In this paper, the propagation of electron acoustic waves in a collision less Fermi plasma is investigated analytically by employing Quantum Hydrodynamic (QHD) model. The plasma system taken into account consists of hot and cold electrons and ions. The modified Korteweg-de Vries Burgers equation is derived in order to study the shock profile of electron acoustic waves numerically in a viscous plasma at the critical regime. The standard reductive perturbation method is employed to derive the mK-dV Burgers equation. Standard soliton solutions are used for quantitative and qualitative study of spatial and temporal evaluation of shock waves.
We present approximate solutions of the both the modified Klein-Gordon (MKGE) and modified Schrodinger equation (MSE) containing the modified Hulthen and modified Kratzer potential using the procedure of Bopp's shift method and perturbation theory in addition to the Greene-Aldrich approximation method of handling centrifugal barriers. This study is conducted in the relativistic and nonrelativistic non-commutative 3-dimensional real space (RNC: 3D-RS) and (NRNC: 3D-RS) symmetries, respectively. The Hulthen-Kratzer potential model is extended to include new radial terms. Furthermore, this potential model is proposed to study some selected diatomic molecules, namely N-2, I-2, CO, NO and HCl. The ordinary Bopp's shift method and perturbation theory are surveyed to get generalized excited states energy as a function of the shift energy and the energy E-nl of the HKP model. Furthermore, the obtained perturbative solutions of the discrete spectrum were dependent on Gamma function, the discreet atomic quantum numbers (j, l, s, m) and the potential parameters (V-0,alpha,r(e), D-e) , and the NC-parameters, which are generated with the effect of (space-space) noncommutative properties. We have also applied our results on diatomic-molecules with spin-0 and spin-1, and have shown that the modified Klein-Gordon equation MKG under the MHKP model becomes similar to the Duffin-Kemmer equation.
The quantum mechanical photon is described as a mathematical point-like elementary bosonic particle that is characterized by its energy (h omega), linear momentum (h), and angular momentum (h), and that propagates a circularly-polarized electromagnetic force at the speed of light (c). The quantum mechanical photon is also considered to be its own antiparticle. With this model of the photon, it is impossible, in principle, to visualize how the photon transfers energy, linear momentum, angular momentum, or the electromagnetic force to matter, and how a photon interacts with nearby photons resulting in interference effects. I have explained the enigmatic properties of the quantum mechanical photon with the model of the binary photon, which postulates that that photon is not an elementary particle and its own antiparticle, but a composite entity composed of a particle of matter and its conjugate antiparticle of antimatter. These conjugate particles are known as semiphotons. Unlike the quantum mechanical photon, the binary photon has extension is space, giving intelligibility and understandability to concepts such as the energy distribution within a photon, the cross-section of a photon, the angular momentum of a photon, the rotational energy of a photon, and the electromagnetic fields of a photon. In this contribution, I depict the wave functions, which are solutions to the Schrodinger equation for a boson, in three-dimensional Euclidean space. The wave functions describe the paths of the corpuscular semiphotons in three-dimensional Euclidean space and unidirectional and absolute Newtonian time. The wave functions that describe the movement of semiphotons give intelligibility and understandability to the wave-particle duality, and they yield the mechanical properties of the binary photon. By assuming that the binary photon is electrically neutral as a consequence of the semiphotons having equal and opposite charge, I show that the propagating binary photon produces a transverse sinusoidal electric field and a three-dimensional magnetic field that are orthogonal to each other and a quadrature out-of-phase with each other. The phase characteristics of the electric and magnetic fields are consistent with Faraday's law and the Ampere-Maxwell law, but inconsistent with Maxwell's electromagnetic waves, which were derived upon the assumption that light is electrically neutral due to the absence of charge (del center dot E = 0). By endowing the quantum of light with equal and opposite charge and using Maxwell's equations, the model of the binary photon offers an alternative way to address the principle of relativity that demands that there are no preferred frames in reckoning the speed of light. In this contribution, I provide animations that are not only consistent with the canonical mechanical and electromagnetic properties of light, but in addition, they give Anschaulichkeit, intelligibility, and understandability to the nature of light. Many people consider that science is the body of existing knowledge and scientists add to this knowledge in a straightforward, logical manner. This commonly accepted viewpoint is at variance with what another Nobelist, Szent-Gyorgyi, said, "A discovery must be, by definition, at variance with existing knowledge." The fact that well-meaning people and good scientists can have such opposing views shows that C. P. Snow's division of our society into two cultures of arts and science is wrong; there are two cultures in science itself. However, there is truly but one culture in which art, literature, music, and science are one, for all the basic attributes of the arts-of beauty, aesthetics, simplicity and the wonderment of the human condition-can be expressed in many ways, but are an essential part of our civilization.
