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Sample records for hard sphere density

  1. Simulation of the consistent Boltzmann equation for hard spheres and its extension to higher densities

    SciTech Connect

    Alexander, F.J.; Garcia, A.L.; Alder, B.J.

    1994-10-01

    The direct simulation Monte Carlo method is modified with a post-collision displacement in order to obtain the hard sphere equation of state. This leads to consistent thermodynamic and transport properties in the low density regime. At higher densities, when the enhanced collision rate according to kinetic theory is introduced, the exact hard sphere equation of state is recovered. and the transport coefficients are comparable to those of the Enskog theory. The computational advantages of this scheme over hard sphere molecular dynamics are that it is significantly faster at low and moderate densities and that it is readily parallelizable.

  2. Free Energy Calculations of Crystalline Hard Sphere Complexes Using Density Functional Theory

    SciTech Connect

    Gunawardana, K. G.S.H.; Song, Xueyu

    2014-12-22

    Recently developed fundamental measure density functional theory (FMT) is used to study binary hard sphere (HS) complexes in crystalline phases. By comparing the excess free energy, pressure and phase diagram, we show that the fundamental measure functional yields good agreements to the available simulation results of AB, AB2 and AB13 crystals. Additionally, we use this functional to study the HS models of five binary crystals, Cu5Zr(C15b), Cu51Zr14(β), Cu10Zr7(φ), CuZr(B2) and CuZr2 (C11b), which are observed in the Cu-Zr system. The FMT functional gives well behaved minimum for most of the hard sphere crystal complexes in the two dimensional Gaussian space, namely a crystalline phase. However, the current version of FMT functional (white Bear) fails to give a stable minimum for the structure Cu10Zr7(φ). We argue that the observed solid phases for the HS models of the Cu-Zr system are true thermodynamic stable phases and can be used as a reference system in perturbation calculations.

  3. Free Energy Calculations of Crystalline Hard Sphere Complexes Using Density Functional Theory

    DOE PAGESBeta

    Gunawardana, K. G.S.H.; Song, Xueyu

    2014-12-22

    Recently developed fundamental measure density functional theory (FMT) is used to study binary hard sphere (HS) complexes in crystalline phases. By comparing the excess free energy, pressure and phase diagram, we show that the fundamental measure functional yields good agreements to the available simulation results of AB, AB2 and AB13 crystals. Additionally, we use this functional to study the HS models of five binary crystals, Cu5Zr(C15b), Cu51Zr14(β), Cu10Zr7(φ), CuZr(B2) and CuZr2 (C11b), which are observed in the Cu-Zr system. The FMT functional gives well behaved minimum for most of the hard sphere crystal complexes in the two dimensional Gaussian space,more » namely a crystalline phase. However, the current version of FMT functional (white Bear) fails to give a stable minimum for the structure Cu10Zr7(φ). We argue that the observed solid phases for the HS models of the Cu-Zr system are true thermodynamic stable phases and can be used as a reference system in perturbation calculations.« less

  4. Free Energy Calculations of Crystalline Hard Sphere Complexes Using Density Functional Theory

    SciTech Connect

    Gunawardana, K. G.S.H.; Song, Xueyu

    2014-12-22

    Recently developed fundamental measure density functional theory (FMT) is used to study binary hard sphere (HS) complexes in crystalline phases. By comparing the excess free energy, pressure and phase diagram, we show that the fundamental measure functional yields good agreements to the available simulation results of AB, AB2 and AB13 crystals. Additionally, we use this functional to study the HS models of five binary crystals, Cu5Zr(C15b), Cu51Zr14(?), Cu10Zr7(?), CuZr(B2) and CuZr2 (C11b), which are observed in the Cu-Zr system. The FMT functional gives well behaved minimum for most of the hard sphere crystal complexes in the two dimensional Gaussian space, namely a crystalline phase. However, the current version of FMT functional (white Bear) fails to give a stable minimum for the structure Cu10Zr7(?). We argue that the observed solid phases for the HS models of the Cu-Zr system are true thermodynamic stable phases and can be used as a reference system in perturbation calculations.

  5. Communication: Dynamical density functional theory for dense suspensions of colloidal hard spheres

    NASA Astrophysics Data System (ADS)

    Stopper, Daniel; Roth, Roland; Hansen-Goos, Hendrik

    2015-11-01

    We study structural relaxation of colloidal hard spheres undergoing Brownian motion using dynamical density functional theory. Contrary to the partial linearization route [D. Stopper et al., Phys. Rev. E 92, 022151 (2015)] which amounts to using different free energy functionals for the self and distinct part of the van Hove function G(r, t), we put forward a unified description employing a single functional for both components. To this end, interactions within the self part are removed via the zero-dimensional limit of the functional with a quenched self component. In addition, we make use of a theoretical result for the long-time mobility in hard-sphere suspensions, which we adapt to the inhomogeneous fluid. Our results for G(r, t) are in excellent agreement with numerical simulations even in the dense liquid phase. In particular, our theory accurately yields the crossover from free diffusion at short times to the slower long-time diffusion in a crowded environment.

  6. Hard spheres out of equilibrium

    NASA Astrophysics Data System (ADS)

    Hermes, M.

    2010-05-01

    In this thesis, experiments and simulations are combined to investigate the nonequilibrium behaviour of hard spheres. In the first chapters we use Molecular Dynamics simulations to investigate the dynamic glass transition of polydisperse hard spheres. We show that this dynamic transition is accompanied by a thermodynamic signature. The higher-order derivatives of the pressure change abruptly at the dynamic glass transition. If a system is compressed beyond this dynamic transition, the pressure increases until it diverges when the system is completely jammed. The density at which the pressure diverges depends on the compression speed. We proceed with experiments on colloidal polymethylmethacrylate (PMMA) particles which closely resemble hard spheres. We investigate the effect of compression using gravity and electric field gradients on the nucleation and on the glass transition. The transition from glass to crystal is gradual and is strongly effected by gravity. We go back to computer simulations to investigate two different techniques to calculate the rate at which a hard-sphere system nucleates. We find that the two techniques yield similar results for the nucleation rate as well as the critical nucleus shape. From this we conclude that the simulation techniques are valid. A combination of simulations and experiments is used to study the nucleation of hard spheres on seed structures. We initiate the nucleation with a seed of particles kept in place by optical tweezers. We show that whereas the nucleation itself can be well described as an equilibrium process, the growth after nucleation can not. We demonstrate that defects play an important role in the growth of the crystal. Colloidal hard spheres can also be driven out of equilibrium using shear. We perform experiments on an equilibrium fluid phase below the coexistence density of the fluid. We show that we can induce order in an equilibrium fluid using oscillatory shear. We find five different phases for varying frequency and amplitude: four known phases and one new phase. The formation of all phases occurs via nucleation and growth and the melting, when the shear is stopped, starts on the edges and near the defects of the crystal phases. In the final chapter, we investigate the interactions between rough colloidal particles in the presence of polymers. We investigate whether surface roughness can be used to reduce the depletion attraction. We find that when the polymer is smaller than the surface roughness the attraction can be reduced significantly compared to smooth colloids.

  7. Hard sphere packings within cylinders.

    PubMed

    Fu, Lin; Steinhardt, William; Zhao, Hao; Socolar, Joshua E S; Charbonneau, Patrick

    2016-02-23

    Arrangements of identical hard spheres confined to a cylinder with hard walls have been used to model experimental systems, such as fullerenes in nanotubes and colloidal wire assembly. Finding the densest configurations, called close packings, of hard spheres of diameter σ in a cylinder of diameter D is a purely geometric problem that grows increasingly complex as D/σ increases, and little is thus known about the regime for D > 2.873σ. In this work, we extend the identification of close packings up to D = 4.00σ by adapting Torquato-Jiao's adaptive-shrinking-cell formulation and sequential-linear-programming (SLP) technique. We identify 17 new structures, almost all of them chiral. Beyond D ≈ 2.85σ, most of the structures consist of an outer shell and an inner core that compete for being close packed. In some cases, the shell adopts its own maximum density configuration, and the stacking of core spheres within it is quasiperiodic. In other cases, an interplay between the two components is observed, which may result in simple periodic structures. In yet other cases, the very distinction between the core and shell vanishes, resulting in more exotic packing geometries, including some that are three-dimensional extensions of structures obtained from packing hard disks in a circle. PMID:26843132

  8. Equilibrium equation of state of a hard sphere binary mixture at very large densities using replica exchange Monte Carlo simulations.

    PubMed

    Odriozola, Gerardo; Berthier, Ludovic

    2011-02-01

    We use replica exchange Monte Carlo simulations to measure the equilibrium equation of state of the disordered fluid state for a binary hard sphere mixture up to very large densities where standard Monte Carlo simulations do not easily reach thermal equilibrium. For the moderate system sizes we use (up to N = 100), we find no sign of a pressure discontinuity near the location of dynamic glass singularities extrapolated using either algebraic or simple exponential divergences, suggesting they do not correspond to genuine thermodynamic glass transitions. Several scenarios are proposed for the fate of the fluid state in the thermodynamic limit. PMID:21303135

  9. Anisotropic pair correlations in binary and multicomponent hard-sphere mixtures in the vicinity of a hard wall: A combined density functional theory and simulation study

    NASA Astrophysics Data System (ADS)

    Härtel, Andreas; Kohl, Matthias; Schmiedeberg, Michael

    2015-10-01

    The fundamental measure approach to classical density functional theory has been shown to be a powerful tool to predict various thermodynamic properties of hard-sphere systems. We employ this approach to determine not only one-particle densities but also two-particle correlations in binary and six-component mixtures of hard spheres in the vicinity of a hard wall. The broken isotropy enables us to carefully test a large variety of theoretically predicted two-particle features by quantitatively comparing them to the results of Brownian dynamics simulations. Specifically, we determine and compare the one-particle density, the total correlation functions, their contact values, and the force distributions acting on a particle. For this purpose, we follow the compressibility route and theoretically calculate the direct correlation functions by taking functional derivatives. We usually observe an excellent agreement between theory and simulations, except for small deviations in cases where local crystal-like order sets in. Our results set the course for further investigations on the consistency of functionals as well as for structural analysis on, e.g., the primitive model. In addition, we demonstrate that due to the suppression of local crystallization, the predictions of six-component mixtures are better than those in bidisperse or monodisperse systems. Finally, we are confident that our results of the structural modulations induced by the wall lead to a deeper understanding of ordering in anisotropic systems in general, the onset of heterogeneous crystallization, caging effects, and glassy dynamics close to a wall, as well as structural properties in systems with confinement.

  10. Hard-sphere fluid in infinite dimensions

    NASA Technical Reports Server (NTRS)

    Wyler, D.; Rivier, N.; Frisch, H. L.

    1987-01-01

    The exact Mayer series is derived for the pressure, density, and equation of state of a hard-sphere fluid in the limit of infinite space dimensions D. The Mayer series can be analytically continued into the full (cut) activity plane, and there is no sign of a phase transition. The quantum-mechanical system is also treated. For D = infinity, the fluid behaves like an ideal Bose gas and undergoes a Bose-Einstein condensation.

  11. Segregation of Fluidized Binary Hard-Sphere Systems Under Gravity

    NASA Astrophysics Data System (ADS)

    Kim, Soon-Chul

    We have derived an analytic expression for the contact value of the local density of binary hard-sphere systems under gravity. We have obtained the crossover conditions for the Brazil-nut type segregation of binary hard-sphere mixtures and binary hard-sphere chain mixtures from the segregation criterion, where the segregation occurs when the density (or the pressure) of the small spheres at the bottom is higher than that of the large spheres, or vice versa. For the binary hard-sphere chain mixtures, the crossover condition for the segregation depends on the number of monomers composed of hard-sphere chains as well as the mass and the diameter of each species. The fundamental-measure theories (FMTs) and local density approximation (LDA) are employed to examine the crossover condition for the segregation of the gravity-induced hard-sphere mixtures. The calculated results show that the LDA does not explain the density oscillation near the bottom, whereas the modified fundamental-measure theory (MFMT) compares with molecular dynamics simulations.

  12. Substitutionally ordered solid solutions of hard spheres

    SciTech Connect

    Cottin, X.; Monson, P.A. )

    1995-02-22

    A recently developed cell theory for multicomponent solid solutions is applied to the study of substitutionally ordered binary hard sphere solid solutions. Solid phase thermodynamic properties and solid--fluid phase diagrams have been determined for a range of particle size ratios. The theoretical predictions agree well with available Monte Carlo simulation results. From the phase diagrams we draw some conclusions about the domains of stability of some simple compounds such as AB, AB[sub 2], and AB[sub 13] in terms of the size ratio, density, and overall composition of the mixture.

  13. Structure of hard-sphere metastable fluids

    NASA Astrophysics Data System (ADS)

    Yuste, S. Bravo; Haro, M. Lpez; Santos, A.

    1996-05-01

    A rational-function approximation method to analytically derive the radial distribution function g(r) and the structure factor S(q) of a hard-sphere fluid is revisited. The method provides a fluid structure thermodynamically consistent with a given equation of state. The Carnahan-Starling and a recently derived Pad (4,3) equations of state are considered. While the Carnahan-Starling equation leads to functions g(r) and S(q) even for densities larger than the crystalline close-packing density, their physical value is questionable already in the metastable fluid region. In the case of the much more reliable Pad equation of state, the method shows the existence of a threshold density, beyond which no meaningful fluid structure can be derived. This threshold value, whose signature is a diverging slope of g(r) at the contact distance, coincides with the one associated in the literature with the glass transition.

  14. Local structure in hard-sphere chain-molecule fluids

    NASA Astrophysics Data System (ADS)

    Wasti, Sambid; Taylor, Mark

    2012-04-01

    The conformation of a polymer chain in solvent is coupled to the local structure of the solvent environment. For hard-sphere systems, a monomeric solvent acts to compress a flexible hard-sphere-solute chain and, for a dense system, the local solvent structure is imprinted onto the chain. Here we use Monte Carlo simulation, including bond-rebridging moves, to study the size and conformation of a hard sphere chain in a hard-sphere solvent as a function of both solvent density and solvent diameter. We also study the structure of a hard-sphere-chain solute in a hard-sphere-chain solvent. In the case of a 5-mer chain in 5-mer solvent we show that the effects of solvent can be mapped to a set of two-body solvation potentials. Following our previous work on hard-sphere chains in monomeric solvent [1], we explore the application of these short chain potentials to the study of longer chain-molecule fluids. [4pt] [1] M.P. Taylor and S. Ichida, J. Polym. Sci. B: Polym. Phys. 45, 3319 (2007).

  15. Demixing in binary mixtures of apolar and dipolar hard spheres

    NASA Astrophysics Data System (ADS)

    Almarza, N. G.; Lomba, E.; Martn, C.; Gallardo, A.

    2008-12-01

    We study the demixing transition of mixtures of equal size hard spheres and dipolar hard spheres using computer simulation and integral equation theories. Calculations are carried out at constant pressure, and it is found that there is a strong correlation between the total density and the composition. The critical temperature and the critical total density are found to increase with pressure. The critical mole fraction of the dipolar component on the contrary decreases as pressure is augmented. These qualitative trends are reproduced by the theoretical approaches that on the other hand overestimate by far the value of the critical temperature. Interestingly, the critical parameters for the liquid-vapor equilibrium extrapolated from the mixture results in the limit of vanishing neutral hard sphere concentration agree rather well with recent estimates based on the extrapolation of charged hard dumbbell phase equilibria when dumbbell elongation shrinks to zero [G. Ganzenmller and P. J. Camp, J. Chem. Phys. 126, 191104 (2007)].

  16. Hard spheres on the gyroid surface

    PubMed Central

    Dotera, Tomonari; Kimoto, Masakiyo; Matsuzawa, Junichi

    2012-01-01

    We find that 48/64 hard spheres per unit cell on the gyroid minimal surface are entropically self-organized. Striking evidence is obtained in terms of the acceptance ratio of Monte Carlo moves and order parameters. The regular tessellations of the spheres can be viewed as hyperbolic tilings on the Poincar disc with a negative Gaussian curvature, one of which is, equivalently, the arrangement of angels and devils in Escher's Circle Limit IV. PMID:24098841

  17. A Monte Carlo simulation study of binary mixtures of charged hard spherocylinders and charged hard spheres

    NASA Astrophysics Data System (ADS)

    Avendao, Carlos; Gil-Villegas, Alejandro; Gonzlez-Tovar, Enrique

    2009-02-01

    In this work, we report Monte Carlo results for thermodynamic and structural properties of an electroneutral binary mixture of charged hard spherocylinders and charged hard spheres. We have examined the effects of the presence of charged hard spheres on the liquid crystalline phases of charged hard spherocylinders for two different models, namely, with charges located at the end or at the center of the spherocylinders. In both cases isotropic and nematic phases are observed. However, at higher densities the systems present nematic-smectic-A and nematic-columnar phase transitions for the first and second models, respectively, according to the simulated structure factor.

  18. Regularized 13 moment equations for hard spheres

    NASA Astrophysics Data System (ADS)

    Struchtrup, Henning; Torrilhon, Manuel

    2012-11-01

    The regularized 13 moment equations (R13) of rarefied gas dynamics for a monatomic hard sphere gas in the linear regime are presented. The equations are based on an extended Grad-type moment system, which was systematically reduced by means of the Order of Magnitude Method [Struchtrup, Phys. Fluids 16(11), 3921-3934 (2004)]. The linear Burnett and super-Burnett equations are derived from Chapman-Enskog expansion of the R13 equations. While the Burnett coefficients agree with literature values, this seems to be the first time that super-Burnett coefficients are computed for a hard sphere gas. The equations are considered for stability, and dispersion and damping of sound waves. Boundary conditions are given, and solutions of simple boundary value problems are briefly discussed.

  19. Thermodynamic properties of non-conformal soft-sphere fluids with effective hard-sphere diameters.

    PubMed

    Rodrguez-Lpez, Tonalli; del Ro, Fernando

    2012-01-28

    In this work we study a set of soft-sphere systems characterised by a well-defined variation of their softness. These systems represent an extension of the repulsive Lennard-Jones potential widely used in statistical mechanics of fluids. This type of soft spheres is of interest because they represent quite accurately the effective intermolecular repulsion in fluid substances and also because they exhibit interesting properties. The thermodynamics of the soft-sphere fluids is obtained via an effective hard-sphere diameter approach that leads to a compact and accurate equation of state. The virial coefficients of soft spheres are shown to follow quite simple relationships that are incorporated into the equation of state. The approach followed exhibits the rescaling of the density that produces a unique equation for all systems and temperatures. The scaling is carried through to the level of the structure of the fluids. PMID:22158949

  20. Packing of hard spheres in cylinders and applications

    NASA Astrophysics Data System (ADS)

    Mughal, Adil; Weaire, Denis; Hutzler, Stefan; Chan, Ho Kei

    2014-03-01

    We study the optimal packing of hard spheres in an infinitely long cylinder. Our simulations have yielded dozens of periodic, mechanically stable, structures as the ratio of the cylinder (D) to sphere (d) diameter is varied. Up to D/d =2.715 the densest structures are composed entirely of spheres which are in contact with the cylinder. The density reaches a maximum at discrete values of D/d when a maximum number of contacts are established. These maximal contact packings are of the classic ``phyllotactic'' type, familiar in biology. However, between these points we observe another type of packing, termed line-slip. An analytic understanding of these rigid structures follows by recourse to a yet simpler problem: the packing of disks on a cylinder. We show that maximal contact packings correspond to the perfect wrapping of a honeycomb arrangement of disks around a cylindrical tube. While line-slip packings are inhomogeneous deformations of the honeycomb lattice modified to wrap around the cylinder. Beyond D/d =2.715 the structures are more complex, since they incorporate internal spheres. We review some relevant experiments with hard spheres, small bubbles and discuss similar structures found in nature. We discuss the chirality of these packings and potential applications in photonics.

  1. Fundamental measure theory for the inhomogeneous hard-sphere system based on Santos' consistent free energy.

    PubMed

    Hansen-Goos, Hendrik; Mortazavifar, Mostafa; Oettel, Martin; Roth, Roland

    2015-05-01

    Based on Santos' general solution for the scaled-particle differential equation [Phys. Rev. E 86, 040102(R) (2012)], we construct a free-energy functional for the hard-sphere system. The functional is obtained by a suitable generalization and extension of the set of scaled-particle variables using the weighted densities from Rosenfeld's fundamental measure theory for the hard-sphere mixture [Phys. Rev. Lett. 63, 980 (1989)]. While our general result applies to the hard-sphere mixture, we specify remaining degrees of freedom by requiring the functional to comply with known properties of the pure hard-sphere system. Both for mixtures and pure systems, the functional can be systematically extended following the lines of our derivation. We test the resulting functionals regarding their behavior upon dimensional reduction of the fluid as well as their ability to accurately describe the hard-sphere crystal and the liquid-solid transition. PMID:26066133

  2. Quantum-hard-sphere system equations of state revisited

    SciTech Connect

    Keller, C.; de Llano, M.; Ren, S.Z.; Solis, M.A.; Baker, G.A. Jr.

    1996-10-01

    Analytical equations of state for boson and fermion hard-sphere fluids ranging from very low to very high densities are constructed. Such equations of state serve as a zero-order (reference) state upon which to build so-called quantum-thermodynamic-perturbation corrections in describing real but simple quantum fluids at zero temperature. The fluid branch extrapolations from the exact low-density series expansions for the energy are carried out by incorporating various physical arguments, such as close packing densities and residues. Modified London equations of state for the high-density crystalline branch agree very well with computer simulations, and at close packing with certain experimental results at high pressure. Copyright {copyright} 1996 Academic Press, Inc.

  3. Dynamics of hard sphere colloidal dispersions

    NASA Technical Reports Server (NTRS)

    Zhu, J. X.; Chaikin, Paul M.; Phan, S.-E.; Russel, W. B.

    1994-01-01

    Our objective is to perform on homogeneous, fully equilibrated dispersions the full set of experiments characterizing the transition from fluid to solid and the properties of the crystalline and glassy solid. These include measurements quantifying the nucleation and growth of crystallites, the structure of the initial fluid and the fully crystalline solid, and Brownian motion of particles within the crystal, and the elasticity of the crystal and the glass. Experiments are being built and tested for ideal microgravity environment. Here we describe the ground based effort, which exploits a fluidized bed to create a homogeneous, steady dispersion for the studies. The differences between the microgravity environment and the fluidized bed is gauged by the Peclet number Pe, which measures the rate of convection/sedimentation relative to Brownian motion. We have designed our experiment to accomplish three types of measurements on hard sphere suspensions in a fluidized bed: the static scattering intensity as a function of angle to determine the structure factor, the temporal autocorrelation function at all scattering angles to probe the dynamics, and the amplitude of the response to an oscillatory forcing to deduce the low frequency viscoelasticity. Thus the scattering instrument and the colloidal dispersion were chosen such as that the important features of each physical property lie within the detectable range for each measurement.

  4. Tunable Long Range Forces Mediated by Self-Propelled Colloidal Hard Spheres

    NASA Astrophysics Data System (ADS)

    Ni, Ran; Cohen Stuart, Martien A.; Bolhuis, Peter G.

    2015-01-01

    Using Brownian dynamics simulations, we systematically study the effective interaction between two parallel hard walls in a 2D suspension of self-propelled (active) colloidal hard spheres, and we find that the effective force between two hard walls can be tuned from a long range repulsion into a long range attraction by changing the density of active particles. At relatively high densities, the active hard spheres can form a dynamic crystalline bridge, which induces a strong oscillating long range dynamic wetting repulsion between the walls. With decreasing density, the dynamic bridge gradually breaks, and an intriguing long range dynamic depletion attraction arises. A similar effect occurs in a quasi-2D suspension of self-propelled colloidal hard spheres by changing the height of the confinement. Our results open up new possibilities to manipulate the motion and assembly of microscopic objects by using active matter.

  5. The hard sphere view of the outer core

    NASA Astrophysics Data System (ADS)

    Helffrich, George

    2015-12-01

    The hard sphere model for liquids attempts to capture the physical behavior of a real liquid in a simple conceptual model: a fluid of fixed size spheres that only interact repulsively when they come into contact. Is the model good enough to use for modeling internal planetary structure? To answer this question, I survey variants of hard sphere liquid theory by applying them to the Earth's outer core to determine which of them explains wavespeeds in the outer core best. The variants explored here are the Carnahan-Starling hard sphere model, the Mansoori-Canfield extension to hard sphere mixtures, the transition metal hard sphere liquid, and the Lennard-Jones hard sphere liquid with attractive forces. With an empirical addition of a temperature dependence to the liquid's hard sphere diameter, all of the variants explored can replicate wavespeeds in most of the radius range of the outer core. The hard sphere model for liquid transition metals explains the wavespeed best because it yields a mean liquid atomic weight of 48.8 g mo l -1 at 10 wt% light element abundance in the core which is in good cosmochemical agreement with core light element models. Other variants also fit core wavespeeds but require implausibly low liquid mean atomic weight implying excessive incorporation of hydrogen or helium in the core. Applied to the detailed wavespeed structure of the Earth's outermost outer core, the model suggests that the mean atomic weight could be reduced by up to 1.74% or the temperature could be increased by up to 400 K relative to an adiabatic profile, or there could be 8% fewer valence electrons in the liquid.

  6. Simple heuristic for the viscosity of polydisperse hard spheres

    NASA Astrophysics Data System (ADS)

    Farr, Robert S.

    2014-12-01

    We build on the work of Mooney [Colloids Sci. 6, 162 (1951)] to obtain an heuristic analytic approximation to the viscosity of a suspension any size distribution of hard spheres in a Newtonian solvent. The result agrees reasonably well with rheological data on monodispserse and bidisperse hard spheres, and also provides an approximation to the random close packing fraction of polydisperse spheres. The implied packing fraction is less accurate than that obtained by Farr and Groot [J. Chem. Phys. 131(24), 244104 (2009)], but has the advantage of being quick and simple to evaluate.

  7. Gibbs ensemble Monte Carlo of nonadditive hard-sphere mixtures.

    PubMed

    Pellicane, Giuseppe; Pandaram, Owen D

    2014-07-28

    In this article, we perform Gibbs ensemble Monte Carlo (GEMC) simulations of liquid-liquid phase coexistence in nonadditive hard-sphere mixtures (NAHSMs) for different size ratios and non-additivity parameters. The simulation data are used to provide a benchmark to a number of theoretical and mixed theoretical/computer simulation approaches which have been adopted in the past to study phase equilibria in NAHSMs, including the method of the zero of the Residual Multi-Particle Entropy, Integral Equation Theories (IETs), and classical Density Functional Theory (DFT). We show that while the entropic criterium is quite accurate in predicting the location of phase equilibrium curves, IETs and DFT provide at best a semi-quantitative reproduction of GEMC demixing curves. PMID:25084927

  8. Inhomogeneous quasistationary state of dense fluids of inelastic hard spheres.

    PubMed

    Fouxon, Itzhak

    2014-05-01

    We study closed dense collections of freely cooling hard spheres that collide inelastically with constant coefficient of normal restitution. We find inhomogeneous states (ISs) where the density profile is spatially nonuniform but constant in time. The states are exact solutions of nonlinear partial differential equations that describe the coupled distributions of density and temperature valid when inelastic losses of energy per collision are small. The derivation is performed without modeling the equations' coefficients that are unknown in the dense limit (such as the equation of state) using only their scaling form specific for hard spheres. Thus the IS is the exact state of this dense many-body system. It captures a fundamental property of inelastic collections of particles: the possibility of preserving nonuniform temperature via the interplay of inelastic cooling and heat conduction that generalizes previous results. We perform numerical simulations to demonstrate that arbitrary initial state evolves to the IS in the limit of long times where the container has the geometry of the channel. The evolution is like a gas-liquid transition. The liquid condenses in a vanishing part of the total volume but takes most of the mass of the system. However, the gaseous phase, which mass grows only logarithmically with the system size, is relevant because its fast particles carry most of the energy of the system. Remarkably, the system self-organizes to dissipate no energy: The inelastic decay of energy is a power law [1+t/t(c)](-2), where t(c) diverges in the thermodynamic limit. This is reinforced by observing that for supercritical systems the IS coincide in most of the space with the steady states of granular systems heated at one of the walls. We discuss the relation of our results to the recently proposed finite-time singularity in other container's geometries. PMID:25353790

  9. Phase behavior of dipolar hard and soft spheres.

    PubMed

    Hynninen, Antti-Pekka; Dijkstra, Marjolein

    2005-11-01

    We study the phase behavior of hard and soft spheres with a fixed dipole moment using Monte Carlo simulations. The spheres interact via a pair potential that is a sum of a hard-core Yukawa (or screened-Coulomb) repulsion and a dipole-dipole interaction. The system can be used to model colloids in an external electric or magnetic field. Two cases are considered: (i) colloids without charge (or dipolar hard spheres) and (ii) colloids with charge (or dipolar soft spheres). The phase diagram of dipolar hard spheres shows fluid, face-centered-cubic (fcc), hexagonal-close-packed (hcp), and body-centered-tetragonal (bct) phases. The phase diagram of dipolar soft spheres shows, in addition to the above mentioned phases, a body-centered-orthorhombic (bco) phase, and is in agreement with the experimental phase diagram [Nature (London) 421, 513 (2003)]. In both cases, the fluid phase is inhomogeneous but we find no evidence of a gas-liquid phase separation. The validity of the dipole approximation is verified by a multipole moment expansion. PMID:16383604

  10. Compact anisotropic spheres with prescribed energy density

    NASA Astrophysics Data System (ADS)

    Chaisi, M.; Maharaj, S. D.

    2005-07-01

    New exact interior solutions to the Einstein field equations for anisotropic spheres are found. We utilise a procedure that necessitates a choice for the energy density and the radial pressure. This class contains the constant density model of Maharaj and Maartens (Gen. Rel. Grav. 21, 899 905 (1989)), and the variable density model of Gokhroo and Mehra (Gen. Rel. Grav. 26, 75 84 (1994)), as special cases. These anisotropic spheres match smoothly to the Schwarzschild exterior and gravitational potentials are well behaved in the interior. A graphical analysis of the matter variables is performed which points to a physically reasonable matter distribution.

  11. New phase for one-component hard spheres.

    PubMed

    Wu, Guang-Wen; Sadus, Richard J

    2004-06-22

    A completely new phase for one-component hard spheres is reported in an unexpected region of the phase diagram. The new phase is observed at compressibility factors intermediate between the solid and the metastable branches. It can be obtained from either Monte Carlo simulations alone or a combination of Monte Carlo and molecular dynamics calculations. An analysis of the intermediate scattering function data shows that the new phase is in a stable equilibrium. Radial distribution function data, configurational snapshots, bond order parameters, and translational order parameters obtained from molecular simulations indicate that the new phase is significantly different from the isotropic liquid, metastable, or crystalline phases traditionally observed in hard sphere systems. This result significantly changes our previous understanding of the behavior of hard spheres. PMID:15268204

  12. Steady Shear Viscosities of Two Hard Sphere Colloidal Dispersions

    NASA Astrophysics Data System (ADS)

    Cheng, Zhengdong; Chaikin, Paul M.; Phan, See-Eng; Russel, William B.; Zhu, Jixiang

    1996-03-01

    Though hard spheres have the simplest inter-particle potential, the many body hydrodynamic interactions are complex and the rheological properties of dispersions are not fully understood in the concentrated regime. We studied two model systems: colloidal poly-(Methyl Methacrylate) spheres with a grafted layer of poly-(12-hydroxy stearic acid) (PMMA/PHSA) and spherical Silica particles (PST-5, Nissan Chemical Industries, Ltd, Tokyo, Japan). Steady shear viscosities were measured by a Zimm viscometer. The high shear relative viscosity of the dispersions compares well with other hard sphere systems, but the low shear relative viscosity of PMMA/PHSA dispersions is ? / ? 0 = 50 at ? = 0.5 , higher than ? / ? 0 = 22 for other hard sphere systems, consistent with recently published data (Phys. Rev. Lett. 75(1995)958). Bare Silica spheres are used to clarify the effect of the grafted layer. With the silica spheres, volume fraction can be determined independent of intrinsic viscosity measurements; also, higher concentrated dispersions can be made.

  13. Investigating hard sphere interactions through spin echo scattering angle measurement

    NASA Astrophysics Data System (ADS)

    Washington, Adam

    Spin Echo Scattering Angle Measurement (SESAME) allows neutron scattering instruments to perform real space measurements on large micron scale samples by encoding the scattering angle into the neutron's spin state via Larmor precession. I have built a SESAME instrument at the Low Energy Neutron Source. I have also assisted in the construction of a modular SESAME instrument on the ASTERIX beamline at Los Alamos National lab. The ability to tune these instruments has been proved mathematically and optimized and automated experimentally. Practical limits of the SESAME technique with respect to polarization analyzers, neutron spectra, Larmor elements, and data analysis were investigated. The SESAME technique was used to examine the interaction of hard spheres under depletion. Poly(methyl methacrylate) spheres suspended in decalin had previously been studied as a hard sphere solution. The interparticle correlations between the spheres were found to match the Percus-Yevick closure, as had been previously seen in dynamical light scattering experiments. To expand beyond pure hard spheres, 900kDa polystyrene was added to the solution in concentrations of less than 1% by mass. The steric effects of the polystyrene were expected to produce a short-range, attractive, "sticky" potential. Experiment showed, however, that the "sticky" potential was not a stable state and that the spheres would eventually form long range aggregates.

  14. A generalized hard-sphere model for Monte Carlo simulation

    NASA Technical Reports Server (NTRS)

    Hassan, H. A.; Hash, David B.

    1993-01-01

    A new molecular model, called the generalized hard-sphere, or GHS model, is introduced. This model contains, as a special case, the variable hard-sphere model of Bird (1981) and is capable of reproducing all of the analytic viscosity coefficients available in the literature that are derived for a variety of interaction potentials incorporating attraction and repulsion. In addition, a new procedure for determining interaction potentials in a gas mixture is outlined. Expressions needed for implementing the new model in the direct simulation Monte Carlo methods are derived. This development makes it possible to employ interaction models that have the same level of complexity as used in Navier-Stokes calculations.

  15. Thermodynamic stability in elastic systems: Hard spheres embedded in a finite spherical elastic solid.

    PubMed

    Solano-Altamirano, J M; Goldman, Saul

    2015-12-01

    We determined the total system elastic Helmholtz free energy, under the constraints of constant temperature and volume, for systems comprised of one or more perfectly bonded hard spherical inclusions (i.e. "hard spheres") embedded in a finite spherical elastic solid. Dirichlet boundary conditions were applied both at the surface(s) of the hard spheres, and at the outer surface of the elastic solid. The boundary conditions at the surface of the spheres were used to describe the rigid displacements of the spheres, relative to their initial location(s) in the unstressed initial state. These displacements, together with the initial positions, provided the final shape of the strained elastic solid. The boundary conditions at the outer surface of the elastic medium were used to ensure constancy of the system volume. We determined the strain and stress tensors numerically, using a method that combines the Neuber-Papkovich spherical harmonic decomposition, the Schwartz alternating method, and Least-squares for determining the spherical harmonic expansion coefficients. The total system elastic Helmholtz free energy was determined by numerically integrating the elastic Helmholtz free energy density over the volume of the elastic solid, either by a quadrature, or a Monte Carlo method, or both. Depending on the initial position of the hard sphere(s) (or equivalently, the shape of the un-deformed stress-free elastic solid), and the displacements, either stationary or non-stationary Helmholtz free energy minima were found. The non-stationary minima, which involved the hard spheres nearly in contact with one another, corresponded to lower Helmholtz free energies, than did the stationary minima, for which the hard spheres were further away from one another. PMID:26701708

  16. On the impossibility of defining adhesive hard spheres as sticky limit of a hard-sphere-Yukawa potential.

    PubMed

    Gazzillo, Domenico

    2011-03-28

    For fluids of molecules with short-ranged hard-sphere-Yukawa (HSY) interactions, it is proven that the Noro-Frenkel "extended law of corresponding states" cannot be applied down to the vanishing attraction range, since the exact HSY second virial coefficient diverges in such a limit. It is also shown that, besides Baxter's original approach, a fully correct alternative definition of "adhesive hard spheres" can be obtained by taking the vanishing-range-limit (sticky limit) not of a Yukawa tail, as is commonly done, but of a slightly different potential with a logarithmic-Yukawa attraction. PMID:21456673

  17. Effect of H[subscript 2]O on the density of silicate melts at high pressures: Static experiments and the application of a modified hard-sphere model of equation of state

    SciTech Connect

    Jing, Zhicheng; Karato, Shun-ichiro

    2012-04-20

    Density of ultramafic silicate melts was determined using the sink/float technique at high pressures. Seven melt compositions were studied, among which three were dry compositions with different Mg's (molar MgO/(MgO + FeO) x 100) and the other four were hydrous compositions synthesized by adding 2-7 wt.% H{sub 2}O to the anhydrous ones. Experimental conditions range from 9 to 15 GPa and from 2173 to 2473 K. The sinking and floatation of density markers were observed for all melt compositions. Melt density data were analyzed by applying the Birch-Murnaghan equation of state and a newly developed equation of state for silicate melts based on the model of hard sphere mixtures. The presence of water can significantly reduce the density of melts due to its small molecular mass. On the other hand, water makes hydrous silicate melts more compressible than anhydrous melts and therefore the effect of H{sub 2}O on melt density is less significant at high pressures. The density of hydrous melts was then calculated as a function of H{sub 2}O content at the conditions of the bottom of the upper mantle, and was compared with the density of the dominant upper mantle minerals. Results show that the conditions for a negatively buoyant melt that coexists with a pyrolite mantle atop the 410 km discontinuity are marginally satisfied if H{sub 2}O is the only volatile component to facilitate melting, but such conditions will be satisfied by a broader range of conditions when other heavier volatile elements (C, K, etc.) are also present.

  18. Effect of H2O on the density of silicate melts at high pressures: Static experiments and the application of a modified hard-sphere model of equation of state

    NASA Astrophysics Data System (ADS)

    Jing, Zhicheng; Karato, Shun-ichiro

    2012-05-01

    Density of ultramafic silicate melts was determined using the sink/float technique at high pressures. Seven melt compositions were studied, among which three were dry compositions with different Mg#'s (molar MgO/(MgO + FeO) × 100) and the other four were hydrous compositions synthesized by adding 2-7 wt.% H2O to the anhydrous ones. Experimental conditions range from 9 to 15 GPa and from 2173 to 2473 K. The sinking and floatation of density markers were observed for all melt compositions. Melt density data were analyzed by applying the Birch-Murnaghan equation of state and a newly developed equation of state for silicate melts based on the model of hard sphere mixtures. The presence of water can significantly reduce the density of melts due to its small molecular mass. On the other hand, water makes hydrous silicate melts more compressible than anhydrous melts and therefore the effect of H2O on melt density is less significant at high pressures. The density of hydrous melts was then calculated as a function of H2O content at the conditions of the bottom of the upper mantle, and was compared with the density of the dominant upper mantle minerals. Results show that the conditions for a negatively buoyant melt that coexists with a pyrolite mantle atop the 410 km discontinuity are marginally satisfied if H2O is the only volatile component to facilitate melting, but such conditions will be satisfied by a broader range of conditions when other heavier volatile elements (C, K, etc.) are also present.

  19. Structural and mechanical features of the order-disorder transition in experimental hard-sphere packings

    NASA Astrophysics Data System (ADS)

    Hanifpour, M.; Francois, N.; Robins, V.; Kingston, A.; Vaez Allaei, S. M.; Saadatfar, M.

    2015-06-01

    Here we present an experimental and numerical investigation on the grain-scale geometrical and mechanical properties of partially crystallized structures made of macroscopic frictional grains. Crystallization is inevitable in arrangements of monosized hard spheres with packing densities exceeding Bernal's limiting density ?Bernal?0.64 . We study packings of monosized hard spheres whose density spans over a wide range (0.59 sphere packings. We show that clear geometrical transitions coincide with modifications of the mechanical backbone of the packing both at the grain and global scale. Notably, two transitions are identified at ?Bernal?0.64 and ?c?0.68 . These results provide insights on how geometrical and mechanical features at the grain scale conspire to yield partially crystallized structures that are mechanically stable.

  20. Structural and mechanical features of the order-disorder transition in experimental hard-sphere packings.

    PubMed

    Hanifpour, M; Francois, N; Robins, V; Kingston, A; Allaei, S M Vaez; Saadatfar, M

    2015-06-01

    Here we present an experimental and numerical investigation on the grain-scale geometrical and mechanical properties of partially crystallized structures made of macroscopic frictional grains. Crystallization is inevitable in arrangements of monosized hard spheres with packing densities exceeding Bernal's limiting density ?(Bernal)?0.64. We study packings of monosized hard spheres whose density spans over a wide range (0.59sphere packings. We show that clear geometrical transitions coincide with modifications of the mechanical backbone of the packing both at the grain and global scale. Notably, two transitions are identified at ?(Bernal)?0.64 and ?(c)?0.68. These results provide insights on how geometrical and mechanical features at the grain scale conspire to yield partially crystallized structures that are mechanically stable. PMID:26172700

  1. Probing the evolution and morphology of hard carbon spheres

    SciTech Connect

    Pol, Vilas G.; Wen, Jianguo; Lau, Kah Chun; Callear, Samantha; Bowron, Daniel T.; Lin, Chi-Kai; Deshmukh, Sanket A.; Sankaranarayanan, Subramanian; Curtiss, Larry A.; David, William; Miller, Dean J.; Thackeray, Michael M.

    2014-03-01

    Monodispersed hard carbon spheres can be synthesized quickly and reproducibly by autogenic reactions of hydrocarbon precursors, notably polyethylene (including plastic waste), at high temperature and pressure. The carbon microparticles formed by this reaction have a unique spherical architecture, with a dominant internal nanometer layered motif, and they exhibit diamond-like hardness and electrochemical properties similar to graphite. In the present study, in-situ monitoring by X-ray diffraction along with electron microscopy, Raman spectroscopy, neutron pair-distribution function analysis, and computational modeling has been used to elucidate the morphology and evolution of the carbon spheres that form from the autogenic reaction of polyethylene at high temperature and pressure. A mechanism is proposed on how polyethylene evolves from a linear chain-based material to a layered carbon motif. Heating the spheres to 2400-2800 °C under inert conditions increases their graphitic character, particularly at the surface, which enhances their electrochemical and tribological properties.

  2. Fundamental measure theory for the inhomogeneous hard-sphere system based on Santos' consistent free energy

    NASA Astrophysics Data System (ADS)

    Hansen-Goos, Hendrik; Mortazavifar, Mostafa; Oettel, Martin; Roth, Roland

    2015-05-01

    Based on Santos' general solution for the scaled-particle differential equation [Phys. Rev. E 86, 040102(R) (2012), 10.1103/PhysRevE.86.040102], we construct a free-energy functional for the hard-sphere system. The functional is obtained by a suitable generalization and extension of the set of scaled-particle variables using the weighted densities from Rosenfeld's fundamental measure theory for the hard-sphere mixture [Phys. Rev. Lett. 63, 980 (1989), 10.1103/PhysRevLett.63.980]. While our general result applies to the hard-sphere mixture, we specify remaining degrees of freedom by requiring the functional to comply with known properties of the pure hard-sphere system. Both for mixtures and pure systems, the functional can be systematically extended following the lines of our derivation. We test the resulting functionals regarding their behavior upon dimensional reduction of the fluid as well as their ability to accurately describe the hard-sphere crystal and the liquid-solid transition.

  3. Weighted correlation approach: An extended version with applications to the hard-sphere fluid

    NASA Astrophysics Data System (ADS)

    Wang, Zhao; Liu, Longcheng

    2012-09-01

    The purpose of this study is to extend the weighted correlation approach (WCA) for inhomogeneous fluids. It now introduces a generic expression to evaluate the single-particle direct correlation function in terms of a series of pair direct correlation functions weighted by different correlation-weight functions and adjustable weight factors. When applied for practical use, however, approximations of the pair direct correlation functions have to be made, together with appropriate definitions of the weighted densities and the choices of the correlation-weight functions. The WCA approach would, then, not only help us to connect and compare different strategies and their underlying assumptions in the density functional approaches, but also enable us to propose and apply density functional theory methods to predict the density profile of, e.g., the hard-sphere fluid confined between a pair of parallel planar hard walls. Numerical results of the extended WCA approach, against the Monte Carlo (MC) simulations in a range of surface separations and bulk densities, suggest that it is capable of representing the fine features of the hard-sphere density distributions. The WCA results also agree well with the calculations from the fundamental measure theory. In addition, the thermodynamic self-consistency of the WCA approach is confirmed by its fairly good agreement with the MC fitted data for the surface tension of a hard-sphere fluid at a planar hard wall. All these tests show that a pure WCA approach can be constructed to investigate the states of ionic hard-sphere fluids.

  4. Improved quantum hard-sphere ground-state equations of state

    SciTech Connect

    Solis, M. A.; Llano, M. de; Clark, J. W.; Baker, George A. Jr.

    2007-09-15

    The London ground-state energy formula as a function of number density for a system of identical boson hard spheres, corrected for the reduced mass of a pair of particles in a 'sphere-of-influence' picture, and generalized to fermion hard-sphere systems with two and four intrinsic degrees of freedom, has a double-pole at the ultimate regular (or periodic, e.g., face-centered-cubic) close-packing density usually associated with a crystalline branch. Improved fluid branches are constructed based upon exact, field-theoretic perturbation-theory low-density expansions for many-boson and many-fermion systems, extrapolated to intermediate densities via Pade and other approximants, but whose ultimate density is irregular or random closest close-packing as suggested in studies of a classical system of hard spheres. Results show substantially improved agreement with the best available Green-function Monte Carlo and diffusion Monte Carlo simulations for bosons, as well as with ladder, variational Fermi hypernetted chain, and so-called L-expansion data for two-component fermions.

  5. Phase behavior of two colloidal suspensions: A hard sphere system and a hard disk system

    NASA Astrophysics Data System (ADS)

    Zhao, Kun

    This thesis investigates the phase behavior of two colloidal systems. In the first part, a hard sphere system consisting of PMMA-PHSA spheres(poly-(methyl methacrylate) spheres with a grafted layer of poly-(12-hydroxy steric acid)) in organic solvent is studied using the electric bottle method. A wedge-shaped cell is used in this method. By applying the electric field, a density gradient of the system is obtained and the liquid-crystal transition is found. The experimental results agree with those from a quantitative theory. The wedge cell is also very useful in the studying of glass transitions. In the second part, an anisotropic colloidal system consisting of plate-like(disk) particles is investigated. The plate-like particles are fabricated using photolithography. These particles are birefringent. Their response to an AC electric field is also studied. In a horizontal field they will form ribbon-like chains while in a vertical field they can stand on their edges when the field is high enough. These standing disks behave similar to two dimensional rectangles. The phase diagram of these standing disks is obtained and a Kosterlitz-Thouless(KT) transition from isotropic to nematic phase is found. Near the KT transition, a tetratic-like region is also found, where the tetratic correlations are of a longer range than the nematic. The results from the analysis of topological defects show that this occurs due to the proliferation of Ising-like grain boundaries that disrupt the nematic order but preserve tetratic correlations, at lengths shorter than the spacing between free disclinations.

  6. Replica exchange Monte Carlo applied to hard spheres.

    PubMed

    Odriozola, Gerardo

    2009-10-14

    In this work a replica exchange Monte Carlo scheme which considers an extended isobaric-isothermal ensemble with respect to pressure is applied to study hard spheres (HSs). The idea behind the proposal is expanding volume instead of increasing temperature to let crowded systems characterized by dominant repulsive interactions to unblock, and so, to produce sampling from disjoint configurations. The method produces, in a single parallel run, the complete HS equation of state. Thus, the first order fluid-solid transition is captured. The obtained results well agree with previous calculations. This approach seems particularly useful to treat purely entropy-driven systems such as hard body and nonadditive hard mixtures, where temperature plays a trivial role. PMID:19831433

  7. Tunable long range forces mediated by self-propelled colloidal hard spheres

    NASA Astrophysics Data System (ADS)

    Ni, Ran; Cohen Stuart, Martien; Bolhuis, Peter

    2015-03-01

    Most colloidal interactions can be tuned by changing properties of the medium. Here we show that activating colloidal particles with random self-propulsion can induce giant effective interactions between large objects immersed in such a suspension. Using Brownian dynamics simulations we find that the effective force between two hard walls in a 2D suspension of self-propelled (active) colloidal hard spheres can be tuned from a long range repulsion into a long range attraction by changing the active particle density. At relatively high densities, the active hard spheres can form a dynamic crystalline bridge, which induces a strong oscillating long range dynamic wetting repulsion between the walls. With decreasing density, the dynamic bridge gradually breaks, and an intriguing long range dynamic depletion attraction arises. A similar effect occurs in a quasi-2D suspension of self-propelled colloidal hard spheres by changing the height of the confinement. Our results open up new possibilities to manipulate the motion and assembly of microscopic objects by using active matter.

  8. Physics of Hard Spheres Experiment: Significant and Quantitative Findings Made

    NASA Technical Reports Server (NTRS)

    Doherty, Michael P.

    2000-01-01

    Direct examination of atomic interactions is difficult. One powerful approach to visualizing atomic interactions is to study near-index-matched colloidal dispersions of microscopic plastic spheres, which can be probed by visible light. Such spheres interact through hydrodynamic and Brownian forces, but they feel no direct force before an infinite repulsion at contact. Through the microgravity flight of the Physics of Hard Spheres Experiment (PHaSE), researchers have sought a more complete understanding of the entropically driven disorder-order transition in hard-sphere colloidal dispersions. The experiment was conceived by Professors Paul M. Chaikin and William B. Russel of Princeton University. Microgravity was required because, on Earth, index-matched colloidal dispersions often cannot be density matched, resulting in significant settling over the crystallization period. This settling makes them a poor model of the equilibrium atomic system, where the effect of gravity is truly negligible. For this purpose, a customized light-scattering instrument was designed, built, and flown by the NASA Glenn Research Center at Lewis Field on the space shuttle (shuttle missions STS 83 and STS 94). This instrument performed both static and dynamic light scattering, with sample oscillation for determining rheological properties. Scattered light from a 532- nm laser was recorded either by a 10-bit charge-coupled discharge (CCD) camera from a concentric screen covering angles of 0 to 60 or by sensitive avalanche photodiode detectors, which convert the photons into binary data from which two correlators compute autocorrelation functions. The sample cell was driven by a direct-current servomotor to allow sinusoidal oscillation for the measurement of rheological properties. Significant microgravity research findings include the observation of beautiful dendritic crystals, the crystallization of a "glassy phase" sample in microgravity that did not crystallize for over 1 year in 1g (Earth's gravity), and the emergence of face-centered-cubic (FCC) crystals late in the coarsening process (as small crystallites lost particles to the slow ripening of large crystallites). Significant quantitative findings from the microgravity experiments have been developed describing complex interactions among crystallites during the growth process, as concentration fields overlap in the surrounding disordered phase. Time-resolved Bragg scattering under microgravity captures one effect of these interactions quite conclusively for the sample at a volume fraction of 0.528. From the earliest time until the sample is almost fully crystalline, the size and overall crystallinity grow monotonically, but the number of crystallites per unit volume (number density) falls. Apparently nucleation is slower than the loss of crystallites because of the transfer of particles from small to large crystals. Thus, coarsening occurs simultaneously with growth, rather than following the completion of nucleation and growth as is generally assumed. In the same sample, an interesting signature appears in the apparent number density of crystallites and the volume fraction within the crystallites shortly before full crystallinity is reached. A brief upturn in both indicates the creation of more domains of the size of the average crystallite simultaneous with the compression of the crystallites. Only the emergence of dendritic arms offers a reasonable explanation. The arms would be "seen" by the light scattering as separate domains whose smaller radii of curvature would compress the interior phase. In fiscal year 1999, numerous papers, a doctoral dissertation, and the PHaSE final report were produced. Although this flight project has been completed, plans are in place for a follow-on colloid experiment by Chaikin and Russel that employs a light microscope within Glenn's Fluids and Combustion Facility on the International Space Station. PHaSE is providing us with a deeper understanding of the nure of phase transitions. The knowledge derived has added to the understanding of condensed matter. In addition, the burgeoning study of the dynamics of colloidal self-assembly may lead to the development of a range of photonic materials that control the desirable properties of light. Thus, applications of ordered colloidal structures include not only ultrastructure ceramics, but also photonic crystals and photothermal nanosecond light-switching devices. Industries dealing with semiconductors, electro-optics, ceramics, and composites stand to benefit from such advancements.

  9. Self-consistent phonon theory of the crystallization and elasticity of attractive hard spheres.

    PubMed

    Shin, Homin; Schweizer, Kenneth S

    2013-02-28

    We propose an Einstein-solid, self-consistent phonon theory for the crystal phase of hard spheres that interact via short-range attractions. The approach is first tested against the known behavior of hard spheres, and then applied to homogeneous particles that interact via short-range square well attractions and the Baxter adhesive hard sphere model. Given the crystal symmetry, packing fraction, and strength and range of attractive interactions, an effective harmonic potential experienced by a particle confined to its Wigner-Seitz cell and corresponding mean square vibrational amplitude are self-consistently calculated. The crystal free energy is then computed and, using separate information about the fluid phase free energy, phase diagrams constructed, including a first-order solid-solid phase transition and its associated critical point. The simple theory qualitatively captures all the many distinctive features of the phase diagram (critical and triple point, crystal-fluid re-entrancy, low-density coexistence curve) as a function of attraction range, and overall is in good semi-quantitative agreement with simulation. Knowledge of the particle localization length allows the crystal shear modulus to be estimated based on elementary ideas. Excellent predictions are obtained for the hard sphere crystal. Expanded and condensed face-centered cubic crystals are found to have qualitatively different elastic responses to varying attraction strength or temperature. As temperature increases, the expanded entropic solid stiffens, while the energy-controlled, fully-bonded dense solid softens. PMID:23464163

  10. On the jamming phase diagram for frictionless hard-sphere packings.

    PubMed

    Baranau, Vasili; Tallarek, Ulrich

    2014-10-21

    We computer-generated monodisperse and polydisperse frictionless hard-sphere packings of 10(4) particles with log-normal particle diameter distributions in a wide range of packing densities ? (for monodisperse packings ? = 0.46-0.72). We equilibrated these packings and searched for their inherent structures, which for hard spheres we refer to as closest jammed configurations. We found that the closest jamming densities ?(J) for equilibrated packings with initial densities ? ? 0.52 are located near the random close packing limit ?(RCP); the available phase space is dominated by basins of attraction that we associate with liquid. ?(RCP) depends on the polydispersity and is ? 0.64 for monodisperse packings. For ? > 0.52, ?(J) increases with ?; the available phase space is dominated by basins of attraction that we associate with glass. When ? reaches the ideal glass transition density ?(g), ?(J) reaches the ideal glass density (the glass close packing limit) ?(GCP), so that the available phase space is dominated at ?(g) by the basin of attraction of the ideal glass. For packings with sphere diameter standard deviation ? = 0.1, ?(GCP) ? 0.655 and ?(g) ? 0.59. For monodisperse and slightly polydisperse packings, crystallization is superimposed on these processes: it starts at the melting transition density ?(m) and ends at the crystallization offset density ?(off). For monodisperse packings, ?(m) ? 0.54 and ?(off) ? 0.61. We verified that the results for polydisperse packings are independent of the generation protocol for ? ? ?(g). PMID:25155116

  11. Geometrical frustration: a study of four-dimensional hard spheres.

    PubMed

    van Meel, J A; Frenkel, D; Charbonneau, P

    2009-03-01

    The smallest maximum-kissing-number Voronoi polyhedron of three-dimensional (3D) Euclidean spheres is the icosahedron, and the tetrahedron is the smallest volume that can show up in Delaunay tessellation. No periodic lattice is consistent with either, and hence these dense packings are geometrically frustrated. Because icosahedra can be assembled from almost perfect tetrahedra, the terms "icosahedral" and "polytetrahedral" packing are often used interchangeably, which leaves the true origin of geometric frustration unclear. Here we report a computational study of freezing of 4D Euclidean hard spheres, where the densest Voronoi cluster is compatible with the symmetry of the densest crystal, while polytetrahedral order is not. We observe that, under otherwise comparable conditions, crystal nucleation in four dimensions is less facile than in three dimensions, which is consistent with earlier observations [M. Skoge, Phys. Rev. E 74, 041127 (2006)]. We conclude that it is the geometrical frustration of polytetrahedral structures that inhibits crystallization. PMID:19391883

  12. Characterization of void space in polydisperse sphere packings: Applications to hard-sphere packings and to protein structure analysis.

    PubMed

    Maiti, Moumita; Lakshminarayanan, Arun; Sastry, Srikanth

    2013-01-01

    The implementation of a method for the exact evaluation of the volume and surface area of cavities and free volumes in polydisperse sphere packings is described. The generalization of an algorithm for Voronoi tessellation by Tanemura et al. is presented, employing the radical plane construction, as a part of the method. We employ this method to calculate the equation of state for monodisperse and polydisperse hard-sphere fluids, crystals, and for the metastable amorphous branch up to random close packing or jamming densities. We compute the distribution of free volumes, and compare with previous results employing a heuristic definition of free volume. We show the efficacy of the method for analyzing protein structure, by computing various quantities such as the distribution of sizes of buried cavities and pockets, the scaling of solvent accessible area to the corresponding occupied volume, the composition of residues lining cavities, etc. PMID:23355091

  13. Using compressibility factor as a predictor of confined hard-sphere fluid dynamics

    PubMed Central

    Mittal, Jeetain

    2009-01-01

    We study the correlations between the diffusivity (or viscosity) and the compressibility factor of bulk hard-sphere fluid as predicted by the ultralocal limit of the barrier hopping theory. Our specific aim is to determine if these correlations observed in the bulk equilibrium hard-sphere fluid can be used to predict the self-diffusivity of fluid confined between a slit-pore or a rectangular channel. In this work, we consider a single-component and a binary mixture of hard spheres. To represent confining walls, we use purely reflecting hard walls and interacting square-well walls. Our results clearly show that the correspondence between the diffusivity and the compressibility factor can be used along with the knowledge of the confined fluid's compressibility factor to predict its diffusivity with quantitative accuracy. Our analysis also suggests that a simple measure, the average fluid density, can be an accurate predictor of confined fluid diffusivity for very tight confinements (? 2-3 particle diameters wide) at low to intermediate density conditions. Together, these results provide further support for the idea that one can use robust connections between thermodynamic and dynamic quantities to predict dynamics of confined fluids from their thermodynamics. PMID:19702285

  14. Transport properties of the Fermi hard-sphere system

    NASA Astrophysics Data System (ADS)

    Mecca, Angela; Lovato, Alessandro; Benhar, Omar; Polls, Artur

    2016-03-01

    The transport properties of neutron star matter play an important role in many astrophysical processes. We report the results of a calculation of the shear viscosity and thermal conductivity coefficients of the hard-sphere fermion system of degeneracy ν =2 , that can be regarded as a model of pure neutron matter. Our approach is based on the effective interaction obtained from the formalism of correlated basis functions and the cluster expansion technique. The resulting transport coefficients show a strong sensitivity to the quasiparticle effective mass, reflecting the effect of second-order contributions to the self-energy that are not taken into account in nuclear matter studies available in the literature.

  15. Direct calculationof the crystal/melt interfacial free energy for a system of hard-spheres

    NASA Astrophysics Data System (ADS)

    Laird, Brian; Davidchack, Ruslan

    2001-03-01

    We present a direct calculation by molecular-dynamics computer simulation of the crystal/melt interfacial free energy, ?, for a system of hard spheres of diameter ?. The calculation is performed by thermodynamic integration along a reversible path defined by cleaving, using specially constructed movable hard-sphere walls, separate bulk crystal and fluid systems, which are then merged to form an interface. We find the interfacial free energy to be slightly anisotropic with ? = 0.62 0.01, 0.64 0.01 and 0.58 0.01 k_BT/?^2 for the (100), (110) and (111) fcc crystal/fluid interfaces, respectively. These values are consistent with earlier density functional calculations and recent experiments measuring the crystal nucleation rates from colloidal fluids of silica spheres that have been interpreted [Marr and Gast, Langmuir 10, 1348 (1994)] to give an estimate of ? for the hard-sphere system of 0.55 0.02 k_BT/?^2, slightly lower than the directly determined value reported here.

  16. The entropies of the hard sphere alkali halide crystals

    NASA Astrophysics Data System (ADS)

    Cox, John W.; Beyerlein, Adolph L.

    1982-08-01

    An asymptotic expansion for the entropy of hard-sphere alkali halide crystals with N small and large particle pairs is obtained: SN/NkB ???13 ln(?ls2e)/(?l?s) +3 ln(?1/3-1)+3 ln ?-C-D?-E?2+???, where kB is the Boltzman constant, e is the natural number, ? is the ratio of the system volume to its high compression limiting volume, ?l and ?s are the mean thermal de Broglie wavelengths [?=(h2/2?mkBT)1/2, m being the mass] of the large and small particles, respectively, ?ls is the hard-sphere collision diameter of nearest neighbor large and small particles; C, D, E, etc. are well-defined parameters dependent on the small to large particle radius ratio and the lattice structure, and ?=[(?1/3-1)+(1-?ls/?ls')], where ?ls' is the average distance between nearest neighbor large and small particles in the high compression limit. If the small to large particle radius ratio is less than ?2-1 for the ''NaCl'' lattice and less than ?3-1 for the ''CsCl'' lattice ?lsspheres obtained by Salsburg, Stillinger, and co-workers [J. Chem. Phys. 49, 4857 (1968)] in that it contains the additional logarithmic term 3 ln ? and a smallness parameter ? that differs from ?1/3-1, used by the earlier workers. Estimates of the leading parameter C were made using the modified cell cluster expansion. The predicted entropies of the alkali metal fluoride salts approach the experimental values at temperatures approaching the melting point which is consistent with the contention that the hard sphere contribution to the entropy dominates other contributions at high temperatures. The predicted difference between the entropies of the two alkali halide lattices is also consistent with the experimental data at higher temperatures.

  17. A Monte Carlo study of the freezing transition of hard spheres

    NASA Astrophysics Data System (ADS)

    Nayhouse, Michael; Amlani, Ankur M.; Orkoulas, G.

    2011-08-01

    A simulation method for fluid-solid transitions, which is based on a modification of the constrained cell model of Hoover and Ree, is developed and tested on a system of hard spheres. In the fully occupied constrained cell model, each particle is confined in its own Wigner-Seitz cell. Constant-pressure simulations of the constrained cell model for a system of hard spheres indicate a point of mechanical instability at a density which is about 64% of the density at the close packed limit. Below that point, the solid is mechanically unstable since without the confinement imposed by the cell walls it will disintegrate to a disordered, fluid-like phase. Hoover and Ree proposed a modified cell model by introducing an external field of variable strength. High values of the external field variable favor configurations with one particle per cell and thus stabilize the solid phase. In this work, the modified cell model of a hard-sphere system is simulated under constant-pressure conditions using tempering and histogram reweighting techniques. The simulations indicate that as the strength of the field is reduced, the transition from the solid to the fluid phase is continuous below the mechanical instability point and discontinuous above. The fluid-solid transition of the hard-sphere system is determined by analyzing the field-induced fluid-solid transition of the modified cell model in the limit in which the external field vanishes. The coexistence pressure and densities are obtained through finite-size scaling techniques and are in good accord with previous estimates.

  18. Compact Collision Kernels for Hard Sphere and Coulomb Cross Sections; Fokker-Planck Coefficients

    SciTech Connect

    Chang Yongbin; Shizgal, Bernie D.

    2008-12-31

    A compact collision kernel is derived for both hard sphere and Coulomb cross sections. The difference between hard sphere interaction and Coulomb interaction is characterized by a parameter {eta}. With this compact collision kernel, the calculation of Fokker-Planck coefficients can be done for both the Coulomb and hard sphere interactions. The results for arbitrary order Fokker-Planck coefficients are greatly simplified. An alternate form for the Coulomb logarithm is derived with concern to the temperature relaxation in a binary plasma.

  19. A comparison of some variational formulas for the free energy as applied to hard-sphere crystals

    NASA Astrophysics Data System (ADS)

    Barnes, C. Daniel; Kofke, David A.

    2002-11-01

    We examine several variational methods for determining bounds on the free energy of model crystalline phases, as applied to hard spheres in one and three dimensions. Cell- and harmonic-based reference systems are considered. Methods that provide the tightest bounds on the free energy are similar in form to free-energy perturbation, and are prone to inaccuracy from inadequate sampling. Gibbs-Bogoliubov formulas are reliable but weaker. For hard potentials they can give only a lower bound, indicating that their ability to provide upper bounds for other potentials is limited. Nevertheless, bounds given by Gibbs-Bogoliubov when applied with the optimal harmonic system prescribed by Morris and Ho [Phys. Rev. Lett. 74, 940 (1995)] yields impressive results; for hard spheres at higher density it is, within confidence limits, equal to the exact hard-sphere free energy.

  20. Hard-sphere crystallization gets rarer with increasing dimension.

    PubMed

    van Meel, J A; Charbonneau, B; Fortini, A; Charbonneau, P

    2009-12-01

    We recently found that crystallization of monodisperse hard spheres from the bulk fluid faces a much higher free-energy barrier in four than in three dimensions at equivalent supersaturation, due to the increased geometrical frustration between the simplex-based fluid order and the crystal [J. A. van Meel, D. Frenkel, and P. Charbonneau, Phys. Rev. E 79, 030201(R) (2009)]. Here, we analyze the microscopic contributions to the fluid-crystal interfacial free energy to understand how the barrier to crystallization changes with dimension. We find the barrier to grow with dimension and we identify the role of polydispersity in preventing crystal formation. The increased fluid stability allows us to study the jamming behavior in four, five, and six dimensions and to compare our observations with two recent theories [C. Song, P. Wang, and H. A. Makse, Nature (London) 453, 629 (2008); G. Parisi and F. Zamponi, Rev. Mod. Phys. (to be published)]. PMID:20365121

  1. Detecting Phase Boundaries in Hard-Sphere Suspensions

    NASA Technical Reports Server (NTRS)

    McDowell, Mark; Rogers, Richard B.; Gray, Elizabeth

    2009-01-01

    A special image-data-processing technique has been developed for use in experiments that involve observation, via optical microscopes equipped with electronic cameras, of moving boundaries between the colloidal-solid and colloidal-liquid phases of colloidal suspensions of monodisperse hard spheres. During an experiment, it is necessary to adjust the position of a microscope to keep the phase boundary within view. A boundary typically moves at a speed of the order of microns per hour. Because an experiment can last days or even weeks, it is impractical to require human intervention to keep the phase boundary in view. The present image-data-processing technique yields results within a computation time short enough to enable generation of automated-microscope-positioning commands to track the moving phase boundary

  2. Diffusion of concentrated neutral hard-sphere colloidal suspensions

    SciTech Connect

    Verberg, R.; Schepper, I. M. de; Cohen, E. G. D.

    2000-03-01

    We evaluate theoretical expressions for the long-time wave-number-dependent self-diffusion and collective diffusion coefficients D{sub S}{sup L}(k,{phi}) and D{sup L}(k,{phi}), respectively, as a function of volume fraction {phi} and wave vector k for neutral monodisperse hard-sphere colloidal suspensions over the entire fluid range. The theory is based on the Smoluchowski equation with mean-field-like hydrodynamic interactions, cage diffusion, and is free of adjustable parameters. The basic physical mechanisms underlying our formulas are discussed and the results are compared with recent experimental results by Segre and Pusey [Phys. Rev. Lett. 77, 771 (1996)]. (c) 2000 The American Physical Society.

  3. Nature of the breakdown in the Stokes-Einstein relationship in a hard sphere fluid

    NASA Astrophysics Data System (ADS)

    Kumar, Sanat K.; Szamel, Grzegorz; Douglas, Jack F.

    2006-06-01

    Molecular dynamics simulations of high density hard sphere fluids clearly show a breakdown of the Stokes-Einstein equation (SE). This result has been conjectured to be due to the presence of mobile particles, i.e., ones which have the propensity to "hop" distances that are integer multiples of the interparticle distance. We conclusively show that the sedentary particles, i.e., ones complementary to the "hoppers," obey the SE relationship to a good approximation, even though the fluid as a whole violates the SE equation at high densities. These results support the notion that the unusual diffusive behavior of supercooled liquids is dominated by the hopping particles.

