Exact Solutions of Axially Symmetric Bianchi Type-I Cosmological Model in Lyr...IOSR Journals
In this paper we have obtained axially symmetric Bianchi type-I cosmological models for perfect
fluid distribution in the context of Lyra’s manifold. Exact solutions of the field equations are obtained by
assuming the expansion in the model is proportional to the shear . This leads to the condition
A Bn
where A and B are scale factors and n( 0) is a constant. Some kinematical and physical parameters of the
model have been discussed. The solutions are compatible with recent observations.
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Existence and Stability of the Equilibrium Points in the Photogravitational M...ijceronline
In this article we have discussed the equilibrium points in the photogravitational magnetic binaries problem when the bigger primary is a oblate spheroid and source of radiation and the small primary is a oblate body and have investigated the stability of motion around these points.
An exact solution of einstein equations for interior field of an anisotropic ...eSAT Journals
Abstract
In this paper, an anisotropic relativistic fluid sphere with variable density, which decreases along the radius and is maximum at
the centre, is discussed. Spherically symmetric static space-time with spheroidal physical 3-space is considered. The source is an
anisotropic fluid.
The solution is an anisotropic generalization of the solution discussed by Vaidya and Tikekar [1]. The physical three space
constant time has spheroidal solution. The line element of the solution can be expressed in the form Patel and Desai [2]. The
material density is always positive. The solution efficiently matches with Schwarzschild exterior solution across the boundary. It is
shown that the model is physically reasonable by studying the numerical estimates of various parameters. The density vs radial
pressure relation in the interior is discussed numerically. An anisotropy effect on the redshift is also studied numerically.
Key Words: Cosmology, Anisotropic fluid sphere, Radial pressure, Radial density, Relativistic model.
Exact Solutions of Axially Symmetric Bianchi Type-I Cosmological Model in Lyr...IOSR Journals
In this paper we have obtained axially symmetric Bianchi type-I cosmological models for perfect
fluid distribution in the context of Lyra’s manifold. Exact solutions of the field equations are obtained by
assuming the expansion in the model is proportional to the shear . This leads to the condition
A Bn
where A and B are scale factors and n( 0) is a constant. Some kinematical and physical parameters of the
model have been discussed. The solutions are compatible with recent observations.
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Existence and Stability of the Equilibrium Points in the Photogravitational M...ijceronline
In this article we have discussed the equilibrium points in the photogravitational magnetic binaries problem when the bigger primary is a oblate spheroid and source of radiation and the small primary is a oblate body and have investigated the stability of motion around these points.
An exact solution of einstein equations for interior field of an anisotropic ...eSAT Journals
Abstract
In this paper, an anisotropic relativistic fluid sphere with variable density, which decreases along the radius and is maximum at
the centre, is discussed. Spherically symmetric static space-time with spheroidal physical 3-space is considered. The source is an
anisotropic fluid.
The solution is an anisotropic generalization of the solution discussed by Vaidya and Tikekar [1]. The physical three space
constant time has spheroidal solution. The line element of the solution can be expressed in the form Patel and Desai [2]. The
material density is always positive. The solution efficiently matches with Schwarzschild exterior solution across the boundary. It is
shown that the model is physically reasonable by studying the numerical estimates of various parameters. The density vs radial
pressure relation in the interior is discussed numerically. An anisotropy effect on the redshift is also studied numerically.
Key Words: Cosmology, Anisotropic fluid sphere, Radial pressure, Radial density, Relativistic model.
-type and -type four dimensional plane wave solutions of Einstein's field eq...inventy
In the present paper, we have studied - type and -type plane wave solutions of Einstein's field equations in general theory of relativity in the case where the zero mass scalar field coupled with gravitational field and zero mass scalar field coupled with gravitational & electromagnetic field and established the existence of these two types of plane wave solutions in . Furthermore we have considered the case of massive scalar field and shown that the non-existence of these two types of plane wave solutions in GR theory.
On the Mathematical Structure of the Fundamental Forces of NatureRamin (A.) Zahedi
The main idea of this article is based on my previous articles (references [1], [2], [3]). In this work by introducing a new mathematical approach based on the algebraic structure of integers (the domain of integers), and assuming the “discreteness” of physical quantities such as the components of the relativistic n-momentum, we derive all the mathematical laws governing the fundamental forces of nature. These obtained laws that are unique, distinct and in the form of the complex tensor equations, represent the force of gravity, the electromagnetic (including electroweak) force, and the (strong) nuclear force (and only these three kinds of forces, for all dimensions D ≥2). Each derived tensor equation contains the term of the mass m_0 (as the invariant mass of the supposed force carrier particle), as well as the term of the external current (as the external source of the force field). In some special cases, these tensor equations are turned into the wave equations that are similar to the Pauli and Dirac equations. In fact, the mathematical laws obtained in this paper, are the corrected and generalized forms of the current field equations including Maxwell equations, Yang-Mils equations and Einstein equations, as well as (in some special conditions) Pauli equation, Dirac equation, and so on. A direct proof of the absence of magnetic monopoles in nature is one of the outcomes of this research, according to the unique formulations of the laws of the fundamental forces that we have derived.
