Stiff Fluid Research Articles

Dynamics of some cosmological solutions in modified f(R) gravity

This paper is devoted to investigate the modified f(R) theory of gravity, where R represents the Ricci scalar respectively. For our current work, we consider the Friedmann-Robertson-Walker (FRW) space-time for finding solutions of field equations. Furthermore, some numerical solutions are examined by taking the Klein-Gordon Equation and using distinct values of the equation of state (EoS) parameter. In this way, we have discussed the solutions for acceleration expansion of the Universe, sub-relativistic Universe, radiation Universe, ultra-relativistic Universe, dust Universe, and stiff fluid Universe respectively. Moreover, their behaviours are examined by using power-law and exponential law techniques. The bouncing scenario is also discussed by choosing some particular values of the model parameters and observed the energy conditions, which are satisfied for a successful bouncing model. It is also concluded that some solution in f(R) theory of gravity supports the concept of exotic matter and accelerated expansion of the Universe due to a large amount of negative pressure.

Deciphering ascending thoracic aortic aneurysm hemodynamics in relation to biomechanical properties

The degeneration of the arterial wall at the basis of the ascending thoracic aortic aneurysm (ATAA) is a complex multifactorial process, which may lead to clinical complications and, ultimately, death. Individual genetic, biological or hemodynamic factors are inadequate to explain the heterogeneity of ATAA development/progression mechanisms, thus stimulating the analysis of their complex interplay.Here the disruption of the hemodynamic environment in the ATAA is investigated integrating patient-specific computational hemodynamics, CT-based in vivo estimation of local aortic stiffness and advanced fluid mechanics methods of analysis. The final aims are (1) deciphering the ATAA spatiotemporal hemodynamic complexity and its link to near-wall topological features, and (2) identifying the existing links between arterial wall degeneration and hemodynamic insult. Technically, two methodologies are applied to computational hemodynamics data, the wall shear stress (WSS) topological skeleton analysis, and the Complex Networks theory. The same analysis was extended to the healthy aorta.As main findings of the study, we report that: (1) different spatiotemporal heterogeneity characterizes the ATAA and healthy hemodynamics, that markedly reflect on their WSS topological skeleton features; (2) a link (stronger than canonical WSS-based descriptors) emerges between the variation of contraction/expansion action exerted by WSS on the endothelium along the cardiac cycle, and ATAA wall stiffness. The findings of the study suggest the use of advanced methods for a deeper understanding of the hemodynamics disruption in ATAA, and candidate WSS topological skeleton features as promising indicators of local wall degeneration.

Seismic Control of Cable-stayed Bridge Using Negative Stiffness Device and Fluid Viscous Damper under Near-field Ground Motions

ABSTRACT Under near-field ground motions, fluid viscous dampers (FVDs) are effective in controlling deck longitudinal displacement but lead to the increase of bending moment and shear force at tower base. Negative stiffness (NS) devices are introduced in combination of FVDs for the bridge. The NS devices lengthen the fundamental vibration period of the bridge to reduce the spectrum acceleration whereas FVDs introduce extra damping to the bridge system to reduce the deck displacement. After implementing NS devices, designers have more options of designing FVDs for seismic control of the cable-stayed bridges while maintaining the design requirements under near-field seismic excitations.

Remarks on Cosmological Bulk Viscosity in Different Epochs

The intention of this paper is mainly two-fold. First, we point out a striking numerical agreement between the bulk viscosity in the lepton era calculated by Husdal (2016) and our own calculations of the present-day bulk viscosity when the functional form is ζ ∼ ρ . From a phenomenological point of view, we thus seem to have an ansatz for the viscosity, which bridges the infancy of the Universe (∼1 s) with the present. This can also be looked upon as a kind of symmetry between the early-time cosmology and the present-day cosmology: it is quite remarkable that the kinetic theory-based bulk viscosity in the early universe and the experimentally-based bulk viscosity in the present universe can be covered by the same simple analytical formula. Second, we consider the Kasner universe as a typical anisotropic model of Bianchi-Type I, investigating whether this geometrical model is compatible with constant viscosity coefficients in the fluid. Perhaps surprisingly, the existence of a shear viscosity turns out to be incompatible with the Kasner model. By contrast, a bulk viscosity is non-problematic in the isotropic version of the model. In the special case of a Zel’dovich (stiff) fluid, the three equal exponents in the Kasner metric are even determined by the bulk viscosity alone, independent of the value of the fluid energy density. We also give a brief comparison with some other recent approaches to viscous cosmology.

