Classical photometry of prefractal surfaces

Using the scale invariance of classical photometry, we develop an approach to finding the photometric function of prefractal structures that form a random topography. The photometric function of the prefractal surfaces is found as the general solution of the resulting differential equation in partial derivatives. The function depends on two parameters: the number of hierarchical levels of the prefractal structures and the roughness parameter of the single-level generation. As a limiting case, the approach includes our previous theory that considered fractoids.     

Numerical Analysis of Quasioptical Multireflector Antennas in 2-D With the Method of Discrete Singularities: E-Wave Case

Numerical method for modeling the E-polarized wave scattering by electrically large quasioptical two-dimensional (2-D) reflectors is presented. Reflectors are assumed zero-thickness and perfectly electrically conducting. Efficient numerical solution is obtained from the coupled singular integral equations discretized using new quadrature formulas of interpolation type. It has controlled accuracy and deals with small-size matrices. To simulate a small-horn feeding, the incident field is taken as a beam generated by a complex-source-point (CSP) current. Presented numerical results validate empirical rule of -10 dB edge illumination needed to provide the best electromagnetic performance of reflector     

Axisymmetric oscillations of a cupola-shaped shell

A spectral boundary problem on axisymmetric eigenoscillations of a cupola-shaped shell is considered with emphasis on small shell thickness. The problem deals with a singularly perturbed system of ordinary differential equations. The paper examines analytical properties of the solution and, based on that, constructs an appropriate functional basis for Ritz’ method. Employing this basis provides fast convergence in the C ³-metrics.     

Magnetometric Studies of Catalyst Refuses in Nanocarbon Materials

It is shown that magnetometry can be employed as an effective tool to control the content of a ferromagnetic constituent in nanocarbon materials. We propose a thermochemical treatment protocol to achieve extensive cleaning of the source nanocarbon materials from ferromagnetic refuses.     

Bose-Einstein Condensation of Magnons in Superfluid 3He

The possibility of Bose-Einstein condensation of excitations has been discussed for a long time. The phenomenon of the phase-coherent precession of magnetization in superfluid ³He and the related effects of spin superfluidity are based on the true Bose-Einstein condensation of magnons. Several different states of coherent precession has been observed in ³He-B: homogeneously precessing domain (HPD); persistent signal formed by Q-balls at very low temperatures; coherent precession with fractional magnetization; and a mode of the coherent precession in compressed aerogel. The coherent precession has been also found in ³He-A in compressed aerogel. Here we demonstrate that all these cases are examples of a Bose-Einstein condensation of magnons, with the magnon interaction term in the Gross-Pitaevskii equation being provided by different types of spin-orbit coupling in the background of the coherent precession.      

Conductivity of highly sulfonated polyphenylene sulfide in the powder form as a function of temperature and humidity

Block-copolymers with highly sulfonated ionomer blocks are considered as leading candidates for low-humidity high-temperature Polymer Electrolyte Fuel Cell membranes. We present a new approach that allows for faster measurement of conductivity of powdered ionomers in a wide range of temperature and humidity with a single 10–30 mg sample. Our method is exemplified by a case study of polyphenylenesufide with a degree of sulfonation 0.70. This material shows 0.12 S/cm conductivity at 127 °C and 50% relative humidity. At higher temperatures and lower humidities, this polymer undergoes irreversible cross-linking. Further routes to improving conductivity, chemical and mechanical properties of the polymer are discussed.     

Silicon Vibrating Wires at Low Temperatures

Nowadays microfabrication techniques originating from micro-electro nics enable to create mechanical objects of micron-size. The field of Micro-Electro-Mechanical devices (MEMs) is continuously expanding, with an amazingly broad range of applications at room temperature. Vibrating objects (torsional oscillators, vibrating wires) widely used at low temperatures to study quantum fluids, can be replaced advantageously by Silicon MEMs. In this letter we report on the study of Silicon vibrating wire devices. A goal-post structure covered with a metal layer is driven at resonance by the Laplace force acting on a current in a magnetic field, while the induced voltage arising from the cut magnetic flux allows to detect the motion. The characteristics of the resonance have been studied from 10 mK to 30 K, in vacuum and in ⁴He gas. In this article, we focus on the results obtained above 1.5 K, in vacuum and gas, and introduce some features observed at lower temperatures. The resonant properties can be quantitatively understood by means of simple models, from the linear regime to a highly non-linear response at strong drives. We demonstrate that the non-linearity is mostly due to the geometry of the vibrators. We also show that in our device the friction mechanisms originate in the metallic layers, and can be fully characterized. The interaction with ⁴He gas is fit to theory without adjustable parameters.      

Decomposition of Fe5C2 catalyst particles in carbon nanofibers during TEM observation

The effect of an electron beam on nanoparticles of two Fe carbide catalysts inside a carbon nanofiber was investigated in a transmission electron microscope. Electron beam exposure does not result in significant changes for cementite (θ-Fe₃C). However, for Hägg carbide nanoparticles (χ-Fe₅C₂), explosive decay is observed after exposure for 5–10 s. This produces small particles of cementite and γ-Fe, each covered with a multilayer carbon shell, and significantly modifies the carbon-fiber structure. It is considered that the decomposition of Hägg carbide is mostly due to the damage induced by high-energy electron collisions with the crystal lattice, accompanied by the heating of the particle and by mechanical stress provided by the carbon layers of the nanofiber.     

Book Reviews

This paper discusses ongoing research to formulate, develop and test a reliability assessment model (GenRel) based on genetic algorithms (GAs). GAs are powerful and broadly applicable stochastic search techniques based on the principles of natural selection, heredity and genetics. The reason for selecting GAs is the fact that the reliability of mining equipment changes over time due to its dependence upon several covariates/factors (e.g. equipment age, operating environment, number and quality of repairs). These factors combine to create a complex impact on a piece of equipment's reliability function. This impact encapsulates and inherits to some degree the individual characteristics of the factors as they evolve over time.

Theoretical probability distributions are commonly used to fit equipment failure data. GenRel uses the exponential probability distribution as its engine to generate predictive patterns based upon historical failure data.

Overall, this paper suggests a methodology for applying GAs for reliability assessment of mining equipment. An example is given to demonstrate the effectiveness of using GAs in reliability studies. The research discussed in this paper was carried out by the Laurentian University Mining Automation Laboratory (LUMAL).