In the present work the classical problem about a particle in a central field is quantized using Chirkov's method. According to this method, in contrast to classical one, quantization is carried out directly in spatial spherical coordinates. The generalization of Schrodinger equation for a case of spatial spherical coordinates is obtained. The expansion formulas of arbitrary functions via the eigenfunctions of this equation are obtained on the basis of Titchmarsh's method. It is proved that the Parseval equality is fulfilled directly in curvilinear coordinates.

Oscillatory motion and propagation of the quantum packet for an electron in a box and through the background positive charge are investigated. The initial velocity of the Gaussian packet is a finite value. The discussion of such simple systems is needed to understand the more complicated nonlinear processes of electron motion in the medium including the effects of self-organization.

Full-potential linearized augmented plane wae (FLAPW) method is used to investigate absorption of K, Na, and Cs on GaAs (110) and (001) -- oriented surfaces. The layer-resolved densities of states, electron energy spectrum and valence charge-densities are analyzed. Coverage dependence of the work function is obtained and is found to be in satisfactory agreement with experiments. The role of oxygen adsorption in GaAs activation to negative electron affinity state is discussed.

A one-dimensional phase-field method was developed that allowed us to observe the evolution of electric potential, charge density, concentration of holes and electrons, as well as distribution of temperature and temperature-related effects across the p-n junction of a model semiconductor diode.

In this paper the influence of work parameter of magnetic force microscopy (MFM) on the magnetic contrast of the stray field measured in soft magnetic amorphous Fe-based ribbons using two-pass technique has been analyzed. It was proved that an increase in ΔZ separation of sample-tip during the second scan affects considerably the quality, contrast of obtained micrograph of the stray field image. Increase in &ΔZ causes smaller interaction between the cantilever's tip and tested field. It is caused by smaller influence of the source field emitted from the sample on the magnetic tip. Detirioration and contrast's broadening of obtained pictures allows to analyze and detect the areas which have positive as well as negative magnetization.

Short overview of various microelectromechanical (MEMS) varactor types potentially suitable for mobile communications of the new generation is given. Special attention is given to MEMS varactors with electrostatic drive which are mostly widespread. Important varactor characteristics are compared for different varactor types.

Microelectromechanical capacitive radiofrequency switches are considered. Design and technological process are reported. Switching characteristics and thermal behavior are investigated. Ways to improve the measured parameters are shown. The switches are prospective for wireless telecommunication systems, in particular for mobile communications.

In this work we have investigated radiation hardness of the big (with length 26.5 cm) crystals of the BaF₂. These crystals were proposed for Two/Three Arm Spectrometer (TAPS). The crystals produced by two different manufactories in Germany and China have been compared. The nature of radiation defects is discussed.

In this contribution we present the renewed results of calculations on electron photodetachment from inner shell of Li^- negative ion and results of preliminary calculations of 1s C^- photodetachment.

Elastic scattering of electrons by negative ion Li^- is studied within the single-electron model and Hartree-Fock approximations and many-body approach. The diffraction peculiarities appeared in the behavior of scattering phases and differential cross section are discussed.

Results of many electron calculations of 3p-subshell photoionization cross section for neutral potassium and calcium are presented. Resonance structure associated with excitation of autoionizing 3s3p⁶4s^1,2np states has been studied. The dynamic polarization and screening contribution to resonance parameters has been taken into account. A crucial role of double-electron excitations has been shown.

In this contribution, we report on a study of the growth of fullerens and nanotubes from small clusters. A key factor in molecular dynamics modeling is the choice of interatomic potential. Ab initio molecular dynamics requires extensive computer resources, so that is outside the scope of most complex systems. We have developed simpler molecular dynamics model of charges at bonds that takes into account the electronic and atomic degrees of freedom and which can be implemented using a personal computer. Our approach has the possibility of studying the excited states formed by electronic transitions. The fundamental difference is that previously one only considered the static atomic subsystem whereas now we investigate both subsystems, atomic and electronic, simultaneously. We have found that the cluster growth is accompanied by the resonance of the electronic and atomic degrees of freedom.

Molecular motors are of nm scale they are the smallest motors known. They are quasi-omnipresent in the biological organism and among their most promiment functions are muscle contraction, flagellar motion, intracellular transport and cellular motion. In most cases the "fuel" for these motors is provided by the cleavage of a molecule named adenosinetri-phosphate (ATP) to its diphosphate (ADP). How this chemically stored energy is transformed into motion, although a subject of major research all over the world, is only partly understood. Motor function is a dynamical problem, and no technique today is capable of monitoring dynamics at nm scale. The energies involved are close to thermal, making a good signal to noise ratio difficult to achieve. Last not not least, a great deal of knowledge is needed to understand the multiple facets of this problem, ranging from biochemistry, nm technology to theoretical physics.

