Resonances and O-curves in Hamiltonian systems

We investigate the problem of the existence of trajectories asymptotic to elliptic equilibria of Hamiltonian systems in the presence of resonances.Comment: 12 page

Pulse Current Treatment Effect on the Strength of Reinforcing Steel and Its Weld Joint under Impact Loading

Приведены результаты испытаний на статическое и ударное растяжение образцов из строительной арматурной стали в состоянии поставки, образцов со стыковым сварным соединением в рабочей части, а также образцов, предварительно обработанных пропус­канием импульсного электрического тока высокой плотности. Показано, что повышенная скорость деформации вызывает увеличение прочности, а обработка импульсным электри­ческим током существенно влияет на прочность и пластичность металла с дефектами в области сварного шва как при статическом, так и при ударном растяжении.Наведено результати випробувань на статичний та ударний розтяг зразків із будівельної сталі у стані поставки, зразків зі стиковим зварним з’єднанням у робочій частині та зразків, що попередньо обробляли пропусканням імпульсного електричного струму високої густини. Показано, що підвищена швидкість деформації призводить до збільшення міцності, а обробка імпульсним електричним струмом суттєво впливає на міцність і пластичність металу з дефектами в області зварного шва як за статичного, так і ударного розтягу.We present results o f static and impact tension tests o f as-received reinforcing steel specimens, specimens with weld joints in their test portion, as well as specimens pretreated by high-density pulse current. As test results demonstrate, an increased strain rate enhances strength, and the pulse current treatment greatly influences the strength and plasticity o f a defect-containing weld metal under static and impact tension

Diagnosability of Fuzzy Discrete Event Systems

In order to more effectively cope with the real-world problems of vagueness, {\it fuzzy discrete event systems} (FDESs) were proposed recently, and the supervisory control theory of FDESs was developed. In view of the importance of failure diagnosis, in this paper, we present an approach of the failure diagnosis in the framework of FDESs. More specifically: (1) We formalize the definition of diagnosability for FDESs, in which the observable set and failure set of events are {\it fuzzy}, that is, each event has certain degree to be observable and unobservable, and, also, each event may possess different possibility of failure occurring. (2) Through the construction of observability-based diagnosers of FDESs, we investigate its some basic properties. In particular, we present a necessary and sufficient condition for diagnosability of FDESs. (3) Some examples serving to illuminate the applications of the diagnosability of FDESs are described. To conclude, some related issues are raised for further consideration.Comment: 14 pages; revisions have been mad

Multichannel Approach to Clustering Matter

An approach is developed, combining the ideas of quantum statistical mechanics and multichannel theory of scattering, for treating statistical systems whose constituents can possess different bound states realized as compact clusters. The main principles for constructing multichannel cluster Hamiltonians are formulated: principle of statistical correctness, principle of cluster coexistence, and principle of potential scaling. The importance of the principle of statistical correctness is emphasized by showing that when it does not hold the behaviour of thermodynamic functions becomes essentially distorted. And moreover, unphysical instabilities can appear. The ideas are carefully illustrated by a statistical model of hot nuclear matter.Comment: 1 file, LaTex, no figure

Temporal Dynamics in Perturbation Theory

Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our attention on the stability conditions permitting to control the convergence of approximation sequences. We show that several types of mapping multipliers and Lyapunov exponents can be introduced and, respectively, several types of conditions controlling local stability can be formulated. The ideas are illustrated by calculating the energy levels of an anharmonic oscillator.Comment: 1 file, 21 pages, RevTex, 2 table

