PROPAGATION OF ELECTROMAGNETIC WAVES IN MULTILAYER MEDIUM
Osama M. AboSeida
Mathematics Department, Faculty of Science, Kafrelshikh University, Egypt
ABSTRACT
Objectives and Motivations
The main goal of this work is to study the effect of certain factors ( boundary conditions, frequency range, propagation constant, electric field, magnetic field ) on some media to improve their physical behavior and to broaden the range of their applications. Also, the improvements of the evaluation of the electric and magnetic fields open new areas of their use in practice and industry. The materials taken into consideration are:
IFarField in Sea
The boundaries of the sea is stratified
The upper surface of the sea is rough
II Buried object
III Radio waves in Atmosphere
Electric and magnetic fields at any height above the duct
Transient field in the upper ionosphere
IV Communication in tunnels
Zewail City of Science and Technology, Egypt Faculty of Science, Sohag University, Egypt
ABSTRACT
In this communication we discuss different aspects of Bioinformatics models and its application quantum information and quantum computer. We focus on the dynamics of charge qubits coupled to a nanomechanical resonator under influence of both a phonon bath in contact with the resonator and irreversible decay of the qubits. Even in the presence of enviroment, the inherent entanglement is found to be rather robust. Due to this fact, together with control of system parameters, the system may therefore be especially suited for quantum computer. Our findings also shed light on the evolution of open quantum manybody systems..
On Wave Propagation of TwoTemperature Generalized Thermoelasticity Theory
Alaa Abdelbary , Umm AlQura Univ., Makkah, Saudi Arabia
Arab Academy of Science and Technology, Po. Box 1029, Alexandria, EGYPT
ABSTRACT
The generalized thermoelasticity model based on two distinct temperatures; the conductive temperature and the thermodynamics temperature where the two temperatures coincide when the heat supply vanishes has been improved. The numerical application of this theorem represented that, the discontinuous points of stress and displacement distributions disappeared still has one paradox, where the thermal wave propagation has an infinite speed. This paradox comes from the equation of the two types of temperature that is a parabolic differential equation. So, this work discusses analytically and numerically the speed of the wave propagation on the context of the twotemperature generalized thermoelasticity theory.
The collapsing of vapour bubbles between twophase bubbly flow
Selim Ali Mohammadein ,  ,  ,  , 
Fluid Mechanics





ABSTRACT
The paper analyses the behaviour of vapour bubble collapse between two finite boundaries. The physical problem is obtained by extended of Plesset and Zwick theory. The collapse problem is solved analytically by using Florschuetz and Chao method. The rate of bubble collapse is affected by initial bubble radius, initial bubble velocity, superheating, thermal diffusivity, and initial void fraction. This study is very important to avoid vapour bubbles in many in some industries.
The effect of shearing stress on the growth of gas bubbles with variant surface tension
Mamdouh Hussein Omran , Selim Ali Mohammadein
lecturer of Applied Mathematics of Suez Canal Universityn  Faculty of Science AlArish
Professor Applied Mathematics of Tanta UniversityFaculty of Science tanta
ABSTRACT
In this paper , we studied the growth of gas bubbles between two phase nonNewtonian fluids flow when the surface tension is variant. The growth problem is discussed for an aqueous solution of carboxymethyl cellulose (CMC) in water at concentration 1.2%w/w and temperature 〖20〗^0 C. The mathematical model is performed by mass, momentum and diffusion equations and solved analytically to derive the growth of a gas bubble between twophase nonNewtonian fluids flow in terms of void fraction and void fraction values. The growth of a gas bubble in nonNewtonian fluids flow performs lower values than that in case of Newtonian one Moreover, the results satisfy the growth model in Newtonian and nonNewtonian fluids given by Mohammadein et al [19,20] for limited values of physical parameters.
The Growing of Vapour Bubbles between TwoPhase Flow under the Effect of Magnetic Field
Selim Ali Mohammadein ,  ,  ,  , 
Fluid Mechanics





ABSTRACT
The paper analysis the growth of a vapour bubble within a superheated liquid under the effect of radical magnetic field. The extended Rayleigh equation is solved analytically on the basis of the modification of Mohammadein model. The growth problem is studied under the influence of independent and dependent magnetic field. The different values of a magnetic field affected the growth. Results are compared with some previous theories with good agreement for a certain values of physical parameters.
