ISRN High Energy Physics http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. A Study of Pion-Nucleus Interactions in terms of Compound Particles Mon, 10 Mar 2014 07:55:07 +0000 http://www.hindawi.com/journals/isrn.hep/2014/604730/ We report some results on the compound multiplicity distribution at 340 GeV/c nucleus interactions. Compound multiplicity distribution is found to depend on the target size and the distribution becomes broader. The peak of the distribution shifts towards higher values of the compound particle multiplicity. Mean compound multiplicity is found to vary linearly with grey, heavy, and shower particle multiplicity. Correlations between different particle multiplicities have been studied in detail. Dispersion of compound multiplicity distributions and its ratio with the mean value is observed to obey a linear relationship with different particle multiplicities except for shower particles where dispersion is almost independent of shower particles. Mean normalized multiplicity has also been studied in terms of created charged particles. Tufail Ahmad Copyright © 2014 Tufail Ahmad. All rights reserved. Analytical Evaluation of the Neutrino-Nucleon Interaction Cross-Sections at Ultrahigh Energy Sun, 02 Feb 2014 13:46:58 +0000 http://www.hindawi.com/journals/isrn.hep/2014/462824/ The ultrahigh energy (UHE) neutrino-nucleon interaction cross-sections are evaluated analytically in one loop by using the solutions of Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations. Since the genesis of the UHE neutrinos is various sources which have energy more than 105 GeV, so parton distributions are extrapolated at ultralow to determine the charged current and the neutral current cross-sections. We then compare our analytically obtained extrapolated results with the next-to-leading order (NLO) results of various other authors. A good agreement between the two reflects the veracity of our approach of extrapolation at ultralow . Pijush Kanti Dhar and D. K. Choudhury Copyright © 2014 Pijush Kanti Dhar and D. K. Choudhury. All rights reserved. A Dark Energy Model with Higher Order Derivatives of in the Modified Gravity Model Wed, 29 Jan 2014 13:14:18 +0000 http://www.hindawi.com/journals/isrn.hep/2014/535010/ We consider a model of dark energy (DE) which contains three terms (one proportional to the squared Hubble parameter, one to the first derivative, and one to the second derivative with respect to the cosmic time of the Hubble parameter) in the light of the modified gravity model, with and being two constant parameters. and represent the curvature and torsion scalars, respectively. We found that the Hubble parameter exhibits a decaying behavior until redshifts (when it starts to increase) and the time derivative of the Hubble parameter goes from negative to positive values for different redshifts. The equation of state (EoS) parameter of DE and the effective EoS parameter exhibit a transition from to (showing a quintom-like behavior). We also found that the model considered can attain the late-time accelerated phase of the universe. Using the statefinder parameters and , we derived that the studied model can attain the phase of the universe and can interpolate between dust and phase of the universe. Finally, studying the squared speed of sound , we found that the considered model is classically stable in the earlier stage of the universe but classically unstable in the current stage. Antonio Pasqua, Surajit Chattopadhyay, and Ratbay Myrzakulov Copyright © 2014 Antonio Pasqua et al. All rights reserved. Dirac Particle in External Non-Abelian Gauge Field Wed, 22 Jan 2014 08:55:42 +0000 http://www.hindawi.com/journals/isrn.hep/2014/375695/ The Green function of a Dirac particle in interaction with a non-Abelian SU(N) gauge fi…eld exactly and analytically determined via the path integral formalism by using the approach so-called “global projection.” The essential steps in the calculation are the choice of a convenient gauge (Lorentz gauge) and the introduction of two constraints, (related to space) and Grassmannian (related to Dirac matrices). Furthermore, it is shown that certain selected equations obtained during the integrations can also be classically derived. Bilel Hamil and Lyazid Chetouani Copyright © 2014 Bilel Hamil and Lyazid Chetouani. All rights reserved. Retracted: Multiplication of Fast Neutrons Source Flux by Using Deuterium-Helium-3 Plasma Wed, 22 Jan 2014 07:17:01 +0000 http://www.hindawi.com/journals/isrn.hep/2014/431429/ ISRN High Energy Physics Copyright © 2014 ISRN High Energy Physics. All