On entire nonnegative solutions of quasilinear inequalities of elliptic type that vanish on a set of positive measure

In the article, it is proved that any nonnegative solution of an elliptic quasilinear inequality that vanishes on a subset of positive measure is trivial. __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 112–118, 2005.     

Loss in a rectangular optical waveguide induced by the crossover of a second waveguide

We calculate the loss induced in a single-mode rectangular optical waveguide by the presence of a second waveguide, perpendicular to the first, which crosses over the first waveguide at a variable distance d. Our calculation is applied to the analysis of several doped silica waveguides of practical importance for optical circuit design.     

Discontinuous travelling wave solutions for certain hyperbolic systems

In an earlier paper on a malignant cell invasion model (Marchantet al., SIAM J. Appl. Math, 60, 2000) we introduced a novelform of discontinuous travelling wave solution. These solutionscould be studied easily by combining behaviour within a phaseplane with the Rankine–Hugoniot shock conditions, whichdescribe properties (such as the ratio of the jump discontinuitiesto the speed of propagation) that solutions may possess. Theseresults were new for several reasons. The shock conditions relateto hyperbolic equations (which the model is) but were appliedin a travelling wave ordinary differential equation phase planeusing techniques that usually apply to parabolic reaction–diffusionsystems. In addition the solutions possess singular behaviournear several points in the phase plane but in spite of thisthere exists a robust and stable family of physically interestingsolutions. In this paper we discuss two previously studied models, oneof detonation theory and one of angiogenesis. We show that eachof these models also possesses a family of discontinuous travellingwave solutions which was not previously discovered. Of particularinterest is the solution which has a blunt interface at thefront of the invading profile. In all three models it is thissolution that is seen to stably evolve from physically relevantinitial data, and for physically relevant parameter values. This work confirms the robustness of these novel travellingwave solutions and their applicability to a wider range of mathematicalmodelling situations.     

Threshold electrical switching in As45Te55-xInx and As50Te50-xInx glasses

The electrical switching behaviour of As₄₅Te_55-xIn_x (5≤x≤15) and As₅₀Te_50-xIn_x (2.5≤x≤11.5) has been studied over a wide range of compositions. These glasses are found to exhibit threshold switching. The composition dependence of switching voltage (V_t) has been found to exhibit a change in slope and a local minimum at compositions x=10 and 12.5 for As₄₅Te_55-xIn_x and x=7.5 and 10.8 for As₅₀Te_50-xIn_x, respectively. The slope change in V_t verses x and the local minimum have been identified using two network topological effects, namely the rigidity percolation threshold and the chemical threshold. Received: 23 August 2001 / Accepted: 27 August 2001 / Published online: 11 February 2002     

Magnetic properties of mechanically alloyed Co–Ti powder

An amorphous phase containing traces of non-transformed Co and Ti powders was obtained by mechanical alloying nominal compositions of Co₆₇Ti₃₃ and Co₅₀Ti₅₀ in a high-energy ball-mill. These alloys were prepared from elemental powders of Co and Ti. The heat treatment of Co₆₇Ti₃₃ at 573, 873 and 1173 K crystallized nanoparticles of Co₂Ti and Co₃Ti compounds, while the same treatments conducted on Co₅₀Ti₅₀ resulted in the formation of Co₂Ti and CoTi nanoparticles. The saturation magnetizations reached a maximum value in the amorphous state and they decreased when the temperatures of the heat treatment rose. Demagnetizing interparticle interaction effects were estimated through hysteresis loops and initial magnetization curves using the Fourier technique.     

Carbon diffusion between the volume and surface of (100) molybdenum

The diffusion of carbon atoms between the volume and the surface of (100) molybdenum is directly studied at temperatures between 1400 and 2000 K (i.e., at process temperatures) for the first time. The balance of carbon atoms in the system is determined. The difference in the activation energies of carbon dissolution and precipitation, ΔE=E s 1-E1s, is found for the case when the diffusion fluxes of dissolved and precipitated carbon atoms are in equilibrium. This difference defines the enrichment of the surface by carbon relative to the bulk. The experimentally found activation energy of carbon dissolution is Es1=3.9 eV. The activation energy of carbon precipitation is estimated at E 1 s=1.9 eV. The latter value is close to the energy of bulk diffusion of carbon in molybdenum.     

Generation of 3rd and 5th harmonics in a thin superconducting film by temperature oscillations and isothermal nonlinear current response

The generation of harmonics of the voltage response is considered when an AC current is applied through a superconducting film above T_c. It is shown that almost at all temperatures the mechanism of the temperature oscillations created by the AC current and the temperature dependence of the resistance dominates over the isothermal nonlinear electric conductivity. Only in a narrow critical region close to T_c the latter is essential for the generation of the harmonics. A detailed investigation of harmonics generation provides an accurate method for measuring the thermal boundary conductance between the film and the insulating substrate. The critical behaviour of the third harmonic will give a new method for the determination of the lifetime of metastable Cooper pairs above T_c. The comparison of the calculated fifth harmonics of the voltage with the experiment is proposed as an important test for the applicability of the employed theoretical models. Received 8 September 2001     

Controlling global stochasticity of Hamiltonian systems by nonlinear perturbation

A method of controlling global stochasticity in Hamiltonian systems by applying nonlinear perturbation is proposed. With the well-known standard map we demonstrate that this control method can convert global stochasticity into regular motion in a wide chaotic region for arbitrary initial condition, in which the control signal remains very weak after a few kicks. The system in which chaos has been controlled approximates to the original Hamiltonian system, and this approach appears robust against small external noise. The mechanism underlying this high control efficiency is intuitively explained. Received 15 January 2002 Published online 6 June 2002