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1

Density functional theory for Baxter's sticky hard spheres in confinement

It has recently been shown that a free energy for Baxter's sticky hard sphere fluid is uniquely defined within the framework of fundamental measure theory (FMT) for the inhomogeneous hard sphere fluid, provided that it obeys scaled-particle theory and the Percus-Yevick (PY) result for the direct correlation function [Hansen-Goos and Wettlaufer, J. Chem. Phys. {\\bf 134}, 014506 (2011)]. Here, combining weighted densities from common versions of FMT with a new vectorial weighted density, we derive a regularization of the divergences of the associated strongly confined limit. Moreover, the simple free energy that emerges is exact in the zero-dimensional limit, leaves the underlying equation of state unaffected, and yields a direct correlation function distinct from the PY expression. Comparison with simulation data for both the bulk pair correlation function and the density profiles in confinement shows that the new theory is significantly more accurate than the PY-based results. Finally, the resulting free energy is applicable to a glass of adhesive hard spheres.

Hendrik Hansen-Goos; Mark A. Miller; J. S. Wettlaufer

2011-12-15

2

Density functional for ternary non-additive hard sphere mixtures

Based on fundamental measure theory, a Helmholtz free energy density functional for three-component mixtures of hard spheres with general, non-additive interaction distances is constructed. The functional constitutes a generalization of the previously given theory for binary non-additive mixtures. The diagrammatic structure of the spatial integrals in both functionals is of star-like (or tree-like) topology. The ternary diagrams possess a higher degree of complexity than the binary diagrams. Results for partial pair correlation functions, obtained via the Ornstein-Zernike route from the second functional derivatives of the excess free energy functional, agree well with Monte Carlo simulation data.

Matthias Schmidt

2011-08-31

3

Poisson's ratio of the fcc hard sphere crystal at high densities

NASA Astrophysics Data System (ADS)

Elastic constants and the Poisson ratio of the fcc hard-sphere crystalline phases, free of defects and with vacancies, are determined by two Monte Carlo methods: (i) the analysis of the box fluctuations in the constant pressure ensemble with variable box shape (N-P-T) and (ii) by the free-energy differentiation with respect to deformation in the fixed box ensemble (N-V-T). Very good agreement is observed for the extrapolated to the infinitely large system limit results of both the methods. The coefficients of the leading singularities of the elastic constants near close packing are estimated; they are well described by the free volume approximation. Two mechanisms influencing the Poisson ratio are studied. (i) It is shown that at high densities particle motions decrease the Poisson ratio with respect to the static case which corresponds to zero temperature. Simulations performed for systems of soft spheres, interacting through n-inverse-power potentials, r-n, show that the elastic constants of the hard spheres can be obtained in the limit n ??. When T ?0 the elastic constants of the soft spheres tend to those of the static model. (ii) It is also shown that vacancies decrease C11 and C44 and increase C12 and, hence, increase the Poisson ratio with respect to the defect-free state of the system.

Tretiakov, Konstantin V.; Wojciechowski, Krzysztof W.

2005-08-01

4

Fundamental measure density functional theory study of hard spheres solid-liquid interface

NASA Astrophysics Data System (ADS)

Interfacial free energy is an important characteristic of solid-liquid interface as it is one of the crucial parameters in many formula of interface thermodynamics such the nucleation theory. Previously different aspects of crystal-melt interfaces were intensively studied with simulations [1,2,3], but theoretical studies with Density Functional Theories (DFT) are inconclusive [4,5]. In this report the structure of hard spheres fcc crystal-melt interfaces and the anisotropy of the interfacial free energies are studied using the Rosenfeld's Fundamental Measure DFT as such a functional leads to reliable coexistence results not only for the hard sphere system but also for the Lennard-Jones systems [6]. The parameters of interfacial density profile were calculated by a proper minimization procedure. For the equilibrium density profile the interfacial free energies were compared with simulation results. 1. R.L.Davidchak and B.B.Laird, Phys.Rev.Lett., 85, 4751(2000). 2. J.J. Hoyt, M. Asta and A. Karma, Phys.Rev.Lett., 86, 5530 (2001). 3. J.R.Morris and X.Song, J.Chem.Phys., 119, 3920 (2003). 4. W.A.Curtin, Phys.Rev.B, 39, 6775(1989). 5. R.Ohnesorge, H.Lowen, and H.Wagner, Phys.Rev.E, 50, 4801 (1994). 6. V.Warshavsky and X.Song, Phys.Rev.E, 69, 061113 (2004).

Warshavsky, Vadim

2005-03-01

5

Properties of non-FCC hard-sphere solids predicted by density functional theory

The free energies of the FCC, BCC, HCP and Simple Cubic phases for hard spheres are calculated as a function of density using the Fundamental Measure Theory models of Rosenfeld et al (PRE 55, 4245 (1997)), Tarazona (PRL 84, 694 (2001)) and Roth et al (J. Phys.: Cond. Matt. 14, 12063 (2002)) in the Gaussian approximation. For the FCC phase, the present work confirms the vanishing of the Lindemann parameter (i.e. vanishing of the width of the Gaussians) near close packing for all three models and the results for the HCP phase are nearly identical. For the BCC phase and for packing fractions above $\\eta \\sim 0.56$, all three theories show multiple solid structures differing in the widths of the Gaussians. In all three cases, one of these structures shows the expected vanishing of the Lindemann parameter at close packing, but this physical structure is only thermodynamically favored over the unphysical structures in the Tarazona theory and even then, some unphysical behavior persists at lower densities. The simple cubic phase is stabilized in the model of Rosenfeld et al. for a range of densities and in the Tarazona model only very near close-packing.

James F. Lutsko

2006-04-20

6

Two versions of the fundamental measure density functionals together with a new interfacial density profile parametrization were used to study the hard-sphere crystal-melt interface in the framework of the fundamental measure density functional theory. The equilibrium interfacial density profiles and interfacial free energies were found as a result of minimization of grand canonical potential of system with respect to parameters of density profile. We found that the average interfacial free energy is about 0.78, which is in reasonable agreement with simulation results. PMID:16605503

Warshavsky, Vadim B; Song, Xueyu

2006-03-01

7

Mode expansion for the density profiles of crystal-fluid interfaces: hard spheres as a test case.

We present a technique for analyzing the full three-dimensional density profiles of planar crystal-fluid interfaces in terms of density modes. These density modes can also be related to crystallinity order parameter profiles which are used in coarse-grained, phase field type models of the statics and dynamics of crystal-fluid interfaces and are an alternative to crystallinity order parameters extracted from simulations using local crystallinity criteria. We illustrate our results for the hard sphere system using finely resolved, three-dimensional density profiles from a density functional theory of fundamental measure type. PMID:23114279

Oettel, M

2012-11-21

8

NSDL National Science Digital Library

The Ejs Hard Sphere Gas model displays a three-dimensional (ideal) gas made out of hard disks. Particles are initialized with a random speed and in a random direction and move with constant velocity until a collision occurs. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting âOpen Ejs Modelâ from the pop-up menu item. Ejs Hard Sphere Gas model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_newton_HardShpereGas.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models for statistical mechanics are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs.

Christian, Wolfgang

2008-07-06

9

We perform a comparative study of the free energies and the density distributions in hard sphere crystals using Monte Carlo simulations and density functional theory (employing Fundamental Measure functionals). Using a recently introduced technique (Schilling and Schmid, J. Chem. Phys 131, 231102 (2009)) we obtain crystal free energies to a high precision. The free energies from Fundamental Measure theory are in good agreement with the simulation results and demonstrate the applicability of these functionals to the treatment of other problems involving crystallization. The agreement between FMT and simulations on the level of the free energies is also reflected in the density distributions around single lattice sites. Overall, the peak widths and anisotropy signs for different lattice directions agree, however, it is found that Fundamental Measure theory gives slightly narrower peaks with more anisotropy than seen in the simulations. Among the three types of Fundamental Measure functionals studied, only the White Bear II functional (Hansen-Goos and Roth, J. Phys.: Condens. Matter 18, 8413 (2006)) exhibits sensible results for the equilibrium vacancy concentration and a physical behavior of the chemical potential in crystals constrained by a fixed vacancy concentration.

M. Oettel; S. Goerig; A. Haertel; H. Loewen; M. Radu; T. Schilling

2010-09-03

10

NASA Astrophysics Data System (ADS)

This article applies the density functional theory to confined liquid crystals, comprised of ellipsoidal shaped particles interacting through the hard Gaussian overlap (HGO) potential. The extended restricted orientation model proposed by Moradi and co-workers [J. Phys.: Condens. Matter 17, 5625 (2005)] is used to study the surface anchoring. The excess free energy is calculated as a functional expansion of density around a reference homogeneous fluid. The pair direct correlation function (DCF) of a homogeneous HGO fluid is approximated, based on the optimized sum of Percus-Yevick and Roth DCF for hard spheres; the anisotropy introduced by means of the closest approach parameter, the expression proposed by Marko [Physica B 392, 242 (2007)] for DCF of HGO, and hard ellipsoids were used. In this study we extend an our previous work [Phys. Rev. E 72, 061706 (2005)] on the anchoring behavior of hard particle liquid crystal model, by studying the effect of changing the particle-substrate contact function instead of hard needle-wall potentials. We use the two particle-surface potentials: the HGO-sphere and the HGO-surface potentials. The average number density and order parameter profiles of a confined HGO fluid are obtained using the two particle-wall potentials. For bulk isotropic liquid, the results are in agreement with the Monte Carlo simulation of Barmes and Cleaver [Phys. Rev. E 71, 021705 (2005)]. Also, for the bulk nematic phase, the theory gives the correct density profile and order parameter between the walls.

Avazpour, A.; Avazpour, L.

2010-12-01

11

Free energies and correlation functions of liquid and solid hard-sphere (HS) mixtures are calculated using the fundamental measure density functional theory. Using the thermodynamic perturbation theory the free energies of solid and liquid Lennard-Jones (LJ) mixtures are obtained from correlation functions of HS systems within a single theoretical approach. The resulting azeotrope- and spindle-type solid-liquid phase diagrams of HS and LJ binary mixtures are in good agreement with the corresponding ones from computer simulations. PMID:18647030

Warshavsky, Vadim B; Song, Xueyu

2008-07-21

12

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

Odriozola, Gerardo; Berthier, Ludovic

2011-02-01

13

Hard Spheres Monte Carlo Model

NSDL National Science Digital Library

The Hard Sphere Monte Carlo Model performs canonical Monte Carlo simulations of 256 or 500 hard spheres covering the fluid and solid states. The results are analysed through the radial distributions functions from which the equation of state (EOS) is estimated. This is done by fitting a polynomial to the radial distribution functions in order to exrapolate them to the hard spheres distance of contact. The consistency of the simulations is assessed by the errors of the predicted compressibility factors relatively to the accurate EOS reported by Wu and Sadus. The Hard Sphere Monte Carlo Model was developed using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the jar file will run the program if Java is installed. You can modify this simulation if you have EJS installed by right-clicking within the map and selecting "Open Ejs Model" from the pop-up menu item.

Fernandes, Fernando S.; Freitas, Filomena

2013-02-20

14

We consider the theory of the glass phase and jamming of hard spheres in the large space dimension limit. Building upon the exact expression for the free-energy functional obtained previously, we find that the random first order transition (RFOT) scenario is realized here with two thermodynamic transitions: the usual Kauzmann point associated with entropy crisis and a further transition at higher pressures in which a glassy structure of microstates is developed within each amorphous state. This kind of glass-glass transition into a phase dominating the higher densities was described years ago by Elisabeth Gardner, and may well be a generic feature of RFOT. Microstates that are small excitations of an amorphous matrix-separated by low entropic or energetic barriers-thus emerge naturally, and modify the high pressure (or low temperature) limit of the thermodynamic functions. PMID:23581562

Kurchan, Jorge; Parisi, Giorgio; Urbani, Pierfrancesco; Zamponi, Francesco

2013-10-24

15

Structure of a hard-sphere fluid near a rough surface: A density-functional approach

NASA Astrophysics Data System (ADS)

The density-functional theory of Evans [in Fundamentals of Inhomogeneous Fluids, edited by D. Henderson (Dekker, New York, 1992)] and Tarazona [Phys. Rev. A 31, 2672 (1985)] is used to study an inhomogeneous fluid near a rough surface or pore composed of grooves consisting of a periodic array of saw-toothed wedges. This involves a two-dimensional formulation of this approach, in contrast to the one-dimensional formulations that generally have been used previously. The agreement with the simulations of Schoen and Dietrich [Phys. Rev. E 56, 499 (1997)] is good.

Henderson, D.; Soko?owski, S.; Wasan, D.

1998-05-01

16

Transport coefficients of hard sphere fluids

NASA Astrophysics Data System (ADS)

New calculations have been made of the self-diffusion coefficient D, the shear viscosity ?s , the bulk viscosity ?b and thermal conductivity ? of the hard sphere fluid, using molecular dynamics (MD) computer simulation. A newly developed hard sphere MD scheme was used to model the hard sphere fluid over a wide range up to the glass transition (~0.57 packing fraction). System sizes of up to 32 000 hard spheres were considered. This set of transport coefficient data was combined with others taken from the literature to test a number of previously proposed analytical formulae for these quantities together with some new ones given here. Only the self-diffusion coefficient showed any substantial n dependence for N > 500 at equilibrium fluid densities ( ? < 0.494). D increased with N , especially at intermediate densities in the range ? ~ 0.3-0.35. The expression for the packing fraction dependence of D proposed by Speedy, R. J., 1987, Molec. Phys. , 62 , 509 was shown to fit these data well for N ~ 500 particle systems. We found that the packing fraction ? dependence of the two viscosities and thermal conductivity, generically denoted by X , were represented well by the simple formula X/X0 = 1/[1 -( ? / gr;1)]m within the equilibrium fluid range 0 < ? <0.493. This formula has two disposable parameters, ?1 and m, and X0 is the value of the property X in the limit of zero density. This expression has the same form as the Krieger-Dougherty formula (Kreiger, I. M., 1972,Adv. Colloid. Interface Sci. , 3, 111) which is used widely in the colloid literature to represent the packing fraction dependence of the Newtonian shear viscosity of monodisperse colloidal near-hard spheres. Of course, in the present case, X0 was the dilute gas transport coefficient of the pure liquid rather than the solvent viscosity. It was not possible to fit the transport coefficient normalized by their Enskog values with such a simple expression because these ratios are typically of order unity until quite high packing fractions and then diverge rapidly at higher values over a relatively narrow density range. At the maximum equilibrium fluid packing fraction ? = 0.494 for both the hard sphere fluid and the corresponding colloidal case a very similar value was found for ?s/?0~ 30-40, suggesting that the 'crowding' effects and their consequences for the dynamics in this region of the phase diagram in the two types of liquid have much in common. For the hard sphere by MD, D0/D ~ 11 at the same packing fraction, possibly indicating the contribution from 'hydrodynamic enhancement' of this transport coefficient, which is largely absent for the shear viscosity. Interestingly the comparable ratio for hard sphere colloids is the same.

Sigurgeirsson, H.; Heyes, D. M.

17

Structural properties of dense hard sphere packings.

We numerically study structural properties of mechanically stable packings of hard spheres (HS), in a wide range of packing fractions 0.53 ? ? ? 0.72. Detailed structural information is obtained from the analysis of orientational order parameters, which clearly reveals a disorder-order phase transition at the random close packing (RCP) density, ?c ? 0.64. Above ?c, the crystalline nuclei form 3D-like clusters, which upon further desification transform into alternating planar-like layers. We also find that particles with icosahedral symmetry survive only in a narrow density range in the vicinity of the RCP transition. PMID:25098389

Klumov, Boris A; Jin, Yuliang; Makse, Hernán A

2014-09-11

18

NASA Astrophysics Data System (ADS)

Radial and triplet correlation functions of the reference hard sphere system are determined at several solid densities by canonical Monte Carlo (MC) simulations. These customized data are used to extend the second order thermodynamic perturbation theory (TPT) to the solid phase of flexible hard chain systems. In order to test the accuracy of the TPT equation of state (EOS) for hard chains, MC simulations are carried out for systems of chain length 4 to 15. Several simulations are performed in the isobaric-isothermal ensemble to obtain the high-density EOS of hard chains in the fluid and solid phases. To determine solid-fluid equilibrium (SFE), Helmholtz free energies of solid crystals at a reference density are determined in a series of canonical MC simulations. As the chain length increases, asymptotic behaviors are observed in the coexistence pressure and densities of fluid and solid phases. It is found that the accuracy of TPT for EOS and SFE in systems of hard chains greatly improves by extending it to second order.

Alavi, Farzad; Feyzi, Farzaneh

2013-01-01

19

Hard spheres on the gyroid surface

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 Poincaré 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

Dotera, Tomonari; Kimoto, Masakiyo; Matsuzawa, Junichi

2012-01-01

20

NASA Astrophysics Data System (ADS)

The points where the fluid-solid (face-centered-cubic) transition takes place in the quantum hard-sphere system, for reduced densities 0.85>?N*>0.5 (reduced de Broglie wavelengths ?B*?0.8), have been determined via calculations of Helmholtz free energies. A number of complementary methods have been utilized, namely, path-integral Monte Carlo simulations for fixing the basic thermodynamic and structural quantities, Ornstein-Zernike computations of the fluid isothermal compressibilities using the centroid correlations, and applications of the Einstein crystal technique. Attention is paid to the evaluation of the statistical uncertainties in the isothermal compressibilities and also to the quantum implementation of the Einstein crystal technique by including explicitly the constraint of fixed center of mass. The equation of state along the fluid ?B* branches studied has been determined with two methods, one based on the isothermal compressibilities and the other on the usual virial estimator. Along the solid ?B* branches the equation of state has been fixed with the virial estimator. The results indicate that the phase transition investigated is governed by entropic effects and that the fluid-solid coexistence densities are arranged along a straight line ?FCC*=?(?F*), a behavior which at least holds even for ?B*<2, as revealed by completing the present analysis with data available in the literature.

Sesé, Luis M.

2007-04-01

21

Conformal Solution Theory: Hard-Sphere Mixtures

Conformal solution theory is examined. It is suggested that most difficulties associated with previous applications of this theory arise from the use of concentration-independent reference fluids. For the particular case of a hard-sphere mixture, it is shown that if the reference fluid is chosen so as to make the first-order term in the theory vanish, good results are obtained.

Douglas Henderson; Peter J. Leonard

1971-01-01

22

Density functional study of pressure profile for hard-sphere fluids confined in a nano-cavity

NASA Astrophysics Data System (ADS)

To gain a deeper understanding and to master the mechanical properties of classical fluids confined in nano-geometry, the pressure tensor applicable to confined fluids is derived by taking into account more correlation among the particles. First, based on classical statistical theory, the expression for the pressure tensor is calculated by expanding the stress tensor and considering further the correlation effect among the particles. Our numerical result is compared with that of molecular dynamics simulation and the agreement between them is quite good. Then, the dependence of the bulk density and the dimension of the cavity on the pressure profile is computed and studied. The curvature dependence of contact pressure and net pressure on the cavity wall is also studied. Finally, the solid-fluid interfacial tension is calculated and compared with Monte Carlo results. The results derived in this work indicate the importance and necessity of correlation among particles in the prediction of the mechanical properties of confined fluids.

Sun, Zongli; Kang, Yanshuang; Zhang, Junxia

2014-03-01

23

Prediction of binary hard-sphere crystal structures

NASA Astrophysics Data System (ADS)

We present a method based on a combination of a genetic algorithm and Monte Carlo simulations to predict close-packed crystal structures in hard-core systems. We employ this method to predict the binary crystal structures in a mixture of large and small hard spheres with various stoichiometries and diameter ratios between 0.4 and 0.84. In addition to known binary hard-sphere crystal structures similar to NaCl and AlB2 , we predict additional crystal structures with the symmetry of CrB, ?CuTi , ?IrV , HgBr2 , AuTe2 , Ag2Se , and various structures for which an atomic analog was not found. In order to determine the crystal structures at infinite pressures, we calculate the maximum packing density as a function of size ratio for the crystal structures predicted by our GA using a simulated annealing approach.

Filion, Laura; Dijkstra, Marjolein

2009-04-01

24

Prediction of binary hard-sphere crystal structures.

We present a method based on a combination of a genetic algorithm and Monte Carlo simulations to predict close-packed crystal structures in hard-core systems. We employ this method to predict the binary crystal structures in a mixture of large and small hard spheres with various stoichiometries and diameter ratios between 0.4 and 0.84. In addition to known binary hard-sphere crystal structures similar to NaCl and AlB2, we predict additional crystal structures with the symmetry of CrB, gammaCuTi, alphaIrV, HgBr2, AuTe2, Ag2Se, and various structures for which an atomic analog was not found. In order to determine the crystal structures at infinite pressures, we calculate the maximum packing density as a function of size ratio for the crystal structures predicted by our GA using a simulated annealing approach. PMID:19518387

Filion, Laura; Dijkstra, Marjolein

2009-04-01

25

Chemical potential of hard-sphere fluids by Monte Carlo methods

The ‘potential distribution’ expressions derived by Widom for the pressure and chemical potential of a fluid are developed for the special case of a hard-sphere fluid. The exact equations produced are closely related to those used in Scaled Particle Theory. They have been used to determine the chemical potential of hard-sphere fluids over the reduced density range 0·1 ? ??

D. J. Adams

1974-01-01

26

Evolution of Correlation Functions in the Hard Sphere Dynamics

NASA Astrophysics Data System (ADS)

The series expansion for the evolution of the correlation functions of a finite system of hard spheres is derived from direct integration of the solution of the Liouville equation, with minimal regularity assumptions on the density of the initial measure. The usual BBGKY hierarchy of equations is then recovered. A graphical language based on the notion of collision history originally introduced by Spohn is developed, as a useful tool for the description of the expansion and of the elimination of degrees of freedom.

Simonella, Sergio

2014-06-01

27

Variational approach to hard sphere segregation under gravity

NASA Astrophysics Data System (ADS)

It is demonstrated that the minimization of the free energy functional for hard spheres and hard disks yields the result that excited granular materials under gravity segregate not only in the widely known "Brazil nut" fashion, i.e. with the larger particles rising to the top, but also in reverse "Brazil nut" fashion. Specifically, the local density approximation is used to investigate the crossover between the two types of segregation occurring in the liquid state, and the results are found to agree qualitatively with previously published results of simulation and of a simple model based on condensation.

Both, Joseph A.; Hong, Daniel C.

2002-03-01

28

Variational Approach to Hard Sphere Segregation under Gravity

NASA Astrophysics Data System (ADS)

It is demonstrated that the minimization of the free energy functional for hard spheres and hard disks yields the result that excited granular materials under gravity segregate not only in the widely known ``Brazil nut'' fashion, i.e., with the larger particles rising to the top, but also in reverse ``Brazil nut'' fashion. Specifically, the local density approximation is used to investigate the crossover between the two types of segregation occurring in the liquid state, and the results are found to agree qualitatively with previously published results of simulation and of a simple model based on condensation.

Both, Joseph A.; Hong, Daniel C.

2002-03-01

29

Modified BBGKY hierarchy for the hard-sphere system

NASA Astrophysics Data System (ADS)

In this paper a statistical approach is formulated for classical N-body systems formed by smooth hard spheres. Based on the emerging new axiomatic approach to Classical Statistical Mechanics recently developed, modified collision boundary conditions for the N-body probability density are introduced, which apply also to dense or locally dense hard-sphere systems. As a result, a modified form is determined for the BBGKY hierarchy, which is characterized by a new representation for the s-body collision operator. The same hierarchy, obtained here in differential form starting from the differential Liouville equation, is found to admit both stochastic and deterministic particular solutions. As an application, in the Boltzmann-Grad limit the hierarchy is shown to recover the ordinary Boltzmann equation holding in the case of rarefied gases. Comparison with literature and physical implications of the theory are pointed out.

Tessarotto, Massimo; Cremaschini, Claudio

2014-11-01

30

Structural properties of dense hard spheres near random close packing

We numerically study structural properties of mechanically stable packings of hard spheres (HS), in a wide range of packing fractions $0.53 \\le \\phi \\le 0.72$. Detailed structural information is obtained from the analysis of orientational order parameters, which clearly reveals a disorder-order phase transition at the random close packing (RCP) density, $\\phi_{\\rm c} \\simeq 0.64$. Above $\\phi_{\\rm c}$ the crystalline nuclei form 3D-like clusters, which upon further desification, transform into alternating planar-like layers. We also find that particles with icosahedral symmetry survive only in a narrow density range in the vicinity of the RCP transition.

Boris A. Klumov; Yuliang Jin; Hernan A. Makse

2014-07-29

31

Compressing nearly hard sphere fluids increases glass fragility

OFFPRINT Compressing nearly hard sphere fluids increases glass fragility L. Berthier and T. A.1209/0295-5075/86/10001 Compressing nearly hard sphere fluids increases glass fragility L. Berthier1(a) and T. A. Witten2 1 to that of a very fragile glass as increases beyond 0. Correlations between fragility and various physical

Berthier, Ludovic

32

Viscosity, hard sphere diameter and interionic potential for liquid lead

L-347 Viscosity, hard sphere diameter and interionic potential for liquid lead G. Chaussemy The Macedo-Litovitz equation for a hard sphere liquid provides a satisfactory model for the viscosity of lead and molecular dynamics. The activation energy for viscosity (0.07 eV) is similar to the height of the interionic

Boyer, Edmond

33

Rosenfeld functional for non-additive hard spheres

The fundamental measure density functional theory for hard spheres is generalized to binary mixtures of arbitrary positive and moderate negative non-additivity between unlike components. In bulk the theory predicts fluid-fluid phase separation into phases with different chemical compositions. The location of the accompanying critical point agrees well with previous results from simulations over a broad range of non-additivities and both for symmetric and highly asymmetric size ratios. Results for partial pair correlation functions show good agreement with simulation data.

Matthias Schmidt

2004-07-01

34

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

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. PMID:25615510

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

2015-01-01

35

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

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.

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

2014-12-11

36

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

NASA Astrophysics Data System (ADS)

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.

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

2015-01-01

37

Dynamics of hard sphere colloidal dispersions

NASA Technical Reports Server (NTRS)

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.

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

1994-01-01

38

Hard Spheres: Crystallization and Glass Formation

Motivated by old experiments on colloidal suspensions, we report molecular dynamics simulations of assemblies of hard spheres, addressing crystallization and glass formation. The simulations cover wide ranges of polydispersity s (standard deviation of the particle size distribution divided by its mean) and particle concentration. No crystallization is observed for s > 0.07. For 0.02 stabilise the fluid but to destabilise the crystal. At a given polydispersity (< 0.07) we find three regimes of nucleation: standard nucleation and growth at concentrations in and slightly above the coexistence region; "spinodal nucleation", where the free energy barrier to nucleation appears to be negligible, at intermediate concentrations; and, at the highest concentrations, a new mechanism, still to be fully understood, which only requires small re-arrangement of the particle positions. The cross-over between the second and third regimes occurs at a concentration, around 58% by volume, where the colloid experiments show a marked change in the nature of the crystals formed and the particle dynamics indicate an "ideal" glass transition.

P. N. Pusey; E. Zaccarelli; C. Valeriani; E. Sanz; W. C. K. Poon; M. E. Cates

2009-08-12

39

Multiple reentrant glass transitions in confined hard-sphere glasses

Glass forming liquids exhibit a rich phenomenology upon confinement. This is often related to the effects arising from wall-fluid interactions. Here we focus on the interesting limit where the separation of the confining walls becomes of the order of a few particle diameters. For a moderately polydisperse, densely packed hard-sphere fluid confined between two smooth hard walls, we show via event-driven molecular dynamics simulations the emergence of a multiple reentrant glass transition scenario upon a variation of the wall separation. Using thermodynamic relations, this reentrant phenomenon is shown to persist also under constant chemical potential. This allows straightforward experimental investigation and opens the way to a variety of applications in micro- and nanotechnology, where channel dimensions are comparable to the size of the contained particles. The results are in-line with theoretical predictions obtained by a combination of density functional theory and the mode-coupling theory of the glass transition.

S. Mandal; S. Lang; M. Gross; M. Oettel; D. Raabe; T. Franosch; F. Varnik

2014-06-20

40

Self-diffusion in liquid gallium and hard sphere model

NASA Astrophysics Data System (ADS)

Incoherent and coherent components of quasielastic neutron scattering have been studied in the temperature range of T = 313 K - 793 K aiming to explore the applicability limits of the hard-sphere approach for the microscopic dynamics of liquid gallium, which is usually considered as a non-hard-sphere system. It was found that the non-hard-sphere effects come into play at the distances shorter than the average interatomic distance. The longer range diffusive dynamics of liquid Ga is dominated by the repulsive forces between the atoms.

Blagoveshchenskii, Nikolay; Novikov, Arkady; Puchkov, Alexander; Savostin, Vadim; Sobolev, Oleg

2015-01-01

41

Revisit of interfacial free energy of the hard sphere system near hard wall

We propose a simple Monte Carlo method to calculate the interfacial free energy between the substrate and the material. Using this method we investigate the interfacial free energys of the hard sphere fluid and solid phases near a smooth hard wall. According to the obtained interfacial free energys of the coexisting fluid and solid phases and the Young equation we are able to determine the contact angle with high accuracy, cos$\\theta$ = 1:010(31), which indicates that a smooth hard wall can be wetted completely by the hard sphere crystal at the interface between the wall and the hard sphere fluid.

Mingcheng Yang; Hongru Ma

2008-06-23

42

Isobaric molecular dynamics simulations of hard sphere systems.

We describe an implementation of the Andersen algorithm for simulating the molecular dynamics in the isobaric isoenthalpic (NPH) ensemble for the hard sphere potential. The work is based on the adaptation of the Andersen algorithm to hard spheres by de Smedt et al. For a hard sphere system in the NPH ensemble, the particle velocities are not constant between collisions and we describe an efficient method for handling this part of the dynamics. The method is extended to give an NPT ensemble simulation of hard sphere systems by applying an ad hoc rescaling of the velocities. The accuracy of the algorithms is tested by comparison with traditional NVE simulation results for the structural, thermodynamic, and transport properties. PMID:11415067

Gruhn, T; Monson, P A

2001-06-01

43

On polydispersity and the hard sphere glass transition.

We investigate the dynamics of polydisperse hard spheres at high packing fractions ?. We use extensive numerical simulations based on an experimentally-realistic particle size distribution (PSD) and compare to commonly-used PSDs such as Gaussian or top hat distribution. We find that the mode of kinetic arrest depends on the PSD's shape and not only on its variance. For the experimentally-realistic PSD we find ageing dynamics even though the density correlators decay fully to zero for ? ? 0.59. We observe substantial decoupling of the dynamics of the smallest and largest particles. While the smallest particles remain diffusive in all our simulations, a power-law describes the largest-particle diffusion, suggesting an ideal arrest at ?c ? 0.588. The latter is however averted just before ?c, due to the presence of the mobile smallest particles. In addition, we identify that a partial aging mechanism is at work, whose effects are most pronounced for the largest particles. By comparing our results with recent experimental observations of ergodic behavior up to ? ? 0.6 in a hard-sphere system, we argue that this is an effect of polydispersity, which smears out the glass transition. PMID:25412138

Zaccarelli, Emanuela; Liddle, Siobhan M; Poon, Wilson C K

2014-12-10

44

Scaled particle theory for hard sphere pairs. I. Mathematical structure.

We develop an extension of the original Reiss-Frisch-Lebowitz scaled particle theory that can serve as a predictive method for the hard sphere pair correlation function g(r). The reversible cavity creation work is analyzed both for a single spherical cavity of arbitrary size, as well as for a pair of identical such spherical cavities with variable center-to-center separation. These quantities lead directly to a prediction of g(r). Smooth connection conditions have been identified between the small-cavity situation where the work can be exactly and completely expressed in terms of g(r), and the large-cavity regime where macroscopic properties become relevant. Closure conditions emerge which produce a nonlinear integral equation that must be satisfied by the pair correlation function. This integral equation has a structure which straightforwardly generates a solution that is a power series in density. The results of this series replicate the exact second and third virial coefficients for the hard sphere system via the contact value of the pair correlation function. The predicted fourth virial coefficient is approximately 0.6% lower than the known exact value. Detailed numerical analysis of the nonlinear integral equation has been deferred to the subsequent paper. PMID:17144712

Stillinger, Frank H; Debenedetti, Pablo G; Chatterjee, Swaroop

2006-11-28

45

Stochastic model of a dense spinless hard-sphere gas

Summary The motion of a spinless quantum particle subjected to random hard-sphere scatterings is studied in the framework of stochastic\\u000a mechanics. The result is applied to the case of a generic particle of a dense spinless hard-sphere gas leading to a description\\u000a that displays the competition between the thermal and the quantum noise. Finally, the model is discussed in connection with

L. M. Morato; G. Galilei

1991-01-01

46

Gibbs ensemble Monte Carlo of nonadditive hard-sphere mixtures.

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

Pellicane, Giuseppe; Pandaram, Owen D

2014-07-28

47

Inhomogeneous quasistationary state of dense fluids of inelastic hard spheres.

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

Fouxon, Itzhak

2014-05-01

48

Exact second virial coefficient for dipolar hard spheres

NASA Astrophysics Data System (ADS)

The second virial coefficient B2 for a fluid of dipolar hard spheres has been given several approximate forms valid in the limits of weak and strong interactions. They have been formulated as asymptotic expressions in a dimensionless interaction parameter ?. In this paper, B2 is determined exactly for all values of ? in both the three-dimensional case, where spheres may access the whole space and their dipole moments may be oriented in all directions, and in the quasi-two-dimensional case, where spheres have their centres bound to glide on a plane, while their dipole moments are still freely orientable in space.

Virga, Epifanio G.

2013-11-01

49

Packing Confined Hard Spheres Denser with Adaptive Prism Phases

We show that hard spheres confined between two parallel hard plates pack denser with periodic adaptive prismatic structures which are composed of alternating prisms of spheres. The internal structure of the prisms adapts to the slit height which results in close packings for a range of plate separations, just above the distance where three intersecting square layers fit exactly between the plates. The adaptive prism phases are also observed in real-space experiments on confined sterically stabilized colloids and in Monte Carlo simulations at finite pressure.

Erdal C. O?uz; Matthieu Marechal; Fernando Ramiro-Manzano; Isabelle Rodriguez; René Messina; Francisco J. Meseguer; Hartmut Löwen

2012-11-27

50

Free volume distribution of nearly jammed hard sphere packings

NASA Astrophysics Data System (ADS)

We calculate the free volume distributions of nearly jammed packings of monodisperse and bidisperse hard sphere configurations. These distributions differ qualitatively from those of the fluid, displaying a power law tail at large free volumes, which constitutes a distinct signature of nearly jammed configurations, persisting for moderate degrees of decompression. We reproduce and explain the observed distribution by considering the pair correlation function within the first coordination shell for jammed hard sphere configurations. We analyze features of the equation of state near jamming, and discuss the significance of observed asphericities of the free volumes to the equation of state.

Maiti, Moumita; Sastry, Srikanth

2014-07-01

51

Free volume distribution of nearly jammed hard sphere packings.

We calculate the free volume distributions of nearly jammed packings of monodisperse and bidisperse hard sphere configurations. These distributions differ qualitatively from those of the fluid, displaying a power law tail at large free volumes, which constitutes a distinct signature of nearly jammed configurations, persisting for moderate degrees of decompression. We reproduce and explain the observed distribution by considering the pair correlation function within the first coordination shell for jammed hard sphere configurations. We analyze features of the equation of state near jamming, and discuss the significance of observed asphericities of the free volumes to the equation of state. PMID:25084929

Maiti, Moumita; Sastry, Srikanth

2014-07-28

52

Free volume distribution of nearly jammed hard sphere packings

We calculate the free volume distributions of nearly jammed packings of monodisperse and bidisperse hard sphere configurations. These distributions differ qualitatively from those of the fluid, displaying a power law tail at large free volumes, which constitutes a distinct signature of nearly jammed configurations, persisting for moderate degrees of decompression. We reproduce and explain the observed distribution by considering the pair correlation function within the first coordination shell for jammed hard sphere configurations. We analyze features of the equation of state near jamming, and discuss the significance of observed asphericities of the free volumes to the equation of state.

Moumita Maiti; Srikanth Sastry

2014-07-25

53

Extended hard-sphere model and collisions of cohesive particles.

In two earlier papers the present authors modified a standard hard-sphere particle-wall and particle-particle collision model to account for the presence of adhesive or cohesive interaction between the colliding particles: the problem is of importance for modeling particle-fluid flow using the Lagrangian approach. This technique, which involves a direct numerical simulation of such flows, is gaining increasing popularity for simulating, e.g., dust transport, flows of nanofluids and grains in planetary rings. The main objective of the previous papers was to formally extend the impulse-based hard-sphere model, while suggestions for quantifications of the adhesive or cohesive interaction were made. This present paper gives an improved quantification of the adhesive and cohesive interactions for use in the extended hard-sphere model for cases where the surfaces of the colliding bodies are "dry," e.g., there is no liquid-bridge formation between the colliding bodies. This quantification is based on the Johnson-Kendall-Roberts (JKR) analysis of collision dynamics but includes, in addition, dissipative forces using a soft-sphere modeling technique. In this way the cohesive impulse, required for the hard-sphere model, is calculated together with other parameters, namely the collision duration and the restitution coefficient. Finally a dimensional analysis technique is applied to fit an analytical expression to the results for the cohesive impulse that can be used in the extended hard-sphere model. At the end of the paper we show some simulation results in order to illustrate the model. PMID:22060357

Kosinski, Pawel; Hoffmann, Alex C

2011-09-01

54

Direct measurement of stacking disorder in hard-sphere colloidal crystals

At high densities, suspensions of nearly hard sphere colloidal particles show a disorder-order, or crystallization, transition. The resulting colloidal crystals are made up of a more or less randomly-stacked sequence of hexagonal layers. There are three lateral positions, A, B, C, which layers can occupy, but each individual layer has a choice of only the two sites not occupied by

M. S. Elliot; B. T. F. Bristol; W. C. K. Poon

1997-01-01

55

Physics of Hard Spheres Experiment: Significant and Quantitative Findings Made

NASA Technical Reports Server (NTRS)

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 understandin

Doherty, Michael P.

