Showing papers on "Compressibility published in 2012"

Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas

Abstract: Fermi gases, collections of fermions such as neutrons and electrons, are found throughout nature, from solids to neutron stars. Interacting Fermi gases can form a superfluid or, for charged fermions, a superconductor. We have observed the superfluid phase transition in a strongly interacting Fermi gas by high-precision measurements of the local compressibility, density, and pressure. Our data completely determine the universal thermodynamics of these gases without any fit or external thermometer. The onset of superfluidity is observed in the compressibility, the chemical potential, the entropy, and the heat capacity, which displays a characteristic lambda-like feature at the critical temperature T(c)/T(F) = 0.167(13). The ground-state energy is 3/5ξN E(F) with ξ = 0.376(4). Our measurements provide a benchmark for many-body theories of strongly interacting fermions.

Force Field Benchmark of Organic Liquids: Density, Enthalpy of Vaporization, Heat Capacities, Surface Tension, Isothermal Compressibility, Volumetric Expansion Coefficient, and Dielectric Constant

Abstract: The chemical composition of small organic molecules is often very similar to amino acid side chains or the bases in nucleic acids, and hence there is no a priori reason why a molecular mechanics force field could not describe both organic liquids and biomolecules with a single parameter set. Here, we devise a benchmark for force fields in order to test the ability of existing force fields to reproduce some key properties of organic liquids, namely, the density, enthalpy of vaporization, the surface tension, the heat capacity at constant volume and pressure, the isothermal compressibility, the volumetric expansion coefficient, and the static dielectric constant. Well over 1200 experimental measurements were used for comparison to the simulations of 146 organic liquids. Novel polynomial interpolations of the dielectric constant (32 molecules), heat capacity at constant pressure (three molecules), and the isothermal compressibility (53 molecules) as a function of the temperature have been made, based on expe...

Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas

Abstract: Fermi gases, collections of fermions such as neutrons and electrons, are found throughout nature, from solids to neutron stars. Interacting Fermi gases can form a superfluid or, for charged fermions, a superconductor. We have observed the superfluid phase transition in a strongly interacting Fermi gas by high-precision measurements of the local compressibility, density, and pressure. Our data completely determine the universal thermodynamics of these gases without any fit or external thermometer. The onset of superfluidity is observed in the compressibility, the chemical potential, the entropy, and the heat capacity, which displays a characteristic lambda-like feature at the critical temperature T(c)/T(F) = 0.167(13). The ground-state energy is 3/5ξN E(F) with ξ = 0.376(4). Our measurements provide a benchmark for many-body theories of strongly interacting fermions.

Mechanical metamaterials with negative compressibility transitions

Abstract: Most materials expand along the direction of an external pulling force, but there are no materials that compress instead. The proposal of mechanical metamaterials that show such negative compressibility promises new artificial materials with designed functionalities.

Ab Initio Simulations for Material Properties along the Jupiter Adiabat

Abstract: We determine basic thermodynamic and transport properties of hydrogen-helium-water mixtures for the extreme conditions along Jupiter's adiabat via ab initio simulations, which are compiled in an accurate and consistent data set. In particular, we calculate the electrical and thermal conductivity, the shear and longitudinal viscosity, and diffusion coefficients of the nuclei. We present results for associated quantities like the magnetic and thermal diffusivity and the kinematic shear viscosity along an adiabat that is taken from a state-of-the-art interior structure model. Furthermore, the heat capacities, the thermal expansion coefficient, the isothermal compressibility, the Gruneisen parameter, and the speed of sound are calculated. We find that the onset of dissociation and ionization of hydrogen at about 0.9 Jupiter radii marks a region where the material properties change drastically. In the deep interior, where the electrons are degenerate, many of the material properties remain relatively constant. Our ab initio data will serve as a robust foundation for applications that require accurate knowledge of the material properties in Jupiter's interior, e.g., models for the dynamo generation.

