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1

Density Functional Theory for Baxter's Sticky Hard Spheres in Confinement

NASA Astrophysics Data System (ADS)

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 [H. Hansen-Goos and J. S. Wettlaufer, J. Chem. Phys. 134, 014506 (2011)JCPSA60021-960610.1063/1.3528226]. Here, combining FMT weighted densities with a new vectorial weighted density, we regularize the divergences of the associated strongly confined limit. The 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 that of PY. 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.

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

2012-01-01

2

Density functional theory for colloidal mixtures of hard platelets, rods, and spheres

NASA Astrophysics Data System (ADS)

A geometry-based density-functional theory is presented for mixtures of hard spheres, hard needles, and hard platelets; both the needles and platelets are taken to be of vanishing thickness. Geometrical weight functions that are characteristic for each species are given, and it is shown how convolutions of pairs of weight functions recover each Mayer bond of the ternary mixture and hence ensure the correct second virial expansion of the excess free-energy functional. The case of sphere-platelet overlap relies on the same approximation as does Rosenfeld’s functional for strictly two-dimensional hard disks. We explicitly control contributions to the excess free energy that are of third order in density. Analytic expressions relevant for the application of the theory to states with planar translational and cylindrical rotational symmetry—e.g., to describe behavior at planar smooth walls—are given. For binary sphere-platelet mixtures, in the appropriate limit of small platelet densities, the theory differs from that used in a recent treatment [L. Harnau and S. Dietrich, Phys. Rev. E 71, 011504 (2004)]. As a test case of our approach we consider the isotropic-nematic bulk transition of pure hard platelets, which we find to be weakly first order, with values for the coexistence densities and the nematic order parameter that compare well with simulation results.

Esztermann, Ansgar; Reich, Hendrik; Schmidt, Matthias

2006-01-01

3

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

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-->infinity. 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. PMID:16229603

Tretiakov, Konstantin V; Wojciechowski, Krzysztof W

2005-08-15

4

Bose-Einstein-condensed systems of hard spheres at high density

NASA Astrophysics Data System (ADS)

The properties of Bose-Einstein-condensed systems of hard spheres at high density are studied by taking into account higher-order corrections beyond the Hartree-Fock-Bogoliubov approximation. Based on a diagrammatic technique of the perturbation expansion starting from the Bogoliubov approximation, we show that the effective interactions separate into two distinct parts: the screened and condensate-mediated interactions. The latter is described by the exchange of virtual quasiparticles between noncondensate bosons via the Bose-Einstein condensate and is attractive for small energy transfer. We calculate the condensation temperature, excitation spectrum, and condensate density in the whole region of the gas parameter. It is shown that the condensate temperature decreases compared to that of an ideal Bose gas due to hard-sphere interactions. We find that the condensate-mediated attraction between noncondensate bosons leads to an enhancement of the anomalous self-energy and, as a consequence, to the emergence of a roton minimum in the excitation spectrum and to the strong suppression of the condensate fraction in the region of high density.

Kim, Ha; Kim, Cheng-Song; Huang, Chang-Lyol; Song, He-Shan; Yi, Xue-Xi

2012-05-01

5

The inverse grand-canonical Monte Carlo (IGCMC) technique is used to calculate the activity coefficients of the following hard-sphere systems: one-component fluid, binary mixture and solvent primitive model (SPM) electrolyte. The calculations for a one-component fluid are performed at different densities. The components of a binary mixture differ in diameters (300 and 500 pm) with the results being presented for different density

S. Lamperski; M. P?uciennik

2010-01-01

6

Hard spheres out of equilibrium

NASA Astrophysics Data System (ADS)

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

Hermes, M.

2010-05-01

7

Hard sphere gas state equation

NASA Astrophysics Data System (ADS)

The dynamic evolution of a gas of N hard spheres determines the equation of state once the equilibrium is reached, after a short transient. The system is investigated in the thermodynamic limit. The algorithms based on a tricky management of the collisions list allow to simulate up to N=10 spheres, rendering the statistical error sufficiently small in simulations involving 10 collisions. The effect of boundaries is discussed, and, to avoid any dependence, periodic boundary conditions are chosen in a box, whose edge is much larger than the spheres radius. The initial state is the symmetric close packing and, by reducing the hard spheres radius, we follow the evolution of the mean free path as a function of the density y (where y is the ratio between the volume of the spheres and the total volume). We observe the solid-fluid first-order phase transition and follow the fluid branch until the hard spheres gas is very dilute. The phase transition is well resolved due to the improved statistics and to the choice, as order parameter, of the mean free path rather than Z=PV/NkT, which has a singularity at zero mean free path. The equations of state in the fluid and solid branches are compared with the Taylor series for the mean free path, obtained from the virial expansions of Z. The second-order truncations P2(y), appear to provide the best fit to the mean free path. This suggests an approximation to Z as Z=1+B2y/P2(y), where B2 is the second virial coefficient.