.
Unsteady Couette Flow of OneComponent Plasma Between Two Parallel Plates Under The Effect of Nonlinear External Magnetic Field.
Dr Taha Zakaraia Abdel Wahid
Basic Sciences Department, October High Institute for Engineering and Technology, 6th October City, Giza, Egypt.
ABSTRACT
The unsteady Couette flow of one component rarefied plasma between two parallel plates under the effect of nonlinear external magnetic field is considered. The two parallel plates one is stationary and the other is moving with a variable velocity depends on time. The plate motion is inducing electric and magnetic fields plus the eternal field. The effect of all fields on the plasma particles is studied. This research is based on the analytic solution of the BGK (Bhatnager–Gross–Krook) model of the nonlinear partial differential Boltzmann equation coupled with Maxwell’s partial differential equation. The initialboundary value problem of the Couette flow problem applied to the system is investigated. For this purpose, the method of moments with a two sided distribution function of Liu and Lee's type is used to get the exact solution of the nonlinear partial differential equations system. In addition, the accurate formula of the electron–electron collision frequency term is presented. The entropy, entropy production, entropy flux, thermodynamic forces, and kinetic coefficients are calculated. The Boltzmann Htheorem for nonequilibrium thermodynamic properties of the system is verified. The distinction between the perturbed velocity distribution functions and the equilibrium velocity distribution function at different time values is illustrated. The ratios between the different contributions of the internal energy changes are predicted via the extended Gibbs equation for diamagnetic plasma. The results are applied to a typical model of laboratory argon plasma. 3DGraphics illustrating the calculated variables are drawn to predict their behavior and the results are discussed.
Hydromagnetic Natural Convection Flow with Heat and Mass Transfer of Heat Absorbing, Radiating and Chemically Reactive Fluid past an Accelerated Moving Vertical Plate with Arbitrary Ramped Temperature
Syed Modassir Hussain
Department of Mathematics, O. P. Jindal Institute of Technology, Raigarh (C.G.) 496109, INDIA
ABSTRACT
The unsteady hydromagnetic natural convection flow with heat and mass transfer of a viscous, incompressible, electrically conducting, temperature dependent heat absorbing, radiating and chemically reactive fluid past an accelerated moving vertical plate with arbitrary ramped temperature and arbitrary ramped surface concentration in a fluid saturated porous medium is studied. The derived governing equations are solved analytically with the help of Laplace Transform Technique. The unified closedform expressions are obtained for fluid velocity, fluid temperature, species concentration, skin friction, Nusselt number and Sherwood numbers. The effects of various parameters on fluid velocity, fluid temperature and species concentration are discussed by graphs whereas numerical values of skin friction, Nusselt and Sherwood numbers are presented in tabular form for different values of pertinent flow parameters. The numerical results are also compared to natural convection flow near an arbitrary ramped temperature plate with arbitrary ramped surface concentration with the corresponding flow near isothermal plate with uniform surface concentration.
Hall effects on MHD Natural Convection Flow with Heat and Mass Transfer of Heat Absorbing, Radiating and Chemically Reactive Fluid past an Accelerated Moving Vertical Plate with Arbitrary Ramped Temperature
Jainendra Jain , Syed Modassir Hussain
Department of Mathematics, O. P. Jindal Institute of Technology, Raigarh (C.G.) 496109, INDIA
Department of Mathematics, O. P. Jindal Institute of Technology, Raigarh (C.G.) 496109, INDIA
ABSTRACT
The effects of Hall current unsteady hydromagnetic natural convection flow with heat and mass transfer of a viscous, incompressible, electrically conducting, temperature dependent heat absorbing, radiating and chemically reactive fluid past an accelerated moving vertical plate with arbitrary ramped temperature and arbitrary ramped surface concentration in a fluid saturated porous medium is studied. The derived governing equations are solved analytically with the help of Laplace Transform Technique. The unified closedform expressions are obtained for fluid velocity, fluid temperature, species concentration, skin friction, Nusselt number and Sherwood numbers. The effects of various parameters on fluid velocity, fluid temperature and species concentration are discussed by graphs whereas numerical values of skin friction, Nusselt and Sherwood numbers are presented in tabular form for different values of pertinent flow parameters. The numerical results are also compared to natural convection flow near an arbitrary ramped temperature plate with arbitrary ramped surface concentration with the corresponding flow near isothermal plate with uniform surface concentration.
