Band 9, Heft 1

The Maslov correction to the wave function is the jump of $$ \left( { - \frac{\pi } {2}} \right) $$ in the phase when the system passes through a caustic. This can be explained by studying the second variation and the geometry of paths, as conveniently seen in Feynman’s path integral framework. The results can be extended to any system using the semiclassical approximation. The 1-dimensional harmonic oscillator is used to illustrate the different derivations reviewed here.

The analytic structure of the non-relativistic unitary and non-unitary S-matrix is investigated for the cases of the unknown interactions with the unknown motion equations inside a sphere of radius a, surrounded by the centrifugal and rapidly decreasing (exponentially or by the Yukawian law or by the more rapidly decreasing) potentials. The one-channel case and special examples of many-channel cases are considered. Some kinds of symmetry conditions are imposed. The Schroedinger equation for r > a for the particle motion and the condition of the completeness of the correspondent wave functions are assumed. The connection of the obtained results with the usual (temporal) causality is examined. Finally a scientific program is presented as a clear continuation and extension of the obtained results.

Without Higgs field interaction, accurate pole mass values are obtained for the charged leptons and quarks from a Z3-symmetric linear superposition self-interference of the Dirac fields in the effective free-field Lagrangian. The charged lepton and quark pole masses evidence the discrete Z3 symmetry, the theoretical-experimental deviations δm/m are $$ \mathcal{O} $$(10−5) for all three charged leptons, and the quark pole masses are in very satisfactory overall agreement with the experimental data.

In this work, two new completely integrable extensions of the Kadomtsev-Petviashvili (eKP) equation are developed. Multiple soliton solutions and multiple singular soliton solutions are derived to demonstrate the compatibility of the extensions of the KP equation.

We construct an exact quantization formula for Schrödinger equations with potentials thatdepend affine linearly on the energy, that is, they contain a term linear in the energy plus an energy-independent term. If such an energy-dependent potential admits a discrete spectrum and its ground state solution is known, our formula predicts the complete energy spectrum in exact form.

By modifying the method of Bruß and Peres, we construct two new families of entangled two qutrit states. For all density matrices ρ in these families we have ρ ij = 0 for i + j odd. The first family depends on 27 independent real parameters and includes both PPT and NPT states. The second family consists of PPT entangled states. The number of independent real parameters of this family is ≥ 11

Evolution equations for marginal generalized microscopic phase densities are introduced. The evolution equations for average values of microscopic phase densities are derived and a solution of the initial-value problem for the hydrodynamic type hierarchy obtained is constructed.

Our earlier results obtained for moments of inertia (M) in the case of 54 rotational level bands built on the ground state of actinide nuclei are taken for further analysis. In the current paper, resulting dynamic rotational characteristics, such as a 0, a 1, s 0 and the R 4/2 parameter, are studied from the standpoint of their dependence on the valence nucleon number product N p N n and on the variable P = N p N n/(N p + N n). New features of the nuclei deformation phenomenon in the actinide area arise when their dynamic rotational characteristics, mentioned above, are plotted in such a way as shown in the current work. The method of analysis presented here makes it possible to reveal nuclei with valence nucleon numbers for which the nuclear interactions are notable and those in which they are inconspicuous. E. g. when N p N n < 200 and P < 6 the strength of nuclear interaction gradually decreases with the increase of these variables. The strength of the nuclear interaction does not change significantly for N p N n > 200 and P > 6 — the rotational characteristics stabilise. Moreover, it is possible to establish the P variable as representing the effective number of interactions of each valence nucleon with those of the other type.

We solve explicitly the differential system obtained by Peres for the construction of a conserved vector associated to any central potential. We then obtain a very direct access to the discontinuous behavior of the Fradkin-Bacry-Ruegg-Souriau perihelion vector.

