Electronic Journal of Theoretical Physics

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ISSN 1729-5254

 

Volume 5, Issue 17 (March 2008)

 

Full text: Acrobat PDF (3,010 KB)

 

Number 

Articles Title

Abstract

 

A Review of Leading Quantum Gravitational Corrections to Newtonian Gravity

 

Arif Akhundov and Anwar Shiekh

 

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In this review we present the theoretical background for treating General Relativity as an effective field theory and focus on the concrete results of such a treatment. As a result we present the calculations of the low-energy leading gravitational corrections to the Newtonian potential between two sources.

 

 

Radiation Reaction at Extreme Intensity

Richard T. Hammond

 

 

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The radiation reaction force is examined for an idealized short pulse of electromagnetic radiation and for a plane wave.  Exact solutions (without radiation reaction) are discussed, the total radiated power is calculated. A new and simpler approach to the approximate form of the equation of motion is presented that automatically removes the runaway solutions. Finally, analytical solutions are presented for the equations of motion that include the radiation reaction forces in the very high intensity regime. A classical scattering angle is defined and it shows  that the electron is scattered in a small cone in the forward direction. The radiation reaction corrections to this angle are also considered.

 

Super-Light Electromagnetic Wave With Longitudinal And Transversal Modes

 

M.M. Kononenko

 

 

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The transformation converting equations invariant under Lorentz into the equations invariant under Galileo is obtained. On this basis:(1) the super-light electromagnetic wave with longitudinal and transversal modes is found out; (2) it is shown the wave velocity coincides with that of de Broglie's wave; (3) the connection between Maxwell's electrodynamics and Shr\"{o}dinger's equation is established; (4) structural elements of space are discovered and ``a horizon of visibility'' is found. It is shown Bell's inequalities and the principle of the light speed constancy are based on the SRT artifact and ``Einstein's local realism'' is determined by the wave referred above. Objectivity of results for quantum and classical objects is discussed.

 

Non Commutative Geometry Constraints and the Standard Renormalization Group Approach: Two Doublets Higgs Model as An Example.

 

N.Mebarki and M.Harrat

 

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The Chamssedine-Fr\"{o}hlich Approach to Noncommutative Geometry (NCG) is extended and applied to the reformulation of the two doublets Higgs model. The Fuzzy mass, coupling and unitarity relations are derived. It is shown that the latter are no more preserved under the renormalization group equations obtained from the standard quantization method. This suggests to look for an appropriate NCG quantization procedure.

 

Hamilton-Jacobi Formulation of a Non-Abelian Yang-Mills Theories

 

W. I. Eshraim and N. I. Farahat

 

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A non-Abelian theory of fermions interacting with gauge bosons is treated as a constrained system using the Hamilton-Jacobi approach. The equations of motion are obtained as total differential equations in many variables. The integability conditions are satisfied, and the set of equations of motion is integrable. A comparison with Dirac's method is done

 

Physical Form of The Clustering Parameter And Gravitational Galaxy Clustering

 

Sajad Masood , Manzoor A Malik, Shakeel Ahmad and N. A. Rather

 

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A theory for a system clustering under gravity is developed for the clustering parameter b(n,T), in terms of a partial differential equation using thermodynamic technique.  Various solutions of the differential equation relate b(n,T) with density n and temperature T of the gravitating system.  The physical validity of various solutions of b(n,T) on the basis of certain boundary conditions and probability density distribution function is discussed.  Results indicate that the clustering parameter depends on the specific combination nT^{-3}.  The theory also provides a new insight into gravitational clustering.

 

Penrose Model Potential, Compared With Coleman- Weinberg Potential for Early Universe Scalar Evolution

A.W. Beckwith

 

 

 

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We present evidence in terms of a D'Alembertain operator acting on a scalar field minus the first derivative of a potential system, with respect to an inflaton scalar field, that the Penrose model as outlined as an alternative to cosmological big crunch models gives us emergent behavior for an inflaton scalar field in early universe cosmological models. This is in contrast to the Coleman-Weinberg potential which in low temperature conditions is always presenting almost non existent emergent scalar fields. This permits us to state that Penrose's cyclic universe model in its initial conditions gives us scalar field dynamics consistent with emergent scalar fields which die out quickly as temperature drops after the onset of inflation. We make no attempt to find the particulars of the conformal mapping which allows the alternative to the big crunch Penrose (2007) lectured upon in the inaugural meeting of the IGC at Penn State.