Analytic Solution of The Unsteady BGK Model for Rarefied Gas between two parallel plates Affected by a Thermal Radiation Field.
Dr Taha Zakaraia Abdel Wahid
Basic Sciences Department, October High Institute for Engineering and Technology, 6th October City, Giza, Egypt.
ABSTRACT
The nonstationary BGK (Bhatnager Gross Krook) model of the kinetic equations for a rarefied gas confined between two parallel plates where the rarefied gas is affected by nonlinear thermal radiation field is presented. The travelling wave solution method is used to get the exact solution of the nonlinear partial differential equations system. These equations were produced from applying the moment method to the unsteady BGK model. Now, a system of nonlinear partial differential equations should be solved which represent an arduous task. The unsteady solution gives the problem a great generality and more applications. The problem is investigated to follow the behavior of the macroscopic properties of the rarefied gas such as the temperature and concentration. The new problem is investigated to follow the behavior of the macroscopic properties of the rarefied gas such as the temperature and concentration. The nonequilibrium thermodynamic properties of the system (gas + the heated plate) are inspected. The entropy, entropy flux, entropy production, thermodynamic forces, kinetic coefficients are obtained. The verification of the Boltzmann Htheorem, Le Chatelier principle and the second law of thermodynamic are presented. The ratios between the different contributions of the internal energy changes based upon the total derivatives of the extensive parameters are estimated via the Gibbs formula. 3Dgraphics illustrating the calculated variables are drawn to predict their behavior and the results are discussed.
A boundary integral method is used to obtain an approximate solution for a plane problem of uncoupled thermoelasticity with mixed thermal and mechanical boundary conditions. The unknown functions in the crosssection are obtained in the form of series in Cartesian harmonics, enriched with harmonic functions that have a singular behavior at the transition points of the mechanical boundary conditions. Boundary collocation is then used to find the coefficients of the expansions. The results are discussed and the functions of practical interest are represented on the boundary and also inside the domain. The locations where possible debonding may take place are noted.
An Alternative Formulation for the Scattering of Electromagnetic Waves
From Vertically Stratified Media
Ehab Adel Mahmoud El_Fayome , Aladin H. Kamel , Hadia S. ElHennawy
Ministry of Interior
Advanced Industrial, Technical and Engineering Center
Electronics and Communications Department, Faculty of Engineering, Ain Shams University
ABSTRACT
A new semianalytical formulation for the computation of the scattered electromagnetic fields from vertically stratified lossy dielectric media is presented. We developed this approach to overcome some of the limitations and difficulties of the existing approaches (FiniteDifference TimeDomain, Finite Element Method, Boundary Element Method, …).
The derivation of the scattered electromagnetic field proceeds through three steps.
In the first step, the Maxwell’s equations are recasted in the form of a volume integral equation on the induced electric polarization current inside the scattering lossy dielectric medium. The volume integral equation method has established itself as a reliable formulation approach for scientific problems and engineering applications related to wave phenomena.
In the second step, a 1D integral eign value problem, on the direction of the stratification, is solved. Using Green’s functions techniques, we show that the resulting set of eign functions form a complete orthonormal set; the orthogonality of the complete set is used to recast the volume integral equation into a linear system; the expansion coefficients are found by solving the linear system.
In the final step, the scattered electromagnetic field is computed by applying Green’s function to the found expansion of the induced electric polarization current.
The results of the proposed scheme are compared with those for a number of cases with known analytical solutions. The comparison is done for a wide range of stratified scatterer size, permittivity and conductivity as well as source operating frequency.
Faculty of Science, Port Said University, Port Said 42521, Egypt
Department of Mathematics, Faculty of Science, Mansoura University, Damietta ElGedida 34517, Egypt
Faculty of Science, Port Said University, Port Said 42521, Egypt
ABSTRACT
Properties of plasma expansion that propagates in an opposite polarity dusty plasma are investigated. Suitable hydrodynamic equations for the dust grains, positive ions, negative ions, and electrons are used. Using selfsimilar transformation, the basic set of nonlinear equations is solved numerically to obtain the expansion properties of the dust dynamics. The relevance of our theoretical model to galactic disk expansion is highlighted.
