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Volume 12 Issue 2

February 2014

Issue of Open Physics

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Open Access February 15, 2014

Nonlinear self-adjointness and invariant solutions of a 2D Rossby wave equation

Rodica Cimpoiasu, Radu Constantinescu

Page range: 81-89

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Abstract

The paper investigates the nonlinear self-adjointness of the nonlinear inviscid barotropic nondivergent vorticity equation in a beta-plane. It is a particular form of Rossby equation which does not possess variational structure and it is studied using a recently method developed by Ibragimov. The conservation laws associated with the infinite-dimensional symmetry Lie algebra models are constructed and analyzed. Based on this Lie algebra, some classes of similarity invariant solutions with nonconstant linear and nonlinear shears are obtained. It is also shown how one of the conservation laws generates a particular wave solution of this equation.

Open Access February 15, 2014

The one-dimensional Hulthén potential in the quantum phase space representation

Jerzy Stanek

Page range: 90-96

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Abstract

The analytic expression of the Wigner function for bound eigenstates of the Hulthén potential in quantum phase space is obtained and presented by plotting this function for a few quantum states. In addition, the correct marginal distributions of the Wigner function in spherical coordinates are determined analytically.

Open Access February 15, 2014

Time-dependent density functional theory molecular dynamics simulation of doubly charged uracil in gas phase

Pablo López-Tarifa, Marie-Anne Hervé du Penhoat, Rodophe Vuilleumier, Marie-Pierre Gaigeot, Ursula Rothlisberger, Ivano Tavernelli, Arnaud Le Padellec, Jean-Philippe Champeaux, Manuel Alcamí, Patrick Moretto-Capelle, Fernando Martín, Marie-Françoise Politis

Page range: 97-102

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Abstract

We use time-dependent density functional theory and Born-Oppenheimer molecular dynamics methods to investigate the fragmentation of doubly ionized uracil in gas phase. Different initial electronic excited states of the dication are obtained by removing electrons from different inner-shell orbitals of the neutral species. We show that shape-equivalent orbitals lead to very different fragmentation patterns revealing the importance of the intramolecular chemical environment. The results are in good agreement with ionion coincidence measurements of uracil collision with 100 keV protons.

Open Access February 15, 2014

An alternative solution of diatomic molecules

Özgür Öztemel, Eser Olğar

Page range: 103-110

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Abstract

The spectrum of r −1 and r −2 type potentials of diatomic molecules in radial Schrödinger equation are calculated by using the formalism of asymptotic iteration method. The alternative method is used to solve eigenvalues and eigenfunctions of Mie potential, Kratzer-Fues potential, Coulomb potential, and Pseudoharmonic potential by determining the α, β, γ and σ parameters.

Open Access February 15, 2014

A Jacobi collocation approximation for nonlinear coupled viscous Burgers’ equation

Eid Doha, Ali Bhrawy, Mohamed Abdelkawy, Ramy Hafez

Page range: 111-122

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Abstract

This article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers’ equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nyström (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers’ equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.

Open Access February 15, 2014

Einstein equation at singularities

Ovidiu-Cristinel Stoica

Page range: 123-131

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Abstract

Einstein’s equation is rewritten in an equivalent form, which remains valid at the singularities in some major cases. These cases include the Schwarzschild singularity, the Friedmann-Lemaître-Robertson-Walker Big Bang singularity, isotropic singularities, and a class of warped product singularities. This equation is constructed in terms of the Ricci part of the Riemann curvature (as the Kulkarni-Nomizu product between Einstein’s equation and the metric tensor).

Open Access February 15, 2014

Dilepton creation based on an analytic hydrodynamic solution

Máté Csanád, Levente Krizsán

Page range: 132-140

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Abstract

High-energy collisions of various nuclei, so called “Little Bangs” are observed in various experiments of heavy ion colliders. The time evolution of the strongly interacting quark-gluon plasma created in heavy ion collisions can be described by hydrodynamical models. After expansion and cooling, the hadrons are created in a freeze-out. Their distribution describes the final state of this medium. To investigate the time evolution one needs to analyze penetrating probes, such as direct photon or dilepton observables, as these particles are created throughout the evolution of the medium. In this paper we analyze an 1+3 dimensional analytic solution of relativistic hydrodynamics, and we calculate dilepton transverse momentum and invariant mass distributions. We investigate the dependence of dilepton production on time evolution parameters, such as emission duration and equation of state. Using parameters from earlier fits of this model to photon and hadron spectra, we compare our calculations to measurements as well. The most important feature of this work is that dilepton observables are calculated from an exact, analytic, 1+3D solution of relativistic hydrodynamics that is also compatible with hadronic and direct photon observables.

Open Access February 15, 2014

The separation of TM and TE wave in multi-layer metamaterial structure

Lijuan Xia, Guanxia Yu, Qian Wang

Page range: 141-146

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Abstract

A mixed-structure form of one-dimensional metamaterial structure composed of single negative permittivity material and anisotropic metamaterial has been investigated in this paper. Such a multi-layer metamaterial structure constitutes special resonant structures, which can be used to control wave propagation and realize the complete separation of TM and TE wave by choosing specific parameters. Theoretical analysis and numerical calculations have been performed to confirm the above results. Specifically, augments in incident angles of TM and TE waves make complete transmission frequencies right shift, and the thicknesses of this resonant structure determine propagation modes and propagation frequencies.

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Open Physics is a peer-reviewed, open access, electronic journal devoted to the publication of fundamental research results in all fields of physics. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-time preservation, no space constraints and immediate publication.
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Astrophysics,
Atomic and Molecular Physics,
Biological and Medical Physics,
Complex Networks, Socio- and Econophysics,
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Statistical and Nonlinear Physics,
Surface Physics,
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