rights reserved. Could a Reported 2007 Analysis of Super-Kamiokande Data Have Missed a Detectable Supernova Signal from Andromeda? Tue, 14 Jan 2014 07:06:21 +0000 http://www.hindawi.com/journals/isrn.hep/2014/408508/ According to a 2007 paper there was no evidence for a neutrino burst of two or more events in Super-Kamiokande (SK) during the entire period of data taking from 1996 to 2005 from Andromeda or anywhere else. There is, however, a scenario under which a detectable signal could have been missed given the search method employed by the analysis, and it would have been found using an alternate method. The alternate method depends on the hypothesis that two of the neutrino mass eigenstates have masses 4.0 eV and 21.4 eV which was inferred from an analysis of the SN 1987A data. Although one might argue that the hypothesis of such large neutrino masses is remote, there is a way they could be compatible with observed constraints on neutrino masses involving a third tachyonic () eigenstate, plus three sterile neutrinos. Given the importance of a positive supernova search result and the ease of conducting it using existing SK data, there would seem to be little reason not to do it. Robert Ehrlich Copyright © 2014 Robert Ehrlich. All rights reserved. Semiclassical Strings in -Dimensional Backgrounds Thu, 19 Dec 2013 08:41:03 +0000 http://www.hindawi.com/journals/isrn.hep/2013/517858/ This study analyzes the geometrical relationship between a classical string and its semiclassical quantum model. From an arbitrary -dimensional geometry, a specific ansatz for a classical string is used to generate a semi-classical quantum model. In this framework, examples of quantum oscillations and quantum free particles are presented that uniquely determine a classical string and the space-time geometry where its motion takes place. Sergio Giardino Copyright © 2013 Sergio Giardino. All rights reserved. Free Energy Evolution and Photon Radiation from QGP Tue, 05 Nov 2013 15:07:10 +0000 http://www.hindawi.com/journals/isrn.hep/2013/156747/ We investigate a simple statistical model of quark-gluon plasma (QGP) formation. In the model, we use a phenomenological parameter which enhances the growth of quark droplet formation and also stabilizes the formation of the QGP droplet. Then, we study direct photon radiation through annihilation and Compton processes from these stabilized QGP incorporating the parametrized momentum factor in the quark mass. The production rate of thermal photon is found to be dominated in the low transverse momentum and increases a little in comparison to the recent development of direct photon radiation of other theoretical and experimental works. Yogesh Kumar and S. Somorendro Singh Copyright © 2013 Yogesh Kumar and S. Somorendro Singh. All rights reserved. A Study on Some Special Forms of Holographic Ricci Dark Energy in Fractal Universe Mon, 28 Oct 2013 10:18:11 +0000 http://www.hindawi.com/journals/isrn.hep/2013/251498/ We have considered the modified and the extended holographic Ricci dark energy models (MHRDE and EHRDE) in fractal universe. We have assumed a time-like fractal profile , where . We have reconstructed the Hubble parameter , the energy density, the equations of state parameter and the deceleration parameter for both MHRDE and EHRDE. Surajit Chattopadhyay, Antonio Pasqua, and Sudipto Roy Copyright © 2013 Surajit Chattopadhyay et al. All rights reserved. A Cosmological Model with Varying and in General Relativity—Part III Sun, 27 Oct 2013 13:22:10 +0000 http://www.hindawi.com/journals/isrn.hep/2013/391436/ We are investigating Bianchi type-I cosmological model in perfect fluid. The cosmological model is obtained by assuming proportional to . We also observed some physical properties of the model and discussed them. Harpreet Kaur, Sumeet Goyal, and H. S. Sahota Copyright © 2013 Harpreet Kaur et al. All rights reserved. Extended Holographic Ricci Dark Energy in Chameleon Brans-Dicke Cosmology Wed, 23 Oct 2013 13:41:00 +0000 http://www.hindawi.com/journals/isrn.hep/2013/414615/ In the present work, we have studied some features of the generalized Brans-Dicke (BD) model in which the scalar field is allowed to couple nonminimally with the matter sector. Extended holographic Ricci dark energy (EHRDE) has been considered in the above framework of BD cosmology. Some restrictions have been derived for the BD parameter , and a stronger matter-chameleon coupling has been observed with the expansion of the universe. In this framework, the equation of the state parameter of EHRDE has behaved like quintom. Also, we