Combined Effects of Hall Current and Heat Transfer on Peristaltic Transport of a Nanofluid in a vertical tapered channel Through a porous medium
A. I. Abdellateef , Zahoor ul haque
Caledonian college of engineering Oman, University of Glasgow, Scotland, UK
Caledonian college of engineering Oman, University of Glasgow, Scotland, UK
ABSTRACT
The inﬂuences of Hall currents and heat transfer on peristaltic transport of a Nano
ﬂuid in a vertical porous tapered channel through a porous medium are investigated theoretically
and graphically under the assumptions of low Reynolds number and long wavelength. the ﬂow is
investigated in a wave frame of reference. Analytical solutions have been obtained for temperature,
axial velocity, stream function and pressure gradient. Graphical results are sketched for various
embedded parameters.
Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt
Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt
Physics Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
ABSTRACT
Creation of hillocklike nanostructures on the surface of yttrium iron garnet (YIG) by irradiation with energetic C60 is reported. These structures are explained using a plasma expansion approach as a nonlinear phenomenon of plasma physics. Our theoretical model suggested basic fluid equations contain different positive and negative plasma species, as well as electrons. Solving the nonlinear equations, we have an initial idea about the properties of these hillocks creation.
Selçuk University, Science Faculty, Department of Mathematics KonyaTURKEY
ABSTRACT
The spread of the singless Laplacian of a simple graph G is defined as difference between the maximum and minimum eigenvalues of the signless Laplacian matrix of G. In this work, we will present some new lower and upper bounds for the spread of the singless Laplacian of a simple graph G in terms of clique and independence numbers. In the final section, as an application of the theory obtained in here, we will also show some new upper bounds for the spread of the singless Laplacian of tensor products of any two simple graphs.
The electromagnetic field of a vertical dipole above a conducting earth
adel
ass.proff.
ABSTRACT
An exact representation for the electromagnetic field above a conducting earth is investigated theoretically. The time domain response of a vertical magnetic dipole above a conducting halfspace is of a crucial importance in the interpretation of air borne electromagnetic data. The classical approach in finding a solution is to apply Fourier inversion to the formal time harmonic solution, leading to a representation in the form of a double infinite integral.
The effect of reflection on the field of a pulsed point source
adel
ass.proff.
ABSTRACT
We calculate the electromagnetic field emitted by a pulsed point source above a planar interface. The power density spectrum of the wave that is observed of a certain distance from its emitting source usually differs from that of the source excitation, we mention that the modified Caganard method also yields closedform results of the radiation from a point source in a discretely layer medium. The observed power spectrum depends strongly on the wave speeds in two media and the position of the observation point with respect to the interface and the source.
Application of some quantum measures of information to nonlinear interaction of two twolevel atoms and two modes of radiation field
A. S.F. Obada , M. M. A. Ahmed , H. F. Habeba
Department of Mathematics, Faculty of Science, AlAzher University, Nassr City 11884, Egypt
Department of Mathematics, Faculty of Science, AlAzher University, Nassr City 11884, Egypt
Department of Mathematics, Faculty of Science, Menofia University, Shebin Elkom 32511, Egypt
ABSTRACT
In this paper, we study a system of nonlinear interaction of two twolevel atoms and two modes of radiation field. For this system, we study the effect of Stark shift on some quantum measures of information that are applied to the present system, such as, atomic inversion, linear entropy, squeezing phenomenon, quantum field entropy, Negativity, quantum discord, degree of coherence and Q function. It is observed that the Stark shift parameter play an important role on the evolution of these measures.