Rambaldi, Sandro; Salustri, Giovanna; Benedetti, Carlo

2006-02-01

8

NASA Astrophysics Data System (ADS)

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 [T. Schilling and F. Schmid, J. Chem. Phys. 131, 231102 (2009)10.1063/1.3274951] 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 fundamental measure theory 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 [H. Hansen-Goos and R. Roth, J. Phys.: Condens. Matter 18, 8413 (2006)10.1088/0953-8984/18/37/002] exhibits sensible results for the equilibrium vacancy concentration and a physical behavior of the chemical potential in crystals constrained by a fixed vacancy concentration.

Oettel, M.; Görig, S.; Härtel, A.; Löwen, H.; Radu, M.; Schilling, T.

2010-11-01

9

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

10

Polydisperse hard spheres at a hard wall

NASA Astrophysics Data System (ADS)

The structural properties of polydisperse hard spheres in the presence of a hard wall are investigated via Monte Carlo simulation and density functional theory (DFT). Attention is focused on the local density distribution ?(?,z), measuring the number density of particles of diameter ? at a distance z from the wall. Estimates of ?(?,z) are obtained for bulk volume fractions ?b=0.2 and ?b=0.4, and for two choices of the bulk parent distribution: a top-hat form, which we study for degrees of polydispersity ?=11.5% and ?=40.4%, and a truncated Schulz form having ?=40.7%. Excellent overall agreement is found between the DFT and simulation results, particularly at ?b=0.2. A detailed analysis of ?(?,z) confirms the presence of oscillatory size segregation effects, as observed in a previous DFT study [I. Pagonabarraga, M. E. Cates, and G. J. Ackland, Phys. Rev. Lett. 84, 911 (2000)]. For large ?, the character of these oscillation is observed to depend strongly on the shape of the parent distribution. In the vicinity of the wall, attractive ?-dependent depletion interactions are found to greatly enhance the density of the largest particles. The local degree of polydispersity ?(z) is suppressed in this region, while further from the wall it exhibits oscillations.

Buzzacchi, Matteo; Pagonabarraga, Ignacio; Wilding, Nigel B.

2004-12-01

11

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

2013-05-13

12

National Technical Information Service (NTIS)

The time-evolution for the system of infinitely many particles in space interacting by a hard-sphere potential is constructed. Examples abound of configurations of the infinite system having more than one solution to the Newtonian equations of motion. A r...

R. K. Alexander

1975-01-01

13

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

14

Effective isotropic potential for dipolar hard spheres.

A new effective isotropic potential is proposed for the dipolar hard-sphere fluid, on the basis of recent results by others for its angle-averaged radial distribution function. The new effective potential is shown to exhibit oscillations even for moderately high densities and moderately strong dipole moments, which are absent from earlier effective isotropic potentials. The validity and significance of this result are briefly discussed. PMID:23552475

Teixeira, P I C

2013-04-03

15

Collision statistics in sheared inelastic hard spheres.

The dynamics of sheared inelastic-hard-sphere systems is studied using nonequilibrium molecular-dynamics simulations and direct simulation Monte Carlo. In the molecular-dynamics simulations Lees-Edwards boundary conditions are used to impose the shear. The dimensions of the simulation box are chosen to ensure that the systems are homogeneous and that the shear is applied uniformly. Various system properties are monitored, including the one-particle velocity distribution, granular temperature, stress tensor, collision rates, and time between collisions. The one-particle velocity distribution is found to agree reasonably well with an anisotropic Gaussian distribution, with only a slight overpopulation of the high-velocity tails. The velocity distribution is strongly anisotropic, especially at lower densities and lower values of the coefficient of restitution, with the largest variance in the direction of shear. The density dependence of the compressibility factor of the sheared inelastic-hard-sphere system is quite similar to that of elastic-hard-sphere fluids. As the systems become more inelastic, the glancing collisions begin to dominate over more direct, head-on collisions. Examination of the distribution of the times between collisions indicates that the collisions experienced by the particles are strongly correlated in the highly inelastic systems. A comparison of the simulation data is made with direct Monte Carlo simulation of the Enskog equation. Results of the kinetic model of Montanero [J. Fluid Mech. 389, 391 (1999)] based on the Enskog equation are also included. In general, good agreement is found for high-density, weakly inelastic systems. PMID:19518225

Bannerman, Marcus N; Green, Thomas E; Grassia, Paul; Lue, Leo

2009-04-22

16

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

2012-01-18

17

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.