have reconstructed the potential and coupling function for BD model for the EHRDE. It has been observed that the potential function is increasing as the matter-chameleon coupling is getting stronger. Surajit Chattopadhyay Copyright © 2013 Surajit Chattopadhyay. All rights reserved. Particle Acceleration by an Electromagnetic Wave Mon, 21 Oct 2013 13:25:46 +0000 http://www.hindawi.com/journals/isrn.hep/2013/760983/ The relativistic equation of motion for an electrically charged massive point particle is integrated exactly for the case of a circularly polarized electromagnetic plane wave. The acceleration of the particle by the wave is calculated in detail, however, under neglection of the radiation damping. In spite of this simplification, the results are applied to a typical pulsar, where the maximum kinetic energy of accelerated protons reaches values of the order of the fastest cosmic ray particles. Heinz Dehnen Copyright © 2013 Heinz Dehnen. All rights reserved. Initial Systematic Investigations of the Landscape of Low-Layer NAHE Variation Extensions Tue, 08 Oct 2013 10:48:29 +0000 http://www.hindawi.com/journals/isrn.hep/2013/595070/ The discovery that the number of physically consistent string vacua is on the order of 10500 has prompted several statistical studies of string phenomenology. Focusing on the Weakly Coupled Free Fermionic String formalism, we present systematic extensions of a variation on the NAHE (Nanopoulos, Antoniadis, Hagelin, Ellis) set of basis vectors. This variation is more conducive to the production of “mirrored” models, in which the observable and hidden sector gauge groups (and possibly matter content) are identical. This study is parallel to the extensions of the NAHE set itself and presents statistics related to similar model properties. Statistical coupling between specific gauge groups and spacetime supersymmetry is also examined. Finally, a model with completely mirrored gauge groups is discussed. It is found that the region of the landscape explored generates no physically realistic models due to a lack of three net chiral generations. Timothy Renner, Jared Greenwald, Douglas Moore, and Gerald Cleaver Copyright © 2013 Timothy Renner et al. All rights reserved. A Study on Ricci Dark Energy in Bulk-Brane Interaction Thu, 19 Sep 2013 13:50:55 +0000 http://www.hindawi.com/journals/isrn.hep/2013/895614/ We have investigated the effects of the interaction between a brane universe and the bulk in which it is embedded. Considering the effects of the interaction between a brane universe and the bulk, we have obtained the equation of state for the interacting holographic Ricci dark energy density in the flat universe. We have investigated the impact of on the equation of state . Also, considering the power law for of the scale factor, we have observed that nontrivial contributions of dark energy which differ from the standard matter fields confined to the brane are increasing with the evolution of the universe. Surajit Chattopadhyay Copyright © 2013 Surajit Chattopadhyay. All rights reserved. Green’s Function for Dirac Particle in a Non-Abelian Field: A Path Integral Approach Sun, 14 Jul 2013 15:20:28 +0000 http://www.hindawi.com/journals/isrn.hep/2013/751963/ The Green function for a Dirac particle moving in a non-Abelian field and having a particular form is exactly determined by the path integral approach. The wave functions were deduced from the residues of Green’s function. It is shown that the classical paths contributed mainly to the determination of the Green function. Sami Boudieb and Lyazid Chetouani Copyright © 2013 Sami Boudieb and Lyazid Chetouani. All rights reserved. Gravity with Extra Dimensions and Dark Matter Interpretation: A Straightforward Approach Sun, 14 Jul 2013 08:32:54 +0000 http://www.hindawi.com/journals/isrn.hep/2013/713508/ Any connection between dark matter and extra dimensions can be cognizably evinced from the associated effective energy-momentum tensor. In order to investigate and test such relationship, a higher dimensional spacetime endowed with a factorizable general metric is regarded to derive a general expression for the stress tensor—from the Einstein-Hilbert action—and to elicit the effective gravitational potential. A particular construction for the case of six dimensions is provided, and it is forthwith revealed that the missing mass phenomenon may be explained, irrespective of the dark matter existence. Moreover, the existence of extra dimensions in the universe accrues the possibility of a straightforward mechanism for such explanation. A