**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**3680

# Search results for: Relativistic Mean Field theory

##### 3680 Multisymplectic Geometry and Noether Symmetries for the Field Theories and the Relativistic Mechanics

**Authors:**
H. Loumi-Fergane,
A. Belaidi

**Abstract:**

The problem of symmetries in field theory has been analyzed using geometric frameworks, such as the multisymplectic models by using in particular the multivector field formalism. In this paper, we expand the vector fields associated to infinitesimal symmetries which give rise to invariant quantities as Noether currents for classical field theories and relativistic mechanic using the multisymplectic geometry where the Poincaré-Cartan form has thus been greatly simplified using the Second Order Partial Differential Equation (SOPDE) for multi-vector fields verifying Euler equations. These symmetries have been classified naturally according to the construction of the fiber bundle used. In this work, unlike other works using the analytical method, our geometric model has allowed us firstly to distinguish the angular moments of the gauge field obtained during different transformations while these moments are gathered in a single expression and are obtained during a rotation in the Minkowsky space. Secondly, no conditions are imposed on the Lagrangian of the mechanics with respect to its dependence in time and in q^{i}, the currents obtained naturally from the transformations are respectively the energy and the momentum of the system.

**Keywords:**
Field theories,
relativistic mechanics,
Lagrangian formalism,
multisymplectic geometry,
symmetries,
Noether theorem,
conservation laws.

##### 3679 De Broglie Wavelength Defined by the Rest Energy E0 and Its Velocity

**Authors:**
K. Orozović,
B. Balon

**Abstract:**

In this paper, we take a different approach to de Broglie wavelength, as we relate it to relativistic physics. The quantum energy of the photon radiated by a body with de Broglie wavelength, as it moves with velocity v, can be defined within relativistic physics by rest energy E₀. In this way, we can show the connection between the quantum of radiation energy of the body and the rest of energy E₀ and thus combine what has been incompatible so far, namely relativistic and quantum physics. So, here we discuss the unification of relativistic and quantum physics by introducing the factor k that is analog to the Lorentz factor in Einstein's theory of relativity.

**Keywords:**
de Brogli wavelength,
relativistic physics,
rest energy,
quantum physics.

##### 3678 Shell Closures in Exotic Nuclei

**Authors:**
G. Saxena,
D. Singh,
M. Kaushik,

**Abstract:**

**Keywords:**
Relativistic Mean Field theory,
Magic Nucleus,
Si
isotopes,
Shell Closure.

##### 3677 Phenomenological and Theoretical Analysis of Relativistic Temperature Transformation and Relativistic Entropy

**Authors:**
Marko Popovic

**Abstract:**

**Keywords:**
STR,
relativistic temperature transformation,
Boyle'slaw,
equilibrium constant,
Gibbs energy.

##### 3676 Einstein’s General Equation of the Gravitational Field

**Authors:**
A. Benzian

**Abstract:**

The generalization of relativistic theory of gravity based essentially on the principle of equivalence stipulates that for all bodies, the grave mass is equal to the inert mass which leads us to believe that gravitation is not a property of the bodies themselves, but of space, and the conclusion that the gravitational field must curved space-time what allows the abandonment of Minkowski space (because Minkowski space-time being nonetheless null curvature) to adopt Riemannian geometry as a mathematical framework in order to determine the curvature. Therefore the work presented in this paper begins with the evolution of the concept of gravity then tensor field which manifests by Riemannian geometry to formulate the general equation of the gravitational field.

