Volume 10, Issue 4

The cosmic ray emulsion chamber community has reported several unusual phenomena which are also relevant to experiments at the current high-energy accelerators, in particular the Fermilab Tevatron Collider and the CERN Large Hadron Collider (LHC). A summary of the ”Cosmic Rays at Mountain Altitude” workshop held at Plock (Poland, September 2010) is given.

Barrabés et al. [Physica D, 241(4), 333–349, 2012] consider the problem of the hydrogen atom interacting with a circularly polarized microwave field modeled as a planar perturbed Kepler problem. For different values of the parameter, the authors offer some numerical evidence of the non-integrability of this problem. The objective of the present work is to give an analytical proof of the C1 non-integrability of this problem for any value of the parameter using the averaging theory as a main tool.

In this paper three things are done. (i) We investigate the analogues of Cerenkov radiation for the decay of a superluminal neutrino and calculate the Cerenkov angles for the emission of a photon through a W loop, and for a collinear electron-positron pair, assuming the tachyonic dispersion relation for the superluminal neutrino. The decay rate of a freely propagating neutrino is found to depend on the shape of the assumed dispersion relation, and is found to decrease with decreasing tachyonic mass of the neutrino. (ii)We discuss a few properties of the tachyonic Dirac equation (symmetries and plane-wave solutions), which may be relevant for the description of superluminal neutrinos seen by the OPERA experiment, and discuss the calculation of the tachyonic propagator. (iii) In the absence of a commonly accepted tachyonic field theory, and in view of an apparent “running” of the observed neutrino mass with the energy, we write down a model Lagrangian, which describes a Yukawa-type interaction of a neutrino coupling to a scalar background field via a scalar-minus-pseudoscalar interaction. This constitutes an extension of the standard model. If the interaction is strong, then it leads to a substantial renormalization-group “running” of the neutrino mass and could potentially explain the experimental observations.

The thermal friction force acting on an atom moving relative to a thermal photon bath has recently been calculated on the basis of the fluctuation-dissipation theorem. The thermal fluctuations of the electromagnetic field give rise to a drag force on an atom provided one allows for dissipation of the field energy via spontaneous emission. The drag force exists if the atomic polarizability has a nonvanishing imaginary part. Here, we explore alternative derivations. The damping of the motion of a simple harmonic oscillator is described by radiative reaction theory (result of Einstein and Hopf), taking into account the known stochastic fluctuations of the electromagnetic field. Describing the excitations of the atom as an ensemble of damped harmonic oscillators, we identify the previously found expressions as generalizations of the Einstein-Hopf result. In addition, we present a simple explanation for blackbody friction in terms of a Doppler shift of the thermal radiation in the inertial frame of the moving atom: The atom absorbs blue-shifted photons from the front and radiates off energy in all directions, thereby losing energy. The original plus the two alternative derivations provide for additional confirmation of an intriguing quantum friction effect, and leave no doubt regarding its existence.

In this paper we have examined the ionization of the ground state hydrogen atom in a spherical box with laser pulses of specific shapes. These shapes are predicted assuming correspondence under some conditions with the alternating kicking field. Unusually kicked dynamics is suggested. It is shown that such kicked dynamics leads to generalized Rabi oscillations with the positive energy states included and participation of the excited states. The correspondence with the real pulse is established emphasizing such unusually kicked dynamics. The approach is verified on the one-dimensional (1D) hydrogen atom and calculation of the known results for ionization probability.

The goal of this paper is to investigate the effect that a distribution of kinesin motor velocities could have on cytoskeletal element (CE) concentration waves in slow axonal transport. Previous models of slow axonal transport based on the stop-and-go hypothesis (P. Jung, A. Brown, Modeling the slowing of neurofilament transport along the mouse sciatic nerve, Physical Biology 6 (2009) 046002) assumed that in the anterograde running state all CEs move with one and the same velocity as they are propelled by kinesin motors. This paper extends the aforementioned theoretical approach by allowing for a distribution of kinesin motor velocities; the distribution is described by a probability density function (PDF). For a two kinetic state model (that accounts for the pausing and running populations of CEs) an analytical solution describing the propagation of the CE concentration wave is derived. Published experimental data are used to obtain an analytical expression for the PDF characterizing the kinesin velocity distribution; this analytical expression is then utilized as an input for computations. It is demonstrated that accounting for the kinesin velocity distribution increases the rate of spreading of the CE concentration waves, which is a significant improvement in the two kinetic state model.

