Levenberg–Marquardt Backpropagation for Numerical Treatment of Micropolar Flow in a Porous Channel with Mass Injection

In this research work, an effective Levenberg–Marquardt algorithm-based artificial neural network (LMA-BANN) model is presented to find an accurate series solution for micropolar flow in a porous channel with mass injection (MPFPCMI). The LMA is one of the fastest backpropagation methods used for solving least-squares of nonlinear problems. We create a dataset to train, test, and validate the LMA-BANN model regarding the solution obtained by optimal homotopy asymptotic (OHA) method. The proposed model is evaluated by conducting experiments on a dataset acquired from the OHA method. The experimental results are obtained by using mean square error (MSE) and absolute error (AE) metric functions. The learning process of the adjustable parameters is conducted with efficacy of the LMA-BANN model. The performance of the developed LMA-BANN for the modelled problem is confirmed by achieving the best promise numerical results of performance in the range of E-05 to E-08 and also assessed by error histogram plot (EHP) and regression plot (RP) measures.

Conformal vector fields of Bianchi type-I spacetimes

This paper aims to investigate Conformal Vector Fields (CVFs) of Bianchi type-I spacetimes. A set of 10-coupled Partial Differential Equations (PDEs) is obtained from the conformal Killing equations. These equations are solved by using direct integration techniques to explore the components of CVFs. Utilizing these components, we get a system of three integrability conditions. Finally, we achieve CVFs along with conformal factors for unique possibilities of unknown metric functions from the solution of these conditions. From our results, it is examined that Bianchi type-I spacetimes admit five or fifteen CVFs for specific choices of metric functions.

Killing vector fields of Bianchi type I spacetimes via Rif tree approach

In this paper, we have adopted a new approach to study the Killing vector fields of locally rotationally symmetric and general Bianchi type I spacetimes. Instead of directly integrating the set of Killing’s equations, an algorithm is developed in Maple which converts these equations to the reduced involutive form (Rif) and consequently it imposes some restrictions on the metric functions in the form of a tree, known as Rif tree. The set of Killing’s equations is then solved for each branch of the Rif tree, giving the explicit form of the Killing vector fields. The structure of Lie algebra is presented for each set of the obtained Killing vector fields and some physical implications of the obtained metrics are discussed.

Beyond gravitomagnetism with applications to Mercury’s perihelion advance and the bending of light

The expansion of both sides of Einstein’s field equations in the weak-field approximation, up to terms of order [Formula: see text] is derived. This new approach leads to an extended form of gravitomagnetism (GEM) properly named as Beyond Gravitomagnetism (BGEM). The metric of BGEM includes a quadratic term in the gravitoelectric potential n the time and also space metric functions in contrast with first post-Newtonian [Formula: see text]PN approximation where the quadratic term appears only in the time metric function. This nonlinear term does not appear in conventional GEM, but is essential in achieving the exact value of Mercury’s perihelion advance as we explicitly show. The new BGEM metric is also applied to the classical problem of light deflection by the Sun, but the contribution of the new nonlinear terms produce higher-order terms in this problem and can be neglected, giving the correct result obtained already in the Lense–Thirring (GEM) approximation. The BGEM approximation also provides new terms that depend on the dynamics of the system, which may bring new insights into galactic and stellar physics.

Kundt geometries and memory effects in the Brans–Dicke theory of gravity

Memory effects are studied in the simplest scalar–tensor theory, the Brans–Dicke (BD) theory. To this end, we introduce, in BD theory, novel Kundt spacetimes (without and with gyratonic terms), which serve as backgrounds for the ensuing analysis on memory. The BD parameter $$\omega $$ ω and the scalar field ($$\phi $$ ϕ ) profile, expectedly, distinguishes between different solutions. Choosing specific localised forms for the free metric functions $$H'(u)$$ H ′ ( u ) (related to the wave profile) and J(u) (the gyraton) we obtain displacement memory effects using both geodesics and geodesic deviation. An interesting and easy-to-understand exactly solvable case arises when $$\omega =-2$$ ω = - 2 (with J(u) absent) which we discuss in detail. For other $$\omega $$ ω (in the presence of J or without), numerically obtained geodesics lead to results on displacement memory which appear to match qualitatively with those found from a deviation analysis. Thus, the issue of how memory effects in BD theory may arise and also differ from their GR counterparts, is now partially addressed, at least theoretically, within the context of this new class of Kundt geometries.