Effects of electromagnetic field on the stability of locally isotropic gravastars

We have studied a new solution of charged gravastars with isotropic matter configuration in the framework of f(R, T) theory of gravity. For this purpose, we have assumed the electric charge as a constant. This stellar structure divided into three different regions: The preliminary part shows the interior charged region in which pressure equals to the negative density, second is the intermediate charged shell which is assumed to be very thin and filled with ultrarelativistic stiff fluid and the last corresponds to the electrovacuum region which is defined by an exterior Reissner-Nordström solution. Under these assumptions, we have found some physical aspects like length, energy, entropy and equation of state for charged spherical gravastar distribution. Moreover, we present an exact solution that free from event horizon and non-singular for this our new model.

Choked Accretion onto a Schwarzschild Black Hole: A Hydrodynamical Jet-launching Mechanism

Abstract We present a novel, relativistic accretion model for accretion onto a Schwarzschild black hole. This consists of a purely hydrodynamical mechanism in which, by breaking spherical symmetry, a radially accreting flow transitions into an inflow-outflow configuration. The spherical symmetry is broken by considering that the accreted material is more concentrated on an equatorial belt, leaving the polar regions relatively under-dense. What we have found is a flux-limited accretion regime in which, for a sufficiently large accretion rate, the incoming material chokes at a gravitational bottleneck and the excess flux is redirected by the density gradient as a bipolar outflow. The threshold value at which the accreting material chokes is of the order of the mass-accretion rate found in the spherically symmetric case studied by Bondi and Michel. We describe the choked accretion mechanism first in terms of a general relativistic, analytic toy model based on the assumption of an ultrarelativistic stiff fluid. We then relax this approximation and, by means of numerical simulations, show that this mechanism can operate also for general polytropic fluids. Interestingly, the qualitative inflow-outflow morphology obtained appears as a generic result of the proposed symmetry break, across analytic and numeric results covering both the Newtonian and relativistic regimes. The qualitative change in the resulting steady-state flow configuration appears even for a very small equatorial-to-polar-density contrast (∼0.1%) in the accretion profile. Finally, we discuss the applicability of this model as a jet-launching mechanism in different astrophysical settings.

Relativistic accretion mechanism for some black holes

In this paper, we have explored some interesting aspects of accretion onto static and spherically symmetric black holes. The different behaviors of the fluid flow are analyzed during the accretion process. We have investigated the most general black hole spacetime with isotropic fluid for the generalized expressions of the radial velocity u(r), energy density ρ(r), speed of sound cs2 and mass accretion rate M˙. We have investigated the physical behavior of the radial velocity and energy density of the fluid flow which are positive and negative. The mass accretion rate increases for the cases of dust, stiff fluid and quintessence while it decreases for the phantom fluid.

Study of gravastars under [formula omitted] gravity

In the present paper, we propose a stellar model under the f(T) gravity following the conjecture of Mazur-Mottola [1,2] known in literature as gravastar, a viable alternative to the black hole. This gravastar has three different regions, viz., (A) Interior core region, (B) Intermediate thin shell, and (C) Exterior spherical region. It is assumed that in the interior region the fluid pressure is equal to a negative matter-energy density providing a constant repulsive force over the spherical thin shell. This shell at the intermediate region is assumed to be formed by a fluid of ultrarelativistic plasma and the pressure, which is directly proportional to the matter-energy density according to Zel'dovich's conjecture of stiff fluid [Zel'dovich (1972) [3]], does nullify the repulsive force exerted by the interior core region for a stable configuration. On the other hand, the exterior spherical region can be described by the exterior Schwarzschild-de Sitter solution. With all these specifications we have found out a set of exact and singularity-free solutions of the gravastar which presents several physically interesting as well as valid features within the framework of alternative gravity.

Estimating server utilization rate in single server queuing models using an approximate solution of stiff fluid flow model

Modeling real-life scenarios as differential equation models have displayed numerous advantages as the model is able to infuse more realistic features of the scenario under consideration. Adopting a differential equation flow model to estimate server utilization rate in queuing systems has not attracted much attention due to the challenges to obtain an exact solution to the model. However, this concern is bypassed by adopting approximate methods. Thus, this article adopts a first order differential equation model to calculate the rate at which work arrives and the capacity of workstation. The values were obtained as the independent variable becomes large, which expresses the values of the utilization of resources which is now infused into conventional queuing expressions to obtain the required information about the queuing systems. A new novel and convergent one-step second-derivative method is developed in this article to obtain the required value of the server utilization rate.

Tilted congruences with stiff fluid cosmological models

We have presented tilted Bianchi type-VI0 cosmological models in general theory of relativity. To solve Einstein’s field equation, we have used the stiff fluid $$ \tilde{p}_{r} = \tilde{\rho } $$ , considering time varying radial velocity $$ \omega = T^{\alpha } $$ and uniform radial velocity $$ \omega = \omega_{0} $$ , where $$ \alpha,\,\omega_{0} $$ are constant. We have also investigated the behaviors of some physical parameters.

