Showing papers in "European Physical Journal Plus in 2014"

Bound states of spatially dependent mass Dirac equation with the Eckart potential including Coulomb tensor interaction

Abstract: We investigate the approximate solutions of the Dirac equation with the position-dependent mass particle in the Eckart potential field including the Coulomb tensor interaction by using the parametric Nikiforov-Uvarov method. Taking an appropriate approximation to deal with the centrifugal term, the Dirac energy states and the corresponding normalized two-spinor components of the wave function are obtained in closed form. Some special cases of our solution are investigated. Furthermore, we present the correct solutions obtained via the asymptotic iteration method which are in agreement with the parametric Nikiforov-Uvarov method results.

Effect of spatially variable magnetic field on ferrofluid flow and heat transfer considering constant heat flux boundary condition

Abstract: Ferrofluid flow and heat transfer in the presence of an external variable magnetic field is studied. The inner cylinder is maintained at uniform heat flux and the outer cylinder has constant temperature. The Control Volume based Finite Element Method (CVFEM) is applied to solve the governing equations. Combined magnetohydrodynamic and ferrohydrodynamic effects have been taken into account. The effects of magnetic number, Hartmann number, Rayleigh number and nanoparticle volume fraction on hydrothermal behavior have been examined. Results show that the Nusselt number is an increasing function of Magnetic number, Rayleigh number and nanoparticle volume fraction while it is a decreasing function of the Hartmann number. Also, it can be concluded that the enhancement in heat transfer decreases with an increase in the Rayleigh number and magnetic number but it increases with an increase in the Hartmann number.

Three-dimensional chaotic autonomous system with only one stable equilibrium: Analysis, circuit design, parameter estimation, control, synchronization and its fractional-order form

Abstract: This paper proposes a three-dimensional chaotic autonomous system with only one stable equilibrium. This system belongs to a newly introduced category of chaotic systems with hidden attractors. The nonlinear dynamics of the proposed chaotic system is described through numerical simulations which include phase portraits, bifurcation diagrams and new cost function for parameter estimation of chaotic flows. The coexistence of a stable equilibrium point with a strange attractor is found in the proposed system for specific parameters values. The physical existence of the chaotic behavior found in the proposed system is verified by using the Orcard-PSpice software. A good qualitative agreement is shown between the simulations and the experimental results. Based on the Routh-Hurwitz conditions and for a specific choice of linear controllers, it is shown that the proposed chaotic system is controlled to its equilibrium point. Chaos synchronization of an identical proposed system is achieved by using the unidirectional linear and nonlinear error feedback coupling. Finally, the fractional-order form of the proposed system is studied by using the stability theory of fractional-order systems and numerical simulations. A necessary condition for the commensurate fractional order of this system to remain chaotic is obtained. It is found that chaos exists in this system with order less than three.

Interaction of nanoparticles for the peristaltic flow in an asymmetric channel with the induced magnetic field

Abstract: In the present investigation, we examined the interaction of nanoparticle copper with the base fluid water in an asymmetric channel in the presence of an induced magnetic field. The complexity of equations describing the flow of the nanofluid is reduced by applying the low-Reynolds number and long-wavelength approximations. The resulting equations are solved exactly. The obtained expressions for the velocity and temperature phenomenon are sketched in graphs. The resulting relations for pressure gradient and pressure rise are plotted for various pertinent parameters. The streamlines are drawn for some physical quantities to discuss the trapping phenomenon.

Unsteady boundary layer MHD free convection flow in a porous medium with constant mass diffusion and Newtonian heating

Abstract: In this article, the unsteady boundary layer magnetohydrodynamic (MHD) free convection flow past an oscillating vertical plate embedded in a porous medium with constant mass diffusion and Newtonian heating condition is analysed. By considering the effects of thermal radiation in the energy equation, the problem is first modeled and then written in dimensionless form, which is then solved by using the Laplace transform technique. The expressions for velocity, temperature and concentration fields are obtained and plotted graphically to see the influence of embedded parameters. The results for skin friction, Nusselt number and Sherwood number are also shown in tables. Further a table is included for the comparison of our results with those present in the literature.