We study how the constants G and Λ may vary in different theoretical models (general relativity (GR) with a perfect fluid, scalar cosmological models (SM) (“quintessence”) with and without interacting scalar and matter fields and three scalar-tensor theories (STT) with a dynamical Λ) in order to explain some observational results. We apply the program outlined in section II to study the Bianchi I models, under the self-similarity hypothesis. We put special emphasis on calculating exact power-law solutions which allow us to compare the different models. In all the studied cases we conclude that the solutions are isotropic and noninflationary. We also arrive at the conclusion that in the GR model with time-varying constants, Λ vanishes while G is constant. In the SM all the solutions are massless i.e. the potential vanishes and all the interacting models are inconsistent from the thermodynamical point of view. The solutions obtained in the STT collapse to the perfect fluid one obtained in the GR model where G is a true constant and Λ vanishes as in the GR and SM frameworks.

In an extreme mass-ratio binary black hole system, a non-equatorial orbit will list (i.e. increase its angle of inclination, i) as it evolves in Kerr spacetime. The abutment, a set of evolving, near-polar, retrograde orbits, for which the instantaneous Carter constant (Q) is at its maximum value (Q X) for given values of latus rectum (l̃) and eccentricity (e), has been introduced as a laboratory in which the consistency of dQ/dt with corresponding evolution equations for d l̃/dt and de/dt might be tested independently of a specific radiation back-reaction model. To demonstrate the use of the abutment as such a laboratory, a derivation of dQ/dt, based only on published formulae for d l̃/dt and de/dt, was performed for elliptical orbits on the abutment. The resulting expression for dQ/dt matched the published result to the second order in e. We believe the abutment is a potentially useful tool for improving the accuracy of evolution equations to higher orders of e and l̃−.

We investigate light propagation in the Swiss-cheese model. On both sides of Swiss-cheese sphere surfaces, observers resting in the flat Friedmann-Robertson-Walker (FRW) space and the Schwarzschild space respectively, see the same light ray enclosing different angles with the normal. We examine light refraction at each crossing of the boundary surfaces, showing that the angle of refraction is larger than the angle of incidence for both directions of the light.

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.

In the context of torsion (teleparallel) gravity, we focus on discussing the spin effects of Dirac particles associated with the non-diagonal singularity-free model (Mars space-time). We see that the vector part depends on the radial r and z directions and the axial-vector will be along the radial direction, that is, it will be symmetric about radial direction. Furthermore, the t = 0 case of the Mars metric is considered, thence it is seen that the axial-vector vanishes.

In gold-gold collisions of the Relativistic Heavy Ion Collider a perfect fluid of strongly interacting quark gluon plasma (sQGP) is created. The time evolution of this fluid can be described by hydrodynamical models. After an expansion, hadrons are created during the freeze-out period. Their distribution reveals information about the final state. To investigate the time evolution one needs to analyze penetrating probes: e.g. direct photon observations. In this paper we analyze a 1+3 dimensional solution of relativistic hydrodynamics. We calculate momentum distribution, azimuthal asymmetry and momentum correlations of direct photons. Based on earlier fits to hadronic spectra, we compare photon calculations to measurements to determine the equations of state and the initial temperature of sQGP. We find that the initial temperature in the center of the fireball is 507±12 MeV, while for the sound speed we get c s=0.36±0.02. We also estimate a systematic error of these results. We find that the measured azimuthal asymmetry is also compatible with this model. We also predict a photon source that is significantly larger in the out direction than in the side direction.

We demonstrate a new method to calculate inelastic scattering cross-sections, which in contrary to the Regge-based methods takes into account the energy momentum conservation law. It is shown that the main contribution to integral expressing inelastic scattering cross-sections does not come from the multi-Regge domain. In particular, accounting for the longitudinal momenta contribution to virtualities is sufficient and results in the new mechanism of cross-section growth. The reasons for taking into account the sufficiently high number of interference contributions are shown and the approximate method for this purpose is developed. By fitting single free parameter of the model achieved a qualitative agreement of the total and inelastic cross sections with experimental data.

The effect of gas flow in low pressure inductively coupled Ar/N2 plasmas operating at the rf frequency of 13.56 MHz and the total gas pressure of 20 mTorr is studied at the gas flows of 5–700 sccm by coupling the plasma simulation with the calculation of flow dynamics. The gas temperature is 300 K and input power is 300 W. The Ar fractions are varied from 0% to 95%. The species taken into account include electrons, Ar atoms and their excited levels, N2 molecules and their seven different excited levels, N atoms, and Ar+, N+, N2 +, N4 + ions. 51 chemical reactions are considered. It is found that the electron densities increase and electron temperatures decrease with a rise in gas flow rate for the different Ar fractions. The densities of all the plasma species for the different Ar fractions and gas flow rates are obtained. The collisional power losses in plasma discharges are presented and the effect of gas flow is investigated.