Keywords: Foundations of Physics, Ontology, Discrete Physics, Discrete Mathematics, The Fundamental Forces of Nature.
Comments: 51 Pages. Expanded version of my previous articles:
Ramin (A.) Zahedi, "Linearization Method in the Ring Theory," Bulletin of the Lebedev Physics Institute, Springer-Verlag, No. 5-6, 1997;
Ramin (A.) Zahedi, "On the Connection Between Methods of the Ring Theory and the Group Approach", Bulletin of the Lebedev Physics Institute, Springer-Verlag, No. 7-8, 1997.
PACS Classifications: 04.20.Cv, 04.50.Kd, 04.90.+e, 04.62.+v, 02.10.Hh, 02.10.Yn, 02.20.Bb, 02.90.+p, 03.50.-z, 03.65.Fd, 03.65.Pm, 03.50.Kk, 12.40.-y, 12.60.-i, 12.10.Dm, 12.10.-g.
External URL: http://arXiv.org/abs/1501.01373. (arXiv:1501.01373 [physics.gen-ph])
Copyright: CC Attribution-NonCommercial-NoDerivs 4.0 International
License URL: https://creativecommons.org/licenses/by-nc-nd/4.0/
Exact Solutions of the Klein-Gordon Equation for the Q-Deformed Morse Potenti...ijrap
In this work, we solve the Klein-Gordon (KG) equation for the general deformed Morse potential with
equal scalar and vector potentials by using the Nikiforov-Uvarov (NU) method, which is based on the
solutions of general second-order linear differential equation with special functions. The energy
eigenvalues and corresponding normalized eigenfunctions are obtained. It is found that the eigenfunctions
can be expressed by the Laguerre polynomials. Our solutions have a good agreement with earlier study.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
A pictorial method of visualizing curl & determinant operation utilized i...ijscmcj
Curl and Determinant operations are well known in the field of Electromagnetics and fluid dynamics. Famous Maxwell’s equations involve curl operation. Though this operation is widely used to represent rotation, we do not have sufficient literature explaining how this operation represents rotation.
Most of the books omit detailed discussion on the physical interpretation of the Curl and Determinan operation. In this paper we have attempted to develop a pictorial method to provide a logical proof showing the versatility of this operation to study the rotating vectors. We further show how this pictorial method simplifies the fundamental expression with regard to determinants.
On Rational Physics: a Basic Formalism for Relativistic Physics and "A Unique...Ramin (A.) Zahedi
Copyright: CC Attribution-NonCommercial-NoDerivs 4.0 International.
License URL: https://creativecommons.org/licenses/by-nc-nd/ .
Comments: 99 Pages. A summary of a submitted and accepted research project, Ramin Zahedi, (On "Foundations of Physics"), Japan, 2012 - 2015; (Expanded version).
KeyWords: "A Unique Mathematical (Axiomatic) Prediction of Eight New Elementary Particles, Including: 'Four Charge-less Raight-Handed Spin-1/2 Fermions (Two Leptons and Two Quarks)', 'One Spin-3/2 Fermion', and 'Three Spin-1 (massive) Gauge Bosons';" CPT Symmetry as the Only Combunation of C, P, and T Symmetries Definable for Interacting Fields"; Time-Reversal Symmetry and the Numebr of Space-Time Dimensions; Monopoles and the Issue of their Existence in Nature.
This article has been invited and presented at the following international conferences:
- The 2016 SIAM International Conference on Mathematical Aspects of Materials Science, Philadelphia, USA, 2016. (https://www.siam.org/meetings/ms16)
- The 17th International Conference on Quantum Foundations: Quantum and Beyond, International Centre for Mathematical Modeling in Physics, (ICMM), Linnaeus University, Sweden, 2016. (https://lnu.se/en/qb)
-The 4th International Conference on New Frontiers in Physics, CERN Organized Conference (Europe). (https://indico.cern.ch/e/icnfp2015)
- The 2016 International Conference on Algebraic Geometry and Mathematical Physics, University of Tromsø, Norway, 2016. (https://site.uit.no/)
- The XXXVII Max Born International Symposium, International Conference on Non-commutative Geometry, Quantum Symmetries and Quantum Gravity (II), Wroclaw University, Poland, 2016. (http://ift.uni.wroc.pl/~mborn37)
- The GRavitational-wave Astronomy International Conference in Paris, Institute d‘Astrophysique de Paris (IAP), The University of Paris VI - Sorbonne University, CNRS, LERU, EUA, Paris, France, 'Supported by European Union's 7th Framework Prog.: FP7/PEOPLE-2011-CIG,‘ 2016. (http://www.iap.fr/vie_scientifique/ateliers/GravitationalWave/2016/scripts/abstract.aspx)
- The 22nd Internnational Australian Institute of Physics Congress (AIP), University of Queensland, Australia, 2016. (http://appc-aip2016.org.au)
- The 21st International Conference on General Relativity and Gravitation, Columbia University, New York, USA, 2016. (http://www.gr21.org).