Dotera, Tomonari; Kimoto, Masakiyo; Matsuzawa, Junichi

2012-01-01

18

Depletion Interactions among Hard Spheres inside Vesicles

NASA Astrophysics Data System (ADS)

We demonstrate that hard spheres diffusing inside a rigid vesicle of complex shape are pushed by entropic excluded-volume interactions to the surface of the vesicle and pushed along the vesicle's surface in the direction of increasing curvature(A.D. Dinsmore, A.G. Yodh and D.J. Pine, Nature 383), 239 (1996).. Rigid, multilamellar SOPC vesicles (3 ?m in diameter) contained water, polystyrene spheres and enough salt to screen out long-range electrostatic interactions. A lone 0.47-?m diameter sphere diffused freely inside the vesicle. When smaller spheres (0.08 ?m, volume fraction = 0.3) were present, the free energy of the mixture decreased by ? kT as the larger sphere moved from bulk to flat surface, and further decreased by kT as it moved from a flat surface to a curved region of the surface. The force will be explained within the depletion-force model by considering the volume accessible to the small spheres as a function of large-sphere position and surface shape. The possibility of membrane curvature induced by the particles will be discussed. Supported by NSF Grant No. DMR93-06814 and Materials Research Grant No. DMR91-20668. AGY also supported in part by the NSF PYI program and by the Alfred P. Sloan Foundation.

Dinsmore, A. D.; Wong, D. T.; Yodh, A. G.

1997-03-01

19

Time correlation functions of hard sphere and soft sphere fluids.

We explore the transition between soft particle fluids of increasing steepness to the hard sphere limit. We analyze the analytic forms of the time correlation functions used in determining transport coefficients in Green-Kubo formulas for fluids composed of particles interacting through a repulsive r(-n) potential. We focus on the steeply repulsive n--> infinity limit where the potential tends to the hard sphere interaction. Dufty [Mol. Phys. 100, 2331 (2002)] developed a theoretical framework that can be used to characterize the transition from a steeply repulsive continuous potential toward the hard sphere potential for the shear stress time correlation function. This function was shown to consist of a rapidly decaying contribution (which is singular in the steeply repulsive limit) and a slowly decaying nonsingular part which can be reasonably well represented by Enskog's prediction on times of order and in excess of the mean collision time. We extend this treatment to the bulk viscosity and thermal conductivity. We focus on the bulk viscosity (pressure) correlation function as it is purely singular for hard spheres, and has no kinetic or cross term contributions in this limit. There is no relaxation of this correlation function on the mean collision or Enskog time scale for hard spheres. We show that it is not possible to represent the steeply repulsive behavior of this function entirely in terms of a sech function, i.e., C(B)(t)=sech(a(n)t/tau(n)), where a(n) is a numerical factor, t is time, and tau(n) is a relaxation time proportional to n(-1). An additional singular function, which we call w(t), is required to obtain the correct short-time behavior of C(B)(t) and the Enskog value for the bulk viscosity. With this additional function, the value of a(n) in the n--> infinity limit is a(n)=square root of 2 which is consistent with the second moment of the time expansion of the time correlation function. We compute this function for large n and extrapolate it to n--> infinity, determining one possible analytic form. The shear stress correlation function also gives a(n)=square root of 2 in the hard sphere limit for the singular part when the sech and w functions are used. This function has a nonsingular component, even in the hard sphere limit. We explore various forms for the crossover function X(t/tau(n)) introduced by Dufty, which weights the limiting singular and nonsingular contributions to C(S)(t) particularly at intermediate times. The qualitative behavior for the heat flux time correlation function (used to obtain the thermal conductivity) is much the same as the shear case. The w(t) derived by several self-consistent extrapolations appears, within the simulation statistics, to be the same for the bulk and shear viscosity, and for the thermal conductivity cases. PMID:14995434

Bra?ka, A C; Heyes, D M

2004-02-25

20

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

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

Rodríguez-López, Tonalli; del Río, Fernando

2011-12-09

21

RESEARCH NOTE Radial distribution functions of hard sphere mixtures

A simple method is proposed to determine radial distribution functions of pure hard sphere fluids and mixtures of hard spheres of different diameters. The range of centre-centre distances of a pair of hard spheres is divided into two parts: that from the closest approach up to the distance xm of the first minimum, and that for distances x > xm.

Tomas Boublik

1997-01-01

22

Regularized 13 moment equations for hard spheres

NASA Astrophysics Data System (ADS)

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

Struchtrup, Henning; Torrilhon, Manuel

2012-11-01

23

Structure of crystals of hard colloidal spheres

We report light-scattering measurements of powder diffraction patterns of crystals of essentially hard colloidal spheres. These are consistent with structures formed by stacking close-packed planes of particles in a sequence of permitted lateral positions, {ital A},{ital B},{ital C}, which shows a high degree of randomness. Crystals grown slowly, while still containing many stacking faults, show a tendency towards face-centered-cubic packing: possible explanations for this observation are discussed.

