The limits of hamiltonian structures in three-dimensional elasticity,shells, and rods

Summary This paper uses Hamiltonian structures to study the problem of the limit of three-dimensional (3D) elastic models to shell and rod models. In the case of shells, we show that the Hamiltonian structure for a three-dimensional elastic body converges, in a sense made precise, to that for a shell model described by a one-director Cosserat surface as the thickness goes to zero. We study limiting procedures that give rise to unconstrained as well as constrained Cosserat director models. The case of a rod is also considered and similar convergence results are established, with the limiting model being a geometrically exact director rod model (in the framework developed by Antman, Simo, and coworkers). The resulting model may or may not have constraints, depending on the nature of the constitutive relations and their behavior under the limiting procedure. The closeness of Hamiltonian structures is measured by the closeness of Poisson brackets on certain classes of functions, as well as the Hamiltonians. This provides one way of justifying the dynamic one-director model for shells. Another way of stating the convergence result is that there is an almost-Poisson embedding from the phase space of the shell to the phase space of the 3D elastic body, which implies that, in the sense of Hamiltonian structures, the dynamics of the elastic body is close to that of the shell. The constitutive equations of the 3D model and their behavior as the thickness tends to zero dictates whether the limiting 2D model is a constrained or an unconstrained director model. We apply our theory in the specific case of a 3D Saint Venant-Kirchhoff material andderive the corresponding limiting shell and rod theories. The limiting shell model is an interesting Kirchhoff-like shell model in which the stored energy function is explicitly derived in terms of the shell curvature. For rods, one gets (with an additional inextensibility constraint) a one-director Kirchhoff elastic rod model, which reduces to the well-known Euler elastica if one adds an additional single constraint that the director lines up with the Frenet frame. This paper is dedicated to the memory of Juan C. Simo This paper was solicited by the editors to be part of a volume dedicated to the memory of Juan Simo.     

Characterization of continuous distributions in terms of moments of extremal statistics

We give characterizations of continuous distributions in terms of moments of order statistics when the sample size is random. In particular, we characterize uniform, exponential, Pareto, and logistic distributions. Special cases of a random sample size (logarithmic series, geometrical, truncated binomial, truncated negative binomial, and truncated Poisson distribution) are also considered. Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part I.     

Influence of preparation method on SrMoO4 impurity content and magnetotransport properties of double perovskite Sr2FeMoO6 polycrystals

The magnetic and electric properties of the Sr₂FeMoO₆ compound produced under different preparation conditions were studied. Depending on the preparation condition, a strong variation in the nonmagnetic SrMoO₄ impurity content was found, which in turn determined the metallic or semiconducting behavior of the resistivity of the Sr₂FeMoO₆ compound. There was also evidence that SrMoO₄ played a crucial role in modifying the low magnetic field intergrain tunneling magnetoresistance in Sr₂FeMoO₆. In addition, we have established a simple method to prepare the single phase Sr₂FeMoO₆ polycrystals.     

Synchronization Analysis of Coupled Noncoherent Oscillators

We present two different approaches to detect and quantify phase synchronization in the case of coupled non-phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the R?ssler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators.     

Anomalous behavior of conductivity of the confined Q1D electron system over liquid helium

Conductivity of electrons in a quasi-one-dimensional (Q1D) system over liquid helium in narrow channels with the parabolic profile of the potential well has been investigated at temperature T, from 0.4 to 1.8 K, for different driving electric fields and radius of channel curvature. The interval of linear electron densities varied from 2.18×10³ up to 1.7×10⁶ cm⁻¹.

The inverse mobility (1/μ_eff) in the electron-ripplon scattering region at the high linear densities of charges in the channel increases with temperature decreasing. This anomalous behavior of the electron transport in the low-temperature region has been explained by either the electron ordering or the polaronic effects in confined conducting channels. The nonlinear behavior of the electron velocity as a function of a driving electric field is supposed to be due to Breg–Cherenkov radiation of the ripplons. The radiation occurred if the velocity of electrons in the channel approaches to the critical value.     

Scattering of scalar fields by rough surfaces. Accounting for multiple scattered waves

Physical Engineering Institute, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 5, pp. 565–574, May, 1991.     

Kink propagation induced by multiplicative noise

The influence of spatio-temporal external multiplicative fluctuations on a single kink in a bistable distributed system is studied. For this purpose we derive a stochastic dynamic equation for the position of the shifted kink. An analytical estimate for spatio-temporally uncorrelated fluctuations is represented and discussed. We draw the conclusion that multiplicative noise induces a propagation of the most probable kink into the region of larger noise. This effect is demonstrated in numerical simulations.     

Die Lasker-Bedingung für Nicht Endlich Erzeugte Moduln

Ohne Zusammenfassung

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Growth of InP/InGaAs multiple quantum well structures by chemical beam epitaxy

InP/InGaAs multiple quantum well structures with up to 200 periods have been grown by CBE. These structures exhibit exceptional lateral uniformity, measured as ±1 Å in period, ±13 ppm in lattice mismatch and ±0.5 nm in wavelength across a 2 inch wafer. Good surface morphology, sharp interfaces and excellent growth control have all been demonstrated.