Reduction of three-dimensional dynamical elasticity theory problems with arbitrarily located plane slits to integral equations

By generalizing a method described earlier /1/ for reducing three-dimensional dynamical problems of elasticity theory for a body with a slit to integral equations, integral equations are obtained for an infinite body with arbitrarily located plane slits. The interaction of disc-shaped slits located in one plane is investigated when normal external forces that vary sinusoidally with time (steady vibrations) are given on their surfaces.

Problems of the reduction of dynamical three-dimensional elasticity theory problems to integral equations for an infinite body weakened by a plane slit were examined in /1, 2/. The solution of the initial problem is obtained in /1/ by applying a Laplace integral transform in time to the appropriate equations and constructing the solution in the form of Helmholtz potentials with densities characterizing the opening of the slit during deformation of the body. The problem under consideration is solved in /2/ by using the fundamental Stokes solution /3/ with subsequent construction of the solution in the form of an analogue of the elastic potential of a double layer.     

Determination of some trace elements in the industrial process of aluminium production

Some trace elements in samples from the aluminium industry (Aluminium Kombinat, Titograd, Yugoslavia) were determined by instrumental neutron activation analysis. Samples characteristic for alumina production (bauxite, red sludge), reduction cell components (alumina, anode, AlF₃, cryolite) and aluminium produced (purity 99.5–99.7%) have been analyzed. 10 trace elements were determined under a given set of working conditions and followed through the routine production.     

Constitutive modeling of cyclic stress softening in filled elastomers

Quasi-static cyclic loading tests on filled rubber-like materials reveal a significant stress softening in the first cycle. The magnitude of this softening, widely known as the Mullins effect, reduces in the next cycles until it reaches a stabilized value referred to as hysteresis. In this contribution, we associate the hysteresis with the fracture of carbon bonds in the filler network. In order to calculate the cyclic energy dissipation, we modify the classic concept of network decomposition [1, 2] and add a new network considered to be responsible for the breakage and re-formation of carbon black aggregates during loading and unloading. The proposed model is in-line with a wide range of experimental observations. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the supports of functions

In this paper, finite difference and finite element methods are used with nonlinear SOR to solve the problems of minimizing strict convex functionals. The functionals are discretized by both methods and some numerical quadrature formula. The convergence of such discretization is guaranteed and will be discussed. As for the convergence of the iterative process, it is necessary to vary the relaxation parameter in each iterations. In addition, for the model catenoid problem, boundary grid refinements play an essential role in the proposed nonlinear SOR algorithm. Numerical results which illustrate the importance of the grid refinements will be presented.

     

Simple phase-only optical decryption with misalignment-free input

An improved optical decryption system based on kinogram encoding is proposed. The decrypted phase image is obtained by optically descrambling the encrypted image with the decrypting phase key. Only a single Fourier lens is needed to generate intensity patterns from the decrypted phase image. The design and simulation results have confirmed the proposed technique as a novel, simple, and robust decryption architecture.     

Metalated nitriles: chelation-controlled cyclizations to cis and trans hydrindanes and decalins

Chelation provides a powerful means of stereocontrol in alkylations of metalated nitriles. Doubly deprotonating a series of cyclic beta-hydroxynitriles triggers cyclizations that implicate metalated nitrile intermediates having configurations imposed by chelation with an adjacent, chiral lithium alkoxide. Identifying chelation as a general stereocontrol element explains several previously anomalous alkylations of metalated nitriles and provides a potential solution to the long-standing difficulty of synthesizing trans-hydrindanes. Employing chelation to control the metalated nitrile geometry permits selective cyclizations to cis and trans hydrindanes and decalins and provides key insight into the geometrical requirements of these demanding cyclizations.