Statistical Mechanics of Structural Fluctuations

The theory of mesoscopic fluctuations is applied to inhomogeneous solids consisting of chaotically distributed regions with different crystalline structure. This approach makes it possible to describe statistical properties of such mixture by constructing a renormalized Hamiltonian. The relative volumes occupied by each of the coexisting structures define the corresponding geometric probabilities. In the case of a frozen heterophase system these probabilities should be given a priori. And in the case of a thermal heterophase mixture the structural probabilities are to be defined self-consistently by minimizing a thermodynamical potential. This permits to find the temperature behavior of the probabilities which is especially important near the points of structural phase transitions. The presense of these structural fluctuations yields a softening of a crystal and a decrease of the effective Debye temperature. These effects can be directly seen by nuclear gamma resonance since the occurrence of structural fluctuations is accompanied by a noticeable sagging of the M\"ossbauer factor at the point of structural phase transition. The structural fluctuations also lead to the attenuation of sound and increase of isothermic compressibility.Comment: 1 file, 18 pages, RevTex, no figure

Comparison of pressure, magnetic field and excess manganese effects on transport properties of film and bulk ceramic La–Ca manganites

The pressure, magnetic field and excess manganese effects on transport and magnetoresistance effect (MRE) have been studied in both the epitaxial films and bulk ceramics of manganites (La₀.₇Ca₀.₃)₁₋xMn₁₊xO₃₋y (x = 0–0.2). A comparison of electrical behavior in both kinds of samples of similar composition at hydrostatic pressures of up to 1.8 GPa and in a magnetic fields of up to 8 kOe has been performed. The pressure and magnetic field effects are shown to increase with increasing manganese content. Experimental data show that the pressure and magnetic field effects on temperatures of both metal–insulator transition (TMD) and MRE peak (TMR) are considerably stronger in the films than in ceramics. The hydrostatic pressure increases TMD and TMR. Magnetoresistance effect for both types of samples was shown to be favored by the pressure and magnetic field in an opposite way. A direct correlation is established between TMD and conductivity bandwidth as well as between MRE and concentration of charge carriers at applied pressure. The differences in the values of pressure effect on resistance, MRE and TMD temperature in the films and ceramics are connected with both granular structure of ceramics and the oxygen nonstoichiometry in ceramic and film samples of the same content as well as with the film strain induced by lattice mismatch between the film and the substrate. The origin of pressure–magnetic field effects is analyzed in the framework of double exchange interaction and small polaron hopping, and variable range hopping models

On the thermal vacancy effects on thermodynamic properties and stability of Van der Waals crystals

Reverting to an investigation of thermal vacancies in simple Van der Waals crystals [phys. stat. sol. (b) 101, 95 (1980)] we take into account the possibility of forming their bonded complexes, in particular divacancies. We use the correlative method of the unsymmetrized self-consistent field (CUSF) that enables one to include the strong anharmonicity of the lattice vibrations. We have calculated the parameters of the vacancy formation, the vacancy and divacancy concentration in solid Ar and contribution of the defects to its equilibrium thermodynamic properties, depending on the temperature and pressure, such contributions to components of the elastic tensor are studied for the first time. We also investigate the influence of defects on the thermodynamic stability of crystal lattice. © 2006 WILEY-VCH Verlag GmbH & Co. KGaA

Thermal vacancy effects on the thermodynamic properties and stability of fullerites

We study the influence of thermal vacancies on equilibrium thermodynamic properties of the high-temperature phase of fullerites taking into account the strong anharmonicity of the lattice vibrations. Treating a crystal with point defects as a quasi-multicomponent system and using the correlative method of the unsymmetrized self-consistent field and the Girifalco interaction potential for the molecular subsystem, we have obtained the vacancy formation parameters for the C60 fullerite. We also take into account the divacancies. The influence of the lattice defects on the specific heats of fullerites is negligible, since a dominant contribution to them is given by intramolecular degrees of freedom. We have calculated the contributions of vacancies to various thermodynamic properties, the volume thermal expansion coefficient, the isothermal bulk modulus, and the components of the isothermal elastic tensor, depending on the temperature and pressure. Near the estimated triple point, these contributions run to more than 10% and increase still further at a metastable region. We also discuss the influence of defects on the thermodynamic stability of fullerites. © 2005 American Chemical Society