Spectral diffusion tunneling two-level systems

An investigation is made of spectral diffusion due to flip-flop processes in tunneling two-level systems. It is shown that at low frequencies (2k _B T/) of the pulses that saturate the state of the two-level systems and at low temperatures (T<1°K) the mechanism of excitation energy transport through the spectrum of the systems due to flip-flop processes is effective.Institute of Physics, Georgian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 96, No. 3, pp. 453–458, September, 1993.     

Distribution systems design with two-level routing considerations

In this study, we formulate and analyze a strategic design model for three-echelon distribution systems with two-level routing considerations. The key design decisions considered are: the number and locations of distribution centers (DC’s), which big clients (clients with larger demand) should be included in the first level routing (the routing between plants and DC’s), the first-level routing between plants, DC’s and big clients, and the second-level routing between DC’s and other clients not included in the first-level routing. A hybrid genetic algorithm embedded with a routing heuristic is developed to efficiently find near-optimal solutions. The quality of the solution to a series of small test problems is evaluated—by comparison with the optimal solution solved using LINGO 9.0. In test problems for which exact solutions are available, the heuristic solution is within 1% of optimal. At last, the model is applied to design a national finished goods distribution system for a Taiwan label-stock manufacturer. Through the case study, we find that the inclusion of big clients in the first-level routing in the analysis leads to a better network design in terms of total logistic costs.     

Quantum diffusion in irregular crystals containing two-level tunnel systems

The quantum diffusion problem for admixture particles interacting with two-level tunnel systems (TLS) is investigated. It is shown that for the temperature range ₀ < T 1 K (where ₀ is the mean value of the energy level disturbance for admixture particles in the neighboring wells), and the TLS concentration is N_D 10²⁷ m^–3, the quantum diffusion coefficient for the admixture particles is determined by their interaction with the TLS's.Dedicated to the memory of Dmitri Nikolajevich ZubarevTranslated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 3, pp. 489–497, March, 1996.Translated by A. R. Shirikyan.     

Some properties of the stationary states of two-level systems

It is shown that some function J(x) is a constant at any point on the x axis at arbitrary variation of the potential energy of a two-level system. The application range of the LCAO method for calculating the wave functions of a one-dimensional two-level system is estimated.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 108, No. 1. pp. 69–78, July, 1996.     

Dynamics of quasicontinuous systems

Quasicontinuous functions are continuous on a residual subset of their domain. The class includes many standard examples from dynamical systems, including the baker transformation and interval exchange maps. We present standard results of continuous topological dynamics (such as that sensitive dependence follows from transitivity and dense periodic points) which extend to quasicontinuous dynamics     

A robust two-level domain decomposition preconditioner for systems of PDEs

Coarse spaces are instrumental in obtaining scalability for domain decomposition methods. However, it is known that most popular choices of coarse spaces perform rather weakly in presence of heterogeneities in the coefficients in the partial differential equations, especially for systems. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems which isolate the terms responsible for slow convergence. We give a general theoretical result and then some numerical examples on a heterogeneous elasticity problem.     

Dynamics of coupled systems

A survey in the form of a review of the author’s research results in the area of dynamics of coupled rotations and coupled systems is presented. The theorem on the existence of a trigger of the coupled singularities and the separatrix in the form of the number eight is presented with a few examples of coupled rotations of the simple systems with debalances. Also, a survey of models and dynamics of coupled systems composed of a number of deformable bodies (plates, beams or belts) with different properties of materials and discrete layer properties is presented and mathematically described. The constitutive stress–strain relations for materials of the coupled sandwich structure elements are presented for different properties: elastic, viscoelastic and creeping. The characteristic modes of the coupled system vibrations are obtained and analyzed for different kinds of materials and structure composition. The visualization of the characteristic numbers and modes and eigenamplitude forms are presented. Structural analysis of sandwich structure vibrations is done.     

Dynamics of systems on infinite lattices

The dynamics of infinite-dimensional lattice systems is studied. A necessary and sufficient condition for asymptotic compactness of lattice dynamical systems is introduced. It is shown that a lattice system has a global attractor if and only if it has a bounded absorbing set and is asymptotically null. As an application, it is proved that the lattice reaction-diffusion equation has a global attractor in a weighted l² space, which is compact as well as contains traveling waves. The upper semicontinuity of global attractors is also obtained when the lattice reaction-diffusion equation is approached by finite-dimensional systems.     

Moment functions of processes in some mechanical systems

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 9, pp. 1277–1279, September, 1989.