  4. Phase transition induced by a shock wave in hard-sphere and hard-disk systems.

    PubMed

    Zhao, Nanrong; Sugiyama, Masaru; Ruggeri, Tommaso

    2008-08-01

    Dynamic phase transition induced by a shock wave in hard-sphere and hard-disk systems is studied on the basis of the system of Euler equations with caloric and thermal equations of state. First, Rankine-Hugoniot conditions are analyzed. The quantitative classification of Hugoniot types in terms of the thermodynamic quantities of the unperturbed state (the state before a shock wave) and the shock strength is made. Especially Hugoniot in typical two possible cases (P-1 and P-2) of the phase transition is analyzed in detail. In the case P-1 the phase transition occurs between a metastable liquid state and a stable solid state, and in the case P-2 the phase transition occurs through coexistence states, when the shock strength changes. Second, the admissibility of the two cases is discussed from a viewpoint of the recent mathematical theory of shock waves, and a rule with the use of the maximum entropy production rate is proposed as the rule for selecting the most probable one among the possible cases, that is, the most suitable constitutive equation that predicts the most probable shock wave. According to the rule, the constitutive equation in the case P-2 is the most promising one in the dynamic phase transition. It is emphasized that hard-sphere and hard-disk systems are suitable reference systems for studying shock wave phenomena including the shock-induced phase transition in more realistic condensed matters. PMID:18698913

  5. Simple effective rule to estimate the jamming packing fraction of polydisperse hard spheres

    NASA Astrophysics Data System (ADS)

    Santos, Andrs; Yuste, Santos B.; Lpez de Haro, Mariano; Odriozola, Gerardo; Ogarko, Vitaliy

    2014-04-01

    A recent proposal in which the equation of state of a polydisperse hard-sphere mixture is mapped onto that of the one-component fluid is extrapolated beyond the freezing point to estimate the jamming packing fraction ?J of the polydisperse system as a simple function of M1M3/M22, where Mk is the kth moment of the size distribution. An analysis of experimental and simulation data of ?J for a large number of different mixtures shows a remarkable general agreement with the theoretical estimate. To give extra support to the procedure, simulation data for seventeen mixtures in the high-density region are used to infer the equation of state of the pure hard-sphere system in the metastable region. An excellent collapse of the inferred curves up to the glass transition and a significant narrowing of the different out-of-equilibrium glass branches all the way to jamming are observed. Thus, the present approach provides an extremely simple criterion to unify in a common framework and to give coherence to data coming from very different polydisperse hard-sphere mixtures.

  6. Simple effective rule to estimate the jamming packing fraction of polydisperse hard spheres.

    PubMed

    Santos, Andrés; Yuste, Santos B; López de Haro, Mariano; Odriozola, Gerardo; Ogarko, Vitaliy

    2014-04-01

    A recent proposal in which the equation of state of a polydisperse hard-sphere mixture is mapped onto that of the one-component fluid is extrapolated beyond the freezing point to estimate the jamming packing fraction ϕJ of the polydisperse system as a simple function of M1M3/M22, where Mk is the kth moment of the size distribution. An analysis of experimental and simulation data of ϕJ for a large number of different mixtures shows a remarkable general agreement with the theoretical estimate. To give extra support to the procedure, simulation data for seventeen mixtures in the high-density region are used to infer the equation of state of the pure hard-sphere system in the metastable region. An excellent collapse of the inferred curves up to the glass transition and a significant narrowing of the different out-of-equilibrium glass branches all the way to jamming are observed. Thus, the present approach provides an extremely simple criterion to unify in a common framework and to give coherence to data coming from very different polydisperse hard-sphere mixtures. PMID:24827171

  7. Random sequential addition of hard spheres in high Euclidean dimensions.

    PubMed

    Torquato, S; Uche, O U; Stillinger, F H

    2006-12-01

    Sphere packings in high dimensions have been the subject of recent theoretical interest. Employing numerical and theoretical methods, we investigate the structural characteristics of random sequential addition (RSA) of congruent spheres in d -dimensional Euclidean space R{d} in the infinite-time or saturation limit for the first six space dimensions (1< or =d < or =6) . Specifically, we determine the saturation density, pair correlation function, cumulative coordination number and the structure factor in each of these dimensions. We find that for 2< or =d density phi{s} scales with dimension as phi{s}=c{1}/2{d}+c{2}d/2{d} , where c{1}=0.202048 and c{2}=0.973872 . We also show analytically that the same density scaling is expected to persist in the high-dimensional limit, albeit with different coefficients. A byproduct of this high-dimensional analysis is a relatively sharp lower bound on the saturation density for any d given by phi{s}> or =(d+2)(1-S{0})2;{d+1} , where S{0}[0,1] is the structure factor at k=0 (i.e., infinite-wavelength number variance) in the high-dimensional limit. We demonstrate that a Palsti-type conjecture (the saturation density in R{d} is equal to that of the one-dimensional problem raised to the d th power) cannot be true for RSA hyperspheres. We show that the structure factor S(k) must be analytic at k=0 and that RSA packings for 1< or =d< or =6 are nearly "hyperuniform." Consistent with the recent "decorrelation principle," we find that pair correlations markedly diminish as the space dimension increases up to six. We also obtain kissing (contact) number statistics for saturated RSA configurations on the surface of a d -dimensional sphere for dimensions 2< or =d< or =5 and compare to the maximal kissing numbers in these dimensions. We determine the structure factor exactly for the related "ghost" RSA packing in R{d} and demonstrate that its distance from "hyperuniformity" increases as the space dimension increases, approaching a constant asymptotic value of 12 . Our work has implications for the possible existence of disordered classical ground states for some continuous potentials in sufficiently high dimensions. PMID:17280063

  8. Random-close packing limits for monodisperse and polydisperse hard spheres.

    PubMed

    Baranau, Vasili; Tallarek, Ulrich

    2014-06-01

    We investigate how the densities of inherent structures, which we refer to as the closest jammed configurations, are distributed for packings of 10(4) frictionless hard spheres. A computational algorithm is introduced to generate closest jammed configurations and determine corresponding densities. Closest jamming densities for monodisperse packings generated with high compression rates using Lubachevsky-Stillinger and force-biased algorithms are distributed in a narrow density range from ? = 0.634-0.636 to ?? 0.64; closest jamming densities for monodisperse packings generated with low compression rates converge to ?? 0.65 and grow rapidly when crystallization starts with very low compression rates. We interpret ?? 0.64 as the random-close packing (RCP) limit and ?? 0.65 as a lower bound of the glass close packing (GCP) limit, whereas ? = 0.634-0.636 is attributed to another characteristic (lowest typical, LT) density ?LT. The three characteristic densities ?LT, ?RCP, and ?GCP are determined for polydisperse packings with log-normal sphere radii distributions. PMID:24723008

  9. Ising low-temperature polynomials and hard-sphere gases on cubic lattices of general dimension

    NASA Astrophysics Data System (ADS)

    Butera, P.; Pernici, M.

    2016-02-01

    We derive and analyze the low-activity and low-density expansions of the pressure for the model of a hard-sphere gas on cubic lattices of general dimension d, through the 13th order. These calculations are based on our recent extension to dimension d of the low-temperature expansions for the specific free-energy of the spin-1/2 Ising models subject to a uniform magnetic field on the (hyper-)simple-cubic lattices. Estimates of the model parameters are given also for some other lattices.

  10. A continuum hard-sphere model of protein adsorption

    NASA Astrophysics Data System (ADS)

    Finch, Craig; Clarke, Thomas; Hickman, James J.

    2013-07-01

    Protein adsorption plays a significant role in biological phenomena such as cell-surface interactions and the coagulation of blood. Two-dimensional random sequential adsorption (RSA) models are widely used to model the adsorption of proteins on solid surfaces. Continuum equations have been developed so that the results of RSA simulations can be used to predict the kinetics of adsorption. Recently, Brownian dynamics simulations have become popular for modeling protein adsorption. In this work a continuum model was developed to allow the results from a Brownian dynamics simulation to be used as the boundary condition in a computational fluid dynamics (CFD) simulation. Brownian dynamics simulations were used to model the diffusive transport of hard-sphere particles in a liquid and the adsorption of the particles onto a solid surface. The configuration of the adsorbed particles was analyzed to quantify the chemical potential near the surface, which was found to be a function of the distance from the surface and the fractional surface coverage. The near-surface chemical potential was used to derive a continuum model of adsorption that incorporates the results from the Brownian dynamics simulations. The equations of the continuum model were discretized and coupled to a CFD simulation of diffusive transport to the surface. The kinetics of adsorption predicted by the continuum model closely matched the results from the Brownian dynamics simulation. This new model allows the results from mesoscale simulations to be incorporated into micro- or macro-scale CFD transport simulations of protein adsorption in practical devices.

  11. A CONTINUUM HARD-SPHERE MODEL OF PROTEIN ADSORPTION

    PubMed Central

    Finch, Craig; Clarke, Thomas; Hickman, James J.

    2012-01-01

    Protein adsorption plays a significant role in biological phenomena such as cell-surface interactions and the coagulation of blood. Two-dimensional random sequential adsorption (RSA) models are widely used to model the adsorption of proteins on solid surfaces. Continuum equations have been developed so that the results of RSA simulations can be used to predict the kinetics of adsorption. Recently, Brownian dynamics simulations have become popular for modeling protein adsorption. In this work a continuum model was developed to allow the results from a Brownian dynamics simulation to be used as the boundary condition in a computational fluid dynamics (CFD) simulation. Brownian dynamics simulations were used to model the diffusive transport of hard-sphere particles in a liquid and the adsorption of the particles onto a solid surface. The configuration of the adsorbed particles was analyzed to quantify the chemical potential near the surface, which was found to be a function of the distance from the surface and the fractional surface coverage. The near-surface chemical potential was used to derive a continuum model of adsorption that incorporates the results from the Brownian dynamics simulations. The equations of the continuum model were discretized and coupled to a CFD simulation of diffusive transport to the surface. The kinetics of adsorption predicted by the continuum model closely matched the results from the Brownian dynamics simulation. This new model allows the results from mesoscale simulations to be incorporated into micro- or macro-scale CFD transport simulations of protein adsorption in practical devices. PMID:23729843

  12. Avalanches mediate crystallization in a hard-sphere glass.

    PubMed

    Sanz, Eduardo; Valeriani, Chantal; Zaccarelli, Emanuela; Poon, Wilson C K; Cates, Michael E; Pusey, Peter N

    2014-01-01

    By molecular-dynamics simulations, we have studied the devitrification (or crystallization) of aged hard-sphere glasses. First, we find that the dynamics of the particles are intermittent: Quiescent periods, when the particles simply "rattle" in their nearest-neighbor cages, are interrupted by abrupt "avalanches," where a subset of particles undergo large rearrangements. Second, we find that crystallization is associated with these avalanches but that the connection is not straightforward. The amount of crystal in the system increases during an avalanche, but most of the particles that become crystalline are different from those involved in the avalanche. Third, the occurrence of the avalanches is a largely stochastic process. Randomizing the velocities of the particles at any time during the simulation leads to a different subsequent series of avalanches. The spatial distribution of avalanching particles appears random, although correlations are found among avalanche initiation events. By contrast, we find that crystallization tends to take place in regions that already show incipient local order. PMID:24306932

  13. Interfacial free energy calculation of a binary hard-sphere fluid at a hard wall by Gibbs-Cahn Integration

    NASA Astrophysics Data System (ADS)

    Kern, Jesse; Laird, Brian

    2013-03-01

    The interfacial free energy, ?, of fluids at surfaces is a parameter that is central to a number of technologically important phenomena, such as wetting, nucleation and the stability and self assembly of colloidal particles in solution. In recent years, our group has developed techniques to determine ? from atomistic simulation. In this work, we apply one of these methods, Gibbs-Cahn Integration, to determine ? for a model two-component (binary) mixture of hard spheres. Molecular dynamics simulation is used to characterize a hard-sphere fluid mixture in a slit-pore confined geometry as packing fraction, mole fraction, and diameter ratio are varied. We find that recent theoretical predictions from the White Bear II classical density functional theory [Roth et al., J. Phys.: Condens. Matter, 18, 8413, (2006)] agree well with our computational results We also observe that, for this model system, the preferential adsorption of one particle species over the other contributes negligibly to the interfacial free energy at modest diameter ratios.

  14. Voronoi cell volume distribution and configurational entropy of hard-spheres

    NASA Astrophysics Data System (ADS)

    Senthil Kumar, V.; Kumaran, V.

    2005-09-01

    The Voronoi cell volume distributions for hard-disk and hard-sphere fluids have been studied. The distribution of the Voronoi free volume ?f, which is the difference between the actual cell volume and the minimal cell volume at close packing, is well described by a two-parameter (2?) or a three-parameter (3?) gamma distribution. The free parameter m in both the 2? and 3? models is identified as the "regularity factor." The regularity factor is the ratio of the square of the mean and the variance of the free volume distribution, and it increases as the cell volume distribution becomes narrower. For the thermodynamic structures, the regularity factor increases with increasing density and it increases sharply across the freezing transition, in response to the onset of order. The regularity factor also distinguishes between the dense thermodynamic structures and the dense random or quenched structures. The maximum information entropy (max-ent) formalism, when applied to the gamma distributions, shows that structures of maximum information entropy have an exponential distribution of ?f. Simulations carried out using a swelling algorithm indicate that the dense random-packed states approach the distribution predicted by the max-ent formalism, though the limiting case could not be realized in simulations due to the structural inhomogeneities introduced by the dense random-packing algorithm. Using the gamma representations of the cell volume distribution, we check the numerical validity of the Cohen-Grest expression [M. H. Cohen and G. S. Grest, Phys. Rev. B 20, 1077 (1979)] for the cellular (free volume) entropy, which is a part of the configurational entropy. The expression is exact for the hard-rod system, and a correction factor equal to the dimension of the system, D, is found necessary for the hard-disk and hard-sphere systems. Thus, for the hard-disk and hard-sphere systems, the present analysis establishes a relationship between the precisely defined Voronoi free volume (information) entropy and the thermodynamic entropy. This analysis also shows that the max-ent formalism, when applied to the free volume entropy, predicts an exponential distribution which is approached by disordered states generated by a swelling algorithm in the dense random-packing limit.

  15. Even hard-sphere colloidal suspensions display Fickian yet non-Gaussian diffusion.

    PubMed

    Guan, Juan; Wang, Bo; Granick, Steve

    2014-04-22

    We scrutinize three decades of probability density displacement distribution in a simple colloidal suspension with hard-sphere interactions. In this index-matched and density-matched solvent, fluorescent tracer nanoparticles diffuse among matrix particles that are eight times larger, at concentrations from dilute to concentrated, over times up to when the tracer diffuses a few times its size. Displacement distributions of tracers, Gaussian in pure solvent, broaden systematically with increasing obstacle density. The onset of non-Gaussian dynamics is seen in even modestly dilute suspensions, which traditionally would be assumed to follow classic Gaussian expectation. The findings underscore, in agreement with recent studies of more esoteric soft matter systems, the prevalence of non-Gaussian yet Fickian diffusion. PMID:24646449

  16. Short-time diffusion in concentrated bidisperse hard-sphere suspensions

    NASA Astrophysics Data System (ADS)

    Wang, Mu; Heinen, Marco; Brady, John F.

    2015-02-01

    Diffusion in bidisperse Brownian hard-sphere suspensions is studied by Stokesian Dynamics (SD) computer simulations and a semi-analytical theoretical scheme for colloidal short-time dynamics, based on Beenakker and Mazur's method [Physica A 120, 388-410 (1983); 126, 349-370 (1984)]. Two species of hard spheres are suspended in an overdamped viscous solvent that mediates the salient hydrodynamic interactions among all particles. In a comprehensive parameter scan that covers various packing fractions and suspension compositions, we employ numerically accurate SD simulations to compute the initial diffusive relaxation of density modulations at the Brownian time scale, quantified by the partial hydrodynamic functions. A revised version of Beenakker and Mazur's ??-scheme for monodisperse suspensions is found to exhibit surprisingly good accuracy, when simple rescaling laws are invoked in its application to mixtures. The so-modified ?? scheme predicts hydrodynamic functions in very good agreement with our SD simulation results, for all densities from the very dilute limit up to packing fractions as high as 40%.

  17. Orientational ordering and phase behaviour of binary mixtures of hard spheres and hard spherocylinders

    NASA Astrophysics Data System (ADS)

    Wu, Liang; Malijevsk, Alexandr; Jackson, George; Mller, Erich A.; Avendao, Carlos

    2015-07-01

    We study the structure and fluid-phase behaviour of binary mixtures of hard spheres (HSs) and hard spherocylinders (HSCs) in isotropic and nematic states using the NPnAT ensemble Monte Carlo (MC) approach in which the normal component of the pressure tensor is fixed in a system confined between two hard walls. The method allows one to estimate the location of the isotropic-nematic phase transition and to observe the asymmetry in the composition between the coexisting phases, with the expected enhancement of the HSC concentration in the nematic phase. This is in stark contrast with the previously reported MC simulations where a conventional isotropic NPT ensemble was used. We further compare the simulation results with the theoretical predictions of two analytic theories that extend the original Parsons-Lee theory using the one-fluid and the many-fluid approximations [Malijevsk et al., J. Chem. Phys. 129, 144504 (2008)]. In the one-fluid version of the theory, the properties of the mixture are related to an effective one-component HS system, while in the many-fluid theory, the components of the mixtures are represented as separate effective HS particles. The comparison reveals that both the one- and the many-fluid approaches provide a reasonably accurate quantitative description of the mixture including the predictions of the isotropic-nematic phase boundary and degree of orientational order of the HSC-HS mixture.

  18. Bosonic hard spheres in quasi-one-dimensional bichromatic optical lattices

    NASA Astrophysics Data System (ADS)

    Gordillo, M. C.; Carbonell-Coronado, C.; De Soto, F.

    2015-04-01

    We calculated the phase diagram of a continuous system of hard spheres loaded in a quasi-one-dimensional bichromatic optical lattice. The wavelengths of both lattice-defining lasers were chosen to model an incommensurate arrangement. Densities of one particle and half a particle per potential well were considered. Our results can be compared directly to those of the experimental system [L. Fallani, J. E. Lye, V. Guarrera, C. Fort, and M. Inguscio, Phys. Rev. Lett. 98, 130404 (2007), 10.1103/PhysRevLett.98.130404] from which our initial parameters were taken. The phase diagrams for both densities are significatively different from those obtained by describing the same experimental setup with a Bose-Hubbard model.

  19. Transport coefficients of a granular gas of inelastic rough hard spheres.

    PubMed

    Kremer, Gilberto M; Santos, Andrs; Garz, Vicente

    2014-08-01

    The Boltzmann equation for inelastic and rough hard spheres is considered as a model of a dilute granular gas. In this model, the collisions are characterized by constant coefficients of normal and tangential restitution, and hence the translational and rotational degrees of freedom are coupled. A normal solution to the Boltzmann equation is obtained by means of the Chapman-Enskog method for states near the homogeneous cooling state. The analysis is carried out to first order in the spatial gradients of the number density, the flow velocity, and the granular temperature. The constitutive equations for the momentum and heat fluxes and for the cooling rate are derived, and the associated transport coefficients are expressed in terms of the solutions of linear integral equations. For practical purposes, a first Sonine approximation is used to obtain explicit expressions of the transport coefficients as nonlinear functions of both coefficients of restitution and the moment of inertia. Known results for purely smooth inelastic spheres and perfectly elastic and rough spheres are recovered in the appropriate limits. PMID:25215731

  20. Direct simulation of diatomic gases using the generalized hard sphere model

    NASA Technical Reports Server (NTRS)

    Hash, D. B.; Hassan, H. A.

    1993-01-01

    The generalized hard sphere model which incorporates the effects of attraction and repulsion is used to predict flow measurements in tests involving extremely low freestream temperatures. For the two cases considered, a Mach 26 nitrogen shock and a Mach 20 nitrogen flow over a flat place, only rotational excitation is deemed important, and appropriate modifications for the Borgnakke-Larsen procedure are developed. In general, for the cases considered, the present model performed better than the variable hard sphere model.

  1. Solubilities of Solutes in Ionic Liquids from a SimplePerturbed-Hard-Sphere Theory

    SciTech Connect

    Qin, Yuan; Prausnitz, John M.

    2005-09-20

    In recent years, several publications have provided solubilities of ordinary gases and liquids in ionic liquids. This work reports an initial attempt to correlate the experimental data using a perturbed-hard-sphere theory; the perturbation is based on well-known molecular physics when the solution is considered as a dielectric continuum. For this correlation, the most important input parameters are hard-sphere diameters of the solute and of the cation and anion that constitute the ionic liquid. In addition, the correlation uses the solvent density and the solute's polarizability and dipole and quadrupole moments, if any. Dispersion-energy parameters are obtained from global correlation of solubility data. Results are given for twenty solutes in several ionic liquids at normal temperatures; in addition, some results are given for gases in two molten salts at very high temperatures. Because the theory used here is much simplified, and because experimental uncertainties (especially for gaseous solutes) are often large, the accuracy of the correlation presented here is not high; in general, predicted solubilities (Henry's constants) agree with experiment to within roughly {+-} 70%. As more reliable experimental data become available, modifications in the characterizing parameters are likely to improve accuracy. Nevertheless, even in its present form, the correlation may be useful for solvent screening in engineering design.

  2. Stochastic Hard-Sphere Dynamics for Hydrodynamics of Non-Ideal Fluids

    SciTech Connect

    Donev, A; Alder, B J; Garcia, A L

    2008-02-26

    A novel stochastic fluid model is proposed with a nonideal structure factor consistent with compressibility, and adjustable transport coefficients. This stochastic hard-sphere dynamics (SHSD) algorithm is a modification of the direct simulation Monte Carlo algorithm and has several computational advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD results in an equation of state and a pair correlation function identical to that of a deterministic Hamiltonian system of penetrable spheres interacting with linear core pair potentials. The fluctuating hydrodynamic behavior of the SHSD fluid is verified for the Brownian motion of a nanoparticle suspended in a compressible solvent.

  3. Variational Monte Carlo study of soliton excitations in hard-sphere Bose gases

    NASA Astrophysics Data System (ADS)

    Rota, R.; Giorgini, S.

    2015-10-01

    By using a full many-body approach, we calculate the excitation energy, the effective mass, and the density profile of soliton states in a three-dimensional Bose gas of hard spheres at zero temperature. The many-body wave function used to describe the soliton contains a one-body term, derived from the solution of the Gross-Pitaevskii equation, and a two-body Jastrow term, which accounts for the repulsive correlations between atoms. We optimize the parameters in the many-body wave function via a variational Monte Carlo procedure, calculating the grand-canonical energy and the canonical momentum of the system in a moving reference frame where the soliton is stationary. As the density of the gas is increased, significant deviations from the mean-field predictions are found for the excitation energy and the density profile of both dark and gray solitons. In particular, the soliton effective mass m* and the mass m Δ N of missing particles in the region of the density depression are smaller than the result from the Gross-Pitaevskii equation, their ratio, however, being well reproduced by this theory up to large values of the gas parameter. We also calculate the profile of the condensate density around the soliton notch, finding good agreement with the prediction of the local-density approximation.

  4. Jamming II: Edwards statistical mechanics of random packings of hard spheres

    NASA Astrophysics Data System (ADS)

    Wang, Ping; Song, Chaoming; Jin, Yuliang; Makse, Hernn A.

    2011-02-01

    The problem of finding the most efficient way to pack spheres has an illustrious history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal in the 1960s. This problem finds applications spanning from the mathematicians pencil, the processing of granular materials, the jamming and glass transitions, all the way to fruit packing in every grocery. There are presently numerous experiments showing that the loosest way to pack spheres gives a density of ?55% (named random loose packing, RLP) while filling all the loose voids results in a maximum density of ?63%-64% (named random close packing, RCP). While those values seem robustly true, to this date there is no well-accepted physical explanation or theoretical prediction for them. Here we develop a common framework for understanding the random packings of monodisperse hard spheres whose limits can be interpreted as the experimentally observed RLP and RCP. The reason for these limits arises from a statistical picture of jammed states in which the RCP can be interpreted as the ground state of the ensemble of jammed matter with zero compactivity, while the RLP arises in the infinite compactivity limit. We combine an extended statistical mechanics approach a la Edwards (where the role traditionally played by the energy and temperature in thermal systems is substituted by the volume and compactivity) with a constraint on mechanical stability imposed by the isostatic condition. We show how such approaches can bring results that can be compared to experiments and allow for an exploitation of the statistical mechanics framework. The key result is the use of a relation between the local Voronoi volumes of the constituent grains (denoted the volume function) and the number of neighbors in contact that permits us to simply combine the two approaches to develop a theory of volume fluctuations in jammed matter. Ultimately, our results lead to a phase diagram that provides a unifying view of the disordered hard sphere packing problem and further sheds light on a diverse spectrum of data, including the RLP state. Theoretical results are well reproduced by numerical simulations that confirm the essential role played by friction in determining both the RLP and RCP limits. The RLP values depend on friction, explaining why varied experimental results can be obtained.

  5. Helical Defect Packings in a Quasi-One-Dimensional System of Cylindrically Confined Hard Spheres

    NASA Astrophysics Data System (ADS)

    Yamchi, Mahdi Zaeifi; Bowles, Richard K.

    2015-07-01

    We use a combination of analytical theory and molecular dynamics simulation to study the inherent structure landscape of a system of hard spheres confined to narrow cylindrical channels of diameter 1 +?{3 }/2 density and alters the local packing structure. The helical sections between defects become asymmetrical and are better described as a double helix with angular twists between the first and second nearest neighbors that are determined by the defect separation distance. Increasing the fraction of defects unwinds the two helical strands so that the least dense structure is a nonhelical packing of two zigzag chains. We also show that the packing effects of the helical section induce a long-range, entropically driven attraction between the defects.

  6. General relativistic fluid spheres with nonzero vacuum energy density

    SciTech Connect

    Hiscock, W.A.

    1988-02-01

    Bounds are developed for the ratios M/R and m/R for fluid spheres in asymptotically de Sitter or anti-de Sitter space-times, where M is the mass of the fluid sphere, and m is the total mass interior to R: M plus the interior vacuum energy. This represents a generalization of the work of Buchdahl to the case of a nonvanishing vacuum energy density. In the asymptotically de Sitter case, it is possible to construct models which have m/r..-->.. 1/2 . Further, it is shown that static fluid spheres can exist in an asymptotically de Sitter space with vacuum energy density rho/sub v/ only if their radius satisfies Rless than or equal to(8..pi..rho/sub v/)/sup 1//sup ///sup 2/, a maximum radius smaller by a factor of 3/sup -1//sup ///sup 2/ than the horizon size of the de Sitter space in the absence of a fluid sphere. If the vacuum energy density is negative, then the ratio m/R is shown to be bounded above by the asymptotically flat limit of (4)/(9) , and the radius of a positive total mass (m) sphere is shown to be bounded above by R<(2..pi..chemically bondrho/sub v/chemically bond)/sup -1//sup ///sup 2/.

  7. A Thermodynamically-Consistent Non-Ideal Stochastic Hard-Sphere Fluid

    SciTech Connect

    Donev, A; Alder, B J; Garcia, A L

    2009-08-03

    A grid-free variant of the Direct Simulation Monte Carlo (DSMC) method is proposed, named the Isotropic DSMC (I-DSMC) method, that is suitable for simulating collision-dominated dense fluid flows. The I-DSMC algorithm eliminates all grid artifacts from the traditional DSMC algorithm and is Galilean invariant and microscopically isotropic. The stochastic collision rules in I-DSMC are modified to introduce a non-ideal structure factor that gives consistent compressibility, as first proposed in [Phys. Rev. Lett. 101:075902 (2008)]. The resulting Stochastic Hard Sphere Dynamics (SHSD) fluid is empirically shown to be thermodynamically identical to a deterministic Hamiltonian system of penetrable spheres interacting with a linear core pair potential, well-described by the hypernetted chain (HNC) approximation. We develop a kinetic theory for the SHSD fluid to obtain estimates for the transport coefficients that are in excellent agreement with particle simulations over a wide range of densities and collision rates. The fluctuating hydrodynamic behavior of the SHSD fluid is verified by comparing its dynamic structure factor against theory based on the Landau-Lifshitz Navier-Stokes equations. We also study the Brownian motion of a nano-particle suspended in an SHSD fluid and find a long-time power-law tail in its velocity autocorrelation function consistent with hydrodynamic theory and molecular dynamics calculations.

  8. Noncrystalline compact packings of hard spheres of two sizes: Bipyramids and the geometry of common neighbors.

    PubMed

    Miracle, D B; Harrowell, Peter

    2009-03-21

    Insight into the efficient filling of space in systems of binary spheres is explored using bipyramids consisting of 3spheres. Compact packings are sought in bipyramids consisting of larger hard spheres of unit radius and smaller hard spheres of radius 0.001/=0.9473 and for 0.8493>/=R>/=0.7434. A topological instability eliminates compact packings for R

  9. Depletion force in the infinite-dilution limit in a solvent of nonadditive hard spheres

    NASA Astrophysics Data System (ADS)

    Fantoni, Riccardo; Santos, Andrs

    2014-06-01

    The mutual entropic depletion force felt by two solute "big" hard spheres immersed in a binary mixture solvent of nonadditive "small" hard spheres is calculated as a function of the surface-to-surface distance by means of canonical Monte Carlo simulations and through a recently proposed rational-function approximation [R. Fantoni and A. Santos, Phys. Rev. E 84, 041201 (2011)]. Four representative scenarios are investigated: symmetric solute particles and the limit where one of the two solute spheres becomes a planar hard wall, in both cases with symmetric and asymmetric solvents. In all cases, the influence on the depletion force due to the nonadditivity in the solvent is determined in the mixed state. Comparison between results from the theoretical approximation and from the simulation shows a good agreement for surface-to-surface distances greater than the smallest solvent diameter.

  10. Depletion force in the infinite-dilution limit in a solvent of nonadditive hard spheres.

    PubMed

    Fantoni, Riccardo; Santos, Andrs

    2014-06-28

    The mutual entropic depletion force felt by two solute "big" hard spheres immersed in a binary mixture solvent of nonadditive "small" hard spheres is calculated as a function of the surface-to-surface distance by means of canonical Monte Carlo simulations and through a recently proposed rational-function approximation [R. Fantoni and A. Santos, Phys. Rev. E 84, 041201 (2011)]. Four representative scenarios are investigated: symmetric solute particles and the limit where one of the two solute spheres becomes a planar hard wall, in both cases with symmetric and asymmetric solvents. In all cases, the influence on the depletion force due to the nonadditivity in the solvent is determined in the mixed state. Comparison between results from the theoretical approximation and from the simulation shows a good agreement for surface-to-surface distances greater than the smallest solvent diameter. PMID:24985660

  11. Kernels of the linear Boltzmann equation for spherical particles and rough hard sphere particles

    NASA Astrophysics Data System (ADS)

    Khurana, Saheba; Thachuk, Mark

    2013-10-01

    Kernels for the collision integral of the linear Boltzmann equation are presented for several cases. First, a rigorous and complete derivation of the velocity kernel for spherical particles is given, along with reductions to the smooth, rigid sphere case. This combines and extends various derivations for this kernel which have appeared previously in the literature. In addition, the analogous kernel is derived for the rough hard sphere model, for which a dependence upon both velocity and angular velocity is required. This model can account for exchange between translational and rotational degrees of freedom. Finally, an approximation to the exact rough hard sphere kernel is presented which averages over the rotational degrees of freedom in the system. This results in a kernel depending only upon velocities which retains a memory of the exchange with rotational states. This kernel tends towards the smooth hard sphere kernel in the limit when translational-rotational energy exchange is attenuated. Comparisons are made between the smooth and approximate rough hard sphere kernels, including their dependence upon velocity and their eigenvalues.

  12. Stochastic interactions of two Brownian hard spheres in the presence of depletants

    SciTech Connect

    Karzar-Jeddi, Mehdi; Fan, Tai-Hsi; Tuinier, Remco; Taniguchi, Takashi

    2014-06-07

    A quantitative analysis is presented for the stochastic interactions of a pair of Brownian hard spheres in non-adsorbing polymer solutions. The hard spheres are hypothetically trapped by optical tweezers and allowed for random motion near the trapped positions. The investigation focuses on the long-time correlated Brownian motion. The mobility tensor altered by the polymer depletion effect is computed by the boundary integral method, and the corresponding random displacement is determined by the fluctuation-dissipation theorem. From our computations it follows that the presence of depletion layers around the hard spheres has a significant effect on the hydrodynamic interactions and particle dynamics as compared to pure solvent and uniform polymer solution cases. The probability distribution functions of random walks of the two interacting hard spheres that are trapped clearly shift due to the polymer depletion effect. The results show that the reduction of the viscosity in the depletion layers around the spheres and the entropic force due to the overlapping of depletion zones have a significant influence on the correlated Brownian interactions.

  13. Computation of structure factors of liquid metals by use of the sticky-hard-sphere potential

    NASA Astrophysics Data System (ADS)

    Gopala Rao, R. V.; Venkatesh, R.

    1990-07-01

    The structure factors of several liquid metals have been calculated through the Baxter solution of the Percus-Yevick equation for a sticky-hard-sphere potential. The computed structure factors are in excellent agreement with experiment, thus showing that the sticky-hard-sphere model, which has only two parameters, is quite good in explaining structural properties. From the calculated structure factors the corresponding radial distribution functions g(r) have been computed for different metals and, hence, the nearest-neighbor distance, the coordination number, and the Ashcroft effective number of electrons per metallic atom.

  14. Molecular-scale hydrophobic interactions between hard-sphere reference solutes are attractive and endothermic

    PubMed Central

    Chaudhari, Mangesh I.; Holleran, Sinead A.; Ashbaugh, Henry S.; Pratt, Lawrence R.

    2013-01-01

    The osmotic second virial coefficients, B2, for atomic-sized hard spheres in water are attractive (B2 < 0) and become more attractive with increasing temperature (?B2/?T < 0) in the temperature range 300 K ? T ? 360 K. Thus, these hydrophobic interactions are attractive and endothermic at moderate temperatures. Hydrophobic interactions between atomic-sized hard spheres in water are more attractive than predicted by the available statistical mechanical theory. These results constitute an initial step toward detailed molecular theory of additional intermolecular interaction features, specifically, attractive interactions associated with hydrophobic solutes. PMID:24297918

  15. Phase behavior of a hard sphere interaction site model of benzene

    SciTech Connect

    Schroer, J. W.; Monson, P. A.

    2000-05-22

    We present a study of the phase diagram for a hard sphere interaction site model of benzene using Monte Carlo computer simulation. The investigation considered the fluid phase and three types of solid phases. Two of these are similar to experimentally determined structures of benzene and the third is a structure which allows the system to reach a high packing density at high pressure through a columnar-like arrangement of the molecules. Extensive calculations of the solid and fluid thermodynamic properties were made. The results show that, for the solid phase, the structure which enables the closest packing of molecules is the most stable one. The solid structures similar to those of benzene, while apparently mechanically stable, were found to be thermodynamically metastable for this purely hard core system. The simulation results have been used to test the accuracy of the cell theory for the solid phase and an equation of state for the fluid phase due to Boublik, as well as phase diagram predictions obtained by using these approximations in combination. (c) 2000 American Institute of Physics.

  16. Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension

    NASA Astrophysics Data System (ADS)

    Urrutia, Ignacio; Szybisz, Leszek

    2010-03-01

    This work is devoted to the exact statistical mechanics treatment of simple inhomogeneous few-body systems. The system of two hard spheres (HSs) confined in a hard spherical pore is systematically analyzed in terms of its dimensionality D. The canonical partition function and the one- and two-body distribution functions are analytically evaluated and a scheme of iterative construction of the D +1 system properties is presented. We analyze in detail both the effect of high confinement, when particles become caged, and the low density limit. Other confinement situations are also studied analytically and several relations between the two HSs in a spherical pore, two sticked HSs in a spherical pore, and two HSs on a spherical surface partition functions are traced. These relations make meaningful the limiting caging and low density behavior. Turning to the system of two HSs in a spherical pore, we also analytically evaluate the pressure tensor. The thermodynamic properties of the system are discussed. To accomplish this statement we purposely focus in the overall characteristics of the inhomogeneous fluid system, instead of concentrate in the peculiarities of a few-body system. Hence, we analyze the equation of state, the pressure at the wall, and the fluid-substrate surface tension. The consequences of new results about the spherically confined system of two HSs in D dimension on the confined many HS system are investigated. New constant coefficients involved in the low density limit properties of the open and closed systems of many HS in a spherical pore are obtained for arbitrary D. The complementary system of many HS which surrounds a HS (a cavity inside of a bulk HS system) is also discussed.

  17. Polydispersity and Optimal Relaxation in the Hard Sphere Fluid

    NASA Astrophysics Data System (ADS)

    Barbier, Matthieu; Trizac, Emmanuel

    2014-03-01

    We consider the mass heterogeneity in a gas of polydisperse hard particles as a key to optimizing a dynamical property: the kinetic relaxation rate. Using the framework of the Boltzmann equation, we study the long time approach of a perturbed velocity distribution toward the equilibrium Maxwellian solution. We work out the cases of discrete as well as continuous distributions of masses, as found in dilute fluids of mesoscopic particles such as granular matter and colloids. On the basis of analytical and numerical evidence, we formulate a dynamical equipartition principle that leads to the result that no such continuous dispersion in fact minimizes the relaxation time, as the global optimum is characterized by a finite number of species. This optimal mixture is found to depend on the dimension of space, ranging from five species for to a single one for . The role of the collisional kernel is also discussed, and extensions to dissipative systems are shown to be possible.

  18. Rolling friction for hard cylinder and sphere on viscoelastic solid.

    PubMed

    Persson, B N J

    2010-12-01

    We calculate the friction force acting on a hard cylinder or spherical ball rolling on a flat surface of a viscoelastic solid. The rolling-friction coefficient depends non-linearly on the normal load and the rolling velocity. For a cylinder rolling on a viscoelastic solid characterized by a single relaxation time Hunter has obtained an exact result for the rolling friction, and our result is in very good agreement with his result for this limiting case. The theoretical results are also in good agreement with experiments of Greenwood and Tabor. We suggest that measurements of rolling friction over a wide range of rolling velocities and temperatures may constitute a useful way to determine the viscoelastic modulus of rubber-like materials. PMID:21107881

  19. Comment on ``New phase for one-component hard spheres'' [J. Chem. Phys. 120, 11686 (2004)

    NASA Astrophysics Data System (ADS)

    Blaak, Ronald; Lwen, Hartmut; Barrat, Jean-Louis

    2004-12-01

    We argue that the claim of a third, thermodynamical stable phase in monodisperse hard sphere system is based on a wrong interpretation of the simulation data. Configurations, made available by the authors, are used to demonstrate that it is an artificially, by periodic boundaries stabilized phase with fcc signature and some defects.

  20. Note: equation of state and the freezing point in the hard-sphere model.

    PubMed

    Robles, Miguel; López de Haro, Mariano; Santos, Andrés

    2014-04-01

    The merits of different analytical equations of state for the hard-sphere system with respect to the recently computed high-accuracy value of the freezing-point packing fraction are assessed. It is found that the Carnahan-Starling-Kolafa and the branch-point approximant equations of state yield the best performance. PMID:24712819

  1. How to predict polydisperse hard-sphere mixture behavior using maximally equivalent tridisperse systems

    NASA Astrophysics Data System (ADS)

    Ogarko, Vitaliy; Luding, Stefan

    2013-03-01

    Polydisperse hard sphere mixtures have equilibrium properties which essentially depend on the number density and a reduced number K of moments of the size distribution function. Such systems are equivalent to other systems with different size distributions if the K moments are matched. In particular, a small number s of components, such that 2 s - 1 = K is sufficient to mimic systems with continuous size distributions. For most of the fluid phase K = 3 moments (s = 2 components) are enough to define an equivalent system, while in the glassy states one needs K = 5 moments (s = 3 components) to achieve good agreement between the polydisperse and its maximally-equivalent tridisperse system. With K = 5 matched moments they are also close in number- and volume-fractions of rattlers. Finally, also the jamming density of maximally-equivalent jammed packings is very close, where the tiny differences can be explained by the distribution of rattlers. This research is supported by the Dutch Technology Foundation STW, which is the applied science division of NWO, and the Technology Programme of the Ministry of Economic Affairs, project Nr. STW-MUST 10120.

  2. Hard sphere-like glass transition in eye lens α-crystallin solutions

    PubMed Central

    Savin, Gabriela; Bucciarelli, Saskia; Dorsaz, Nicolas; Thurston, George M.; Stradner, Anna; Schurtenberger, Peter

    2014-01-01

    We study the equilibrium liquid structure and dynamics of dilute and concentrated bovine eye lens α-crystallin solutions, using small-angle X-ray scattering, static and dynamic light scattering, viscometry, molecular dynamics simulations, and mode-coupling theory. We find that a polydisperse Percus–Yevick hard-sphere liquid-structure model accurately reproduces both static light scattering data and small-angle X-ray scattering liquid structure data from α-crystallin solutions over an extended range of protein concentrations up to 290 mg/mL or 49% vol fraction and up to ca. 330 mg/mL for static light scattering. The measured dynamic light scattering and viscosity properties are also consistent with those of hard-sphere colloids and show power laws characteristic of an approach toward a glass transition at α-crystallin volume fractions near 58%. Dynamic light scattering at a volume fraction beyond the glass transition indicates formation of an arrested state. We further perform event-driven molecular dynamics simulations of polydisperse hard-sphere systems and use mode-coupling theory to compare the measured dynamic power laws with those of hard-sphere models. The static and dynamic data, simulations, and analysis show that aqueous eye lens α-crystallin solutions exhibit a glass transition at high concentrations that is similar to those found in hard-sphere colloidal systems. The α-crystallin glass transition could have implications for the molecular basis of presbyopia and the kinetics of molecular change during cataractogenesis. PMID:25385638

  3. Phase diagram of dipolar hard and soft spheres: manipulation of colloidal crystal structures by an external field.

    PubMed

    Hynninen, Antti-Pekka; Dijkstra, Marjolein

    2005-04-01

    Phase diagrams of hard and soft spheres with a fixed dipole moment are determined by calculating the Helmholtz free energy using simulations. The pair potential is given by a dipole-dipole interaction plus a hard-core and a repulsive Yukawa potential for soft spheres. Our system models colloids in an external electric or magnetic field, with hard spheres corresponding to uncharged and soft spheres to charged colloids. The phase diagram of dipolar hard spheres shows fluid, face-centered-cubic (fcc), hexagonal-close-packed (hcp), and body-centered-tetragonal (bct) phases. The phase diagram of dipolar soft spheres exhibits, in addition to the above mentioned phases, a body-centered-orthorhombic (bco) phase, and it agrees well with the experimental phase diagram [Nature (London) 421, 513 (2003)]. Our results show that bulk hcp, bct, and bco crystals can be realized experimentally by applying an external field. PMID:15904046

  4. Predicting side-chain conformations of methionine using a hard-sphere model with stereochemical constraints

    NASA Astrophysics Data System (ADS)

    Virrueta, A.; Gaines, J.; O'Hern, C. S.; Regan, L.

    2015-03-01

    Current research in the O'Hern and Regan laboratories focuses on the development of hard-sphere models with stereochemical constraints for protein structure prediction as an alternative to molecular dynamics methods that utilize knowledge-based corrections in their force-fields. Beginning with simple hydrophobic dipeptides like valine, leucine, and isoleucine, we have shown that our model is able to reproduce the side-chain dihedral angle distributions derived from sets of high-resolution protein crystal structures. However, methionine remains an exception - our model yields a chi-3 side-chain dihedral angle distribution that is relatively uniform from 60 to 300 degrees, while the observed distribution displays peaks at 60, 180, and 300 degrees. Our goal is to resolve this discrepancy by considering clashes with neighboring residues, and averaging the reduced distribution of allowable methionine structures taken from a set of crystallized proteins. We will also re-evaluate the electron density maps from which these protein structures are derived to ensure that the methionines and their local environments are correctly modeled. This work will ultimately serve as a tool for computing side-chain entropy and protein stability. A. V. is supported by an NSF Graduate Research Fellowship and a Ford Foundation Fellowship. J. G. is supported by NIH training Grant NIH-5T15LM007056-28.

  5. Optical experiments on a crystallizing hard-sphere-polymer mixture at coexistence.

    PubMed

    Stipp, Andreas; Schpe, Hans-Joachim; Palberg, Thomas; Eckert, Thomas; Biehl, Ralf; Bartsch, Eckhard

    2010-05-01

    We report on the crystallization kinetics in an entropically attractive colloidal system using a combination of time resolved scattering methods and microscopy. Hard sphere particles are polystyrene microgels swollen in a good solvent (radius a=380 nm, starting volume fraction 0.534) with the short ranged attractions induced by the presence of short polymer chains (radius of gyration r g=3 nm, starting volume fraction 0.0224). After crystallization, stacking faulted face centered cubic crystals coexist with about 5% of melt remaining in the grain boundaries. From the Bragg scattering signal we infer the amount of crystalline material, the average crystallite size and the number density of crystals as a function of time. This allows to discriminate an early stage of conversion, followed by an extended coarsening stage. The small angle scattering (SALS) appears only long after completed conversion and exhibits Furukawa scaling for all times. Additional microscopic experiments reveal that the grain boundaries have a reduced Bragg scattering power but possess an increased refractive index. Fits of the Furukawa function indicate that the dimensionality of the scatterers decreases from 2.25 at short times to 1.65 at late times and the characteristic length scale is slightly larger than the average crystallite size. Together this suggests the SALS signal is due scattering from a foam like grain boundary network as a whole. PMID:20866224

  6. Hard-sphere fluid with tight-binding electronic interactions -- a glue model treatment

    NASA Astrophysics Data System (ADS)

    Reinaldo-Falagan, M.; Tarazona, P.; Velasco, E.; Chacon, E.; Hernandez, J. P.

    2003-03-01

    We have carried out self-consistent Monte-Carlo simulations for a model monovalent-atom fluid, with hard-sphere interactions and attractions due to the free energy of its valence electrons. This energy is obtained in a tight-binding model with electronic hopping which decreases exponentially with distance. The many-body atomic energies in the disordered environment are fitted with a 'glue' model which, unlike its usual treatment, has its parameters obtained from the model itself. The phase diagram and electronic conductivity derived from this self-consistent treatment of atomic and electronic structures are obtained. Ionic correlations induced by the electronic energy are found to play a crucial role in the thermodynamic and electronic properties of the present model. The electrical conductivity evidences a rapid drop with decreasing fluid density, in the vapor, due to the almost classical percolation of the ionic structures. The resulting phase diagram and the electrical conductivity, at vapor-liquid coexistence, give reasonable agreement with experimental data for fluid cesium, for a chosen decay-parametrization of the electronic hopping.

  7. Optical experiments on a crystallizing hard-sphere-polymer mixture at coexistence

    NASA Astrophysics Data System (ADS)

    Stipp, Andreas; Schpe, Hans-Joachim; Palberg, Thomas; Eckert, Thomas; Biehl, Ralf; Bartsch, Eckhard

    2010-05-01

    We report on the crystallization kinetics in an entropically attractive colloidal system using a combination of time resolved scattering methods and microscopy. Hard sphere particles are polystyrene microgels swollen in a good solvent (radius a=380nm , starting volume fraction 0.534) with the short ranged attractions induced by the presence of short polymer chains (radius of gyration rg=3nm , starting volume fraction 0.0224). After crystallization, stacking faulted face centered cubic crystals coexist with about 5% of melt remaining in the grain boundaries. From the Bragg scattering signal we infer the amount of crystalline material, the average crystallite size and the number density of crystals as a function of time. This allows to discriminate an early stage of conversion, followed by an extended coarsening stage. The small angle scattering (SALS) appears only long after completed conversion and exhibits Furukawa scaling for all times. Additional microscopic experiments reveal that the grain boundaries have a reduced Bragg scattering power but possess an increased refractive index. Fits of the Furukawa function indicate that the dimensionality of the scatterers decreases from 2.25 at short times to 1.65 at late times and the characteristic length scale is slightly larger than the average crystallite size. Together this suggests the SALS signal is due scattering from a foam like grain boundary network as a whole.

  8. Absence of Scaling for the Intermediate Scattering Function of a Hard-Sphere Suspension: Static and Dynamic X-Ray Scattering from Concentrated Polystyrene Latex Spheres

    SciTech Connect

    Lurio, L. B.; Lumma, D.; Sandy, A. R.; Borthwick, M. A.; Falus, P.; Mochrie, S. G. J.; Pelletier, J. F.; Sutton, M.; Regan, Lynne; Malik, A.

    2000-01-24

    X-ray photon correlation spectroscopy and small-angle scattering measurements are presented of the dynamics and structure of concentrated suspensions of charge-stabilized polystyrene latex spheres dispersed in glycerol, for volume fractions from 3% to 52% . The static structures of the suspensions show essentially hard-sphere behavior, and the short-time dynamics shows good agreement with predictions for the wave-vector-dependent collective diffusion coefficient. However, the intermediate scattering function is found to violate a scaling behavior found previously for a sterically stabilized hard-sphere suspension [P. N. Segre and P. N. Pusey, Phys. Rev. Lett. 77, 771 (1996)]. (c) 2000 The American Physical Society.

  9. Monte Carlo calculation of interfacial free energy of hard-sphere fluid against structured walls

    NASA Astrophysics Data System (ADS)

    Mori, Atsushi; Laird, Brian

    2001-03-01

    Particle insertion method for evaluating the chemical potential is modified to apply to the calculation of the interfacial free energies of the hard-sphere fluid against fcc (001), (011), and (111) walls, respectively. For hard-body systems a free energy difference, i.e., the chemical potential or the interfacial free energy, is calculated as a logrithm of probability that a hard object is successfully inserted into the system. However, because the direct insertion of a hard wall into a dense fluid is less probable, we calculate the free energy difference by forming a structure on a structurless wall gradually. The interfacial free energy against a flat wall is also evaluated by gradual forming of a wall in a fluid, which is tested by comparing with the literature. These wall interfacial free energies are compared with the direct evaluation of the crystal/fluid interfacial free energies which has been recently published.

  10. Physics of Hard Spheres Experiment (PhaSE) or "Making Jello in Space"

    NASA Technical Reports Server (NTRS)

    Ling, Jerri S.; Doherty, Michael P.

    1998-01-01

    The Physics of Hard Spheres Experiment (PHaSE) is a highly successful experiment that flew aboard two shuttle missions to study the transitions involved in the formation of jellolike colloidal crystals in a microgravity environment. A colloidal suspension, or colloid, consists of fine particles, often having complex interactions, suspended in a liquid. Paint, ink, and milk are examples of colloids found in everyday life. In low Earth orbit, the effective force of gravity is thousands of times less than at the Earth's surface. This provides researchers a way to conduct experiments that cannot be adequately performed in an Earth-gravity environment. In microgravity, colloidal particles freely interact without the complications of settling that occur in normal gravity on Earth. If the particle interactions within these colloidal suspensions could be predicted and accurately modeled, they could provide the key to understanding fundamental problems in condensed matter physics and could help make possible the development of wonderful new "designer" materials. Industries that make semiconductors, electro-optics, ceramics, and composites are just a few that may benefit from this knowledge. Atomic interactions determine the physical properties (e.g., weight, color, and hardness) of ordinary matter. PHaSE uses colloidal suspensions of microscopic solid plastic spheres to model the behavior of atomic interactions. When uniformly sized hard spheres suspended in a fluid reach a certain concentration (volume fraction), the particle-fluid mixture changes from a disordered fluid state, in which the spheres are randomly organized, to an ordered "crystalline" state, in which they are structured periodically. The thermal energy of the spheres causes them to form ordered arrays, analogous to crystals. Seven of the eight PHaSE samples ranged in volume fraction from 0.483 to 0.624 to cover the range of interest, while one sample, having a concentration of 0.019, was included for instrument calibration.

  11. Clusters in sedimentation equilibrium for an experimental hard-sphere-plus-dipolar Brownian colloidal system.

    PubMed

    Newman, Hugh D; Yethiraj, Anand

    2015-01-01

    In this work, we use structure and dynamics in sedimentation equilibrium, in the presence of gravity, to examine, via confocal microscopy, a Brownian colloidal system in the presence of an external electric field. The zero field equation of state (EOS) is hard sphere without any re-scaling of particle size, and the hydrodynamic corrections to the long-time self-diffusion coefficient are quantitatively consistent with the expected value for hard spheres. Care is taken to ensure that both the dimensionless gravitational energy, which is equivalent to a Peclet number Peg, and dipolar strength Λ are of order unity. In the presence of an external electric field, anisotropic chain-chain clusters form; this cluster formation manifests itself with the appearance of a plateau in the diffusion coefficient when the dimensionless dipolar strength Λ ~ 1. The structure and dynamics of this chain-chain cluster state is examined for a monodisperse system for two particle sizes. PMID:26323363

  12. The structural origin of the hard-sphere glass transition in granular packing

    DOE PAGESBeta

    Xia, Chengjie; Li, Jindong; Cao, Yixin; Kou, Binquan; Xiao, Xianghui; Fezzaa, Kamel; Xiao, Tiqiao; Wang, Yujie

    2015-09-28

    Glass transition is accompanied by a rapid growth of the structural relaxation time and a concomitant decrease of configurational entropy. It remains unclear whether the transition has a thermodynamic origin, and whether the dynamic arrest is associated with the growth of a certain static order. Using granular packing as a model hard-sphere glass, we show the glass transition as a thermodynamic phase transition with a ‘hidden’ polytetrahedral order. This polytetrahedral order is spatially correlated with the slow dynamics. It is geometrically frustrated and has a peculiar fractal dimension. Additionally, as the packing fraction increases, its growth follows an entropy-driven nucleationmore » process, similar to that of the random first-order transition theory. In conclusion, our study essentially identifies a long-sought-after structural glass order in hard-sphere glasses.« less

  13. The structural origin of the hard-sphere glass transition in granular packing

    SciTech Connect

    Xia, Chengjie; Li, Jindong; Cao, Yixin; Kou, Binquan; Xiao, Xianghui; Fezzaa, Kamel; Xiao, Tiqiao; Wang, Yujie

    2015-09-28

    Glass transition is accompanied by a rapid growth of the structural relaxation time and a concomitant decrease of configurational entropy. It remains unclear whether the transition has a thermodynamic origin, and whether the dynamic arrest is associated with the growth of a certain static order. Using granular packing as a model hard-sphere glass, we show the glass transition as a thermodynamic phase transition with a ‘hidden’ polytetrahedral order. This polytetrahedral order is spatially correlated with the slow dynamics. It is geometrically frustrated and has a peculiar fractal dimension. Additionally, as the packing fraction increases, its growth follows an entropy-driven nucleation process, similar to that of the random first-order transition theory. In conclusion, our study essentially identifies a long-sought-after structural glass order in hard-sphere glasses.

  14. Phase coexistence in polydisperse charged hard-sphere fluids: mean spherical approximation.

    PubMed

    Kalyuzhnyi, Yurij V; Kahl, Gerhard; Cummings, Peter T

    2004-06-01

    Taking advantage of the availability of the analytic solution of the mean spherical approximation for a mixture of charged hard spheres with an arbitrary number of components we show that the polydisperse fluid mixture of charged hard spheres belongs to the class of truncatable free energy models, i.e., to those systems where the thermodynamic properties can be represented by a finite number of (generalized) moments of the distribution function that characterizes the mixture. Thus, the formally infinitely many equations that determine the parameters of the two coexisting phases can be mapped onto a system of coupled nonlinear equations in these moments. We present the formalism and demonstrate the power of this approach for two systems; we calculate the full phase diagram in terms of cloud and shadow curves as well as binodals and discuss the distribution functions of the coexisting daughter phases and their charge distributions. PMID:15268036

  15. The Dynamics of Disorder-Order Transition in Hard Sphere Colloidal Dispersions

    NASA Technical Reports Server (NTRS)

    Chaikin, Paul M.; Zhu, Jixiang; Cheng, Zhengdong; Phan, See-Eng; Russel, William B.; Lant, Christian T.; Doherty, Michael P.; Meyer, William V.; Rogers, Richard; Cannell, D. S.; Ottewill, R. H.

    1998-01-01

    The Physics of Hard Spheres Experiment (PHaSE) seeks a complete understanding of the entropically driven disorder-order transition in hard sphere colloidal dispersions. The light scattering instrument designed for flight collects Bragg and low angle light scattering in the forward direction via a CCD camera and performs conventional static and dynamic light scattering at 10-160 deg. through fiber optic cables. Here we report on the kinetics of nucleation and growth extracted from time-resolved Bragg images and measurements of the elastic modulus of crystalline phases obtained by monitoring resonant responses to sinusoidal forcing through dynamic light scattering. Preliminary analysis of the former indicates a significant difference from measurements on the ground, while the latter confirms nicely laboratory experiments with the same instrument and predictions from computer simulations.

  16. Communication: Virial coefficients and demixing in highly asymmetric binary additive hard-sphere mixtures.

    PubMed

    López de Haro, Mariano; Tejero, Carlos F; Santos, Andrés

    2013-04-28

    The problem of demixing in a binary fluid mixture of highly asymmetric additive hard spheres is revisited. A comparison is presented between the results derived previously using truncated virial expansions for three finite size ratios with those that one obtains with the same approach in the extreme case in which one of the components consists of point particles. Since this latter system is known not to exhibit fluid-fluid segregation, the similarity observed for the behavior of the critical constants arising in the truncated series in all instances, while not being conclusive, may cast serious doubts as to the actual existence of a demixing fluid-fluid transition in disparate-sized binary additive hard-sphere mixtures. PMID:23635104

  17. Low Variance Particle Simulations of the Boltzmann Transport Equation for the Variable Hard Sphere Collision Model

    NASA Astrophysics Data System (ADS)

    Radtke, G. A.; Hadjiconstantinou, N. G.; Wagner, W.

    2011-05-01

    We present and validate a variance reduced deviational particle method for simulating the Boltzmann transport equation for the variable hard sphere (VHS) collision operator. In comparison with the direct simulation Monte Carlo (DSMC) method, the proposed method is more suitable for simulating transport in regimes where the departure from equilibrium is small, such as dilute gas flows in small-scale devices (MEMS, NEMS). In fact, the proposed method has a constant signal-to-noise ratio in the limit of small departure from equilibrium, and is thus able to simulate arbitrarily small deviations from equilibrium. The approach developed herein combines the variable hard sphere collision algorithm developed by Wagner [1] with an efficient advection routine based on Ref. [2]. The resulting method is stable and highly efficient, and results in dramatically reduced statistical noise in regimes typical of transport in small-scale devices.

  18. Clusters in sedimentation equilibrium for an experimental hard-sphere-plus-dipolar Brownian colloidal system

    PubMed Central

    Newman, Hugh D.; Yethiraj, Anand

    2015-01-01

    In this work, we use structure and dynamics in sedimentation equilibrium, in the presence of gravity, to examine, via confocal microscopy, a Brownian colloidal system in the presence of an external electric field. The zero field equation of state (EOS) is hard sphere without any re-scaling of particle size, and the hydrodynamic corrections to the long-time self-diffusion coefficient are quantitatively consistent with the expected value for hard spheres. Care is taken to ensure that both the dimensionless gravitational energy, which is equivalent to a Peclet number Peg, and dipolar strength Λ are of order unity. In the presence of an external electric field, anisotropic chain-chain clusters form; this cluster formation manifests itself with the appearance of a plateau in the diffusion coefficient when the dimensionless dipolar strength Λ ~ 1. The structure and dynamics of this chain-chain cluster state is examined for a monodisperse system for two particle sizes. PMID:26323363

  19. The structural origin of the hard-sphere glass transition in granular packing

    PubMed Central

    Xia, Chengjie; Li, Jindong; Cao, Yixin; Kou, Binquan; Xiao, Xianghui; Fezzaa, Kamel; Xiao, Tiqiao; Wang, Yujie

    2015-01-01

    Glass transition is accompanied by a rapid growth of the structural relaxation time and a concomitant decrease of configurational entropy. It remains unclear whether the transition has a thermodynamic origin, and whether the dynamic arrest is associated with the growth of a certain static order. Using granular packing as a model hard-sphere glass, we show the glass transition as a thermodynamic phase transition with a ‘hidden' polytetrahedral order. This polytetrahedral order is spatially correlated with the slow dynamics. It is geometrically frustrated and has a peculiar fractal dimension. Additionally, as the packing fraction increases, its growth follows an entropy-driven nucleation process, similar to that of the random first-order transition theory. Our study essentially identifies a long-sought-after structural glass order in hard-sphere glasses. PMID:26412008

  20. The structural origin of the hard-sphere glass transition in granular packing

    NASA Astrophysics Data System (ADS)

    Xia, Chengjie; Li, Jindong; Cao, Yixin; Kou, Binquan; Xiao, Xianghui; Fezzaa, Kamel; Xiao, Tiqiao; Wang, Yujie

    2015-09-01

    Glass transition is accompanied by a rapid growth of the structural relaxation time and a concomitant decrease of configurational entropy. It remains unclear whether the transition has a thermodynamic origin, and whether the dynamic arrest is associated with the growth of a certain static order. Using granular packing as a model hard-sphere glass, we show the glass transition as a thermodynamic phase transition with a `hidden' polytetrahedral order. This polytetrahedral order is spatially correlated with the slow dynamics. It is geometrically frustrated and has a peculiar fractal dimension. Additionally, as the packing fraction increases, its growth follows an entropy-driven nucleation process, similar to that of the random first-order transition theory. Our study essentially identifies a long-sought-after structural glass order in hard-sphere glasses.

  1. Parallelized event chain algorithm for dense hard sphere and polymer systems

    SciTech Connect

    Kampmann, Tobias A. Boltz, Horst-Holger; Kierfeld, Jan

    2015-01-15

    We combine parallelization and cluster Monte Carlo for hard sphere systems and present a parallelized event chain algorithm for the hard disk system in two dimensions. For parallelization we use a spatial partitioning approach into simulation cells. We find that it is crucial for correctness to ensure detailed balance on the level of Monte Carlo sweeps by drawing the starting sphere of event chains within each simulation cell with replacement. We analyze the performance gains for the parallelized event chain and find a criterion for an optimal degree of parallelization. Because of the cluster nature of event chain moves massive parallelization will not be optimal. Finally, we discuss first applications of the event chain algorithm to dense polymer systems, i.e., bundle-forming solutions of attractive semiflexible polymers.

  2. Stability of LS and LS2 crystal structures in binary mixtures of hard and charged spheres.

    PubMed

    Hynninen, A-P; Filion, L; Dijkstra, M

    2009-08-14

    We study by computer simulations the stability of various crystal structures in a binary mixture of large and small spheres interacting either with a hard sphere or a screened-Coulomb potential. In the case of hard-core systems, we consider structures that have atomic prototypes CrB, gammaCuTi, alphaIrV, HgBr2, AuTe2, Ag2Se and the Laves phases (MgCu2, MgNi2, and MgZn2) as well as a structure with space group symmetry 74. By utilizing Monte Carlo simulations to calculate Gibbs free energies, we determine composition versus pressure and constant volume phase diagrams for diameter ratios of q=0.74, 0.76, 0.8, 0.82, 0.84, and 0.85 for the small and large spheres. For diameter ratios 0.76 < or = q < or = 0.84, we find the Laves phases to be stable with respect to the other crystal structures that we considered and the fluid mixture. By extrapolating to the thermodynamic limit, we show that the MgZn2 structure is the most stable one of the Laves structures. We also calculate phase diagrams for equally and oppositely charged spheres for size ratio of 0.73 taking into consideration the Laves phases and CsCl. In the case of equally charged spheres, we find a pocket of stable Laves phases, while in the case of oppositely charged spheres, Laves phases are found to be metastable with respect to the CsCl and fluid phases. PMID:19691406

  3. Tracking three-phase coexistences in binary mixtures of hard plates and spheres.

    PubMed

    Aliabadi, Roohollah; Moradi, Mahmood; Varga, Szabolcs

    2016-02-21

    The stability of demixing phase transition in binary mixtures of hard plates (with thickness L and diameter D) and hard spheres (with diameter ?) is studied by means of Parsons-Lee theory. The isotropic-isotropic demixing, which is found in mixtures of large spheres and small plates, is very likely to be pre-empted by crystallization. In contrast, the nematic-nematic demixing, which is obtained in mixtures of large plates and small spheres, can be stabilized at low diameter ratios (?/D) and aspect ratios (L/D). At intermediate values of ?/D, where the sizes of the components are similar, neither the isotropic-isotropic nor the nematic-nematic demixing can be stabilized, but a very strong fractionation takes place between a plate rich nematic and a sphere rich isotropic phases. Our results show that the excluded volume interactions are capable alone to explain the experimental observation of the nematic-nematic demixing, but they fail in the description of isotropic-isotropic one [M. Chen et al., Soft Matter 11, 5775 (2015)]. PMID:26896997

  4. Random-walk analysis of displacement statistics of particles in concentrated suspensions of hard spheres

    NASA Astrophysics Data System (ADS)

    van Megen, W.

    2006-01-01

    Mean-squared displacements (MSDs) of colloidal fluids of hard spheres are analyzed in terms of a random walk, an analysis which assumes that the process of structural relaxation among the particles can be described in terms of thermally driven memoryless encounters. For the colloidal fluid in thermodynamic equilibrium the magnitude of the stretching of the MSD is able to be reconciled by a bias in the walk. This description fails for the under-cooled colloidal fluid.

  5. The range and nature of effective interactions in hard-sphere solids.

    PubMed

    Schindler, Michael; Maggs, A C

    2016-02-23

    Colloidal systems observed in video microscopy are often analysed using the displacements correlation matrix of particle positions. In non-thermal systems, the inverse of this matrix can be interpreted as a pair-interaction potential between particles. If the system is thermally agitated, however, only an effective interaction is accessible from the correlation matrix. We show how this effective interaction differs from the non-thermal case by comparing with high-statistics numerical data from hard-sphere crystals. PMID:26830000

  6. Fluids confined in wedges and by edges: Virial series for the line-thermodynamic properties of hard spheres

    SciTech Connect

    Urrutia, Ignacio

    2014-12-28

    This work is devoted to analyze the relation between the thermodynamic properties of a confined fluid and the shape of its confining vessel. Recently, new insights in this topic were found through the study of cluster integrals for inhomogeneous fluids that revealed the dependence on the vessel shape of the low density behavior of the system. Here, the statistical mechanics and thermodynamics of fluids confined in wedges or by edges is revisited, focusing on their cluster integrals. In particular, the well known hard sphere fluid, which was not studied in this framework so far, is analyzed under confinement and its thermodynamic properties are analytically studied up to order two in the density. Furthermore, the analysis is extended to the confinement produced by a corrugated wall. These results rely on the obtained analytic expression for the second cluster integral of the confined hard sphere system as a function of the opening dihedral angle 0 < β < 2π. It enables a unified approach to both wedges and edges.

  7. Evolutionary behaviour of miniemulsion phases: I. Hard sphere interaction and bound water on miniemulsion droplets

    NASA Astrophysics Data System (ADS)

    Katsumoto, Yukiteru; Ushiki, Hideharu; Graciaa, Alain; Lachaise, Jean

    2000-01-01

    The interaction between nano sphere droplets in translucent oil in water (O/W) emulsion phases, so-called miniemulsion phases, was investigated by using light scattering measurement techniques. We choose the ternary system of water/hexadecane/Mergital LT7 (the main component is heptaethylene glycol mono-n -dodecyl ether). Rayleigh ratio measurement was performed with changing dispersed phase volume fraction icons/Journals/Common/phi" ALT="phi" ALIGN="TOP"/> , and it revealed the fact that the osmotic compressibility is in good agreement with that of a hard sphere fluid. The dependence of the collective diffusion coefficients, measured by dynamic light scattering experiments, is similar to those observed in colloidal hard sphere suspensions. We found out that the ratio of the hydrodynamic diameter to the hard sphere diameter is 1.19 and the volume fraction of dispersed droplets is given by icons/Journals/Common/phi" ALT="phi" ALIGN="TOP"/> = 1.35icons/Journals/Common/phi" ALT="phi" ALIGN="TOP"/> . Preparing miniemulsions with various water to oil ratios, it was revealed that the ratio icons/Journals/Common/phi" ALT="phi" ALIGN="TOP"/> /icons/Journals/Common/phi" ALT="phi" ALIGN="TOP"/> was varied from 1.01 to 1.33. This indicates that the underestimation of the total volume of droplets calculated by the sum of surfactant and oil volume was not negligible. It is therefore considered that the volume fraction of bound water on miniemulsion droplets should be taken into account. We briefly discuss the idea that bound water plays an important role in obtaining a homogeneous miniemulsion phase.

  8. Response to ``Comment on: `New phase for one-component hard spheres' '' [J. Chem. Phys. 120, 11686 (2004)

    NASA Astrophysics Data System (ADS)

    Wu, Guang-Wen; Sadus, Richard J.