Modeling Coupled Heat and Mass Transfer in Peristaltic Cylindrical Flow of Robertson-Stiff Fluid

The Robertson–Stiff fluid (RS) is a yield-pseudo-plastic model which has been used to describe the rheological properties of drilling fluids, cement slurries and bentonite suspensions. Experimentally, several rheological data showed that this model provides more consistently accurate descriptions of the rheology of such fluids than other viscoplastic models. This result motivates us to study theoretically the peristaltic transport for this shear-thinning model and for other viscoplastic models in the presence of heat and mass transfer in a cylindrical tube. For long wavelength and low Reynolds number approximations, an analytical solution is obtained. The results showed that the velocity and the temperature decrease with increasing the yield parameter and the power index while they increase with the increase in the occlusion parameter. We also observed an opposite behavior of the concentration versus these physical parameters. Moreover, all these parameters enhance the mechanical efficiency of pumping. In addition, the comparison shows that the velocity, temperature and the absolute value of concentration are greater for the proposed model than those of Herschel–Bulkley, Bingham and Casson models, respectively.

Cylindrical wormholes: A search for viable phantom-free models in GR

The well-known problem of wormholes in General Relativity (GR) is the necessity of exotic matter, violating the Weak Energy Condition (WEC), for their support. This problem looks easier if, instead of island-like configurations, one considers string-like ones, among them, cylindrically symmetric spacetimes with rotation. However, for cylindrical wormhole solutions, a problem is the lacking asymptotic flatness, making it impossible to observe their entrances as local objects in our universe. It was suggested to solve this problem by joining a wormhole solution to flat asymptotic regions at some surfaces [Formula: see text] and [Formula: see text] on different sides of the throat. The configuration then consists of three regions, the internal one containing a throat and two flat external ones. We discuss different kinds of source matter suitable for describing the internal regions of such models (scalar fields, isotropic and anisotropic fluids) and present two examples where the internal matter itself and the surface matter on both junction surfaces [Formula: see text] respect the WEC. In one of these models, the internal source is a stiff perfect fluid whose pressure is equal to its energy density, in the other, it is a special kind of anisotropic fluid. Both models are free from closed timelike curves. We thus obtain examples of regular twice asymptotically flat wormhole models in GR without exotic matter and without causality violations.

Constraints on a Bianchi type I spacetime extension of the standard ΛCDM model

We consider the simplest anisotropic generalization, as a correction, to the standard $\Lambda$CDM model, by replacing the spatially flat Robertson-Walker metric by the Bianchi type-I metric, which brings in a new term $\Omega_{\sigma 0}a^{-6}$ (mimicking the stiff fluid) in the average expansion rate $H(a)$ of the Universe. From Hubble and Pantheon data, relevant to the late Universe ($z\lesssim 2.4$), we obtain the constraint $\Omega_{\sigma0}\lesssim10^{-3}$, in line with the model-independent constraints. When the baryonic acoustic oscillations and cosmic microwave background (CMB) data are included, the constraint improves by 12 orders of magnitude, i.e., $\Omega_{\sigma0}\lesssim10^{-15}$. We find that this constraint could alter neither the matter-radiation equality redshift nor the peak of the matter perturbations. Demanding that the expansion anisotropy has no significant effect on the standard big bang nucleosynthesis (BBN), we find the constraint $\Omega_{\sigma0}\lesssim10^{-23}$. We show explicitly that the constraint from BBN renders the expansion anisotropy irrelevant to make a significant change in the CMB quadrupole temperature, whereas the constraint from the cosmological data in our model provides the temperature change up to $\sim11\, \rm mK$, though it is much beyond the CMB quadrupole temperature.

Gravastars with Kuchowicz metric potential

Abstract In the present article we are going to study different features of a Gravitationally Vacuum Condensate Star, i.e., Gravastar with the help of the Kuchowicz metric potential [B. Kuchowicz, Acta. Phys. Pol. 33, 541 (1968)] in ( 3 + 1 ) dimensional spacetime. The gravastar consists of three regions namely the interior, intermediate thin shell and the exterior. Our main objective is to study the non-singular solutions of the system considered here. Also we want to study different features of the shell region, composed of ultra relativistic plasma obeying Zel’dovich’s conjecture of stiff fluid, like the energy, proper length, entropy and surface redshift which will confirm the stability of our model. Using the Kuchowicz metric potential we have found another metric potential (i.e. e λ ) for the interior and shell region which is non-singular in its nature for both of the region. The exterior of the gravastar has been described as the Schwarzschild type. We have found the numerical values of different constants imposing the boundary conditions. This theoretical model of gravastar can completely overcome the singularity problem related to black holes and hence can be taken as a promising alternative to the classical black hole within the framework of Einstein’s General Relativity.

