Shape sensitivity of a plane crack front

The 3D‐elasticity model of a solid with a plane crack under the stress‐free boundary conditions at the crack is considered. We investigate variations of a solution and of energy functionals with respect to perturbations of the crack front in the plane. The corresponding expansions at least up to the second‐order terms are obtained. The strong derivatives of the solution are constructed as an iterative solution of the same elasticity problem with specified right‐hand sides. Using the expansion of the potential and surface energy, we consider an approximate quadratic form for local shape optimization of the crack front defined by the Griffith criterion. To specify its properties, a procedure of discrete optimization is proposed, which reduces to a matrix variational inequality. At least for a small load we prove its solvability and find a quasi‐static model of the crack growth depending on the loading parameter. Copyright © 2003 John Wiley & Sons, Ltd.     

Chaos-controlling technique for suppressing self-modulation in backward-wave tubes

A method for suppressing self-modulation in backward-wave tubes is proposed. Additional delay is introduced into the feedback circuit, owing to which the output signal amplitude affects the electron beam current that enters into the interaction space. Numerical simulations demonstrate that the operating current in the single-frequency oscillation mode may be increased roughly twofold.     

Effects of Moisture and Stresses on the Structure and Properties of Polyester Resin

The results of a complex study of structural changes in a cured Norpol 440 polyester resin under the action of damp environment and mechanical loading are presented. A considerable effect of absorbed moisture on the structure and some characteristics of the material is revealed by using thermophysical methods and X-ray diffractometry. The joint effect of moisture and mechanical stress is estimated by investigating the creep in stationary and nonstationary moisture conditions. The anisotropy of the material structure formed during creep is evaluated from the results of dilatometric measurements. It is found that the degree of anisotropy of the material after creep accompanied by moisture sorption is higher than that after creep in the conditions of moisture equilibrium with atmosphere. It is established that the aftercure and relaxation of the residual creep deformation come to an end at heating to 80-85°C. At a further rise in temperature and repeated heating, changes in the material structure are not observed.     

Improved tabu search algorithm for the handling of route duration constraints in vehicle routing problems with time windows

This note introduces a refinement to a previously proposed tabu search algorithm for vehicle routing problems with time windows. This refinement yields new best known solutions on a set of benchmark instances of the multi-depot, the periodic and the site-dependent vehicle routing problems with time windows.     

Stratifiable Families of Extremals and Sufficient Conditions for Optimality in Optimal Control Problems

It is shown that, if a parametrized fämily of extremals F can be stratified in a way compatible with the flow map generated by F, then those trajectories of the family which realize the minimal values of the cost in F are indeed optimal in comparison with all trajectories which lie in the region R covered by the trajectories of F. It is not assumed that F is a field covering the state space injectively. As illustration, an optimal synthesis is constructed for a system where the flow of extremals exhibits a simple cusp singularity.     

Precise measurement of magnetic moment of short-lived β-emitting nuclei12B ( I π=1+, T 1/2=20.18 ms)

The spin polarized β-emitting nuclei¹²B (I ^π=1⁺,T _1/2=20.18 ms) were produced by the nuclear reaction¹¹B(d, p)¹²B and by the selection technique of the incident deuteron energy and the¹²B recoil angle following the nuclear reaction. The nuclear magnetic moment of the short-lived nuclei¹²B was measured by β-NMR with the β-NMR and β-NQR setup established for the first time in China. The nuclear magnetic moment of¹²B was determined to be μ=0.99993±0.00048 nm org=0.99993±0.00048 after the precise correction of the Knight shift.     

Synthesis and electrical characteristics of polyaniline nanoparticles and their polymeric composite

Monodisperse polyaniline nanoparticles (PAPSSA) were synthesized from an oxidative dispersion polymerization using poly(sodium 4-styrenesulfonate) (PSSA) as both a polymeric stabilizer and a dopant agent due to its acidity. The nanoparticles were being stabilized with two different molecular weight of PSSA. Size effect of PAPSSA particles were examined by scanning electron microscopy (SEM), transmission electron microscopy (TEM) and dynamic light scattering (DLS). The d.c. electrical conductivity of composite films on the glass substrate was measured by a four-probe method. It was found that the electrical properties of the composite films are affected by the content of nano-sized polyaniline and different molecular weights of stabilizer in the poly(vinyl alcohol) (PVA) matrix.     

CuPc molecules adsorbed on Au(1 1 0)-(1 × 2): growth morphology and evolution of valence band states

We present the growth morphology, the long-range ordering, and the evolution of the valence band electronic states of ultrathin films of copper phthalocyanine (CuPc) deposited on the Au(1 1 0)-(1 × 2) reconstructed surface, as a function of the organic molecule coverage. The low energy electron diffraction patterns present a (5 × 3) reconstruction from the early adsorption stages. High-resolution UV photoelectron spectroscopy data show the disappearance of the Au surface states related to the (1 × 2) reconstruction, and the presence of new electronic features related to the molecule-substrate interaction and to the CuPc molecular states. The CuPc highest occupied molecular orbital gradually emerges in the valence band, while the interface electronic states are quenched, upon increasing the coverage.     

Asymptotic stability, ergodicity and other asymptotic properties of the nonlinear filter

In this work we study connections between various asymptotic properties of the nonlinear filter. It is assumed that the signal has a unique invariant probability measure. The key property of interest is expressed in terms of a relationship between the observation σ field and the tail σ field of the signal, in the stationary filtering problem. This property can be viewed as the permissibility of the interchange of the order of the operations of maximum and countable intersection for certain σ-fields. Under suitable conditions, it is shown that the above property is equivalent to various desirable properties of the filter such as

(a) uniqueness of invariant measure for the signal,

(b) uniqueness of invariant measure for the pair (signal, filter),

(c) a finite memory property of the filter,

(d) a property of finite time dependence between the signal and observation σ fields and

(e) asymptotic stability of the filter.

Previous works on the asymptotic stability of the filter for a variety of filtering models then identify a rich class of filtering problems for which the above equivalent properties hold.