scholarly journals Quintom cosmological model and some possible solutions using Lie and Noether symmetries

2016 ◽  
Vol 25 (14) ◽  
pp. 1650110 ◽  
Author(s):  
Sourav Dutta ◽  
Muthusamy Lakshmanan ◽  
Subenoy Chakraborty
Keyword(s):  
Lie Algebra ◽  
Physical System ◽  
Three Dimensional ◽  
Noether Symmetry ◽  
Conserved Quantities ◽  
Considerable Simplification ◽  
Present Context ◽  
Augmented Space ◽  
Constants Of Motion ◽  
Flrw Universe

The present work deals with a quintom model of dark energy in the framework of a spatially flat isotropic and homogeneous Friedmann–Lemaitre–Robertson–Walker (FLRW) universe. At first, Lie point symmetry is imposed to the system and the unknown coupled potential of the model is determined. Then Noether symmetry, which is also a point like symmetry of the Lagrangian, is imposed on the physical system and the potential takes a general form. It is shown that the Lie algebra of Noether symmetry is a sub-algebra of the corresponding Lie algebra of the Lie symmetry. Finally, a point transformation in the three-dimensional augmented space is performed suitably so that one of the variables become cyclic and as a result there is considerable simplification to the physical system. Hence, conserved quantities (i.e. constants of motion) are expressed in a compact form and cosmological solutions are evaluated and analyzed in the present context.

A study of dynamical equations for non-minimally coupled scalar field using Noether symmetric approach

2016 ◽  
Vol 31 (19) ◽  
pp. 1650116 ◽  
Author(s):  
Sourav Dutta ◽  
Madan Mohan Panja ◽  
Subenoy Chakraborty
Keyword(s):  
Scalar Field ◽  
Infinitesimal Generator ◽  
Einstein Gravity ◽  
Matter Content ◽  
The Self ◽  
Noether Symmetry ◽  
Dynamical Equations ◽  
Augmented Space ◽  
Constants Of Motion ◽  
Scalar Field Cosmology

Non-minimally coupled scalar field cosmology has been studied in this work within the framework of Einstein gravity. In the background of homogeneous and isotropic Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime non-minimally coupled scalar field having self-interacting potential is taken as the source of the matter content. The constraint of imposing Noether symmetry on the Lagrangian of the system not only determines the infinitesimal generator (the symmetry vector) but also the coupling function and the self-interacting potential for the scalar field. By choosing appropriately a point transformation in the augmented space, one of the transformed variables is cyclic for the Lagrangian. Finally, using constants of motion, the solutions are analyzed.

A cosmological study of Einstein–Skyrme model in anisotropic Kantowski–Sachs spacetime using Lie and Noether symmetries

2018 ◽  
Vol 15 (06) ◽  
pp. 1850089 ◽  
Author(s):  
Santu Mondal ◽  
Sourav Dutta ◽  
Manjusha Tarafdar ◽  
Subenoy Chakraborty
Keyword(s):  
Lie Algebra ◽  
Evolution Equations ◽  
Einstein Gravity ◽  
Lie Symmetry ◽  
Noether Symmetry ◽  
Noether Symmetries ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Unknown Parameters ◽  
Augmented Space

The present work deals with anisotropic (but zero heat flux) Skyrme fluid in a locally rotational Kantowski–Sachs (KS) spacetime in the background of Einstein gravity. The Lie point symmetry is imposed to the system of Einstein field equations and unknown parameters are either determined or interrelated by the imposition of the symmetry. Subsequently, Noether symmetry, a point-like symmetry of the Lagrangian is used and it is found that the Lie algebra of the Noether symmetry is a subalgebra of the corresponding Lie algebra of the Lie symmetry. Then a point transformation in the 2D augmented space is taken in such a manner that one of the variables becomes cyclic and hence the Lagrangian as well as the evolution equations are simplified to a great extent. Finally, solutions to the physical system are presented and are analyzed physically.

scholarly journals Comparing the perception with the reality of walking in a hilly environment: an accessibility method applied to a University campus in Hong Kong

2015 ◽  
Vol 10 (1) ◽  
Author(s):  
Guibo Sun ◽  
Robert Haining ◽  
Hui Lin ◽  
Nicolas M. Oreskovic ◽  
Jie He
Keyword(s):  
Hong Kong ◽  
Three Dimensional ◽  
University Campus ◽  
Network Modelling ◽  
Walking Behavior ◽  
Individual Perception ◽  
Pedestrian Network ◽  
Present Context ◽  
Public Health Practitioners ◽  
People’S Perceptions

