Fourier-Feynman transform, convolution and first variation

We examine several interesting relationships and expressions involving Fourier-Feynman transform, convolution product and first variation for functionals in the Fresnel class F(B) of an abstract Wiener space B. We also prove a translation theorem and Parseval's identity for the analytic Feynman integral. This revised version was published online in June 2006 with corrections to the Cover Date.     

Spin and quark states in the probability representation of quantum mechanics

A short review of the general principles of constructing tomograms of spin and quark states is presented.     

The glow curve structure for the LiF:Mg,Cu,Na,Si TL detector with dopants concentrations and sintering temperatures

The glow curve structures for LiF:Mg,Cu,Na,Si TL detectors with various dopant concentrations and sintering temperatures were investigated for the improvement of the glow curve structure and sensitivity of the TL detector. The dopant concentrations were varied over the following ranges: Mg (0–0.25 mol%), Cu (0–0.07 mol%), Na and Si (0–1.5 mol%). With increasing Cu concentration, the intensity of the main peak was intensified and reached a maximum at a concentration of 0.05 mol%. The high-temperature peak was reduced. The dependency of the main peak intensity on the Mg concentration exhibits a sharp maximum at 0.2 mol%. The intensity of the high-temperature peak tends to rise slightly with increasing Mg concentration. It was found that the optimum concentrations of the dopants in the LiF:Mg,Cu,Na,Si TL material are Mg: 0.2 mol%, Cu: 0.05 mol%, Na and Si: 0.9 mol%. The dependency of the main peak intensity on sintering temperature exhibits a very sharp maximum at 830°C. The high-temperature peak was rapidly reduced after 825°C.     

Use of ultrafine-dispersed nanodiamond for selective deposition of boron-doped diamond films

A suspension of ultrafine-dispersed nanodiamond was used for introducing (in particular, selectively) high-density centers of diamond nucleation on various substrates. High-quality doped diamond films to be used as electrochemistry electrodes were deposited from the gas phase in a microwave discharge on certain substrates treated using ultrafine-dispersed nanodiamond. A uniform distribution of nucleation centers with concentrations greater than 10¹⁰ cm^-2 on silicon substrates was obtained. Electrochemical current-potential curves were measured for continuous films. Diamond meshes of different transparency were grown using selective nucleation. Successful production of high-quality doped diamond meshes gives grounds to consider them the most promising electrodes for use in electrochemistry.     

Chain decay of low-angle tilt boundaries in nanocrystalline materials

In terms of two-dimensional dislocation-disclination dynamics, a theoretical model is developed to describe the decay of a low-angle tilt boundary in a deformed nanocrystalline material under the action of an externally applied elastic stress and of the elastic field of a neighboring decayed boundary. The critical external stresses are calculated at which the boundary decays and the dislocations making up this boundary either are trapped by the boundary that decayed earlier or break away from both boundaries. The decay of a low-angle tilt boundary is shown to result in a substantial decrease in the critical decay stresses for the neighboring boundaries, which can cause an avalanche-like chain decay of low-angle boundaries yielding high-density ensembles of mobile dislocations capable of carrying substantial plastic deformations and of forming shear bands in deformed nanocrystalline materials.     

Investigation of the X-ray radiation produced by a diffusive discharge in the rod-plane geometry under atmospheric pressure

Spatial parameters of the X-ray radiation produced by a high-voltage nanosecond discharge evolving in air under atmospheric pressure in the rod (cathode)-plane electrode system with a 10-cm electrode spacing are studied experimentally. A ∼170-ns voltage pulse with an amplitude of ∼200 kV and 10-ns rise time is applied to the cathode. The photoelectronic method is used to study, under the same conditions, the integrated (over the gap) characteristics of the radiation, in particular, the duration of its generation. It is found that, when the size of the X-ray source is not smaller than that of the discharge region of diffusive luminescence, radiation from the cathode region of the gap is primarily observed (i.e., from the region where the electric field distribution is sharply inhomogeneous). The X-ray generation is usually observed after the bridging of the discharge gap, the X-ray pulse having a rise time of ∼3 ns, a duration of ∼10 ns, and an effective radiation energy of ∼6 keV.     

Numerical simulation of the translational nonequilibrium zone behind a shock-wave front

The translational nonequilibrium zone in a shock wave is considered for a gas consisting of light particles and a small addition of heavy particles. The gas is taken to be two-dimensional, and long-range forces are assumed to be absent. In the framework of this approximation, a program for molecular dynamics simulation of the gas is developed. It is applied to calculate a particle distribution function in the shock wave, to analyze the time evolution of the distribution function, and to study its dependence on the gas composition.     

The total acoustic impedance of a prolate spheroid performing transverse oscillatory movements

Using the theory of spheroidal wave functions, the total acoustic impedance is determined for a prolate spheroid performing transverse translational and rotational oscillatory movements. Expressions for the radiation resistance, the added mass, and the added moment of inertia are derived. It is shown that, in the lowfrequency approximation, this mass and moment of inertia reach limiting values identical to hydrodynamic ones. The components of the total acoustic impedance are calculated for spheroids of different relative thicknesses at an arbitrary frequency.     

Synthesis of ordered Ge-Si heterostructures containing ultrasmall germanium nanoclusters

Different techniques for the fabrication of structures containing ensembles of ultrasmall germanium nanoclusters distributed with a high density over the substrate surface are discussed. How to control the morphology and ordering of these ensembles is also discussed.