External URLs: https://Cds.CERN.ch/record/1980381/, https://INSPIREHEP.net/record/1387680/, http://Eprints.Lib.Hokudai.ac.jp/dspace/handle/2115/59279/, https://www.OpenAire.EU/search/publication?articleId=dedup_wf_001::422af8dcdfbae42429965b16b61f0e94, https://Hal-UNIV-PARIS3.archives-ouvertes.fr/USPC/hal-01547739 , http://mts-srep.NATURE.com/srep_files/2017/07/20/00174434/00/174434_0_related_ms_4909193_pttcpw.pdf , https://hal-PARIS1.archives-ouvertes.fr/hal-01547739 , https://indico.CERN.ch/event/344173/session/22/contribution/422/attachments/1140145/1646101/R.a.Zahedi--OnDiscretePhysics-Jan.2015-signed.pdf.
Analytical Solution Of Schrödinger Equation With Mie–Type Potential Using Fac...ijrap
we have obtained the analytical solution of Schrödinger wave equation with Mie – type potential
using factorization method. We have also obtained energy eigenvalues of our potential and the
corresponding wave function using an ansatz and then compare the result to standard Laguerre’s
differential equation. Under special cases our potential model reduces two well known potentials such as
Coulomb and the Kratzer Feus potentials.
To the Issue of Reconciling Quantum Mechanics and General RelativityIOSRJAP
The notion of gravitational radiation as a radiation of the same level as the electromagnetic radiation is based on theoretically proved and experimentally confirmed fact of existence of stationary states of an electron in its gravitational field characterized by the gravitational constant K = 1042G (G is the Newtonian gravitational constant) and unrecoverable space-time curvature Λ. If the numerical values of K 5.11031 Nm2 kg-2 and =4.41029 m -2 , there is a spectrum of stationary states of the electron in its own gravitational field (0.511 MeV ... 0.681 MeV).Adjusting according to the known mechanisms of broadening does not disclose the broadening of the registered portion of the emission spectrum of the micropinch. It indicates the presence of an additional mechanism of broadening the registered portion of the spectrum of the characteristic radiation due to the contribution of the excited states of electrons in their own gravitational field. The energy spectrum of the electron in its own gravitational field and the energy spectra of multielectron atoms are such that there is a resonance of these spectra. As obvious, the consequence of such resonant interaction is appearance, including new lines, of electromagnetic transitions not associated with atomic transitions. The manuscript is the review of previously published papers cited in the references.
This paper considers the problem of magneto-hydrodynamics (MHD) Newtonian and non-Newtonian nano fluid flow passing on a magnetic sphere with mixed convection effect. Nano Fluid is a combination of liquid fluid as a base fluid with small solid nano particles. Water is chosen as Newtonian base fluid and oil is chosen as non-Newtonian base fluid. Then, Alumina and Copper are chosen as solid particle in nano fluid. We further construct governing equation by applying continuity equation, momentum equation, and energy equation to obtain dimensional governing equations. The dimensional governing equations that have been obtained are converted into non-dimensional governing equations by substituting non-dimensional variables. The non-dimensional governing equations are further transformed into similarity equations using stream function and solved numerically using Euler Implicit Finite Difference method. We further analyse the effect of magnetic parameter towards velocity and temperature in MHD nano fluid flow. The results show that the increases of magnetic parameter impacts to the decrease of velocity and temperature. Then, the velocity and temperature of Newtonian nano fluid are higher than the velocity and temperature of non-Newtonian nano fluid. Also, the velocity and temperature of copper-water are higher than the velocity and temperature of Alumina-water.
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH INVERSELY QUADRATIC HELLMANN PLUS ...ijrap
The solutions of the Schrödinger equation with inversely quadratic Hellmann plus Mie-type potential for
any angular momentum quantum number have been presented using the Nikiforov-Uvarov method. The
bound state energy eigenvalues and the corresponding un-normalized eigenfunctions are obtained in terms
of the Laguerre polynomials. Several cases of the potential are also considered and their eigen values obtained.
On the Logical Origin of the Laws Governing the Fundamental Forces of Nature:...Ramin (A.) Zahedi
Copyright: CC Attribution-NonCommercial-NoDerivs 4.0 International.
License URL: https://creativecommons.org/licenses/by-nc-nd/ .
Comments: 90 Pages. A summary of a submitted and accepted research project, Ramin Zahedi, (On "Foundations of Physics"), Japan, 2012 - 2015.
KeyWords: "A Unique Mathematical (Axiomatic) Prediction of Eight New Elementary Particles, Including: 'Four Charge-less Raight-Handed Spin-1/2 Fermions (Two Leptons and Two Quarks)', 'One Spin-3/2 Fermion', and 'Three Spin-1 (massive) Gauge Bosons';" CPT Symmetry as the Only Combunation of C, P, and T Symmetries Definable for Interacting Fields"; Time-Reversal Symmetry and the Numebr of Space-Time Dimensions; Monopoles and the Issue of their Existence in Nature.