configuration whose density profile coincides with the Newtonian potential for spiral galaxies is constructed, from a 4-dimensional isotropic metric plus extradimensional components. A Miyamoto-Nagai ansatz is used to solve Einstein equations. The stable rotation curves associated with such system are computed, in full compliance with the observational data, without fitting techniques. The density profiles are reconstructed and compared to the ones obtained from the Newtonian potential. C. H. Coimbra Araújo and Roldão da Rocha Copyright © 2013 C. H. Coimbra Araújo and Roldão da Rocha. All rights reserved. Transverse Spin Structure Function Thu, 27 Jun 2013 13:32:37 +0000 http://www.hindawi.com/journals/isrn.hep/2013/519842/ The transverse spin-dependent nucleon structure function at large is computed within the Wandzura-Wilczek relation, using NLO fit. Also we investigate the twist-3 contribution of via calculating . It turns out that although the twist-3 part of can be negligible for DIS processes, it has a significant value in resonance region. H. Bagherpour and M. Saeedhosseini Copyright © 2013 H. Bagherpour and M. Saeedhosseini. All rights reserved. Impact of High Energy Cosmic Rays on Global Atmospheric Electrical Parameters over Different Orographically Important Places of India Wed, 19 Jun 2013 18:23:05 +0000 http://www.hindawi.com/journals/isrn.hep/2013/831431/ Global atmospheric electrical parameters such as atmospheric conductivity, air-earth current density, atmospheric electric field, and atmospheric potential have been calculated for eighty different orographically important places of India under the influence of cosmic ray modulation factor due to Forbush decrease assuming fair weather conditions. The results have been compared with the earlier work of Kumar et al. (1998) and show that the correlation between cosmic rays and global atmospheric electrical parameters near the earth surface depends upon the relative magnitudes of galactic cosmic ray particles. Adarsh Kumar and H. P. Singh Copyright © 2013 Adarsh Kumar and H. P. Singh. All rights reserved. Solutions and Thermodynamics of Charged Rotating Black Holes in a Fuzzy Space Tue, 18 Jun 2013 09:05:18 +0000 http://www.hindawi.com/journals/isrn.hep/2013/184857/ We investigate the effect of fuzzy space on black hole and its thermodynamic Properties; we also present our results in different types of black holes according to the parameters and representing electric and magnetic charges. Abderrahman El Boukili, Mourad Nach, Hamid Chaqsare, Moulay Driss Aouragh, and Moulay Brahim Sedra Copyright © 2013 Abderrahman El Boukili et al. All rights reserved. Multiplication of Fast Neutrons Source Flux by Using Deuterium-Helium-3 Plasma Thu, 30 May 2013 14:25:43 +0000 http://www.hindawi.com/journals/isrn.hep/2013/689739/ The production of fast neutrons source is examined by using a thermal neutron flux inside plasma. In order to reach a favorable yield of fast neutrons flux, the parameters such as energy loss rate, reaction probability, and neutron absorption length are calculated. The nuclear conversion efficiency, , of thermal neutron to fast neutrons is obtained to be by calculating the physical parameters for the plasma designed. Mohammad Mahdavi and Maryam Shahbahrami Copyright © 2013 Mohammad Mahdavi and Maryam Shahbahrami. All rights reserved. On a Semiclassical Limit of Loop Space Quantum Mechanics Thu, 09 May 2013 13:45:14 +0000 http://www.hindawi.com/journals/isrn.hep/2013/398030/ Following earlier work, we view two-dimensional nonlinear sigma model as single particle quantum mechanics in the free loop space of the target space. In a natural semiclassical limit of this model, the wavefunction localizes on the submanifold of vanishing loops. One would expect that the semiclassical expansion should be related to the tubular expansion of the theory around the submanifold and effective dynamics on the submanifold is obtainable using Born-Oppenheimer approximation. We develop a framework to carry out such an analysis at the leading order. In particular, we show that the linearized tachyon effective equation is correctly reproduced up to divergent terms all proportional to the Ricci scalar. The steps are as follows: first we define a finite dimensional analogue of the loop space quantum mechanics (LSQM) where we discuss its tubular expansion and how that is related to a semiclassical expansion of the Hamiltonian. Then we study an explicit construction of the relevant tubular neighborhood in loop space using exponential maps. Such a tubular geometry is obtained