Isotropic Fluid Research Articles

A Brief analysis of isotropic Karmarkar models in modified gravity theory

This investigation explores the nature of charged compact stars within the modified theory whose functional depends on the Ricci scalar, Lagrangian density of the matter and trace of the energy–momentum tensor. The methodology involves starting with a static spherical spacetime filled with the isotropic fluid. The field equations are then formulated corresponding to a specific minimal model of this extended theory. While developing these equations, we also take into account different choices of the fluid Lagrangian density. Further, we use the Karmarkar condition to deal with the extra degrees of freedom in the equations of motion and construct their corresponding solutions. The metric components obtained from the Karmarkar condition possess three constants which are evaluated through the matching conditions of the interior spherical geometry with the exterior vacuum spacetime. Further, we explore the obtained models for different values of the parameters through a comprehensive graphical analysis. Conclusively, our results agree well with the physical conditions and thus advance our understanding of the impact of the considered gravity theory on the internal composition of stellar objects.

Evolving wormhole geometry from dark matter energy density

We analyse traversable wormholes defined by the dynamic line elements that asymptotically approach Friedmann–Robertson–Walker (FRW) universe. These dynamical wormholes is supported by the galactic dark matter as well as perfect isotropic fluid. We will discuss several evolving Lorentzian wormholes comprising with different perfect isotropic fluids in addition to various scale factors. We will speculate the various significance, features and throat energy conditions for these evolving traversable Lorentzian wormholes.

Black holes immersed in dark matter: Energy condition and sound speed

In this work, we study the impact of the environment around a black hole in detail. We introduce nonvanishing radial pressure in a manner analogous to compact stars. We examine both isotropic and anisotropic fluid configurations with and without radial pressure respectively. Our focus extends beyond just dark matter density to the vital role of the energy condition and sound speed in the spacetime of a black hole immersed in matter. In cases of anisotropic pressure with vanishing radial pressure, all profiles violate the dominant energy condition near the BH, and the tangential sound speed exceeds light speed for all dark matter profiles. In our second approach, without assuming vanishing radial pressure, we observe similar violations and superluminal sound speeds. To rectify this, we introduce a hard cutoff for the sound speed, ensuring it remains subluminal. As a consequence, the energy condition is also satisfied. However, this results in increased density and pressure near the BH. This raises questions about the sound speed and its impact on the density structure, as well as questions about the validity of the model itself. With the matter distribution, we also compute the metric for different configurations. It reveals sensitivity to the profile structure. The metric components point toward the horizon structure. Published by the American Physical Society 2024

Comment on “Source of black bounces in Rastall gravity”

In Atazadeh and Hadi (JCAP 01 (2024) 067), the authors proposed that black bounce solutions, such as the Simpson-Visser and the Bardeen-type spacetimes, can be obtained from Rastall gravity. To achieve these spacetimes, the authors consider the presence of a phantom scalar field with nonlinear electrodynamics. However, in this comment, we obtained different electromagnetic Lagrangians from the original work. The most problematic issue is not the incorrect expression of the electromagnetic Lagrangian itself. We show that the method obtains electromagnetic functions that are inconsistent. To obtain the black bounce spacetimes as solutions of Rastall gravity, it is necessary to consider an isotropic fluid, combined with the nonlinear electrodynamics and the phantom scalar field.

Realistic compact objects in the f(R, T) gravity in the background of polytropic and barotropic gas models

The f(R, T) gravity in the background of the polytropic and barotropic fluid has been investigated in this work. We have selected the TOV equation to determine the internal spacetime of a spherically symmetric galactic object. With the use of the Einstein equation, we have selected KB-spacetime to calculate the mass, compactness, and surface redshift of a spherically symmetric body. Explicit conditions for model parameters have been constructed for the boundary conditions of the interior and exterior spacetime, and the Schwarzschild solution has been employed in the modified f(R, T) gravity theory to evaluate different matching criteria. An increasing pattern in compactness with respect to the different radii is evident in the graphical representation of the compactness evolution for each of the individual star models. After selecting a non-vacuum field equation for higher order curvature, we reformulated f(R, T) for R and T. As a result, the tangential pressure, radial pressure, and matter density have all been calculated. According to the study, as the radius goes to infinity, the tangential and radial pressures display asymptotic flatness and converge to zero. Polytropic and barotropic gas EoS have been adopted since the star model confronts the presence of an isotropic fluid backdrop. It has been noted that in a polytropic background, density and pressure increase with distance from the star’s core, but in a barotropic background, the pressure exhibits an ascending pattern as a function of radius.