Pusey, P.N.; van Megen, W.; Bartlett, P.; Ackerson, B.J.; Rarity, J.G.; Underwood, S.M. (Royal Signals and Radar Establishment, Malvern, WR14 3PS, United Kingsom (GB) Department of Applied Physics, Royal Melbourne Institute of Technology, Melbourne, Victoria, Australia School of Chemistry, Bristol University, Bristol, BS8 1TS, United Kingdom Department of Physics, Oklahoma State University, Stillwater, Oklahoma 74078)

1989-12-18

24

Structure of crystals of hard colloidal spheres

We report light-scattering measurements of powder diffraction patterns of crystals of essentially hard colloidal spheres. These are consistent with structures formed by stacking close-packed planes of particles in a sequence of permitted lateral positions, {ital A},{ital B},{ital C}, which shows a high degree of randomness. Crystals grown slowly, while still containing many stacking faults, show a tendency towards face-centered-cubic packing:

P. N. Pusey; W. van Megen; P. Bartlett; B. J. Ackerson; J. G. Rarity; S. M. Underwood

1989-01-01

25

Structure of crystals of hard colloidal spheres

We report light-scattering measurements of powder diffraction patterns of crystals of essentially hard colloidal spheres. These are consistent with structures formed by stacking close-packed planes of particles in a sequence of permitted lateral positions, A,B,C, which shows a high degree of randomness. Crystals grown slowly, while still containing many stacking faults, show a tendency towards face-centered-cubic packing: possible explanations for

P. N. Pusey; W. van Megen; P. Bartlett; B. J. Ackerson; J. G. Rarity; S. M. Underwood

1989-01-01

26

Interfacial free energy of a hard-sphere fluid in contact with curved hard surfaces

NASA Astrophysics Data System (ADS)

Using molecular-dynamics simulation, we have calculated the interfacial free energy ? between a hard-sphere fluid and hard spherical and cylindrical colloidal particles, as functions of the particle radius R and the fluid packing fraction ?=??3/6, where ? and ? are the number density and hard-sphere diameter, respectively. These results verify that Hadwiger's theorem from integral geometry, which predicts that ? for a fluid at a surface, with certain restrictions, should be a linear combination of the average mean and Gaussian surface curvatures, is valid within the precision of the calculation for spherical and cylindrical surfaces up to ??0.42. In addition, earlier results for ? for this system [Bryk , Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.68.031602 68, 031602 (2003)] using a geometrically based classical density functional theory are in excellent agreement with the current simulation results for packing fractions in the range where Hadwiger's theorem is valid. However, above ??0.42, ?(R) shows significant deviations from the Hadwiger form indicating limitations to its use for high-density hard-sphere fluids. Using the results of this study together with Hadwiger's theorem allows one, in principle, to determine ? for any sufficiently smooth surface immersed in a hard-sphere fluid.

Laird, Brian B.; Hunter, Allie; Davidchack, Ruslan L.

2012-12-01

27

Interfacial free energy of a hard-sphere fluid in contact with curved hard surfaces.

Using molecular-dynamics simulation, we have calculated the interfacial free energy ? between a hard-sphere fluid and hard spherical and cylindrical colloidal particles, as functions of the particle radius R and the fluid packing fraction ?=??(3)/6, where ? and ? are the number density and hard-sphere diameter, respectively. These results verify that Hadwiger's theorem from integral geometry, which predicts that ? for a fluid at a surface, with certain restrictions, should be a linear combination of the average mean and Gaussian surface curvatures, is valid within the precision of the calculation for spherical and cylindrical surfaces up to ? ? 0.42. In addition, earlier results for ? for this system [Bryk et al., Phys. Rev. E 68, 031602 (2003)] using a geometrically based classical density functional theory are in excellent agreement with the current simulation results for packing fractions in the range where Hadwiger's theorem is valid. However, above ? ? 0.42, ?(R) shows significant deviations from the Hadwiger form indicating limitations to its use for high-density hard-sphere fluids. Using the results of this study together with Hadwiger's theorem allows one, in principle, to determine ? for any sufficiently smooth surface immersed in a hard-sphere fluid. PMID:23367884

Laird, Brian B; Hunter, Allie; Davidchack, Ruslan L

2012-12-20

28

Voronoi neighbor statistics of hard-disks and hard-spheres

NASA Astrophysics Data System (ADS)