from a Riemannian structure on the tangent bundle of target space which views the zero-section as a submanifold admitting a tubular neighborhood. Using this result and exploiting an analogy with the toy model, we arrive at the final result for LSQM. Partha Mukhopadhyay Copyright © 2013 Partha Mukhopadhyay. All rights reserved. Generalized Nuclear Woods-Saxon Potential under Relativistic Spin Symmetry Limit Wed, 20 Mar 2013 17:46:26 +0000 http://www.hindawi.com/journals/isrn.hep/2013/987632/ By using the Pekeris approximation, we present solutions of the Dirac equation with the generalized Woods-Saxon potential with arbitrary spin-orbit coupling number under spin symmetry limit. We obtain energy eigenvalues and corresponding eigenfunctions in closed forms. Some numerical results are given too. M. Hamzavi and A. A. Rajabi Copyright © 2013 M. Hamzavi and A. A. Rajabi. All rights reserved. Exact Solution of the Dirac Equation for the Yukawa Potential with Scalar and Vector Potentials and Tensor Interaction Sat, 16 Mar 2013 13:43:23 +0000 http://www.hindawi.com/journals/isrn.hep/2013/310392/ We present exact solutions of the Dirac equation with Yukawa potential in the presence of a Coulomb-like tensor potential. For this goal we expand the Yukawa form of the nuclear potential in its mesonic clouds by using Taylor extension to the power of seventh and bring out its simple form. In order to obtain the energy eigenvalue and the corresponding wave functions in closed forms for this potential (with great powers and inverse exponent), we use ansatz method. We also regard the effects of spin-spin, spin-isospin, and isospin-isospin interactions on the relativistic energy spectra of nucleon. By using the obtained results, we have calculated the deuteron mass. The results of our model show that the deuteron spectrum is very close to the ones obtained in experiments. Mona Azizi, Nasrin Salehi, and Ali Akbar Rajabi Copyright © 2013 Mona Azizi et al. All rights reserved. Super-Liouville Theory from Superstring Theory in the Presence of Gauge Worldsheet Fields Thu, 14 Mar 2013 08:16:03 +0000 http://www.hindawi.com/journals/isrn.hep/2013/364852/ We obtain in this work the super-Liouville theory induced from the action of the superstring theory in the presence of gauge worldsheet fields; such construction is based on a special ansatz that gives a special value of -fields . We discuss the integrability of super-Liouville theory through the Lax formulation, and we establish also the superfields formulation of super-Liouville equations. A. EL Boukili, M. Nach, K. Bilal, and M. B. Sedra Copyright © 2013 A. EL Boukili et al. All rights reserved. From Generalized Dirac Equations to a Candidate for Dark Energy Wed, 06 Mar 2013 11:38:42 +0000 http://www.hindawi.com/journals/isrn.hep/2013/374612/ We consider extensions of the Dirac equation with mass terms and . The corresponding Hamiltonians are Hermitian and pseudo-Hermitian ( Hermitian), respectively. The fundamental spinor solutions for all generalized Dirac equations are found in the helicity basis and brought into concise analytic form. We postulate that the time-ordered product of field operators should yield the Feynman propagator ( prescription), and we also postulate that the tardyonic as well as tachyonic Dirac equations should have a smooth massless limit. These postulates lead to sum rules that connect the form of the fundamental field anticommutators with the tensor sums of the fundamental plane-wave eigenspinors and the projectors over positive-energy and negative-energy states. In the massless case, the sum rules are fulfilled by two egregiously simple, distinguished functional forms. The first sum rule remains valid in the case of a tardyonic theory and leads to the canonical massive Dirac field. The second sum rule is valid for a tachyonic mass term and leads to a natural suppression of the right-handed helicity states for tachyonic particles and left-handed helicity states for tachyonic spin-1/2 antiparticles. When applied to neutrinos, the theory contains a free tachyonic mass parameter. Tachyons are known to be repulsed by gravity. We discuss a possible role of a tachyonic neutrino as a contribution to the accelerated expansion of the Universe “dark energy.” U. D. Jentschura and B. J. Wundt Copyright © 2013 U. D. Jentschura and B. J. Wundt. All rights reserved. Phenomenology of Neutrino Mixing in Vacuum and Matter Wed, 13 Feb 2013 11:44:50 +0000 http://www.hindawi.com/journals/isrn.hep/2013/206516/ The current status and some perspectives of the phenomenology of massive