In this paper, the main focus of discussion is the evolution of the Korteweg-de Vries(KdV) equation by employing the standard reductive perturbation technique. The evolution of the KdV equation was derived using the conservation laws for DAW(Dust Acoustic Wave) mode in plasma containing dust particles and positrons to ascertain the structure of solitons. In this paper, the KdV equation has been solved both numerically and analytically. Further, setting up the NLSE(Non-Linear Schrodinger Equation) studies about Rogue wave and Dynamical system has been carried out from the derived KdV equation. In addition to that, linear and non-linear analysis of Dispersion relation and group velocity profile for the DAW mode in plasma also has been discussed. All studies are supported by graphical representation to show all analytical results follow the theoretical model.
Cosmological models with time dependent displacement field in the cosmological theory based on Lyra's geometry have been discussed. Exact solutions have been obtained for a spatially flat FRW model by considering a particular form for the time dependent displacement field. We have also obtained conditions under which the matter-dominated, flat universe undergoes decelerated or accelerated expansions. Accelerated expansion of the Universe is of particular interest in view of the recent observations.
We have studied a static conformally flat cylindrical symmetric perfect fluid distribution with improved energy-momentum tensor developed by Ray and Smalley and obtain an exact solution in the context of Einstein-Cartan Theory. The explicit expressions for pressure, spin, energy density, expansion, rotation and shear have also been found.
The basic aim of thisstudy is to use one dimensional Quantum hydrodynamics model to analyse the solitary profiles and shock fronts of Electrostatic and Ion acoustic waves in semi classical plasma, by using the governing equations to derive the KdV-Burgers equation with the help of standard perturbation techniques and stretching expressions, and then extending the study of the nonlinearities of the ion acoustic waves to obtain the Non Linear Schrodinger's Equation and studying the formation of rogue waves from it, also analyzing the2D and 3D plots to conclude certain observable and experimental facts. The paper also includes the study of the dynamics of the system and it' sbehavioral changes when subjected to small perturbations.
Images of sub-resolution fluorescent microspheres taken with a laser scanning confocal microscope do not appear as spheres but as prolate ellipsoids relative to the optical axis of a microscope. The full width at half maximum (FWHM) intensity of the major axis of the ellipsoid is greater than the FWHM intensity of the minor axis of the ellipsoid by pi n/NA, where pi is a factor that depends on the geometry of the binary photon and N/NA is a factor that depends on the geometry of the optical system. The standard equations of confocal microscopy are inadequate describers and predictors of these results. However, the lateral and axial resolution equations that are based on Rayleigh's criterion and derived from the Kirchhoff diffraction equation whose assumptions are met by the binary photon are not only better describers and predictors but also explainers of the quantitative spatial aspects of the images. The accuracy of the equations that are based on the model of the binary photon in predicting the FWHM of the images of the fluorescent microspheres support the claim that binary photons, which exhibit wave-particle duality as a consequence of the motions of two oppositely-charged particles that give rise to wave-like electromagnetic fields may be the fundamental and irreducible component of light.