New Algorithms For One Dimensional Differential Transform Method
Eman Anower Elmabrouk , Dr. Fawzi Abdelwahid
Department of Mathematics, Faculty of Education University of Benghazi, Al Marj, Libya
Department of Mathematics, Faculty of Science, University of Benghazi, BenghaziLibya
ABSTRACT
Abstract
In this work, we reviewed the concept of onedimensional differential transform and studied their properties. We also introduced new useful algorithms and applied the differential transform method to selected linear ordinary differential equations. This study showed that this method is powerful and efficient in finding series solutions for linear differential equations and capable of reducing the size of calculations comparing with other methods
Airy Wave Packet for a Particle in a Time Dependant Linear Potential
mounira berrehail , nadjet benchiheub
Département des Sciences de la matière, Université de Bordj Bou Arreridj, Bordj Bou Arreridj 43000, Algérie
Département des Sciences de la matière, Université de Bordj Bou ArreridjBordj Bou Arreridj 43000, Algérie
ABSTRACT
We study the quantum motion of a particle in the presence of a time dependent linear potential using an operator invariant that is quadratic in p and linear in q within the framework of the LewisRiesenfeld invariant, The special invariant operator proposed in this work is demonstrated to be an Hermitian operator which has an Airy wave packet as its eigenfunction
Dust ionacoustic shock waves in a nonMaxwellian magnetoplasma
S. A. ElTantawy , N. A. ElBedwehy
Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt
Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt
ABSTRACT
The nonlinear features of dust ionacoustic shock waves (DIASWs) in a magnetoplasma containing cold viscous positive ions, a nonextensive electrons, and immobile negatively charged dust grains are investigated. By using the fluid model and employing the reductive perturbation method, the ZakharovKuznetsovBurgers (ZKB) equation has been derived which governs the dynamics of the DIASWs. It is observed that the fundamental properties of the DIASWs are significantly modified by the effects of different parameters such as the nonextensive parameter, the ion gyrofrequency, the dust concentration, the viscosity parameter, and the direction cosine are discussed. The implications of our result in space and laboratory dusty plasmas are discussed.
Effects of polarization force and trapped ions on dust acoustic waves
E. I. ElAwady , N. A. ElBedwehy , S. K. ElLabany
Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt
Department of Physics, Faculty of Science, Damietta University, New Damietta 34517, Egypt
Department of Physics, Faculty of Science, Damietta University, New Damietta 34517, Egypt
ABSTRACT
Linear and nonlinear lowfrequency dust acoustic waves in a strongly coupled dusty plasma are investigated. Strong correlation and polarization force effects are examined on the propagation of linear waves. While to describe the nonlinear waves, a reductive perturbation technique is used to reduce the basic equations into one evolution equation. Solving the latter using tanh method, shock solution is obtained. Furthermore, for certain conditions of plasma parameters; only solitary waves can exist. Dependence of solitons and shocks propagation on various plasma parameters are examined.
Entanglement of twocupled atoms in presence of two external magnetic
fields
E.M.Khalil , S. Sanad
Mathematics Department, Faculty of Science, AlAzher University, Nassr City 11884, Cairo, Egypt
Mathematics Department, Faculty of Science (Girls Branch), AlAzhar University, Nasr City 11884, Cairo, Egypt
ABSTRACT
In this paper some aspects through a atomatom interaction in presence
of an external classical fields in and directions are presented. Analytical solution under
a certain parametric conditions are obtained. The dynamical operators are determined
through the equation of motion. After obtained the dynamical operators are employed to
perform a careful investigation of the temporal evolution of the atomic inversion, linear
entropy, variance squeezing and entropy squeezing. The influence of the external classical
fields on the atomic inversion and linear entropy is examined. Our study of the linear
entropy shows that the system is almost in a mixed state, and the maximum value of
entanglement occurs around 0.5. Finally we examine the variance squeezing and entropy
squeezing for different values of the external classical terms parameter leads to different
observation of the squeezing in the quadrature’s. We have also shown that classical terms
lead to an increase of the amount of squeezing for all quadrature’s and squeezing period
Nonlinear waves in Saturn’s ring two temperature dusty plasma
Ms. S. M. Ahmed , W. M. Moslem
Department of Mathematics, Faculty of Science, Suez University, Suez, Egypt
Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt
ABSTRACT
The generation of dustacoustic nonlinear waves in dusty plasma composed of negatively charged dust grains, isothermal electrons, and twotemperature isothermal ions is investigated. Solving the fluid equations using perturbation method,we derivenonlinear evolution equation that enables us to examine the nonlinear phenomena in different Saturn’s rings (i.e.Ering, Fring, and Bring). The existence region of the created waves is defined and different plasma parameters are discussed on the wave propagation.
