Field Equations Research Articles

Eringen’s nonlocal elasticity theory for the analysis of two temperature generalized thermoelastic interactions in an anisotropic medium with memory

PurposeThe purpose of this paper is to investigate the thermoelastic interactions in a homogeneous, transversely isotropic infinite medium with a spherical cavity in the context of two temperature Lord-Shulman (2TLS) generalized theory of thermoelasticity considering Eringen’s nonlocal theory and memory dependent derivative (MDD). Memory-dependent derivative is found to be better than fractional calculus for reflecting the memory effect which leads us to the current investigation.Design/methodology/approachThe governing field equations of the problem are solved analytically using the eigenvalue approach in the transformed domain of Laplace when the cavity’s boundary is being loaded thermomechanically. Using MATLAB software the numerical solution in real space-time domain is obtained by Stehfest method.FindingsNumerical results for the different thermophysical quantities are presented in graphs and the effects of delay time parameter, non-local parameter and two temperature parameters are studied thereafter. The outcomes of this study convince that the displacement u, conductive temperature ϕ, thermodynamic temperature θ are concave upward whereas radial stress τrr is concave downward for every choice of delay time parameter ω, two temperature parameter η and non-local parameter “ζ”. As a specific instance of our findings, the conclusions of an equivalent problem involving integer order thermoelasticity theory can be obtained, and the corresponding results of this article can be readily inferred for isotropic materials.Originality/valueThe novelty of this research lies in the adoption of generalized thermoelastic theory with memory dependent derivative and Eringen’s nonlocality for analyzing the thermoelastic interactions in an infinite body with spherical cavity by employing eigenvalue approach. It has applications to many thermo-dynamical systems.

Constraining hybrid potential scalar field cosmological model in Lyra’s geometry with recent observational data

In this study, we investigate a scalar field cosmological model with Lyra’s geometry to explain the present cosmic expansion in a homogeneous and isotropic flat FRW universe. In Einstein’s field equations, we presupposed a variable displacement vector as an element of Lyra’s geometry. In the context of the conventional theory of gravity, we suggest a suitable parametrization of the scalar field’s dark energy density in the hybrid function of redshift [Formula: see text], confirming the essential transition behavior of the universe from a decelerating era to the present accelerated scenario. We present constraints on model parameters using the most recent observational datasets from OHD, BAO/CMB and Pantheon, taking Markov Chain Monte Carlo (MCMC) analysis into account. For the proposed model, the best estimated values of parameters for the combined dataset (OHD, BAO/CMB and Pantheon) are [Formula: see text][Formula: see text]km/s/Mpc, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. The model exhibits a flipping nature, and the redshift transition occurs at [Formula: see text]. The current value of the decelerated parameter for the proposed model is calculated as [Formula: see text] for the combined dataset. Some dynamical properties of the model like energy density ([Formula: see text]), scalar field pressure ([Formula: see text]), EoS parameter of scalar field ([Formula: see text]), and effective EoS parameter ([Formula: see text]) are analyzed and presented. Further, we have also examined the statefinder diagnosis and jerk parameters of the derived model. The total density parameter for the derived model is found to be unity which is in nice agreement with recent standard findings.

Bifurcation structure of steady states for a cooperative model with population flux by attractive transition

AbstractThis paper studies the steady states to a diffusive Lotka–Volterra cooperative model with population flux by attractive transition. The first result gives many bifurcation points on the branch of the positive constant solution under the weak cooperative condition. The second result shows every steady state approaches a solution of the scalar field equation as the coefficients of the flux tend to infinity. Indeed, the numerical simulation using pde2path exhibits the global bifurcation branch of the cooperative model with large population flux is near that of the scalar field equation.

Analytical solutions to Einstein field equations for spherically symmetric anisotropic matter: a comparative study using Tolman VII metric potential

AbstractIn this paper, we present analytical solutions to the Einstein field equations for spherically symmetric anisotropic matter distributions using the well-established Tolman VII metric potential, chosen for its strong physical and mathematical foundations. Our solutions are derived using three distinct approaches: the vanishing complexity factor condition (VCC), the embedding class I condition (ECC), and the conformally flat condition (CFC). We conduct a comprehensive comparative analysis of these three approaches. By ensuring a smooth match between the interior spacetime metric and the exterior Schwarzschild metric, and applying the condition of vanishing radial pressure at the boundary, we determine the model parameters. We graphically assess the model’s stability by examining conditions such as causality, the adiabatic index, equations of state, and the generalized Tolman–Oppenheimer–Volkov (TOV) equation, considering the forces acting within the system. Additionally, the effects of anisotropy on the stars’ physical characteristics are investigated through graphical representations.

