Band 9, Heft 3

A conventional wisdom often perpetuated in the literature states that: (i) a 3 + 1 decomposition of spacetime into space and time is synonymous with the canonical treatment and this decomposition is essential for any Hamiltonian formulation of General Relativity (GR); (ii) the canonical treatment unavoidably breaks the symmetry between space and time in GR and the resulting algebra of constraints is not the algebra of four-dimensional diffeomorphism; (iii) according to some authors this algebra allows one to derive only spatial diffeomorphism or, according to others, a specific field-dependent and non-covariant four-dimensional diffeomorphism; (iv) the analyses of Dirac [21] and of ADM [22] of the canonical structure of GR are equivalent. We provide some general reasons why these statements should be questioned. Points (i–iii) have been shown to be incorrect in [45] and now we thoroughly re-examine all steps of the Dirac Hamiltonian formulation of GR. By direct calculation we show that Dirac’s references to space-like surfaces are inessential and that such surfaces do not enter his calculations. In addition, we show that his assumption g 0k = 0, used to simplify his calculation of different contributions to the secondary constraints, is unwarranted; yet, remarkably his total Hamiltonian is equivalent to the one computed without the assumption g 0k = 0. The secondary constraints resulting from the conservation of the primary constraints of Dirac are in fact different from the original constraints that Dirac called secondary (also known as the “Hamiltonian” and “diffeomorphism” constraints). The Dirac constraints are instead particular combinations of the constraints which follow directly from the primary constraints. Taking this difference into account we found, using two standard methods, that the generator of the gauge transformation gives diffeomorphism invariance in four-dimensional space-time; and this shows that points (i–iii) above cannot be attributed to the Dirac Hamiltonian formulation of GR. We also demonstrate that ADM and Dirac formulations are related by a transformation of phase-space variables from the metric g μν to lapse and shift functions and the three-metric g km, which is not canonical. This proves that point (iv) is incorrect. Points (i–iii) are mere consequences of using a non-canonical change of variables and are not an intrinsic property of either the Hamilton-Dirac approach to constrained systems or Einstein’s theory itself.

The dynamical properties of a noise-driven tumor cell growth system are investigated when there exist two different kinds of time delays, in the deterministic and fluctuating forces, respectively. Using the approximation probability density approach, the delayed Fokker-Planck equation is obtained. The effects of two different time delays on the stationary probability distribution (SPD), the mean value and the mean passage time (MFPT) are discussed. It is found that the time delay τ1 in the deterministic force can enhance tumor cell number, while the time delay τ2 in the fluctuating force can induce a decrease in tumor cell numbers. On the other hand, while τ1 can hold back the extinction of tumor cells, τ2 can speed up their extinction.

The characteristics of fragment emission in peripheral 197Au+197Au collisions 35 MeV/A are studied using the two clusterization approaches within framework of quantum molecular dynamics model. Our model calculations using minimum spanning tree (MST) algorithm and advanced clusterization method namely simulated annealing clusterization algorithm (SACA) showed that fragment structure can be realized at an earlier time when spectators contribute significantly toward the fragment production even at such a low incident energy. Comparison of model predictions with experimental data reveals that SACA method can nicely reproduce the fragment charge yields and mean charge of the heaviest fragment. This reflects suitability of SACA method over conventional clusterization techniques to investigate spectator matter fragmentation in low energy domain.

The recent WMAP data have confirmed that exotic dark matter together with the vacuum energy (cosmological constant) dominate in the flat Universe. Modern particle theories provide viable cold dark matter candidates with masses in the GeV-TeV region. All such candidates will be called WIMPs (Weakly Interacting Massive Particles). The nature of dark matter can only be unraveled by its direct detection in the laboratory. In this work we present some theoretical elements relevant to the direct dark matter detection experiments, paying particular attention to directional experiments, i.e. experiments in which not only the energy but the direction of the recoiling nucleus is observed. Since the direction of observation is fixed with respect to the Earth, while the Earth is rotating around its axis, in a directional experiment the angle between the direction of observation and the Sun’s direction of motion will change during the day. So, since the event rates sensitively depend on this angle, the observed signal in such experiments will exhibit very interesting and characteristic periodic diurnal variation.