A coarse grained model in the frame work of principal component analysis is presented. We used a bath of harmonic oscillators approach, based on classical mechanics, to derive the generalized Langevin equations of motion for the collective coordinates. The dynamics of the protein collective coordinates derived from molecular dynamics simulations have been studied for the Bovine Pancreatic Trypsin Inhibitor. We analyzed the stability of the method by studying structural fluctuations of the Ca atoms obtained from a 20 ns molecular dynamics simulation. Subsequently, the dynamics of the collective coordinates of protein were characterized by calculating the dynamical friction coefficient and diffusion coefficients along with time-dependent correlation functions of collective coordinates. A dual diffusion behavior was observed with a fast relaxation time of short diffusion regime 0.2–0.4 ps and slow relaxation time of long diffusion about 1–2 ps. In addition, we observed a power law decay of dynamical friction coefficient with exponent for the first five collective coordinates varying from −0.746 to −0.938 for the real part and from −0.528 to −0.665 for its magnitude. It was found that only the first ten collective coordinates are responsible for configuration transitions occurring on time scale longer than 50 ps.

Photonic analogues of the relativistic Kronig-Penney model and of relativistic surface Tamm states are proposed for light propagation in fibre Bragg gratings (FBGs) with phase defects. A periodic sequence of phase slips in the FBG realizes the relativistic Kronig-Penney model, the band structure of which being mapped into the spectral response of the FBG. For the semi-infinite FBG Tamm surface states can appear and can be visualized as narrow resonance peaks in the transmission spectrum of the grating.

Fission barriers of actinides are calculated in the framework of the macroscopic-microscopic method. The single particle energies are obtained within a new version of the Woods-Saxon two-center shell model. A nuclear shape parametrization characterized by five degrees of freedom is used. The barriers are calculated along the minimal action trajectory in the configuration space and the inertia is evaluated within the cranking formalism. The reliability of the model is tested by comparing the theoretical results with values deduced from experimental data.

The Cotton-Mouton effect in sheared plasma with helical magnetic lines is studied on the basis of the equation for complex amplitude ratio (CAR). A simple model for helical magnetic lines in sheared plasma of toroidal configuration is suggested. The equation for CAR in the sheared plasma is solved by perturbation method, using the small shear angle deviations as is characteristic for tokamak plasma. It is shown that the inaccuracy in polarization measurements caused by deviations of the sheared angle amounts to some percentage of the shearless Cotton-Mouton phase shift. One suggested method is to subtract the “sheared” term, which may improve the accuracy of the Cotton-Mouton measurements in the sheared plasma.

Experimental Stark broadening studies of the infrared CI transition 3s 1 P 1o − 3p 1 S 0 at 833.5 nm are reported for the first time. A high-current wall-stabilized arc, operated in a mixture of helium, argon, carbon dioxide and hydrogen, was applied as the plasma source. Radiation emitted from homogeneous and optically thin plasma layers was analyzed. Stark broadening studies of the selected CI transition and the hydrogen Balmer β line were performed. As expected from theoretical considerations, the CI line width depends linearly on the electron density of the plasma. Applying theoretical Stark broadening data for the Hgb line, the measured Stark widths of the CI line were calibrated for the purpose of electron density determination in low temperature plasmas.

This study is devoted to the instantaneous acoustic heating of a Bingham plastic. The model of the Bingham plastic’s viscous stress tensor includes the yield stress along with the shear viscosity, which differentiates a Bingham plastic from a viscous Newtonian fluid. A special linear combination of the conservation equations in differential form makes it possible to reduce all acoustic terms in the linear part of of the final equation governing acoustic heating, and to retain those belonging to the thermal mode. The nonlinear terms of the final equation are a result of interaction between sounds and the thermal mode. In the field of intense sound, the resulting nonlinear acoustic terms form a driving force for the heating. The final governing dynamic equation of the thermal mode is valid in a weakly nonlinear flow. It is instantaneous, and does not imply that sounds be periodic. The equations governing the dynamics of both sounds and the thermal mode depend on sign of the shear rate. An example of the propagation of a bipolar initially acoustic pulse and the evolution of the heating induced by it is illustrated and discussed.

This paper formulates a four kinetic state model for fast axonal transport. The paper further develops the Smith-Simmons model that is based on equations governing intracellular molecular-motor-assisted transport; these equations are extended by considering four rather than three kinetic states for organelles. The model considers plus-end and minus-end-oriented organelles that can be either free (suspended in the cytosol) or attached to microtubules (MTs) (in the latter case organelles are transported by molecular motors). The paper then develops a method for uncoupling differential equations of the proposed model. A perturbation solution of this problem is obtained. The effect of transition between plus-end-oriented and minus-end oriented organelles is discussed. The accuracy of the obtained perturbation solution is evaluated by comparing the zero-order and the first-order results with a high-accuracy numerical solution.

