Stiff Fluid Research Articles

Spikes and matter inhomogeneities in massless scalar field models

We shall discuss the general relativistic generation of spikes in a massless scalar field or stiff perfect fluid model. We first investigate orthogonally transitive (OT) G2 stiff fluid spike models both heuristically and numerically, and give a new exact OT G2 stiff fluid spike solution. We then present a new two-parameter family of non-OT G2 stiff fluid spike solutions, obtained by the generalization of non-OT G2 vacuum spike solutions to the stiff fluid case by applying Geroch’s transformation on a Jacobs seed. The dynamics of these new stiff fluid spike solutions is qualitatively different from that of the vacuum spike solutions in that the matter (stiff fluid) feels the spike directly and the stiff fluid spike solution can end up with a permanent spike. We then derive the evolution equations of non-OT G2 stiff fluid models, including a second perfect fluid, in full generality, and briefly discuss some of their qualitative properties and their potential numerical analysis. Finally, we discuss how a fluid, and especially a stiff fluid or massless scalar field, affects the physics of the generation of spikes.

Performance Analysis of a Nonrecessed Hybrid Conical Journal Bearing Compensated With Capillary Restrictors

The present paper deals with the performance analysis of a nonrecessed hole-entry hydrostatic/hybrid conical journal bearing with capillary restrictors. Finite element method has been used for solving the modified Reynolds equation governing the flow of lubricant in the clearance space of journal and bearing. The hole-entry hybrid conical journal bearing performance characteristics have been depicted for a wide range of radial load parameter (W¯r = 0.25–1.5) with uniform distribution of holes at an angle of 30 deg in the circumferential direction. The numerically simulated results have been presented in terms of maximum fluid film pressure, minimum fluid film thickness, lubricant flow rate, direct fluid film stiffness coefficients, direct fluid film damping coefficients, and stability threshold speed. However, the proposed investigation of nonrecess hole-entry hybrid conical journal bearing shows important performance for bearing stiffness and minimum fluid film thickness at variable radial load and at given operating speed.

Generating time dependent conformally coupled Einstein-scalar solutions

Using the correspondence between a minimally coupled scalar field and an effective stiff perfect fluid with or without a cosmological constant, we present a simple method for generating time dependent Einstein-scalar solutions with a conformally coupled scalar field that has vanishing or non-vanishing potential. This is done by using Bekenstein’s transformation on Einstein-scalar solutions with minimally coupled massless scalar fields, and its later generalization by Abreu et al. to massive fields. In particular we obtain two new spherically symmetric time dependent solutions to the coupled system of Einstein’s and the conformal scalar field equations, with one of the solutions having a Higgs’ type potential for the scalar field, and we study their properties.

Five dimensional spherically symmetric perfect fluid cosmological model in a scalar-tensor theory of gravitation

Five dimensional spherically symmetric space-time is considered in the presence of perfect fluid source in the scalar-tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A 113:467, 1986). An exact solution of the field equations is obtained using a relation between the metric potentials which represents a stiff fluid model in this theory. Some physical properties of the model are also discussed.

LRS Bianchi Type II tilted barotropic fluid cosmological model with heat conduction in general relativity

A tilted cosmological model is studied for a barotropic fluid distribution with heat conduction in the framework of a compact Bianchi Type II space-time. To get a deterministic solution in terms of cosmic time t, we have used the supplementary condition R = S n between the metric potentials R and S, where n is a constant. The shear tensor σ ij for the tilted model satisfies the trace-free condition σ ij v j = 0, where v i is the fluid velocity vector. In a special case, the model becomes non-tilted. The heat conduction vector q i also satisfies the trace-free condition q i v i = 0. The spatial volume increases as time increases, and the model represents an inflationary scenario. The model for a barotropic fluid distribution represents decelerating and accelerating phases of the universe, matching with the astronomical observations. Anisotropy is maintained throughout, but in a special case the model isotropizes. The particle horizon and entropy are discussed. We have also discussed the stiff fluid case with physical and geometrical aspects of the models.