Gaussian black holes in brane-world model

We present regular black hole solutions in the framework of Brane-world gravity sourced by a Gaussian matter distribution. The black hole metric shares all the common features of regular black holes in the modified General Relativity (GR) with some exciting features. Considering the energy momentum tensor for an isotropic fluid on the brane, the modified Einstein field equation results with an effective energy momentum tensor that describes an anisotropic fluid determined by brane world parameters. Although the effective radial pressure and energy density satisfy the vacuum energy condition, the effective transverse pressure behaves differently. Gaussian black hole (GBH) solutions are obtained from a Gaussian matter distribution. In the paper, a new class of GBH solutions are obtained in the brane-world gravity with effective normal matter in addition to exotic matter distribution. In the brane world gravity, the mass of a GBH depends on the brane tension. The mass of a GBH formed in the brane world is greater than that at low energy (i.e., GR). We study the trajectories of the massive and the massless particles that can be trapped around a GBH for a set of model parameters. The radii of the photon spheres around the GBH and the condition for the stability of the trajectories of the photon spheres are determined. The properties of the GBHs are studied in detail, including their possible observable features.

Effect of decoupling parameters on maximum allowable mass of anisotropic stellar structure constructed by mass constraint approach in f(Q)-gravity

In the present article anisotropic solutions with vanishing complexity in the framework of f(Q) gravity are generated. At first, the field equations in f(Q)-gravity are gravitationally decoupled where the isotropic fluid component corresponds to Vlasenko–Pronin space-time. Then, with a new source, the complete geometric deformation is supplemented to an isotropic component, and the related deformation function is derived by the method known as mimicking of mass constraints. Furthermore, the generated anisotropic solution prevails all the physical tests along with the stability analysis with respect to the decoupling parameter as well as the f(Q) gravity parameter and it accomplishes the physical representation of observational constraint related to stars, namely, SMC X-1, 2 S 0921-630, PSR J0437-4715, Vela X-1, PSR J1748-2021B which are reflected in Mass–Radius curves. Hence, the study comes out to be worthy of the fact that the f(Q) gravity parameter directly influences the maximum mass of a compact stellar configuration for the fixed decoupling parameter in the context of gravitational decoupling where it predicts the star PSR J1748-2021B having highest mass 2.74 M⊙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{\\odot }$$\\end{document}. It is noted that when the decoupling parameter (α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}) increases, the central value of the adiabatic index value also increases, while the reverse situation occurs when the f(Q)-parameter (β1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta _1$$\\end{document}) gets increased. This implies that both the parameters α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} and β1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta _1$$\\end{document} have the overall controlling power on the stability of the model.

Incompressible Schrödinger Flow with Heat-Transfer: An Introduction to the Analysis of Isotropic Fluid Dynamics in Sobolev Spaces for an Immersed Arbitrary Isothermal Geometry

This research investigates the intricate interplay of incompressible Schrödinger flow, heat-transfer, and the presence of an immersed isothermal body. The mathematical framework encompasses the Schrödinger equation for incompressible fluids, the heat transfer equation, and introduces a term that represents the thermal influence of an immersed isothermal geometry. Emphasizing the modeling and analysis of isotropic fluid dynamics, the study seeks to unravel the subtle relationship between the principles of quantum mechanics and the classical behavior of fluids. The initial discoveries produce an important theorem that leads the name of the authors, allowing new and valuable insights into the effects of the isothermal body immersed in a fluid medium. As a result, it was found that the term temperature source offers a unique perspective at the intersection of quantum mechanics and fluid dynamics.

Decoupled anisotropic Buchdahl’s relativistic models in f( R,T ) theory

This paper constructs three different anisotropic extensions of the existing isotropic solution to the modified field equations through the gravitational decoupling in f(R,T) theory. For this, we take a static sphere that is initially filled with the isotropic fluid and then add a new gravitational source producing anisotropy in the system. The field equations now correspond to the total matter configuration. We transform the radial metric component to split these equations into two sets characterizing their parent sources. The unknowns comprising in the first set are determined by considering the Buchdahl isotropic solution. On the other hand, we employ different constraints related to the additional gravitational source and make the second system solvable. Further, the constant triplet in Buchdahl solution is calculated by means of matching criteria between the interior and exterior geometries at the spherical boundary. The mass and radius of a compact star LMC X-4 are used to analyze the physical relevancy of the developed models. We conclude that our resulting models II and III are in well-agreement with acceptability conditions for the considered values of the parameters.

