A Note about the Appearance of Non-Hyperbolic Solutions in a Mechanical Pendulum System

The investigation of the behavior of a nonlinear system consists in theanalysis of different stages of its motion, where the complexity varieswith the proximity of a resonance region. Near this region the stabilitydomain of the system undergoes sudden changes due basically tocompetition and interaction between periodic and saddle solutions insidethe phase portrait, leading to the occurrence of the most differentphenomena. Depending of the domain of the chosen control parameter,these events can reveal interesting geometric features of the system sothat the phase portrait is not capable to express all them, since theprojection of these solutions on the two-dimensional surface can hidesome aspects of these events. In this work we will investigate thenumerical solutions of a particular pendulum system close to a secondaryresonance region, where we vary the control parameter in a restrictdomain in order to draw a preliminary identification about what happenswith this system. This domain includes the appearance of non-hyperbolicsolutions where the basin of attraction in the center of the phaseportrait diminishes considerably, almost disappearing, and afterwardsits size increases with the direction of motion inverted. Thisphenomenon delimits a boundary between low and high frequency of theexternal excitation.     

Coulomb drag of conduction electrons in spatially separated two-dimensional layers: An effective-parameter approximation

The Coulomb drag of electrons in spatially separated two-dimensional layers is considered under conditions of electron heating when the nonequilibrium distribution of electrons in the first layer can be described by macroparameters, such as the effective temperature. The nonequilibrium response is calculated using a projection operator that is an obvious generalization of the Mori operator to the case of nonequilibrium systems.     

Efficient discretization of pressure‐correction equations on non‐orthogonal grids

An alternative discretization of pressure‐correction equations within pressure‐correction schemes for the solution of the incompressible Navier–Stokes equations is introduced, which improves the convergence and robustness properties of such schemes for non‐orthogonal grids. As against standard approaches, where the non‐orthogonal terms usually are just neglected, the approach allows for a simplification of the pressure‐correction equation to correspond to 5‐point or 7‐point computational molecules in two or three dimensions, respectively, but still incorporates the effects of non‐orthogonality. As a result a wide range (including rather high values) of underrelaxation factors can be used, resulting in an increased overall performance of the underlying pressure‐correction schemes. Within this context, a second issue of the paper is the investigation of the accuracy to which the pressure‐correction equation should be solved in each pressure‐correction iteration. The scheme is investigated for standard test cases and, in order to show its applicability to practical flow problems, for a more complex configuration of a micro heat exchanger. Copyright © 2003 John Wiley & Sons, Ltd.     

Exchange of stability and finite-dimensional dynamics in a bifurcation problem with marginally stable continuous spectrum

We consider solutions bifurcating from a spatially homogeneous equilibrium under the assumption that the associated linearization possesses continuous spectrum up to the imaginary axis, for all values of the bifurcation parameter, and that a real eigenvalue crosses the imaginary axis. For a model we investigate the nonlinear stability of the trivial solution with respect to spatially localized perturbations, prove the occurrence of a pitchfork bifurcation of equilibria and the nonlinear stability of the bifurcating equilibria, again with respect to spatially localized perturbations.     

A Study of Drop Size Distribution in Multistage Bubble Extractor

Results obtained in determining experimentally the mean volume-surface drop diameter of the dispersed phase in a multistage bubble extractor are presented.     

Optical fractionation of an ensemble of impurity molecules with respect to the magnitude of the piezochromic effect

A method of hole burning in the 0-0 band of the impurity-absorption spectra of polymers and glasses is suggested. This method is selective not only with respect to the transition energy, but also with respect to the magnitude of the piezochromic effect. It is shown that, in combination with the modulation of the wavelength of probe radiation, this method makes it possible to determine the contribution of the impurity molecules with a specified magnitude of the piezochromic effect to the total absorption and luminescence of a sample. This circumstance allows one to study experimentally the correlation of the piezochromic effect with other characteristics of impurity molecules.     

Kinetics of a photoinduced NH tautomerism of free-base porphyrins in crystalline matrices at low temperatures: Computer simulations and experiment

Photoinduced NH tautomerism, along with the reaction pathways of phototautomerization in tetrabenzoporphin and porphin free bases in n-octane polycrystalline matrices at 77 K, is studied by simulation of kinetic processes and their experimental observation. The simulation of the processes is performed by the numerical solution of the system of kinetic equations describing the populations of electronic levels and transitions between them. Kinetic dependences are obtained by measuring the perturbation of stationary fluorescence of one component of the 0-0 doublet origin upon pulsed selective photoexcitation of the other component. For two tautomeric forms related by the reversibility of the photochemical reaction, under the assumption of synchronism of the NH rearrangement, (i) analytical solutions governing the reaction rate are found, (ii) a method of measuring the rate constants of the proton rearrangement is suggested and the constants themselves are estimated, and (iii) direct evidence of the participation of T ₁ levels in the photochemical reaction is obtained. With the aid of numerical simulations, the specific features of kinetic manifestation of an asynchronous mechanism of the photoinduced NH rearrangement are studied.     

Search for the emission of π<Superscript>0</Superscript> mesons from the neutron-induced fission of <Superscript>235</Superscript>U nuclei

A nuclear-reactor experiment on the search for the emission of neutral pions from the neutron-induced fission of ²³⁵U nuclei has been carried out. To this end, an experimental setup for searching for the emission of π⁰ mesons with high sensitivity to this process has been designed and produced. This setup consisted of two Cherenkov total-absorption spectrometers for the detection and measurements of the energy of two gamma-ray photons from π ⁰-meson decay. The spectrometers were placed at the exits of two coaxial horizontal experimental channels. To protect the detectors from low-energy β and γ rays and neutron fluxes, 3.5-m-long water filters were situated in the channels. To reject the cosmic background, large-area scintillation counters operating in the anticoincidence mode were placed over each spectrometer. The energy and time resolution of the spectrometers, as well as the efficiency of detecting charged particles by scintillation counters, were tested on the secondary electron beam of the Tomsk electron synchrotron Sirius. Runs of measurements of the effect on the operating reactor (duration of 805 h) were alternated with runs of measurements of background on the stopped reactor (duration of 403 h). Statistical processing of the experimental results yields an upper limit of ≤5.3×10 ^?12 with a 90% confidence level for the probability of the emission of neutral pions from the neutron-induced fission of ²³⁵U nuclei. This result and results of other works carried out with sources of spontaneously fissioning ²⁵²Cf nuclei show that the probabilities of the emission of π⁰ mesons from spontaneous fission and fission induced by fission-spectrum neutrons are equal to each other.