2000-01-01

56

Probing the evolution and morphology of hard carbon spheres

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.

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

57

Improved Quantum Hard-Sphere Ground-State Equations of State

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 \\textit{regular} (or periodic, e.g., face-centered-cubic) close-packing density usually associated with a crystalline branch. Improved fluid branches are contructed based upon exact, field-theoretic perturbation-theory low-density expansions for many-boson and many-fermion systems, appropriately extrapolated to intermediate densities, but whose ultimate density is irregular or \\textit{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.

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

2007-10-26

58

Self-assembly in colloidal hard-sphere systems

NASA Astrophysics Data System (ADS)

In this thesis, we examine the phase behaviour and nucleation in a variety of hard-sphere systems. In Chapter 1 we present a short introduction and describe some of the simulation techniques used in this thesis. One of the main difficulties in predicting the phase behaviour in colloidal, atomic and nanoparticle systems is in determining the stable crystalline phases. To address this problem, in Chapters 2 and 4 we present two different methods for predicting possible crystal phases. In Chapter 2, we apply a genetic algorithm to binary hard-sphere mixtures and use it to predict the best-packed structures for this system. In Chapter 4 we present a novel method based on Monte Carlo simulations to predict possible crystalline structures for a variety of models. When the possible phases are known, full free-energy calculations can be used to predict the phase diagrams. This is the focus of Chapters 3 and 5. In Chapter 3, we examine the phase behaviour for binary hard-sphere mixtures with size ratios of the large and small spheres between 0.74 and 0.85. Between size ratios 0.76 and 0.84 we find regions where the binary Laves phases are stable, in addition to monodisperse face-centered-cubic (FCC) crystals of the large and small spheres and a binary liquid. For size ratios 0.74 and 0.85 we find only the monodisperse FCC crystals and the binary liquid. In Chapter 5 we examine the phase behaviour of binary hard-sphere mixtures with size ratios between 0.3 and 0.42. In this range, we find an interstitial solid solution (ISS) to be stable, as well as FCC crystals of the small and large spheres, and a binary fluid. The ISS phase consists of an FCC crystal of the large particles with some of the octahedral holes filled by smaller particles. We show that this filling fraction can be tuned from 0 to 100%. Additionally, we examine the diffusive properties of the small particles in the ISS for size ratio 0.3. In contrast to most systems, we find a region where the diffusion increases as a function of the packing fraction. Finally, in Chapters 6, 7, and 8 we examine nucleation in colloidal systems. In Chapter 6, we examine the crystal nucleation for hard spheres using a variety of simulation techniques, namely, umbrella sampling (US), forward flux sampling (FFS), and molecular dynamics (MD). We compare the resulting nucleation rates with previous experimental and simulated rates. and find agreement between all the theoretically predicted nucleation rates. However, the experimental results display a markedly different behaviour for low supersaturation. In Chapter 7, we examine in more detail the FFS technique, in particular, the effect measurement error has on the resulting nucleation rates. In Chapter 8, we examine the crystal nucleation of the Weeks-Chandler-Andersen (WCA) model with ?? = 40 using Brownian dynamics, US and FFS. This WCA potential is softer than the hard-sphere potential, but is frequently used to approximate hard spheres. Our predicted nucleation rates for this potential are in agreement with those found for hard spheres.

Filion, L. C.

2011-01-01

59

Thermodynamic and rheological properties of hard sphere dispersions

NASA Astrophysics Data System (ADS)

We investigate the thermodynamic and rheological properties of hard sphere dispersions with colloidal poly-(methyl methacrylate) particles grafted with a layer of poly-(12-hydroxy stearic acid) (PMMA-PHSA). These spheres are index-matched in a mixture of tetralin and decalin and the absorption of tetralin into the PMMA core is determined with light scattering. The effective hard sphere volume fraction is set by the disorder-order transition, thereby accounting for the polymer layer, any swelling due to the solvent, and polydispersity. The equation of state for the fluid phase, extracted from the equilibrium sediment with x-ray densitometry, conforms to the Carnahan-Starling equation. However, the osmotic pressure of the crystalline phase lies slightly above that calculated for a single FCC crystal. Likewise the high shear viscosity of the fluid compares well with other hard sphere dispersions, but the low shear viscosity for PMMA-PHSA hard spheres exceeds those for polystyrene and silica hard spheres. Our low shear viscosities are consistent with other PMMA-PHSA data after rescaling for both the polymer layer thickness and polydispersity. We use simple models and molecular dynamics simulations to determine that the higher osmotic pressure in the crystalline phase is a direct effect of polydispersity. Polydispersity appears to lower the crystalline close packed volume fraction. The random close packing is almost independent of polydispersity. We measure the high frequency shear modulus and dynamic viscosity for our PMMA-PHSA crystals by detecting the resonant response to oscillatory forcing with a novel dynamic light scattering scheme. The resonant response for colloidal crystals formed in normal and microgravity environments were similar, indicating that the bulk rheological properties are unaffected within experimental error by differing crystal structure and crystallite size. Our high frequency shear modulus seem reasonable, lying close to predictions for the static modulus of hard sphere crystals, whereas our high frequency dynamic viscosity seem high, exceeding measurements on the high frequency dynamic viscosity for metastable fluids. The measurements are in the linear regime for the shear modulus but may not be for the dynamic viscosity, which may explain our anomalously high dynamic viscosity.

Phan, See-Eng

1998-09-01

60

Experiments with Hard, Soft, and Hydrodynamically Interacting Spheres

NASA Astrophysics Data System (ADS)

This thesis presents research on colloidal suspensions of nearly identical spheres and shows that some very interesting phenomena take place while the inter-particle interactions are simple in nature. The work is divided into three areas which explore aspects of hydrodynamic and hard core and electrostatic repulsive interactions. In chapter two hard core interactions are singled out, as we verify the prediction of a remarkable first order phase transition from a disordered fluid of spheres to a long range ordered solid. We accurately measured the full equation of state of a sediment of sub micrometer hard spheres using an X-ray densitometry technique. The measurements prove the existence of hard sphere behavior in a real system with unprecedented accuracy and prove our method a new and accurate probe of colloidal interactions. Chapter three is concerned with the settling state preceding the equilibrium sediments described above. This problem of many-body hydrodynamic interactions at near zero Reynolds number has proven elusive to the extent that even the most rudimentary macroscopic quantities, such as the mean settling velocity < v> , have only been calculated (with limited success) for dilute suspensions of spheres. We created a steady state fluidized suspension of colloidal spheres in which we deliberately controlled particle dynamics and positions by altering their interactions. The measurements are the first to quantitatively confirm calculations for flow through periodic lattices and have introduced a novel way to measure the effects of suspension microstructure and concentration on the average sedimentation rate. The final chapter concentrates on the microscopic, and often locally collective, motions of settling non-Brownian hard spheres. Of interest here were recent measurements of anomalously large sedimentation velocity fluctuations and again the need for observations of the suspension microstructure, whose lack has lead to theoretical speculations on the possibility of infinite sedimentation velocity variances. From digital particle imaging velocimetry on dilute fluidized beds we have found no evidence of a diverging velocity variance, but did observe strong spatial velocity correlations out to 50 particle diameters. The latter discovery should have a significant impact on redirecting theoretical efforts concerning dilute sedimentation.

Rutgers, Maarten Arnold

1995-01-01

61

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

NASA Astrophysics Data System (ADS)

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.

Zhao, Kun

62

Slow dynamics and aging of a colloidal hard sphere glass.

The intermediate scattering function (ISF) is measured for a colloidal hard-sphere glass as functions of the scattering vector and waiting time. For scattering vectors near the structure factor peak, we show that the ISF and the stretching index, defined at the crossover time between the fast and slow processes, depend algebraically on the waiting time. By contrast, the Debye-Waller factor is independent of the waiting time. PMID:18851462

Martinez, V A; Bryant, G; van Megen, W

2008-09-26

63

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

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

Baranau, Vasili; Tallarek, Ulrich

2014-10-21

64

Replica exchange Monte Carlo applied to hard spheres.

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

Odriozola, Gerardo

2009-10-14

65

Tension and stiffness of the hard sphere crystal-fluid interface

A combination of fundamental measure density functional theory and Monte Carlo computer simulation is used to determine the orientation-resolved interfacial tension and stiffness for the equilibrium hard-sphere crystal-fluid interface. Microscopic density functional theory is in quantitative agreement with simulations and predicts a tension of 0.66 kT/\\sigma^2 with a small anisotropy of about 0.025 kT and stiffnesses with e.g. 0.53 kT/\\sigma^2 for the (001) orientation and 1.03 kT/\\sigma^2 for the (111) orientation. Here kT is denoting the thermal energy and \\sigma the hard sphere diameter. We compare our results with existing experimental findings.

Andreas Härtel; Martin Oettel; Roberto E. Rozas; Stefan U. Egelhaaf; Jürgen Horbach; Hartmut Löwen

2012-03-13

66

Theoretical studies of the correlations in moderately asymmetric binary hard-sphere solid mixtures.

A theoretical approach to calculate the correlation functions in binary hard-sphere (HS) solid mixtures is developed. The method is motivated by the theory of correlations in one-component HS solids [Rascon, Phys. Rev. E 54, 1261 (1996)] and the Kirkwood-Buff theory for solutions. Combined with the fundamental measure density functional theory the approach provides correlation functions in good agreement with the numerical simulations results for the moderately asymmetric mixtures. PMID:18643025

Warshavsky, Vadim B; Song, Xueyu

2008-05-01

67

We compute the singular value decomposition of the radial distribution function for hard sphere, and square well solutions. We find that decomposes into a small set of basis vectors allowing for an extremely accurate representation at all interpolated densities and potential strengths. In addition, we find that the coefficient vectors describing the magnitude of each basis vector are well described by a low-order polynomial. We provide a program to calculate in this compact representation for the investigated parameter range. PMID:24143174

Hoppe, Travis

2013-01-01

68

A Monte Carlo study of the freezing transition of hard spheres

NASA Astrophysics Data System (ADS)

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.

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

2011-08-01

69

NASA Astrophysics Data System (ADS)

The crystal-melt interfacial free energy, gamma, is the reversible work per unit area needed to create an interface between a crystal and its melt. The kinetic coefficient, mu, of crystal-melt interface is the ratio of the interface growth velocity to the undercooling (TM - T), where TM is the melting point. These two thermodynamic and kinetic parameters are very important in crystal growth. In this work we determine gamma and mu for the single and binary hard-sphere systems by analyzing capillary fluctuations in interface position using molecular dynamics (MD) simulation [Hoyt et al, Mat. Sci. Eng. R 41, 121-163 (2003)]. Our results of mu for the single hard-sphere system for the three orientations (100), (110), and (111) are in agreement with other simulation and experimental results for metals. The results we obtained give the relation mu100 > mu110 > mu111, which is also consistent with the ordering of experiments and simulations for metals, but is different from the ordering predicted by the density functional theory (DFT) for the hard-sphere system in which the orientation (110) is the lowest. Our results of gamma for the single hard-sphere is also consistent with the previous simulation results for the hard-sphere system, performed by two methods, cleaving method and fluctuation method. It also gives the relation gamma100 > gamma 110 > gamma111, which is also in agreement with the literature. Our simulation result for the binary hard-sphere system also gives the relation gamma 100 > gamma110 > gamma111. The interfacial free energy for the binary hard-sphere system is slightly higher than that for the single hard-sphere system, but after scaling its pressure to the pressure of the single hard-sphere system to keep the pressures the same, it becomes slightly smaller, which is in consistent with the gamma of the Cu-Ni alloy being slightly smaller than that of Ni. Our calculation for the mu of the binary hard-sphere system also gives the relation mu100 > mu 110 > mu111, and its values are smaller than that of the single hard-sphere system.

Amini, Majeed Abdul-Nabi

2006-12-01

70

Fifth to eleventh virial coefficients of hard spheres

NASA Astrophysics Data System (ADS)

Virial coefficients Bn of three-dimensional hard spheres are reported for n=5 to 11, with precision exceeding that presently available in the literature. Calculations are performed using the recursive method due to Wheatley, and a binning approach is proposed to allow more flexibility in where computational effort is directed in the calculations. We highlight the difficulty as a general measure that quantifies performance of an algorithm that computes a stochastic average and show how it can be used as the basis for optimizing such calculations.

Schultz, Andrew J.; Kofke, David A.

2014-08-01

71

The Boltzmann-Grad Limit of a Hard Sphere System: Analysis of the Correlation Error

We present a quantitative analysis of the Boltzmann-Grad (low-density) limit of a hard sphere system. We introduce and study a set of functions (correlation errors) measuring the deviations in time from the statistical independence of particles (propagation of chaos). In the context of the BBGKY hierarchy, a correlation error of order $k$ measures the event where $k$ tagged particles are connected by a chain of interactions preventing the factorization. We prove that, provided $k$ is not too large, such an error flows to zero with the hard spheres diameter $\\varepsilon$, for short times, as $\\varepsilon^{\\gamma k}$, for some $\\gamma>0$. This requires a new analysis of many-recollision events, and improves previous estimates of high order correlation functions.

Mario Pulvirenti; Sergio Simonella

2014-05-19

72

The rheology of bimodal hard-sphere dispersions

NASA Astrophysics Data System (ADS)

The viscosity of a monolayer of a suspension of bimodally distributed hard spheres is determined for area fractions, ?a, from 0.15 to 0.74 with different particle size ratios, ? (diameter of large sphere/diameter of small spheres=1, 2, and 4), and different fractions of small spheres of total solids, ? (0.07, 0.27, 0.49, 0.64, and 0.83). Particle distributions are generated by a Monte Carlo technique and the hydrodynamic interactions are calculated by Stokesian dynamics. These results, which correspond to the high-frequency dynamic viscosities, are compared with those from the dynamic simulation of hydrodynamically interacting spherical particles [Chang and Powell, J. Fluid Mech. 253, 1 (1993)]. Dynamic simulation is found to yield higher relative viscosities, ?r, as compared with the results of Monte Carlo simulation at high concentrations. This results from the absence of long clusters that completely cross a periodic cell in the Monte Carlo simulations that are present in the dynamic simulations. When ?a is normalized by the maximum packing fraction, ?m2-D, all the viscosity data fall onto a master curve. This is the same trend as that found in dynamic simulations, except that the Monte Carlo simulation gives lower relative viscosities for ?a/?m2-D ? 0.3. When ? and ?a are fixed, ?r decreases as ? increases from zero, reaches a minimum, and then increases as ??1, similar to the trend found in the dynamic simulations. Good agreement is found among the results of two-dimensional simulations, experiments, and three-dimensional simulations for monodispersed suspensions.

Chang, Chingyi; Powell, Robert L.

1994-05-01

73

Short-wavelength collective modes and generalized hydrodynamic equations for hard-sphere particles

NASA Astrophysics Data System (ADS)

The extended hydrodynamic modes recently discussed by de Schepper, Cohen, and collaborators using an approximate hard-sphere kinetic equation are computed here with use of approximate hard-sphere generalized hydrodynamic equations. The theory presented here is completely analytic and reproduces the results of de Schepper et al. for dense hard-sphere fluids reasonably well. The connection to previous theories based on generalized hydrodynamics is discussed.

Kirkpatrick, T. R.

1985-11-01

74

ESTIMATING THE DENSITY OF DRY SNOW LAYERS FROM HARDNESS, AND HARDNESS FROM DENSITY

ESTIMATING THE DENSITY OF DRY SNOW LAYERS FROM HARDNESS, AND HARDNESS FROM DENSITY Daehyun Kim 1 ABSTRACT: At the ISSW 2000, Geldsetzer and Jamieson presented empirical relations between the density density and water equivalent (e.g. because the layer was too thin for the density sampler

Jamieson, Bruce

75

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

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. PMID:24827171

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

2014-04-01

76

A simple effective rule to estimate the jamming packing fraction of polydisperse hard spheres

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 $\\phi_\\text{J}$ of the polydisperse system as a simple function of $M_1M_3/M_2^2$, where $M_k$ is the $k$th moment of the size distribution. An analysis of experimental and simulation data of $\\phi_\\text{J}$ 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.

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

2014-02-14

77

Diffusion of concentrated neutral hard-sphere colloidal suspensions

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.

Verberg, R. [IRI Delft University of Technology, 2629 JB Delft (Netherlands)] [IRI Delft University of Technology, 2629 JB Delft (Netherlands); Schepper, I. M. de [IRI Delft University of Technology, 2629 JB Delft (Netherlands)] [IRI Delft University of Technology, 2629 JB Delft (Netherlands); Cohen, E. G. D. [The Rockefeller University, New York, New York 10021 (United States)] [The Rockefeller University, New York, New York 10021 (United States)

2000-03-01

78

Detecting Phase Boundaries in Hard-Sphere Suspensions

NASA Technical Reports Server (NTRS)

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

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

2009-01-01

79

Nested sampling for materials: The case of hard spheres

NASA Astrophysics Data System (ADS)

The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by studying the three-dimensional hard-sphere model. Having obtained the partition function, we show how easy it is to calculate the compressibility and the free energy as functions of the packing fraction and local order, verifying that the transition to crystallinity has a very small barrier, and that the entropic contribution of jammed states to the free energy is negligible for packing fractions above the phase transition. We quantify the previously proposed schematic phase diagram and estimate the extent of the region of jammed states. We find that within our samples, the maximally random jammed configuration is surprisingly disordered.

Pártay, Lívia B.; Bartók, Albert P.; Csányi, Gábor

2014-02-01

80

Transport coefficients of the inelastic variable hard sphere

NASA Astrophysics Data System (ADS)

The transport coefficients of the inelastic variable hard sphere are calculated using infinite Maxwellian iterations of Grad’s 14 moment equations and dimensional analysis on the basis of the Chapman-Enskog expansion. The viscosity coefficient (?) obtained using infinite Maxwellian iterations coincides with that obtained using dimensional analysis on the basis of the Chapman-Enskog expansion. Two transport coefficients (? and ?) calculated using infinite Maxwellian iterations, which define the heat flux, coincide with those calculated using dimensional analysis on the basis of the Chapman-Enskog expansion, only when ? and ? obtained using infinite Maxwellian iterations converge. Divergences of ? and ? occur whenever the dissipating rate of the heat flux, via the inelastic collisional term, is equal to or smaller than the characteristic increasing or decreasing rate of the heat flux via the decrease in the temperature.

Yano, Ryosuke

2013-09-01

81

Glass transition of hard spheres in high dimensions

NASA Astrophysics Data System (ADS)

We have investigated analytically and numerically the liquid-glass transition of hard spheres for dimensions d?? in the framework of mode-coupling theory. The numerical results for the critical collective and self-nonergodicity parameters fc(k;d) and fc(s)(k;d) exhibit non-Gaussian k dependence even up to d=800 . fc(s)(k;d) and fc(k;d) differ for k˜d1/2 , but become identical on a scale k˜d , which is proven analytically. The critical packing fraction ?c(d)˜d22-d is above the corresponding Kauzmann packing fraction ?K(d) derived by a small cage expansion. Its quadratic pre-exponential factor is different from the linear one found earlier. The numerical values for the exponent parameter and therefore the critical exponents a and b depend on d , even for the largest values of d .

Schmid, Bernhard; Schilling, Rolf

2010-04-01

82

Jamming II: Edwards' statistical mechanics of random packings of hard spheres

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 60's. This problem finds applications spanning from the mathematician's 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% (RLP) while filling all the loose voids results in a maximum density of ~63-64% (RCP). While those values seem robustly true, to this date there is no physical explanation or theoretical prediction for them. Here we show that random packings of monodisperse hard spheres in 3d can pack between the densities 4/(4 + 2 \\sqrt 3) or 53.6% and 6/(6 + 2 \\sqrt 3) or 63.4%, defining RLP and RCP, respectively. 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. Ultimately, our results lead to a phase diagram that provides a unifying view of the disordered hard sphere packing problem.

Ping Wang; Chaoming Song; Yuliang Jin; Hernan A. Makse

2010-11-16

83

Analytical expressions for the fourth virial coefficient of a hard-sphere mixture

NASA Astrophysics Data System (ADS)

A method of numerical calculation of the fourth virial coefficients of the mixture of additive hard spheres is proposed. The results are compared with an exact analytical formula for the fourth partial virial coefficient B4[1] (i.e., three spheres of diameters ?1 and one sphere of diameter ?2 ) and a semiempirical expression for B4[2] (i.e., two spheres of each kind). It is shown that the first formula is nonanalytic and the implication to the equations of state for hard-sphere mixtures is discussed.

Labík, Stanislav; Kolafa, Ji?í

2009-11-01

84

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

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

Baranau, Vasili; Tallarek, Ulrich

2014-06-01

85

First-principle proof of the modified collision boundary conditions for the hard-sphere system

NASA Astrophysics Data System (ADS)

A fundamental issue lying at the foundation of classical statistical mechanics is the determination of the collision boundary conditions that characterize the dynamical evolution of multi-particle probability density functions (PDF) and are applicable to systems of hard-spheres undergoing multiple elastic collisions. In this paper it is proved that, when the deterministic N-body PDF is included in the class of admissible solutions of the Liouville equation, the customary form of collision boundary conditions adopted in previous literature becomes physically inconsistent and must actually be replaced by suitably modified collision boundary conditions.

Tessarotto, Massimo; Cremaschini, Claudio

2014-05-01

86

We introduce an approximation for the pair distribution function of the inhomogeneous hard sphere fluid. Our approximation makes use of our recently published averaged pair distribution function at contact which has been shown to accurately reproduce the averaged pair distribution function at contact for inhomogeneous density distributions. This approach achieves greater computational efficiency than previous approaches by enabling the use of exclusively fixed-kernel convolutions and thus allowing an implementation using fast Fourier transforms. We compare results for our pair distribution approximation with two previously published works and Monte-Carlo simulation, showing favorable results.

Paho Lurie-Gregg; Jeff B. Schulte; David Roundy

2014-09-24

87

Approach to approximating the pair distribution function of inhomogeneous hard-sphere fluids

NASA Astrophysics Data System (ADS)

We introduce an approximation for the pair distribution function of the inhomogeneous hard sphere fluid. Our approximation makes use of our recently published averaged pair distribution function at contact, which has been shown to accurately reproduce the averaged pair distribution function at contact for inhomogeneous density distributions. This approach achieves greater computational efficiency than previous approaches by enabling the use of exclusively fixed-kernel convolutions and thus allowing an implementation using fast Fourier transforms. We compare results for our pair distribution approximation with two previously published works and Monte Carlo simulation, showing favorable results.

Lurie-Gregg, Paho; Schulte, Jeff B.; Roundy, David

2014-10-01

88

Avalanches mediate crystallization in a hard-sphere glass

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.

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

2014-04-02

89

Avalanches mediate crystallization in a hard-sphere glass.

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

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

2014-01-01

90

Short-time diffusion in concentrated bidisperse hard-sphere suspensions

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 120A, 388 (1983) & 126A, 349 (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 $\\delta\\gamma$-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 $\\delta\\gamma$ 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 $40\\%$.

Mu Wang; Marco Heinen; John F. Brady

2014-10-31

91

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

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%. PMID:25681941

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

2015-02-14

92

Structure and anomalous solubility for hard spheres in an associating lattice gas model

Structure and anomalous solubility for hard spheres in an associating lattice gas model Marcia M://jcp.aip.org/about/rights_and_permissions #12;THE JOURNAL OF CHEMICAL PHYSICS 137, 064905 (2012) Structure and anomalous solubility for hard July 2012; published online 13 August 2012) In this paper we investigate the solubility of a hard

Barbosa, Marcia C. B.

93

A free-energy functional that contains both the symmetry conserved and symmetry broken parts of the direct pair correlation function has been used to investigate the freezing of a system of hard spheres into crystalline and amorphous structures. The freezing parameters for fluid-crystal transition have been found to be in very good agreement with the results found from simulations. We considered amorphous structures found from the molecular dynamics simulations at packing fractions $\\eta$ lower than the glass close packing fraction $\\eta_{J}$ and investigated their stability compared to that of a homogeneous fluid. The existence of free-energy minimum corresponding to a density distribution of overlapping Gaussians centered around an amorphous lattice depicts the deeply supercooled state with a heterogeneous density profile.

Swarn Lata Singh; Atul S. Bharadwaj; Yashwant Singh

2011-01-31

94

Scattering functions of core-shell-structured hard spheres with Schulz-distributed radii.

The scattering intensity of polydisperse systems of core-shell and layered hard spheres is considered. The Percus-Yevick solution for the partial structure factors is cast in a form suitable for numerical and analytical treatment. Closed-form, analytical expressions are given for an effective hard-sphere model of the scattering intensity of particles with an internal layered structure and a size polydispersity governed by a Schulz distribution. A similar model for polydisperse hard spheres of core-shell structure but with a monodisperse shell thickness is also presented. The models are tested against small-angle X-ray scattering experiments on a hard-sphere-like microemulsion system. PMID:19462945

Nayeri, M; Zackrisson, M; Bergenholtz, J

2009-06-18

95

Kinetic coefficient for hard-sphere crystal growth from the melt

Using molecular-dynamics simulation, we determine the magnitude and anisotropy of the kinetic coefficient (mu) for the crystal growth from the melt for the hard-sphere system through an analysis of equilibrium capillary ...

Laird, Brian Bostian; Amini, M.

2006-11-24

96

Low-noise Monte Carlo simulation of the variable hard sphere gas

We present an efficient particle simulation method for the Boltzmann transport equation based on the low-variance deviational simulation Monte Carlo approach to the variable-hard-sphere gas. The proposed method exhibits ...

Radtke, Gregg A.

97

Direct calculation of the hard-sphere crystal/melt interfacial free energy

We present a direct calculation by molecular-dynamics computer simulation of the crystal/melt interfacial free energy gamma for a system of hard spheres of diameter sigma. The calculation is performed by thermodynamic ...

Laird, Brian Bostian; Davidchack, R. L.

2000-11-27

98

Transport coefficients of a granular gas of inelastic rough hard spheres

NASA Astrophysics Data System (ADS)

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.

Kremer, Gilberto M.; Santos, Andrés; Garzó, Vicente

2014-08-01

99

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

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.

Qin, Yuan; Prausnitz, John M.

2005-09-20

100

Inhomogeneous quasi-stationary state of dense fluid of inelastic hard spheres

We study closed dense collections of hard spheres that collide inelastically with constant coefficient of normal restitution. We find inhomogeneous states (IS) where the density profile is spatially non-uniform but constant in time. The states are exact solutions of non-linear partial differential equations that describe the coupled distributions of density and temperature when inelastic losses of energy per collision are small. The derivation is performed without modelling 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. The IS is exact non-linear state of this many-body system. It captures a fundamental property of inelastic collections of particles: the possibility of preserving non-uniform temperature via the interplay of inelastic cooling and heat conduction, generalizing previous results in the dilute case. 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 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 behavior is caused by unusual spatial distribution of particles: on approach to one of the container's walls the density grows inversely with the distance. We discuss the relation of our results to the recently proposed finite-time singularity in other container's geometries.

Itzhak Fouxon

2014-02-13

101

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

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.

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

2008-02-26

102

Hard-sphere fluid adsorbed in an annular wedge: The depletion force of hard-body colloidal physics

NASA Astrophysics Data System (ADS)

Many important issues of colloidal physics can be expressed in the context of inhomogeneous fluid phenomena. When two large colloids approach one another in solvent, they interact at least partly by the response of the solvent to finding itself adsorbed in the annular wedge formed between the two colloids. At shortest range, this fluid mediated interaction is known as the depletion force/interaction because solvent is squeezed out of the wedge when the colloids approach closer than the diameter of a solvent molecule. An equivalent situation arises when a single colloid approaches a substrate/wall. Accurate treatment of this interaction is essential for any theory developed to model the phase diagrams of homogeneous and inhomogeneous colloidal systems. The aim of our paper is a test of whether or not we possess sufficient knowledge of statistical mechanics that can be trusted when applied to systems of large size asymmetry and the depletion force in particular. When the colloid particles are much larger than a solvent diameter, the depletion force is dominated by the effective two-body interaction experienced by a pair of solvated colloids. This low concentration limit of the depletion force has therefore received considerable attention. One route, which can be rigorously based on statistical mechanical sum rules, leads to an analytic result for the depletion force when evaluated by a key theoretical tool of colloidal science known as the Derjaguin approximation. A rival approach has been based on the assumption that modern density functional theories (DFT) can be trusted for systems of large size asymmetry. Unfortunately, these two theoretical predictions differ qualitatively for hard sphere models, as soon as the solvent density is higher than about 2/3 that at freezing. Recent theoretical attempts to understand this dramatic disagreement have led to the proposal that the Derjaguin and DFT routes represent opposite limiting behavior, for very large size asymmetry and molecular sized mixtures, respectively. This proposal implies that nanocolloidal systems lie in between the two limits, so that the depletion force no longer scales linearly with the colloid radius. That is, by decreasing the size ratio from mesoscopic to molecular sized solutes, one moves smoothly between the Derjaguin and the DFT predictions for the depletion force scaled by the colloid radius. We describe the results of a simulation study designed specifically as a test of compatibility with this complex scenario. Grand canonical simulation procedures applied to hard-sphere fluid adsorbed in a series of annular wedges, representing the depletion regime of hard-body colloidal physics, confirm that neither the Derjaguin approximation, nor advanced formulations of DFT, apply at moderate to high solvent density when the geometry is appropriate to nanosized colloids. Our simulations also allow us to report structural characteristics of hard-body solvent adsorbed in hard annular wedges. Both these aspects are key ingredients in the proposal that unifies the disparate predictions, via the introduction of new physics. Our data are consistent with this proposed physics, although as yet limited to a single colloidal size asymmetry.

Herring, A. R.; Henderson, J. R.

2007-01-01

103

Hard-sphere fluid adsorbed in an annular wedge: the depletion force of hard-body colloidal physics.

Many important issues of colloidal physics can be expressed in the context of inhomogeneous fluid phenomena. When two large colloids approach one another in solvent, they interact at least partly by the response of the solvent to finding itself adsorbed in the annular wedge formed between the two colloids. At shortest range, this fluid mediated interaction is known as the depletion force/interaction because solvent is squeezed out of the wedge when the colloids approach closer than the diameter of a solvent molecule. An equivalent situation arises when a single colloid approaches a substrate/wall. Accurate treatment of this interaction is essential for any theory developed to model the phase diagrams of homogeneous and inhomogeneous colloidal systems. The aim of our paper is a test of whether or not we possess sufficient knowledge of statistical mechanics that can be trusted when applied to systems of large size asymmetry and the depletion force in particular. When the colloid particles are much larger than a solvent diameter, the depletion force is dominated by the effective two-body interaction experienced by a pair of solvated colloids. This low concentration limit of the depletion force has therefore received considerable attention. One route, which can be rigorously based on statistical mechanical sum rules, leads to an analytic result for the depletion force when evaluated by a key theoretical tool of colloidal science known as the Derjaguin approximation. A rival approach has been based on the assumption that modern density functional theories (DFT) can be trusted for systems of large size asymmetry. Unfortunately, these two theoretical predictions differ qualitatively for hard sphere models, as soon as the solvent density is higher than about 23 that at freezing. Recent theoretical attempts to understand this dramatic disagreement have led to the proposal that the Derjaguin and DFT routes represent opposite limiting behavior, for very large size asymmetry and molecular sized mixtures, respectively. This proposal implies that nanocolloidal systems lie in between the two limits, so that the depletion force no longer scales linearly with the colloid radius. That is, by decreasing the size ratio from mesoscopic to molecular sized solutes, one moves smoothly between the Derjaguin and the DFT predictions for the depletion force scaled by the colloid radius. We describe the results of a simulation study designed specifically as a test of compatibility with this complex scenario. Grand canonical simulation procedures applied to hard-sphere fluid adsorbed in a series of annular wedges, representing the depletion regime of hard-body colloidal physics, confirm that neither the Derjaguin approximation, nor advanced formulations of DFT, apply at moderate to high solvent density when the geometry is appropriate to nanosized colloids. Our simulations also allow us to report structural characteristics of hard-body solvent adsorbed in hard annular wedges. Both these aspects are key ingredients in the proposal that unifies the disparate predictions, via the introduction of new physics. Our data are consistent with this proposed physics, although as yet limited to a single colloidal size asymmetry. PMID:17358145

Herring, A R; Henderson, J R

2007-01-01

104

Mean properties and free energy of a few hard spheres confined in a spherical cavity

NASA Astrophysics Data System (ADS)

We use analytical calculations and event-driven molecular dynamics simulations to study a small number of hard sphere particles in a spherical cavity. The cavity is also taken as the thermal bath so that the system thermalizes by collisions with the wall. In that way, these systems of two, three, and four particles, are considered in the canonical ensemble. We characterize various mean and thermal properties for a wide range of number densities. We study the density profiles, the components of the local pressure tensor, the interface tension, and the adsorption at the wall. This spans from the ideal gas limit at low densities to the high-packing limit in which there are significant regions of the cavity for which the particles have no access, due the conjunction of excluded volume and confinement. The contact density and the pressure on the wall are obtained by simulations and compared to exact analytical results. We also obtain the excess free energy for N = 4, by using a simulated-assisted approach in which we combine simulation results with the knowledge of the exact partition function for two and three particles in a spherical cavity.

Urrutia, I.; Pastorino, C.

2014-09-01

105

Mean properties and free energy of a few hard spheres confined in a spherical cavity.

We use analytical calculations and event-driven molecular dynamics simulations to study a small number of hard sphere particles in a spherical cavity. The cavity is also taken as the thermal bath so that the system thermalizes by collisions with the wall. In that way, these systems of two, three, and four particles, are considered in the canonical ensemble. We characterize various mean and thermal properties for a wide range of number densities. We study the density profiles, the components of the local pressure tensor, the interface tension, and the adsorption at the wall. This spans from the ideal gas limit at low densities to the high-packing limit in which there are significant regions of the cavity for which the particles have no access, due the conjunction of excluded volume and confinement. The contact density and the pressure on the wall are obtained by simulations and compared to exact analytical results. We also obtain the excess free energy for N = 4, by using a simulated-assisted approach in which we combine simulation results with the knowledge of the exact partition function for two and three particles in a spherical cavity. PMID:25273472

Urrutia, I; Pastorino, C

2014-09-28

106

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

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.

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

2009-08-03

107

Ratio of effective temperature to pressure controls the mobility of sheared hard spheres

Using molecular dynamics simulation, we calculate fluctuations and response for steadily sheared hard spheres over a wide range of packing fractions $\\phi$ and shear strain rates $\\gamma$, using two different methods to dissipate energy. To a good approximation, shear stress and density fluctuations are related to their associated response functions by a single effective temperature $T_{eff}$ that is equal to or larger than the kinetic temperature $T_{kin}$. We find a crossover in the relationship between the relaxation time $\\tau$ and the the nondimensionalized effective temperature $T_{eff}/p\\sigma^3$, where $p$ is the pressure and $\\sigma$ is the sphere diameter. In the solid response regime, the behavior at fixed packing fraction satisfies $\\tau\\gamma\\propto \\exp(-cp\\sigma^3/T_{eff})$, where $c$ depends weakly on $\\phi$, suggesting that the average local yield strain is controlled by the effective temperature in a way that is consistent with shear transformation zone theory. In the fluid response regime, the relaxation time depends on $T_{eff}/p\\sigma^3$ as it depends on $T_{kin}/p\\sigma^3$ in equilibrium. This regime includes both near-equilibrium conditions where $T_{eff} ~ T_{kin}$ and far-from-equilibrium conditions where $T_{eff} \

Thomas K. Haxton

2011-03-18

108

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

NASA Astrophysics Data System (ADS)

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.

Fantoni, Riccardo; Santos, Andrés

2014-06-01

109

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

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

2013-01-01

110

Self-diffusion coefficients and shear viscosity of inverse power fluids: from hard- to soft-spheres.