A study on nonlinear dynamics of head-on collision of electron acoustic solitons (EASs) in a weakly relativistic unmagnetized plasma composed of stationary ions, cold inertia ions and het Boltzmann distributed electrons is carried out. Two Korteweg-de Vries (KdV) equations are derived by employing extended Poincare Lighthill-Kou (PLK) method. In the given range of plasma parameters, only negative potential EASs are observed. Further, from the solutions of KdV equations dynamics of head-on collision between two EASs has been illustrated. The variation of phase shifts for the different plasma parameters has been analyzed. The results of present investigation may have enormous significance in the context of plasma heating process in astrophysical regions.
An investigation is presented to study the propagation properties of low frequency ion-acoustic shocks in quantum plasma whose constituents are electrons (inertialess), positive ions and negatively charged dust grains both mobile. The Quantum hydrodynamic (QHD) model has been considered to investigate dust-ion acoustic shock structures in two-fluid quantum plasma. The reductive perturbation technique is employed to derive the Korteweg-de Vries-Burgers (KdV-B) equation whose solution has the form of shock structures and in the limiting case, solitons structures are observed. The combined effects of variation of different physical parameters on the characteristics of DIA shock and solitary structures are analyzed. The time evolution analysis of DIA shocks has also been carried out to see the occurrence of monotonic as well as oscillatory shocks in the given quantum plasma system. The results of present investigation may be useful in the and understanding of fundamental plasma phenomenon in an astrophysical plasma environment.
Modulational instability (MI) of ion acoustic waves (IAWs) in a weakly relativistic warm adiabatic unmagnetized plasma whose constitutes are ion fluid and q-non-extensively distributed electrons, using a reductive perturbation technique (multiple scales) is investigated. The domain of the stability and instability is determined. The solution of ion acoustic rogue waves (IARWs) are found. The effect of the physical parameters such as relativistic factor u(0)/C and temperature ratio T-i/T-e (T-i is the ion temperature and T-e is the electron temperature) as well as the distribution parameter q on the instability of the system and rogue wave (RW) width and amplitude are studied. Finally, the validity of our results in various regions in astrophysical plasma is briefly discussed.
We investigate the dual arc volumetric modulated arc therapy (VMAT) technique and its pretreatment quality control for patients with prostate cancer. The forward technique multi-entrance three-dimensional conformal radiation therapy (ME-3DCRT) and VMAT technique were compared with respect to plan quality (homogeneity and conformity indexes, and the organs at risk doses) and treatment efficiency (i.e., treatment time, monitors unity) for Eleven high risk prostate cancer patients treated with dual-arc volumetric modulated arc therapy (one fraction per day and five times a week) in the National Institute of Oncology Rabat-Morocco, between 2017 and 2019. Furthermore, the statistical analysis and the VMAT dosimetric evaluation were done.
Electron Acoustic Solitary structures in Fermi Plasma with two temperature electrons have various applications in space and laboratory-made plasmas. Formulation of an adequate theory is important to understand various physical systems with various physical parameters. The motion of two temperature electrons in a quantum Fermi plasma system highly affects the solitary profile of the system. We study the quantum Fermi plasma system with two temperature electrons where the streaming velocities of two-electron population are opposite. We consider quantum hydrodynamic model (QHD) and derive a linear dispersion relation for the system. For non-linear study of the system, we use standard perturbative technique to derive Kortewegde Vries Burger's equation and show the evolution of solitary profile with different plasma parameters. We analyse the stable Rouge wave structure using NLSE and show simulation results. We study the dynamical properties and phase plot for two-stream quantum Fermi plasma system with two temperature electrons.
We investigate the impact of the table's electronic density on the calculated and received dose for the energy 6MV. And we determine the density of the carbon fiber and foam with the best agreement between the measured and Monaco treatment planning system calculated dose.
Compact star structures are investigated in the framework of General Relativity using a modified TOV equation. The modified TOV equation is derived by incorporating the cosmological constant in the field equations. A quark equation of state signified by a bag constant is used to integrate the TOV equations. Depending on the choice of the cosmological constant and bag constant, stellar properties such as mass and radius of the compact star are found to change effectively. Also, we have obtained the mass-radius and mass-density relationship of compact star.