Some simple models for quark stars

Abstract: We find two new classes of exact solutions for the Einstein-Maxwell equations. The solutions are obtained by considering charged anisotropic matter with a linear equation of state consistent with quark stars. The field equations are integrated by specifying forms for the measure of anisotropy and a gravitational potential which are physically reasonable. The solutions found generalize the Mark-Harko model and the Komathiraj-Maharaj model. A graphical analysis indicates that the matter variables are well behaved.

Magnetohydrodynamic flow of water/ethylene glycol based nanofluids with natural convection through a porous medium

Abstract: In this study, the natural convection boundary layer flow along with inverted cone, magnetic and heat generation on water and ethylene glycol based nanofluids is considered by means of variable wall temperature. Porous medium is also taken into account. The physical problem is first modeled and then the governing equations are transformed into nonlinear ordinary differential equations under the assumptions of the Boussinesq approximation. Analytical solutions of nonlinear coupled equations are obtained by the homotopy analysis method. Correlation of skin friction and heat transfer rate corresponding to active parameters is also presented. Obtained results are illustrated by graphs and tables in order to see the effects of physical parameters.

$ f(R,T_{\mu\nu}T^{\mu\nu})$ gravity and Cardassian-like expansion as one of its consequences

Abstract: We propose a new model of gravity where the Ricci scalar \( (R)\) in the Einstein-Hilbert action is replaced by an arbitrary function of \( R\) and of the norm of energy-momentum tensor, i.e., \( f(R,T_{\mu u}T^{\mu u})\) . Field equations are derived in the metric formalism. We find that the equation of motion of massive test particles is non-geodesic and these test particles are acted upon by a force which is orthogonal to the four-velocity of the particles. We also find the Newtonian limit of the model to calculate the extra acceleration which can affect the perihelion of Mercury. There is a deviation from the general relativistic (GR) result unless the energy density of fluid is constant. Arranging the \( \alpha\) parameter gives an opportunity to cure the inconsistency between the observational values for the abundance of light elements and the standard Big Bang nucleosynthesis results. Even the dust-dominated universe undergoes an accelerated expansion without using a cosmological constant in Model II. With this specific choice of \( f(R,T_{\mu u}T^{\mu u})\), we get Cardassian-like expansion.

Models of universe with a polytropic equation of state: I. The early universe

Abstract: We construct models of universe with a generalized equation of state $ p=(\alpha \rho+k\rho^{1+1/n})c^{2}$ having a linear component and a polytropic component. Concerning the linear equation of state $ p=\alpha\rho c^{2}$ , we assume $ -1\le \alpha\le 1$ . This equation of state describes radiation ( $ \alpha=1/3$ ) or pressureless matter ( $ \alpha=0$ ). Concerning the polytropic equation of state $ p=k\rho^{1+1/n} c^{2}$ , we remain very general allowing the polytropic constant k and the polytropic index n to have arbitrary values. In this paper, we consider negative indices n < 0. In this case, the polytropic component dominates the linear component in the late universe where the density is low. For $ \alpha=0$ , $ n=-1$ and $ k=-\rho_{\Lambda}$ , where $ \rho_{\Lambda}=7.02 10^{-24}$ g/m3 is the cosmological density, we obtain a model of late universe describing the transition from the matter era to the dark energy era. The universe exists at any time in the future and there is no singularity. It undergoes an inflationary expansion (exponential acceleration) with the cosmological density $ \rho_{\Lambda}=7.02 10^{-24}$ g/m3 (dark energy) on a timescale $ t_{\Lambda}=1.46 10^{18}$ s. Coincidentally, we live close to the transition between the matter era and the dark energy era, corresponding to a size $ a_{2}=8.95 10^{25}$ m and a time $ t_{2}=2.97 10^{17}$ s. For $ \alpha=0$ , $ n=-1$ and $ k=\rho_{\Lambda}$ , we obtain a model of cyclic universe appearing and disappearing periodically. If we were living in this universe, it would disappear in about 2.38 billion years. We make the connection between the early and the late universe and propose a simple equation describing the whole evolution of the universe. This leads to a model of universe that is eternal in past and future without singularity (aioniotic universe). It refines the standard $ \Lambda$ CDM model by incorporating naturally a phase of early inflation and removing the primordial singularity (Big Bang). This model exhibits a nice “symmetry” between the early and the late universe, the cosmological constant in the late universe playing the same role as the Planck constant in the early universe. The pressure is successively negative (early inflation), positive (radiation and matter eras), and negative again (late inflation). We interpret the cosmological constant as a fundamental constant of nature describing the “cosmophysics” just like the Planck constant describes the “microphysics”. The Planck density and the cosmological density represent fundamental upper and lower bounds differing by 122 orders of magnitude. The cosmological constant “problem” may be a false problem. We determine the potential of the scalar field (quintessence, tachyon field) corresponding to the generalized equation of state $ p=(\alpha \rho+k\rho^{1+1/n})c^{2}$ . We also propose a unification of vacuum energy, radiation, and dark energy through the quadratic equation of state $ p/c^{2}=-4\rho^{2}/3\rho_{P}+\rho/3 - 4\rho_{\Lambda}/3$ .