Observations of ubiquitous compressive waves in the Sun/'s chromosphere

Abstract: The details of the mechanism(s) responsible for the observed heating and dynamics of the solar atmosphere still remain a mystery. Magnetohydrodynamic waves are thought to have a vital role in this process. Although it has been shown that incompressible waves are ubiquitous in off-limb solar atmospheric observations, their energy cannot be readily dissipated. Here we provide, for the first time, on-disk observation and identification of concurrent magnetohydrodynamic wave modes, both compressible and incompressible, in the solar chromosphere. The observed ubiquity and estimated energy flux associated with the detected magnetohydrodynamic waves suggest the chromosphere is a vast reservoir of wave energy with the potential to meet chromospheric and coronal heating requirements. We are also able to propose an upper bound on the flux of the observed wave energy that is able to reach the corona based on observational constraints, which has important implications for the suggested mechanism(s) for quiescent coronal heating.

A Stabilized Incompressible SPH Method by Relaxing the Density Invariance Condition

Abstract: A stabilized Incompressible Smoothed Particle Hydrodynamics (ISPH) is proposed to simulate free surface flow problems. In the ISPH, pressure is evaluated by solving pressure Poisson equation using a semi-implicit algorithm based on the projection method. Even if the pressure is evaluated implicitly, the unrealistic pressure fluctuations cannot be eliminated. In order to overcome this problem, there are several improvements. One is small compressibility approach, and the other is introduction of two kinds of pressure Poisson equation related to velocity divergence-free and density invariance conditions, respectively. In this paper, a stabilized formulation, which was originally proposed in the framework of Moving Particle Semi-implicit (MPS) method, is applied to ISPH in order to relax the density invariance condition. This formulation leads to a new pressure Poisson equation with a relaxation coefficient, which can be estimated by a preanalysis calculation. The efficiency of the proposed formulation is tested by a couple of numerical examples of dam-breaking problem, and its effects are discussed by using several resolution models with different particle initial distances. Also, the effect of eddy viscosity is briefly discussed in this paper.

Electronic compressibility of layer-polarized bilayer graphene

Abstract: We report on a capacitance study of dual gated bilayer graphene. The measured capacitance allows us to probe the electronic compressibility as a function of carrier density, temperature, and applied perpendicular electrical displacement $\overline{D}$. As a band gap is induced with increasing $\overline{D}$, the compressibility minimum at charge neutrality becomes deeper but remains finite, suggesting the presence of localized states within the energy gap. Temperature dependent capacitance measurements show that compressibility is sensitive to the intrinsic band gap. For large displacements, an additional peak appears in the compressibility as a function of density, corresponding to the presence of a one-dimensional van Hove singularity (vHs) at the band edge arising from the quartic bilayer graphene band structure. For $\overline{D}g0$, the additional peak is observed only for electrons, while for $\overline{D}l0$ the peak appears only for holes. This asymmetry can be understood in terms of the finite interlayer separation and may be useful as a direct probe of the layer polarization.

A New Analytical Method for Analyzing Linear Flow in Tight/Shale Gas Reservoirs: Constant-Flowing-Pressure Boundary Condition

Abstract: Many tight/shale gas wells exhibit linear flow, which can last for several years. Linear flow can be analyzed using a square-root-oftime plot, a plot of rate-normalized pressure vs. the square root of time. Linear flow appears as a straight line on this plot, and the slope of this line can be used to calculate the product of fracture half-length and the square root of permeability. In this paper, linear flow from a fractured well in a tight/shale gas reservoir under a constant-flowing-pressure constraint is studied. It is shown that the slope of the square-root-of-time plot results in an overestimation of fracture half-length, if permeability is known. The degree of this overestimation is influenced by initial pressure, flowing pressure, and formation compressibility. An analytical method is presented to correct the slope of the squareroot-of-time plot to improve the overestimation of fracture halflength. The method is validated using a number of numerically simulated cases. As expected, the square-root-of-time plots for these simulated cases appear as a straight line during linear flow for constant flowing pressure. It is found that the newly developed analytical method results in a more reliable estimate of fracture half-length, if permeability is known. Our approach, which is fully analytical, results in an improvement in linear-flow analysis over previously presented methods. Finally, the application of this method to multifractured horizontal wells is discussed and the method is applied to three field examples.