A unified description of dark ingredients is realized by a vacuum dark fluid defined by symmetry of its stress-energy tensor and allowed by General Relativity. The symmetry is reduced compared with the maximally symmetric de Sitter vacuum, which makes vacuum dark fluid essentially anisotropic and allows its density and pressure to evolve. It represents distributed vacuum dark energy by a time-evolving and spatially inhomogeneous cosmological term, and vacuum dark matter by gravitational vacuum solitons which are regular gravitationally bound structures without horizons (dark particles or dark stars), with the de Sitter centre (Λδki) in de Sitter space (λδki).

Total precession (geodetic precession and frame dragging) depends on the velocity of each source of gravitation, which means that it depends on the choice of the coordinate system. We consider the latter as an anomaly specifically in the Gravity Probe B experiment, we investigated it and solved this anomaly. Thus, we proved that if our present expression for the geodetic precession is correct, then the frame dragging should be 25% less than its predicted value.

This paper presents an analytical solution for slow axonal transport in an axon. The governing equations for slow axonal transport are based on the stop-and-go hypothesis which assumes that organelles alternate between short periods of rapid movement on microtubules (MTs), short on-track pauses, and prolonged off-track pauses, when they temporarily disengage from MTs. The model includes six kinetic states for organelles: two for off-track organelles (anterograde and retrograde), two for running organelles, and two for pausing organelles. An analytical solution is obtained for a steady-state situation. To obtain the analytical solution, the governing equations are uncoupled by using a perturbation method. The solution is validated by comparing it with a high-accuracy numerical solution. Results are presented for neurofilaments (NFs), which are characterized by small diffusivity, and for tubulin oligomers, which are characterized by large diffusivity. The difference in transport modes between these two types of organelles in a short axon is discussed. A comparison between zero-order and first-order approximations makes it possible to obtain a physical insight into the effects of organelle reversals (when organelles change the type of a molecular motor they are attached to, an anterograde versus retrograde motor).

Symmetry analysis was applied in this work to discuss the behavior of the family R6M23 compounds upon hydrogenation (deuteration), where different structural transformations and magnetic properties, depending on the type of R and M atoms and hydrogen (deuterium) concentrations, have been found. The crystallographic structure of these compounds is described by the Fm3m space group and contain 116 atoms per unit cell occupying the positions 24e(R), 4b, 24d, 32f1 and 32f2(M). Additionally in the elementary cell, there could be up to 100 atoms of hydrogen (or deuterium) occupying the interstitial positions 4a, 32f3, 96j1 and 96k1. The symmetry analysis in the frame of the theory of space groups and their representation gives the opportunity to find all possible transformations from high symmetry parent structure to the structures with symmetry belonging to one of its subgroups. For a given transformation it indicates possible displacements of atoms from initial positions in the parent structure, ordering of hydrogen over interstitial sites and also ordering of magnetic moments, described by the smallest possible number of free parameters. The analysis was carried out by means of the MODY computer program for vectors k = (0; 0; 0) and k = (0; 0; 1) describing the changes of translational symmetry and all positions occupied by the R, M and D atoms.

An extended ASYNNNI model, that beside nearest-neighbour and next-nearest neighbour O-O interactions in the basal plane also includes interactions between the three nearest oxygen atoms, is used to describe the statistics of CuO chain fragmentation and to calculate doping and T c in YBa2Cu3O6+x . Calculations were made by the Monte Carlo method employing the recently proposed charge transfer model that assumes only chains whose length is equal to, or exceeds, a characteristic (critical) length, l cr, can provide holes to the layers and contribute to doping p. The obtained p(x) is then combined with a universal T c versus p relation to yield T c(x) characteristics that correlate remarkably with those reported in recent experiments. The best coordination between theoretical and experimental T c(x) characteristics has been achieved for l cr = 2, implying that only isolated basal plane oxygen atoms (trivial chains) do not contribute holes to CuO2 layers.

We apply the phase field crystal method for nonequilibrium patterning to stochastic systems with an external source in which transient dynamics is essential. Considering a prototype model for a one-component periodic system subjected to external influence kind of irradiation we study properties of pattern selection processes and external noise induced pattern-forming transitions. These processes are examined by means of the structure function dynamics analysis. Nonequilibrium pattern-forming transitions are analyzed numerically.

Classical molecular dynamics simulations have been performed for crystalline germanium with the aim to estimate the thermal effects within the first three coordination shells and their influence on the single-scattering and multiple-scattering contributions to the Ge K-edge extended x-ray absorption fine structure (EXAFS).