This article has been invited and presented at the following international conferences:
- The 2016 SIAM International Conference on Mathematical Aspects of Materials Science, Philadelphia, USA, 2016. (https://www.siam.org/meetings/ms16)
- The 17th International Conference on Quantum Foundations: Quantum and Beyond, International Centre for Mathematical Modeling in Physics, (ICMM), Linnaeus University, Sweden, 2016. (https://lnu.se/en/qb)
-The 4th International Conference on New Frontiers in Physics, CERN Organized Conference (Europe). (https://indico.cern.ch/e/icnfp2015)
- The 2016 International Conference on Algebraic Geometry and Mathematical Physics, University of Tromsø, Norway, 2016. (https://site.uit.no/)
- The XXXVII Max Born International Symposium, International Conference on Non-commutative Geometry, Quantum Symmetries and Quantum Gravity (II), Wroclaw University, Poland, 2016. (http://ift.uni.wroc.pl/~mborn37)
- The GRavitational-wave Astronomy International Conference in Paris, Institute d‘Astrophysique de Paris (IAP), The University of Paris VI - Sorbonne University, CNRS, LERU, EUA, Paris, France, 'Supported by European Union's 7th Framework Prog.: FP7/PEOPLE-2011-CIG,‘ 2016. (http://www.iap.fr/vie_scientifique/ateliers/GravitationalWave/2016/scripts/abstract.aspx)
- The 22nd Internnational Australian Institute of Physics Congress (AIP), University of Queensland, Australia, 2016. (http://appc-aip2016.org.au)
- The 21st International Conference on General Relativity and Gravitation, Columbia University, New York, USA, 2016. (http://www.gr21.org).
External URLs: https://Cds.CERN.ch/record/1980381/, https://INSPIREHEP.net/record/1387680/, http://Eprints.Lib.Hokudai.ac.jp/dspace/handle/2115/59279/, https://www.OpenAire.EU/search/publication?articleId=dedup_wf_001::422af8dcdfbae42429965b16b61f0e94, https://Hal-UNIV-PARIS3.archives-ouvertes.fr/USPC/hal-01476703 , http://mts-srep.NATURE.com/srep_files/2017/07/20/00174434/00/174434_0_related_ms_4909193_pttcpw.pdf , https://hal-PARIS1.archives-ouvertes.fr/hal-01476703 , https://indico.CERN.ch/event/344173/session/22/contribution/422/attachments/1140145/1646101/R.a.Zahedi--OnDiscretePhysics-Jan.2015-signed.pdf.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
-type and -type four dimensional plane wave solutions of Einstein's field eq...inventy
In the present paper, we have studied - type and -type plane wave solutions of Einstein's field equations in general theory of relativity in the case where the zero mass scalar field coupled with gravitational field and zero mass scalar field coupled with gravitational & electromagnetic field and established the existence of these two types of plane wave solutions in . Furthermore we have considered the case of massive scalar field and shown that the non-existence of these two types of plane wave solutions in GR theory.
On the Mathematical Structure of the Fundamental Forces of NatureRamin (A.) Zahedi
The main idea of this article is based on my previous articles (references [1], [2], [3]). In this work by introducing a new mathematical approach based on the algebraic structure of integers (the domain of integers), and assuming the “discreteness” of physical quantities such as the components of the relativistic n-momentum, we derive all the mathematical laws governing the fundamental forces of nature. These obtained laws that are unique, distinct and in the form of the complex tensor equations, represent the force of gravity, the electromagnetic (including electroweak) force, and the (strong) nuclear force (and only these three kinds of forces, for all dimensions D ≥2). Each derived tensor equation contains the term of the mass m_0 (as the invariant mass of the supposed force carrier particle), as well as the term of the external current (as the external source of the force field). In some special cases, these tensor equations are turned into the wave equations that are similar to the Pauli and Dirac equations. In fact, the mathematical laws obtained in this paper, are the corrected and generalized forms of the current field equations including Maxwell equations, Yang-Mils equations and Einstein equations, as well as (in some special conditions) Pauli equation, Dirac equation, and so on. A direct proof of the absence of magnetic monopoles in nature is one of the outcomes of this research, according to the unique formulations of the laws of the fundamental forces that we have derived.
Keywords: Foundations of Physics, Ontology, Discrete Physics, Discrete Mathematics, The Fundamental Forces of Nature.
Comments: 51 Pages. Expanded version of my previous articles:
Ramin (A.) Zahedi, "Linearization Method in the Ring Theory," Bulletin of the Lebedev Physics Institute, Springer-Verlag, No. 5-6, 1997;
Ramin (A.) Zahedi, "On the Connection Between Methods of the Ring Theory and the Group Approach", Bulletin of the Lebedev Physics Institute, Springer-Verlag, No. 7-8, 1997.
PACS Classifications: 04.20.Cv, 04.50.Kd, 04.90.+e, 04.62.+v, 02.10.Hh, 02.10.Yn, 02.20.Bb, 02.90.+p, 03.50.-z, 03.65.Fd, 03.65.Pm, 03.50.Kk, 12.40.-y, 12.60.-i, 12.10.Dm, 12.10.-g.