A Jacobi elliptic functions method for constructing travelling wave solutions to nonlinear partial differential equations arising in mathematical physics
S. M. Moawad , O. H. ElKalaawy , E. T. Hussain
Department of Mathematics, Faculty of Science, BeniSuef University, BeniSuef, Egypt
Department of Mathematics, Faculty of Science, BeniSuef University, BeniSuef, Egypt
Department of Mathematics, Faculty of Science, BeniSuef University, BeniSuef, Egypt
ABSTRACT
In this work, we present a Jacobi elliptic functions method to solve the KleinGordon equation, generalized KleinGordon equation, KleinGordonZakharov equations and perturbed nonlinear Schrӧdinger equation with Kerr law nonlinearity. By using this method, we obtain the exact travelling wave solutions to these equations. The proposed method is effective and can be applied to wide classes of partial differential equations arising in mathematical physics.
Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia
Department of Computer Science, CIT College, Taif University, Taif, Saudi Arabia
Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia
ABSTRACT
Realistic quantum systems are not closed in different studies of quantum information due to the rapid destruction of crucial quantum properties. Therefore, it is important to study the dynamical behavior of the different information quantifiers in the case of closed governed by the Tavis Cummings model. Thus, the interaction between composite quantum systems and understanding the correlations between different quantum information quantifiers have attracted more interest. So in the first part of this project, we have discussed the correlation between the quantum Fisher Information and quantum entanglement for the system under consideration. Analytic results under certain parametric conditions are obtained, by means of which we have analyzed the influence of different parameters on the entanglement measures and quantum Fisher information for two types of the estimator parameter. We have investigated the quantum Fisher information flow and nonlocal correlation between the two qubits which is measured by the concurrence and the entanglement between the two qubits and optical field which is measured by the von Neumann entropy in terms of the parameters involved in the whole system. The effect of the qubit motion though the velocity parameter in the evolution of the system dynamics; nonlocal correlation and quantum Fisher information have been discussed.
Derivation of equilibrium equations and threedimensional solutions for nonlinear fieldaligned ideal magnetohydrodynamics with compressible flows
S. M. Moawad , D. A. Ibrahim
Department of Mathematics, Faculty of Science, BeniSuef University, BeniSuef, Egypt
Department of Mathematics, Faculty of Science, BeniSuef University, BeniSuef, Egypt
ABSTRACT
The equilibrium properties of threedimensional ideal magnetohydrodynamics (MHD) with compressible flows are investigated. The governing equations are taken in the steady state with magnetic field parallel to the plasma flow. The equilibrium equations of compressible MHD flows are derived and described in a mathematical mode. The existence of threedimensional exact solutions to these flows is investigated. Several classes of threedimensional exact solutions of several cases of nonlinear equilibrium equations are presented.
CLASSICAL SUMMATION THEOREMS: Generalizations and Applications
Medhat A. Rakha
Mathematics Department  Suez Canal University  Ismailia  Egypt
ABSTRACT
It is well known that classical summation theorems such as of Gauss, Gauss second, Kummer and Bailey for the series 2F1 and Watson, Dixon and Whipple for the series 3F2 play an important role in the theory of hypergeometric and generalized hypergeometric series. Applications of these summation theorems are well known.
The aim of this talk is to provide the generalizations of the abovementioned classical summation theorems in the most general case.
Control of the entanglement of a twolevel atom interacting with radiation field via a phase damping
A.S. F. Obada , E.M. Khalil , M. M. A. Ahmed , M. M. Yousef
Mathematics Department, Faculty of Science, AlAzhar University, Nasr City 11884, Cairo, Egypt.
Mathematics Department, Faculty of Science, AlAzhar University, Nasr City 11884, Cairo, Egypt.
Mathematics Department, Faculty of Science, AlAzhar University, Nasr City 11884, Cairo, Egypt.
Mathematics Department, Faculty of Science, AlAzhar University, Nasr City 11884, Cairo, Egypt.
ABSTRACT
In this context the interaction between twolevel atom and radiation field in the presence of phase damping terms is studied. In particular the temporal evolution of the mutual information, the fidelity and the Qfunction are calculated. The mutual entropy and the fidelity are used as an indicator of the degree of entanglement between the subsystem. The Qfunction has been also considered to give more information in the phase space about the system. The results indicate the sensitivity of these aspects to changes in the decay parameter.