We investigate the electronic and band structure for the (8; 0) single-wall carbon nanotube (SWCNT) with a europium (Eu) and a uranium (U) atom outside by using the first-principles method with the density functional theory (DFT). The calculated band structure (BS), total density of state (TDOS), and projected density of state (PDOS) can elucidate the differences between the pure (8; 0) SWCNT and the nuclei outside the SWCNT. The indirect band gaps are obtained when Eu and U atom are put outside the (8; 0) CNT; they are 0.037 eV and 0.036 eV, respectively, which is much smaller than 0.851 eV for pure CNT. Compared with pure (8; 0) SWCNT, the bottom of the conduction band moves down by 0.383 eV and 0.451 eV with the Eu and U outside, and the top of valence band moves up by 0.127 eV and 0.162 eV, respectively. More significantly, the top of the valence band has exceeded the fermi-level. So, a single nucleus changes the semiconductor character of pure nanotube to semi-metal.

In the lithium-caesium sulphate crystal in the temperature range of ferroelastic phase transition, the uniaxial stress σ X induced changes in velocity and attenuation of the longitudinal ultrasonic wave propagating in the direction [010] are studied. The phase transition is close to the three-critical point and the critical exponent is κ = 0.27 ± 0.02. The stress applied drastically decreases the stepwise change in the wave velocity at T C up to its disappearance at 2 MPa. In the temperature range between T C and T C − 6 K, the stress leads to an increase in the wave velocity and a decrease in its attenuation. This range was interpreted as that of co-existence of ferroelastic and incommensurate ordering, in which the stress influences the density of solitons leading to stiffening of the crystal lattice.

In this paper we presented a new method (Eigen-Coordinates (ECs)) that can be used for calculations of the critical points (CPs) energy of the interband-transition edges of the heterostructures. This new method is more accurate and complete in comparison with conventional ones and has a wide range of application for the calculation of the fitting parameters related to nontrivial functions that initially have nonlinear fitting parameters that are difficult to evaluate. The new method was applied to determine the CPs energies from the dielectric functions of the MBE grown GaAs1−xPx ternary alloys obtained using spectroscopic ellipsometry (SE) measurements at room temperature in the 0.5-5 eV photon energy region. The obtained results are in good agreement with the results of the other methods.

Nonlinear stimulation of the vorticity mode caused by losses in the momentum of sound in a chemically reacting gas is considered. The instantaneous dynamic equation for the vorticity mode is derived. It includes a quadratic nonlinear acoustic source, which reflects the fact that the reason for the interaction between sound and the vorticity mode is nonlinear. Both periodic and aperiodic sound may be considered as the origin of the vorticity flow. The equation governing the mean flow (the acoustic streaming) in the field of periodic sound is also derived. In the non-equilibrium regime of a chemical reaction, there may exist streaming vortices whose direction of rotation is opposite to that of the vortices in the standard thermoviscous flows. For periodic sound, this is illustrated by an example. The theory and the example describe both equilibrium and non-equilibrium chemical reactions.

A three-particle operator in a second quantized form is studied systematically and comprehensively. The operator is transformed into irreducible tensor form. Possible coupling schemes, identified by the classes of symmetric group S6, are presented. Recoupling coefficients that make it possible to transform a given scheme into another are produced by using the angular momentum theory combined with quasispin formalism. The classification of the three-particle operator which acts on n = 1, 2,..., 6 open shells of equivalent electrons of atom is considered. The procedure to construct three-particle matrix elements are examined.

Density functional theory methods were used to investigate various self-assembled photoactive bioorganic systems of interest for artificial minimal cells. The cell systems studied are based on nucleotides or their compounds and consisted of up to 123 atoms (not including the associated water or methanol solvent shells) and are up to 2.5 nm in diameter. The electron correlation interactions responsible for the weak hydrogen and Van derWaals chemical bonds increase due to the addition of a polar solvent (water or methanol). The precursor fatty acid molecules of the system also play a critical role in the quantum mechanical interaction based self-assembly of the photosynthetic center and the functioning of the photosynthetic processes of the artificial minimal cells. The distances between the separated sensitizer, fatty acid precursor, and methanol molecules are comparable to Van derWaals and hydrogen bonding radii. As a result the associated electron correlation interactions compress the overall system, resulting in an even smaller gap between the highest occupied molecular orbital (HOMO), and lowest unoccupied molecular orbital (LUMO) electron energy levels and photoexcited electron tunnelling occurs from the sensitizer (either Ru(bpy)32+ or [Ru(bpy)2(4-Bu-4’-Me-2,2’-bpy)]2++ derivatives) to the precursor fatty acid molecules (notation used: Me = methyl; Bu = butyl; bpy = bipyridine). The shift of the absorption spectrum to the red for the artificial protocell photosynthetic centers might be considered as the measure of the complexity of these systems.