The influence of hilliness on walking behavior could be a consequence of the real effect of the local topography, but individual perception of the difficulties associated with walking in a hilly environment may also be important. Previous studies have found that people’s perceptions do not necessarily match well with the realities of walking in hilly environments. There are a few methods that can be used to visualize the geography of that difference for use by urban planners and public health practitioners. A walking accessibility measure that allows comparison of perception and reality is proposed and implemented in this study. We note that difficulties in calculating accessibility measures in the present context arise primarily from problems with data quality, three-dimensional pedestrian network modelling and the adequacy of accessibility methods for describing and predicting walking behavior. We present practical strategies for addressing these issues using geographic information systems. Our method is illustrated by calculating accessibility for a hilly university campus in Hong Kong. Walking behaviors on, and people’s perceptions of, this hilly environment were obtained through walking diaries and a survey. The article concludes with suggested directions for the future development of walking accessibility measures along with some ideas about their applicability to the practice of planning and designing a walkable environment.

scholarly journals Complete set of quasi-conserved quantities for spinning particles around Kerr

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Geoffrey Compère ◽  
Adrien Druart
Keyword(s):  
Linear Order ◽  
Conserved Quantities ◽  
Killing Tensor ◽  
Kerr Geometry ◽  
Spinning Particles ◽  
Kerr Spacetime ◽  
Killing Tensors ◽  
Mixed Symmetry ◽  
Constants Of Motion ◽  
Complete Set

We revisit the conserved quantities of the Mathisson-Papapetrou-Tulczyjew equations describing the motion of spinning particles on a fixed background. Assuming Ricci-flatness and the existence of a Killing-Yano tensor, we demonstrate that besides the two non-trivial quasi-conserved quantities, i.e. conserved at linear order in the spin, found by Rüdiger, non-trivial quasi-conserved quantities are in one-to-one correspondence with non-trivial mixed-symmetry Killing tensors. We prove that no such stationary and axisymmetric mixed-symmetry Killing tensor exists on the Kerr geometry. We discuss the implications for the motion of spinning particles on Kerr spacetime where the quasi-constants of motion are shown not to be in complete involution.

scholarly journals GROUP PROPERTIES OF A ONE-DIMENSIONAL NONLINEAR POROELASTICITY EQUATION

2019 ◽  
Vol 4 (1) ◽  
pp. 149-155
Author(s):  
Kholmatzhon Imomnazarov ◽  
Ravshanbek Yusupov ◽  
Ilham Iskandarov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Lie Algebra ◽  
Three Dimensional ◽  
Group Classification ◽  
Second Order ◽  
Partial Differential ◽  
One Dimensional ◽  
Preliminary Group

This paper studies a class of partial differential equations of second order , with arbitrary functions and , with the help of the group classification. The main Lie algebra of infinitely infinitesimal symmetries is three-dimensional. We use the method of preliminary group classification for obtaining the classifications of these equations for a one-dimensional extension of the main Lie algebra.

scholarly journals Some exact solutions in f(𝒢,T) gravity via Noether symmetries

2017 ◽  
Vol 32 (16) ◽  
pp. 1750086 ◽  
Author(s):  
M. Farasat Shamir ◽  
Mushtaq Ahmad
Keyword(s):  
Exact Solutions ◽  
Momentum Tensor ◽  
Gravity Models ◽  
Noether Symmetry ◽  
Type I ◽  
Conserved Quantities ◽  
Rotationally Symmetric ◽  
Bianchi Type I Universe ◽  
Modified Formula ◽  
Bonnet Term

This paper is devoted to investigate the recently proposed modified Gauss–Bonnet [Formula: see text] gravity, with [Formula: see text], the Gauss–Bonnet term, coupled with [Formula: see text], the trace of energy–momentum tensor. We have used the Noether symmetry methodology to discuss some cosmologically important [Formula: see text] gravity models with anisotropic background. In particular, the Noether symmetry equations for modified [Formula: see text] gravity are reported for locally rotationally symmetric Bianchi type I universe. Explicitly, two models have been proposed to explore the exact solutions and the conserved quantities. It is concluded that the specific models of modified Gauss–Bonnet gravity may be used to reconstruct [Formula: see text]CDM cosmology without involving any cosmological constant.

Conservation laws corresponding to the Noether symmetries of the geodetic Lagrangian in spherically symmetric spacetimes

2017 ◽  
Vol 26 (05) ◽  
pp. 1741006 ◽  
Author(s):  
Bismah Jamil ◽  
Tooba Feroze
Keyword(s):  
Conservation Laws ◽  
Noether Symmetry ◽  
Complete List ◽  
Spherically Symmetric ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Symmetric Spacetimes ◽  
Spherically Symmetric Spacetimes

In this paper, we present a complete list of spherically symmetric nonstatic spacetimes along with the generators of all Noether symmetries of the geodetic Lagrangian for such metrics. Moreover, physical and geometrical interpretations of the conserved quantities (conservation laws) corresponding to each Noether symmetry are also given.

scholarly journals Three-dimensional higher-order Schrödinger algebras and Lie algebra expansions

2020 ◽  
Vol 2020 (4) ◽  
Author(s):  
Oguzhan Kasikci ◽  
Nese Ozdemir ◽  
Mehmet Ozkan ◽  
Utku Zorba
Keyword(s):  
Lie Algebra ◽  
Three Dimensional ◽  
Higher Order
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