Certain constructions of asymptotic analysis related to the Stone-Čcech compactification

The paper considers the representations of attraction sets in topological spaces and their relations with the relaxation of accessibility problems under the conditions of sequentially relaxed constraints. The author studies the structure of approximate (in essence, asymptotic) solutions and generalized elements and establishes the possibility of their real identification for a certain version (related to the Stone-Čech compactification and the Wallman relaxation) of relaxation of the initial problem. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 26, Nonlinear Dynamics, 2005.     

Influence of ionizing radiation on the magnetically sensitive properties of planar triacs

Changes in the magnetically sensitive properties of multilayer semiconductors devices, such as planar diffusion triacs, that are related to atomic-displacement-induced defects and ionization by irradiation are considered. It is shown that irradiation may significantly raise the magnetic sensitivity of the triacs. Processes and underlying mechanisms responsible for the improvement of the magnetic sensitivity under the action of a number of galvanomagnetic effects are studied.     

Ab-initio simulation of elastic constants for some ceramic materials

Athermal elasticity for some ceramic materials (α-Al₂O₃, SiC (α and β phases), TiO₂ (rutile and anatase), hexagonal AlN and TiB₂, cubic BN and CaF₂, and monoclinic ZrO₂) have been investigated via density functional theory. Energy-volume equation-of-state computations to obtain the zero pressure equilibrium volume and bulk modulus as well as computations of the full elastic constant tensor of these ceramics at the experimental zero pressure volume have been performed. The present results for the single crystal elasticity are in good agreement with experiments both for the aggregate properties (bulk and shear modulus) and the elastic anisotropy. In contrast, a considerable discrepancy for the zero pressure bulk modulus of some ceramics evaluated from the energy-volume fit to the computational zero pressure volume has been observed.     

Ultrafast creation and annihilation of space-charge domains in a semiconductor superlattice observed by use of Terahertz fields

We report an experimental study indicating ultrafast creation and annihilation of space-charge domains in a semiconductor superlattice under the action of a THz field. Our experiment was performed for an InGaAs/InAlAs superlattice with the conduction electrons undergoing miniband transport. We applied to a superlattice a dc bias that was slightly smaller than a critical bias necessary for the formation of space-charge domains caused by a static negative differential conductivity. Additionally subjecting the superlattice to a strong THz field, resulted in a dc transport governed by the formation of domains if the frequency of the field was smaller than an upper frequency limit (~3 THz). From this frequency limit for the creation and annihilation of domains we determined the characteristic time of the domain buildup. Our analysis shows that the buildup time of domains in a wide miniband and heavily doped superlattice is limited by the relaxation time due to scattering of the miniband electrons at polar optic phonons. Our results are of importance for both an understanding of ultrafast dynamics of pattern formation in nanostructures and the development of THz electronic devices.Received: 25 March 2004, Published online: 23 July 2004PACS: 72.20.Ht High-field and nonlinear effects - 72.30. + q High-frequency effects; plasma effects - 73.21.Cd SuperlatticesK.N. Alekseev: Permanent address: Department of Physical Sciences, P.O. Box 3000, University of Oulu FIN-90014, Finland.     

Study of the Structure and Sorption Properties of Some Types of Cellulose

The pulsed NMR, isopiestic and pycnometric methods are applied to investigate the physicochemical properties of softwood [GOST (State Standard) 9571-89] and hardwood [GOST 28172-89] celluloses, as well as flax cellulose [GOST 10330-76, 9394-76], both in the initial state and subjected to chemical treatment. Possible changes occurring in the supramolecular structure of a polymer are analyzed. The structural and sorption characteristics of the investigated samples are calculated. Their water absorption capacities are determined.     

Formation of Supersonic Zones and Local Separation Zones in Transonic Steady-State Flow Past Surface Roughness in the Free Interaction Regime

Within the framework of free interaction theory numerical methods are used to investigate the occurrence of supersonic zones with shocks in the outer inviscid region for flow past roughness in the lower viscous sublayer, with and without the formation of local separation zones.     

Derivation of the k–ε model for locally homogeneous turbulence by homogenization techniques

We derive the incompressible and compressible k–ε model for locally homogeneous turbulence. The model is rigorously derived on formal mathematical grounds using the MPP modelling technique. This lets us calculate by either analytical or numerical means the closure constants of the model. To cite this article: T. Chacón Rebollo, D. Franco Coronil, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Some properties of multi-degree-of-freedom potential systems and application to statistical equivalent non-linearization

This paper presents some properties of two restricted classes of multi-degree-of-freedom potential systems subjected to Gaussian white-noise excitations. Specifically, potential systems which exhibit damping terms with energy-dependent polynomial form are referred to. In this context, first systems with coupled stiffness terms and damping terms depending on the total energy are investigated. Then, systems with uncoupled stiffness terms and damping terms depending on the total energy in each degree-of-freedom are considered. For these two classes, it is found that algebraic relations among the stationary statistical moments of the energy functions can be derived by applying standard tools of Itô calculus. Further, it is noted that these relations are very useful within the framework of an equivalent statistical non-linearization technique to build approximate solutions for arbitrary non-linear systems.     

Spinors, Inflation, and Non-Singular Cyclic Cosmologies

We consider toy cosmological models in which a classical, homogeneous, spinor field provides a dominant or sub-dominant contribution to the energy-momentum tensor of a flat Friedmann-Robertson-Walker universe. We find that, if such a field were to exist, appropriate choices of the spinor self-interaction would generate a rich variety of behaviors, quite different from their widely studied scalar field counterparts. We first discuss solutions that incorporate a stage of cosmic inflation and estimate the primordial spectrum of density perturbations seeded during such a stage. Inflation driven by a spinor field turns out to be unappealing as it leads to a blue spectrum of perturbations and requires considerable fine-tuning of parameters. We next find that, for simple, quartic spinor self-interactions, non-singular cyclic cosmologies exist with reasonable parameter choices. These solutions might eventually be incorporated into a successful past- and future-eternal cosmological model free of singularities. In an Appendix, we discuss the classical treatment of spinors and argue that certain quantum systems might be approximated in terms of such fields.