Model-based analysis of micropolar nanofluid flow over a stretching surface

Abstract: This article deals with the study of micropolar nanofluids flow over a stretching sheet. This study uses the compatible models to deal with the effects of two different kinds of nanoparticles (copper (Cu) and silver (Ag)) within the base fluids (water and Kerosene oil). Developed governing boundary layer equations and the boundary conditions are transformed into the system of coupled nonlinear ordinary differential equations. Numerical results are constructed for velocity, temperature, skin friction coefficient and local Nusselt number by considering the thermo-physical properties of both base fluids and particles. Fluid flow behavior is analyzed through stream lines and a conclusion has been developed under the observation of fluid flow behavior.

VSR symmetries in the DKP algebra: The interplay between Dirac and Elko spinor fields

Abstract: VSR symmetries are here naturally incorporated in the DKP algebra on the spin-0 and the spin-1 DKP sectors. We show that the Elko (dark) spinor fields structure plays an essential role in accomplishing this aim, unravelling hidden symmetries on the bosonic DKP fields under the action of discrete symmetries.

Axially symmetric cosmological model in f(R, T) gravity

Abstract: An axially symmetric space-time is considered in the presence of a perfect fluid source in the framework of f (R, T) gravity, where R is the Ricci scalar and T is the trace of the energy-momentum tensor proposed by Harko et al. (Phys. Rev. D 84, 024020, (2011)). We assume the variation law of mean Hubble parameter to obtain the exact solutions of the field equations. The geometrical and physical parameters for both the models are studied.

Quantum dot in a graphene layer with topological defects

Abstract: In this paper we use an exactly solvable model in order to investigate a magnetization and persistent current of massless Dirac fermions confined in a quantum dot in a graphene layer with a topological defect. We study the low-energy electronic spectrum of a graphene layer structure using the continuum approach and introduce a disclination by means of the geometric theory of defects. The model of the confining potential is introduced into the system via the Dirac oscillator, which provides a harmonic confinement for quasiparticles, in order to study a behaviour of quantum dots in graphene. The exact energy spectrum and wave functions are obtained analytically for the model, in the case where a thin magnetic flux confined to the dot centre, and the arising of persistent currents is investigated. A uniform magnetic field is introduced in a quantum dot, and this model is used to study persistent currents and magnetization in the graphene dot. We have derived exact expressions both for the magnetic moment and for the current carried by quasiparticle states.

A new Jacobi spectral collocation method for solving 1+1 fractional Schrödinger equations and fractional coupled Schrödinger systems

Abstract: The Jacobi spectral collocation method (JSCM) is constructed and used in combination with the operational matrix of fractional derivatives (described in the Caputo sense) for the numerical solution of the time-fractional Schrodinger equation (T-FSE) and the space-fractional Schrodinger equation (S-FSE). The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations, which greatly simplifies the solution process. In addition, the presented approach is also applied to solve the time-fractional coupled Schrodinger system (T-FCSS). In order to demonstrate the validity and accuracy of the numerical scheme proposed, several numerical examples with their approximate solutions are presented with comparisons between our numerical results and those obtained by other methods.