External URL: http://arXiv.org/abs/1501.01373. (arXiv:1501.01373 [physics.gen-ph])
Copyright: CC Attribution-NonCommercial-NoDerivs 4.0 International
License URL: https://creativecommons.org/licenses/by-nc-nd/4.0/
Exact Solutions of the Klein-Gordon Equation for the Q-Deformed Morse Potenti...ijrap
In this work, we solve the Klein-Gordon (KG) equation for the general deformed Morse potential with
equal scalar and vector potentials by using the Nikiforov-Uvarov (NU) method, which is based on the
solutions of general second-order linear differential equation with special functions. The energy
eigenvalues and corresponding normalized eigenfunctions are obtained. It is found that the eigenfunctions
can be expressed by the Laguerre polynomials. Our solutions have a good agreement with earlier study.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
A pictorial method of visualizing curl & determinant operation utilized i...ijscmcj
Curl and Determinant operations are well known in the field of Electromagnetics and fluid dynamics. Famous Maxwell’s equations involve curl operation. Though this operation is widely used to represent rotation, we do not have sufficient literature explaining how this operation represents rotation.
Most of the books omit detailed discussion on the physical interpretation of the Curl and Determinan operation. In this paper we have attempted to develop a pictorial method to provide a logical proof showing the versatility of this operation to study the rotating vectors. We further show how this pictorial method simplifies the fundamental expression with regard to determinants.
On Rational Physics: a Basic Formalism for Relativistic Physics and "A Unique...Ramin (A.) Zahedi
Copyright: CC Attribution-NonCommercial-NoDerivs 4.0 International.
License URL: https://creativecommons.org/licenses/by-nc-nd/ .
Comments: 99 Pages. A summary of a submitted and accepted research project, Ramin Zahedi, (On "Foundations of Physics"), Japan, 2012 - 2015; (Expanded version).
KeyWords: "A Unique Mathematical (Axiomatic) Prediction of Eight New Elementary Particles, Including: 'Four Charge-less Raight-Handed Spin-1/2 Fermions (Two Leptons and Two Quarks)', 'One Spin-3/2 Fermion', and 'Three Spin-1 (massive) Gauge Bosons';" CPT Symmetry as the Only Combunation of C, P, and T Symmetries Definable for Interacting Fields"; Time-Reversal Symmetry and the Numebr of Space-Time Dimensions; Monopoles and the Issue of their Existence in Nature.
This article has been invited and presented at the following international conferences:
- The 2016 SIAM International Conference on Mathematical Aspects of Materials Science, Philadelphia, USA, 2016. (https://www.siam.org/meetings/ms16)
- The 17th International Conference on Quantum Foundations: Quantum and Beyond, International Centre for Mathematical Modeling in Physics, (ICMM), Linnaeus University, Sweden, 2016. (https://lnu.se/en/qb)
-The 4th International Conference on New Frontiers in Physics, CERN Organized Conference (Europe). (https://indico.cern.ch/e/icnfp2015)
- The 2016 International Conference on Algebraic Geometry and Mathematical Physics, University of Tromsø, Norway, 2016. (https://site.uit.no/)
- The XXXVII Max Born International Symposium, International Conference on Non-commutative Geometry, Quantum Symmetries and Quantum Gravity (II), Wroclaw University, Poland, 2016. (http://ift.uni.wroc.pl/~mborn37)
- The GRavitational-wave Astronomy International Conference in Paris, Institute d‘Astrophysique de Paris (IAP), The University of Paris VI - Sorbonne University, CNRS, LERU, EUA, Paris, France, 'Supported by European Union's 7th Framework Prog.: FP7/PEOPLE-2011-CIG,‘ 2016. (http://www.iap.fr/vie_scientifique/ateliers/GravitationalWave/2016/scripts/abstract.aspx)
- The 22nd Internnational Australian Institute of Physics Congress (AIP), University of Queensland, Australia, 2016. (http://appc-aip2016.org.au)
- The 21st International Conference on General Relativity and Gravitation, Columbia University, New York, USA, 2016. (http://www.gr21.org).
External URLs: https://Cds.CERN.ch/record/1980381/, https://INSPIREHEP.net/record/1387680/, http://Eprints.Lib.Hokudai.ac.jp/dspace/handle/2115/59279/, https://www.OpenAire.EU/search/publication?articleId=dedup_wf_001::422af8dcdfbae42429965b16b61f0e94, https://Hal-UNIV-PARIS3.archives-ouvertes.fr/USPC/hal-01547739 , http://mts-srep.NATURE.com/srep_files/2017/07/20/00174434/00/174434_0_related_ms_4909193_pttcpw.pdf , https://hal-PARIS1.archives-ouvertes.fr/hal-01547739 , https://indico.CERN.ch/event/344173/session/22/contribution/422/attachments/1140145/1646101/R.a.Zahedi--OnDiscretePhysics-Jan.2015-signed.pdf.
Analytical Solution Of Schrödinger Equation With Mie–Type Potential Using Fac...ijrap
we have obtained the analytical solution of Schrödinger wave equation with Mie – type potential
using factorization method. We have also obtained energy eigenvalues of our potential and the
corresponding wave function using an ansatz and then compare the result to standard Laguerre’s
differential equation. Under special cases our potential model reduces two well known potentials such as
Coulomb and the Kratzer Feus potentials.