Fluid-responsive tunable metasurfaces for high-fidelity optical wireless communication.

Optical wireless communication (OWC), with its blazing data transfer speed and unparalleled security, is a futuristic technology for wireless connectivity. Despite the significant advancements in OWC, the realization of tunable devices for on-demand and versatile connectivity still needs to be explored. This presents a considerable limitation in utilizing adaptive technologies to improve signal directivity and optimize data transfer. This study proposes a unique platform that utilizes tunable, fluid-responsive multifunctional metasurfaces offering dynamic and unprecedented control over electromagnetic wave manipulation to enhance the performance of OWC networks. We have achieved real-time, on-demand beam steering with vary-focusing capability by integrating the fabricated metasurfaces with different isotropic fluids. Furthermore, the designed metasurfaces are capable of polarization-based switching of the diffracted light beams to enhance overall productivity. Our research has showcased the potential of fluid-responsive tunable metasurfaces in revolutionizing OWC networks by significantly improving transmission reliability and signal quality through real-time adjustments. The proposed methodology is verified by designing and fabricating an all-dielectric metasurface measuring 500 μm × 500 μm and experimentally investigating its fluid-responsive vary-focal capability. By incorporating fluid-responsive properties into spin-decoupled metasurfaces, we aim to develop advanced high-tech optical devices and systems to simplify beam-steering and improve performance, adaptability, and functionality, making the devices suitable for various practical applications.

An OrthoBoXY-method for various alternative box geometries.

We have shown in a recent contribution [Busch and Paschek, J. Phys. Chem. B, 2023 127, 7983-7987] that for molecular dynamics (MD) simulations of isotropic fluids based on orthorhombic periodic boundary conditions with "magical" box length ratios of Lz/Lx = Lz/Ly = 2.7933596497, the computed self-diffusion coefficients Dx and Dy in x- and y-direction become system size independent. They thus represent the true self-diffusion coefficient D0 = (Dx + Dy)/2, while the shear viscosity can be determined from diffusion coefficients in x-, y-, and z-direction, using the expression η = kBT·8.1711245653/[3πLz(Dx + Dy - 2Dz)]. Here we present a more generalized version of this "OrthoBoXY"-approach, which can be applied to any orthorhombic MD box of any shape. In particular, we would like to test, how the efficiency is affected by using a shape more akin to the cubic form, albeit with different box length ratios Lx/Lz ≠ Ly/Lz and Lx < Ly < Lz. We use NVT and NpT simulations of systems of 1536 TIP4P/2005 water molecules as a benchmark and explore different box geometries to determine the influence of the box shape on the computed statistical uncertainties for D0 and η. Moreover, another "magical" set of box length ratios is discovered with Ly/Lz = 0.57804765578 and Lx/Lz = 0.33413909235, where the self-diffusion coefficient in x-direction becomes system size independent, such that D0 = Dx.

Hydrodynamic cavitation of nematic liquid crystal in Stokes flow behind bluff body with different shapes in microchannel

Hydrodynamic cavitation, which occurs when the local pressure is below the saturated vapor pressure in hydrodynamic flow, is ubiquitous in fluid dynamics and implicated in a myriad of industrial and biomedical applications. Although extensively studied in isotropic liquids, corresponding investigations in anisotropic liquids are largely lacking. In this paper, the hydrodynamic cavitation in the bluff body bypass flow of nematic liquid crystal 5CB in the microchannel is experimentally investigated. By 5CB, we mean the thermotropic liquid crystal 4′-pentyl-4-biphenylcarbonitrile. When the Reynolds number is in the range of 3 × 10−4 &amp;lt; Re &amp;lt; 1.2 × 10−3, a special flow phenomenon behind the bluff body is observed, namely, the disclination loop. The critical Reynolds number of cavitation inception varies with the shape of the bluff body, while the lowest value corresponds to the triangular bluff body. The hydrodynamic cavitation occurs in the Stokes flow regime with the Reynolds number significantly lower than 0.1 for all bluff bodies. There is a close relation between the oscillation behavior of cavitation domains and the structure of the bluff body. In addition, the pressure difference between the inlet and outlet of the microchannel shows linear relation with the Reynolds number rather than the quadratic relation for isotropic fluids, which proves the presence of shear thinning in the flow of nematic liquid crystals. The study in this paper on the hydrodynamic cavitation of nematic liquid crystal can broaden the research on providing new approaches for the enhancement of fluid mixing and heat transfer in microfluidic chips.