Bounds on Eccentricity Version of Atom Bond Connectivity Index of Graphs
Yasar Nacaroglu , A. Dilek Maden
Selçuk University, Science Faculty, Department of Mathematics KonyaTURKEY
Selçuk University, Science Faculty, Department of Mathematics KonyaTURKEY
ABSTRACT
Let G be a connected graph with vertex set V(G) and edge set E(G).
Farahani (2013) defined eccentricity version of Atom Bond Connectivity Index. They exhibited this new index and introduced a closed formula of ABC5 for a famous family of Benzenoid. In
this paper, we establish bounds for eccentricity atom bond connectivity
index.
A Moving Threelevel Atom Interacting with a TwoMode Field in Squeezed Coherent States with a Nonlinear Kerrlike Medium and Stark Effect: some atomfield aspects
A.S. F. Obada , M. M. A. Ahmed , Ahmed Salah , Ahmed M. Farouk
Mathematics Department, Faculty of Science, AlAzher University, Nassr City 11884, Cairo, Egypt
Mathematics Department, Faculty of Science, AlAzher University, Nassr City 11884, Cairo, Egypt
Mathematics & Theoretical Physics Department, Nuclear Research Center, Atomic Energy Authority, Cairo, Egypt
Mathematics Department, Faculty of Science, AlAzher University, Nassr City 11884, Cairo, Egypt
ABSTRACT
In this paper, the interaction of a moving threelevel atom and a twomode quantized electromagnetic cavity field is extended to involve the effects of the atomic motion. Detuning parameters, Kerr nonlinearity, Stark Shift contributions and arbitrary forms of intensitydependent atomfield coupling have been taken into account. The constants of motion and the wave function when the atom is initially prepared in superposition states have been obtained. We calculate some statistical aspects such as purity, Mandel factor, momentum increment and momentum diffusion.
A Cosmological Inﬂationary Model Using Optimal Control
Moutaz Ramadan
Faculty of Science, Port Said University, Egypt.
ABSTRACT
The evolution of a cosmological inﬂationary model, driven by a selfinteracting scalar ﬁeld, is considered. The problem is formulated as an optimal control problem. By applying Pontryagin’s maximum principle, a new solution is obtained.
Electromagnetohydrodynamic peristaltic flow of blood through a flexible channel with a slip velocity.
Kh. S. Mekheimer , R. E. AboElkhair , A. M. A. Moawad
Mathematics and Statistics Department, Faculty of Science, Taif University, Hawia 888, Taif, KSA and Mathematical Department, Faculty of Science (Men), AlAzhar University, Nasr City 11884, Cairo, Egypt.
Mathematical Department, Faculty of Science (Men), AlAzhar University, Nasr City 11884, Cairo, Egypt.
Mathematical Department, Faculty of Science (Men), AlAzhar University, Nasr City 11884, Cairo, Egypt.
ABSTRACT
In the present investigation, the effects of both wall slip conditions and electrokinetic effects (electroosmosis) on electromagnetohydrodynamic peristaltic flow of Newtonian fluid in a channel have been studied under the assumptions of long wavelength and lowReynolds number. The flow is measured in wave frame of reference moving with uniform velocity. The analytical results are acquired for the velocity pro file and pressure gradient distribution. The linearlized PoissonBoltzmann equation is solved to obtain the (electrical double layer)EDL potential distribution.The pressure rise data is extracted by numerical technique. The graphical effect of various observing parameters on pressure rise, frictionless force axial velocity are sketched manually. The expansion and contraction phenomenon of the whole bolus is also displayed in the end.
Lie point symmetries for a magneto couple stress fluid in a porous channel with expanding or
contracting walls and slip boundary condition.
R. E. AboElkhair
Mathematics Department, Faculty of Science, AlAzhar University, Nasr City, 11448, Cairo, Egypt.
ABSTRACT
In this paper, an incompressible flow of a couple stress fluid with magnetic field in a porous channel with expanding or contracting walls and slip boundary condition is considered. Lie group analysis has been employed and the group invariant solutions are obtained, the governing equations are reduced to nonlinear ordinary differential equations. The resulting equations are solved analytically. The graphs for velocity components and pressure distribution for different values of the fluid and geometric parameters are plotted and discussed.