Showing papers in "Central European Journal of Physics in 2015"

On the Solution of Burgers’ Equation with the New Fractional Derivative

Abstract: Abstract Firstly in this article, the exact solution of a time fractional Burgers’ equation, where the derivative is conformable fractional derivative, with dirichlet and initial conditions is found byHopf-Cole transform. Thereafter the approximate analytical solution of the time conformable fractional Burger’s equation is determined by using a Homotopy Analysis Method(HAM). This solution involves an auxiliary parameter ~ which we also determine. The numerical solution of Burgers’ equation with the analytical solution obtained by using the Hopf-Cole transform is compared.

Novel measures based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis

Abstract: We propose novel metrics based on the Kol- mogorov complexity for use in complex system behav- ior studies and time series analysis. We consider the ori- gins of the Kolmogorov complexity and discuss its physi- cal meaning. To get better insights into the nature of com- plex systems and time series analysis we introduce three novel measures based on the Kolmogorov complexity: (i) the Kolmogorov complexity spectrum, (ii) the Kolmogorov complexity spectrum highest value and (iii) the overall Kolmogorov complexity. The characteristics of these mea- sures have been tested using a generalized logistic equa- tion. Finally, the proposed measures have been applied to dierent time series originating from: a model output (the biochemical substance exchange in a multi-cell system), four dierent geophysical phenomena (dynamics of: river ow, long term precipitation, indoor 222 Rn concentration and UV radiation dose) and the economy (stock price dy- namics).Theresultsobtainedoerdee perinsightsintothe

Numerical solutions of the reaction diffusion system by using exponential cubic B-spline collocation algorithms

Abstract: Abstract The solutions of the reaction-diffusion system are given by method of collocation based on the exponential B-splines. Thus the reaction-diffusion systemturns into an iterative banded algebraic matrix equation. Solution of the matrix equation is carried out byway of Thomas algorithm. The present methods test on both linear and nonlinear problems. The results are documented to compare with some earlier studies by use of L∞ and relative error norm for problems respectively.

Primacy analysis in the system of Bulgarian cities

Abstract: This work has been performed in the framework of COST Action IS1104 "The EU in the new economic complex geography: models, tools and policy evaluation". We acknowledge some support through the project ’Evolution spatiale et temporelle d’infrastructures regionales et economiques en Bulgarie et en Federation Wallonie-Bruxelles’ within the intergovernemental agreement for cooperation between the Republic of Bulgaria and the Communaute Francaise de Belgique.

Stagnation point flow of carbon nanotubes over stretching cylinder with slip conditions

Abstract: Abstract This work concentrates on stagnation point flow of a nanofluid over an impermeable stretching cylinder with mass transfer and slip effects. Carbon nanotubes (CNTs) and water are used as a nanofluid in the present investigation. Two types of CNTs are used as nanoparticles (i) Single-wall carbon nanotubes (SWCNTs) and (ii) multiwall carbon nanotubes (MWCNTs). Appropriate transformations are used to achieve a system of ordinary differential equations. Convergent series solutions are obtained. Behavior of various parameters on the velocity, temperature and concentration profiles are discussed graphically. Numerical values of skin friction coefficient, Nusselt number and Sherwood number are computed and analyzed.

An Effective Schema for Solving Some Nonlinear Partial Differential Equation Arising In Nonlinear Physics

Abstract: Abstract In this paper, a new computational algorithm called the "Improved Bernoulli sub-equation function method" has been proposed. This algorithm is based on the Bernoulli Sub-ODE method. Firstly, the nonlinear evaluation equations used for representing various physical phenomena are converted into ordinary differential equations by using various wave transformations. In this way, nonlinearity is preserved and represent nonlinear physical problems. The nonlinearity of physical problems together with the derivations is seen as the secret key to solve the general structure of problems. The proposed analytical schema, which is newly submitted to the literature, has been expressed comprehensively in this paper. The analytical solutions, application results, and comparisons are presented by plotting the two and three dimensional surfaces of analytical solutions obtained by using the methods proposed for some important nonlinear physical problems. Finally, a conclusion has been presented by mentioning the important discoveries in this study.

Kantowski-Sachs Cosmological model with quark and strange quark matter in f(R) theory of gravity

Abstract: In this paper we have studied the Kantowski- Sachs cosmological model with the quark and strange quark matter in thef(R) theory of gravity. The general so- lutionsoftheelde quationsareobtainedbyassumingthe physical condition shear scalar is proportional to scalar expansion , which leads to the relation B = A n between metric coecients B andA. The physical and geometrical aspects of the model are also discussed.