Probing kinematics and fate of the Universe with linearly time-varying deceleration parameter

Abstract: The parametrizations q = q 0+q 1 z and q = q 0+q 1(1 − a/a 0) (Chevallier-Polarski-Linder parametrization) of the deceleration parameter, which are linear in cosmic redshift z and scale factor a , have been frequently utilized in the literature to study the kinematics of the Universe. In this paper, we follow a strategy that leads to these two well-known parametrizations of the deceleration parameter as well as an additional new parametrization, q = q 0+q 1(1 − t/t 0), which is linear in cosmic time t. We study the features of this linearly time-varying deceleration parameter in contrast with the other two linear parametrizations. We investigate in detail the kinematics of the Universe by confronting the three models with the latest observational data. We further study the dynamics of the Universe by considering the linearly time-varying deceleration parameter model in comparison with the standard ΛCDM model. We also discuss the future of the Universe in the context of the models under consideration.

Heat transfer in the boundary layer flow of a Casson fluid over a permeable shrinking sheet with viscous dissipation

Abstract: In this paper the dual solutions in the flow of a Casson fluid over a porous shrinking surface are numerically discussed. Viscous dissipation in the heat transfer analysis is presented. Appropriate similarity transformations are used to convert governing nonlinear partial differential equations of flow and heat transfer into the system of nonlinear ordinary differential equations. The shooting technique with the Runge-Kutta method is employed to solve the resulting equations. Graphical results for dimensionless velocity and temperature are reported and examined very carefully. The study reveals that the existence of dual solutions is possible for some range of the suction parameter. For both solutions, the momentum boundary layer thickness decreases with the Casson fluid parameter. The thermal boundary layer thickness decreases with the Prandtl number and increases with the Eckert number (in both solutions). Further, the thermal boundary layer thickness decreases with increasing values of wall mass suction for the first solution, whereas it increases with increasing values of the mass suction parameter for the second solution.

Envelope periodic solutions for a discrete network with the Jacobi elliptic functions and the alternative (G′/G)-expansion method including the generalized Riccati equation

Abstract: Using the Jacobi elliptic functions and the alternative (G′/G-expansion method including the generalized Riccati equation, we derive exact soliton solutions for a discrete nonlinear electrical transmission line in (2+1) dimension. More precisely, these methods are general as they lead us to diverse solutions that have not been previously obtained for the nonlinear electrical transmission lines. This study seeks to show that it is not often necessary to transform the equation of the network into a well-known differential equation before finding its solutions. The solutions obtained by the current methods are generalized periodic solutions of nonlinear equations. The shape of solutions can be well controlled by adjusting the parameters of the network. These exact solutions may have significant applications in telecommunication systems where solitons are used to codify or for the transmission of data.

Cu-doped ZnO nanoparticles synthesized by simple co-precipitation route

Abstract: Cu-doped zinc oxide (CuxZn1-x O, x = 0–3%) nanoparticles were synthesized using the simple direct co-precipitation method with Zn(CH3COO)2 . H2O, Cu(CH3COO)2 and polyvinylenepyroliden (PVP) as raw materials. Structure, size distribution and morphology of the Cu-doped ZnO nanoparticles were studied by X-ray diffraction, transmission electron microscope (TEM) and scanning electron microscope (SEM), respectively. The optical and photoluminescence photospectroscopy were utilized to analyze the crystal defects of the ZnO nanoparticles. Cu addition does not change the hexagonal wurtzite structure of ZnO nanoparticles. The mean particle size is around 10 nm. The 0.01% Cu concentration causes maximal photoluminescence. The bandgap of ZnO nanoparticles was obtained around 3.93eV due to quantum size effects.

Work cost of thermal operations in quantum thermodynamics

Abstract: Adopting a resource theory framework of thermodynamics for quantum and nano systems pioneered by Janzing et al. (Int. J. Th. Phys. 39, 2717 (2000)), we formulate the cost in the useful work of transforming one resource state into another as a linear program of convex optimization. This approach is based on the characterization of thermal quasiorder given by Janzing et al. and later by Horodecki and Oppenheim (Nat. Comm. 4, 2059 (2013)). Both characterizations are related to an extended version of majorization studied by Ruch, Schranner and Seligman under the name mixing distance (J. Chem. Phys. 69, 386 (1978)).

