Structure evaluation of materials by electrical methods

A theoretical and practical framework of different problems has been discussed to explain advantages and limitations of techniques based on electrical sensing methods which are consistent to implement structure evaluation of materials. The term structure evaluation is generally used here to mean extracting the quantitative information of interest of a material or an object to be examined from a physical measurement, or more typically from a set of physical measurements, that themselves may be only indirectly related to the quantitative information desired. The paper emphasizes the point that the structure evaluation is a typical inverse problem and as such is made more difficult, since inverse problems are characteristically illconditioned, that is, small errors in the measurement typically lead to large errors in the solution. Use of physically motivated a priori information to diminishing such ill-conditioning is discussed. Features of updated electrical sensing methods, particularly those used for nondestructive testing (NDT) are considered. Potential advantages of the electrical methods compared to other NDT techniques are that they offer inexpensive, safe, nonharmful, and fast testing. Some novel achievements including excitation with a number of complex electric field excitation patterns on the object together with computer-assisted information acquisition have considerably extended both the potential and the scope of the electrical methods which will still be recognized. In order to present an up-to-date perspective, some conceptual and methodologic aspects have been considered for two structure evaluation problems, i.e., for generating a) algorithms for determining structural parameters of materials, such as density, moisture content, polymerization degree, etc., from dielectric spectra; b) tomographic cross-sectional maps of electrical parameters of the object to be examined.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Institute of Polymer Mechanics, Riga, Latvia. Published in Mekhanika Kompozitnykh Materialov, No. 1, pp. 124–134, January–February, 1996.     

Structure,properties, and tests of carbonreinforced plastics

The effect has been examined of various factors on the realization of mean values of mechanical properties in monofilaments in composites; the necessity has been pointed out of taking account of specific characteristics of the structure and behavior of reinforced polymers based on carbon fibers during determination of strain and tensile properties of these materials.     

Structure and properties of polymers

The history of the development of the structural mechanics of polymers is reviewed and the more important of its future tasks are noted.Institute of Heteroorganic Compounds, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 387–394, May–June, 1972.     

Structure of quasi-Newton minimization methods

A scheme for the design of quasi-Newton methods for unconstrained optimization problems is examined. A criterion for the positive definiteness of the quasi-Newton modification of the Hessian matrix is given. Quasi-Newton methods are described that cannot be placed within the classical scheme specified by the family of Broyden methods.     

Numerical methods for eighth-, tenth- and twelfth-order eigenvalue problems arising in thermal instability

Second-order finite-difference methods are developed for the numerical solutions of the eighth-, tenth- and twelfth-order eigenvalue problems arising in the study of the effect of rotation on a horizontal layer of fluid heated from below. Instability setting-in as overstability may be modelled by an eighth-order ordinary differential equation. When a uniform magnetic field also acts across the fluid in the same direction as gravity, instability setting-in as ordinary convection may be modelled by a tenth-order differential equation, while instability setting-in as overstability may be modelled by a twelfth-order differential equation. The numerical methods are developed by making direct replacements of the derivatives in the differential equations and then by computing the eigenvalues, which may incorporate Rayleigh number, horizontal wave speed and a time constant, from the resulting algebraic eigenvalue problem. The eigenvalues are also computed by writing the differential equations as systems of second-order differential equations and then using second- and fourth-order methods to obtain the eigenvalues. Numerical results obtained using the two approaches are compared with estimates appearing in the literature.     

Some properties of frames of subspaces obtained by operator theory methods

We study the relationship among operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space H. We get sufficient conditions on an orthonormal basis of subspaces E={Ei}_i∈I of a Hilbert space K and a surjective T∈L(K,H) in order that {T(Ei)}_i∈I is a frame of subspaces with respect to a computable sequence of weights. We also obtain generalizations of results in [J.A. Antezana, G. Corach, M. Ruiz, D. Stojanoff, Oblique projections and frames, Proc. Amer. Math. Soc. 134 (2006) 1031-1037], which relate frames of subspaces (including the computation of their weights) and oblique projections. The notion of refinement of a fusion frame is defined and used to obtain results about the excess of such frames. We study the set of admissible weights for a generating sequence of subspaces. Several examples are given.     

