Dynamics of film

The general theory of films as two-dimensional continua are elaborated upon. As physical realizations of such a model this paper examines: inextensible films, elastic films, and nets.The suggested dynamic equations have enabled us to find out the characteristic speeds of wave propagation of the invariants of external and internal geometry and formulate the criteria of instability of their shape. Also included herein is a detailed account of the equation describing the film motions beyond the limits of the shape stability accompanied by the formation of wrinkles.The theory is illustrated by examples.The effort was supported by Dr. A. Amos, Materials and Structures Division, Office of Aeronautics and Space Technology, National Aeronautics and Space Administration.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS7-100 sponsored by the National Aeronautics and Space Administration.     

The supersonic motion of a crowdion. The one-dimensional model with nonlinear interaction between the nearest neighbours

An anharmonic Frenkel-Kontorova model is used for the investigation of a moving crowdion. The dynamic equations are solved exactly in the case of a special kind of anharmonicity. It is shown that the crowdion described by such model can move with supersonic velocities. The dependence of the crowdion width on the velocity is found.     

Nanomechanical magnetization reversal

The dynamics of the ferromagnetic order parameter in thin magnetic films is strongly affected by the magnetomechanical coupling at certain resonance frequencies. By solving the equation of motion of the coupled mechanical and magnetic degrees of freedom we show that the magnetic field induced magnetization switching can be strongly accelerated by the lattice and illustrate the possibility of magnetization reversal by mechanical actuation.     

Spectral broadening of continuous-wave monochromatic pump radiation caused by stimulated Brillouin scattering in optical fiber

We experimentally show that, when stimulated Brillouin scattering is generated in optical fiber by use of monochromatic cw pump radiation, the transmitted pump radiation exhibits spectral broadening that is much narrower than the classical homogeneous gain-narrowed Brillouin bandwidth. The bandwidth is practically independent of the pump strength, fiber characteristics, and the waveguide-induced inhomogeneously broadened bandwidth of the Stokes emission. We show that these properties arise from strong parametric coupling of the Stokes and pump signals in the pump-depletion region.     

Matching of asymptotic models in scattering of a plane acoustic wave by an elastic cylindrical shell

Scattering of a plane harmonic acoustic wave by an elastic cylindrical shell is considered. The procedure based on matching of asymptotic models is developed. The long-wave models (the Kirchhoff-Love theory (or its refinement) and the long-wave high-frequency approximation) are exploited in the vicinities of zero frequency and thickness resonance frequencies, whilst the model of a fluid-loaded flat elastic layer is utilized outside the aforementioned vicinities. Comparison with the exact solution demonstrates that the proposed approach is highly efficient for total synthesis of the scattered pressure as well as for uniform approximation of the resonant curves associated with partial modes.     

The Role of Singlet and Triplet Dioxygen Molecules in the EPR and 1H NMR Spectrum Line Broadening

In the Mo^(VI)/H₂O₂/H₂O system, the relaxation time (T ₁) of protons in a water molecule and in a CH₃ group decreases 10 to 30 times under conditions of dismutation of H₂O₂ with the formation of ¹O₂(¹_g). It is experimentally found that the overequilibrium concentration of triplet dioxygen cannot be the reason behind a decrease in T ₁ in the ¹H NMR spectra. Neither can it explain the anomalous line broadening in ESR spectra under conditions of ¹O₂(¹_g) formation in the systems V^(V)/H₂O₂/AcOH and Mo^(VI)/H₂O₂/H₂O. Ab initio calculations showed that it is principle possible that the ³O₄(³·^- _g-¹_g) molecule exists in a snake-like form and is formed by the reaction between ³O₂(³·^- _g) and ¹O₂(¹_g), which is the product of H₂O₂ decomposition in the systems V^(V)/H₂O₂/AcOH and Mo^(IV)/H₂O₂/H₂O. The interaction of ¹O₂ with the ·OOH radical is exothermic (Q = 2.30 kcal/mol) and leads to the formation of ·OOOOH. It is assumed that the paramagnetic species of type ·OOOOH or ³O₄(³ A ₁) that is formed in the reaction might be responsible for the spectral effects observed.     

Monotonicity of the Generalized Reduced Module

In terms of polar sets, we complement some Dubinin's inequalities expressing the monotonicity of the generalized reduced module for open subsets of and by equality cases. These results are applied to extremal problems of geometric function theory. Bibliography: 19 titles.     

Ballistic technique to model interaction of a freely flying body with the blast area

Experimental modeling of processes taking place when a freely flying object experiences the influence of explosion is considered. The basic factors acting on the object in the blast area and disturbing its trajectory are revealed. The explosion energy transferred to a conic body flying with a supersonic velocity is estimated. Analysis of similarity criteria allows one to estimate the feasibility of modeling such full-scale processes under the condition of ballistic experiment.