 

Increasing Effective Gravitational Constant In Fractional Add Brane Cosmology

 

El-Nabulsi Ahmad Rami

 

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Arkani--Hamed--Dimopoulos--Dvali brane model with time--increasing scaling gravitational constant is constructed within the framework of fractional action--like variational approach with one positive parameter `\alpha'.

 

A Two-Dimensional Discrete Mapping with C^{Infinity} Multifold Chaotic Attractors

 

Zeraoulia Elhadj and J. C. Sprott

 

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This paper introduces a two-dimensional, C^{\infinity} discrete bounded map capable of generating "multi- fold"      strange attractors via period-doubling bifurcation routes to chaos.

 

Bosons-Parafermions Wess-Zumino Model

 

L. Maghlaoui and N. Belaloui

 

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A Wess-Zumino model in terms of bosons and parafermions of order p=2 is investigated.\,We show that the parasupercharges associated to the parasupersymmetric transformations satisfy the p=2 trilinear relations. The closure of the transformations algebra is established with a trilinear product rule for the fermionic elements. Finally, we verify that these parasupercharges are really the generators of the parasupersymmetric transformations.

 

Geometrodynamics of Information on Curved Statistical Manifolds and Its Applications to Chaos

 

C. Cafaro and S. A. Ali

 

 

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A novel information-geometrodynamical approach to chaotic dynamics (IGAC) on curved statistical manifolds based on Entropic Dynamics (ED) is presented and a new definition of information geometrodynamical entropy (IGE) as a measure of chaoticity is proposed. The general classical formalism is illustrated in a relatively simple example. It is shown that the hyperbolicity of a non-maximally symmetric 6N-dimensional statistical manifold {M}_{s} underlying an ED Gaussian model describing an arbitrary system of 3N degrees of freedom leads to linear information-geometric entropy growth and to exponential divergence of the Jacobi vector field intensity, quantum and classical features of chaos respectively. An information-geometric analogue of the Zurek-Paz quantum chaos criterion in the classical reversible limit is proposed. This analogy is illustrated applying the IGAC to a set of n-uncoupled three-dimensional anisotropic inverted harmonic oscillators characterized by a Ohmic distributed frequency spectrum.

 

Stochastic Measures and Modular Evolution in Non-Equilibrium Thermodynamics

 

Enrique Hernandez-Lemus, and Jesus K. Estrada-Gil

 

 

 

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We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical structure for (physical) correlation functions and non-equilibrium thermodynamical potentials. It is proposed that macroscopic evolution equations (such as dynamic correlation functions) may be obtained from a non-equilibrium thermodynamical description, by using the fact that extended thermodynamical potentials belong to a certain class of statistical systems whose probability distribution functions are defined by a {\it stationary measure}; although a measure which is, in general, {\sl different} from the equilibrium Gibbs measure. These probability measures obey a certain hierarchy on its stochastic evolution towards the most probable (stationary) measure. This in turns defines a convergence sequence. We propose a formalism which considers the mesoscopic stage (typical of non-local dissipative processes such as the ones described by extended irreversible thermodynamics) as being governed by stochastic dynamics due to the effect of non-equilibrium fluctuations. Some applications of the formalism are described.

 

Beltrami Flow of an Unsteady Dusty Fluid between Parallel Plates in Anholonomic Co-Ordinate System

 

B.J.Gireesha, C.S.Bagewadi and C.S.Vishalakshi

 

 

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An analytical study of Beltrami flow of viscous dusty fluid between two parallel plates has been studied. The flow is due to influence of movement of plates. Flow analysis is carried out using differential geometry techniques and exact solutions of the problem are obtained using Laplace Transform technique also which are discussed with the help of graphs drawn for different values of Reynolds number. Further the expressions for skin-friction are obtained at the boundaries.

 

Factorization Method and Solution of the Non- Central Modified Kratzer Potential

 

J. Sadeghi and B. Pourhassan

 

 

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In this paper, we study the Schr\"odinger equation with a non - central modified Kratzer potential plus a ring – shaped like potential, which is not spherically symmetric. Thus, the standard methods for separation of variables do not quite apply. However we are able to separate variables using a simple extension of the standard method, which leads to solutions in the associated Laguerre function for the radial part and Jacobi polynomials for the polar angle part. We also introduce an interesting pair of first order ladder operators, which allow us to generate the energy eigenvalues for all states of the system. The obtained results show that the lack of spherical symmetry removes the degeneracy of second quantum number m which completely expected.