Cosmology and thermodynamics of FLRW universe with bulk viscous stiff fluid

We consider a cosmological model dominated by a stiff fluid with a constant bulk viscosity. We classify all the possible cases of the universe predicted by the model and analyze the scale factor and the density as well as the curvature scalar. We find that when the dimensionless constant bulk viscous parameter is in the range $$0 < \bar{\zeta }<6$$ the model begins with a big bang and makes a transition from the decelerating expansion epoch to an accelerating epoch and then tends to the de Sitter phase as $$ t\rightarrow \infty $$ . The transition into the accelerating epoch would be in the recent past when $$4<\bar{\zeta }<6.$$ For $$\bar{\zeta }>6$$ the model does not have a big bang and shows an increase in the fluid density and scalar curvature as the universe expands which eventually saturates as the scale factor $$a \rightarrow \infty $$ in the future. We have analyzed the model with statefinder diagnostics and find that the model is different from the $$\Lambda $$ CDM model but approaches the $$\Lambda $$ CDM point as $$a \rightarrow \infty $$ . We have also analyzed the status of the generalized second law of thermodynamics with an apparent horizon as the boundary of the universe and found that the law is generally satisfied when $$0 \le \bar{\zeta }<6$$ , and for $$\bar{\zeta }>6$$ the law is satisfied when the scale factor is larger than a minimum value.

Cosmic backgrounds of relic gravitons and their absolute normalization

Provided the consistency relations are not violated, the recent BICEP2 observations pin down the absolute normalization, the spectral slope and the maximal frequency of the cosmic graviton background produced during inflation. The properly normalized spectra are hereby computed from the lowest frequencies (of the order of the present Hubble rate) up to the highest frequency range in the GHz region. Deviations from the conventional paradigm cannot be excluded and are examined by allowing for different physical possibilities including, in particular, a running of the tensor spectral index, an explicit breaking of the consistency relations and a spike in the high-frequency tail of the spectrum coming either from a post-inflationary phase dominated by a stiff fluid or from the contribution of waterfall fields in a hybrid inflationary context. The direct determinations of the tensor to scalar ratio at low frequencies, if confirmed by the forthcoming observations, will also affect and constrain the high-frequency uncertainties. The limits on the cosmic graviton backgrounds coming from wide-band interferometers (such as LIGO/Virgo, LISA and BBO/DECIGO) together with a more accurate scrutiny of the tensor B-mode polarization at low frequencies will set direct bounds on the post-inflationary evolution and on other unconventional completions of the standard lore.

Testing facility concepts for the material characterization of porous media consisting of relatively limp foam and stiff fluid

Fluid filled foams are important components of acoustical systems. Most are made up of a stiff skeleton medium relative to the fluid considered, usually air. Biot’s theory of poroelasticity is appropriate for characterizing and modeling these foams. The use of relatively stiff fluid (such as water) and limp foam media pose a greater challenge. Recently modifications to Biot's theory have generated the mechanical relationships required to model these systems. Necessary static material properties for the model can be obtain through in vacuo measurement. Frequency dependent properties are more difficult to obtain. Traditional impedance tube methods suffer from fluid structure interaction when the bulk modulus of the fluid media approaches that of the waveguide. The current investigation derives the theory for, and investigates the feasibility of, several rigid impedance tube alternatives for characterizing limp foams in stiff fluid media. Alternatives considered include a sufficiently rigid impedance tube, a pressure relief impedance tube and, the most promising, a piston excited oscillating chamber of small aspect ratio. The chamber concept can recover the descriptive properties of a porous medium described by Biot’s theory or by complex-impedance equivalent-fluid models. The advantages of this facility are small facility size, low cost, and small sample size.

Bulk viscous cosmological models in f(R,T) theory of gravity

We have constructed Locally Rotationally Symmetric Bianchi type I (LRSBI) cosmological models in the f(R,T) theory of gravity when the source of gravitation is the bulk viscous fluid. The models are constructed for f(R,T)=R+2f(T) and f(R,T)=f1(R)+f2(T). We found that in the first case the model degenerates into effective stiff fluid model of the universe. In the second case we obtained degenerate effective stiff fluid model as well as general bulk viscous models of the universe. Some physical and kinematical properties of the models are also discussed.

Vapor-liquid equilibrium and critical asymmetry of square well and short square well chain fluids.

The critical behavior of square well fluids with variable interaction ranges and of short square well chain fluids have been investigated by grand canonical ensemble Monte Carlo simulations. The critical temperatures and densities were estimated by a finite-size scaling analysis with the help of histogram reweighting technique. The vapor-liquid coexistence curve in the near-critical region was determined using hyper-parallel tempering Monte Carlo simulations. The simulation results for coexistence diameters show that the contribution of |t|(1-α) to the coexistence diameter dominates the singular behavior in all systems investigated. The contribution of |t|(2β) to the coexistence diameter is larger for the system with a smaller interaction range λ. While for short square well chain fluids, longer the chain length, larger the contribution of |t|(2β). The molecular configuration greatly influences the critical asymmetry: a short soft chain fluid shows weaker critical asymmetry than a stiff chain fluid with same chain length.

