• Issue front cover thumbnail

      Volume 80, Issue 5

      May 2013,   pages  739-915

    • The symmetries and conservation laws of some Gordon-type equations in Milne space-time

      S Jamal A H Kara A H Bokhari F D Zaman

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      In this letter, the Lie point symmetries of a class of Gordon-type wave equations that arise in the Milne space-time are presented and analysed. Using the Lie point symmetries, it is showed how to reduce Gordon-type wave equations using the method of invariants, and to obtain exact solutions corresponding to some boundary values. The Noether point symmetries and conservation laws are obtained for the Klein–Gordon equation in one case. Finally, the existence of higher-order variational symmetries of a projection of the Klein–Gordon equation is investigated using the multiplier approach.

    • Exact travelling wave solutions for some important nonlinear physical models

      Jonu Lee Rathinasamy Sakthivel

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      The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical studies. In this paper, the Kudryashov method is used to seek exact travelling wave solutions of such physical models. Further, three-dimensional plots of some of the solutions are also given to visualize the dynamics of the equations. The results reveal that the method is a very effective and powerful tool for solving nonlinear partial differential equations arising in mathematical physics.

    • Classification of single travelling wave solutions to the generalized Zakharov–Kuznetsov equation

      Jin-Yan Hu

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      By the complete discrimination system for the polynomial method, the classification of single travelling wave solutions to the generalized Zakharov–Kuznetsov equation with $p = 2$ was obtained.

    • Collapse revival behaviour of the entanglement between V-type three-level atoms and two-mode photons in nonlinear Jaynes–Cummings model

      M Mohjoei M M Golshan H Safari

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      In this paper the time evolution of von Neumann entropy, as a measure of entanglement between V-type three-level atoms and the union of a two-mode field, is studied. The atom–field interaction is assumed to occur in a Kerr-type medium with an intensity-dependent coupling. Introducing a Casmir operator whose eigenvalues, 𝑁, give total excitations in the system and commutes with the governing Hamiltonian, it is concluded that the latter is block-diagonal with ever growing dimensions. As we shall show, however, each block consists of two $2 \times 2$ blocks while all the others, $(N −1)$ in number, are $3 \times 3$. We then proceed to analytically calculate the time-evolution operator which is also block-diagonal, each block with the same properties as that of the Hamiltonian. Our calculations show that, as expected, the atom–field entanglement oscillates which, depending upon the initial state, exhibits the phenomenon of collapse revivals. It is further shown that collapse revivals occur whenever both $2 \times 2$ blocks are involved in the time evolution of the system. Properties of such behaviour in the entanglement are also discussed in detail.

    • Confinement, average forces, and the Ehrenfest theorem for a one-dimensional particle

      Salvatore De Vincenzo

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      The topics of confinement, average forces, and the Ehrenfest theorem are examined for a particle in one spatial dimension. Two specific cases are considered: (i) A free particle moving on the entire real line, which is then permanently confined to a line segment or `a box' (this situation is achieved by taking the limit $V_{0} \rightarrow \infty$ in a finite well potential). This case is called `a particle-in-an-infinite-square-well-potential'. (ii) A free particle that has always been moving inside a box (in this case, an external potential is not necessary to confine the particle, only boundary conditions). This case is called `a particle-in-a-box'. After developing some basic results for the problem of a particle in a finite square well potential, the limiting procedure that allows us to obtain the average force of the infinite square well potential from the finite well potential problem is re-examined in detail. A general expression is derived for the mean value of the external classical force operator for a particle-in-an-infinite-square-well-potential, $\hat{F}$. After calculating similar general expressions for the mean value of the position ($\hat{X}$) and momentum ($\hat{P}$) operators, the Ehrenfest theorem for a particle-in-an-infinite-square-well-potential (i.e., $d\langle \hat{X} \rangle /dt = \langle \hat{P} \rangle /M$ and $d\langle \hat{P} \rangle /dt = \langle \hat{F} \rangle$) is proven. The formal time derivatives of the mean value of the position ($\hat{x}$) and momentum ($\hat{p}$) operators for a particle-in-a-box are re-introduced. It is verified that these derivatives present terms that are evaluated at the ends of the box. Specifically, for the wave functions satisfying the Dirichlet boundary condition, the results, $d\langle \hat{x} \rangle /dt = \langle \hat{p} \rangle /M$ and $d\langle \hat{p} \rangle /dt = b.t. + \langle \hat{f} \rangle$, are obtained where b.t. denotes a boundary term and $\hat{f}$ is the external classical force operator for the particle-in-a-box. Thus, it appears that the expected Ehrenfest theorem is not entirely verified. However, by considering a normalized complex general state that is a combination of energy eigen-states to the Hamiltonian describing a particle-in-a-box with $\nu(x) = 0(\Rightarrow \hat{f} = 0)$, the result that the b.t. is equal to the mean value of the external classical force operator for the particle-in-an-infinite-square-well-potential is obtained, i.e., $d\langle \hat{p} \rangle /dt$ is equal to $\langle \hat{F} \rangle$. Moreover, the b.t. is written as the mean value of a quantity that is called boundary quantum force, $f_{B}$. Thus, the Ehrenfest theorem for a particle-in-a-box can be completed with the formula $d\langle \hat{p} \rangle /dt = \langle f_{B} \rangle$.