Structure and rheological properties of polymers

The viscoelastic properties of linear flexible-chain polymers with a narrow distribution, for which M > 5M_c (M_c corresponds to the formation of a three-dimensional entanglement network), their mixtures, and concentrated solutions are examined. It is established that under the influence of deformation the polymer may undergo a transition to the rubbery state, which thus defines the limit of its flow state; this transition is also observed in mixtures and concentrated solutions of high-molecular-weight polymers with a narrow distribution. The relative simplicity of the rheological properties of linear high-molecular-weight polymers and their mixtures is determined by the sharpness of the transition to the rubbery state. It has been found that in mixtures of high-molecular-weight polymers the apparent viscosity mechanism associated with a decrease in dissipative losses on transition of the high-molecular-weight components to the rubbery state is dominant; on a broad range of molecular weights (M > M_c), and moreover for polymer solutions, the decrease in entanglement network density under the influence of deformation acquires considerable importance. It is established that the separate effect of the high-molecular-weight components on the viscoelastic properties of their mixtures contradicts the idea of a random network of macromolecular chains. Attention is drawn to the temperature dependence of the viscosity of polymers with a narrow distribution and the dynamic properties of their mixtures. Problems of theoretical and practical interest associated with the particular rheological properties of polymer systems at high deformation rates are defined.     

Stability properties of collocation methods

Lower bounds for are given for which equidistant s-point collocation methods areA()-stable for arbitrarys.     

Order and stability properties of explicit multivalue methods

Recent papers by Burrage and Moss [1] and Burrage [2] have studied in some detail the order properties of implicit multivalue (or general linear) methods and certain classes of these methods were proposed as being suitable for solving stiff differential equations. In this present paper we study the order and stability of explicit multivalue methods with a view to deriving new families of methods suitablefor solving non stiff problems.     

Some relationships between implicit Runge-Kutta,collocation and Lanczosτ methods,and their stability properties

In this paper relationships between various one-step methods for the initial value problem in ordinary differential equations are discussed and a unified treatment of the stability properties of the methods is given. The analysis provides some new results on stability as well as alternative derivations for some known results. The term stability is used in the sense ofA-Stability as introduced by Dahlquist. Conditions for any polynomial collocation method or its equivalent to beA-Stable are derived. These conditions may be easily checked in any particular case.     

Preserving geometric properties of the exponential matrix by block Krylov subspace methods

Given a large square real matrix A and a rectangular tall matrix Q, many application problems require the approximation of the operation . Under certain hypotheses on A, the matrix preserves the orthogonality characteristics of Q; this property is particularly attractive when the associated application problem requires some geometric constraints to be satisfied. For small size problems numerical methods have been devised to approximate while maintaining the structure properties. On the other hand, no algorithm for large A has been derived with similar preservation properties. In this paper we show that an appropriate use of the block Lanczos method allows one to obtain a structure preserving approximation to when A is skew-symmetric or skew-symmetric and Hamiltonian. Moreover, for A Hamiltonian we derive a new variant of the block Lanczos method that again preserves the geometric properties of the exact scheme. Numerical results are reported to support our theoretical findings, with particular attention to the numerical solution of linear dynamical systems by means of structure preserving integrators. AMS subject classification (2000) 65F10, 65F30, 65D30     

Prediction properties of some extrapolation methods

Convergence acceleration methods consist in the construction of a sequence converging faster than the initial sequence. Each member of the new sequence is a guess for the limit and it is computed from a restricted number of terms of the initial sequence. It is shown herein how convergence acceleration methods can be used to predict the next (unknown) term of the initial sequence instead of its limit. Particular emphasis on Aitken's △² process and the E-algorithm is placed.     

Mapping properties of matrix summability methods

Summary Conditions on a complex matrix A are given which are necessary and sufficient for A to have the property that if x belongs to the complex linear space generated by the set of all convergent real sequences having nonnegative kth differences, then Ax belongs to the complex linear space generated by the set of all convergent real sequences having nonnegative jth differences. Entrata in Redazione il 18 giugno 1970.     

Change in the optical properties of ski-3 rubber in deformation,fatigue, and thermal and radiation aging

Conclusion Optical methods can be used in studying the kinetics of mechanical fatigue, thermal, and radiation aging; some general characteristics and differences in the development of these processes in elastomers with higher extinction can be detected with them. The sensitivity of the measurements is increased by the rational selection of the light wave-length of preliminary homogeneous biaxial stretching. A decrease in the thickness attained by deformation by one order of magnitude did not convert the optical medium to the class of singly scattering media, but the changes in the optical properties in aging were more pronounced against the background of decreasing extinction.Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 261–265, March–April, 1991.