    2004-12-01

    The nature of the phases observed in a hard-sphere system is considered. Simulation data, obtained via both Monte Carlo simulation and molecular dynamics support the existence of a new phase for hard spheres. The data include configurational snapshots, compressibility factors, radial distribution functions, order parameters, and self-intermediate scattering functions. To facilitate further investigation of the new phase, the relevant configuration files are available on the internet.

  9. Elastically cooperative activated barrier hopping theory of relaxation in viscous fluids. I. General formulation and application to hard sphere fluids.

    PubMed

    Mirigian, Stephen; Schweizer, Kenneth S

    2014-05-21

    We generalize the force-level nonlinear Langevin equation theory of single particle hopping to include collective effects associated with long range elastic distortion of the liquid. The activated alpha relaxation event is of a mixed spatial character, involving two distinct, but inter-related, local and collective barriers. There are no divergences at volume fractions below jamming or temperatures above zero Kelvin. The ideas are first developed and implemented analytically and numerically in the context of hard sphere fluids. In an intermediate volume fraction crossover regime, the local cage process is dominant in a manner consistent with an apparent Arrhenius behavior. The super-Arrhenius collective barrier is more strongly dependent on volume fraction, dominates the highly viscous regime, and is well described by a nonsingular law below jamming. The increase of the collective barrier is determined by the amplitude of thermal density fluctuations, dynamic shear modulus or transient localization length, and a growing microscopic jump length. Alpha relaxation time calculations are in good agreement with recent experiments and simulations on dense fluids and suspensions of hard spheres. Comparisons of the theory with elastic models and entropy crisis ideas are explored. The present work provides a foundation for constructing a quasi-universal, fit-parameter-free theory for relaxation in thermal molecular liquids over 14 orders of magnitude in time. PMID:24852549

  10. Monte Carlo simulation and equation of state for flexible charged hard-sphere chain fluids: Polyampholyte and polyelectrolyte solutions

    SciTech Connect

    Jiang, Hao; Adidharma, Hertanto

    2014-11-07

    The thermodynamic modeling of flexible charged hard-sphere chains representing polyampholyte or polyelectrolyte molecules in solution is considered. The excess Helmholtz energy and osmotic coefficients of solutions containing short polyampholyte and the osmotic coefficients of solutions containing short polyelectrolytes are determined by performing canonical and isobaric-isothermal Monte Carlo simulations. A new equation of state based on the thermodynamic perturbation theory is also proposed for flexible charged hard-sphere chains. For the modeling of such chains, the use of solely the structure information of monomer fluid for calculating the chain contribution is found to be insufficient and more detailed structure information must therefore be considered. Two approaches, i.e., the dimer and dimer-monomer approaches, are explored to obtain the contribution of the chain formation to the Helmholtz energy. By comparing with the simulation results, the equation of state with either the dimer or dimer-monomer approach accurately predicts the excess Helmholtz energy and osmotic coefficients of polyampholyte and polyelectrolyte solutions except at very low density. It also well captures the effect of temperature on the thermodynamic properties of these solutions.

  11. Elastically Cooperative Activated Hopping Theory of Relaxation in Viscous Liquids. I. General Formulation and Application to Hard Sphere Fluids.

    SciTech Connect

    Mirigian, Stephen; Schweizer, Kenneth

    2014-01-01

    We generalize the force-level nonlinear Langevin equation theory of single particle hopping to include collective effects associated with long range elastic distortion of the liquid. The activated alpha relaxation event is of a mixed spatial character, involving two distinct, but inter-related, local and collective barriers. There are no divergences at volume fractions below jamming or temperatures above zero Kelvin. The ideas are first developed and implemented analytically and numerically in the context of hard sphere fluids. In an intermediate volume fraction crossover regime, the local cage process is dominant in a manner consistent with an apparent Arrhenius behavior. The super-Arrhenius collective barrier is more strongly dependent on volume fraction, dominates the highly viscous regime, and is well described by a nonsingular law below jamming. The increase of the collective barrier is determined by the amplitude of thermal density fluctuations, dynamic shear modulus or transient localization length, and a growing microscopic jump length. Alpha relaxation time calculations are in good agreement with recent experiments and simulations on dense fluids and suspensions of hard spheres. Comparisons of the theory with elastic models and entropy crisis ideas are explored. The present work provides a foundation for constructing a quasi-universal, fit-parameter-free theory for relaxation in thermal molecular liquids over 14 orders of magnitude in time.

  12. Elastically cooperative activated barrier hopping theory of relaxation in viscous fluids. I. General formulation and application to hard sphere fluids

    NASA Astrophysics Data System (ADS)

    Mirigian, Stephen; Schweizer, Kenneth S.

    2014-05-01

    We generalize the force-level nonlinear Langevin equation theory of single particle hopping to include collective effects associated with long range elastic distortion of the liquid. The activated alpha relaxation event is of a mixed spatial character, involving two distinct, but inter-related, local and collective barriers. There are no divergences at volume fractions below jamming or temperatures above zero Kelvin. The ideas are first developed and implemented analytically and numerically in the context of hard sphere fluids. In an intermediate volume fraction crossover regime, the local cage process is dominant in a manner consistent with an apparent Arrhenius behavior. The super-Arrhenius collective barrier is more strongly dependent on volume fraction, dominates the highly viscous regime, and is well described by a nonsingular law below jamming. The increase of the collective barrier is determined by the amplitude of thermal density fluctuations, dynamic shear modulus or transient localization length, and a growing microscopic jump length. Alpha relaxation time calculations are in good agreement with recent experiments and simulations on dense fluids and suspensions of hard spheres. Comparisons of the theory with elastic models and entropy crisis ideas are explored. The present work provides a foundation for constructing a quasi-universal, fit-parameter-free theory for relaxation in thermal molecular liquids over 14 orders of magnitude in time.

  13. The Physics of Hard Spheres Experiment on MSL-1: Required Measurements and Instrument Performance

    NASA Technical Reports Server (NTRS)

    Doherty, Michael P.; Lant, Christian T.; Ling, Jerri S.

    1998-01-01

    The Physics of HArd Spheres Experiment (PHaSE), one of NASA Lewis Research Center's first major light scattering experiments for microgravity research on complex fluids, flew on board the Space Shuttle's Microgravity Science Laboratory (MSL-1) in 1997. Using colloidal systems of various concentrations of micron-sized plastic spheres in a refractive index-matching fluid as test samples, illuminated by laser light during and after crystallization, investigations were conducted to measure the nucleation and growth rate of colloidal crystals as well as the structure, rheology, and dynamics of the equilibrium crystal. Together, these measurements support an enhanced understanding of the nature of the liquid-to-solid transition. Achievement of the science objectives required an accurate experimental determination of eight fundamental properties for the hard sphere colloidal samples. The instrument design met almost all of the original measurement requirements, but with compromise on the number of samples on which data were taken. The instrument performs 2-D Bragg and low angle scattering from 0.4 deg. to 60 deg., dynamic and single-channel static scattering from 10 deg. to 170 deg., rheology using fiber optics, and white light imaging of the sample. As a result, PHaSE provided a timely microgravity demonstration of critical light scattering measurement techniques and hardware concepts, while generating data already showing promise of interesting new scientific findings in the field of condensed matter physics.

  14. On the definition of an ideal amorphous solid of uniform hard spheres

    NASA Astrophysics Data System (ADS)

    To, Long-Thang; Daley, Daryl J.; Stachurski, Zbigniew H.

    2006-08-01

    Perfection of structure is defined firstly by the definition of imperfections that may occur in that structure, and secondly by the strict requirement of absence of those imperfections. An ideal amorphous solid is a geometrical structure with perfectly random (as distinct from disordered) packing of spheres/atoms. This is achieved by requiring all spheres to be in fixed positions (no rattlers) and the packing to obey certain statistical rules (without exceptions). The random configurations of local clusters are described by the mathematics of self-avoiding random walks, and the distribution of mutual contacts (coordination numbers) is described by combinatorics developed in connection with an earlier work on the structure of liquids. Flaws in the structure are defined. An ideal amorphous solid, based on packing of identical spheres and without any flaws, appears to have packing density close to approximately 0.61. Flaws which form clusters with close packing configurations (fcc and hcp) have the effect of increasing the packing density, whereas other type of flaws, i.e., loose spheres or vacancies will inevitably decrease the packing density. This relationship is revealed by analysis of recently published experimental packings and computer simulations. In that sense, the ideal amorphous solid described here is entirely new and original.

  15. An Automatic Phase-Change Detection Technique for Colloidal Hard Sphere Suspensions

    NASA Technical Reports Server (NTRS)

    McDowell, Mark; Gray, Elizabeth; Rogers, Richard B.

    2005-01-01

    Colloidal suspensions of monodisperse spheres are used as physical models of thermodynamic phase transitions and as precursors to photonic band gap materials. However, current image analysis techniques are not able to distinguish between densely packed phases within conventional microscope images, which are mainly characterized by degrees of randomness or order with similar grayscale value properties. Current techniques for identifying the phase boundaries involve manually identifying the phase transitions, which is very tedious and time consuming. We have developed an intelligent machine vision technique that automatically identifies colloidal phase boundaries. The algorithm utilizes intelligent image processing techniques that accurately identify and track phase changes vertically or horizontally for a sequence of colloidal hard sphere suspension images. This technique is readily adaptable to any imaging application where regions of interest are distinguished from the background by differing patterns of motion over time.

  16. The role of bond tangency and bond gap in hard sphere crystallization of chains.

    PubMed

    Karayiannis, Nikos Ch; Foteinopoulou, Katerina; Laso, Manuel

    2015-03-01

    We report results from Monte Carlo simulations on dense packings of linear, freely-jointed chains of hard spheres of uniform size. In contrast to our past studies where bonded spheres along the chain backbone were tangent, in the present work a finite tolerance in the bond is allowed. Bond lengths are allowed to fluctuate in the interval [?, ? + dl], where ? is the sphere diameter. We find that bond tolerance affects the phase behaviour of hard-sphere chains, especially in the close vicinity of the melting transition. First, a critical dl(crit) exists marking the threshold for crystallization, whose value decreases with increasing volume fraction. Second, bond gaps enhance the onset of phase transition by accelerating crystal nucleation and growth. Finally, bond tolerance has an effect on crystal morphologies: in the tangent limit the majority of structures correspond to stack-faulted random hexagonal close packing (rhcp). However, as bond tolerance increases a wealth of diverse structures can be observed: from single fcc (or hcp) crystallites to random hcp/fcc stackings with multiple directions. By extending the simulations over trillions of MC steps (10(12)) we are able to observe crystal-crystal transitions and perfection even for entangled polymer chains in accordance to the Ostwald's rule of stages in crystal polymorphism. Through simple geometric arguments we explain how the presence of rigid or flexible constraints affects crystallization in general atomic and particulate systems. Based on the present results, it can be concluded that proper tuning of bond gaps and of the connectivity network can be a controlling factor for the phase behaviour of model, polymer-based colloidal and granular systems. PMID:25594158

  17. Thermodynamics and structure of liquid metals from the charged hard-sphere reference fluid

    NASA Astrophysics Data System (ADS)

    Akinlade, O.; Lai, S. K.; Tosi, M. P.

    1990-10-01

    Perturbative variational calculations of thermodynamic and structural properties of liquid metals, based on the use of ab initio and highly reliable nonlocal pseudopotentials for the electron-ion interactions and of the fluid of charged hard spheres as a reference system, have been reported recently for the liquid alkali metals from Na to Cs near the freezing point. We extend in this work the above-mentioned calculations in two directions. Firstly, we discuss the predicted temperature dependence of the liquid structure factor for the same alkali metals over a limited temperature range above the freezing point. Secondly, we examine the usefulness of the approach for metals with relatively strong electron-ion interactions, namely Li and several polyvalent metals (Mg, Cd, Al, In, Tl and Pb). The charged hard-sphere reference system leads to lower values of the Helmholtz free energy and to slightly improved values of the excess entropy for all the liquid metals that we evaluate, even though polyvalent ones overall appear to be relatively close to fluids of neutral hard spheres. For the liquid alkali metals at elevated temperatures, the calculated structure factors are of similar quality as in our previous work, that is, they show a systematic shift in the positions of peaks and valleys to slightly larger wave numbers and peak heights that are somewhat underestimated with increasing temperature. However, for liquid polyvalent metals, our approach yields quite good agreement with experiment for the positions of maxima and minima in the liquid structure factor, while it tends to overemphasize somewhat these structures.

  18. Static lengths in glass-forming monodisperse hard-sphere fluids from periodic array pinning.

    PubMed

    Zhou, Yuxing; Milner, Scott T

    2015-12-23

    We explore the static length in glass-forming hard-sphere liquids revealed by the response of dynamical properties (diffusion coefficient D and α relaxation time τα) to a regular array of pinned particles. By assuming a universal scaling form, we find data can be excellently collapsed onto a master curve, from which relative length scales can be extracted. By exploiting a crystal-avoiding simulation method that suppresses crystallization while preserving dynamics, we can study monodisperse as well as polydisperse systems. The static length obtained from dynamical property Q (τα and D) scales as log Q ∼ ξ, with ψ ≈ 1. PMID:26473276

  19. Non-polytropic effect on shock-induced phase transitions in a hard-sphere system

    NASA Astrophysics Data System (ADS)

    Zheng, Yue; Zhao, Nanrong; Ruggeri, Tommaso; Sugiyama, Masaru; Taniguchi, Shigeru

    2010-07-01

    By adopting a simplified model of a non-polytropic hard-sphere system where heat capacity depends on the temperature, we demonstrate the importance of non-polytropic effect on the shock-induced phase transitions. We show explicitly that with the increase of the shock strength the perturbed temperature (the temperature after a shock) increases and the vibrational modes are gradually excited, and as a result, shock-induced phase transitions are qualitatively and quantitatively different from the phase transitions observed in a simple polytropic model. The effect on the admissibility (stability) of a shock wave is also analyzed.

  20. Temperature Dependence of the Pairwise Association of Hard Spheres in Water

    NASA Astrophysics Data System (ADS)

    Graziano, Giuseppe

    2016-02-01

    It is shown that the Gibbs energy change associated with the formation of the contact-minimum configuration of two hard spheres in water becomes more negative on increasing the temperature, at 1 atm, by extending the geometric approach previously developed [G. Graziano, Chem. Phys. Lett. 499, 79 (2010)].. This is because the decrease in water accessible surface area accompanying the association leads to a gain in translational entropy of water molecules. The process is exothermic, due to the release of some water molecules from the hydration shell to the bulk. This water reorganization is characterized by a complete enthalpy-entropy compensation and does not affect the Gibbs energy change.

  1. Phase transitions in self-gravitating systems: self-gravitating fermions and hard-sphere models.

    PubMed

    Chavanis, Pierre-Henri

    2002-05-01

    We discuss the nature of phase transitions in self-gravitating systems both in the microcanonical and in the canonical ensemble. We avoid the divergence of the gravitational potential at short distances by considering the case of self-gravitating fermions and hard-sphere models. Depending on the values of the parameters, three kinds of phase transitions (of zero, first, and second order) are evidenced. They separate a "gaseous" phase with a smoothly varying distribution of matter from a "condensed" phase with a core-halo structure. We propose a simple analytical model to describe these phase transitions. We determine the value of energy (in the microcanonical ensemble) and temperature (in the canonical ensemble) at the transition point and we study their dependence on the degeneracy parameter (for fermions) or on the size of the particles (for a hard-sphere gas). Scaling laws are obtained analytically in the asymptotic limit of a small short distance cutoff. Our analytical model captures the essential physics of the problem and compares remarkably well with the full numerical solutions. We also stress some analogies with the liquid-gas transition and with the Blume-Emery-Griffiths model with infinite range interactions. In particular, our system presents two tricritical points at which the transition passes from first order to second order. PMID:12059663

  2. Physics of Hard Sphere Experiment: Scattering, Rheology and Microscopy Study of Colloidal Particles

    NASA Technical Reports Server (NTRS)

    Cheng, Z.-D.; Zhu, J.; Phan, S.-E.; Russel, W. B.; Chaikin, P. M.; Meyer, W. V.

    2002-01-01

    The Physics of Hard Sphere Experiment has two incarnations: the first as a scattering and rheology experiment on STS-83 and STS-94 and the second as a microscopy experiment to be performed in the future on LMM on the space station. Here we describe some of the quantitative and qualitative results from previous flights on the dynamics of crystallization in microgravity and especially the observed interaction of growing crystallites in the coexistance regime. To clarify rheological measurements we also present ground based experiments on the low shear rate viscosity and diffusion coefficient of several hard sphere experiments at high volume fraction. We also show how these experiments will be performed with confocal microscopy and laser tweezers in our lab and as preparation for the phAse II experiments on LMM. One of the main aims of the microscopy study will be the control of colloidal samples using an array of applied fields with an eye toward colloidal architectures. Temperature gradients, electric field gradients, laser tweezers and a variety of switchable imposed surface patterns are used toward this control.

  3. Crystal nucleation in binary hard sphere mixtures: A Monte Carlo simulation study

    NASA Astrophysics Data System (ADS)

    Punnathanam, S.; Monson, P. A.

    2006-07-01

    We present calculations of the nucleation barrier during crystallization in binary hard sphere mixtures under moderate degrees of supercooling using Monte Carlo simulations in the isothermal-isobaric semigrand ensemble in conjunction with an umbrella sampling technique. We study both additive and negatively nonadditive binary hard sphere systems. The solid-fluid phase diagrams of such systems show a rich variety of behavior, ranging from simple spindle shapes to the appearance of azeotropes and eutectics to the appearance of substitutionally ordered solid phase compounds. We investigate the effect of these types of phase behavior upon the nucleation barrier and the structure of the critical nucleus. We find that the underlying phase diagram has a significant effect on the mechanism of crystal nucleation. Our calculations indicate that fractionation of the species upon crystallization increases the difficulty of crystallization of fluid mixtures and in the absence of fractionation (azeotropic conditions) the nucleation barrier is comparable to pure fluids. We also calculate the barrier to nucleation of a substitutionally ordered compound solid. In such systems, which also show solid-solid phase separation, we find that the phase that nucleates is the one whose equilibrium composition is closer to the composition of the fluid phase.

  4. Crystal nucleation in binary hard sphere mixtures: a Monte Carlo simulation study.

    PubMed

    Punnathanam, S; Monson, P A

    2006-07-14

    We present calculations of the nucleation barrier during crystallization in binary hard sphere mixtures under moderate degrees of supercooling using Monte Carlo simulations in the isothermal-isobaric semigrand ensemble in conjunction with an umbrella sampling technique. We study both additive and negatively nonadditive binary hard sphere systems. The solid-fluid phase diagrams of such systems show a rich variety of behavior, ranging from simple spindle shapes to the appearance of azeotropes and eutectics to the appearance of substitutionally ordered solid phase compounds. We investigate the effect of these types of phase behavior upon the nucleation barrier and the structure of the critical nucleus. We find that the underlying phase diagram has a significant effect on the mechanism of crystal nucleation. Our calculations indicate that fractionation of the species upon crystallization increases the difficulty of crystallization of fluid mixtures and in the absence of fractionation (azeotropic conditions) the nucleation barrier is comparable to pure fluids. We also calculate the barrier to nucleation of a substitutionally ordered compound solid. In such systems, which also show solid-solid phase separation, we find that the phase that nucleates is the one whose equilibrium composition is closer to the composition of the fluid phase. PMID:16848593

  5. Thermodynamic Functions of Solvation of Hydrocarbons, Noble Gases, and Hard Spheres in Tetrahydrofuran-Water Mixtures.

    PubMed

    Sedov, I A; Magsumov, T I

    2015-07-16

    Thermodynamic solvation properties of mixtures of water with tetrahydrofuran at 298 K are studied. The Gibbs free energies and enthalpies of solvation of n-octane and toluene are determined experimentally. For molecular dynamics simulations of the binary solvent, we have modified a TraPPE-UA model for tetrahydrofuran and combined it with the SPC/E potential for water. The excess thermodynamic functions of neon, xenon, and hard spheres with two different radii are calculated using the particle insertion method. Simulated and real systems share the same characteristic trends for the thermodynamic functions. A maximum is present on dependencies of the enthalpy of solvation from the composition of solvent at 70-90 mol % water, making it higher than in both of the cosolvents. It is caused by a high enthalpy of cavity formation in the mixtures rich with water due to solvent reorganization around the cavity, which is shown by calculation of the enthalpy of solvation of hard spheres. Addition of relatively small amounts of tetrahydrofuran to water effectively suppresses the hydrophobic effect, leading to a quick increase of both the entropy and enthalpy of cavity formation and solvation of low polar molecules. PMID:26115405

  6. Theory of gelation, vitrification, and activated barrier hopping in mixtures of hard and sticky spheres.

    PubMed

    Viehman, Douglas C; Schweizer, Kenneth S

    2008-02-28

    Naive mode coupling theory (NMCT) and the nonlinear stochastic Langevin equation theory of activated dynamics have been generalized to mixtures of spherical particles. Two types of ideal nonergodicity transitions are predicted corresponding to localization of both, or only one, species. The NMCT transition signals a dynamical crossover to activated barrier hopping dynamics. For binary mixtures of equal diameter hard and attractive spheres, a mixture composition sensitive "glass-melting" type of phenomenon is predicted at high total packing fractions and weak attractions. As the total packing fraction decreases, a transition to partial localization occurs corresponding to the coexistence of a tightly localized sticky species in a gel-like state with a fluid of hard spheres. Complex behavior of the localization lengths and shear moduli exist because of the competition between excluded volume caging forces and attraction-induced physical bond formation between sticky particles. Beyond the NMCT transition, a two-dimensional nonequilibrium free energy surface emerges, which quantifies cooperative activated motions. The barrier locations and heights are sensitive to the relative amplitude of the cooperative displacements of the different species. PMID:18315063

  7. Simulation of a Solid-Solid Transition in Confined Colloidal Hard Spheres

    NASA Astrophysics Data System (ADS)

    Qi, Weikai; Peng, Yi; Han, Yilong; Bowles, Richard; Dijkstra, Marjolein

    2015-03-01

    Recent experiments on a system of colloidal particles confined between two flat plates showed a two-stage nucleation process involving the transition of a solid, consisting of n +1 crystalline layers with a square symmetry (n +1 s-phase), to another solid consisting of n triangular layers (n t-phase), via an intermediate metastable liquid droplet. Using event-driven molecular dynamics and Monte Carlo simulations, we study the 5s --> 4t solid-solid transition in colloidal hard spheres confined between two planar hard walls. The 5s solid initially melts, forming a liquid droplet, within which the 4t solid nucleates. Calculations of the free-energy landscape confirm that the optimal kinetic pathway is a two-stage nucleation process with a critical nucleus consisting of liquid-like and t-solid-like particles. In addition, we find that the t-solid-like cluster nucleates near the planar hard walls, and contains both face-centered-cubic and hexagonal-close-packed ordered particles. Current Address: Dept. Chemistry, University of Saskatchewan, Canada.

  8. Combined temperature and density series for fluid-phase properties. I. Square-well spheres

    NASA Astrophysics Data System (ADS)

    Elliott, J. Richard; Schultz, Andrew J.; Kofke, David A.

    2015-09-01

    Cluster integrals are evaluated for the coefficients of the combined temperature- and density-expansion of pressure: Z = 1 + B2(?) ? + B3(?) ?2 + B4(?) ?3 + ⋯, where Z is the compressibility factor, ? is the packing fraction, and the Bi(?) coefficients are expanded as a power series in reciprocal temperature, ?, about ? = 0. The methodology is demonstrated for square-well spheres with ? = [1.2-2.0], where ? is the well diameter relative to the hard core. For this model, the Bi coefficients can be expressed in closed form as a function of ?, and we develop appropriate expressions for i = 2-6; these expressions facilitate derivation of the coefficients of the ? series. Expanding the Bi coefficients in ? provides a correspondence between the power series in density (typically called the virial series) and the power series in ? (typically called thermodynamic perturbation theory, TPT). The coefficients of the ? series result in expressions for the Helmholtz energy that can be compared to recent computations of TPT coefficients to fourth order in ?. These comparisons show good agreement at first order in ?, suggesting that the virial series converges for this term. Discrepancies for higher-order terms suggest that convergence of the density series depends on the order in ?. With selection of an appropriate approximant, the treatment of Helmholtz energy that is second order in ? appears to be stable and convergent at least to the critical density, but higher-order coefficients are needed to determine how far this behavior extends into the liquid.

  9. On the calculation of the thermodynamics of liquid metals using the charged-hard-sphere reference system

    NASA Astrophysics Data System (ADS)

    Iwamatsu, M.

    1989-09-01

    We have two-parameter variational calculations of the free energy of simple liquid metals using the charged-hard-sphere (CHS) reference system and the Ashcroft local pseudopotential. The results are compared with those obtained using the hard-sphere (HS) and the one-component-plasma (OCP) reference system. It is shown that the CHS reference gives the lowest bound of the free energy among the three references for the polyvalent metals, while the OCP reference gives the lowest energy for the alkali metals.

  10. Quantitative analysis of the correlations in the Boltzmann-Grad limit for hard spheres

    NASA Astrophysics Data System (ADS)

    Pulvirenti, M.

    2014-12-01

    In this contribution I consider the problem of the validity of the Boltzmann equation for a system of hard spheres in the Boltzmann-Grad limit. I briefly review the results available nowadays with a particular emphasis on the celebrated Lanford's validity theorem. Finally I present some recent results, obtained in collaboration with S. Simonella, concerning a quantitative analysis of the propagation of chaos. More precisely we introduce a quantity (the correlation error) measuring how close a j-particle rescaled correlation function at time t (sufficiently small) is far from the full statistical independence. Roughly speaking, a correlation error of order k, measures (in the context of the BBKGY hierarchy) the event in which k tagged particles form a recolliding group.

  11. Perturbation theory for multicomponent fluids based on structural properties of hard-sphere chain mixtures

    NASA Astrophysics Data System (ADS)

    Hlushak, Stepan

    2015-09-01

    An analytical expression for the Laplace transform of the radial distribution function of a mixture of hard-sphere chains of arbitrary segment size and chain length is used to rigorously formulate the first-order Barker-Henderson perturbation theory for the contribution of the segment-segment dispersive interactions into thermodynamics of the Lennard-Jones chain mixtures. Based on this approximation, a simple variant of the statistical associating fluid theory is proposed and used to predict properties of several mixtures of chains of different lengths and segment sizes. The theory treats the dispersive interactions more rigorously than the conventional theories and provides means for more accurate description of dispersive interactions in the mixtures of highly asymmetric components.

  12. Quantitative analysis of the correlations in the Boltzmann-Grad limit for hard spheres

    SciTech Connect

    Pulvirenti, M.

    2014-12-09

    In this contribution I consider the problem of the validity of the Boltzmann equation for a system of hard spheres in the Boltzmann-Grad limit. I briefly review the results available nowadays with a particular emphasis on the celebrated Lanford’s validity theorem. Finally I present some recent results, obtained in collaboration with S. Simonella, concerning a quantitative analysis of the propagation of chaos. More precisely we introduce a quantity (the correlation error) measuring how close a j-particle rescaled correlation function at time t (sufficiently small) is far from the full statistical independence. Roughly speaking, a correlation error of order k, measures (in the context of the BBKGY hierarchy) the event in which k tagged particles form a recolliding group.

  13. Apparent wall slip in non-Brownian hard-sphere suspensions.

    PubMed

    Korhonen, Marko; Mohtaschemi, Mikael; Puisto, Antti; Illa, Xavier; Alava, Mikko J

    2015-05-01

    We analyze apparent wall slip, the reduction of particle concentration near the wall, in hard-sphere suspensions at concentrations well below the jamming limit utilizing a continuum level diffusion model. The approach extends a constitutive equation proposed earlier with two additional potentials describing the effects of gravitation and wall-particle repulsion. We find that although both mechanisms are shear independent by nature, due to the shear-rate-dependent counter-balancing particle migration fluxes, the resulting net effect is non-linearly shear dependent, causing larger slip at small shear rates. In effect, this shows up in the classically measured flow curves as a mild shear thickening regime at the transition from small to intermediate shear rates. PMID:25998170

  14. Direct measurement of the free energy of aging hard sphere colloidal glasses.

    PubMed

    Zargar, Rojman; Nienhuis, Bernard; Schall, Peter; Bonn, Daniel

    2013-06-21

    The nature of the glass transition is one of the most important unsolved problems in condensed matter physics. The difference between glasses and liquids is believed to be caused by very large free energy barriers for particle rearrangements; however, so far it has not been possible to confirm this experimentally. We provide the first quantitative determination of the free energy for an aging hard sphere colloidal glass. The determination of the free energy allows for a number of new insights in the glass transition, notably the quantification of the strong spatial and temporal heterogeneity in the free energy. A study of the local minima of the free energy reveals that the observed variations are directly related to the rearrangements of the particles. Our main finding is that the probability of particle rearrangements shows a power law dependence on the free energy changes associated with the rearrangements similar to the Gutenberg-Richter law in seismology. PMID:23829762

  15. Single-particle fluctuations and directional correlations in driven hard-sphere glasses.

    PubMed

    Mandal, Suvendu; Chikkadi, Vijaykumar; Nienhuis, Bernard; Raabe, Dierk; Schall, Peter; Varnik, Fathollah

    2013-08-01

    Via event-driven molecular dynamics simulations and experiments, we study the packing-fraction and shear-rate dependence of single-particle fluctuations and dynamic correlations in hard-sphere glasses under shear. At packing fractions above the glass transition, correlations increase as shear rate decreases: the exponential tail in the distribution of single-particle jumps broadens and dynamic four-point correlations increase. Interestingly, however, upon decreasing the packing fraction, a broadening of the exponential tail is also observed, while dynamic heterogeneity is shown to decrease. An explanation for this behavior is proposed in terms of a competition between shear and thermal fluctuations. Building upon our previous studies [Chikkadi et al., Europhys. Lett. 100, 56001 (2012)], we further address the issue of anisotropy of the dynamic correlations. PMID:24032797

  16. Polymer induced changes of the crystallization scenario in suspensions of hard sphere like microgel particles

    NASA Astrophysics Data System (ADS)

    Beyer, Richard; Iacopini, Sara; Palberg, Thomas; Schpe, Hans Joachim

    2012-06-01

    We investigated the crystallization scenario of highly cross linked polystyrene particles dispersed in the good solvent 2-ethylnaphtalene and their mixtures with non-adsorbing low molecular weight polysterene polymer using time resolved static light scattering. The samples were prepared slightly below the melting volume fraction of the polymer free system. For the polymer free samples, we obtained polycrystalline solids via crystallization scenario known from hard sphere suspensions with little competition of wall crystal formation. Addition of non-adsorbing low molecular weight polystyrene polymer leads to a considerably slowing down of the bulk crystallization kinetics. We observed a delay of the precursor to crystal conversion for the bulk crystallization while the induction times for the wall nucleation are reduced. The increased polymer concentration thus shifts the balance between the two competing crystallization pathways giving the possibility to tune the relative amount of wall based crystals.

  17. Effect of Hydrodynamic Interactions on Self-Diffusion of Quasi-Two-Dimensional Colloidal Hard Spheres

    NASA Astrophysics Data System (ADS)

    Thorneywork, Alice L.; Rozas, Roberto E.; Dullens, Roel P. A.; Horbach, Jürgen

    2015-12-01

    We compare experimental results from a quasi-two-dimensional colloidal hard sphere fluid to a Monte Carlo simulation of hard disks with small particle displacements. The experimental short-time self-diffusion coefficient DS scaled by the diffusion coefficient at infinite dilution, D0, strongly depends on the area fraction, pointing to significant hydrodynamic interactions at short times in the experiment, which are absent in the simulation. In contrast, the area fraction dependence of the experimental long-time self-diffusion coefficient DL/D0 is in quantitative agreement with DL/D0 obtained from the simulation. This indicates that the reduction in the particle mobility at short times due to hydrodynamic interactions does not lead to a proportional reduction in the long-time self-diffusion coefficient. Furthermore, the quantitative agreement between experiment and simulation at long times indicates that hydrodynamic interactions effectively do not affect the dependence of DL/D0 on the area fraction. In light of this, we discuss the link between structure and long-time self-diffusion in terms of a configurational excess entropy and do not find a simple exponential relation between these quantities for all fluid area fractions.

  18. Two-stage melting induced by dislocations and grain boundaries in monolayers of hard spheres.

    PubMed

    Qi, Weikai; Gantapara, Anjan P; Dijkstra, Marjolein

    2014-08-14

    Melting in two-dimensional systems has remained controversial as theory, simulations, and experiments show contrasting results. One issue that obscures this discussion is whether or not theoretical predictions on strictly 2D systems describe those on quasi-2D experimental systems, where out-of-plane fluctuations may alter the melting mechanism. Using event-driven molecular dynamics simulations, we find that the peculiar two-stage melting scenario of a continuous solid-hexatic and a first-order hexatic-liquid transition as observed for a truly 2D system of hard disks [Bernard and Krauth, Phys. Rev. Lett., 2011, 107, 155704] persists for a quasi-2D system of hard spheres with out-of-plane particle motions as high as half the particle diameter. By calculating the renormalized Young's modulus, we show that the solid-hexatic transition is of the Kosterlitz-Thouless type and occurs via dissociation of bound dislocation pairs. In addition, we find a first-order hexatic-liquid transition that seems to be driven by spontaneous proliferation of grain boundaries. PMID:24752821

  19. Qualitative Observations Concerning Packing Densities for Liquids, Solutions, and Random Assemblies of Spheres

    ERIC Educational Resources Information Center

    Duer, W. C.; And Others

    1977-01-01

    Discusses comparisons of packing densities derived from known molar volume data of liquids and solutions. Suggests further studies for using assemblies of spheres as models for simple liquids and solutions. (MLH)

  20. Coordinated HArd Sphere Model (CHASM): A Simplified Model for Silicate and Oxide Liquids at Mantle Conditions

    NASA Astrophysics Data System (ADS)

    Wolf, A. S.; Asimow, P. D.; Stevenson, D. J.

    2013-12-01

    Recent first-principles theoretical calculations (Stixrude 2009) and experimental shock-wave investigations (Mosenfelder 2009) indicate that melting perovskite requires significantly less energy than previously thought, supporting the idea of a deep-mantle magma ocean early in Earth's history. The modern-day solid Earth is thus likely the result of crystallization from an early predominantly molten state, a process that is primarily controlled by the poorly understood behavior of silicate melts at extreme pressures and temperatures. Probing liquid thermodynamics at mantle conditions is difficult for both theory and experiment, and further challenges are posed by the large relevant compositional space including at least MgO, SiO2, and FeO. First-principles molecular dynamics has been used with great success to determine the high P-T properties of a small set of fixed composition silicate-oxide liquids including MgO (Karki 2006), SiO2 (Karki 2007), Mg2SiO4 (de Koker 2008), MgSiO3 (Stixrude 2005), and Fe2SiO4 (Ramo 2012). While extremely powerful, this approach has limitations including high computational cost, lower bounds on temperature due to relaxation constraints, as well as restrictions to length scales and time scales that are many orders of magnitude smaller than those relevant to the Earth or experimental methods. As a compliment to accurate first-principles calculations, we have developed the Coordinated HArd Sphere Model (CHASM). We extend the standard hard sphere mixture model, recently applied to silicate liquids by Jing (2011), by accounting for the range of oxygen coordination states available to liquid cations. Utilizing approximate analytic expressions for the hard sphere model, the method can predict complex liquid structure and thermodynamics while remaining computationally efficient. Requiring only minutes on standard desktop computers rather than months on supercomputers, the CHASM approach is well-suited to providing an approximate thermodynamic map of the wide compositional space relevant to early Earth evolution. As a first step on this path, we apply the CHASM formalism to the MgO system. We first demonstrate that the model parameters can be obtained by training on equation of state data for a variety of crystal polymorphs, which discretely sample the continuous range of coordination states available to the liquid; training only on solid data, CHASM thus provides a fully predictive model for oxide liquids. Using the best-fit parameter values, the coordination evolution and equation of state of MgO liquid is determined by free-energy minimization over a wide P-T range. These results are evaluated by favorable comparison with predictions from published first-principles molecular dynamics calculations, indicating that CHASM is accurately capturing the dominant physical mechanism controlling the behavior of high pressure oxide liquids. By combining the CHASM description of MgO liquid with a thermodynamic model for solid MgO periclase, we also compare the MgO melting curve with both first principles computations and shock wave measurements. Future development of the CHASM model will incorporate SiO2, FeO, and Al2O3, providing a simple physical framework that enables both interpretation of experiments and prediction of behavior currently outside our technical or computational capabilities.

  1. A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson-Nernst-Planck Equations to Account for Hard Sphere Repulsion Among Ions

    NASA Astrophysics Data System (ADS)

    Qiao, Yu; Liu, Xuejiao; Chen, Minxin; Lu, Benzhuo

    2016-02-01

    The hard sphere repulsion among ions can be considered in the Poisson-Nernst-Planck (PNP) equations by combining the fundamental measure theory (FMT). To reduce the nonlocal computational complexity in 3D simulation of biological systems, a local approximation of FMT is derived, which forms a local hard sphere PNP (LHSPNP) model. In the derivation, the excess chemical potential from hard sphere repulsion is obtained with the FMT and has six integration components. For the integrands and weighted densities in each component, Taylor expansions are performed and the lowest order approximations are taken, which result in the final local hard sphere (LHS) excess chemical potential with four components. By plugging the LHS excess chemical potential into the ionic flux expression in the Nernst-Planck equation, the three dimensional LHSPNP is obtained. It is interestingly found that the essential part of free energy term of the previous size modified model (Borukhov et al. in Phys Rev Lett 79:435-438, 1997; Kilic et al. in Phys Rev E 75:021502, 2007; Lu and Zhou in Biophys J 100:2475-2485, 2011; Liu and Eisenberg in J Chem Phys 141:22D532, 2014) has a very similar form to one term of the LHS model, but LHSPNP has more additional terms accounting for size effects. Equation of state for one component homogeneous fluid is studied for the local hard sphere approximation of FMT and is proved to be exact for the first two virial coefficients, while the previous size modified model only presents the first virial coefficient accurately. To investigate the effects of LHS model and the competitions among different counterion species, numerical experiments are performed for the traditional PNP model, the LHSPNP model, the previous size modified PNP (SMPNP) model and the Monte Carlo simulation. It's observed that in steady state the LHSPNP results are quite different from the PNP results, but are close to the SMPNP results under a wide range of boundary conditions. Besides, in both LHSPNP and SMPNP models the stratification of one counterion species can be observed under certain bulk concentrations.

  2. Assembly of vorticity-aligned hard-sphere colloidal strings in a simple shear flow

    PubMed Central

    Cheng, Xiang; Xu, Xinliang; Rice, Stuart A.; Dinner, Aaron R.; Cohen, Itai

    2012-01-01

    Colloidal suspensions self-assemble into equilibrium structures ranging from face- and body-centered cubic crystals to binary ionic crystals, and even kagome lattices. When driven out of equilibrium by hydrodynamic interactions, even more diverse structures can be accessed. However, mechanisms underlying out-of-equilibrium assembly are much less understood, though such processes are clearly relevant in many natural and industrial systems. Even in the simple case of hard-sphere colloidal particles under shear, there are conflicting predictions about whether particles link up into string-like structures along the shear flow direction. Here, using confocal microscopy, we measure the shear-induced suspension structure. Surprisingly, rather than flow-aligned strings, we observe log-rolling strings of particles normal to the plane of shear. By employing Stokesian dynamics simulations, we address the mechanism leading to this out-of-equilibrium structure and show that it emerges from a delicate balance between hydrodynamic and interparticle interactions. These results demonstrate a method for assembling large-scale particle structures using shear flows. PMID:22198839

  3. Crystal nucleation in the hard-sphere system revisited: a critical test of theoretical approaches.

    PubMed

    Tth, Gyula I; Grnsy, Lszl

    2009-04-16

    The hard-sphere system is the best known fluid that crystallizes: the solid-liquid interfacial free energy, the equations of state, and the height of the nucleation barrier are known accurately, offering a unique possibility for a quantitative validation of nucleation theories. A recent significant downward revision of the interfacial free energy from approximately 0.61kT/sigma(2) to (0.56 +/- 0.02)kT/sigma(2) [Davidchack, R.; Morris, J. R.; Laird, B. B. J. Chem. Phys. 2006, 125, 094710] necessitates a re-evaluation of theoretical approaches to crystal nucleation. This has been carried out for the droplet model of the classical nucleation theory (CNT), the self-consistent classical theory (SCCT), a phenomenological diffuse interface theory (DIT), and single- and two-field variants of the phase field theory that rely on either the usual double-well and interpolation functions (PFT/S1 and PFT/S2, respectively) or on a Ginzburg-Landau expanded free energy that reflects the crystal symmetries (PFT/GL1 and PFT/GL2). We find that the PFT/GL1, PFT/GL2, and DIT models predict fairly accurately the height of the nucleation barrier known from Monte Carlo simulations in the volume fraction range of 0.52 < varphi < 0.54, whereas the CNT, SCCT, PFT/S1, and PFT/S2 models underestimate it significantly. PMID:19320450

  4. Shock-induced phase transition in systems of hard spheres with internal degrees of freedom

    NASA Astrophysics Data System (ADS)

    Taniguchi, Shigeru; Mentrelli, Andrea; Zhao, Nanrong; Ruggeri, Tommaso; Sugiyama, Masaru

    2010-06-01

    Shock waves and shock-induced phase transitions are theoretically and numerically studied on the basis of the system of Euler equations with caloric and thermal equations of state for a system of hard spheres with internal degrees of freedom. First, by choosing the unperturbed state (the state before the shock wave) in the liquid phase, the Rankine-Hugoniot conditions are studied and their solutions are classified on the basis of the phase of the perturbed state (the state after the shock wave), being a shock-induced phase transition possible under certain conditions. With this regard, the important role of the internal degrees of freedom is shown explicitly. Second, the admissibility (stability) of shock waves is studied by means of the results obtained by Liu in the theory of hyperbolic systems. It is shown that another type of instability of a shock wave can exist even though the perturbed state is thermodynamically stable. Numerical calculations have been performed in order to confirm the theoretical results in the case of admissible shocks and to obtain the actual evolution of the wave profiles in the case of inadmissible shocks (shock splitting phenomena).

  5. Shock-induced phase transition in systems of hard spheres with internal degrees of freedom.

    PubMed

    Taniguchi, Shigeru; Mentrelli, Andrea; Zhao, Nanrong; Ruggeri, Tommaso; Sugiyama, Masaru

    2010-06-01

    Shock waves and shock-induced phase transitions are theoretically and numerically studied on the basis of the system of Euler equations with caloric and thermal equations of state for a system of hard spheres with internal degrees of freedom. First, by choosing the unperturbed state (the state before the shock wave) in the liquid phase, the Rankine-Hugoniot conditions are studied and their solutions are classified on the basis of the phase of the perturbed state (the state after the shock wave), being a shock-induced phase transition possible under certain conditions. With this regard, the important role of the internal degrees of freedom is shown explicitly. Second, the admissibility (stability) of shock waves is studied by means of the results obtained by Liu in the theory of hyperbolic systems. It is shown that another type of instability of a shock wave can exist even though the perturbed state is thermodynamically stable. Numerical calculations have been performed in order to confirm the theoretical results in the case of admissible shocks and to obtain the actual evolution of the wave profiles in the case of inadmissible shocks (shock splitting phenomena). PMID:20866522

  6. Disappearance of a Stacking Fault in Hard-Sphere Crystals under Gravity

    NASA Astrophysics Data System (ADS)

    Mori, A.; Suzuki, Y.; Matsuo, S.

    In the first part of this paper, a review is given on the mechanismfor the disappearance of an intrinsic stacking fault in a hard-sphere (HS) crystal under gravity, which we recently discovered by Monte Carlo (MC) simulations [A. Mori et al., J. Chem. Phys. 124 (2006), 17450; Mol. Phys. 105 (2007), 1377]. We have observed, in the case of fcc (001) stacking, that the intrinsic stacking fault running along an oblique direction shrunk through the gliding of a Shockley partial dislocation at the lower end of the stacking fault. In order to address the shortcomings and approximations of previous simulations, such as the use of periodic ] boundary condition (PBC) and the fact that the fcc (001) stacking had been realized by the stress from the small PBC box, we present an elastic strain energy calculation for an infinite system and a MC simulation result for HSs in a pyramidal pit under gravity. In particular, the geometry of the latter has already been tested experi mentally [S. Matsuo et al., Appl. Phys. Lett. 82 (2003), 4283]. The advantage of using a pyramidal pit as a template as well as the feasibility of the mechanism we describe is demonstrated.

  7. Electrical conductivity of a tight-binding hard-sphere model for hot fluid metals

    NASA Astrophysics Data System (ADS)

    Tarazona, P.; Chacn, E.; Vergs, J. A.; Reinaldo-Falagn, M.; Velasco, E.; Hernandez, J. P.

    2005-01-01

    Hot fluid metals are represented using a tight-binding hard-sphere model. Various treatments of the electrical conductivity of those disordered systems are presented and results are compared for equilibrium ionic configurations near the liquid-vapor phase coexistence. The configurations are obtained from self-consistent Monte Carlo simulations, with the cohesive energy being due to exact calculations of the valence electron delocalization. The disorder in the electronic hopping elements arises from that of the ionic positions, since the hopping is assumed to decay exponentially with distance. Calculated values of the electrical conductivity are found to span several orders of magnitude along the liquid-vapor coexistence curve, from typical metallic values in the low-temperature dense liquid metal, to a percolation-limited transition, to an insulator on the vapor branch. We compare the results based on the Kubo-Greenwood treatment, formulated appropriately for the model, with those of a mesoscopic approach based on the Greens function method for the quantum-coherent transport between two voltages leads, and examine results from two versions of the randomized phase model, which assumes a rapid decay of the quantum coherence. The various conductivity results are also compared with the experimental data for cesium.

  8. Preparation of PHSA-PMMA stabilizer for model hard sphere systems

    NASA Astrophysics Data System (ADS)

    Hollingsworth, Andrew; Russel, William; van Kats, Carlos; van Blaaderen, Alfons

    2006-03-01

    Sterically-stabilized colloidal particles are an excellent model hard-sphere system used by many groups. One of the original stabilizers used for such systems was developed and patented by ICI more than 30 years ago. It consists of a `comb-like' stabilizer of a poly(12-hydroxystearic acid) which is soluble in aliphatic hydrocarbons. These pendant PHSA chains are grafted to an insoluble poly(methyl methacrylate) backbone that strongly adsorbs to polymer particles and thus provides a means of anchoring stabilizer to particle surfaces. Unfortunately, the PHSA-g-PMMA stabilizer is not commercially available. Furthermore, the three-step procedure (Antl, et al. 1986) is generally regarded by non-chemists as technique intensive and time-consuming. We have systematically studied the PHSA-PMMA stabilizer synthesis with the goal of taking the mystery out of the protocol and making the entire synthesis reproducible. Several important details, not published in the literature, will be discussed, along with the analytical results from mass spectroscopy, proton NMR, acid titration and gel permeation chromatography, all of which were used to characterize the polymer and its precursors.

  9. Dynamical arrest in adhesive hard-sphere dispersions driven by rigidity percolation

    NASA Astrophysics Data System (ADS)

    Valadez-Pérez, Néstor E.; Liu, Yun; Eberle, Aaron P. R.; Wagner, Norman J.; Castañeda-Priego, Ramón

    2013-12-01

    One major goal in condensed matter is identifying the physical mechanisms that lead to arrested states of matter, especially gels and glasses. The complex nature and microscopic details of each particular system are relevant. However, from both scientific and technological viewpoints, a general, consistent and unified definition is of paramount importance. Through Monte Carlo computer simulations of states identified in experiments, we demonstrate that dynamical arrest in adhesive hard-sphere dispersions is the result of rigidity percolation with coordination number equal to 2.4. This corresponds to an established mechanism leading to mechanical transitions in network-forming materials [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.54.2107 54, 2107 (1985)]. Our findings connect the concept of critical gel formation in colloidal suspensions with short-range attractive interactions to the universal concept of rigidity percolation. Furthermore, the bond, angular, and local distributions along the gelation line are explicitly studied in order to determine the topology of the structure at the critical gel state.

  10. Assembly of vorticity-aligned hard-sphere colloidal strings in a simple shear flow.

    PubMed

    Cheng, Xiang; Xu, Xinliang; Rice, Stuart A; Dinner, Aaron R; Cohen, Itai

    2012-01-01

    Colloidal suspensions self-assemble into equilibrium structures ranging from face- and body-centered cubic crystals to binary ionic crystals, and even kagome lattices. When driven out of equilibrium by hydrodynamic interactions, even more diverse structures can be accessed. However, mechanisms underlying out-of-equilibrium assembly are much less understood, though such processes are clearly relevant in many natural and industrial systems. Even in the simple case of hard-sphere colloidal particles under shear, there are conflicting predictions about whether particles link up into string-like structures along the shear flow direction. Here, using confocal microscopy, we measure the shear-induced suspension structure. Surprisingly, rather than flow-aligned strings, we observe log-rolling strings of particles normal to the plane of shear. By employing Stokesian dynamics simulations, we address the mechanism leading to this out-of-equilibrium structure and show that it emerges from a delicate balance between hydrodynamic and interparticle interactions. These results demonstrate a method for assembling large-scale particle structures using shear flows. PMID:22198839

  11. Cavity averages for hard spheres in the presence of polydispersity and incomplete data.

    PubMed

    Schindler, Michael; Maggs, A C

    2015-09-01

    We develop a cavity-based method which allows to extract thermodynamic properties from position information in hard-sphere/disk systems. So far, there are available-volume and free-volume methods. We add a third one, which we call available volume after take-out, and which is shown to be mathematically equivalent to the others. In applications, where data sets are finite, all three methods show limitations, and they do this in different parameter ranges. We illustrate the principal equivalence and the limitations on data from molecular dynamics: In particular, we test robustness against missing data. We have in mind experimental limitations where there is a small polydispersity, say 4% in the particle radii, but individual radii cannot be determined. We observe that, depending on the used method, the errors in such a situation are easily 100% for the pressure and 10kT for the chemical potentials. Our work is meant as guideline to the experimentalists for choosing the right one of the three methods, in order to keep the outcome of experimental data analysis meaningful. PMID:26359237

  12. Thermodynamics and dynamics of the hard-sphere system: From stable to metastable states

    NASA Astrophysics Data System (ADS)

    Bomont, Jean-Marc; Bretonnet, Jean-Louis

    2014-08-01

    A set of three different scaling laws is investigated, which are devoted to link the transport properties, i.e. diffusion coefficient, shear viscosity, bulk viscosity and thermal conductivity, to the thermodynamic properties for the athermal hard-sphere system, over the wider range of packing fraction covering the stable and metastable regimes. Except for the thermal conductivity, the Rosenfeld (1999) [15] relation is found to be applicable to the stable states while the Adam and Gibbs (1965) [24] relation holds well for the metastable states. In contrast, the modified Cohen and Turnbull (1959) [25] relation proposed here gives sound support for a universal scaling law connecting the dynamic and thermodynamic properties, over the domain of packing fraction including the stable and metastable states. In particular, it is found that the most relevant control parameter is not the excess entropy, but the logarithm derivative of the excess entropy with respect to the packing fraction. In the same context, the Stokes-Einstein relation between the diffusion coefficient and the shear viscosity is also examined. The possible violation of the Stokes-Einstein relation is investigated over a large domain of packing fractions.

  13. Combined temperature and density series for fluid-phase properties. I. Square-well spheres.

    PubMed

    Elliott, J Richard; Schultz, Andrew J; Kofke, David A

    2015-09-21

    Cluster integrals are evaluated for the coefficients of the combined temperature- and density-expansion of pressure: Z = 1 + B2(?) ? + B3(?) ?(2) + B4(?) ?(3) + ?, where Z is the compressibility factor, ? is the packing fraction, and the B(i)(?) coefficients are expanded as a power series in reciprocal temperature, ?, about ? = 0. The methodology is demonstrated for square-well spheres with ? = [1.2-2.0], where ? is the well diameter relative to the hard core. For this model, the B(i) coefficients can be expressed in closed form as a function of ?, and we develop appropriate expressions for i = 2-6; these expressions facilitate derivation of the coefficients of the ? series. Expanding the B(i) coefficients in ? provides a correspondence between the power series in density (typically called the virial series) and the power series in ? (typically called thermodynamic perturbation theory, TPT). The coefficients of the ? series result in expressions for the Helmholtz energy that can be compared to recent computations of TPT coefficients to fourth order in ?. These comparisons show good agreement at first order in ?, suggesting that the virial series converges for this term. Discrepancies for higher-order terms suggest that convergence of the density series depends on the order in ?. With selection of an appropriate approximant, the treatment of Helmholtz energy that is second order in ? appears to be stable and convergent at least to the critical density, but higher-order coefficients are needed to determine how far this behavior extends into the liquid. PMID:26395690

  14. On the accurate direct computation of the isothermal compressibility for normal quantum simple fluids: Application to quantum hard spheres

    NASA Astrophysics Data System (ADS)

    Ses, Luis M.

    2012-06-01

    A systematic study of the direct computation of the isothermal compressibility of normal quantum fluids is presented by analyzing the solving of the Ornstein-Zernike integral (OZ2) equation for the pair correlations between the path-integral necklace centroids. A number of issues related to the accuracy that can be achieved via this sort of procedure have been addressed, paying particular attention to the finite-N effects and to the definition of significant error bars for the estimates of isothermal compressibilities. Extensive path-integral Monte Carlo computations for the quantum hard-sphere fluid (QHS) have been performed in the (N, V, T) ensemble under temperature and density conditions for which dispersion effects dominate the quantum behavior. These computations have served to obtain the centroid correlations, which have been processed further via the numerical solving of the OZ2 equation. To do so, Baxter-Dixon-Hutchinson's variational procedure, complemented with Baumketner-Hiwatari's grand-canonical corrections, has been used. The virial equation of state has also been obtained and several comparisons between different versions of the QHS equation of state have been made. The results show the reliability of the procedure based on isothermal compressibilities discussed herein, which can then be regarded as a useful and quick means of obtaining the equation of state for fluids under quantum conditions involving strong repulsive interactions.

  15. Near-wall dynamics of concentrated hard-sphere suspensions: comparison of evanescent wave DLS experiments, virial approximation and simulations.

    PubMed

    Liu, Yi; B?awzdziewicz, Jerzy; Cichocki, Bogdan; Dhont, Jan K G; Lisicki, Maciej; Wajnryb, Eligiusz; Young, Y-N; Lang, Peter R

    2015-10-01

    In this article we report on a study of the near-wall dynamics of suspended colloidal hard spheres over a broad range of volume fractions. We present a thorough comparison of experimental data with predictions based on a virial approximation and simulation results. We find that the virial approach describes the experimental data reasonably well up to a volume fraction of ?? 0.25 which provides us with a fast and non-costly tool for the analysis and prediction of evanescent wave DLS data. Based on this we propose a new method to assess the near-wall self-diffusion at elevated density. Here, we qualitatively confirm earlier results [Michailidou, et al., Phys. Rev. Lett., 2009, 102, 068302], which indicate that many-particle hydrodynamic interactions are diminished by the presence of the wall at increasing volume fractions as compared to bulk dynamics. Beyond this finding we show that this diminishment is different for the particle motion normal and parallel to the wall. PMID:26264420

  16. Application of the Born-Mayer Potential with a Hard-Sphere Scattering Kernel to Rarefied Hyperthermal Gas Flow Modeling

    NASA Astrophysics Data System (ADS)

    Dimpfl, William L.; Wysong, Ingrid J.; Gimelshein, Sergey F.; Braunstein, Matthew; Bernstein, Lawrence S.

    2008-12-01

    Direct Simulation Monte Carlo (DSMC) modeling of spacecraft engine plume radiance in low earth orbit shows significant errors in plume size and shape. These errors are mainly due to deficiencies in extrapolating low energy (<1 eV) Variable Hard-Sphere (VHS) and Variable Soft-Sphere (VSS) collision models to hyperthermal collision energies (>1 eV) important in plume modeling. The VHS and VSS scattering treatments are based on repulsive inverse-power-law inter-particle potential energy functions, which are not adequate at hyperthermal energies. In this work, we integrate the more physically realistic and accurate repulsive Born-Mayer exponential-interaction potential into the DSMC framework. We introduce the new Extended Variable Hard-Sphere (EVHS) and Extended Variable Soft-Sphere (EVSS) collision models, which significantly improve DSMC modeling at hyperthermal energies without an added computational penalty. Comparisons between VHS and EVHS modeling and data for argon over a range of energies and high altitude plume radiance data demonstrate the validity of the new treatment.

  17. Essential roles of protein-solvent many-body correlation in solvent-entropy effect on protein folding and denaturation: Comparison between hard-sphere solvent and water

    NASA Astrophysics Data System (ADS)

    Oshima, Hiraku; Kinoshita, Masahiro

    2015-04-01

    In earlier works, we showed that the entropic effect originating from the translational displacement of water molecules plays the pivotal role in protein folding and denaturation. The two different solvent models, hard-sphere solvent and model water, were employed in theoretical methods wherein the entropic effect was treated as an essential factor. However, there were similarities and differences in the results obtained from the two solvent models. In the present work, to unveil the physical origins of the similarities and differences, we simultaneously consider structural transition, cold denaturation, and pressure denaturation for the same protein by employing the two solvent models and considering three different thermodynamic states for each solvent model. The solvent-entropy change upon protein folding/unfolding is decomposed into the protein-solvent pair (PA) and many-body (MB) correlation components using the integral equation theories. Each component is further decomposed into the excluded-volume (EV) and solvent-accessible surface (SAS) terms by applying the morphometric approach. The four physically insightful constituents, (PA, EV), (PA, SAS), (MB, EV), and (MB, SAS), are thus obtained. Moreover, (MB, SAS) is discussed by dividing it into two factors. This all-inclusive investigation leads to the following results: (1) the protein-water many-body correlation always plays critical roles in a variety of folding/unfolding processes; (2) the hard-sphere solvent model fails when it does not correctly reproduce the protein-water many-body correlation; (3) the hard-sphere solvent model becomes problematic when the dependence of the many-body correlation on the solvent number density and temperature is essential: it is not quite suited to studies on cold and pressure denaturating of a protein; (4) when the temperature and solvent number density are limited to the ambient values, the hard-sphere solvent model is usually successful; and (5) even at the ambient values, however, the many-body correlation plays significant roles in the β-sheet formation and argument of relative stabilities of very similar structures of a protein. These results are argued in detail with respect to the four physically insightful constituents and the two factors mentioned above. The relevance to the absence or presence of hydrogen-bonding properties in the solvent is also discussed in detail.

  18. Essential roles of protein-solvent many-body correlation in solvent-entropy effect on protein folding and denaturation: Comparison between hard-sphere solvent and water

    SciTech Connect

    Oshima, Hiraku; Kinoshita, Masahiro

    2015-04-14

    In earlier works, we showed that the entropic effect originating from the translational displacement of water molecules plays the pivotal role in protein folding and denaturation. The two different solvent models, hard-sphere solvent and model water, were employed in theoretical methods wherein the entropic effect was treated as an essential factor. However, there were similarities and differences in the results obtained from the two solvent models. In the present work, to unveil the physical origins of the similarities and differences, we simultaneously consider structural transition, cold denaturation, and pressure denaturation for the same protein by employing the two solvent models and considering three different thermodynamic states for each solvent model. The solvent-entropy change upon protein folding/unfolding is decomposed into the protein-solvent pair (PA) and many-body (MB) correlation components using the integral equation theories. Each component is further decomposed into the excluded-volume (EV) and solvent-accessible surface (SAS) terms by applying the morphometric approach. The four physically insightful constituents, (PA, EV), (PA, SAS), (MB, EV), and (MB, SAS), are thus obtained. Moreover, (MB, SAS) is discussed by dividing it into two factors. This all-inclusive investigation leads to the following results: (1) the protein-water many-body correlation always plays critical roles in a variety of folding/unfolding processes; (2) the hard-sphere solvent model fails when it does not correctly reproduce the protein-water many-body correlation; (3) the hard-sphere solvent model becomes problematic when the dependence of the many-body correlation on the solvent number density and temperature is essential: it is not quite suited to studies on cold and pressure denaturating of a protein; (4) when the temperature and solvent number density are limited to the ambient values, the hard-sphere solvent model is usually successful; and (5) even at the ambient values, however, the many-body correlation plays significant roles in the β-sheet formation and argument of relative stabilities of very similar structures of a protein. These results are argued in detail with respect to the four physically insightful constituents and the two factors mentioned above. The relevance to the absence or presence of hydrogen-bonding properties in the solvent is also discussed in detail.

  19. Inquiry into thermodynamic behavior of hard sphere plus repulsive barrier of finite height

    NASA Astrophysics Data System (ADS)

    Zhou, Shiqi; Solana, J. R.

    2009-11-01

    A bridge function approximation is proposed to close the Ornstein-Zernike (OZ) integral equation for fluids with purely repulsive potentials. The performance of the bridge function approximation is then tested by applying the approximation to two kinds of repulsive potentials, namely, the square shoulder potential and the triangle shoulder potential. An extensive comparison between simulation and the OZ approach is performed over a wide density range for the fluid phase and several temperatures. It is found that the agreement between the two routes is excellent for not too low temperatures and satisfactory for extremely low temperatures. Then, this globally trustworthy OZ approach is used to investigate the possible existence or not of a liquid anomaly, i.e., a liquid-liquid phase transition at low temperatures and negative values of the thermal expansion coefficient in certain region of the phase diagram. While the existence of the liquid anomaly in the square shoulder potential has been previously predicted by a traditional first-order thermodynamic perturbation theory (TPT), the present investigation indicates that the liquid-liquid phase transition disappears in the OZ approach, so that its prediction by the first-order TPT is only an artifact originating from the low temperature inadequacy of the first-order TPT. However, the OZ approach indeed predicts negative thermal expansion coefficients. The present bridge function approximation, free of adjustable parameters, is suitable to be used within the context of a recently proposed nonhard sphere perturbation scheme.

  20. Tomography-based parameter estimation for sticky hard spheres as microstructure model for microwave modeling of snow

    NASA Astrophysics Data System (ADS)

    Lwe, Henning; Picard, Ghislain

    2014-05-01

    Within dense media radiative transfer (DMRT) simulations for microwave modeling of snow, the microstructure is often modeled as a discrete sphere assembly, e.g. sticky hard spheres (SHS). An objective mapping of this simplified microstructural model onto the bicontinuous structure of real snow is however missing. This ambiguity in the structural representation actually hinders a compelling comparison of DMRT with other models, such as the microwave emission model of layered snowpacks (MEMLS) which is formulated in terms of the two-point correlation function for continuous microstructures. To connect the different approaches, we have derived an analytical expression for the two-point correlation function for monodisperse SHS in the Percus-Yevick approximation. The analytical form of the two-point correlation function allows both, the evaluation of the scattering coefficient for SHS in the improved Born approximation for MEMLS, and an objective retrieval of the SHS parameters (sphere diameter and stickiness) from micro-computed tomography for DMRT. The parameter estimation is demonstrated for a comprehensive set of 167 different snow samples by providing stickiness values and comparing estimated sphere diameters to the specific surface area.

  1. PRELIMINARY COMMUNICATION The fourth and fifth virial coefficients of an additive hard sphere mixture from the Henderson-Chan formulae

    NASA Astrophysics Data System (ADS)

    Henderson Kwong-Yu Chan, Douglas

    The fourth and fifth virial coefficients of an additive hard sphere mixture, predicted from our recent formulae, are compared with the values calculated by Saija et al. and Enciso et al. Our formulae are supported by recent simulation and theoretical results. The Saija et al. and Enciso et al. values are calculated from what are purported to be exact formulae but differ drastically. In particular, Saija et al. claim that the fifth virial coefficient can be negative whereas Enciso et al. question this result. Our estimates agree closely with the results of Enciso et al. and the estimates of Boublik and Mansouri et al. This does not mean that the Boublik and Mansoori et al. equation of state is accurate under all circumstances, as our formulae lead to rather different results, including demixing, when the large spheres are present in small concentrations.

  2. Coordinated Hard Sphere Mixture (CHaSM): A simplified model for oxide and silicate melts at mantle pressures and temperatures

    NASA Astrophysics Data System (ADS)

    Wolf, Aaron S.; Asimow, Paul D.; Stevenson, David J.

    2015-08-01

    We develop a new model to understand and predict the behavior of oxide and silicate melts at extreme temperatures and pressures, including deep mantle conditions like those in the early Earth magma ocean. The Coordinated Hard Sphere Mixture (CHaSM) is based on an extension of the hard sphere mixture model, accounting for the range of coordination states available to each cation in the liquid. By utilizing approximate analytic expressions for the hard sphere model, this method is capable of predicting complex liquid structure and thermodynamics while remaining computationally efficient, requiring only minutes of calculation time on standard desktop computers. This modeling framework is applied to the MgO system, where model parameters are trained on a collection of crystal polymorphs, producing realistic predictions of coordination evolution and the equation of state of MgO melt over a wide range of pressures and temperatures. We find that the typical coordination number of the Mg cation evolves continuously upward from 5.25 at 0 GPa to 8.5 at 250 GPa. The results produced by CHaSM are evaluated by comparison with predictions from published first-principles molecular dynamics calculations, indicating that CHaSM is accurately capturing the dominant physics controlling the behavior of oxide melts at high pressure. Finally, we present a simple quantitative model to explain the universality of the increasing Grneisen parameter trend for liquids, which directly reflects their progressive evolution toward more compact solid-like structures upon compression. This general behavior is opposite that of solid materials, and produces steep adiabatic thermal profiles for silicate melts, thus playing a crucial role in magma ocean evolution.

  3. Wave functions of the super-Tonks-Girardeau gas and the trapped one-dimensional hard-sphere Bose gas

    SciTech Connect

    Girardeau, M. D.; Astrakharchik, G. E.

    2010-06-15

    Recent theoretical and experimental results demonstrate a close connection between the super-Tonks-Girardeau (STG) gas and a one-dimensional (1D) hard-sphere Bose (HSB) gas with hard-sphere diameter nearly equal to the 1D scattering length a{sub 1D} of the STG gas, a highly excited gaslike state with nodes only at interparticle separations |x{sub jl}|=x{sub node{approx_equal}}a{sub 1D}. It is shown herein that when the coupling constant g{sub B} in the Lieb-Liniger interaction g{sub B{delta}}(x{sub jl}) is negative and |x{sub 12}|{>=}x{sub node}, the STG and HSB wave functions for N=2 particles are not merely similar, but identical; the only difference between the STG and HSB wave functions is that the STG wave function allows a small penetration into the region |x{sub 12}|hard-sphere diameter a{sub hs}=x{sub node}, the HSB wave function vanishes when |x{sub 12}|2. The STG and HSB wave functions for N=2 are given exactly in terms of a parabolic cylinder function, and for N{>=}2, x{sub node} is given accurately by a simple parabola. The metastability of the STG phase generated by a sudden change of the coupling constant from large positive to large negative values is explained in terms of the very small overlap between the ground state of the Tonks-Girardeau gas and collapsed cluster states.

  4. Perturbation and variational approach for the equation of state for hard-sphere and LennardJones fluids

    NASA Astrophysics Data System (ADS)

    B. Khasare, S.

    2012-04-01

    The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state (EOS) for a mixture of hard sphere (HS), LennardJones (LJ) fluids. A suitable flexible functional form for the radial distribution function G(R) is assumed for the mixture, with R as a variable. The function G(R) has an arbitrary parameter m and a different equation of state can be obtained with a suitable choice of m. For m = 0.75 and m = 0.83 results are close to molecular dynamics (MD) result for pure HS and LJ fluid respectively.

  5. Many-fluid Onsager density functional theories for orientational ordering in mixtures of anisotropic hard-body fluids.

