Central European Journal of Physics

In the 10-dimensional pp-waves background we have found using T-duality a 4-dimensional space-time in which closed time-like curves appear in the region bounded by two coaxial elliptic cylinders. This 4-dimensional space-time is similar to the Gödel-type space-time only in this region. Outside of this region the causal pathology does not appear.

We examine the problem of flow and heat transfer in a second grade fluid over a stretching sheet [K. Vajravelu, T. Roper, Int. J. Nonlinear Mech. 34, 1031 (1999)]. The equations considered by Vajravelu and Roper [K. Vajravelu, T. Roper, Int. J. Nonlinear Mech. 34, 1031 (1999)], are found to be incorrect in the literature. In this paper, we not only corrected the equation but found a useful analytic solution to this important problem. We also extended the problem for hydromagnetic flow and heat transfer with Hall effect. The explicit analytic homotopy solution for the velocity field and heat transfer are presented. Graphs for the velocity field, skin friction coefficient, and rate of heat transfer are presented. Tables for the skin friction coefficient and rate of heat transfer are also presented. The convergence of the solution is also properly checked 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.

We have solved exactly the two-component Dirac equation in the presence of a spatially one-dimensional Hulthén potential, and presented the Dirac spinors of scattering states in terms of hypergeometric functions. We have derived the reflection and transmission coefficients using the matching condition on the wavefunctions, and investigated the condition for the existence of transmission resonance. Furthermore, we have demonstrated how the transmission resonance depends on the shape of the potential.

Quantum-chemical testing of donor-acceptor properties of binary molecular complexes, related to the singlet state, is suggested as QCh calculations of studied systems and their constituents by using both spin-nondependent (RHF) and spindependent (UHF) versions of the exploited computational tool. The avoided crossing of intermolecular interaction terms of neutral moleculesE int (A 0 B 0) and molecular ionsE int (A + B −) causes a multi-mode character of the ground state term. The dependence of D-A complex properties on the type of the term, space positions of the term minimum, and the interrelation of the corresponding energies are discussed. The suggested approach has been applied to binary complexes C60+X (X=TAE, TDAE, DMMA, COANP, 2Li, Mg).

In this paper, we apply certain measure of noncompactness and fixed point theorem of Darbo type to derive the existence and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order with three parameters. Moreover, we also present the uniqueness and another existence results of the solutions to the above equations. Finally, two examples are given to illustrate the obtained results.

A classical and a relativistic law of motion for an advancing shell are deduced applying the thin layer approximation. A new parameter connected with the quantity of absorbed matter in the expansion is introduced; this allows the matching of theory with observation.

Tetracationic porphyrin dyes TMPyP and ZnPyP were intercalated into hydrophobized layered silicate films of three smectites. The smectites represented the layered silicate specimens of high (Fluorohectorite, Corning; FHT), medium (Kunipia F montmorillonite; KF) and low layer charge (Laponite, Laporte; LAP). The molecular orientations of the dye cations were studied by means of linearly-polarized ultraviolet-visible (UV-VIS) spectroscopy. The spectral analysis and consequent calculations of tilting angles of the transition moments at the wavelengths of Soret band transitions were in the range of 25°-35°. The determined angles indicated molecular orientation of the dye cations being almost parallel to the surface of the silicates. Slightly higher values (above 35°), determined for a FHT film, indicated either a slightly tilted orientation of the dye cations or the change of molecular comformation after the intercalation of the dye.

We explore two- and three-state Markov models driven out of thermal equilibrium by non-potential forces, to demonstrate basic properties of the steady heat capacity based on the concept of quasistatic excess heat. It is shown that large enough driving forces can make the steady heat capacity negative. For both the low- and high-temperature regimes we propose an approximative thermodynamic scheme in terms of “dynamically renormalized” effective energy levels.

Results of radionuclide activity concentration measurements in deposition and ground-level air conducted at the station of the Institute of Physics situated 3.5 km from the Ignalina Nuclear Power Plant (Ignalina NPP) in 2005 are analyzed. Atmospheric depositional fluxes of 7Be, 60Co and 137Cs are estimated. Radionuclide particle deposition rates are calculated. The Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model of the global dispersion and deposition is used to explain variations in the 137Cs activity concentration in the ground-level air in the Ignalina NPP region in 2005. An increase in the 137Cs activity concentration of up to 17.4 µBq m−3 on 30 October-5 November is studied. Modelling results show that the Chernobyl NPP Unit 4 Sarcophagus and the radiocaesium resuspension from the Chernobyl NPP accident polluted regions are sources of 137Cs to the environment of the Ignalina NPP. Results on solubility in water of aerosols — carriers of 137Cs — are discussed.