Open Access Published by De Gruyter Open Access

Volume 11 Issue 3

March 2013

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Open Access March 28, 2013

Interpretations of cosmological spectral shifts

Dag Østvang

Page range: 269-278

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Abstract

It is shown that for Robertson-Walker models with flat or closed space sections, all of the cosmological spectral shift can be attributed to the non-flat connection (and thus indirectly to space-time curvature). For Robertson-Walker models with hyperbolic space sections, it is shown that cosmological spectral shifts uniquely split up into “kinematic” and “gravitational” parts provided that distances are small. For large distances no such unique split-up exists in general. A number of common, but incorrect assertions found in the literature regarding interpretations of cosmological spectral shifts, is pointed out.

Open Access March 28, 2013

Exact and approximate solutions to Schrödinger’s equation with decatic potentials

David Brandon, Nasser Saad

Page range: 279-290

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Abstract

The one-dimensional Schrödinger’s equation is analysed with regard to the existence of exact solutions for decatic polynomial potentials. Under certain conditions on the potential’s parameters, we show that the decatic polynomial potential V (x) = ax 10 + bx 8 + cx 6 + dx 4 + ex 2, a > 0 is exactly solvable. By examining the polynomial solutions of certain linear differential equations with polynomial coefficients, the necessary and sufficient conditions for corresponding energy-dependent polynomial solutions are given in detail. It is also shown that these polynomials satisfy a four-term recurrence relation, whose real roots are the exact energy eigenvalues. Further, it is shown that these polynomials generate the eigenfunction solutions of the corresponding Schrödinger equation. Further analysis for arbitrary values of the potential parameters using the asymptotic iteration method is also presented.

Open Access March 28, 2013

Multiple soliton solutions for the integrable couplings of the KdV and the KP equations

Abdul-Majid Wazwaz

Page range: 291-295

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Abstract

In this work, we study the nonlinear integrable couplings of the KdV and the Kadomtsev-Petviashvili (KP) equations. The simplified Hirota’s method will be used for this study. We show that these couplings possess multiple soliton solutions the same as the multiple soliton solutions of the KdV and the KP equations, but differ only in the coefficients of the transformation used. This difference exhibits soliton solutions for some equations and anti-soliton solutions for others.

Open Access March 28, 2013

On the geometry of the space-time and motion of the spinning bodies

Kostadin Trenčevski

Page range: 296-316

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Abstract

In this paper an alternative theory about space-time is given. First some preliminaries about 3-dimensional time and the reasons for its introduction are presented. Alongside the 3-dimensional space (S) the 3-dimensional space of spatial rotations (SR) is considered independently from the 3-dimensional space. Then it is given a model of the universe, based on the Lie groups of real and complex orthogonal 3 × 3 matrices in this 3+3+3-dimensional space. Special attention is dedicated for introduction and study of the space S × SR, which appears to be isomorphic to SO(3,ℝ) × SO(3,ℝ) or S 3 × S 3. The influence of the gravitational acceleration to the spinning bodies is considered. Some important applications of these results about spinning bodies are given, which naturally lead to violation of Newton’s third law in its classical formulation. The precession of the spinning axis is also considered.

Open Access March 28, 2013

Measurement interpretation and information measures in general probabilistic theory

Zhaoqi Wu, Chuanxi Zhu, Xiaozhi Zhang

Page range: 317-324

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Abstract

The incompatibility of dynamics postulate (unitary evolution) and the measurement postulate (wave-packet collapse) of quantum mechanics has recently been solved by Zurek from an information transfer perspective. Luo gave his derivation by relaxing the repeatability postulate. In this paper, we reconsider Luo’s derivation in the setting of general probabilistic theory (GPT). We also introduce the concept of sub- and super-fidelity in GPT and discuss their properties.

Open Access March 28, 2013

Singularity-free model of electric charge in physical vacuum: non-zero spatial extent and mass generation

Vladimir Dzhunushaliev, Konstantin Zloshchastiev

Page range: 325-335

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Abstract

We propose a model of a spinless electrical charge as a self-consistent field configuration of the electromagnetic (EM) field interacting with a physical vacuum effectively described by the logarithmic quantum Bose liquid. We show that, in contrast to the EM field propagating in a trivial vacuum, a regular solution does exist, and both its mass and spatial extent emerge naturally from dynamics. It is demonstrated that the charge and energy density distribution acquire Gaussian-like form. The solution in the logarithmic model is stable and energetically favourable, unlike that obtained in a model with a quartic (Higgs-like) potential.

Open Access March 28, 2013

Analysis of inter-quark interactions in classical chromodynamics

Jurij Darewych, Askold Duviryak

Page range: 336-344

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Abstract

The QCD gluon equation of motion is solved approximately by means of a Green function. This solution is used to reformulate the Lagrangian of QCD such that the gluon propagator appears directly in the interaction terms of the Lagrangian. The nature of the interactions is discussed. A coordinate-space form of the interactions is presented and analyzed in the static, non-relativistic case.

Open Access March 28, 2013

An approximation to the cross sections of Z l boson production at CLIC by using neural networks

Serkan Akkoyun, Seyit Kara

Page range: 345-349

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Abstract

In this work, the possible dynamics associated with leptophilic Z l boson at CLIC (Compact Linear Collider) have been investigated by using artificial neural networks (ANNs). These hypotetic massive boson Z l have been shown through the process e + e −→µ+µ−. Furthermore, the invariant mass distributions for final muons have been consistently predicted by using ANN. For these highly non-linear data, we have constructed consistent empirical physical formulas (EPFs) by appropriate feed-forward ANN. These ANNEPFs can be used to derive further physical functions which could be relevant to studying Z l.