Michael Faraday discovered that linearly polarized light could be rotated by a magnetic field as it propagated through a piece of "heavy glass." Since the effect could not be observed in air, Faraday assumed that the magnetic field acted on the glass and that the glass influenced the magnetic properties of light itself. According to the standard theory, the magnetic field causes the glass, which has a single refractive index in the absence of a magnetic field, to become optically active as a result of the Lorentz force acting on the electrons in the glass. As a result, the glass develops one refractive index for right circularly polarized (RCP) light and another refractive index for left circularly polarized (LCP) light. This results in the rotation of the azimuth of polarization. While the discovery of the Faraday effect was important evidence for the electromagnetic theory of light, the magnetic property of light itself that responds to the changes in the refractive index remains enigmatic. Here we suggest that if light be described as being composed of equal and opposite moving charges within each binary photon, the magnetic field would act both on the glass and on the light itself. The binary photon model proposes that the photon is not an elementary particle but a complex of two particles that are conjugate in terms of mass, electric charge, and sense of rotation, whose movements generate a linearly polarized transverse electric field and a circularly polarized magnetic field that is orthogonal to the electric field and phase shifted by one quarter wavelength. The binary photon contains an electric dipole and a magnetic moment, which logically seem to be a sine qua non for the carrier of the electromagnetic force. As a result of the electromagnetic properties of the binary photon, the force exerted on the binary photons by the applied magnetic field used to demonstrate the Faraday effect would result in the transformation of binary photons with a single wavelength into binary photons with two different wavelengths. The binary photons with two different wavelengths would no longer experience the same refractive index as they propagated through the glass because by necessity, the glass required to show the Faraday effect with a relatively short geometrical path length must have high dispersion and a low Abbe number. As a result of the high dispersion and low Abbe number, the transformed binary photons with the shorter wavelength would experience a higher refractive index and the transformed binary photons with the longer wavelength would experience a lower refractive index. Consequently, as they propagated through the glass, the shorter wavelength binary photons would be retarded relative to the longer wavelength binary photons and the azimuth of polarization would be rotated. The model of the binary photon and its response to a magnetic field describes and explains the magnetic properties of light proposed by Faraday and the requirement for high dispersion glass to observe the Faraday effect. In addition, the electromagnetic properties of the binary photon have the required number of degrees of freedom to account for other magneto-optical phenomena such as the Zeeman effect.
Relativistic theory has been successful in describing nuclear phenomena. Therefore, this article investigated shell and cluster models in a relativistic manner In this regards, considering appropriate potential for a few-body system by Jacobean coordinate, Klein-Gordon equation was solved by Nikiforov-Uvarov method. Then ground state energy and the first excited state of several light nuclei were calculated and compared with experimental values, which showed the efficiency of this model for investigation of energy levels of different nuclei.
In this paper we consider the propagation of electron acoustic solitary waves in semi-classical plasma. Using quantum hydrodynamic model we obtain the dispersion relation and study the parametric variations of the dispersion curve. We further study the solitary profiles and its evolution by using the Korteweg-de Vries Burger equation. We extended our work to the study of Rogue waves. The results provide with interesting findings that has laboratory and astrophysical importance.
Stationary nonlinear localized electrostatic (ES) waves may be excited when an electron beam is injected into a plasma. In the present investigation, the propagation properties of two dimensional ion-acoustic solitons have been studied in a plasma composed of ion fluid, hot electrons obeying Cairns distribution and embedded with electron beam. Electron beams exist in different space and astrophysical environments and influence the properties of nonlinear structures. In this paper, we consider model equations and derive the KP equation using reductive perturbation technique. Using its solution, numerical analysis is carried out. It is seen that negative potential ion-acoustic solitons are observed under the influence of variation of beam density, beam velocity and non-thermal parameter. The findings of this investigation may be of great importance to understand the nonlinear phenomena in the upper layer of the magnetosphere where Cairns distributed hot electrons, ions and electron beam may exist.