**Keywords:**
Inertia,
principle of equivalence,
tensors,
Riemannian geometry.

##### 3675 The Self-Energy of an Ellectron Bound in a Coulomb Field

**Authors:**
J. Zamastil,
V. Patkos

**Abstract:**

Recent progress in calculation of the one-loop selfenergy of the electron bound in the Coulomb field is summarized. The relativistic multipole expansion is introduced. This expansion is based on a single assumption: except for the part of the time component of the electron four-momentum corresponding to the electron rest mass, the exchange of four-momentum between the virtual electron and photon can be treated perturbatively. For non Sstates and normalized difference n3En −E1 of the S-states this itself yields very accurate results after taking the method to the third order. For the ground state the perturbation treatment of the electron virtual states with very high three-momentum is to be avoided. For these states one can always rearrange the pertinent expression in such a way that free-particle approximation is allowed. Combination of the relativistic multipole expansion and free-particle approximation yields very accurate result after taking the method to the ninth order. These results are in very good agreement with the previous results obtained by the partial wave expansion and definitely exclude the possibility that the uncertainity in determination of the proton radius comes from the uncertainity in the calculation of the one-loop selfenergy.

**Keywords:**
Hydrogen-like atoms,
self-energy.

##### 3674 A Computer Model of Quantum Field Theory

**Authors:**
Hans H. Diel

**Abstract:**

This paper describes a computer model of Quantum Field Theory (QFT), referred to in this paper as QTModel. After specifying the initial configuration for a QFT process (e.g. scattering) the model generates the possible applicable processes in terms of Feynman diagrams, the equations for the scattering matrix, and evaluates probability amplitudes for the scattering matrix and cross sections. The computations of probability amplitudes are performed numerically. The equations generated by QTModel are provided for demonstration purposes only. They are not directly used as the base for the computations of probability amplitudes. The computer model supports two modes for the computation of the probability amplitudes: (1) computation according to standard QFT, and (2) computation according to a proposed functional interpretation of quantum theory.

**Keywords:**
Computational Modeling,
Simulation of Quantum Theory,
Quantum Field Theory,
Quantum Electrodynamics

##### 3673 Exploring the Nature and Meaning of Theory in the Field of Neuroeducation Studies

**Authors:**
Ali Nouri

**Abstract:**

Neuroeducation is one of the most exciting research fields which is continually evolving. However, there is a need to develop its theoretical bases in connection to practice. The present paper is a starting attempt in this regard to provide a space from which to think about neuroeducational theory and invoke more investigation in this area. Accordingly, a comprehensive theory of neuroeducation could be defined as grouping or clustering of concepts and propositions that describe and explain the nature of human learning to provide valid interpretations and implications useful for educational practice in relation to philosophical aspects or values. Whereas it should be originated from the philosophical foundations of the field and explain its normative significance, it needs to be testable in terms of rigorous evidence to fundamentally advance contemporary educational policy and practice. There is thus pragmatically a need to include a course on neuroeducational theory into the curriculum of the field. In addition, there is a need to articulate and disseminate considerable discussion over the subject within professional journals and academic societies.

**Keywords:**
Neuroeducation studies,
neuroeducational theory,
theory building,
neuroeducation research.

##### 3672 Value from Environmental and Cultural Perspectives or Two Sides of the Same Coin

**Authors:**
Vilém Pařil,
Dominika Tóthová

**Abstract:**

This paper discusses the value theory in cultural heritage and the value theory in environmental economics. Two economic views of the value theory are compared, within the field of cultural heritage maintenance and within the field of the environment. The main aims are to find common features in these two differently structured theories under the layer of differently defined terms as well as really differing features of these two approaches; to clear the confusion which stems from different terminology as in fact these terms capture the same aspects of reality; and to show possible inspiration these two perspectives can offer one another. Another aim is to present these two value systems in one value framework. First, important moments of the value theory from the economic perspective are presented, leading to the marginal revolution of (not only) the Austrian School. Then the theory of value within cultural heritage and environmental economics are explored. Finally, individual approaches are compared and their potential mutual inspiration searched for.