    PubMed

    Malijevsk, Alexandr; Jackson, George; Varga, Szabolcs

    2008-10-14

    The extension of Onsager's second-virial theory [L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949)] for the orientational ordering of hard rods to mixtures of nonspherical hard bodies with finite length-to-breadth ratios is examined using the decoupling approximations of Parsons [Phys. Rev. A 19, 1225 (1979)] and Lee [J. Chem. Phys. 86, 6567 (1987); 89, 7036 (1988)]. Invariably the extension of the Parsons-Lee (PL) theory to mixtures has in the past involved a van der Waals one-fluid treatment in which the properties of the mixture are approximated by those of a reference one-component hard-sphere fluid with an effective diameter which depends on the composition of the mixture and the molecular parameters of the various components; commonly this is achieved by equating the molecular volumes of the effective hard sphere and of the components in the mixture and is referred to as the PL theory of mixtures. It is well known that a one-fluid treatment is not the most appropriate for the description of the thermodynamic properties of isotropic fluids, and inadequacies are often rectified with a many-fluid (MF) theory. Here, we examine MF theories which are developed from the virial theorem and the virial expansion of the Helmholtz free energy of anisotropic fluid mixtures. The use of the decoupling approximation of the pair distribution function at the level of a multicomponent hard-sphere reference system leads to our MF Parsons (MFP) theory of anisotropic mixtures. Alternatively the mapping of the virial coefficients of the hard-body mixtures onto those of equivalent hard-sphere systems leads to our MF Lee (MFL) theory. The description of the isotropic-nematic phase behavior of binary mixtures of hard Gaussian overlap particles is used to assess the adequacy of the four different theories, namely, the original second-virial theory of Onsager, the usual PL one-fluid theory, and the MF theories based on the Lee (MFL) and Parsons (MFP) approaches. A comparison with the simulation data for the mixtures studied by Zhou et al. [J. Chem. Phys. 120, 1832 (2004)] suggests that the Parsons MF description (MFP) provides the most accurate representation of the properties of the isotropic-nematic ordering transition and density (pressure) dependence of the order parameters. PMID:19045155

  6. Disordered strictly jammed binary sphere packings attain an anomalously large range of densities.

    PubMed

    Hopkins, Adam B; Stillinger, Frank H; Torquato, Salvatore

    2013-08-01

    Previous attempts to simulate disordered binary sphere packings have been limited in producing mechanically stable, isostatic packings across a broad spectrum of packing fractions. Here we report that disordered strictly jammed binary packings (packings that remain mechanically stable under general shear deformations and compressions) can be produced with an anomalously large range of average packing fractions 0.634???0.829 for small to large sphere radius ratios ? restricted to ??0.100. Surprisingly, this range of average packing fractions is obtained for packings containing a subset of spheres (called the backbone) that are exactly strictly jammed, exactly isostatic, and also generated from random initial conditions. Additionally, the average packing fractions of these packings at certain ? and small sphere relative number concentrations x approach those of the corresponding densest known ordered packings. These findings suggest for entropic reasons that these high-density disordered packings should be good glass formers and that they may be easy to prepare experimentally. We also identify an unusual feature of the packing fraction of jammed backbones (packings with rattlers excluded). The backbone packing fraction is about 0.624 over the majority of the ?-x plane, even when large numbers of small spheres are present in the backbone. Over the (relatively small) area of the ?-x plane where the backbone is not roughly constant, we find that backbone packing fractions range from about 0.606 to 0.829, with the volume of rattler spheres comprising between 1.6% and 26.9% of total sphere volume. To generate isostatic strictly jammed packings, we use an implementation of the Torquato-Jiao sequential linear programming algorithm [Phys. Rev. E 82, 061302 (2010)], which is an efficient producer of inherent structures (mechanically stable configurations at the local maxima in the density landscape). The identification and explicit construction of binary packings with such high packing fractions could have important practical implications for granular composites where density is critical both to material properties and fabrication cost, including for solid propellants, concrete, and ceramics. The densities and structures of jammed binary packings at various ? and x are also relevant to the formation of a glass phase in multicomponent metallic systems. PMID:24032826

  7. A New Approach to the Equation of State of Silicate Melts: An Application of a Hard-Sphere Model to a Multi-Component System

    NASA Astrophysics Data System (ADS)

    Jing, Z.; Karato, S.

    2009-12-01

    Compressional properties of silicate liquids including density and bulk modulus at elevated pressures and temperatures (i.e., equation of state) are crucial to our understanding of melting processes such as the generation and differentiation of silicate melts in Earth and hence to explore the geophysical and geochemical consequences of melting. Unlike the solid and gaseous states of a matter for which there are widely accepted idealized models like crystal lattice and ideal gas, describing the properties of liquids are challenging because they are as dense as solids yet there is no long-range order in atomic positions. In the past, equations of state of silicate melts were treated in analogy with that of solids for which the change in internal energy due to the change in inter-atomic distance plays an important role. However, a comparison of compressional properties reveals fundamental differences between silicate liquids and solids: (1) Liquids have much smaller bulk moduli than solids; (2) Liquids do not follow Birch’s law (the relationship between bulk modulus and density) as opposed to solids; (3) The Grüneisen parameter increases with increasing pressure for (non-metallic) liquids but decreases for solids. (4) The radial distribution functions of liquids show that the inter-atomic distances in liquids do not change upon compression as much as solids do. In this work, we show that these differences are due to the different compressional mechanisms of liquids and solids. That is, liquids have the ability of changing structures, and hence the compression of liquids is largely controlled by the entropic contribution of the free energy in addition to the internal energy contribution (reduction in the inter-atomic distances) that is available to solids. In order to account for the role of entropic contribution, we propose a new equation of state for multi-component silicate liquids based on the theory of hard-sphere mixtures. In this model, the cation-anion polyhedra for oxide components in liquids such as the SiO2 tetrahedra and MgO octahedra are considered as impenetrable rigid spheres. The geometrical arrangements of these spheres give the entropic contribution to compression, while the attraction between the spheres give the internal energy contribution to compression. We calibrate the equation of state using the experimental measurements on room-pressure density and bulk modulus of liquids. This equation of state provides a unified explanation for the experimental observations cited above including the bulk moduli of liquids as well as the pressure dependence of Grüneisen parameter. We will also discuss the effect of composition on melt density and other compressional properties based on this equation of state.

  8. A method for treating the passage of a charged hard sphere ion as it passes through a sharp dielectric boundary.

    PubMed

    Boda, Dezso; Henderson, Douglas; Eisenberg, Bob; Gillespie, Dirk

    2011-08-14

    In the implicit solvent models of electrolytes (such as the primitive model (PM)), the ions are modeled as point charges in the centers of spheres (hard spheres in the case of the PM). The surfaces of the spheres are not polarizable which makes these models appropriate to use in computer simulations of electrolyte systems where these ions do not leave their host dielectrics. The same assumption makes them inappropriate in simulations where these ions cross dielectric boundaries because the interaction energy of the point charge with the polarization charge induced on the dielectric boundary diverges. In this paper, we propose a procedure to treat the passage of such ions through dielectric interfaces with an interpolation method. Inspired by the "bubble ion" model (in which the ion's surface is polarizable), we define a space-dependent effective dielectric coefficient, ?(eff)(r), for the ion that overlaps with the dielectric boundary. Then, we replace the "bubble ion" with a point charge that has an effective charge q/?(eff)(r) and remove the portion of the dielectric boundary where the ion overlaps with it. We implement the interpolation procedure using the induced charge computation method [D. Boda, D. Gillespie, W. Nonner, D. Henderson, and B. Eisenberg, Phys. Rev. E 69, 046702 (2004)]. We analyze the various energy terms using a spherical ion passing through an infinite flat dielectric boundary as an example. PMID:21842924

  9. Liquid theory with high accuracy and broad applicability: Coupling parameter series expansion and non hard sphere perturbation strategy

    NASA Astrophysics Data System (ADS)

    Zhou, Shiqi

    2011-12-01

    Thermodynamic and structural properties of liquids are of fundamental interest in physics, chemistry, and biology, and perturbation approach has been fundamental to liquid theoretical approaches since the dawn of modern statistical mechanics and remains so to this day. Although thermodynamic perturbation theory (TPT) is widely used in the chemical physics community, one of the most popular versions of the TPT, i.e. Zwanzig (Zwanzig, R. W. J. Chem. Phys. 1954, 22, 1420-1426) 1st-order high temperature series expansion (HTSE) TPT and its 2nd-order counterpart under a macroscopic compressibility approximation of Barker-Henderson (Barker, J. A.; Henderson, D. J. Chem. Phys. 1967, 47, 2856-2861), have some serious shortcomings: (i) the nth-order term of the HTSE is involved with reference fluid distribution functions of order up to 2n, and the higher-order terms hence progressively become more complicated and numerically inaccessible; (ii) the performance of the HTSE rapidly deteriorates and the calculated results become even qualitatively incorrect as the temperature of interest decreases. This account deals with the developments that we have made over the last five years or so to advance a coupling parameter series expansion (CPSE) and a non hard sphere (HS) perturbation strategy that has scored some of its greatest successes in overcoming the above-mentioned difficulties. In this account (i) we expatiate on implementation details of our schemes: how input information indispensable to high-order truncation of the CPSE in both the HS and non HS perturbation schemes is calculated by an Ornstein-Zernike integral equation theory; how high-order thermodynamic quantities, such as critical parameters and excess constant volume heat capacity, are extracted from the resulting excess Helmholtz free energy with irregular and inevitable numerical errors; how to select reference potential in the non HS perturbation scheme. (ii) We give a quantitative analysis on why convergence speed of the CPSE in both the HS and non HS perturbation schemes is certainly faster than that of the HTSE and the HS perturbation scheme. (iii) We illustrate applications of the CPSE TPT in both the HS and non HS perturbation schemes in calculating thermodynamic properties of various coarse-grained potential function models and as input information of other liquid state theories such as a classical density functional theory (DFT), and also discuss, in the framework of classical DFT, the potential of our CPSE scheme in several typical problems of chemical physics interest. (iv) Finally, we consider several topics which are possibly expected to be settled in the immediate future and possible integration with other liquid state theory frameworks aiming to solve problems in complex fluids in both bulk and inhomogeneous states.

  10. Dynamics of Disorder-Order Transitions in Hard Sphere Colloidal Dispersions in micro-g

    NASA Technical Reports Server (NTRS)

    Zhu, J. X.; Li, M.; Phan, S. E.; Russel, W. B.; Chaikin, Paul M.; Rogers, Rick; Meyers, W.

    1996-01-01

    We performed a series of experiments on 0.518 millimeter PMMA spheres suspended in an index matching mixture of decalin and tetralin the microgravity environment provided by the Shuttle Columbia on mission STS-73. The samples ranged in concentration from 0.49 to 0.62. volume fraction (phi) of spheres, which covers the range in which liquid, coexistence, solid and glass phases are expected from Earth bound experiments. Light scattering was used to probe the static structure, and the particle dynamics. Digital and 35 mm photos provided information on the morphology of the crystals. In general, the crystallites grew considerably larger (roughly an order of magnitude larger) than the same samples with identical treatment in 1 g. The dynamic light scattering shows the typical short time diffusion and long time caging effects found in 1 g. The surprises that were encountered in microgravity include the preponderance of random hexagonal close packed (RHCP) structures and the complete absence of the expected face centered cubic (FCC) structure, existence of large dendritic crystals floating in the coexistence samples (where liquid and solid phases coexist) and the rapid crystallization of samples which exist only in glass phase under the influence of one g. These results suggest that colloidal crystal growth is profoundly effected by gravity in yet unrecognized ways. We suspect that the RCHP structure is related to the nonequilibrium growth that is evident from the presence of dendrites. An analysis of the dendritic growth instabilities is presented within the framework of the Ackerson-Schatzel equation.

  11. Further development of the approach of Peralta and Zwanzig. II. The drag on a sphere as a function of density

    NASA Astrophysics Data System (ADS)

    Keyes, T.; Morita, Terumitsu

    1981-11-01

    Our modification of the method of Peralta and Zwanzig for the calculation of the drag on a sphere is applied at high and low bath densities. We obtain Stokes law at high density and 0.82 times the exact result at low density. Thus, our theory gives a unified framework for calculation of the drag as a function of density.

  12. Uniform electron gases. III. Low-density gases on three-dimensional spheres

    NASA Astrophysics Data System (ADS)

    Agboola, Davids; Knol, Anneke L.; Gill, Peter M. W.; Loos, Pierre-Franois

    2015-08-01

    By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of Cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGF centers are found by solving the Thomson problem (i.e., the minimum-energy arrangement of n point charges) on the 3-sphere for various values of n. We have found 11 special values of n whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids the hyper-tetrahedron (n = 5), the hyper-octahedron (n = 8), and the 24-cell (n = 24) and a fourth is a highly symmetric structure (n = 13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy.

  13. Segregation in hard-sphere mixtures under gravity. An extension of Edwards approach with two thermodynamical parameters

    NASA Astrophysics Data System (ADS)

    Nicodemi, M.; Fierro, A.; Coniglio, A.

    2002-12-01

    We study segregation patterns in a hard-sphere binary model under gravity subject to sequences of taps. We discuss the appearance of the "Brazil nut" effect (where large particles move up) and the "reverse Brazil nut" effects in the stationary states reached by "tap" dynamics. In particular, we show that the stationary state depends only on two thermodynamical quantities: the gravitational energy of the first and of the second species, and not on the sample history. To describe the properties of the system, we generalize Edwards' approach by introducing a canonical distribution characterized by two configurational temperatures, conjugate to the energies of the two species. This is supported by Monte Carlo calculations showing that the average of several quantities over the tap dynamics and over such distribution coincide. The segregation problem can then be understood as an equilibrium statistical-mechanics problem with two control parameters.

  14. Direct Simulation of the Phase Behavior of Binary Hard-Sphere Mixtures: Test of the Depletion Potential Description

    NASA Astrophysics Data System (ADS)

    Dijkstra, Marjolein; van Roij, Ren; Evans, Robert

    1999-01-01

    We study the phase behavior of additive binary hard-sphere mixtures by direct computer simulation, using a new technique which exploits an analog of the Gibbs adsorption equation. The resulting phase diagrams, for size ratios q = 0.2,0.1, and 0.05, are in remarkably good agreement with those obtained from an effective one-component Hamiltonian based on pairwise additive depletion potentials, even in regimes of high packing (solid phases) and for relatively large size ratios ( q = 0.2) where one might expect the approximation of pairwise additivity to fail. Our results show that the depletion potential description accounts for the key features of the phase equilibria for q<=0.2.

  15. Testing a simple method for computing directly the bulk modulus by NPT simulation: The case of polydisperse hard sphere solids

    NASA Astrophysics Data System (ADS)

    Li, Da; Xu, Hong

    2015-10-01

    The bulk modulus of hard sphere solids has been computed directly by constant pressure Monte-Carlo simulations, using the histogram of the volume fluctuations. In considering first the one-component system, we show that the method is accurate in a large range of pressures, including high-pressure regime. The method is then applied to a polydisperse solid with relatively low polydispersity index. For illustrative purpose, we took a three-component mixture with symmetric size-distribution, and we studied the solid phase (fcc crystal) of this system. Our results show that the equation of state is very sensitive to the polydispersity. Furthermore, in the high-pressure region, where no (accurate) analytical fit for the equation of state exists, our simulations are able to predict the bulk modulus of such systems.

  16. Following the evolution of hard sphere glasses in infinite dimensions under external perturbations: compression and shear strain.

    PubMed

    Rainone, Corrado; Urbani, Pierfrancesco; Yoshino, Hajime; Zamponi, Francesco

    2015-01-01

    We consider the adiabatic evolution of glassy states under external perturbations. The formalism we use is very general. Here we use it for infinite-dimensional hard spheres where an exact analysis is possible. We consider perturbations of the boundary, i.e., compression or (volume preserving) shear strain, and we compute the response of glassy states to such perturbations: pressure and shear stress. We find that both quantities overshoot before the glass state becomes unstable at a spinodal point where it melts into a liquid (or yields). We also estimate the yield stress of the glass. Finally, we study the stability of the glass basins towards breaking into sub-basins, corresponding to a Gardner transition. We find that close to the dynamical transition, glasses undergo a Gardner transition after an infinitesimal perturbation. PMID:25615481

  17. Effective diffusion coefficients in random packings of polydisperse hard spheres from two-point and three-point correlation functions

    NASA Astrophysics Data System (ADS)

    Hlushkou, D.; Liasneuski, H.; Tallarek, U.; Torquato, S.

    2015-09-01

    We evaluate the effective diffusion coefficient Deff in random packings of polydisperse hard spheres with an analytical formula involving the three-point microstructural parameter ζ2. Bulk packings with solid volume fraction between ϕ = 0.54 and ϕ = 0.634 were computer-generated using experimentally determined particle size distributions characterized by different mean particle diameter and associated standard deviation. The parameter ζ2 was calculated from two- and three-point correlation functions S2 and S3, respectively, via an approach based on sampling templates. Results of the asymptotic analysis for S2 and S3 compare favorably with theoretical predictions. Effective diffusivities calculated by the approximate analytical formula are close to those obtained from simulations using a random-walk particle-tracking technique. The values of Deff are affected by the packings' solid volume fraction, the spatial positions of the spheres, and to a far lesser extent by the particles' polydispersity. The proposed numerical approach can be applied to evaluate effective diffusive transport properties of general two-phase materials just from the geometrical information embodied in ϕ and ζ2.

  18. Stability, Convergence to Self-Similarity and Elastic Limit for the Boltzmann Equation for Inelastic Hard Spheres

    NASA Astrophysics Data System (ADS)

    Mischler, S.; Mouhot, C.

    2009-06-01

    We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres, in the framework of so-called constant normal restitution coefficients {? in [0,1]} . In the physical regime of a small inelasticity (that is {? in [?_*,1)} for some constructive {?_* in [0,1)}) we prove uniqueness of the self-similar profile for given values of the restitution coefficient {? in [?_*,1)} , the mass and the momentum; therefore we deduce the uniqueness of the self-similar solution (up to a time translation). Moreover, if the initial datum lies in {L^1_3} , and under some smallness condition on {(1-?_*)} depending on the mass, energy and {L^1 _3} norm of this initial datum, we prove time asymptotic convergence (with polynomial rate) of the solution towards the self-similar solution (the so-called homogeneous cooling state). These uniqueness, stability and convergence results are expressed in the self-similar variables and then translate into corresponding results for the original Boltzmann equation. The proofs are based on the identification of a suitable elastic limit rescaling, and the construction of a smooth path of self-similar profiles connecting to a particular Maxwellian equilibrium in the elastic limit, together with tools from perturbative theory of linear operators. Some universal quantities, such as the quasi-elastic self-similar temperature and the rate of convergence towards self-similarity at first order in terms of (1-?), are obtained from our study. These results provide a positive answer and a mathematical proof of the Ernst-Brito conjecture [16] in the case of inelastic hard spheres with small inelasticity.

  19. Acoustic field induced in spheres with inhomogeneous density by external sources.

    PubMed

    Kokkorakis, Gerassimos C; Fikioris, John G

    2004-02-01

    Acoustic or electromagnetic fields induced in the interior of inhomogeneous penetrable bodies by external sources can be evaluated via well-known volume integral equations. For bodies of arbitrary shape and/or composition, for which separation of variables fails, a direct attack for the solution of these integral equations is the only available approach. In a previous paper by the same authors the scalar (acoustic) field in inhomogeneous spheres of arbitrary compressibility, but with constant density, was considered. In the present one the direct hybrid (analytical-numerical) method applied to the much simpler integral equation for spheres with constant density is generalized to densities that vary with r, theta, or even psi. This extension is by no means trivial, owing to the appearance of the derivatives of both the density and the unknown function in the volume integral, a fact necessitating a more subtle and accuracy-sensitive approach. Again, the spherical shape allows use of the orthogonal spherical harmonics and of Dini's expansions of a general type for the radial functions. The convergence of the latter, shown to be superior to other possible sets of orthogonal expansions, can be further optimized by the proper selection of a crucial parameter in their eigenvalue equation. PMID:15000160

  20. Nanopatterned ferroelectrics for ultrahigh density rad-hard nonvolatile memories.

    SciTech Connect

    Brennecka, Geoffrey L.; Stevens, Jeffrey; Scrymgeour, David; Gin, Aaron V.; Tuttle, Bruce Andrew

    2010-09-01

    Radiation hard nonvolatile random access memory (NVRAM) is a crucial component for DOE and DOD surveillance and defense applications. NVRAMs based upon ferroelectric materials (also known as FERAMs) are proven to work in radiation-rich environments and inherently require less power than many other NVRAM technologies. However, fabrication and integration challenges have led to state-of-the-art FERAMs still being fabricated using a 130nm process while competing phase-change memory (PRAM) has been demonstrated with a 20nm process. Use of block copolymer lithography is a promising approach to patterning at the sub-32nm scale, but is currently limited to self-assembly directly on Si or SiO{sub 2} layers. Successful integration of ferroelectrics with discrete and addressable features of {approx}15-20nm would represent a 100-fold improvement in areal memory density and would enable more highly integrated electronic devices required for systems advances. Towards this end, we have developed a technique that allows us to carry out block copolymer self-assembly directly on a huge variety of different materials and have investigated the fabrication, integration, and characterization of electroceramic materials - primarily focused on solution-derived ferroelectrics - with discrete features of {approx}20nm and below. Significant challenges remain before such techniques will be capable of fabricating fully integrated NVRAM devices, but the tools developed for this effort are already finding broader use. This report introduces the nanopatterned NVRAM device concept as a mechanism for motivating the subsequent studies, but the bulk of the document will focus on the platform and technology development.

  1. Development of a method for measuring the density of liquid sulfur at high pressures using the falling-sphere technique

    SciTech Connect

    Funakoshi, Ken-ichi; Nozawa, Akifumi

    2012-10-15

    We describe a new method for the in situ measurement of the density of a liquid at high pressure and high temperature using the falling-sphere technique. Combining synchrotron radiation X-ray radiography with a large-volume press, the newly developed falling-sphere method enables the determination of the density of a liquid at high pressure and high temperature based on Stokes' flow law. We applied this method to liquid sulfur and successfully obtained the density at pressures up to 9 GPa. Our method could be used for the determination of the densities of other liquid materials at higher static pressures than are currently possible.

  2. A Bhatnagar-Gross-Krook-like Model Kinetic Equation for a Granular Gas of Inelastic Rough Hard Spheres

    SciTech Connect

    Santos, Andres

    2011-05-20

    The Boltzmann collision operator for a dilute granular gas of inelastic rough hard spheres is much more intricate than its counterpart for inelastic smooth spheres. Now the one-body distribution function depends not only on the translational velocity v of the center of mass but also on the angular velocity {omega} of the particle. Moreover, the collision rules couple v and {omega}, involving not only the coefficient of normal restitution {alpha} but also the coefficient of tangential restitution {beta}. The aim of this paper is to propose an extension to inelastic rough particles of a Bhatnagar-Gross-Krook-like kinetic model previously proposed for inelastic smooth particles. The Boltzmann collision operator is replaced by the sum of three terms representing: (i) the relaxation to a two-temperature local equilibrium distribution, (ii) the action of a nonconservative drag force F proportional to v-u(u being the flow velocity), and (iii) the action of a nonconservative torque M equal to a linear combination of {omega} and {Omega}({Omega} being the mean angular velocity). The three coefficients in F and M are fixed to reproduce the Boltzmann collisional rates of change of {Omega} and of the two granular temperatures (translational and rotational). A simpler version of the model is also constructed in the form of two coupled kinetic equations for the translational and rotational velocity distributions. The kinetic model is applied to the simple shear flow steady state and the combined influence of {alpha} and {beta} on the shear and normal stresses and on the translational velocity distribution function is analyzed.

  3. Arrest scenarios in concentrated protein solutions - from hard sphere glasses to arrested spinodal decomposition

    NASA Astrophysics Data System (ADS)

    Stradner, Anna; Bucciarelli, Saskia; Casal, Lucia; Foffi, Giuseppe; Thurston, George; Farago, Bela; Schurtenberger, Peter

    2014-03-01

    The occurrence of an arrest transition in concentrated colloid suspensions and its dependence on the interaction potential is a hot topic in soft matter. Such arrest transitions can also occur in concentrated protein solutions, as they exist e.g. in biological cells or are increasingly used in pharmaceutical formulations. Here we demonstrate the applicability of concepts from colloid science to understand the dynamics of concentrated protein solutions. In this presentation we report a combination of 3D light scattering, small-angle X-ray scattering and neutron spin echo measurements to study the structural properties as well as the collective and self diffusion of proteins in highly concentrated solutions on the relevant length and time scales. We demonstrate that various arrest scenarios indeed exist for different globular proteins. The proteins chosen are different bovine lens crystallins. We report examples of hard and attractive glass transitions and arrested spinodal decomposition directly linked to the effective pair potentials determined in static scattering experiments for the different proteins. We discuss these different arrest scenarios in view of possible applications of dense protein solutions as well as in view of their possible relevance for living systems.

  4. The power of hard-sphere models for proteins: Understanding side-chain conformations and predicting thermodynamic stability

    NASA Astrophysics Data System (ADS)

    Zhou, Alice; O'Hern, Corey; Regan, Lynne

    2013-03-01

    We seek to dramatically improve computational protein design using minimal models that include only the dominant physical interactions. By modeling proteins with hard-sphere interactions and stereochemical constraints, we are able to explain the side-chain dihedral angle distributions for Leu, Ile, and other hydrophobic residues that are observed in protein crystal structures. We also consider inter-residue interactions on the distribution of side-chain dihedral angles for residues in the hydrophobic core of T4 lysozyme. We calculate the energetic and entropic contributions to the free energy differences between wildtype T4 lysozyme and several mutants involving Leu to Ala substitutions. We find a strong correlation between the entropy difference and the decrease in the melting temperature of the mutatants. These results emphasize that considering both entropy and enthalpy is crucial for obtaining a quantitative understanding of protein stability. NSF DMR-1006537 and PHY-1019147, the Raymond and Beverly Sackler Institute for Biological, Physical and Engineering Sciences, and Howard Hughes Medical Institute International Research Fellowship

  5. Quadrature-based moment closures for non-equilibrium flows: Hard-sphere collisions and approach to equilibrium

    NASA Astrophysics Data System (ADS)

    Icardi, M.; Asinari, P.; Marchisio, D. L.; Izquierdo, S.; Fox, R. O.

    2012-08-01

    Recently the Quadrature Method of Moments (QMOM) has been extended to solve several kinetic equations, in particular for gas-particle flows and rarefied gases in which the non-equilibrium effects can be important. In this work QMOM is tested as a closure for the dynamics of the Homogeneous Isotropic Boltzmann Equation (HIBE) with a realistic description for particle collisions, namely the hard-sphere model. The behaviour of QMOM far away and approaching the equilibrium is studied. Results are compared to other techniques such as the Grad's moment method (GM) and the off-Lattice Boltzmann Method (oLBM). Comparison with a more accurate and computationally expensive approach, based on the Discrete Velocity Method (DVM), is also carried out. Our results show that QMOM describes very well the evolution when it is far away from equilibrium, without the drawbacks of the GM and oLBM or the computational costs of DVM, but it is not able to accurately reproduce equilibrium and the dynamics close to it. Static and dynamic corrections to cure this behaviour are here proposed and tested.

  6. Global validity of the Master kinetic equation for hard-sphere systems

    NASA Astrophysics Data System (ADS)

    Tessarotto, M.; Cremaschini, C.; Asci, C.; Soranzo, A.; Tironi, G.

    2015-08-01

    Following the recent establishment of an exact kinetic theory realized by the Master kinetic equation which describes the statistical behavior of the Boltzmann-Sinai Classical Dynamical System (CDS), in this paper the problem is posed of the construction of the related global existence and regularity theorems. For this purpose, based on the global prescription of the same CDS for arbitrary single- and multiple-collision events, first global existence is extablished for the N-body Liouville equation which is written in Lagrangian differential and integral forms. This permits to reach the proof of global existence both of generic N-body probability density functions (PDF) as well as of particular solutions which maximize the statistical Boltzmann-Shannon entropy and are factorized in terms of the corresponding 1-body PDF. The latter PDF is shown to be uniquely defined and to satisfy the Master kinetic equation globally in the extended 1-body phase space. Implications concerning the global validity of the asymptotic Boltzmann equation and Boltzmann H-theorem are discussed.

  7. Molecular dynamics simulation of a piston driven shock wave in a hard sphere gas. Final Contractor ReportPh.D. Thesis

    NASA Technical Reports Server (NTRS)

    Woo, Myeung-Jouh; Greber, Isaac

    1995-01-01

    Molecular dynamics simulation is used to study the piston driven shock wave at Mach 1.5, 3, and 10. A shock tube, whose shape is a circular cylinder, is filled with hard sphere molecules having a Maxwellian thermal velocity distribution and zero mean velocity. The piston moves and a shock wave is generated. All collisions are specular, including those between the molecules and the computational boundaries, so that the shock development is entirely causal, with no imposed statistics. The structure of the generated shock is examined in detail, and the wave speed; profiles of density, velocity, and temperature; and shock thickness are determined. The results are compared with published results of other methods, especially the direct simulation Monte-Carlo method. Property profiles are similar to those generated by direct simulation Monte-Carlo method. The shock wave thicknesses are smaller than the direct simulation Monte-Carlo results, but larger than those of the other methods. Simulation of a shock wave, which is one-dimensional, is a severe test of the molecular dynamics method, which is always three-dimensional. A major challenge of the thesis is to examine the capability of the molecular dynamics methods by choosing a difficult task.

  8. The isotropic-nematic and nematic-nematic phase transition of binary mixtures of tangent hard-sphere chain fluids: an analytical equation of state.

    PubMed

    van Westen, Thijs; Vlugt, Thijs J H; Gross, Joachim

    2014-01-21

    An analytical equation of state (EoS) is derived to describe the isotropic (I) and nematic (N) phase of linear- and partially flexible tangent hard-sphere chain fluids and their mixtures. The EoS is based on an extension of Onsager's second virial theory that was developed in our previous work [T. van Westen, B. Oyarzn, T. J. H. Vlugt, and J. Gross, J. Chem. Phys. 139, 034505 (2013)]. Higher virial coefficients are calculated using a Vega-Lago rescaling procedure, which is hereby generalized to mixtures. The EoS is used to study (1) the effect of length bidispersity on the I-N and N-N phase behavior of binary linear tangent hard-sphere chain fluid mixtures, (2) the effect of partial molecular flexibility on the binary phase diagram, and (3) the solubility of hard-sphere solutes in I- and N tangent hard-sphere chain fluids. By changing the length bidispersity, two types of phase diagrams were found. The first type is characterized by an I-N region at low pressure and a N-N demixed region at higher pressure that starts from an I-N-N triphase equilibrium. The second type does not show the I-N-N equilibrium. Instead, the N-N region starts from a lower critical point at a pressure above the I-N region. The results for the I-N region are in excellent agreement with the results from molecular simulations. It is shown that the N-N demixing is driven both by orientational and configurational/excluded volume entropy. By making the chains partially flexible, it is shown that the driving force resulting from the configurational entropy is reduced (due to a less anisotropic pair-excluded volume), resulting in a shift of the N-N demixed region to higher pressure. Compared to linear chains, no topological differences in the phase diagram were found. We show that the solubility of hard-sphere solutes decreases across the I-N phase transition. Furthermore, it is shown that by using a liquid crystal mixture as the solvent, the solubility difference can by maximized by tuning the composition. Theoretical results for the Henry's law constant of the hard-sphere solute are in good agreement with the results from molecular simulation. PMID:25669397

  9. The isotropic-nematic and nematic-nematic phase transition of binary mixtures of tangent hard-sphere chain fluids: An analytical equation of state

    NASA Astrophysics Data System (ADS)

    van Westen, Thijs; Vlugt, Thijs J. H.; Gross, Joachim

    2014-01-01

    An analytical equation of state (EoS) is derived to describe the isotropic (I) and nematic (N) phase of linear- and partially flexible tangent hard-sphere chain fluids and their mixtures. The EoS is based on an extension of Onsager's second virial theory that was developed in our previous work [T. van Westen, B. Oyarzn, T. J. H. Vlugt, and J. Gross, J. Chem. Phys. 139, 034505 (2013)]. Higher virial coefficients are calculated using a Vega-Lago rescaling procedure, which is hereby generalized to mixtures. The EoS is used to study (1) the effect of length bidispersity on the I-N and N-N phase behavior of binary linear tangent hard-sphere chain fluid mixtures, (2) the effect of partial molecular flexibility on the binary phase diagram, and (3) the solubility of hard-sphere solutes in I- and N tangent hard-sphere chain fluids. By changing the length bidispersity, two types of phase diagrams were found. The first type is characterized by an I-N region at low pressure and a N-N demixed region at higher pressure that starts from an I-N-N triphase equilibrium. The second type does not show the I-N-N equilibrium. Instead, the N-N region starts from a lower critical point at a pressure above the I-N region. The results for the I-N region are in excellent agreement with the results from molecular simulations. It is shown that the N-N demixing is driven both by orientational and configurational/excluded volume entropy. By making the chains partially flexible, it is shown that the driving force resulting from the configurational entropy is reduced (due to a less anisotropic pair-excluded volume), resulting in a shift of the N-N demixed region to higher pressure. Compared to linear chains, no topological differences in the phase diagram were found. We show that the solubility of hard-sphere solutes decreases across the I-N phase transition. Furthermore, it is shown that by using a liquid crystal mixture as the solvent, the solubility difference can by maximized by tuning the composition. Theoretical results for the Henry's law constant of the hard-sphere solute are in good agreement with the results from molecular simulation.

  10. PREFACE: Classical density functional theory methods in soft and hard matter Classical density functional theory methods in soft and hard matter

    NASA Astrophysics Data System (ADS)

    Haataja, Mikko; Gránásy, László; Löwen, Hartmut

    2010-08-01

    Herein we provide a brief summary of the background, events and results/outcome of the CECAM workshop 'Classical density functional theory methods in soft and hard matter held in Lausanne between October 21 and October 23 2009, which brought together two largely separately working communities, both of whom employ classical density functional techniques: the soft-matter community and the theoretical materials science community with interests in phase transformations and evolving microstructures in engineering materials. After outlining the motivation for the workshop, we first provide a brief overview of the articles submitted by the invited speakers for this special issue of Journal of Physics: Condensed Matter, followed by a collection of outstanding problems identified and discussed during the workshop. 1. Introduction Classical density functional theory (DFT) is a theoretical framework, which has been extensively employed in the past to study inhomogeneous complex fluids (CF) [1-4] and freezing transitions for simple fluids, amongst other things. Furthermore, classical DFT has been extended to include dynamics of the density field, thereby opening a new avenue to study phase transformation kinetics in colloidal systems via dynamical DFT (DDFT) [5]. While DDFT is highly accurate, the computations are numerically rather demanding, and cannot easily access the mesoscopic temporal and spatial scales where diffusional instabilities lead to complex solidification morphologies. Adaptation of more efficient numerical methods would extend the domain of DDFT towards this regime of particular interest to materials scientists. In recent years, DFT has re-emerged in the form of the so-called 'phase-field crystal' (PFC) method for solid-state systems [6, 7], and it has been successfully employed to study a broad variety of interesting materials phenomena in both atomic and colloidal systems, including elastic and plastic deformations, grain growth, thin film growth, solid-liquid interface properties, glassy dynamics, nucleation and growth, and diffusive phase transformations at the nano- and mesoscales [8-16]. The appealing feature of DDFT (as applied to solid-state systems) is that it automatically incorporates diffusive dynamics with atomic scale spatial resolution, and it naturally incorporates multiple components, elastic strains, dislocations, free surfaces, and multiple crystalline orientations; all of these features are critical in modeling the behavior of solid-state systems. Similarities between the problems of interest to the two communities and the complementary nature of the methods they apply suggest that a direct interaction between them should be highly beneficial for both parties. Here we summarize some of the discussions during a three-day CECAM workshop in Lausanne (21-23 October 2009) which was organized in order to bring together researchers from the complex fluids and materials science communities and to foster the exchange of ideas between these two communities. During the course of the workshop, several open problems relevant to both fields (DFT and PFC) were identified, including developing better microscopically-informed density functionals, incorporating stochastic fluctuations, and accounting for hydrodynamic interactions. The goal of this special issue is to highlight recent progress in DFT and PFC approaches, and discuss key outstanding problems for future work. The rest of this introductory paper is organized as follows. In section 2, we give a brief overview of the current research topics addressed in this special issue. Then, in section 3, we present a collection of outstanding problems, which have been identified as important for further developments of the two fields and intensely debated at the CECAM workshop. Finally, we close the paper with a few concluding remarks. 2. Research topics addressed in this special issue This special issue consists of research papers that cover a broad range of interesting subjects, about a half of which are related to the theoretical materials science community and the other half came from the soft-matter community. We begin by discussing papers related to PFC. Diverse subjects related to the phase-field crystal model include exciting topics such as predicting/controlling the equilibrium phase behavior [19, 18, 17] and kinetics of epitaxial island formation on nano-membranes [20]. Moreover, phase-field crystal modeling has proved to be very successful in simulating homogeneous and heterogeneous crystal nucleation and growth, and several aspects of these phenomena are discussed in this issue [18, 21]. Finally, it is shown how to incorporate additional orientational degrees of freedom within the PFC approach to model liquid crystals [22]. On the DFT side, the other papers in this special issue deal with problems associated with advanced DFT techniques and applications. The existence of a structural instability in sub-critical crystalline fluctuations in a supercooled liquid within a square-gradient theory is discussed in [23]. Fundamental measure theory for hard-body systems is improved by discussing a correction term in detail, as discussed in [24]. A mean-field-like density functional for charges is applied to the effective interaction between charged colloids obtained within a cell model [25]. The remaining articles provide fundamental insight into how to supplement DDFT-type methods with hydrodynamics [26, 27], highlight the role of the projection operator technique in deriving dynamical density functional theories [28], and demonstrate how perturbation methods can be employed to compute the properties of solid-liquid interfaces [29]. This particular collection of papers demonstrates rather convincingly the significant potential that classical density functional techniques possess in modeling complex systems built of either soft or hard matter (or combinations thereof). While the PFC approach offers a simple and appealing means to simulate evolving microstructures in spatially extended system with atomic scale spatial resolution over diffusive time scales, DFT provides both its theoretical underpinning and (hopefully) the means to construct microscopically more quantitative density functionals for use in engineering materials. Outstanding issues within the PFC and DFT approaches, discussed next, will provide further opportunities for interactions between the PFC and DFT communities. 3. Important open issues and exciting avenues for further research In the following we summarize some of the exciting topics for future research, which were discussed during the CECAM workshop. They concern both fundamental problems and applications, all within the framework of DFT and PFC. Addressing these issues will provide a framework for future work in these two overlapping fields. (a) How to construct a reliable density functional (DF) for soft repulsions? Most of the recent developments in classical density functional theory were focussed on hard-sphere-like interactions in the framework of fundamental-measure-theory (FMT) [30-33]. While this approach can be extended to additive and nonadditive mixtures [34, 35] and to non-spherical hard objects [36, 37], it is much more difficult to include soft-core interactions, such as inverse-power-law pair-potentials. There have been attempts to include those, mainly using the Ramakrishnan-Yussouff [38] or the weighted-density [39-41] approximation, or other modifications (see e.g., [42, 43]), but the accuracy of these functionals are inferior to that of FMT for hard spheres. Clearly the FMT of Rosenfeld needs an extension for the hard-core Coulomb system. A complementary approach is to start from a density functional for hard orientable objects [36] and to integrate out the orientational degrees of freedom. This would lead to a softened effective repulsion between spherical objects. We mention finally that in the extreme limit of ultrasoft pair potentials, which are penetrable, the mean-field approximation provides a reliable functional [44]. (b) How to construct a reliable DF beyond perturbation theory? This is the key to developing accurate, predictive functionals for use in materials science problems. Typically an attractive tail in the interparticle interaction is treated within thermodynamic hard-sphere perturbation theory [45, 46], in most cases at the mean-field level. As this perturbative approach is only justified for weak attraction strengths, there is a great need to go beyond this perturbation theory. A general non-perturbative route, which could be helpful here, is to consider a functional for a mixture and reducing it to an effective one-component system. Following this idea, for example effective depletion attractions can be modeled for a one-component system by starting from the binary Asakura-Oosawa functional [34, 35]. This idea still needs to be exploited in a more general sense, i.e. for more general cross-interactions in the mixture. It could also be combined with the idea of using non-spherical hard objects and integrating out the orientational degrees of freedom. (c) How to apply the fundamental measure theory to the full phase diagram of lyotropic liquid crystals? There are already density-functional investigations of liquid-crystal phases of hard spherocylinders [47, 48], but the novel fundamental-measure-theory which was recently proposed for non-spherical objects[36] has never been applied to this problem. In fact, this new functional now needs numerical evaluation for liquid-crystal phases different from isotropic and nematic ones, such as smectic, columnar, plastic crystalline and full orientational ordered crystalline phases [49, 50]. This is mainly a pure numerical resolution problem since the density fields are sharply peaked in the solid phases and need enough grid points, which is at the moment a rather formidable challenge in three spatial dimensions. However, if only orientational degrees of freedoms are considered, the computational effort is greatly reduced; see, e.g., [36, 51, 52]. (d) The role of fluctuations in DDFT and PFC. There is a continuing debate about the role of noise in the dynamical density functional theory (see e.g. [53]) and correspondingly also in the phase-field crystal models. Derivations of DDFT from the Smoluchowski level [54] and also within the projection operator technique [5] quite naturally lead to a deterministic equation without any noise. Clearly this is an approximation, which becomes problematic in the vicinity of a critical point or in the case of nucleation problems, where the system has to leave a metastable minimum of the free energy; in the former case, fluctuations are required in order to capture the correct critical behavior (i.e., critical exponents), while in the latter case, fluctuations are needed to establish an escape route of the system from a metastable phase. Other approaches add noise on a more phenomenological level. However, the actual strength of the noise, though fundamentally correlated with the thermal energy, is not known exactly and is treated in most applications as a phenomenological fit parameter; see, e.g., [55, 56]. This problem is a very fundamental one, and, of course, shared by the DDFT and PFC approaches. In more general terms, the addition of noise to the equation of motion in continuum models is not without conceptual difficulties (see [57]), even if noise is properly discretized in the course of the numerical integration. With the noise added, the equilibrium physical properties of the system change. Furthermore, transformation kinetics generally depend on the spatial and temporal steps, and in the limit of infinitely small steps an ultraviolet 'catastrophe' (divergence of the free energy) may occur. Evidently, an 'ultraviolet cut-off', i.e. filtering out the highest frequencies, is required to regularize the unphysical singularity. In the PFC case, a straightforward choice for the cut-off length is the interparticle distance, which is expected to remove the unphysical, small wavelength fluctuations [58, 16, 59, 18]. Perhaps a more elegant way to handle this problem is via renormalizing the model parameters so that with noise one recovers the 'bare' physical properties (see the application of this approach for the Swift-Hohenberg model in [60]). However, further systematic investigations are needed in order to settle this issue. (e) The need to clarify the role of the adiabatic approximation. While DDFT can be derived from more microscopic equations, such as the Smoluchowski equation [54] or the Langevin equations [61] for the individual particles, a major approximation is invoked in the derivation, namely the so-called 'adiabatic approximation'. This approximation assumes that all other observables relax much faster than the one-particle density field [5]. Therefore, the nonequilibrium correlations are replaced by equilibrium ones corresponding to an inhomogeneous reference one-particle density [54]. This enables one to formulate the theory in terms of the time-dependent one-particle density field alone. What is still needed here is a more general theory which provides the next-leading order beyond the adiabatic approximation. This improved theory would not only provide more fundamental insight into the DDFT itself; it would also pave the way to many applications where the simpleDDFT fails. (f) How to apply and exploit DDFT for active matter? The collective behavior of self-propelled particles with internal driving motors is a topic of active research [62, 62]. Given that the particle dynamics can be described in terms of driven Brownian motion, a dynamical density functional theory can be derived in a straightforward manner. In a first application, DDFT was employed to describe aggregation phenomena near system boundaries for driven rod-like colloidal particles [64]. The potential of DDFT for 'active' particles should be exploited more in the future, as it provides a microscopic approach to investigate nonequilibrium effects, such as swarming and jamming. (g) How to construct a PFC model for inhomogeneous liquid crystals? The traditional PFC model [6, 7] describes a two-dimensional one-component solid phase by a single inhomogeneous sinusoidal density field. The PFC approach has been generalized to mixtures by including more than a single density field [11] and to anisotropic particles with a fixed orientation [65]. However, it has never been applied to liquid crystals which are made by particles with intrinsic orientational degrees of freedom. Based on discussion during the CECAM workshop, a link towards the PFC model has been elaborated and the corresponding PFC model for liquid crystals was derived, see article [22] in this special issue. The extended PFC model contains both the translational density and the local orientational degree of ordering as well as a local director field. The model exhibits stable isotropic, nematic, smectic A, columnar, plastic crystalline and orientationally ordered crystalline phases and bears therefore much richer phases than the original PFC. A large-scale numerical exploration of this PFC model still needs to be performed. The derivation exploits the connection between DDFT and PFC, which was highlighted in [66] for spherical particles, and is based on recent generalizations of DDFT to rod-like Brownian particles [67, 64]. (h) How to incorporate hydrodynamic interactions between particles in dense driven systems of colloids? In dense colloidal dispersions, hydrodynamic interactions between the particles play a major role in their collective behavior. While these interactions affect neither structural correlations nor the equilibrium phase behavior, they have a profound effect on the dynamics both in equilibrium and non-equilibrium [68]. Recently, DDFT was extended to include hydrodynamic interactions on the pairwise level of the mobility tensors [69]. This kind of DDFT needs more applications as well as a fundamental development towards higher-order mobility tensors beyond the pairwise level or to a description, which includes lubrication forces between colloidal particles at small interparticle separations. (i) How to systematically construct effective, low-frequency representations from DFT/DDFT? Given an accurate and predictive density functional, which incorporates interaction potentials between the constituent species in a multi-component system, building an effective description would be highly desirable as it would provide an alternative to purely atomistic approaches (e.g., molecular dynamics simulations) and enable the simulation of quantitative, microscopically-informed, continuum systems across diffusive time scales. The first challenge, of course, is the development of such functionals, as already discussed in item (b) above. Once this challenge has been overcome, the next step would be to project out the dynamics of the relevant degrees of freedom from the full DDFT description. Physically, one would expect that the shape of a single peak in the density would relax much faster than, say, the distance between peak centers. Therefore, it should be possible to `slave' the high-frequency modes associated with the peak shapes to the more slowly evolving modes with low spatial frequencies. (j) How to build numerically efficient, quantitative PFC models for a broad spectrum of metallic materials? Viewed as an extension of the traditional phase-field method (see, e.g., [70-74]. for comprehensive reviews), PFC incorporates microscopic physics (crystal symmetry, grain orientation, topological defects) in a phenomenological manner. A practical issue in numerically integrating the dynamic PFC equation is that the grid spacing is constrained to be a fraction of the lattice spacing (typically Δ x ~ a/8), making large-scale simulations challenging in three spatial dimensions. It is thus highly desirable to develop a methodology that would allow one to tune important materials parameters such as crystal symmetry, lattice spacing, elastic constants, surface energies and stresses, dislocation core energy, and dislocation mobility, without sacrificing numerical efficiency. The issue of constructing PFC free energies, which give rise to a given crystal symmetry, has been addressed very recently; see, e.g., [17-19]. Going beyond the question of crystal symmetry, an appealing possibility is to further develop the so-called amplitude equation approach [75-77]., in which the density field is essentially expressed in terms of slowly-varying envelope functions (i.e., amplitudes), modulated by the fundamental spatial periodicity of the density. In fact, it has been demonstrated recently that such an approach provides a truly multi-scale approach to studying phase transformations in solid-liquid systems [78]. The goal is to construct amplitude equations, which accurately incorporate, e.g., surface tension anisotropies for simulations of solid-solid, solid-liquid, and solid-vapor systems. Alternatively, one can work directly with the PFC density field and introduce additional model parameters which can be fitted so that a required set of physical properties is recovered, such as the properties of the solid-liquid interface in pure iron [79]. (k) How to simulate electronic materials with PFC? Ferroelectrics comprise an interesting class of materials, which undergo a structural phase transformation (typically cubic-to-tetragonal) below a Curie temperature and acquire a non-zero electric polarization. It has been suggested that the manipulation of these polarization domains by means of an external field can be exploited in novel non-volatile memory devices [80, 81]. The PFC approach would present an appealing means to study ferroelectrics exhibiting one or more (ferroic) order parameters, provided that the crystal lattice can be coupled to the local order parameter(s) in a physically-based manner. 4. Concluding remarks The workshop 'Classical density functional theory methods in soft and hard matter' has established the first contact between the soft-matter community working with advanced classical density functional techniques and a theoretical materials science community working with engineering materials and armed with a simple but numerically very efficient dynamical density functional technique, the phase-field crystal method. A large number of common problems have been identified, which represent challenges for both communities during the coming years. This has been borne out by the lively discussions and some of the provocative talks. The organizers think that the workshop proved to be a truly successful event, matching to the high standards of the CECAM workshops, and hope that the workshop will indeed catalyze a long-term interaction between the two communities. As a final note, we would like to emphasize that progress in the areas highlighted in this special issue will positively impact both fields, and we expect that these issues will provide the natural link for collaborations and intellectual exchanges between these traditionally separate-yet-allied fields. In particular, such activities would lead to significant improvements in the applicability and versatility of classical DFT methods in both soft and hard matter systems, for the common benefit of physicists, chemists, and materials scientists. References [1] Evans R 1979 Adv. Phys. 28 143 [2] Oxtoby D W 1991 Liquids, Freezing and the Glass Transition (Session LI (1989) of Les Houches Summer Schools of Theoretical Physics) (Amsterdam: North Holland) p 147 [3] Singh Y 1991 Phys. Rep. 207 351 [4] Löwen H 1994 Phys. Rep. 237 249 [5] Español P and Löwen H 2009 J. Chem. Phys. 131 244101 [6] Elder K R, Katakowski M, Haataja M and Grant M 2002 Phys. Rev. Lett. 88 245701 [7] Elder K R and Grant M 2004 Phys. Rev. E 70 051605 [8] Berry J, Grant M and Elder K R 2006 Phys. Rev. E 73 031609 [9] Stefanovic P, Haataja M and Provatas N 2006 Phys. Rev. Lett. 96 225504 [10] Wu K-A and Karma A 2007 Phys. Rev. B 76 184107 [11] Elder K R, Provatas N, Berry J, Stefanovic P and Grant M 2007 Phys. Rev. B 75 064107 [12] Berry J, Elder K R and Grant M 2008 Phys. Rev. E 77 061506 [13] Huang Z-F and Elder K R 2008 Phys. Rev. Lett. 101 158701 [14] Wu K-A and Voorhees P W 2009 Phys. Rev. B 80 125408 [15] Stefanovic P, Haataja M and Provatas N 2009 Phys. Rev. E 80 046107 [16] Tegze G, Gránásy L, Tóth G I, Podmaniczky F, Jaatinen A, Ala-Nissial T and Pusztai T 2009 Phys. Rev. Lett. 103 035702 [17] Jaatinen A and Ala-Nissila T 2010 Extended phase diagram of the three-dimensional phase field crystal model J. Phys.: Condens. Matter 22 205402 [18] Tóth G I, Tegze G, Pusztai T, Tóth G and Gránásy L 2010 Polymorphism, crystal nucleation and growth in the phase-field crystal model in 2D and 3D J. Phys.: Condens. Matter 22 364101 [19] Wu K-A, Plapp M and Voorhees P 2010 Controlling crystal symmetries in phase-field crystal models J. Phys.: Condens. Matter 22 364102 [20] Elder K R and Huang Z-F 2010 A phase field crystal study of epitaxial island formation on nanomembranes J. Phys.: Condens. Matter 22 364103 [21] Backofen R and Voigt A 2010 A phase-field-crystal approach to critical nuclei J. Phys.: Condens. Matter 22 364104 [22] Löwen H 2010 A phase-field-crystal model for liquid crystals J. Phys.: Condens. Matter 22 364105 [23] Harrowell P 2010 On the existence of a structural instability in sub-critical crystalline fluctuations in a supercooled liquid J. Phys.: Condens. Matter 22 364106 [24] Hansen-Goos H and Mecke K 2010 Tensorial density functional theory for non-spherical hard-body fluids J. Phys.: Condens. Matter 22 364107 [25] Denton A R 2010 Poisson-Boltzmann theory of charged colloids: limits of the cell model for salty suspensions J. Phys.: Condens. Matter 22 364108 [26] Rauscher M 2010 DDFT for Brownian particles and hydrodynamics J. Phys.: Condens. Matter 22 364109 [27] Marini Bettolo Marconi U and Melchionna S 2010 Dynamic density functional theory versus kinetic theory of simple fluids J. Phys.: Condens. Matter 22 364110 [28] Majaniemi S, Provatas N and Nonomura M 2010 Effective model hierarchies for dynamic and static classical density functional theories J. Phys.: Condens. Matter 22 364111 [29] Warshavsky V B and Song X 2010 Perturbation theory for solid-liquid interfacial free energies J. Phys.: Condens. Matter 22 364112 [30] Rosenfeld Y, Schmidt M, Löwen H and Tarazona P 1997 Phys. Rev. E 55 4245 [31] Roth R, Evans R, Lang A and Kahl G 2002 J. Phys: Condens. Matter 14 12063 [32] Tarazona P, Cuesta J A and Martinez-Raton Y 2008 Density Functional Theories of Hard Particle Systems (Springer Lecture Notes in Physics vol 753) (Berlin: Springer) p 247 [33] Roth R 2010 J. Phys: Condens. Matter 22 063102 [34] Schmidt M, Löwen H, Brader J M and Evans R 2000 Phys. Rev. Lett. 85 1934 [35] Schmidt M, Löwen H, Brader J M and Evans R 2002 J. Phys.: Condens. Matter 14 9353 [36] Hansen-Goos H and Mecke K 2009 Phys. Rev. Lett. 102 018302 [37] Esztermann A, Reich H and Schmidt M 2006 Phys. Rev. E 73 011409 [38] Ramakrishnan T V and Yussouff M 1979 Phys. Rev. B 19 2775 [39] Denton A R and Ashcroft N W 1989 Phys. Rev. A 39 4701 [40] Hasegawa M 1994 J. Phys. Soc. Japan 63 2215 [41] Kol A and Laird B B 1997 Mol. Phys. 90 951 [42] van Teeffelen S, Löwen H and Likos C N 2008 J. Phys.: Condens. Matter 20 404217 [43] van Teeffelen S, Hoffmann N, Likos C N and Löwen H 2006 Europhys. Lett. 75 583 [44] Likos C N, Hoffmann N, Löwen H and Louis A A 2002 J. Phys.: Condens. Matter 14 7681 [45] Curtin W A and Ashcroft N W 1986 Phys. Rev. Lett. 56 2775 [46] Likos C N, Németh Z T and Löwen H 1994 J. Phys.: Condens. Matter 6 10965 [47] Poniewierski A and Holyst R 1988 Phys. Rev. Lett. 61 2461 [48] Graf H and Löwen H 1999 J. Phys.: Condens. Matter 11 1435 [49] Bolhuis P and Frenkel D 1997 J. Chem. Phys. 106 666 [50] Frenkel D, Mulder B M and McTague J P 1984 Phys. Rev. Lett. 52 287 [51] Härtel A and Löwen H 2010 J. Phys.: Condens. Matter 22 104112 [52] Härtel A, Blaak R and Löwen H 2010 Towing, breathing, splitting, and overtaking in driven colloidal liquid crystals Phys. Rev. E 81 051703 [53] Archer A J and Rauscher M 2004 J. Phys. A: Math. Gen. 37 9325 [54] Archer A J and Evans R 2004 J. Chem. Phys. 121 4246 [55] Ramos J A P, Granato E, Achim C V, Ying S C, Elder K R and Ala-Nissila T 2008 Phys. Rev. E 78 031109 [56] Hubert J, Cheng M and Emmerich H 2009 J. Phys.: Condens. Matter 21 464108 [57] Plapp M 2010 Philos. Mag. submitted [58] Pusztai T, Tegze G, Tóth G I, Környei L, Bansel G, Fan Z and Gránásy L 2008 J. Phys.: Condens. Matter 20 404205 [59] Tegze G, Bansel G, Tóth G I, Pusztai T, Fan Z and Gránásy L 2009 J. Comput. Phys. 228 1612 [60] Gross N A, Ignatiev M and Chakraborty B 2000 Phys. Rev. E 62 6116 [61] Marconi V M B and Tarazona P 2000 J. Phys.: Condens. Matter 12 A413 [62] Toner J, Tu Y and Ramaswamy S 2005 Ann. Phys. 318 170 [63] Lauga E and Powers T R 2009 Rep. Prog. Phys. 72 096601 [64] Wensink H H and Löwen H 2008 Phys. Rev. E 78 031409 [65] Prieler R, Hubert J, Li D, Verleye B, Haberkern R and Emmerich H 2009 J. Phys.: Condens. Matter 21 464110 [66] van Teeffelen S, Backofen R, Voigt A and Löwen H 2009 Phys. Rev. E 79 051404 [67] Rex M, Wensink H H and Löwen H 2007 Phys. Rev. E 76 021403 [68] Dhont J K G 1996 An Introduction to Dynamics of Colloids (Amsterdam: Elsevier) [69] Rex M and Löwen H 2008 Phys. Rev. Lett. 101 148302 [70] Elder K R, Grant M, Provatas N and Kosterlitz J M 2001 Phys. Rev. E 64 021604 [71] Chen L Q 2002 Annu. Rev. Mat. Res. 32 113 [72] Boettinger W J, Warren J A, Beckermann C and Karma A 2002 Annu. Rev. Mat. Res. 32 163 [73] Gránásy L, Pusztai T and Warren J A 2004 J. Phys.: Condens. Matter 16 R1205 [74] Singer-Loginova I and Singer H M 2008 Rep. Prog. Phys. 71 106501 [75] Goldenfeld N, Athreya B P and Dantzig J A 2005 Phys. Rev. E 72 020601 [76] Yeon D-H, Huang Z-F, Elder K R and Thornton K 2010 Phil. Mag. 90 237 [77] Elder K R, Huang Z-F and Provatas N 2010 Phys. Rev. E 81 011602 [78] Athreya B P, Goldenfeld N, Dantzig J A, Greenwood M and Provatas N 2007 Phys. Rev. E 76 056706 [79] Jaatinen A, Achim C V, Elder K R and Ala-Nissila T 2009 Phys. Rev. E 80 031602 [80] Chu M-W et al 2004 Nat. Mater. 3 87 [81] Rudiger A and Waser J 2008 J. Alloy Compounds 449 2

  11. An effective medium approach for the elongational viscosity of non-colloidal and non-Brownian hard-sphere suspensions

    NASA Astrophysics Data System (ADS)

    Housiadas, Kostas D.

    2015-08-01

    An effective-medium fluid mechanics model based on the original idea first presented by Brinkman ["A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles," Appl. Sci. Res. 1, 27-34 (1949)] for the viscous force exerted by a flowing fluid on a dense swarm of fixed spherical particles is utilized for the prediction of the elongational viscosity of a non-colloidal, non-Brownian hard-sphere suspension in an incompressible Newtonian matrix fluid. The same model was explored by Housiadas and Tanner ["A model for the shear viscosity of non-colloidal suspensions with Newtonian matrix fluids," Rheol. Acta 53, 831-841 (2014)] for the derivation of an analytical formula for the bulk shear viscosity of the suspension as a function of the volume fraction of the solid phase, a formula which is in very good agreement with widely used semi-empirical relationships and available experimental data from the literature. In the present paper, it is assumed that a spherical particle is subject, in an average sense, to a far-field uniform uniaxial elongational flow and a suitable pressure gradient. Under steady, isothermal, creeping conditions, and imposing no-slip and no-penetration conditions at the surface of a particle in a stagnation point of the fluid and the far-field velocity and pressure profiles, the solution of the three-dimensional Brinkman equations is found analytically. The solution shows a faster decay of the velocity disturbances around a reference particle than the single-particle case. A volume average of the total stress tensor gives an analytical formula for the bulk elongational viscosity of the complex system as a function of the particle concentration. A significant increase of the elongation viscosity with increasing the particle concentration is predicted. The increase is larger than the corresponding increase of the shear viscosity, in qualitative accordance with the theoretical formula of Batchelor and Green ["The determination of the bulk stress in a suspension of spherical particles to order c2" J. Fluid Mech. 56(3), 401-427 (1972)]. The new formula reduces to Einstein's expression in the infinite dilution limit and agrees well with other theoretical formulas in the semi-dilute regime. Moreover, the agreement of the new formula with recently developed semi-empirical formulas over the whole concentration regime is remarkable. Finally, the model predictions perform very well, and better than other formulas, when compared with a few experimental data for extensional measurements of hard-particle suspensions from the literature.

  12. Plane Poiseuille flow of a sedimenting suspension of Brownian hard-sphere particles: Hydrodynamic stability and direct numerical simulations

    NASA Astrophysics Data System (ADS)

    Yiantsios, Stergios G.

    2006-05-01

    The pressure driven flow of a suspension of sedimenting Brownian hard-sphere particles in a plane channel is considered. The balance of gravity and Brownian forces leads to a stationary state where a concentration profile of the particles is established in the channel, with a transition from a viscous sediment to clear fluid. The hydrodynamic stability of the flow and the nonlinear evolution of unstable disturbances are studied numerically by spectral element/Fourier expansion techniques. Two modes of instability with different characteristics are identified. The first is of the Tollmien-Schlichting type, similar to the one present in single-fluid parallel shear flows. This instability appears at much lower Reynolds numbers than for a single fluid when the transition in viscosity is gradual and the sediment is receptive to the fluid motion in the bulk, that is, for relatively small colloidal particles well into the submicron range. An interesting feature, observed through three-dimensional numerical simulations, is the formation of longitudinal striation patterns in the sediment, reminiscent of drag reducing surfaces with organized roughness known as riblets. The second type of instability is similar to the interfacial instability in stratified shear flows with a jump in viscosity. This type of instability appears also at low Reynolds numbers, when the transition from sediment to clear fluid is sharper, that is, for relatively larger particles. This instability results in slow waves traveling with velocities characteristic of those in the sediment, and gives rise to a significant resuspension and formation of low concentration regions in the vicinity of the sediment. An interesting feature is the formation of patterns in the sediment reminiscent of sand ripples.

  13. Crystallization of Hard Sphere Colloids in Microgravity: Results of the Colloidal Disorder-Order Transition, CDOT on USML-2. Experiment 33

    NASA Technical Reports Server (NTRS)

    Zhu, Ji-Xiang; Chaikin, P. M.; Li, Min; Russel, W. B.; Ottewill, R. H.; Rogers, R.; Meyer, W. V.

    1998-01-01

    Classical hard spheres have long served as a paradigm for our understanding of the structure of liquids, crystals, and glasses and the transitions between these phases. Ground-based experiments have demonstrated that suspensions of uniform polymer colloids are near-ideal physical realizations of hard spheres. However, gravity appears to play a significant and unexpected role in the formation and structure of these colloidal crystals. In the microgravity environment of the Space Shuttle, crystals grow purely via random stacking of hexagonal close-packed planes, lacking any of the face-centered cubic (FCC) component evident in crystals grown in 1 g beyond melting and allowed some time to settle. Gravity also masks 33-539 the natural growth instabilities of the hard sphere crystals which exhibit striking dendritic arms when grown in microgravity. Finally, high volume fraction "glass" samples which fail to crystallize after more than a year in 1 g begin nucleation after several days and fully crystallize in less than 2 weeks on the Space Shuttle.

  14. Deriving snow hardness from density and its application to the 1-D snow cover model SNOWPACK

    NASA Astrophysics Data System (ADS)

    Monti, F.; Schweizer, J.

    2012-04-01

    Estimating snow density (?s) based on snow hardness and grain type is often exploited in snow science. In snow hydrology snow water equivalent (SWE) that strongly depends on ?s needs to be determined; in avalanche forecasting an appropriate calculation of ?s is crucial to assess the load on a possible weak layer. However, collecting ?s is time consuming and difficult to do for very thin layers, and thus a parameterisation of ?son hand hardness is useful. On the other hand, the 1D snow cover model SNOWPACK derives snow hardness on simulated snow density. Recently, a new snow settling parameterization was introduced in the model which affects the simulation of density so that a new calibration is needed. We established a relation between ?sand hand hardness which is representative for various climatic regions of the European Alps. Two data sets including 14'455 dry-snow layers with measured density, grain type and hand hardness were used to relate density to hand hardness for the major grain types. The data were collected in the surroundings of Davos (Switzerland) and in the Veneto region (Italy), and cover different climatic regions and elevations. We applied least square and robust regressions to explore the data. The regression equations for both data sets were generally in reasonable agreement. The data collected in the Veneto region showed a higher variance than those of Davos; nevertheless the Veneto data was normally distributed and the mean values of ?s and hand hardness were highly correlated (R2? 0.9). Only for the grain type melt forms the correlation was lower. The linear relations were then used for the model calibration of SNOWPACK. First hardness simulations obtained with the different settings of the model are promising as simulated hardness is in fair agreement with observed values

  15. Analytic Equations of State for the Generalized Lennard-Jones Fluid Based on the Ross Variational Perturbation Theory and the Percus-Yevick Radial Distribution Function of Hard Spheres

    NASA Astrophysics Data System (ADS)

    Xue, Xin-Ying; Sun, Jiu-Xun

    2009-04-01

    Analytic expressions for the equation of state and thermodynamic properties have been derived for a generalized Lennard-Jones fluid, based on the Ross variational perturbation theory and the analytic Percus-Yevick (PY) expression for the radial distribution function of hard spheres. It is shown that the variational procedure is absolutely convergent and the calculations are convenient and fast. Numerical calculations have been made within wide temperature and density ranges. The results show that the precision is equivalent to the non-analytic modified Weeks-Chandler- Anderson (mWCA) and complete analytic mean spherical approximation (MSA) theories as compared with computer simulation results. It is concluded that the analytic theory can be applied to research practical fluids within wide temperature and density ranges.

  16. A model for the post-collapse equilibrium of cosmological structure: truncated isothermal spheres from top-hat density perturbations

    NASA Astrophysics Data System (ADS)

    Shapiro, Paul R.; Iliev, Ilian T.; Raga, Alejandro C.

    1999-07-01

    The post-collapse structure of objects that form by gravitational condensation out of the expanding cosmological background universe is a key element in the theory of galaxy formation. Towards this end, we have reconsidered the outcome of the non-linear growth of a uniform, spherical density perturbation in an unperturbed background universe - the cosmological `top-hat' problem. We adopt the usual assumption that the collapse to infinite density at a finite time predicted by the top-hat solution is interrupted by a rapid virialization caused by the growth of small-scale inhomogeneities in the initial perturbation. We replace the standard description of the post-collapse object as a uniform sphere in virial equilibrium by a more self-consistent one as a truncated, non-singular, isothermal sphere in virial and hydrostatic equilibrium, including for the first time a proper treatment of the finite-pressure boundary condition on the sphere. The results differ significantly from both the uniform sphere and the singular isothermal sphere approximations for the post-collapse objects. The virial temperature that results is more than twice the previously used `standard value' of the post-collapse uniform sphere approximation, but 1.4 times smaller than that of the singular, truncated isothermal sphere approximation. The truncation radius is 0.554 times the radius of the top-hat at maximum expansion, and the ratio of the truncation radius to the core radius is 29.4, yielding a central density that is 514 times greater than at the surface and 1.8x10^4 times greater than that of the unperturbed background density at the epoch of infinite collapse predicted by the top-hat solution. For the top-hat fractional overdensity delta_L predicted by extrapolating the linear solution into the non-linear regime, the standard top-hat model assumes that virialization is instantaneous at delta_Ldelta_c=1.686 i.e. the epoch at which the non-linear top-hat reaches infinite density. The surface of the collapsing sphere meets that of the post-collapse equilibrium sphere slightly earlier, however, when delta_L=1.52. These results will have a significant effect on a wide range of applications of the Press-Schechter and other semi-analytical models to cosmology. We discuss the density profiles obtained here in relation to the density profiles for a range of cosmic structures, from dwarf galaxies to galaxy clusters, indicated by observation and by N-body simulation of cosmological structure formation, including the recent suggestion of a universal density profile for haloes in the cold dark matter (CDM) model. The non-singular isothermal sphere solution presented here predicts the virial temperature and integrated mass distribution of the X-ray clusters formed in the CDM model as found by detailed, 3D, numerical gas and N-body dynamical simulations remarkably well. This solution allows us to derive analytically the numerically calibrated mass-temperature and radius-temperature scaling laws for X-ray clusters, which were derived empirically by Evrard, Metzler & Navarro from simulation results for the CDM model.

  17. Analytic equation of state for exponential-six fluid based on the Ross variational perturbation theory and the Percus Yevick radial distribution function of hard spheres

    NASA Astrophysics Data System (ADS)

    Sun, Jiu-xun; Wu, Qiang; Cai, Lingcang; Jing, Fuqian

    2007-11-01

    The analytic expressions for equation of state and thermodynamic properties have been derived for the exp-6 fluids, by using the Ross variational perturbation theory and the analytic Percus-Yevick (PY) expression of radial distribution function of hard spheres. It is shown that the variational procedure is absolutely convergent and the calculations are fast. The comparison of the numerical results with the computer simulations shows that the precision of the analytic Ross theory is equivalent to the non-analytic modified Weeks-Chandler-Anderson (mWCA) theory, and is slightly better than the complicated optimized reference hypernetted chain (RHNC) theory.