An All-Speed Asymptotic-Preserving Method for the Isentropic Euler and Navier-Stokes Equations

Abstract: The computation of compressibleflows becomes more challenging when the Mach number has different orders of magnitude. When the Mach number is of order one, modern shock capturing methods are able to capture shocks and other complex structures with high numerical resolutions. However, if the Mach number is small, the acoustic waves lead to stiffness in time and excessively large numerical viscosity, thus demanding much smaller time step and mesh size than normally needed for incom- pressible flow simulation. In this paper, we develop an all-speed asymptotic preserv- ing (AP) numerical scheme for the compressible isentropic Euler and Navier-Stokes equations that is uniformly stable and accurate for all Mach numbers. Our idea is to split the system into two parts: one involves a slow, nonlinear and conservative hyper- bolic system adequate for the use of modern shock capturing methods and the other a linear hyperbolic system which contains the stiff acoustic dynamics, to be solved im- plicitly. This implicit part is reformulated into a standard pressure Poisson projection system and thus possesses sufficient structure for efficient fast Fourier transform solu- tion techniques. In the zero Mach number limit, the scheme automatically becomes a projection method-like incompressible solver. We present numerical results in one and two dimensions in both compressible and incompressible regimes. AMS subject classifications: 35Q35, 65M08, 65M99, 76M12, 76N99

Knots and links in steady solutions of the Euler equation

Abstract: Given any possibly unbounded, locally nite link, we show that there exists a smooth dieomorphism transforming this link into a set of stream (or vortex) lines of a vector eld that solves the steady incompressible Euler equation in R 3 . Furthermore, the dieomorphism can be chosen arbitrarily close to the identity in any C r norm.

Interaction of a planar shock wave with a dense particle curtain: Modeling and experiments

Abstract: The interaction of a planar shock wave with a dense particle curtain is investigated through modeling and experiments. The physics in the interaction between a shock wave with a dense gas-particle mixture is markedly differently from that with a dilute mixture. Following the passage of the shock wave, the dense particle curtain expands rapidly as it propagates downstream and pressures equilibrate throughout the flow field. In the simulations, the particles are viewed as point-particles and are traced in a Lagrangian framework. A physics-based model is then developed to account for interphase coupling. Compared to the standard drag law, four major improvements are made in the present interphase coupling model to take into account: (1) unsteady force contributions to particle force; (2) effect of compressibility on hydrodynamic forces; (3) effect of particle volume fraction on hydrodynamic forces; (4) effect of inter-particle collision. The complex behavior of the dense particle curtain is due to the interplay between two-way coupling, finite particle inertia, and unsteady forces. Incorporation of these effects through significant modeling improvements is essential for the simulation results to agree well with the experimental data. As a result of the large pressure gradient inside the particle curtain, the unsteady forces remain significant for a long time compared to the quasi-steady force and greatly influence the particle curtain motion.

Sinking, merging and stationary plumes in a coupled chemotaxis-fluid model: a high-resolution numerical approach