Erosion and evolution of Ni and Cu(111) surface topography under impact of small N-atomic clusters (N=1÷55) with energies of 500 eV/atom is studied at atomic scale using a many-body potential. To provide final thermodynamics equilibrium state at non-zero (room) temperature, the Molecular Dynamics (MD) simulation was combined with statistical data sampling techniques in the frame of Metropolis Monte-Carlo (MMC) method. It was demonstrated that pronounced micro-crater surrounded by rim of ad-atoms is formed in the impact region above a threshold cluster size of around N=9. The impact of smaller clusters leads to formation of shallow craters or vacancies and ad-atom islands on a surface.

Sputtering of Ni and Cu fcc metals under impact of small N-atomic clusters (N=1÷55) with energies of 500 eV/atom is studied by means of classical molecular dynamics (MD) method. The mechanisms responsible on observed non-linear effects in sputtering (like non-additive enhancement of sputtering yield, late emission, etc.) are analyzed at atomic scale. The role of electronic subsystem of the metals is also discussed in respect to observed spike effects that take place both at collisional and post-collisional cascade stages. It is demonstrated that electron-phonon coupling may significantly influence on post-cascade heat spike development reducing non-additive enhancement of sputtering yields of metals in course of cluster bombardment.

EAM interatomic potential to be used for radiation effect simulations in the Fe-Cr system has been recently proposed. In the present work, this potential is used to calculate by means of classical molecular dynamics (MD) the diffusivity of solute Cr atoms in Fe-12%Cr random alloy. Fe self-diffusivity is calculated as well, both in the alloy and in the pure metal, for comparison. In addition, the melting point for both the pure metal and the alloy, as predicted by the potential, has been determined and a comparison between the efficiency of vacancy and interstitial mechanisms for diffusion has been performed. This study allows the validity of the potential to be checked against experimental data outside its fitting range, while providing some insight into the description that this potential gives of irradiation effects. A correct prediction of the diffusivity of solute atoms at high temperature and the melting point are indeed an important pre-requisite for a correct prediction of ion mixing and point defect clustering within a displacement cascade during the thermal spike phase. The conclusion of the study is that the present potential is capable of reproducing with excellent accuracy both the diffusion coefficient and the melting point in Fe and in the Fe-Cr alloy. Atomic diffusion through interstitials is also seen to be a more efficient mechanism than through vacancies in the materials considered.

In this paper, the transferability of a pseudopotential proposed by Fiolhais et al. is assessed. This model, developed for simple metals in the solid state, is used to predict the behavior of these elements in the liquid state by means of molecular dynamic simulations. Comparisons between simulation predictions and experimental results for static structural properties, as well as available self-diffusion coefficients demonstrate its adequacy for the description of the interatomic interactions of all the alkali and alkaline-earth metals, as well as of the polyvalent metals Al, Tl, and Pb, and alloys of alkali metals.

The binding energies of vacancies to copper-vacany clusters in ferritic alloys containing Cu are of great importance as parameters for Object Kinetic Monte Carlo (OKMC) or Rate Equation (RE) models for the prediction of Cu precipitation under irradiation. Copper-vacancy complexes created after irradiation influence the mechanic properties of irradiated steels since they are obstacles to dislocation motion and lead to hardening and embrittlement of the material. The main purpose of this work is to find an efficient computational procedure to perform the calculation of copper-vacancy complex formation energies and corresponding vacancy binding energies in bcc Fe-Cu alloys, in order to calculate a whole matrix of values, from small to large complex sizes.

In this contribution, we report on a study of the mechanical properties of carbon nanotubes. We have developed a rather simple molecular dynamics model of charges at bonds which takes into account the electronic and atomic degrees of freedom, and which can be implemented using a personal computer. Our approach has the possibility of studying the excited states formed by electronic transitions and to investigate both subsystems, atomic and electronic, simultaneously. We observed structure changes of carbon nanotubes during deformation as well as stress-strain diagrams at low and high temperatures.

The continuing miniaturization of microelectronic devices is reaching of their physical limits. Discovery of carbon fullerenes and nanotubes opened a challenging new field in nano-scale devices and materials. Algorithms for the construction of nano-objects, as the initial configurations for the following molecular dynamics simulation, are proposed. Own graphic interface for the spatial visualization of simulated nano-objects is described and some illustrations are presented.