On the Lorentz symmetry breaking effects on a Dirac neutral particle inside a two-dimensional quantum ring

Abstract: We study the effects of the Lorentz symmetry violation in the nonrelativistic quantum dynamics of a spin-1/2 neutral particle interacting with external fields confined to a two-dimensional quantum ring (W.-C. Tan, J.C. Inkson, Semicond. Sci. Technol. 11, 1635 (1996)). We show a possible scenario for the Lorentz symmetry breaking that permits us to make an analogy with the Landau-Aharonov-Casher system (M. Ericsson, E. Sjoqvist, Phys. Rev. A 65, 013607 (2001)), where a change in the angular frequency characteristic of the confinement of a quantum particle to a two-dimensional ring is obtained. Then, we show that an upper bound for the Lorentz symmetry breaking parameters may be set up. Besides, we analyse another possible scenario of the Lorentz symmetry violation by showing the presence of an analogue of the Coulomb potential. We obtain the bound states solutions to the Schrodinger-Pauli equation and discuss a quantum effect characterized by the dependence of the angular frequency on the quantum numbers of the system.

Meshless local radial point interpolation (MLRPI) on the telegraph equation with purely integral conditions

Abstract: In this paper, the meshless local radial point interpolation (MLRPI) method is applied to the one-dimensional telegraph equation with purely integral conditions In MLRPI, it does not require any background integration cells but it requires all integrations be carried out locally over small quadrature domains of regular shapes, such as lines in one dimension, circles or squares in two dimensions and spheres or cubes in three dimensions A technique is proposed to construct shape functions using point interpolation method augmented to the radial basis functions The time derivatives are approximated by the finite difference method Some numerical experiments for the mentioned problem are carried out as well

Influence of heat generation and heat flux on peristaltic flow with interacting nanoparticles

Abstract: In the current study, we have examined the peristaltic flow of three different nanoparticles with water as base fluid under the influence of slip boundary conditions through a vertical asymmetric porous channel in the presence of MHD. The selected nanoparticles are titanium dioxide ( TiO2 , copper oxide (CuO) and silicon dioxide ( SiO2 . The Brownian motion shows that the effective conductivity increases to result in a lower temperature gradient for a given heat flux. To examine these transport phenomena thoroughly, we also consider the thermal conductivity model of Brownian motion for nanofluids, this increases the effect of the particle size, particle volume fraction and temperature dependence. The mathematical formulation is presented. Exact solutions are obtained from the resulting equations. The obtained expressions for pressure gradient, temperature and velocity profile are described through graphs for the various relevant parameters. The streamlines are drawn for some physical quantities to discuss the trapping phenomenon.

Mixed convection flow of nanofluid with Newtonian heating

Abstract: This article explores the flow of viscous nanofluid over a stretching sheet with mixed convection. The main objective here is to examine the Newtonian heating effect. The partial differential equations are reduced to the ordinary differential equations (ODE). The resulting ODEs are computed for the convergent series solutions. Plots for physical quantities of interest are displayed and discussed. Local Nusselt and Sherwood numbers are computed and analyzed.

Discovering forgeries of modern art by the 14C Bomb Peak

Abstract: Exploiting the anomalous behaviour of the atmospheric radiocarbon concentration in the years after 1955 (so-called “Bomb Peak”), an alleged painting by Fernard Leger was unambiguously proven to be a fake just by dating the canvas support. Some art historians had questioned the authenticity of the painting, and their suspicions were fuelled by some scientific examinations of the paint materials (X-ray radiography, SEM-EDS), compared to those of another work unquestionably attributed to Leger. The decisive argument to prove that it was a fake was provided by the radiocarbon date obtained from a sample of canvas of the painting, using Accelerator Mass Spectrometry at the INFN-Labec laboratory in Florence. Beyond any doubt, the cotton plant from which the canvas was produced was cut no earlier than 1959, i.e. four years after Leger's death, thus definitely confirming the concerns of a fake.

Electricity by intermittent sources: An analysis based on the German situation 2012

Abstract: The 2012 data of the German load, the on- and offshore and the photo-voltaic energy production are used and scaled to the limit of supplying the annual demand (100% case). The reference mix of the renewable energy (RE) forms is selected such that the remaining back-up energy is minimised. For the 100% case, the RE power installation has to be about 3 times the present peak load. The back-up system can be reduced by 12% in this case. The surplus energy corresponds to 26% of the demand. The back-up system and more so the grid must be able to cope with large power excursions. All components of the electricity supply system operate at low capacity factors. Large-scale storage can hardly be motivated by the effort to further reduce CO2 emission. Demand-side management will intensify the present periods of high economic activities. Its rigorous implementation will expand the economic activities into the weekends. On the basis of a simple criterion, the increase of periods with negative electricity prices in Germany is assessed. It will be difficult with RE to meet the low CO2 emission factors which characterise those European Countries which produce electricity mostly by nuclear and hydro power.