The neighbor distribution in hard-sphere and hard-disk fluids is analyzed using Voronoi tessellation. The statistical measures analyzed are the nth neighbor coordination number (Cn), the nth neighbor distance distribution [fn(r)], and the distribution of the number of Voronoi faces (Pn). These statistics are sensitive indicators of microstructure, and they distinguish thermodynamic and annealed structures. A sharp rise in the hexagon population marks the onset of hard-disk freezing transition, and Cn decreases sharply to the hexagonal lattice values. In hard-disk random structures the pentagon and heptagon populations remain significant even at high volume fraction. In dense hard-sphere (three-dimensional) structures at the freezing transition, C1 is close to 14, instead of the value of 12 expected for a face-centered-cubic lattice. This is found to be because of a topological instability, where a slight perturbation of the positions in the centers of a pair of particles transforms a vertex in the Voronoi polyhedron into a Voronoi surface. We demonstrate that the pair distribution function and the equation-of-state obtained from Voronoi tessellation are equal to those obtained from thermodynamic calculations. In hard-sphere random structures, the dodecahedron population decreases with increasing density. To demonstrate the utility of the neighbor analysis, we estimate the effective hard-sphere diameter of the Lennard-Jones fluid by identifying the diameter of the spheres in the hard-sphere fluid which has C1 equal to that for the Lennard-Jones fluid. The estimates are within 2% deviation from the theoretical results of Barker-Henderson and Weeks-Chandler-Andersen.

Kumar, V. Senthil; Kumaran, V.

2005-08-01

29

Dynamics of heterogeneous hard spheres in a file.

Normal dynamics in a quasi-one-dimensional channel of length L (??) of N hard spheres are analyzed. The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W?D(-?) for small D, where 0??<1. The initial spheres' density ? is nonuniform and scales with the distance (from the origin) l as ??l(-?), 0???1. An approximation for the N-particle PDF for this problem is derived. From this solution, scaling law analysis and numerical simulations, we show here that the mean square displacement for a particle in such a system obeys

Flomenbom, Ophir

2010-09-21

30

Quench rate independence of the hard sphere glass transition

NASA Astrophysics Data System (ADS)

About 200 glasses were made by compressing the hard sphere fluid. The location of the glass transition is not measurably changed when the rate at which the fluid is compressed through the transition is varied by a factor of 500. There is small variance in the properties of the glasses but no statistically significant effects of compression rate. The equation of state of each glass can be expressed as PV/NkT = Ci/(1 - z/zi) where Ci = 2·67 ± 0·05 is the configurational heat capacity in units of Nk, and the limiting density of the glasses zi = 0·875 ± 0·003 (relative to the close packed crystal). The reproducibility of the glasses suggests that either the glass transition in hard spheres is not simply a kinetic phenomenon, or that the structural relaxation time in the fluid diverges near the glass transition density.

Speedy, Robin J.

31

Hard-Sphere Approach to the Excitation Spectrum in Liquid Helium II.

National Technical Information Service (NTIS)

The excitation spectrum of a Bose system of hard spheres is obtained in a high-density-calculation-including multiple scattering processes. The hard-sphere interaction is represented by a non-Hermitian pseudopotential constructed in a previous work, and t...

L. Liu L. S. Liu

1964-01-01

32

Haptic Search for Hard and Soft Spheres

In this study the saliency of hardness and softness were investigated in an active haptic search task. Two experiments were performed to explore these properties in different contexts. In Experiment 1, blindfolded participants had to grasp a bundle of spheres and determine the presence of a hard target among soft distractors or vice versa. If the difference in compliance between target and distractors was small, reaction times increased with the number of items for both features; a serial strategy was found to be used. When the difference in compliance was large, the reaction times were independent of the number of items, indicating a parallel strategy. In Experiment 2, blindfolded participants pressed their hand on a display filled with hard and soft items. In the search for a soft target, increasing reaction times with the number of items were found, but the location of target and distractors appeared to have a large influence on the search difficulty. In the search for a hard target, reaction times did not depend on the number of items. In sum, this showed that both hardness and softness are salient features.

van Polanen, Vonne; Bergmann Tiest, Wouter M.; Kappers, Astrid M. L.

2012-01-01

33

Controlling the jamming transition of sheared hard spheres

NASA Astrophysics Data System (ADS)

Many applications require understanding how disordered materials flow under an external load such as a shear stress. Since external loads drive systems out of equilibrium, their behavior cannot be described solely in terms of equilibrium parameters like temperature and pressure. However, simulations and experiments show that sheared spherical particles possess an effective temperature that relates low-frequency fluctuations of various observable quantities to their associated response functions. Here, we show that the mobility of a mixture of sheared hard spheres is largely controlled by the dimensionless ratio of effective temperature to pressure, Teff/p3?, where ? is the sphere diameter. We define the effective temperature as the consistent value that relates the amplitudes of low-frequency shear stress and density fluctuations to their associated response functions. We find that the relaxation time ? characterizing the mobility depends on Teff/p3? according to two distinct mechanisms in two distinct regimes. In the solid response regime, the behavior at fixed packing fraction ? satisfies ??(-cp3?/Teff), where ? is the strain rate and c depends weakly on ?, suggesting that the effective temperature controls the average local yield strain. In the fluid response regime, ? depends on Teff/p3? as it depends on T/p3? in equilibrium. This regime comprises a large part of the hard-sphere jamming phase diagram including both near-equilibrium conditions where Teff is similar to the kinetic temperature Tkin and far-from-equilibrium conditions where TeffTkin. In particular, the dynamic jamming transition is largely controlled by the fluid-response mechanism; like equilibrium hard spheres, sheared hard spheres can flow only if low-frequency fluctuations are large enough compared to the pressure. By presenting our results in terms of the dimensionless jamming phase diagram, we show how these mechanisms likely apply to systems with soft repulsive interactions.