In this contribution we report on a study of structure changes of cyclic molecules, naphthalene in three states: normal, fully and partly ionized, in the temperature range from 100° to 1200° C for a normal and from 100 K to 1000 K for the ionized forms. We have used a new molecular dynamics with charges at bonds and have studied time dependence of interatomic distances at these temperatures. It was found that the interatomic distances can serve as a criterion for conformation transitions between different conformations. Explanation is based on the theory of stability and the theory of parametric resonance.

In this contribution we report on a study of structure changes of polycyclic molecules C₁₃H₉ and C₁₄H₁₀ in the temperature range from 100 to 1400 K. We have used a new molecular dynamics with charges at bonds and have studied time dependence of interatomic distances at these temperatures. It was found that the interatomic distances can serve as a criterion for conformation transitions between different conformations. Explanation is based on the theory of stability and the theory of parametric resonance.

In this contribution, we report on a study of the self-organization of Cro protein. The process is computer simulated by the method of molecular dynamics. We investigated folding of the Cro regulatory protein of bacteriophage λ. Spontaneous transition of α-spiral structure into a globule was observed. In some cases the self-organization was similar to that obtained earlier for simple organic polymers and proteins. We have developed a graphical way of analysis of three-dimensional protein structures that transforms three-dimensional structures into quasi two-dimensional ones. With the help of this method we have found that the folding consists of three stages which incorporate formation of transverse waves in an elongated helix rectilinear structure taken as an initial conformation, compression and collapse of these waves, and reptile motion of helices in regions with bad local order or search of a native conformation.

We describe a computer simulation method of the holographic repeated recording process that is feasible for the fan-out element synthesis. Such fan-out elements or beam splitters represent complex spatial periodical structures possessing a wide diffraction spectrum. In the study the methods of extending the diffraction spectrum, the enhancement of the uniformity of the energy distribution in diffraction orders, increasing the diffraction efficiency of synthesized structures are discussed. The experimental results on the fan-out element synthesis are also presented.

A novel analytical approach is proposed for an accurate estimation of a broad range of Gaussian laser beam diameters. The new approach is used to study the performance of most recently proposed periodic and aperiodic rulings. Further, for spot-size measurement applications, which range from very small to very large beam diameters, a new single aperiodic exponential ruling is proposed.

The light beam propagation in the system "transparent sphere -- mirrored surface" is described in a ray approximation. The indicatrixes of back scattering are determined using the method of the numerical simulation. The coefficients of retroreflection in candelas per lux per square meter are calculated. Usage of the diffuse scatterer is offered as the standard sample.

In this contribution it is reported on aggregate nano- and micro-particles optical properties such as refractive index, light extinction and light scattering intensity. The experimental model of aggregate glass spheres was used. The results of study can be applied for characterization of aggregation-disaggregation processes for three-dimensional disperse systems with nanoparticles of different nature: latexes, viruses, biological cells, etc.

Portable apparatus presented in this paper is an x-ray equipment permitting to carry out traditional stress determination by x-ray diffraction method both in-laboratory and in-field conditions. The portability of apparatus is achieved by construction of compact and light high voltage source coupled with special x-ray tube and using of coordinate sensitive detector. Other distinctive characteristic of apparatus is an absence of a goniometer. Special collimator and simple meter of incidence angle permit to substitute the goniometer and to carry out the stress measurements of different industrial equipments such as pipelines, tanks. Software program executes a control of measurement procedure and carries out data processing experimental results.

Difficulties of determination of surface stress gradients using X-ray diffraction technique are connected with interpretation of non-linearity of θ_φ,ψ versus sin²ψ experimental curves. The problem is that the scattering of experimental data conceals a non-linear character of sin²ψ dependency and does not allow to determine correctly the parameters of stress gradient. The solution of this problem can be resolved experimentally by stress analysis of a sample with known parameters of stress gradients or by computer simulation of a diffraction profile created by surface layers with stress gradient. The first is not successful because of the difficulty to make the samples with the known parameters of stress gradient. The second is more productive because it allows to simulate an experimental θ_φ,ψ versus sin²ψ dependency and to obtain the relationships between stress gradient parameters and non-linearity of sin²ψ plots. Computer simulation of diffraction data presented in this paper permits also to analyze directly the broadening of diffraction line caused by stress gradient.

Shape memory alloys (SMA's) have become one of the major elements of intelligent structures and mechanisms (e.g. sensors, actuators, and active biomaterials) due to their unique thermo-mechanical properties. The main features of SMA's are related to a reversible martensitic transformation that can be induced either thermally or by applying stress. In this study, crystalline structure and changes in phase composition of TiNiCu samples were investigated mainly using an X-ray diffraction (XRD) method. Amorphous ribbons with the composition of Ti₅₀Ni₂₅Cu₂₅ were characterized under various temperatures during annealing. Changes in crystalline structure have been shown to be dependent on the executed processes. XRD measurement results revealed that heat treatment annealing yields totally the crystalline structure of amorphous structure and martensite is the major phase.