Impact of charge and non-minimal fluid-geometry coupling on anisotropic interiors

This paper explores the interior configuration of various charged anisotropic compact models within the framework of f(R,T,RληTλη) gravity. The chosen model in this theory is represented by R+γRληTλη , where γ is a real-valued parameter. We adopt a static spherical metric to describe the interior of compact strange stars and derive the corresponding field equations. The solution to these equations is then obtained using the Finch-Skea metric and a linear equation of state. Taking the radius and mass of the compact star model 4U 1820-30 as a case study, we investigate the impact of charge and modified corrections on its internal distribution. The stability of the resulting model is also determined within a specific range of γ. Additionally, we determine the values of the model parameter through the vanishing radial pressure constraint, aligning with the experimental data of eight different stars. Our findings indicate that the resulting model adheres to the conditions necessary for physically relevant interiors, particularly in the case of lower charge.

A Microlocal Investigation of Stochastic Partial Differential Equations for Spinors with an Application to the Thirring Model

AbstractOn a d-dimensional Riemannian, spin manifold (M, g) we consider non-linear, stochastic partial differential equations for spinor fields, driven by a Dirac operator and coupled to an additive Gaussian, vector-valued white noise. We extend to the case in hand a procedure, introduced in Dappiaggi et al (Commun Contemp Math 27(07):2150075, 2022), for the scalar counterpart, which allows to compute at a perturbative level the expectation value of the solutions as well as the associated correlation functions accounting intrinsically for the underlying renormalization freedoms. This framework relies strongly on tools proper of microlocal analysis and it is inspired by the algebraic approach to quantum field theory. As a concrete example we apply it to a stochastic version of the Thirring model proving in particular that it lies in the subcritical regime if $$d\le 2$$ d ≤ 2 .

Constraints and time evolution in generic f(Riemann) gravity

Abstract We give a detailed canonical analysis of the n-dimensional f(Riemann)
gravity, correcting the earlier results in the literature. We also
write the field equations in the Fischer-Marsden form which is amenable
to identifying the non-stationary energy on a spacelike hypersurface.
We give pure R^2 and R_{\mu\nu}R^{\mu\nu} theories as examples.

Galactic dynamics in the presence of scalaron: a perspective from f(R) gravity

We consider f(R) modified gravity theory incorporating the chameleon mechanism to address galactic dynamics. By employing the metric formalism and utilizing a conformal transformation, we simplify the field equations and describe the extra degree of freedom f R via a scalar field (scalaron) with chameleonic behavior. A recently proposed f(R) model is analyzed to illustrate this behavior effectively. Subsequently, the rotational velocity equation including the scalaron’s contribution is derived for a test particle in a static, spherically symmetric spacetime. Then we generate rotation curves and fit them to observational data of thirty seven galaxies using two fitting parameters, M 0 and r c , the total mass and core radius of a galaxy respectively.

Apparent horizon tracking in supercritical solutions of the Einstein-scalar field equations in spherical symmetry in affine-null coordinates

Apparent horizon tracking in supercritical solutions of the Einstein-scalar field equations in spherical symmetry in affine-null coordinates

Stability Analysis of Static Spherical Spacetime in Extended Symmetric Teleparallel Gravity

Abstract Our manuscript aims to analysis the viability and stability of
anisotropic stellar objects in the modified symmetric teleparallel
gravity. A particular model of this extended theory is considered to
formulate explicit field equations which govern the interaction
between matter and geometry. The configuration of static spherical
symmetric structures is examined through the Finch-Skea solution.
However, the values of unknown constants in the metric potentials
are evaluated by the Darmois junction conditions. For the viability
of proposed stellar objects, the physical parameters including
density, pressure, anisotropy, mass, energy constraints, compactness
function and redshift are analyzed. Furthermore, stability of the
proposed stellar objects is investigated by causality condition,
Herrera cracking approach and adiabatic index. Our findings indicate
that the proposed stellar objects are viable as well as stable in
the presence of correction terms.

Various exact solutions of the (4+1)-dimensional Boiti–Leon–Manna–Pempinelli-like equation by using bilinear neural network method

In this paper, Bilinear neural network method is used to investigate the (4+1)-dimensional Boiti–Leon–Manna–Pempinelli-like (BLMP-like) equation, which can be utilized to model wave phenomena in incompressible fluids and in the study of fluid mechanics. On the basis of the generalized bilinear operators, the generalized bilinear equation is formulated. In the bilinear neural network method, a variety of neural network structures, including the single hidden layer and multiple hidden layers neural network are employed to investigate the exact solutions. By considering the special values of the parameters involved, the dynamical behavior of the solution is analyzed graphically. The effective method adopted significantly contributes to the understanding of nonlinear evolution equations in various fields, including plasma physics, mathematical physics, electromagnetism, and fluid dynamics.