  18. Co-pelletization of sewage sludge and biomass: the density and hardness of pellet.

    PubMed

    Jiang, Longbo; Liang, Jie; Yuan, Xingzhong; Li, Hui; Li, Changzhu; Xiao, Zhihua; Huang, Huajun; Wang, Hou; Zeng, Guangming

    2014-08-01

    In the present study, the effects of process parameters on pellet properties were investigated for the co-pelletization of sludge and biomass materials. The relaxed pellet density and Meyer hardness of pellets were identified. Scanning electron microscopy, FT-IR spectra and chemical analysis were conducted to investigate the mechanisms of inter-particular adhesion bonding. Thermogravimetric analysis was applied to investigate the combustion characteristics. Results showed that the pellet density was increased with the parameters increasing, such as pressure, sludge ratio and temperature. High hardness pellets could be obtained at low pressure, temperature and biomass size. The optimal moisture content for co-pelletization was 10-15%. Moreover, the addition of sludge can reduce the diversity of pellet hardness caused by the heterogeneity of biomass. Increasing ratio of sludge in the pellet would slow down the release of volatile. Synergistic effects of protein and lignin can be the mechanism in the co-pelletization of sludge and biomass. PMID:24935004

  19. Intercomparison of density and temperature profiles obtained by lidar, ionizatoin gauges, falling spheres, datasondes and radiosondes during the DYANA campaign

    NASA Technical Reports Server (NTRS)

    Lubken, F.-J.; Hillert, W.; Lehmacher, G.; Von Zahn, U.; Bittner, M.; Offermann, D.; Schmidlin, F. J.; Hauchecorne, A.; Mourier, M.; Czechowsky, P.

    1994-01-01

    During the course of the DYnamics Adapted Network for the Atmosphere (DYANA) campaign in early 1990, various techniques to measure densities and temperatures from the ground up to the lower thermosphere were employed. Some of these measurements were performed near simultaneously (maximum allowed time difference: 1 h) and at the same location, and therefore offered the unique chance of intercomparison of different techniques. In this study, we will report on intercomparisons of data from ground-based instruments (Rayleigh- and sodium-lidar), balloon-borne methods (datasondes and radiosondes) and rocket-borne techniques (falling spheres and ionization gauges). The main result is that there is good agreement between the various measurements when considering the error bars. Only occasionally did we notice small but systematic differences (e.g. for the datasondes above 65 km). The most extensive intercomparison was possible between the Rayleigh lidar and the falling sphere technique, both employed in Biscarrosse (44 deg N, 1 deg W). Concerning densities, excellent agreement was found below 63 km: the mean of the deviations is less than 1% and the root mean square (RMS) is approximately 3%. Systematic differences of the order of 5% were noticed around 67 km and above 80 km. The former can be accounted for by an instrumental effect of the falling sphere (Ma = 1 transition; Ma = Mach number), whereas the latter is tentatively explained by the presence of Mie scatterers in the upper mesosphere. Concerning temperatures, the agreement is excellent between 35 and 65 km: the mean of the deviations is less than +/- 3 K and the variability is +/- 5 K. The two systematic density differences mentioned above also affect the temperatures: between 65 and 80 km, the Rayleigh lidar temperatures are systematically lower than the falling sphere values by approximately 5 K.

  20. Resolving uncertainties in snow microstructure representation: The two-point correlation function for sticky hard spheres and tomography-based estimation of stickiness

    NASA Astrophysics Data System (ADS)

    Loewe, H.; Picard, G.

    2013-12-01

    The necessity of a grain size scaling factor and the interpretation of the stickiness parameter in dense media radiative transfer (DMRT) simulations has led to some controversy in microwave emission modeling of snow. Ambiguities originate from the representation of snow microstructure within DMRT as a discrete sphere assembly, e.g. sticky hard spheres (SHS), which is difficult to identify with the random, bicontinuous structure of real snow. This uncertainty in structural representation also hinders a compelling comparison of DMRT with other models, such as the microwave emission model of layered snowpacks (MEMLS) which is based on the two-point correlation function for continuous microstructures. As a remedy, we have derived an exact expression for the two-point correlation function for monodisperse SHS in the Percus-Yevick approximation as required to evaluate the scattering coefficient in the improved Born approximation in MEMLS. The SHS parameters, namely sphere diameter and stickiness, are objectively estimated for various snow samples by fitting the analytical expression to experimental data from micro-computed tomography.

  1. Microwave scattering coefficient of snow in MEMLS and DMRT-ML revisited: the relevance of sticky hard spheres and tomography-based estimates of stickiness

    NASA Astrophysics Data System (ADS)

    Lwe, H.; Picard, G.

    2015-04-01

    The description of snow microstructure in microwave models is often simplified to facilitate electromagnetic calculations. Within dense media radiative transfer (DMRT), the microstructure is commonly described by sticky hard spheres (SHS). An objective mapping of real snow onto SHS is however missing which prevents to use measured input parameters for DMRT. In contrast, the microwave emission model of layered snowpacks (MEMLS) employs a conceptually different approach, based on the two-point correlation function which is accessible by tomography. Here we show the equivalence of both electromagnetic approaches by reformulating their microstructural models in a common framework. Using analytical results for the two-point correlation function of hard spheres we show that the scattering coefficient in both models only differs by a factor which is close to unity, weakly dependent on ice volume fraction and independent of other microstructural details. Additionally, our analysis provides an objective retrieval method for the SHS parameters (diameter and stickiness) from tomography images. For a comprehensive data set we demonstrate the variability of stickiness and compare the SHS diameter to the optical equivalent diameter. Our results confirm the necessity of a large grain-size scaling when relating both diameters in the non-sticky case, as previously suggested by several authors.

  2. A variable hard sphere-based phenomenological inelastic collision model for rarefied gas flow simulations by the direct simulation Monte Carlo method

    NASA Astrophysics Data System (ADS)

    Prasanth, P. S.; Kakkassery, Jose K.; Vijayakumar, R.

    2012-04-01

    A modified phenomenological model is constructed for the simulation of rarefied flows of polyatomic non-polar gas molecules by the direct simulation Monte Carlo (DSMC) method. This variable hard sphere-based model employs a constant rotational collision number, but all its collisions are inelastic in nature and at the same time the correct macroscopic relaxation rate is maintained. In equilibrium conditions, there is equi-partition of energy between the rotational and translational modes and it satisfies the principle of reciprocity or detailed balancing. The present model is applicable for moderate temperatures at which the molecules are in their vibrational ground state. For verification, the model is applied to the DSMC simulations of the translational and rotational energy distributions in nitrogen gas at equilibrium and the results are compared with their corresponding Maxwellian distributions. Next, the Couette flow, the temperature jump and the Rayleigh flow are simulated; the viscosity and thermal conductivity coefficients of nitrogen are numerically estimated and compared with experimentally measured values. The model is further applied to the simulation of the rotational relaxation of nitrogen through low- and high-Mach-number normal shock waves in a novel way. In all cases, the results are found to be in good agreement with theoretically expected and experimentally observed values. It is concluded that the inelastic collision of polyatomic molecules can be predicted well by employing the constructed variable hard sphere (VHS)-based collision model.

  3. Microwave scattering coefficient of snow in MEMLS and DMRT-ML revisited: the relevance of sticky hard spheres and tomography-based estimates of stickiness

    NASA Astrophysics Data System (ADS)

    Lwe, H.; Picard, G.

    2015-11-01

    The description of snow microstructure in microwave models is often simplified to facilitate electromagnetic calculations. Within dense media radiative transfer (DMRT), the microstructure is commonly described by sticky hard spheres (SHS). An objective mapping of real snow onto SHS is however missing which prevents measured input parameters from being used for DMRT. In contrast, the microwave emission model of layered snowpacks (MEMLS) employs a conceptually different approach, based on the two-point correlation function which is accessible by tomography. Here we show the equivalence of both electromagnetic approaches by reformulating their microstructural models in a common framework. Using analytical results for the two-point correlation function of hard spheres, we show that the scattering coefficient in both models only differs by a factor which is close to unity, weakly dependent on ice volume fraction and independent of other microstructural details. Additionally, our analysis provides an objective retrieval method for the SHS parameters (diameter and stickiness) from tomography images. For a comprehensive data set we demonstrate the variability of stickiness and compare the SHS diameter to the optical equivalent diameter. Our results confirm the necessity of a large grain-size scaling when relating both diameters in the non-sticky case, as previously suggested by several authors.

  4. General Solution of Static Sphere of Perfect Fluid and Dust of Uniform Density Using Isotropic Line Element

    NASA Astrophysics Data System (ADS)

    Marathe, C. D.; Rawa, J. J.; Nikouravan, Bijan

    2012-12-01

    The general solution of a static sphere of perfect fluid of uniform density using isotropic line element has been obtained by using the additional condition of continuity at the boundary. Here it is shown that, this solution is a solution of equation of Wyman with an additional integrating constant. If we do not put the condition of continuity at the boundary, then it can be shown that as using equation of Wyman so the solution of static sphere of dust can be obtained using Wyman's solution by putting 0 in the solution, so that in terms 0 is for dust instead of in terms of fluid obtained by Wyman. The anomalies discussed in the present paper can be removed by new field equation. The new proposed field equation is given and it is shown that the new proposed equation can bring Newtonian approximation.

  5. Comparison of I-131 radioimmunotherapy tumor dosimetry: unit density sphere model versus patient-specific Monte Carlo calculations.

    PubMed

    Howard, David M; Kearfott, Kimberlee J; Wilderman, Scott J; Dewaraja, Yuni K

    2011-10-01

    High computational requirements restrict the use of Monte Carlo algorithms for dose estimation in a clinical setting, despite the fact that they are considered more accurate than traditional methods. The goal of this study was to compare mean tumor absorbed dose estimates using the unit density sphere model incorporated in OLINDA with previously reported dose estimates from Monte Carlo simulations using the dose planning method (DPMMC) particle transport algorithm. The dataset (57 tumors, 19 lymphoma patients who underwent SPECT/CT imaging during I-131 radioimmunotherapy) included tumors of varying size, shape, and contrast. OLINDA calculations were first carried out using the baseline tumor volume and residence time from SPECT/CT imaging during 6 days post-tracer and 8 days post-therapy. Next, the OLINDA calculation was split over multiple time periods and summed to get the total dose, which accounted for the changes in tumor size. Results from the second calculation were compared with results determined by coupling SPECT/CT images with DPM Monte Carlo algorithms. Results from the OLINDA calculation accounting for changes in tumor size were almost always higher (median 22%, range -1%-68%) than the results from OLINDA using the baseline tumor volume because of tumor shrinkage. There was good agreement (median -5%, range -13%-2%) between the OLINDA results and the self-dose component from Monte Carlo calculations, indicating that tumor shape effects are a minor source of error when using the sphere model. However, because the sphere model ignores cross-irradiation, the OLINDA calculation significantly underestimated (median 14%, range 2%-31%) the total tumor absorbed dose compared with Monte Carlo. These results show that when the quantity of interest is the mean tumor absorbed dose, the unit density sphere model is a practical alternative to Monte Carlo for some applications. For applications requiring higher accuracy, computer-intensive Monte Carlo calculation is needed. PMID:21939358

  6. Comparison of I-131 Radioimmunotherapy Tumor Dosimetry: Unit Density Sphere Model Versus Patient-Specific Monte Carlo Calculations

    PubMed Central

    Howard, David M.; Kearfott, Kimberlee J.; Wilderman, Scott J.

    2011-01-01

    Abstract High computational requirements restrict the use of Monte Carlo algorithms for dose estimation in a clinical setting, despite the fact that they are considered more accurate than traditional methods. The goal of this study was to compare mean tumor absorbed dose estimates using the unit density sphere model incorporated in OLINDA with previously reported dose estimates from Monte Carlo simulations using the dose planning method (DPMMC) particle transport algorithm. The dataset (57 tumors, 19 lymphoma patients who underwent SPECT/CT imaging during I-131 radioimmunotherapy) included tumors of varying size, shape, and contrast. OLINDA calculations were first carried out using the baseline tumor volume and residence time from SPECT/CT imaging during 6 days post-tracer and 8 days post-therapy. Next, the OLINDA calculation was split over multiple time periods and summed to get the total dose, which accounted for the changes in tumor size. Results from the second calculation were compared with results determined by coupling SPECT/CT images with DPM Monte Carlo algorithms. Results from the OLINDA calculation accounting for changes in tumor size were almost always higher (median 22%, range −1%–68%) than the results from OLINDA using the baseline tumor volume because of tumor shrinkage. There was good agreement (median −5%, range −13%–2%) between the OLINDA results and the self-dose component from Monte Carlo calculations, indicating that tumor shape effects are a minor source of error when using the sphere model. However, because the sphere model ignores cross-irradiation, the OLINDA calculation significantly underestimated (median 14%, range 2%–31%) the total tumor absorbed dose compared with Monte Carlo. These results show that when the quantity of interest is the mean tumor absorbed dose, the unit density sphere model is a practical alternative to Monte Carlo for some applications. For applications requiring higher accuracy, computer-intensive Monte Carlo calculation is needed. PMID:21939358

  7. Hardness of FeB{sub 4}: Density functional theory investigation

    SciTech Connect

    Zhang, Miao; Du, Yonghui; Gao, Lili; Lu, Mingchun; Lu, Cheng; Liu, Hanyu

    2014-05-07

    A recent experimental study reported the successful synthesis of an orthorhombic FeB{sub 4} with a high hardness of 62(5) GPa [H. Gou et al., Phys. Rev. Lett. 111, 157002 (2013)], which has reignited extensive interests on whether transition-metal borides compounds will become superhard materials. However, it is contradicted with some theoretical studies suggesting transition-metal boron compounds are unlikely to become superhard materials. Here, we examined structural and electronic properties of FeB{sub 4} using density functional theory. The electronic calculations show the good metallicity and covalent Fe–B bonding. Meanwhile, we extensively investigated stress-strain relations of FeB{sub 4} under various tensile and shear loading directions. The calculated weakest tensile and shear stresses are 40 GPa and 25 GPa, respectively. Further simulations (e.g., electron localization function and bond length along the weakest loading direction) on FeB{sub 4} show the weak Fe–B bonding is responsible for this low hardness. Moreover, these results are consistent with the value of Vickers hardness (11.7–32.3 GPa) by employing different empirical hardness models and below the superhardness threshold of 40 GPa. Our current results suggest FeB{sub 4} is a hard material and unlikely to become superhard (>40 GPa)

  8. Effective densities of hard coals as a function of their genetic characteristics

    SciTech Connect

    Dobronravov, V.F.

    1985-01-01

    A quantitative analysis has been made of the change in the effective densities of hard coals as a function of the stage of metamorphism, petrographic composition, and degree of reduction. In the sintering and in the leaning components, this index changes along a curve with a minimum at the medium states of metamorphism. The influence of the petrographic composition is a maximum in the region of fat coals and is the range of 0.04-0.07 g/cm/sup 3/. The influence of the degree of reduction is small and decreases with a rise in rank. A formula is proposed for calculating the effective densities of hard coals from their genetic parameters.

  9. Facile Route Using Highly Arrayed PMMA Spheres as Hard Template for the Fabrication of 3D Ordered Nanoporous MgO

    NASA Astrophysics Data System (ADS)

    Li, Hui-ning; Dai, Hong-xing; He, Hong; Tong Au, Chak

    2007-12-01

    Using magnesium nitrate as Mg source and regularly packed polymethyl methacrylate (PMMA) spheres were synthesized via a combined strategy of emulsifier-free emulsion polymerization and water floating technique as hard template, we fabricated ordered nanoporous magnesium oxide. The synthesized PMMA and MgO samples were characterized by N2 adsorption-desorption, X-ray diffraction, high-resolution scanning electron microscopy, transmission electron microscopy, and selected area electron diffraction. It was observed that the synthesized PMMA spheres possessed a uniform diameter of approximately 284 nm and were in a highly ordered array, and the MgO generated by using the PMMA-templating method exhibited polycrystallinity with three-dimensionally ordered pores. BET surface area of the synthesized MgO sample is 100.7 m2/g, pore volume is 0.46 cm3/g, wall thickness is 4-24 nm, and pore sizes are in the range of 10-120 nm. Such a 3D high-surface-area nanoporous strongly basic MgO is useful in the applications of catalyst supports and acidic gas adsorbents.

  10. A comparison of measured and predicted sphere shock shapes in hypersonic flows with density ratios from 4 to 19

    NASA Technical Reports Server (NTRS)

    Miller, C. G., III

    1975-01-01

    Measured shock shapes are presented for sphere and hemisphere models in helium, air, CF4, C2F6, and CO2 test gases, corresponding to normal-shock density ratios (primary factor governing shock detachment distance of blunt bodies at hypersonic speeds) from 4 to 19. These shock shapes were obtained in three facilities capable of generating the high density ratios experienced during planetary entry at hypersonic conditions; namely, the 6-inch expansion tube, with hypersonic CF4 tunnel, and pilot CF4 Mach 6 tunnel (with CF4 replaced by C2F6). Measured results are compared with several inviscid perfect-gas shock shape predictions, in which an effective ratio of specific heats is used as input, and with real-gas predictions which include effects of a laminar viscous layer and thermochemical nonequilibrium.

  11. First Results from a New Rigid Falling Sphere Probe to Measure Winds, Density, and Temperature in the Mesosphere and Lower Thermosphere

    NASA Astrophysics Data System (ADS)

    Fish, C. S.; Larsen, M. F.; Pfaff, R. F., Jr.; Fullmer, R.; Swenson, C.; Martineau, R.; Sanderson, W.; Pilinski, M.

    2014-12-01

    We outline the development, test, calibration, and results from the first flights of a new rigid falling sphere probe which were launched in the summers of 2011 and 2013 as part of the NASA Daytime Dynamo sounding rocket campaign at Wallops Island, Virginia. Using highly sensitive accelerometers in conjunction with GPS data, the new rigid falling sphere probe provides a new means to detect the neutral wind, density, and temperature measurements, primarily below approximately 130 km. Initial results will be shown and the accuracy of this technique will be assessed. The maturing of the falling sphere technique provides a possible complement to the well-established vapor trail technique.

  12. Unit-Sphere Anisotropic Multiaxial Stochastic-Strength Model Probability Density Distribution for the Orientation of Critical Flaws

    NASA Technical Reports Server (NTRS)

    Nemeth, Noel

    2013-01-01

    Models that predict the failure probability of monolithic glass and ceramic components under multiaxial loading have been developed by authors such as Batdorf, Evans, and Matsuo. These "unit-sphere" failure models assume that the strength-controlling flaws are randomly oriented, noninteracting planar microcracks of specified geometry but of variable size. This report develops a formulation to describe the probability density distribution of the orientation of critical strength-controlling flaws that results from an applied load. This distribution is a function of the multiaxial stress state, the shear sensitivity of the flaws, the Weibull modulus, and the strength anisotropy. Examples are provided showing the predicted response on the unit sphere for various stress states for isotropic and transversely isotropic (anisotropic) materials--including the most probable orientation of critical flaws for offset uniaxial loads with strength anisotropy. The author anticipates that this information could be used to determine anisotropic stiffness degradation or anisotropic damage evolution for individual brittle (or quasi-brittle) composite material constituents within finite element or micromechanics-based software

  13. COLLAPSE AND FRAGMENTATION OF MAGNETIC MOLECULAR CLOUD CORES WITH THE ENZO AMR MHD CODE. I. UNIFORM DENSITY SPHERES

    SciTech Connect

    Boss, Alan P.; Keiser, Sandra A.

    2013-02-20

    Magnetic fields are important contributors to the dynamics of collapsing molecular cloud cores, and can have a major effect on whether collapse results in a single protostar or fragmentation into a binary or multiple protostar system. New models are presented of the collapse of magnetic cloud cores using the adaptive mesh refinement code Enzo2.0. The code was used to calculate the ideal magnetohydrodynamics (MHD) of initially spherical, uniform density, and rotation clouds with density perturbations, i.e., the Boss and Bodenheimer standard isothermal test case for three-dimensional (3D) hydrodynamics codes. After first verifying that Enzo reproduces the binary fragmentation expected for the non-magnetic test case, a large set of models was computed with varied initial magnetic field strengths and directions with respect to the cloud core axis of rotation (parallel or perpendicular), density perturbation amplitudes, and equations of state. Three significantly different outcomes resulted: (1) contraction without sustained collapse, forming a denser cloud core; (2) collapse to form a single protostar with significant spiral arms; and (3) collapse and fragmentation into binary or multiple protostar systems, with multiple spiral arms. Comparisons are also made with previous MHD calculations of similar clouds with a barotropic equations of state. These results for the collapse of initially uniform density spheres illustrate the central importance of both magnetic field direction and field strength for determining the outcome of dynamic protostellar collapse.

  14. Expansion-free evolving spheres must have inhomogeneous energy density distributions

    SciTech Connect

    Herrera, L.; Le Denmat, G.; Santos, N. O.

    2009-04-15

    In a recent paper a systematic study on shearing expansion-free spherically symmetric distributions was presented. As a particular case of such systems, the Skripkin model was mentioned, which corresponds to a nondissipative perfect fluid with a constant energy density. Here we show that such a model is inconsistent with junction conditions. It is shown that in general for any nondissipative fluid distribution, the expansion-free condition requires the energy density to be inhomogeneous. As an example we consider the case of dust, which allows for a complete integration.

  15. The concept of collision strength and a unified kinetic calculation for hard-sphere interactions and inverse square force law interactions

    NASA Astrophysics Data System (ADS)

    Chang, Yongbin

    2003-12-01

    With a concept of collision strength and other associated definitions, a unified kinetic theory for both hard-sphere interactions and inverse square force law interactions is developed. Collision frequencies that associate with many kinds of physical terms are calculated and expressed by a series special function Υj(α,x). Among them are arbitrary higher order linear Fokker-Planck coefficients, collision frequency, and energy exchange frequency. In case of a two-temperature system, the total collision rate, energy exchange rate, and collision strength rate are calculated and expressed in a uniform expression. A primitive form of Coulomb logarithm 1/2Γ(0,hmin) is found by comparing the exact form of equilibration time with Spitzer's result. Many unifications are found from the unified expression. The threshold value of collision strength has unified activation energy in chemical reaction rate theory and ionization energy in Thomson's classical ionization theory. An incomplete gamma function has unified Arrhenius exponential coefficient in chemical reaction rate theory and Coulomb logarithm in plasma physics.

  16. Equilibrium theory of the hard sphere fluid and glasses in the metastable regime up to jamming. II. Structure and application to hopping dynamics.

    PubMed

    Jadrich, Ryan; Schweizer, Kenneth S

    2013-08-01

    Building on the equation-of-state theory of Paper I, we construct a new thermodynamically consistent integral equation theory for the equilibrium pair structure of 3-dimensional monodisperse hard spheres applicable up to the jamming transition. The approach is built on a two Yukawa generalized mean spherical approximation closure for the direct correlation function (DCF) beyond contact that reproduces the exact contact value of the pair correlation function and isothermal compressibility. The detailed construction of the DCF is guided by the desire to capture its distinctive features as jamming is approached. Comparison of the theory with jamming limit simulations reveals good agreement for many, but not all, of the key features of the pair correlation function. The theory is more accurate in Fourier space where predictions for the structure factor and DCF are accurate over a wide range of wavevectors from significantly below the first cage peak to very high wavevectors. New features of the equilibrium pair structure are predicted for packing fractions below jamming but well above crystallization. For example, the oscillatory DCF decays very slowly at large wavevectors for high packing fractions as a consequence of the unusual structure of the radial distribution function at small separations. The structural theory is used as input to the nonlinear Langevin equation theory of activated dynamics, and calculations of the alpha relaxation time based on single particle hopping are compared to recent colloid experiments and simulations at very high volume fractions. PMID:23927265

  17. Computational stability ranking of mutated hydrophobic cores in staphylococcal nuclease and T4 lysozyme using hard-sphere and stereochemical constraints

    NASA Astrophysics Data System (ADS)

    Virrueta, Alejandro; Zhou, Alice; O'Hern, Corey; Regan, Lynne

    2014-03-01

    Molecular dynamics methods have significantly advanced the understanding of protein folding and stability. However, current force-fields cannot accurately calculate and rank the stability of modified or de novo proteins. One possible reason is that current force-fields use knowledge-based corrections that improve dihedral angle sampling, but do not satisfy the stereochemical constraints for amino acids. I propose the use of simple hard-sphere models for amino acids with stereochemical constraints taken from high-resolution protein crystal structures. This model can enable a correct consideration of the entropy of side-chain rotations, and may be sufficient to predict the effects of single residue mutations in the hydrophobic cores of staphylococcal nuclease and T4 lysozyme on stability changes. I will computationally count the total number of allowed side-chain conformations Ω and calculate the associated entropy, S = kBln(Ω) , before and after each mutation. I will then rank the stability of the mutated cores based on my computed entropy changes, and compare my results with structural and thermodynamic data published by the Stites and Matthews groups. If successful, this project will provide a novel framework for the evaluation of entropic protein stabilities, and serve as a possible tool for computational protein design.

  18. Equilibrium and shear induced nonequilibrium phase behavior of PMMA microgel spheres

    SciTech Connect

    Paulin, S.E.; Ackerson, B.J.; Wolfe, M.S.

    1996-03-01

    Polymethylmethacrylate (PMMA) spheres suspended in benzyl alcohol are found to swell to more than two times that of their dry radius and have been observed to undergo an equilibrium phase transition from liquid to crystalline structure with increasing concentration. The width of the coexistence region is found to be narrower by nearly half compared to simulation results for hard sphere systems. Comparison of the measured freezing point and fractional density change upon melting with those calculated from soft sphere simulations are consistent with a purely repulsive interparticle potential on the order of 1/r{sup 20}. Analysis of powder pattern scattering profiles from samples in the crystallized region of the equilibrium phase diagram indicates crystallites made up of a registered random stacking of hexagonal close packed planes, similar to that found in monodisperse suspensions of hard spheres. With the application of oscillatory shear, nonequilibrium microstructures similar to those found in model hard sphere systems have been observed in these suspensions.

  19. Compressibility and hardness of Co-based bulk metallic glass: A combined experimental and density functional theory study

    SciTech Connect

    Wang Jianfeng; Li Ran; Xu Tao; Li Yan; Liu Zengqian; Huang Lu; Hua Nengbin; Zhang Tao; Xiao Ruijuan; Li Gong; Li Yanchun

    2011-10-10

    An incompressible Co{sub 54}Ta{sub 11}B{sub 35} bulk metallic glass (BMG) was investigated using in situ high-pressure synchrotron diffraction and nanoindendation. The elastic constants were deduced from the experiments based on the isotropic model. The Vickers hardness was measured to be 17.1 GPa. The elastic moduli and hardness are the highest values known in BMGs. The theoretically calculated elastic properties by density-functional study were well consistent with experimental measurements. The analysis of charge density and bonding character indicates the covalent character of Co-B and B-B bonds, underlying the unusually high elastic modulus and hardness in this material.

  20. THE FIRST HARD X-RAY POWER SPECTRAL DENSITY FUNCTIONS OF ACTIVE GALACTIC NUCLEUS

    SciTech Connect

    Shimizu, T. Taro; Mushotzky, Richard F.

    2013-06-10

    We present results of our power spectral density (PSD) analysis of 30 active galactic nuclei (AGNs) using the 58 month light curves from Swift's Burst Alert Telescope (BAT) in the 14-150 keV band. PSDs were fit using a Monte Carlo based algorithm to take into account windowing effects and measurement error. All but one source were found to be fit very well using an unbroken power law with a slope of {approx} - 1, consistent at low frequencies with previous studies in the 2-10 keV band, with no evidence of a break in the PSD. For five of the highest signal-to-noise ratio sources, we tested the energy dependence of the PSD and found no significant difference in the PSD at different energies. Unlike previous studies of X-ray variability in AGNs, we do not find any significant correlations between the hard X-ray variability and different properties of the AGN including luminosity and black hole mass. The lack of break frequencies and correlations seem to indicate that AGNs are similar to the high state of Galactic black holes.

  1. Applications of Robust, Radiation Hard AlGaN Optoelectronic Devices in Space Exploration and High Energy Density Physics

    SciTech Connect

    Sun, K.

    2011-05-04

    This slide show presents: space exploration applications; high energy density physics applications; UV LED and photodiode radiation hardness; UV LED and photodiode space qualification; UV LED AC charge management; and UV LED satellite payload instruments. A UV LED satellite will be launched 2nd half 2012.

  2. Structure and phase behaviors of confined two penetrable soft spheres

    NASA Astrophysics Data System (ADS)

    Kim, Eun-Young; Kim, Soon-Chul

    2016-04-01

    We study the phase behaviors of two penetrable soft spheres, whose interactions include the soft repulsion and attraction, in a hard spherical pore. The exact partition function, one-body density, and equation of state for the confined two penetrable soft spheres have been calculated using the Fourier transform method. The phase diagrams have been determined from the negative compressibility of the van der Waals type, which imitates the phase transition of many particle system. The addition of the soft repulsion and attraction beyond the soft-core potential gives rise to the van der Waals instability. The soft attraction beyond the soft-core potential significantly enhances the van der Waals instability, whereas the soft repulsion reduces the van der Waals instability. For two hard spheres and hard square-well spheres, the van der Waals instability is not observed. However, the addition of a short-range soft repulsion beyond the hard-core gives rise to the van der Waals instability.

  3. Low-dislocation-density epitatial layers grown by defect filtering by self-assembled layers of spheres

    DOEpatents

    Wang, George T.; Li, Qiming

    2013-04-23

    A method for growing low-dislocation-density material atop a layer of the material with an initially higher dislocation density using a monolayer of spheroidal particles to bend and redirect or directly block vertically propagating threading dislocations, thereby enabling growth and coalescence to form a very-low-dislocation-density surface of the material, and the structures made by this method.

  4. Halogen bonding from a hard and soft acids and bases perspective: investigation by using density functional theory reactivity indices.

    PubMed

    Pinter, Balazs; Nagels, Nick; Herrebout, Wouter A; De Proft, Frank

    2013-01-01

    Halogen bonds between the trifluoromethyl halides CF(3)Cl, CF(3)Br and CF(3)I, and dimethyl ether, dimethyl sulfide, trimethylamine and trimethyl phosphine were investigated using Pearson's hard and soft acids and bases (HSAB) concept with conceptual DFT reactivity indices, the Ziegler-Rauk-type energy-decomposition analysis, the natural orbital for chemical valence (NOCV) framework and the non-covalent interaction (NCI) index. It is found that the relative importance of electrostatic and orbital (charge transfer) interactions varies as a function of both the donor and acceptor molecules. Hard and soft interactions were distinguished and characterised by atomic charges, electrophilicity and local softness indices. Dual-descriptor plots indicate an orbital ? hole on the halogen similar to the electrostatic ? hole manifested in the molecular electrostatic potential. The predicted high halogen-bond-acceptor affinity of N-heterocyclic carbenes was evidenced in the highest complexation energy for the hitherto unknown CF(3) INHC complex. The dominant NOCV orbital represents an electron-density deformation according to a n??*-type interaction. The characteristic signal found in the reduced density gradient versus electron-density diagram corresponds to the non-covalent interaction between contact atoms in the NCI plots, which is the manifestation of halogen bonding within the NCI theory. The unexpected C-X bond strengthening observed in several cases was rationalised within the molecular orbital framework. PMID:23169478

  5. Catalytic, hollow, refractory spheres

    NASA Technical Reports Server (NTRS)

    Wang, Taylor G. (Inventor); Elleman, Daniel D. (Inventor); Lee, Mark C. (Inventor); Kendall, Jr., James M. (Inventor)

    1987-01-01

    Improved, heterogeneous, refractory catalysts are in the form of gas-impervious, hollow, thin-walled spheres (10) suitable formed of a shell (12) of refractory such as alumina having a cavity (14) containing a gas at a pressure greater than atmospheric pressure. The wall material may be itself catalytic or a catalytically active material coated onto the sphere as a layer (16), suitably platinum or iron, which may be further coated with a layer (18) of activator or promoter. The density of the spheres (30) can be uniformly controlled to a preselected value within .+-.10 percent of the density of the fluid reactant such that the spheres either remain suspended or slowly fall or rise through the liquid reactant.

  6. Catalytic hollow spheres

    NASA Technical Reports Server (NTRS)

    Wang, Taylor G. (Inventor); Elleman, Daniel D. (Inventor); Lee, Mark C. (Inventor); Kendall, Jr., James M. (Inventor)

    1986-01-01

    The improved, heterogeneous catalysts are in the form of gas-impervious, hollow, thin-walled spheres (10) suitably formed of a shell (12) of metal such as aluminum having a cavity (14) containing a gas at a pressure greater than atmospheric pressure. The wall material may be, itself, catalytic or the catalyst can be coated onto the sphere as a layer (16), suitably platinum or iron, which may be further coated with a layer (18) of activator or promoter. The density of the spheres (30) can be uniformly controlled to a preselected value within .+-.10 percent of the density of the fluid reactant such that the spheres either remain suspended or slowly fall or rise through the liquid reactant.

  7. Catalytic hollow spheres

    NASA Technical Reports Server (NTRS)

    Wang, Taylor G. (Inventor); Elleman, Daniel D. (Inventor); Lee, Mark C. (Inventor); Kendall, Jr., James M. (Inventor)

    1989-01-01

    The improved, heterogeneous catalysts are in the form of gas-impervious, hollow, thin-walled spheres (10) suitably formed of a shell (12) of metal such as aluminum having a cavity (14) containing a gas at a pressure greater than atmospheric pressure. The wall material may be, itself, catalytic or the catalyst can be coated onto the sphere as a layer (16), suitably platinum or iron, which may be further coated with a layer (18) of activator or promoter. The density of the spheres (30) can be uniformly controlled to a preselected value within .+-.10 percent of the density of the fluid reactant such that the spheres either remain suspended or slowly fall or rise through the liquid reactant.

  8. AlGaN UV LED and Photodiodes Radiation Hardness and Space Qualifications and Their Applications in Space Science and High Energy Density Physics

    SciTech Connect

    Sun, K. X.

    2011-05-31

    This presentation provides an overview of robust, radiation hard AlGaN optoelectronic devices and their applications in space exploration & high energy density physics. Particularly, deep UV LED and deep UV photodiodes are discussed with regard to their applications, radiation hardness and space qualification. AC charge management of UV LED satellite payload instruments, which were to be launched in late 2012, is covered.

  9. INFLUENCE OF ENERGY DENSITY OF DIFFERENT LIGHT SOURCES ON KNOOP HARDNESS OF A DUAL-CURED RESIN CEMENT

    PubMed Central

    Piva, Evandro; Correr, Loureno; Sinhoreti, Mario Alexandre Coelho; Consani, Simonides; Demarco, Flvio Fernando; Powers, John Michael

    2008-01-01

    The purpose of this study was to evaluate the Knoop hardness of a dual-cured resin-based luting cement irradiated with different light sources as well energy density through a ceramic sample. Three light-curing unit (LCUs) were tested: tungsten halogen light (HAL), light-emitting diode (LED) and xenon plasma-arc (PAC) lamp. Disc-shaped specimens were fabricated from a resin-based cement (Enforce). Three energy doses were used by modifying the irradiance (I) of each LCU and the irradiation time (T): 24 Jcm-2 (I/2x2T), 24 Jcm-2 (IxT) and 48 Jcm-2 (Ix2T). Energy doses were applied through a 2.0-mm-thick ceramic sample (Duceram Plus). Three groups underwent direct irradiation over the resin cement with the different LCUs and a chemically-activated group served as a control. Thirteen groups were tested (n=10). Knoop hardness number (KHN) means were obtained from cross-sectional areas. Two-way ANOVA and the Holm-Sidak method were used for statistical comparisons of activation mode and energy doses (?=5%). Application of 48 J.cm-2 energy dose through the ceramic using LED (50.52.8) and HAL (50.93.7) produced significantly higher KHN means (p<0.05) than the control (44.73.8). LED showed statistically similar performance to HAL. Only HAL showed a relationship between the increase of LCU energy dose and hardness increase. PMID:19089216

  10. A classical density-functional theory for describing water interfaces.

    PubMed

    Hughes, Jessica; Krebs, Eric J; Roundy, David

    2013-01-14

    We develop a classical density functional for water which combines the White Bear fundamental-measure theory (FMT) functional for the hard sphere fluid with attractive interactions based on the statistical associating fluid theory variable range (SAFT-VR). This functional reproduces the properties of water at both long and short length scales over a wide range of temperatures and is computationally efficient, comparable to the cost of FMT itself. We demonstrate our functional by applying it to systems composed of two hard rods, four hard rods arranged in a square, and hard spheres in water. PMID:23320706

  11. Colloidal rod-sphere mixtures: fluid-fluid interfaces and the Onsager limit.

    PubMed

    Brader, Joseph M; Esztermann, Ansgar; Schmidt, Matthias

    2002-09-01

    Using a geometry-based density functional theory we investigate the free interface between demixed bulk fluid phases of a colloidal mixture of hard spheres and vanishingly thin needles. Results are presented for the spatial and orientational density distributions of the particles, as well as for the interface tension. Density profiles display oscillations on the sphere-rich side of the interface provided the sphere liquid phase is on the oscillatory side of the Fisher-Widom line in the bulk phase diagram. Needles tend to align parallel (perpendicular) to the interface on the needle-rich (sphere-rich) side displaying biaxial (uniaxial) order. Furthermore, we generalize the theory to the Onsager limit for interacting rods, and give explicit expressions for the functional in simple geometries. PMID:12366111

  12. Volumetric density trends (TB/in.3) for storage components: TAPE, hard disk drives, NAND, and Blu-ray

    NASA Astrophysics Data System (ADS)

    Fontana, R. E.; Decad, G. M.; Hetzler, S. R.

    2015-05-01

    Memory storage components, i.e., hard disk drives, tape cartridges, solid state drives using Flash NAND chips, and now optical cartridges using Blu-ray disks, have provided annual increases in memory capacity by decreasing the area of the memory cell associated with the technology of these components. The ability to reduce bit cell sizes is now being limited by nano-technology physics so that in order for component manufacturers to continue to increase component capacity, volumetric enhancements to the storage component are now being introduced. Volumetric enhancements include adding more tape per cartridge, more disk platters per drive, and more layers of memory cells on the silicon NAND substrate or on the optical disk substrate. This paper describes these volumetric strategies, projects density trends at the bit cell level, and projects volumetric trends at the component level in order to forecast future component capacity trends.

  13. Confined disordered strictly jammed binary sphere packings

    NASA Astrophysics Data System (ADS)

    Chen, D.; Torquato, S.

    2015-12-01

    Disordered jammed packings under confinement have received considerably less attention than their bulk counterparts and yet arise in a variety of practical situations. In this work, we study binary sphere packings that are confined between two parallel hard planes and generalize the Torquato-Jiao (TJ) sequential linear programming algorithm [Phys. Rev. E 82, 061302 (2010), 10.1103/PhysRevE.82.061302] to obtain putative maximally random jammed (MRJ) packings that are exactly isostatic with high fidelity over a large range of plane separation distances H , small to large sphere radius ratio α , and small sphere relative concentration x . We find that packing characteristics can be substantially different from their bulk analogs, which is due to what we term "confinement frustration." Rattlers in confined packings are generally more prevalent than those in their bulk counterparts. We observe that packing fraction, rattler fraction, and degree of disorder of MRJ packings generally increase with H , though exceptions exist. Discontinuities in the packing characteristics as H varies in the vicinity of certain values of H are due to associated discontinuous transitions between different jammed states. When the plane separation distance is on the order of two large-sphere diameters or less, the packings exhibit salient two-dimensional features; when the plane separation distance exceeds about 30 large-sphere diameters, the packings approach three-dimensional bulk packings. As the size contrast increases (as α decreases), the rattler fraction dramatically increases due to what we call "size-disparity" frustration. We find that at intermediate α and when x is about 0.5 (50-50 mixture), the disorder of packings is maximized, as measured by an order metric ψ that is based on the number density fluctuations in the direction perpendicular to the hard walls. We also apply the local volume-fraction variance στ2(R ) to characterize confined packings and find that these packings possess essentially the same level of hyperuniformity as their bulk counterparts. Our findings are generally relevant to confined packings that arise in biology (e.g., structural color in birds and insects) and may have implications for the creation of high-density powders and improved battery designs.

  14. Numerical simulation of a sphere moving down an incline with identical spheres placed equally apart

    USGS Publications Warehouse

    Ling, Chi-Hai; Jan, Chyan-Deng; Chen, Cheng-lung; Shen, Hsieh Wen

    1992-01-01

    This paper describes a numerical study of an elastic sphere moving down an incline with a string of identical spheres placed equally apart. Two momentum equations and a moment equation formulated for the moving sphere are solved numerically for the instantaneous velocity of the moving sphere on an incline with different angles of inclination. Input parameters for numerical simulation include the properties of the sphere (the radius, density, Poison's ratio, and Young's Modulus of elasticity), the coefficient of friction between the spheres, and a damping coefficient of the spheres during collision.

  15. The importance of precision radar tracking data for the determination of density and winds from the high-altitude inflatable sphere

    NASA Technical Reports Server (NTRS)

    Schmidlin, F. J.; Michel, W. R.

    1985-01-01

    Analysis of inflatable sphere measurements obtained during the Energy Budget and MAP/WINE campaigns led to questions concerning the precision of the MPS-36 radar used for tracking the spheres; the compatibility of the sphere program with the MPS-36 radar tracking data; and the oversmoothing of derived parameters at high altitudes. Simulations, with winds having sinusoidal vertical wavelengths, were done with the sphere program (HIROBIN) to determine the resolving capability of various filters. It is concluded that given a precision radar and a perfectly performing sphere, the HIROBIN filters can be adjusted to provide small-scale perturbation information to 70 km (i.e., sinusoidal wavelengths of 2 km). It is recommended that the HIROBIN program be modified to enable it to use a variable length filter, that adjusts to fall velocity and accelerations to provide wind data with small perturbations.

  16. Beyond packing of hard spheres: The effects of core softness, non-additivity, intermediate-range repulsion, and many-body interactions on the glass-forming ability of bulk metallic glasses

    NASA Astrophysics Data System (ADS)

    Zhang, Kai; Fan, Meng; Liu, Yanhui; Schroers, Jan; Shattuck, Mark D.; O'Hern, Corey S.

    2015-11-01

    When a liquid is cooled well below its melting temperature at a rate that exceeds the critical cooling rate Rc, the crystalline state is bypassed and a metastable, amorphous glassy state forms instead. Rc (or the corresponding critical casting thickness dc) characterizes the glass-forming ability (GFA) of each material. While silica is an excellent glass-former with small Rc < 10-2 K/s, pure metals and most alloys are typically poor glass-formers with large Rc > 1010 K/s. Only in the past thirty years have bulk metallic glasses (BMGs) been identified with Rc approaching that for silica. Recent simulations have shown that simple, hard-sphere models are able to identify the atomic size ratio and number fraction regime where BMGs exist with critical cooling rates more than 13 orders of magnitude smaller than those for pure metals. However, there are a number of other features of interatomic potentials beyond hard-core interactions. How do these other features affect the glass-forming ability of BMGs? In this manuscript, we perform molecular dynamics simulations to determine how variations in the softness and non-additivity of the repulsive core and form of the interatomic pair potential at intermediate distances affect the GFA of binary alloys. These variations in the interatomic pair potential allow us to introduce geometric frustration and change the crystal phases that compete with glass formation. We also investigate the effect of tuning the strength of the many-body interactions from zero to the full embedded atom model on the GFA for pure metals. We then employ the full embedded atom model for binary BMGs and show that hard-core interactions play the dominant role in setting the GFA of alloys, while other features of the interatomic potential only change the GFA by one to two orders of magnitude. Despite their perturbative effect, understanding the detailed form of the intermetallic potential is important for designing BMGs with cm or greater casting thickness.

  17. Beyond packing of hard spheres: The effects of core softness, non-additivity, intermediate-range repulsion, and many-body interactions on the glass-forming ability of bulk metallic glasses.

    PubMed

    Zhang, Kai; Fan, Meng; Liu, Yanhui; Schroers, Jan; Shattuck, Mark D; O'Hern, Corey S

    2015-11-14

    When a liquid is cooled well below its melting temperature at a rate that exceeds the critical cooling rate Rc, the crystalline state is bypassed and a metastable, amorphous glassy state forms instead. Rc (or the corresponding critical casting thickness dc) characterizes the glass-forming ability (GFA) of each material. While silica is an excellent glass-former with small Rc < 10(-2) K/s, pure metals and most alloys are typically poor glass-formers with large Rc > 10(10) K/s. Only in the past thirty years have bulk metallic glasses (BMGs) been identified with Rc approaching that for silica. Recent simulations have shown that simple, hard-sphere models are able to identify the atomic size ratio and number fraction regime where BMGs exist with critical cooling rates more than 13 orders of magnitude smaller than those for pure metals. However, there are a number of other features of interatomic potentials beyond hard-core interactions. How do these other features affect the glass-forming ability of BMGs? In this manuscript, we perform molecular dynamics simulations to determine how variations in the softness and non-additivity of the repulsive core and form of the interatomic pair potential at intermediate distances affect the GFA of binary alloys. These variations in the interatomic pair potential allow us to introduce geometric frustration and change the crystal phases that compete with glass formation. We also investigate the effect of tuning the strength of the many-body interactions from zero to the full embedded atom model on the GFA for pure metals. We then employ the full embedded atom model for binary BMGs and show that hard-core interactions play the dominant role in setting the GFA of alloys, while other features of the interatomic potential only change the GFA by one to two orders of magnitude. Despite their perturbative effect, understanding the detailed form of the intermetallic potential is important for designing BMGs with cm or greater casting thickness. PMID:26567672

  18. Improved association in a classical density functional theory for water.

    PubMed

    Krebs, Eric J; Schulte, Jeff B; Roundy, David

    2014-03-28

    We present a modification to our recently published statistical associating fluid theory-based classical density functional theory for water. We have recently developed and tested a functional for the averaged radial distribution function at contact of the hard-sphere fluid that is dramatically more accurate at interfaces than earlier approximations. We now incorporate this improved functional into the association term of our free energy functional for water, improving its description of hydrogen bonding. We examine the effect of this improvement by studying two hard solutes (a hard hydrophobic rod and a hard sphere) and a Lennard-Jones approximation of a krypton atom solute. The improved functional leads to a moderate change in the density profile and a large decrease in the number of hydrogen bonds broken in the vicinity of the hard solutes. We find an improvement of the partial radial distribution for a krypton atom in water when compared with experiment. PMID:24697459

  19. Improved association in a classical density functional theory for water

    SciTech Connect

    Krebs, Eric J.; Schulte, Jeff B.; Roundy, David

    2014-03-28

    We present a modification to our recently published statistical associating fluid theory-based classical density functional theory for water. We have recently developed and tested a functional for the averaged radial distribution function at contact of the hard-sphere fluid that is dramatically more accurate at interfaces than earlier approximations. We now incorporate this improved functional into the association term of our free energy functional for water, improving its description of hydrogen bonding. We examine the effect of this improvement by studying two hard solutes (a hard hydrophobic rod and a hard sphere) and a Lennard-Jones approximation of a krypton atom solute. The improved functional leads to a moderate change in the density profile and a large decrease in the number of hydrogen bonds broken in the vicinity of the hard solutes. We find an improvement of the partial radial distribution for a krypton atom in water when compared with experiment.

  20. Multiple reentrant glass transitions of soft spheres at high densities: Monotonicity of the curves of constant relaxation time in jamming phase diagrams depending on temperature over pressure and pressure

    NASA Astrophysics Data System (ADS)

    Schmiedeberg, Michael

    2013-05-01

    By using molecular-dynamics simulations, we determine the jamming phase diagrams at high densities for a bidisperse mixture of soft spheres that interact according to repulsive power-law pair potentials. We observe that the relaxation time varies nonmonotonically as a function of density at constant temperature. Therefore, the jamming phase diagrams contain multiple reentrant glass transitions if temperature and density are used as control parameters. However, if we consider a new formulation of the jamming phase diagrams where temperature over pressure and pressure are employed as control parameters, no nonmonotonic behavior is observed.

  1. Free Volume of the Hard Spheres Gas

    ERIC Educational Resources Information Center

    Shutler, P. M. E.; Martinez, J. C.; Springham, S. V.

    2007-01-01

    The Enskog factor [chi] plays a central role in the theory of dense gases, quantifying how the finite size of molecules causes many physical quantities, such as the equation of state, the mean free path, and the diffusion coefficient, to deviate from those of an ideal gas. We suggest an intuitive but rigorous derivation of this fact by showing how

  2. A simple real space density functional theory of freezing, with implications for the glass transition

    SciTech Connect

    Stoessel, J.P.; Wolynes, P.G.

    1989-01-01

    With analogy to the ''highly accurate'' summation of cluster diagrams for hard sphere fluids a la Carnahan-Starling, we present a simple, real space free energy density functional for arbitrary potential systems, based on the generalization of the second virial coefficient to inhomogeneous systems which, when applied to hard sphere, soft-sphere, and Lennard-Jones freezing, yield melting characteristics in remarkable agreement with experiment. Implications for the liquid-glass transition in all three potential systems are also presented. 45 refs., 7 figs., 1 tab.

  3. Enhancement of electromechanical coupling coefficient and acoustic power density in conventional "Hard" Pb(Zr1-xTix)O3 ceramics by application of uniaxial stress

    NASA Astrophysics Data System (ADS)

    Viehland, D.; Tito, F.; McLaughlin, E.; Robinson, H.; Janus, R.; Ewart, L.; Powers, J.

    2001-08-01

    Investigations of the polarization versus electric field (P-E) and strain versus electric field (?-E) responses for "hard" Pb(Zr1-xTix)O3 piezoelectric ceramics have been performed under various uniaxial stresses (?) and ac electrical drive fields. Investigations revealed a significant decrease in the remanent polarization of specimens with increasing ?. Subsequent calculations of the longitudinal electromechanical coupling coefficient (k33) and acoustic power density revealed significant enhancements with increasing ?.

  4. FROM THE HISTORY OF PHYSICS: The physics of a thermonuclear explosion of a normal-density liquefied deuterium sphere (On the impossibility of a spherically symmetric thermonuclear explosion in liquid deuterium at normal density)

    NASA Astrophysics Data System (ADS)

    Marchuk, Gurii I.; Imshennik, Vladimir S.; Basko, Mikhail M.

    2009-03-01

    The hydrodynamic problem of a thermonuclear explosion in a sphere of normal-density liquid deuterium was solved (Institute for Physics and Power Engineering, Obninsk) in 1952-1954 in the framework of the Soviet Atomic Project. The principal result was that the explosion shockwave in deuterium strongly decayed because of radiation energy loss and nonlocal energy release by fast neutrons. At that time, this negative result implied in essence that the straightforward approach to creating a thermonuclear weapon was in fact a blind alley. This paper describes a numerical solution to the stated problem, obtained with the modern DEIRA code developed for numerical modeling of inertially confined fusion. Detailed numerical calculations have confirmed the above 'historic' result and shed additional light on the physical causes of the detonation wave decay. The most pernicious factor is the radiation energy loss due to the combined effect of bremsstrahlung and the inverse Compton scattering of the emitted photons on the hot electrons. The impact of energy transfer by fast neutrons which was already quite adequately accounted for in the above-cited historical work is less significant. We present a more rigorous (compared to that of the 1950s) study of the role of inverse Compton scattering for which, in particular, an independent analytic estimate is obtained.

  5. Electronic structure of C and N co-doped TiO{sub 2}: A combined hard x-ray photoemission spectroscopy and density functional theory study

    SciTech Connect

    Ruzybayev, Inci; Baik, Seung Su; Choi, Hyoung Joon; Rumaiz, Abdul K. Sterbinsky, G. E.; Woicik, J. C.; Ismat Shah, S.

    2014-12-01

    We have studied the electronic structure of C and N co-doped TiO{sub 2} using hard x-ray photoelectron spectroscopy and first-principles density functional theory calculations. Our results reveal overlap of the 2p states of O, N, and C in the system which shifts the valence band maximum towards the Fermi level. Combined with optical data we show that co-doping is an effective route for band gap reduction in TiO{sub 2}. Comparison of the measured valence band with theoretical photoemission density of states reveals the possibility of C on Ti and N on O site.

  6. Generating perfect fluid spheres in general relativity

    NASA Astrophysics Data System (ADS)

    Boonserm, Petarpa; Visser, Matt; Weinfurtner, Silke

    2005-06-01

    Ever since Karl Schwarzschilds 1916 discovery of the spacetime geometry describing the interior of a particular idealized general relativistic stara static spherically symmetric blob of fluid with position-independent densitythe general relativity community has continued to devote considerable time and energy to understanding the general-relativistic static perfect fluid sphere. Over the last 90 years a tangle of specific perfect fluid spheres has been discovered, with most of these specific examples seemingly independent from each other. To bring some order to this collection, in this article we develop several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. These transformation theorems sometimes lead to unexpected connections between previously known perfect fluid spheres, sometimes lead to new previously unknown perfect fluid spheres, and in general can be used to develop a systematic way of classifying the set of all perfect fluid spheres.

  7. Fabrication and application of inorganic hollow spheres.

    PubMed

    Hu, Jing; Chen, Min; Fang, Xiaosheng; Wu, Limin

    2011-11-01

    Inorganic hollow spheres have attracted considerable interest due to their singular properties and wide range of potential applications. In this critical review, we provide a comprehensive overview of the preparation and applications of inorganic hollow spheres. We first discuss the syntheses of inorganic hollow spheres by use of polymers, inorganic nonmetals, metal-based hard templates, small-molecule emulsion, surfactant micelle-based soft-templates, and the template-free approach. For each method, a critical comment is given based on our knowledge and related research experience. We go on to discuss some important applications of inorganic hollow spheres in 0D, 2D, and 3D arrays. We conclude this review with some perspectives on the future research and development of inorganic hollow spheres (235 references). PMID:21799974

  8. Rotary Multilayer Split MorphA Piezoelectric Microactuator for Dual-Stage Actuation Systems in High Track Density Hard Disk Drives

    NASA Astrophysics Data System (ADS)

    Wang, Zhihong; Zhu, Weiguang; Tan, Ooi Kiang; Yao, Xi

    2001-09-01

    A novel annular rotary piezoelectric microactuator has been proposed for a dual-stage actuation system for future high track density hard disk drives. The microactuator is designed to be mounted on a flexure tongue and drives a slider directly to perform high-frequency track following. The configuration and operation of the microactuator are described. The controllable stroke and the resonance frequency of the slider/actuator assembly have been evaluated and optimized by finite-element analysis. The results reveal that the designed actuator/slider assembly should be a promising addition to the dual-stage actuation system.

  9. Plasmonic lateral forces on chiral spheres

    NASA Astrophysics Data System (ADS)

    Canaguier-Durand, Antoine; Genet, Cyriaque

    2016-01-01

    We show that the optical force exerted on a finite size chiral sphere by a surface plasmon mode has a component along a direction perpendicular to the plasmon linear momentum. We reveal how this chiral lateral force, pointing in opposite directions for opposite enantiomers, stems from an angular-to-linear crossed momentum transfer involving the plasmon transverse spin angular momentum density and mediated by the chirality of the sphere. Our multipolar approach allows us discussing the inclusion of the recoil term in the force on a small sphere taken in the dipolar limit and observing sign inversions of the lateral chiral force when the size of the sphere increases.

  10. Molecular solvent model of cylindrical electric double layers: a systematic study by Monte Carlo simulations and density functional theory.

    PubMed

    Goel, Teena; Patra, Chandra N; Ghosh, Swapan K; Mukherjee, Tulsi

    2008-10-21

    We present the Monte Carlo simulation and density functional study of structure of cylindrical double layers considering solvent as the third component. We have chosen molecular solvent model, where ions and solvent molecules are considered as charged and neutral hard spheres, respectively, having equal diameter. The polyionic cylinder is modeled as an infinite, rigid, and impenetrable charged hard cylinder surrounded by the electrolyte and the solvent spheres. The theory is partially perturbative where the hard-sphere interactions are treated within the weighted density approach, the corresponding ionic interactions have been evaluated through second-order functional Taylor expansion with respect to the bulk electrolyte. The Monte Carlo simulations have been performed in canonical ensemble. The system is studied at varying concentrations of electrolyte ions and the solvent molecules, at different valences of the electrolyte, at different sizes of hard spheres, and at varying surface charge density. The theory and the simulation results are found to be in good agreement at different parametric conditions. The hard-sphere exclusion effects due to molecular nature of the solvent are shown to have special implications in characterizing diffuse layer phenomena such as layering and charge inversion. PMID:19045218

  11. The Surface Free Energy of Hard Chain Fluids against a Hard Planar Wall

    NASA Astrophysics Data System (ADS)

    van Swol, Frank

    2000-03-01

    We present the first data for the interfacial properties of the simplest possible polymer fluid substrate interface, namely that of a hard chain fluid against a planar hard wall. We use molecular dynamics to calculate the surface free energy and the adsorption isotherms for hard chains of 2, 8, 20, 100, 400 and 1000 beads. We find that chain fluids differ markedly from the simple spheres in that both the adsorption and the surface free energy change sign and display an extremum as a function of density. The surface free energy exhibits a ‘Boyle density’ where at a nonzero density the surface free energy is equal to that of an ideal gas. The combined data can be fitted to a simple surface equation of state that expresses the free energy as a function of chain length and density. The results that we present here are the first of its kind for polymer fluids should proof particularly useful in further developing approximate density functional and integral equation approaches to polymer interfaces. We observe over most of the pressure range is linear with pressure.

  12. Specific surface area of overlapping spheres in the presence of obstructions.

    PubMed

    Jenkins, D R

    2013-02-21

    This study considers the random placement of uniform sized spheres, which may overlap, in the presence of another set of randomly placed (hard) spheres, which do not overlap. The overlapping spheres do not intersect the hard spheres. It is shown that the specific surface area of the collection of overlapping spheres is affected by the hard spheres, such that there is a minimum in the specific surface area as a function of the relative size of the two sets of spheres. The occurrence of the minimum is explained in terms of the break-up of pore connectivity. The configuration can be considered to be a simple model of the structure of a porous composite material. In particular, the overlapping particles represent voids while the hard particles represent fillers. Example materials are pervious concrete, metallurgical coke, ice cream, and polymer composites. We also show how the material properties of such composites are affected by the void structure. PMID:23445025

  13. Specific surface area of overlapping spheres in the presence of obstructions

    NASA Astrophysics Data System (ADS)

    Jenkins, D. R.

    2013-02-01

    This study considers the random placement of uniform sized spheres, which may overlap, in the presence of another set of randomly placed (hard) spheres, which do not overlap. The overlapping spheres do not intersect the hard spheres. It is shown that the specific surface area of the collection of overlapping spheres is affected by the hard spheres, such that there is a minimum in the specific surface area as a function of the relative size of the two sets of spheres. The occurrence of the minimum is explained in terms of the break-up of pore connectivity. The configuration can be considered to be a simple model of the structure of a porous composite material. In particular, the overlapping particles represent voids while the hard particles represent fillers. Example materials are pervious concrete, metallurgical coke, ice cream, and polymer composites. We also show how the material properties of such composites are affected by the void structure.

  14. Improved Iterative Hard- and Soft-Reliability Based Majority-Logic Decoding Algorithms for Non-Binary Low-Density Parity-Check Codes

    NASA Astrophysics Data System (ADS)

    Xiong, Chenrong; Yan, Zhiyuan

    2014-10-01

    Non-binary low-density parity-check (LDPC) codes have some advantages over their binary counterparts, but unfortunately their decoding complexity is a significant challenge. The iterative hard- and soft-reliability based majority-logic decoding algorithms are attractive for non-binary LDPC codes, since they involve only finite field additions and multiplications as well as integer operations and hence have significantly lower complexity than other algorithms. In this paper, we propose two improvements to the majority-logic decoding algorithms. Instead of the accumulation of reliability information in the existing majority-logic decoding algorithms, our first improvement is a new reliability information update. The new update not only results in better error performance and fewer iterations on average, but also further reduces computational complexity. Since existing majority-logic decoding algorithms tend to have a high error floor for codes whose parity check matrices have low column weights, our second improvement is a re-selection scheme, which leads to much lower error floors, at the expense of more finite field operations and integer operations, by identifying periodic points, re-selecting intermediate hard decisions, and changing reliability information.

  15. Understanding the Electronic Structure of IrO2 Using Hard-X-ray Photoelectron Spectroscopy and Density-Functional Theory

    NASA Astrophysics Data System (ADS)

    Kahk, J. M.; Poll, C. G.; Oropeza, F. E.; Ablett, J. M.; Colin, D.; Rueff, J.-P.; Agrestini, S.; Utsumi, Y.; Tsuei, K. D.; Liao, Y. F.; Borgatti, F.; Panaccione, G.; Regoutz, A.; Egdell, R. G.; Morgan, B. J.; Scanlon, D. O.; Payne, D. J.

    2014-03-01

    The electronic structure of IrO2 has been investigated using hard x-ray photoelectron spectroscopy and density-functional theory. Excellent agreement is observed between theory and experiment. We show that the electronic structure of IrO2 involves crystal field splitting of the iridium 5d orbitals in a distorted octahedral field. The behavior of IrO2 closely follows the theoretical predictions of Goodenough for conductive rutile-structured oxides [J. B. Goodenough, J. Solid State Chem. 3, 490 (1971)]. Strong satellites associated with the core lines are ascribed to final state screening effects. A simple plasmon model for the satellites applicable to many other metallic oxides appears to be not valid for IrO2.

  16. An application of the grazing-angle incidence hard x-ray optical nanoscope in ultra-high density digital data read-out device

    NASA Astrophysics Data System (ADS)

    Bezirganyan, Hakob P.; Bezirganyan, Siranush E.; Bezirganyan, Petros H., Jr.; Bezirganyan, Hayk H., Jr.

    2008-08-01

    We present in this theoretical paper a set-up of grazing-angle incidence hard x-ray nanoscope (GIXN), which is the essential part of ultra-high density digital data read-out device. The GIXN consists of the asymmetrically cut single crystal, which is operating like an image magnifier. The X-ray high-resolution diffractive optical lens (zone plate) and spatially resolving detector (CCD camera) are arranged like in classical schemes of the X-ray imaging microscopy. Proposed nanoscope operates based on grazing-angle incidence x-ray backscattering diffraction (GIXB) technique applied in the specular beam suppression mode. Grazing-angle incident X-ray configuration allows the handling of data from very large surface area of the X-ray optical memory disk (X-ROM) and, consequently, the data read-out speed is much faster than in optical data read-out systems.

  17. Transfer-matrix study of a hard-square lattice gas with two kinds of particles and density anomaly

    NASA Astrophysics Data System (ADS)

    Oliveira, Tiago J.; Stilck, Jrgen F.

    2015-09-01

    Using transfer matrix and finite-size scaling methods, we study the thermodynamic behavior of a lattice gas with two kinds of particles on the square lattice. Only excluded volume interactions are considered, so that the model is athermal. Large particles exclude the site they occupy and its four first neighbors, while small particles exclude only their site. Two thermodynamic phases are found: a disordered phase where large particles occupy both sublattices with the same probability and an ordered phase where one of the two sublattices is preferentially occupied by them. The transition between these phases is continuous at small concentrations of the small particles and discontinuous at larger concentrations, both transitions are separated by a tricritical point. Estimates of the central charge suggest that the critical line is in the Ising universality class, while the tricritical point has tricritical Ising (Blume-Emery-Griffiths) exponents. The isobaric curves of the total density as functions of the fugacity of small or large particles display a minimum in the disordered phase.

  18. Transfer-matrix study of a hard-square lattice gas with two kinds of particles and density anomaly.

    PubMed

    Oliveira, Tiago J; Stilck, Jrgen F

    2015-09-01

    Using transfer matrix and finite-size scaling methods, we study the thermodynamic behavior of a lattice gas with two kinds of particles on the square lattice. Only excluded volume interactions are considered, so that the model is athermal. Large particles exclude the site they occupy and its four first neighbors, while small particles exclude only their site. Two thermodynamic phases are found: a disordered phase where large particles occupy both sublattices with the same probability and an ordered phase where one of the two sublattices is preferentially occupied by them. The transition between these phases is continuous at small concentrations of the small particles and discontinuous at larger concentrations, both transitions are separated by a tricritical point. Estimates of the central charge suggest that the critical line is in the Ising universality class, while the tricritical point has tricritical Ising (Blume-Emery-Griffiths) exponents. The isobaric curves of the total density as functions of the fugacity of small or large particles display a minimum in the disordered phase. PMID:26465420

  19. Dry etching of nanosized Ge1Sb2Te4 patterns using TiN hard mask for high density phase-change memory.

    PubMed

    Feng, Gaoming; Liu, Bo; Song, Zhitang; Lv, Shilong; Wu, Liangcai; Feng, Songlin; Chen, Bomy

    2009-02-01

    Being able to pattern and etch chalcogenide materials in nanometer scale is essential for the integration of high density chalcogenide random access memory. We investigated dry etching methods for the patterning of Ge1Sb2Te4 films in CHF3/O2 gas mixture using reactive-ion etching system. The gas species CHF3/O2 can reach good etched features with smooth sidewall and a taper angle of 86 degrees. The nanosized Ge1Sb2Te4 patterns were defined by electron-beam lithography using hydrogen silsesquioxane as negative type e-beam resist. A hard mask of TiN, to which the selectivity of Ge1Sb2Te4 is as high as 12, was chosen for employing a CHF3/O2 gas mixture for Ge1Sb2Te4 etching. The Ge1Sb2Te4 line with width of 170 nm could be successfully obtained with good profiles and uniformity using these optimized patterning conditions, which could be very helpful for fabricating high density chalcogenide random access memory based on Ge1Sb2Te4. PMID:19441562

  20. Hard convex lens-shaped particles: Densest-known packings and phase behavior

    NASA Astrophysics Data System (ADS)

    Cinacchi, Giorgio; Torquato, Salvatore

    2015-12-01

    By using theoretical methods and Monte Carlo simulations, this work investigates dense ordered packings and equilibrium phase behavior (from the low-density isotropic fluid regime to the high-density crystalline solid regime) of monodisperse systems of hard convex lens-shaped particles as defined by the volume common to two intersecting congruent spheres. We show that, while the overall similarity of their shape to that of hard oblate ellipsoids is reflected in a qualitatively similar phase diagram, differences are more pronounced in the high-density crystal phase up to the densest-known packings determined here. In contrast to those non-(Bravais)-lattice two-particle basis crystals that are the densest-known packings of hard (oblate) ellipsoids, hard convex lens-shaped particles pack more densely in two types of degenerate crystalline structures: (i) non-(Bravais)-lattice two-particle basis body-centered-orthorhombic-like crystals and (ii) (Bravais) lattice monoclinic crystals. By stacking at will, regularly or irregularly, laminae of these two crystals, infinitely degenerate, generally non-periodic in the stacking direction, dense packings can be constructed that are consistent with recent organizing principles. While deferring the assessment of which of these dense ordered structures is thermodynamically stable in the high-density crystalline solid regime, the degeneracy of their densest-known packings strongly suggests that colloidal convex lens-shaped particles could be better glass formers than colloidal spheres because of the additional rotational degrees of freedom.

  1. Hard convex lens-shaped particles: Densest-known packings and phase behavior.

    PubMed

    Cinacchi, Giorgio; Torquato, Salvatore

    2015-12-14

    By using theoretical methods and Monte Carlo simulations, this work investigates dense ordered packings and equilibrium phase behavior (from the low-density isotropic fluid regime to the high-density crystalline solid regime) of monodisperse systems of hard convex lens-shaped particles as defined by the volume common to two intersecting congruent spheres. We show that, while the overall similarity of their shape to that of hard oblate ellipsoids is reflected in a qualitatively similar phase diagram, differences are more pronounced in the high-density crystal phase up to the densest-known packings determined here. In contrast to those non-(Bravais)-lattice two-particle basis crystals that are the densest-known packings of hard (oblate) ellipsoids, hard convex lens-shaped particles pack more densely in two types of degenerate crystalline structures: (i) non-(Bravais)-lattice two-particle basis body-centered-orthorhombic-like crystals and (ii) (Bravais) lattice monoclinic crystals. By stacking at will, regularly or irregularly, laminae of these two crystals, infinitely degenerate, generally non-periodic in the stacking direction, dense packings can be constructed that are consistent with recent organizing principles. While deferring the assessment of which of these dense ordered structures is thermodynamically stable in the high-density crystalline solid regime, the degeneracy of their densest-known packings strongly suggests that colloidal convex lens-shaped particles could be better glass formers than colloidal spheres because of the additional rotational degrees of freedom. PMID:26671389

  2. Catalytic, hollow, refractory spheres, conversions with them

    NASA Technical Reports Server (NTRS)

    Wang, Taylor G. (Inventor); Elleman, Daniel D. (Inventor); Lee, Mark C. (Inventor); Kendall, Jr., James M. (Inventor)

    1989-01-01

    Improved, heterogeneous, refractory catalysts are in the form of gas-impervious, hollow, thin-walled spheres (10) suitable formed of a shell (12) of refractory such as alumina having a cavity (14) containing a gas at a pressure greater than atmospheric pressure. The wall material may be itself catalytic or a catalytically active material coated onto the sphere as a layer (16), suitably platinum or iron, which may be further coated with a layer (18) of activator or promoter. The density of the spheres (30) can be uniformly controlled to a preselected value within .+-.10 percent of the density of the fluid reactant such that the spheres either remain suspended or slowly fall or rise through the liquid reactant.