Cylindrical symmetric, non-rotating and non-static or static black hole solutions and the naked singularities

In this work, a four-dimensional cylindrical symmetric and non-static or static space-times in the backgrounds of anti-de Sitter (AdS) spaces with perfect stiff fluid, anisotropic fluid and electromagnetic field as the stress–energy tensor, is presented. For suitable parameter conditions in the metric function, the solution represents non-static or static non-rotating black hole solution. In addition, we show for various parameter conditions, the solution represents static and/or non-static models with a naked singularity without an event horizon.

Rotating Cylinders with Anisotropic Fluids in General Relativity

We consider anisotropic fluids with directional pressures $p_i = w_i \rho$ ($\rho$ is the density, $w_i = $const, $i = 1,2,3$) as sources of gravity in stationary cylindrically symmetric space-times. We describe a general way of obtaining exact solutions with such sources, where the main features are splitting of the Ricci tensor into static and rotational parts and using the harmonic radial coordinate. Depending on the values of $w_i$, it appears possible to obtain general or special solutions to the Einstein equations, thus recovering some known solutions and finding new ones. Three particular examples of exact solutions are briefly described: with a stiff isotropic perfect fluid ($p = \rho$), with a distribution of cosmic strings of azimuthal direction (i.e., forming circles around the $z$ axis), and with a stationary combination of two opposite radiation flows along the $z$ axis.

Nonlinear vibration isolation for fluid-conveying pipes using quasi-zero stiffness characteristics

Abstract Fluid-conveying pipes are always subjected to various excitations to cause unwanted vibrations. A quasi-zero stiffness system consisting of three linear springs is adopted as the nonlinear isolator to attenuate the transverse vibrations of fluid-conveying pipes induced by foundation excitations. A dynamic model of nonlinear forced vibration of the fluid-conveying pipe coupled with two nonlinear isolators is established for the nonlinear continuous system and validated by using two methods, Galerkin method and the finite difference method. The influence of the quasi-zero stiffness isolators on the vibration characteristics and vibration transmission of the pipe is investigated by analyzing the natural frequency, vibration mode, and nonlinear vibration response. The effects of flow speed of the fluid and the system parameters of the isolator are studied to evaluate the isolation performance. It is found that the quasi-zero stiffness isolator and fluid flow can shift several natural frequencies of vibration of the pipeline to the low-frequency region. When the linear stiffness of the vibration isolation is zero in the vertical direction, the first two modes of the bending vibration of the fluid-conveying pipe tend to become rigid mode. While achieving high-efficiency vibration isolation in the high-frequency region, the vibration in the low-frequency region is complicated. The flow speed of the fluid can deteriorate the performance of vibration isolation.

Black holes/naked singularities in four-dimensional non-static space-time and energy-momentum distributions

In this article, we discuss four dimensional non-static space-times in the background of de-Sitter and anti-de Sitter spaces with the matter-energy sources a stiff fluid, anisotropic fluid, and an electromagnetic field. Under various parameter conditions the solutions may represent models of naked singularity and/or black holes. Finally, the energy-momentum distributions using the complexes of Landau-Lifshitz, Einstein, Papapetrou, and M{\o}ller prescriptions, were evaluated.

Classical Incompressible Fluid Dynamics as a Limit of Relativistic Compressible Fluid Dynamics

Properly scaled, the relativistic Euler system for an arbitrary isentropic, causally compressible fluid is shown to formally converge, as c → ∞, to the non-relativistic Euler system for the homogeneously incompressible fluid. The limit is particularly interesting in the case of the relativistic stiff fluid, for which all modes are linearly degenerate in the sense of the theory of hyperbolic systems of conservation laws. This case connects the continuation problem for regular solutions to the incompressible version of the classical Euler equations with the old conjecture that for hyperbolic systems linear degeneracy of all modes prevent gradient blowup. One could say that questions in two different areas of the theory of partial differential equations are linked to each other through Einstein’s theory of relativity.

A model of the late universe with viscous Zel’ldovich fluid and decaying vacuum

Many have speculated about the presence of a stiff fluid in very early stage of the universe. Such a stiff fluid was first introduced by Zel’dovich. Recently the late acceleration of the universe was studied by taking bulk viscous stiff fluid as the dominant cosmic component, but the age predicted by such a model is less than the observed value. We consider a flat universe with viscous stiff fluid and decaying vacuum energy as the cosmic components and found that the model predicts a reasonable background evolution of the universe with de Sitter epoch as end phase of expansion. More over, the model also predicts a reasonable value for the age of the present universe. We also performed a dynamical system analysis of the model and found that the end de Sitter phase predicted by the model is stable.