Molecular dynamics computer simulation has been used to compute the self-diffusion coefficient, D, and shear viscosity, eta(s), of soft-sphere fluids, in which the particles interact through the soft-sphere or inverse power pair potential, phi(r) = epsilon(sigma/r)(n), where n measures the steepness or stiffness of the potential, and epsilon and sigma are a characteristic energy and distance, respectively. The simulations were carried out on monodisperse systems for a range of n values from the hard-sphere (n --> infinity) limit down to n = 4, and up to densities in excess of the fluid-solid co-existence value. A new analytical procedure is proposed which reproduces the transport coefficients at high densities, and can be used to extrapolate the data to densities higher than accurately accessible by simulation or experiment, and tending to the glass transition. This formula, DX(c-1) proportional, variant A/X + B, where c is an adjustable parameter, and X is either the packing fraction or the pressure, is a development of one proposed by Dymond. In the expression, -A/B is the value of X at the ideal glass transition (i.e., where D and eta(s)(-1) --> 0). Estimated values are presented for the packing fraction and the pressure at the glass transition for n values between the hard and soft particle limits. The above expression is also shown to reproduce the high density viscosity data of supercritical argon, krypton and nitrogen. Fits to the soft-sphere simulation transport coefficients close to solid-fluid co-existence are also made using the analytic form, ln(D) = alpha(X)X, and n-dependence of the alpha(X) is presented (X is either the packing fraction or the pressure). PMID:18597018

Heyes, D M; Bra?ka, A C

2008-07-21

111

NASA Astrophysics Data System (ADS)

Understanding the origin of flow heterogeneity in glassy systems is of high interest both due to its importance from theoretical standpoint as well as due to its occurrence in a large number of practical situations such as the flow of the so-called soft-glassy materials (foams, colloidal suspensions, granular media, etc). Detailed experimental investigations do indeed confirm that the flow of driven amorphous solids is not homogeneous, even if the macroscopic stress is constant across the system. We study this issue via large scale event driven molecular dynamics simulations of a hard sphere glass. We observe significant fluctuations of the velocity profile with a time scale of the order of a few hundreds percent strain. Furthermore, there appears to be a correlation between the fluctuations of the local volume fraction and the fluctuations of the local shear rate. The time scales of the fluctuations of density and shear rate are practically identical. These observations motivate an interpretation of our results via the shear concentration coupling (SCC) theory. A detailed comparison, however, reveals serious inconsistencies. In particular, the amplitude of the fluctuations of the shear rate seems to be decoupled from that of density, a feature which is rather unexpected within the SCC picture. An alternative interpretation of our observations is also discussed invoking dynamic heterogeneity.

Mandal, Suvendu; Gross, Markus; Raabe, Dierk; Varnik, Fathollah

2013-02-01

112

One and Two-Fluid van der Waals Theories of Liquid Mixtures, I. Hard Sphere Mixtures

The equation of state of a mixture of hard spheres is calculated using the one- and two-fluid van der Waals theories and the three-fluid theory. The one-fluid theory is found to be in the best agreement with the machine-simulation results.

Douglas Henderson; Peter J. Leonard

1970-01-01

113

The potential energy landscape and inherent dynamics of a hard-sphere fluid

Hard-sphere models exhibit many of the same kinds of supercooled-liquid behavior as more realistic models of liquids, but the highly non-analytic character of their potentials makes it a challenge to think of that behavior in potential-energy-landscape terms. We show here that it is possible to calculate an important topological property of hard-sphere landscapes, the geodesic pathways through those landscapes, and to do so without artificially coarse-graining or softening the potential. We show, moreover, that the rapid growth of the lengths of those pathways with increasing packing fraction quantitatively predicts the precipitous decline in diffusion constants in a glass-forming hard-sphere mixture model. The geodesic paths themselves can be considered as defining the intrinsic dynamics of hard spheres, so it is also revealing to find that they (and therefore the features of the underlying potential-energy landscape) correctly predict the occurrence of dynamic heterogeneity and non-zero values of the non-Gaussian parameter. The success of these landscape predictions for the dynamics of such a singular model emphasizes that there is more to potential energy landscapes than is revealed by looking at the minima and saddle points.

Qingqing Ma; Richard M. Stratt

2014-08-13

114

Rolling friction for hard cylinder and sphere on viscoelastic solid

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 an useful way to determine the viscoelastic modulus of rubber-like materials.

B. N. J. Persson

2010-08-26

115

Disorder and excess modes in hard-sphere colloidal systems

NASA Astrophysics Data System (ADS)

The anomalous thermodynamic properties of glasses remain incompletely understood, notably the anomalous peak in the heat capacity at low temperatures; it is believed to be due to an excess of low-frequency vibrational modes and a manifestation of the structural disorder in these systems. We study the thermodynamics and vibrational dynamics of colloidal glasses and (defected) crystals. The experimental determination of the vibrational density of states allows us to directly observe a strong enhancement of low-frequency modes. Using a novel method (Zargar R. et al., Phys. Rev. Lett. 110 (2013) 258301) to determine the free energy, we also determine the entropy and the specific heat experimentally. It follows that the emergence of the excess modes and high values of the specific heat are directly related and are specific to the glass: even for solids containing a very large amount of defects, both the low-frequency density of states and the specific heat are significantly smaller than for the glass.

Zargar, R.; Russo, J.; Schall, P.; Tanaka, H.; Bonn, D.

2014-11-01

116

The microstructures of cold dense systems as informed by hard sphere models and optimal packings

NASA Astrophysics Data System (ADS)

Sphere packings, or arrangements of "billiard balls" of various sizes that never overlap, are especially informative and broadly applicable models. In particular, a hard sphere model describes the important foundational case where potential energy due to attractive and repulsive forces is not present, meaning that entropy dominates the system's free energy. Sphere packings have been widely employed in chemistry, materials science, physics and biology to model a vast range of materials including concrete, rocket fuel, proteins, liquids and solid metals, to name but a few. Despite their richness and broad applicability, many questions about fundamental sphere packings remain unanswered. For example, what are the densest packings of identical three-dimensional spheres within certain defined containers? What are the densest packings of binary spheres (spheres of two different sizes) in three-dimensional Euclidean space R3 ? The answers to these two questions are important in condensed matter physics and solid-state chemistry. The former is important to the theory of nucleation in supercooled liquids and the latter in terms of studying the structure and stability of atomic and molecular alloys. The answers to both questions are useful when studying the targeted self-assembly of colloidal nanostructures. In this dissertation, putatively optimal answers to both of these questions are provided, and the applications of these findings are discussed. The methods developed to provide these answers, novel algorithms combining sequential linear and nonlinear programming techniques with targeted stochastic searches of conguration space, are also discussed. In addition, connections between the realizability of pair correlation functions and optimal sphere packings are studied, and mathematical proofs are presented concerning the characteristics of both locally and globally maximally dense structures in arbitrary dimension d. Finally, surprising and unexpected findings are presented concerning structural signatures inherent to nonequilibrium glassy states of matter, as modeled using a prototypical glass of 1,000,000 identical spheres.

Hopkins, Adam Bayne

117

Importance of many-body correlations in glass transition: an example from polydisperse hard spheres.

Most of the liquid-state theories, including glass-transition theories, are constructed on the basis of two-body density correlations. However, we have recently shown that many-body correlations, in particular, bond orientational correlations, play a key role in both the glass transition and the crystallization transition. Here we show, with numerical simulations of supercooled polydisperse hard spheres systems, that the length-scale associated with any two-point spatial correlation function does not increase toward the glass transition. A growing length-scale is instead revealed by considering many-body correlation functions, such as correlators of orientational order, which follows the length-scale of the dynamic heterogeneities. Despite the growing of crystal-like bond orientational order, we reveal that the stability against crystallization with increasing polydispersity is due to an increasing population of icosahedral arrangements of particles. Our results suggest that, for this type of systems, many-body correlations are a manifestation of the link between the vitrification and the crystallization phenomena. Whether a system is vitrified or crystallized can be controlled by the degree of frustration against crystallization, polydispersity in this case. PMID:23556787

Leocmach, Mathieu; Russo, John; Tanaka, Hajime

2013-03-28

118

NASA Astrophysics Data System (ADS)

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 < ? < 2?. It enables a unified approach to both wedges and edges.

Urrutia, Ignacio

2014-12-01

119

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 < ? < 2?. It enables a unified approach to both wedges and edges. PMID:25554179

Urrutia, Ignacio

2014-12-28

120

NASA Astrophysics Data System (ADS)

Two-dimensional hard disks are a fundamentally important many-body model system in classical statistical mechanics. Despite their significance, a comprehensive experimental data set for two-dimensional single component and binary hard disks is lacking. Here, we present a direct comparison between the full set of radial distribution functions and the contact values of a two-dimensional binary colloidal hard sphere model system and those calculated using fundamental measure theory. We find excellent quantitative agreement between our experimental data and theoretical predictions for both single component and binary hard disk systems. Our results provide a unique and fully quantitative mapping between experiments and theory, which is crucial in establishing the fundamental link between structure and dynamics in simple liquids and glass forming systems.

Thorneywork, Alice L.; Roth, Roland; Aarts, Dirk G. A. L.; Dullens, Roel P. A.

2014-04-01

121

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

NASA Technical Reports Server (NTRS)

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.

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

122

NASA Astrophysics Data System (ADS)

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.

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

2013-04-01

123

Parallelized event chain algorithm for dense hard sphere and polymer systems

NASA Astrophysics Data System (ADS)

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.

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

2015-01-01

124

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

NASA Technical Reports Server (NTRS)

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.

Ling, Jerri S.; Doherty, Michael P.

1998-01-01

125

Two hard spheres in a pore: Exact Statistical Mechanics for different shaped cavities

The Partition function of two Hard Spheres in a Hard Wall Pore is studied appealing to a graph representation. The exact evaluation of the canonical partition function, and the one-body distribution function, in three different shaped pores are achieved. The analyzed simple geometries are the cuboidal, cylindrical and ellipsoidal cavities. Results have been compared with two previously studied geometries, the spherical pore and the spherical pore with a hard core. The search of common features in the analytic structure of the partition functions in terms of their length parameters and their volumes, surface area, edges length and curvatures is addressed too. A general framework for the exact thermodynamic analysis of systems with few and many particles in terms of a set of thermodynamic measures is discussed. We found that an exact thermodynamic description is feasible based in the adoption of an adequate set of measures and the search of the free energy dependence on the adopted measure set. A relation similar to the Laplace equation for the fluid-vapor interface is obtained which express the equilibrium between magnitudes that in extended systems are intensive variables. This exact description is applied to study the thermodynamic behavior of the two Hard Spheres in a Hard Wall Pore for the analyzed different geometries. We obtain analytically the external work, the pressure on the wall, the pressure in the homogeneous zone, the wall-fluid surface tension, the line tension and other similar properties.

Ignacio Urrutia

2010-05-05

126

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

NASA Astrophysics Data System (ADS)

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, ?CuTi, ?IrV, 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?q?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.

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

2009-08-01

127

Thermodynamic scaling law for the diffusion coefficient in hard-sphere system

NASA Astrophysics Data System (ADS)

Two scaling laws are investigated, which are devoted to link the diffusion coefficient to the thermodynamic properties for the athermal hard-sphere system, over the wide range of packing fraction covering the stable and metastable regimes. It is found that the most relevant control parameter is not the excess entropy, but the compressibility factor, i.e. the logarithm derivative of the excess entropy with respect to the packing fraction.

Bomont, Jean-Marc; Bretonnet, Jean-Louis

2015-02-01

128

A two-stage approach to relaxation in billiard systems of locally confined hard spheres

We consider the three-dimensional dynamics of systems of many interacting hard spheres, each individually confined to a dispersive environment, and show that the macroscopic limit of such systems is characterized by a coefficient of heat conduction whose value reduces to a dimensional formula in the limit of vanishingly small rate of interaction. It is argued that this limit arises from an effective loss of memory. Similarities with the diffusion of a tagged particle in binary mixtures are emphasized.

Pierre Gaspard; Thomas Gilbert

2011-11-27

129

NASA Astrophysics Data System (ADS)

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.

Jiang, Hao; Adidharma, Hertanto

2014-11-01

130

NASA Astrophysics Data System (ADS)

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.

Mirigian, Stephen; Schweizer, Kenneth S.

2014-05-01

131

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

Mirigian, Stephen; Schweizer, Kenneth S

2014-05-21

132

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.

Mirigian, Stephen [University of Illinois, Urbana-Champaign] [University of Illinois, Urbana-Champaign; Schweizer, Kenneth [University of Illinois] [University of Illinois

2014-01-01

133

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

NASA Technical Reports Server (NTRS)

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.

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

1998-01-01

134

Impact of microstructure on the effective diffusivity in random packings of hard spheres

NASA Astrophysics Data System (ADS)

We present results of computer simulations of the effective diffusion coefficient in bulk random packings of hard monosized spheres with solid volume fraction between 0.54 (random-loose packing) and 0.634 (maximally random jammed). Six types of sphere packings were generated with different protocols and parameters resulting in a systematically varied degree of microstructural heterogeneity. The packing morphology is qualitatively characterized by statistical analyses of Voronoi cells obtained from spatial tessellation of the packing space. Diffusive transport of point-like tracers in the pore space of the packings was simulated with a random-walking particle-tracking technique. Our results indicate that the effective transport characteristics of the random sphere packings are not fully defined from the solid volume fraction but also depend on the packing microstructure. For the first time, we compared (i) the values of the effective diffusion coefficient Deff simulated in packings with different morphologies, and (ii) the corresponding values of Deff obtained from an approximate analytical formula involving the three-point microstructural parameter ?2. This analysis reveals that this approximation involving ?2 clearly reflects key morphological specificity of individual sphere packings and provides a sufficiently accurate estimate of the effective diffusion coefficient.

Liasneuski, H.; Hlushkou, D.; Khirevich, S.; Höltzel, A.; Tallarek, U.; Torquato, S.

2014-07-01

135

Hard spheres revisited: Accurate calculation of the solid-liquid interfacial free energy

NASA Astrophysics Data System (ADS)

We revise the earlier [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 85, 4751 (2000)] direct calculation of the hard sphere solid-liquid interfacial free energy by the cleaving walls method. The revisions of the method include modified interactions with the cleaving walls and the use of a nonequilibrium work measurements approach, which allows for a more robust control of the accuracy of the obtained results. We find that the new values are lower compared to the original ones, which is consistent with the more recent indirect estimates based on extrapolation from the soft-sphere results [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 94, 086102 (2005)], as well as those obtained using the capillary fluctuations method [R. L. Davidchack, J. R. Morris, and B. B. Laird, J. Chem. Phys. 125, 094710 (2006)].

Davidchack, Ruslan L.

2010-12-01

136

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

NASA Technical Reports Server (NTRS)

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.

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

2005-01-01

137

NASA Astrophysics Data System (ADS)

We present a novel application of the expanded ensemble Monte Carlo (EEMC) simulation method to calculation of the chemical potential of nanocolloidal particles in nanocolloid-polymer mixtures. This approach uses an expanded canonical ensemble in which the colloidal particle diameter is an additional ensemble variable, allowed to vary between zero and the maximum colloid size desired. Using a hard-sphere model system, we demonstrate that this approach is superior to the Widom method for calculating chemical potentials in colloid-polymer systems. Specifically the EEMC leads to lower uncertainties and is capable of calculating accurate colloid chemical potentials for particle sizes where Widom insertion fails due to overlap. The EEMC method is applied to calculate the colloid chemical potential for an infinitely dilute colloidal particle (hard-sphere) in a dilute polymer (hard-sphere chain) solution over a wide range of relative sizes, 0.1g/R<12, where Rg is the polymer radius of gyration and R is the colloid radius. The simulation results are compared to the predictions of models developed by others: an integral equation model (FS) [Fuchs and Schweizer, Europhys. Lett. 51, 621 (2000)] and a field theoretic (FT) approach [Eisenriegler [et al.], Phys. Rev. E 54, 1134 (1996)]. Very good agreement is observed with the FS model over a wide range of Rg/R values, whereas the FT model agrees well only at large Rg/R. An empirical power law function is found to represent the simulation results well, potentially useful for analysis of free energy data for colloid-polymer mixtures.

Tej, Marla Krishna; Meredith, J. Carson

2002-09-01

138

Glass-transition properties of Yukawa potentials: from charged point particles to hard spheres.

The glass transition is investigated in three dimensions for single and double Yukawa potentials for the full range of control parameters. For vanishing screening parameter, the limit of the one-component plasma is obtained; for large screening parameters and high coupling strengths, the glass-transition properties cross over to the hard-sphere system. Between the two limits, the entire transition diagram can be described by analytical functions. Unlike other potentials, the glass-transition and melting lines for Yukawa potentials are found to follow shifted but otherwise identical curves in control-parameter space. PMID:25019902

Yazdi, Anoosheh; Ivlev, Alexei; Khrapak, Sergey; Thomas, Hubertus; Morfill, Gregor E; Löwen, Hartmut; Wysocki, Adam; Sperl, Matthias

2014-06-01

139

Structural properties of liquid lanthanides using charge hard sphere reference system

NASA Astrophysics Data System (ADS)

In the present paper Charge Hard Sphere (CHS) system is employed to investigate the structural properties like long wavelength limit S(0), isothermal compressibility (?T) and coordination number n for some liquid lanthanides viz.: La, Ce, Pr, Nd, Eu, Gd, Tb, Dy, Ho, Er, Yb and Lu. Our well established parameter free model potential is used to describe the electron-ion interaction alongwith sarkar et al. dielectric function. From the present results, it is seen that good agreement between present results and available experimental data have been achieved. At last, we establish the applicability of our parameter free model potential and CHS method to account such structural properties.

Thakora, P. B.; Sonvane, Y. A.; Patel, H. P.; Gajjar, P. N.; Jani, A. R.

2012-06-01

140

Structural Properties of Some Semiconductor Liquid Metals Using Charged Hard Sphere Reference System

NASA Astrophysics Data System (ADS)

The structural properties like pair distribution function g(r), long wavelength limit of structure factor S(0) and isothermal compressibility ?T of some semiconductor liquid metals (Si, Ga, Ge, In, Sn, Tl and Bi) are calculated using our well established single parametric model potential alongwith charged hard sphere (CHS) reference system. To see the influence of exchange and correlation effect, Taylor local field correlation function is used. Lastly we conclude that our model potential successfully explains the structural properties of semiconductor liquid metals (Si, Ga, Ge, In, Sn, Tl and Bi).

Sonvane, Y. A.; Thakor, P. B.; Kanawade, Sandhya; Gajjar, P. N.; Jani, A. R.

2011-07-01

141

Crystal-liquid interfacial free energy of hard spheres via a novel thermodynamic integration scheme

The hard sphere crystal-liquid interfacial free energy, ($\\gamma_{\\rm cl}$), is determined from molecular dynamics simulations using a novel thermodynamic integration (TI) scheme. The advantage of this TI scheme compared to previous methods is to successfully circumvent hysteresis effects due to the movement of the crystal-liquid interface. This is accomplished by the use of extremely short-ranged and impenetrable Gaussian flat walls which prevent the drift of the interface while imposing a negligible free-energy penalty. We find that it is crucial to analyze finite-size effects in order to obtain reliable estimates of $\\gamma_{\\rm cl}$ in the thermodynamic limit.

Ronald Benjamin; Jürgen Horbach

2014-10-31

142

Convergence of spherical harmonic expansions for the evaluation of hard-sphere cluster integrals

NASA Astrophysics Data System (ADS)

For N particles ( N>2), by means of a spherical harmonic expansion of Silverstone and Moats, a 3 N-dimensional cluster may be reduced to 2 N+1 trivial integrals and N-1 interesting integrals. For hard spheres, the N-1 interesting integrals are products of polynomials integrated between binomial bounds. With simple clusters, closed forms are obtained; for more complex clusters, infinite series in l (of Y lm ) appear. It is here shown for representative cases that these series converge exponentially rapidly, the leading pair of terms accounting for all but a few tenths of a percent of the total cluster integral.

Phillies, George D. J.

1991-02-01

143

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

NASA Technical Reports Server (NTRS)

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.

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

2002-01-01

144

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

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

Chavanis, Pierre-Henri

2002-05-01

145

Determination of the melting point of hard spheres from direct coexistence simulation methods

NASA Astrophysics Data System (ADS)

We consider the computation of the coexistence pressure of the liquid-solid transition of a system of hard spheres from direct simulation of the inhomogeneous system formed from liquid and solid phases separated by an interface. Monte Carlo simulations of the interfacial system are performed in three different ensembles. In a first approach, a series of simulations is carried out in the isothermal-isobaric ensemble, where the solid is allowed to relax to its equilibrium crystalline structure, thus avoiding the appearance of artificial stress in the system. Here, the total volume of the system fluctuates due to changes in the three dimensions of the simulation box. In a second approach, we consider simulations of the inhomogeneous system in an isothermal-isobaric ensemble where the normal pressure, as well as the area of the (planar) fluid-solid interface, are kept constant. Now, the total volume of the system fluctuates due to changes in the longitudinal dimension of the simulation box. In both approaches, the coexistence pressure is estimated by monitoring the evolution of the density along several simulations carried out at different pressures. Both routes are seen to provide consistent values of the fluid-solid coexistence pressure, p =11.54(4)kBT/?3, which indicates that the error introduced by the use of the standard constant-pressure ensemble for this particular problem is small, provided the systems are sufficiently large. An additional simulation of the interfacial system is conducted in a canonical ensemble where the dimensions of the simulation box are allowed to change subject to the constraint that the total volume is kept fixed. In this approach, the coexistence pressure corresponds to the normal component of the pressure tensor, which can be computed as an appropriate ensemble average in a single simulation. This route yields a value of p =11.54(4)kBT/?3. We conclude that the results obtained for the coexistence pressure from direct simulations of the liquid and solid phases in coexistence using different ensembles are mutually consistent and are in excellent agreement with the values obtained from free energy calculations.

Noya, Eva G.; Vega, Carlos; de Miguel, Enrique

2008-04-01

146

NASA Astrophysics Data System (ADS)

Using both molecular simulation and theory, we examine fluid-phase thermodynamic and structural properties of on-lattice hard-sphere fluids. Our purpose in this work is to provide reference data for on-lattice density functional theories [D. W. Siderius and L. D. Gelb, Langmuir 25, 1296 (2009)] and related perturbation theories. In this model, hard spheres are located at sites on a finely discretized cubic lattice where the spacing between lattice sites is between one-tenth and one-third the hard-sphere diameter. We calculate exactly the second, third, and fourth virial coefficients as functions of the lattice spacing. Via Monte Carlo simulation, we measure the excess chemical potential as a function of density for several lattice spacings. These results are then parametrized with a convenient functional form and can immediately be used in on-lattice density functional theories. Of particular interest is to identify those lattice spacings that yield properties similar to those of the off-lattice fluid. We find that the properties of the on-lattice fluid are strongly dependent on lattice spacing, generally approaching those of the off-lattice fluid with increasing lattice resolution, but not smoothly. These observations are consistent with results for larger lattice spacings [A. Z. Panagiotopoulos, J. Chem. Phys. 123, 104504 (2005)]. Certain lattice spacings are found to yield fluid properties in particularly good agreement with the off-lattice fluid. We also find that the agreement of many different on- and off-lattice hard-sphere fluid properties is predicted quite well by that of the virial coefficients, suggesting that they may be used to identify favorable lattice spacings. The direct correlation function at a few lattice spacings and a single density is obtained from simulation. The on-lattice fluid is structurally anisotropic, exhibiting spherical asymmetry in correlation functions. Interestingly, the anisotropies are properly captured in the Percus-Yevick-based calculation of the direct correlation function. Lastly, we speculate on the possibility of obtaining a theoretical equation of state of the on-lattice hard-sphere fluid computed in the Percus-Yevick approximation.

Siderius, Daniel W.; Gelb, Lev D.

2009-08-01

147

NASA Astrophysics Data System (ADS)

We investigate the dynamic structure factor of a system of Bose particles at zero temperature using quantum Monte Carlo methods. Interactions are modeled using a hard-sphere potential of size a and simulations are performed for values of the gas parameter na3 ranging from the dilute regime up to densities n where the thermodynamically stable phase is a solid. With increasing density, we observe a crossover of the dispersion of elementary excitations from a Bogoliubov-type spectrum to a phonon-maxon-roton curve and the emergence of a broad multiphonon contribution accompanying the single-quasiparticle peak. In particular, for na3=0.2138, which corresponds to superfluid 4He at equilibrium density, the extracted spectrum turns out to be in good agreement with the experimental energy-momentum dispersion relation in the roton region and for higher momenta. The behavior of the spectral function at the same density in the stable solid and metastable gas phase above the freezing point is also discussed.

Rota, R.; Tramonto, F.; Galli, D. E.; Giorgini, S.

2013-12-01

148

Fluctuations, structure factor and polytetrahedra in random packings of sticky hard spheres

Sequentially-built random sphere-packings have been numerically studied in the packing fraction interval $0.329 structure factors $S(Q)$ of the aggregates. Among various parameters (Voronoi tessellation, contact coordination number distribution,...), fluctuations were quantitatively evaluated by the direct evaluation of the fluctuations of the local sphere number density, which appears to follow a power law. The FWHM of the Voronoi cells volume shows a regular variation over the whole packing fraction range. Dirac peaks appear on the pair correlation function as the packing fraction of the aggregates decreases, indicating the growth of larger and larger polytetrahedra, which manifest in two ways on the structure factor, at low and large $Q$values. These low PF aggregates have a composite structure made of regular polytetrahedra embedded in a more disordered matrix. Incidentally, the irregularity index of the building tetrahedron appears as a better parameter than the packing fraction to describe various features of the aggregates structure.

Marc Bletry; Jean Bletry

2014-09-08

149

NASA Astrophysics Data System (ADS)

Even though ionic liquids are composed of nonspherical ions, it is shown here that the general features of the capacitance of an electrical double layer can be obtained using a charged hard sphere model. We have shown in our earlier studies that at high electrolyte concentrations or large magnitudes of the electrode charge density the fact that the ions have a finite size, and are not point ions, cause the capacitance near the potential of zero charge to increase and change from a minimum to a maximum as the ionic concentration is increased and to decrease as the magnitude of the electrode charge density increases. Here, we show that the asymmetry of the capacitance of an ionic liquid can be explained qualitatively by using spherical ions of different size without attempting to introduce the ionic shape in a detailed manner. This means that the general features of the capacitance of the double layer of an ionic liquid can be studied without using a complex model, although the study of the density or charge profiles of an ionic fluid would require one. However, this is often unnecessary in the analysis of many experiments.

Lamperski, Stanis?aw; Sosnowska, Joanna; Bhuiyan, Lutful Bari; Henderson, Douglas

2014-01-01

150

We consider a slit-like pore filled with a disordered hard-sphere matrix. The diameter of matrix species is chosen almost equal to the pore width. Another hard-sphere fluid species, of smaller diameter, enters, at a given chemical potential, into this confined quenched microporous medium. The model is similar to the experimental setup; see G. Cruz de Leon et al. Phys. Rev. Lett. 81, 1122 (1998). The model is solved by using the inhomogeneous replica Ornstein-Zernike equations with Percus-Yevick approximation. We discuss the effective interactions between species in a confined medium on the chemical potential and matrix microporosity. Copyright 1999 Academic Press. PMID:10489311

Sokolowski; Rzysko; Pizio

1999-10-01

151

Towards a general definition of gelation for adhesive hard-sphere dispersions

One major goal in condensed matter physics 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 adhesive hard-sphere dispersions are the result of rigidity percolation with average number of bonds, $$, equals to 2.4. This corresponds to an established mechanism leading to phase transitions in network-forming materials. 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 of the critical gel state.

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

2013-06-25

152

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

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

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

2013-06-21

153

NASA Astrophysics Data System (ADS)

Different theoretical approaches for the thermodynamic properties and the equation of state for multicomponent mixtures of nonadditive hard spheres in d dimensions are presented in a unified way. These include the theory by Hamad, our previous formulation, the original MIX1 theory, a recently proposed modified MIX1 theory, as well as a nonlinear extension of the MIX1 theory proposed in this paper. Explicit expressions for the compressibility factor, Helmholtz free energy, and second, third, and fourth virial coefficients are provided. A comparison is carried out with recent Monte Carlo data for the virial coefficients of asymmetric mixtures and with available simulation data for the compressibility factor, the critical consolute point, and the liquid-liquid coexistence curves. The merits and limitations of each theory are pointed out.

Santos, Andrés; López de Haro, Mariano; Yuste, Santos B.

2010-05-01

154

Disordered Solids without Well-Defined Transverse Phonons: The Nature of Hard-Sphere Glasses

NASA Astrophysics Data System (ADS)

We probe the Ioffe-Regel limits of glasses with repulsions near the zero-temperature jamming transition by calculating the dynamical structure factors. The Ioffe-Regel limit (frequency) is reached when the phonon wavelength is comparable to the mean free path, beyond which phonons are no longer well defined. At zero temperature, the transverse Ioffe-Regel frequency vanishes at the jamming transition with a diverging length, but the longitudinal one does not, which excludes the existence of a diverging length associated with the longitudinal excitations. At low temperatures, the transverse and longitudinal Ioffe-Regel frequencies approach zero at the jamminglike transition and glass transition, respectively. As a consequence, glasses between the glass transition and the jamminglike transition, which are hard-sphere glasses in the low temperature limit, can only carry well-defined longitudinal phonons and have an opposite pressure dependence of the ratio of the shear modulus to the bulk modulus from glasses beyond the jamminglike transition.

Wang, Xipeng; Zheng, Wen; Wang, Lijin; Xu, Ning

2015-01-01

155

NASA Astrophysics Data System (ADS)

Molecular dynamics simulations of a hard sphere crystal are performed for volume fractions ranging from solidification point to melting point. A local bond order parameter is chosen to assign a nature, liquid or solid, to a particle. The probability for a liquid or solid particle to change state presents a typical sigmoid shape as the nature of its neighbors changes. Using this property, I propose a reaction-like mechanism and introduce a small number of rate constants. A mean-field approach to melting and a kinetic Monte Carlo algorithm on a lattice are derived from these chemical processes. The results of these models successfully compare with molecular dynamics simulations, proving that the main properties of melting can be captured by a small number of dynamical parameters.

Lemarchand, C. A.

2012-06-01

156

Shear rheology of hard-sphere, dispersed, and aggregated suspensions, and filler-matrix composites.

This paper reviews the shear rheology of suspensions of microscopic particles. The nature of interparticle forces determines the microstructure, and hence the deformation and flow behavior of suspensions. Consequently, suspensions were classified according to the resulting microstructure: hard-spheres, stabilized, or aggregated particles. This study begins with the most simple case: flowing suspensions of inert, rigid, monomodal spherical particles (called hard-spheres), at low shear rates. Even for inert particles, we reviewed the effect of several factors that produce deviations from this ideal case, namely: shear rate, particle shape, particle size distribution, and particle deformability. Then we moved to suspensions of colloidal particles, where interparticle forces play a significant role. First we studied the case of dispersed or stabilized suspensions (colloidal dispersions), where long range repulsive forces keep particles separated, leading to a crystalline order. Second we studied the more common case of aggregated or flocculated suspensions, where net attractive forces lead to the formation of fractal clusters. Above the gelation concentration (which depends on the magnitude of the attractive forces), clusters are interconnected into a network, forming a gel. We differentiate between weak and strong aggregation, which may lead to weak or strong gels, respectively. Finally, we reviewed the case of filler/matrix composite suspensions or gels, where rigid or viscoelastic particles (fillers) are dispersed in a continuous viscoelastic material (matrix), usually a gel. For each type of suspension, predictive curves of fundamental rheological properties (viscosity, yield stress, elastic and complex moduli) vs. particle volume fraction and shear rate were obtained from theoretical or empirical models and sound experimental data, covering ranges of practical interest. PMID:22304831

Genovese, Diego B

2012-01-01

157

NASA Astrophysics Data System (ADS)

DWS-based tracer particle microrheology is demonstrated to be a useful way to study the dynamics of aqueous Pluronic L64 solutions, which is viewed as a model adhesive hard sphere (AHS) system. The short-time dynamics of aqueous Pluronic L64 solutions indicate a purely hydrodynamic high frequency microviscosity as predicted by Batchelor for colloidal dispersions. The evolution of the micellar dynamics reveals a zero shear microviscosity in good agreement with steady shear viscosity measurements. As the temperature is increased, the dynamics become dominated by an apparent attractive intermicellar potential observed in microscopic creep measurements. While Pluronic L64 solutions have been reported to form a percolated micellar network, DWS-based microviscoelasticity measurements do not detect the previously observed G'˜G?˜?? scaling expected for a static percolated network at low frequencies. This most likely owes to the fact that tracer particle microrheology is dominated by local Pluronic L64 micelle dynamics in the near sphere region and not the bulk mechanical properties as measured by traditional rheometry. The sensitivity of tracer particle microrheological measurements to the true dynamic nature of the percolated network in weak physical gels highlights the distinct differences between these micro- and macrorheology measurement techniques. Such discrepancies should be most evident in systems that are dominated by association processes such as those occurring in AHS solutions or polymer solutions approaching a phase boundary. Despite this, the AHS potential is qualitatively consistent with the results found here.

Kloxin, Christopher J.; van Zanten, John H.

2009-10-01

158

Fast decay of the velocity autocorrelation function in dense shear flow of inelastic hard spheres

We find in complementary experiments and event driven simulations of sheared inelastic hard spheres that the velocity autocorrelation function $\\psi(t)$ decays much faster than $t^{-3/2}$ obtained for a fluid of elastic spheres at equilibrium. Particle displacements are measured in experiments inside a gravity driven flow sheared by a rough wall. The average packing fraction obtained in the experiments is 0.59, and the packing fraction in the simulations is varied between 0.5 and 0.59. The motion is observed to be diffusive over long times except in experiments where there is layering of particles parallel to boundaries, and diffusion is inhibited between layers. Regardless, a rapid decay of $\\psi(t)$ is observed, indicating that this is a feature of the sheared dissipative fluid, and is independent of the details of the relative particle arrangements. An important implication of our study is that the non-analytic contribution to the shear stress may not be present in a sheared inelastic fluid, leading to a wider range of applicability of kinetic theory approaches to dense granular matter.

Ashish V. Orpe; V. Kumaran; K. Anki Reddy; Arshad Kudrolli

2008-11-18

159

Uniform density static fluid sphere in Einstein-Gauss-Bonnet gravity and its universality

In Newtonian theory, gravity inside a constant density static sphere is independent of spacetime dimension. Interestingly this general result is also carried over to Einsteinian as well as higher order Einstein-Gauss-Bonnet (Lovelock) gravity notwithstanding their nonlinearity. We prove that the necessary and sufficient condition for universality of the Schwarzschild interior solution describing a uniform density sphere for all n{>=}4 is that its density is constant.

Dadhich, Naresh; Molina, Alfred; Khugaev, Avas [Inter-University Centre for Astronomy and Astrophysics, Post Bag 4 Pune 411 007 (India); Departament de Fisica Fonamental, Universitat de Barcelona, Barcelona (Spain); Institute of Nuclear Physics, Tashkent, 100214 (Uzbekistan)

2010-05-15

160

Using molecular dynamics (MD) and Monte Carlo (MC) simulations interfacial properties of crystal-fluid interfaces are investigated for the hard sphere system and the one-component metallic system Ni (the latter modeled by a potential of the embedded atom type). Different local order parameters are considered to obtain order parameter profiles for systems where the crystal phase is in coexistence with the

T. Zykova-Timan; R. E. Rozas; J. Horbach; K. Binder

2009-01-01

161

The effect of inertial normal force on the rolling friction of a soft sphere on a hard plane

Previously, in the rolling-friction analysis, the normal compression force was assumed to be independent of the rolling speed. In this study, it is found that the normal compression force of a soft sphere on a hard plane depends on its rolling speed as the inertial force is taken into consideration. A new expression of the rolling frictional torque, which is

Y. Xu; K. L. Yung

2003-01-01

162

NASA Astrophysics Data System (ADS)

Based on the expansion and extension of the virial equation of state (EOS) of hard-sphere fluids solved by the Percus-Yevick integration equation, a universal cubic (UC) EOS is developed. The UC EOS is applied to model hard-sphere and Lennard-Jones (LJ) fluids, simple Ar and N2 liquids at low temperatures, and supercritical Ar and N2 fluids at high temperatures, as well as ten solids, respectively. The three parameters are determined for the hard-sphere fluid by fitting molecular dynamics (MD) simulation data of the third to eighth virial coefficients in the literature; for other fluids by fitting isothermal compression data; and for solids by using the Einstein model. The results show that the UC EOS gives better results than the Carnahan-Starling EOS for compressibility of hard-sphere fluids. The Helmholtz free energy and internal energy for LJ fluids are predicted and compared with MD simulation data. The calculated pressures for simple Ar and N2 liquids are compared with experimental data. The agreement is fairly good. Eight three-parameter EOSs are applied to describe isothermals of ten typical solids. It is shown that the UC EOS gives the best precision with correct behavior at high-pressure limitation. The UC EOS considering thermal effects is used to analytically evaluate the isobaric thermal expansivity and isothermal compressibility coefficients. The results are in good agreement with experimental data.

Sun, Jiu-Xun; Cai, Ling-Cang; Wu, Qiang; Jin, Ke

2013-09-01

163

into jammed pack- ings as a function of the compression rate R, size ratio , and number fraction xS of smallarXiv:submit/0947842[cond-mat.mtrl-sci]2Apr2014 Can the packing efficiency of binary hard spheres (Dated: April 2, 2014) We perform molecular dynamics simulations to compress binary hard spheres

O'Hern, Corey S.

164

NASA Astrophysics Data System (ADS)

A method for calculation of the free energy of dipolar hard spheres under the presence of an applied magnetic field is presented. The method is based on the virial expansion in terms of density as well as the dipolar coupling constant ?, and it uses diagram technique. The formulas and the diagrams, needed to calculate the second B2 and third B3 virial coefficients, are derived up to the order of ˜?3, and compared to the zero-field case. The formula for B2 is the same as in the zero-field case; the formula for B3, however, is different in an applied field, and a derivation is presented. This is a surprising result which is not emphasized in standard texts, but which has been noticed before in the virial expansion for flexible molecules (Caracciolo et al., 2006; Caracciolo et al., 2008). To verify the correctness of the obtained formulas, B2 and B3 were calculated within the accuracy of ?2, which were applied to initial magnetic susceptibility. The obtained expression fully coincides with the well-known theories (Morozov and Lebedev, 1990; Huke and Lücke, 2000; Ivanov and Kuznetsova, 2001), which used different methods to calculate the initial magnetic susceptibility.

