On Decidability of List Structures

Siberian Mathematical Journal - The paper studies computability-theoretic complexity of various structures that are based on the list data type. The list structure over a structure S consists of...     

The Moment Finite-Element Scheme in Problems of Nonlinear Continuum Mechanics

The conceptual and theoretical fundamentals of the original moment finite-element scheme (MFES) developed to solve problems of nonlinear continuum mechanics are presented. Typical examples of model problems are given to illustrate the advantages of the MFES over other traditional finite-element schemes. The basic relationships for studying the nonlinear deformation and distortion of mechanical continuum systems are formulated in an invariant tensor form. Also, some mathematical algorithms specially developed to solve systems of nonlinear equations of high order are described. The numerical solutions obtained are proved reliable and rapidly converging to the exact solutions for a sufficient number of test problems. Results of strength, postbuckling stability, vibration, fracture, and high-speed influence analyses of real mechanical systems are illustrated.     

Experimental–Theoretical Technique for Determining the Equation-of-State Parameters for Soils

This paper considers an experimental–theoretical technique for determining pressure–strain curves and curves of yield strength versus pressure for soils based on disagreement between data of physical and numerical modeling of wave processes in a system of split Hopkinson bars with a soil sample in a holder. A convergent iterative procedure was developed to refine the equation-of-state parameters of soils obtained by the Kolsky method. The error of the technique is analyzed, the role of friction and the coefficient of sliding friction between the soil and the deformed holder.     

Temperature increase with neck propagation in polymers

The heating arising in the neck propagation in polymers is investigated. The heat equation describing the neck temperature is modified. An analytic solution describing the maximum temperature of the neck is obtained. A method for determining the heat transfer coefficient is developed. The neck heating temperature in polyethylene terephthalate can attain 155°C which is much greater than it is usually thought. The corresponding value for polycarbonate is only 31°C.     

Analysis of photoconductivity spectra with a strongly delayed photoresponse

The problem of recording the photoresponse spectra in semiconductors with the persistent photoconductivity effect is considered for heterostructures with ??slow?? charge states at the heterointerface. The proposed versions of the solution of this problem include the use of modulation of excitation or reconstruction of the true shape of the spectrum recorded in the direct-current mode.     

Solution of problems of oblique penetration of axisymmetric projectiles into soft soil based on local interaction models

A comparative analysis of the solutions of the three-dimensional problem of the oblique penetration of a rigid body into soft soil is carried out arsing interaction models based on one-dimensional solutions of the problem of the spherical cavity expansion. Both the well-known self-similar analytical solutions for an incompressible medium as well as the generalized solution for a compressible elastoplastic medium with separation of the shock wave which arises are considered. Use of the incompressible medium hypothesis, disregarding flow separation, in estimating the maximum values of the resistive forces leads to large errors. Taking account of compressibility enables the resistive forces to be refined appreciably and enables a satisfactory estimate of the deviation of the trajectories of bodies from the initial direction of motion to the obtained. In the proposed method of solving oblique penetration problems, a three-dimensional problem is reduced, on the basis of the plane sections hypothesis and disregarding peripheral mass and momentum flows, to the combined solution of a number of axisymmetric problems for each meridional section. It is shown that, with well-known local interaction models, this approach enables the reliability of the calculation of both the force and the kinematic characteristics of the penetration process to be increased considerably due to the fact that the dynamics of the free surface and cavitation effects of the covitating flow are taken into account.