To the Issue of Reconciling Quantum Mechanics and General RelativityIOSRJAP
The notion of gravitational radiation as a radiation of the same level as the electromagnetic radiation is based on theoretically proved and experimentally confirmed fact of existence of stationary states of an electron in its gravitational field characterized by the gravitational constant K = 1042G (G is the Newtonian gravitational constant) and unrecoverable space-time curvature Λ. If the numerical values of K 5.11031 Nm2 kg-2 and =4.41029 m -2 , there is a spectrum of stationary states of the electron in its own gravitational field (0.511 MeV ... 0.681 MeV).Adjusting according to the known mechanisms of broadening does not disclose the broadening of the registered portion of the emission spectrum of the micropinch. It indicates the presence of an additional mechanism of broadening the registered portion of the spectrum of the characteristic radiation due to the contribution of the excited states of electrons in their own gravitational field. The energy spectrum of the electron in its own gravitational field and the energy spectra of multielectron atoms are such that there is a resonance of these spectra. As obvious, the consequence of such resonant interaction is appearance, including new lines, of electromagnetic transitions not associated with atomic transitions. The manuscript is the review of previously published papers cited in the references.
This paper considers the problem of magneto-hydrodynamics (MHD) Newtonian and non-Newtonian nano fluid flow passing on a magnetic sphere with mixed convection effect. Nano Fluid is a combination of liquid fluid as a base fluid with small solid nano particles. Water is chosen as Newtonian base fluid and oil is chosen as non-Newtonian base fluid. Then, Alumina and Copper are chosen as solid particle in nano fluid. We further construct governing equation by applying continuity equation, momentum equation, and energy equation to obtain dimensional governing equations. The dimensional governing equations that have been obtained are converted into non-dimensional governing equations by substituting non-dimensional variables. The non-dimensional governing equations are further transformed into similarity equations using stream function and solved numerically using Euler Implicit Finite Difference method. We further analyse the effect of magnetic parameter towards velocity and temperature in MHD nano fluid flow. The results show that the increases of magnetic parameter impacts to the decrease of velocity and temperature. Then, the velocity and temperature of Newtonian nano fluid are higher than the velocity and temperature of non-Newtonian nano fluid. Also, the velocity and temperature of copper-water are higher than the velocity and temperature of Alumina-water.
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH INVERSELY QUADRATIC HELLMANN PLUS ...ijrap
The solutions of the Schrödinger equation with inversely quadratic Hellmann plus Mie-type potential for
any angular momentum quantum number have been presented using the Nikiforov-Uvarov method. The
bound state energy eigenvalues and the corresponding un-normalized eigenfunctions are obtained in terms
of the Laguerre polynomials. Several cases of the potential are also considered and their eigen values obtained.
On the Logical Origin of the Laws Governing the Fundamental Forces of Nature:...Ramin (A.) Zahedi
Copyright: CC Attribution-NonCommercial-NoDerivs 4.0 International.
License URL: https://creativecommons.org/licenses/by-nc-nd/ .
Comments: 90 Pages. A summary of a submitted and accepted research project, Ramin Zahedi, (On "Foundations of Physics"), Japan, 2012 - 2015.
KeyWords: "A Unique Mathematical (Axiomatic) Prediction of Eight New Elementary Particles, Including: 'Four Charge-less Raight-Handed Spin-1/2 Fermions (Two Leptons and Two Quarks)', 'One Spin-3/2 Fermion', and 'Three Spin-1 (massive) Gauge Bosons';" CPT Symmetry as the Only Combunation of C, P, and T Symmetries Definable for Interacting Fields"; Time-Reversal Symmetry and the Numebr of Space-Time Dimensions; Monopoles and the Issue of their Existence in Nature.
This article has been invited and presented at the following international conferences:
- The 2016 SIAM International Conference on Mathematical Aspects of Materials Science, Philadelphia, USA, 2016. (https://www.siam.org/meetings/ms16)
- The 17th International Conference on Quantum Foundations: Quantum and Beyond, International Centre for Mathematical Modeling in Physics, (ICMM), Linnaeus University, Sweden, 2016. (https://lnu.se/en/qb)
-The 4th International Conference on New Frontiers in Physics, CERN Organized Conference (Europe). (https://indico.cern.ch/e/icnfp2015)
- The 2016 International Conference on Algebraic Geometry and Mathematical Physics, University of Tromsø, Norway, 2016. (https://site.uit.no/)
- The XXXVII Max Born International Symposium, International Conference on Non-commutative Geometry, Quantum Symmetries and Quantum Gravity (II), Wroclaw University, Poland, 2016. (http://ift.uni.wroc.pl/~mborn37)
- The GRavitational-wave Astronomy International Conference in Paris, Institute d‘Astrophysique de Paris (IAP), The University of Paris VI - Sorbonne University, CNRS, LERU, EUA, Paris, France, 'Supported by European Union's 7th Framework Prog.: FP7/PEOPLE-2011-CIG,‘ 2016. (http://www.iap.fr/vie_scientifique/ateliers/GravitationalWave/2016/scripts/abstract.aspx)
- The 22nd Internnational Australian Institute of Physics Congress (AIP), University of Queensland, Australia, 2016. (http://appc-aip2016.org.au)
- The 21st International Conference on General Relativity and Gravitation, Columbia University, New York, USA, 2016. (http://www.gr21.org).