    • Space-time algebra for the generalization of gravitational field equations

      Süleyman Demir

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      The Maxwell–Proca-like field equations of gravitolectromagnetism are formulated using space-time algebra (STA). The gravitational wave equation with massive gravitons and gravitomagnetic monopoles has been derived in terms of this algebra. Using space-time algebra, the most generalized form of gravitoelectromagnetic Klein–Gordon equation has been obtained. Finally, the analogy in formulation between massive gravitational theory and electromagnetism has been discussed.

    • Comparison of backstepping and modified active control in projective synchronization of chaos in an extended Bonhöffer–van der Pol oscillator

      K S Ojo A N Njah S T Ogunjo

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      In this article, projective synchronization of double–scroll attractor of an extended Bonöffer–van der Pol oscillator (BVPO) is considered via the backstepping and active control techniques. In each synchronization scheme, a single control function is designed to achieve projective synchronization between two Bonhöffer–van der Pol oscillator evolving from different initial conditions. To obtain a single control function via the active control, the coefficient of the error dynamics is chosen such that the number of control functions is reduced from three to one, thereby, reducing control function complexity in design. The results show that the transient error dynamics convergence and synchronization time are achieved faster via the backstepping than that of the active control technique. However, the control function obtained via the active control is simpler with a more stable synchronization time and hence, it is more suitable for practical implementation. Numerical simulations are presented to confirm the effectiveness of the analytical results.

    • Investigation of the zenith angle dependence of cosmic-ray muons at sea level

      Mehmet Bektasoglu Halil Arslan

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      Angular distribution of cosmic-ray muons at sea level has been investigated using the Geant4 simulation package. The model used in the simulations was tested by comparing the simulation results with the measurements made using the Berkeley Lab cosmic ray detector. Primary particles’ energy and fluxes were obtained from the experimental measurements. Simulations were run at each zenith angle starting from $\theta = 0^{\circ}$ up to $\theta = 70^{\circ}$ with $5^{\circ}$ increment. The angular distribution of muons at sea level has been estimated to be in the form $I(\theta) = I(0^{\circ}) \cos^{n}(\theta)$, where $I(0^{\circ})$ is the muon intensity at 0° and 𝑛 is a function of the muon momentum. The exponent $n = 1.95 \pm 0.08$ for muons with energies above 1 GeV is in good agreement, within error, with the values reported in the literature.

    • Effect of the isovector coupling channel on the macroscopic part of the nuclear binding energy

      S Haddad

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      The effect of isovector coupling channel on the macroscopic part of the nuclear binding energy is studied using the relativistic density-dependent Thomas–Fermi approach. The dependency of this effect on the number of neutrons and protons is also studied. The isovector coupling channel leads to increased nuclear binding energy, and this effect increases with the increasing neutron number in the nucleus.