Abstract: Aquatic bacteria like Bacillus subtilis are heavier than water yet they are able to swim up an oxygen gradient and concentrate in a layer below the water surface, which will undergo Rayleigh–Taylor-type instabilities for sufficiently high concentrations. In the literature, a simplified chemotaxis–fluid system has been proposed as a model for bio-convection in modestly diluted cell suspensions. It couples a convective chemotaxis system for the oxygen-consuming and oxytactic bacteria with the incompressible Navier–Stokes equations subject to a gravitational force proportional to the relative surplus of the cell density compared to the water density. In this paper, we derive a high-resolution vorticity-based hybrid finite-volume finite-difference scheme, which allows us to investigate the nonlinear dynamics of a two-dimensional chemotaxis–fluid system with boundary conditions matching an experiment of Hillesdon et al. (Bull. Math. Biol., vol. 57, 1995, pp. 299–344). We present selected numerical examples, which illustrate (i) the formation of sinking plumes, (ii) the possible merging of neighbouring plumes and (iii) the convergence towards numerically stable stationary plumes. The examples with stable stationary plumes show how the surface-directed oxytaxis continuously feeds cells into a high-concentration layer near the surface, from where the fluid flow (recurring upwards in the space between the plumes) transports the cells into the plumes, where then gravity makes the cells sink and constitutes the driving force in maintaining the fluid convection and, thus, in shaping the plumes into (numerically) stable stationary states. Our numerical method is fully capable of solving the coupled chemotaxis–fluid system and enabling a full exploration of its dynamics, which cannot be done in a linearised framework.

Slip effects on MHD flow of a generalized Oldroyd-B fluid with fractional derivative

Abstract: This paper presents an analysis for magnetohydrodynamic (MHD) flow of an incompressible generalized Oldroyd-B fluid inducing by an accelerating plate. Where the no-slip assumption between the wall and the fluid is no longer valid. The fractional calculus approach is introduced to establish the constitutive relationship of a viscoelastic fluid. Closed form solutions for velocity and shear stress are obtained in terms of Fox H-function by using the discrete Laplace transform of the sequential fractional derivatives. The solutions for no-slip condition and no magnetic field can be derived as the special cases. Furthermore, the effects of various parameters on the corresponding flow and shear stress characteristics are analyzed and discussed in detail.

A new density variance–Mach number relation for subsonic and supersonic isothermal turbulence

Abstract: The probability density function of the gas density in subsonic and supersonic, isothermal, driven turbulence is analyzed using a systematic set of hydrodynamical grid simulations with resolutions of up to 10243 cells. We perform a series of numerical experiments with root-mean-square (rms) Mach number ranging from the nearly incompressible, subsonic () to the highly compressible, supersonic () regime. We study the influence of two extreme cases for the driving mechanism by applying a purely solenoidal (divergence-free) and a purely compressive (curl-free) forcing field to drive the turbulence. We find that our measurements fit the linear relation between the rms Mach number and the standard deviation (std. dev.) of the density distribution in a wide range of Mach numbers, where the proportionality constant depends on the type of forcing. In addition, we propose a new linear relation between the std. dev. of the density distribution ?? and that of the velocity in compressible modes, i.e., the compressible component of the rms Mach number, . In this relation the influence of the forcing is significantly reduced, suggesting a linear relation between ?? and , independent of the forcing, and ranging from the subsonic to the supersonic regime.

Super-Compressibility of Ultralow-Density Nanoporous Silica

Abstract: Porosity generally embrittles ceramics, and low-density nanoporous oxides typically exhibit very brittle behavior. In contrast to such expectations, we find that an effective fracture strain of nanoporous silica increases with increasing porosity. At ultralow relative densities of <0.5%,[1] nanoporous monoliths start exhibiting super-compressible deformation with large effective fracture strains of >50%. We attribute such a super-compressible behavior to consequences of an increase in the average aspect ratio of ligaments with decreasing monolith density. These results have important implications for designing novel supercompressive materials and for understanding observations of super-compressibility for other low-density nanoporous systems such as carbon-nanotube-based nanofoams. Understanding effects of porosity on mechanical properties of solids has been a subject of numerous previous investigations, driven by their important technological implications. Indeed, most brittle structural materials, such as masonry materials, ceramics, and bones, are to some extent porous, with the size of pores and/or ligaments often being at the nanoscale. Porosity of different materials covers a very wide range, from zero (i.e., full density solids) to >99% for aerogels (AGs). The AGs are representative materials for the limiting case of low-density/high-porosity systems with submicron uniformity. They are sol-gel-derived solids made from nanoscale ligaments randomly interconnected into a macroscopic three-dimensional structure with open-cell porosity tunable up to ∼99.95%.[2] Numerous previous studies[2] have focused on conventional silica AGs with densities above ∼50 mg cm−3, first made by Kistler a number of decades ago.[3] Ligaments in these AGs are made of amorphous SiO2 with variable surface hydroxylation. Successful synthesis of ultralow-density[4] silica AGs has also been reported.[5–7] Ultralow-density nanofoams are currently of interest for thermonuclear fusion energy applications as scaffolds for condensed hydrogen fuel layers in fusion targets.[8] They are also attractive materials for solid-state targets for ultrabright x-ray lasers,[9] energy absorbing structures,[10] compliant electrical contacts,[11] and electromechanical devices.[12] Poor mechanical properties of nanofoams limit their use in these applications.

