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.     

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.     

The Fermi Level Pinning in Semiconductors (Interphase Boundaries,Clusters, and Radiation Modification)

The original results are presented, and the current status of the Fermi level pinning in semiconductors is reviewed for different physical phenomena (interphase boundaries, semiconductor clusters, and radiation modification of semiconductors).     

PDE with Random Coefficients and Euclidean Field Theory

In this paper a new proof of an identity of Giacomin, Olla, and Spohn is given. The identity relates the 2 point correlation function of a Euclidean field theory to the expectation of the Green's function for a pde with random coefficients. The Euclidean field theory is assumed to have convex potential. An inequality of Brascamp and Lieb therefore implies Gaussian bounds on the Fourier transform of the 2 point correlation function. By an application of results from random pde, the previously mentioned identity implies pointwise Gaussian bounds on the 2 point correlation function.     

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.     

Modification of GaAs by medium-energy N<Stack><Subscript>2</Subscript><Superscript>+</Superscript></Stack> ions

The modification of GaAs with a 2500-eV beam containing N ₂ ⁺ and Ar⁺ ions is examined with Auger electron spectroscopy. Most implanted nitrogen atoms are found to react with the matrix, substituting arsenic atoms to produce a several-nanometer-thick layer of the single-phase GaAs_1−x N_x (x=6%) solid solution. The GaN phase is absent. Displaced arsenic atoms and nitrogen atoms unreacted with the matrix are present in the layer and on its surface. The former segregate, whereas the latter form molecules.     

Spontaneous Surgery on the Borromean Rings

We study the cone-manifolds whose singular sets are obtained by orbifold and spontaneous surgeries on components of the Borromean rings. We establish existence of geometric structures on these manifolds. For manifolds with hyperbolic structure we obtain an integral representation for volumes.     

Aftereffect in microhardness testing of corundum

Cleavage near microhardness indentations on the surface of corundum is found to appear long (20–30 days) after unloading.