Elfimova, Ekaterina A.; Karavaeva, Tatyana E.; Ivanov, Alexey O.

2014-12-01

165

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

In the first part of this paper, a review is given on the mechanism for 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 experimentally [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.

Atsushi Mori; Yoshihisa Suzuki; Shikegi Matsuo

2008-05-12

166

NASA Astrophysics Data System (ADS)

Algorithms to search for crystal structures that optimize some extensive property (energy, volume, etc) typically make use of random particle reorganizations in the context of one or more numerical techniques such as simulated annealing, genetic algorithms or biased random walks, applied to the coordinates of every particle in the unit cell, together with the cell angles and lengths. In this paper we describe the restriction of such searches to predefined isopointal sets, breaking the problem into countable sub-problems which exploit crystal symmetries to reduce the dimensionality of the search space. Applying this method to the search for maximally packed mixtures of hard spheres of two sizes, we demonstrate that the densest packed structures can be identified by searches within a couple of isopointal sets. For the A2B system, the densest known packings over the entire tested range 0.2 < rA/rB < 2.5, including some improvements on previous optima, can all be identified by searches within a single isopointal set. In the case of the AB composition, searches of two isopointal sets generate the densest packed structures over the radius ratio range 0.2 < rA/rB < 5.0.

Hudson, Toby S.; Harrowell, Peter

2011-05-01

167

The dielectric virial expansion and the models of dipolar hard-sphere fluid.

The virial expansion technique to determine the dielectric constant epsilon of dipolar hard-sphere fluid is developed. It is shown that the formalism allows to bring into agreement the results of Debye's, Onsager's, and Langevin's to the problem. The third virial coefficient of epsilon is considered as a series over dipolar parameter lambda=m(2)d(3)kT. The terms up to O(lambda(11)) are calculated analytically providing a correct description of the third virial coefficient for small and intermediate values of lambda (0

Morozov, Konstantin I

2007-05-21

168

NASA Astrophysics Data System (ADS)

Diffusive transport is a ubiquitous process that is typically understood in terms of a classical random walk of non-interacting particles. Here we present the results for a model of hard-sphere colloids in a Newtonian incompressible solvent at various volume fractions below the ordering transition (˜50%). We numerically simulate the colloidal systems via Fast Lubrication Dynamics -- a Brownian Dynamics approach with corrected mean-field hydrodynamic interactions. Colloid-colloid interactions are also included so that we effectively solve a system of interacting Langevin equations. The results of the simulations are analyzed in terms of the diffusion coefficient as a function of time with the early and late time diffusion coefficients comparing well with experimental results. An interpretation of the full time dependent behavior of the diffusion coefficient and mean-squared displacement is given in terms of a continuous time random walk. Therefore, the deterministic, continuum diffusion equation which arises from the discrete, interacting random walkers is presented. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Lechman, Jeremy; Pierce, Flint

2012-02-01

169

Local shear transformations in deformed and quiescent hard-sphere colloidal glasses

NASA Astrophysics Data System (ADS)

We perform a series of deformation experiments on a monodisperse, hard-sphere colloidal glass while simultaneously following the three-dimensional trajectories of roughly 50000 individual particles with a confocal microscope. In each experiment, we deform the glass in pure shear at a constant strain rate [(1-5)×10-5 s-1] to maximum macroscopic strains (5%-10%) and then reverse the deformation at the same rate to return to zero macroscopic strain. We also measure three-dimensional particle trajectories in an identically prepared quiescent glass in which the macroscopic strain is always zero. We find that shear transformation zones exist and are active in both sheared and quiescent colloidal glasses, revealed by a distinctive fourfold signature in spatial autocorrelations of the local shear strain. With increasing shear, the population of local shear transformations develops more quickly than in a quiescent glass and many of these transformations are irreversible. When the macroscopic strain is reversed, we observe partial elastic recovery, followed by plastic deformation of the opposite sign, required to compensate for the irreversibly transformed regions. The average diameter of the shear transformation zones in both strained and quiescent glasses is slightly more than two particle diameters.

Jensen, K. E.; Weitz, D. A.; Spaepen, F.

2014-10-01

170

Coherent crystallography of shear-aligned crystals of hard-sphere colloids

The structure of colloidal crystals formed from suspensions of hard-sphere colloids is studied. The samples are contained in a thin cell. By rocking the samples, we are able to form shear-aligned colloidal crystals with extended, long-range order. The aligned crystals persist after the shear ceases, enabling us to use laser-light crystallography to determine their structure. We observe an unusual ordering, wherein the structure is a nearly perfect single twin of a face-centered cubic crystal, with crystals of different twins formed on each side of the cell. We exploit the coherence of the laser source to observe a specklelike fluctuation of the intensity in the Bragg peaks. However, this fluctuation occurs only in one scattering direction, and therefore reflects a remnant disorder in the stacking of the hcp planes. We introduce a simple model which accounts for both the nature of the disorder in the stacking as well as the specklelike fluctuations. Our observation of this speckle also confirms recent predictions.

Liu, J. (Department of Physics, California State University at Long Beach, Long Beach, California 90840 (United States)); Weitz, D.A. (Exxon Research and Engineering Co., Route 22E, Annandale, New Jersey 08801 (United States)); Ackerson, B.J. (Department of Physics, Oklahama State University, Stillwater, Oklahoma 74078 (United States))

1993-08-01

171

Local shear transformations in deformed and quiescent hard-sphere colloidal glasses.

We perform a series of deformation experiments on a monodisperse, hard-sphere colloidal glass while simultaneously following the three-dimensional trajectories of roughly 50,000 individual particles with a confocal microscope. In each experiment, we deform the glass in pure shear at a constant strain rate [(1-5)×10(-5) s(-1)] to maximum macroscopic strains (5%-10%) and then reverse the deformation at the same rate to return to zero macroscopic strain. We also measure three-dimensional particle trajectories in an identically prepared quiescent glass in which the macroscopic strain is always zero. We find that shear transformation zones exist and are active in both sheared and quiescent colloidal glasses, revealed by a distinctive fourfold signature in spatial autocorrelations of the local shear strain. With increasing shear, the population of local shear transformations develops more quickly than in a quiescent glass and many of these transformations are irreversible. When the macroscopic strain is reversed, we observe partial elastic recovery, followed by plastic deformation of the opposite sign, required to compensate for the irreversibly transformed regions. The average diameter of the shear transformation zones in both strained and quiescent glasses is slightly more than two particle diameters. PMID:25375492

Jensen, K E; Weitz, D A; Spaepen, F

2014-10-01

172

The power of simple hard-sphere models in protein structure prediction

NASA Astrophysics Data System (ADS)

There are several force-fields that are currently used to describe the potential energy of biological macromolecules such as proteins. These typically include many parameters, derived from a combination of statistical, experimental sources. These work on average to describe a protein, but the large number of parameters moves this description further away from a true physical understanding than is desirable. Our approach is to investigate to what extent simple hard sphere models can be used to model and predict the behavior of different aspects of protein structure. We present the results of specific calculations. The distributions of the side-chain dihedral angle chi1 of Val and Thr in proteins of known structure show distinctive features: Val side chains predominantly adopt dihedral angle, chi1, of 180, whereas Thr side chains typically adopt a dihedral angle, chi1, of 60 or 300. Several hypotheses have been proposed to explain these differences, including inter-residue steric clashes and hydrogen-bonding interactions. In contrast, we show that the observed side-chain dihedral angle distributions for both Val and Thr can be explained using only local steric interactions in a dipeptide mimetic. Our results emphasize the power of a simple physics-based approaches and their importance for future advances in protein engineering and design.

Regan, Lynne

2012-02-01

173

A series of density-controlled graphene oxide-coated mesoporous silica spheres (GO/SiO2) are successfully synthesized to investigate the influence of the particle density on electrorheological (ER) activity. The particle density of mesoporous silica spheres is controlled by creating different sized pores via surfactant template and swelling agent incorporation method. Additionally, ball-milled graphene oxide is successfully coated onto the surface of various silica spheres (SiO2) through amine-modification to enhance ER efficiency. In this study, we investigate that mesoporous silica spheres-based ER fluid (GO/epSiO2) with lowest particle density exhibit most increased ER performance, which is 3-fold higher than that of similar sized neat silica spheres-based ER fluid (GO/nSiO2) without pore. In addition, the relationship between particle density, anti-sedimentation property, and ER performance is examined by applying Stokes' law and practical sedimentation observation. Furthermore, dielectric loss model is used to clarify the influence of dielectric property on ER activity. This newly designed ER study offers insight into the influence of the particle density on the performance of ER fluids. PMID:25454420

Yoon, Chang-Min; Lee, Seungae; Hong, Seung Hee; Jang, Jyongsik

2015-01-15

174

Fabrication of thin-wall hollow nickel spheres and low density syntactic foams

A process has been developed to fabricate thin-wall hollow spheres from conventional oxide powders at room temperature. The polymer- bonded powder shells are fired in air to sinter the walls, leaving the shells either impervious or porous. Alternatively, the oxide shells can be preferentially reduced to produce thin-wall hollow metal spheres which can be bonded together to produce an ultra light weight closed-cell foam. Processing and properties of this class of low density structures will be discussed.

Clancy, R.B.; Sanders, T.H. Jr.; Cochran, J.K.

1991-12-31

175

We perform molecular dynamics simulations to compress binary hard spheres into jammed packings as a function of the compression rate $R$, size ratio $\\alpha$, and number fraction $x_S$ of small particles to determine the connection between the glass-forming ability (GFA) and packing efficiency in bulk metallic glasses (BMGs). We define the GFA by measuring the critical compression rate $R_c$, below which jammed hard-sphere packings begin to form "random crystal" structures with defects. We find that for systems with $\\alpha \\gtrsim 0.8$ that do not de-mix, $R_c$ decreases strongly with $\\Delta \\phi_J$, as $R_c \\sim \\exp(-1/\\Delta \\phi_J^2)$, where $\\Delta \\phi_J$ is the difference between the average packing fraction of the amorphous packings and random crystal structures at $R_c$. Systems with $\\alpha \\lesssim 0.8$ partially de-mix, which promotes crystallization, but we still find a strong correlation between $R_c$ and $\\Delta \\phi_J$. We show that known metal-metal BMGs occur in the regions of the $\\alpha$ and $x_S$ parameter space with the lowest values of $R_c$ for binary hard spheres. Our results emphasize that maximizing GFA in binary systems involves two competing effects: minimizing $\\alpha$ to increase packing efficiency, while maximizing $\\alpha$ to prevent de-mixing.

Kai Zhang; W. Wendell Smith; Minglei Wang; Yanhui Liu; Jan Schroers; Mark D. Shattuck; Corey S. O'Hern

2014-04-02

176

NASA Astrophysics Data System (ADS)

We perform molecular dynamics simulations to compress binary hard spheres into jammed packings as a function of the compression rate R, size ratio ?, and number fraction xS of small particles to determine the connection between the glass-forming ability (GFA) and packing efficiency in bulk metallic glasses (BMGs). We define the GFA by measuring the critical compression rate Rc, below which jammed hard-sphere packings begin to form "random crystal" structures with defects. We find that for systems with ? ?0.8 that do not demix, Rc decreases strongly with ??J, as Rc˜exp(-1/??J2), where ??J is the difference between the average packing fraction of the amorphous packings and random crystal structures at Rc. Systems with ? ?0.8 partially demix, which promotes crystallization, but we still find a strong correlation between Rc and ??J. We show that known metal-metal BMGs occur in the regions of the ? and xS parameter space with the lowest values of Rc for binary hard spheres. Our results emphasize that maximizing GFA in binary systems involves two competing effects: minimizing ? to increase packing efficiency, while maximizing ? to prevent demixing.

Zhang, Kai; Smith, W. Wendell; Wang, Minglei; Liu, Yanhui; Schroers, Jan; Shattuck, Mark D.; O'Hern, Corey S.

2014-09-01

177

We perform molecular dynamics simulations to compress binary hard spheres into jammed packings as a function of the compression rate R, size ratio ?, and number fraction x(S) of small particles to determine the connection between the glass-forming ability (GFA) and packing efficiency in bulk metallic glasses (BMGs). We define the GFA by measuring the critical compression rate R(c), below which jammed hard-sphere packings begin to form "random crystal" structures with defects. We find that for systems with ??0.8 that do not demix, R(c) decreases strongly with ??(J), as R(c)?exp(-1/??(J)(2)), where ??(J) is the difference between the average packing fraction of the amorphous packings and random crystal structures at R(c). Systems with ??0.8 partially demix, which promotes crystallization, but we still find a strong correlation between R(c) and ??(J). We show that known metal-metal BMGs occur in the regions of the ? and x(S) parameter space with the lowest values of R(c) for binary hard spheres. Our results emphasize that maximizing GFA in binary systems involves two competing effects: minimizing ? to increase packing efficiency, while maximizing ? to prevent demixing. PMID:25314450

Zhang, Kai; Smith, W Wendell; Wang, Minglei; Liu, Yanhui; Schroers, Jan; Shattuck, Mark D; O'Hern, Corey S

2014-09-01

178

Fractal Weyl law for three-dimensional chaotic hard-sphere scattering systems.

The fractal Weyl law connects the asymptotic level number with the fractal dimension of the chaotic repeller. We provide the first test for the fractal Weyl law for a three-dimensional open scattering system. For the four-sphere billiard, we investigate the chaotic repeller and discuss the semiclassical quantization of the system by the method of cycle expansion with symmetry decomposition. We test the fractal Weyl law for various symmetry subspaces and sphere-to-sphere separations. PMID:21230359

Eberspächer, Alexander; Main, Jörg; Wunner, Günter

2010-10-01

179

Casein micelles as hard spheres: limitations of the model in acidified gel formation

In many situations casein micelles can be treated as adhesive spheres and milk gels are often considered as particle gels. In this study of acidified milk gels, produced over a wide range of acidification conditions using glucono-?-lactone as acidulant, we show that adhesive sphere and particle gel theories are of limited applicability. Internal micellar integrity and the rates of change

David S Horne

2003-01-01

180

NASA Astrophysics Data System (ADS)

Results are presented from our simulation study of flexible, tangent hard-sphere polymer chains, using a Monte Carlo technique with a reptation algorithm. We examine the crossover region from the swollen (dilute) region to the semidilute regime using chains of degree up to N=2000. The (average) chain end-to-end distance is analyzed as a function of the number of chain links, as is a correlation function for the internal separation of segments, expressed in terms of their connectivity. We study the structure of the polymer chains using scattering functions, which are presented in addition to the segment-segment distribution functions from which they are calculated. Not surprisingly, the Flory exponent ? changes gradually from the dilute value of ??0.59 to ?1/2 at high density. We find that for chains of 2000 segments, this transition begins at the very low molecular volume fraction of about 0.1%. An analysis of the correlation function for internal segments provides a similar but more detailed picture, in that the role of the screening length ? becomes explicit. The pair distribution and scattering functions in the swollen, crossover, and melt regions are determined and the scaling behavior is reexamined in the context of these functions. The system considered will form a reference system for subsequent studies in which the model will be broadened to include a network and/or attractive interactions. In this paper we seek first of all to establish that reference, and to relate our work to previous studies in this area of interest. As an important technical point, we also note that the use of an inappropriate random number generator can cause the complete failure of simulations of this type.

Haslam, Andrew J.; Jackson, George; McLeish, Tom C. B.

1999-07-01

181

A new Monte Carlo method to study the fluid-solid phase transition of polydisperse hard spheres

A new Monte Carlo approach is proposed to investigate the fluid-solid phase transition of the polydisperse system. By using the extended ensemble, a reversible path was constructed to link the monodisperse and corresponding polydisperse system. Once the fluid-solid coexistence point of the monodisperse system is known, the fluid-solid coexistence point of the polydisperse system can be obtained from the simulation. The validity of the method is checked by the simulation of the fluid-solid phase transition of a size-polydisperse hard sphere colloid. The results are in agreement with the previous studies.

Mingcheng Yang; Hongru Ma

2008-07-04

182

NASA Astrophysics Data System (ADS)

In the Brazil nut problem (BNP), hard spheres with larger diameters rise to the top. In a previous paper, a theory was presented for the crossover from BNP to the reverse Brazil nut problem (RBNP) using a relationship between the mass and diameter ratios of the different species of particles. In this paper, we investigate the effects of the inital layer number and the geometry of the container on the segregation of particles. New crossover conditions are determined for these parameters, and the theoretical predictions are compared to Molecular Dynamics simulations in two and three dimensions.

Quinn, Paul V.; Hong, Daniel C.; Luding, Stefan

2002-03-01

183

NASA Astrophysics Data System (ADS)

The fourth virial coefficient of additive hard-sphere mixtures, as predicted by the Percus-Yevick (PY) and hypernetted-chain (HNC) theories, is derived via the compressibility, virial, and chemical-potential routes, the outcomes being compared with exact results. Except in the case of the HNC compressibility route, the other five expressions exhibit a common structure involving the first three moments of the size distribution. In both theories, the chemical-potential route is slightly better than the virial one and the best behavior is generally presented by the compressibility route. Moreover, the PY results with any of the three routes are more accurate than any of the HNC results.

Beltrán-Heredia, Elena; Santos, Andrés

2014-04-01

184

NASA Astrophysics Data System (ADS)

In the mode-coupling approximation, we consider the transition to the glass state in a system of collapsing hard spheres (a system with the hard-core potential to which a repulsive step is added). We propose an approximation for the structure factor of the system, which we use to construct the phase diagram of the transition to the glass state. We show that there exists a maximum on the liquid-glass curve corresponding to the reentrant transition to the glass state in the system. In the framework of the proposed model, we consider bifurcations of solutions of the equations describing the transition to the glass state and show that there exist bifurcations of the "swallow-tail" type corresponding to the glass-glass transition.

Ryzhov, V. N.; Tareyeva, E. E.; Fomin, Yu. D.

2011-05-01

185

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

NASA Astrophysics Data System (ADS)

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. EPLEEE81539-375510.1103/PhysRevE.82.061302 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.

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

2013-08-01

186

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

Boda, Dezs?; Henderson, Douglas; Eisenberg, Bob; Gillespie, Dirk

2011-01-01

187

NASA Astrophysics Data System (ADS)

Measurements are reported of the diffusion constant D(T) for xenon gas, in the form of the radioisotope 133Xe, through liquid n-octane, n-decane, and n-tetradecane, in the range 10-40 °C. The values range from D (10.0 °C, Xe?n-C14H30)=1.32×10-5 cm2/s to D (40.0 °C, Xe?n-C8H18)=6.02×10-5 cm2/s. A new experimental method is used in which D is obtained by monitoring the decrease in concentration as gas diffuses into the liquid in an effectively one-dimensional geometry. As expected, the results do not agree with the Stokes-Einstein law. They do follow the usual correlation D?p=AT, with p=0.708 and A=9.80×10-8, where ? is the liquid viscosity in centipoises and T is in K. Application to these results of the rough-hard-sphere theory of diffusion is discussed. A quantitative analysis cannot be made until molecular dynamics results for smooth-hard-sphere diffusion are available.

Pollack, Gerald L.; Kennan, Richard P.; Himm, Jeffrey F.; Stump, Daniel R.

1990-01-01

188

NASA Astrophysics Data System (ADS)

We obtain ab-initio estimations of the dynamic structure factor, S(q,?), of Bose gases at zero temperature. More precisely, we use the Genetic Inversion via Falsification of Theories (GIFT) algorithm to perform analytic continuations of imaginary time correlation functions computed via an exact Path Integral projector method. Using the hard-sphere potential to model the two-body interactions between the atoms, we compute S(q,?) changing the gas parameter from the dilute regime (na3 = 10-4) up to the density corresponding to superfluid 4He at equilibrium (na3 = 0.2138). With increasing density, we observe the emergence of a broad multiphonon contribution accompanying the quasiparticle peak and a crossover of the dispersion of elementary excitations from a Bogoliubov-like spectrum to a phonon-maxon- roton curve. Apart from the low wave vector region, for na3 = 0.2138 the energy-momentum dispersion relation and the static density response function, ?(q), turns out to be in good agreement with the superfluid 4He experimental data at equilibrium density.

Rota, R.; Tramonto, F.; Galli, D. E.; Giorgini, S.

2014-08-01

189

Nanopatterned ferroelectrics for ultrahigh density rad-hard nonvolatile memories.

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.

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

2010-09-01

190

Calculation of the interfacial free energy of a binary hard-sphere fluid at a planar hard wall

+ ?2, (3) where ? i is the number density of species i. Without loss of generality, we assume ? 1 > ? 2. The mole fraction of each species is xi = ? i/?, with x1 + x2 = 1. The total packing frac- tion ? for the mixture is ? = ?1 + ?2, where ?i = ?6 ? 3... the integration of Eq. (16) is also quite small, so the scatter in 0 0.1 0.2 0.3 0.4 0.5 ? -0.02 0 ? 1 |N ? 12 x1 = 0.75 x1 = 0.50 x1 = 0.25 ? = 0.7 FIG. 5. Interfacial excess particle number 1|N as a function of packing frac- tion for the ? = 0.7 systems...

Kern, Jesse L.; Laird, Brian Bostian

2014-01-08

191

Disappearance of a stacking fault in the hard-sphere crystal under gravity, such as reported by Zhu et al. [Nature 387 (1997) 883], has successfully been demonstrated by Monte Carlo simulations. We previously found that a less ordered (or defective) crystal formed above a bottom ordered crystal under stepwise controlled gravity [Mori et al. J. Chem. Phys. 124 (2006) 174507]. A defect in the upper defective region has been identified with a stacking fault for the (001) growth. We have looked at the shrinking of a stacking fault mediated by the motion of the Shockley partial dislocation; the Shockley partial dislocation terminating the lower end of the stacking fault glides. In addition, the presence of crystal strain, which cooperates with gravity to reduce stacking faults, has been observed.

Atsushi Mori; Yoshihisa Suzuki; Shin-ichiro Yanagiya; Tsutomu Sawada; Kensaku Ito

2006-06-26

192

NASA Astrophysics Data System (ADS)

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.

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

2015-01-01

193

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

Mikko Haataja; László Gránásy; Hartmut Löwen

2010-01-01

194

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

NASA Technical Reports Server (NTRS)

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.

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

1996-01-01

195

NASA Astrophysics Data System (ADS)

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 ? of the particle. Moreover, the collision rules couple v and ?, involving not only the coefficient of normal restitution ? but also the coefficient of tangential restitution ?. 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 ? and ? (? being the mean angular velocity). The three coefficients in F and M are fixed to reproduce the Boltzmann collisional rates of change of ? 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 ? and ? on the shear and normal stresses and on the translational velocity distribution function is analyzed.

Santos, Andrés

2011-05-01

196

Nature of the divergence in low shear viscosity of colloidal hard-sphere dispersions Zhengdong 2002 Measurements of the low-shear viscosity o with a Zimm-Crothers viscometer for dispersions not capture the divergence. However, the nonhydrodynamic contribution to the relative viscosity o

Weeks, Eric R.

197

On the thermodynamics of hard spheres near a soft repulsive wall

We extend the variational method based on the Gibbs-Bogolioubov inequality to the case of fluids against a wall. We investigate the influence of the softness of the wall on the free energy of the system. For small packing fraction we consider a density expansion. The variational results are compared with the exact ones which are given by a direct expansion

J.-P. Badiali; M.-E. Boudh-Hir

1984-01-01

198

NASA Astrophysics Data System (ADS)

In a recent paper [Phys. Rev. EPRESCM1539-375510.1103/PhysRevE.86.040102 86, 040102(R) (2012)], Santos presented a self-consistency condition that can be used to limit the possible forms of fundamental measure theory. Here, the direct correlation function, resulting from the Santos functional, is derived, and it is found to be very close to the result of the White Bear density functional, except near the origin where it diverges.

Lutsko, James F.

2013-01-01

199

NASA Technical Reports Server (NTRS)

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.

Woo, Myeung-Jouh; Greber, Isaac

1995-01-01

200

NASA Astrophysics Data System (ADS)

We present a comprehensive study of the solidification scenario in suspensions of colloidal hard spheres for three polydispersities between 4.8% and 5.8%, over a range of volume fractions from near freezing to near the glass transition. From these results, we identify four stages in the crystallization process: (i) an induction stage where large numbers of precursor structures are observed, (ii) a conversion stage as precursors are converted to close packed structures, (iii) a nucleation stage, and (iv) a ripening stage. It is found that the behavior is qualitatively different for volume fractions below or above the melting volume fraction. The main effect of increasing polydispersity is to increase the duration of the induction stage, due to the requirement for local fractionation of particles of larger or smaller than average size. Near the glass transition, the nucleation process is entirely frustrated, and the sample is locked into a compressed crystal precursor structure. Interestingly, neither polydispersity nor volume fraction significantly influences the precursor stage, suggesting that the crystal precursors are present in all solidifying samples. We speculate that these precursors are related to the dynamical heterogeneities observed in a number of dynamical studies.

Schöpe, Hans Joachim; Bryant, Gary; van Megen, William

2007-08-01

201

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

NASA Astrophysics Data System (ADS)

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

Monti, F.; Schweizer, J.

2012-04-01

202

Hardness and density distributions of pharmaceutical tablets measured by terahertz pulsed imaging.

We present terahertz pulsed imaging (TPI) as a novel tool to quantify the hardness and surface density distribution of pharmaceutical tablets. Good agreement between the surface refractive index (SRI) measured by TPI and the crushing force measured from diametral compression tests was found using a set of tablets that were compacted at various compression forces. We also found a strong correlation between TPI results and tablet bulk density, and how these relate to tablet hardness. Numerical simulations of tablet surface density distribution by finite element analysis exhibit excellent agreement with the TPI measured SRI maps. These results show that TPI has an advantage over traditional diametral compression and is more suitable for nondestructive hardness and density distribution monitoring and control of pharmaceutical manufacturing processes. PMID:23609052

May, Robert K; Su, Ke; Han, Lianghao; Zhong, Shuncong; Elliott, James A; Gladden, Lynn F; Evans, Mike; Shen, Yaochun; Zeitler, J Axel

2013-07-01

203

NASA Technical Reports Server (NTRS)

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.

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

1998-01-01

204

Flow-induced instabilities that lead to non-uniform stationary flow profiles have been observed in many different soft-matter systems. Two types of instabilities that lead to banded stationary states have been identified, which are commonly referred to as gradient- and vorticity-banding. The molecular origin of these instabilities is reasonably well understood. A third type of instability that has been proposed phenomenologically [Europhys. Lett., 1986, 2, 129 and Phys. Rev. E, 1995, 52, 4009] is largely unexplored. Essential to this "Shear-gradient Concentration Coupling" (SCC-) instability is a mass flux that is induced by spatial gradients of the shear rate. A possible reason that this instability has essentially been ignored is that the molecular origin of the postulated mass flux is not clear, and no explicit expressions for the shear-rate and concentration dependence of the corresponding transport coefficient exist. It is therefore not yet known what types of flow velocity- and concentration-profiles this instability gives rise to. In this paper, an expression for the transport coefficient corresponding to the shear-gradient induced mass flux is derived in terms of the shear-rate dependent pair-correlation function, and Brownian dynamics simulations for hard-spheres are presented that specify the shear-rate and concentration dependence of the pair-correlation function. This allows to explicitly formulate the coupled advection-diffusion equation and an equation of motion for the suspension flow velocity. The inclusion of a non-local contribution to the stress turns out to be essential to describe the SCC-banding transition. The coupled equations of motion are solved numerically, and flow- and concentration-profiles are discussed. It is shown that the SCC-instability occurs within the glass state at sufficiently small shear rates, leading to a banded flow-profile where one of the bands is non-flowing. PMID:25346243

Jin, Howon; Kang, Kyongok; Ahn, Kyung Hyun; Dhont, Jan K G

2014-12-21

205

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

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

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

2014-08-01

206

DENSITY PROFILES OF SEMI-DILUTE POLYMER SOLUTIONS NEAR A HARD WALL: MONTE CARLO SIMULATION

169 DENSITY PROFILES OF SEMI-DILUTE POLYMER SOLUTIONS NEAR A HARD WALL: MONTE CARLO SIMULATION WAN of Washington, Seattle, WA 98195 Introduction A semi-dilute polymer solution is one in which polymers overla1p. The bulk properties of semi-dilute polymer solutions have been studied extensively - and much has been

Aksay, Ilhan A.

207

Single-crystal silicon MEMS microactuator for high-density hard disk drive

A single crystal silicon MEMS microactuator for high density hard disk drives is described in this paper. The microactuator is located between a slider and a suspension, and drives the slider on which a magnetic head is attached. The MEMS actuator is fabricated by improved LISA process. It has an electrically isolated 20:1 (40micrometers thick, 2micrometers width) high aspect ratio

Jianqiang Mou; Shixin Chen; Yi Lu

2001-01-01

208

Fluids in contact with a hard surface: University of the bridge functions for the density profile

NASA Astrophysics Data System (ADS)

The modified hypernetted chain theory (MHNC) for density profiles of fluids in contact with a hard, smooth surface is found to possess a remarkably simple and interesting property: The accuracy of the MHNC and the universality of the bridge functions for the density profiles can be tested without resort to any detailed solution of the integral equations. It is given by the degree of universality of the bulk bridge parameter when expressed in terms of the second partial derivative of the free energy with respect to a certain density equation. This function (F) as obtained from MHNC calculations for bulk simple fluids is found to be remarkably independent of the pair potential. As an example for the accuracy of the resulting method, the one component plasma near a hard wall is discussed.

Rosenfeld, Y.; Blum, L.

1986-05-01

209

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

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)

Zhang, Miao; Du, Yonghui; Gao, Lili [Department of Physics, Beihua University, Jilin 132013 (China)] [Department of Physics, Beihua University, Jilin 132013 (China); Lu, Mingchun [Department of Aeronautical Engineering Professional Technology, Jilin Institute of Chemical Technology, Jilin 132102 (China)] [Department of Aeronautical Engineering Professional Technology, Jilin Institute of Chemical Technology, Jilin 132102 (China); Lu, Cheng [Department of Physics, Nanyang Normal University, Nanyang 473061 (China)] [Department of Physics, Nanyang Normal University, Nanyang 473061 (China); Liu, Hanyu, E-mail: hal420@mail.usask.ca [Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5E2 (Canada)] [Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5E2 (Canada)

2014-05-07

210

Steel and titanium hollow sphere foams

Metal hollow sphere foams are fabricated by bonding millimeter sized metal alloy hollow spheres at points of contact. The spheres are formed as powder shells from slurries. For stainless steel spheres, the starting powder is a mixture of iron and chromium oxide. Thermal treatment in hydrogen reduces the oxides to Fe/Cr alloys with less than 2% porosity in sphere walls. The nominal composition is close to that of 405 stainless. Carburization in CO/CO{sub 2} atmosphere followed by heat treatment produces foams of either 410 or 420 type stainless steels depending on carbon content. Compressive stress-strain behavior was measured on point contact bonded stainless foams both before and after carburization. Hardness measurements on steel sphere walls were used to estimate the yield strength. Relative strengths of the foams were positioned between open and closed cell models. This was encouraging because bonding in the foams was less than optimum and the hollow sphere walls contained defects. As processing improves, strengths should increase. To produce titanium alloy spheres, the starting powder is titanium alloy hydride. Thermal treatment in an inert atmosphere decomposes the hydride and sinters the titanium powder in the sphere walls to greater than 96% relative density. Both titanium and Ti-6V-4V spheres and foams have been produced. Oxygen contents are a concern for titanium compositions and processing is being altered to reduce oxygen levels to increase ductility.

Hurysz, K.M.; Clark, J.L.; Nagel, A.R.; Lee, K.J.; Cochran, J.K.; Sanders, T.H. Jr. [Georgia Inst. of Tech., Atlanta, GA (United States); Hardwicke, C.U. [General Electric Corp., Schenectady, NY (United States). Physical Metallurgy Lab.

1998-12-31

211

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

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.

Dobronravov, V.F.

1985-01-01

212

NASA Technical Reports Server (NTRS)

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.

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

213

increased surface hardness on two of the 11 rating dates. When the rate was increased to 7.5 g kg 1 , significant This study was conducted to determine the effect of various types increases in surface hardness were reported on eight of and rates of soil reinforcing materials on soil bulk density, soil water the 11 rating dates. During dry

A. S. McNitt; P. J. Landschoot

2003-01-01

214

In this paper, we have successfully identified the triangular-shaped defect structures with stacking fault tetrahedra. These structure often appeared in hard-sphere (HS) crystals grown on a square pattern under gravity. We have, so far, performed Monte Carlo simulations of the HS crystals under gravity. Single stacking faults as observed previously in the HS crystals grown on a flat wall were not seen in the case of square template. Instead, defect structures with triangular appearance in $xz$- and $yz$- projections were appreciable. We have identified them by looking layer by layer. Those structures are surrounded by stacking faults along face-centered cubic (fcc) {111}. Also, we see isolated vacancies and vacancy-interstitial pairs, and we have found octahedral structures surrounded by stacking faults along fcc {111}.

Atsushi Mori; Yoshihisa Suzuki

2014-06-30

215

NASA Astrophysics Data System (ADS)

The equation of state (EOS) for hard-sphere fluid derived from compressibility routes of Percus-Yevick theory (PYC) is extended. The two parameters are determined by fitting well-known virial coefficients of pure fluid. The extended cubic EOS can be directly extended to multi-component mixtures, merely demanding the EOS of mixtures also is cubic and combining two physical conditions for the radial distribution functions at contact (RDFC) of mixtures. The calculated virial coefficients of pure fluid and predicted compressibility factors and RDFC for both pure fluid and mixtures are excellent as compared with the simulation data. The values of RDFC for mixtures with extremely large size ratio 10 are far better than the BGHLL expressions in literature.

Sun, Jiu-Xun; Jin, Ke; Cai, Ling-Cang; Wu, Qiang

2014-08-01

216

NASA Technical Reports Server (NTRS)

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

Nemeth, Noel

2013-01-01

217

a fundamental measure density functional theory we investigate both bulk and inhomogeneous systems of the binary in the electronic version) 1. Introduction Liquids can consist of a mixture of components which in molecular systems particles with differing shapes or sizes, or mixtures of colloids and non-adsorbing polymer. Besides gas

Schmidt, Matthias

218

acting on particles of species i. The ideal a)Electronic mail: hendrik.hansen-goos@yale.edu. gas part of the inhomogeneous SHS fluid SHS is uniquely defined when (a) it is solely a function of the weighted densities from

Wettlaufer, John S.

219

Expansion-free evolving spheres must have inhomogeneous energy density distributions

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.

Herrera, L. [Escuelade Fisica Facultadde Ciencias, Universidad Central de Venezuela, Caracas (Venezuela, Bolivarian Republic of); Le Denmat, G. [LERMA-PVI, Universite Paris 06, Observatoire de Paris, CNRS, 3 rue Galilee, Ivry sur Seine 94200 (France); Santos, N. O. [LERMA-PVI, Universite Paris 06, Observatoire de Paris, CNRS, 3 rue Galilee, Ivry sur Seine 94200 (France); Laboratorio Nacional de Computacao Cientifica, 25651-070 Petropolis Rio de Janeiro (Brazil)

2009-04-15

220

NASA Astrophysics Data System (ADS)

We present in this paper a general analytical solution to the integral equations of liquid state theories (Born-Green-Yvon, hyper-netted-chain, and Percus-Yevick Equations) at low-density limit for potentials with a hard core. For the specific case of the Lennard-Jones potential with a hard core, we have derived an analytical function for the radial distribution function at high temperature and low density. We have noted that this function has two humps which is the characteristic feature of the radial distribution function at low densities. In addition, this function has been used to calculate the third virial coefficient for such a fluid exactly. We see that for the especial case of Lennard-Jones fluid with a hard core, which its radial distribution function has explicitly been calculated at high temperatures, the correct behavior of the third virial coefficient with temperature is obtained. The magnitude of hard-core diameter has significant effect on the thermodynamic properties of fluid: for instance, when the diameter changes only by a few percent the third virial coefficient may change more than 100%. The hard-core diameter decreases when temperature increases. The reduction is less than 20%. For the supercritical fluid, the calculated compression factor and internal energy are in good agreement with those obtained from the simulation for the Lennard-Jones fluid.

Khanpour, Mehrdad; Parsafar, G. A.; Najafi, B.

2004-05-01

221

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.

Sun, K.

2011-05-04

222

The First Hard X-Ray Power Spectral Density Functions of Active Galactic Nucleus

NASA Astrophysics Data System (ADS)

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 ~ - 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.

Shimizu, T. Taro; Mushotzky, Richard F.

2013-06-01

223

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

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.