 

Discrete Self-Similarity between Rr Lyrae Stars And Singly-Excited Helium Atoms

 

Robert L. Oldershaw

 

 

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Classical variable stars called RR Lyrae stars have pulsating outer envelopes constituted of excited atoms. Here we demonstrate that the qualitative and quantitative properties of RR Lyrae variables and one subclass of their atomic scale constituents: singly-excited helium atoms undergoing transitions between Rydberg states, share a remarkable degree of self-similarity. In terms of masses, radii, oscillation periods, morphologies and kinematics the stellar and atomic analogues obey a simple set of discrete self-similar scaling equations. The concept of stellar/atomic self-similarity may prove useful in the search for a deeper understanding of both stellar and atomic systems.

 

Brownian Dynamics of Nanoparticles Moving Near a Fluctuating Membrane

 

A. Bendouch, M. Benhamou, and H. Kaidi

 

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This work deals with Brownian dynamics study of small nanoparticles moving near an attractive penetrable fluid membrane. As consequence, these particles are pushed towards the interface, under a change of a suitable physical parameter, such as temperature, pressure or membrane environment. For simplicity, we assume that the particle size is small enough in comparison to the roughness of the membrane. In addition, the particles are supposed to be of very low density (their mutual interactions can be ignored). Then, the only remaining interaction is a mean-force external potential computed exactly in some recent work. The latter that originates from the strong membrane undulations, is a function of the perpendicular distance $z$. Brownian dynamics are studied through the time particle density, which solves the Smoluchowski equation. This density is determined exactly around the fluid membrane, where the essential of phenomenon takes place. In particular, far from the interface, the beads diffuse as usual. But inside the thermal fluctuations region, the Brownian particles diffuse and effectuate small oscillations, with a frequency \omega scaling as \omega \thicksim \kappa ^{3/8}, where \kappa  accounts for the bending rigidity constant of the membrane. We emphasize that the present Brownian dynamics study reveals the existence of a characteristic time \tau \thicksim \kappa ^{-3/4}, which can be interpreted as the time beyond which the particles reach their final equilibrium state. For early times \left( t<\tau \right) , however, the particles are out equilibrium. After a long time \left( t>\tau \right) , the beads reach their final equilibrium state, and occupy new holes and valleys.\ Finally, this work must be considered as a natural extension of a recent one that was concerned with the static study of the colloidal organization in contact with a fluctuating fluid membrane.

 

Influence of Third Order Perturbation on Heisenberg Hamiltonian Of Thick Ferromagnetic Films

 

P. Samarasekara

 

 

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The effect of third order perturbation on the classical Heisenberg Hamiltonian of thick ferromagnetic has been investigated for the first time. Energy of thick films with layers up to 10000 has been plotted for sc(001) and fcc(001) ferromagnetic compounds. Unlike the second order perturbation, the third order perturbation does not increase the total energy by any considerable amount. For the thicknesses approximately N=45 and 40, the anisotropy energy is small for sc(001) and fcc(001), respectively, indicating that the energy required to rotate from easy to hard direction is really small at theses thicknesses. The energy curves of sc (001) and fcc(001) with N=10000 have been flattened by reducing the smooth part of the curve compared with those of second order perturbation. The angle between the easy and hard direction is 97.4^{0} and 32.45^{0 }for sc(001) and fcc(001) thick film with N=10000, respectively. The overshooting parts began to appear after introducing second or third order perturbation, and hence the angle between easy and hard directions is not 90^{0} in the overshooting part of curves. The third and second order perturbation vanish at \theta =0^{0} and 90^{0} directions.

 

Viscous Dusty Fluid Flow with Constant Velocity Magnitude

 

Siddabasappa, Venkateshappa, Rudraswamy, Gopinath

 

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We consider the viscous dusty fluid, where the velocity of the dust particle is everywhere parallel to that of the fluid with velocity magnitude of the fluid is constant along each individual streamline. Also it is assumed that number density of the dust particle is constant and the dust particles are uniform in size and shape and bulk concentration of the dust is small. Hodograph and Legendre transform of stream function is employed to get the solutions and the geometry of streamlines for these flows by using the resulting partial differential equations when the Jacobian is zero and nonzero cases. In each case the variation of pressure is analyzed graphically.

 

The Influence of Long-Range Interaction on Critical Behavior of Some Alloys

 

S. V. Belim

 

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The critical behavior of some alloys are analyzed within the framework of Heisenbergs model with long-range interaction. On based experimental values of the critical exponent \gamma we calculate the value of paerameter of long-range interaction.

 

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