Narrow Results

This paper is the continuation of the groundwork laid in [A. Iram, A. A. Siddiqui and T. Feroze, Int. J. Mod. Phys. D31(11) (2022) 2240006], where the Segre classification scheme was applied to categorize spherically symmetric static spacetime metrics into four possible Segre types $[(1,111)],$$[1,(111)],$$[(1,1)(11)],$ or $[1,1(11)]$. The solution for type $[(1,111)]$ leads to the Schwarzschild de-Sitter/anti de-Sitter metrics. The eigenvalue degeneracy in Segre types identifies the kind of matter distribution in space and aid in the consideration of novel solutions for the corresponding energy momentum tensor. We deal with an anisotropic distribution of matter correlated with electric field intensity for types $[(1,1)(11)]$ and $[1,1(11)]$. The type $[1,(111)]$ refers to ideal fluid characterized by uniformly distributed pressure. A comprehensive examination is conducted in scenarios where all physical and stability criteria are satisfied. Nevertheless, for type $[(1,1)(11)]$, the strong energy and causality prerequisites are breached due to negative pressure, suggesting the existence of dark energy where the attributes of standard matter cannot be met. Furthermore, the numerical test for models is conducted for the compact objects $4\text{U}1538-52$, $\text{PSR}\text{J}1614-2230$, $4\text{U}1608-52$, and $\text{EXO}1785-248$. Each star’s density, pressure, and compactness factor are observed, showing the regularity at the origin. These observations impart that the discover models are plausible since they accurately represent the observable system.

This research paper aims to redefine the complexity factor in $f(R,G)$ gravity and the appearance of electric charge, where $R$ is the Ricci scalar and $G$ is the Gauss–Bonnet term. In this context, we intend to analyze the splitting of the Riemann tensor after considering the anisotropic distribution of the charged fluid related to the spherically symmetric spacetime. We interpret $Y_{\mathrm{\text{TF}}}$ as the complexity factor among all the determined structural scalars that encompasses the characteristics of anisotropic pressure and the effective representation of the energy density. The correction terms associated with modified theory are considered to calculate some significant results related to the Weyl scalar, Tolman mass, and the complexity factor (CF). Moreover, the expression for CF is established by using the structure scalars determined in our paper, and the diminishing complexity restraint is utilized to determine the solutions for the various models. The celestial object having non-uniform energy density and anisotropic pressure asserts the maximum intricacy. But, if the effects of non-uniform energy density and anisotropic distribution of pressure are eradicated due to the presence of dark source terms associated with modified gravity then these fluids may not exhibit any complexity. Consequently, it is revealed that the constituents of effective and electromagnetic parts directly influence the structure scalars and CF.

This paper explores a comprehensive approach to modeling compact stars that incorporates both normal matter and dark energy. We employ the Durgapal–Fuloria ansatz within the context of Rastall gravity to derive a relativistic analytical solution. The model is thoroughly analyzed both analytically and graphically, to assess its physical properties and facilitates a comparison with the results of classical general relativity. Our findings demonstrate that the model we have put forward is in substantial agreement with observational data for three different compact star representatives like Her X-1, PSR J0348+0432, and RX J1856.3-37.2. We evaluate the model’s viability by examining its energy conditions, stability, and adherence to the Buchdahl limit, all of which are found to be satisfactory. The analysis confirms the stable solution for Rastall parameter spanning −0.005 to 0.11, and it converges to standard general relativity when the coupling parameter approaches to zero.

The changes of the structure in the energy range of the interplanetary magnetic field (IMF) turbulence versus solar activity can be considered as one of the important reasons of the long period (11-year) modulation of galactic cosmic ray (GCR) intensity; the amplitude of the 27-day variation of GCR anisotropy is greater in the qA > 0 periods than in the qA < 0 periods of the solar magnetic cycles in a good correlation with the similar changes of the 27-day variation of GCR intensity.

We summarize the main results reported by EAS-TOP in the study of cosmic rays in the energy range 10¹² – 10¹⁶ eV (from the direct measurements up to above the "knee"), i.e. the region which is generally considered to represent the high energy galactic radiation.

Anisotropies in the arrival directions of cosmic rays reflect their source distribution and propagation properties. In the presented analysis extensive air shower measurements with KASCADE are analyzed with respect to large and small scale anisotropies. The resulting upper limits on large scale anisotropy amplitudes of 10^-3 to 10^-2 restrict the parameter space of several propagation models. No cosmic ray point sources could be found in a sky survey of the northern hemisphere. Typical upper flux limits for point sources are around 10^-10m^-2s^-1.

