Hydrodynamic Solution Research Articles

New exact solutions of relativistic hydrodynamics

A new class of simple and exact solutions of relativistic hydrodynamics is presented, and the consequences are explored in data analysis. The effects of longitudinal work and acceleration are taken into account in an advanced estimate of the initial energy density and the life-time of the reaction.

Impurity in a granular gas under nonlinear Couette flow

We study in this work the transport properties of an impurity immersed in a granular gasunder stationary nonlinear Couette flow. The starting point is a kinetic model forlow-density granular mixtures recently proposed by the authors (Vega Reyes et al 2007 Phys. Rev. E 75 061306). Two routes have been considered. First, a hydrodynamic ornormal solution is found by exploiting a formal mapping between the kinetic equations forthe gas particles and for the impurity. We show that the transport properties of theimpurity are characterized by the ratio between the temperatures of the impurity and gasparticles and by five generalized transport coefficients: three related to the momentum flux(a nonlinear shear viscosity and two normal stress differences) and two related to the heatflux (a nonlinear thermal conductivity and a cross-coefficient measuring a component of theheat flux orthogonal to the thermal gradient). Second, by means of a Monte Carlosimulation method we numerically solve the kinetic equations and show that ourhydrodynamic solution is valid in the bulk of the fluid when realistic boundary conditionsare used. Furthermore, the hydrodynamic solution applies to arbitrarily (inside thecontinuum regime) large values of the shear rate, of the inelasticity, and of therest of the parameters of the system. Preliminary simulation results of the trueBoltzmann description show the reliability of the nonlinear hydrodynamic solution ofthe kinetic model. This shows again the validity of a hydrodynamic descriptionfor granular flows, even under extreme conditions, beyond the Navier–Stokesdomain.

Charge‐separation Effect on Dielectric and Electro‐optical Properties of 6‐arm Polystyrene Stars with Fullerene Core in Solutions

Experimental results on the study of electro‐optical, dielectric and hydrodynamic solution properties of 6‐arm polystyrene stars A6C60(PS)6 with a variable structure of low molecular addend, A, are reported. Strong dielectric polarization of A6C60(PS)6 have been detected in external electric fields of radio frequency range and explained by intermolecular long lifetime charge‐separated state of highly symmetric fullere adducts situated at the central part of polystyrene stars.

Slip coefficient in nanoscale pore flow

The hydrodynamic solutions based on Maxwell's boundary conditions include an empirical slip coefficient (SC), which depends on properties of the adsorbate and adsorbent. Existing kinetic theory derivations of the SC are usually formulated for half-space flow and do not include finite-size effects, which dominate the flow in nanopores. We present an expression for the SC applicable to flow in nanoscale pores, which has been verified by nonequilibrium molecular-dynamics simulation. Our results show that the slip coefficient depends strongly on the pore width for small pores tending to a constant value for pores of width >20 molecular diameters for our systems, in contrast to the linear scaling predicted by Maxwell's theory of slip.

A Newton-Krylov solver for implicit solution of hydrodynamics in core collapse supernovae

This paper describes an implicit approach and nonlinear solver for solution of radiation-hydrodynamic problems in the context of supernovae and proto-neutron star cooling. The robust approach applies Newton-Krylov methods and overcomes the difficulties of discontinuous limiters in the discretized equations and scaling of the equations over wide ranges of physical behavior. We discuss these difficulties, our approach for overcoming them, and numerical results demonstrating accuracy and efficiency of the method.

Dynamical modeling of relativistic heavy ion collisions

It is quite important to describe space-time evolution of matter created in relativistic heavy ion collisions toward understanding bulk and transport properties of the quark gluon plasma (QGP). We discuss current status of dynamical modeling in relativistic heavy ion collisions based on fully three dimensional ideal hydrodynamics. We obtain local temperature of the QGP by numerically solving hydrodynamic equations. We also utilize hydrodynamic solutions to estimate other observables such as high p T spectra for hadrons, J / ψ suppression, string formation between a jet parton and a fluid parton and electro-magnetic spectra.