On global well-posedness for the Einstein-Maxwell-Euler system in Bondi coordinates

Weanalyze the Einstein-Maxwell equations for an irrotational stiff fluid. Under the spherical symmetry assumption on the space-time, in Bondi coordinates, the considered model is reduced to a nonlinear evolution system of partial integrodifferential equations. Assuming regularity at the center of symmetry and that the matter content of the initial light cone is the so-called null dust, the characteristic initial value problem associated to the obtained system is solved globally by a contraction mapping argument. In future work we will address the issue of global well-posedness for the considered model in other physically interesting cases where the matter content of the initial light cone is not the null dust.

Performance of hydrostatic tilted thrust pad bearings of various recess shapes operating with non-Newtonian lubricant

Hydrostatic thrust bearings are an integral part of hydroelectric power stations. These bearings are usually designed to work under parallel operation, but tilt is inevitable due to manufacturing errors, assembly errors, structural vibrations and structural deformations. Owing to the advent of latest advancements in manufacturing techniques, any geometric shape of recess can be easily manufactured and the designer has a greater flexibility. The geometric shape of recess significantly affects the performance of a bearing. Therefore, the present study is aimed to numerically analyze the influence of the tilt and recess shape on the static and dynamic performance characteristics of the hydrostatic thrust pad bearing system having Rabinowitsch fluid model lubricant. The lubricant obeying Rabinowitsch fluid model with tilt makes the Reynolds equation highly non-linear therefore, finite element method is used to analyze. Three different types of recess shapes of equal area A¯b/A¯oc=4 have been analyzed to model hydrostatic thrust pad compensated by orifice compensator. The numerically simulated results indicate that the tilt angle significantly affects the dynamic and static characteristic parameters. The value of pocket pressure and fluid film reaction of a hydrostatic thrust pad bearing has been found to significantly decrease with tilt whereas the value of lubricant flow, fluid film stiffness coefficient and fluid damping coefficient increase with tilt.

LRS Bianchi type I stiff fluid inflationary universe with variable bulk viscosity

Stiff fluid inflationary cosmological model with variable bulk viscosity in the frame work of locally rotationally symmetric (LRS) Bianchi type I space–time, is investigated. To get the deterministic solution, we have also assumed that σ is proportional to θ and ζθ = constant = α where σ is shear, θ the expansion, and ζ the coefficient of bulk viscosity. The ansatz ζθ = constant, was found to connect with the occurrence of Little Rip cosmology using Friedmann–Robertson–Walker metric given by Brevik et al. (Phys. Rev. D, 84, 103508 (2011)). We find that the model has constant expansion but represents accelerating phase. The model in general represents an anisotropic universe but in special case, it leads to an isotropic one. The spatial volume increases exponentially with time representing the inflationary scenario. The presence of bulk viscosity tends to increase the inflationary phase. Also, the model leads to the de Sitter model in a special case. The presence of bulk viscosity prevents the matter density to vanish at late time. The energy conditions as given by Kolassis et al. (Classical Quantum Gravity, 5, 1129 (1988)). Chatterjee and Banerjee (Gen. Relativ. Gravitation, 36, 303 (2004)) are also discussed. We find that the energy conditions are satisfied for stiff fluid inflationary universe with variable bulk viscosity.

MULTI-COMPONENT BIANCHI I COSMOLOGIES WITH TORSION

The Bianchi I cosmological models containing radiation, stiff fluid and a nonminimally coupled material scalar field with polynomial potentials of the fourth degree are considered in the framework of the Einstein–Cartan theory (ECT). Exact partial solutions are obtained for arbitrary positive values of the coupling constant ξ. The restrictions on ξ are found from the integrability conditions. It is demonstrated that singular models with the asymptotical isotropization by the de Sitter type and by the power-law (t4/3) type at late-times are possible. It is shown that the bouncing models with the isotropization by the de Sitter law of expansion at late-times are admissible. The role of sources in the evolution of models is elucidated.