Haxton, Thomas

2012-02-01

34

Densest columnar structures of hard spheres from sequential deposition.

The rich variety of densest columnar structures of identical hard spheres inside a cylinder can surprisingly be constructed from a simple and computationally fast sequential deposition of cylinder-touching spheres, if the cylinder-to-sphere diameter ratio is D is an element of [1,2.7013]. This provides a direction for theoretically deriving all these densest structures and for constructing such densest packings with nano-, micro-, colloidal, or charged particles, which all self-assemble like hard spheres. PMID:22181358

Chan, Ho-Kei

2011-11-14

35

Phase diagrams of nearly-hard-sphere binary colloids

We have investigated the equilibrium compositions and structures of the phases of nearly-hard-sphere binary colloids and obtained experimental phase diagrams. Aqueous dispersions of charge-stabilized polystyrene spheres were studied in the hard-sphere limit, with sphere-diameter ratios ranging from 2 to 12 and total volume fractions less than 0.4. At sufficiently high volume fractions, the samples separated into two phases. One phase,

A. D. Dinsmore; A. G. Yodh; D. J. Pine

1995-01-01

36

NASA Astrophysics Data System (ADS)

The liquid crystal phase behavior of linear and partially flexible hard-sphere chain fluids and the solubility of hard spheres in hard-sphere chain fluids are studied by constant pressure Monte Carlo simulations. An extensive study on the phase behavior of linear fluids with a length of 7, 8, 9, 10, 11, 12, 13, 14, 15, and 20 beads is carried out. The phase behavior of partially flexible fluids with a total length of 8, 10, 14, and 15 beads and with different lengths for the linear part is also determined. A precise description of the reduced pressure and of the packing fraction change at the isotropic-nematic coexistence was achieved by performing long simulation runs. For linear fluids, a maximum in the isotropic to nematic packing fraction change is observed for a chain length of 15 beads. The infinite dilution solubility of hard spheres in linear and partially flexible hard-sphere chain fluids is calculated by the Widom test-particle insertion method. To identify the effect of chain connectivity and molecular anisotropy on free volume, solubility is expressed relative to that of hard spheres in a hard sphere fluid at same packing fraction as relative Henry's law constants. A linear relationship between relative Henry's law constants and packing fraction is observed for all linear fluids. Furthermore, this linearity is independent of liquid crystal ordering and seems to be independent of chain length for linear chains of 10 beads and longer. The same linear relationship was observed for the solubility of hard spheres in nematic forming partially flexible fluids for packing fractions up to a value slightly higher than the nematic packing fraction at the isotropic-nematic coexistence. At higher packing fractions, the small flexibility of these fluids seems to improve solubility in comparison with the linear fluids.

Oyarzún, Bernardo; van Westen, Thijs; Vlugt, Thijs J. H.

2013-05-01

37

The liquid crystal phase behavior of linear and partially flexible hard-sphere chain fluids and the solubility of hard spheres in hard-sphere chain fluids are studied by constant pressure Monte Carlo simulations. An extensive study on the phase behavior of linear fluids with a length of 7, 8, 9, 10, 11, 12, 13, 14, 15, and 20 beads is carried out. The phase behavior of partially flexible fluids with a total length of 8, 10, 14, and 15 beads and with different lengths for the linear part is also determined. A precise description of the reduced pressure and of the packing fraction change at the isotropic-nematic coexistence was achieved by performing long simulation runs. For linear fluids, a maximum in the isotropic to nematic packing fraction change is observed for a chain length of 15 beads. The infinite dilution solubility of hard spheres in linear and partially flexible hard-sphere chain fluids is calculated by the Widom test-particle insertion method. To identify the effect of chain connectivity and molecular anisotropy on free volume, solubility is expressed relative to that of hard spheres in a hard sphere fluid at same packing fraction as relative Henry's law constants. A linear relationship between relative Henry's law constants and packing fraction is observed for all linear fluids. Furthermore, this linearity is independent of liquid crystal ordering and seems to be independent of chain length for linear chains of 10 beads and longer. The same linear relationship was observed for the solubility of hard spheres in nematic forming partially flexible fluids for packing fractions up to a value slightly higher than the nematic packing fraction at the isotropic-nematic coexistence. At higher packing fractions, the small flexibility of these fluids seems to improve solubility in comparison with the linear fluids. PMID:23742514