Solving nonlinear evolution equation system using two different methods

Abstract: Abstract This paper deals with constructing more general exact solutions of the coupled Higgs equation by using the (G0/G, 1/G)-expansion and (1/G0)-expansion methods. The obtained solutions are expressed by three types of functions: hyperbolic, trigonometric and rational functions with free parameters. It has been shown that the suggested methods are productive and will be used to solve nonlinear partial differential equations in applied mathematics and engineering. Throughout the paper, all the calculations are made with the aid of the Maple software.

Raman modes in transferred bilayer CVD graphene

Abstract: A systematic experimental Raman spectroscopic study of twisted bilayer graphene (tBLG) domains local- ized inside wide-area single layer graphene (SLG) pro- duced by low-pressure CVD on Cu foil and transferred onto SiO2/Si substrate has been performed. According to the Raman characterization the tBLG domains had a great variety of twisting angles between the bottom and top graphene layers (6 < < 25 ). The twisting angle was estimated from the spectral position of the rotating R and R 0 modesintheRamanspectrum.UnderGbandresonance conditionsthebreathing modeZO 0 withafrequency of95- 97cm 1 was detected, and a breathing mode ZO was found in the spectra between 804cm 1 and 836cm 1 , its posi- tion depending on the twisting angle . An almost linear relationship was found between the frequencies !ZO and !R. Also a few other spectral peculiarities were found, e.g. a high-energy excitation of the G band resonance, the 2G overtone appearing at 3170-3180cm 1 by the G band res- onance, revealing a linear dispersion of 80cm 1 /eV of the 2D band in tBLG

Unification Principle and a Geometric Field Theory

Abstract: Abstract In the context of the geometrization philosophy, a covariant field theory is constructed. The theory satisfies the unification principle. The field equations of the theory are constructed depending on a general differential identity in the geometry used. The Lagrangian scalar used in the formalism is neither curvature scalar nor torsion scalar, but an alloy made of both, the W-scalar. The physical contents of the theory are explored depending on different methods. The analysis shows that the theory is capable of dealing with gravity, electromagnetism and material distribution with possible mutual interactions. The theory is shown to cover the domain of general relativity under certain conditions.

Mixed spectral AKNS hierarchy from linear isospectral problem and its exact solutions

Abstract: Abstract In this paper, the AKNS isospectral problem and its corresponding time evolution are generalized by embedding three coefficient functions. Starting from the generalizedAKNS isospectral problem, a mixed spectralAKNS hierarchy with variable coefficients is derived. Thanks to the selectivity of these coefficient functions, the mixed spectral AKNS hierarchy contains not only isospectral equations but also nonisospectral equations. Based on a systematic analysis of the related direct and inverse scattering problems, exact solutions of the mixed spectral AKNS hierarchy are obtained through the inverse scattering transformation. In the case of reflectionless potentials, the obtained exact solutions are reduced to n-soliton solutions. This paper shows that the AKNS spectral problem being nonisospectral is not a necessary condition to construct a nonisospectral AKNS hierarchy and that the inverse scattering transformation can be used for solving some other variable-coefficient mixed hierarchies of isospectral equations and nonisospectral equations.

Application of Metal-Oxide-Semiconductor structures containing silicon nanocrystals in radiation dosimetry

Abstract: This article makes a brief review of the most im- portant results obtained by the authors and their collabo- rators during the last four years in the field of the devel- opment of metal-insulator-silicon structures with dielec- tric film containing silicon nanocrystals, which are suit- able for applications in radiation dosimetry. The prepara- tion of SiOx films is briefly discussed and the annealing conditions used for the growth of silicon nanocrystals are presented. A two-step annealing process for preparation of metal-oxide-semiconductor structures with three-layer gate dielectrics is described. Electron Microscopy investi- gations prove the Si nanocrystals growth, reveal the crys- tal spatial distribution in the gate dielectric and provide evidences for the formation of a top SiO2 layer when apply- ing the two-step annealing. Two types of MOS structures with three region gate dielectrics were fabricated and char- acterized by high frequency capacitance/conductance- voltage (C/G-V) measurements. The effect of gamma and ultraviolet radiation on the flatband voltage of preliminary charged metal-oxide-semiconductor structures is investi- gated and discussed.

