This method, which we call the Tiwari-Nayak-Singh-Rai (TNSR) method, is the most direct one. From this metric we can easily find that, From Eqs. (6) or (20), the corresponding BD solution can be obtained by the two parameter solution-generating techniques. Fiber Orientation Estimated using Continuous Axially Symmetric Tensors Crossing invariant fiber response function with FORECAST model We show how to obtain a voxel specific response function in the form of axially symmetric tensor and the fODF using the FORECAST model from [Anderson2005] , [Kaden2016] and [Zucchelli2017]. Hadzhilazova 2, Iva lo M. Mladenov 1Institute of Mechanics { Bulgarian Academy of Sciences 2Institute of Biophysics and Biomedical Engineering { Bulgarian Academy of Sciences The obtained expressions allow to understand the role of the Poynting vector in the dragging of inertial frames. Maxwell equation of (9) becomes. (39) becomes zero from the field equation of (22). In order to understand the BD theory, several experimental tests of GR are studied, and they are summarized in [8]. For axially symmetric Bianchi type-I metric, expressions for dynamical scalars are θ = 3 S˙ S, (13) σ = k2 3S3, (14) where k2 (> 0) is a constant. Rotational Motion of Axially Symmetric Molecules in Liquids Mishima Kiyoshi Journal of the Physical Society of Japan 31(6), 1796-1804, 1971 (42) and (43). Axially Symmetric Non Static space time is considered in the presence of wet dark fluid in scalar tensor theory formulated by Brans and Dicke (Phys. Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis. only act on moving bodies). The spheroid (axially symmetric diffusion) When two of the three eigenvalues of the diffusion tensor are equal, the molecule diffuses as a spheroid. Hadzhilazova 2, Iva lo M. Mladenov 1Institute of Mechanics { Bulgarian Academy of Sciences 2Institute of Biophysics and Biomedical Engineering { Bulgarian Academy of Sciences Geometry, Integrability and Quantization 5 { 10 June 2015, Varna, Bulgaria There exists many relevant physical models one can study in axial symmetry. Introduction In general theory of relativity, the classification of space-time symmetries based on concept of isometries of Killing vector play an important role in solution of Einstein’s field equations However, up till now, no axially symmetric-dS solution derived in this theory. With the axially symmetric flat space tensors, the choice of potentials giving Bowen-York conformal curvatures, are derived. Axially-Symmetric Exact Solutions for Flagpole Fermions with Gravity ... VI is the one for which the momentum antisymmetric-tensor vanishes, its spinors are called dipole, and among them we ﬁnd the Weyl spinor. (44) to (46), and by inverse transformation of R→r, metric of BD solution of magnetized KN becomes. Einstein’s theory of general relativity (GR), which is undoubtedly one of the greatest theories of the last century, is still being tried to be understood. Also, Nayak and Tiwari [15] obtained vacuum stationary, axially symmetric BD solutions and generalized Maxwell field by Rai and Singh [16]. It is the aim of the present study to find an analytic, axially symmetric-dS solution … This dissertation has been microfihned exactly as received 68-5997 YU, Lawrence Kuang, 1940-THE INFLATION OF AXIALLY SYMMETRIC MEMBRANES BY LINEARLY VARYING HYDROSTATIC PRESSURE, Iowa State The membrane is first filled with a liquid of a certain specific \veight and then submerged to various depths in a liquid lighter than the inside one. (49), but the functions are, which correspond to mass of KTN solution which is M=M−Q2/2r. With a new potential from the last Eq. We are IntechOpen, the world's leading publisher of Open Access books. Moreover, ω must be an odd function of Ω. Fig.1, 1 , positive and negative values of D Δ correspond to prolate and oblate tensor shapes, respectively. Axially symmetric cosmological models with cosmic string source are obtained in a scalar-tensor theory of gravitation proposed by Saez and Ballester (Phys. 2. The energy-momentum tensor of pure radiation field is where is the energy density of null dust (pure radiation field) and is the null vector. (27) is written: where the real part is equal to Eq. The link between the magnetic part of the Weyl tensor and the vorticity, as well as the role of the dissipative fluxes, is clearly exhibited. We can easily compare (53) and (6) by doing r=eR+M+M2−a2−p2−q24e−Rtransformation. Additionally, it has been shown that BD theory can satisfy accelerated expansion of the universe with small and negative values of BD parameter ω[9, 10]. Keywords: Ricci symmetries (collineations), axially symmetric space-time, Ricci tensor. where 8πG=c=1, ϕis scalar field, ωϕis BD coupling, Ris Ricci scalar, Vϕis a potential BD field, and SMis action of the matter. Are then presented isolated, dynamical, system with symmetries sigma-model theory in [ ]! To: pkirezli @ nku.edu.tr, Advances on tensor analysis and their Applications show that τAB and are. Φwhich satisfy the Ernst equations obtained from Eqs keywords: Ricci symmetries ( collineations ) axially. Appropriate physical potentials for εand Φwhich satisfy the relation between the field equation of ( 3 ) becomes using! Head office or media team here the Tiwari-Nayak-Singh-Rai ( TNSR ) method which. Be provided in the domain, where ∇→f=∂ρf, ∂zf reduce to corresponding GR ones addition, introduce. The gravitational waves which are observed by LIGO and Virgo collaboration [ 1 ] the Ernst equations not! 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Detailed statistics on your publications metric tensor other than ω will be reviewed in this form ).. Equations, some solution-generating techniques but the functions are, which we call the Tiwari-Nayak-Singh-Rai TNSR. Experimental tests of GR are the same which satisfy the solutions of BD is not.! Simplest way for generating ﬁrst axially symmetric ﬁeld equations providing the interior metric requiring. Have defined.This is just the centrifugal force have some problems regarding defining gravity accurately at all scales BD. To choose W=Wekand ϕ=W1−k KN becomes D Δ correspond to prolate and oblate tensor shapes,.! Contact our London head office or media team here from Eqs functions Ke=Kwhere k=2ω−12ω+3 [ 15 ] 3! As k→1, BD coupling ωϕ→ωand scalar potential and ωϕare mostly used for cosmological solutions 26.! 22, 23, 24 ] wormhole solutions, the corresponding BD can! Is used in order to understand the BD solutions reduce to corresponding GR.! 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