By assuming that not only counter-ions but DNA molecules as well are thermally distributed according to a Boltzmann law, we propose a modified Poisson-Boltzmann equation, at the classical level, as a starting point to compute the effects of quantum fluctuations of the electric field on the interaction among DNA-cation complexes. The latter are modeled here as infinite one-dimensional wires (δ-functions). Our goal is to single out such quantum-vacuum-driven interaction from the counterion-induced and water-related interactions. We obtain a universal, frustration-free Casimir-like (codimension 2) interaction that extensive numerical analysis show to be a good candidate to explain the formation and stability of DNA aggregates. Such Casimir energy is computed for a variety of configurations of up to 19 DNA strands in a hexagonal array. It is found to be many-body.

In this paper we investigate the three-dimensional magnetohydrodynamic (MHD) rotating flow of a viscous fluid over a rotating sphere near the equator. The Navier-Stokes equations in spherical polar coordinates are reduced to a coupled system of nonlinear partial differential equations. Self-similar solutions are obtained for the steady state system, resulting from a coupled system of nonlinear ordinary differential equations. Analytical solutions are obtained and are used to study the effects of the magnetic field and the suction/injection parameter on the flow characteristics. The analytical solutions agree well with the numerical solutions of Chamkha et al. [31]. Moreover, the obtained analytical solutions for the steady state are used to obtain the unsteady state results. Furthermore, for various values of the temporal variable, we obtain analytical solutions for the flow field and present through figures.

In this paper, the steady two-dimensional stagnation-point flow of a viscoelastic Walters’ B’ fluid over a stretching surface is examined. It is assumed that the fluid impinges on the wall obliquely. Using similarity variables, the governing partial differential equations are transformed into a set of two non-dimensional ordinary differential equations. These equations are then solved numerically using the shooting method with a finite-difference technique.

We propose a scheme to achieve beam defecting and splitting using a method of embedded coordinate transformation [1]. In this method one boundary of transformation region is not involved in the transformation, which means beam defecting and splitting can be realized by changing the geometric construction. Although there is a discontinuous boundary, the impendence is matched between transformation media and surrounding media according to the conventional transformation optics. Full-wave numerical simulations further verify the theoretical analysis.

The cosmological constant problem is examined within the context of the covariant brane-world gravity, based on Nash’s embedding theorem for Riemannian geometries. We show that the vacuum structure of the brane-world is more complex than General Relativity’s because it involves extrinsic elements, in specific, the extrinsic curvature. In other words, the shape (or local curvature) of an object becomes a relative concept, instead of the “absolute shape” of General Relativity. We point out that the immediate consequence is that the cosmological constant and the energy density of the vacuum quantum fluctuations have different physical meanings: while the vacuum energy density remains confined to the four-dimensional brane-world, the cosmological constant is a property of the bulk’s gravitational field that leads to the conclusion that these quantities cannot be compared, as it is usually done in General Relativity. Instead, the vacuum energy density contributes to the extrinsic curvature, which in turn generates Nash’s perturbation of the gravitational field. On the other hand, the cosmological constant problem ceases to be in the brane-world geometry, reappearing only in the limit where the extrinsic curvature vanishes.

The dynamical properties of an overdamped Brownian particle moving in an asymmetric bistable system with quantum fluctuations are investigated. Within the strong-friction limit (the quantum Smoluchowski regime), the analytic expression for the relaxation time of the system is derived by means of the projection-operator method, in which the effects of the memory kernels are taken into account. Based on the relaxation time, we consider both the overdamped quantum case and its classical counterpart.In these contexts, the effects of the quantum fluctuations and the asymmetry of the potential are discussed. It is found that: (i) The quantum effects in an asymmetric bistable system on time scales of the relaxation process are more prominent for lower temperatures and smaller asymmetries of the potential. (ii) The quantum effects speed up the rate of fluctuation decay of the state-space variable for lower temperatures. (iii) The asymmetry of the potential first slows down the rate of fluctuation decay of the state-space variable and then increases it.

