On linear and nonlinear aspects of dynamic mode decomposition

The approximation of reduced linear evolution operator (propagator) via dynamic mode decomposition (DMD) is addressed for both linear and nonlinear events. The 2D unsteady supersonic underexpanded jet, impinging the flat plate in nonlinear oscillating mode, is used as the first test problem for both modes. Large memory savings for the propagator approximation are demonstrated. Corresponding prospects for the estimation of receptivity and singular vectors are discussed. The shallow water equations are used as the second large‐scale test problem. Excellent results are obtained for the proposed optimized DMD method of the shallow water equations when compared with recent POD‐based/discrete empirical interpolation‐based model reduction results in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Heat capacity of the PbFe1/2Ta1/2O3 perovskite-like compound

Physics of the Solid State - The heat capacity C p(T) of the complex perovskite PbFe1/2Ta1/2O3 has been studied using adiabatic calorimetry in the temperature range 150–370 K. Three diffuse...     

Functional law of iterated logarithm for normalized integrals of processes with weak dependence

For normalized integrals of processes with weak dependence, we prove the law of iterated logarithm in the Strassen form. The results obtained are used for the construction of a curvilinear confidence region in which a solution of an equation with small parameter is sought. Donetsk University, Donetsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 4, pp. 490–499, April, 1997.     

Ferroelasticity of materials with a mechanical shape memory

It is extremely difficult to take into account the variety of aspects of the behavior of solids when they are deformed. Hence, when designing constructions, simplifying models are introduced which take into account only the most important properties of the materials in each specific case (creep, aftereffect, plasticity, etc.), and the corresponding phenomenological theories are employed [1], In this paper we attempt to construct the fundamentals of a theory which describes the phenomenon of ferroelasticity due to the behavior of thermoelastic martensite, first discovered in [2], The apparatus of this theory will be necessary when designing self-recovering constructions which can be manufactured from materials with a mechanical shape memory.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 122–126, May–June, 1979.     

Influence of Solvent Polarity and Viscosity on Nonradiative Processes in Oligothiophenes with Intramolecular Charge Transfer

By the methods of luminescence, picosecond spectroscopy, and quantumchemical calculations the mechanisms of electron excitation energy deactivation in some oligothiophenes with intramolecular charge transfer depending on the solvent polarity and viscosity have been investigated. While for 2Npiperidino5(2,2dicyanovinyl)thiophene (PDCVT) the main channel of nonradiative deactivation is the transition to a lower intermediate state with a twisted double bond controlled by the medium viscosity, in the case of (E){2[25piperidino2thienyl]6(trifluoridemethyl)4H4pyranylidene}propanedinitryl (PTFDN) fluorescence quenching is initiated by the solvent polarity. For two other oligothiophenes, 2Npiperidino5cyanothiophene (PCT) and 2Npiperidino5cyanoterthiophene (PCTT), differing in the length of the thiophene chain, we have revealed, along with the effective quenching of fluorescence in shortchain PCT (independent of the solvent polarity and viscosity), an increase in the radiation capacity in PCTT with increasing polarity of the solvent. The possible mechanisms of nonradiative deactivation in the investigated oligothiophenes are discussed.     

Multiphoton absorption controlled by the resonance optical stark effect in crystals

Probabilities of n-photon transitions between upper valence and lower conduction bands under conditions in which the frequency of light is in resonance with the frequency of adjacent transition between two conduction bands are calculated for arbitrary integer n. The case of n = 3 is investigated in detail. Effects caused by transformation of the electronic band spectrum due to the resonance optical Stark effect are analyzed. It is shown that the rate of photogeneration of electron-hole pairs as a function of radiation intensity j is nonmonotonic and includes areas of extremely fast rise and/or decrease due to the appearance of new van Hove singularities in the modified band spectrum.