Detecting extra dimensions by Hydrogen-like atoms

Abstract: We reconsider the idea in spectroscopy of de- tecting extra dimensions by regarding the nucleus as a homogeneous sphere In our results, it turns out that the gravitationalpotentialinsidethenucleusismuchstronger thanthepotentialinducedbyaparticleinthesameregime in ref (16), and thus a more signicant correction of the ground state energy of hydrogen-like atoms is obtained, which can be used to determine the existence of ADD's ex- tra dimensions In order to get a larger order of magnitude for the correction, it is better to apply our theory to high-Z atoms or muonic atoms, where the volume of the nucleus can'tbeignoredandtherelativisticeectisimportant Our workisbasedontheDiracequationinaweakgravityeld, and the result is more precise

Evaluation of absorbed dose in Gadolinium neutron capture therapy

Abstract: Gadolinium neutron capture therapy (GdNCT) is usedfortreatmentofradioresistantmalignanttumors.The absorbed dose in GdNCT can be divided into four primary dose components: thermal neutron, fast neutron, pho- ton and natural gadolinium doses. The most signicant is the dose created by natural gadolinium. The amount of gadolinium at the irradiated region is changeable and de- pends on the gadolinium delivery agent and on the struc- ture of the location where the agent is injected. To de- ne the time dependence of the gadolinium concentra- tion (t) in the irradiated region the pharmacokinetics of gadolinium delivery agent (Magnevist) was studied at in- tratumoral injection in mice and intramuscular injection inrats.Apolynomialapproximationwasappliedtotheex- perimental data and the inuence of (t) on the relative change of the absorbed dose of gadolinium was studied.

Painlevé analysis and exact solutions of bosonized N = 1 supersymmetric Burgers equation

Abstract: Abstract Based on the bosonization approach, the N = 1 supersymmetric Burgers (SB) system is transformed to a coupled pure bosonic system. The Painlevé property and the Bäcklund transformations (BT) of the bosonized SB (BSB) system are obtained through standard singularity analysis. Explicit solutions such as the muti-solitarywaves and error functionwaves are provided for the BT. The exact solutions of the BSB system are obtained from the generalized tanh expansion method.

Response of a fractional nonlinear system to harmonic excitation by the averaging method

Abstract: Abstract In this work, we consider a fractional nonlinear vibration system of Duffing type with harmonic excitation by using the fractional derivative operator -∞−1Dαt and the averaging method. We derive the steady-state periodic response and the amplitude-frequency and phase-frequency relations. Jumping phenomena caused by the nonlinear term and resonance peaks are displayed, which is similar to the integer-order case. It is possible that a minimum of the amplitude exists before the resonance appears for some values of the modelling parameters, which is a feature for the fractional case. The effects of the parameters in the fractional derivative term on the amplitude-frequency curve are discussed.

Erlang Strength Model for Exponential Effects

Abstract: Abstract All technical systems have been designed to perform their intended tasks in a specific ambient. Some systems can perform their tasks in a variety of distinctive levels. A system that can have a finite number of performance rates is called a multi-state system. Generally multi-state system is consisted of components that they also can be multi-state. The performance rates of components constituting a system can also vary as a result of their deterioration or in consequence of variable environmental conditions. Components failures can lead to the degradation of the entire multi-state system performance. The performance rates of the components can range from perfect functioning up to complete failure. The quality of the system is completely determined by components. In this article, a possible state for the single component system, where component is subject to two stresses, is considered under stress-strength model which makes the component multi-state. The probabilities of component are studied when strength of the component is Erlang random variables and the stresses are independent exponential random variables. Also, the probabilities of component are considered when the stresses are dependent exponential random variables.

Age-density relation of Main galaxies at fixed parameters or for different galaxy families

Abstract: Abstract Using two volume-limited Main galaxy samples of the Sloan Digital Sky Survey Data Release 10 (SDSS DR10), we examine the environmental dependence of galaxy age at fixed parameters or for different galaxy families. Statistical results show that the environmental dependence of galaxy age is stronger for late type galaxies, but can be still observed for the early types: the age of galaxies in the densest regime is preferentially older than that in the lowest density regime with the same morphological type. We also find that the environmental dependence of galaxy age for red galaxies and Low Stellar Mass (LSM) galaxies is stronger, while the one for blue galaxies and High Stellar Mass ( HSM ) galaxies is very weak.

