A geometrical interpretation of parity violation in gravity with torsion

In a space-time with torsion, the action for the gravitational field can be extended with a parity-violating piece. We show how to obtain such a piece from geometry itself, by suitably modifying the affine connection so as to include a pseudo-tensorial part. The merit of such an approach is that it provides one with a consistent method for incorporating parity-violation in the Lagrangians for matter fields with arbitrary spin in a space-time background with torsion.     

Intensity cross-correlation in light scattered by the rotational motion of macromolecules

Intensity cross-correlation in light scattered by the rotational motion of macromolecules is discussed in terms of pair- pair correlation. Expressions are given for a single pair for comparison with a rod, an equilateral triangle for comparison with a flat macromolecule, and a regular tetrahedron for comparison with other shapes. Anticorrelation occurs for the pair and triangle and correlation for the tetrahedron.     

Kinetics of crystalline configurations: III. An alloy that is inhomogeneous in one crystal direction

The new theory of crystal kinetics, developed in two earlier papers (Physica 111A (1982) 591 and Physica 113A (1982) 117), here is applied to an alloy model with inhomogeneities. The latter are restricted to one crystal direction. Macroscopic rate equations are derived for the concentrations and for the nearest neigbour correlations. In a linearized form these are solved, with results that (for a positive interaction) closely agree with Cahn's macroscopic theory of spinodal decomposition. In systems with a negative interaction a long range order with a domain structure will develop below the transition temperature. In the limit of long.waves Fick's second law is recovered, with a diffusion coefficient depending on composition and temperature, but with a value for the associated nearest neighbour correlation that does not correspond to local equilibrium. For a few cases the full, non-linear, rate equations are integrated numerically. After an initially exponential growth, in agreement with the small amplitude analysis, the solutions show a rather sudden transition to a much slower coarsening process. The latter is markedly more sluggish for the ordering alloys than for the decomposing ones.     

Effect of pressure on the Raman spectra of synthetic diamonds with boron impurity

The raman scattering technique is used for studying diamonds with a 0.04–0.1 at % boron impurity under a pressure up to 3 GPa in a chamber with sapphire anvils. The Raman frequency increases linearly with pressure for all samples with pressure coefficients of 2.947 cm^?1/GPa for pure diamond and 3.01 cm^?1/GPa for boron-doped samples. The Raman linewidths remain unchanged for pure diamond and for diamond with a boron concentration of about 0.04 at % and decrease linearly upon an increase in pressure for samples with a boron concentration of about 0.1 at %. The Raman spectra with a line profile corresponding to the Fano resonance do not change qualitatively up to a pressure of 3 GPa. In diamond samples with a boron impurity exceeding 0.1 at %, the boron concentration in the surface layer can be substantially higher than at the center of the sample.     

Constants of Motion for Several One-Dimensional Systems and Problems Associated with Getting Their Hamiltonians

The constants of motion of the following systems are deduced: a relativistic particle with linear dissipation; a no-relativistic particle with a time explicitly depending force; a no-relativistic particle with a constant force and time depending mass; and a relativistic particle under a conservative force with position depending mass. The Hamiltonian for these systems, which is determined by getting the velocity as a function of position and generalized linear momentum, can be found explicitly at first approximation for the first system. The Hamiltonians for the other systems are kept implicitly in their expressions for their constants of motion.     

Approach to the quantum evolution for underdamped, critically damped, and overdamped driven harmonic oscillators using unitary transformation

Exact solution of the Schrödinger equation is derived for underdamped, critically damped, and overdamped harmonic oscillators with a driving force. A unitary operator transforming Hamiltonian into a simple form is introduced. The transformed Hamiltonian, represented in terms of a modified frequency ω, is identical with the Hamiltonian of the standard harmonic oscillator for the underdamped oscillator, with the Hamiltonian of a free particle for the critically damped oscillator, and with the Hamiltonian of a system with a harmonic parabolic potential for the overdamped oscillator. The eigenvalues of underdamped oscillator are discrete while those of the critically damped and the overdamped oscillators are continuous.     

Feynman propagator for an arbitrary half—integral spin

Based on the solution to Bargmann－Wigner equation for a particle with arbitrary half-integral spin, a direct derivation of the projection operator and propagator for a particle with arbitrary half-integral spin is worked out. The projection operator constructed by Behrends and Fronsdal is re-deduced and confirmed and simplified, the general commutation rules and Feynman propagator with additional non-covariant terms for a free particle with arbitrary half-integral spin are derived, and explicit expressions for the propagators for spins 3/2, 5/2 and 7/2 are provided.     