**Keywords:**
Cultural heritage,
environmental economics,
existence value,
value theory.

##### 3671 Generalized Mean-field Theory of Phase Unwrapping via Multiple Interferograms

**Authors:**
Yohei Saika

**Abstract:**

On the basis of Bayesian inference using the maximizer of the posterior marginal estimate, we carry out phase unwrapping using multiple interferograms via generalized mean-field theory. Numerical calculations for a typical wave-front in remote sensing using the synthetic aperture radar interferometry, phase diagram in hyper-parameter space clarifies that the present method succeeds in phase unwrapping perfectly under the constraint of surface- consistency condition, if the interferograms are not corrupted by any noises. Also, we find that prior is useful for extending a phase in which phase unwrapping under the constraint of the surface-consistency condition. These results are quantitatively confirmed by the Monte Carlo simulation.

**Keywords:**
Bayesian inference,
generalized mean-field theory,
phase unwrapping,
statistical mechanics.

##### 3670 Propagation of Electron-Acoustic Solitary Waves in Weakly Relativistically Degenerate Fermi Plasma

**Authors:**
Swarniv Chandra,
Basudev Ghosh,
S. N. Paul

**Abstract:**

**Keywords:**
Relativistic Degeneracy,
Electron-Acoustic Waves,
Quantum Plasma,
KdV Equation.

##### 3669 Absorption Spectra of Artificial Atoms in Presence of THz Fields

**Authors:**
B. Dahiya,
K.Batra,
V.Prasad

**Abstract:**

Artificial atoms are growing fields of interest due to their physical and optoelectronicapplications. The absorption spectra of the proposed artificial atom inpresence of Tera-Hertz field is investigated theoretically. We use the non-perturbativeFloquet theory and finite difference method to study the electronic structure of ArtificialAtom. The effect of static electric field on the energy levels of artificial atom is studied.The effect of orientation of static electric field on energy levels and diploe matrix elementsis also highlighted.

**Keywords:**
Absorption spectra,
Artificial atom,
Floquet Theory,
THz fields

##### 3668 Half-Circle Fuzzy Number Threshold Determination via Swarm Intelligence Method

**Authors:**
P.-W. Tsai,
J.-W. Chen,
C.-W. Chen,
C.-Y. Chen

**Abstract:**

In recent years, many researchers are involved in the field of fuzzy theory. However, there are still a lot of issues to be resolved. Especially on topics related to controller design such as the field of robot, artificial intelligence, and nonlinear systems etc. Besides fuzzy theory, algorithms in swarm intelligence are also a popular field for the researchers. In this paper, a concept of utilizing one of the swarm intelligence method, which is called Bacterial-GA Foraging, to find the stabilized common P matrix for the fuzzy controller system is proposed. An example is given in in the paper, as well.

**Keywords:**
Half-circle fuzzy numbers,
predictions,
swarm
intelligence,
Lyapunov method.

##### 3667 Propagation of Nonlinear Surface Waves in Relativistically Degenerate Quantum Plasma Half-Space

**Authors:**
Swarniv Chandra,
Parthasona Maji,
Basudev Ghosh

**Abstract:**

The nonlinear self-interaction of an electrostatic surface wave on a semibounded quantum plasma with relativistic degeneracy is investigated by using quantum hydrodynamic (QHD) model and the Poisson’s equation with appropriate boundary conditions. It is shown that a part of the second harmonic generated through self-interaction does not have a true surface wave character but propagates obliquely away from the plasma-vacuum interface into the bulk of plasma.

**Keywords:**
Harmonic Generation,
Quantum Plasma,
Quantum Hydrodynamic Model,
Relativistic Degeneracy,
Surface waves.

##### 3666 Action Functional of the Electomagnetic Field: Effect of Gravitation

**Authors:**
Arti Vaish,
Harish Parthasarathy

**Abstract:**

The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equations for the four electromagnetic potentials given by the metric of space-time. Similar to the Einstein-s formulation of the field equations of gravitation, these equations are also derived from an action principle. In this paper, the expressions for the action functional of the electromagnetic field have been derived in the presence of gravitational field.

**Keywords:**
General theory of relativity,
electromagnetism,
metric tensor,
Maxwells equations,
test functions,
finite element method.