PIV-based pressure fluctuations in the turbulent boundary layer

Abstract: The unsteady pressure field is obtained from time-resolved tomographic particle image velocimetry (Tomo-PIV) measurement within a fully developed turbulent boundary layer at free stream velocity of U ∞ = 9.3 m/s and Reθ = 2,400. The pressure field is evaluated from the velocity fields measured by Tomo-PIV at 10 kHz invoking the momentum equation for unsteady incompressible flows. The spatial integration of the pressure gradient is conducted by solving the Poisson pressure equation with fixed boundary conditions at the outer edge of the boundary layer. The PIV-based evaluation of the pressure field is validated against simultaneous surface pressure measurement using calibrated condenser microphones mounted behind a pinhole orifice. The comparison shows agreement between the two pressure signals obtained from the Tomo-PIV and the microphones with a cross-correlation coefficient of 0.6 while their power spectral densities (PSD) overlap up to 3 kHz. The impact of several parameters governing the pressure evaluation from the PIV data is evaluated. The use of the Tomo-PIV system with the application of three-dimensional momentum equation shows higher accuracy compared to the planar version of the technique. The results show that the evaluation of the wall pressure can be conducted using a domain as small as half the boundary layer thickness (0.5δ99) in both the streamwise and the wall normal directions. The combination of a correlation sliding-average technique, the Lagrangian approach to the evaluation of the material derivative and the planar integration of the Poisson pressure equation results in the best agreement with the pressure measurement of the surface microphones.

Pseudo hard-sphere potential for use in continuous molecular-dynamics simulation of spherical and chain molecules.

Abstract: We present a continuous pseudo-hard-sphere potential based on a cut-and-shifted Mie (generalized Lennard-Jones) potential with exponents (50, 49). Using this potential one can mimic the volumetric, structural, and dynamic properties of the discontinuous hard-sphere potential over the whole fluid range. The continuous pseudo potential has the advantage that it may be incorporated directly into off-the-shelf molecular-dynamics code, allowing the user to capitalise on existing hardware and software advances. Simulation results for the compressibility factor of the fluid and solid phases of our pseudo hard spheres are presented and compared both to the Carnahan-Starling equation of state of the fluid and published data, the differences being indistinguishable within simulation uncertainty. The specific form of the potential is employed to simulate flexible chains formed from these pseudo hard spheres at contact (pearl-necklace model) for mc = 4, 5, 7, 8, 16, 20, 100, 201, and 500 monomer segments. The compres...

A modified SPH method for simulating motion of rigid bodies in Newtonian fluid flows

Abstract: A weakly compressible smoothed particle hydrodynamics (WCSPH) method is used along with a new no-slip boundary condition to simulate movement of rigid bodies in incompressible Newtonian fluid flows. It is shown that the new boundary treatment method helps to efficiently calculate the hydrodynamic interaction forces acting on moving bodies. To compensate the effect of truncated compact support near solid boundaries, the method needs specific consistent renormalized schemes for the first and second-order spatial derivatives. In order to resolve the problem of spurious pressure oscillations in the WCSPH method, a modification to the continuity equation is used which improves the stability of the numerical method. The performance of the proposed method is assessed by solving a number of two-dimensional low-Reynolds fluid flow problems containing circular solid bodies. Wherever possible, the results are compared with the available numerical data.