Oyarzún, Bernardo; van Westen, Thijs; Vlugt, Thijs J H

2013-05-28

38

Thermodynamic and rheological properties of hard sphere dispersions

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

See-Eng Phan

1998-01-01

39

Quantum-hard-sphere system equations of state revisited

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

Keller, C. [Physics Department, University of South Dakota, Vermillion, South Dakota 57069 (United States); de Llano, M. [Physics Department, North Dakota State University, Fargo, North Dakota 58105 (United States); Ren, S.Z. [Physics Department, University of South Dakota, Vermillion, South Dakota 57069 (United States); Solis, M.A. [Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Apdo. Postal 20-364, 01000 Mexico, DF. (Mexico); Baker, G.A. Jr. [Theoretical Division, University of California, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

1996-10-01

40

Cavities in the hard sphere crystal and fluid

NASA Astrophysics Data System (ADS)

The number, size, surface area and shape of cavities in the hard-sphere crystal and dense fluid were studied by simulation. The number nc of cavities per sphere is given over about 60 orders of magnitude by -ln{nc} = pV/NkT - 1 + F(z) with F(z) ? - 0·6 + ln {z} in the crystal and F(z) ? - 2·5 in the dense fluid. The average cavity volume ~~ and nc, for the crystal, to within their uncertainties.~~

Bowles, Richard K.; Speedy, Robin J.

41

Stacking in sediments of colloidal hard spheres.

We use computer simulations to investigate the crystallization dynamics of sedimenting hard spheres in large systems (hundreds of thousands of particles). We show that slow sedimentation results primarily in face-centered cubic (fcc) stacked crystals, instead of random hexagonal close packed or hexagonal close packed (hcp) crystals. We also find slanted stacking faults, in the fcc regions. However, we attribute the formation of fcc to the free energy difference between fcc and hcp and not to the presence of these slanted stacking faults. Although the free energy difference between hcp and fcc per particle is small (only 10(-3) times the thermal energy), it can become considerable, when multiplied by the number of particles in each domain. The ratio of fcc to hcp obtained from dynamic simulations is in excellent agreement with well-equilibrated Monte Carlo simulations, in which no slanted stacking faults were found. Our results explain a range of experiments on colloids, in which the amount of fcc increases upon lowering the sedimentation rate or decreasing the initial volume fraction. PMID:21787016

Marechal, Matthieu; Hermes, Michiel; Dijkstra, Marjolein

2011-07-21

42

Gravitational Effects on the Crystallization of Colloidal Hard Spheres

NASA Astrophysics Data System (ADS)

Hard sphere systems, in which the interaction energy between two spheres is zero when they do not touch and infinity when they touch, provides a fundamental model system for the structures of liquid, solid (crystal and glass) and the transition between them. Gravity affects the colloidal hard sphere system by sedimentation and convection. I will report the equilibrium phase diagram, the crystallization kinetics of colloidal hard spheres measured from space shuttle missions and compare with identical experiments on the ground. Detailed quantitative nucleation and growth measurements were performed on the space shuttle Columbia in flight STS-83 and STS-94. Gravity suppresses coarsening between crystallites and accelerates nucleation. More and smaller crystallites are produced on ground. The dendritic growth instability of hard sphere crystals, which is absent in ground experiments, were observed by photography and measured by time resolved Bragg scattering. In contrast to the conventional picture that crystallization progresses by isolated growth of individual crystallites followed by a coarsening process, we found that simultaneous coarsening and growth. This indicates strong long-ranged interaction between the diffusion field of the growing crystallites. FCC structure is strongly indicated as the equilibrium structure of hard sphere crystals. Finally, controlled crystal growth by temperature gradients will be discussed.(PHaSE, Physics of Hard Spheres Experiment or Fruit-fly of Condensed Matter Physics)

Cheng, Zhengdong

2000-03-01

43

A mixed hard sphere interference function for molten Ge

NASA Astrophysics Data System (ADS)

The interference function of molten semiconductor Ge is calculated up to the Fermi diameter using the mixed hard sphere model developed recently by Canessa, Mariani and Vignolo. A good agreement with experiment is obtained.

Araos, J.; Canessa, E.; Vignolo, J.

1985-01-01

44

A model for repulsive hard spheres with surface adhesion

NASA Astrophysics Data System (ADS)

We have adapted Baxter's Sticky Hard Sphere (SHS) model so that it more adequately describes systems where the interparticle potential well is preceded by an energy barrier. In the original model the particles interact via a pair potential with a narrow attractive region next to a repulsive core. As such it is most suited for atomic and molecular systems at low densities. Colloidal particles, however, often exhibit long range respulsing whereas they do attract each other at shorter ranges. This motivated our effort to extend the model. It is shown that the Percus-Yevick equation can also be solved analytically for this particular potential, provided that the region of attraction is sufficiently small. The new feature of this Repulsive Sticky Hard Sphere (RSHS) model is that the fraction of aggregated particles increases with temperature as is experimentally observed in such systems. Structure functions from small angle X-ray studies on water/AOT/iso-octane microemulsions can be fit to those predicted by the RSHS model. The thus obtained binding enthalpy is in good agreement with earlier determinations from dielectric studies.