    • Beam lifetime measurement and analysis in Indus-2 electron storage ring

      Pradeep Kumar A D Ghodke Gurnam Singh

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      In this paper, the beam lifetime measurement and its theoretical analysis are presented using measured vacuum pressure and applied radio frequency (RF) cavity voltage in Indus-2 electron storage ring at 2 GeV beam energy. Experimental studies of the effect of RF cavity voltage and bunched beam filling pattern on beam lifetime are also presented. An equation of stable beam current decay is evolved and this equation closely follows the observed beam current decay pattern. It shows that the beam is stable and the beam current decay is due to the beam–residual gas interaction (vacuum lifetime) and electron–electron interaction within a bunch (Touschek lifetime). The estimated vacuum, Touschek and total beam lifetimes from analytical formulations are also compared with the measured beam lifetime.

    • The measurements of thermal neutron flux distribution in a paraffin phantom

      Parisa Akhlaghi Laleh Rafat-Motavalli Seyed Hashem Miri-Hakimabad

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      The term `thermal flux' implies a Maxwellian distribution of velocity and energy corresponding to the most probable velocity of 2200 ms-1 at 293.4 K. In order to measure the thermal neutron flux density, the foil activation method was used. Thermal neutron flux determination in paraffin phantom by counting the emitted rays of indium foils with two different detectors (Geiger–Muller counter and NaI(Tl)) was the aim of this project. The relative differences of the outcome of the experiments were between 2.5% and 5%. The final results were compared with MCNP4C outputs and the best agreement was generated using NaI(Tl) by a minimum discrepancy of about 0.6% for the foil placed 8.5 cm from the neutron source.

    • Nonlinear properties of a graded-index photonic heterostructure

      B Tavakkoly Moghaddam S Roshan Entezar H Pashei Adl

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      The optical properties of a one-dimensional (1D) photonic heterostructure with gradedindex nonlinear materials are demonstrated theoretically. The influence of the gradation profile of the graded-index nonlinear layers on the linear and nonlinear responses of the structure are analysed. It is shown that the 𝑄-factor of the defect mode and the threshold input intensity to achieve the optical bistability in the used photonic heterostructure depend on the gradation profile of the gradedindex nonlinear layers.

    • Construction of an exact solution of time-dependent Ginzburg–Landau equations and determination of the superconducting–normal interface propagation speed in superconductors

      Neelufar Panna Jamal Nazrul Islam

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      A new approach is taken to calculate the speed of front propagation at which the interface moves from a superconducting to a normal region in a superconducting sample. Using time-dependent Ginzburg–Landau (TDGL) equations we have calculated the speed by constructing a new exact solution. This approach is based on a method given by Di Bartolo and Dorsey. Our result for the speed agrees with the result of Di Bartolo and Dorsey.

    • Nanoscale experimental study of the morphology of a microcrack in silicon by transmission electron microscopy

      D S Liu C W Zhao X H Hou

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      A microcrack in a silicon single crystal was experimentally investigated using highresolution transmission electron microscopy (HRTEM). In particular, the numerical Moiré (NM) method was used to visualize the deformations and defects. The lattice structure of the microcrack was carefully observed at the nanoscale. HRTEM images of the microcrack demonstrated that the lattice structure of most of the microcrack regions is regular with good periodicity. In addition, the microcrack cleavage expands alternately along different crystal planes, where the principal cleavage plane is the (1 1 1) crystal plane. The NM maps showed no sharp plastic deformation around the microcrack, but discrete edge dislocations can be found only near the crack tip.

    • A cellular automata model for ant trails

      Sibel Gokce Ozhan Kayacan

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      In this study, the unidirectional ant traffic flow with U-turn in an ant trail was investigated using one-dimensional cellular automata model. It is known that ants communicate with each other by dropping a chemical, called pheromone, on the substrate. Apart from the studies in the literature, it was considered in the model that (i) ant colony consists of two kinds of ants, goodand poor-smelling ants, (ii) ants might make U-turn for some special reasons. For some values of densities of good- and poor-smelling ants, the flux and mean velocity of the colony were studied as a function of density and evaporation rate of pheromone.

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