Non-local symmetries of first-order equations

It is shown how one can transform scalar first-order ordinarydifferential equations which admit non-local symmetries of theexponential type to integrable equations admitting canonicalexponential non-local symmetries. As examples we invoke theAbel equation of the second kind, the Riccati equation and naturalgeneralizations of these. Moreover, our method describes howa double reduction of order for a second-order ordinary differentialequation which admits a two-dimensional Lie algebra of generatorsof point symmetries can be affected if the second-order equationis first reduced in order once by a symmetry which does notspan an ideal of the two-dimensional Lie algebra.     

Electro-elastic interactions and second order anisotropic constitutive equations

Piezoelectricity is usually expressed as an interaction between mechanical and electrical variables. The physics involved is hence governed by a coupling between Maxwell's equations of electromagnetism and the equations of elasticity. Such a coupling takes us through the piezoelectric constitutive relations. In this work, the second order anisotropic constitutive equations are treated, and in particular, the number of independent material constants is computed for all the 32 crystallographic classes.Paper presented, in reduced version, at the 12th Italian National Congress of Theoretical and Applied Mechanics (AIMETA '95), October 1995, Naples, Italy.     

Anisotropic effects in surface acoustic wave propagation from a point source in a crystal

Strong anisotropic effects in the propagation of surface acoustic waves (SAWs) from a point-like source are studied experimentally and theoretically. Nanosecond SAW pulses are generated by focused laser pulses and detected with a cw probe laser beam at a large distance from the source compared to the SAW wavelength, which allows us to resolve fine intricate features in SAW wavefronts. In our theoretical model, we represent the laser excitation by a localized impulsive force acting on the sample surface and calculate the far-field surface response of an elastically anisotropic solid to such a force. The model simulates the measured SAW waveforms very well and accounts for all experimentally observed features. Using the data obtained for the (111) and (001) surfaces of GaAs, we describe a variety of effects encountered in the SAW propagation from a point source in crystals. The most interesting phenomenon is the existence of cuspidal structures in SAW wavefronts resulting in multiple SAW arrivals for certain ranges of the observation angle. Cuspidal edges correspond to the phonon focusing directions yielding sharp peaks in the SAW amplitude. A finite SAW wavelength results in internal diffraction whereby the SAW wavefront spreads beyond the group velocity cusps. Degeneration of a SAW into a transverse bulk wave is another strong effect influencing the anisotropy of the SAW amplitude and making whole sections of the SAW wavefront including some phonon focusing directions unobservable in the experiment. The propagation of a leaky SAW mode (pseudo-SAW) is affected by a specific additional effect i.e. anisotropic attenuation. We also demonstrate that many of the discussed features are reproduced in powder patterns, a simple technique developed by us earlier for visualization of SAW amplitude anisotropy.Received: 17 June 2003, Published online: 15 October 2003PACS: 43.35.+d Ultrasonics, quantum acoustics, and physical effects of sound - 68.35.Gy Mechanical properties; surface strains - 62.65.+k Acoustical properties of solidsA.M. Lomonosov: On leave from the General Physics Institute, 117942 Moscow, Russia     

Transition to Chaos in the Floating Half Zone Convection

The transition process from steady convection to chaos is experimentally studied in thermocapillary convections of floating half zone. The onset of temperature oscillations in the liquid bridge of floating half zone and further transitions of the temporal convective behaviour are detected by measuring the temperature in the liquid bridge. The fast Fourier transform reveals the frequency and amplitude characteristics of the flow transition. The experimental results indicate the existence of a sequence of period-doubling bifurcations that culminate in chaos. The measured Feigenbaum numbers are δ2 =4.69 and δ4 = 4.6, which are comparable with the theoretical asymptotic value δ=4.669.     

Experimental Setup for Neutron Lifetime Measurements with a Large Gravitational Trap at Low Temperatures

Technical Physics - Currently the most accurate measurements of neutron lifetime are being performed at the Petersburg Nuclear Physics Institute with ultracold neutrons (UCNs) stored in a...     