CNT suspended nanofluid analysis in a flexible tube with ciliated walls

Abstract: The current investigation is carried out to analyze the effect of heat transfer in a flexible tube with ciliated walls and carbon nanotubes. The problem has been formulated in the form of non-linear partial differential equations, which are then reduced to ordinary differential equation form using the dimensionless variables and the conditions of low Reynolds number and long wavelength. Exact solutions have been obtained for velocity, temperature and pressure gradient and graphs for velocity, temperature and pressure gradient have been plotted for a better analysis of the solution.

Thim’s experiment and exact rotational space-time transformations

Abstract: Thim measured the transverse Doppler shift using a system consisting of a stationary antenna and pickup, in addition to a number of intermediate antennas mounted on the rim of a rotating disk. No such shift was detected, although the experiment should have had enough sensitivity to measure it, as predicted by the Lorentz transformations. However, using the Lorentz transformations to analyze the results of experiments involving circular motion, while commonly done, is inappropriate because such an analysis involves non-inertial frames, which are outside the range of validity of special relativity. In this paper, we re-analyze Thim's experiment using exact rotational space-time transformations, finding that his null result is consistent with theoretical predictions.

Quintessence scalar field: A dynamical systems study

Abstract: The present work deals with a dynamical systems study of quintessence potentials leading to the present accelerated expansion of the universe. The principal interest is to check for late time attractors which give an accelerated expansion for the universe. Two examples are worked out, namely the exponential and the power-law potentials.

On the origins and the historical roots of the Higgs boson research from a bibliometric perspective

Abstract: The subject of our present paper is the analysis of the origins or historical roots of the Higgs boson research from a bibliometric perspective, using a segmented regression analysis in combination with a method named reference publication year spectroscopy (RPYS). Our analysis is based on the references cited in the Higgs boson publications published since 1974. The objective of our analysis consists of identifying specific individual publications in the Higgs boson research context to which the scientific community frequently had referred to. We are interested in seminal works which contributed to a high extent to the discovery of the Higgs boson. Our results show that researchers in the Higgs boson field preferably refer to more recently published papers —particularly papers published since the beginning of the sixties. For example, our analysis reveals seven major contributions which appeared within the sixties: Englert and Brout (1964), Higgs (1964, 2 papers), and Guralnik et al. (1964) on the Higgs mechanism as well as Glashow (1961), Weinberg (1967), and Salam (1968) on the unification of weak and electromagnetic interaction. Even if the Nobel Prize award highlights the outstanding importance of the work of Peter Higgs and Francois Englert, bibliometrics offer the additional possibility of getting hints to other publications in this research field (especially to historical publications), which are of vital importance from the expert point of view.

Positron-acoustic Gardner solitons and double layers in electron-positron-ion plasmas with nonthermal electrons and positrons

Abstract: A theoretical investigation has been made on positron-acoustic (PA) Gardner solitons (GSs) and double layers (DLs) in four-component plasma system consisting of immobile positive ions, mobile cold positrons, nonthermal hot positrons, and nonthermal hot electrons. The reductive perturbation method has been used to derive Korteweg-de Vries (K-dV), modified K-dV (mK-dV), and Gardner equations. The basic features (viz. amplitude, polarity, speed, etc.) of the PA GSs as well as PA DLs are examined. The analytical comparison among K-dV solitons, mK-dV solitons, and GSs are also made. It has been identified that the amplitude, polarity, speed, thickness of such PA solitons and DLs are significantly modified due to the presence of nonthermal distributed hot electrons and hot positrons. The results of our investigation should be useful for understanding various interstellar space plasma environments (viz. ionosphere, lower part of magnetosphere, auroral acceleration regions, supernovas, pulsar environments, cluster explosions, active galactic nuclei, etc.).