  3. Ordering of hard particles between hard walls

    NASA Astrophysics Data System (ADS)

    Chrzanowska, A.; Teixeira, P. I. C.; Ehrentraut, H.; Cleaver, D. J.

    2001-05-01

    The structure of a fluid of hard Gaussian overlap particles of elongation ? = 5, confined between two hard walls, has been calculated from density-functional theory and Monte Carlo simulations. By using the exact expression for the excluded volume kernel (Velasco E and Mederos L 1998 J. Chem. Phys. 109 2361) and solving the appropriate Euler-Lagrange equation entirely numerically, we have been able to extend our theoretical predictions into the nematic phase, which had up till now remained relatively unexplored due to the high computational cost. Simulation reveals a rich adsorption behaviour with increasing bulk density, which is described semi-quantitatively by the theory without any adjustable parameters.

  4. Thermodynamic properties and entropy scaling law for diffusivity in soft spheres.

    PubMed

    Pieprzyk, S; Heyes, D M; Bra?ka, A C

    2014-07-01

    The purely repulsive soft-sphere system, where the interaction potential is inversely proportional to the pair separation raised to the power n, is considered. The Laplace transform technique is used to derive its thermodynamic properties in terms of the potential energy and its density derivative obtained from molecular dynamics simulations. The derived expressions provide an analytic framework with which to explore soft-sphere thermodynamics across the whole softness-density fluid domain. The trends in the isochoric and isobaric heat capacity, thermal expansion coefficient, isothermal and adiabatic bulk moduli, Grneisen parameter, isothermal pressure, and the Joule-Thomson coefficient as a function of fluid density and potential softness are described using these formulas supplemented by the simulation-derived equation of state. At low densities a minimum in the isobaric heat capacity with density is found, which is a new feature for a purely repulsive pair interaction. The hard-sphere and n = 3 limits are obtained, and the low density limit specified analytically for any n is discussed. The softness dependence of calculated quantities indicates freezing criteria based on features of the radial distribution function or derived functions of it are not expected to be universal. A new and accurate formula linking the self-diffusion coefficient to the excess entropy for the entire fluid softness-density domain is proposed, which incorporates the kinetic theory solution for the low density limit and an entropy-dependent function in an exponential form. The thermodynamic properties (or their derivatives), structural quantities, and diffusion coefficient indicate that three regions specified by a convex, concave, and intermediate density dependence can be expected as a function of n, with a narrow transition region within the range 5 < n < 8. PMID:25122250

  5. Thermodynamic properties and entropy scaling law for diffusivity in soft spheres

    NASA Astrophysics Data System (ADS)

    Pieprzyk, S.; Heyes, D. M.; Bra?ka, A. C.

    2014-07-01

    The purely repulsive soft-sphere system, where the interaction potential is inversely proportional to the pair separation raised to the power n, is considered. The Laplace transform technique is used to derive its thermodynamic properties in terms of the potential energy and its density derivative obtained from molecular dynamics simulations. The derived expressions provide an analytic framework with which to explore soft-sphere thermodynamics across the whole softness-density fluid domain. The trends in the isochoric and isobaric heat capacity, thermal expansion coefficient, isothermal and adiabatic bulk moduli, Grneisen parameter, isothermal pressure, and the Joule-Thomson coefficient as a function of fluid density and potential softness are described using these formulas supplemented by the simulation-derived equation of state. At low densities a minimum in the isobaric heat capacity with density is found, which is a new feature for a purely repulsive pair interaction. The hard-sphere and n =3 limits are obtained, and the low density limit specified analytically for any n is discussed. The softness dependence of calculated quantities indicates freezing criteria based on features of the radial distribution function or derived functions of it are not expected to be universal. A new and accurate formula linking the self-diffusion coefficient to the excess entropy for the entire fluid softness-density domain is proposed, which incorporates the kinetic theory solution for the low density limit and an entropy-dependent function in an exponential form. The thermodynamic properties (or their derivatives), structural quantities, and diffusion coefficient indicate that three regions specified by a convex, concave, and intermediate density dependence can be expected as a function of n, with a narrow transition region within the range 5

  6. Density functional theory calculations on the active site of biotin synthase: mechanism of S transfer from the Fe(2)S(2) cluster and the role of 1st and 2nd sphere residues.

    PubMed

    Rana, Atanu; Dey, Subal; Agrawal, Amita; Dey, Abhishek

    2015-10-01

    Density functional theory (DFT) calculations are performed on the active site of biotin synthase (BS) to investigate the sulfur transfer from the Fe(2)S(2) cluster to dethiobiotin (DTB). The active site is modeled to include both the 1st and 2nd sphere residues. Molecular orbital theory considerations and calculation on smaller models indicate that only an S atom (not S?) transfer from an oxidized Fe(2)S(2) cluster leads to the formation of biotin from the DTB using two adenosyl radicals generated from S-adenosyl-L-methionine. The calculations on larger protein active site model indicate that a 9-monothiobiotin bound reduced cluster should be an intermediate during the S atom insertion from the Fe(2)S(2) cluster consistent with experimental data. The Arg260 bound to Fe1, being a weaker donor than cysteine bound to Fe(2), determines the geometry and the electronic structure of this intermediate. The formation of this intermediate containing the C9-S bond is estimated to have a ?G(?) of 17.1 kcal/mol while its decay by the formation of the 2nd C6-S bond is calculated to have a ?G(?) of 29.8 kcal/mol, i.e. the 2nd C-S bond formation is calculated to be the rate determining step in the cycle and it leads to the decay of the Fe(2)S(2) cluster. Significant configuration interaction (CI), present in these transition states, helps lower the barrier of these reactions by ~30-25 kcal/mol relative to a hypothetical outer-sphere reaction. The conserved Phe285 residue near the Fe(2)S(2) active site determines the stereo selectivity at the C6 center of this radical coupling reaction. Reaction mechanism of BS investigated using DFT calculations. Strong CI and the Phe285 residue control the kinetic rate and stereochemistry of the product. PMID:26369537

  7. Hard-pan soils - Management

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Hard pans, hard layers, or compacted horizons, either surface or subsurface, are universal problems that limit crop production. Hard layers can be caused by traffic or soil genetic properties that result in horizons with high density or cemented soil particles; these horizons have elevated penetrati...

  8. Molecular orbital studies (hardness, chemical potential, electrophilicity, and first electron excitation), vibrational investigation and theoretical NBO analysis of 2-hydroxy-5-bromobenzaldehyde by density functional method

    NASA Astrophysics Data System (ADS)

    Nataraj, A.; Balachandran, V.; Karthick, T.

    2013-01-01

    In this work, the vibrational spectral analysis was carried out using Raman and infrared spectroscopy in the range 4000-400 cm-1 and 3500-100 cm-1, respectively, for the 2-hydroxy-5-bromobenzaldehyde (HBB). The experimental spectra were recorded in the solid phase. The fundamental vibrational frequencies and intensity of vibrational bands were evaluated using density functional theory (DFT) with the standard B3LYP/6-311G++(d,p) method and basis set. Normal co-ordinate calculations were performed with the DFT force field corrected by a recommended set of scaling factors yielding fairly good agreement between observed and calculated frequencies. Simulation of infrared and Raman spectra utilizing the results of these calculations led to excellent overall agreement with the observed spectral patterns. The complete assignments were performed on the basis of the potential energy distribution (PED) of the vibrational modes, calculated with scaled quantum mechanics (SQM) method. The optimized geometric parameters (bond lengths and bond angles) were compared with experimental values of related compound. The stability of the molecule arising from hyper conjugative interactions and the charge delocalization has been analyzed using natural bond orbital (NBO) analysis. The directly calculated ionization potential (IP), electron affinity (EA), electronegativity (?), electrophilicity index (?), hardness (?), chemical potential (?), and first electron excitation (?) are all correlated with the HOMO and LUMO energies with their molecular properties. These show that charge transfer occurs within the molecule. Furthermore, molecular electrostatic potential maps (MESP) of the molecule have been calculated.

  9. Active swarms on a sphere

    NASA Astrophysics Data System (ADS)

    Sknepnek, Rastko; Henkes, Silke

    2015-02-01

    We show that coupling to curvature nontrivially affects collective motion in active systems, leading to motion patterns not observed in flat space. Using numerical simulations, we study a model of self-propelled particles with polar alignment and soft repulsion confined to move on the surface of a sphere. We observe a variety of motion patterns with the main hallmarks being polar vortex and circulating band states arising due to the incompatibility between spherical topology and uniform motiona consequence of the "hairy ball" theorem. We provide a detailed analysis of density, velocity, pressure, and stress profiles in the circulating band state. In addition, we present analytical results for a simplified model of collective motion on the sphere showing that frustration due to curvature leads to stable elastic distortions storing energy in the band.

  10. Active swarms on a sphere.

    PubMed

    Sknepnek, Rastko; Henkes, Silke

    2015-02-01

    We show that coupling to curvature nontrivially affects collective motion in active systems, leading to motion patterns not observed in flat space. Using numerical simulations, we study a model of self-propelled particles with polar alignment and soft repulsion confined to move on the surface of a sphere. We observe a variety of motion patterns with the main hallmarks being polar vortex and circulating band states arising due to the incompatibility between spherical topology and uniform motion-a consequence of the "hairy ball" theorem. We provide a detailed analysis of density, velocity, pressure, and stress profiles in the circulating band state. In addition, we present analytical results for a simplified model of collective motion on the sphere showing that frustration due to curvature leads to stable elastic distortions storing energy in the band. PMID:25768504

  11. Local thermodynamic mapping for effective liquid density-functional theory

    NASA Technical Reports Server (NTRS)

    Kyrlidis, Agathagelos; Brown, Robert A.

    1992-01-01

    The structural-mapping approximation introduced by Lutsko and Baus (1990) in the generalized effective-liquid approximation is extended to include a local thermodynamic mapping based on a spatially dependent effective density for approximating the solid phase in terms of the uniform liquid. This latter approximation, called the local generalized effective-liquid approximation (LGELA) yields excellent predictions for the free energy of hard-sphere solids and for the conditions of coexistence of a hard-sphere fcc solid with a liquid. Moreover, the predicted free energy remains single valued for calculations with more loosely packed crystalline structures, such as the diamond lattice. The spatial dependence of the weighted density makes the LGELA useful in the study of inhomogeneous solids.

  12. Balls and Spheres

    ERIC Educational Resources Information Center

    Szekely, George

    2011-01-01

    This article describes an art lesson that allows students to set up and collect sphere canvases. Spheres move art away from a rectangular canvas into a dimension that requires new planning and painting. From balls to many other spherical canvases that bounce, roll, float and fly, art experiences are envisioned by students. Even if adults recognize

  13. Balls and Spheres

    ERIC Educational Resources Information Center

    Szekely, George

    2011-01-01

    This article describes an art lesson that allows students to set up and collect sphere canvases. Spheres move art away from a rectangular canvas into a dimension that requires new planning and painting. From balls to many other spherical canvases that bounce, roll, float and fly, art experiences are envisioned by students. Even if adults recognize…

  14. Lorentzian fuzzy spheres

    NASA Astrophysics Data System (ADS)

    Chaney, A.; Lu, Lei; Stern, A.

    2015-09-01

    We show that fuzzy spheres are solutions of Lorentzian Ishibashi-Kawai-Kitazawa-Tsuchiya-type matrix models. The solutions serve as toy models of closed noncommutative cosmologies where big bang/crunch singularities appear only after taking the commutative limit. The commutative limit of these solutions corresponds to a sphere embedded in Minkowski space. This "sphere" has several novel features. The induced metric does not agree with the standard metric on the sphere, and, moreover, it does not have a fixed signature. The curvature computed from the induced metric is not constant, has singularities at fixed latitudes (not corresponding to the poles) and is negative. Perturbations are made about the solutions, and are shown to yield a scalar field theory on the sphere in the commutative limit. The scalar field can become tachyonic for a range of the parameters of the theory.

  15. Soft Spheres Make More Mesophases

    NASA Astrophysics Data System (ADS)

    Santangelo, Christian; Glaser, Matthew; Grason, Gregory; Kamien, Randall; Kosmrlj, Andreij; Ziherl, Primoz

    2008-03-01

    We use both mean-field methods and numerical simulation to study the phase diagram of classical particles interacting with a hard-core and repulsive, soft shoulder. Despite the purely repulsive interaction, this system displays a remarkable array of aggregate phases arising from the competition between the hard-core and shoulder length scales. In the limit of large shoulder width to core size, we argue that this phase diagram has a number of universal features, and classify the set of repulsive shoulders that lead to aggregation at high density. Surprisingly, the phase sequence and aggregate size adjusts so as to keep almost constant inter-aggregate separation.

  16. SPHERES National Lab Facility

    NASA Technical Reports Server (NTRS)

    Benavides, Jose

    2014-01-01

    SPHERES is a facility of the ISS National Laboratory with three IVA nano-satellites designed and delivered by MIT to research estimation, control, and autonomy algorithms. Since Fall 2010, The SPHERES system is now operationally supported and managed by NASA Ames Research Center (ARC). A SPHERES Program Office was established and is located at NASA Ames Research Center. The SPHERES Program Office coordinates all SPHERES related research and STEM activities on-board the International Space Station (ISS), as well as, current and future payload development. By working aboard ISS under crew supervision, it provides a risk tolerant Test-bed Environment for Distributed Satellite Free-flying Control Algorithms. If anything goes wrong, reset and try again! NASA has made the capability available to other U.S. government agencies, schools, commercial companies and students to expand the pool of ideas for how to test and use these bowling ball-sized droids. For many of the researchers, SPHERES offers the only opportunity to do affordable on-orbit characterization of their technology in the microgravity environment. Future utilization of SPHERES as a facility will grow its capabilities as a platform for science, technology development, and education. XXXX

  17. StenniSphere

    NASA Technical Reports Server (NTRS)

    2000-01-01

    The John C. Stennis Space Center's visitor center, StenniSphere, is one of Mississippi's leading tourist attractions and features a 14,000-square-foot interactive review of Stennis Space Center's role in America's space program. Designed to entertain while educating, StenniSphere includes informative displays and exhibits from NASA, the Naval Meteorology and Oceanography Command, and other resident agencies located at Stennis Space Center in Hancock County, Miss.

  18. Chinese Armillary Spheres

    NASA Astrophysics Data System (ADS)

    Sun, Xiaochun

    The armillary sphere was perhaps the most important type of astronomical instrument in ancient China. It was first invented by Luoxia Hong in the first century BC. After Han times, the structure of the armillary sphere became increasingly sophisticated by including more and more rings representing various celestial movements as recognized by the Chinese astronomers. By the eighth century, the Chinese armillary sphere consisted of three concentric sets of rings revolving on the south-north polar axis. The relative position of the rings could be adjusted to reflect the precession of the equinoxes and the regression of the Moon's nodes along the ecliptic. To counterbalance the defect caused by too many rings, Guo Shoujing from the late thirteenth century constructed the Simplified Instruments which reorganized the rings of the armillary sphere into separate instruments for measuring equatorial coordinates and horizontal coordinates. The armillary sphere was still preserved because it was a good illustration of celestial movements. A fifteenth-century replica of Guo Shoujing's armillary sphere still exists today.

  19. Density functional theory for carbon dioxide crystal

    SciTech Connect

    Chang, Yiwen; Mi, Jianguo Zhong, Chongli

    2014-05-28

    We present a density functional approach to describe the solid?liquid phase transition, interfacial and crystal structure, and properties of polyatomic CO{sub 2}. Unlike previous phase field crystal model or density functional theory, which are derived from the second order direct correlation function, the present density functional approach is based on the fundamental measure theory for hard-sphere repulsion in solid. More importantly, the contributions of enthalpic interactions due to the dispersive attractions and of entropic interactions arising from the molecular architecture are integrated in the density functional model. Using the theoretical model, the predicted liquid and solid densities of CO{sub 2} at equilibrium triple point are in good agreement with the experimental values. Based on the structure of crystal-liquid interfaces in different planes, the corresponding interfacial tensions are predicted. Their respective accuracies need to be tested.

  20. Density functional theory for carbon dioxide crystal.

    PubMed

    Chang, Yiwen; Mi, Jianguo; Zhong, Chongli

    2014-05-28

    We present a density functional approach to describe the solid-liquid phase transition, interfacial and crystal structure, and properties of polyatomic CO2. Unlike previous phase field crystal model or density functional theory, which are derived from the second order direct correlation function, the present density functional approach is based on the fundamental measure theory for hard-sphere repulsion in solid. More importantly, the contributions of enthalpic interactions due to the dispersive attractions and of entropic interactions arising from the molecular architecture are integrated in the density functional model. Using the theoretical model, the predicted liquid and solid densities of CO2 at equilibrium triple point are in good agreement with the experimental values. Based on the structure of crystal-liquid interfaces in different planes, the corresponding interfacial tensions are predicted. Their respective accuracies need to be tested. PMID:24880310

  1. Cosymplectic p-spheres

    NASA Astrophysics Data System (ADS)

    Cappelletti-Montano, Beniamino; De Nicola, Antonio; Yudin, Ivan

    2016-02-01

    We introduce cosymplectic circles and cosymplectic spheres, which are the analogues in the cosymplectic setting of contact circles and contact spheres. We provide a complete classification of compact 3-manifolds that admit a cosymplectic circle. The properties of tautness and roundness for a cosymplectic p-sphere are studied. To any taut cosymplectic circle on a three-dimensional manifold M we are able to canonically associate a complex structure and a conformal symplectic couple on M R. We prove that a cosymplectic circle in dimension three is round if and only if it is taut. On the other hand, we provide examples in higher dimensions of cosymplectic circles which are taut but not round and examples of cosymplectic circles which are round but not taut.

  2. Gearing up the SPHERE

    NASA Astrophysics Data System (ADS)

    Kasper, M.; Beuzit, J.-L.; Feldt, M.; Dohlen, K.; Mouillet, D.; Puget, P.; Wildi, F.; Abe, L.; Baruffolo, A.; Baudoz, P.; Bazzon, A.; Boccaletti, A.; Brast, R.; Buey, T.; Chesneau, O.; Claudi, R.; Costille, A.; Delboulb, A.; Desidera, S.; Dominik, C.; Dorn, R.; Downing, M.; Feautrier, P.; Fedrigo, E.; Fusco, T.; Girard, J.; Giro, E.; Gluck, L.; Gonte, F.; Gojak, D.; Gratton, R.; Henning, T.; Hubin, N.; Lagrange, A.-M.; Langlois, M.; Mignant, D. L.; Lizon, J.-L.; Lilley, P.; Madec, F.; Magnard, Y.; Martinez, P.; Mawet, D.; Mesa, D.; Mller-Nilsson, O.; Moulin, T.; Moutou, C.; O'Neal, J.; Pavlov, A.; Perret, D.; Petit, C.; Popovic, D.; Pragt, J.; Rabou, P.; Rochat, S.; Roelfsema, R.; Salasnich, B.; Sauvage, J.-F.; Schmid, H. M.; Schuhler, N.; Sevin, A.; Siebenmorgen, R.; Soenke, C.; Stadler, E.; Suarez, M.; Turatto, M.; Udry, S.; Vigan, A.; Zins, G.

    2012-09-01

    Direct imaging and spectral characterisation of exoplanets is one of the most exciting, but also one of the most challenging areas, in modern astronomy. The challenge is to overcome the very large contrast between the host star and its planet seen at very small angular separations. This article reports on the progress made in the construction of the second generation VLT instrument SPHERE, the Spectro-Polarimetric High-contrast Exoplanet REsearch instrument. SPHERE is expected to be commissioned on the VLT in 2013.

  3. Relativistically spinning charged sphere

    NASA Astrophysics Data System (ADS)

    Lynden-Bell, D.

    2004-11-01

    When the equatorial spin velocity v of a charged conducting sphere approaches c, the Lorentz force causes a remarkable rearrangement of the total charge q. Charge of that sign is confined to a narrow equatorial belt at latitudes b??(3)(1-v2/c2)1/2 while charge of the opposite sign occupies most of the spheres surface. The change in field structure is shown to be a growing contribution of the magic electromagnetic field of the charged Kerr-Newman black hole with Newtons G set to zero. The total charge within the narrow equatorial belt grows as (1-v2/c2)-(1/4) and tends to infinity as v approaches c. The electromagnetic field, Poynting vector, field angular momentum, and field energy are calculated for these configurations. Gyromagnetic ratio, g factor, and electromagnetic mass are illustrated in terms of a 19th century electron model. Classical models with no spin had the small classical electron radius e2/mc2 a hundredth of the Compton wavelength, but models with spin take that larger size but are so relativistically concentrated to the equator that most of their mass is electromagnetic. The method of images at inverse points of the sphere is shown to extend to charges at points with imaginary coordinates.

  4. Poisson-Boltzmann thermodynamics of counterions confined by curved hard walls.

    PubMed

    Šamaj, Ladislav; Trizac, Emmanuel

    2016-01-01

    We consider a set of identical mobile pointlike charges (counterions) confined to a domain with curved hard walls carrying a uniform fixed surface charge density, the system as a whole being electroneutral. Three domain geometries are considered: a pair of parallel plates, the cylinder, and the sphere. The particle system in thermal equilibrium is assumed to be described by the nonlinear Poisson-Boltzmann theory. While the effectively one-dimensional plates and the two-dimensional cylinder have already been solved, the three-dimensional sphere problem is not integrable. It is shown that the contact density of particles at the charged surface is determined by a first-order Abel differential equation of the second kind which is a counterpart of Enig's equation in the critical theory of gravitation and combustion or explosion. This equation enables us to construct the exact series solutions of the contact density in the regions of small and large surface charge densities. The formalism provides, within the mean-field Poisson-Boltzmann framework, the complete thermodynamics of counterions inside a charged sphere (salt-free system). PMID:26871116

  5. Poisson-Boltzmann thermodynamics of counterions confined by curved hard walls

    NASA Astrophysics Data System (ADS)

    Šamaj, Ladislav; Trizac, Emmanuel

    2016-01-01

    We consider a set of identical mobile pointlike charges (counterions) confined to a domain with curved hard walls carrying a uniform fixed surface charge density, the system as a whole being electroneutral. Three domain geometries are considered: a pair of parallel plates, the cylinder, and the sphere. The particle system in thermal equilibrium is assumed to be described by the nonlinear Poisson-Boltzmann theory. While the effectively one-dimensional plates and the two-dimensional cylinder have already been solved, the three-dimensional sphere problem is not integrable. It is shown that the contact density of particles at the charged surface is determined by a first-order Abel differential equation of the second kind which is a counterpart of Enig's equation in the critical theory of gravitation and combustion or explosion. This equation enables us to construct the exact series solutions of the contact density in the regions of small and large surface charge densities. The formalism provides, within the mean-field Poisson-Boltzmann framework, the complete thermodynamics of counterions inside a charged sphere (salt-free system).

  6. Soft spheres make more mesophases

    NASA Astrophysics Data System (ADS)

    Glaser, M. A.; Grason, G. M.; Kamien, R. D.; Komrlj, A.; Santangelo, C. D.; Ziherl, P.

    2007-05-01

    We use both mean-field methods and numerical simulation to study the phase diagram of classical particles interacting with a hard core and repulsive, soft shoulder. Despite the purely repulsive and isotropic interaction, this system displays a remarkable array of aggregate phases arising from the competition between the hard-core and soft-shoulder length scales, including fluid and crystalline phases with micellar, lamellar, and inverse micellar morphology. In the limit of large shoulder width to core size, we argue that this phase diagram has a number of universal features, and classify the set of repulsive shoulders that lead to aggregation at high density. Surprisingly, the phase sequence and aggregate size adjust so as to keep almost constant inter-aggregate separation.

  7. Effect of ionic size on the structure of cylindrical electric double layers: a systematic study by Monte Carlo simulations and density functional theory.

    PubMed

    Goel, Teena; Patra, Chandra N; Ghosh, Swapan K; Mukherjee, Tulsi

    2011-09-22

    The effect of ionic size on the diffuse layer characteristics of a cylindrical electric double layer is studied using density functional theory and Monte Carlo simulations for the restricted primitive model and solvent primitive model. The double layer is comprised of an infinitely long, rigid, impenetrable charged cylinder also referred to as the polyion, located at the center of a cylindrical cell containing the electrolyte, which is composed of charged hard spheres and the solvent molecules as neutral hard spheres (in the case of the solvent primitive model). The diameters of all the hard spheres are taken to be the same. The theory is based on a partially perturbative scheme, where perturbation is used to approximate the ionic interactions and the hard sphere contribution is treated within the weighted density approach. The Monte Carlo simulations are performed in the canonical ensemble. The zeta potential profiles as a function of the polyion surface charge density are presented for cylindrical double layers at different ionic concentrations, ionic valences, and different hard sphere (ionic and the solvent) diameters of 2, 3, and 4 . The theory agrees quite well with the simulation results for a wide range of system parametric conditions and is capable of showing the maximum and minimum in the zeta potential value for systems having divalent counterions. The steric effects due to the presence of solvent molecules play a major role in characterizing the zeta potential and the ionic density profiles. A noticeable change in the concavity of the zeta potential plots with increasing particle size at very low concentrations of monovalent electrolytes is suggestive of the occurrence of infinite differential capacitance for such systems. PMID:21827170

  8. Axiomatic foundations of entropic theorems for hard-sphere systems

    NASA Astrophysics Data System (ADS)

    Tessarotto, Massimo; Cremaschini, Claudio

    2015-05-01

    Following the recent establishment of an exact kinetic theory describing the statistical behavior of the Boltzmann-Sinai Classical Dynamical System and realized by the Master kinetic equation, in this paper the problem is posed of the construction of related appropriate entropic theorems. The same equation is proved to warrant, in particular, an exact constant H-theorem, referred to here as Master constant H-theorem, which holds for the 1-body ( i.e., kinetic) Boltzmann-Shannon entropy. The relationship with the customary Boltzmann H-theorem holding for the Boltzmann equation and the physical origin of the related phenomenon of macroscopic irreversibility are investigated.

  9. Parallel sphere rendering

    SciTech Connect

    Krogh, M.; Painter, J.; Hansen, C.

    1996-10-01

    Sphere rendering is an important method for visualizing molecular dynamics data. This paper presents a parallel algorithm that is almost 90 times faster than current graphics workstations. To render extremely large data sets and large images, the algorithm uses the MIMD features of the supercomputers to divide up the data, render independent partial images, and then finally composite the multiple partial images using an optimal method. The algorithm and performance results are presented for the CM-5 and the M.

  10. Relativistically spinning charged sphere

    SciTech Connect

    Lynden-Bell, D.

    2004-11-15

    When the equatorial spin velocity v of a charged conducting sphere approaches c, the Lorentz force causes a remarkable rearrangement of the total charge q. Charge of that sign is confined to a narrow equatorial belt at latitudes b{<=}{radical}(3)(1-v{sup 2}/c{sup 2}){sup 1/2} while charge of the opposite sign occupies most of the sphere's surface. The change in field structure is shown to be a growing contribution of the 'magic' electromagnetic field of the charged Kerr-Newman black hole with Newton's G set to zero. The total charge within the narrow equatorial belt grows as (1-v{sup 2}/c{sup 2}){sup -(1/4)} and tends to infinity as v approaches c. The electromagnetic field, Poynting vector, field angular momentum, and field energy are calculated for these configurations. Gyromagnetic ratio, g factor, and electromagnetic mass are illustrated in terms of a 19th century electron model. Classical models with no spin had the small classical electron radius e{sup 2}/mc{sup 2}{approx} a hundredth of the Compton wavelength, but models with spin take that larger size but are so relativistically concentrated to the equator that most of their mass is electromagnetic. The method of images at inverse points of the sphere is shown to extend to charges at points with imaginary coordinates.

  11. Dynamics of an aspherical bubble oscillating near a rigid sphere

    NASA Astrophysics Data System (ADS)

    Kurihara, Eru; Fujino, Kuninori; Hamakawa, Hiromitsu

    2015-10-01

    Behavior of a non-spherical bubble oscillating near a rigid sphere was investigated in the framework of the Lagrangian formalism and multipole expansion of the bubble boundary. In this study, shape oscillations of the bubble are taken into account up to the third oscillation mode (octupole mode) to illustrate the liquid jet formation on the bubble surface. To account for interaction between the bubble and the rigid sphere, corrections of the velocity potential in a liquid containing the bubble and the sphere will be considered up to terms of fifth order in the inverse separation distance. Derived equations describes typical bubble behavior such as volume oscillations, translation, and shape oscillations. This paper presents the motion of the bubble in the vicinity of the rigid sphere by using numerical computations of the equations. In particular, it is discussed that the dependencies of bubble behavior on the density and radius of the sphere.

  12. Critical levitation loci for spheres on cryogenic fluids.

    NASA Technical Reports Server (NTRS)

    Hendricks, R. C.; Ohm, S. A.

    1972-01-01

    The conditions which allow a fluid to support a sphere having a higher specific gravity than its own are investigated. Three basic parameters which together define the maximum floating conditions are considered, including the Bond number, the wetting angle of the interface, and the ratio of solid-liquid specific gravities. The Bond number represents the ratio of buoyancy to surface tension forces. An analysis of the forces at the sphere-liquid interface is conducted to determine the optimum levitation loci, that is, the conditions permitting flotation of a maximum density sphere. Data for glycerine, carbon tetrachloride, and water spheres floating on a liquid nitrogen surface appear to be in good agreement with the analysis. Data for Teflon spheres on water also appear to be in agreement with the analytical results.

  13. Weighted energy problem on the unit sphere

    NASA Astrophysics Data System (ADS)

    Bilogliadov, Mykhailo

    2016-02-01

    We consider the minimal energy problem on the unit sphere {{S}}^2 in the Euclidean space {{R}}^3 immersed in an external field Q, where the charges are assumed to interact via Newtonian potential 1/r, r being the Euclidean distance. The problem is solved by finding the support of the extremal measure, and obtaining an explicit expression for the equilibrium density. We then apply our results to an external field generated by a point charge, and to a quadratic external field.

  14. Theoretical study of miscibility and glass-forming trends in mixtures of polystyrene spheres

    NASA Technical Reports Server (NTRS)

    Shih, W.-H.; Stroud, D.

    1984-01-01

    A theoretical study of glass-forming trends and miscibility in mixtures of polystyrene spheres (polyballs) of different diameters, suspended in an aqueous solution, is presented. The polyballs are assumed to be charged and to interact via a Debye-Hueckel screened Coulomb potential. The Helmholtz free energy is calculated from a variational principle based on the Gibbs-Bogoliubov inequality, in which a mixture of hard spheres of different diameters is chosen as the reference system. It is found that when the charges of the two types of polyballs are sufficiently different, the variationally determined ratio of hard-sphere diameters differs substantially, leading to packing difficulties characteristic of glass formation. The experimentally observed range of glass formation corresponds to a ratio of hard-sphere diameters of 0.8 or less. Calculations of the free energy as a function of concentration indicate that the liquid polyball mixture is stable against the phase separation, even for widely different polyball charges.

  15. Ellipsoids beat Spheres: Experiments with Candies, Colloids and Crystals

    NASA Astrophysics Data System (ADS)

    Chaikin, Paul

    2006-04-01

    How many gumballs fit in the glass sphere of a gumball machine? Scientists have been puzzling over problems like this since the Ancient Greeks. Yet it was only recently proven that the standard way of stacking oranges at a grocery store--with one orange on top of each set of three below--is the densist packing for spheres, with a packing fraction ? 0.74. Random (amorphous) packings of spheres have a lower density, with ? 0.64. The density of crystalline and random packings of atoms is intimately related to the melting transition in matter. We have studied the crystal-liquid transition in spherical colloidal systems on earth and in microgravity. The simplest objects to study after spheres are squashed spheres -- ellipsoids. Surprisingly we find that ellipsoids can randomly pack more densely than spheres, up to ?0.68 - 0.71 for a shape close to that of M&M's^ Candies, and even approach ?0.75 for general ellipsoids. The higher density relates directly to the higher number of neighbors needed to prevent the more asymetric ellipsoid from rotating. We have also found the ellipsoids can be packed in a crystalline array to a density, ?.7707 which exceeds the highest previous packing. Our findings provide insights into granular materials, rigidity, crystals and glasses, and they may lead to higher quality ceramic materials.

  16. Hard metal composition

    DOEpatents

    Sheinberg, Haskell (Los Alamos, NM)

    1986-01-01

    A composition of matter having a Rockwell A hardness of at least 85 is formed from a precursor mixture comprising between 3 and 10 weight percent boron carbide and the remainder a metal mixture comprising from 70 to 90 percent tungsten or molybdenum, with the remainder of the metal mixture comprising nickel and iron or a mixture thereof. The composition has a relatively low density of between 7 to 14 g/cc. The precursor is preferably hot pressed to yield a composition having greater than 100% of theoretical density.

  17. Hard metal composition

    DOEpatents

    Sheinberg, H.

    1983-07-26

    A composition of matter having a Rockwell A hardness of at least 85 is formed from a precursor mixture comprising between 3 and 10 wt % boron carbide and the remainder a metal mixture comprising from 70 to 90% tungsten or molybdenum, with the remainder of the metal mixture comprising nickel and iron or a mixture thereof. The composition has a relatively low density of between 7 and 14 g/cc. The precursor is preferably hot pressed to yield a composition having greater than 100% of theoretical density.

  18. Studying Density VS Ar-pressures for optimization of DC-magnetron sputter deposition of Ni/C multilayers for hard x-ray telescopes

    NASA Astrophysics Data System (ADS)

    Hussain, Ahsen M.; Romaine, Suzanne E.; Gorenstein, Paul; Everett, J.; Bruni, Ricardo J.; Clark, Anna M.; Ruane, Michael F.; Fedyunin, Y.

    1997-07-01

    The influence of varying the Ar-pressure in the process of depositing Ni/C multilayers by dc-magnetron sputtering has been studied, and atomic force microscopy (AFM) measurements, x-ray characterization results and transmission electron microscopy (TEM) results are presented. Single Ni and C films and Ni/C multilayers were deposited at Ar-pressures of 1.5, 3, 5 and 7 mTorr. The one-dimensional power spectral density data from the AFM measurements clearly indicate that the best densities and thin film qualities for both materials are obtained at lower Ar-pressure, i.e. 1.5 mTorr.

  19. Production of high energy-solid density electron bunches and hard ? -quanta and positron fluxes by ultrarelativistic lasers in solid-plasma targets

    NASA Astrophysics Data System (ADS)

    Avetissian, H. K.; Matevosyan, H. H.; Mkrtchian, G. F.; Sedrakian, Kh. V.

    2015-12-01

    We consider nonlinear interaction of superpower laser pulses of relativistic intensities with nanolayers and solid-plasma targets toward the production of high energy-density electron and positron bunches along with high energy photon fluxes. It is shown that petawatt lasers are capable of producing via two-target scheme high density field-free electron/positron bunches and substantial amounts of ? -quanta with energies up to 200 MeV. For actual supershort and tightly focused-strongly nonplane ultrarelativistic laser pulses of linear and circular polarizations, the 3D3V problem is solved via numerical simulations.

  20. Fill tube fitted spheres

    SciTech Connect

    Ives, B.H.

    1981-07-13

    The high temperature diffusion technique for fuel filling of some future direct drive cryogenic ICF targets may be unacceptable. The following describes a technique of fitting a 1 mm diameter x 6 ..mu..m thick glass microsphere with an approx. 50 ..mu..m O.D. glass fill tube. The process of laser drilling a 50 ..mu..m diameter hole in the microsphere wall, technique for making the epoxy joint between the sphere and fill tube, as well as the assembly procedure are also discussed.

  1. SPHERE Science Verification

    NASA Astrophysics Data System (ADS)

    Leibundgut, B.; Beuzit, J.-L.; Gibson, N.; Girard, J.; Kasper, M.; Kerber, F.; Lundin, L.; Mawet, D.; McClure, M.; Milli, J.; Petr-Gotzens, M.; Siebenmorgen, R.; van den Ancker, M.; Wahhaj, Z.

    2015-03-01

    Science Verification (SV) for the latest instrument to arrive on Paranal, the high-contrast and spectro-polarimetric extreme adaptive optics instrument SPHERE, is described. The process through which the SV proposals were solicited and evaluated is briefly outlined; the resulting observations took place in December 2014 and February 2015. A wide range of targets was observed, ranging from the Solar System, young stars with planets and discs, circumstellar environments of evolved stars to a galaxy nucleus. Some of the first results are previewed.

  2. Parallel sphere rendering

    SciTech Connect

    Krogh, M.; Hansen, C.; Painter, J.; de Verdiere, G.C.

    1995-05-01

    Sphere rendering is an important method for visualizing molecular dynamics data. This paper presents a parallel divide-and-conquer algorithm that is almost 90 times faster than current graphics workstations. To render extremely large data sets and large images, the algorithm uses the MIMD features of the supercomputers to divide up the data, render independent partial images, and then finally composite the multiple partial images using an optimal method. The algorithm and performance results are presented for the CM-5 and the T3D.

  3. Forming MOFs into spheres by use of molecular gastronomy methods.

    PubMed

    Spjelkavik, Aud I; Aarti; Divekar, Swapnil; Didriksen, Terje; Blom, Richard

    2014-07-14

    A novel method utilizing hydrocolloids to prepare nicely shaped spheres of metal-organic frameworks (MOFs) has been developed. Microcrystalline CPO-27-Ni particles are dispersed in either alginate or chitosan solutions, which are added dropwise to solutions containing, respectively, either divalent group 2 cations or base that act as gelling agents. Well-shaped spheres are immediately formed, which can be dried into spheres containing mainly MOF (>95?wt?%). The spheronizing procedures have been optimized with respect to maximum specific surface area, shape, and particle density of the final sphere. At optimal conditions, well-shaped 2.5-3.5?mm diameter CPO-27-Ni spheres with weight-specific surface areas <10?% lower than the nonformulated CPO-27-Ni precursor, and having sphere densities in the range 0.8 to 0.9?g?cm(-3) and particle crushing strengths above 20?N, can be obtained. The spheres are well suited for use in fixed-bed catalytic or adsorption processes. PMID:24964774

  4. High pressure gas spheres for neutron and photon experiments

    NASA Astrophysics Data System (ADS)

    Rupp, G.; Petrich, D.; Kppeler, F.; Kaltenbaek, J.; Leugers, B.; Reifarth, R.

    2009-09-01

    High pressure gas spheres have been designed and successfully used in several nuclear physics experiments on noble gases. The pros and cons of this solution are the simple design and the high reliability versus the fact that the density is limited to 40-60% of liquid or solid gas samples. Originally produced for neutron capture studies at keV energies, the comparably small mass of the gas spheres were an important advantage, which turned out to be of relevance for other applications as well. The construction, performance, and operation of the spheres are described and examples for their use are presented.

  5. Experimental Investigation of Mechanical Properties of Metallic Hollow Sphere Structures

    NASA Astrophysics Data System (ADS)

    Friedl, O.; Motz, C.; Peterlik, H.; Puchegger, S.; Reger, N.; Pippan, R.

    2008-02-01

    Metallic foam was fabricated from 316L stainless steel spheres, where the bonding of the spheres was achieved by a sintering process. The mechanical behavior of a low-density material (0.3 g/cm3) with 2- and 4-mm sphere diameter and a high-density material (0.6 g/cm3) with 4-mm sphere diameter was investigated in compression and tension. The cell wall material of this hollow sphere structure (HSS) had different morphologies: dense and porous sintered walls were investigated. The cell wall morphology affects the Youngs modulus (stiffness) and the ductility of the HSS material. Defects, such as the cell wall porosity, lower the ductility of the material. Besides the quasi-static measurements, the HSS material was tested with a resonance frequency method (dynamic measurement), to obtain detailed information on the stiffness at different temperatures up to 700 C. In-situ compression and tension tests were carried out to understand the deformation mechanisms on the scale of the single hollow spheres. The failure mechanisms in the vicinity of the sintering neck of the spheres was investigated. A doubling of the density leads to an increase of the plateau stress and the ultimate tensile stress of the material, whereas the ductility (strain to fracture) depended mainly on the cell wall morphology. Due to the mainly tensile loading of the cell walls in the vicinity of the sinter neck, the ultimate tensile strength doubled for the high-density HSS, in good agreement with theoretical considerations. In compression, the gain in the plateau stress was not as distinctive compared with the theoretical considerations assuming a bending dominated deformation. The influence of structural parameters, such as cell wall morphology, cell wall thickness, and sphere diameter, on the mechanical behavior is discussed.

  6. Science on a Sphere exhibit

    NASA Technical Reports Server (NTRS)

    2009-01-01

    Students from Xavier University Preparatory School in New Orleans view the newest exhibit at StenniSphere, the visitor center at NASA's John C. Stennis Space Center - Science on a Sphere, a 68-inch global presentation of planetary data. StenniSphere is only the third NASA visitor center to offer the computer system, which uses four projectors to display data on a globe and present a dynamic, revolving, animated view of Earth and other planets.

  7. Magnetic spheres in microwave cavities

    NASA Astrophysics Data System (ADS)

    Zare Rameshti, Babak; Cao, Yunshan; Bauer, Gerrit E. W.

    2015-06-01

    We apply Mie scattering theory to study the interaction of magnetic spheres with microwaves in cavities beyond the magnetostatic and rotating wave approximations. We demonstrate that both strong and ultrastrong coupling can be realized for stand alone magnetic spheres made from yttrium iron garnet (YIG), acting as an efficient microwave antenna. The eigenmodes of YIG spheres with radii of the order mm display distinct higher angular momentum character that has been observed in experiments.

  8. Determination of meteor flux distribution over the celestial sphere

    NASA Technical Reports Server (NTRS)

    Andreev, V. V.; Belkovich, O. I.; Filimonova, T. K.; Sidorov, V. V.

    1992-01-01

    A new method of determination of meteor flux density distribution over the celestial sphere is discussed. The flux density was derived from observations by radar together with measurements of angles of arrival of radio waves reflected from meteor trails. The role of small meteor showers over the sporadic background is shown.

  9. Panoramic stereo sphere vision

    NASA Astrophysics Data System (ADS)

    Feng, Weijia; Zhang, Baofeng; Röning, Juha; Zong, Xiaoning; Yi, Tian

    2013-01-01

    Conventional stereo vision systems have a small field of view (FOV) which limits their usefulness for certain applications. While panorama vision is able to "see" in all directions of the observation space, scene depth information is missed because of the mapping from 3D reference coordinates to 2D panoramic image. In this paper, we present an innovative vision system which builds by a special combined fish-eye lenses module, and is capable of producing 3D coordinate information from the whole global observation space and acquiring no blind area 360°×360° panoramic image simultaneously just using single vision equipment with one time static shooting. It is called Panoramic Stereo Sphere Vision (PSSV). We proposed the geometric model, mathematic model and parameters calibration method in this paper. Specifically, video surveillance, robotic autonomous navigation, virtual reality, driving assistance, multiple maneuvering target tracking, automatic mapping of environments and attitude estimation are some of the applications which will benefit from PSSV.

  10. Nitrogen-doped hierarchically porous carbon spheres as efficient metal-free electrocatalysts for an oxygen reduction reaction

    NASA Astrophysics Data System (ADS)

    Liu, You-Lin; Shi, Cheng-Xiang; Xu, Xue-Yan; Sun, Ping-Chuan; Chen, Tie-Hong

    2015-06-01

    Using hierarchically mesoporous silica spheres as a hard template and methyl violet as carbon and nitrogen source, nitrogen-doped hierarchically porous carbon spheres (N-HCS) are successfully prepared via a nanocasting method. The nitrogen-doped carbon spheres obtained after carbonization at 1000 C (N-HCS-1000) exhibit a hierarchically micro-meso-macroporous structure with a relatively high surface area (BET) of 1413 m2 g-1 and a notably large pore volume of 2.96 cm3 g-1. In an oxygen reduction reaction (ORR) in alkaline media, the N-HCS-1000 material exhibits excellent activity with high current density, and its onset potential is notably close to that of the commercial Pt/C catalyst. The efficient catalytic activity of this catalyst could be attributed to the high electrical conductivity of the nitrogen-doped carbon matrix as well as the hierarchically porous framework. This catalyst also exhibits better methanol crossover resistance and higher stability than the commercial Pt/C catalyst.

  11. Laser-assisted electron scattering on a nano-sphere

    NASA Astrophysics Data System (ADS)

    Varr, Sndor; Szab, Lrnt Zs.; Czirjk, Attila

    2016-02-01

    We investigate the scattering of electrons on a hard sphere in the presence of a laser field of arbitrary intensity. We use spherical Gordon-Volkov states, and we present a novel method for the computation of a key quantity in this theory. We compute and analyze some additional results regarding the total differential scattering cross sections in the case of the weak field limit.

  12. Strong and weak adsorptions of polyelectrolyte chains onto oppositely charged spheres

    NASA Astrophysics Data System (ADS)

    Cherstvy, Andrey; Winkler, Roland

    2007-03-01

    We investigate the complexation of long thin polyelectrolyte chains with the oppositely charged sphere. In the limit of strong adsorption, when strongly charged polyelectrolyte chains adapt definite wrapped conformations on the sphere surface (solenoidal, tennis-ball-like, etc.), we analytically solve the linear Poisson-Boltzmann equation and calculate the electrostatic potential and energy of the complex. We discuss some biological applications of the obtained results, including those for DNA wrapping in the nucleosome core particles and for aggregate formation of DNA with oppositely charged nano-spheres studied in vitro. For weak adsorption, when a flexible weakly charged polyelectrolyte chain is localized next to the sphere in solution, we solve the Edwards equation for the chain conformations in the Hulth'en potential. The latter is used as an approximation for the screened Debye-H"uckel potential of the sphere. For arbitrary sphere radius, we predict the critical conditions for polyelectrolyte adsorption as a coupling between critical sphere and polyelectrolyte charge densities, sphere radius, temperature, and ionic strength in solution. We find that the critical charge density of the sphere exhibits a distinctively different dependence on the Debye screening length than for polyelectrolyte adsorption onto a flat surface. We compare our findings with experimental measurements on complex formation of various polyelectrolytes (DNA, PSS, AMPS, etc.) with oppositely charged colloidal particles and cationic micelles, where similar universal scaling relations for the sphere charge density have been revealed.

  13. Low Velocity Sphere Impact of a Soda Lime Silicate Glass

    SciTech Connect

    Wereszczak, Andrew A; Fox, Ethan E; Morrissey, Timothy G; Vuono, Daniel J

    2011-10-01

    This report summarizes TARDEC-sponsored work at Oak Ridge National Laboratory (ORNL) during the FY11 involving low velocity (< 30 m/s or < 65 mph) ball impact testing of Starphire soda lime silicate glass. The intent was to better understand low velocity impact response in the Starphire for sphere densities that bracketed that of rock. Five sphere materials were used: borosilicate glass, soda-lime silicate glass, steel, silicon nitride, and alumina. A gas gun was fabricated to produce controlled velocity delivery of the spheres against Starphire tile targets. Minimum impact velocities to initiate fracture in the Starphire were measured and interpreted in context to the kinetic energy of impact and the elastic property mismatch between the any of the five sphere-Starphire-target combinations. The primary observations from this low velocity (< 30 m/s or < 65 mph) testing were: (1) Frictional effects contribute to fracture initiation. (2) Spheres with a lower elastic modulus require less force to initiate fracture in the Starphire than spheres with a higher elastic modulus. (3) Contact-induced fracture did not initiate in the Starphire SLS for impact kinetic energies < 150 mJ. Fracture sometimes initiated or kinetic energies between {approx} 150-1100 mJ; however, it tended to occur when lower elastic modulus spheres were impacting it. Contact-induced fracture would always occur for impact energies > 1100 mJ. (4) The force necessary to initiate contact-induced fracture is higher under dynamic or impact conditions than it is under quasi-static indentation conditions. (5) Among the five used sphere materials, silicon nitride was the closest match to 'rock' in terms of both density and (probably) elastic modulus.

  14. Spheres of spheres of azafullerene in the solid state

    SciTech Connect

    Prassides, K.; Keshavarz-K., M.; Beer, E.

    1996-10-01

    This work is concerned with the structural characterization of azafullerene, (C{sub 59}N){sub 2}. The material forms largely non-crystalline spheres approximately 1 {mu}m in diameter. The structure of these spheres was probed through X-ray diffraction and electron microscopy. An oxidized version of the azafullerene, (C{sub 59}N){sub 2}O, was studied as well.

  15. Microwave-Assisted Solvothermal Synthesis of VO2 Hollow Spheres and Their Conversion into V2 O5 Hollow Spheres with Improved Lithium Storage Capability.

    PubMed

    Pan, Jing; Zhong, Li; Li, Ming; Luo, Yuanyuan; Li, Guanghai

    2016-01-01

    Monodispersed hierarchically structured V2 O5 hollow spheres were successfully obtained from orthorhombic VO2 hollow spheres, which are in turn synthesized by a simple template-free microwave-assisted solvothermal method. The structural evolution of VO2 hollow spheres has been studied and explained by a chemically induced self-transformation process. The reaction time and water content in the reaction solution have a great influence on the morphology and phase structure of the resulting products in the solvothermal reaction. The diameter of the VO2 hollow spheres can be regulated simply by changing vanadium ion content in the reaction solution. The VO2 hollow spheres can be transformed into V2 O5 hollow spheres with nearly no morphological change by annealing in air. The nanorods composed of V2 O5 hollow spheres have an average length of about 70?nm and width of about 19?nm. When used as a cathode material for lithium-ion batteries, the V2 O5 hollow spheres display a diameter-dependent electrochemical performance, and the 440?nm hollow spheres show the highest specific discharge capacity of 377.5?mAhg(-1) at a current density of 50 mAg(-1) , and are better than the corresponding solid spheres and nanorod assemblies. PMID:26749240

  16. Mechanical Properties and Uniformity of Nanocrystalline Diamond Coating Deposited Around a Sphere by MPCVD

    NASA Astrophysics Data System (ADS)

    Chen, Hongyun; Gou, Li

    2015-12-01

    Nanocrystalline diamond coatings were deposited by MPCVD on the spheres used for a ball bearing. The nanocrystalline coatings with a grain size of 50 nm were confirmed by the surface morphology and composition analysis. The hardness of the coating is 20–40 GPa tested by nanoindentation, which is higher than that of tungsten carbide and silicon nitride substrates. The coating around the sphere observed from the Micro CT images is uniform with a thickness of 12 μm.

  17. Frontal Impact of Rolling Spheres.

    ERIC Educational Resources Information Center

    Domenech, A.; Casasus, E.

    1991-01-01

    A model of the inelastic collision between two spheres rolling along a horizontal track is presented, taking into account the effects of frictional forces at impact. This experiment makes possible direct estimates of the coefficients of restitution and friction. (Author)

  18. Molecular-Scale Density Oscillations in Water Adjacent to a Mica Surface

    SciTech Connect

    Cheng, L.; Fenter, P.; Nagy, K. L.; Schlegel, M. L.; Sturchio, N. C.

    2001-10-08

    High-resolution specular x-ray reflectivity of the mica(001)-water interface under ambient conditions reveals oscillations in water oxygen density in the surface-normal direction, giving evidence of interfacial water ordering. The spacings between neighboring water layers in the near-surface, strongly oscillatory region are 2.5(2)--2.7(2){angstrom}, approximately the size of the water molecule. The density oscillations extend to about 10{angstrom} above the surface and do not strictly maintain a solvent-size periodicity as that in interfacial liquid metal and hard-sphere molecular liquids. We interpret this oscillatory density profile of the interfacial water as due to the ''hard-wall'' effect of the molecularly smooth mica surface.

  19. High-Sensitivity Measurement of Density by Magnetic Levitation.

    PubMed

    Nemiroski, Alex; Kumar, A A; Soh, Siowling; Harburg, Daniel V; Yu, Hai-Dong; Whitesides, George M

    2016-03-01

    This paper presents methods that use Magnetic Levitation (MagLev) to measure very small differences in density of solid diamagnetic objects suspended in a paramagnetic medium. Previous work in this field has shown that, while it is a convenient method, standard MagLev (i.e., where the direction of magnetization and gravitational force are parallel) cannot resolve differences in density <10(-4) g/cm(3) for macroscopic objects (>mm) because (i) objects close in density prevent each other from reaching an equilibrium height due to hard contact and excluded volume, and (ii) using weaker magnets or reducing the magnetic susceptibility of the medium destabilizes the magnetic trap. The present work investigates the use of weak magnetic gradients parallel to the faces of the magnets as a means of increasing the sensitivity of MagLev without destabilization. Configuring the MagLev device in a rotated state (i.e., where the direction of magnetization and gravitational force are perpendicular) relative to the standard configuration enables simple measurements along the axes with the highest sensitivity to changes in density. Manipulating the distance of separation between the magnets or the lengths of the magnets (along the axis of measurement) enables the sensitivity to be tuned. These modifications enable an improvement in the resolution up to 100-fold over the standard configuration, and measurements with resolution down to 10(-6) g/cm(3). Three examples of characterizing the small differences in density among samples of materials having ostensibly indistinguishable densities-Nylon spheres, PMMA spheres, and drug spheres-demonstrate the applicability of rotated Maglev to measuring the density of small (0.1-1 mm) objects with high sensitivity. This capability will be useful in materials science, separations, and quality control of manufactured objects. PMID:26815205

  20. Rebound and jet formation of a fluid-filled sphere

    NASA Astrophysics Data System (ADS)

    Killian, Taylor W.; Klaus, Robert A.; Truscott, Tadd T.

    2012-12-01

    This study investigates the impact dynamics of hollow elastic spheres partially filled with fluid. Unlike an empty sphere, the internal fluid mitigates some of the rebound through an impulse driven exchange of energy wherein the fluid forms a jet inside the sphere. Surprisingly, this occurs on the second rebound or when the free surface is initially perturbed. Images gathered through experimentation show that the fluid reacts more quickly to the impact than the sphere, which decouples the two masses (fluid and sphere), imparts energy to the fluid, and removes rebound energy from the sphere. The experimental results are analyzed in terms of acceleration, momentum and an energy method suggesting an optimal fill volume in the neighborhood of 30%. While the characteristics of the fluid (i.e., density, viscosity, etc.) affect the fluid motion (i.e., type and size of jet formation), the rebound characteristics remain similar for a given fluid volume independent of fluid type. Implications of this work are a potential use of similar passive damping systems in sports technology and marine engineering.

  1. Nematic ordering and defects on the surface of a sphere: A Monte Carlo simulation study

    NASA Astrophysics Data System (ADS)

    Bates, Martin A.

    2008-03-01

    We examine the ordering of hard rods on the surface of a sphere using computer simulations. As predicted by previous theories of thin nematic shells we observe four s =+1/2 defects. However, the predicted tetrahedral symmetry for the defects and the "baseball" director configuration is not observed. Instead the four defects are located, on average, on a great circle which splits the sphere into two hemispheres, each of which has a splay dominated director configuration. We argue that this result occurs as the bend elastic constant for hard rods is much larger than the splay elastic constant.

  2. Density in a Bottle.

    ERIC Educational Resources Information Center

    Roser, Charles E.; McCluskey, Catherine L.

    1998-01-01

    Explains how the Canadian soft drink Orbitz can be used for explorations of density in the classroom. The drink has colored spheres suspended throughout that have a density close to that of the liquid. Presents a hands-on activity that can be easily done in two parts. (DDR)

  3. Porous Ceramic Spheres From Cation Exchange Beads

    NASA Technical Reports Server (NTRS)

    Dynys, Fred

    2005-01-01

    This document is a slide presentation that examines the use of a simple templating process to produce hollow ceramic spheres with a pore size of 1 to 10 microns. Using ion exchange process it was determined that the method produces porous ceramic spheres with a unique structure: (i.e., inner sphere surrounded by an outer sphere.)

  4. Structure, thermodynamics, and position-dependent diffusivity in fluids with sinusoidal density variations.

    PubMed

    Bollinger, Jonathan A; Jain, Avni; Truskett, Thomas M

    2014-07-22

    Molecular dynamics simulations and a stochastic method based on the Fokker-Planck equation are used to explore the consequences of inhomogeneous density profiles on the thermodynamic and dynamic properties of the hard-sphere fluid and supercooled liquid water. Effects of the inhomogeneity length scale are systematically considered via the imposition of sinusoidal density profiles of various wavelengths. For long-wavelength density profiles, bulk-like relationships between local structure, thermodynamics, and diffusivity are observed as expected. However, for both systems, a crossover in behavior occurs as a function of wavelength, with qualitatively different correlations between the local static and dynamic quantities emerging as density variations approach the scale of a particle diameter. Irrespective of the density variation wavelength, average diffusivities of hard-sphere fluids in the inhomogeneous and homogeneous directions are coupled and approximately correlate with the volume available for insertion of another particle. Unfortunately, a quantitatively reliable static predictor of position-dependent dynamics has yet to be identified for even the simplest of inhomogeneous fluids. PMID:24984592

  5. Perfect fluid spheres in general relativity

    NASA Astrophysics Data System (ADS)

    Srivastava, D. C.; Prasad, S. S.

    1983-01-01

    Spherically symmetric perfect fluid distributions in general relativity have been investigated under the assumptions of (1) uniform expansion or contraction and (2) the validity of an equation of state of the form p = p(rho) with nonuniform density. An exact solution which is equivalent to a solution found earlier by Wyman (1946) is obtained, and it is shown that the solution is unique. The boundary conditions at the interface of fluid distribution and the exterior vacuum are discussed, and as a consequence the following theorem is established: uniform expansion or contraction of a perfect fluid sphere obeying an equation of state with nonuniform density is not admitted by the field equations. It is further shown that the Wyman metric is not suitable on physical grounds to represent a cosmological solution.

  6. Casimir energy and entropy in the sphere-sphere geometry

    SciTech Connect

    Rodriguez-Lopez, Pablo

    2011-08-15

    We calculate the Casimir energy and entropy for two spheres described by the perfect-metal model, plasma model, and Drude model in the large-separation limit. We obtain nonmonotonic behavior of the Helmholtz free energy as a function of separation and temperature for the perfect-metal and plasma models, leading to parameter ranges with negative entropy, and also we obtain nonmonotonic behavior of the entropy as a function of temperature and the separation between the spheres. This nonmonotonic behavior has not been found for the Drude model. The appearance of this anomalous behavior of the entropy as well as its thermodynamic consequences are discussed.

  7. Process development and fabrication for sphere-pac fuel rods. [PWR; BWR

    SciTech Connect

    Welty, R.K.; Campbell, M.H.

    1981-06-01

    Uranium fuel rods containing sphere-pac fuel have been fabricated for in-reactor tests and demonstrations. A process for the development, qualification, and fabrication of acceptable sphere-pac fuel rods is described. Special equipment to control fuel contamination with moisture or air and the equipment layout needed for rod fabrication is described and tests for assuring the uniformity of the fuel column are discussed. Fuel retainers required for sphere-pac fuel column stability and instrumentation to measure fuel column smear density are described. Results of sphere-pac fuel rod fabrication campaigns are reviewed and recommended improvements for high throughput production are noted.

  8. Project CONDOR: Middle atmosphere wind structure obtained with lightweight inflatable spheres near the equatorial electrojet

    NASA Technical Reports Server (NTRS)

    Schmidlin, F. J.

    1987-01-01

    Observed correlations between the atmospheric electric field and the neutral wind were studied using additional atmospheric measurements during Project CONDOR. Project CONDOR obtained measurements near the equatorial electrojet (12 S) during March 1983. Neutral atmosphere wind measurements were obtained using lightweight inflatable spheres and temperatures were obtained using a datasonde. The lightweight sphere technology, the wind structure, and temperature structure are described. Results show that the lightweight sphere gives higher vertical resolution of winds below 75 km compared with the standard sphere, but gives little or no improvement above 80 km, and no usable temperature and density data.

  9. Depletion, melting and reentrant solidification in mixtures of soft and hard colloids.

    PubMed

    Marzi, Daniela; Capone, Barbara; Marakis, John; Merola, Maria Consiglia; Truzzolillo, Domenico; Cipelletti, Luca; Moingeon, Firmin; Gauthier, Mario; Vlassopoulos, Dimitris; Likos, Christos N; Camargo, Manuel

    2015-11-14

    We present extensive experimental and theoretical investigations on the structure, phase behavior, dynamics and rheology of model soft-hard colloidal mixtures realized with large, multiarm star polymers as the soft component and smaller, compact stars as the hard one. The number and length of the arms in star polymers control their softness, whereas the size ratio, the overall density and the composition are additional parameters varied for the mixtures. A coarse-grained theoretical strategy is employed to predict the structure of the systems as well as their ergodicity properties on the basis of mode coupling theory, for comparison with rheological measurements on the samples. We discovered that dynamically arrested star-polymer solutions recover their ergodicity upon addition of colloidal additives. At the same time the system displays demixing instability, and the binodal of the latter meets the glass line in a way that leads, upon addition of a sufficient amount of colloidal particles, to an arrested phase separation and reentrant solidification. We present evidence for a subsequent solid-to-solid transition well within the region of arrested phase separation, attributed to a hard-sphere-mixture type of glass, due to osmotic shrinkage of the stars at high colloidal particle concentrations. We systematically investigated the interplay of star functionality and size ratio with glass melting and demixing, and rationalized our findings by the depletion of the big stars due to the smaller colloids. This new depletion potential in which, contrary to the classic colloid-polymer case, the hard component depletes the soft one, has unique and novel characteristics and allows the calculation of phase diagrams for such mixtures. This work covers a broad range of soft-hard colloidal mixture compositions in which the soft component exceeds the hard one in size and provides general guidelines for controlling the properties of such complex mixtures. PMID:26356800

  10. Local hardness equalization: Exploiting the ambiguity

    NASA Astrophysics Data System (ADS)

    Ayers, Paul W.; Parr, Robert G.

    2008-05-01

    In the density-functional theory of chemical reactivity, the local hardness is known to be an ambiguous concept. The mathematical structure associated with this problematic situation is elaborated and three common definitions for the local hardness are critically examined: the frontier local hardness [S. K. Ghosh, Chem. Phys. Lett. 172, 77 (1990)], the total local hardness [S. K. Ghosh and M. Berkowitz, J. Chem. Phys. 83, 2976 (1985)], and the unconstrained local hardness [P. W. Ayers and R. G. Parr, J. Am. Chem. Soc. 122, 2010 (2000)]. The frontier local hardness has particularly nice properties: (a) it has smaller norm than most, if not all, other choices of the local hardness and (b) it is "unbiased" in an information-theoretic sense. For the ground electronic state of a molecular system, the frontier local hardness is equal to the global hardness. For an electronic system in its ground state, both the chemical potential and the frontier local hardness are equalized. The frontier local hardness equalization principle provides a computational approach for designing reagents with desirable chemical reactivity profiles.

  11. Sphere forming method and apparatus

    NASA Technical Reports Server (NTRS)

    Youngberg, C. L.; Miller, C. G.; Stephens, J. B.; Finnerty, A. A. (Inventor)

    1983-01-01

    A system is provided for forming small accurately spherical objects. Preformed largely spherical objects are supported at the opening of a conduit on the update of hot gas emitted from the opening, so the object is in a molten state. The conduit is suddenly jerked away at a downward incline, to allow the molten object to drop in free fall, so that surface tension forms a precise sphere. The conduit portion that has the opening, lies in a moderate vacuum chamber, and the falling sphere passes through the chamber and through a briefly opened valve into a tall drop tower that contains a lower pressure, to allow the sphere to cool without deformation caused by falling through air.

  12. How dense can one pack spheres of arbitrary size distribution?

    NASA Astrophysics Data System (ADS)

    Reis, S. D. S.; Arajo, N. A. M.; Andrade, J. S., Jr.; Herrmann, Hans J.

    2012-01-01

    We present the first systematic algorithm to estimate the maximum packing density of spheres when the grain sizes are drawn from an arbitrary size distribution. With an Apollonian filling rule, we implement our technique for disks in 2d and spheres in 3d. As expected, the densest packing is achieved with power-law size distributions. We also test the method on homogeneous and on empirical real distributions, and we propose a scheme to obtain experimentally accessible distributions of grain sizes with low porosity. Our method should be helpful in the development of ultra-strong ceramics and high-performance concrete.

  13. Theoretical study of the freezing of polystyrene sphere suspensions

    NASA Technical Reports Server (NTRS)

    Shih, W.-H.; Stroud, D.

    1983-01-01

    A theoretical study of melting in aqueous suspensions of polystyrene spheres is presented. The Helmholtz free energies of the liquid and solid phase of the suspensions are calculated as functions of sphere number density and electrolyte concentrations. The results tend to show that the freezing curve of such suspensions is that of a conventional classical liquid with repulsive short-range interactions. The interactions can be treated satisfactorily within a slightly modified Debye-Hueckel approximation. The modifications include size correction and a correction for nonlinear screening. The results are confirmed by analogous calculations for the solid phase, and for the line along which liquid and solid free energies are equal.

  14. Thermoinertial bouncing of a relativistic collapsing sphere: A numerical model

    SciTech Connect

    Herrera, L.; Di Prisco, A.; Barreto, W.

    2006-01-15

    We present a numerical model of a collapsing radiating sphere, whose boundary surface undergoes bouncing due to a decreasing of its inertial mass density (and, as expected from the equivalence principle, also of the 'gravitational' force term) produced by the 'inertial' term of the transport equation. This model exhibits for the first time the consequences of such an effect, and shows that under physically reasonable conditions this decreasing of the gravitational term in the dynamic equation may be large enough as to revert the collapse and produce a bouncing of the boundary surface of the sphere.

  15. Density dependence and composition dependence of the viscosity of neon-helium and neon-argon mixtures

    NASA Astrophysics Data System (ADS)

    Kestin, J.; Korfali, .; Sengers, J. V.; Kamgar-Parsi, B.

    1981-04-01

    In this paper we present a detailed experimental study of the density dependence of the viscosity of He?Ne and Ne?Ar mixtures at various compositions. The data are analyzed in terms of a density expansion including a logarithmic contribution whose presence is predicted by the kinetic theory of gases. The composition dependence of the viscosity of the dense gas mixtures is compared with estimated values predicted on the basis of the Enskog-Thorne theory for dense mixtures of gases of hard spheres.

  16. Effect of the cluster integrals on three particles on the calculated electron density of a hydrogen plasma

    NASA Technical Reports Server (NTRS)

    Mcintyre, R. G.; Bruce, R. E.

    1974-01-01

    The effect of the calculation of the cluster integrals on three particles is analyzed and evaluated for a hydrogen plasma where a pairwise-additive hard sphere-Coulomb potential is assumed. The Mayer cluster integral method was used to calculate the Helmholtz free energy which was then applied to the calculation of the electron number density through an iterative technique using a corrected Saha equation. It is seen that the three particle integrals provide a substantial correction to the calculations in the low energy-high density region of the hydrogen plasma.

  17. Abradable dual-density ceramic turbine seal system

    NASA Technical Reports Server (NTRS)

    Clingman, D. L.; Schechter, B.; Cross, K. R.; Cavanagh, J. R.

    1981-01-01

    A plasma sprayed dual density ceramic abradable seal system for direct application to the HPT seal shroud of small gas turbine engines. The system concept is based on the thermal barrier coating and depends upon an additional layer of modified density ceramic material adjacent to the gas flow path to provide the desired abradability. This is achieved by codeposition of inert fillers with yttria stabilized zirconia (YSZ) to interrupt the continuity of the zirconia struture. The investigation of a variety of candidate fillers, with hardness values as low as 2 on Moh's scale, led to the conclusion that solid filler materials in combination with a YSZ matrix, regardless of their hardness values, have a propensity for compacting rather than shearing as originally expected. The observed compaction is accompanied by high energy dissipation in the rub interaction, usually resulting in the adhesive transfer of blade material to the stationary seal member. Two YSZ based coating systems which incorported hollow alumino silicate spheres as density reducing agents were surveyed over the entire range of compositions from 100 percent filler to 100 percent YSZ. Abradability and erosion characteristics were determined, hardness and permeability characterized, and engine experience acquired with several system configurations.