Noether symmetries and conservation laws in some analytic spherically symmetric spacetimes of f(R, L m ) gravity

In general relativity, dark energy is usually illustrated by a cosmological constant(Λ), but f(R, L m ) gravity provides a different approach to cosmic acceleration by modifying the gravitational theory. In the present paper, the non-static spherically symmetric spacetimes have been derived by taking into account f(R, L m ) = f 1(R) + H(L m )f 2(R). Lie symmetry approach is operated to reduce the order of the partial differential equations corresponding to the field equations, which are further solved. Killing and Noether symmetries provides insights into the conservation laws. So, the obtained spacetimes have been investigated to obtain the Killing and Noether symmetries. The Lagrangian approach have been used to obtain the Noether symmetries. This study is well-structured, as it provides a justification for the well-established result that Noether symmetries encompass Killing symmetries [1]. Also the conserved quantities and commutators of Noether symmetries have been calculated.

The de Broglie-Einstein-Rosen gravitational wave

de Broglie gravitational waves are solutions of the linearized Einstein's field equations in vacuum, with intriguing properties. They are axially symmetric and have an effective mass, which is responsible for longitudinal effects that are absent in standard gravity waves. Moreover, they represent a classical realization of a form of dynamics proposed for quantum particles by de Broglie one hundred years ago. In this paper we will show that this perturbation field can be obtained, apart from a proportionality constant, in the weak field limit of a particular Einstein-Rosen field, which we call the de Broglie-Einstein-Rosen wave. Some properties of this exact solution are also discussed.

Metric-Affine F(T,Q) gravity: cosmological implications and constraints

Abstract In this paper, we investigate some exact cosmological models in Metric-Affine $F(T,Q)$ gravity, with observational constraints. The Metric-Affine $F(T,Q)$ gravity is some kind of unification of two known gravity theories, namely, the $F(T)$ gravity and the $F(Q)$ gravity. We obtain the field equations of the Metric-Affine theory by considering the metric tensor and the general affine connection as independent variables. We then focus on the particular case in which the $F(T,Q)$ function characterizing the aforementioned metric-affine models is linear, that is, $F(T,Q)=\lambda T+\mu Q$. We investigate this linear case and consider a Friedmann-Lema\^{i}tre-Robertson-Walker background to study cosmological aspects and applications. We have obtained three exact solutions of the modified field equations in two different cases, $T$ and $Q$, using the Hubble function $H(t)$ and the scale factor $a(t)$. We then placed observational constraints on these solutions using the Hubble $H(z)$ datasets and the MCMC analysis. We have investigated the deceleration parameter $q(z)$ and effective EoS parameters, and a comparative study of all three models with $\Lambda$CDM model has been carried out.

Conservation laws of stress–energy tensor in Yang–Mills theory

In this paper we present a new identity to associate the conservation laws of stress–energy tensor with the field equations in Yang–Mills theory. The Lorentz force is included with a consistent formulation as in Maxwell theory.

Phase velocity shifts of shear surface waves in flexoelectric wave-guide clamped on piezomagnetic base

Surface acoustic wave devices featuring periodic layers of piezomagnetic and piezoelectric-flexoelectric layers are subject to intense investigation. In miniaturized devices, large strain gradients are possible that produce significant flexoelectric fields in piezoelectric components. In the present theoretical research, surface acoustic wave transference has been manifested in a flexoelectric waveguide clamped over a piezomagnetic base. This endeavor involves the formulation and solution of coupled magneto-electro-elastic field equations governing the structure’s behavior. Coupled magneto-electro-elastic field equations for the structure have been derived and solved utilizing analytical techniques. By accounting for pertinent boundary conditions, the dispersion relations characterizing the velocity of surface waves, both in scenarios with and without electrodes have been obtained. Based on proper numerical examples, the frequency and phase velocity spectrum have been plotted offering insights into key parameters i.e. modal frequency, phase velocity, and wave attenuation. The outcomes of the theoretical study may be helpful in providing insights into mechanical wave propagation in coupled piezoelectric/piezomagnetic structures.