Neutrino Anomalies and Chiral Flipping in Anisotropic Einstein-Cartan Cosmology

Recently Palle has investigated the chiral vorticity and Cartan torsion in neutrino asymmetries. In his case he addressed this problem in Goedel s like anisotropic Einstein-Catan cosmology. In this paper we discusse how these ideas applied to sheared Bianchi types I Einstein-Cartan (EC) neutrino amisotropic cosmology, affect the handness of neutrinos in the universe. Actually here a novel concept of the chiral metric is introduced where metric functions also possess two distinct signs as in neutrino flipping or helicity. The axial anomaly equation for neutrinos in the presence of torsion and metric chirality is shown to produce left-handed neutrinos from right-handed torsion. Metric chirality is shown to be able to define how the metric would behave far away of neutrino density. Chiral flipping of the chiral neutrinos in the presence of torsion is also investigated. It is shown that when the chiral torsion is left-handed the chemical chiral potential vanishes as the universe expands.

An efficient method to detect communities in social networks

Social networks represent the social structure, which is composed of individuals having social interactions among them. The interactions between the units in a social network represent the relations of the various social contacts and aim at finding different individuals in that network, with similar interests. It is a challenging problem to detect the social interactions between individuals with comparable considerations and desires from a large social network, which can be termed as community detection. Detection of the communities from social networks has been done by other authors previously, and many community identification algorithms were also proposed, but those communities' identification has been achieved on the online available data sets. The proposed algorithm in this paper has been named as Average Degree Newman Girvan (ADNG) algorithm, which can easily identify the communities from the real-time data sets, collected from the social network websites. The approach presented here is based on first determining the average degree of the network graph and then identifying the communities using the Newman Girvan algorithm. The proposed algorithm has been compared with four community detection algorithms, i.e., Leading eigenvector (LEC) algorithm, Fastgreedy (FG) algorithm, Leiden algorithm and Kernighan-Lin (KL) algorithm based on a few metric functions. This algorithm helps to detect communities for different domains, like for any proposed government policy, online shopping products, newly launched products in a market, etc.

Acceptability conditions and relativistic barotropic equations of state

We sketch an algorithm to generate exact anisotropic solutions starting from a barotropic EoS and setting an ansatz on the metric functions. To illustrate the method, we use a generalization of the polytropic equation of state consisting of a combination of a polytrope plus a linear term. Based on this generalization, we develop two models which are not deprived of physical meaning as well as fulfilling the stringent criteria of physical acceptability conditions. We also show that some relativistic anisotropic polytropic models may have singular tangential sound velocity for polytropic indexes greater than one. This happens in anisotropic matter configurations when the polytropic equation of state is implemented together with an ansatz on the metric functions. The generalized polytropic equation of state is free from this pathology in the tangential sound velocity.

Erratum: Dispersion of gravitational waves in cold spherical interstellar medium

The study published in IJMPD 27(4):1850040, 2018 provided a numerical result for the frequency-shift of GWs due to dispersion in interstellar medium. In order to adjust the metric functions of the originally improperly matched ‘background’ spacetime in Sec. 2.1, the authors have adopted Darmois–Israel junction conditions. In Sec. 4.1 the code used in the original paper erroneously computed the magnitude of frequency-shift for the transient event GW150914 due to a missing conversion factor. In both cases where numerical errors and potential contradictions have been identified and eliminated, adjustments were undertaken in order to maintain consistency with closely-related earlier studies.

Quasi-normal modes and stability of Einstein–Born–Infeld black holes in de Sitter space

We study gravitational perturbations of electrically charged black holes in (3+1)-dimensional Einstein–Born–Infeld gravity with a positive cosmological constant. For the axial perturbations, we obtain a set of decoupled Schrödinger-type equations, whose formal expressions, in terms of metric functions, are the same as those without cosmological constant, corresponding to the Regge–Wheeler equation in the proper limit. We compute the quasi-normal modes (QNMs) of the decoupled perturbations using the Schutz–Iyer–Will’s WKB method. We discuss the stability of the charged black holes by investigating the dependence of quasi-normal frequencies on the parameters of the theory, correcting some errors in the literature. It is found that all the axial perturbations are stable for the cases where the WKB method applies. There are cases where the conventional WKB method does not apply, like the three-turning-points problem, so that a more generalized formalism is necessary for studying their QNMs and stabilities. We find that, for the degenerate horizons with the “point-like” horizons at the origin, the QNMs are quite long-lived, close to the quasi-resonance modes, in addition to the “frozen” QNMs for the Nariai-type horizons and the usual (short-lived) QNMs for the extremal black hole horizons. This is a genuine effect of the branch which does not have the general relativity limit. We also study the exact solution near the (charged) Nariai limit and find good agreements even far beyond the limit for the imaginary frequency parts.