The results of X-ray diffraction analysis of three Zr-based alloys are presented in this contribution. The tubular samples of ZrlNb, Zry4 W and ZIRLO alloys were simultaneously oxidized for various exposures in both pressurized VVER 1000 imitating water and water with 70 ppm Li as LiOH at 360°C. The effect of Li-environment was observed for all the characteristics obtained by means of XRD, i.e. residual stresses σ, krystallite size D and microstrains ε of oxide layers. The change of all the characteristics correspond to changes of corrosion kinetics in Li-environment for two types of the alloys: Zry4 W and ZIRLO. The behavior of ZrlNb alloy was found to be different. No effect of Li-environment was observed on stresses σ in metal underlying of alloys investigated.

One of characteristic feature of stress determination by X-ray diffraction technique is the possibility to analyze stress state in individual phases of a multiphase material. Duplex steel widely used in chemistry and oil refinery equipments is an example of this kind multiphase material consisting of approximately equal quantities of ferrite and austenite. These phases have different mechanical properties that cause a different stress distribution under loading. In the present paper mechanical behavior of a duplex steel and their ferrite and austenite phases have been studied by X-ray diffraction technique. Stress distribution has been analyzed both in elastic and plastic region.

One can exploit different approaches to describe gas, liquid or solid state. It is possible to consider medium as population of separate molecules, the motion of each molecule being investigated by Newton's or quantum laws. More rough description can be applied through the distribution function of the molecules, but the simplest way is to write the conservation laws in continuous mechanics. In classical mechanics these are the laws for mass, linear momentum, energy, but the law of angular momentum is also fundamental. For particles without structure this law is not formulated. For particles with structure this law is formulated as a local law. The conservation laws are found experimentally and expressed in an integral form. It is possible to pass from the integral form to differential form for smooth functions. This assumes the possibility to pinch a volume to a point. Often the conservation laws are received as balance relations for an elementary volume put in infinity space. Every law deals with its own elementary volume. However, the angular momentum conservation law assumes the exsitence of a coordinate system and radius vector from the origin to an elementary volume. So the symmetry of the angular momentum law is postulated in spite of the fact that in general case the movement of mass points is noninertial. Large gradients lead to large remainder terms when we turn from an integral form to a differential one. One of the aims of our analysis is to define relation between the conservation laws in continuum mechanics and the variation of the angular momentum in an elementary volume. Passage from the description of motion of a system of mass points to the motion of the elementary volume as a whole is insufficiently studied in mechanics. This question is advanced mostly for a rarefied gas by Bogolubove N.N., his pupils and co-workers who use N-partial distribution function to describe motion of a system of N mass points. It was done to receive an equation for one-partial distribution function in kinetics. It is essentially that Hamiltonian formalism must be exploited for deduction the equation for N-partial distribution function. The latter supposition provides transition from the Liouville equation to the kinetic equation for the mass points at known additional conditions. However the Hamiltonian formalism can be used in the case of mechanics without dissipation. For large gradients and perturbing surfaces the formalism is absent.

In this contribution we report on a study of the transient subsided volume for granular half-space and layer. The subsidence trough arises from axial symmetric normal dynamic surface loading. Two models of medium are investigated: standard linear Kandaurov solid and viscogranular solid. We have derived an analytical expression of subsided volume for three types of loading: (1) suddenly applied constant load, (2) instantaneous impulsive load, (3) harmonic oscillating load. The results are compared with corresponding solutions for elastic and viscoelastic media.

A model describing the motion of a layer of granular medium on a rigid foundation is under cosideration. The motion is caused by a normal load which is applied to the plane covering the layer. The process of stresses propagation is represented by Kandaurov model. The model of standard linear solid is used to take in account the internal friction. The last includes Maxwell and Voigt models of anelasticity.

The motion of a half of a space filled with granular medium is under consideration. The motion is caused by a normal band load applied to the plane covering the half of the space. The process of stresses propagation is represented by Kandaurov model. The model of standard linear solid is used to take in account the internal friction. The last includes Maxwell and Voigt models of anelasticity.

Approximated value for the vertical displacement of a surface bounding a half space and a layer laying on rigid foundation filled with granular medium caused by a vertical symmetric load is received here. The results obtained for Kandaurov standard linear medium model are used. This model takes in account an internal friction. The Papoulis method of numerical inversion of the Laplace transform is applied.