Elasto-Dynamic Behavior of a Two-Dimensional Square Lattice With Entrained Fluid II: Microstructural and Homogenized Models

This paper presents a detailed study of the pressure waves and effective mechanical properties of a closed-cell cellular solid with entrained fluid. Plane-harmonic-waves are analyzed in a periodic square with a finite-element model of a representative-volume element, which explicitly considers fluid-structure interactions, structural deformations, and the fluid dynamics of entrained fluid. The wall, cavity, and coupled-system resonance frequencies are identified as key parameters that describe the propagation characteristics. A tube-piston model based on computed microstructural deformations allows us to determine the effective stiffness tensor of an equivalent continuum at the macroscale. The analysis of dispersion surfaces indicates a single isotropic pressure mode for frequencies below resonance of the lattice walls, unlike Biot's theory which predicts two pressure modes. Shear modes are instead strongly anisotropic for all values of relative density ρ* describing both cellular ρ*&lt;0.3 and porous solids ρ*≥0.3. The dependence of the pressure wave phase velocity on the relative density is analyzed for varying properties of the entrained fluid. Depending on the relative density and mass coupling of the solid and fluid phases, the microstructural deformations can be of three types: bending, through-the-thickness, and the combination of the two. For heavy and stiff entrained fluid, the bending regime is confined to extremely small values of relative density, whereas for light fluid such as a gas, deformations are of the bending-type for ρ*&lt;0.1. Through-the-thickness deformations appear only for the heavy entrained fluid for large values of ρ*.

LRS Bianchi Type II Massive String Cosmological Model for Stiff Fluid Distribution with Decaying Vacuum Energy (Λ)

An LRS Bianchi Type II model formed by massive strings with decaying vacuum energy (Λ) for stiff fluid distribution is studied in the context of general relativity. To get the deterministic model, we have assumed that \(\frac{\sigma}{\theta} =\mathrm{constant}\) where σ is shear and θ the expansion in the model and decaying vacuum energy (Λ) is proportional to H2 (H is Hubble parameter) as used in Arbab (Gen. Relativ. Gravit. 29:51, 1997). We find that the model represents decelerating and accelerating phases of universe. The decaying vacuum energy (Λ) is proportional to \(\frac{1}{\tau^{2}}\) as obtained by Bertolami (Nuovo Cimento B 93:36, 1986) and Hubble parameter is proportional to \(\frac{1}{\tau}\) which matches with the observation. The model in general represents anisotropic space-time. However, in special case, it isotropizes. The particle density (ρp) and string tenson (λ) are initially large but decrease due to lapse of time. The model also admits particle horizon and entropy is inversely proportional absolute temperature. Thus the model is in good agreement with present age of universe.

Anisotropic Bianchi Type-I and Type-II Bulk Viscous String Cosmological Models Coupled with Zero Mass Scalar Field

The LRS Bianchi type-I and type-II string cosmological models are studied when the source for the energy momentum tensor is a bulk viscous stiff fluid containing one dimensional strings together with zero-mass scalar field. We have obtained the solutions of the field equations assuming a functional relationship between metric coefficients when the metric is Bianchi type-I and constant deceleration parameter in case of Bianchi type-II metric. The physical and kinematical properties of the models are discussed in each case. The effects of Viscosity on the physical and kinematical properties are also studied.

Stiff Fluid Cosmological Models in Five Dimensional Space-Time Based On Lyra Geometry

In this paper we have constructed stiff fluid cosmological models by considering five dimensional Kaluza-Klein space-time based on Lyra geometry in the frame work of scalar tensor theory of gravitation proposed by Saez and Ballester, which are obtained for two different cases: constant displacement vector and time dependent displacement vector. Also some physical and kinametical properties of the models are discussed.

Non-static plane symmetric massive string magnetized perfect fluid cosmological models in bimetric theory of gravitation

In this paper,we investigate the non-static massive string magnetized barotropic perfect fluid cosmological models in Rosen's (Gen.Rel.Grav.Vol.4 (1973) 435) bimetric theory of gravitation. Using the relation isotropic pressure 'p' directly proportional to energy density 'ρ' ( i.e p = Є1 ρ , where -1 ≤ Є1 ≤ 1) , dust filled geometric string model and stiff fluid filled model of the universe are obtained. Some physical and geometrical behavior of the exhibited models are also discussed.

Bianchi Type I Magnetized Stiff Fluid Models with Bulk Viscosity in Lyra Geometry

In the present study, we have investigated Bianchi Type I cosmological model for stiff fluid or Zel’dovich fluid distribution with magnetic field and bulk viscosity in the frame work of Lyra geometry. To get the deterministic model, we have also assumed a condition that eigen value (\( \sigma_{1}^{1} \)) of shear tensor (\( \sigma_{\text{i}}^{\text{j}} \)) is proportional to the expansion (θ) in the model. This leads to A = (BC)n where A, B, C are metric potentials and n is a constant. The physical and geometrical aspects of the model in presence and absence of magnetic field and bulk viscosity are also discussed.