Shimizu, T. Taro; Mushotzky, Richard F., E-mail: tshimizu@astro.umd.edu [Department of Astronomy, University of Maryland, College Park, MD 20742 (United States)

2013-06-10

224

Single-crystal silicon MEMS microactuator for high-density hard disk drive

NASA Astrophysics Data System (ADS)

A single crystal silicon MEMS microactuator for high density hard disk drives is described in this paper. The microactuator is located between a slider and a suspension, and drives the slider on which a magnetic head is attached. The MEMS actuator is fabricated by improved LISA process. It has an electrically isolated 20:1 (40micrometers thick, 2micrometers width) high aspect ratio structure directly processed from a single crystal silicon substrate. The overall dimension of the micro-actuator is 1.4mm by 1.4mm and by a thickness of 0.15mm. Experiments show that +/- 0.6 micrometers displacement stroke of the Read/Write magnetic head, which is attached on the MEMS actuator, can be achieved when input voltage is 40V. The dynamic performances of the MEMS actuator integrated with a Head Gimbal Assembly (HGA) are analyzed by FEM Simulation. The simulation results demonstrated that the controllable in-plane resonance frequency of the MEMS actuator is 1.5 kHz, and the first uncontrollable out-of- plane resonance frequency of the MEMS actuator integrated with the HGA is 16.6kHz. The single crystal silicon microactuator has good shock reliability, and eliminates large material creep and thermal mismatch problems.

Mou, Jianqiang; Chen, Shixin; Lu, Yi

2001-11-01

225

Crystal growth rates in colloidal alloy crystallization of binary mixtures of monodispersed polystyrene and\\/or silica spheres\\u000a having different sizes and densities are studied in microgravity by parabolic flights of an aircraft. The crystal growth rates\\u000a are obtained by time-resolved reflection spectroscopy with a continuous circulating-type stopped-flow-cell system. The growth\\u000a rates of alloy crystallization increase substantially in microgravity up to about

T. Okubo; A. Tsuchida; S. Takahashi; K. Taguchi; M. Ishikawa

2000-01-01

226

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.

Sun, K. X.

2011-05-31

227

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) I·NHC 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

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

2013-01-01

228

Characterization of maximally random jammed sphere packings: Voronoi correlation functions

We characterize the structure of maximally random jammed (MRJ) sphere packings by computing the Minkowski functionals (volume, surface area, and integrated mean curvature) of their associated Voronoi cells. The probability distribution functions of these functionals of Voronoi cells in MRJ sphere packings are qualitatively similar to those of an equilibrium hard-sphere liquid and partly even to the uncorrelated Poisson point process, implying that such local statistics are relatively structurally insensitive. This is not surprising because the Minkowski functionals of a single Voronoi cell incorporate only local information and are insensitive to global structural information. To improve upon this, we introduce descriptors that incorporate nonlocal information via the correlation functions of the Minkowski functionals of two cells at a given distance as well as certain cell-cell probability density functions. We evaluate these higher-order functions for our MRJ packings as well as equilibrium hard spheres and the Poisson point process. We find strong anticorrelations in the Voronoi volumes for the hyperuniform MRJ packings, consistent with previous findings for other pair correlations [A. Donev et al., Phys. Rev. Lett. 95, 090604 (2005)], indicating that large-scale volume fluctuations are suppressed by accompanying large Voronoi cells with small cells, and vice versa. In contrast to the aforementioned local Voronoi statistics, the correlation functions of the Voronoi cells qualitatively distinguish the structure of MRJ sphere packings (prototypical glasses) from that of the correlated equilibrium hard-sphere liquids. Moreover, while we did not find any perfect icosahedra (the locally densest possible structure in which a central sphere contacts 12 neighbors) in the MRJ packings, a preliminary Voronoi topology analysis indicates the presence of strongly distorted icosahedra.

Michael Andreas Klatt; Salvatore Torquato

2015-01-03

229

NASA Technical Reports Server (NTRS)

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.

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

1986-01-01

230

A density functional theory is presented to study the effect of attractions on the structure of polymer solutions confined between surfaces. The polymer molecules have been modeled as a pearl necklace of freely jointed hard spheres and the solvent as hard spheres, both having Yukawa-type attractions and the mixture being confined between attractive Yukawa-type surfaces. The present theory treats the ideal gas free energy functional exactly and uses weighted density approximation for the hard chain and hard sphere contributions to the excess free energy functional. The attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions on the density profiles of the polymer and the solvent molecules are found to agree quite well with the Monte Carlo simulation results for varying densities, chain lengths, wall separations, and different sets of interaction potentials. PMID:17328632

Patra, Chandra N

2007-02-21

231

NASA Technical Reports Server (NTRS)

Energy-independent first-flight transport kernels are evaluated for a spherical region with an R(-2) density distribution. The uncollided angular-flux distribution is obtained and integrated for a source distribution that is proportional to the density to give the uncollided emitted particle flux and current density. These are useful for the calculation of mass, energy, and momentum carried away by fast particles born in the medium. The data are relevant to estimate escape from weakly bound atmospheres such as comet comae, dilute circumstellar envelopes, and some unconfined laboratory plasmas.

Huebner, W. F.; Keady, J. J.

1984-01-01

232

Improved association in a classical density functional theory for water

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.

Krebs, Eric J.; Schulte, Jeff B.; Roundy, David [Department of Physics, Oregon State University, Corvallis, Oregon 97331 (United States)] [Department of Physics, Oregon State University, Corvallis, Oregon 97331 (United States)

2014-03-28

233

Using a barley mapping population, 'Vlamingh' × 'Buloke' (V × B), whole grain analyses were undertaken for physical seed traits and malting quality. Grain density and size were predicted by digital image analysis (DIA), while malt extract and protein content were predicted using near infrared (NIR) analysis. Validation of DIA and NIR algorithms confirmed that data for QTL analysis was highly correlated (R (2) > 0.82), with high RPD values (the ratio of the standard error of prediction to the standard deviation, 2.31-9.06). Endosperm hardness was measured on this mapping population using the single kernel characterisation system. Grain density and endosperm hardness were significantly inter-correlated in all three environments (r > 0.22, P < 0.001); however, other grain components were found to interact with the traits. QTL for these traits were also found on different genomic regions, for example, grain density QTLs were found on chromosomes 2H and 6H, whereas endosperm hardness QTLs were found on 1H, 5H, and 7H. In this study, the majority of the genomic regions associated with grain texture were also coincident with QTLs for grain size, yield, flowering date and/or plant development genes. This study highlights the complexity of genomic regions associated with the variation of endosperm hardness and grain density, and their relationships with grain size traits, agronomic-related traits, and plant development loci. PMID:23884598

Walker, Cassandra K; Ford, Rebecca; Muñoz-Amatriaín, María; Panozzo, Joe F

2013-10-01

234

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

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

2001-01-01

235

NASA Astrophysics Data System (ADS)

We study the asymptotic behavior of the conserved densities deduced form the Lagrangian corresponding to the nonlinear two-dimensional Euler equations describing nonviscous incompressible fluid flows on a three-dimensional rotating spherical surface superimposed by a particular stationary latitude dependent flow. Under the assumption of no friction and a distribution of temperature dependent only upon latitude, the equations in question can be used to model zonal west-to-east flows in the upper atmosphere between the Ferrel and Polar cells. The conserved densities were analyzed and visualized by using the exact invariant solutions associated with the given model for the particular form of finite disturbances for which the invariant solutions are also exact solutions of Navier-Stokes equations.

Ibragimov, Ranis N.; Dameron, Michael; Dannangoda, Chamath

2014-06-01

236

Thermodynamics of quantum photon spheres

Photon spheres, surfaces where massless particles are confined in closed orbits, are expected to be common astrophysical structures surrounding ultracompact objects. In this paper a semiclassical treatment of a photon sphere is proposed. We consider the quantum Maxwell field and derive its energy spectra. A thermodynamic approach for the quantum photon sphere is developed and explored. Within this treatment, an expression for the spectral energy density of the emitted radiation is presented. Our results suggest that photon spheres, when thermalized with their environment, have nonusual thermodynamic properties, which could lead to distinct observational signatures.

M. C. Baldiotti; Walace S. Elias; C. Molina; Thiago S. Pereira

2014-10-07

237

NSDL National Science Digital Library

This learning object from Wisc-Online covers the sphere, examining the properties and components of the shape. The lesson uses the geometric formulas for finding the volume and surface area of the shape. Practice questions are also included.

Jensen, Douglas; Reed, Allen

2005-01-01

238

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

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.

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

1992-01-01

239

Kinetic density functional theory of freezing

NASA Astrophysics Data System (ADS)

A theory of freezing of a dense hard sphere gas is presented. Starting from a revised Enskog theory, hydrodynamic equations that account for non-local variations in the density but local variations in the flow field are derived using a modified Chapman Enskog procedure. These hydrodynamic equations, which retain structural correlations, are shown to be effectively a time dependent density functional theory. The ability of this theory to capture the solid liquid phase transition is established through analysis and numerical simulations.

Baskaran, Arvind; Baskaran, Aparna; Lowengrub, John

2014-11-01

240

Hard body amphiphiles at a hard wall JOSEPH M. BRADER1y

Hard body amphiphiles at a hard wall JOSEPH M. BRADER1y , CHRISTIAN VON FERBER2 and MATTHIAS 2003) We investigate the structure of amphiphilic molecules exposed to a substrate that is modelled by a hard wall. Our simple model amphiphiles consist of a hard sphere head group to which a vanishingly thin

Ott, Albrecht

241

NASA Astrophysics Data System (ADS)

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.

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

2001-09-01

242

NSDL National Science Digital Library

What is Density? Density is the amount of "stuff" in a given "space". In science terms that means the amount of "mass" per unit "volume". Using units that means the amount of "grams" per "centimeters cubed". Check out the following links and learn about density through song! Density Beatles Style Density Chipmunk Style Density Rap Enjoy! ...

Miss Witcher

2011-10-06

243

NSDL National Science Digital Library

What is density? Density is a relationship between mass (usually in grams or kilograms) and volume (usually in L, mL or cm 3 ). Below are several sights to help you further understand the concept of density. Click the following link to review the concept of density. Be sure to read each slide and watch each video: Chemistry Review: Density Watch the following video: Pop density video The following is a fun interactive sight you can use to review density. Your job is #1, to play and #2 to calculate the density of the ...

Mr. Hansen

2010-10-26

244

The objective of this study was to determine whether dietary boron (B) affects the strength, density and mineral composition of teeth and mineral density of alveolar bone in rabbits with apparent obesity induced by a high-energy diet. Sixty female, 8-month-old, New Zealand rabbits were randomly assigned for 7 months into five groups as follows: (1) control 1, fed alfalfa hay only (5.91MJ/kg and 57.5mgB/kg); (2) control 2, high energy diet (11.76MJ and 3.88mgB/kg); (3) B10, high energy diet+10mgB gavage/kg body weight/96h; (4) B30, high energy diet+30mgB gavage/kg body weight/96h; (5) B50, high energy diet+50mgB gavage/kg body weight/96h. Maxillary incisor teeth of the rabbits were evaluated for compression strength, mineral composition, and micro-hardness. Enamel, dentin, cementum and pulp tissue were examined histologically. Mineral densities of the incisor teeth and surrounding alveolar bone were determined by using micro-CT. When compared to controls, the different boron treatments did not significantly affect compression strength, and micro-hardness of the teeth, although the B content of teeth increased in a dose-dependent manner. Compared to control 1, B50 teeth had decreased phosphorus (P) concentrations. Histological examination revealed that teeth structure (shape and thickness of the enamel, dentin, cementum and pulp) was similar in the B-treated and control rabbits. Micro CT evaluation revealed greater alveolar bone mineral density in B10 and B30 groups than in controls. Alveolar bone density of the B50 group was not different than the controls. Although the B treatments did not affect teeth structure, strength, mineral density and micro-hardness, increasing B intake altered the mineral composition of teeth, and, in moderate amounts, had beneficial effects on surrounding alveolar bone. PMID:25468191

Hakki, Sema S; Malkoc, Siddik; Dundar, Niyazi; Kayis, Seyit Ali; Hakki, Erdogan E; Hamurcu, Mehmet; Baspinar, Nuri; Basoglu, Abdullah; Nielsen, Forrest H; Götz, Werner

2014-10-28

245

Sticky surface: sphere-sphere adhesion dynamics.

We present a multi-scale model to study the attachment of spherical particles with a rigid core, coated with binding ligands and suspended in the surrounding, quiescent fluid medium. This class of fluid-immersed adhesion is widespread in many natural and engineering settings, particularly in microbial surface adhesion. Our theory highlights how the micro-scale binding kinetics of these ligands, as well as the attractive/repulsive surface potential in an ionic medium affects the eventual macro-scale size distribution of the particle aggregates (flocs). The bridge between the micro-macro model is made via an aggregation kernel. Results suggest that the presence of elastic ligands on the particle surface lead to the formation of larger floc aggregates via efficient inter-floc collisions (i.e. non-zero sticking probability, g). Strong electrolytic composition of the surrounding fluid favours large floc formation as well. The kernel for the Brownian diffusion for hard spheres is recovered in the limit of perfect binding effectiveness (g?1) and in a neutral solution with no dissolved salts. PMID:25159830

Sircar, Sarthok; Younger, John G; Bortz, David M

2014-08-27

246

Numerical Investigation of Glassy Dynamics in Low-Density Systems Emanuela Zaccarelli,1

to this low-density (Wigner) glass transition share many features with their hard-sphere counterparts of intense scrutiny. Model systems often form the basis for detailed investigations that include the core fea, theoretical and computational studies of the glass transition [1Â3]. Many of the most interesting properties

Zaccarelli, Emanuela

247

Calculations of free energies in liquid and solid phases: Fundamental measure density, a theoretical description of the free energies and correlation functions of hard-sphere (HS) liquid and solid-Chandler-Andersen perturbation theory, free energies of liquid and solid phases with many interaction potentials can be obtained

Song, Xueyu

248

The Van-der-Waals Gas EOS for the Lorentz Contracted Spheres

The relativistic equation of state (EOS) of the Van-der-Waals gas is suggested and analyzed. In contrast to the usual case, the Lorentz contraction of the sphere's volume is taken into account. It is proven that the suggested EOS obeys the causality in the limit of high densities, i.e., the value of sound velocity of such a media is subluminar. The pressure obtained for the high values of chemical potential has an interesting kinetic interpretation. The suggested EOS shows that for high densities the most probable configuration corresponds to the smallest value of the relativistic excluded volume. In other words, for high densities the configurations with the collinear velocities of the neighboring hard core particles are the most probable ones. This, perhaps, may shed light on the coalescence process of any relativistic hard core constituents.

Kyrill A. Bugaev

2008-01-17

249

The van der Waals gas EOS for the Lorentz contracted rigid spheres

NASA Astrophysics Data System (ADS)

The relativistic equation of state (EOS) of the van der Waals gas is suggested and analyzed. In contrast to the usual case, the Lorentz contraction of the sphere's volume is taken into account. It is proven that the suggested EOS obeys the causality in the limit of high densities, i.e., the value of sound velocity of such a media is subluminar. The pressure obtained for the high values of chemical potential has an interesting kinetic interpretation. The suggested EOS shows that for high densities the most probable configuration corresponds to the smallest value of the relativistic excluded volume. In other words, for high densities the configurations with the collinear velocities of the neighboring hard core particles are the most probable ones. This, perhaps, may shed light on the coalescence process of any relativistic hard core constituents.

Bugaev, Kyrill A.

2008-07-01

250

Representative atomic and molecular systems, including various inorganic and organic molecules with covalent and ionic bonds, have been studied by using density functional theory. The calculations were done with the commonly used exchange-correlation functional B3LYP followed by a comprehensive analysis of the calculated highest-occupied and lowest-unoccupied Kohn-Sham orbital (HOMO and LUMO) energies. The basis set dependence of the DFT results

Chang-Guo Zhan; Jeffrey A. Nichols; David A. Dixon

2003-01-01

251

Specific surface area of overlapping spheres in the presence of obstructions

NASA Astrophysics Data System (ADS)

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.

Jenkins, D. R.

2013-02-01

252

Since their discovery by Milnor in 1956, exotic spheres have pro- vided a fascinating object of study for geometers. In this article we survey what is known about the curvature of exotic spheres. 1. Introduction Exotic spheres are manifolds which are homeomorphic but not diffeomorphic to a standard sphere. In this introduction our aims are twofold: First, to give a

M. Joachim; D. J. Wraith

2008-01-01

253

On the laser beam cutting of metallic hollow sphere structures

NASA Astrophysics Data System (ADS)

Metal hollow sphere structures (MHSS) represent a group of advanced composite materials. A high geometric reproducibility leads to relatively constant mechanical and physical properties. Therefore MHSS combine the advantages of cellular metals without a big scattering of the material properties. Several joining technologies can be used to assemble single metallic hollow spheres to a interdependent structure like sintering, soldering and adhering. This allows adjusting of variable macroscopic attitudes. A cutting process for MHSS needs to reflect the special characteristic of the composite material. In this paper laser beam cutting is presented as an efficient technology. The small amount of heat being involved during the process results in a small heat affected zone. All investigations were done with MHSS having different macroscopic dimensions (length, width, thickness, joining technology). The experimental work was done by a CO2-laser. The cut depth is governed by the heat input per unit length and the MHSS density. Finite element analysis was used to predict heat flux and temperature level for different geometric parameters of the spheres (diameter, wall thickness). The numerical simulation allows a detailed analysis of the physical process in the zone that is influenced by the laser beam and which can hardly be analysed by measuring technique. The models for the static and transient finite element analysis consider heat conduction and convection.

Riegel, H.; Fruhstuck, J.; Merkel, M.; Winkler, R.; Öchsner, A.

2013-02-01

254

Falling Spheres in Stratified Fluids

NASA Astrophysics Data System (ADS)

Low settling rates are observed for small particulate matter in strongly, stably stratified fluid. As the particle passes through an interface between two layers of fluid, it entrains lighter, upper fluid. The significance of this entrained fluid in the low Reynolds regime, along with a model for the behavior of the particle, has not yet been fully explored. We present careful measurements performed in stratified corn syrup showing the effects of the enhanced drag due to entrained fluid on the sphere at low Reynolds. We explore the theory for modeling sphere behavior and also discuss the hydrodynamics, which involve a strong coupling between the variable density fluid and moving solid boundary.

Lin, Joyce; Camassa, Roberto; Falcon, Claudia; McLaughlin, Richard

2008-11-01

255

Impulse Absorption by Tapered Alignments of Elastic Spheres

A numerical parametric study of 1D granular systems with Hertzian spheres is investigated. The relevant and always-repulsive interaction potential is nonlinearly dependent upon the overlap of adjacent grains. Specifically, we report our extensive investigation of two distinct systems and provide hard- sphere approximations as well as results from the numerical solution to the equations of motion. Chains can be characterized

Robert Doney; Surajit Sen

2005-01-01

256

NSDL National Science Digital Library

This web page introduces the concepts of density and buoyancy. The discovery in ancient Greece by Archimedes is described. The densities of various materials are given and temperature effects introduced. Links are provided to news and other resources related to mass density. This is part of the Vision Learning collection of short online modules covering topics in a broad range of science and math topics.

Day, Martha M.

2008-05-26

257

SPHERE MODEL FOR MOLTEN SEMICONDUCTORS AND SEMIMETALS B.R. Orton Physics Department, BruneZ University,2,3,4/ and the semimetals Ga /5,6,7/, Sn /2,8,10/, Sb /11,12,13,14/ and Bi /8,15,16/ give interference functions, I(K) (K semiconductors 1181 and semimetals /19/, 1201, /21/ contains the Â£0110- wing features. (a) The atoms

Paris-Sud XI, UniversitÃ© de

258

Local thermodynamic mapping for effective liquid density-functional theory

NASA Technical Reports Server (NTRS)

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.

Kyrlidis, Agathagelos; Brown, Robert A.

1992-01-01

259

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

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, Grüneisen 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

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

2014-07-01

260

Using the Clifford algebra formalism we extend the quantum jumps algorithm of the Event Enhanced Quantum Theory (EEQT) to convex state figures other than those stemming from convex hulls of complex projective spaces that form the basis for the standard quantum theory. We study quantum jumps on n-dimensional spheres, jumps that are induced by symmetric configurations of non-commuting state monitoring detectors. The detectors cause quantum jumps via geometrically induced conformal maps Moebius transformations) and realize iterated function systems (IFS) with fractal attractors located on n-dimensional spheres. We also extend the formalism to mixed states, represented by "density matrices" in the standard formalism, (the n-balls), but such an extension does not lead to new results, as there is a natural mechanism of purification of states. As a numerical illustration we study quantum fractals on the circle (one-dimensional sphere and pentagon), two-sphere (octahedron), and on three-dimensional sphere (hypercube-...

Jadczyk, A

2006-01-01

261

NASA Astrophysics Data System (ADS)

We investigate the effects of concavo-convex walls of a nanopore on the structure and certain thermodynamic properties of confined fluids. Adsorption, solvation force, and capillary condensation in a nanopore formed between two homocentric spheres will be determined using the MFMT. For hard sphere fluids, contact density is greater at the concave wall than it is at the convex wall. In Yukawa fluids, for the thermodynamic state in which the energy effect is the dominant factor, contact density at a concave wall is less than that at a convex wall; this will be reversed for the thermodynamic state in which the entropy effect is the dominant factor. It is possible to find thermodynamic states in which contact densities at concave and convex walls become identical. The adsorption and solvation force of hard sphere fluid show an oscillatory behavior versus H. Capillary condensation is in certain cases observed for Yukawa fluids.

Helmi, Abbas; Keshavarzi, Ezat

2014-03-01

262

Catalytic, hollow, refractory spheres, conversions with them

NASA Technical Reports Server (NTRS)

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.

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

1989-01-01

263

Largest Lyapunov Exponent for Many Particle Systems at Low Densities

NASA Astrophysics Data System (ADS)

The largest Lyapunov exponent ?+ for a dilute gas with short range interactions in equilibrium is studied by a mapping to a clock model, in which every particle carries a watch, with a discrete time that is advanced at collisions. This model has a propagating front solution with a speed that determines ?+, for which we find a density dependence as predicted by Krylov, but with a larger prefactor. Simulations for the clock model and for hard sphere and hard disk systems confirm these results and are in excellent mutual agreement. They show a slow convergence of ?+ with increasing particle number, in good agreement with a prediction by Brunet and Derrida.

van Zon, R.; van Beijeren, H.; Dellago, Ch.

1998-03-01

264

Density functional theory for carbon dioxide crystal

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.

Chang, Yiwen; Mi, Jianguo, E-mail: mijg@mail.buct.edu.cn; Zhong, Chongli [State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029 (China)

2014-05-28

265

NSDL National Science Digital Library

Module covering Earth's three fluid spheres: oceans, atmosphere and cryosphere (glaciers). An event seen in each sphere illustrates processes and concepts: El Nino events for oceans; thunderstorm formation for atmosphere; and global temperature change impacts on glaciers. Concepts covered include: properties of air, water, ice as fluids; flow of energy and matter between spheres; short and long-term cycles; and others. Activities include on-line literature research, use of maps and other data sources.

266

Sound scattering from two concentric fluid spheres (L)

The solution to the problem of plane wave and point source scattering by two concentric fluid spheres is derived. The effect of differences in sound speed, density, and absorption coefficient is taken into account. The scattered field is then found in the limit as the outer sphere becomes an infinitely thin shell and compared to the solution for a single fluid sphere for verification. A simulation is then performed using the concentric fluid sphere solution as an approximation to the human head and compared to the solution of a single fluid sphere with the properties of either bone or water. The solutions were found to be similar outside of the spheres but differ significantly inside the spheres. PMID:21743603

McNew, Jared; Lavarello, Roberto; O’Brien, William D.

2011-01-01

267

Soft Spheres Make More Mesophases

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.

Matthew A. Glaser; Gregory M. Grason; Randall D. Kamien; A. Kosmrlj; Christian D. Santangelo; P. Ziherl

2006-09-22

268

Periodically oscillating plasma sphere

The periodically oscillating plasma sphere, or POPS, is a novel fusion concept first proposed by D. C. Barnes and R. A. Nebel [Fusion Technol. 38, 28 (1998)]. POPS utilizes the self-similar collapse of an oscillating ion cloud in a spherical harmonic oscillator potential well formed by electron injection. Once the ions have been phase-locked, their coherent motion simultaneously produces very high densities and temperatures during the collapse phase of the oscillation. A requirement for POPS is that the electron injection produces a stable harmonic oscillator potential. This has been demonstrated in a gridded inertial electrostatic confinement device and verified by particle simulation. Also, the POPS oscillation has been confirmed experimentally through observation that the ions in the potential well exhibit resonance behavior when driven at the POPS frequency. Excellent agreement between the observed POPS frequencies and the theoretical predictions has been observed for a wide range of potential well depths and three different ion species. Practical applications of POPS require large plasma compressions. These large compressions have been observed in particle simulations, although space charge neutralization remains a major issue.

Park, J.; Nebel, R.A.; Stange, S.; Murali, S. Krupakar [Los Alamos National Laboratory, Los Alamos, New Mexico 87544 (United States); University of Wisconsin, Madison, Wisconsin 53706 (United States)

2005-05-15

269

ERIC Educational Resources Information Center

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…

Szekely, George

2011-01-01

270

Density profiles of a colloidal liquid at a wall under shear flow

Using a dynamical density functional theory we analyze the density profile of a colloidal liquid near a wall under shear flow. Due to the symmetries of the system considered, the naive application of dynamical density functional theory does not lead to a shear induced modification of the equilibrium density profile, which would be expected on physical grounds. By introducing a physically motivated dynamic mean field correction we incorporate the missing shear induced interparticle forces into the theory. We find that the shear flow tends to enhance the oscillations in the density profile of hard-spheres at a hard-wall and, at sufficiently high shear rates, induces a nonequilibrium transition to a steady state characterized by planes of particles parallel to the wall. Under gravity, we find that the center-of-mass of the density distribution increases with shear rate, i.e., shear increases the potential energy of the particles.

J. M. Brader; M. Krüger

2010-10-13

271

Electromagnetically revolving sphere viscometer

NASA Astrophysics Data System (ADS)

In this paper, we propose a new method of low viscosity measurement, in which the rolling of a probe sphere on the flat solid bottom of a sample cell is driven remotely and the revolution speed of the probe in a sample liquid gives the viscosity measurements. The principle of this method is based on the electromagnetically spinning technique that we developed, and the method is effective especially for viscosity measurements at levels below 100 mPa·s with an accuracy higher than 1%. The probe motion is similar to that in the well-known rolling sphere (ball) method. However, our system enables a steady and continuous measurement of viscosity, which is problematic using the conventional method. We also discuss the limits of the measurable viscosity range common to rolling-sphere-type viscometers by considering the accelerating motion of a probe sphere due to gravity, and we demonstrate the performance of our methods.

Hosoda, Maiko; Sakai, Keiji

2014-12-01

272

NASA Technical Reports Server (NTRS)

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.

2000-01-01

273

NASA Astrophysics Data System (ADS)

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.

Sun, Xiaochun

274

Generalized Density Functional Theory

NASA Astrophysics Data System (ADS)

Positionally dependent(See for example W.A. Curtin and N.W. Ashcroft, Phys. Rev. A 32), 2909 (1985). R.D. Groot and J.P. van de Eerden, Phys. Rev A 36, 4356 (1987). R. Leidl and H. Wagner, J. Chem. Phys. 98, 4142 (1993). and positionally independent(See for example A.R. Denton and N.W. Ashcroft, Phys. Rev. B 39), 4701 (1989) weighted density approximations of classical density functional theories are each shown to represent limits of a more general approach. The resulting flexibility is used to improve on the results obtained so far for inhomogeneous systems, the hard-sphere crystal being given as an example. The inherent physical limitations of such mappings are shown to arise from the resulting weight functions which remain proportional to the second order direct correlation function. The physical arguments apply also to electronic density functional theory(Supported by the National Science Foundation). http://www.msc.cornell.edu/ akhein/physics.html

Khein, A.; Ashcroft, N. W.

1997-03-01

275

Amphiphilic hard body mixtures Matthias Schmidt and Christian von Ferber

Amphiphilic hard body mixtures Matthias Schmidt and Christian von Ferber Institut fuÂ¨r Theoretische Received 16 June 2001; published 29 October 2001 In order to study ternary amphiphilic mixtures, we and amphiphilic particles, where the hydrophilic head is modeled as a hard sphere and the hydrophobic tail

Ott, Albrecht

276

Densest binary sphere packings

NASA Astrophysics Data System (ADS)

The densest binary sphere packings in the ?-x plane of small to large sphere radius ratio ? and small sphere relative concentration x have historically been very difficult to determine. Previous research had led to the prediction that these packings were composed of a few known “alloy” phases including, for example, the AlB2 (hexagonal ?), HgBr2, and AuTe2 structures, and to XYn structures composed of close-packed large spheres with small spheres (in a number ratio of n to 1) in the interstices, e.g., the NaCl packing for n=1. However, utilizing an implementation of the Torquato-Jiao sphere-packing algorithm [Torquato and Jiao, Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.82.061302 82, 061302 (2010)], we have discovered that many more structures appear in the densest packings. For example, while all previously known densest structures were composed of spheres in small to large number ratios of one to one, two to one, and very recently three to one, we have identified densest structures with number ratios of seven to three and five to two. In a recent work [Hopkins , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.107.125501 107, 125501 (2011)], we summarized these findings. In this work, we present the structures of the densest-known packings and provide details about their characteristics. Our findings demonstrate that a broad array of different densest mechanically stable structures consisting of only two types of components can form without any consideration of attractive or anisotropic interactions. In addition, the structures that we have identified may correspond to currently unidentified stable phases of certain binary atomic and molecular systems, particularly at high temperatures and pressures.

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

2012-02-01

277

Freezing of parallel hard cubes with rounded edges.

The freezing transition in a classical three-dimensional system of rounded hard cubes with fixed, equal orientations is studied by computer simulation and fundamental-measure density functional theory. By switching the rounding parameter s from zero to one, one can smoothly interpolate between cubes with sharp edges and hard spheres. The equilibrium phase diagram of rounded parallel hard cubes is computed as a function of their volume fraction and the rounding parameter s. The second order freezing transition known for oriented cubes at s = 0 is found to be persistent up to s = 0.65. The fluid freezes into a simple-cubic crystal which exhibits a large vacancy concentration. Upon a further increase of s, the continuous freezing is replaced by a first-order transition into either a sheared simple cubic lattice or a deformed face-centered cubic lattice with two possible unit cells: body-centered orthorhombic or base-centered monoclinic. In principle, a system of parallel cubes could be realized in experiments on colloids using advanced synthesis techniques and a combination of external fields. PMID:22502532

Marechal, Matthieu; Zimmermann, Urs; Löwen, Hartmut

2012-04-14

278

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.

Sheinberg, H.

1983-07-26

279

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.

Sheinberg, Haskell (Los Alamos, NM)

1986-01-01

280

1.1 Conversion Table 1 presents data in the Rockwell C hardness range on the relationship among Brinell hardness, Vickers hardness, Rockwell hardness, Rockwell superficial hardness, Knoop hardness, and Scleroscope hardness of non-austenitic steels including carbon, alloy, and tool steels in the as-forged, annealed, normalized, and quenched and tempered conditions provided that they are homogeneous. 1.2 Conversion Table 2 presents data in the Rockwell B hardness range on the relationship among Brinell hardness, Vickers hardness, Rockwell hardness, Rockwell superficial hardness, Knoop hardness, and Scleroscope hardness of non-austenitic steels including carbon, alloy, and tool steels in the as-forged, annealed, normalized, and quenched and tempered conditions provided that they are homogeneous. 1.3 Conversion Table 3 presents data on the relationship among Brinell hardness, Vickers hardness, Rockwell hardness, Rockwell superficial hardness, and Knoop hardness of nickel and high-nickel alloys (nickel content o...

American Society for Testing and Materials. Philadelphia

2007-01-01

281

Structural Correlations in Glass-Forming Hard Spheres Fluids

NASA Astrophysics Data System (ADS)

Recent studies have detected the presence of a growing static length scale associated with the glassy dynamical slowdown. Yet no fully satisfying microscopic description of such a length scale has yet been formulated. We critically evaluate the hypothesis that correlated structural defects could underlie the growing relaxation time in deeply supersaturated fluid. Though a clear structural signature of a developing order in these systems is found, the resulting defect geometry does not lead quite match the Frank- Kasper defect scenario. The dimensionally generalizable nature of the defects, however, make them promising options for defining static observables.

Charbonneau, Patrick; Charbonneau, Benoit

2011-03-01

282

Discontinuous Shear Thickening of Frictional Hard-Sphere Suspensions

NASA Astrophysics Data System (ADS)

Discontinuous shear thickening (DST) observed in many dense athermal suspensions has proven difficult to understand and to reproduce by numerical simulation. By introducing a numerical scheme including both relevant hydrodynamic interactions and granularlike contacts, we show that contact friction is essential for having DST. Above a critical volume fraction, we observe the existence of two states: a low viscosity, contactless (hence, frictionless) state, and a high viscosity frictional shear jammed state. These two states are separated by a critical shear stress, associated with a critical shear rate where DST occurs. The shear jammed state is reminiscent of the jamming phase of granular matter. Continuous shear thickening is seen as a lower volume fraction vestige of the jamming transition.

Seto, Ryohei; Mari, Romain; Morris, Jeffrey F.; Denn, Morton M.

2013-11-01

283

Particle Diffusion and Crystallisation in Suspensions of Hard Spheres

We report Brownian dynamics simulation results on binarycolloidal mixtures of particles of two different diameters interacting via a repulsive DLVO potential. As the effective temperature is lowered by reducing charged impurity concentration, a transition from liquid to crystal at a total volume fraction phi of 0.2 and to glassy state at phi = 0.3 are observed. The mean squared displacements

W. van Megen; S. M. Underwood; J. Müller; T. C. Mortensen; S. I. Henderson; J. L. Harland; P. Francis

1997-01-01

284

Phase diagram of colloidal spheres in a biaxial electric or magnetic field.

Colloidal particles with a dielectric constant mismatch with the surrounding solvent in an external biaxial magnetic or electric field experience an "inverted" dipolar interaction. We determine the phase behavior of such a system using Helmholtz free energy calculations in Monte Carlo simulations for colloidal hard spheres as well as for charged hard spheres interacting with a repulsive Yukawa potential. The phase diagram of colloidal hard spheres with inverted dipolar interactions shows a gas-liquid transition, a hexagonal ABC stacked crystal phase, and a stretched hexagonal-close-packed crystal. The phase diagram for charged spheres is very similar, but displays an additional layered-fluid phase. We compare our results with recent experimental observations. PMID:20515101

Smallenburg, Frank; Dijkstra, Marjolein

2010-05-28

285

NASA Astrophysics Data System (ADS)

We apply the logic of the quench action to give an exact analytical expression for the time evolution of the one-body density matrix after an interaction quench in the Lieb–Liniger model from the ground state of the free theory (BEC state) to the infinitely repulsive regime. In this limit there exists a mapping between the bosonic wavefuntions and the free fermionic ones but this does not help the computation of the one-body density matrix which is sensitive to particle statistics. The final expression, given in terms of the difference of two Fredholm Pfaffians, can be numerically evaluated and is valid in the thermodynamic limit and for all times after the quench.

De Nardis, J.; Caux, J.-S.

2014-12-01

286

Diffusion of a sphere in a dilute solution of polymer coils

We calculate the short time and the long time diffusion coefficient of a spherical tracer particle in a polymer solution in the low density limit by solving the Smoluchowski equation for a two-particle system and applying a generalized Einstein relation (fluctuation dissipation theorem). The tracer particle as well as the polymer coils are idealized as hard spheres with a no-slip boundary condition for the solvent but the hydrodynamic radius of the polymer coils is allowed to be smaller than the direct-interaction radius. We take hydrodynamic interactions up to 11th order in the particle distance into account. For the limit of small polymers, the expected generalized Stokes-Einstein relation is found. The long time diffusion coefficient also roughly obeys the generalized Stokes-Einstein relation for larger polymers whereas the short time coefficient does not. We find good qualitative and quantitative agreement to experiments.

Matthias Krüger; Markus Rauscher

2009-08-12

287

This paper presents the density measurement of tridecane by using hydrostatic weighing system, which is currently practised in Density Laboratory of National Metrology Laboratory (NML), SIRIM Berhad. This system weighed the crystal sphere while the crystal sphere was immersed in the tridecane. The volume and mass in air of the crystal sphere were calibrated at KRISS, Korea. The uncertainties of volume and mass in air of the crystal sphere were 4 ppm and 0.3 ppm respectively.

Nor, Mohd. Fazrul Hisyam Mohd.; Othman, Hafidzah; Abidin, Abd. Rashid Zainal [National Metrology Laboratory, SIRIM Berhad (Malaysia)

2009-07-07

288

Impulse Absorption by Tapered Alignments of Elastic Spheres

NASA Astrophysics Data System (ADS)

A numerical parametric study of 1D granular systems with Hertzian spheres is investigated. The relevant and always-repulsive interaction potential is nonlinearly dependent upon the overlap of adjacent grains. Specifically, we report our extensive investigation of two distinct systems and provide hard- sphere approximations as well as results from the numerical solution to the equations of motion. Chains can be characterized by the number of grains, N, the successive decrease in particle size or tapering, q, and restitutive losses, ?. By increasing the tapering, these chains act as shock absorbers by converting well-defined pulses into noise and spreading the energy among all members in the chain.

Doney, Robert; Sen, Surajit

2005-07-01

289

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.

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

1996-10-01

290

Relativistically spinning charged sphere

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.