Wrinkling of workpiece is one of the major problems occurring at application of impulse drawing of thin sheet metal. The loss of shell stability appears in the areas with compressive stresses and is basis of buckling phenomenon. The nonlinear explicit finite element code LS-DYNA was used for prediction wrinkling. Pulse pressure and strain hardening of a material were given from experiment. The modeling of shell such as Belytschko-Wong has given the good consent of results of finite element simulation of sheet metal forming process with experimental data at electrohydraulic thin brass drawing.

The results of experimental analysis of elasto-plastic deforming of steel tubular specimens are presented. The proportional and complex cyclical loading, including partial and full unloading, were considered. The comparison is performed for the test data and the predictions obtained with using of some variations of plastic theory.

Method of computer aided technique was used for estimation of interaction forces of tessellated charged planes. It is shown that interfering to crack restitution is caused by geometrical factors, detrusion and rotational displacement.

Plasticity and microhardness of annealed metallic glass (MG) on the basis of cobalt were investigated. Pursuant to specificity of geometry of ribbon samples and amorphous state, measurement regime of true microhardness of MG is detected. It was found abnormal behavior of microhardness at the stage of transition from amorphous to crystalline state at practically zero plasticity. It was established that crystallization of MG consists of two stages.

Evolution of surface structure of metallic glass subjected to etching was investigated. The changes of surface structure of metallic glass 82K3XCP after chemical etching and different modes of annealing were studied. Samples of metallic glass were etched in solutions of sulphurous acid with different concentration. Corrosion-resistance was determined. The dependence of corrosion rate on acid concentration was found. Characteristic concentric circumferences on the etching surface were investigated. Their formation mechanism is discussed. Crystallization on surface stimulated by both acid and annealing was examined. The formation of first dendrites on surface of annealed metallic glass and their evolution were investigated.

This paper is dedicated to the simulation of waves in the near-shore zone (the zone where wave height is comparable with the depth). The method described allows simulating waves transformation and destruction phenomena. At the same time, it satisfies computer performance restrictions in real time applications. The method solves 2D problem and is based on boundary element method. To simplify calculations and increase performance, we use piecewise constant elements which does not have essential influence upon precision, as we modify the method properly. Results of this method -- 2D profiles -- can be easily used for imitation of 3D problem solution by interpolation between 2D profiles for different bathymetric charts. The paper contains the model description, drawings of wave profiles and 3D waves screenshots.

We present an information-theoretic approach to the image interpretation problems. In the context of this approach such tasks as contour extracting, constructing the most informative image features and image matching are described as a single unified problem. Our approach is based primarily on the interpretation of the image (or image set) representation problem as a Minimum Description Length (MDL) problem. The image matching turns out to be a generally adopted method of images alignment by maximization of their mutual information. However, instead of using the pixels intensities themselves a more condensed data representation form can be used to reduce the dimensionality of input data and to extract the invariant information: hierarchical image structural description. Though we developed and successfully applied the information-theoretic approach for the images matching, it can be extended to the other problems, e.g. the changes detection.

Pixelation problem of textures in Virtual Reality can be resolved by using theory of J.A. Wheeler, affirming that our consciousness densely interacts with the objective world even in a very large scale. Despite of uncertainty with correctness of this hypothesis to the real world, this idea looks very attractive for computer based virtual worlds modeling as a method of local environment detailing just "when we are looking."

In this contribution we report on a set of methods to obtain and classify new algebraic surfaces of three variables of third and fourth degree. These methods are used to create a software library of cubic and quartic surfaces that can be further expanded with surfaces of higher degrees. There is a short observation of what is available in literature regarding these surfaces, and there are three methods to generate new surfaces. These surfaces are to be studied, classified and they can be used in CAD and other systems for modeling real-life objects, artificial constructions and futuristic elements.

In this contribution we report on a problem of defense construction against an attack, with "Substitution of one of the TCP-connection subjects in the Internet (hijacking)," carried out for the first time by Kevin Mitnik (December 12, 1994) and which remains its potential danger till now. In this work the mathematical models of the remote attacks represented in earlier publications are expanded and specified.

The methods used for modification of separate speech signals fragments in the process of speech synthesis by arbitrary text are described in this report. Three groups of sounds differ in the modification methods of frequency characteristics. Two groups of sounds differ in that they need different methods of duration changes. To modify the samples of a speaker's voice by the methods used it is necessary to make pre-marking, so called segementation. As variable speech fragments, the allophones are taken. The modification methods described allow form arbitrary speech successions in the wide intonation diapason on the basis of limited amount of the speaker's voice patterns.