External URLs: https://Cds.CERN.ch/record/1980381/, https://INSPIREHEP.net/record/1387680/, http://Eprints.Lib.Hokudai.ac.jp/dspace/handle/2115/59279/, https://www.OpenAire.EU/search/publication?articleId=dedup_wf_001::422af8dcdfbae42429965b16b61f0e94, https://Hal-UNIV-PARIS3.archives-ouvertes.fr/USPC/hal-01476703 , http://mts-srep.NATURE.com/srep_files/2017/07/20/00174434/00/174434_0_related_ms_4909193_pttcpw.pdf , https://hal-PARIS1.archives-ouvertes.fr/hal-01476703 , https://indico.CERN.ch/event/344173/session/22/contribution/422/attachments/1140145/1646101/R.a.Zahedi--OnDiscretePhysics-Jan.2015-signed.pdf.
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Bianchi type i wet dark universe in bimetric relativity
1. Mathematical Theory and Modeling www.iiste.org
ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)
Vol.3, No.9, 2013-Special issue, International Conference on Recent Trends in Applied Sciences with Engineering Applications
30
Bianchi Type-I Wet Dark Universe in Bimetric Relativity
S.D.Deo1
, S.P.Singh2
( 1) Head Department Of Mathematics, N.S. Science and Arts College, Bhadrawati , Dist.: Chandrapur(M.S.),
Pin- 442902 , India.
Email: S_deo01@yahoo.in
(2) Department of Mathematics, Anandibai Damodar Kale Degree college of Arts & Commerce,
Saibaba Nagar , Borivali (west), Mumbai-400092, Maharashtra, India.
Email: spsinghcollege@gmail.com
Abstract
In this paper , we have investigated the role of Wet Dark Fluid in Bianchi Type-I cosmological model within the
framework of bimetric theory of relativity proposed by Rosen N. Here we have used a new equation of state for
the matter dark energy component of the universe known as Wet Dark Fluid given by = ϒ( - ∗ )
which can describe a liquid for example water. It is further observed the non existence of Wet Dark Fluid in
bimetric relativity.
Keywords: Bianchi Type-I Universe , Wet Dark Fluid , Bimetric Relativity
AMS Subject Code- 83C05 ( general relativity)
1. INTRODUCTION:-
Einstein’s theory of general relativity is one of the most beautiful structures of theoretical physics which
describes the theory of gravitation in terms of geometry. In the last decades, several theories of gravitation have
been proposed as alternatives to Einstein’s theory of general relativity.The most popular among them is Rosen’s
(1973) bimetric theory of relativity.
Rosen(1) proposed the bimetric theory of relativity to remove some of the unsatisfactory features of the general
theory of relativity. In the bimetric theory , there exist two metric tensors at each point of space-time , which
describes the gravitation and the background metric which enters into the field equation and interacts
with , ℎ ℎ .
One can regard ℎ ℎ no matter were present. Accordingly , at each
space-time point ,one has two line elements:
=
and ! =
where ds is the interval between two neighbouring events as measured by means of a clock and a measuring rod.
The interval ! is an abstract or geometrical quantity not directly measurable .One can regard it as describing
the geometry that would exist if no matter were present.
When we study the Bianchi type models , we observed that the models contain isotropic special cases and they
permit arbitrarily small anisotropic levels at some instant of cosmic times. Hence these models are to be known
as suitable models of our universe. Therefore study of Bianchi type models creates much more interest.
One of the mysteries of cosmology is the nature of dark energy component of the universe. There is , definitely
no lack of cosmological constant, phantom energy , quintessence k-essence etc. To explain the acceleration of
the universe, modified Friedmann equation such as cardassion expansion and also what might be derived from
brane cosmology have been used. In this work , Wet Dark Fluid ( WDF) as a model for dark energy is used in
Bimetric Relativity. This model is generalized Chaplygin gas( GCG) where an equation of state is offered with
properties relevant for the dark energy problem.
Riess et al (2) , Perimuttar et al (3) and Sahani(4) have studied the nature of the dark component of the universe
as one of the deepest mysteries of cosmology. We are motivated to use the wet dark fluid (WDF) as a model for
dark energy which stems from an equation of state proposed by Tait(5) and Hayward(6) to treat water and
aqueous solutions.
The equation of state for Wet Dark Fluid is = ϒ( - ∗ ) (1.1)
Where the parameters ϒ and ∗ " # #
0 ≤ ≤ 1.
We have energy conservation equation as:
+ 3)* + + = 0 -1.2/
Using equation of state and 3H = 0
.
1
in the above equation , we get
2. Mathematical Theory and Modeling www.iiste.org
ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)
Vol.3, No.9, 2013-Special issue, International Conference on Recent Trends in Applied Sciences with Engineering Applications
31
=
2
342 ∗ +
5
6 -342/
(1.3)
ℎ ℎ 7 # ℎ # .
Wet Dark Fluid ( WDF) has two components : one behaves as cosmological constant and other as standard fluid
with equation of state p= Type equation here.
If we take c>0 then this fluid will not violet the strong energy condition p + ≥ 0 ;
* + + = - 1 + / − ∗
* + += - 1 + /
5
6 -342/
- 1.4/
Holman and Naidu (7) used the wet dark fluid as dark energy in the homogeneous isotropic FRW case . Singh
and Chaubey (8) studied Bianchi type-I universe with wet dark fluid. And also Deo S. D. (9) studied Bianchi
type-I universe with Wet Dark Energy in Bimetric Relativity. This work concludes that the Bianchi Type-I
cosmological model in Bimetric Relativity does not accommodate Wet Dark Energy .