Lynden-Bell, D. [Institute of Astronomy, The Observatories, Madingley Road, Cambridge, CB3 0HA (United Kingdom) and Clare College, Cambridge (United Kingdom)

2004-11-15

291

Mechanics of BCC and FCC hollow-sphere foams

Hollow-sphere foams provide an alternative microstructure for low-density metal structures with the potential for improved properties. In a recent companion paper, the mechanical properties of hollow-sphere foams with simple cubic packing (SC) were shown to be close to the theoretical values for closed-cell foams and well above the measured modulus and strength of metallic closed-cell foams. Here, we analyze the

W. S. Sanders; L. J. Gibson

2003-01-01

292

Hollow silica spheres: synthesis and mechanical properties.

Core-shell polystyrene-silica spheres with diameters of 800 nm and 1.9 microm were synthesized by soap-free emulsion and dispersion polymerization of the polystyrene core, respectively. The polystyrene spheres were used as templates for the synthesis of silica shells of tunable thickness employing the Stöber method [Graf et al. Langmuir 2003, 19, 6693]. The polystyrene template was removed by thermal decomposition at 500 degrees C, resulting in smooth silica shells of well-defined thickness (15-70 nm). The elastic response of these hollow spheres was probed by atomic force microscopy (AFM). A point load was applied to the particle surface through a sharp AFM tip, and successively increased until the shell broke. In agreement with the predictions of shell theory, for small deformations the deformation increased linearly with applied force. The Young's modulus (18 +/- 6 GPa) was about 4 times smaller than that of fused silica [Adachi and Sakka J. Mater. Sci. 1990, 25, 4732] but identical to that of bulk silica spheres (800 nm) synthesized by the Stöber method, indicating that it yields silica of lower density. The minimum force needed to irreversibly deform (buckle) the shell increased quadratically with shell thickness. PMID:19437752

Zhang, Lijuan; D'Acunzi, Maria; Kappl, Michael; Auernhammer, Günter K; Vollmer, Doris; van Kats, Carlos M; van Blaaderen, Alfons

2009-03-01

293

NASA Astrophysics Data System (ADS)

Classical density functional theory (DFT) of fluids is a fast and efficient theory to compute the structure of the electrical double layer in the primitive model of ions where ions are modeled as charged, hard spheres in a background dielectric. While the hard-core repulsive component of this ion-ion interaction can be accurately computed using well-established DFTs, the electrostatic component is less accurate. Moreover, many electrostatic functionals fail to satisfy a basic theorem, the contact density theorem, that relates the bulk pressure, surface charge, and ion densities at their distances of closest approach for ions in equilibrium at a smooth, hard, planar wall. One popular electrostatic functional that fails to satisfy the contact density theorem is a perturbation approach developed by Kierlik and Rosinberg [Phys. Rev. A 44, 5025 (1991), 10.1103/PhysRevA.44.5025] and Rosenfeld [J. Chem. Phys. 98, 8126 (1993), 10.1063/1.464569], where the full free-energy functional is Taylor-expanded around a bulk (homogeneous) reference fluid. Here, it is shown that this functional fails to satisfy the contact density theorem because it also fails to satisfy the known low-density limit. When the functional is corrected to satisfy this limit, a corrected bulk pressure is derived and it is shown that with this pressure both the contact density theorem and the Gibbs adsorption theorem are satisfied.

Gillespie, Dirk

2014-11-01

294

Classical density functional theory (DFT) of fluids is a fast and efficient theory to compute the structure of the electrical double layer in the primitive model of ions where ions are modeled as charged, hard spheres in a background dielectric. While the hard-core repulsive component of this ion-ion interaction can be accurately computed using well-established DFTs, the electrostatic component is less accurate. Moreover, many electrostatic functionals fail to satisfy a basic theorem, the contact density theorem, that relates the bulk pressure, surface charge, and ion densities at their distances of closest approach for ions in equilibrium at a smooth, hard, planar wall. One popular electrostatic functional that fails to satisfy the contact density theorem is a perturbation approach developed by Kierlik and Rosinberg [Phys. Rev. A 44, 5025 (1991)PLRAAN1050-294710.1103/PhysRevA.44.5025] and Rosenfeld [J. Chem. Phys. 98, 8126 (1993)JCPSA60021-960610.1063/1.464569], where the full free-energy functional is Taylor-expanded around a bulk (homogeneous) reference fluid. Here, it is shown that this functional fails to satisfy the contact density theorem because it also fails to satisfy the known low-density limit. When the functional is corrected to satisfy this limit, a corrected bulk pressure is derived and it is shown that with this pressure both the contact density theorem and the Gibbs adsorption theorem are satisfied. PMID:25493766

Gillespie, Dirk

2014-11-01

295

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

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.

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

2001-10-08

296

Facile assembly of 3D binary colloidal crystals from soft microgel spheres.

It still remains a big challenge to fabricate binary colloidal crystals (binary CCs) from hard colloidal spheres, although a lot of efforts have been made. Here, for the first time, binary CCs are assembled from soft hydrogel spheres, PNIPAM microgels, instead of hard spheres. Different from hard spheres, microgel binary CCs can be facilely fabricated by simply heating binary microgel dispersions to 37 °C and then allowing them to cool back to room temperature. The formation of highly ordered structure is indicated by the appearance of an iridescent color and a sharp Bragg diffraction peak. Compared with hard sphere binary CCs, the assembly of PNIPAM microgel binary CCs is much simpler, faster and with a higher "atom" economy. The easy formation of PNIPAM microgel binary CC is attributed to the thermosensitivity and soft nature of the PNIPAM microgel spheres. In addition, PNIPAM microgel binary CCs can respond to temperature change, and their stop band can be tuned by changing the concentration of the dispersion. PMID:24497429

Liu, Yang; Guan, Ying; Zhang, Yongjun

2014-03-01

297

STP Hard Disks Metropolis Program

NSDL National Science Digital Library

The STP Hard Disks Metropolis program is a Monte Carlo simulation of hard disks in two dimensions. The default initial condition is a rectangular configuration of N=64 particles in a box of length L = 40. You can slowly increase the density of the gas (by setting the minimum scale length between centers to a value slightly less than 1) to explore phase transitions. STP HardDisksMetropolis is part of a suite of Open Source Physics programs that model aspects of Statistical and Thermal Physics (STP). The program is distributed as a ready-to-run (compiled) Java archive. Double-clicking the stp_HardDisksMetropolis.jar file will run the program if Java is installed on your computer. Additional programs can be found by searching ComPADRE for Open Source Physics, STP, or Statistical and Thermal Physics.

Gould, Harvey; Tobochnik, Jan; Christian, Wolfgang; Cox, Anne

2009-03-06

298

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.

Krogh, M.; Hansen, C.; Painter, J. [Los Alamos National Lab., NM (United States); de Verdiere, G.C. [CEA Centre d`Etudes de Limeil, 94 - Villeneuve-Saint-Georges (France)

1995-05-01

299

Preliminary Health Assessment of Cultured Hard Clams,

Preliminary Health Assessment of Cultured Hard Clams, Mercenaria mercenaria, in Florida Ruth for cultured hard clams in Floridaclams in Florida #12;Health Monitoring Program: SamplingSampling Â· 60 animals Density lease area Indian River Aquaculture Use Zone represent the majority of the clam production Sand

Florida, University of

300

DSMC Simulation and Experimental Validation of Shock Interaction in Hypersonic Low Density Flow

Direct simulation Monte Carlo (DSMC) of shock interaction in hypersonic low density flow is developed. Three collision molecular models, including hard sphere (HS), variable hard sphere (VHS), and variable soft sphere (VSS), are employed in the DSMC study. The simulations of double-cone and Edney's type IV hypersonic shock interactions in low density flow are performed. Comparisons between DSMC and experimental data are conducted. Investigation of the double-cone hypersonic flow shows that three collision molecular models can predict the trend of pressure coefficient and the Stanton number. HS model shows the best agreement between DSMC simulation and experiment among three collision molecular models. Also, it shows that the agreement between DSMC and experiment is generally good for HS and VHS models in Edney's type IV shock interaction. However, it fails in the VSS model. Both double-cone and Edney's type IV shock interaction simulations show that the DSMC errors depend on the Knudsen number and the models employed for intermolecular interaction. With the increase in the Knudsen number, the DSMC error is decreased. The error is the smallest in HS compared with those in the VHS and VSS models. When the Knudsen number is in the level of 10?4, the DSMC errors, for pressure coefficient, the Stanton number, and the scale of interaction region, are controlled within 10%. PMID:24672360

2014-01-01

301

Using the flotation of a single sphere to measure and model capillary forces.

The flotation of small polymer spheres in lower density liquids was studied to better understand the capillary forces associated with curved surfaces. A sphere composed of poly(tetrafluoroethylene) (PTFE) or polycarbonate (PC) was placed in a clear container, and liquid (water, formamide, or ethylene glycol) was slowly added. The progression of liquid rising and ultimately floating or engulfing the sphere was observed. Capillary forces aided buoyancy, allowing some of the spheres to float. A combination of greater lyophobicity and surface tension enabled water to suspend larger spheres than the other two liquids. As compared to PTFE, a smaller density difference between water and PC permitted much larger PC spheres to be buoyed. The largest PTFE that floated was approximately 5 mm in diameter versus 10 mm for PC. Maximum flotation diameters were estimated by an iterative method as well as a closed solution. Both gave reasonable estimates, falling within the range bracketed by the largest floater and the smallest sinker. PMID:19338330

Extrand, C W; Moon, Sung In

2009-06-01

302

Low Velocity Sphere Impact of a Soda Lime Silicate Glass

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.

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

2011-10-01

303

NASA Technical Reports Server (NTRS)

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.

Mcintyre, R. G.; Bruce, R. E.

1974-01-01

304

Efficient implementation of sphere demodulation

We provide new results on the sphere demodulator (SD) and its new variant, the list sphere demodulator (LSD). A new reduced complexity SD algorithm is presented. We suggest implementing the necessary sorting of constellation symbols through a look up table. In addition, we propose the use of a modified QR algorithm which tries to begin the search in the layers

Ami Wiesel; Xavier Mestre; A. Pages; Javier R. Fonollosa

2003-01-01

305

The theory of the vortex motion of two-dimensional incompressible inviscid flow on a sphere is presented. Vorticity and stream function, which are related by the Laplace-Beltrami operator, are initially outlined. Green's function of the equation is obtained in which the stream function is expressed as integral form. The equations of motion for two vortex models on a sphere are derived.

Yoshifumi Kimura; Hisashi Okamoto

1987-01-01

306

Panoramic stereo sphere vision

NASA Astrophysics Data System (ADS)

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.

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

2013-01-01

307

Impulse absorption by tapered horizontal alignments of elastic spheres

NASA Astrophysics Data System (ADS)

We present an analytical and numerical study of the problem of mechanical impulse propagation through a horizontal alignment of progressively shrinking (tapered) elastic spheres that are placed between two rigid end walls. The studies are confined to cases where initial loading between the spheres is zero (i.e., in the “sonic vacuum” region). The spheres are assumed to interact via the Hertz potential. Force and energy as a function of time for selected grains that comprise the solitary wave are provided and shed light on the system’s behavior. Propagation of energy is analytically studied in the hard-sphere approximation and phase diagrams plotting normalized kinetic energy of the smallest grain at the tapered end are developed for various chain lengths and tapering factors. These details are then compared to kinetic energy phase diagrams obtained via extensive dynamical simulations. Our figures indicate that the ratios of the kinetic energies of the smallest to largest grains possess a Gaussian dependence on tapering and an exponential decay when the number of grains increases. The conclusions are independent of system size, thus being applicable to tapered alignments of micron-sized spheres as well as those that are macroscopic and more easily realizable in the laboratory. Results demonstrate the capabililty of these chains to thermalize propagating impulses and thereby act as potential shock absorbing devices.

Doney, Robert L.; Sen, Surajit

2005-10-01

308

Scattering of sound by a penetrable sphere above a plane boundary

NASA Astrophysics Data System (ADS)

The problem of acoustic scattering by a penetrable sphere irradiated by a point source is investigated. A theoretical model is developed for the case of scattering by a sphere placed above an acoustically hard and an impedance boundary. The sphere is made of an extended reaction material that is assumed to be acoustically penetrable. The problems are tackled by using the technique of variables separation and appropriate wave field expansions. By adopting an image source method, the solutions can be formulated in form of multiscattering interaction between the sphere and the image sphere near a hard and an impedance boundary. The effect of boundary impedance on the reflected sound fields is incorporated in the numerical model by using the well-known Wely-van der Pol formula. Preliminary indoor measurements are conducted in an anechoic chamber for the characterization of the acoustical properties of the penetrable sphere as well as the impedance boundary. A further set of experimental measurements is carried out to demonstrate the validity of the proposed theoretical models for various receiver locations around the sphere above the impedance boundary. [Work sponsored by the Innovation & Technology Commission, MTR Corp. Ltd., and The Hong Kong Polytechnic University under Project No. ZM07.

Lui, Wai Keung; Li, Kai Ming

2002-11-01

309

Role of bit patterned media in future of hard disk drives

The hard disk industry has traditionally stayed competitive by competing on the means of price alone by cutting down aggressively on cost via increase of areal density. Continuing increases in the areal density of hard ...

Aravindakshan, Vibin

2007-01-01

310

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.

Medasani, Bharat; Ovanesyan, Zaven; Thomas, Dennis G.; Sushko, Maria L.; Marucho, Marcelo

2014-05-29

311

NASA Technical Reports Server (NTRS)

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.

Schmidlin, F. J.

1987-01-01

312

In this paper, a theoretical description of the free energies and correlation functions of hard-sphere (HS) liquid and solid phases is developed using fundamental measure density-functional theory. Within the framework of Weeks-Chandler-Andersen perturbation theory, free energies of liquid and solid phases with many interaction potentials can be obtained from these characteristics of the HS system within a single theoretical description. An application to the Lennard-Jones system yields liquid-solid coexistence results in good agreement with the ones from simulations. PMID:15244546

Warshavsky, Vadim B; Song, Xueyu

2004-06-01

313

In this paper we investigate the solubility of a hard - sphere gas in a solvent modeled as an associating lattice gas (ALG). The solution phase diagram for solute at 5% is compared with the phase diagram of the original solute free model. Model properties are investigated thr ough Monte Carlo simulations and a cluster approximation. The model solubility is computed via simulations and shown to exhibit a minimum as a function of temperature. The line of minimum solubility (TmS) coincides with the line of maximum density (TMD) for different solvent chemical potentials.

Marcia M. Szortyka; Maurício Girardi; Vera B. Henriques; Marcia C. Barbosa

2012-05-09

314

Frontal Impact of Rolling Spheres.

ERIC Educational Resources Information Center

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)

Domenech, A.; Casasus, E.

1991-01-01

315

Nucleation-Mode Localization in Hard-Soft Nanocomposites

NASA Astrophysics Data System (ADS)

Aligned hard-soft nanocomposites continue to be an active research area in permanent magnetism, challenged by demanding processing requirements but also encouraged by experimental proofs of principle. The approach was initially outlined by Kneller and Hawig (1991), who advocated hard-soft multilayers. Skomski and Coey (1993) considered three-dimensional nanostructures, such as soft spheres in a hard matrix, and predicted an upper energy-product limit of about 1000 kJ/m^3. It is well-established that the dimensions of the soft regions cannot be larger than twice the domain-wall width of the hard phase, but otherwise it was believed that geometry has a rather secondary effect. However, our recent research reveals substantial differences. Soft-in-hard geometries are better than hard-in-soft geometries and embedded soft spheres are better than multilayers. This is in close analogy to the dimensionality-dependent quantum-mechanical delocalization of electrons in an inhomogeneous potential and to the behavior of impurity states in the band gaps of solids. Transparent analytical nucleation-field solutions are found for some geometries and in the limit of very small soft inclusion as a function of the hard-phase coercivity and hysteresis-loop shape.

Skomski, Ralph; Balasubramanian, Balamurugan; Das, Bhaskar; Sellmyer, D. J.

2013-03-01

316

The gravitomagnetic field of a sphere, Gravity Probe B and the LAGEOS satellites

The gravitomagnetic field generated by a rotating sphere is usually calculated from the ideal dipole model. However, for a sphere with a homogeneous mass density, this model is not generally valid. Trying to obtain a more accurate value of the gravitomagnetic field inside and outside the sphere, series expansions for this field are presented in this paper. The calculated polar gravitomagnetic field of the sphere and that from the ideal dipole model appear to coincide, but the field in the vicinity of the sphere may deviate. The deduced field within the sphere strongly deviates from the ideal dipole result. As an illustration, the gravitomagnetic precession rate (or frame-dragging effect) of a gyroscope moving in the gravitomagnetic field from a large rotating sphere is calculated. For the Gravity Probe B experiment the result may coincide with the prediction from the ideal dipole model and in fair agreement with observations. In addition, the obtained Lense-Thirring precession rate for the LAGEOS satellites probably coincides with the standard prediction. For both experiments alternative predictions are calculated, when the gravitomagnetic field and the magnetic field from moving charge are equivalent. Theoretical and observational indications for such an equivalence are summarized. The obtained series expansions for the gravitomagnetic field of a sphere can also be applied to the calculation of the magnetic field, generated by a rotating sphere with a homogeneous charge density. Results for this case are also discussed.

Jacob Biemond

2008-02-22

317

Analysis of principal nested spheres

Summary A general framework for a novel non-geodesic decomposition of high-dimensional spheres or high-dimensional shape spaces for planar landmarks is discussed. The decomposition, principal nested spheres, leads to a sequence of submanifolds with decreasing intrinsic dimensions, which can be interpreted as an analogue of principal component analysis. In a number of real datasets, an apparent one-dimensional mode of variation curving through more than one geodesic component is captured in the one-dimensional component of principal nested spheres. While analysis of principal nested spheres provides an intuitive and flexible decomposition of the high-dimensional sphere, an interesting special case of the analysis results in finding principal geodesics, similar to those from previous approaches to manifold principal component analysis. An adaptation of our method to Kendall’s shape space is discussed, and a computational algorithm for fitting principal nested spheres is proposed. The result provides a coordinate system to visualize the data structure and an intuitive summary of principal modes of variation, as exemplified by several datasets. PMID:23843669

Jung, Sungkyu; Dryden, Ian L.; Marron, J. S.

2012-01-01

318

A density functional approach to model highly charged spherical colloids in electrolyte mixtures

NASA Astrophysics Data System (ADS)

We present a classical density functional (DFT) approach to study the effects of ion size asymmetry, ion-ion correlation and solvent excluded volume on the structural and thermodynamic properties of strongly interacting charged systems. The hard sphere correlation effects are modeled non-perturbatively with weighted density approximation, where as electrostatic correlations are modeled perturbatively within the mean spherical approximation. The present DFT approach is able to describe macro-ions in electrolytes comprising neutral hard sphere mimicking water molecules and ions with dissimilar valence and realistic sizes and densities. We applied the theory to study spherical electric double layers and obtained results in good agreement with simulations. We calculated ion profiles, integrated charge, mean electrostatic potential, ionic coordination number, zeta potential, and inverse differential capacity at different conditions. For higher surface charge on macromolecule, charge inversion is noticed and when the counter-ions are bigger than co-ions, surface charge amplification is observed. Layering and screening effects are more pronounced when water molecules are explicitly considered. This work has potential applications in bio-electrostatics and colloidal engineering.

Medasani, Bharat; Ovanesyan, Zaven; Marucho, Marcelo

2013-03-01

319

Thermoinertial bouncing of a relativistic collapsing sphere: A numerical model

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.

Herrera, L.; Di Prisco, A.; Barreto, W. [Centro de Fisica Teorica y Computacional, Facultad de Ciencias, Universidad Central de Venezuela, Caracas (Venezuela); Centro de Fisica Fundamental, Facultad de Ciencias, Universidad de los Andes, Merida (Venezuela)

2006-01-15

320

Baryonic sphere: A spherical domain wall carrying baryon number

NASA Astrophysics Data System (ADS)

We construct a spherical domain wall which has baryon charge distributed on a sphere of finite radius in a Skyrme model with a sixth-order derivative term and a modified mass term. Its distribution of energy density likewise takes the form of a sphere. In order to localize the domain wall at a finite radius we need a negative coefficient in front of the Skyrme term and a positive coefficient of the sixth order derivative term to stabilize the soliton. Increasing the pion mass pronounces the shell-like structure of the configuration.

Gudnason, Sven Bjarke; Nitta, Muneto

2014-01-01

321

Viscosity, entropy and the viscosity to entropy density ratio; how perfect is a nucleonic fluid?

The viscosity of hadronic matter is studied using a classical evaluation of the scattering angle and a quantum mechanical discussion based on phase shifts from a potential. Semi classical limits of the quantum theory are presented. A hard sphere and an attractive square well potential step are each considered as well as the combined effects of both. The lowest classical value of the viscosity for an attractive potential is shown to be a hard sphere limit. The high wave number-short wavelength limits of the quantum result have scaling laws associated with it for both the viscosity and entropy. These scaling laws are similar to the Fraunhoher diffraction increase for the hard sphere geometric cross section. Specific examples for nuclear collisions are given. The importance of the nuclear tensor force and hard core is mentioned. The viscosity (eta), entropy density (s) and eta/s ratio are calculated for a gas of dilute neutrons in the unitary limit of large scattering length. Away from the unitary limit, the ratio of the interaction radius or the scattering length to the interparticle spacing introduces a variable y besides the fugacity z. The isothermal compressibility is shown to impose important constraints. The results for eta/s are compared to the AdS/CFT string theory minimum of (1/4Pi)hbar/kb to see how close a nucleonic gas is to being a perfect fluid. The eta/s ~1hbar/kb for a neutron gas in its unitary limit. The eta/s 3hbar/kb treating the nuclear scattering as billiard ball collisions. The minimum eta/s for a neutron gas occurs in regions of negative isothermal compressibility and high fugacity where higher virial terms are important. In a neutron-proton system higher virial terms are associated with a liquid-gas phase transition and critical opalescent phenomena.The type of flow-laminar,vortex, turbulent- is investigated.

Aram Z. Mekjian

2010-09-29

322

The need for calibrated sonar targets is addressed in connection with the development and testing of a set of thin-walled spheres filled with a high-density fluid. Using historical research information as a guide, a set of thin-walled metal spheres was developed and filled with a high-density fluid. The combination of the spherical shape and the acoustic focusing effects of the

David M. Deveau

2000-01-01

323

We measured ultra-small-angle neutron scattering (USANS) from polymethylmethacrylate spheres tamped down in air. Two slightly polydisperse pure sphere sizes (1.5 and 7.5 microm diameters) and five mixtures of these were used. All were loose packed (packing fractions of 0.3-0.6) with nongravitational forces (e.g., friction) important, preventing close packing. The USANS data are rich in information on powder packing. A modified Percus-Yevick fluid model was used to parametrize the data-adequately but not well. The modifications required the introduction of small voids, less than the sphere size, and a parameter reflecting substantial deviation from the Percus-Yevick prediction of the sphere-sphere correlation function. The mixed samples fitted less well, and two further modifying factors were necessary. These were local inhomogeneities, where the concentration of same-size spheres, both large and small, deviated from the mean packing, and a factor accounting for the presence within these "clusters" of self-avoidance of the large spheres (that is, large spheres coated with more small spheres than Percus-Yevick would predict). The overall deviations from the hard-sphere Percus-Yevick model that we find here suggest that fluid models of loose packed powders are unlikely to be successful but lay the ground work for future theoretical and computational works. PMID:19658692

Reynolds, Philip A; McGillivray, Duncan J; Jackson, Andrew J; White, John W

2009-07-01

324

Configurational entropy of binary hard-disk glasses: Nonexistence of an ideal glass transition

NASA Astrophysics Data System (ADS)

We study the thermodynamics of a binary hard-disk mixture in which the ratio of disk diameters is ? =1.4. We use a recently developed molecular dynamics algorithm to calculate the free-volume entropy of glassy configurations and obtain the configurational entropy (degeneracy) of the supercompressed liquid as a function of density. We find that the configurational entropy of the glasses near the kinetic glass transition is very close to the mixing entropy, suggesting that the degeneracy is zero only for the phase-separated crystal. We explicitly construct an exponential number of jammed packings with densities spanning the spectrum from the accepted "amorphous" glassy state to the phase-separated crystal, thus showing that there is no ideal glass transition in binary hard-disk mixtures. This construction also demonstrates that the ideal glass, defined as having zero configurational entropy, is not amorphous, but instead is nothing more than a phase-separated crystal. This critique of the presumed existence of an ideal glass parallels our previous critique of the idea that there is a most-dense random (close) packing for hard spheres [Torquato et al., Phys. Rev. Lett. 84, 2064 (2000)]. We also perform free-energy calculations to determine the equilibrium phase behavior of the system. The calculations predict a first-order freezing transition at a density below the kinetic glass transition. However, this transition appears to be strongly kinetically suppressed and is not observed directly. New simulation techniques are needed in order to gain a more complete understanding of the thermodynamic and kinetic behavior of the binary disk mixture and, in particular, of the demixing process during crystallization.

Donev, Aleksandar; Stillinger, Frank H.; Torquato, Salvatore

2007-09-01

325

Accelerated Simulation of a Heavy Particle in a Gas of Elastic Spheres

A new, accelerated algorithm for a system of elastic hard-spheres in which one of the particles (a colloid) is significantly heavier than the others is presented. The algorithm follows the framework of the stochastic heterogeneous multiscale method. It is shown that, in the limit in which the ratio between the light and the heavy particles approaches zero, the dynamics of

Gil Ariel; Eric Vanden-Eijnden

2008-01-01

326

ORSPHERE: CRITICAL, BARE, HEU(93.2)-METAL SPHERE

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.

Margaret A. Marshall

2013-09-01

327

Helical packings and phase transformations of soft spheres in cylinders.

The phase behavior of helical packings of thermoresponsive microspheres inside glass capillaries is studied as a function of the volume fraction. Stable packings with long-range orientational order appear to evolve abruptly to disordered states as the particle volume fraction is reduced, consistent with recent hard-sphere simulations. We quantify this transition using correlations and susceptibilities of the orientational order parameter psi6. The emergence of coexisting metastable packings, as well as coexisting ordered and disordered states, is also observed. These findings support the notion of phase-transition-like behavior in quasi-one-dimensional systems. PMID:20481667

Lohr, M A; Alsayed, A M; Chen, B G; Zhang, Z; Kamien, R D; Yodh, A G

2010-04-01

328

Helical Packings and Phase Transformations of Soft Spheres in Cylinders

The phase behavior of helical packings of thermoresponsive microspheres inside glass capillaries is studied as a function of volume fraction. Stable packings with long-range orientational order appear to evolve abruptly to disordered states as particle volume fraction is reduced, consistent with recent hard sphere simulations. We quantify this transition using correlations and susceptibilities of the orientational order parameter psi_6. The emergence of coexisting metastable packings, as well as coexisting ordered and disordered states, is also observed. These findings support the notion of phase transition-like behavior in quasi-1D systems.

Matthew A. Lohr; Ahmed M. Alsayed; Bryan G. Chen; Zexin Zhang; Randall D. Kamien; Arjun G. Yodh

2010-04-02

329

Chiral Structures of Thermoresponsive Soft Spheres in Hollow Cylinders

NASA Astrophysics Data System (ADS)

We experimentally observe the formation of closely packed crystalline structures in hollow cylinders. The structures have varying degrees of chiral order. The systems are created from aqueous suspensions of thermoresponsive N-isopropylacrylamide (NIPA) microgel particles packed in micron-diameter glass capillaries. We categorize these structures according to classifications used by Erickson for tubular packings of hard spheres [1]. By varying the temperature-tunable diameter of these particles, the system's volume fraction is changed, permitting observations of the resilience of these structures and their melting transitions. Melting of these thermal crystalline structures is observed. [1] R. O. Erickson, Science 181 (1973) 705-716.

Lohr, Matthew A.; Alsayed, Ahmed; Zhang, Zexin; Yodh, Arjun G.

2009-03-01

330

Hydrodynamic force between a sphere and a soft, elastic surface.

The hydrodynamic drainage force between a spherical silica particle and a soft, elastic polydimethylsiloxane surface was measured using the colloidal probe technique. The experimental force curves were compared to finite element simulations and an analytical model. The hydrodynamic repulsion decreased when the particle approached the soft surface as compared to a hard substrate. In contrast, when the particle was pulled away from the surface again, the attractive hydrodynamic force was increased. The hydrodynamic attraction increased because the effective area of the narrow gap between sphere and the plane on soft surfaces is larger than on rigid ones. PMID:25198777

Kaveh, Farzaneh; Ally, Javed; Kappl, Michael; Butt, Hans-Jürgen

2014-10-01

331

Density functional theory is used to explore the solvation properties of a spherical solute immersed in a supercritical diatomic fluid. The solute is modeled as a hard core Yukawa particle surrounded by a diatomic Lennard-Jones fluid represented by two fused tangent spheres using an interaction site approximation. The authors' approach is particularly suitable for thoroughly exploring the effect of different interaction parameters, such as solute-solvent interaction strength and range, solvent-solvent long-range interactions, and particle size, on the local solvent structure and the solvation free energy under supercritical conditions. Their results indicate that the behavior of the local coordination number in homonuclear diatomic fluids follows trends similar to those reported in previous studies for monatomic fluids. The local density augmentation is particularly sensitive to changes in solute size and is affected to a lesser degree by variations in the solute-solvent interaction strength and range. The associated solvation free energies exhibit a nonmonotonous behavior as a function of density for systems with weak solute-solvent interactions. The authors' results suggest that solute-solvent interaction anisotropies have a major influence on the nature and extent of local solvent density inhomogeneities and on the value of the solvation free energies in supercritical solutions of heteronuclear molecules. PMID:17302486

Husowitz, B; Talanquer, V

2007-02-01

332

Equilibration and aging of dense soft-sphere glass-forming liquids.

The recently developed nonequilibrium extension of the self-consistent generalized Langevin equation theory of irreversible relaxation [Ramírez-González and Medina-Noyola, Phys. Rev. E 82, 061503 (2010); Ramírez-González and Medina-Noyola, Phys. Rev. E 82, 061504 (2010)] is applied to the description of the irreversible process of equilibration and aging of a glass-forming soft-sphere liquid that follows a sudden temperature quench, within the constraint that the local mean particle density remains uniform and constant. For these particular conditions, this theory describes the nonequilibrium evolution of the static structure factor S(k;t) and of the dynamic properties, such as the self-intermediate scattering function F(S)(k,?;t), where ? is the correlation delay time and t is the evolution or waiting time after the quench. Specific predictions are presented for the deepest quench (to zero temperature). The predicted evolution of the ?-relaxation time ?(?)(t) as a function of t allows us to define the equilibration time t(eq)(?), as the time after which ?(?)(t) has attained its equilibrium value ?(?)(eq)(?). It is predicted that both, t(eq)(?) and ?(?)(eq)(?), diverge as ???((a)), where ?((a)) is the hard-sphere dynamic-arrest volume fraction ?((a))(?0.582), thus suggesting that the measurement of equilibrium properties at and above ?((a)) is experimentally impossible. The theory also predicts that for fixed finite waiting times t, the plot of ?(?)(t;?) as a function of ?exhibits two regimes, corresponding to samples that have fully equilibrated within this waiting time (???((c))(t)), and to samples for which equilibration is not yet complete (???((c))(t)). The crossover volume fraction ?((c))(t) increases with t but saturates to the value ?((a)). PMID:23767539

Sánchez-Díaz, Luis Enrique; Ramírez-González, Pedro; Medina-Noyola, Magdaleno

2013-05-01

333

Equilibration and aging of dense soft-sphere glass-forming liquids

NASA Astrophysics Data System (ADS)

The recently developed nonequilibrium extension of the self-consistent generalized Langevin equation theory of irreversible relaxation [Ramírez-González and Medina-Noyola, Phys. Rev. E10.1103/PhysRevE.82.061503 82, 061503 (2010); Ramírez-González and Medina-Noyola, Phys. Rev. E10.1103/PhysRevE.82.061504 82, 061504 (2010)] is applied to the description of the irreversible process of equilibration and aging of a glass-forming soft-sphere liquid that follows a sudden temperature quench, within the constraint that the local mean particle density remains uniform and constant. For these particular conditions, this theory describes the nonequilibrium evolution of the static structure factor S(k;t) and of the dynamic properties, such as the self-intermediate scattering function FS(k,?;t), where ? is the correlation delay time and t is the evolution or waiting time after the quench. Specific predictions are presented for the deepest quench (to zero temperature). The predicted evolution of the ?-relaxation time ??(t) as a function of t allows us to define the equilibration time teq(?), as the time after which ??(t) has attained its equilibrium value ??eq(?). It is predicted that both, teq(?) and ??eq(?), diverge as ???(a), where ?(a) is the hard-sphere dynamic-arrest volume fraction ?(a)(?0.582), thus suggesting that the measurement of equilibrium properties at and above ?(a) is experimentally impossible. The theory also predicts that for fixed finite waiting times t, the plot of ??(t;?) as a function of ? exhibits two regimes, corresponding to samples that have fully equilibrated within this waiting time (???(c)(t)), and to samples for which equilibration is not yet complete (???(c)(t)). The crossover volume fraction ?(c)(t) increases with t but saturates to the value ?(a).

Sánchez-Díaz, Luis Enrique; Ramírez-González, Pedro; Medina-Noyola, Magdaleno

2013-05-01

334

Fuel Fabrication for Surrogate Sphere-Pac Rodlet

Sphere-pac fuel consists of a blend of spheres of two or three different size fractions contained in a fuel rod. The smear density of the sphere-pac fuel column can be adjusted to the values obtained for light-water reactor (LWR) pellets (91-95%) by using three size fractions, and to values typical of the fast-reactor oxide fuel column ({approx}85%) by using two size fractions. For optimum binary packing, the diameters of the two sphere fractions must differ by at least a factor of 7 (ref. 3). Blending of spheres with smaller-diameter ratios results in difficult blending, nonuniform loading, and lower packing fractions. A mixture of about 70 vol% coarse spheres and 30 vol% fine spheres is needed to obtain high packing fractions. The limiting smear density for binary packing is 86%, with about 82% achieved in practice. Ternary packing provides greater smear densities, with theoretical values ranging from 93 to 95%. Sphere-pac technology was developed in the 1960-1990 period for thermal and fast spectrum reactors of nearly all types (U-Th and U-Pu fuel cycles, oxide and carbide fuels), but development of this technology was most strongly motivated by the need for remote fabrication in the thorium fuel cycle. The application to LWR fuels as part of the DOE Fuel Performance Improvement Program did not result in commercial deployment for a number of reasons, but the relatively low production cost of existing UO{sub 2} pellet fuel is probably the most important factor. In the case of transmutation fuels, however, sphere-pac technology has the potential to be a lower-cost alternative while also offering great flexibility in tailoring the fuel elements to match the exact requirements of any particular reactor core at any given time in the cycle. In fact, the blend of spheres can be adjusted to offer a different composition for each fuel pin or group of pins in a given fuel element. Moreover, it can even provide a vertical gradient of composition in a single fuel pin. For minor-actinide-bearing fuels, the sphere-pac form is likely to accept the large helium release from {sup 241}Am transmutation with less difficulty than pellet forms and is especially well suited to remote fabrication as a dustless fuel form that requires a minimum number of mechanical operations. The sphere-pac (and vi-pac) fuel forms are being explored for use as a plutonium-burning fuel by the European Community, the Russian Federation, and Japan. Sphere-pac technology supports flexibility in the design and fabrication of fuels. For example, the blend composition can be any combination of fissile, fertile, transmutation, and inert components. Since the blend of spheres can be used to fill any geometric form, nonconventional fuel geometries (e.g., annular fuels rods, or annular pellets with the central region filled with spheres) are readily fabricated using sphere-pac loading methods. A project, sponsored by the U.S. Department of Energy Advanced Fuel Cycle Initiative (AFCI), has been initiated at Oak Ridge National Laboratory (ORNL) with the objective of conducting the research and development necessary to evaluate sphere-pac fuel for transmutation in thermal and fast-spectrum reactors. This AFCI work is unique in that it targets minor actinide transmutation and explores the use of a resin-loading technology for the fabrication of the remote-handled minor actinide fraction. While there are extensive data on sphere-pac fuel performance for both thermal-spectrum and fast-spectrum reactors, there are few data with respect to their use as a transmutation fuel. The sphere-pac fuels developed will be tested as part of the AFCI LWR-2 irradiations. This report provides a review of development efforts related to the fabrication of a sphere-pac rodlet containing surrogate fuel materials. The eventual goal of this activity is to develop a robust process that can be used to fabricate fuels or targets containing americium. The report also provides a review of the materials, methods, and techniques to be used in the fabrication of the surrogate fuel rodlet that will also b

Del Cul, G.D.

2005-07-19

335

The Fukui potential is a measure of the chemical hardness

NASA Astrophysics Data System (ADS)

The chemical hardness is, after the chemical potential, the most important concept in describing the chemical reactivity of atoms and molecules. Recently, we showed that the Fukui potential at the nucleus of an atom is proportional to its hardness. Based on this, we speculated that the Fukui potential at the nucleus could be an alternative definition of the hardness. In this Letter we verify that the Fukui potential successfully describe the hardness of atoms. It is surprising that a property that depends only on the density at the nucleus can give such a good description of the chemical hardness.