The anisotropy of cosmic rays, produced by Galactic supernovae is calculated. It is a factor 100 ÷ 1000 larger than the observed value at 1 PeV. It is shown that this contradiction can be explained if a cosmic ray diffusion coefficient is small in the local vicinity of the Sun.

The fluid models mentioned in the title are studied in a modified approach, based on two formulas for the mass function. All characteristics of the fluid are expressed through a master potential, satisfying an ordinary second-order differential equation. Different constraints are imposed on this core of relations, finding new solutions and deriving the classical results for perfect fluids as particular cases. All charged anisotropic solutions, all conformally flat and all uniform density solutions are found. A large class of solutions with linear equation among the two pressures is derived, including the case of vanishing tangential pressure. The mechanism responsible for the appearance of equation of state is elucidated.

We have studied the thermal suppression of the bottomonium states in relativistic heavy-ion collision at LHC energies as function of centrality, rapidity, transverse momentum. First, we address the effects of the nonperturbative confining force and the momentum anisotropy together on heavy quark potential at finite temperature, which are resolved by correcting both the perturbative and nonperturbative terms of the potential at T = 0 in a weakly-anisotropic medium, not its perturbative term alone as usually done in the literature. Second, we model the expansion of medium by the Bjorken hydrodynamics in the presence of both shear and bulk viscosity, followed by an additional pre-equilibrium anisotropic evolution. Finally, we couple them together to quantify the yields of bottomonium production in nucleus–nucleus collisions at LHC energies and found a better agreement with the CMS data. Our estimate of the inclusive ϒ(1S) production indirectly constrains both the uncertainties in isotropization time and the shear-to-entropy density ratio and favors the values as 0.3 fm/c and 0.3 (perturbative result), respectively.

In this paper, we study the behavior of static spherically symmetric relativistic model of the strange star SAX J1808.4-3658 by exploring a new exact solution for anisotropic matter distribution. We analyze the comprehensive structure of the space–time within the stellar configuration by using the Einstein field equations amalgamated with quadratic equation of state (EoS). Further, we compare solutions of quadratic EoS model with modified Bose–Einstein condensation EoS and linear EoS models which can be generated by a suitable choice of parameters in quadratic EoS model. Subsequently, we compare the properties of strange star SAX J1808.4-3658 for all the three EoS models with the help of graphical representations.

In this paper, we develop a complexity factor for static sphere in modified Gauss–Bonnet gravity with anisotropic and nonhomogeneous configuration. We use the field equations as well as equation of continuity to derive expressions for mass function in $f({𝒢})$ gravity. The Riemann tensor is split using Bel’s approach to formulate structure scalars that exhibit fundamental properties of the system. A complexity factor is developed on the basis of these scalars and the condition of vanishing complexity is used to obtain solutions of two different models. It is observed that modified terms increase complexity of the matter distribution.

In this paper, we consider a new solution to discuss the physical aspects of anisotropic compact celestial bodies in the background of $f({𝒢},{𝒯})$ theory. We take static spherically symmetric metric to describe the internal region of the stellar objects and apply the embedding class-I method to get the metric solution corresponding to a specific $f({𝒢},{𝒯})$ model. By matching the interior and exterior geometries at the boundary, we find the values of unknown constants. We check the stability and viability of the resulting solution through various parameters that include energy bounds, causality condition, Herrera’s condition, role of adiabatic index, redshift and compactness factor. The graphical interpretation is done for some particular compact star candidates, i.e. LMC X-4, Cen X-3, 4U 1820-30 and Vela X-1. We conclude that our model provides physically acceptable structure of the considered compact objects and is also stable.

In this paper, we explore the behavior and anisotropic structure of quark stellar models in the framework of massive Brans–Dicke gravity. The system of field equations, representing a static sphere, is formulated by incorporating the MIT bag model. We use the Karmarkar condition for embedding class-one to formulate a relativistic model corresponding to a well-behaved radial metric function. The values of unknown parameters are determined through the matching of internal and external space–times at the hypersurface. The observed masses and radii of the strange star candidates (RXJ 1856-37, Her X-1 and PSR J1614-2230) specify the solution. Further, we evaluate the impact of the massive scalar field on state parameters and investigate the viability as well as stability of the self-gravitating objects. It is found that the obtained values of the bag constant (corresponding to each star) lie within the accepted range. Moreover, the anisotropic structure meets the necessary viability and stability criteria.

