Relativistic form factor in terms of wave functions of composite systems at rest

Joint Institute for Nuclear Research, Dubna. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 78, no. 2, pp. 227–233, February, 1989.     

Relativistic coulomb quasipotential and new narrow resonances in systems of charged particles

Scientific-Research Institute of Nuclear Physics at the Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 83, No. 2, pp. 175–185, May, 1990     

Infrared singularities of gluon Green's functions and two-quark interaction quasipotential in quantum chromodynamics

Institute of High Energy Physics, Serpukhov. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 86, No. 1, pp. 53–73, January, 1991.     

Fundamentals of the statistical mechanics of composite systems

Conclusions The proposed variant of the statistical theory of composite media makes it possible to derive relations between the effective parameters of the medium and the dispersion characteristics of the structure, and also to account for the effect of specimen shape and variable structural heterogeneity on these parameters. In the limiting case of an infinitely large specimen, all relationships comply with the results of the traditional theory of composite systems.Presented at the Sixth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, November, 1986).Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 21–30, January–February, 1988.     

Mechanics of composite materials in fuel cell systems

The science and technology that are fundamental to the concept of composite materials are also the foundation for the construction and function of fuel cells and fuel cell systems. The present paper outlines this relationship in the context of the physics and chemistry that are enabled by the specific selection and arrangement of constituents of the functional composite fuel cell. General principles of operation are described, and fundamental issues are defined that must be addressed by the composites community if the fuel cell science and engineering is to advance. Examples of several types of functional composite fuel cells are presented, with emphasis on polymer electrolyte (PEM) and solid-oxide (SOFC) systems. Specific needs for continued research are identified.Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 3–16, January–February, 2005.     

One dynamic model of a composite material

A model has been constructed for the propagation of waves orthogonally to the layers or fibers of a composite material and based on the Voltaire equation of state with oscillating kernels. The results of treatment of experimental data are presented.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 2, pp. 364–367, March–April, 1976.     

Stabilization of a class of nonlinear composite stochastic systems

This paper deals with the stability for a class of nonlinear composite stochastic systems by feedback laws.Firstly,we give sufficient conditions for the existence of feedback laws which render the equilibrium solution of the stochastic system globally asymptotically stable in probability.Secondly,for stochastic systems of the same type,we prove that there exists a linear feedback law which exponentially stabilizes in mean square the closed–loop stochastic system at its equilibrium.     

Relativistic Kronig-Penney-type Hamiltonians

The relativistic Kronig-Penney model is extended to a wide class of point interactions introduced in the nonrelativisfic case by Paul Chernoff and the author. A generalized Kronig-Penney relation, which converges to the standard Kronig-Penney relation in the nonrelativistic limit, is shown to determine the spectrum of the corresponding Hamiltonian. Several examples are considered, including the well-known special cases of electrostatic and Lorentz scalar point interactions, as well as several new solvable models.     

A model of general systems

In this paper a mathematical model of general systems with not only one, but also more than one relation between the objects of the systems, was introduced. Among others, the concepts of partial systems, similarity of systems, embeddability of systems and free sum of systems were introduced. The following theorem was proved: there is no system whose object set consists of all systems.     

Gradient estimates for parabolic systems from composite material

In this paper, we derive W~(1,∞) and piecewise C~(1,α) estimates for solutions, and their t-derivatives, of divergence form parabolic systems with coefficients piecewise H¨older continuous in space variables x and smooth in t. This is an extension to parabolic systems of results of Li and Nirenberg [Comm Pure Appl Math, 2003, 56:892–925] on elliptic systems. These estimates depend on the shape and the size of the surfaces of discontinuity of the coefficients, but are independent of the distance between these surfaces.     

A composite model for municipal solid waste

The mechanical behaviour of municipal solid waste is very complex due to the internal structure and differs considerably from ordinary materials. The fundamental idea of the presented mechanical constitutive model is the split of the material into two solid phases, justified by experimental observations, where fibrous particles signi.cantly influence the composite behaviour. Constitutive laws are independently introduced for each phase. A .nite deformation theory is applied, whereas the concept of elastoplasticity allows reproducing the highly non-linear stress-strain relations. A creep law describes time-depending deformation under compression loads. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)