New family of simple solutions of relativistic perfect fluid hydrodynamics

A new class of accelerating, exact and explicit solutions of relativistic hydrodynamics is found—more than 50 years after the previous similar result, the Landau–Khalatnikov solution. Surprisingly, the new solutions have a simple form, that generalizes the renowned, but accelerationless, Hwa–Bjorken solution. These new solutions take into account the work done by the fluid elements on each other, and work not only in one temporal and one spatial dimensions, but also in arbitrary number of spatial dimensions. They are applied here for an advanced estimation of initial energy density and life-time of the reaction in ultra-relativistic heavy ion collisions. New formulas are also conjectured, that yield further important increase of the initial energy density estimate and the measured life-time of the reaction if the value of the speed of sound is in the realistic range.

Similar final states from different initial states using new exact solutions of relativistic hydrodynamics

We present exact, analytic and simple solutions of relativistic perfect fluid hydrodynamics. The solutions allow us to calculate the rapidity distribution of the particles produced at the freeze-out, and fit them to the measured rapidity distribution data. We also give an advanced estimation of the energy density reached in heavy ion collisions, and an improved estimation of the life-time of the reaction.

Detailed description of accelerating, simple solutions of relativistic perfect fluid hydrodynamics

In this paper we describe in full details a new family of recently found exact solutions of relativistic, perfect fluid dynamics. With an ansatz that generalizes the well-known Hwa-Bjorken solution we obtain a wide class of new exact, explicit, and simple solutions, which have a remarkable advantage as compared to presently known exact and explicit solutions: they do not lack acceleration. They can be utilized for the description of the evolution of the matter created in high energy heavy ion collisions. Because these solutions are accelerating, they provide a more realistic picture than the well-known Hwa-Bjorken solution, and give more insight into the dynamics of the matter. We exploit this by giving an advanced simple estimation of the initial energy density of the produced matter in high energy collisions, which takes acceleration effects, i.e., the work done by the pressure, and the modified change of the volume elements, into account. We also give an advanced estimation of the life-time of the reaction. Our new solutions can also be used to test numerical hydrodynamical codes reliably. In the end, we also give an exact, $1+1$ dimensional, relativistic hydrodynamical solution, where the initial pressure and velocity profile is arbitrary, and we show that this general solution is stable for perturbations.

LATTICE BOLTZMANN METHOD WITH OPTIMIZED BOUNDARY LAYER AT FINITE KNUDSEN NUMBERS

We present an optimization procedure in high-order lattice Boltzmann models in order to fine-tune the method for micro-channel flows in the transition region. Both the first and second slip coefficients are tunable, and the hydrodynamic and Knudsen layer solutions can be tailored. Very good results are obtained in comparison with the continuous solution for hard sphere molecules. For the first time, we provide an accurate description of Poiseuille flow in the transition region.

Hydrodynamic Solution of the Virtual Mass Coefficient of a Vortex Ring Moving in a Fluid

1. IntroductionA vortex ring (or as it is also called, a dipolar vortex ortoroidal bubble) can be formed by ejecting a puff of smokefrom a mouth of rounded lips. The vortex ring rises upwardwith a smoke-filled core. Two stationary vortex rings appearin the wake of the solid sphere at Reynolds number (Re) equalto eight. The rings progressively increase in size with Re untilthey become unstable and change into a spiral ring. A spherical-cap bubble can change into a vortex ring under certaincircumstances.Isolated vortex rings found applications in the chemicalengineering industry where they can be regarded as efficientmeans of transporting fluids over relatively large distances. Onthe laboratory scale, the vortex rings were found effective inmixing of stratified liquids and in agitating a liquid surface topromote gas absorption. The significant contributions in thisregard derive from the experiments and analyses done byProfessor Baird and his colleagues at the University of Mc-Master (Rao et al.,

Numerical simulation of colloid dead-end filtration: Effect of membrane characteristics and operating conditions on matter accumulation