##### 3665 Image Modeling Using Gibbs-Markov Random Field and Support Vector Machines Algorithm

**Authors:**
Refaat M Mohamed,
Ayman El-Baz,
Aly A. Farag

**Abstract:**

**Keywords:**
Image Modeling,
MRF,
Parameters Estimation,
SVM Learning.

##### 3664 Central Finite Volume Methods Applied in Relativistic Magnetohydrodynamics: Applications in Disks and Jets

**Authors:**
Raphael de Oliveira Garcia,
Samuel Rocha de Oliveira

**Abstract:**

We have developed a new computer program in Fortran 90, in order to obtain numerical solutions of a system of Relativistic Magnetohydrodynamics partial differential equations with predetermined gravitation (GRMHD), capable of simulating the formation of relativistic jets from the accretion disk of matter up to his ejection. Initially we carried out a study on numerical methods of unidimensional Finite Volume, namely Lax-Friedrichs, Lax-Wendroff, Nessyahu-Tadmor method and Godunov methods dependent on Riemann problems, applied to equations Euler in order to verify their main features and make comparisons among those methods. It was then implemented the method of Finite Volume Centered of Nessyahu-Tadmor, a numerical schemes that has a formulation free and without dimensional separation of Riemann problem solvers, even in two or more spatial dimensions, at this point, already applied in equations GRMHD. Finally, the Nessyahu-Tadmor method was possible to obtain stable numerical solutions - without spurious oscillations or excessive dissipation - from the magnetized accretion disk process in rotation with respect to a central black hole (BH) Schwarzschild and immersed in a magnetosphere, for the ejection of matter in the form of jet over a distance of fourteen times the radius of the BH, a record in terms of astrophysical simulation of this kind. Also in our simulations, we managed to get substructures jets. A great advantage obtained was that, with the our code, we got simulate GRMHD equations in a simple personal computer.

**Keywords:**
Finite Volume Methods,
Central Schemes,
Fortran
90,
Relativistic Astrophysics,
Jet.

##### 3663 A Unification and Relativistic Correction for Boltzmann’s Law

**Authors:**
Lloyd G. Allred

**Abstract:**

The distribution of velocities of particles in plasma is a well understood discipline of plasma physics. Boltzmann’s law and the Maxwell-Boltzmann distribution describe the distribution of velocity of a particle in plasma as a function of mass and temperature. Particles with the same mass tend to have the same velocity. By expressing the same law in terms of energy alone, the author obtains a distribution independent of mass. In summary, for particles in plasma, the energies tend to equalize, independent of the masses of the individual particles. For high-energy plasma, the original law predicts velocities greater than the speed of light. If one uses Einstein’s formula for energy (*E=mc ^{2}*), then a relativistic correction is not required.

**Keywords:**
Cosmology,
EMP,
Euclidean,
plasma physics,
relativity.

##### 3662 Study on Electrohydrodynamic Capillary Instability with Heat and Mass Transfer

**Authors:**
D. K. Tiwari,
Mukesh Kumar Awasthi,
G. S. Agrawal

**Abstract:**

The effect of an axial electric field on the capillary instability of a cylindrical interface in the presence of heat and mass transfer has been investigated using viscous potential flow theory. In viscous potential flow, the viscous term in Navier-Stokes equation vanishes as vorticity is zero but viscosity is not zero. Viscosity enters through normal stress balance in the viscous potential flow theory and tangential stresses are not considered. A dispersion relation that accounts for the growth of axisymmetric waves is derived and stability is discussed theoretically as well as numerically. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, heat transfer capillary number, conductivity ratio, permittivity ratio on the stability of the system. It has been observed that the axial electric field and heat and mass transfer both have stabilizing effect on the stability of the system.