The time-dependent density functional theory (TDDFT) method was performed to investigate the hydrogenbonding dynamics of methyl cyanide (MeNC) as hydrogen bond acceptor in hydrogen donating methanol (MeOH) solvent. The ground-state geometry optimizations and electronic transition energies and corresponding oscillation strengths of the low-lying electronically excited states for the isolated MeNC and MeOH monomers, the hydrogen-bonded MeNC-MeOH dimer and MeNC-2MeOH trimer are calculated by the DFT and TDDFT methods, respectively. An intermolecular hydrogen bond N≡C…H-O is formed between MeNC and methanol molecule. According to Zhao’s rule on the excited-state hydrogen bonding dynamics, we find the intermolecular hydrogen bonds N≡C…H-O are strengthened in electronically excited states of the hydrogen-bonded MeNC-MeOH dimer and MeNC-2MeOH trimer, with the excitation energy of a related excited state being lowered and electronic spectral redshifts being induced. Furthermore, the hydrogen bond strengthening in the electronically excited state plays an important role on the photophysics and photochemistry of MeNC in solutions

We have calculated relativistic energies and Landé factors for 5d6s 2, 5d 26s, 6s6p 2, 6s 27s, 5d 3, 5d6s7s, 6s 26p, 5d6s6p, 5d 26p and 6s 27p excited levels outside the core [Xe]4f 14 in neutral lutetium (Lu I, Z = 71). These calculations are based on the multiconfiguration Hartree-Fock (MCHF) method, within the framework of the Breit-Pauli relativistic corrections. Moreover, the results obtained have been compared with other works.

Analysis is carried out to study the convection heat transfer in an upper convected Maxwell fluid at a non-isothermal stretching surface. This is a generalization of the paper by Sadeghy et al. [21] to study the effects of free convection currents, variable thermal conductivity and the variable temperature at the stretching surface. Unlike in Sadeghy et al., here the governing nonlinear partial differential equations are coupled. These coupled equations are transformed in to a system of nonlinear ordinary differential equations and are solved numerically by a finite difference scheme (known as the Keller-Box method) and the numerical results are presented through graphs and tables for a wide range of governing parameters. The results obtained for the flow and heat transfer characteristics reveal many interesting behaviors that warrant further study of nonlinear convection heat transfer.

The velocity field corresponding to the unsteady motion of a viscous fluid between two side walls perpendicular to a plate is determined by means of the Fourier transforms. The motion of the fluid is produced by the plate which after the time t = 0, applies an oscillating shear stress to the fluid. The solutions that have been obtained, presented as a sum of the steady-state and transient solutions satisfy the governing equation and all imposed initial and boundary conditions. In the absence of the side walls they are reduced to the similar solutions corresponding to the motion over an infinite plate. Finally, the influence of the side walls on the fluid motion, the required time to reach the steady-state, as well as the distance between the walls for which the velocity of the fluid in the middle of the channel is unaffected by their presence, are established by means of graphical illustrations.

The flow of a micropolar fluid in a porous channel with expanding or contracting walls is investigated. The governing equations are reduced to ordinary ones by using similar transformations. Homotopy analysis method (HAM) is employed to obtain the expressions for the velocity fields and microrotation fields. Graphs are sketched for the effects of some values of parameters, especially the expansion ratio, on the velocity and microrotation fields and associated dynamic characteristics are analyzed in detail.

The integrability of coupled KdV equations is examined. The simplified form of Hirota’s bilinear method is used to achieve this goal. Multiple-soliton solutions and multiple singular soliton solutions are formally derived for each coupled KdV equation. The resonance phenomenon of each model will be examined.

The $$ \mathcal{N} $$-extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible. For even $$ \mathcal{N} $$ one can identify the 1D $$ \mathcal{N} $$-extended superalgebra with the fermionic Heisenberg algebra. Alternatively, supersymmetry generators can be realized as operators belonging to the Universal Enveloping Superalgebra of one bosonic and several fermionic oscillators. The deformed system is described in terms of twisted operators satisfying twist-deformed (anti)commutators. The main differences between an abelian twist defined in terms of fermionic operators and an abelian twist defined in terms of bosonic operators are discussed.