Trigonometric quadratic B-spline subdomain Galerkin algorithm for the Burgers’ equation

Abstract: Abstract A variant of the subdomain Galerkin method has been set up to find numerical solutions of the Burgers’ equation. Approximate function consists of the combination of the trigonometric B-splines. Integration of Burgers’ equation has been achived by aid of the subdomain Galerkin method based on the trigonometric B-splines as an approximate functions. The resulting first order ordinary differential system has been converted into an iterative algebraic equation by use of the Crank-Nicolson method at successive two time levels. The suggested algorithm is tested on somewell-known problems for the Burgers’ equation.

Study of Grodzins product (E(2 + 1 ) * B(E2)↑) in the framework of the Asymmetric Rotor Model

Abstract: Abstract A systematic dependence of Grodzins product (E(2+1) * B(E2)↑) on the asymmetry parameter Υ0 is studied in the Z = 50 − 82, N = 82 − 126 major shell space. The Grodzins product provides contributions of E(2+1) and B(E2) \" simultaneously, which further reflects the shape phase transitions with asymmetry parameter 0. In the region of deformed nuclei, Grodzins product (E(2+1)*B(E2)↑) shows direct dependence on the asymmetry parameter 0. We discuss here for the first time the correlation between Grodzins product (E(2+1) * B(E2)↑) and the asymmetry parameter Υ0.

Unsteady MHD boundary layer flow and heat transfer over the stretching sheets submerged in a moving fluid with Ohmic heating and frictional heating

Abstract: Abstract This paper is devoted to the analysis of the unsteady magnetohydrodynamic (MHD) boundary layer flow and heat transfer on a permeable stretching sheet embedded in a moving incompressible viscous fluid. The combined effects of Ohmic heating, thermal radiation, frictional heating and internal heat absorption/generation are taken into account. The governing time dependent nonlinear boundary layer equations are converted into a systemof nonlinear ordinary differential equations by similarity transformations. Some analytical results that give the characteristics of the velocity field in the boundary layer are presented and proved. The governing equations are then solved by using the shooting technique along with the fourth order Runge-Kutta method. The analytical properties proved in this paper are consistent with those obtained by the numerical method. Furthermore, the effects of the various parameters on the velocity and temperature fields are presented graphically and discussed in detail.

Pulse Propagation in a Non-Linear Medium

Abstract: This paper considers a novel approach to solv- ing the general propagation equation of optical pulses in an arbitrary non-linear medium. Using a suitable change of variable and applying the Adomian decomposition method to the non-linear Schrodinger equation, an ana- lytical solution can be obtained which takes into account- parameters such as attenuation factor, the second order dispersive parameter, the third order dispersive parameter and the non-linear Kerr effect coefficient. By analysing the solution, this paper establishes that this method is suit- able for the study of light pulse propagation in a non-linear optical medium. on the envelope. In a series of remarkable papers (1-3) solutions to NLSEs are considered using a variety of ap- proaches. These methods can be classified into two broad categories known as the finite-difference methods and the pseudo spectral methods. The split-step Fourier method is a finite-difference method which has recently been used extensively due to its faster calculation speedcompared to other methods. This paper considers the use of the Ado- mian decomposition method for solving the NLSE for pulse propagation in non-linear media. It has previously been used to solve a wide range of physical problems (4-7) and is a semi-exact method which does not require lineariza- tion or discretization. The method has gone through a se- ries of modification in the following references (8-16). An advantage of this method is that it can provide analyti- cal approximation or an approximated solution to a wide class of non-linear equations without linearization, per- turbation, closure approximation or discretization meth- ods. Its abilities attracted many authors to use this method for solving physical problems. In this paper analytical solutions to NLSEs are investi- gated by using the Adomian decomposition method, tak- ing into account the input pulse propagation and param- eters such as attenuation factor, the second order disper- sive parameter, the third order dispersive parameter and the non-linear Kerr effect coefficient. The rest of this paper is organized as follows: the next section presents details of the model and the Adomian decomposition method, sec- tion 3 compares the results using this method to classic an- alytical solutions and the paper is finished with conclud- ing remarks.