Equation of State of Charged Rod Dispersions.

We study the accuracy of the theory of Stroobants, Lekkerkerker, and Odijk [Macromolecules 1986, 19, 2232-2238], called SLO theory, to describe the thermodynamic properties of an isotropic fluid of charged rods. By incorporation of the effective diameter of the rods according to SLO theory into scaled particle theory (SPT), we obtain an expression for the rod concentration-dependent free volume fraction and the osmotic pressure of a collection of charged hard spherocylinders. The results are compared to Monte Carlo simulations. We find close agreement between the simulation results and the SLO-SPT predictions for not too large values of the Debye length and for high rod charge densities. The deviations increase with rod density, particularly at concentrations above which isotropic-nematic phase transitions are expected.

Construction of thin-shell wormhole models in the geometric representation of [formula omitted](ℛ,[formula omitted]) gravity

The “cut and paste” approach is applied to construct static thin-shell wormhole models for f(R,T)=R+ηR2+β4R+λT, where η,β,λ are arbitrary constants and R is the Ricci scalar, as well as T, stand for the trace of the stress–energy tensor of the matter fields. We use matching conditions of the theory in geometric representation in an attempt to connect two space–times across separation hypersurface Σ. Firstly, we discuss the junction conditions for the considered specific form of f(R,T) function using distribution formalism. We assume isotropic perfect fluid and the polytropic equation of state which supports the exotic matter at the throat of the shell. We study distinct components of the Lanczos equation in the context of considered gravity model and the equation of state by employing symmetry-preserving radial perturbation. The widest possible ranges of parametric values and the influence of mass are explored to check the stability and instability of static wormhole models. This is defined via 2nd derivative of potential at throat radius and acquired constraint equation in the background of f(R,T) gravity. We examine the stable and unstable behavior of constructed wormhole solutions via theoretical and graphical approaches.

Traversable wormholes with static spherical symmetry and their stability in higher-curvature gravity

The solutions of traversable wormholes and their geometries are investigated in higher-curvature gravity with boundary terms for each case under the presence of anisotropic, isotropic and barotropic fluids in detail. For each case, the effective energy-momentum tensor violates the null energy condition throughout the wormhole throat. The null and weak energy conditions are also analyzed for ordinary matters. The regions that physically viable wormhole solutions can exist are explicitly shown. Furthermore, it is found that the range of the viable regions exhibits an alternating pattern of expansion and contraction. The present analyses can reveal the regions in which traversable wormholes can be constructed for anisotropic, isotropic and barotropic fluids cases with incorporating realistic matter contents, leading to fundamental physics insights into the feasible construction of wormholes in higher-curvature gravity with boundary term. The main achievements of this work, in contrast to previous studies, are its thorough investigation of traversable wormholes within the framework of higher-curvature gravity with boundary terms, its extensive consideration of various fluid types, and the explicit identification of regions where stable wormhole solutions can exist.

Isotropic Durgapal IV fluid sphere in bigravity

We analyze an isotropic uncharged fluid sphere model within bigravity considering the Durgapal IV metric (M.C. Durgapal, J. Phys. A: Math. Gen. 15, 2637 (1982)). In this work, we investigate the effects of the scale parameter k on the local matter distribution. Here, we have chosen the compact star candidate SMC X-1 with observed values of mass = (1.29 ± 0.05) M⊙ and radius [Formula: see text] km, respectively, to analyze our results analytically as well as graphically. For smaller values of k, we get the stiff (or hard) equation of state (EoS). Here, we solve the modified Einstein field equations in the presence of the background metric γμν. Due to this constant curvature background, the density and pressure terms are modified by adding an extra term, which affects the EoS. For r ≪ k, the background de Sitter space–time reduces into Minkowski form, and the coupling vanishes. We discuss certain physical quantities of our obtained solution, such as density, isotropic pressure, sound speed, pressure-density gradients, compactness, and surface redshift, to claim the physical viability of our model. It is found that our model clearly satisfies all the energy conditions, the causality condition, and the dynamical equilibrium via a modified Tolman–Oppenheimer–Volkov equation. Finally, we can conclude that our proposed model is physically realistic and well behaved.