Krypton Separation from Ambient Air for Application in Collinear Fast Beam Laser Spectroscopy

A portable apparatus for the separation of krypton from environmental air samples was tested. The apparatus is based on the cryogenic trapping of gases at liquid nitrogen temperature followed by controlled releases at higher temperatures. The setup consists of a liquid nitrogen trap for the removal of H(2)O and CO(2), followed by charcoal-filled coils that sequentially collect and release krypton and other gases providing four stages of gas chromatography to achieve separation and purification of krypton from mainly N(2), O(2), and Ar. Residual reactive gases remaining after the final stage of chromatography are removed with a hot Ti sponge getter. A thermal conductivity detector is used to monitor the characteristic elution times of the various components of condensed gases in the traps during step-wise warming of the traps from liquid nitrogen temperatures to 0?°C, and then to 100?°C. This allows optimizing the switching times of the valves between the stages of gas chromatography so that mainly krypton is selected and loaded to the next stage while exhausting the other gases using a He carrier. A krypton separation efficiency of ~80?% was determined using a quadrupole mass spectrometer.     

Obliquely propagating ion-acoustic shock waves in a degenerate quantum plasma

A theoretical investigation has been carried out on the propagation of non-linear ion-acoustic shock waves (IASHWs) in a magnetized degenerate quantum plasma system composed of inertial non-relativistic positively charged light and heavy ions, inertialess non-relativistically or ultra-relativistically degenerate electrons and positrons. The reductive perturbation method has been employed to derive the Burgers' equation. It has been observed that under consideration, our plasma model supports only positive potential shock structure. It is also found that the amplitude and steepness of the IASHWs have been significantly modified by the variation of ion kinematic viscosity, oblique angle, number density, and charge state of the plasma species. The results of our present investigation will be helpful for understanding the propagation of IASHWs in white dwarfs and neutron stars.     

Commensurability oscillations in NdBa2Cu3Oy single crystals

Commensurability between inter-vortex distance and crystal lattice constant is investigated by angular dependent magnetization in very pure twinned and twin-free NdBa₂ Cu₃ O_y single crystals. With increasing temperature the incommensurate states split up and become finally commensurate with half the vortex distance. These new commensurate states are related to a substructure of the intrinsic pinning potential within the unit cell and discussed with respect to temperature, field, anisotropy, and twin structure.     

Determining a 'safe' high-mass limit in matrix-assisted laser desorption/ionisation time-of-flight mass spectra of coal derived materials with reference to instrument noise

Three methods for determining a 'safe' estimate for high-mass limits of MALDI spectra of coal derived liquids were explored, using a sample of coal-tar pitch and its pyridine-insoluble fraction. Co-addition of increasing numbers of single-shot spectra (10, 30, 50 and 100 pulses) showed visually observable reductions in noise levels, consistent with robust and statistically meaningful signals. Three separate types of post-acquisition calculation were used to identify high-mass limits of the spectra. (i) A literature method indicated high-mass limits similar to those observed visually-as a shift from baseline at the highest masses, nearly 350 000 u for the coal tar pitch and about 390 000 u for its pyridine insoluble fraction. (ii) Comparing instrument signal with pre-selected multiples of the standard deviation, upper mass estimates of between 40-60 000 u for the coal-tar pitch and about 95 000 u for its pyridine-insoluble fraction were found. (iii) Calculation of the slope was used to identify 'lift-off' of the spectrum from baseline. The angle between the smoothed spectrum and the baseline was matched to a pre-selected value (e.g. 0.5 degrees and 1 degrees ). However, the arbitrary specification of the key parameter did not establish this last method on a firm basis. The choice of a criterion for estimating high-mass limits of MALDI spectra remains a semi-quantitative procedure; a reasonably conservative high-mass limit may be estimated by comparison of signal with five times the standard deviation. However, evaluation of size exclusion chromatograms of the present samples using polystyrene standards suggests that molecular mass distributions of pitch samples arrived at by MALDI mass spectrometry are, at least partly, determined by the limitations of available instruments. Copyright 1999 John Wiley & Sons, Ltd.