  18. Combustion of a Polymer (PMMA) Sphere in Microgravity

    NASA Technical Reports Server (NTRS)

    Yang, Jiann C.; Hamins, Anthony; Donnelly, Michelle K.

    1999-01-01

    A series of low gravity, aircraft-based, experiments was conducted to investigate the combustion of supported thermoplastic polymer spheres under varying ambient conditions. The three types of thermoplastic investigated were polymethylmethacrylate (PMMA), polypropylene (PP). and polystyrene (PS). Spheres with diameters ranging from 2 mm to 6.35 mm were tested. The total initial pressure varied from 0.05 MPa to 0. 15 MPa whereas the ambient oxygen concentration varied from 19 % to 30 % (by volume). The ignition system consisted of a pair of retractable energized coils. Two CCD cameras recorded the burning histories of the spheres. The video sequences revealed a number of dynamic events including bubbling and sputtering, as well as soot shell formation and break-up during combustion of the spheres at reduced gravity. The ejection of combusting material from the burning spheres represents a fire hazard that must be considered at reduced gravity. The ejection process was found to be sensitive to polymer type. All average burning rates were measured to increase with initial sphere diameter and oxygen concentration, whereas the initial pressure had little effect. The three thermoplastic types exhibited different burning characteristics. For the same initial conditions, the burning rate of PP was slower than PMMA, whereas the burning rate of PS was comparable to PMMA. The transient diameter of the burning thermoplastic exhibited two distinct periods: an initial period (enduring approximately half of the total burn duration) when the diameter remained approximately constant, and a final period when the square of the diameter linearly decreased with time. A simple homogeneous two-phase model was developed to understand the changing diameter of the burning sphere. Its value is based on a competition between diameter reduction due to mass loss from burning and sputtering, and diameter expansion due to the processes of swelling (density decrease with heating) and bubble growth. The model relies on empirical parameters for input, such as the burning rate and the duration of the initial and final burning periods.

  19. Microstructure and Rheology in Suspensions of Swollen PMMA Spheres

    NASA Astrophysics Data System (ADS)

    Paulin, Steven Edward

    Scope and method of study. Rheological properties of materials are generally observed as macroscopic manifestations of microscopic behavior. However, there are very few systems in which both may be simultaneously monitored and correlated. Colloidal suspensions, due to their comparatively similar size to the wavelength of visible light and usually well defined characteristics, make nearly perfect systems upon which to study microstructure and rheology. Suspensions of polymethylmethacrylate spheres swollen in benzyl alcohol have been characterized via static and dynamic light scattering techniques. Monitoring of microstructure under the application of applied shear was achieved utilizing a Bohlin Constant Stress Rheometer fitted with an optical couette. Here, a range of both steady state and oscillatory rheological measurements are made on the suspension while microstructure was monitored via light scattering. Scattering images from shear induced structures were video taped and later digitized for enhancement and analysis. Findings and conclusions. PMMA microgel suspensions have been observed to undergo an equilibrium order/disorder phase transition similar to that found in simulations of soft spheres interacting via a 1/r^{20 } type interparticle potential. Here, the width of the coexistence region is narrower than that for a purely hard sphere repulsion. Bragg scattering from samples in the coexistence region of the equilibrium phase diagram indicate crystallites composed of random stacked hexagonal close packed planes, nearly identical to that found in hard sphere like sterically stabilized suspensions of PMMA. Shear induced microstructures similar to those found in sterically stabilized suspensions of PMMA are observed. Although the linear viscoelastic region can be examined, swollen PMMA exhibit microstructural evolution in the nonlinear region. Nonlinear creep and creep recovery measurements indicate a strain dependent dissipative process derived from sample microstructure, with an elastic relaxation due to local microstructure or particle deformation.

  20. ORSPHERE: CRITICAL, BARE, HEU(93.2)-METAL SPHERE

    SciTech Connect

    Margaret A. Marshall

    2013-09-01

    In the early 1970’s Dr. John T. Mihalczo (team leader), J.J. Lynn, and J.R. Taylor performed experiments at the Oak Ridge Critical Experiments Facility (ORCEF) with highly enriched uranium (HEU) metal (called Oak Ridge Alloy or ORALLOY) in an attempt to recreate GODIVA I results with greater accuracy than those performed at Los Alamos National Laboratory in the 1950’s (HEU-MET-FAST-001). The purpose of the Oak Ridge ORALLOY Sphere (ORSphere) experiments was to estimate the unreflected and unmoderated critical mass of an idealized sphere of uranium metal corrected to a density, purity, and enrichment such that it could be compared with the GODIVA I experiments. “The very accurate description of this sphere, as assembled, establishes it as an ideal benchmark for calculational methods and cross-section data files.” (Reference 1) While performing the ORSphere experiments care was taken to accurately document component dimensions (±0. 0001 in. for non-spherical parts), masses (±0.01 g), and material data The experiment was also set up to minimize the amount of structural material in the sphere proximity. A three part sphere was initially assembled with an average radius of 3.4665 in. and was then machined down to an average radius of 3.4420 in. (3.4425 in. nominal). These two spherical configurations were evaluated and judged to be acceptable benchmark experiments; however, the two experiments are highly correlated.

  1. Ionic asymmetry and solvent excluded volume effects on spherical electric double layers: A density functional approach

    PubMed Central

    Medasani, Bharat; Ovanesyan, Zaven; Thomas, Dennis G.; Sushko, Maria L.; Marucho, Marcelo

    2014-01-01

    In this article, we present a classical density functional theory for electrical double layers of spherical macroions that extends the capabilities of conventional approaches by accounting for electrostatic ion correlations, size asymmetry, and excluded volume effects. The approach is based on a recent approximation introduced by Hansen-Goos and Roth for the hard sphere excess free energy of inhomogeneous fluids [J. Chem. Phys. 124, 154506 (2006); Hansen-Goos and Roth, J. Phys.: Condens. Matter 18, 8413 (2006)]. It accounts for the proper and efficient description of the effects of ionic asymmetry and solvent excluded volume, especially at high ion concentrations and size asymmetry ratios including those observed in experimental studies. Additionally, we utilize a leading functional Taylor expansion approximation of the ion density profiles. In addition, we use the mean spherical approximation for multi-component charged hard sphere fluids to account for the electrostatic ion correlation effects. These approximations are implemented in our theoretical formulation into a suitable decomposition of the excess free energy which plays a key role in capturing the complex interplay between charge correlations and excluded volume effects. We perform Monte Carlo simulations in various scenarios to validate the proposed approach, obtaining a good compromise between accuracy and computational cost. We use the proposed computational approach to study the effects of ion size, ion size asymmetry, and solvent excluded volume on the ion profiles, integrated charge, mean electrostatic potential, and ionic coordination number around spherical macroions in various electrolyte mixtures. Our results show that both solvent hard sphere diameter and density play a dominant role in the distribution of ions around spherical macroions, mainly for experimental water molarity and size values where the counterion distribution is characterized by a tight binding to the macroion, similar to that predicted by the Stern model. PMID:24880304

  2. Ionic Asymmetry and Solvent Excluded Volume Effects on Spherical Electric Double Layers: A Density Functional Approach

    SciTech Connect

    Medasani, Bharat; Ovanesyan, Zaven; Thomas, Dennis G.; Sushko, Maria L.; Marucho, Marcelo

    2014-05-29

    In this article we present a classical density functional theory for electrical double layers of spherical macroions that extends the capabilities of conventional approaches by accounting for electrostatic ion correlations, size asymmetry and excluded volume effects. The approach is based on a recent approximation introduced by Hansen-Goos and Roth for the hard sphere excess free energy of inhomogeneous fluids (J. Chem. Phys. 124, 154506). It accounts for the proper and efficient description of the effects of ionic asymmetry and solvent excluded volume, especially at high ion concentrations and size asymmetry ratios including those observed in experimental studies. Additionally, we utilize a leading functional Taylor expansion approximation of the ion density profiles. In addition, we use the Mean Spherical Approximation for multi-component charged hard sphere fluids to account for the electrostatic ion correlation effects. These approximations are implemented in our theoretical formulation into a suitable decomposition of the excess free energy which plays a key role in capturing the complex interplay between charge correlations and excluded volume effects. We perform Monte Carlo simulations in various scenarios to validate the proposed approach, obtaining a good compromise between accuracy and computational cost. We use the proposed computational approach to study the effects of ion size, ion size asymmetry and solvent excluded volume on the ion profiles, integrated charge, mean electrostatic potential, and ionic coordination number around spherical macroions in various electrolyte mixtures. Our results show that both solvent hard sphere diameter and density play a dominant role in the distribution of ions around spherical macroions, mainly for experimental water molarity and size values where the counterion distribution is characterized by a tight binding to the macroion, similar to that predicted by the Stern model.

  3. Ionic asymmetry and solvent excluded volume effects on spherical electric double layers: A density functional approach

    NASA Astrophysics Data System (ADS)

    Medasani, Bharat; Ovanesyan, Zaven; Thomas, Dennis G.; Sushko, Maria L.; Marucho, Marcelo

    2014-05-01

    In this article, we present a classical density functional theory for electrical double layers of spherical macroions that extends the capabilities of conventional approaches by accounting for electrostatic ion correlations, size asymmetry, and excluded volume effects. The approach is based on a recent approximation introduced by Hansen-Goos and Roth for the hard sphere excess free energy of inhomogeneous fluids [J. Chem. Phys. 124, 154506 (2006); Hansen-Goos and Roth, J. Phys.: Condens. Matter 18, 8413 (2006)]. It accounts for the proper and efficient description of the effects of ionic asymmetry and solvent excluded volume, especially at high ion concentrations and size asymmetry ratios including those observed in experimental studies. Additionally, we utilize a leading functional Taylor expansion approximation of the ion density profiles. In addition, we use the mean spherical approximation for multi-component charged hard sphere fluids to account for the electrostatic ion correlation effects. These approximations are implemented in our theoretical formulation into a suitable decomposition of the excess free energy which plays a key role in capturing the complex interplay between charge correlations and excluded volume effects. We perform Monte Carlo simulations in various scenarios to validate the proposed approach, obtaining a good compromise between accuracy and computational cost. We use the proposed computational approach to study the effects of ion size, ion size asymmetry, and solvent excluded volume on the ion profiles, integrated charge, mean electrostatic potential, and ionic coordination number around spherical macroions in various electrolyte mixtures. Our results show that both solvent hard sphere diameter and density play a dominant role in the distribution of ions around spherical macroions, mainly for experimental water molarity and size values where the counterion distribution is characterized by a tight binding to the macroion, similar to that predicted by the Stern model.

  4. Particle sizing in highly turbid dispersions by Photon Density Wave spectroscopy: Bidisperse systems

    NASA Astrophysics Data System (ADS)

    Bressel, L.; Wolter, J.; Reich, O.

    2015-09-01

    Photon Density Wave (PDW) spectroscopy is applied for characterizing the scattering properties, i.e. the reduced scattering coefficient ?s?, of highly concentrated mono- and bidisperse polymer latices. The theory for dependent scattering is reviewed and analytical expressions for the structure factors for hard sphere interaction in mono- (HSPYA) and bidisperse (BHSPYA) systems are given. From the scattering properties particle sizes of mono- and bidisperse polystyrene latices are determined as well as the relative amount of small and large particles for the bidisperse case.

  5. Porous Si spheres encapsulated in carbon shells with enhanced anodic performance in lithium-ion batteries

    SciTech Connect

    Wang, Hui; Wu, Ping Shi, Huimin; Lou, Feijian; Tang, Yawen; Zhou, Tongge; Zhou, Yiming Lu, Tianhong

    2014-07-01

    Highlights: • In situ magnesiothermic reduction route for the formation of porous Si@C spheres. • Unique microstructural characteristics of both porous sphere and carbon matrix. • Enhanced anodic performance in term of cycling stability for lithium-ion batteries. - Abstract: A novel type of porous Si–C micro/nano-hybrids, i.e., porous Si spheres encapsulated in carbon shells (porous Si@C spheres), has been constructed through the pyrolysis of polyvinylidene fluoride (PVDF) and subsequent magnesiothermic reduction methodology by using SiO{sub 2} spheres as precursors. The as-synthesized porous Si@C spheres have been applied as anode materials for lithium-ion batteries (LIBs), and exhibit enhanced anodic performance in term of cycling stability compared with bare Si spheres. For example, the porous Si@C spheres are able to exhibit a high reversible capacity of 900.0 mA h g{sup −1} after 20 cycles at a current density of 0.05 C (1 C = 4200 mA g{sup −1}), which is much higher than that of bare Si spheres (430.7 mA h g{sup −1})

  6. Complexation of DNA with positive spheres: Phase diagram of charge inversion and reentrant condensation

    NASA Astrophysics Data System (ADS)

    Nguyen, T. T.; Shklovskii, B. I.

    2001-10-01

    The phase diagram of a water solution of DNA and oppositely charged spherical macroions is studied. DNA winds around spheres to form beads-on-a-string complexes resembling the chromatin 10 nm fiber. At small enough concentration of spheres these "artificial chromatin" complexes are negative, while at large enough concentrations of spheres the charge of DNA is inverted by the adsorbed spheres. Charges of complexes stabilize their solutions. In the plane of concentrations of DNA and spheres the phases with positive and negative complexes are separated by another phase, which contains the condensate of neutral DNA-spheres complexes. Thus, when the concentration of spheres grows, DNA-spheres complexes experience condensation and resolubilization (or reentrant condensation). Phenomenological theory of the phase diagram of reentrant condensation and charge inversion is suggested. Parameters of this theory are calculated by microscopic theory. It is shown that an important part of the effect of a monovalent salt on the phase diagram can be described by the nontrivial renormalization of the effective linear charge density of DNA wound around a sphere, due to the Onsager-Manning condensation. We argue that our phenomenological phase diagram or reentrant condensation is generic to a large class of strongly asymmetric electrolytes. Possible implications of these results for the natural chromatin are discussed.

  7. Handbook of hard coatings

    SciTech Connect

    Bunshah, R.; Weissmantel, C.

    2000-07-01

    This book discusses the hard coatings classified as tribologically hard, which are wear resistant and low friction. Three sections discuss tribological properties and new developments. With the development of modern technology in the areas of optical, optoelectronic, and defense related applications, the traditional term hard coatings can be extended. Thus, a system which operates satisfactorily, in a given environment can be said to be hard with respect to that environment. Many hard coatings are ceramic compounds such as oxides, carbides, nitrides, ceramic alloys, cements, diamonds and cubic nitride.

  8. The unconstrained local hardness: an intriguing quantity, beset by problems.

    PubMed

    Cuevas-Saavedra, Rogelio; Rabi, Nataly; Ayers, Paul W

    2011-11-21

    Developing a mathematical approach to the local hard/soft acid/base principle requires an unambiguous definition for the local hardness. One such quantity, which has aroused significant interest in recent years, is the unconstrained local hardness. Key identities are derived for the unconstrained local hardness, ??/??(r). Several identities are presented which allow one to determine the unconstrained local hardness either explicitly using the hardness kernel and the inverse-linear response function, or implicitly by solving a system of linear equations. One result of this analysis is that the problem of determining the unconstrained local hardness is infinitely ill-conditioned because arbitrarily small changes in electron density can cause enormous changes in the chemical potential. This is manifest in the exponential divergence of the unconstrained local hardness as one moves away from the system. This suggests that one should be very careful when using the unconstrained local hardness for chemical interpretation. PMID:21984043

  9. Excluded volume effects in compressed polymer brushes: A density functional theory

    SciTech Connect

    Chen, Cangyi; Tang, Ping E-mail: fengqiu@fudan.edu.cn; Qiu, Feng E-mail: fengqiu@fudan.edu.cn; Shi, An-Chang

    2015-03-28

    A classical density functional theory (DFT) is applied to investigate the behavior of compressed polymer brushes composed of hard-sphere chains. The excluded volume interactions among the chain segments are explicitly treated. Two compression systems are used to study the behavior of brush-wall and brush-brush interactions. For the brush-brush systems, an obvious interpenetration zone has been observed. The extent of the interpenetration depends strongly on the grafting density. Furthermore, the repulsive force between the brush and wall or between the two brushes has been obtained as a function of the compression distance. Compared to the prediction of the analytic self-consistent field theory, such force increases more rapidly in the brush-wall compression with high polymer grafting densities or at higher compressions. In the brush-brush compression system, the interpenetration between the two compressed brushes creates a “softer” interaction. The influence of hard-sphere solvents on the behavior of compressed brushes is also discussed.

  10. Vortex interaction with a moving sphere

    NASA Astrophysics Data System (ADS)

    Allen, J. J.; Jouanne, Y.; Shashikanth, B. N.

    This paper details the experimental results of the axisymmetric collision of a vortex ring with a sphere. The experiments were conducted in water and a neutrally buoyant sphere was free to move in response to the impulse delivered by the vortex ring during the interaction. Good agreement has been achieved between kinematic data for the sphere speed and acceleration and the behaviour of the moment and rate of change of the moment of vorticity, measured using particle image velocimetry (PIV). The interaction of the vortex ring with the sphere creates secondary vorticity on the sphere surface. This initially results in a reduction of the fluid impulse and an acceleration of the sphere. However, within the measurement window of the interaction, the rate of increase of the positive moment of vorticity is slightly larger than the rate of increase of the negative moment of vorticityand the sphere gradually slows. A movie is available with the online version of the paper.

  11. Open-cluster density profiles derived using a kernel estimator

    NASA Astrophysics Data System (ADS)

    Seleznev, Anton F.

    2016-03-01

    Surface and spatial radial density profiles in open clusters are derived using a kernel estimator method. Formulae are obtained for the contribution of every star into the spatial density profile. The evaluation of spatial density profiles is tested against open-cluster models from N-body experiments with N = 500. Surface density profiles are derived for seven open clusters (NGC 1502, 1960, 2287, 2516, 2682, 6819 and 6939) using Two-Micron All-Sky Survey data and for different limiting magnitudes. The selection of an optimal kernel half-width is discussed. It is shown that open-cluster radius estimates hardly depend on the kernel half-width. Hints of stellar mass segregation and structural features indicating cluster non-stationarity in the regular force field are found. A comparison with other investigations shows that the data on open-cluster sizes are often underestimated. The existence of an extended corona around the open cluster NGC 6939 was confirmed. A combined function composed of the King density profile for the cluster core and the uniform sphere for the cluster corona is shown to be a better approximation of the surface radial density profile.The King function alone does not reproduce surface density profiles of sample clusters properly. The number of stars, the cluster masses and the tidal radii in the Galactic gravitational field for the sample clusters are estimated. It is shown that NGC 6819 and 6939 are extended beyond their tidal surfaces.

  12. The sphere-in-contact model of carbon materials.

    PubMed

    Zeinalipour-Yazdi, Constantinos D; Pullman, David P; Catlow, C Richard A

    2016-01-01

    A sphere-in-contact model is presented that is used to build physical models of carbon materials such as graphite, graphene, carbon nanotubes and fullerene. Unlike other molecular models, these models have correct scale and proportions because the carbon atoms are represented by their atomic radius, in contrast to the more commonly used space-fill models, where carbon atoms are represented by their van der Waals radii. Based on a survey taken among 65 undergraduate chemistry students and 28 PhD/postdoctoral students with a background in molecular modeling, we found misconceptions arising from incorrect visualization of the size and location of the electron density located in carbon materials. Based on analysis of the survey and on a conceptual basis we show that the sphere-in-contact model provides an improved molecular representation of the electron density of carbon materials compared to other molecular models commonly used in science textbooks (i.e., wire-frame, ball-and-stick, space-fill). We therefore suggest that its use in chemistry textbooks along with the ball-and-stick model would significantly enhance the visualization of molecular structures according to their electron density. Graphical Abstract A sphere-in-contact model of C60-fullerene. PMID:26791534

  13. Gravitational instability of finite isothermal spheres

    NASA Astrophysics Data System (ADS)

    Chavanis, P. H.

    2002-01-01

    We investigate the stability of bounded self-gravitating systems in the canonical ensemble by using a thermodynamical approach. Our study extends the earlier work of Padmanabhan (\\cite{pad89}) in the microcanonical ensemble. By studying the second variations of the free energy, we find that instability sets in precisely at the point of minimum temperature in agreement with the theorem of Katz (\\cite{kat78}). The perturbation that induces instability at this point is calculated explicitly; it has not a ``core-halo'' structure contrary to what happens in the microcanonical ensemble. We also study Jeans type gravitational instability of isothermal gaseous spheres described by Navier-Stokes equations. The introduction of a container and the consideration of an inhomogeneous distribution of matter avoids the Jeans swindle. We show analytically the equivalence between dynamical stability and thermodynamical stability and the fact that the stability of isothermal gas spheres does not depend on the viscosity. This confirms the findings of Semelin et al. (\\cite{sem01}) who used numerical methods or approximations. We also give a simpler derivation of the geometric hierarchy of scales inducing instability discovered by these authors. The density profiles that trigger these instabilities are calculated explicitly; high order modes of instability present numerous oscillations whose nodes also follow a geometric progression. This suggests that the system will fragment in a series of ``clumps'' and that these ``clumps'' will themselves fragment in substructures. The fact that both the domain sizes leading to instability and the ``clumps'' sizes within a domain follow a geometric progression with the same ratio suggests a fractal-like behavior. This gives further support to the interpretation of de Vega et al. (1996) concerning the fractal structure of the interstellar medium.

  14. The dynamic sphere test problem

    SciTech Connect

    Chabaud, Brandon M.; Brock, Jerry S.; Smith, Brandon M.

    2012-05-16

    In this manuscript we define the dynamic sphere problem as a spherical shell composed of a homogeneous, linearly elastic material. The material exhibits either isotropic or transverse isotropic symmetry. When the problem is formulated in material coordinates, the balance of mass equation is satisfied automatically. Also, the material is assumed to be kept at constant temperature, so the only relevant equation is the equation of motion. The shell has inner radius r{sub i} and outer radius r{sub o}. Initially, the shell is at rest. We assume that the interior of the shell is a void and we apply a time-varying radial stress on the outer surface.

  15. Development of a Falling Sphere Technique for E-region Wind Measurements

    NASA Astrophysics Data System (ADS)

    Cannon, B. K.; Fish, C. S.; Larsen, M. F.; Swenson, C.

    2009-12-01

    In this presentation we outline the development of a new falling sphere technique sensor for measuring the lower E-region neutral winds and density, which are critical for many of the electrodynamics and plasma physics studies that are carried out as part of the NASA suborbital rocket program. Currently, chemical releases are the primary technique for measuring winds in the lower E-region. Chemical release wind measurements provide detailed wind profiles with good accuracy and have a long flight history. However, they have a number of operational drawbacks, including the need for clear skies over a broad area for camera observations, limited viewing windows (e.g., only at nighttime in the case of trimethyl aluminum), and the need to follow strict handling procedures. Recent advances in low-cost commercial technology have made the falling sphere technique an attractive option to chemical release for E-region measurements. Falling sphere instruments (typically inflatable devices) have been used extensively to make wind measurements in the D-region. Similar measurements in the lower E-region require higher sensitivity accelerometers and a more careful design of the sphere (e.g., solid sphere structure for hypersonic speeds). This presentation demonstrates the design and laboratory testing and calibration of a next-generation solid falling sphere instrument for E-region measurements. Ultimately, the development of this new falling sphere instrument will enable the deployment of multiple falling spheres from one rocket for 3D volume determination of neutral wind measurements.

  16. Ormosils of high hardness

    SciTech Connect

    Iwamoto, Takashi; Mackenzie, J.D.

    1994-12-31

    Organically modified silicates (ormosils) of high hardness were prepared by the reactions of tetraethoxysilane (TEOS) and polydimethylsiloxane (PDMS) aided by ultrasonic irradiation. The mechanisms leading to the hard ormosil formation were investigated by liquid state {sup 29}Si NMR spectroscopy. PDMS chains were found to be broken into shorter chains and/or 4-membered siloxane rings during the reaction and finally, all PDMS chains were chemically incorporated as short chains into silica networks. Vickers hardnesses of the hard ormosils were measured and compared with those of the hardest transparent plastics. Whereas the hardest transparent plastics have Vickers hardness values of less than 25 kg/mm{sup 2}, the hard ormosils have Vickers hardnesses tip to higher than 150 kg/mm{sup 2}. A theoretical model was developed for the calculation of Vickers hardnesses of the hard ormosils and agreed well with experimental results. Predictions based on this theory indicate that even harder ormosils can be made when Al{sub 2}O{sub 3}, ZrO{sub 2} and TiO{sub 2} are substituted for SiO{sub 2}. Results based on these new ormosils are also presented.

  17. Collective excitations in soft-sphere fluids

    NASA Astrophysics Data System (ADS)

    Bryk, Taras; Gorelli, Federico; Ruocco, Giancarlo; Santoro, Mario; Scopigno, Tullio

    2014-10-01

    Despite that the thermodynamic distinction between a liquid and the corresponding gas ceases to exist at the critical point, it has been recently shown that reminiscence of gaslike and liquidlike behavior can be identified in the supercritical fluid region, encoded in the behavior of hypersonic waves dispersion. By using a combination of molecular dynamics simulations and calculations within the approach of generalized collective modes, we provide an accurate determination of the dispersion of longitudinal and transverse collective excitations in soft-sphere fluids. Specifically, we address the decreasing rigidity upon density reduction along an isothermal line, showing that the positive sound dispersion, an excess of sound velocity over the hydrodynamic limit typical for dense liquids, displays a nonmonotonic density dependence strictly correlated to that of thermal diffusivity and kinematic viscosity. This allows rationalizing recent observation parting the supercritical state based on the Widom line, i.e., the extension of the coexistence line. Remarkably, we show here that the extremals of transport properties such as thermal diffusivity and kinematic viscosity provide a robust definition for the boundary between liquidlike and gaslike regions, even in those systems without a liquid-gas binodal line. Finally, we discuss these findings in comparison with recent results for Lennard-Jones model fluid and with the notion of the "rigid-nonrigid" fluid separation lines.

  18. Collective excitations in soft-sphere fluids.

    PubMed

    Bryk, Taras; Gorelli, Federico; Ruocco, Giancarlo; Santoro, Mario; Scopigno, Tullio

    2014-10-01

    Despite that the thermodynamic distinction between a liquid and the corresponding gas ceases to exist at the critical point, it has been recently shown that reminiscence of gaslike and liquidlike behavior can be identified in the supercritical fluid region, encoded in the behavior of hypersonic waves dispersion. By using a combination of molecular dynamics simulations and calculations within the approach of generalized collective modes, we provide an accurate determination of the dispersion of longitudinal and transverse collective excitations in soft-sphere fluids. Specifically, we address the decreasing rigidity upon density reduction along an isothermal line, showing that the positive sound dispersion, an excess of sound velocity over the hydrodynamic limit typical for dense liquids, displays a nonmonotonic density dependence strictly correlated to that of thermal diffusivity and kinematic viscosity. This allows rationalizing recent observation parting the supercritical state based on the Widom line, i.e., the extension of the coexistence line. Remarkably, we show here that the extremals of transport properties such as thermal diffusivity and kinematic viscosity provide a robust definition for the boundary between liquidlike and gaslike regions, even in those systems without a liquid-gas binodal line. Finally, we discuss these findings in comparison with recent results for Lennard-Jones model fluid and with the notion of the "rigid-nonrigid" fluid separation lines. PMID:25375488

  19. Spectroscopic and electronic structure properties of CdSe nanocrystals: spheres and cubes.

    PubMed

    Proshchenko, Vitaly; Dahnovsky, Yuri

    2014-04-28

    In this work we study the electronic structure of CdmSem quantum dots of various sizes and different shapes such as spheres and cubes using DFT, TDDFT, and CIS methods. This work requires a careful computational analysis where a proper exchange-correlation functional has to be chosen to fit the experimental optical gap. We find some differences in the optical and HOMO-LUMO gap values between spheres and cubes. In general, the gaps for the cubes have higher values than those for the spheres. We also calculate optical absorption spectra using the data for energy levels and oscillator strengths for optical transitions. We find that DFT yields some discrepancy in the density of states for the spheres and cubes. However, the density of states calculated by TDDFT and CIS provide better agreement. The results of the calculation can be useful for quantum dots synthesized in laser ablation experiments. PMID:24634919

  20. Measuring the phase of vibration of spheres in a viscoelastic medium as an image contrast modality

    NASA Astrophysics Data System (ADS)

    Urban, Matthew W.; Kinnick, Randall R.; Greenleaf, James F.

    2005-12-01

    Detection of calcifications in breast is an important problem in the diagnosis of breast cancer. Vibro-acoustography is a recently developed method that uses the radiation force of ultrasound to create images of the mechanical response of an object at a low frequency using the magnitude or phase of the response. Small spheres are used to explore the use of the phase of vibration as a contrast modality for use in detection and identification of calcifications in breast tissue. An experiment is presented to measure the magnitude and phase of vibration at different frequencies. The theoretical and experimental results are compared for spheres of two different sizes. Phase images are shown in which five spheres of different density can be clearly distinguished from each other. With phase measurements and images, it is demonstrated that predictable image contrast exists for spheres of different density embedded in a viscoelastic medium.

  1. Sphere Drag and Heat Transfer

    PubMed Central

    Duan, Zhipeng; He, Boshu; Duan, Yuanyuan

    2015-01-01

    Modelling fluid flows past a body is a general problem in science and engineering. Historical sphere drag and heat transfer data are critically examined. The appropriate drag coefficient is proposed to replace the inertia type definition proposed by Newton. It is found that the appropriate drag coefficient is a desirable dimensionless parameter to describe fluid flow physical behavior so that fluid flow problems can be solved in the simple and intuitive manner. The appropriate drag coefficient is presented graphically, and appears more general and reasonable to reflect the fluid flow physical behavior than the traditional century old drag coefficient diagram. Here we present drag and heat transfer experimental results which indicate that there exists a relationship in nature between the sphere drag and heat transfer. The role played by the heat flux has similar nature as the drag. The appropriate drag coefficient can be related to the Nusselt number. This finding opens new possibilities in predicting heat transfer characteristics by drag data. As heat transfer for flow over a body is inherently complex, the proposed simple means may provide an insight into the mechanism of heat transfer for flow past a body. PMID:26189698

  2. Sphere Drag and Heat Transfer

    NASA Astrophysics Data System (ADS)

    Duan, Zhipeng; He, Boshu; Duan, Yuanyuan

    2015-07-01

    Modelling fluid flows past a body is a general problem in science and engineering. Historical sphere drag and heat transfer data are critically examined. The appropriate drag coefficient is proposed to replace the inertia type definition proposed by Newton. It is found that the appropriate drag coefficient is a desirable dimensionless parameter to describe fluid flow physical behavior so that fluid flow problems can be solved in the simple and intuitive manner. The appropriate drag coefficient is presented graphically, and appears more general and reasonable to reflect the fluid flow physical behavior than the traditional century old drag coefficient diagram. Here we present drag and heat transfer experimental results which indicate that there exists a relationship in nature between the sphere drag and heat transfer. The role played by the heat flux has similar nature as the drag. The appropriate drag coefficient can be related to the Nusselt number. This finding opens new possibilities in predicting heat transfer characteristics by drag data. As heat transfer for flow over a body is inherently complex, the proposed simple means may provide an insight into the mechanism of heat transfer for flow past a body.

  3. Sphere Drag and Heat Transfer.

    PubMed

    Duan, Zhipeng; He, Boshu; Duan, Yuanyuan

    2015-01-01

    Modelling fluid flows past a body is a general problem in science and engineering. Historical sphere drag and heat transfer data are critically examined. The appropriate drag coefficient is proposed to replace the inertia type definition proposed by Newton. It is found that the appropriate drag coefficient is a desirable dimensionless parameter to describe fluid flow physical behavior so that fluid flow problems can be solved in the simple and intuitive manner. The appropriate drag coefficient is presented graphically, and appears more general and reasonable to reflect the fluid flow physical behavior than the traditional century old drag coefficient diagram. Here we present drag and heat transfer experimental results which indicate that there exists a relationship in nature between the sphere drag and heat transfer. The role played by the heat flux has similar nature as the drag. The appropriate drag coefficient can be related to the Nusselt number. This finding opens new possibilities in predicting heat transfer characteristics by drag data. As heat transfer for flow over a body is inherently complex, the proposed simple means may provide an insight into the mechanism of heat transfer for flow past a body. PMID:26189698

  4. Sphere-Pac Evaluation for Transmutation

    SciTech Connect

    Icenhour, A.S.

    2005-05-19

    The U.S. Department of Energy Advanced Fuel Cycle Initiative (AFCI) is sponsoring a project at Oak Ridge National Laboratory with the objective of conducting the research and development necessary to evaluate the use of sphere-pac transmutation fuel. Sphere-pac fuels were studied extensively in the 1960s and 1970s. More recently, this fuel form is being studied internationally as a potential plutonium-burning fuel. For transmutation fuel, sphere-pac fuels have potential advantages over traditional pellet-type fuels. This report provides a review of development efforts related to the preparation of sphere-pac fuels and their irradiation tests. Based on the results of these tests, comparisons with pellet-type fuels are summarized, the advantages and disadvantages of using sphere-pac fuels are highlighted, and sphere-pac options for the AFCI are recommended. The Oak Ridge National Laboratory development activities are also outlined.

  5. Mesoporous carbon spheres with controlled porosity for high-performance lithium-sulfur batteries

    NASA Astrophysics Data System (ADS)

    Wang, Dexian; Fu, Aiping; Li, Hongliang; Wang, Yiqian; Guo, Peizhi; Liu, Jingquan; Zhao, Xiu Song

    2015-07-01

    Mesoporous carbon (MC) spheres with hierarchical pores, controlled pore volume and high specific surface areas have been prepared by a mass-producible spray drying assisted template method using sodium alginate as carbon precursor and commercial colloidal silica particles as hard template. The resulting MC spheres, possessing hierarchical pores in the range of 3-30 nm, are employed as conductive matrices for the preparation of cathode materials for lithium-sulfur batteries. A high pressure induced one-step impregnation of elemental sulfur into the pore of the MC spheres has been exploited. The electrochemical performances of sulfur-impregnated MC spheres (S-MC) derived from MC spheres with different pore volume and specific surface area but with the same sulfur loading ratio of 60 wt% (S-MC-X-60) have been investigated in details. The S-MC-4-60 composite cathode material displayed a high initial discharge capacity of 1388 mAhg-1 and a good cycling stability of 857 mAhg-1 after 100 cycles at 0.2C, and shows also excellent rate capability of 864 mAhg-1 at 2C. More importantly, the sulfur loading content in MC-4 spheres can reach as high as 80%, and it still can deliver a capacity of 569 mAhg-1 after 100 cycles at 0.2C.

  6. Mixtures of ions and amphiphilic molecules in slit-like pores: A density functional approach

    SciTech Connect

    Pizio, O.; Rżysko, W. Sokołowski, S.; Sokołowska, Z.

    2015-04-28

    We investigate microscopic structure and thermodynamic properties of a mixture that contains amphiphilic molecules and charged hard spheres confined in slit-like pores with uncharged hard walls. The model and the density functional approach are the same as described in details in our previous work [Pizio et al., J. Chem. Phys. 140, 174706 (2014)]. Our principal focus is in exploring the effects brought by the presence of ions on the structure of confined amphiphilic particles. We have found that for some cases of anisotropic interactions, the change of the structure of confined fluids occurs via the first-order transitions. Moreover, if anions and cations are attracted by different hemispheres of amphiphiles, a charge at the walls appears at the zero value of the wall electrostatic potential. For a given thermodynamic state, this charge is an oscillating function of the pore width.

  7. Microgravity and the Formation of Latex Spheres

    NASA Technical Reports Server (NTRS)

    1982-01-01

    This set of photographs illustrates the value of microgravity in the formation of latex spheres. The image at left shows irregular spheres produced on Earth, while the photograph at right shows uniform spheres produced during the STS-3 mission, March 22 - 30, 1982, in the Monodisperse Latex Reactor, developed by the Marshall Space Flight Center and Lehigh University. The Marshall-managed MLR experiment demonstrated the feasibility of producing monodisperse polystyrene latex microspheres in space and their application to medicine and industry.

  8. Porous Ceramic Spheres from Ion Exchange Resin

    NASA Technical Reports Server (NTRS)

    Dynys, Fred

    2005-01-01

    A commercial cation ion exchange resin, cross-linked polystyrene, has been successfully used as a template to fabricate 20 to 50 micron porous ceramic spheres. Ion exchange resins have dual template capabilities. Pore architecture of the ceramic spheres can be altered by changing the template pattern. Templating can be achieved by utilizing the internal porous structure or the external surface of the resin beads. Synthesis methods and chemical/physical characteristics of the ceramic spheres will be reported.

  9. Process for making hollow carbon spheres

    DOEpatents

    Luhrs, Claudia C.; Phillips, Jonathan; Richard, Monique N.; Knapp, Angela Michelle

    2013-04-16

    A hollow carbon sphere having a carbon shell and an inner core is disclosed. The hollow carbon sphere has a total volume that is equal to a volume of the carbon shell plus an inner free volume within the carbon shell. The inner free volume is at least 25% of the total volume. In some instances, a nominal diameter of the hollow carbon sphere is between 10 and 180 nanometers.

  10. Crystalline assembly of hard polyhedra via directional entropic forces

    NASA Astrophysics Data System (ADS)

    Damasceno, Pablo F.; Engel, Michael; Glotzer, Sharon C.

    2012-02-01

    Entropic forces are effective forces that result from a system's statistical tendency to increase its entropy. Hard rods and disks spontaneously align and can assemble into layers and columns if those structures increase the configurational space available to the particles. Hard spheres, cubes and even tetrahedra order for the same reason. Here we extend those findings by showing that hard polyhedra can self-assemble into a variety of complex phases, most of them never before reported in systems of single-component hard particles. The role of shape and directional entropic forces in stabilizing these structures will be discussed. Our results suggest new possibilities for self-assembling complex target structures from colloidal building blocks. [4pt] [1] Damasceno, PF; Engel, M; Glotzer, SC. arXiv:1109.1323v1

  11. Session: Hard Rock Penetration

    SciTech Connect

    Tennyson, George P. Jr.; Dunn, James C.; Drumheller, Douglas S.; Glowka, David A.; Lysne, Peter

    1992-01-01

    This session at the Geothermal Energy Program Review X: Geothermal Energy and the Utility Market consisted of five presentations: ''Hard Rock Penetration - Summary'' by George P. Tennyson, Jr.; ''Overview - Hard Rock Penetration'' by James C. Dunn; ''An Overview of Acoustic Telemetry'' by Douglas S. Drumheller; ''Lost Circulation Technology Development Status'' by David A. Glowka; ''Downhole Memory-Logging Tools'' by Peter Lysne.

  12. Hardness Tester for Polyur

    NASA Technical Reports Server (NTRS)

    Hauser, D. L.; Buras, D. F.; Corbin, J. M.

    1987-01-01

    Rubber-hardness tester modified for use on rigid polyurethane foam. Provides objective basis for evaluation of improvements in foam manufacturing and inspection. Typical acceptance criterion requires minimum hardness reading of 80 on modified tester. With adequate correlation tests, modified tester used to measure indirectly tensile and compressive strengths of foam.

  13. Density functional theory of fluids in the isothermal-isobaric ensemble.

    PubMed

    Gonzlez, A; White, J A; Romn, F L; Velasco, S

    2004-06-01

    We present a density functional theory for inhomogeneous fluids at constant external pressure. The theory is formulated for a volume-dependent density, n(r,V), defined as the conjugate variable of a generalized external potential, nu(r,V), that conveys the information on the pressure. An exact expression for the isothermal-isobaric free-energy density functional is obtained in terms of the corresponding canonical ensemble functional. As an application we consider a hard-sphere system in a spherical pore with fluctuating radius. In general we obtain very good agreement with simulation. However, in some situations a peak develops in the center of the cavity and the agreement between theory and simulation becomes worse. This happens for systems where the number of particles is close to the magic numbers N=13, 55, and 147. PMID:15268089

  14. Equations of state for many-body systems at high densities

    NASA Astrophysics Data System (ADS)

    Khan, Imran; Gao, Bo

    2004-05-01

    For a many-body system at high densities, the equation of state depends not only on the scattering length, but also on further details of the inter-particle potential. For a many-atom system, in particular, its behavior at high densities will depend on the van der Waals interaction. We are exploring the behavior of a many-atom system in this density regime using the variational Monte Carlo method, in combination with the concept of effective potential introduced in a recent work(B. Gao, J. Phys. B 36), 2111 (2003).. As an initial test, we will compare our hard-sphere results with those of Gross-Pitevaskii equation and diffussion Monte Carlo method(D. Blume and C. H. Greene, Phys. Rev. A 63), 063601 (2001)..

  15. Density functional theory for crystal-liquid interfaces of Lennard-Jones fluid.

    PubMed

    Wang, Xin; Mi, Jianguo; Zhong, Chongli

    2013-04-28

    A density functional approach is presented to describe the crystal-liquid interfaces and crystal nucleations of Lennard-Jones fluid. Within the theoretical framework, the modified fundamental measure theory is applied to describe the free energy functional of hard sphere repulsion, and the weighted density method based on first order mean spherical approximation is used to describe the free energy contribution arising from the attractive interaction. The liquid-solid equilibria, density profiles within crystal cells and at liquid-solid interfaces, interfacial tensions, nucleation free energy barriers, and critical cluster sizes are calculated for face-centered-cubic and body-centered-cubic nucleus. Some results are in good agreement with available simulation data, indicating that the present model is quantitatively reliable in describing nucleation thermodynamics of Lennard-Jones fluid. PMID:23635162

  16. Anisotropic fluid spheres in general relativity

    SciTech Connect

    Bayin, S.S.

    1982-09-15

    We present various analytic solutions for anisotropic fluid spheres in general relativity. First we consider generalizations of the P = ..cap alpha..rho solution to the case where pressure is anisotropic, and study the effects of anisotropy on the structure of neutron stars. Next we study radiating anisotropic fluid spheres and present three classes of analytic solutions. We also study slowly rotating anisotropic fluid spheres and present two analytic solutions corresponding to the nonradiating case. One of these solutions corresponds to uniform rotation, while the other corresponds to differential rotation. We also present differential equations to be solved for slowly rotating and radiating anisotropic fluid spheres.

  17. Radiometric levitation of micron sized spheres

    NASA Astrophysics Data System (ADS)

    Lewittes, M.; Arnold, S.; Oster, G.

    1982-03-01

    Radiometric levitation of a 20-?-diam dye-impregnated glycerol sphere has been observed at intensities as low as 1 W/cm2 in air at 30 Torr. The levitation has been effected on both strongly absorbing spheres in the direction of the light and weakly absorbing spheres in the opposite sense. Both strongly and weakly absorbing spheres are found to laterally seek an intensity minimum. Consequently particles were stably held in the focused beam of an Ar+ laser (4880 ) operating in the TEM*01 (doughnut) mode.

  18. The hard metal diseases

    SciTech Connect

    Cugell, D.W. )

    1992-06-01

    Hard metal is a mixture of tungsten carbide and cobalt, to which small amounts of other metals may be added. It is widely used for industrial purposes whenever extreme hardness and high temperature resistance are needed, such as for cutting tools, oil well drilling bits, and jet engine exhaust ports. Cobalt is the component of hard metal that can be a health hazard. Respiratory diseases occur in workers exposed to cobalt--either in the production of hard metal, from machining hard metal parts, or from other sources. Adverse pulmonary reactions include asthma, hypersensitivity pneumonitis, and interstitial fibrosis. A peculiar, almost unique form of lung fibrosis, giant cell interstitial pneumonia, is closely linked with cobalt exposure.66 references.

  19. Molecular density functional theory for water with liquid-gas coexistence and correct pressure

    SciTech Connect

    Jeanmairet, Guillaume Levesque, Maximilien; Sergiievskyi, Volodymyr; Borgis, Daniel

    2015-04-21

    The solvation of hydrophobic solutes in water is special because liquid and gas are almost at coexistence. In the common hypernetted chain approximation to integral equations, or equivalently in the homogenous reference fluid of molecular density functional theory, coexistence is not taken into account. Hydration structures and energies of nanometer-scale hydrophobic solutes are thus incorrect. In this article, we propose a bridge functional that corrects this thermodynamic inconsistency by introducing a metastable gas phase for the homogeneous solvent. We show how this can be done by a third order expansion of the functional around the bulk liquid density that imposes the right pressure and the correct second order derivatives. Although this theory is not limited to water, we apply it to study hydrophobic solvation in water at room temperature and pressure and compare the results to all-atom simulations. The solvation free energy of small molecular solutes like n-alkanes and hard sphere solutes whose radii range from angstroms to nanometers is now in quantitative agreement with reference all atom simulations. The macroscopic liquid-gas surface tension predicted by the theory is comparable to experiments. This theory gives an alternative to the empirical hard sphere bridge correction used so far by several authors.

  20. Molecular density functional theory for water with liquid-gas coexistence and correct pressure

    NASA Astrophysics Data System (ADS)

    Jeanmairet, Guillaume; Levesque, Maximilien; Sergiievskyi, Volodymyr; Borgis, Daniel

    2015-04-01

    The solvation of hydrophobic solutes in water is special because liquid and gas are almost at coexistence. In the common hypernetted chain approximation to integral equations, or equivalently in the homogenous reference fluid of molecular density functional theory, coexistence is not taken into account. Hydration structures and energies of nanometer-scale hydrophobic solutes are thus incorrect. In this article, we propose a bridge functional that corrects this thermodynamic inconsistency by introducing a metastable gas phase for the homogeneous solvent. We show how this can be done by a third order expansion of the functional around the bulk liquid density that imposes the right pressure and the correct second order derivatives. Although this theory is not limited to water, we apply it to study hydrophobic solvation in water at room temperature and pressure and compare the results to all-atom simulations. The solvation free energy of small molecular solutes like n-alkanes and hard sphere solutes whose radii range from angstroms to nanometers is now in quantitative agreement with reference all atom simulations. The macroscopic liquid-gas surface tension predicted by the theory is comparable to experiments. This theory gives an alternative to the empirical hard sphere bridge correction used so far by several authors.

  1. Tandem spheres in hypersonic flow

    SciTech Connect

    Laurence, Stuart J; Deiterding, Ralf; Hornung, Hans G

    2009-01-01

    The problem of determining the forces acting on a secondary body when it is travelling at some point within the shocked region created by a hypersonic primary body is of interest in such situations as store or stage separation, re-entry of multiple vehicles, and atmospheric meteoroid fragmentation. The current work is concerned with a special case of this problem, namely that in which both bodies are spheres and are stationary with respect to one another. We first present an approximate analytical model of the problem; subsequently, numerical simulations are described and results are compared with those from the analytical model. Finally, results are presented from a series of experiments in the T5 hypervelocity shock tunnel in which a newly-developed force-measurement technique was employed.

  2. Efflux time of soap bubbles and liquid spheres.

    PubMed

    Grosse, A V

    1967-06-01

    The efflux time, T, of gas from soap bubbles of radius, R, through their blow tube of length, 1, and radius, p, is given by the equation see pdf for equation where eta is the viscosity of the gas and omicron the surface tension of the bubble solution, all in centimeter-gram-second units. Similar relations between time and diameter were established for the flow from one bubble to another or from one bubble within another. The same relations hold for the flow of liquid spheres, suspended in another liquid of equal density, following Plateau's classic method. They have been extended to the flow of spheres to cylinders and catenoids of rotation. In all these cases the driving force is the surface or interfacial tension, creating an excess pressure as defined by Laplace's equation. PMID:17792780

  3. Special purpose reflectometer uses modified ulbricht sphere

    NASA Technical Reports Server (NTRS)

    Gorstein, M.

    1967-01-01

    Modified Ulbricht sphere measures stray radiation caused by irregularities in the reflective surface of an optical test specimen. The test specimen is positioned between a light source and exit port and all diffusely scattered radiation is measured by a photomultiplier tube in the sphere.

  4. The "Magical" Sphere: Uncovering the Secret

    ERIC Educational Resources Information Center

    Petruševski, Vladimir M.; Bukleski, Miha

    2006-01-01

    A red sphere is seen at the bottom of a sealed glass tube filled with a colorless, transparent liquid. Holding the tube for a short period makes the sphere rise slowly from the bottom until it finally floats on the surface of the liquid. Instructions for preparing the demonstration are given, together with an explanation of the phenomenon. A…

  5. Spontaneous Symmetry Breakdown in Fuzzy Spheres

    NASA Astrophysics Data System (ADS)

    Das, C. R.; Digal, S.; Govindarajan, T. R.

    We study and analyse the questions regarding breakdown of global symmetry on noncommutative sphere. We demonstrate this by considering a complex scalar field on a fuzzy sphere and isolating Goldstone modes. We discuss the role of nonlocal interactions present in these through geometrical considerations.

  6. C{sub 60}: Sphere or polyhedron?

    SciTech Connect

    Haddon, R.C.

    1997-02-19

    In the original publication on the subject, C{sub 60} was depicted with the aid of a soccer ball, but this representation soon gave way to the familiar line drawing of chemical bonds between nucleii. To a large extent the dichotomy in the representation of the fullerenes remains today, and it is the purpose of this paper to pose and address the question that appears in the title. Of course, in reality the answer is well-known, and neither the sphere nor the polyhedron represent C{sub 60}, which like other molecules exists as a collection of nuclei with an associated distribution of electron density. Nevertheless, it is of interest to consider which of these conventional representations is most relevant for the fullerenes and in particular the language most appropriate to the description of the shape of these molecules and the geometry of the carbon atoms. The analysis presented here shows that topology of the molecule is paramount, and hence, C{sub 60} (and the fullerenes) are best modeled as polyhedra. 16 refs., 3 figs.

  7. Cavitation due to an impacting sphere

    NASA Astrophysics Data System (ADS)

    de Graaf, K. L.; Brandner, P. A.; Pearce, B. W.; Lee, J. Y.

    2015-12-01

    Cavitation associated with the impact of a sphere on a flat surface is investigated using high-speed photography. The sphere, of diameter 15 or 45 mm and made from Ertacetal® or stainless steel, was fully submerged and accelerated using a spring-loaded mechanism to achieve Reynolds numbers based on impact velocity and sphere radius of up to 7.2×104. The static pressure and impact velocity were varied to achieve cavitation numbers ranging from 8.9 to 120.9. High-speed photography of the impacting sphere and induced cavitation bubble was filmed at 105-140 kHz. A log law relationship was found between the non-dimensional maximum bubble radius and the cavitation number. The relationship was modulated by the material properties. Interaction between the sphere and the bubble was also noted.

  8. Organizing Your Hard Disk.

    ERIC Educational Resources Information Center

    Stocker, H. Robert; Hilton, Thomas S. E.

    1991-01-01

    Suggests strategies that make hard disk organization easy and efficient, such as making, changing, and removing directories; grouping files by subject; naming files effectively; backing up efficiently; and using PATH. (JOW)

  9. Hard Constraints in Optimization Under Uncertainty

    NASA Technical Reports Server (NTRS)

    Crespo, Luis G.; Giesy, Daniel P.; Kenny, Sean P.

    2008-01-01

    This paper proposes a methodology for the analysis and design of systems subject to parametric uncertainty where design requirements are specified via hard inequality constraints. Hard constraints are those that must be satisfied for all parameter realizations within a given uncertainty model. Uncertainty models given by norm-bounded perturbations from a nominal parameter value, i.e., hyper-spheres, and by sets of independently bounded uncertain variables, i.e., hyper-rectangles, are the focus of this paper. These models, which are also quite practical, allow for a rigorous mathematical treatment within the proposed framework. Hard constraint feasibility is determined by sizing the largest uncertainty set for which the design requirements are satisfied. Analytically verifiable assessments of robustness are attained by comparing this set with the actual uncertainty model. Strategies that enable the comparison of the robustness characteristics of competing design alternatives, the description and approximation of the robust design space, and the systematic search for designs with improved robustness are also proposed. Since the problem formulation is generic and the tools derived only require standard optimization algorithms for their implementation, this methodology is applicable to a broad range of engineering problems.

  10. Radiation Hard AlGaN Detectors and Imager

    SciTech Connect

    2012-05-01

    Radiation hardness of AlGaN photodiodes was tested using a 65 MeV proton beam with a total proton fluence of 3x10{sup 12} protons/cm{sup 2}. AlGaN Deep UV Photodiode have extremely high radiation hardness. These new devices have mission critical applications in high energy density physics (HEDP) and space explorations. These new devices satisfy radiation hardness requirements by NIF. NSTec is developing next generation AlGaN optoelectronics and imagers.

  11. Stochastic Interactions of Two Brownian Spheres in the Presence of Depletants

    NASA Astrophysics Data System (ADS)

    Karzar-Jeddi, Mehdi; Tuinier, Remco; Taniguchi, Takashi; Fan, Tai-Hsi

    2014-03-01

    The pair interactions between hard spheres play an essential role in many processes such as macromolecular crowding, binding, self-assembly of particles, and many chemical and food processes. Here we focus on theoretical analysis of the long-time correlated stochastic motion of two hard spheres in a non-adsorbing polymer solution. The hard spheres are held by hypothetical optical traps. The pair mobility tenser is found using a two-layer approximation with pure solvent in the depletion zone surrounding the particle and uniform polymer solution elsewhere. The resulting mobility computed by the boundary integral analysis is used to define the level of thermal fluctuation. Results show how the mobility and the decay of displacement correlation functions modified by the polymer depletion effect. The attractive osmotic potential increases the auto-correlation of the pair particle motion, while reduces the cross-correlation of the particles. This work gives better understanding of the pair interactions in a suspension of non-adsorbing polymers as an essential step toward many-particle interactions.

  12. Shape transitions in soft spheres regulated by elasticity

    NASA Astrophysics Data System (ADS)

    Fogle, Craig; Rowat, Amy; Levine, Alex; Rudnick, Joseph

    2014-03-01

    Soft core shell structures abound in nature. Examples of these structures, comprised of a thin outer membrane bounding an elastic core, include raisins, gel-filled vesicles, and a variety of membrane-bound organelles in the cell. We study the elasticity-driven morphological transitions of spherical core shell structures when either their surface area is increased or their interior volume is decreased. We demonstrate a transition, which is related to the Euler buckling, from the spherical initial shape to a lower symmetry one. We discuss the dependence of the critical excess surface area (relative to that of a bounding sphere) for buckling, the internal stresses in the core, and the symmetry of the buckled state on the elastic parameters of the system. We compare these predictions to a variety of observed morphological transitions in hard and soft materials, and discuss extensions of this work to growing viscoelastic media.

  13. Anomalies, conformal manifolds, and spheres

    NASA Astrophysics Data System (ADS)

    Gomis, Jaume; Hsin, Po-Shen; Komargodski, Zohar; Schwimmer, Adam; Seiberg, Nathan; Theisen, Stefan

    2016-03-01

    The two-point function of exactly marginal operators leads to a universal contribution to the trace anomaly in even dimensions. We study aspects of this trace anomaly, emphasizing its interpretation as a sigma model, whose target space {M} is the space of conformal field theories (a.k.a. the conformal manifold). When the underlying quantum field theory is supersymmetric, this sigma model has to be appropriately supersymmetrized. As examples, we consider in some detail {N}=(2,2) and {N}=(0,2) supersymmetric theories in d = 2 and {N}=2 supersymmetric theories in d = 4. This reasoning leads to new information about the conformal manifolds of these theories, for example, we show that the manifold is Kähler-Hodge and we further argue that it has vanishing Kähler class. For {N}=(2,2) theories in d = 2 and {N}=2 theories in d = 4 we also show that the relation between the sphere partition function and the Kähler potential of {M} follows immediately from the appropriate sigma models that we construct. Along the way we find several examples of potential trace anomalies that obey the Wess-Zumino consistency conditions, but can be ruled out by a more detailed analysis.

  14. Ceramic Spheres From Cation Exchange Beads

    NASA Technical Reports Server (NTRS)

    Dynys, F. W.

    2003-01-01

    Porous ZrO2 and hollow TiO2 spheres were synthesized from a strong acid cation exchange resin. Spherical cation exchange beads, polystyrene based polymer, were used as a morphological-directing template. Aqueous ion exchange reaction was used to chemically bind (ZrO)(2+) ions to the polystyrene structure. The pyrolysis of the polystyrene at 600 C produces porous ZrO2 spheres with a surface area of 24 sq m/g with a mean sphere size of 42 microns. Hollow TiO2 spheres were synthesized by using the beads as a micro-reactor. A direct surface reaction - between titanium isopropoxide and the resin beads forms a hydrous TiO2 shell around the polystyrene core. The pyrolysis of the polystyrene core at 600 C produces hollow anatase spheres with a surface area of 42 sq m/g with a mean sphere size of 38 microns. The formation of ceramic spheres was studied by XRD, SEM and B.E.T. nitrogen adsorption measurements.

  15. Numerical Simulations of Falling Sphere Viscometry Experiments.

    NASA Astrophysics Data System (ADS)

    O Dwyer, L.; Kellogg, L. H.; Lesher, C. E.

    2007-12-01

    The falling sphere technique based on Stokes' law is widely used to determine the viscosities of geologically relevant melts at high pressures. Stokes' law is valid when a rigid sphere falls slowly and steadily through a stationary and infinite Newtonian medium of uniform properties. High-pressure falling sphere experiments however, usually involve dropping a dense, refractory sphere through a liquid contained by a cylindrical capsule of finite size. The sphere velocity is influenced by the walls (Faxen correction) and ends of the capsule, and possible convective motion of the fluid. Efforts are made to minimize thermal gradients in laboratory experiments, but small temperature differences within the capsule can lead to convection complicating interpretation. We utilize GALE (Moresi et al., 2003;), a finite element particle-in-cell code, to examine these factors in numerical models of conditions similar to those of high-pressure experiments. Our modeling considers a three- dimensional box or cylinder containing a cluster of particles that represent the dense sphere in laboratory experiments surrounded by low viscosity particles representing the melt. GALE includes buoyancy forces, heat flow, and viscosity variations so our model can be used to assess the effects of the capsule's walls and ends, and the consequences of thermal gradients on the sphere's velocity and trajectory. Comparisons between our numerical simulations and real-time falling sphere experiments involving lower viscosity molten komatiite are made to assess the validity of Stokes' law with the standard Faxen correction included, and formulations considering end effects. The modeling also permits an evaluation of the uncertainties in recovering accurate liquid viscosities from Stokes' law when a dense sphere falls through a convecting low viscosity melt. It also allows us to assess acceleration to a terminal velocity that can provide constraints on melt viscosity in experiments in which the terminal velocity was not reached.

  16. Agglomerate-of-spheres model: Theoretical considerations

    NASA Astrophysics Data System (ADS)

    Winsel, A.; Bashtavelova, E.

    1993-10-01

    The 'agglomerate-of-spheres' (AOS) model associates the resistivity and the mechanical strength of PbO2 with the narrow zones between the sphere-like agglomerates. Some fundamentals of the electric contact theory are reported. During the formation of the PbO2 active material a so-called electroformative force is represented. It represents the force, which is needed to create the new order of the agglomerate-of-spheres. The nature of this force is similar to that one which in winter time cracks freezing water pipes.

  17. Bzier curves on the shape sphere

    NASA Astrophysics Data System (ADS)

    Georgiev, Georgi H.

    2012-11-01

    There are two important models of the simplicial shape space of order (2,3). The first model introduced by D. Kendall is a two-dimensional sphere with radius 1/2. Therefore, this model is called the shape sphere. The second model introduced by F. Bookstein is a one-point extension of the Euclidean plane. Using a natural conformal mapping between these models we investigate curves on the shape sphere which correspond to Bzier curves in the Euclidean plane. We also describe two different types of rational spherical curves and their plane pre-images.

  18. Charged-current reactions in the supernova neutrino-sphere

    NASA Astrophysics Data System (ADS)

    Rrapaj, Ermal; Holt, J. W.; Bartl, Alexander; Reddy, Sanjay; Schwenk, A.

    2015-03-01

    We calculate neutrino absorption rates due to charged-current reactions ?e+n ?e-+p and ?e+p ?e++n in the outer regions of a newly born neutron star called the neutrino-sphere. To improve on recent work which has shown that nuclear mean fields enhance the ?e cross section and suppress the ?e cross section, we employ realistic nucleon-nucleon interactions that fit measured scattering phase shifts. Using these interactions we calculate the momentum-, density-, and temperature-dependent nucleon self-energies in the Hartree-Fock approximation. A potential derived from chiral effective field theory and a pseudopotential constructed to reproduce nucleon-nucleon phase shifts at the mean-field level are used to study the equilibrium proton fraction and charged-current rates. We compare our results to earlier calculations obtained using phenomenological mean-field models and to those obtained in the virial expansion valid at low density and high temperature. In the virial regime our results are consistent with previous calculations, and at higher densities relevant for the neutrino-sphere, ? ?1012 g/cm 3, we find the difference between the ?e and ?e absorption rates to be larger than predicted earlier. Our results may have implications for heavy-element nucleosynthesis in supernovae, and for supernova neutrino detection.

  19. Green's function of radial inhomogeneous spheres excited by internal sources.

    PubMed

    Zouros, Grigorios P; Kokkorakis, Gerassimos C

    2011-01-01

    Green's function in the interior of penetrable bodies with inhomogeneous compressibility by sources placed inside them is evaluated through a Schwinger-Lippmann volume integral equation. In the case of a radial inhomogeneous sphere, the radial part of the unknown Green's function can be expanded in a double Dini's series, which allows analytical evaluation of the involved cumbersome integrals. The simple case treated here can be extended to more difficult situations involving inhomogeneous density as well as to the corresponding electromagnetic or elastic problem. Finally, numerical results are given for various inhomogeneous compressibility distributions. PMID:21302984

  20. Simple technique determines ac properties of hard superconductive materials

    NASA Technical Reports Server (NTRS)

    Harper, C. M.; Hecht, R.

    1966-01-01

    Critical current density of neodymium-titanium alloy samples is analyzed from magnetization curves to determine the ac properties of hard semiconductive materials. A complete family of magnetization curves is obtained, each curve representing performance at a different temperature.

  1. Hard superconducting nitrides

    PubMed Central

    Chen, Xiao-Jia; Struzhkin, Viktor V.; Wu, Zhigang; Somayazulu, Maddury; Qian, Jiang; Kung, Simon; Christensen, Axel Nrlund; Zhao, Yusheng; Cohen, Ronald E.; Mao, Ho-kwang; Hemley, Russell J.

    2005-01-01

    Detailed study of the equation of state, elasticity, and hardness of selected superconducting transition-metal nitrides reveals interesting correlations among their physical properties. Both the bulk modulus and Vickers hardness are found to decrease with increasing zero-pressure volume in NbN, HfN, and ZrN. The computed elastic constants from first principles satisfy c11 > c12 > c44 for NbN, but c11 > c44 > c12 for HfN and ZrN, which are in good agreement with the neutron scattering data. The cubic ?-NbN superconducting phase possesses a bulk modulus of 348 GPa, comparable to that of cubic boron nitride, and a Vickers hardness of 20 GPa, which is close to sapphire. Theoretical calculations for NbN show that all elastic moduli increase monotonically with increasing pressure. These results suggest technological applications of such materials in extreme environments. PMID:15728352

  2. Thermodynamics of the low-density excluded-volume hadron gas

    NASA Astrophysics Data System (ADS)

    Redlich, Krzysztof; Zalewski, Kacper

    2016-01-01

    We consider the thermodynamics of excluded-volume particles at finite temperature and chemical potential in the low-density approximation. We assume Boltzmann statistics and study the influence of the excluded volume on an ideal gas thermodynamics at the same temperature, pressure, and number of particles. We show that considering the change of the free enthalpy due to the excluded volume, and using the Maxwell identities, one can derive relevant thermodynamic functions and parameters of multicomponent gases. The derivation is quite general, because particles may have different sizes and shapes which can also depend on their momenta. Besides its simplicity and generality, our approach has the advantage of eliminating the transcendental equations occurring in earlier studies. A representative example of the excluded-volume thermodynamics is the single-component gas of hard spheres. For this case, using a virial expansion, the validity limits of the low-density approximation are also discussed.

  3. Ionic density distributions near the charged colloids: Spherical electric double layers

    SciTech Connect

    Kim, Eun-Young; Kim, Soon-Chul

    2013-11-21

    We have studied the structure of the spherical electric double layers on charged colloids by a density functional perturbation theory, which is based both on the modified fundamental-measure theory for the hard spheres and on the one-particle direct correlation functional (DCF) for the electronic residual contribution. The contribution of one-particle DCF has been approximated as the functional integration of the second-order correlation function of the ionic fluids in a bulk phase. The calculated result is in very good agreement with the computer simulations for the ionic density distributions and the zeta potentials over a wide range of macroion sizes and electrolyte concentrations, and compares with the results of Yu et al. [J. Chem. Phys. 120, 7223 (2004)] and modified Poisson-Boltzmann approximation [L. B. Bhuiyan and C. W. Outhwaite, Condens. Matter Phys. 8, 287 (2005)]. The present theory is able to provide interesting insights about the charge inversion phenomena occurring at the interface.

  4. Electric Double-Layer Structure in Primitive Model Electrolytes. Comparing Molecular Dynamics with Local-Density Approximations

    DOE PAGESBeta

    Giera, Brian; Lawrence Livermore National Lab.; Henson, Neil; Kober, Edward M.; Shell, M. Scott; Squires, Todd M.

    2015-02-27

    We evaluate the accuracy of local-density approximations (LDAs) using explicit molecular dynamics simulations of binary electrolytes comprised of equisized ions in an implicit solvent. The Bikerman LDA, which considers ions to occupy a lattice, poorly captures excluded volume interactions between primitive model ions. Instead, LDAs based on the Carnahan–Starling (CS) hard-sphere equation of state capture simulated values of ideal and excess chemical potential profiles extremely well, as is the relationship between surface charge density and electrostatic potential. Excellent agreement between the EDL capacitances predicted by CS-LDAs and computed in molecular simulations is found even in systems where ion correlations drivemore » strong density and free charge oscillations within the EDL, despite the inability of LDAs to capture the oscillations in the detailed EDL profiles.« less

  5. Electric Double-Layer Structure in Primitive Model Electrolytes. Comparing Molecular Dynamics with Local-Density Approximations

    SciTech Connect

    Giera, Brian; Henson, Neil; Kober, Edward M.; Shell, M. Scott; Squires, Todd M.

    2015-02-27

    We evaluate the accuracy of local-density approximations (LDAs) using explicit molecular dynamics simulations of binary electrolytes comprised of equisized ions in an implicit solvent. The Bikerman LDA, which considers ions to occupy a lattice, poorly captures excluded volume interactions between primitive model ions. Instead, LDAs based on the Carnahan–Starling (CS) hard-sphere equation of state capture simulated values of ideal and excess chemical potential profiles extremely well, as is the relationship between surface charge density and electrostatic potential. Excellent agreement between the EDL capacitances predicted by CS-LDAs and computed in molecular simulations is found even in systems where ion correlations drive strong density and free charge oscillations within the EDL, despite the inability of LDAs to capture the oscillations in the detailed EDL profiles.

  6. Electric Double-Layer Structure in Primitive Model Electrolytes. Comparing Molecular Dynamics with Local-Density Approximations

    SciTech Connect

    Giera, Brian; Henson, Neil; Kober, Edward M.; Shell, M. Scott; Squires, Todd M.

    2015-02-27

    We evaluate the accuracy of local-density approximations (LDAs) using explicit molecular dynamics simulations of binary electrolytes comprised of equisized ions in an implicit solvent. The Bikerman LDA, which considers ions to occupy a lattice, poorly captures excluded volume interactions between primitive model ions. Instead, LDAs based on the CarnahanStarling (CS) hard-sphere equation of state capture simulated values of ideal and excess chemical potential profiles extremely well, as is the relationship between surface charge density and electrostatic potential. Excellent agreement between the EDL capacitances predicted by CS-LDAs and computed in molecular simulations is found even in systems where ion correlations drive strong density and free charge oscillations within the EDL, despite the inability of LDAs to capture the oscillations in the detailed EDL profiles.

  7. Polarizability of the dielectric double-sphere

    NASA Astrophysics Data System (ADS)

    Pitkonen, Mikko

    2006-10-01

    An explicit solution for the longitudinal and transverse polarizability of the symmetric dielectric intersecting double sphere is obtained as a rapidly converging series of integral operators, which is fast enough for real time calculation in Java Applet.

  8. StenniSphere reopens after Hurricane Katrina

    NASA Technical Reports Server (NTRS)

    2006-01-01

    StenniSphere reopened Jan. 18, 2006, almost five months after Hurricane Katrina damaged the basement of the building that houses the visitor center. Thanks to the staff's careful preparations before the storm, no artifacts or exhibits were harmed.