**Keywords:**
Capillary instability,
Viscous potential flow,
Heat and mass transfer,
Axial electric field.

##### 3661 Viscous Potential Flow Analysis of Electrohydrodynamic Capillary Instability through Porous Media

**Authors:**
Mukesh Kumar Awasth,
Mohammad Tamsir

**Abstract:**

The effect of porous medium on the capillary instability of a cylindrical interface in the presence of axial electric field has been investigated using viscous potential flow theory. In viscous potential flow, the viscous term in Navier-Stokes equation vanishes as vorticity is zero but viscosity is not zero. Viscosity enters through normal stress balance in the viscous potential flow theory and tangential stresses are not considered. A dispersion relation that accounts for the growth of axisymmetric waves is derived and stability is discussed theoretically as well as numerically. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, viscosity ratio, permittivity ratio on the stability of the system. It has been observed that the axial electric field and porous medium both have stabilizing effect on the stability of the system.

**Keywords:**
Capillary instability,
Viscous potential flow,
Porous
media,
Axial electric field.

##### 3660 The Effect of the Crystal Field Interaction on the Critical Temperatures and the Sublattice Magnetizations of a Mixed Spin-3/2 and Spin-5/2 Ferrimagnetic System

**Authors:**
Fathi Abubrig,
Mohamed Delfag,
Suad M. Abuzariba

**Abstract:**

The influence of the crystal field interactions on the mixed spin-3/2 and spin-5/2 ferrimagnetic Ising system is considered by using the mean field theory based on Bogoliubov inequality for the Gibbs free energy. The ground-state phase diagram is constructed, the phase diagrams of the second-order critical temperatures are obtained, and the thermal variation of the sublattice magnetizations is investigated in detail. We find some interesting phenomena for the sublattice magnetizations at particular values of the crystal field interactions.

**Keywords:**
Crystal field,
Ising system,
Ferrimagnetic,
magnetization,
phase diagrams.

##### 3659 A Refined Nonlocal Strain Gradient Theory for Assessing Scaling-Dependent Vibration Behavior of Microbeams

**Authors:**
Xiaobai Li,
Li Li,
Yujin Hu,
Weiming Deng,
Zhe Ding

**Abstract:**

**Keywords:**
Euler-Bernoulli Beams,
free vibration,
higher order
inertia,
nonlocal strain gradient theory,
velocity gradient.

##### 3658 Temperature Field Study of Brake Disc in a Belt Conveyor Brake

**Authors:**
Hou Youfu,
Wang Daoming,
Meng Qingrui

**Abstract:**

**Keywords:**
Downward belt conveyor,
Disc brake,
Temperature
field,
Numerical simulation.

##### 3657 An Evolutionary Statistical Learning Theory

**Authors:**
Sung-Hae Jun,
Kyung-Whan Oh

**Abstract:**

**Keywords:**
Evolutionary computing,
Local optima,
Over-fitting,
Statistical learning theory

##### 3656 Flexure of Cantilever Thick Beams Using Trigonometric Shear Deformation Theory

**Authors:**
Yuwaraj M. Ghugal,
Ajay G. Dahake

**Abstract:**

A trigonometric shear deformation theory for flexure of thick beams, taking into account transverse shear deformation effects, is developed. The number of variables in the present theory is same as that in the first order shear deformation theory. The sinusoidal function is used in displacement field in terms of thickness coordinate to represent the shear deformation effects. The noteworthy feature of this theory is that the transverse shear stresses can be obtained directly from the use of constitutive relations with excellent accuracy, satisfying the shear stress free conditions on the top and bottom surfaces of the beam. Hence, the theory obviates the need of shear correction factor. Governing differential equations and boundary conditions are obtained by using the principle of virtual work. The thick cantilever isotropic beams are considered for the numerical studies to demonstrate the efficiency of the. Results obtained are discussed critically with those of other theories.

**Keywords:**
Trigonometric shear deformation,
thick beam,
flexure,
principle of virtual work,
equilibrium equations,
stress.

