Loop Variables for a Class of Conical Spacetimes

Loop variables are used to describe the presence of topological defects in spacetime. In particular we study the dependence of the holonomy transformation on angular momentum and torsion for a multi-chiral cone. We also compute the holonomies for multiple moving crossed cosmic strings and two plane topological defects-crossed by a cosmic string.Comment: 17 pages, LATE

On the BV structure on the cohomology of moduli space

The question of vanishing of the BV operator on the cohomology of the moduli space of Riemann surfaces is investigated. The BV structure, which comprises a BV operator and an antibracket, is identified, vanishing theorems are proven, and a counterexample is provided

Dirac equation in the magnetic-solenoid field

We consider the Dirac equation in the magnetic-solenoid field (the field of a solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using von Neumann's theory of deficiency indices. We find self-adjoint extensions of the Dirac Hamiltonian in both above dimensions and boundary conditions at the AB solenoid. Besides, for the first time, solutions of the Dirac equation in the magnetic-solenoid field with a finite radius solenoid were found. We study the structure of these solutions and their dependence on the behavior of the magnetic field inside the solenoid. Then we exploit the latter solutions to specify boundary conditions for the magnetic-solenoid field with Aharonov-Bohm solenoid.Comment: 23 pages, 2 figures, LaTex fil

The influence of vibroacoustics on Self-organizing of Sige nanostructures onto silicon substrate

Microprocessor electronics is based on silicon technology. The growth of microprocessor circuit’s speed, the increase of elements integration, the development of Si light-emitting semiconductor devices demands the introduction of new functional principles and technologies in silicon electronics. Recently optical lithography cannot provide the necessary level of miniaturization. Electron-beam and scanning lithography are also unproductive. The object of researches was Ge/Si (001) heterosystems with nanoislands obtained using different technological conditions. In Ge/Si heterosystems the kinetics of formation of nanoislands is still not completely clear, beginning from the definition of critical thickness of nanolayer, vibroacustics, temperatures. Raman spectroscopy (RS), high resolution X-ray diffractometry and scanning atomic force microscopy (AFM) for research of physical mechanisms of nanoislands formation, character of deformation fields and processes of diffusion of silicon from substrate in wetting layer and nanoislands were applied. Such combination of analysis methods has allowed to obtain structure’s parameters as elastic deformations, structure, density of nanoislands, their sizes and form variation generated at different physical conditions (temperature, acoustic vibration). The photon (optical and acoustic) spectrums of self-organized nanostructures, generated during molecular-beam epitaxy (MBE) growth of Ge on Si substrate have been investigated using method of RS. The componental structure and values of elastic deformations in nanoislands obtained by the variation of epitaxial temperature at identical thickness of deposited Ge layer and by variation of Ge layer thickness at identical temperature has been estimated by atomic force microscopy metho

Simulation of chip-formation by a single grain of pyramid shape

The article focuses on the analysis of thermomechanical modeling of cutting by single abrasive micro-size grain while the process of grinding. In this research, applying the Johnson-Cook” material model, which relates the intensity of stress with strain rate, temperature and the accumulated plastic strain. Using arbitrary Lagrangian-Eulerian (ALE) approach makes it possible avoid the distortion of finite elements in the simulation of chip-formation under large deformations. The simulation allows predicting cutting force for processing workpiece of titanium alloy Ti6Al4V by single grain grinding

Path space forms and surface holonomy

We develop parallel transport on path spaces from a differential geometric approach, whose integral version connects with the category theoretic approach. In the framework of 2-connections, our approach leads to further development of higher gauge theory, where end points of the path need not be fixed.Comment: 6 pages, 2 figures. Talk delivered by S. Chatterjee at XXVIII WGMP, 28th June-4th July, 2009. Bialowieza, Polan

Piezo-and pyroelectric GAAS sensors integrated in one crystal with GAAS FET

One of important problems of recent electronics is non-cooled pyroelectric and piezoelectric sensors. They are realized usually in a hybrid integrated chip where thousands of ferroelectric ceramic elements are integrated with transistor matrix. Reported research work is devoted to the possibility of realization of one-crystal pyroelectric sensor. We revealed new effect of symmetry decrease that is used as a basis to develop one-crystal pyroelectric or piezoelectric sensor array using III-V crystals. In feasible sensor devices, the transducer, the amplifier and read-out electronics would be the various parts of one crystal chip. Voltage sensitivity of semi-insulating GaAs-type temperature sensor is the same as one of PZT pyroelectric ceramics. However, proposed device will be fully made from GaAs and related crystal layers by the standard in the micro-electronics technolog

Acoustic emission and methods of its registration (review)

Lately a tendency is observed for the steady growth of requirements applied both to construction materials as well as to the methods of estimation of their reliability and quality. Particular attention is paid to the development of new, physically reasonable criteria of structural durability of materials, based on comprehensive study of the phenomena, which form the basis of processes of deformation and fracture. Such approach is supposed to enhance our understanding of the nature of durability and mechanisms of fracture of materials on different scale levels. This is possible only when analysis of these phenomena is accomplished by means of modern physical research methods as well as applying acoustic emission techniques for diagnostics of the fractures

The Path Integral Quantization And The Construction Of The S-matrix In The Abelian And Non-Abelian Chern-Simons Theories

The cvariant path integral quantization of the theory of the scalar and spinor particles interacting through the abelian and non-Abelian Chern-Simons gauge fields is carried out and is shown to be mathematically ill defined due to the absence of the transverse components of these gauge fields. This is remedied by the introduction of the Maxwell or the Maxwell-type (in the non-Abelian case)term which makes the theory superrenormalizable and guarantees its gauge-invariant regularization and renormalization. The generating functionals are constructed and shown to be formally the same as those of QED (or QCD) in 2+1 dimensions with the substitution of the Chern-Simons propagator for the photon (gluon) propagator. By constructing the propagator in the general case, the existence of two limits; pure Chern-Simons and QED (QCD) after renormalization is demonstrated. By carrying out carefully the path integral quantization of the non-Abelian Chern-Simons theories using the De Witt-Fadeev-Popov and the Batalin-Fradkin- Vilkovisky methods it is demonstrated that there is no need to quantize the dimensionless charge of the theory. The main reason is that the action in the exponent of the path integral is BRST-invariant which acquires a zero winding number and guarantees the BRST renormalizability of the model. The S-matrix operator is constructed, and starting from this S-matrix operator novel topological unitarity identities are derived that demand the vanishing of the gauge-invariant sum of the imaginary parts of the Feynman diagrams with a given number of intermediate on-shell topological photon lines in each order of perturbation theory. These identities are illustrated by an explicit example.Comment: LaTex file, 31 pages, two figure

The analysis of defects propagation in navigating electronic devices

Defects in the form of microcracks in ??8?12 contacts of passive electronic components of navigating devices operating at different temperatures and pressure were analyzed. Research results have demonstrated the possibility of early prevention of potential accidents. Microscopic studies are systematized depending on various physical and chemical influences on devices. The mathematical model for defects definition in local points of contacts with an error of about 5 – 7.5 % has been applie