Geometrical Form Factor Improvement for Receiving System of Infrared Lidar

Improvement of an infrared light detection and ranging (IR-lidar) system for a short range (0–1000 m) and with high resolution is studied to enhance a geometrical form factor. Theoretical modeling of Mie scattering echo signals agrees with the experimental results. Introduction of a lens in front of the detector is effective for increasing the geometrical form factor, and a significant improvement in the received signal intensity is achieved, especially for short-range measurements around 100 m. This is useful for the IR-lidar system with a detector diameter of less than 1 mm. In the theoretical model, a ray-tracing technique was applied and a transmitting laser beam with Gaussian profile was considered for better accuracy.     

Using a focused ion beam for the creation of a molecular single-electron transistor

Blank chips for a molecular single-electron transistor were created with the use of etching technology with a focused ion beam. Etching can be characterized as a process with a high speed of production, great reproducibility, mild requirements for prior lithographic operations, and rather good possibilities for decreasing gap width. The optimal parameters of scission of the metallic jumper of the electrodes were found, so that it is possible to create a 70 nm gap suitable for the production of a system with “overhanging” electrodes.     

A primitive-variable Riemann method for solution of the shallow water equations with wetting and drying

A Riemann flux that uses primitive variables rather than conserved variables is developed for the shallow water equations with nonuniform bathymetry. This primitive-variable flux is both conservative and well behaved at zero depth. The unstructured finite-volume discretization used is suitable for highly nonuniform grids that provide resolution of complex geometries and localized flow structures. A source-term discretization is derived for nonuniform bottom that balances the discrete flux integral both for still water and in dry regions. This primitive-variable formulation is uniformly valid in wet and dry regions with embedded wetting and drying fronts. A fully nonlinear implicit scheme and both nonlinear and time-linearized explicit schemes are developed for the time integration. The implicit scheme is solved by a parallel Newton-iterative algorithm with numerically computed flux Jacobians. A concise treatment of characteristic-variable boundary conditions with source terms is also given. Computed results obtained for the one-dimensional dam break on wet and dry beds and for normal-mode oscillations in a circular parabolic basin are in very close agreement with the analytical solutions. Other results for a forced breaking wave with friction interacting with a sloped bottom demonstrate a complex wave motion with wetting, drying and multiple interacting wave fronts. Finally, a highly nonuniform, coastline-conforming unstructured grid is used to demonstrate an unsteady simulation that models an artificial coastal flooding due to a forced wave entering the Gulf of Mexico.     

Sound waves in a liquid with polydisperse vapor–gas bubbles

A mathematical model is presented for the propagation of plane, spherical, and cylindrical sound waves in a liquid containing polydisperse vapor–gas bubbles with allowance for phase transitions. A system of integro-differential equations is constructed to describe perturbed motion of a two-phase mixture, and a dispersion relation is derived. An expression for equilibrium sound velocity is obtained for a gas–liquid or vapor–liquid mixture. The theoretical results agree well with the known experimental data. The dispersion curves obtained for the phase velocity and the attenuation coefficient in a mixture of water with vapor–gas bubbles are compared for various values of vapor concentration in the bubbles and various bubble distributions in size. The evolution of pressure pulses of plane and cylindrical waves is demonstrated for different values of the initial vapor concentration in bubbles. The calculated frequency dependence of the phase sound velocity in a mixture of water with vapor bubbles is compared with experimental data.     

Hydrodynamics of binary fluid phase segregation

Starting with the Vlasov-Boltzmann equation for a binary fluid mixture, we derive an equation for the velocity field u when the system is segregated into two phases (at low temperatures) with a sharp interface between them. u satisfies the incompressible Navier-Stokes equations together with a jump boundary condition for the pressure across the interface which, in turn, moves with a velocity given by the normal component of u. Numerical simulations of the Vlasov-Boltzmann equations for shear flows parallel and perpendicular to the interface in a phase segregated mixture support this analysis. We expect similar behavior in real fluid mixtures.     

Improved measurements of thermally induced birefringence effects in a laser material using a half-wave plate

The polarization dependence of a probe beam for use in measuring thermally induced birefringence effects in a laser-diode end-pumped Nd:YAG ceramic laser has been investigated. The variation in intensity of the probe beam was found to be 10.2% for a linearly polarized probe beam, 20.6% for a circularly polarized probe beam, and 31.4% for a circularly polarized probe beam using a half-wave plate with a pump power of 12 W. The angle between the analyzer and the inclination of the major axis of the elliptical polarization with respect to the x axis was controlled using a half-wave plate. By combining a half-wave plate with a circularly polarized probe beam, the variation in intensity increased compared with conventional methods.     