The aim of this work is to develop a simulation capability applicable to dead-end filtration of colloidal dispersions in order to investigate the effect of process conditions, such as membrane configuration and operating parameters, on filtration efficiency through the analysis of the appearance of a deposit on the membrane. To reach this goal, a model describing the transport behaviour of a concentrated colloidal dispersion is implemented in a commercial CFD code (ANSYS-CFX). The collective diffusion induced by inter-particle interactions is accounted for from knowledge of the variation of the osmotic pressure with the particle volume fraction. Coupled with a transient, two dimensional hydrodynamic solution, such a model allows description of the mass transport properties both in the dispersed (concentration polarisation) and the condensed (deposit) forms of accumulation. Two-dimensional concentration profiles along the membrane are obtained. Simulations are used to understand the role of operating parameters and membrane characteristics on the appearance of a deposit at the membrane surface. This formation is controlled by the hollow fibre configuration, where there are zones working in both cross-flow and dead-end mode due to the particular hydrodynamic conditions.

Computation of phonation aeroacoustics by an INS/PCE splitting method

In this study, an INS/PCE splitting method is exploited to compute vocal sound generated within the glottis by a pulsating air jet at maximum speed less than Mach number of 0.1. The acoustic field is computed by solving the perturbed compressible equations (PCE), with acoustic sources acquired from the transient hydrodynamic solutions obtained by the incompressible Navier–Stokes equations (INS). The governing equations are spatially discretized with a sixth-order compact scheme and time-integrated by a four-stage Runge–Kutta method. The computed results show that a voice quality is closely related to the vortical structure in the shear layer of the pulsating jet and the jet characteristics are determined by its local Reynolds number, pulsating frequency (or fundamental frequency), and glottis closure. It is also found that the rotational motion of the glottis controls the glottal impedance by changing the flow separation points between the leading- and trailing-edge of the vocal folds and this increases the mechanical efficiency of the glottis as a sound generator in the phonation process.

The Pressure‐confined Wind of the Massive and Compact Super Star Cluster M82‐A1

The observed parameters of the young super star cluster M82-A1 and its associated compact H II region are here shown to indicate a low heating efficiency or immediate loss, through radiative cooling, of a large fraction of the energy injected by stellar winds and supernovae during the early evolution of the cluster. This implies a bimodal hydrodynamic solution, which leads to a reduced mass deposition rate into the ISM, with a much reduced outflow velocity. We also show here that in order to match the observed parameters of the H II region associated with M82-A1, the resulting star cluster wind should be confined by a high-pressure interstellar medium. The cluster wind parameters, together with the location of the reverse shock, its cooling length, and the radius of the standing outer H II region, are derived analytically. All of these properties are then confirmed with a semianalytical integration of the flow equations, which provides also us with the run of the hydrodynamic variables as a function of radius. The impact of the results is discussed and extended to other massive and young super star clusters surrounded by a compact H II region.

Angiopoietin-1 Requires p190 RhoGAP to Protect against Vascular Leakage in Vivo

Angiopoietin-1 (Ang-1), a ligand of the endothelium-specific receptor Tie-2, inhibits permeability in the mature vasculature, but the mechanism remains unknown. Here we show that Ang-1 signals Rho family GTPases to organize the cytoskeleton into a junction-fortifying arrangement that enhances the permeability barrier function of the endothelium. Ang-1 phosphorylates Tie-2 and its downstream effector phosphatidylinositol 3-kinase. This induces activation of one endogenous GTPase, Rac1, and inhibition of another, RhoA. Loss of either part of this dual effect abrogates the cytoskeletal and anti-permeability actions of Ang-1, suggesting that coordinated GTPase regulation is necessary for the vessel-sealing effects of Ang-1. p190 RhoGAP, a GTPase regulatory protein, provides this coordinating function as it is phosphorylated by Ang-1 treatment, requires Rac1 activation, and is necessary for RhoA inhibition. Ang-1 prevents the cytoskeletal and pro-permeability effects of endotoxin but requires p190 RhoGAP to do so. Treatment with p190 RhoGAP small interfering RNA completely abolishes the ability of Ang-1 to rescue endotoxemia-induced pulmonary vascular leak and inflammation in mice. We conclude that Ang-1 prevents vascular permeability by regulating the endothelial cytoskeleton through coordinated and opposite effects on the Rho GTPases Rac1 and RhoA. By linking Rac1 activation and RhoA inhibition, p190 RhoGAP is critical to the protective effects of Ang-1 against endotoxin. These results provide mechanistic evidence that targeting the endothelium through Tie-2 may offer specific therapeutic strategies in life-threatening endotoxemic conditions such as sepsis and acute respiratory distress syndrome.