The method of paraxial complex geometrical optics (PCGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing in smoothly inhomogeneous and nonlinear saturable media of cylindrical symmetry. PCGO reduces the problem of Gaussian beam diffraction in nonlinear and inhomogeneous media to the system of the first order ordinary differential equations for the complex curvature of the wave front and for GB amplitude, which can be readily solved both analytically and numerically. As a result, PCGO radically simplifies the description of Gaussian beam diffraction in inhomogeneous and nonlinear media as compared to the numerical and analytical methods of nonlinear optics. The power of PCGO method is presented on the example of Gaussian beam evolution in logarithmically saturable medium with either focusing and defocusing refractive profile. Besides, the influence of initial curvature of the wave front on GB evolution in nonlinear saturable medium is discussed in this paper.

We discuss the one-dimensional Hubbard model, on finite sites spin chain, in context of the action of the direct product of two unitary groups SU(2)×SU(2). The symmetry revealed by this group is applicable in the procedure of exact diagonalization of the Hubbard Hamiltonian. This result combined with the translational symmetry, given as the basis of wavelets of the appropriate Fourier transforms, provides, besides the energy, additional conserved quantities, which are presented in the case of a half-filled, four sites spin chain. Since we are dealing with four elementary excitations, two quasiparticles called “spinons”, which carry spin, and two other called “holon” and “antyholon”, which carry charge, the usual spin-SU(2) algebra for spinons and the so called pseudospin-SU(2) algebra for holons and antiholons, provide four additional quantum numbers.

We describe a pseudospectral approach which combines a mapping procedure with the principle of minimal sensitivity to obtain accurate estimates for the eigenvalues of non-uniform strings and both uniform and nonuniform membranes. We illustrate the method on specific examples, including the case of a cross shaped membrane, with arms of infinite length.

Fracture patterns resulting from point-like impact acting perpendicularly on the plane of a commercial sodalime glass plate is modelled by a spring-block system. The characteristic patterns consist of crack lines that are spreading radially from the impact point and concentric arcs intersecting these radial lines. Experimental results suggest that the number of radial crack lines is scaling linearly with the energy dissipated during the crack formation process. The elaborated spring-block model reproduces with success the observed fracture patterns and scaling law.

In this paper, a modification of the successive linearization method (SLM) for solving nonlinear initial value problems is introduced for the first time. The proposed method is based on a novel technique of extending the standard SLM and adapting it to a sequence of multiple intervals. In this new application the method is referred to as the piecewise successive linearization method(PSLM). This new algorithm is applied to chaotic and non-chaotic differential equations that model the Lotka-Volterra, Lorenz, Rössler and Genesio-Tesi systems. A comparative study between the new algorithm and the MATLAB Runge-Kutta based in-built solver (ode45) method is presented. The results demonstrate accuracy and reliability of the proposed PSLM algorithm.

Taking a two-level system interacting with a two-band environment as an example, we discuss the non-Markovianity and initial system-environment correlations for the generalized Lindblad master equation by using a recently introduced measure given by Breuer et al. Our results show that the initial states of the environment and initial system-environment correlations have strong effects on the non-Markovianity of the reduced system. Moreover, we also show that information and energy can flow in different directions, i.e., energy flows to the system while information flows from the system, which is quite different from previous results.

We investigate the effect of the isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Morse potential for any quantum states. When the velocity-dependent term is used as a constant parameter, ρ(r) = ρ 0, the energy eigenvalues can be obtained analytically by using the Pekeris approximation. When the velocity-dependent term is considered as an harmonic oscillator type, ρ(r) = ρ 0 r 2, we show how to obtain the energy eigenvalues of the Morse potential without any approximation for any n and ℓ quantum states by using numerical calculations. The calculations have been performed for different energy eigenvalues and different numerical values of ρ 0, in order to show the contribution of the velocity-dependent potential on the energy eigenvalues of the Morse potential.

The asymptotic iteration method is employed to calculate the any ℓ-state solutions of the Schrödinger equation with the Eckart potential by proper approximation of the centrifugal term. Energy eigenvalues and corresponding eigenfunctions are obtain explicitly. The energy eigenvalues are calculated numerically for some values of ℓ and n. Our results are in excellent agreement with the findings of other methods for short potential ranges.

In this manuscript the homotopy perturbation method, the new iterative method, and the variational iterative method have been successively used to obtain approximate analytical solutions of nonlinear Sturm-Liouville, Navier-Stokes and Burgers’ equations. It is shown that the homotopy perturbation method gives approximate analytical solution near to the exact one. We have illustrated the obtained results by sketching the graph of the solutions.