Effect of the varying repulsive core of Gay–Berne pair potential on the structure and freezing transition in a two-dimensional system of soft ellipses

ABSTRACT We have investigated the effect of the strength of repulsive core of Gay–Berne (GB) ( n − 6 ) pair potential on the pair correlations and isotropic-nematic ( I − N ) freezing transition in a system of soft ellipses confined to a two-dimensional plane. The power n has been varied in the range 8 ≤ n ≤ 16 at an interval of two. Percus–Yevick (PY) integral equation theory (IET) has been solved to calculate the pair correlations of the isotropic fluid, which has been then used in the density functional theory to determine the isotropic-nematic transition parameters. The pair correlations obtained by PY theory have been compared with those obtained by NVT Monte-Carlo (MC) simulation. We observe a better agreement between PY and MC correlations at lower n -values of the interaction potential. An increase in the values of n results in more intricate structures manifested in both the radial distribution part and the higher order correlations. The I − N transition parameters are found to be sensitive to the value of the exponent n . The transition density is found to decrease, whereas the corresponding orientational order parameter is found to increase with the increase in n for a given temperature. At a given temperature, we observe a cut-off of n , below which the nematic does not stabilise. The smaller value of change in density at the transition indicates that the I − N transition is of weakly first order.

Jetting and Droplet Formation Driven by Interfacial Electrohydrodynamic Effects Mediated by Solitons in Liquid Crystals.

Solitons are highly confined, propagating waves that arise from nonlinear feedback in natural (e.g., shallow and confined waters) and engineered systems (e.g., optical wave propagation in fibers). Solitons have recently been observed in thin films of liquid crystals (LCs) in the presence of ac electric fields, where localized LC director distortions arise and propagate due to flexoelectric polarization. Here we report that collisions between LC solitons and interfaces to isotropic fluids can generate a range of interfacial hydrodynamic phenomena. We find that single solitons can either generate single droplets or, alternatively, form jets of LC that subsequently break up into organized assemblies of droplets. We show that the influence of key parameters, such as electric field strength, LC film thickness, and LC-oil interfacial tension, map onto a universal state diagram that characterizes the transduction of soliton flexoelectric energy into droplet interfacial energy. Overall, we reveal that solitons in LCs can be used to focus the energy of nonlocalized electric fields to generate a new class of nonlinear electrohydrodynamic effects at fluid interfaces, including jetting and emulsification.

Spontaneous Chiral Symmetry Breaking and Lane Formation in Ferromagnetic Ferrofluids.

Ferromagnetic ferrofluids are synthetic materials consisting of magnetic nanoplatelets dispersed in an isotropic fluid. Their main characteristics are the formation of stable magnetic domains and the presence of macroscopic magnetization even in the absence of a magnetic field. Here, the authors report on the experimental observation of spontaneous stripe formation in a ferromagnetic ferrofluid in the presence of an oscillating external magnetic field. The striped structure is identified as elongated magnetic domains, which exhibit reorientation upon reversal of the magnetic field. The stripes are oriented perpendicular to the magnetic field and are separated by alternating flow lanes. The velocity profile is measured using a space-time correlation technique that follows the motion of the thermally excited fluctuations in the sample. The highest velocities are found in the depleted regions between individual domains and reach values up to several µms-1 . The fluid in adjacent lanes moves in the opposite directions despite the applied magnetic field being uniform. The formation of bidirectional flow lanes can be explained by alternating rotation of magnetic nanoparticles in neighboring stripes, which indicates spontaneous breaking of the chiral symmetry in the sample.

Stability of the static-fluid cylindrical regular spacetime

In this paper, we study the mechanical stability of a static cylindrically symmetric regular solution to Einstein’s field equations that is supported by a static uniform perfect fluid with the equation of state p=−13ɛ in which p and ɛ are the pressure and the energy density of the uniform and isotropic perfect fluid. With the line-element ds2=−dt2+sech2ξρdρ2+dz2+1ξ2sinh2ξρdϕ2, this spacetime contains only one parameter, namely, ξ=8πɛ3 such that for small ρ or ξ→0 limit, the spacetime becomes flat. This solution belongs to a class of solutions found long ago by Bronnikov in the context of a static cylindrically symmetric perfect fluid, however, its interesting properties have not been noticed previously. Particularly, we show that this special cylindrically symmetric solution to the Einstein equations describes a regular distribution of gas of disordered cosmic strings. Moreover, with detailed calculations, we prove that the spacetime is unstable against a radial linear perturbation of its perfect fluid source.