Cárdenas, Carlos

2011-09-01

336

Precise algorithm to generate random sequential addition of hard hyperspheres at saturation

NASA Astrophysics Data System (ADS)

The study of the packing of hard hyperspheres in d-dimensional Euclidean space Rd has been a topic of great interest in statistical mechanics and condensed matter theory. While the densest known packings are ordered in sufficiently low dimensions, it has been suggested that in sufficiently large dimensions, the densest packings might be disordered. The random sequential addition (RSA) time-dependent packing process, in which congruent hard hyperspheres are randomly and sequentially placed into a system without interparticle overlap, is a useful packing model to study disorder in high dimensions. Of particular interest is the infinite-time saturation limit in which the available space for another sphere tends to zero. However, the associated saturation density has been determined in all previous investigations by extrapolating the density results for nearly saturated configurations to the saturation limit, which necessarily introduces numerical uncertainties. We have refined an algorithm devised by us [S. Torquato, O. U. Uche, and F. H. Stillinger, Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.74.061308 74, 061308 (2006)] to generate RSA packings of identical hyperspheres. The improved algorithm produce such packings that are guaranteed to contain no available space in a large simulation box using finite computational time with heretofore unattained precision and across the widest range of dimensions (2?d?8). We have also calculated the packing and covering densities, pair correlation function g2(r), and structure factor S(k) of the saturated RSA configurations. As the space dimension increases, we find that pair correlations markedly diminish, consistent with a recently proposed “decorrelation” principle, and the degree of “hyperuniformity” (suppression of infinite-wavelength density fluctuations) increases. We have also calculated the void exclusion probability in order to compute the so-called quantizer error of the RSA packings, which is related to the second moment of inertia of the average Voronoi cell. Our algorithm is easily generalizable to generate saturated RSA packings of nonspherical particles.

Zhang, G.; Torquato, S.

2013-11-01

337

Definite affine spheres and loop groups

NASA Astrophysics Data System (ADS)

We obtain the Weierstrass-type representation and the dressing transformation for definite affine spheres in this paper. As an application of the Weierstrass-type representation, we construct the entire family of finite-Symes type affine spheres.

Liang, Mingheng; Ji, Qingchun

2010-05-01

338

NSDL National Science Digital Library

Hardness is probably a concept you are well familiar with. You already know that certain materials are harder than others; in fact, you prove it everyday when you chew your food and your teeth don’t break (because your teeth are harder than the foods you chew). Hardness can be defined as a material's ability to resist a change in shape. Modern hardness testers take a well-defined shape and press it into a material with a certain force, observing the indent it leaves in the material when it is removed. In this lesson, you will be performing hardness testing on different bars of chocolate.

2007-12-20

339

Eddy currents in a conducting sphere

NASA Technical Reports Server (NTRS)

This report analyzes the eddy current induced in a solid conducting sphere by a sinusoidal current in a circular loop. Analytical expressions for the eddy currents are derived as a power series in the vectorial displacement of the center of the sphere from the axis of the loop. These are used for first order calculations of the power dissipated in the sphere and the force and torque exerted on the sphere by the electromagnetic field of the loop.

Bergman, John; Hestenes, David

1986-01-01

340

Control of Strong-Laser-Field Coupling to Electrons in Solid Targets with Wavelength-Scale Spheres

Irradiation of a planar solid by an intense laser pulse leads to fast electron acceleration and hard x-ray production. We have investigated whether this high field production of fast electrons can be controlled by introducing dielectric spheres of well-defined size on the target surface. We find that the presence of spheres with a diameter slightly larger than half the laser wavelength leads to Mie enhancements of the laser field which, accompanied by multipass stochastic heating of the electrons, leads to significantly enhanced hard x-ray yield and temperature.

Sumeruk, H. A.; Kneip, S.; Symes, D. R.; Churina, I. V.; Belolipetski, A. V.; Ditmire, T. [Texas Center for High Intensity Laser Science, Dept. of Physics, University of Texas at Austin, Austin, Texas 78712 (United States); Donnelly, T. D. [Physics Department, Harvey Mudd College, Claremont, California (United States)

2007-01-26

341

Vortex interaction with a moving sphere

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

J. J. A LLEN; Y. J OUANNE; B. N. S HASHIKANTH

2007-01-01

342

Miniature piezoelectric hollow sphere transducers (BBs)

Miniature piezoelectric transducers were prepared from millimeter size hollow spheres which were formed from PZT-5A powder slurries using a coaxial nozzle process. After sintering, the spheres were poled in two ways: radially and tangentially. Principal modes of vibration were found to be a breathing mode near 700 kHz and a thickness mode near 13 MHz for the radially poled spheres,

Sedat Alkoy; Aydin Dogan; Anne-Christine Hladky; P. Langlet; J. E. Cochran; N. E. Newnham

1997-01-01

343

Vacuum energies on spheres and in cubes

The vacuum energy of a conformally coupled scalar field on the d-dimensional sphere is calculated. On even spheres it is zero and on odd spheres it oscillates in sign. Results for the d-torus and d-cube are also given.

J. S. Dowker

2011-06-18

344

The viscosity of suspensions of rigid spheres

An explanation is given of the dependence of the relative viscosity on the size distribution of the suspended spheres, an effect recently observed by Ward and Whitmore.(1) It is shown theoretically that if the spheres are of very diverse sizes, the relative viscosity is (1 - c)-2.5 for all values of the volume concentration c. For spheres of equal size,

R. Roscoe

1952-01-01

345

Geometrical quantities on a fuzzy sphere

In this paper, we consider the geometrical quantities on the fuzzy sphere from the spectral point of view, such as the area and the dimension. We find that, in contract to the standard sphere, the area and the dimension are the functions of the energy scale of the fuzzy sphere.

Jingbo Wang; Yanshen Wang

2010-07-12

346

Soft spheres make more mesophases

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,

Matthew A. Glaser; Gregory M. Grason; Randall D. Kamien; A. Košmrlj; Christian D. Santangelo; P. Ziherl

2007-01-01

347

Session: Hard Rock Penetration

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.

Tennyson, George P. Jr.; Dunn, James C.; Drumheller, Douglas S.; Glowka, David A.; Lysne, Peter

1992-01-01

348

1! CSI3131 Topics CPU Memory Hard Drive Peripherals Computing Systems OS Overview StructureDeadlocks M em ory M anagem ent Basic Memory Managermtn Virtual Memory Storage and I/O File Systems Hard Drive Management Swap I/O Management 2 Module 7: Memory Management Reading: Chapter 8 Â§ To provide a detailed

Stojmenovic, Ivan

349

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.

Cugell, D.W. (Department of Medicine, Northwestern University Medical School, Chicago, IL (United States))

1992-06-01

350

Poincaré Sphere and Decoherence Problems

Henri Poincar\\'e formulated the mathematics of the Lorentz transformations, known as the Poincar\\'e group. He also formulated the Poincar\\'e sphere for polarization optics. It is shown that these two mathematical instruments can be combined into one mathematical device which can address the internal space-time symmetries of elementary particles, decoherence problems in polarization optics, entropy problems, and Feynman's rest of the universe.

Y. S. Kim

2012-10-12

351

Vortex interaction with a moving sphere

NASA Astrophysics Data System (ADS)

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.

Allen, J. J.; Jouanne, Y.; Shashikanth, B. N.

352

Sedimentation of spheres at small Reynolds number.

The effect of fluid inertia on the settling of spheres in a viscous incompressible fluid is studied in the limit of small Reynolds number. The kinetic energy of flow depends on the positions of the spheres, and gives rise to forces on the spheres. In the dilute limit it suffices to study the corresponding pair interaction. The interaction is calculated from the Stokes flow for two spheres settling between plane walls in the point particle limit. The dissipative interaction between a pair of spheres is calculated from the Proudman-Pearson [I. Proudman and J. R. A. Pearson, J. Fluid Mech. 2, 237 (1957)] solution of the Navier-Stokes equations for flow about a sphere in unbounded geometry. The combination of kinetic and dissipative interaction gives rise to a repulsive force of range of the order of the sphere diameter divided by the Reynolds number. PMID:15974788

Felderhof, B U

2005-06-01

353

Radiation Hard AlGaN Detectors and Imager

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.

None

2012-05-01

354

Instabilities in Very Young Neutron Stars: Density

NSDL National Science Digital Library

This simulation shows the first 20 milliseconds in the life of a neutron star which is formed in a Type II supernova. After an initial collapse phase, the neutron star becomes unstable to convection. The resulting convective motions destroy the spherical symmetry of the star and rapidly mix the inner regions. In addition, the neutrino flux from the neutron star will be non-spherical and will be significantly enhanced by the convective motions. This may have major implications for the Type II supernova mechanism. The calculation was performed using the Piecewise-Parabolic Method for hydrodynamics. The computational grid contained 300 zones in radius and 200 zones in angle. The inner 200 zones in radius were uniformly spaced, ranging from the inner boundary at 25 km to 175 km. The outer 100 zones were non-uniformly spaced and stretched to 2000 km. Only the inner 200 zones are plotted. The inner boundary was treated as a hard sphere. At the outer boundary, zero gradients for all the variables were assumed. Periodic boundary conditions were used along the sides of the grid. The following sequence shows the density evolution for 20 milliseconds after the shock stalls. The density is plotted on a log scale. Values range from 10^9 gm-cm^3 at the outer boundary to 1.4 x 10^12 gm-cm^3 at the inner boundary.

Pamela ONeil

1994-02-12

355

Collective excitations in soft-sphere fluids

NASA Astrophysics Data System (ADS)

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.

Bryk, Taras; Gorelli, Federico; Ruocco, Giancarlo; Santoro, Mario; Scopigno, Tullio

2014-10-01

356

Collective excitations in soft-sphere fluids.

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

Bryk, Taras; Gorelli, Federico; Ruocco, Giancarlo; Santoro, Mario; Scopigno, Tullio

2014-10-01

357

NASA Astrophysics Data System (ADS)

The nucleation kinetics of the rotator phase in hard cuboctahedra, truncated octahedra, and rhombic dodecahedra is simulated via a combination of forward flux sampling and umbrella sampling. For comparable degrees of supersaturation, the polyhedra are found to have significantly lower free-energy barriers and faster nucleation rates than hard spheres. This difference primarily stems from localized orientational ordering, which steers polyhedral particles to pack more efficiently. Orientational order hence fosters here the growth of orientationally disordered nuclei.

Thapar, Vikram; Escobedo, Fernando A.

2014-01-01

358

Self-assembly of amphiphilic Janus particles at planar walls: A density functional study

We investigate the structure formation of amphiphilic molecules at planar walls using density functional theory. The molecules are modeled as (hard) spheres composed of a hydrophilic and hydrophobic part. The orientation of the resulting Janus-particles is described as a vector representing an internal degree of freedom. Our density functional approach involves Fundamental Measure Theory combined with a mean-field approximation for the anisotropic interaction. Considering neutral, hydrophilic and hydrophobic walls, we study the adsorption of the particles, focussing on the competition between the surface field and interact ion-induced ordering phenomena. Finally, we consider systems confined between two planar walls. It is shown that the anisotropic Janus interaction yields pronounced frustration effects at low temperatures.

Gerald Rosenthal; Sabine H. L. Klapp

2010-12-06

359

Crystalline Phases of Polydisperse Spheres

NASA Astrophysics Data System (ADS)

We use specialized Monte Carlo simulation methods and moment free energy calculations to provide conclusive evidence that dense polydisperse spheres at equilibrium demix into coexisting fcc phases, with more phases appearing as the spread of diameters increases. We manage to track up to four coexisting phases. Each of these is fractionated: it contains a narrower distribution of particle sizes than is present in the system overall. We also demonstrate that, surprisingly, demixing transitions can be nearly continuous, accompanied by fluctuations in local particle size correlated over many lattice spacings.

Sollich, Peter; Wilding, Nigel B.

2010-03-01

360

The dynamic sphere test problem

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.

Chabaud, Brandon M. [Los Alamos National Laboratory; Brock, Jerry S. [Los Alamos National Laboratory; Smith, Brandon M. [Los Alamos National Laboratory

2012-05-16

361

Quantum fractals on n-spheres. Clifford Algebra approach

Using the Clifford algebra formalism we extend the quantum jumps algorithm of the Event Enhanced Quantum Theory (EEQT) to convex state figures other than those stemming from convex hulls of complex projective spaces that form the basis for the standard quantum theory. We study quantum jumps on n-dimensional spheres, jumps that are induced by symmetric configurations of non-commuting state monitoring detectors. The detectors cause quantum jumps via geometrically induced conformal maps (Mobius transformations) and realize iterated function systems (IFS) with fractal attractors located on n-dimensional spheres. We also extend the formalism to mixed states, represented by "density matrices". As a numerical illustration we study quantum fractals on the circle, two--sphere (octahedron), and on three-dimensional sphere (hypercube-tesseract, 24 cell, 600 cell,and 120 cell). The invariant measure on the attractor is approximated by the powers of the Markov operator. In the appendices we calculate the Radon-Nikodym derivative of the SO(n+1) invariant measure on S^n under SO(1,n+1) transformations and discuss the Hamilton's "icossian calculus" as well as its application to quaternionic realization of the binary icosahedral group that is at the basis of the 600 cell and its dual, the 120 cell. As a by-product of this work we obtain several Clifford algebraic results, such as a characterization of positive elements in a Clifford algebra Cl(n+1) as generalized Lorentz boosts, and their action as Moebius transformation on n-sphere, and a decomposition of any element of Spin^+(1,n+1) into a boost and a rotation, including the explicit formula for the pullback of the O(n+1) invariant Riemannian metric with respect to the associated Mobius transformation.

Arkadiusz Jadczyk

2007-05-25

362

Sphere-Pac Evaluation for Transmutation

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.

Icenhour, A.S.

2005-05-19

363

Detecting dark energy with wavelets on the sphere

Dark energy dominates the energy density of our Universe, yet we know very little about its nature and origin. Although strong evidence in support of dark energy is provided by the cosmic microwave background, the relic radiation of the Big Bang, in conjunction with either observations of supernovae or of the large scale structure of the Universe, the verification of dark energy by independent physical phenomena is of considerable interest. We review works that, through a wavelet analysis on the sphere, independently verify the existence of dark energy by detecting the integrated Sachs-Wolfe effect. The effectiveness of a wavelet analysis on the sphere is demonstrated by the highly statistically significant detections of dark energy that are made. Moreover, the detection is used to constrain properties of dark energy. A coherent picture of dark energy is obtained, adding further support to the now well established cosmological concordance model that describes our Universe.

J. D. McEwen

2007-08-29

364

SPHERES Smartphone Workbench - Duration: 4:19.

The Smart SPHERES space robot (Synchronized Position Hold, Engage, Reorient, Experimental Satellites) equipped with an Android smartphone performs a video survey inside of the International Space S...

365

Aperture correction for a sphere interferometer

NASA Astrophysics Data System (ADS)

Considerations have been made to derive a correction for the diameter measurements of a sphere by means of a special sphere interferometer. This correction is caused by the finite diameter of the light source acting as the entrance 'pinhole' aperture in the light collimating system. The finite diameter has the effect that the wave which is incident on the sphere is a superposition of spherical waves which are slightly inclined with respect to each other. The resulting correction is essential for high accuracy dimensional measurements of silicon spheres to determine the Avogadro constant—a new determination of which is a contribution to a new definition of the kilogram.

Arnold Nicolaus, R.; Bönsch, Gerhard

2009-12-01

366

Contact mechanics of rough spheres

NASA Astrophysics Data System (ADS)

We use large scale numerical calculations to study the contact mechanics of rough spheres on flat elastic solids. Such geometries are encountered in systems that range from ball bearings to atomic force microscope tips, but the influence of roughness is seldom considered explicitly. Our calculations show that the contact area A grows linearly with load N at small loads and crosses over to Hertzian behavior A N^2/3 at large loads. The total contact stiffness is defined as K = dN/dz where z is the normal displacement of the sphere. It shows power-law K N^? behavior at all loads with an exponent ? that is close to the value of 1/3 expected from Hertzian contact mechanics. The results are discussed in the context of recent theories for flat rough contacts [1] and Greenwood-Williams theory as modified for spherical contacts [2]. [4pt] [1] B.N.J. Persson, J. Chem. Phys. 115, 3840 (2001); S. Hyun, L. Pei, J.-F. Molinari, M.O. Robbins, Phys. Rev. E 70, 026117 (2004); S. Akarapu, T. Sharp, M.O. Robbins, Phys. Rev. Lett. 106, 204301 (2011) [0pt] [2] K.L. Johnson, Contact Mechanics, Cambridge University Press, 1987

Pastewka, Lars; Robbins, Mark

2013-03-01

367

NASA Astrophysics Data System (ADS)

TiO2/carbon hollow composite spheres with mesoporous structure were successfully prepared by using a conventional hard template method but without an on-purpose etching process to remove the core material. A possible surface-protected dissolution mechanism was proposed to account for the spontaneous dissolution of the silica core. The thickness of carbon layer could be well controlled by adjusting the concentration of glucose in the hydrothermal reaction. Moreover, the as-prepared TiO2/C hollow spheres had remarkable light absorption in the visible region. As compared with the SiO2@TiO2 solid spheres prepared without the addition of glucose, the TiO2/C hollow spheres exhibited enhanced photocatalytic efficiency for the visible-light photodegradation of Rhodamine B.

Zhang, Zewu; Zhou, Yuming; Zhang, Yiwei; Sheng, Xiaoli; Zhou, Shijian; Xiang, Sanming

2013-12-01

368

NASA Astrophysics Data System (ADS)

Measurements of jets and heavy ?avour, the so called hard probes, play a crucial role in understanding properties of hot and dense nuclear matter created in high energy heavy-ion collisions. The measurements at the Relativistic Heavy Ion Collider (RHIC) showed that in central Au+Au collisons at RHIC energy ( ?sNN = 200 GeV) the nuclear matter created has properties close to those of perfect liquid, manifests partonic degrees of freedom and is opaque to hard probes. In order to draw quantitative conclusions on properties of this hot and dense nuclear matter reference measurements in proton-proton collisions and d+Au collisions are essential to estimate cold nuclear matter effects. In this proceedings a review of recent results on hard probes measurements in p+p, d+Au and A+A collisions as well as of beam energy dependence of jet quenching from STAR and PHENIX experiments at RHIC is presented.

Biel?íková, Jana

2014-04-01

369

Packing densification of binary mixtures of spheres and cubes subjected to 3D mechanical vibrations

NASA Astrophysics Data System (ADS)

Packing densification of binary mixtures of spheres and cubes, which are large cubes/small spheres and large spheres/small cubes packing systems, under 3D vibrations was studied physically. The influences of vibration conditions such as vibration time, frequency, amplitude, vibration intensity, volume fraction of large particles, and container size on the packing densification were systematically analyzed, and the optimal processing parameters were identified. And the proposed analytical model was validated as well. The results show that the influences of each operating parameter on the packing densification of different binary mixtures have similar trends; however, the maximum packing densities and corresponding optimal parameters are different. The good agreement between physical and analytical results proves the effectiveness of the proposed analytical model. The results provide meaningful information and references for the random dense packings of binary mixtures of cubes and spheres both in industry and in scientific research.

An, X. Z.; He, S. S.; Feng, H. D.; Qian, Q.

2015-01-01

370

Multiple Ferromagnetic Resonance in Ferrite Spheres

Ferromagnetic resonance experiments have been performed on single crystal spheres of manganese and manganese-zinc ferrites placed in field configurations having large gradients in the rf magnetic field at the sample site. Five major and several minor resonant absorptions are observed extending over a region of 700 oersteds at room temperature. The line spacings are essentially independent of sphere size. The

Robert L. White; Irvin H. Solt

1956-01-01

371

Acoustic Scattering from a Sphere Steve Turley

Acoustic Scattering from a Sphere Steve Turley November 24, 2006 Contents 1 Introduction 2 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 References 26 List of Figures 1 Dierential cross section for scattering from an acoustically soft sphere of radius 0.1 wavelengths. 13 2 Dierential cross section for scattering from an acoustically soft

Hart, Gus

372

Practical wavelet design on the sphere

We address the question of designing isotropic analysis functions on the sphere which are perfectly limited in the spectral domain and optimally localized in the spatial domain. This work is motivated by the need of localized analysis tools in domains where the data is lying on the sphere, e.g.{} the science of the Cosmic Microwave Background. Our construction is derived

Frédéric Guilloux; Gilles Fay; Jean-François Cardoso

2007-01-01

373

The periodically oscillating plasma sphere

A new method of operating an inertial electrostatic confinement (IEC) device is proposed, and its performance is evaluated. The scheme involved an oscillating thermal cloud of ions immersed in a bath of electrons that form a harmonic oscillator potential. The scheme is called the periodically oscillating plasma sphere, and it appears to solve many of the problems that may limit other IEC systems to low gain. A set of self-similar solutions to the ion fluid equations is presented, and plasma performance is evaluated. Results indicate that performance enhancement of gridded IEC systems such as the Los Alamos intense neutron source device is possible as well as high-performance operation for low-loss systems such as the Penning trap experiment. Finally, a conceptual idea for a massively modular Penning trap reactor is also presented.

Nebel, R.A.; Barnes, D.C. [Los Alamos National Lab., NM (United States)

1998-08-01

374

Here we show that coupling to curvature has profound effects on collective motion in active systems, leading to patterns not observed in flat space. Biological examples of such active motion in curved environments are numerous: curvature and tissue folding are crucial during gastrulation, epithelial and endothelial cells move on constantly growing, curved crypts and vili in the gut, and the mammalian corneal epithelium grows in a steady-state vortex pattern. On the physics side, droplets coated with actively driven microtubule bundles show active nematic patterns. We study a model of self-propelled particles with polar alignment on a sphere. Hallmarks of these motion patterns are a polar vortex and a circulating band arising due to the incompatibility between spherical topology and uniform motion - a consequence of the hairy ball theorem. We present analytical results showing that frustration due to curvature leads to stable elastic distortions storing energy in the band.

Rastko Sknepnek; Silke Henkes

2014-07-31

375

ERIC Educational Resources Information Center

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.…

Sturgeon, Julie

2008-01-01

376

ERIC Educational Resources Information Center

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,…

Mathews, Jay

2009-01-01

377

ERIC Educational Resources Information Center

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,…

Berry, John N., III

2009-01-01

378

21 CFR 886.3320 - Eye sphere implant.

Code of Federal Regulations, 2011 CFR

...8 2011-04-01 2011-04-01 false Eye sphere implant. 886.3320 Section 886...DEVICES Prosthetic Devices § 886.3320 Eye sphere implant. (a) Identification. An eye sphere implant is a device intended to...

2011-04-01

379

21 CFR 886.3320 - Eye sphere implant.

Code of Federal Regulations, 2012 CFR

...8 2012-04-01 2012-04-01 false Eye sphere implant. 886.3320 Section 886...DEVICES Prosthetic Devices § 886.3320 Eye sphere implant. (a) Identification. An eye sphere implant is a device intended to...

2012-04-01

380

21 CFR 886.3320 - Eye sphere implant.

Code of Federal Regulations, 2010 CFR

...8 2010-04-01 2010-04-01 false Eye sphere implant. 886.3320 Section 886...DEVICES Prosthetic Devices § 886.3320 Eye sphere implant. (a) Identification. An eye sphere implant is a device intended to...

2010-04-01

381

382

21 CFR 886.3320 - Eye sphere implant.

Code of Federal Regulations, 2013 CFR

...8 2013-04-01 2013-04-01 false Eye sphere implant. 886.3320 Section 886...DEVICES Prosthetic Devices § 886.3320 Eye sphere implant. (a) Identification. An eye sphere implant is a device intended to...

2013-04-01

383

Monodisperse PEGylated spheres: an aqueous colloidal model system.

Fluorinated core-shell spheres have been synthesized using a novel semibatch emulsion polymerization protocol employing slow feeding of the initiator. The synthesis results in aqueous dispersions of highly monodisperse spheres bearing a well-defined poly(ethylene glycol) graft (PEGylation). Measurements are consistent with the synthesis achieving a high grafting density that moreover consists of a single PEG layer with the polymer significantly elongated beyond its radius of gyration in bulk. The fluorination of the core of the particles confers a low index of refraction such that the particles can be refractive index matched in water through addition of relatively small amounts of a cosolvent, which enables the use of optical and laser-based methods for studies of concentrated systems. The systems exhibit an extreme stability in NaCl solutions, but attractions among particles can be introduced by addition of other salts, in which case aggregation is shown to be reversible. The PEGylated sphere dispersions are expected to be ideally suited as model systems for studies of the effect of PEG-mediated interactions on, for instance, structure, dynamics, phase behavior, and rheology. PMID:24533774

Ulama, Jeanette; Zackrisson Oskolkova, Malin; Bergenholtz, Johan

2014-03-01

384

Non-axisymmetric wind-accretion simulations. II. Density gradients

The hydrodynamics of a variant of classical Bondi-Hoyle-Lyttleton accretion is investigated: a totally absorbing sphere moves at various Mach numbers (3 and 10) relative to a medium, which is taken to be an ideal gas having a density gradient (of 3%, 20% or 100% over one accretion radius) perpendicular to the relative motion. Similarly to the 3D models published previously, both with velocity gradients and without, the models with a density gradient presented here exhibit non-stationary flow patterns, although the Mach cone remains fairly stable. The accretion rates of mass, linear and angular momenta do not fluctuate as strongly as published previously for 2D models. No obvious trend of the dependency of mass accretion rate fluctuations on the density gradient can be discerned. The average specific angular momentum accreted is roughly between zero and 70% of the total angular momentum available in the accretion cylinder in the cases where the average is prograde. Due to the large fluctuations during accretion, the average angular momentum of some models is retrograde by up to 25%. Small gradients hardly influence the average accretion rates as compared to accretion from a homogeneous medium, while very large ones succeed to dominate and form an accretion flow in which the sense of rotation is not inverted.

M. Ruffert

1999-03-19

385

Green's function of radial inhomogeneous spheres excited by internal sources.

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

Zouros, Grigorios P; Kokkorakis, Gerassimos C

2011-01-01

386

In this study the Singlet Reference Interaction Site Model (SRISM) is employed to the study of the electrode charge dependence of the capacitance of a planar electric double layer using the primitive model of the double layer for a high density electrolyte that mimics an ionic liquid. The ions are represented by charged hard spheres and the electrode is a uniformly charged flat surface. The capacitance of this model fluid is calculated with the SRISM approach with closures based on the hypernetted chain (HNC) and Kovalenko-Hirata (KH) closures and compared with simulations. As long as the magnitude of the electrode charge is not too great, the HNC closure shows the most promise. The KH results are reasonably good for a high density electrolyte but are poor when applied at low densities.

S. Woelki; D. Henderson

2012-02-22

387

Ceramic Spheres From Cation Exchange Beads

NASA Technical Reports Server (NTRS)

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.

Dynys, F. W.

2003-01-01

388

Application of micromachine technologies to hard disk drives

We propose applications of micromachine technologies to increase the areal density of Hard Disk Drives (HDDs). The most attractive ways to increase the density are head positioning with high accuracy and ultra-low flying height of head sliders. We propose two micro actuators and a non-assembly micro structure. One of micro actuators is essential to achieve highly accurate positioning of head.

S. Nakamura

1998-01-01

389

Wake formation behind a rolling sphere

NASA Astrophysics Data System (ADS)

Experimental flow visualizations are presented depicting the flow behind a spherical body moving on a plane wall. In the Reynolds number range of 100

Stewart, B. E.; Leweke, T.; Hourigan, K.; Thompson, M. C.

2008-07-01

390

Representation of Qudits on a Riemann Sphere

In quantum computation and information science, the geometrical representations based on the Bloch sphere representation for transformations of two state systems have been traditionally used. While this representation is very useful for the two state qubit, it cannot be generalized easily to multiple states like that of qudits and when it is generalized, it looses its simple geometrical representation. This paper proposes the use of an alternative representation in quantum information and computation for qubits as well as qudits based on the Majorana representation on the Riemann Sphere, which preserves the simple sphere representation.

Rahul Bijurkar

2007-03-20

391

NASA Technical Reports Server (NTRS)

StenniSphere, the John C. Stennis Space Center's visitor center in Hancock County, Miss., features a 14,000-square-foot museum and outdoor exhibits about Stennis Space Center. Designed to entertain while educating, StenniSphere includes informative displays and exhibits from NASA, the Naval Meteorology and Oceanography Command, and other resident agencies. Recently named Mississippi's Travel Attraction of the Year, StenniSphere hosted a quarter of a million visitors in its first year and is a major school field trip destination.

2001-01-01

392

Manipulator for rotating and examining small spheres

A manipulator is disclosed which provides fast, accurate rotational positioning of a small sphere, such as an inertial confinement fusion target, which allows inspecting of the entire surface of the sphere. The sphere is held between two flat, flexible tips which move equal amounts in opposite directions. This provides rolling of the ball about two orthogonal axes without any overall translation. The manipulator may be controlled, for example, by an x- and y-axis driven controlled by a mini-computer which can be programmed to generate any desired scan pattern. 8 figs.

Weinstein, B.W.; Willenborg, D.L.

1980-02-12

393

Manipulator for rotating and examining small spheres

A manipulator which provides fast, accurate rotational positioning of a small sphere, such as an inertial confinement fusion target, which allows inspecting of the entire surface of the sphere. The sphere is held between two flat, flexible tips which move equal amounts in opposite directions. This provides rolling of the ball about two orthogonal axes without any overall translation. The manipulator may be controlled, for example, by an x- and y-axis driven controlled by a mini-computer which can be programmed to generate any desired scan pattern.

Weinstein, Berthold W. [Livermore, CA; Willenborg, David L. [Livermore, CA

1980-02-12

394

Density Functional Theory (DFT) Rob Parrish

Density Functional Theory (DFT) Rob Parrish robparrish@gmail.com 1 #12;Agenda Â· The mechanism Â· References 2 #12;Wavefunction Approach 3 Hydrogen 421 Wavefunction at Density Isosurface. Really hard to find Easy to do this Why? Because of Hermitian Operators: Kinetic Energy Density: #12;Density Functional

Sherrill, David

395

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.

Mansur, Louis K [ORNL] [ORNL; Bhattacharya, R [UES, Incorporated, Dayton, OH] [UES, Incorporated, Dayton, OH; Blau, Peter Julian [ORNL] [ORNL; Clemons, Art [ORNL] [ORNL; Eberle, Cliff [ORNL] [ORNL; Evans, H B [UES, Incorporated, Dayton, OH] [UES, Incorporated, Dayton, OH; Janke, Christopher James [ORNL] [ORNL; Jolly, Brian C [ORNL] [ORNL; Lee, E H [Consultant, Milpitas, CA] [Consultant, Milpitas, CA; Leonard, Keith J [ORNL] [ORNL; Trejo, Rosa M [ORNL] [ORNL; Rivard, John D [ORNL] [ORNL

2010-01-01

396

NASA Astrophysics Data System (ADS)

SPHERE is an extrasolar planet imager whose goal is to detect giant extrasolar planets in the vicinity of bright stars and to characterize them through spectroscopic and polarimetric observations. It is a complete system with a core made of an extreme-Adaptive Optics (AO) turbulence correction, a pupil tracker and NIR and Visible coronagraph devices. At its back end, a differential dual imaging camera and an integral field spectrograph (IFS) work in the Near Infrared (NIR) (0.95 <=?<=2.32 ?m) and a high resolution polarization camera covers the visible (0.6 <=?<=0.9 ?m). The IFS is a low resolution spectrograph (R~50) operates in the near IR (0.95<=?<=1.6 ?m), an ideal wavelength range for the detection of planetary features, over a field of view of about 1.7 x 1.7 square arcsecs. Form spectra it is possible to reconstruct monochromatic images with high contrast (10-7) and high spatial resolution, well inside the star PSF. In this paper we describe the IFS, its calibration and the results of several performance which IFS underwent. Furthermore, using the IFS characteristics we give a forecast on the planetary detection rate.

Claudi, R.; Giro, E.; Turatto, M.; Baruffolo, A.; Bruno, P.; Cascone, E.; DeCaprio, V.; Desidera, S.; Dorn, R.; Fantinel, D.; Finger, G.; Gratton, R.; Lessio, L.; Lizon, J. L.; Maire, A. L.; Mesa, D.; Salasnich, B.; Scuderi, S.; Zurlo, A.; Dohlen, K.; Beuzit, J. L.; Mouillet, D.; Puget, P.; Wildi, Francois; Hubin, N.; Kasper, M.

2014-07-01

397

Local hardness equalization and the principle of maximum hardness.

The chemical potential, hardness, and hyperhardnesses equalization principles are used to show that the leading term associated with charge transfer in the total interaction energy among the fragments in which a molecule is divided is directly proportional to minus the hardness of the molecule in its ground state, as established by the principle of maximum hardness. The additional terms in the interaction energy, associated with the changes in the external potential of the fragments, provide explanation for deviations between the point of maximum hardness and the point of minimum energy. It is also found that the dual descriptor plays a very important role in hardness equalization. PMID:23758354

Gázquez, José L; Vela, Alberto; Chattaraj, Pratim K

2013-06-01

398

NASA Astrophysics Data System (ADS)

Monte Carlo (MC) simulation and classical density functional theory (DFT) results are reported for the structural and electrostatic properties of a planar electric double layer containing ions having highly asymmetric diameters or valencies under extreme concentration condition. In the applied DFT, for the excess free energy contribution due to the hard sphere repulsion, a recently elaborated extended form of the fundamental measure functional is used, and coupling of Coulombic and short range hard-sphere repulsion is described by a traditional second-order functional perturbation expansion approximation. Comparison between the MC and DFT results indicates that validity interval of the traditional DFT approximation expands to high ion valences running up to 3 and size asymmetry high up to diameter ratio of 4 whether the high valence ions or the large size ion are co- or counter-ions; and to a high bulk electrolyte concentration being close to the upper limit of the electrolyte mole concentration the MC simulation can deal with well. The DFT accuracy dependence on the ion parameters can be self-consistently explained using arguments of liquid state theory, and new EDL phenomena such as overscreening effect due to monovalent counter-ions, extreme layering effect of counter-ions, and appearance of a depletion layer with almost no counter- and co-ions are observed.

Zhou, Shiqi; Lamperski, Stanis?aw; Zydorczak, Maria

2014-08-01

399

Detecting dark energy with wavelets on the sphere Jason D. McEwen

Detecting dark energy with wavelets on the sphere Jason D. McEwen Astrophysics Group, Cavendish Laboratory, Cambridge CB3 0HE, UK ABSTRACT Dark energy dominates the energy density of our Universe, yet we know very little about its nature and origin. Although strong evidence in support of dark energy

McEwen, Jason

400

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.

Yi, Bin [College of Materials Science and Engineering, Hunan University, Changsha 410082 (China)] [College of Materials Science and Engineering, Hunan University, Changsha 410082 (China); Chen, Xiaohua, E-mail: hudacxh62@yahoo.com.cn [College of Materials Science and Engineering, Hunan University, Changsha 410082 (China)] [College of Materials Science and Engineering, Hunan University, Changsha 410082 (China); Guo, Kaimin [College of Physics and Electronic Science, Changsha University of Science and Technology (China)] [College of Physics and Electronic Science, Changsha University of Science and Technology (China); Xu, Longshan [Department of Mechanical Engineering, Xiamen University of Technology, Xiamen 361024 (China)] [Department of Mechanical Engineering, Xiamen University of Technology, Xiamen 361024 (China); Chen, Chuansheng [College of Physics and Electronic Science, Changsha University of Science and Technology (China)] [College of Physics and Electronic Science, Changsha University of Science and Technology (China); Yan, Haimei; Chen, Jianghua [College of Materials Science and Engineering, Hunan University, Changsha 410082 (China)] [College of Materials Science and Engineering, Hunan University, Changsha 410082 (China)

2011-11-15

401

Water entry of small hydrophobic spheres

We present the results of a combined experimental and theoretical investigation of the normal impact of hydrophobic spheres on a water surface. Particular attention is given to characterizing the shape of the resulting air ...

Bush, John W. M.

402

StenniSphere reopens after Hurricane Katrina

NASA Technical Reports Server (NTRS)

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.

2006-01-01

403

The objective of this study was to attempt to deliver glipizide from spheres and compacts containing the natural polymer Carrageenan (Gelcarin, GP 812) and prepared by extruder/marumerizer technique. A second objective was to evaluate the mucoadhesive strength of the bioadhesive spheres onto the mucus membrane of rabbit. The effects of polymer, drug level, and type of spheronizing material were evaluated. All sphere formulations were compacted into tablets using a rotary Manesty B-3B machine equipped with 12/32 flat face tooling. Results show drug release from spheres and compacts decreased as the level of Carrageenan was increased. However as the level of drug was increased drug release also increased. Spheres containing Avicel PH-101 gave higher drug release than spheres of the same composition but prepared with Avicel RC-581. In general, the drug release from tablets was higher than its corresponding spheres and drug release from spheres and tablets containing Carrageenan was higher than control spheres and tablets of the same composition but without Carrageenan. Tablet formulations compacted from spheres containing Avicel RC-581 gave higher release rate constants than tablet formulations of the same composition but prepared with Avicel PH-101. The bioadhesion study showed that mucoadhesion strength between spheres and mucus membrane of the rabbit depends on the levels of polymer, drug, and type of spheronizing material. Developed bioadhesive spheres and tablets increase the solubility of glipizide which may increase its bioavailability and also increased the adherence of the bioadhesive systems to the mucous membrane so that once daily dose can be administered. PMID:11485182

Garcia, J; Ghaly, E S

2001-08-01

404

Isospectral deformations of metrics on spheres

NASA Astrophysics Data System (ADS)

We construct non-trivial continuous isospectral deformations of Riemannian metrics on the ball and on the sphere in $\\R^n$ for every $n\\geq 9$. The metrics on the sphere can be chosen arbitrarily close to the round metric; in particular, they can be chosen to be positively curved. The metrics on the ball are both Dirichlet and Neumann isospectral and can be chosen arbitrarily close to the flat metric.