Europium-doped barium aluminate (BaAlxOy:Eu2+) phosphors were obtained at low temperatures (500°C) using the solution — combustion of corresponding metal nitrate-urea solution mixtures. The particle size and morphology and the structural and luminescent properties of the synthesized phosphors were examined by means of scanning electron microscopy (SEM), X-ray diffraction (XRD), Electron diffraction spectroscopy (EDS) and photoluminescence (PL). It was found that the change in Ba: Al molar ratios showed greatly influence not only on the particle size and morphology, but also on their PL spectra and crystalline structure. The structure of BaAlxOy nanophosphors changes from a hexagonal Ba2Al10O17 phase for samples with 6:100 molar ratios to a hexagonal BaAl2O4 one with an increase in Ba content. The peak of the emission band occurs at a longer wavelength (around 615 nm) with a decrease in Ba concentration but displays a broad blue-green emission band composed from two emissions with the maximum at 495 and 530nm coming from Eu2+ in two sites for increasing Ba content. The blue-green emission is probably due to the influence of 5d electron states of Eu2+ in the crystal field because of atomic size variation causing crystal defects while the red emission is due to f - f transitions. These findings clearly demonstrate the possibility of fine tuning the colour emission.

We present a quantized model of a harmonically confined dot atom with inherent damping in the presence of a transverse magnetic field. The model leads to a non-Hermitian Hamiltonian in coordinate space. We have analytically studied the effects of damping on Rabi type oscillations of the system. The model explains the decoherence of Rabi oscillations in a Josephson Junction.

The present work deals with experimental studies to examine the theoretical model of thermodiffusion of electrically charged nanoparticles. Three different ionic magnetic colloid samples have been synthesized and profoundly analyzed. The theoretical model is a classical one, based on the calculation of the temperature and the electric potential distribution around nanoparticles. The discrepancy between experimental data and theory turns out not to exceed 20%. We focus on applying different approximations between calculated electrical double layer in the theoretical model and experimental determination of the surface charge density of colloidal particles. We assume this is the main reason for obtained discrepancy.

A comparative study of the excitation of luminescence by VUV radiation as well as of thermally and photostimulated luminescence has been carried out for CaSO4:Tb3+ and CaSO4:Gd3+ phosphors, where Na+ or F− ions are used for charge compensation. The distinction in hole processes for the phosphors with Na+ or F− compensators is determined by the differing thermal stability of the holes localized at/near Tb3+Na+ and Gd3+Na+ (up to 100–160 K) or at/near Tb3+F− V Ca and Gd3+F− V Ca centers involving also a cation vacancy (up to 400–550 K). Tunnel luminescence in the pairs of localized electrons and holes nearby Tb3+ or Gd3+ has been detected. The mechanisms of electron-hole, hole-electron and tunnel recombination luminescence as well as a subsequent released energy transfer to RE3+ ions are considered.

The analytical expressions for the three-dimensional spatial distribution of excitons and luminescence decay kinetics of wide band-gap crystals were derived taking into account the saturation effect for absorption near the centre of the incident laser beam with Gaussian transversal profile. The model is verified for the excitonic emission of CdWO4 crystals under excitation by ultra-short laser pulses in the region of weak excitonic absorption.

Lithium fluoride (LiF), one of the most pervasive alkali halides in optical device research, is routinely used in optical data storage and radiation protection. LiF crystals may contain different aggregate defects produced by several types of ionizing radiation, with the number of defects being proportional to the cumulative radiation dose. Stimulation of irradiated LiF detectors by heating or with blue light causes thermoluminescence (TL) or photoluminescence (PL), respectively. We developed a new PL reader equipped with a blue light-emitting diode for stimulation and a Hamamatsu photomultiplier for registering green emissions, dedicated to examining LiF detectors as well as more broadly investigating TL/PL emission from standard LiF detectors irradiated with gamma rays, 60 MeV protons and alpha particles. The results confirmed very high efficiency PL signal from alpha-irradiated LiF detectors corresponding to their low efficiency after gamma irradiation, and vice versa for TL readout. Combining the TL and PL readouts permits us to discriminate between how different kinds of radiation affect efficiency in LiF detectors.

In this work, we explore more applications of the simplified form of the bilinear method to the seventhorder Caudrey-Dodd-Gibbon (CDG) and the Caudrey-Dodd-Gibbon-KP (CDG-KP) equation. We formally derive one and two soliton solutions for each equation. We also show that the two equations do not show resonance.