2.METRIC AND SOLUTIONS OF FIELD EQUATIONS:-
We consider Bianchi type-I Metric in the form:
= I - − / + J d + K L (2.1)
ℎ I, J, K ℎ 7 of t only.
Mℎ background flat metric corresponding to equation (2.1) is
! = − + + d + L (2.2)
The field equations in bimetric theory of gravitation proposed by Rosen (1973) are:
N -
3
O = -8P"M (2.3)
ℎ N =
3 QR
( S
.
S ⃒Q
)⃒U
and k=-
V
2
/
W
X
together with g=det( ) and = det - )
Here the vertical bar (⃒) denotes the covariant differentiation with respect to
and M is the energy momentum tensor of the matter field.
Rosen’s field equation in bimetric theory for the metric (2.1) with the help of equations
(2.2)-(2.3) , can be written in the form:
Z
[
[
]
.
+ Z
^
^
]
.
= -16P"M3
3
(2.4)
2 Z
_
_
]
.
− Z
[
[
]
.
+ Z
^
^
]
.
= -16P"M (2.5)
2 Z
_
_
]
.
+ Z
[
[
]
.
− Z
^
^
]
.
= -16P"M`
`
(2.6)
Z
[
[
]
.
+ Z
^
^
]
.
= -16P"Ma
a
(2.7)
Here the overhead dot( . ) denotes differentiation with respect to t.
The energy momentum tensor by Singh and Chaubey(2008) for the Wet Dark Fluid source is given by,
M = * + + - O (2.8)
Here
ℎ is the matter density and is the flow vector of the fluid. The
flow of the matter is taken orthogonal to the hyper surfaces of the homogenity so that
. = 1 (2.9)
b # 7 , 7 c -2.8) &(2.9) ℎ # ,
M3
3
= M = M`
`
= - & Ma
a
= (2.10)
Now using equation (2.10), equations (2.4)-(2.7) becomes,
3. Mathematical Theory and Modeling www.iiste.org
ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)
Vol.3, No.9, 2013-Special issue, International Conference on Recent Trends in Applied Sciences with Engineering Applications
32
Z
[
[
]
.
+ Z
^
^
]
.
= 16P" (2.11)
− Z
[
[
]
.
+ Z
^
^
]
.
= 16P" (2.12)
2 Z
_
_
]
.
+ Z
[
[
]
.
− Z
^
^
]
.
= 16P" (2.13)
Z
[
[
]
.
+ Z
^
^
]
.
= -16P" (2.14)
d c -2.11) & (2.14) ,we get
+ = 0 ( 2.15)
e ℎ , ℎ ,
> 0
> 0 ℎ .
Mℎ # c -2.15/ 7 ℎ ,
=0 and = 0 (2.16)
ℎ ℎ ℎ ℎ ℎ # L. h i " e
( ) and wet dark fluid energy density( /, both are identically zero. Thus Bianchi type-I universe with
wet dark fluid in bimetric theory of relativity does not survive and hence only vacuum model is obtained.
For vacuum case, =0 = , the field equations (2.11)-(2.14),gives the solution of the form,
A=B=C= jk
(2.17)
Where n is the constant of integration.
Thus in view of equation (2.17), the metric (2.1) takes the form:
d = jk
( + d + L -d ) (2.18)
This can be transformed through a proper choice of coordinates to
d = l
( m + dn + L -dM ) (2.19)
3.CONCLUSION:-
Here we have constructed Bianchi Type-I cosmological model in Rosen’s bimetric theory of relativity with a
new equation of state for the dark energy component of the universe known as Wet Dark Fluid. Further, we
conclude the nil contribution of Wet Dark Fluid in Bianchi Type-I cosmological model in Rosen’s theory and
hence only vacuum model is obtained.
ACKNOWLEDGEMENT
The authors are thankful to Dr. R.D.Giri , Professor Emiratus , PGTD (Mathematics) ,RTM Nagpur
University,Nagpur (M.S.), India , for his constant inspiration and guidance. Also special thanks is given to
Principal, Dr. Yasmeen Bhatia of Anandibai Damodar Kale Degree college, Mumbai (M.S.), India.
REFERENCES:-
(1) Rosen , N: Gen. Rel.Grav.,4,435(1973).
(2)Riess , A.G. et al. 1009(1998).
(3)Perimutter , S.et al : Astrophys.J.,157,565(1998).
(4)Sahni,V.:arXiv:astro-ph/0403324(2004).
(5)Tait,P.G.: The Voyage of HMS Challenger( H.M.S.O. , London,1998).
(6)Hayward,A.T.J.,Brit.J.Appl.Phys.18,965,(1967).
(7)Holman,R. and Naidu,S., arXiv: Astro-phy/0408102(preprint)(2005).
(8)Singh,T. and Chaubey,R.: Pramana Journal of Physics,71,No.3(2008).
(9)Deo,S.D.: OIIRJ,II(1), 104-107(2012).
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