##### 3655 Photon Localization inside a Waveguide Modeled by Uncertainty Principle

**Authors:**
Shilpa N. Kulkarni,
Sujata R. Patrikar

**Abstract:**

**Keywords:**
photon localization in waveguide,
photon tunneling,
quantum confinement of light,
Schrödinger wave equation,
uncertainty principle.

##### 3654 Flexure of Simply Supported Thick Beams Using Refined Shear Deformation Theory

**Authors:**
Yuwaraj M. Ghugal,
Ajay G. Dahake

**Abstract:**

A trigonometric shear deformation theory for flexure of thick beams, taking into account transverse shear deformation effects, is developed. The number of variables in the present theory is same as that in the first order shear deformation theory. The sinusoidal function is used in displacement field in terms of thickness coordinate to represent the shear deformation effects. The noteworthy feature of this theory is that the transverse shear stresses can be obtained directly from the use of constitutive relations with excellent accuracy, satisfying the shear stress free conditions on the top and bottom surfaces of the beam. Hence, the theory obviates the need of shear correction factor. Governing differential equations and boundary conditions are obtained by using the principle of virtual work. The thick simply supported isotropic beams are considered for the numerical studies to demonstrate the efficiency of the results obtained is discussed critically with those of other theories.

**Keywords:**
Trigonometric shear deformation,
thick beam,
flexure,
principle of virtual work,
equilibrium equations,
stress.

##### 3653 A New Developed Formula to Determine the Shear Buckling Stress in Welded Aluminum Plate Girders

**Authors:**
Badr Alsulami,
Ahmed S. Elamary

**Abstract:**

This paper summarizes and presents main results of an in-depth numerical analysis dealing with the shear buckling resistance of aluminum plate girders. The studies conducted have permitted the development of a simple design expression to determine the critical shear buckling stress in aluminum web panels. This expression takes into account the effects of reduction of strength in aluminum alloys due to welding process. Ultimate shear resistance (USR) of plate girders can be obtained theoretically using Cardiff theory or Hӧglund’s theory. USR of aluminum alloy plate girders predicted theoretically using BS8118 appear inconsistent when compared with test data. Theoretical predictions based on Hӧglund’s theory, are more realistic. Cardiff theory proposed to predict the USR of steel plate girders only. Welded aluminum alloy plate girders studied experimentally by others; the USR resulted from tests are reviewed. Comparison between the test results with the values obtained from Hӧglund’s theory, BS8118 design method and Cardiff theory performed theoretically. Finally, a new equation based on Cardiff tension-field theory, proposed to predict theoretically the USR of aluminum plate girders.

**Keywords:**
Shear resistance,
Aluminum,
Cardiff theory,
Hӧglund's theory,
Plate girder.

##### 3652 Advancing the Theory of Planned Behavior within Dietary and Physical Domains among Type 2 Diabetics: A Mixed Methods Approach

**Authors:**
D.O. Omondi,
M.K. Walingo,
G.M. Mbagaya,
L.O.A. Othuon

**Abstract:**

**Keywords:**
Physical activity,
diet,
Type 2 diabetes,
behaviorchange theory,
model.

##### 3651 Newtonian Mechanics Descriptions for General Relativity Experimental Tests, Dark Matter and Dark Energy

**Authors:**
Jing-Gang Xie

**Abstract:**

As the continuation to the previous studies of gravitational frequency shift, gravitational time dilation, gravitational light bending, gravitational waves, dark matter, and dark energy are explained in the context of Newtonian mechanics. The photon is treated as the particle with mass of hν/C^{2} under the gravitational field of much larger mass of M. Hence the quantum mechanics theory could be applied to gravitational field on cosmology scale. The obtained results are the same as those obtained by general relativity considering weak gravitational field approximation; however, the results are different when the gravitational field is substantially strong.

**Keywords:**
Gravitational time dilation,
gravitational light bending,
gravitational waves,
dark matter,
dark energy,
General Relativity,
gravitational frequency shift.