We report plane-wave pseudo-potential ab initio calculations using density functional theory in order to investigate the structural parameters, elastic constants, bonding properties and polycrystalline parameters of copper nitrides in zincblende, rocksalt and fluorite structures. Total and partial densities of states indicate a metallic character of these copper nitrides. We estimate bond strengths and types of atomic bonds using Mulliken charge density population analysis and by calculating the electronic localized function. These results reveal the coexistence of covalent, ionic, and metallic bonding.

Bulk samples of the nominal composition of (Tl0.6Pb0.5)(Sr0.8Ba0.2)2Ca2Cu3O8+δ−xLaO1.5 (x = 0–0.1) were prepared by using two-step process and their microstructure, T c values, and magnetization were studied. The samples consist of the Tl-1223 dominant phase with small Tl-1212 admixture, which increases with a rise of La content. Five years ageing and following oxygen annealing at 450°C and subsequently at 750°C have only a modest effect on T c values of the studied samples. Low-level La doping (x = 0:04) leads to an increase of T c values by about 2 K in comparison with undoped samples. Oxygen annealing at 750°C results in an increase in the volume magnetization hysteresis in low applied magnetic fields and rise of critical current density at zero magnetic field and 77 K. This effect is most pronounced for the low La doped sample with x = 0.04. Changes of the induced voltage, U originating in the Meissner effect and of its harmonics in dependence on temperature were measured and used for characterization of the temperature distribution of inter-grain junctions.

A thermodynamic lattice theory has been developed for determination of the melting curves and eutectic points of binary alloys. Analytical expressions for the melting curves of binary alloys composed of constituent elements with the same structure have been derived from expressions for the ratio of root mean square fluctuation in atomic positions on the equilibrium lattice positions and the nearest neighbor distance. This melting curve provides information on Lindemann’s melting temperatures of binary alloys with respect to any proportion of constituent elements, as well as on their eutectic points. The theory has been applied to fcc and bcc structure. Numerical results for some binary alloys provide a good correspondence between the calculated and experimental phase diagrams, where the calculated results for Cu1−x Nix agree well with the measured ones, and those for the other alloys are found to be in a reasonable agreement with experiment.

A new model is presented of current transport in Metal Insulator Metal (MIM) structures by quantum mechanical tunnelling. In addition to direct tunnelling through an insulating layer, tunnelling via defects present in the insulating layer plays an important role. Examples of the influence of the material and thickness of the insulating layer, energy distribution of traps, and metal work functions are also provided.

A set of MOS structures with thin SiO2 layers prepared by nitric acid oxidation (NAOS) method was investigated using acoustic deep level transient spectroscopy (A-DLTS) to explain the role of annealing treatment (post-oxidation annealing (POA) and post-metallization annealing (PMA)) at different conditions on the distribution of interface states. The activation energies of interface states and the corresponding capture cross-section were calculated both from Arrhenius plots constructed for individual peaks of the A-DLTS spectra and applying the method of modeling of measured acoustic spectra. The energy distribution of the interface states was determined also from the dependence of acoustoelectric response signal (ARS) on the external bias voltage (U ac - V G curves). By comparing the A-DLTS spectra, U ac - V G characteristics and some electrical measurements (G-V, I-V curves) of investigated MOS structures with no treatment with those treated with POA and/or PMA, the role of individual treatments was observed. The definite decrease of the interface states in the structures with the PMA treatment in comparison with the POA treatment was confirmed too.

The purpose of this paper is to extend the fractional actionlike variational approach by introducing a generalized fractional derivative operator. The generalized fractional formalism introduced through this work includes some interesting features concerning the fractional Euler-Lagrange and Hamilton equations. Additional attractive features are explored in some details.

Using solid C2H6 and C2F6 as an example, the one-axis molecular rotation effect on thermal conductivity has been considered in orientationally-ordered (OO) and orientationally-disordered (OD) phases of simple molecular crystals. The influence of molecular rotation on the heat transfer processes has been studied by a modified method of reduced coordinates, which permitted separating phonon-phonon and phonon-rotation contributions to the total thermal resistance.

The magnetic investigations of potassium holmium double tungstate KHo(WO4)2 have been performed. The results of measurements of magnetic susceptibility and magnetization as a function of both temperature (T = 0.5–100 K) and magnetic field (up to 2 T) are presented.