Generalized binomial distribution in photon statistics

Abstract: This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 30 License Open Phys 2015; 13:41–49 Research Article Open Access Aleksey Ilyin* Generalized binomial distribution in photon statistics Abstract: The photon-number distribution between two parts of a given volume is found for an arbitrary photon statistics This problem is related to the interaction of a light beam with a macroscopic device, for example a diaphragm, that separates the photon ux into two parts with known probabilities To solve this problem, a Generalized Binomial Distribution (GBD) is derived that is applicable to an arbitrary photon statistics satisfying probability convolution equations It is shown that if photons obey Poisson statistics then the GBD is reduced to the ordinary binomial distribution, whereas in the case of BoseEinstein statistics the GBD is reduced to the Polya distribution In this case, the photon spatial distribution depends on the phase-space volume occupied by the photons This result involves a photon bunching e ect, or collective behavior of photons that sharply di ers from the behavior of classical particles It is shown that the photon bunching e ect looks similar to the quantum interference e ect

Neutrinos from the Early Universe and physics beyond standard models

Abstract: Neutrino oscillations present the only robust ex- ampleofexperimentallydetectedphysicsbeyondthestan- dardmodel.Thisreviewdiscussestheestablishedandsev- eral hypothetical beyond standard models neutrino char- acteristics and their cosmological eects and constraints. Particularly, the contemporary cosmological constraints on the number of neutrino families, neutrino mass dier- ences and mixing, lepton asymmetry in the neutrino sec- tor, neutrino masses, light sterile neutrino are briey re-

Fractional thermal diffusion and the heat equation

Abstract: Abstract Fractional calculus is the branch of mathematical analysis that deals with operators interpreted as derivatives and integrals of non-integer order. This mathematical representation is used in the description of non-local behaviors and anomalous complex processes. Fourier’s lawfor the conduction of heat exhibit anomalous behaviors when the order of the derivative is considered as 0 < β,ϒ ≤ 1 for the space-time domain respectively. In this paper we proposed an alternative representation of the fractional Fourier’s law equation, three cases are presented; with fractional spatial derivative, fractional temporal derivative and fractional space-time derivative (both derivatives in simultaneous form). In this analysis we introduce fractional dimensional parameters σx and σt with dimensions of meters and seconds respectively. The fractional derivative of Caputo type is considered and the analytical solutions are given in terms of the Mittag-Leffler function. The generalization of the equations in spacetime exhibit different cases of anomalous behavior and Non-Fourier heat conduction processes. An illustrative example is presented.

The analysis of the suction/injection on the MHD Maxwell fluid past a stretching plate in the presence of nanoparticles by Lie group method

Abstract: Abstract In this paper, the magnetohydrodynamic (MHD) Maxwell fluid past a stretching plate with suction/ injection in the presence of nanoparticles is investigated. The Lie symmetry group transformations are used to convert the boundary layer equations into non-linear ordinary differential equations. The dimensionless governing equations are solved numerically using Bvp4c with MATLAB, which is a collocation method equivalent to the fourth order mono-implicit Runge-Kutta method. The effects of some physical parameters, such as the elastic parameter K, the Hartmann number M, the Prandtl number Pr, the Brownian motion Nb, the thermophoresis parameter Nt and the Lewis number Le, on the velocity, temperature and nanoparticle fraction are studied numerically especially when suction and injection at the sheet are considered.

Peristaltic transport of a fractional Burgers’ fluid with variable viscosity through an inclined tube

Abstract: Abstract In the present study,we investigate the unsteady peristaltic transport of a viscoelastic fluid with fractional Burgers’ model in an inclined tube. We suppose that the viscosity is variable in the radial direction. This analysis has been carried out under low Reynolds number and long-wavelength approximations. An analytical solution to the problem is obtained using a fractional calculus approach. Figures are plotted to show the effects of angle of inclination, Reynolds number, Froude number, material constants, fractional parameters, parameter of viscosity and amplitude ratio on the pressure gradient, pressure rise, friction force, axial velocity and on the mechanical efficiency.

Numerical study on the standing morphology of an oblique detonation wave under the influence of an incoming boundary layer

Abstract: Abstract The influence of an incoming boundary layer to the standing morphology of an oblique detonation wave (ODW) induced by a compression ramp is numerically studied in this paper. The Spalart-Allmaras (SA) turbulence model is used to perform simulation of detonationboundary- layer interactions. Three different wall conditions are applied to realize control on the boundary-layer separation scales. Accordingly, different standing morphologies of the ODWs are obtained, including smooth ODW (without transverse wave) under no-slip, adiabatic wall condition with large-scale separation, abrupt ODW (with transverse wave) under no-slip, cold wall condition with moderate-scale separation, and bow-shaped detached ODW under slipwall condition without a boundary layer.

Oscillation of fractional order functional differential equations with nonlinear damping

Abstract: Abstract In this paper, we are concerned with the oscillatory behavior of a class of fractional differential equations with functional terms. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. Based on a certain variable transformation, by using a generalized Riccati transformation, generalized Philos type kernels, and averaging techniques we establish new interval oscillation criteria. Illustrative examples are also given.