neutrinos is reviewed. We start with the phenomenology of neutrino oscillations in vacuum and in matter. We summarize the results of neutrino experiments using solar, atmospheric. The fundamental theory of flavor changing neutrinos that has confirmed the neutrino oscillations and the various parameters affecting these oscillations have been discussed in detail. Specifically we will take the solar and atmospheric neutrino case. The oscillation plots will be discussed in detail, based on their behavior in vacuum and matter. Both normal and inverted mass hierarchy hypotheses are tested and both are consistent with observation. Finally the sensitivity of theta 13 over these probability oscillations has been analyzed and commented. A. Upadhyay and M. Batra Copyright © 2013 A. Upadhyay and M. Batra. All rights reserved. Neutrino Dispersion Relations from a Dark Energy Model Thu, 17 Jan 2013 17:02:24 +0000 http://www.hindawi.com/journals/isrn.hep/2013/497071/ We consider a model in which the neutrino is kinetically coupled to a scalar field and study its implications for environmentally dependent neutrino velocities. Following the usual effective field theory logic, this coupling is expected to arise in neutrino dark energy models. It leads to a Lorentz violation in the neutrino sector. The coupling of the scalar field to the stress tensor of the Earth yields terrestrial neutrino dispersion relations distinct from those in interstellar space. Emilio Ciuffoli, Jarah Evslin, Jie Liu, and Xinmin Zhang Copyright © 2013 Emilio Ciuffoli et al. All rights reserved. Analysis of Lateral Distribution of Atmospheric Cherenkov Light at High Mountain Altitude Towards Event Reconstruction Thu, 13 Dec 2012 09:43:54 +0000 http://www.hindawi.com/journals/isrn.hep/2012/906358/ Air shower simulations with CORSIKA6.990 code using FLUKA 2011 and QGSJET II hadron generators are performed. The simulations are carried out at high mountain observation level, namely, Chacaltaya cosmic ray station. The lateral distribution of atmospheric Cherenkov light produced by various primary particles, namely, proton, helium, oxygen, and iron nuclei, is obtained over wide energy range, between 1011 eV and 1017 eV. The lateral distribution is obtained, integrating over time and angle Cherenkov photons till 800 m from the shower axis. The shapes of the obtained distributions are compared and parameterized. Three different approximations of lateral distribution of Cherenkov light are compared. On the basis of inverse problem solution an event analysis, towards mass composition and energy reconstruction of the primary particle, is carried out. The applications and scientific potential for HECRE experiment proposal are discussed. Alexander Mishev Copyright © 2012 Alexander Mishev. All rights reserved. Approximate Complete Solutions of DKP Equation under a Vector Exponential Interaction via a Pekeris-Type Approximation Tue, 04 Dec 2012 09:07:02 +0000 http://www.hindawi.com/journals/isrn.hep/2012/987196/ The DKP equation for an exponential potential is exactly solved via an appropriate approximation using the methodology of supersymmetric quantum mechanics. We see that the solutions are already known without any cumbersome algebra we face in any numerical or analytical approach. Closed forms of eigenfunctions and eigenvalues are reported. S. Zarrinkamar, A. A. Rajabi, and H. Hassanabadi Copyright © 2012 S. Zarrinkamar et al. All rights reserved. The Effect of Energy Leakage Probability on Burn Propagation in an Optically Thick Fusion Plasma Thu, 29 Nov 2012 08:48:07 +0000 http://www.hindawi.com/journals/isrn.hep/2012/838394/ In an optically thick plasma, the mean free path of bremsstrahlung photons is smaller than the plasma radius, and radiation can be treated as a photon gas in thermal equilibrium. In these conditions, the black body radiation spectrum exceeds the number of hot photons, and reabsorption processes such as inverse bremsstrahlung radiation and inverse Compton scattering become important. It has been shown that a dense fusion plasma like the one being used in ICF method is initially optically thick. When the fuel pellet is burning, the temperature of its electrons rises (approximately greater than 90 KeV), and the pellet becomes rapidly optically thin. In this paper, we have shown that the energy leakage probability makes electron temperature remain low (approximately smaller than 55 KeV), and as a result the fuel pellet remains optically thick during burning. M. Mahdavi, T. Koohrokhi, and Z. Barfami Copyright © 2012 M. Mahdavi et al. All rights reserved.