Gordon, Carolyn S.

2001-08-01

405

Particle sizing in highly turbid dispersions by Photon Density Wave spectroscopy

NASA Astrophysics Data System (ADS)

Photon Density Wave (PDW) spectroscopy is presented as a fascinating technology for the independent determination of scattering (??s) and absorption (?a) properties of highly turbid liquid dispersions. The theory is reviewed introducing new expressions for the PDW coefficients kI and k?. Furthermore, two models for dependent scattering, namely the hard sphere model in the Percus-Yevick Approximation (HSPYA) and the Yukawa model in the Mean Spherical Approximation (YMSA), are experimentally examined. On the basis of the HSPYA particle sizing is feasible in dispersions of high ionic strength. It is furthermore shown that in dialyzed dispersions or in technical copolymers with high particle charge only the YMSA allows for correct dilution-free particle sizing.

Bressel, L.; Hass, R.; Reich, O.

2013-09-01

406

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.

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. [Texas Center for High Intensity Laser Science, Department of Physics, University of Texas, Austin, Texas 78712 (United States); Department of Physics, Harvey Mudd College, Claremont, California 91711 (United States); Institut fuer Theoretische Physik I, Heinrich-Heine-University of Dusseldorf, 40225 Dusseldorf (Germany); Texas Center for High Intensity Laser Science, Department of Physics, University of Texas, Austin, Texas 78712 (United States)

2007-06-15

407

As a common used and hardly emulsified amorphous thermoplastic, the bisphenol-A polycarbonates were used as the polymer candidate to form a novel monodispersed sub-micrometer mesoporous polymer-silica spheres with full interpenetrating structure. The synthesis procedure was based on a modified sol-gel approach in which the polycarbonate was plasticized in advanced by the surfactant of polymer emulsion. The mesoporous spheres possess a perfect uniform particle size and the polymer-silica spheres are held together by permanent entanglement in three dimensions. The defined crystallization of the polycarbonate was occurred when it was entrapped in the silica laminated matrix due to the plasticizing effect of the surfactant, and directly affected the thermal stability of the mesoporous spheres. The specific surface areas and pore diameters of mesoporous sphere were affected by the mass content and crystallization behavior of the polycarbonate. The p-phenylenediamine was used as adsorbate to investigate the cationic organics adsorption ability of the mesoporous spheres. The results shown that the polycarbonate-silica possess a well adsorption capacity for p-phenylenediamine by virtue of two kinds of hydrogen bond, and the maximum adsorption capacity was nearly 7.5 times larger than that of the hollow mesoporous silica. PMID:24491338

Zu, Lei; Li, Ruirui; Shi, Yue; Lian, Huiqin; Liu, Yang; Cui, Xiuguo; Bai, Zongwu

2014-04-01

408

We analyze the geometric structure and mechanical stability of a complete set of isostatic and hyperstatic sphere packings obtained via exact enumeration. The number of nonisomorphic isostatic packings grows exponentially with the number of spheres $N$, and their diversity of structure and symmetry increases with increasing $N$ and decreases with increasing hyperstaticity $H \\equiv N_c - N_{ISO}$, where $N_c$ is the number of pair contacts and $N_{ISO} = 3N-6$. Maximally contacting packings are in general neither the densest nor the most symmetric. Analyses of local structure show that the fraction $f$ of nuclei with order compatible with the bulk (RHCP) crystal decreases sharply with increasing $N$ due to a high propensity for stacking faults, 5- and near-5-fold symmetric structures, and other motifs that preclude RHCP order. While $f$ increases with increasing $H$, a significant fraction of hyperstatic nuclei for $N$ as small as 11 retain non-RHCP structure. Classical theories of nucleation that consider only spherical nuclei, or only nuclei with the same ordering as the bulk crystal, cannot capture such effects. Our results provide an explanation for the failure of classical nucleation theory for hard-sphere systems of $N\\lesssim 10$ particles; we argue that in this size regime, it is essential to consider nuclei of unconstrained geometry. Our results are also applicable to understanding kinetic arrest and jamming in systems that interact via hard-core-like repulsive and short-ranged attractive interactions.

Robert S. Hoy; Jared Harwayne-Gidansky; Corey S. O'Hern

2012-05-02

409

NASA Astrophysics Data System (ADS)

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 500°C 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.

Yao, Ran-Ran; Zhao, Dong-Lin; Bai, Li-Zhong; Yao, Ning-Na; Xu, Li

2014-07-01

410

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 500°C 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. PACS 81.05.ue; 61.48.Gh; 72.80.Vp PMID:25114657

2014-01-01

411

We review recent results on hard observables in p+p, d+A and A+A collisions obtained by the PHENIX experiment. Emphasis is put on those measurements that provide insight into the properties of hot QCD media expected to be created in nucleus-nucleus collisions at RHIC energies. Direct photon spectra, jet properties and heavy quarks production measured in p+p and d+Au collisions are compared to the same observables extracted in heavy ion collisions to find modifications due to the presence of hot QCD matter.

D. Peressounko; for the PHENIX collaboration

2005-12-08

412

Hardness of Materials- Introduction

NSDL National Science Digital Library

This lesson plan from Edmonds Community College will serve as an excellent introduction to the hardness of materials. The module illustrates the differences in properties between different materials. Students will determine property differences between different types of materials, observe property differences between materials of the same class, measure, record and report their results and observe differences in results due to operator error. Student, instructor and course evaluation questions are included. This document will serve as a framework for instructors and may be downloaded in PDF format.

2012-10-12

413

We have studied interfacial structure and properties of liquid-vapor interfaces of dipolar fluids and quadrupolar fluids, respectively, using the classical density functional theory (DFT). Towards this end, we employ the fundamental measure DFT for a reference hard-sphere (HS) part of free energy and the modified mean field approximation for the correlation function of dipolar or quadrupolar fluid. At low temperatures we find that both the liquid-vapor interfacial density profile and orientational order parameter profile exhibit weakly damped oscillatory decay into the bulk liquid. At high temperatures the decay of interfacial density and order parameter profiles is entirely monotonic. The scaled temperature ? = 1 - T/T(c) that separates the two qualitatively different interfacial structures is in the range 0.10-0.15. At a given (dimensionless) temperature, increasing the dipolar or quadrupolar moment enhances the density oscillations. Application of an electric field (normal to the interface) will damp the oscillations. Likewise, at the given temperature, increasing the strength of any multipolar moment also increases the surface tensions while increasing the strength of the applied electric field will reduce the surface tensions. The results are compared with those based on the local-density approximations (LDA) for the reference HS part of free energy as well as with results of numerical experiments. PMID:24116570

Warshavsky, V B; Zeng, X C

2013-10-01

414

NASA Astrophysics Data System (ADS)

We present a Fourier space density functional approach for hard particles with attractive interactions, which is based on a previously developed two-dimensional approach [S. Hlushak, W. R?ysko, and S. Soko?owski, J. Chem. Phys. 131, 094904 (2009), 10.1063/1.3213623] for hard-sphere chains. The interactions are incorporated by means of a three-dimensional Fourier image of the direct correlation function that is obtained from the first-order mean-spherical approximation. In order to improve the computational efficiency, we make extensive use of fast Fourier transforms for calculating density convolution integrals. A two-dimensional implementation of the new density functional approach, based on the expansion of the functional around the bulk fluid density, is used to study structure and adsorption of two model fluids in narrow cylindrical pores. We also investigate two methods that improve the accuracy of the theory as compared to the conventional DFT approach, which expands the free energy functional around the bulk fluid density: One a variant of the reference fluid density functional theory used by Gillespie et al. [Phys. Rev. E 68, 031503 (2003), 10.1103/PhysRevE.68.031503], and the second a weighted density approach with energy route thermodynamics. Results from these two methods are compared to the conventional approach and also to the results of Monte Carlo simulations. We find that the method of Gillespie et al. and the weighted density approach with energy route thermodynamics yield significant improvement over the conventional approach.

Hlushak, Stepan P.; McCabe, Clare; Cummings, Peter T.

2012-09-01

415

Collinear swimmer propelling a cargo sphere at low Reynolds number.

The swimming velocity and rate of dissipation of a linear chain consisting of two or three little spheres and a big sphere is studied on the basis of low Reynolds number hydrodynamics. The big sphere is treated as a passive cargo, driven by the tail of little spheres via hydrodynamic and direct elastic interaction. The fundamental solution of Stokes equations in the presence of a sphere with a no-slip boundary condition, as derived by Oseen, is used to model the hydrodynamic interactions between the big sphere and the little spheres. PMID:25493887

Felderhof, B U

2014-11-01

416

Terminal energy distribution of blast waves from bursting spheres

NASA Technical Reports Server (NTRS)

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.

Adamczyk, A. A.; Strehlow, R. A.

1977-01-01

417

Recent researches on the air resistance of spheres

NASA Technical Reports Server (NTRS)

The following conclusions on air resistance of spheres are drawn: 1) disturbances in front of the sphere and even single fine wires affect the critical Reynolds Number; 2) disturbances around the sphere increased the drag of the sphere without martially affecting the value of the Reynolds Number(sub crith); 3) great disturbances of the boundary layer of the sphere likewise change R.N.(sub crith); 4) turbulence of the approaching air stream lowers critical R.N.

Flachsbart, O

1928-01-01

418

Effective density and atomic number determined from diffraction profiles

NASA Astrophysics Data System (ADS)

X-ray diffraction (XRD) profiles are conventionally used to determine lattice spacings via Bragg's law in order to characterize crystalline materials. It does not appear to be widely known that they also permit compositional information, such as effective atomic number and a density descriptor, to be determined from materials having little or no crystal structure. A ratio method is introduced that relates x-ray scatter intensities in two adjacent momentum transfer bands of the diffraction profile corresponding to the "tip" region of the primary x-ray spectrum. It is shown that this ratio depends on the effective atomic number, Z, of the scattering sample. Conversely, Z may be derived from measurement of the ratio. Error sources in this ratio method are briefly analyzed. Once Z is known, the IAM (independent atom model) cross section can be extrapolated from the high momentum transfer region to lower values, where molecular interference effects manifest themselves in the XRD profile. This procedure enables the molecular interference function, s(x), to be determined. On the assumption that the structure of liquids and amorphous materials can be represented by the hard sphere (HS) model, the packing fraction, ?, of atoms in the scattering sample can be ascertained from the second moment of s(x). The effective atomic number, Z and the density descriptor, ?, usefully complement information provided by more traditional material analysis techniques based on XRD profiles.

Harding, Geoffrey

2006-08-01

419

We extend previous analysis of data for the melt-nucleus interfacial free energy, $\\gamma$, gained from optical experiments on suspensions of charged colloidal spheres, which crystallize with body centred cubic (bcc) crystal structures. Compiling data from five pure species with different polydispersities and one binary mixture, we find the equilibrium melt-crystal interfacial energy to be considerably larger than the hard sphere reference value. Both this quantity and the entropy of freezing decrease with increasing polydispersity. Moreover, we give a first experimental determination of the Turnbull coefficient for a bcc crystallizing material. The observed value $C_{T, bcc} \\approx 0.3$ agrees well with theoretical expectations for bcc systems with short to medium ranged interactions.

Thomas Palberg; Patrick Wette; Dieter M. Herlach

2014-03-25

420

Non-axisymmetric wind-accretion simulations. II. Density gradients

NASA Astrophysics Data System (ADS)

The hydrodynamics of a variant of classical Bondi-Hoyle-Lyttleton accretion is investigated: a totally absorbing sphere moves at various Mach numbers (3 and 10) relative to a medium, which is taken to be an ideal gas having a density gradient (of 3%, 20% or 100% over one accretion radius) perpendicular to the relative motion. I examine the influence of the Mach number, the adiabatic index, and the strength of the gradient upon the physical behaviour of the flow and the accretion rates of the angular momentum in particular. The hydrodynamics is modeled by the ``Piecewise Parabolic Method'' (PPM). The resolution in the vicinity of the accretor is increased by multiply nesting several grids around the sphere. Similarly to the 3D models published previously, both with velocity gradients and without, the models with a density gradient presented here exhibit non-stationary flow patterns, although the Mach cone remains fairly stable. The accretion rates of mass, linear and angular momenta do not fluctuate as strongly as published previously for 2D models. No obvious trend of the dependency of mass accretion rate fluctuations on the density gradient can be discerned. The average specific angular momentum accreted is roughly between zero and 70% of the total angular momentum available in the accretion cylinder in the cases where the average is prograde. Due to the large fluctuations during accretion, the average angular momentum of some models is retrograde by up to 25%. The magnitude is always smaller than the value of a vortex with Kepler velocity around the surface of the accretor. The models with small density gradients initially display a transient quasi-stable accretion phase in which the specific angular momentum accreted is within 10% of the total angular momentum available in the accretion cylinder. Later, when the flow becomes unstable, the average decreases. I conclude that for accretion from a medium with both density and/or velocity gradients, most of the angular momentum that is available in the accretion cylinder is accreted together with mass. Small gradients hardly influence the average accretion rates as compared to accretion from a homogeneous medium, while very large ones succeed to dominate and form an accretion flow in which the sense of rotation is not inverted.

Ruffert, M.

1999-06-01

421

Analytic expressions that describe Casimir interactions over the entire range of separations have been limited to planar surfaces. Here we derive analytic expressions for the classical or high-temperature limit of Casimir interactions between two spheres (interior and exterior configurations), including the sphere-plane geometry as a special case, using bispherical coordinates. We consider both Dirichlet boundary conditions and metallic boundary conditions described by the Drude model. At short distances, closed-form expansions are derived from the exact result, displaying an intricate structure of deviations from the commonly employed proximity force approximation. PMID:23215058

Bimonte, Giuseppe; Emig, Thorsten

2012-10-19

422

Free Cooling Phase-Diagram of Hard-Spheres with Short- and Long-Range Interactions

We study the stability, the clustering and the phase-diagram of free cooling granular gases. The systems consist of mono-disperse particles with additional non-contact (long-range) interactions, and are simulated here by the event-driven molecular dynamics algorithm with discrete (short-range shoulders or wells) potentials (in both 2D and 3D). Astonishingly good agreement is found with a mean field theory, where only the energy dissipation term is modified to account for both repulsive or attractive non-contact interactions. Attractive potentials enhance cooling and structure formation (clustering), whereas repulsive potentials reduce it, as intuition suggests. The system evolution is controlled by a single parameter: the non-contact potential strength scaled by the fluctuation kinetic energy (granular temperature). When this is small, as expected, the classical homogeneous cooling state is found. However, if the effective dissipation is strong enough, structure formation proceeds, before (in the repulsive case) non-contact forces get strong enough to undo the clustering (due to the ongoing dissipation of granular temperature). For both repulsive and attractive potentials, in the homogeneous regime, the cooling shows a universal behaviour when the (inverse) control parameter is used as evolution variable instead of time. The transition to a non-homogeneous regime, as predicted by stability analysis, is affected by both dissipation and potential strength. This can be cast into a phase diagram where the system changes with time, which leaves open many challenges for future research.

S. Gonzalez; A. R. Thornton; S. Luding

2014-07-09

423

Calculation of the entropy of binary hard sphere mixtures from pair correlation functions

. Frenkel, Mol. Phys. 72, 715 (1991). 23 A. Baranyai and D. J. Evans, Z. Narturforsch. 46a, 27 (1990). 24W. G. T. Kranendonk and D. Frenkel, Mol. Phys. 72, 679 (1991). 2SB. B. Laird and A. D. J. Haymet, J. Phys. Chern., in preparation (1992). 26T...

Laird, Brian Bostian; Haymet, A. D. J.

1992-06-01

424

A MATHEMATICAL MODEL FOR THE HARD SPHERE REPULSION IN IONIC SOLUTIONS

in the concentrated solutions near electrodes, active sites of enzymes, and selectivity filters of proteins. Finally. For example, in electrochemistry ions are highly concentrated near electrodes. In biology ions are highly Solutions well summarized in a recent book [65] and indee

Hyon, YunKyong

425

Periodic and Aperiodic Close Packing: A Spontaneous Hard-Sphere Model.

ERIC Educational Resources Information Center

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…

van de Waal, B. W.

1985-01-01

426

Crossover Behavior in the Packing and Assembly of Concave Hard Spheres

Particle shape plays an important role in assembly and packing. The combination of concave and convex surfaces in particular influence the way particles arrange, both entropically and in the limit of infinite pressure. We study recently synthesized spheroidal particles with up to six symmetric concavities (dimples) between the convex and concave extents of their shape. These particles exhibit a crossover in behavior during both packing and assembly arising from a competition between their convex and concave features. We identify the shape features that control this crossover as the total circumference to depth ratio of dimples in packing, and the individual dimple volume in assembly.

N. Khalid Ahmed; Greg van Anders; Elizabeth R. Chen; Sharon C. Glotzer

2015-01-13

427

Sticky red spheres can be used to capture western cherry fruit fly, Rhagoletis indifferens Curran (Diptera: Tephritidae), but red spheres have not been definitively shown to be more attractive than yellow traps. The objective of this study was to compare fly captures on ammonia-baited red spheres and yellow spheres and panels so that sensitive detection traps for fly management can be identified. Nontarget insects could interfere with fly captures, so weights of nontarget insects on traps were also determined. Yellow spheres and panels generally caught more flies than red spheres. More males than females were caught on nearly all red and yellow traps. Saffron Thread, Marigold, Sunny Summer, and Yam Yellow spheres and panels were bright yellow and generally caught more flies, especially females, than Cherry Cobbler Red or Tartar Red spheres. Twenty Carat Yellow and Glorious Gold spheres and panels were less bright and caught fewer flies than bright yellow traps and similar numbers of flies as Tartar Red spheres, respectively. Dry weights of nontarget insects on at least one yellow trap type were greater than on red spheres in only 4 of 10 tests. Results show that bright yellow spheres and panels capture more R. indifferens than red spheres and do not consistently capture greater amounts of nontarget insects than red spheres, suggesting that they should be used instead of red spheres for detecting this fly. PMID:24224253

Yee, Wee L

2013-10-01

428

Surface layer determination for the Si spheres of the Avogadro project

NASA Astrophysics Data System (ADS)

For the accurate determination of the Avogadro constant, two 28Si spheres were produced, whose macroscopic density, in addition to other values, must be determined. To make a contribution to the new definition of the kilogram, a relative standard uncertainty of less than 2 × 10-8 has to be achieved. Each silicon surface is covered by a surface layer (SL). Consequently, correction parameters for the SL are determined to be applied to the mass and volume determination of the enriched spheres. With the use of a large set of surface analysing techniques, the structure of the SL is investigated. An unexpected metallic contamination existing on the sphere surface enlarges the uncertainty contribution of the correction parameters above the originally targeted value of 1 × 10-8. In the framework of this investigation this new obstacle is resolved in two ways. A new combination of analytical methods is applied to measure the SL mass mSL and the thickness dSL, including this new contamination, with an uncertainty of u(mSL) = 14.5 µg and 14.4 µg, respectively, and u(dSL) = 0.33 nm and 0.32 nm for the 28Si spheres AVO28-S5 and AVO28-S8, respectively. In the second part of the work, the chemical composition of these metallic contaminations is found to be Cu, Ni and Zn silicide compounds. For the removal of this contamination, a special procedure is developed, tested and applied to the spheres to produce the originally expected surface structure on the spheres. After the application of this new procedure the use of x-ray reflectometry directly at the spheres will be possible. It is expected to reduce the uncertainty contribution due to the SL down to 1 × 10-8.

Busch, I.; Azuma, Y.; Bettin, H.; Cibik, L.; Fuchs, P.; Fujii, K.; Krumrey, M.; Kuetgens, U.; Kuramoto, N.; Mizushima, S.

2011-04-01

429

Outer-sphere electron transfer kinetics of metal ion oxidation by molecular oxygen

NASA Astrophysics Data System (ADS)

Density functional theory molecular orbital calculations and Marcus theory have been combined to assess the rates and physicochemical factors controlling the outer-sphere oxidation of divalent V, Cr, Mn, Fe, and Co aquo and hydroxo ions by O 2 in homogeneous aqueous solution. Key quantities in the elementary oxidation step include the inner-sphere component of the reorganization energy, the thermodynamic driving force, and electrostatic work terms describing the interactions occurring, in this case, between the net charges on the product species. Collectively, these factors and their interplay have a large influence on the rate of the oxidation cross-reaction. An inner-sphere pathway for the self-exchange reactions and oxidation by O 2 of Mn 2+ and Cr 2+ ions has been supported indirectly in this study by comparing predicted outer-sphere rates with the results of previous experiments. Likewise, an outer-sphere pathway is suggested for the similar sets of reactions involving the V, Fe, and Co ions. An assessment of the self-exchange reaction for the oxygen/superoxide couple has led to predicted rates in excellent agreement with direct measurements. Predicted rates of oxidation for the hexaquo Fe ion are also in agreement with experiment, while the predicted rates for the outer-sphere oxidation of its hydrolysis products are ˜2 to 3 (monohydroxo) and ˜4 (dihydroxo) orders of magnitude slower than the observed rates. This suggests an inner-sphere pathway is appropriate to explain the relatively fast rates observed for the hydrolyzed Fe species.

Rosso, Kevin M.; Morgan, James J.

2002-12-01

430

Detailed characterization of rattlers in exactly isostatic, strictly jammed sphere packings

NASA Astrophysics Data System (ADS)

We generate jammed disordered packings of 100?N?2000 monodisperse hard spheres in three dimensions whose strictly jammed backbones are demonstrated to be exactly isostatic with unprecedented numerical accuracy. This is accomplished by using the Torquato-Jiao (TJ) packing algorithm as a means of studying the maximally random jammed (MRJ) state. The rattler fraction of these packings converges towards 0.015 in the infinite-system limit, which is markedly lower than previous estimates for the MRJ state using the Lubachevsky-Stillinger protocol. This is because the packings that the TJ algorithm creates are closer to the true MRJ state, as shown using bond-orientational and translational order metrics. The rattler pair correlation statistics exhibit strongly correlated behavior contrary to the conventional understanding that they be randomly (Poisson) distributed. Dynamically interacting "polyrattlers" may be found imprisoned in shared cages as well as interacting through "bottlenecks" in the backbone and these clusters are mainly responsible for the sharp increase in the rattler pair correlation function near contact. We discover the surprising existence of polyrattlers with cluster sizes of up to five rattlers (which is expected to increase with system size) and present a distribution of polyrattler occurrence as a function of cluster size and system size. We also enumerate all of the rattler interaction topologies we observe and present images of several examples, showing that MRJ packings of monodisperse spheres can contain large rattler cages while still obeying the strict jamming criterion. The backbone spheres that encage the rattlers are significantly hypostatic, implying that correspondingly hyperstatic regions must exist elsewhere in these isostatic packings. We also observe that rattlers in hard-sphere packings share an apparent connection with the low-temperature two-level system anomalies that appear in real amorphous insulators and semiconductors.

Atkinson, Steven; Stillinger, Frank H.; Torquato, Salvatore

2013-12-01

431

ORSPHERE: PHYSICS MEASUREMENTS FOR BARE, HEU(93.2)-METAL SPHERE

In the early 1970s 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 1950s (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 inches), masses (±0.01 g), and material data. The experiment was also set up to minimize the amount of structural material in the sphere proximity. Two, correlated spheres were evaluated and judged to be acceptable as criticality benchmark experiments. This evaluation is given in HEU-MET-FAST-100. The second, smaller sphere was used for additional reactor physics measurements. Worth measurements (Reference 1, 2, 3 and 4), the delayed neutron fraction (Reference 3, 4 and 5) and surface material worth coefficient (Reference 1 and 2) are all measured and judged to be acceptable as benchmark data. The prompt neutron decay (Reference 6), relative fission density (Reference 7) and relative neutron importance (Reference 7) were measured, but are not evaluated. Information for the evaluation was compiled from References 1 through 7, the experimental logbooks 8 and 9 ; additional drawings and notes provided by the experimenter; and communication with the lead experimenter, John T. Mihalczo.

Margaret A. Marshall

2014-03-01

432

We investigate the electric double layer formed between charged walls of a slit-like pore and a solvent primitive model (SPM) for electrolyte solution. The recently developed version of the weighted density functional approach for electrostatic interparticle interaction is applied to the study of the density profiles, adsorption and selectivity of adsorption of ions and solvent species. Our principal focus, however, is in the dependence of differential capacitance on the applied voltage, on the electrode and on the pore width. We discuss the properties of the model with respect to the behavior of a primitive model, i.e., in the absence of a hard-sphere solvent. We observed that the differential capacitance of the SPM on the applied electrostatic potential has the camel-like shape unless the ion fraction is high. Moreover, it is documented that the dependence of differential capacitance of the SPM on the pore width is oscillatory, which is in close similarity to the primitive model.

O. Pizio; S. Soko?owski

2014-07-11

433

Chromium, Nickel, and Iron in Deep-Sea Spheres

NASA Astrophysics Data System (ADS)

Spheres of iron and nickel oxides from deep sea sediments are thought to be extra-terrestrial material which was melted and oxidized during atmospheric passage [1]. The heavy isotopes of oxygen, iron, and nickel are often highly enriched in these "Type I" spheres [2-6]. From the fractionation of the Ni and Fe isotopic compositions, Xue et al. [6] inferred pre-atmospheric Fe/Ni ~13 for such spheres. This result does not uniquely determine the source material as several types of meteoritic metal have similar Fe/Ni ratios. We have analyzed some deep-sea spheres for chromium as well as for nickel and iron. The vapor pressure of metallic Cr, a possible measure of its tendency to evaporate, exceeds that of Fe and Ni. Type I spheres KK1-9 (256 micrograms) and KK1-10 (222 micrograms) were dissolved in 500 microliters 6N HCl and a 5% aliquot of each solution was taken for elemental analysis by ICP/MS [6]. The Fe, Ni, and Cr in the remaining solutions were separated by ion exchange. The isotopic abundances of Fe and Cr were determined by thermal ionization MS [7,8] and those of Ni by ICP/MS [6]. Elemental concentrations were: KK1-9 -- Fe 64.6%, Ni 5.5%, Cr 160 ppm; KK1-10 -- Fe 63.3%, Ni 0.038%, Cr 450 ppm. The composition of KK1-9 is typical of Type I spheres. The low nickel content of KK1-10 is unusual among spheres we have analyzed [6], but not unprecedented (cf [9]). The isotopic mass fractionation, Phi, in sphere KK1-9 is 2.2+/-0.4%/AMU for Fe (Fig. 1) and 1.9+/-0.4%/AMU for Ni. Assuming Rayleigh-type distillation, these values correspond to evaporative losses of ~90% for each element, and a source Fe/Ni ratio similar to that measured; i.e., ~12. The Ni data conform to the anticorrelation of Phi with Ni concentration [4,5]. Cr in KK1-9 was too low for isotopic analysis, but Cr/Fe = 0.00025, slightly higher than in most iron meteorites. This result is consistent with iron meteorite source materials, if Fe was lost somewhat preferentially to Cr, counter to expectations from the vapor pressures of the metals. The Ni available from KK1-10 was insufficient for isotopic analysis, but Fe was unfractionated (Fig. 1). Phi(Cr) = 0.27+/-0.21%/AMU, implying a modest Cr loss of ~30%. A terrestrial origin for KK1-10, suggested by low Ni/Fe <10^-3, is counter to mass fractionation of Cr and the presence of cosmogenic 53Mn in similar spherules [10]. The possibility of an extra-terrestrial source with low Ni/Fe merits further investigation. The Fe isotopic abundances in KK1-10 were within error limits of the terrestrial composition when normalized to 54Fe/56Fe = 0.062669 [11], but the data for KK1-9 hint at an 57Fe deficit of -2+/-1 epsilon-units, similar to values reported for non-FUN inclusions of Allende [11]. References:[ 1] Blanchard M. B. et al. (1980) EPSL, 46, 178-190. [2] Davis A. M. and Brownlee D. E. (1993) LPS XXIV, 373-374. [3] Davis A. M. et al. (1991) LPS XXII, 281-282. [4] Clayton R. N. et al. (1986) EPSL, 79, 235-240. [5] Herzog et al. (1994) GCA, 58, 5319-5323. [6] Xue et al. (1995) LPS XXVI, 1527-1528. [7] Shih C.-Y. et al. (1995) LPS XXVI, 1289-1290. [8] Nyquist L. E. et al. (1994) Meteoritics, 29, 872-885. [9] Czajkowski J. (1987) Ph.D. dissertation, Univ. of California, San Diego. [10] Nishiizumi K. (1983) EPSL, 63, 223-228. [11] Volkening J. and Papanastassiou D. A., Astrophys. J., 347, L43-L46. Figure 1 showing the Fe-isotopic fractionation in two Type I spheres appears here in the hard copy.

Nyquist, L. E.; Shih, C.-Y.; Wiesmann, H.; Brownlee, D. E.; Xue, S.; Hall, G. S.; Herzog, G. F.

1995-09-01

434

Two-sphere low Reynold's propeller

A three-dimensional model of a low-Reynold's swimmer is introduced and analyzed in this paper. This model consists of two large and small spheres connected by two perpendicular thin rods. The geometry of this system is motivated by the microorganisms that use a single tail to swim, the large sphere represents the head of microorganism and the small sphere resembles its tail. Each rod changes its length and orientation in a non-reciprocal manner that effectively propel the system. Translational and rotational velocities of the swimmer are studied for different values of parameters. Our findings show that by changing the parameters we can adjust both the velocity and the direction of motion of the swimmer.

Ali Najafi; Rojman Zargar

2010-09-29

435

Mutual information on the fuzzy sphere

We numerically calculate entanglement entropy and mutual information for a massive free scalar field on commutative (ordinary) and noncommutative (fuzzy) spheres. We regularize the theory on the commutative geometry by discretizing the polar coordinate, whereas the theory on the noncommutative geometry naturally posseses a finite and adjustable number of degrees of freedom. Our results show that the UV-divergent part of the entanglement entropy on a fuzzy sphere does not follow an area law, while the entanglement entropy on a commutative sphere does. Nonetheless, we find that mutual information (which is UV-finite) is the same in both theories. This suggests that nonlocality at short distances does not affect quantum correlations over large distances in a free field theory.

Philippe Sabella-Garnier

2014-09-24

436

Experimental study of the oscillation of spheres in an acoustic levitator.

The spontaneous oscillation of solid spheres in a single-axis acoustic levitator is experimentally investigated by using a high speed camera to record the position of the levitated sphere as a function of time. The oscillations in the axial and radial directions are systematically studied by changing the sphere density and the acoustic pressure amplitude. In order to interpret the experimental results, a simple model based on a spring-mass system is applied in the analysis of the sphere oscillatory behavior. This model requires the knowledge of the acoustic pressure distribution, which was obtained numerically by using a linear finite element method (FEM). Additionally, the linear acoustic pressure distribution obtained by FEM was compared with that measured with a laser Doppler vibrometer. The comparison between numerical and experimental pressure distributions shows good agreement for low values of pressure amplitude. When the pressure amplitude is increased, the acoustic pressure distribution becomes nonlinear, producing harmonics of the fundamental frequency. The experimental results of the spheres oscillations for low pressure amplitudes are consistent with the results predicted by the simple model based on a spring-mass system. PMID:25324056

Andrade, Marco A B; Pérez, Nicolás; Adamowski, Julio C

2014-10-01

437

NASA Astrophysics Data System (ADS)

A new hard-core potential model was recently used to calculate thermodynamic properties of some model fluids, including equilibrium properties, such as compressibility factor and internal energy. A Lennard-Jones (LJ) like potential has been used to modify the repulsive part of the potential. The modified potential contains five parameters, namely, ?, R, ?, ?, and ?HS. The parameter ? is the tail of the attractive branch whose value changes from zero to one. In this work, we have chosen ? = 1 to make the potential continuous at separation r = R?, where the parameter R is the well width. R lies in the range 1.2 to 2.5, and R = 1.3 was found to be the best value for all real gases studied. The parameter ? is the well depth of potential function, and ? is the separation at which the potential function is zero. ?HS is the effective hard sphere diameter, which depends on temperature and an additional parameter. Using statistical mechanics along with the Boltzmann factor criterion (BFC) for the effective hard sphere diameter, an analytical expression has been derived for the reduced second virial coefficient in terms of the reduced temperature. Fitting experimental data to expression derived for the second virial coefficient, the potential parameters ? and ? are obtained. Since this potential is spherical (depending only on distance), three types of species are chosen, namely Ar and He (monoatomic), N2and O2 (diatomic), and methane (spherical molecule), to show how appropriate this potential model is for them. This model predicts an inversion temperature for the second virial coefficient (temperature at which the second virial coefficient pass through a maximum) at ILM0001, where T1 is the inversion temperature, and TB is the Boyle temperature. The predicted value is better than that of the L-J model (for which ILM0002). The maximum percentage deviation of the second virial coefficient is about 2%, except around the Boyle temperature. Then the transport properties of the fluids at the zero density limit, including viscosity, thermal conductivity, and self-diffusion coefficients, are calculated using the same values of the potential parameters. Maximum percentage deviation of transport properties at the zero density limit is about 3% for viscosity (except for Ar, with 5%), about 2.5% for thermal conductivity (except for N2 and Ar, at 8 and 5%, respectively), and about 8% for the self-diffusion coefficient. In comparison with experimental data, the modified potential model gives more accurate results than those obtained from the hard-core and modified hard-core potential models, especially at high temperatures.

Parsafar, G. A.; Shokouhi, M.

438

Cell-mimetic coatings for immune spheres.

Extrinsically induced or engineered cells are providing new therapeutic means in emerging fields such as cell therapeutics, immunomodulation and regenerative medicine. We are demonstrating a spatial induction method using lipid coatings, which can change signal presentation strength from material surface to adherent macrophage cells, that induce early cell-cell interaction leading to organotypic morphology. For that, we have developed a cell mimetic lipid coating with a rafts size to the order of transmembrane proteins (<10 nm) with enhanced lateral elastic properties. Such surface coatings are capable of reducing adherent macrophage spreading, while enabling early induction of cell-cell interaction to form organotypic macrophage colonies or "spheres" (M-spheres). PMID:25454756

Kaladhar, K; Renz, H; Sharma, C P

2014-11-01

439

Orientationally Glassy Crystals of Janus Spheres

NASA Astrophysics Data System (ADS)

Colloidal Janus spheres in water (one hemisphere attractive and the other repulsive) assemble into two-dimensional hexagonal crystals with orientational order controlled by anisotropic interactions. We exploit the decoupled translational and rotational order to quantify the orientational dynamics. Via imaging experiments and Monte Carlo simulations we demonstrate that the correlations in the orientation of individual Janus spheres exhibit glasslike dynamics that can be controlled via the ionic strength. Thus, these colloidal building blocks provide a particularly suitable model glass system for elucidating nontrivial dynamics arising from directional interactions, not captured by the consideration of just translational order.

Jiang, Shan; Yan, Jing; Whitmer, Jonathan K.; Anthony, Stephen M.; Luijten, Erik; Granick, Steve

2014-05-01

440

Hypervelocity shock standoff on spheres in air

NASA Astrophysics Data System (ADS)

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.

Zander, F.; Gollan, R. J.; Jacobs, P. A.; Morgan, R. G.

2014-03-01

441

Dependence on sphere size of the phase behavior of mixtures of rods and spheres

NASA Astrophysics Data System (ADS)

By the addition of chondroitin sulfate (Chs) to the aqueous suspension of tobacco mosaic virus (TMV), the aggregation of TMV occurs at very dilute TMV concentration compared with the addition of polyethylene oxide (PEO). The difference of physical behavior between Chs and PEO is the chain conformation in solution. The Chs chain has a semirigid nature, whereas the PEO chain has a flexible nature. In this study, the Chs and PEO chains are simplified to spherical particles having different size, and we use the spherocylinder model for TMV particle. The effect of the sphere size on the phase behaviors in the mixtures of rods and spheres is investigated by Monte Carlo simulations. By the addition of small spheres, the system transforms from the miscible isotropic phase to the miscible nematic phase. On the other hand, by the addition of large spheres, the system changes from the miscible isotropic phase to the immiscible nematic phase through the immiscible isotropic phase. The different phase behaviors between the small and the large spheres originate from the difference of overlapping volume of the depletion zone. In addition, we perform the Monte Carlo simulations in the case that semirigid chains are used as the Chs chain models. The same phase behaviors are observed as the mixtures of rods and large spheres. Thus the sphere model captures the phase behaviors of rod and polymer mixture systems.

Urakami, Naohito; Imai, Masayuki

2003-07-01

442

Impact velocity vs target hardness relationships for equivalent response of cask structures

In this paper, impact velocity vs. target hardness relationships for cask structures are reviewed. The relationships are based on equivalent cask responses in terms of equal deceleration or similar cask damages. By examining several past cask or container tests as well as some analytical results, some conclusions can be drawn about the relationship between target hardness and equivalent impact velocities. This relationship clearly shows that the cask response to impact is cask-dependent and that the rigid sphere impact model results in an unconservative estimate of equivalent velocity.

Chen, T.F.; Chen, J.C.; Witte, M.C.; Fischer, L.E.

1993-06-01