In this paper, we study the effects of anisotropy on phase transitions in graphene. We work with a low-energy effective field theory which is strongly coupled, and solves a coupled set of Schwinger–Dyson equations. We show that the effect of anisotropy is to reduce the critical coupling.

This paper describes a new computational method of fully automated anisotropic triangulation of a trimmed parametric surface. Given as input: (1) a domain geometry and (2) a 3×3 tensor field that specifies a desired anisotropic node-spacing, this new approach first packs ellipsoids closely in the domain by defining proximity-based interacting forces among the ellipsoids and finding a force-balancing configuration using dynamic simulation. The centers of the ellipsoids are then connected by anisotropic Delaunay triangulation for a complete mesh topology. Since a specified tensor field controls the directions and the lengths of the ellipsoids' principal axes, the method generates a graded anisotropic mesh whose elements conform precisely to the given tensor field.

We consider the macroscopic model derived by Degond and Motsch from a time-continuous version of the Vicsek model, describing the interaction orientation in a large number of self-propelled particles. In this paper, we study the influence of a slight modification at the individual level, letting the relaxation parameter depend on the local density and taking in account some anisotropy in the observation kernel (which can model an angle of vision).

The main result is a certain robustness of this macroscopic limit and of the methodology used to derive it. With some adaptations to the concept of generalized collisional invariants, we are able to derive the same system of partial differential equations, the only difference being in the definition of the coefficients, which depend on the density. This new feature may lead to the loss of hyperbolicity in some regimes.

We then provide a general method which enables us to get asymptotic expansions of these coefficients. These expansions shows, in some effective situations, that the system is not hyperbolic. This asymptotic study is also useful to measure the influence of the angle of vision in the final macroscopic model, when the noise is small.

We consider an anisotropic first-order ODE aggregation model in two dimensions and its approximation by a second-order relaxation system. The relaxation model contains a small parameter $𝜀$, which can be interpreted as inertia or (non-dimensionalized) response time. We examine rigorously the limit $𝜀\to 0$ of solutions to the relaxation system. Of major interest is how discontinuous (in velocities) solutions to the first-order model are captured in the zero-inertia limit. We find that near such discontinuities, solutions to the second-order model perform fast transitions within a time layer of size ${𝒪}({𝜀}^{2/3})$. We validate this scale with numerical simulations.

The paper presents estimates of the S-wave velocity and the crack density at which fractured reservoirs begin to play an important role in oil exploration. Transverse isotropy with a horizontal axis of symmetry (HTI) is the simplest azimuthally anisotropic model used to describe fractured reservoirs that contain parallel vertical cracks. A double profile concept is used to develop an equation for the P-S wave normal-moveout (NMO) velocity. The azimuthal NMO velocities of the P- and P-S waves can then be used to estimate the velocities of the S-waves and Thomsen's coefficient, γ. For multilayered media, a recursive equation is developed for the NMO velocity in each layer. The numerical results indicate that the S-wave NMO velocity can be accurately estimated using the P- and P-S wave NMO velocities in HTI media. An important parameter of fracture systems that can be measured from seismic data is the crack density which can be estimated using the NMO velocities of the P- and S-waves from horizontal reflectors. Therefore, fractures can be completely characterized by the joint inversion of P-waves and converted P-S waves in HTI media.

A simple model of seismic wave attenuation combining anisotropy with anelastic effects is constructed. The anelastic response is based on the Cole–Cole relaxation function. Time-stepping finite-difference and ray-asymptotic methods of numerical solution are discussed.

A novel adaptive strategy, dubbed m-adaptation, is developed for solving the acoustic wave equation (in the time domain) on square meshes. The finite element, the finite difference and a few other more recent methods are shown to be particular members of the mimetic family. Analysis of the parametric family of mimetic discretization methods is performed to find the optimal member that eliminates the numerical dispersion at the fourth-order (as in Ref. 1) and the numerical anisotropy at the sixth-order (higher than in Ref. 1). The stability condition for the optimal method is derived that turns out to be comparable to the classical Courant condition. The numerical experiments show that the new approach is consistently better than the classical methods for reducing a long-time integration error.