Open Access March 28, 2013

Investigation of superexcited states in molecular deuterium

Andrey Smolin, Juan Li, Yuxiang Mo, Oleg Vasyutinskii

Page range: 350-356

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Abstract

A high-resolution VUV laser absorption spectroscopy is used to investigate the photon-induced ion-pair formation in D2 in the spectral region from 140117.4 to 140732.0 cm−1. We report determination of photoionization efficiency in ortho-para D2 in supersonic molecular beam with energy resolution of 0.1 cm−1. The assignment of the superexcited D2 Rydberg states is done based on the quantum defect theory.

Open Access March 28, 2013

A Lennard-Jones-like perspective on first order transitions in biological helices

Nikolay Oskolkov, Jakob Bohr

Page range: 357-362

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Abstract

Helical structures with Lennard-Jones self-interactions are studied for optimal conformations. For this purpose, their self-energy is analyzed for extrema with respect to the geometric parameters of the helices. It is found that Lennard-Jones helices exhibit a first order phase transition from a state with large curvature of the helical backbone to one with a small curvature. I.e. from a dense helix to an extended helix. A transition from one helical structure to another is a phenomenon known to take place in self-assembling helices formed in multicomponent solutions with cholesterol.

Open Access March 28, 2013

On spectral relaxation method approach for steady von Kármán flow of a Reiner-Rivlin fluid with Joule heating, viscous dissipation and suction/injection

Sandile Motsa, Zodwa Makukula

Page range: 363-374

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Abstract

In this study we use the spectral relaxation method (SRM) for the solution of the steady von Kármán flow of a Reiner-Rivlin fluid with Joule heating and viscous dissipation. The spectral relaxation method is a new Chebyshev spectral collocation based iteration method that is developed from the Gauss-Seidel idea of decoupling systems of equations. In this work, we investigate the applicability of the method in solving strongly nonlinear boundary value problems of von Kármán flow type. The SRM results are validated against previous results present in the literature and with those obtained using the bvp4c, a MATLAB inbuilt routine for solving boundary value problems. The study highlights the accuracy and efficiency of the proposed SRM method in solving highly nonlinear boundary layer type equations.

Open Access March 28, 2013

Dipole-exchange spin excitations in a thin ferromagnetic nanoshell

Yuri Gorobets, Volodymyr Kulish

Page range: 375-379

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Abstract

In this paper spin excitations in spherical ferromagnetic nanoshells are investigated. The magnetic dipoledipole interaction, the exchange interaction and the anisotropy effects are taken into consideration. For such spin excitations, an equation for the magnetic potential perturbation is obtained. For a nanoshell that is thin compared to its size, the dispersion relation for nonzero spin excitation modes and the only possible frequency for zero-mode spin excitations are found. Limitations on the mode numbers are derived.

Open Access March 28, 2013

Acoustic field and the entropy mode induced by it in a waveguide filled with some non-equilibrium gases

Anna Perelomova

Page range: 380-386

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Abstract

The non-linear propagation of an acoustic beam in a rectangular waveguide is considered. The medium of sound propagation, is a gas where thermodynamically non-equilibrium processes take place: such as exothermic chemical reactions or excitation of vibrational degrees of a molecule’s freedom. The incident and reflected compounds of the acoustic field do not interact in the leading order in the case of periodic weakly nonlinear sound with zero mean value of velocity. The acoustic heating or cooling in a waveguide is discussed.

Open Access March 28, 2013

First-principles study of electronic structure and optical properties of Sr(Ti,Zr)O3

Gulden Celik, Suleyman Cabuk

Page range: 387-393

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Abstract

Electronic and optical properties of Sr(Ti,Zr)O3 crystals in the cubic (Pm-3m) and tetragonal (I4/mcm) phase were calculated by the first-principles calculations using the density functional theory and the local density approximation. The band structure of cubic and tetragonal phases show an indirect band gap at (R-Γ) point and at (M-Γ) point in the Brillouin zone, respectively. The linear photon-energy dependent dielectric functions and some optical properties such as the absorption coefficient, energy-loss function and reflectivity are calculated for both phases. The optical properties of tetragonal phase of Sr(Ti,Zr)O3 were investigated by theoretical methods for the first time. We have also made some comparisons with the available related experimental and theoretical data.

Open Access March 28, 2013

Magnetic phase transition in KGd(WO4)2 double tungstate

Mieczysław Borowiec, Tetyana Zayarnyuk, Maria Gutowska, Jarosław Więckowski, Andrzej Szewczyk, Vladimir Dyakonov, Eduard Zubov, Marek Barański, Viktor Domukhovski, Maria Pujol, Magdalena Aguiló, Francesc Díaz, Henryk Szymczak

Page range: 394-396

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Abstract

Investigations of the specific heat of the potassium gadolinium double tungstate KGd(WO4)2 have been performed over the temperature range from 0.05 K up to 4 K in zero magnetic field. The λ -type anomaly observed at T = 0.42 K was interpreted as an indication of a second order magnetic phase transition within the Gadolinium sublattice. The critical exponent α was determined from experimental data.

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