Constraining the variable generalized Chaplygin gas model in matter creation cosmology

We explore the variable generalized Chaplygin gas (VGCG) model in the theory of matter creation cosmology within the framework of a spatially homogeneous and isotropic flat Friedmann—Lemaître—Robertson—Walker space-time. Matter creation cosmology is based on reinterpretation of the energy–momentum tensor in Einstein’s field equations. This creation corresponds to an irreversible energy flow from the gravitational field to the created matter constituents. The variable Chaplygin gas (VCG) is also studied as a particular solution. We use the Markov chain Monte Carlo method to constrain the free parameters of three models, namely, Lambda-Cold-Dark matter (ΛCDM), VGCG and VCG models with and without matter creation from the latest observational data from baryon acoustic oscillations, cosmic chronometer, type Ia supernovae (Pantheon) including gamma-ray bursts, quasars and the local measurement of H 0 from R21 data. Two different combinations of dataset provide a fairly tight constraint on the parameters of the ΛCDM, VGCG and VCG models. The present values of various cosmological parameters are obtained, which are very close to the ΛCDM model. Furthermore, we perform stability analysis, Bayesian evidence analysis and information criteria analysis for these models through studying the sound speed, Bayes factor, and Akaike information criteria (AIC) and Bayesian information criteria (BIC) selection criteria. The values of sound speed for VGCG and VCG models shows that both the models are stable. According to AIC, it is observed that VGCG and VCG models with matter creation are supported considerably less by current observations, while BIC shows that these models are not favoured by observational data.

Self-bound isotropic models in [formula omitted] gravity and effect of [formula omitted] parameter on mass–radius relation and stability of compact objects

The present article investigates the effect of f(Q) parameters on two classes of exact spherically symmetric self-bound isotropic solutions for compact objects. The field equation in f(Q) gravity is solved using Korkina–Orlyanskii and Buchdahl models. The physical validity of both models has been verified using regularity, stability, and hydrostatic equilibrium tests. We have also shown the effect of f(Q) gravity parameter α on the stability and mass–radius relation. We predicted the radii of observable compact objects GW 190814, PSR J0740+6620 PSR J1614, 2230, Cen X-3, and LMC X-4. In the absence of β, the massive neutron star GW 190814 is detected at greater values of α=1.5 and 1.2 for models I and II respectively. The corresponding estimated radii for both models are 15.30−0.29+0.18km and 15.03−0.25+0.17km. Additionally, as the non-metricity scalar α increases, the mass–radius decreases, and when β increases with fix α, the reverse scenario arises. Our finding indicates that a lower mass−gap can be achieved in f(Q) gravity theory as compared to the standard theory of gravity.

Maximum-correntropy-based sequential method for fast neural population activity reconstruction in the cortex from incomplete abnormally-disturbed noisy measurements

This paper continues to explore the membrane potential reconstruction and pattern recognition problem in a neural tissue modeled by Stochastic Dynamic Neural Field (SDNF) equation. Although recent research has suggested an efficient solution based on the state-space approach through nonlinear Bayesian filtering framework, it is becoming extremely difficult to ignore the existence of non-Gaussian uncertainties in the SDNFs as well as the stability problem of neuronal population dynamics to outliers. Motivated by recent events in signal processing and mathematical neuroscience, this paper explores the SDNFs in a presence of non-Gaussian uncertainties, which is the shot noise case, where the corrupted data might appear due to broken sensors. We derive the “distributionally robust” state estimator for the membrane potential reconstruction process that is the Maximum Correntropy Criterion Extended Kalman Filter (MCC-EKF) as well as its fast and numerically robust (to roundoff) implementation method by using the sequential principle of processing the measurement vectors. The numerical experiments are provided to illustrate the performance of the novel estimation methods.

Inflation scenario in a non-minimal f(Q) gravity model

In the context of f(Q) gravity, cosmological inflation takes a different turn. f(Q) gravity is a modified theory of gravity, where the Lagrangian is a function of the non-metricity scalar Q. f(Q) gravity theory is part of an extensive class of modified gravity theories designed to explain the accelerated expansion of the universe without the requirement for dark energy. In this paper, we study the modified gravity f(Q) in which the scalar field is non-minimally coupled with the matter (it has a new interaction term αQ(1+ϕ2) with the inflaton scalar field (ϕ) and non-metricity scalar (Q)). In pursuit, an inflationary model is extended and investigated by determining the slow-roll parameters and obtaining the model's linear perturbations after calculating the field equation. By comparing the model parameters with the CMB observational data, the model is adapted to observational data through the constraint of the parameters. After some numerical calculations, we show our model is consistent with observational data and free of the phantom if 1<α<1.5 and 1.42<γ2<1.75.