Early time dynamics in heavy-ion collisions from AdS/CFT correspondence

We study the matter produced in heavy-ion collisions, assuming that this matter is strongly interacting and employing AdS/CFT correspondence to investigate its dynamics. At late proper times \ensuremath{\tau} we show that Bjorken hydrodynamics solution, obtained recently by Janik and Peschanski using gauge-gravity duality [1], can be singled out by simply requiring that the metric tensor is a real and single-valued function of the coordinates everywhere in the bulk, without imposing any constraints on the curvature invariant. At early proper times we use a similar strategy to show that the energy density $\ensuremath{\epsilon}$ approaches a constant as $\ensuremath{\tau}\ensuremath{\rightarrow}0$. We therefore demonstrate that the strong coupling dynamics incorporates the isotropization transition in heavy-ion collisions. By matching our early-time regime with the late-time one of Janik and Peschanski we estimate the isotropization time at RHIC to be approximately ${\ensuremath{\tau}}_{\mathrm{iso}}\ensuremath{\approx}0.3$ fm/$c$, in good agreement with results of hydrodynamic simulations.

Super stellar clusters with a bimodal hydrodynamic solution: an approximate analytic approach

Aims. We look for a simple analytic model to distinguish between stellar clusters undergoing a bimodal hydrodynamic solution from those able to drive only a stationary wind. Clusters in the bimodal regime undergo strong radiative cooling within their densest inner regions, which results in the accumulation of the matter injected by supernovae and stellar winds and eventually in the formation of further stellar generations, while their outer regions sustain a stationary wind. Methods. The analytic formulae are derived from the basic hydrodynamic equations. Our main assumption, that the density at the star cluster surface scales almost linearly with that at the stagnation radius, is based on results from semi-analytic and full numerical calculations. Results. The analytic formulation allows for the determination of the threshold mechanical luminosity that separates clusters evolving in either of the two solutions. It is possible to fix the stagnation radius by simple analytic expressions and thus to determine the fractions of the deposited matter that clusters evolving in the bimodal regime blow out as a wind or recycle into further stellar generations.

Accelerating solutions of perfect fluid hydrodynamics for initial energy density and life-time measurements in heavy ion collisions

A new class of accelerating, exact, explicit and simple solutions of relativistic hydrodynamics is presented. Since these new solutions yield a finite rapidity distribution, they lead to an advanced estimate of the initial energy density and life-time of high energy heavy ion collisions. Accelerating solutions are also given for spherical expansions in arbitrary number of spatial dimensions.

Dynamical Instability of a Rotating Dipolar Bose-Einstein Condensate

We analyze the hydrodynamic solutions for a dilute Bose-Einstein condensate with long-range dipolar interactions in a rotating, elliptical harmonic trap. The static solutions and their regimes of dynamical instability vary nontrivially with the strength of the dipolar interactions. We comprehensively map out this behavior, and, in particular, examine the experimental routes toward unstable dynamics, which, in analogy to conventional condensates, may lead to vortex lattice formation.

Distribution of copper deposited under forced-convection conditions at a contour cathode

The effect of hydrodynamic conditions and solution composition on the distribution of copper electrodeposited on a contour cathode (profile parameters: a cylindrical cavity 1.5–3 mm in diameter and 0.55–2.56 mm in depth) is studied. In the case of high stability of the intermediate reduction product, Cu(I), a purposeful decrease in the current efficiency for metal at Reynolds numbers 50 to 250 has a pronounced leveling effect. When reduction Fe(III) + e → Fe(II) occurs in parallel to the main cathodic process, the coating’s uniformity significantly improves.