Quasi-equilibrium lattice Boltzmann method

A general lattice Boltzmann method for simulation of fluids with tailored transport coefficients is presented. It is based on the recently introduced quasi-equilibrium kinetic models, and a general lattice Boltzmann implementation is developed. Lattice Boltzmann models for isothermal binary mixtures with a given Schmidt number, and for a weakly compressible flow with a given Prandtl number are derived and validated.     

The forced vibrational response of a rectangular parallelepiped with rigid-lubricated boundaries

The Green function for a rectangular parallelepiped with rigid-lubricated boundaries is developed by a normal mode approach, the free vibration solutions being used. Explicit solutions are presented for a concentrated impulse, which serves as a model for an acoustic emission stress wave, and for a concentrated step force. Numerical results for short times show good agreement with the infinite space solution. Analogous solutions are developed for the inverse boundary conditions.     

Numerical simulation of continuum models for fluid-fluid interface dynamics

This paper is concerned with numerical methods for two-phase incompressible flows assuming a sharp interface model for interfacial stresses. Standard continuum models for the fluid dynamics in the bulk phases, for mass transport of a solute between the phases and for surfactant transport on the interface are given. We review some recently developed finite element methods for the appropriate discretization of such models, e.?g., a pressure extended finite element (XFE) space which is suitable to represent the pressure jump, a space-time extended finite element discretization for the mass transport equation of a solute and a surface finite element method (SurFEM) for surfactant transport. Numerical experiments based on level set interface capturing and adaptive multilevel finite element discretization are presented for rising droplets with a clean interface model and a spherical droplet in a Poisseuille flow with a Boussinesq-Scriven interface model.     

Angular momentum and cross sections for fusion with weakly bound nuclei: breakup,a coherent effect

Results for the cross section and average angular momentum for complete fusion at energies around the Coulomb barrier are presented for 7Li with 165Ho. Comparison of the cross sections with a one-dimensional barrier penetration model, using a potential consistent with the measured elastic scattering, showed a reduction above the barrier and an enhancement below it. An increase in the measured average angular momentum, , above the barrier and its consistency with that obtained from the fusion excitation function for weakly bound nuclei, is reported. These results together with a reanalysis of existing data conclusively demonstrate that the effect of breakup on fusion is coherent, like coupling to any nonelastic channel.     

Optical inhomogeneity model for evaporated Y2O3 obtained from physical thickness measurement

A multiparameter fitting with additional parameters for film inhomogeneity based on transmission results is used to get film inhomogeneity information and to compare different models for film structure. For a number of evaporated materials similar results from transmission fitting have been obtained by using a model consisting of two sublayers with a constant difference in refractive indices between them, either with a thin sublayer in the contact with a substrate or with air. As additional information, we obtained the film physical thickness result from step profile measurements for an oxygen-doped Y₂O₃ film on a fused silica and we compared it with the fit results for this coating. The result closest to the profilometry one has been achieved for a model with a thinner sublayer in contact with the substrate. The differences are great enough to assert that Y₂O₃ films on a fused silica possess a higher refractive index in the first stages of growth and then, after some transition, the main material with smaller refractive index grows on it.     

Electrodynamic calculation of spirals contacting the cavity ends

We calculate the eigenfrequencies of a cylindrical cavity with spirals contacting its ends. Explicit expressions are obtained for the case of a long cavity with one spiral contacting both ends and for the case of a cavity with one short spiral contacting one end. Calculations are also performed for the structures without constraints on the length and for a cavity with both spirals having close eigenfrequencies.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 47, No. 9, pp. 761–768, September, 2004.     

Fourier analysis for rotating-element ellipsometers

We introduce a Fourier analysis of the waveform of periodic light-irradiance variation to capture Fourier coefficients for multichannel rotating-element ellipsometers. In this analysis, the Fourier coefficients for a sample are obtained using a discrete Fourier transform on the exposures. The analysis gives a generic function that encompasses the discrete Fourier transform or the Hadamard transform, depending on the specific conditions. Unlike the Hadamard transform, a well-known data acquisition method that is used only for conventional multichannel rotating-element ellipsometers with line arrays with specific readout-mode timing, this Fourier analysis is applicable to various line arrays with either nonoverlap or overlap readout-mode timing. To assess the effects of the novel Fourier analysis, the Fourier coefficients for a sample were measured with a custom-built rotating-polarizer ellipsometer, using this Fourier analysis with various numbers of scans, integration times, and rotational speeds of the polarizer.