Investigation and reduction of variance of a weighted estimate in numerical statistical simulation

The efficiency of the “value” and “partial value” modeling related to the construction of a modeling distribution for an auxiliary random variable by multiplying the initial density by a value function is investigated. The value function usually corresponds to a solution of the adjoint equation. Conditions under which the value modeling of the initial distribution reduces the variance compared to the direct simulation are obtained. It is proved that the variance of the weighted estimate is bounded in the case of the partial value modeling. This proposition provides a basis for a method for determining whether or not the variance of the weighted estimate is bounded. This method uses the majorizing adjoint equation. Using a practically important problem in transport theory as an example, the asymptotic optimization of the distribution of the mean free path is presented. The application of the proposed method of the investigation of the variance boundedness for the analysis of the classical exponential transformation method of simulating the mean free path of a particle in the one-dimensional and the spherical variants is discussed.     

Growth kinetics of iron boride layers: Dimensional analysis

Dimensional analysis is presented as a powerful tool in the study of the paste boriding process. In particular, a dimensional method is used to study the growth kinetics of the boride layers FeB and Fe₂B. Experiments were performed in AISI 1045 steel and AISI M2 steel, to test the suggested model. Samples of 1045 steel were prepared and treated using boron paste thickness of 3-5 mm, at temperatures of 1193, 1223 and 1273 K, with 2, 4 and 6 h of treatment time. The M2 specimens had boron paste thickness of 3 and 4 mm and temperatures of 1223, 1253 and 1273 K for 2 and 6 h. Results indicate that the growth of boron layers obeys power laws of the form y = αx^β, where α and β constants are a function of the material and the interface of interest. Validation of the model was carried out using experimental data with an average error percentage of 7.6% for Fe₂B in 1045 steel, 15.8% for FeB and 3.4% for Fe₂B in M2 steel.     

Study of the dielectric properties of water in the frequency range 75–120 GHz

We study experimentally the frequency dependences of the refractive index n and the absorption coefficient k of distilled, sea, and river water. The measurements were performed using a quasioptical device with a backward-wave oscillator as the radiation source and OAP-7 optical-acoustic receivers at a water temperature of 27°C in the cell. The quantities n and k were determined from the measured transmission and reflection coefficients of the cell with water by means of joint numerical solution of the equations for these quantities. For distilled water in the frequency range f = 75–120 GHz, we obtained n = 6.142–3.926 · 10–2f[GHz] + 1.307 · 10–4(f[GHz])² and k = 3.607–2.101 · 10⁻² f[GHz] + 5.252 · 10–5(f[GHz])². On the whole, these data are in good agreement with the measurement results obtained by other authors at several frequencies of the indicated range and coincide with the calculation data based on the models by Meissner and Wentz and by Liebe et al. within the limits of the rms determination errors 0.05 and 0.02 for the parameters n and k, respectively. The values of n and k for different seawater samples and river water containing insoluble admixtures coincide with the values of these quantities for distilled water within the limits of the experimental measurement errors 3–5% and 1–2%, respectively. The dependences n(f) and k(f) obtained experimentally for seawater are compared with those calculated on the basis of the developed models. Measurements of the transmission spectrum of a cell with double distilled water were performed for low power density of radiation (less than μW/cm²) to reproduce the effect of water resonant transparency reported many times in the literature. Our measurements did not reveal any resonant features in the spectral behavior of the refractive index n and the absorption coefficient k of water and gave the same result as for a power density exceeding the threshold of appearance of this effect. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 6, pp. 489–501, June 2006.     

High-power excimer laser systems

Two-high power excimer laser systems with square (25 × 25 cm) and circular (with a diameter of 40 cm) cross sections of the output laser beam are described. The first (second) system consists of four (five) excimer lasers. The experimental results on the generation of the high-quality high-power laser pulses are presented. Laser beams with a pulse duration of 1–250 ns, a divergence of 0.01 mrad, a spectral line width of 0.01 cm⁻¹, and a pulse energy of up to 330 J are obtained. Original Text ? Astro, Ltd., 2006.