In this paper, we report some experimental results concerning several types of loss measurements of Er3+:Ti:LiNbO3 optical waveguides by using optical methods. Using the Fabry-Pérot interferometry method, we evaluated the attenuation coefficient of an optical waveguide resonator for a laser radiation having λ = 1.55 µm. We also evaluated the insertion losses, polarization dependent losses, and coupling with external losses. Additionally, from the transmitted spectra of the symmetrical monomode Fabry-Pérot optical waveguide resonator, we were able to evaluate the value of the group effective refractive index.

We show that a non-local form of the Gross-Pitaevskii equation describes not only long-wave excitations, but also the short-wave ones in Bose-condensate systems. At certain parameter values, the excitation spectrum mimics the Landau spectrum of quasi-particle excitations in superfluid helium with roton minimum. The excitation wavelength, at which the roton minimum exists, is close to the inter-particle interaction range. We determine how the roton gap and the effective roton mass depend on the interaction potential parameters, and show that the existence domain of the spectrum with a roton minimum is reduced if one accounts for an inter-particle attraction.

In this paper we present a deterministic and a probabilistic model of the dynamics of the price relations for a number of assets on the market. The formalism is based on the asset space introduced in a theory by Illinski. We derive, from an action functional for the system of price relations in that space, the corresponding difference equations, which constitute the deterministic description. Furthermore, we obtain the probability density function of the probabilistic model of market dynamics from the same action functional. The deterministic solution corresponds to a geometric sequence for the interest, whereas the derived probability density describes the probability of the next value of the price relations in dependence on their prior value. The formalism is completely developed for systems (markets) with two and three assets, but exactly the same approach is applicable to the systems consisting of an arbitrary number of assets.

The aim of the present work is to use one of the machine learning techniques named the genetic programming (GP) to model the p-p interactions through discovering functions. In our study, GP is used to simulate and predict the multiplicity distribution of charged pions (P(n ch)), the average multiplicity (〈n ch〉) and the total cross section (σ tot) at different values of high energies. We have obtained the multiplicity distribution as a function of the center of mass energy ($$ \sqrt s $$) and charged particles (n ch). Also, both the average multiplicity and the total cross section are obtained as a function of $$ \sqrt s $$. Our discovered functions produced by GP technique show a good match to the experimental data. The performance of the GP models was also tested at non-trained data and was found to be in good agreement with the experimental data.

The Blume-Emery-Griffiths model with the dipole-quadrupole interaction ($$ \ell = \frac{I} {J} $$) has been simulated using a cellular automaton algorithm improved from the Creutz cellular automaton (CCA) on the face centered cubic (fcc) lattice. The finite-size scaling relations and the power laws of the order parameter (M) and the susceptibility (χ) are proposed for the dipole-quadrupole interaction (ℓ). The dipole-quadrupole critical exponent δχ has been estimated from the data of the order parameter (M) and the susceptibility (χ). The simulations have been done in the interval $$ 0 \leqslant \ell = \frac{I} {J}0 \leqslant 0.01 $$ for $$ d = \frac{D} {J} = 0,k = \frac{K} {J} = 0 $$ and $$ h = \frac{H} {J} = 0 $$ parameter values on a face centered cubic (fcc) lattice with periodic boundary conditions. The results indicate that the effect of the ℓ parameter is similar to the external magnetic field (h). The critical exponent δℓ are in good agreement with the universal value (δh = 5) of the external magnetic field.

The aim of this paper is to introduce a new approximate method, namely the Optimal Parametric Iteration Method (OPIM) to provide an analytical approximate solution to Thomas-Fermi equation. This new iteration approach provides us with a convenient way to optimally control the convergence of the approximate solution. A good agreement between the obtained solution and some well-known results has been demonstrated. The proposed technique can be easily applied to handle other strongly nonlinear problems.

The original version of the article was published in Central European Journal of Physics 8, 94–960 (2010), DOI: 10.2478/s11534-010-0011-2. Unfortunately, due to an editorial processing error the original version of this article contains mistakes in Eqs. (23) and (25). Here we display the corrected version of these equations.

The original version of the article was published in Central European Journal of Physics 9, 45–48 (2011), DOI: 10.2478/s11534-010-0061-5. Unfortunately, due to an editorial processing error the original version of this article contains a mistake in Eq. (5). Here we display the corrected version of this equation.