Three-dimensional cellular structures with negative Poisson's ratio and negative compressibility properties

Abstract: A three-dimensional cellular system that may be made to exhibit some very unusual but highly useful mechanical properties, including negative Poisson’s ratio (auxetic), zero Poisson’s ratio, negative linear and negative area compressibility, is proposed and discussed. It is shown that such behaviour is scale-independent and may be obtained from particular conformations of this highly versatile system. This model may be used to explain the auxetic behaviour in auxetic foams and in other related cellular systems; such materials are widely known for their superior performance in various practical applications. It may also be used as a blueprint for the design and manufacture of new man-made multifunctional systems, including auxetic and negative compressibility systems, which can be made to have tailor-made mechanical properties.

Modeling of Hydraulic Fracturing in a Poroelastic Cohesive Formation

Abstract: This paper investigates the main parameters that affect the propagation of a fluid driven-fracture in a poroelastic medium. The fracture results from the pumping of an incompressible Newtonian viscous fluid at the fracture inlet, and the flow in the fracture is modelled by the lubrication theory. Rock deformation is assumed as porous-elastic. Leak-off in the host rock is considered to account for the diffusion effects in the surrounding formation. The propagation criterion is of the cohesive type. Finite element analysis was performed to compute the fracturing pressure and fracture dimensions as a function of the time and length. It was found that higher pressures are needed to extend a fracture in a poroelastic medium than in an elastic medium, and the created profiles of poroelastic fracture are wider. It was found that grain compressibility plays a minor role and does not result any significant difference in the fluid pressures and fracture dimensions. Wider fracture profiles are obtained with ...

Long wavelength gradient drift instability in Hall plasma devices. I. Fluid theory

Abstract: The problem of long wavelength instabilities in Hall thruster plasmas is revisited. A fluid model of the instabilities driven by the E0×B drift in plasmas with gradients of density, electron temperature, and magnetic field is proposed. It is shown that full account of compressibility of the electron flow in inhomogeneous magnetic field leads to quantitative modifications of earlier obtained instability criteria and characteristics of unstable modes. Modification of the stability criteria due to finite temperature fluctuations is investigated.

Equation of motion for a sphere in non-uniform compressible flows

Abstract: Linearized viscous compressible Navier–Stokes equations are solved for the transient force on a spherical particle undergoing unsteady motion in an inhomogeneous unsteady ambient flow. The problem is formulated in a reference frame attached to the particle and the force contributions from the undisturbed ambient flow and the perturbation flow are separated. Using a density-weighted velocity transformation and reciprocal relation, the total force is first obtained in the Laplace domain and then transformed to the time domain. The total force is separated into the quasi-steady, inviscid unsteady, and viscous unsteady contributions. The above rigorously derived particle equation of motion can be considered as the compressible extension of the Maxey–Riley–Gatignol equation of motion and it incorporates interesting physics that arises from the combined effects of inhomogeneity and compressibility.

Immersed smoothed finite element method for two dimensional fluid–structure interaction problems

Abstract: SUMMARY A novel method called immersed smoothed FEM using three-node triangular element is proposed for two-dimensional fluid–structure interaction (FSI) problems with largely deformable nonlinear solids placed within incompressible viscous fluid. The fluid flows are solved using the semi-implicit characteristic-based split method. Smoothed FEMs are employed to calculate the transient responses of solids based on explicit time integration. The fictitious fluid with two assumptions is introduced to achieve the continuous form of the FSI conditions. The discrete formulations to calculate the FSI forces are obtained in terms of the characteristic-based split scheme, and the algorithm based on a set of fictitious fluid mesh is proposed for evaluating the FSI force exerted on the solid. The accuracy, stability, and convergence properties of immersed smoothed FEM are verified by numerical examples. Investigations on the mesh size ratio indicate that the stability is fairly independent of the wide range of the mesh size ratio. No additional volume correction is required to satisfy the incompressible constraints. Copyright © 2012 John Wiley & Sons, Ltd.