  9. Elastic spheres can walk on water

    PubMed Central

    Belden, Jesse; Hurd, Randy C.; Jandron, Michael A.; Bower, Allan F.; Truscott, Tadd T.

    2016-01-01

    Incited by public fascination and engineering application, water-skipping of rigid stones and spheres has received considerable study. While these objects can be coaxed to ricochet, elastic spheres demonstrate superior water-skipping ability, but little is known about the effect of large material compliance on water impact physics. Here we show that upon water impact, very compliant spheres naturally assume a disk-like geometry and dynamic orientation that are favourable for water-skipping. Experiments and numerical modelling reveal that the initial spherical shape evolves as elastic waves propagate through the material. We find that the skipping dynamics are governed by the wave propagation speed and by the ratio of material shear modulus to hydrodynamic pressure. With these insights, we explain why softer spheres skip more easily than stiffer ones. Our results advance understanding of fluid-elastic body interaction during water impact, which could benefit inflatable craft modelling and, more playfully, design of elastic aquatic toys. PMID:26842860

  10. Magnetization of small iron-nickel spheres

    NASA Technical Reports Server (NTRS)

    Wasilewski, P.

    1981-01-01

    Magnetic properties of small iron-nickel alloy spheres, having compositions which cover the entire Fe-Ni binary, are presented. The spheres were formed during solidification in free fall following the melting of electropolished wires of appropriate composition. The spheres with Ni not greater than 25% acquired a martensitic thermal remanence while those with Ni not less than 30% acquired a thermoremanent magnetization. A magnetic remanence-composition diagram and a coercive force-composition diagram are constructed. Magnetic hysteresis loops and derived parameters demonstrate the difference between metal-bearing and oxide-bearing natural samples. The magnetic remanence varies as the sphere size in conjunction with the microstructure. These results help to explain why coercive force is generally low, remanent coercive force is generally high, and their ratio (R/C) is always large in fine metal dispersions, such as lunar samples and chondrite meteorites.

  11. ISS Update: Smart SPHERES - Duration: 11 minutes.

    NASA Video Gallery

    NASA Public Affairs Officer Kelly Humphries conducts a phone interview with Mark Micire, SPHERES Engineering Manager at Ames Research Center. Questions? Ask us on Twitter @NASA_Johnson and include ...

  12. Elastic spheres can walk on water.

    PubMed

    Belden, Jesse; Hurd, Randy C; Jandron, Michael A; Bower, Allan F; Truscott, Tadd T

    2016-01-01

    Incited by public fascination and engineering application, water-skipping of rigid stones and spheres has received considerable study. While these objects can be coaxed to ricochet, elastic spheres demonstrate superior water-skipping ability, but little is known about the effect of large material compliance on water impact physics. Here we show that upon water impact, very compliant spheres naturally assume a disk-like geometry and dynamic orientation that are favourable for water-skipping. Experiments and numerical modelling reveal that the initial spherical shape evolves as elastic waves propagate through the material. We find that the skipping dynamics are governed by the wave propagation speed and by the ratio of material shear modulus to hydrodynamic pressure. With these insights, we explain why softer spheres skip more easily than stiffer ones. Our results advance understanding of fluid-elastic body interaction during water impact, which could benefit inflatable craft modelling and, more playfully, design of elastic aquatic toys. PMID:26842860

  13. Self healing: solid spheres impacting soap bubbles

    NASA Astrophysics Data System (ADS)

    Killian, Taylor; Bryson, Joshua; Huey, Jordan; Bird, James C.; Nave, Jean-Christophe; Truscott, Tadd

    2012-11-01

    Under the right conditions a moving sphere may pass through a stationary soap bubble without rupturing it. At impact, the sphere forms a cavity in the soap film that often facilitates reparation after collapse. This interaction leaves a small film surrounding the sphere as it passes through the center of the bubble. In contrast, as the sphere passes through the opposite side of the bubble, rupture is more likely. The physics behind this phenomenon are not well understood, nor the limiting factors of this interaction. We explore the phenomenon using high-speed photography. Our observations reveal that there are several distinct cavity regimes. We present the parameters for drainage, rupture and reparation each of which are related to curvature gradients.

  14. "schwinger Model" on the Fuzzy Sphere

    NASA Astrophysics Data System (ADS)

    Harikumar, E.

    In this paper, we construct a model of spinor fields interacting with specific gauge fields on the fuzzy sphere and analyze the chiral symmetry of this "Schwinger model". In constructing the theory of gauge fields interacting with spinors on the fuzzy sphere, we take the approach that the Dirac operator Dq on the q-deformed fuzzy sphere SqF2 is the gauged Dirac operator on the fuzzy sphere. This introduces interaction between spinors and specific one-parameter family of gauge fields. We also show how to express the field strength for this gauge field in terms of the Dirac operators Dq and D alone. Using the path integral method, we have calculated the 2n-point functions of this model and show that, in general, they do not vanish, reflecting the chiral non-invariance of the partition function.

  15. Elastic spheres can walk on water

    NASA Astrophysics Data System (ADS)

    Belden, Jesse; Hurd, Randy C.; Jandron, Michael A.; Bower, Allan F.; Truscott, Tadd T.

    2016-02-01

    Incited by public fascination and engineering application, water-skipping of rigid stones and spheres has received considerable study. While these objects can be coaxed to ricochet, elastic spheres demonstrate superior water-skipping ability, but little is known about the effect of large material compliance on water impact physics. Here we show that upon water impact, very compliant spheres naturally assume a disk-like geometry and dynamic orientation that are favourable for water-skipping. Experiments and numerical modelling reveal that the initial spherical shape evolves as elastic waves propagate through the material. We find that the skipping dynamics are governed by the wave propagation speed and by the ratio of material shear modulus to hydrodynamic pressure. With these insights, we explain why softer spheres skip more easily than stiffer ones. Our results advance understanding of fluid-elastic body interaction during water impact, which could benefit inflatable craft modelling and, more playfully, design of elastic aquatic toys.

  16. Liouville Quantum Gravity on the Riemann Sphere

    NASA Astrophysics Data System (ADS)

    David, François; Kupiainen, Antti; Rhodes, Rémi; Vargas, Vincent

    2016-03-01

    In this paper, we rigorously construct Liouville Quantum Field Theory on the Riemann sphere introduced in the 1981 seminal work by Polyakov. We establish some of its fundamental properties like conformal covariance under PSL{_2({C})}-action, Seiberg bounds, KPZ scaling laws, KPZ formula and the Weyl anomaly formula. We also make precise conjectures about the relationship of the theory to scaling limits of random planar maps conformally embedded onto the sphere.

  17. Dynamical density functional theory for colloidal dispersions including hydrodynamic interactions

    NASA Astrophysics Data System (ADS)

    Rex, M.; Lwen, H.

    2009-02-01

    A dynamical density functional theory (DDFT) for translational Brownian dynamics is derived which includes hydrodynamic interactions. The theory reduces to the simple Brownian DDFT proposed by Marconi and Tarazona (U. Marini Bettolo Marconi and P. Tarazona, J. Chem. Phys. 110, 8032 (1999); J. Phys.: Condens. Matter 12, A413 (2000)) when hydrodynamic interactions are neglected. The derivation is based on Smoluchowskis equation for the time evolution of the probability density with pairwise hydrodynamic interactions. The theory is applied to hard-sphere colloids in an oscillating spherical optical trap which switches periodically in time from a stable confining to an unstable potential. Rosenfelds fundamental measure theory for the equilibrium density functional is used and hydrodynamics are incorporated on the Rotne-Prager level. The results for the time-dependent density profiles are compared to extensive Brownian dynamics simulations which are performed on the same Rotne-Prager level and excellent agreement is obtained. It is further found that hydrodynamic interactions damp and slow the dynamics of the confined colloid cluster in comparison to the same situation with neglected hydrodynamic interactions.

  18. 1500 Gate standard cell compatible radiation hard gate array

    SciTech Connect

    Mills, B.D.; Shafer, B.D.; Melancon, E.P.

    1984-11-01

    The G1500 gate array combines Sandia Labs' 4/3..mu.. CMOS silicon gate radiation hard process with a novel gate isolated standard cell compatible design for quick turnaround time, low cost, and radiation hardness. This device is hard to 5 x 10/sup 5/ rads, utilizes a configuration that provides high packing density, and is supported on both the Daisy and Mentor workstations. This paper describes Sandia Labs' radiation hard 4/3..mu.. process, the G1500's unique design, and the complete design capabilities offered by the workstations.

  19. Inverse Magnus effect on a rotating sphere

    NASA Astrophysics Data System (ADS)

    Kim, Jooha; Park, Hyungmin; Choi, Haecheon; Yoo, Jung Yul

    2011-11-01

    In this study, we investigate the flow characteristics of rotating spheres in the subcritical Reynolds number (Re) regime by measuring the drag and lift forces on the sphere and the two-dimensional velocity in the wake. The experiment is conducted in a wind tunnel at Re = 0 . 6 105 - 2 . 6 105 and the spin ratio (ratio of surface velocity to the free-stream velocity) of 0 (no spin) - 0.5. The drag coefficient on a stationary sphere remains nearly constant at around 0.52. However, the magnitude of lift coefficient is nearly zero at Re < 2 . 0 105 , but rapidly increases to 0.3 and then remains constant with further increasing Reynolds number. On the other hand, with rotation, the lift coefficient shows negative values, called inverse Magnus effect, depending on the magnitudes of the Reynolds number and spin ratio. The velocity field measured from a particle image velocimetry (PIV) indicates that non-zero lift coefficient on a stationary sphere at Re > 2 . 0 105 results from the asymmetry of separation line, whereas the inverse Magnus effect for the rotating sphere results from the differences in the boundary-layer growth and separation along the upper and lower sphere surfaces. Supported by the WCU, Converging Research Center and Priority Research Centers Program, NRF, MEST, Korea.

  20. CSI: Hard Drive

    ERIC Educational Resources Information Center

    Sturgeon, Julie

    2008-01-01

    Acting on information from students who reported seeing a classmate looking at inappropriate material on a school computer, school officials used forensics software to plunge the depths of the PC's hard drive, searching for evidence of improper activity. Images were found in a deleted Internet Explorer cache as well as deleted file space.…

  1. CSI: Hard Drive

    ERIC Educational Resources Information Center

    Sturgeon, Julie

    2008-01-01

    Acting on information from students who reported seeing a classmate looking at inappropriate material on a school computer, school officials used forensics software to plunge the depths of the PC's hard drive, searching for evidence of improper activity. Images were found in a deleted Internet Explorer cache as well as deleted file space.

  2. Work Hard. Be Nice

    ERIC Educational Resources Information Center

    Mathews, Jay

    2009-01-01

    In 1994, fresh from a two-year stint with Teach for America, Mike Feinberg and Dave Levin inaugurated the Knowledge Is Power Program (KIPP) in Houston with an enrollment of 49 5th graders. By this Fall, 75 KIPP schools will be up and running, setting children from poor and minority families on a path to college through a combination of hard work,

  3. Budgeting in Hard Times.

    ERIC Educational Resources Information Center

    Parrino, Frank M.

    2003-01-01

    Interviews with school board members and administrators produced a list of suggestions for balancing a budget in hard times. Among these are changing calendars and schedules to reduce heating and cooling costs; sharing personnel; rescheduling some extracurricular activities; and forming cooperative agreements with other districts. (MLF)

  4. Running in Hard Times

    ERIC Educational Resources Information Center

    Berry, John N., III

    2009-01-01

    Roberta Stevens and Kent Oliver are campaigning hard for the presidency of the American Library Association (ALA). Stevens is outreach projects and partnerships officer at the Library of Congress. Oliver is executive director of the Stark County District Library in Canton, Ohio. They have debated, discussed, and posted web sites, Facebook pages,…

  5. Running in Hard Times

    ERIC Educational Resources Information Center

    Berry, John N., III

    2009-01-01

    Roberta Stevens and Kent Oliver are campaigning hard for the presidency of the American Library Association (ALA). Stevens is outreach projects and partnerships officer at the Library of Congress. Oliver is executive director of the Stark County District Library in Canton, Ohio. They have debated, discussed, and posted web sites, Facebook pages,

  6. Structure and dynamics of concentrated dispersions of polystyrene latex spheres in glycerol: Static and dynamic x-ray scattering

    SciTech Connect

    Lumma, D.; Lurio, L. B.; Borthwick, M. A.; Falus, P.; Mochrie, S. G. J.

    2000-12-01

    X-ray photon correlation spectroscopy and small-angle x-ray scattering measurements are applied to characterize the dynamics and structure of concentrated suspensions of charge-stabilized polystyrene latex spheres dispersed in glycerol, for volume fractions between 2.7% and 52%. The static structures of the suspensions show essentially hard-sphere behavior. The short-time dynamics shows good agreement with predictions for the wave-vector-dependent collective diffusion coefficient, which are based on a hard-sphere model [C. W. J. Beenakker and P. Mazur, Physica A 126, 349 (1984)]. However, the intermediate scattering function is found to violate a scaling behavior found previously for a sterically stabilized hard-sphere suspension [P. N. Segre and P. N. Pusey, Phys. Rev. Lett. 77, 771 (1996)]. Our measurements are parametrized in terms of a viscoelastic model for the intermediate scattering function [W. Hess and R. Klein, Adv. Phys. 32, 173 (1983)]. Within this framework, two relaxation modes are predicted to contribute to the decay of the dynamic structure factor, with mode amplitudes depending on both wave vector and volume fraction. Our measurements indicate that, for particle volume fractions smaller than about 0.30, the intermediate scattering function is well described in terms of single-exponential decays, whereas a double-mode structure becomes apparent for more concentrated systems.

  7. Surface modification and characterization of carbon spheres by grafting polyelectrolyte brushes

    NASA Astrophysics Data System (ADS)

    Zhang, Qi; Li, Houbin; Zhang, Pan; Liu, Liangliang; He, Yuhang; Wang, Yali

    2014-06-01

    Modified carbon spheres (CSPBs) were obtained by grafting poly(diallyl dimethyl ammonium chloride) (p-DMDAAC) on the surface of carbon spheres (CSs). It can be viewed as a kind of cation spherical polyelectrolyte brushes (CSPBs), which consist of carbon spheres as core and polyelectrolytes as shell. The method of synthesizing carbon spheres was hydrothermal reaction. Before the polyelectrolyte brushes were grafted, azo initiator [4,4'-Azobis(4-cyanovaleric acyl chloride)] was attached to the carbon spheres' surface through hydroxyl groups. CSPBs were characterized by scanning electron microscope (SEM), Fourier transform infrared spectroscopy (FTIR), gel permeation chromatography (GPC), conductivity meter, and system zeta potential. The results showed that compared with carbon spheres, the conductivity and zeta potential on CSPBs increased from 9.98 to 49.24 μS/cm and 11.6 to 42.5 mV, respectively, after the polyelectrolyte brushes were grafted. The colloidal stability in water was enhanced, and at the same time, the average diameter of the CSPBs was found to be 173 nm, and the average molecular weight and grafted density of the grafted polyelectrolyte brushes were 780,138 g/mol and 4.026 × 109/nm2, respectively.

  8. Surface modification and characterization of carbon spheres by grafting polyelectrolyte brushes.

    PubMed

    Zhang, Qi; Li, Houbin; Zhang, Pan; Liu, Liangliang; He, Yuhang; Wang, Yali

    2014-01-01

    Modified carbon spheres (CSPBs) were obtained by grafting poly(diallyl dimethyl ammonium chloride) (p-DMDAAC) on the surface of carbon spheres (CSs). It can be viewed as a kind of cation spherical polyelectrolyte brushes (CSPBs), which consist of carbon spheres as core and polyelectrolytes as shell. The method of synthesizing carbon spheres was hydrothermal reaction. Before the polyelectrolyte brushes were grafted, azo initiator [4,4'-Azobis(4-cyanovaleric acyl chloride)] was attached to the carbon spheres' surface through hydroxyl groups. CSPBs were characterized by scanning electron microscope (SEM), Fourier transform infrared spectroscopy (FTIR), gel permeation chromatography (GPC), conductivity meter, and system zeta potential. The results showed that compared with carbon spheres, the conductivity and zeta potential on CSPBs increased from 9.98 to 49.24 ?S/cm and 11.6 to 42.5mV, respectively, after the polyelectrolyte brushes were grafted. The colloidal stability in water was enhanced, and at the same time, the average diameter of the CSPBs was found to be 173nm, and the average molecular weight and grafted density of the grafted polyelectrolyte brushes were 780,138g/mol and 4.026??10(9)/nm(2,) respectively. PMID:24948900

  9. The Separate Spheres Model of Gendered Inequality.

    PubMed

    Miller, Andrea L; Borgida, Eugene

    2016-01-01

    Research on role congruity theory and descriptive and prescriptive stereotypes has established that when men and women violate gender stereotypes by crossing spheres, with women pursuing career success and men contributing to domestic labor, they face backlash and economic penalties. Less is known, however, about the types of individuals who are most likely to engage in these forms of discrimination and the types of situations in which this is most likely to occur. We propose that psychological research will benefit from supplementing existing research approaches with an individual differences model of support for separate spheres for men and women. This model allows psychologists to examine individual differences in support for separate spheres as they interact with situational and contextual forces. The separate spheres ideology (SSI) has existed as a cultural idea for many years but has not been operationalized or modeled in social psychology. The Separate Spheres Model presents the SSI as a new psychological construct characterized by individual differences and a motivated system-justifying function, operationalizes the ideology with a new scale measure, and models the ideology as a predictor of some important gendered outcomes in society. As a first step toward developing the Separate Spheres Model, we develop a new measure of individuals' endorsement of the SSI and demonstrate its reliability, convergent validity, and incremental predictive validity. We provide support for the novel hypotheses that the SSI predicts attitudes regarding workplace flexibility accommodations, income distribution within families between male and female partners, distribution of labor between work and family spheres, and discriminatory workplace behaviors. Finally, we provide experimental support for the hypothesis that the SSI is a motivated, system-justifying ideology. PMID:26800454

  10. The Separate Spheres Model of Gendered Inequality

    PubMed Central

    Miller, Andrea L.; Borgida, Eugene

    2016-01-01

    Research on role congruity theory and descriptive and prescriptive stereotypes has established that when men and women violate gender stereotypes by crossing spheres, with women pursuing career success and men contributing to domestic labor, they face backlash and economic penalties. Less is known, however, about the types of individuals who are most likely to engage in these forms of discrimination and the types of situations in which this is most likely to occur. We propose that psychological research will benefit from supplementing existing research approaches with an individual differences model of support for separate spheres for men and women. This model allows psychologists to examine individual differences in support for separate spheres as they interact with situational and contextual forces. The separate spheres ideology (SSI) has existed as a cultural idea for many years but has not been operationalized or modeled in social psychology. The Separate Spheres Model presents the SSI as a new psychological construct characterized by individual differences and a motivated system-justifying function, operationalizes the ideology with a new scale measure, and models the ideology as a predictor of some important gendered outcomes in society. As a first step toward developing the Separate Spheres Model, we develop a new measure of individuals’ endorsement of the SSI and demonstrate its reliability, convergent validity, and incremental predictive validity. We provide support for the novel hypotheses that the SSI predicts attitudes regarding workplace flexibility accommodations, income distribution within families between male and female partners, distribution of labor between work and family spheres, and discriminatory workplace behaviors. Finally, we provide experimental support for the hypothesis that the SSI is a motivated, system-justifying ideology. PMID:26800454

  11. Terminal energy distribution of blast waves from bursting spheres

    NASA Technical Reports Server (NTRS)

    Adamczyk, A. A.; Strehlow, R. A.

    1977-01-01

    The calculation results for the total energy delivered to the surroundings by the burst of an idealized massless sphere containing an ideal gas are presented. The logic development of various formulas for sphere energy is also presented. For all types of sphere bursts the fraction of the total initial energy available in the sphere that is delivered to the surroundings is shown to lie between that delivered for the constant pressure addition of energy to a source region and that delivered by isentropic expansion of the sphere. The relative value of E sub/Q increases at fixed sphere pressure/surrounding pressure as sphere temperature increases because the velocity of sound increases.

  12. Isomorphic multifractal shear flows for hard disks via adiabatic and isokinetic nonequilibrium molecular dynamics

    SciTech Connect

    Dellago, C.; Hoover, W.G.; Posch, H.A.

    1998-05-01

    Identical particle trajectories can result from driven shear flows of two different types: (i) thermostatted flows, simulating a nonequilibrium steady state, and (ii) adiabatic flows, in which the irreversible heating associated with viscous work is not extracted from the system. This trajectory isomorphism applies to shears of hard particles, such as hard disks and spheres. Here we simulate such isomorphic shear flows. We also discuss the associated instantaneous Lyapunov spectra, which are not isomorphic. We extrapolate the dissipative hard-disk spectra to the large-system limit. {copyright} {ital 1998} {ital The American Physical Society}

  13. High-performance carbon nanotube-implanted mesoporous carbon spheres for supercapacitors with low series resistance

    SciTech Connect

    Yi, Bin; Chen, Xiaohua; Guo, Kaimin; Xu, Longshan; Chen, Chuansheng; Yan, Haimei; Chen, Jianghua

    2011-11-15

    Research highlights: {yields} CNTs-implanted porous carbon spheres are prepared by using gelatin as soft template. {yields} Homogeneously distributed CNTs form a well-develop network in carbon spheres. {yields} CNTs act as a reinforcing backbone assisting the formation of pore structure. {yields} CNTs improve electrical conductivity and specific capacitance of supercapacitor. -- Abstract: Carbon nanotube-implanted mesoporous carbon spheres were prepared by an easy polymerization-induced colloid aggregation method using gelatin as a soft template. Scanning electron microscopy, transmission electron microscopy and nitrogen adsorption-desorption measurements reveal that the materials are mesoporous carbon spheres, with a diameter of {approx}0.5-1.0 {mu}m, a specific surface area of 284 m{sup 2}/g and average pore size of 3.9 nm. Using the carbon nanotube-implanted mesoporous carbon spheres as electrode material for supercapacitors in an aqueous electrolyte solution, a low equivalent series resistance of 0.83 {Omega} cm{sup 2} and a maximum specific capacitance of 189 F/g with a measured power density of 8.7 kW/kg at energy density of 6.6 Wh/kg are obtained.

  14. Random Packings Of Rod-Sphere Mixtures Simulated By Mechanical Contraction

    NASA Astrophysics Data System (ADS)

    Kyrylyuk, Andriy V.; Wouterse, Alan; Philipse, Albert P.

    2009-06-01

    We study the random close packing of a binary mixture of spheres and rod-like particles (spherocylinders) by the mechanical contraction computer simulation. We investigate the universality in packing of near-spheres by monitoring the position and the value of the maximum in the mixture packing density as a function of the mixture composition and the rod aspect ratio. We find that independently of the mixture composition the particles pack more efficiently/densely as the rod aspect ratio is perturbed slightly from zero and the maximum density is always reached at one unique rod aspect ratio of about 0.45. The dependence of the value of the maximum packing fraction on the mixture composition (the relative rod volume fraction) is linear, exhibiting some ideality in packing of near-spheres. This counter-intuitive finding suggests that even for high rod concentrations in a rod-sphere mixture the packing is governed by local contacts between the neighboring particles, which is usually observed for dilute colloidal suspensions and granular gases, where there is no correlation between the particles. The plausible explanation for this intriguing behavior is that the correlations between the particles are completely lost in the range of distances of several particle diameters, which can be originated from the decoupling of the orientational and translational degrees of freedom of the nearly spherical rods. This gives rise to the universality and locality of random close packing of the rod-sphere mixtures.

  15. Decoherence of a qubit as a diffusion on the Bloch sphere

    NASA Astrophysics Data System (ADS)

    Siudzi?ska, Katarzyna; Chru?ci?ski, Dariusz

    2015-10-01

    We analyze qubit decoherence in the framework of geometric quantum mechanics. In this framework the qubit density operators are represented by probability distributions which are also the Khler functions on the Bloch sphere. Interestingly, the complete positivity of the quantum evolution is recovered as ellipticity of the second order differential operator (deformed Laplacian) which governs the evolution of the probability distribution.

  16. Uniform hollow magnetite spheres: Facile synthesis, growth mechanism, and their magnetic properties

    SciTech Connect

    Zhou, Xing; Zhao, Guizhe; Liu, Yaqing

    2014-11-15

    Highlights: • Uniform Fe{sub 3}O{sub 4} hollow spheres with high saturation magnetization were synthesized through a simple solvothermal process. • Without using any hard templates or external magnetic field. • The as-prepared magnetite hollow spheres exhibit a ferromagnetic behavior with high Ms of ca. 85.9 emu/g at room temperature. • The morphology of Fe{sub 3}O{sub 4} with nanoparticles, hollow, and irregular structures could be adjusted by changing the reactive conditions. - Abstract: Hierarchical porous Fe{sub 3}O{sub 4} hollow spheres with high saturation magnetization were synthesized through a simple solvothermal process in ethylene glycol (EG) in the presence of Tetrabutylammonium chloride (TBAC) and urea. By investigating the effect of reaction temperature, time, the amount of urea, and concentration of iron ion on the formation of hollow spheres, it was proposed that the main formation mechanism of hollow spheres is Ostwald ripening process combined with assembly-then-inside-out evacuation process. Additionally, it is found that the morphology of Fe{sub 3}O{sub 4} with nanoparticles, hollow, and irregular structures could be adjusted by changing the above factors. The resulting products were characterized by means of scanning electron microscopy (SEM), transmission electron microscopy (TEM), X-ray powder diffraction (XRD), high resolution transmission electron microscopy (HRTEM), energy dispersive X-ray spectroscopy (EDX), and vibrating sample magnetometer (VSM). The hierarchical porous Fe{sub 3}O{sub 4} hollow spheres exhibited enhanced saturation magnetization as compared with Fe{sub 3}O{sub 4} nanoparticles.

  17. Facile fabrication of monodisperse polymer hollow spheres.

    PubMed

    Lv, Hui; Lin, Quan; Zhang, Kai; Yu, Kui; Yao, Tongjie; Zhang, Xuehai; Zhang, Junhu; Yang, Bai

    2008-12-01

    This article reports the facile synthesis of monodisperse polymer hollow spheres by seeded emulsion polymerization without additional treatment. In this method, P(St-MMA-MAA) copolymer latex particles were first prepared by emulsifier-free emulsion polymerization and then used as seeds to carry out emulsion polymerization of methyl methacrylate (MMA), divinyl benzene (DVB), and 2-hydroxyethyl methacrylate (HEMA) with potassium persulfate (KPS) as initiator at 80 degrees C. The void of hollow spheres was readily adjusted by changing the monomer/seed weight ratio, and it could be enlarged while the diameters of hollow spheres changed little after etching by dimethyl formamide (DMF). The effects of synthetic parameters including the monomer composition and the properties of seeds on the morphology of hollow spheres were investigated in detail. On the basis of the experimental results, it seemed reasonable to conclude that the formation of hollow spheres was due to the "dissolution" of seeds in monomers and phase separation between the constituent polymers. As a thermodynamic factor, sodium dodecyl sulfate (SDS) would allow the preparation of solid particles depending on its level. PMID:18954151

  18. Data Comparison: Satellite and Falling Sphere Temperatures

    NASA Technical Reports Server (NTRS)

    Schmidlin, Francis J.; Schauer, Allison G.; Remsberg, Ellis E.; Gerlach, John C. (Technical Monitor)

    2001-01-01

    Small meteorological rocketsondes providing temperature data have beam used for comparison with, and validation of measurements from satellite-borne instruments. A significant number of rocket-borne falling spheres were launched in conjunction with the Upper Atmosphere Research Satellite (UARS) for validation of the Halogen Occultation Experiment (HALOE), High Resolution Doppler Interferometer (HRDI), and the Microwave Limb Sounder (MLS) instruments. Upper stratosphere and mesosphere temperatures measured with these instruments on UARS are compared with inflatable spheres launched from Wallops Island (1992-1999), Brazil (1994), Hawaii (1992), Norway (1992), and Sweden (1993 and 1996). Time and space differences varied between the satellite measurement and the rocketsonde launch, for example HALOE overpasses occurred within 5 days and in some cases there were spatial differences of up to 30 degrees longitude. Validation measurements of the HRDI instrument occurred at Wallops Island when it passed within 20 minutes and 330 kilometers of the launch site. Because of discontinuity in the falling sphere drag coefficients when fall speed neared MACH 1 falling sphere temperatures near 70 kilometers attitude are biased toward lower temperatures. Availability of improved software and a new atmospheric model have helped to reduce this bias. The validated remote instrument measurements permit a new perspective of atmospheric structure to be formed, not always possible with the limited number of falling sphere measurements. Features of the remote measurement temperature profiles and their possible use to extend the climatological data base at the rocketsonde sites will be discussed.

  19. SPHERES flight operations testing and execution

    NASA Astrophysics Data System (ADS)

    Mohan, Swati; Saenz-Otero, Alvar; Nolet, Simon; Miller, David W.; Sell, Steven

    2009-10-01

    Synchronized Position Hold Engage Reorient Experimental Satellites (SPHERES) is a formation flight testing facility consisting of three satellites operating inside the International Space Station (ISS). The goal is to use the long term microgravity environment of the ISS to mature formation flight and docking algorithms. The operations processes of SPHERES have also matured over the course of the first seven test sessions. This paper describes the evolution of the SPHERES program operations processes from conception to implementation to refinement through flight experience. Modifications to the operations processes were based on experience and feedback from Marshall Space Flight Center Payload Operations Center, USAF Space Test Program office at Johnson Space Center, and the crew of Expedition 13 (first to operate SPHERES on station). Important lessons learned were on aspects such as test session frequency, determination of session success, and contingency operations. This paper describes the tests sessions; then it details the lessons learned, the change in processes, and the impact on the outcome of later test sessions. SPHERES had very successful initial test sessions which allowed for modification and tailoring of the operations processes to streamline the code delivery and to tailor responses based on flight experiences.

  20. Hard Times Hit Schools

    ERIC Educational Resources Information Center

    McNeil, Michele

    2008-01-01

    Hard-to-grasp dollar amounts are forcing real cuts in K-12 education at a time when the cost of fueling buses and providing school lunches is increasing and the demands of the federal No Child Left Behind Act still loom larger over states and districts. "One of the real challenges is to continue progress in light of the economy," said Gale Gaines,…

  1. Hot electron and x-ray production from intense laser irradiation of wavelength-scale polystyrene spheres

    SciTech Connect

    Sumeruk, H. A.; Kneip, S.; Symes, D. R.; Churina, I. V.; Belolipetski, A. V.; Dyer, G.; Landry, J.; Bansal, G.; Bernstein, A.; Donnelly, T. D.; Karmakar, A.; Pukhov, A.; Ditmire, T.

    2007-06-15

    Hot electron and x-ray production from solid targets coated with polystyrene-spheres which are irradiated with high-contrast, 100 fs, 400 nm light pulses at intensity up to 2x10{sup 17} W/cm{sup 2} have been studied. The peak hard x-ray signal from uncoated fused silica targets is an order of magnitude smaller than the signal from targets coated with submicron sized spheres. The temperature of the x-rays in the case of sphere-coated targets is twice as hot as that of uncoated glass. A sphere-size scan of the x-ray yield and observation of a peak in both the x-ray production and temperature at a sphere diameter of 0.26 {mu}m, indicate that these results are consistent with Mie enhancements of the laser field at the sphere surface and multipass stochastic heating of the hot electrons in the oscillating laser field. These results also match well with particle-in-cell simulations of the interaction.

  2. SUPER HARD SURFACED POLYMERS

    SciTech Connect

    Mansur, Louis K; Bhattacharya, R; Blau, Peter Julian; Clemons, Art; Eberle, Cliff; Evans, H B; Janke, Christopher James; Jolly, Brian C; Lee, E H; Leonard, Keith J; Trejo, Rosa M; Rivard, John D

    2010-01-01

    High energy ion beam surface treatments were applied to a selected group of polymers. Of the six materials in the present study, four were thermoplastics (polycarbonate, polyethylene, polyethylene terephthalate, and polystyrene) and two were thermosets (epoxy and polyimide). The particular epoxy evaluated in this work is one of the resins used in formulating fiber reinforced composites for military helicopter blades. Measures of mechanical properties of the near surface regions were obtained by nanoindentation hardness and pin on disk wear. Attempts were also made to measure erosion resistance by particle impact. All materials were hardness tested. Pristine materials were very soft, having values in the range of approximately 0.1 to 0.5 GPa. Ion beam treatment increased hardness by up to 50 times compared to untreated materials. For reference, all materials were hardened to values higher than those typical of stainless steels. Wear tests were carried out on three of the materials, PET, PI and epoxy. On the ion beam treated epoxy no wear could be detected, whereas the untreated material showed significant wear.

  3. Softeners for hardness removal.

    PubMed

    Shetty, Rashma; Manjunath, N T; Babu, B T Suresh

    2005-10-01

    The depletion of water resources, both surface and subsurface and deterioration of water quality made researchers and policy makers to think of the possible remedies to make water sources potable / wholesome. There is a need to address the problems of hardness and fluoride in subsurface water on priority basis. In this direction, bench scale studies were conducted to evaluate the performance of water softeners. Indepth studies were carried out at University B.D.T College of Engineering, Davangere, Karnataka, to assess the performance of bench scale softeners of D to H ratio 1:2, 1:3, 1:4 in removing hardness of varied concentrations from both synthetic and natural water samples. Studies revealed that irrespective of D to H ratio of softeners, the waters having hardness concentration up to 1000 mg/l can be treated to the same degree (81.68% and above). The findings of regeneration studies and cost economics are also summarized in this paper. PMID:17051915

  4. Density patterns and energy-angle distributions from a simple cascade scheme for last 20Ne + 238U collisions

    NASA Astrophysics Data System (ADS)

    Halbert, E. C.

    1981-01-01

    A simple but fully three-dimensional cascade approach, appropriate for considering heavy-ion collisions at a few hundred MeV per projectile nucleon, is applied to 20Ne + 238U. For impact parameters bNeU of 0 and 5 fm the calculated results include densities ρ(r-->,t) of nucleon masses during the collision and energy-angle distributions d2ndEdΩ of scattered nucleon masses emerging from the collision. All of the present calculations use idealized nucleon-nucleon interactions implying cross sections σNN that are purely elastic, isotropic, and independent of the initial NN state. Some of these calculations also introduce excluded-volume effects, such as those associated with a classical hard core in the NN interaction. The calculated density ρ(r-->,t) is quite sensitive to changes in the size of the excluded volume (we tried hard cores of radius 0, 0.5, and 0.9 fm). However, it is only in the case of zero excluded volume that ρ(r-->,t) shows much sensitivity to changes in σNN (we tried σNN=15.4, 25.4, and 53.1 mb). The distribution d2ndEdΩ is rather insensitive to the excluded-volume feature but does depend sensitively on σNN, on the impact parameter bNeU, and on the emitted-nucleon characteristics E and Ω. For one particular set of NN parameters-hard-core radius = 0.9 fm, σNN=25.4 mb-our cascade calculation reduces to a case in which each nucleon is modeled precisely as a classical frictionless billiard ball (a "hard sphere") of diameter equal to the hard-core radius. For this case our cascade results would be especially suitable for comparison with analogous fluid-dynamic results-these latter to be computed using the known equation of state of a hard-sphere gas. NUCLEAR REACTIONS High-energy heavy-ion reactions. Intranuclear cascade calculations. 20Ne + 238U collisions at laboratory energies of about 200-400 MeV per nucleon of the projectile. Density of nuclear matter. Energy-angle distributions of emitted nucleons.

  5. A range of spin-crossover temperature T1/2>300 K results from out-of-sphere anion exchange in a series of ferrous materials based on the 4-(4-imidazolylmethyl)-2-(2-imidazolylmethyl)imidazole (trim) ligand, [Fe(trim)2]X2 (X=F, Cl, Br, I): comparison of experimental results with those derived from density functional theory calculations.

    PubMed

    Lemercier, Gilles; Brfuel, Nicolas; Shova, Sergiu; Wolny, Juliusz A; Dahan, Franoise; Verelst, Marc; Paulsen, Hauke; Trautwein, Alfred X; Tuchagues, Jean-Pierre

    2006-09-25

    The synthesis and characterization of [FeII(trim)2]Cl2 (2), [FeII(trim)2]Br2MeOH (3), and [FeII(trim)2]I2MeOH (4), including the X-ray crystal structure determinations of 2 (50 and 293 K) and 4 (293 K), have been performed and their properties have been examined. In agreement with the magnetic susceptibility results, the Mssbauer data show the presence of high-spin (HS) to low-spin (LS) crossover with a range of T1/2 larger than 300 K (from approximately 20 K for [FeII(trim)2]F2 (1) to approximately 380 K for 4). All complexes in this series include the same [Fe(trim)2]2+ complex cation: the ligand field comprises a constant contribution from the trim ligands and a variable one originating from the out-of-sphere anions, which is transmitted to the metal center by the connecting imidazole rings and hydrogen bonds. The impressive variation in the intrinsic characteristics of the spin-crossover (SCO) phenomenon in this series is then interpreted as an inductive effect of the anions transmitted to the nitrogen donors through the hydrogen bonds. Based on this qualitative analysis, an increased inductive effect of the out-of-sphere anion corresponds to a decreased SCO temperature T1/2, in agreement with the experimental results. Electronic structure calculations with periodic boundary conditions have been performed that show the importance of intermolecular effects in tuning the ligand field, and thus in determining the transition temperature. Starting with the geometries obtained from the X-ray studies, the [FeII(trim)2]X2 complex molecules 1-4 have been investigated both for the single molecules and the crystal lattices with the local density approximation of density functional theory. The bulk geometries of the complex cations deduced from the X-ray studies and those calculated are in fair agreement for both approaches. However, the trend observed for the transition temperatures of 1-4 disagrees with the trend for the spin-state splittings ES (difference EHS-ELS between the energy of the HS and LS isomers) calculated for the isolated molecules, whereas it agrees with the trend for ES calculated with periodic boundary conditions. The latter calculations predict the strongest stabilization of the HS state for the fluoride complex, which actually is essentially HS above T=50 K, while the most pronounced stabilization of the LS state is predicted for 4, in line with the experimental results. PMID:16874821

  6. Turbulence generator using a precessing sphere

    NASA Astrophysics Data System (ADS)

    Goto, Susumu; Ishii, Nobukazu; Kida, Shigeo; Nishioka, Michio

    2007-06-01

    We propose a precessing sphere as a tabletop turbulence generator, which has less uncertainty in the setting of control parameters and the resulting high flow-reproducibility. The precession is realized by rotating the spin axis of a sphere around another axis (the precession axis). In our experiments, the two axes are fixed at right angles. The flow inside the sphere is governed only by two nondimensional parameters, one being ? (the rate of precession). The range of parameters for sustaining turbulence is revealed by the time-series analysis of velocity fields measured by particle image velocimetry. Well-developed turbulence can be sustained even for ? of the order of a few percent when Re is beyond a few thousands.

  7. Facile synthesis and electrochemical performances of hollow graphene spheres as anode material for lithium-ion batteries

    PubMed Central

    2014-01-01

    The hollow graphene oxide spheres have been successfully fabricated from graphene oxide nanosheets utilizing a water-in-oil emulsion technique, which were prepared from natural flake graphite by oxidation and ultrasonic treatment. The hollow graphene oxide spheres were reduced to hollow graphene spheres at 500C for 3h under an atmosphere of Ar(95%)/H2(5%). The first reversible specific capacity of the hollow graphene spheres was as high as 903 mAh g-1 at a current density of 50 mAh g-1. Even at a high current density of 500 mAh g-1, the reversible specific capacity remained at 502 mAh g-1. After 60cycles, the reversible capacity was still kept at 652 mAh g-1 at the current density of 50 mAh g-1. These results indicate that the prepared hollow graphene spheres possess excellent electrochemical performances for lithium storage. The high rate performance of hollow graphene spheres thanks to the hollow structure, thin and porous shells consisting of graphene sheets. PACS 81.05.ue; 61.48.Gh; 72.80.Vp PMID:25114657

  8. Facile synthesis and electrochemical performances of hollow graphene spheres as anode material for lithium-ion batteries

    NASA Astrophysics Data System (ADS)

    Yao, Ran-Ran; Zhao, Dong-Lin; Bai, Li-Zhong; Yao, Ning-Na; Xu, Li

    2014-07-01

    The hollow graphene oxide spheres have been successfully fabricated from graphene oxide nanosheets utilizing a water-in-oil emulsion technique, which were prepared from natural flake graphite by oxidation and ultrasonic treatment. The hollow graphene oxide spheres were reduced to hollow graphene spheres at 500C for 3 h under an atmosphere of Ar(95%)/H2(5%). The first reversible specific capacity of the hollow graphene spheres was as high as 903 mAh g-1 at a current density of 50 mAh g-1. Even at a high current density of 500 mAh g-1, the reversible specific capacity remained at 502 mAh g-1. After 60 cycles, the reversible capacity was still kept at 652 mAh g-1 at the current density of 50 mAh g-1. These results indicate that the prepared hollow graphene spheres possess excellent electrochemical performances for lithium storage. The high rate performance of hollow graphene spheres thanks to the hollow structure, thin and porous shells consisting of graphene sheets.

  9. Tracer diffusion of hard-sphere binary mixtures under nano-confinement

    NASA Astrophysics Data System (ADS)

    Marini Bettolo Marconi, Umberto; Malgaretti, Paolo; Pagonabarraga, Ignacio

    2015-11-01

    The physics of diffusion phenomena in nano- and microchannels has attracted a lot of attention in recent years, due to its close connection with many technological, medical, and industrial applications. In the present paper, we employ a kinetic approach to investigate how the confinement in nanostructured geometries affects the diffusive properties of fluid mixtures and leads to the appearance of properties different from those of bulk systems. In particular, we derive an expression for the friction tensor in the case of a bulk fluid mixture confined to a narrow slit having undulated walls. The boundary roughness leads to a new mechanism for transverse diffusion and can even lead to an effective diffusion along the channel larger than the one corresponding to a planar channel of equivalent section. Finally, we discuss a reduction of the previous equation to a one dimensional effective diffusion equation in which an entropic term encapsulates the geometrical information on the channel shape.

  10. Periodic and Aperiodic Close Packing: A Spontaneous Hard-Sphere Model.

    ERIC Educational Resources Information Center

    van de Waal, B. W.

    1985-01-01

    Shows how to make close-packed models from balloons and table tennis balls to illustrate structural features of clusters and organometallic cluster-compounds (which are of great interest in the study of chemical reactions). These models provide a very inexpensive and tactile illustration of the organization of matter for concrete operational

  11. Periodic and Aperiodic Close Packing: A Spontaneous Hard-Sphere Model.

    ERIC Educational Resources Information Center

    van de Waal, B. W.

    1985-01-01

    Shows how to make close-packed models from balloons and table tennis balls to illustrate structural features of clusters and organometallic cluster-compounds (which are of great interest in the study of chemical reactions). These models provide a very inexpensive and tactile illustration of the organization of matter for concrete operational…

  12. Tracer diffusion of hard-sphere binary mixtures under nano-confinement.

    PubMed

    Marini Bettolo Marconi, Umberto; Malgaretti, Paolo; Pagonabarraga, Ignacio

    2015-11-14

    The physics of diffusion phenomena in nano- and microchannels has attracted a lot of attention in recent years, due to its close connection with many technological, medical, and industrial applications. In the present paper, we employ a kinetic approach to investigate how the confinement in nanostructured geometries affects the diffusive properties of fluid mixtures and leads to the appearance of properties different from those of bulk systems. In particular, we derive an expression for the friction tensor in the case of a bulk fluid mixture confined to a narrow slit having undulated walls. The boundary roughness leads to a new mechanism for transverse diffusion and can even lead to an effective diffusion along the channel larger than the one corresponding to a planar channel of equivalent section. Finally, we discuss a reduction of the previous equation to a one dimensional effective diffusion equation in which an entropic term encapsulates the geometrical information on the channel shape. PMID:26567671

  13. Shear viscosity and structural scalings in model adhesive hard-sphere gels.

    PubMed

    Eberle, Aaron P R; Martys, Nicos; Porcar, Lionel; Kline, Steven R; George, William L; Kim, Jung M; Butler, Paul D; Wagner, Norman J

    2014-05-01

    We present experiments and simulations that show a fundamental scaling for both the rheology and microstructure of flowing gels. Unique flow-SANS measurements demonstrate that the structure orients along both the neutral and compression axis. We quantify the anisotropy using a single parameter, α, that scales by a dimensionless number, M^{'}, that arises from a force balance on a particle. Simulations support the scalings and confirm the results are independent of the shape and range of the potential suggesting a universal for colloidal gels with short-ranged attractions. PMID:25353728

  14. Wave-induced motion of magnetic spheres

    NASA Astrophysics Data System (ADS)

    Gissinger, Christophe

    2015-12-01

    We report an experimental study of the motion of magnetized beads driven by a travelling-wave magnetic field. For sufficiently large wave speed, we report the existence of a backward motion, in which the sphere can move in the direction opposite to the driving wave. We show that the transition to this new state is strongly subcritical and can lead to chaotic motion of the bead. For some parameters, this counterpropagation of the sphere can be one order of magnitude faster than the driving-wave speed. These results are understood in the framework of a model based on the interplay among solid friction, air resistance and magnetic torque.

  15. Mesoporous hollow spheres from soap bubbling.

    PubMed

    Yu, Xianglin; Liang, Fuxin; Liu, Jiguang; Lu, Yunfeng; Yang, Zhenzhong

    2012-02-01

    The smaller and more stable bubbles can be generated from the large parent bubbles by rupture. In the presence of a bubble blowing agent, hollow spheres can be prepared by bubbling a silica sol. Herein, the trapped gas inside the bubble acts as a template. When the porogen, i.e., other surfactant, is introduced, a mesostructured shell forms by the co-assembly with the silica sol during sol-gel process. Morphological evolution emphasizes the prerequisite of an intermediate interior gas flow rate and high exterior gas flow rate for hollow spheres. The method is valid for many compositions from inorganic, polymer to their composites. PMID:22078340

  16. Integrable point vortex motion on a sphere

    NASA Astrophysics Data System (ADS)

    Kidambi, Rangachari

    This dissertation is concerned with integrable point vortex motion on a sphere. First, we solve the equations governing the relative motion of three point vortices of arbitrary strength moving on the surface of a sphere of radius R. The system is more general than the corresponding one in the plane and reduces to it in the limit R ? infinity, as long as the three vortices remain sufficiently close to each other during the course of their motion. We then fully characterize all fixed and relative equilibria and more general relative motions on the sphere. We then describe self-similar vortex collapse on the sphere, stating necessary and sufficient conditions for collapse to occur, computing the collapse times and vortex trajectories on the route towards collapse. Collapse trajectories occur in pairs, called 'partner states', which have two distinct collapse times tau -- < tau+. In the plane, there is only one collapse time associated with a given configuration---the partner state is one that expands self-similarly. The instantaneous streamline patterns that can occur are then considered. After stating some general results based on the spherical topology, we categorize all possible instantaneous streamline patterns and describe their stagnation point structure for the cases of two and three vortices. For the case of two vortices, the only non-degenerate patterns that can arise are a figure eight (lemniscate) or a limacon, which are homotopically equivalent. For the case of three vortices, there: are 12 topologically distinct primitives, from which an additional 23 patterns can be produced via continuous deformations on the sphere (homotopies). All possible streamline patterns that arise from three vortex motion can be obtained via linear superposition of the primitives and their homotopic equivalents. In this sense, the primitives can be viewed as the 'building blocks' for the general instantaneous flow topology. We describe streamline patterns for three vortex fixed equilibria and relative equilibria as seen in both a fixed and a rotating frame of reference. Finally, we examine vortex motion on the sphere with solid boundaries. For highly symmetric domains, we show that known solutions in the plane, obtained by the method of images, can be used to generate solutions on the sphere by stereographic projection. We explicitly compute the particle and vortex motion for several domains on the sphere, including a spherical cap, a longitudinal wedge, channel and rectangle.

  17. Hypervelocity shock standoff on spheres in air

    NASA Astrophysics Data System (ADS)

    Zander, F.; Gollan, R. J.; Jacobs, P. A.; Morgan, R. G.

    2014-03-01

    To provide data for the validation of computational fluid dynamics models, measurements of the shock standoff distance on spheres in hypervelocity flows have been made. Test flows of air at 8.7 and 9.7 km/s were generated in the X2 expansion tunnel fitted with a Mach 10 nozzle. High-speed video images were analysed with a least-squares shape-fitting algorithm. Assuming a spherical shock shape near the nose enabled increased resolution measurements beyond the native pixel size. Normalised shock standoff distances, /, in the range 0.03-0.04 were measured, with sphere diameters, , of 40, 60 and 80 mm.

  18. Equation of state and critical point behavior of hard-core double-Yukawa fluids.

    PubMed

    Montes, J; Robles, M; López de Haro, M

    2016-02-28

    A theoretical study on the equation of state and the critical point behavior of hard-core double-Yukawa fluids is presented. Thermodynamic perturbation theory, restricted to first order in the inverse temperature and having the hard-sphere fluid as the reference system, is used to derive a relatively simple analytical equation of state of hard-core multi-Yukawa fluids. Using such an equation of state, the compressibility factor and phase behavior of six representative hard-core double-Yukawa fluids are examined and compared with available simulation results. The effect of varying the parameters of the hard-core double-Yukawa intermolecular potential on the location of the critical point is also analyzed using different perspectives. The relevance of this analysis for fluids whose molecules interact with realistic potentials is also pointed out. PMID:26931708

  19. A green chemical approach to the synthesis of photoluminescent ZnO hollow spheres with enhanced photocatalytic properties

    SciTech Connect

    Patrinoiu, Greta; Tudose, Madalina; Calderon-Moreno, Jose Maria; Birjega, Ruxandra; Budrugeac, Petru; Ene, Ramona; Carp, Oana

    2012-02-15

    ZnO hollow spheres have been synthesized by a simple and environmentally friendly template assisted route. Starch-derived carbonaceous spheres were used as template, impregnated with Zn(CH{sub 3}COO){sub 2}{center_dot}2H{sub 2}O to obtain zinc-containing precursor spheres and thermally treatment at 600 Degree-Sign C, yielding hollow ZnO spherical shells. The precursor spheres and hollow shells were characterized by X-ray diffraction, FTIR spectroscopy, scanning electron microscopy, thermal analysis and room-temperature photoluminescence measurements. The hollow spherical shells with diameters of {approx}150 nm and wall thickness of {approx}20 nm, are polycrystalline, with a mean crystallite size of 22 nm, exhibiting interesting emission features, with a wide multi-peak band covering blue and green regions of the visible spectrum. The photocatalytic activities (under UV and visible light irradiations) of the ZnO spherical shells evaluated for the phenol degradation reaction in aqueous solutions are outstanding, a total phenol conversion being registered in the case of UV irradiation experiments. - Graphical abstract: The photocatalytic reaction initiated by the photoexcitation of the semiconductor (ZnO), leads to the formation of electron-hole, while part of the electron-hole pairs recombine, some holes combine with water to form {center_dot}OH radicals and some electrons convert oxygen to super oxide radical ({center_dot}O{sub 2}{sup -}). Highlights: Black-Right-Pointing-Pointer Green synthesis of ZnO hollow spheres. Black-Right-Pointing-Pointer Starch-derived carbonaceous spheres as spherical hard template. Black-Right-Pointing-Pointer ZnO hollow spheres with notable visible photoluminescence properties. Black-Right-Pointing-Pointer ZnO hollow spheres with photocatalytical activity in degradation/mineralization of phenol.

  20. On the role of ambient environments in the collapse of Bonnor-Ebert spheres

    SciTech Connect

    Kaminski, Erica; Frank, Adam; Carroll, Jonathan; Myers, Phil E-mail: pmyers@cfa.harvard.edu

    2014-07-20

    We consider the interaction between a marginally stable Bonnor-Ebert (BE) sphere and the surrounding ambient medium. In particular, we explore how the infall from an evolving ambient medium can trigger the collapse of the sphere using three-dimensional adaptive mesh refinement simulations. We find the resulting collapse dynamics to vary considerably with ambient density. In the highest ambient density cases, infalling material drives a strong compression wave into the cloud. It is the propagation of this wave through the cloud interior that triggers the subsequent collapse. For lower ambient densities, we find the main trigger of collapse to be a quasistatic adjustment of the BE sphere to gravitational settling of the ambient gas. In all cases, we find that the classic 'outside-in' collapse mode for super-critical BE spheres is recovered before a protostar (i.e., sink particle) forms. Our work supports scenarios in which BE dynamics naturally begins with either a compression wave or infall dominated phase, and only later assumes the usual outside-in collapse behavior.

  1. Viscosity of bimodal suspensions with hard spherical particles

    NASA Astrophysics Data System (ADS)

    Spangenberg, Jon; Scherer, George W.; Hopkins, Adam B.; Torquato, Salvatore

    2014-11-01

    We analyze two equations for their ability to predict the viscosity of bimodal suspensions with hard spherical particles. The equations express the viscosity as a function of the particle loading and the packing (or, volume) fraction at which the viscosity diverges (viscosity threshold). The latter is found from previously published experimental studies for a variety of sphere diameter ratios and fractions of small particles in total solids. A comparison between the viscosity thresholds and the maximally random jammed packing verifies their interconnection and permits accurate viscosity prediction of bimodal suspensions.

  2. Weighted density-functional theory for simple fluids: Prewetting of a Lennard-Jones fluid

    NASA Astrophysics Data System (ADS)

    Sweatman, M. B.

    2002-01-01

    The prewetting of a Lennard-Jones fluid is studied using weighted density-functional theory. The intrinsic Helmholtz free-energy functional is separated into repulsive and attractive contributions. An accurate functional for hard spheres is used for the repulsive functional and a weighted density-functional method is used for the attractive part. The results for this theory are compared against mean-field density-functional theory, the theory of Velasco and Tarazona [E. Velasco and P. Tarazona, J. Chem. Phys. 91, 7916 (1989)] and grand canonical ensemble simulation results. The results demonstrate that the weighted density functional for attractive forces may offer a significant increase in accuracy over the other theories. The density-functional and simulation results also indicate that a previous estimate of the wetting temperature for a model of the interaction of argon with solid carbon dioxide, obtained from simulations [J. E. Finn and P. A. Monson, Phys. Rev. A, 39, 6402 (1989)], is incorrect. The weighted density-functional method indicates that triple-point prewetting is observed for this model potential.

  3. Trapping of a mie sphere by acoustic pulses: effects of pulse length.

    PubMed

    Kang, Shih-Tsung; Yeh, Chih-Kuang

    2013-07-01

    The acoustic counterpart of optical tweezers shows great promise as a single-particle manipulator using a highly focused acoustic beam. Understanding the dependence of the trapping performance of the acoustic beam on the acoustic pulse length may facilitate its development and extend the applications. Herein, we propose a ray-based model for the time-course simulation of instantaneous forces exerted on single Mie spheres by highly focused acoustic pulses of arbitrary lengths. The simulations considered single fat/lipid spheres with a density of 950 kg/m3 and speed of sound of 1450 m/s, suspended in water and located on the beam axis. Simulation was used to establish the spatial and temporal pressure data of pulsed acoustic fields transmitted from a 100-MHz transducer with a half-power bandwidth of 50% and an f-number of 1. The instantaneous intensity vectors were calculated to represent rays for estimating forces exerted by consecutive wave-particle interactions. The results suggest that short acoustic pulses can exert negative forces pulling spheres beyond the focus in the direction opposite to that of wave propagation. Varying the excitation pulse duration has no effect on the region where the exerted forces are averagely negative. Lengthening the excitation pulse duration rapidly increases the amplitude of the average force. A smaller sphere experiences a greater average force when the spatial length of a transmitted acoustic pulse is comparable to the sphere diameter. The amplitude of the instantaneous force can be maximized as long as the acoustic pulse length is longer than the sphere diameter. Regulating the relation between acoustic pulse length and sphere size may be advantageous in particle sorting applications. PMID:25004516

  4. How to control Chaplygin's sphere using rotors

    NASA Astrophysics Data System (ADS)

    Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S.

    2012-05-01

    In the paper we study the control of a balanced dynamically non-symmetric sphere with rotors. The no-slip condition at the point of contact is assumed. The algebraic controllability is shown and the control inputs that steer the ball along a given trajectory on the plane are found. For some simple trajectories explicit tracking algorithms are proposed.

  5. 3-Dimensional Colloidal Crystals From Hollow Spheres

    NASA Astrophysics Data System (ADS)

    Zhang, Jian; Work, William J.; Sanyal, Subrata; Lin, Keng-Hui; Yodh, A. G.

    2000-03-01

    We have succeeded in synthesizing submicron-sized, hollow PMMA spheres and self-assembling them into colloidal crystalline structures using the depletion force. The resulting structures can be used as templates to make high refractive-index contrast, porous, inorganic structures without the need to use calcination or chemical-etching. With the method of emulsion polymerization, we managed to coat a thin PMMA shell around a swellable P(MMA/MAA/EGDMA) core. After neutralization and heating above the glass transition temperature of PMMA, we obtained water-swollen hydrogel particles encapsulated in PMMA shells. These composite particles become hollow spheres after drying. We characterized the particles with both transmission electron microscopy (TEM) and dynamic light scattering (DLS). The TEM results confirmed that each sphere has a hollow core. The DLS results showed that our hollow spheres are submicron-sized, with a swelling ratio of at least 25%, and with a polydispersity less than 5%. We anticipate using this method in the near-future to encapsulate ferrofluid emulsion droplets and liquid crystal droplets.

  6. Propulsion of a Two-Sphere Swimmer.

    PubMed

    Klotsa, Daphne; Baldwin, Kyle A; Hill, Richard J A; Bowley, R M; Swift, Michael R

    2015-12-11

    We describe experiments and simulations demonstrating the propulsion of a neutrally buoyant swimmer that consists of a pair of spheres attached by a spring, immersed in a vibrating fluid. The vibration of the fluid induces relative motion of the spheres which, for sufficiently large amplitudes, can lead to motion of the center of mass of the two spheres. We find that the swimming speed obtained from both experiment and simulation agree and collapse onto a single curve if plotted as a function of the streaming Reynolds number, suggesting that the propulsion is related to streaming flows. There appears to be a critical onset value of the streaming Reynolds number for swimming to occur. We observe a change in the streaming flows as the Reynolds number increases, from that generated by two independent oscillating spheres to a collective flow pattern around the swimmer as a whole. The mechanism for swimming is traced to a strengthening of a jet of fluid in the wake of the swimmer. PMID:26705658

  7. Charged static fluid spheres in general relativity.

    NASA Astrophysics Data System (ADS)

    Mak, M. K.; Fung, P. C. W.

    1995-08-01

    In this paper, the authors present a new method to extend Pant's work (1994) to the case of charged fluid spheres. A number of previously known solutions has been rediscovered in the process. Two classes of solutions are obtained and matched at the boundary with the Reissner-Nordstrm metric.

  8. Electromagnetic resonant modes of dielectric sphere bilayers

    NASA Astrophysics Data System (ADS)

    Andueza, A.; Pérez-Conde, J.; Sevilla, J.

    2015-05-01

    Sphere bilayers have been proposed as promising structures for electromagnetic management in photonic crystal devices. These arrangements are made of two intertwined subsets of spheres of different size and refractive index, one subset filling the interstitial sites of the other. We present a systematic study of the electromagnetic resonant modes of the bilayers, in comparison with those of the constituent subsets of spheres. Three samples were built with glass and Teflon spheres and their transmission spectra measured in the microwave range (10-25 GHz). Simulations with finite integration time-domain method are in good agreement with experiments. Results show that the bilayer presents the same resonances as one of the subsets but modified by the presence of the other in its resonant frequencies and in the electric field distributions. As this distortion is not very large, the number of resonances in a selected spectral region is determined by the dominant subset. The degree of freedom that offers the bilayer could be useful to fine tune the resonances of the structure for different applications. A map of modes useful to guide this design is also presented. Scale invariance of Maxwell equations allows the translation of these results in the microwave range to the visible region; hence, some possible applications are discussed in this framework.

  9. Electromagnetic resonant modes of dielectric sphere bilayers

    SciTech Connect

    Andueza, A. Pérez-Conde, J.; Sevilla, J.

    2015-05-28

    Sphere bilayers have been proposed as promising structures for electromagnetic management in photonic crystal devices. These arrangements are made of two intertwined subsets of spheres of different size and refractive index, one subset filling the interstitial sites of the other. We present a systematic study of the electromagnetic resonant modes of the bilayers, in comparison with those of the constituent subsets of spheres. Three samples were built with glass and Teflon spheres and their transmission spectra measured in the microwave range (10–25 GHz). Simulations with finite integration time-domain method are in good agreement with experiments. Results show that the bilayer presents the same resonances as one of the subsets but modified by the presence of the other in its resonant frequencies and in the electric field distributions. As this distortion is not very large, the number of resonances in a selected spectral region is determined by the dominant subset. The degree of freedom that offers the bilayer could be useful to fine tune the resonances of the structure for different applications. A map of modes useful to guide this design is also presented. Scale invariance of Maxwell equations allows the translation of these results in the microwave range to the visible region; hence, some possible applications are discussed in this framework.

  10. Surface polaritons on left-handed spheres

    NASA Astrophysics Data System (ADS)

    Ancey, Stphane; Dcanini, Yves; Folacci, Antoine; Gabrielli, Paul

    2007-11-01

    We consider the interaction of an electromagnetic field with a left-handed sphere, i.e., with a sphere fabricated from a left-handed material, in the framework of complex angular momentum techniques. We emphasize more particularly, from a semiclassical point of view, the resonant aspects of the problem linked to the existence of surface polaritons. We prove that the long-lived resonant modes can be classified into distinct families, each family being generated by one surface polariton propagating close to the sphere surface, and we physically describe all the surface polaritons by providing, for each one, its dispersion relation and its damping. This can be achieved by noting that each surface polariton corresponds to a particular Regge pole of the electric part (TM) or the magnetic part (TE) of the S matrix of the sphere. Moreover, for both polarizations, we find that there exists a particular surface polariton which corresponds, in the large radius limit, to that supported by the plane interface. There also exists, for both polarizations, an infinite family of surface polaritons of whispering gallery type having no analogs in the plane interface case and specific to left-handed materials. They present a left-handed behavior" (phase and group velocities are opposite) as well as a very weak damping. They could be very useful in the context of plasmonics or cavity quantum electrodynamics.

  11. Chromatographic NMR Spectroscopy with Hollow Silica Spheres.

    PubMed

    Gonzlez-Garca, Tania; Margola, Tommaso; Silvagni, Adriano; Mancin, Fabrizio; Rastrelli, Federico

    2016-02-01

    The use of micrometric hollow silica spheres is described as a strategy to reduce magnetic field inhomogeneities in the context of NMR chromatography. When employed as a stationary phase, hollow silica microspheres allow the use of common solution-state NMR instruments to measure the diffusion coefficient perturbation induced by the interaction of the analytes with the silica surface. PMID:26809047

  12. More transition amplitudes on the Riemann sphere

    SciTech Connect

    Dimock, J.

    2008-06-15

    We consider a conformal field theory for bosons on the Riemann sphere. Correlation functions are defined as singular limits of functional integrals. The main result is that these amplitudes define transition amplitudes, that is multilinear Hilbert-Schmidt functionals on a fixed Hilbert space.

  13. Some analytical models of radiating collapsing spheres

    SciTech Connect

    Herrera, L.; Di Prisco, A; Ospino, J.

    2006-08-15

    We present some analytical solutions to the Einstein equations, describing radiating collapsing spheres in the diffusion approximation. Solutions allow for modeling physical reasonable situations. The temperature is calculated for each solution, using a hyperbolic transport equation, which permits to exhibit the influence of relaxational effects on the dynamics of the system.

  14. TEACHING PHYSICS: Biking around a hollow sphere

    NASA Astrophysics Data System (ADS)

    Mak, Se-yuen; Yip, Din-yan

    1999-11-01

    The conditions required for a cyclist riding a motorbike in a horizontal circle on or above the equator of a hollow sphere are derived using concepts of equilibrium and the condition for uniform circular motion. The result is compared with an empirical analysis based on a video show. Some special cases of interest derived from the general solution are elaborated.

  15. Experimentation on recurrent sphere collision with Audacity

    NASA Astrophysics Data System (ADS)

    Muradoglu, Murat; Ng, Enoch Ming Wei; Ng, Tuck Wah

    2014-11-01

    Under the theme of collisions that occur repeatedly, we conducted easy and inexpensive experiments of rebounding spheres and Newtons cradle with two spheres to determine the coefficients of restitution using the sound record feature in modern laptops and a free and open source software called Audacity. In the rebounding sphere experiment, the coefficients of restitution of the golf and ping pong balls used were found to be 0.727 0.025 and 0.816 0.041 respectively. With the Netwons cradle experiment, the coefficient of restitution of two steel sphere balls was found to be 0.987 0.003. The contrasts in the results obtained from both experiments permit the operational principles of a pendulum to be emphasized, and engagements to be made to consider the transfer of kinetic energy in the form of vibrational energy of the bodies constituents. Using a one-dimensional two-mass model with spring and damper linkages to account for harmonic motions that occur during impact, we found it possible to perform a simple analysis to account for this, and how it can be linked to high energy transfer modes such as the phenomenon of resonance and impedance matching.

  16. Metal-Matrix/Hollow-Ceramic-Sphere Composites

    NASA Technical Reports Server (NTRS)

    Baker, Dean M.

    2011-01-01

    A family of metal/ceramic composite materials has been developed that are relatively inexpensive, lightweight alternatives to structural materials that are typified by beryllium, aluminum, and graphite/epoxy composites. These metal/ceramic composites were originally intended to replace beryllium (which is toxic and expensive) as a structural material for lightweight mirrors for aerospace applications. These materials also have potential utility in automotive and many other terrestrial applications in which there are requirements for lightweight materials that have high strengths and other tailorable properties as described below. The ceramic component of a material in this family consists of hollow ceramic spheres that have been formulated to be lightweight (0.5 g/cm3) and have high crush strength [40.80 ksi (.276.552 MPa)]. The hollow spheres are coated with a metal to enhance a specific performance . such as shielding against radiation (cosmic rays or x rays) or against electromagnetic interference at radio and lower frequencies, or a material to reduce the coefficient of thermal expansion (CTE) of the final composite material, and/or materials to mitigate any mismatch between the spheres and the matrix metal. Because of the high crush strength of the spheres, the initial composite workpiece can be forged or extruded into a high-strength part. The total time taken in processing from the raw ingredients to a finished part is typically 10 to 14 days depending on machining required.

  17. Propulsion of a Two-Sphere Swimmer

    NASA Astrophysics Data System (ADS)

    Klotsa, Daphne; Baldwin, Kyle A.; Hill, Richard J. A.; Bowley, R. M.; Swift, Michael R.

    2015-12-01

    We describe experiments and simulations demonstrating the propulsion of a neutrally buoyant swimmer that consists of a pair of spheres attached by a spring, immersed in a vibrating fluid. The vibration of the fluid induces relative motion of the spheres which, for sufficiently large amplitudes, can lead to motion of the center of mass of the two spheres. We find that the swimming speed obtained from both experiment and simulation agree and collapse onto a single curve if plotted as a function of the streaming Reynolds number, suggesting that the propulsion is related to streaming flows. There appears to be a critical onset value of the streaming Reynolds number for swimming to occur. We observe a change in the streaming flows as the Reynolds number increases, from that generated by two independent oscillating spheres to a collective flow pattern around the swimmer as a whole. The mechanism for swimming is traced to a strengthening of a jet of fluid in the wake of the swimmer.

  18. Life in the E-Sphere.

    ERIC Educational Resources Information Center

    Pelton, Joseph N.

    2002-01-01

    Discusses the survival of the human race in the Third Millennium. Considers environmental issues; shifting from a focus on economic growth to human development; the rate of technological change; the e-sphere, which goes beyond a global village to a global brain; technology in education and in health care; and educational reform. (LRW)

  19. The Public Sphere and Online, Independent Journalism

    ERIC Educational Resources Information Center

    Beers, David

    2006-01-01

    The rapid evolution of online, independent journalism affords educators an opportunity to increase students' understanding of the nature and power of the news media. Drawing from Habermas's theories of the role of the public sphere in democratic discourse, the author, as founder of an online news publication, traces trends in concentrated

  20. Steel Spheres and Skydiver--Terminal Velocity

    ERIC Educational Resources Information Center

    Costa Leme, J.; Moura, C.; Costa, Cintia

    2009-01-01

    This paper describes the use of open source video analysis software in the study of the relationship between the velocity of falling objects and time. We discuss an experiment in which a steel sphere falls in a container filled with two immiscible liquids. The motion is similar to that of a skydiver falling through air.