Approximate Noether gauge symmetries of Bardeen model

We investigate the approximate Noether gauge symmetries of the geodesic Lagrangian for the Bardeen spacetime model. This is accommodated by a set of new approximate Noether gauge symmetry relations for the perturbed geodesic Lagrangian in the spacetime. A detailed analysis to the spacetime of Bardeen model up to third-order approximate Noether gauge symmetries is presented.Comment: 7 pages, 1 table, submitted to the EPJ

New Exact Spherically Symmetric Solutions in f(R,ϕ,X)f(R,\phi,X) gravity by Noether's symmetry approach

The exact solutions of spherically symmetric space-times are explored by using Noether symmetries in $f(R,\phi,X)$ gravity with $R$ the scalar curvature, $\phi$ a scalar field and $X$ the kinetic term of $\phi$. Some of these solutions can represent new black holes solutions in this extended theory of gravity. The classical Noether approach is particularly applied to acquire the Noether symmetry in $f(R,\phi,X)$ gravity. Under the classical Noether theorem, it is shown that the Noether symmetry in $f(R,\phi,X)$ gravity yields the solvable first integral of motion. With the conservation relation obtained from the Noether symmetry, the exact solutions for the field equations can be found. The most important result in this paper is that, without assuming $R=\textrm{constant}$, we have found new spherically symmetric solutions in different theories such as: power-law $f(R)=f_0 R^n$ gravity, non-minimally coupling models between the scalar field and the Ricci scalar $f(R,\phi,X)=f_0 R^n \phi^m+f_1 X^q-V(\phi)$, non-minimally couplings between the scalar field and a kinetic term $f(R,\phi,X)=f_0 R^n +f_1\phi^mX^q$ , and also in extended Brans-Dicke gravity $f(R,\phi,X)=U(\phi,X)R$. It is also demonstrated that the approach with Noether symmetries can be regarded as a selection rule to determine the potential $V(\phi)$ for $\phi$, included in some class of the theories of $f(R,\phi,X)$ gravity.Comment: Accepted for publication in JCAP. The title and the abstract have been changed and new exact solutions have been added with more cases. The existence of horizons of our solutions has been discussed to

Classification of Static Plane Symmetric Spacetimes according to their Matter Collineations

In this paper we classify static plane symmetric spacetimes according to their matter collineations. These have been studied for both cases when the energy-momentum tensor is non-degenerate and also when it is degenerate. It turns out that the non-degenerate case yields either {\it four}, {\it five}, {\it six}, {\it seven} or {\it ten} independent matter collineations in which {\it four} are isometries and the rest are proper. There exists three interesting cases where the energy-momentum tensor is degenerate but the group of matter collineations is finite-dimensional. The matter collineations in these cases are either {\it four}, {\it six} or {\it tenComment: 15 pages, LaTex, no figure

Physics-based prognostic modelling of filter clogging phenomena

In industry, contaminant filtration is a common process to achieve a desired level of purification, since contaminants in liquids such as fuel may lead to performance drop and rapid wear propagation. Generally, clogging of filter phenomena is the primary failure mode leading to the replacement or cleansing of filter. Cascading failures and weak performance of the system are the unfortunate outcomes due to a clogged filter. Even though filtration and clogging phenomena and their effects of several observable parameters have been studied for quite some time in the literature, progression of clogging and its use for prognostics purposes have not been addressed yet. In this work, a physics based clogging progression model is presented. The proposed model that bases on a well-known pressure drop equation is able to model three phases of the clogging phenomena, last of which has not been modelled in the literature yet. In addition, the presented model is integrated with particle filters to predict the future clogging levels and to estimate the remaining useful life of fuel filters. The presented model has been implemented on the data collected from an experimental rig in the lab environment. In the rig, pressure drop across the filter, flow rate, and filter mesh images are recorded throughout the accelerated degradation experiments. The presented physics based model has been applied to the data obtained from the rig. The remaining useful lives of the filters used in the experimental rig have been reported in the paper. The results show that the presented methodology provides significantly accurate and precise prognostic results

Classification of Spherically Symmetric Static Spacetimes according to their Matter Collineations

The spherically symmetric static spacetimes are classified according to their matter collineations. These are studied when the energy-momentum tensor is degenerate and also when it is non-degenerate. We have found a case where the energy-momentum tensor is degenerate but the group of matter collineations is finite. For the non-degenerate case, we obtain either {\it four}, {\it five}, {\it six} or {\it ten} independent matter collineations in which four are isometries and the rest are proper. We conclude that the matter collineations coincide with the Ricci collineations but the constraint equations are different which on solving can provide physically interesting cosmological solutions.Comment: 15 pages, no figure, Late