Some observations on uncertainty propagation through a simple nonlinear system

This paper discusses a number of issues relating to the analysis of uncertain systems or data in the context of (low-frequency) structural dynamics. In order to illustrate potential problems in applying ‘classical’ uncertainty analysis methods to nonlinear systems, a simple nonlinear system is simulated and the breakdown of two standard approaches is demonstrated on data from the system. By relaxing the requirements of the analysis, it is shown that an alternative uncertainty theory gives useful qualitative information about the system. This motivates a discussion of how uncertainty frameworks should be chosen to suit the problem in hand and leads to a clustering of uncertainty problems in structural dynamics into three types: quantification, fusion and propagation.     

100-TW femtosecond laser based on parametric amplification

In experiments on the parametrical amplification of femtosecond pulses in wide-aperture DKDP crystals, a power of more than 100 TW has been reached, which is much higher than the record level achieved in such lasers. The energy efficiency obtained for the parametric amplifier is equal to 27%. The energy of a 72-fs pulse is equal to 10 J.     

On a Modification of the Scintillation Method

We solve the problem of diffraction of fluctuating radiation by an optically thin irregular layer (phase screen) with developed turbulent structure. It is shown that in the case of diffraction of radiation with saturated fluctuations and a narrow-band frequency spectrum by a weakly turbulent moving phase screen, the measured frequency spectrum of intensity fluctuations in the observation plane allows one to obtain information on the form of the spectrum of irregularities of an optically thin irregular layer in a wide size range significantly exceeding the size of the first Fresnel zone. Similarly to the well-known phase method of diagnostics of randomly irregular media, the conventional scintillation method modified in such a way yields undistorted information on the form of the irregularity spectrum. However, in contrast to the phase method, it also allows one to obtain data on the drift velocity of irregularities in the studied irregular layer.     

Comparative analysis of heterogeneous solid and soft materials by adsorption, NMR and thermally stimulated depolarisation current methods

Structural characterisation of such bio-objects as fibrinogen solution, yeast cells, wheat seeds and bone tissues has been done using two versions of cryoporometry based on the integral Gibbs-Thomson (IGT) equation for freezing point depression of pore liquids and the measurements by ¹H NMR spectroscopy (180-200 < T < 273 K) and the thermally stimulated depolarisation current (TSDC) method (90 < T < 273 K) of structured water. The IGT equation was solved using a self-consisting regularization procedure including the maximum entropy principle applied to the distribution function of pore size (PSD). Both methods give clear pictures of changes in the structural characteristics caused, e.g., by hydration and swelling of wheat seeds and yeast cells, coagulation and interaction of fibrinogen with solid nanoparticles in the aqueous media, and the human bone tissue disease.     

Determination of electron temperature based on a semicoronal model in Hall accelerator plasma flows

We present the results of a spectroscopic study of a nonequilibrium plasma in a Hall accelerator, in particular for such an important parameter as the electron temperature. For the studied conditions, we used the semicoronal equilibrium model, which relates the intensity ratios for two successive ionization steps for the same element. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 1, pp. 93–96, January–February, 2007.     

QUALITATIVE AND QUANTITATIVE ANALYSIS OF STOCHASTIC PROCESSES BASED ON MEASURED DATA, II: APPLICATIONS TO EXPERIMENTAL DATA

Analysis of stochastic processes governed by the Langevin equation is discussed. The analysis is based on a general method for non-parametric estimation of deterministic and random terms of the Langevin equation directly from given data. Separate estimation of the terms corresponds to the decomposition of process dynamics into deterministic and random components. Part I of the paper presented several possibilities for qualitative and quantitative analysis of process dynamics based on such decomposition. In Part II, some of these analysis possibilities are applied to experimental datasets from metal cutting and laser-beam welding.     

Aeolian Tones of a Honeycomb Lattice Cell

Aeroacoustic resonant oscillations (aeolian tones) are studied for flow past two plates forming a cross in a square cross section channel. Possible oscillation modes are classified on the basis of admissible symmetry groups and the existence of the modes is proved. The infinite linear system of equations for these modes obtained by the sewing method was simplified and studied numerically. Curves of eigenfrequency versus plate length are constructed. The form of the eigenfunctions is studied.     

Scientific heritage of Boris Lukich Laptev (4/23/05–1/15/89)

Biographical information on the eminent Soviet geometer Boris Lukich Laptev (4/23/05–1/15-89) is given as well as a survey of his research in the areas of differential geometry and history of mathematics.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 21, pp.27–42, 1989.