasized.     

Non-ideal behavior of mixed micelles of cationic gemini surfactants with varying spacer length and anionic surfactants: A conductimetric study

Mixtures of cationic and anionic surfactants (catanionic mixtures) are often highly non-ideal, exhibiting strong synergism in their interfacial properties, manifested for instance in significant reduction of the mixture critical micelle concentration (cmc) and enhanced adsorption onto surfaces. The magnitude of such effects is of fundamental interest and has important application-related uses (e.g. in detergent formulation). In this work, the micellization process of mixtures of cationic gemini surfactants of the alkanediyl-α,ω-bis(alkyl dimethylammonium bromide) type, denoted by 12–n–12 (where n is the spacer length), with several common anionic surfactants has been investigated by electric conductivity. For the purpose of comparison, cationic–cationic mixtures, where dodecyltrimethylammonium bromide is the second cationic surfactant, have also been investigated. The cationic/anionic mixtures show relatively significant deviations from ideal behavior, depending on the structure of the gemini surfactant and the anionic surfactant. The interaction parameter β₁₂, within Rubingh's non-ideal model for mixed micelles, has been calculated for each mixture, as well as the mixed micelle composition as a function of mixture composition. The observed synergism in the different mixtures is interpreted in terms of the molecular structure of the surfactants and corresponding head–head and chain–chain interactions.     

Dirac–Kähler Equation

Tensor, matrix, and quaternion formulations of Dirac–Kähler equation for massive and massless fields are considered. The equation matrices obtained are simple linear combinations of matrix elements in the 16-dimensional space. The projection matrix-dyads defining all the 16 independent equation solutions are found. A method of computing the traces of 16-dimensional Petiau–Duffin–Kemmer matrix product is considered. We show that the symmetry group of the Dirac–Kähler tensor fields for charged particles is SO(4, 2). The conservation currents corresponding this symmetry are constructed. We analyze transformations of the Lorentz group and quaternion fields. Supersymmetry of the Dirac–Kähler fields with tensor and spinor parameters is investigated. We show the possibility of constructing a gauge model of interacting Dirac–Kähler fields where the gauge group is the noncompact group under consideration.