Bedeaux, D.; Koper, G. J. M.

1992-05-01

45

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

NASA Astrophysics Data System (ADS)

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.

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

2006-11-01

46

Hard sphere crystal nucleation and growth near large spherical impurities

NASA Astrophysics Data System (ADS)

We report how large spherical impurities affect the nucleation and growth of hard sphere colloidal crystals. Both the impurities and the colloids are fluorescently labelled polymethylmetacrylate particles and are dispersed in an optically and density matching solvent mixture. Crystal growth, initiated either at the impurity surface, or at the sample bottom, was studied by imaging sequences of two-dimensional xy-slices in the plane of the impurity's centre of mass with a laser scanning confocal microscope. At least two factors determine whether a large impurity can function as a seed for heterogeneous nucleation: timescales and impurity curvature. The curvature needs to be sufficiently low for crystal nuclei to form on the impurity surface. If bulk crystal growth has already approached the impurity, bulk growth is dominant over growth of crystallites on the impurity surface. Such surface crystallites eventually reorient to adapt to the overall bulk crystal symmetry.

de Villeneuve, V. W. A.; Verboekend, D.; Dullens, R. P. A.; Aarts, D. G. A. L.; Kegel, W. K.; Lekkerkerker, H. N. W.

2005-11-01

47

New phase for one-component hard spheres

NASA Astrophysics Data System (ADS)

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

Wu, Guang-Wen; Sadus, Richard J.

2004-06-01

48

Exact second virial coefficient for dipolar hard spheres.

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. PMID:24158678

Virga, Epifanio G

2013-10-24

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. PMID:23215619

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

2012-11-21

50

Slip and flow of hard-sphere colloidal glasses.

We study the flow of concentrated hard-sphere colloidal suspensions along smooth, nonstick walls using cone-plate rheometry and simultaneous confocal microscopy. In the glass regime, the global flow shows a transition from Herschel-Bulkley behavior at large shear rate to a characteristic Bingham slip response at small rates, absent for ergodic colloidal fluids. Imaging reveals both the "solid" microstructure during full slip and the local nature of the "slip to shear" transition. Both the local and global flow are described by a phenomenological model, and the associated Bingham slip parameters exhibit characteristic scaling with size and concentration of the hard spheres. PMID:19113756

Ballesta, P; Besseling, R; Isa, L; Petekidis, G; Poon, W C K

2008-12-15

51

Compact anisotropic spheres with prescribed energy density

NASA Astrophysics Data System (ADS)

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

Chaisi, M.; Maharaj, S. D.

2005-07-01

52

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

Gazzillo, Domenico

2011-03-28

53

Clustering and gelation of hard spheres induced by the Pickering effect.

A mixture of hard-sphere particles and model emulsion droplets is studied with a Brownian dynamics simulation. We find that the addition of nonwetting emulsion droplets to a suspension of pure hard spheres can lead to both gas-liquid and fluid-solid phase separations. Furthermore, we find a stable fluid of hard-sphere clusters. The stability is due to the saturation of the attraction that occurs when the surface of the droplets is completely covered with colloidal particles. At larger emulsion droplet densities a percolation transition is observed. The resulting networks of colloidal particles show dynamical and mechanical properties typical of a colloidal gel. The results of the model are in good qualitative agreement with recent experimental findings [E. Koos and N. Willenbacher, Science 331, 897 (2011)] in a mixture of colloidal particles and two immiscible fluids. PMID:22680411

Fortini, Andrea

2012-04-02

54

The glass transition in binary mixtures of hard colloidal spheres

Particle dynamics have been measured by dynamic light scattering for mixtures of colloidal particles with hard sphere interactions. The diameter ratio (small:large) is 0.6. The optical properties of the suspended particles are such that the relative contrast of the two species is very sensitive to temperature, a feature we exploit to obtain the three partial intermediate scattering functions. The glass

S. R. Williams; W. van Megen

2000-01-01

55

Physics of Hard Spheres Experiment -2 (Phase-2).

National Technical Information Service (NTIS)

The Physics of Hard Spheres Experiment-2 (PH(sup A)SE-2) seeks to answer fundamental questions about how model atoms change their behavior as more and more neighbors are moved into their neighborhood. The PH(sup A)SE-2 experiment will use an enhanced micr...

P. M. Chaikin W. B. Russel M. T. Sullivan A. D. Hollingsworth A. vanBlaaderen W. V. Meyer M. P. Doherty A. H. Resnick

2001-01-01

56

New phase for one-component hard spheres

A completely new phase for one-component hard spheres is reported in an unexpected region of the phase diagram. The new phase is observed at compressibility factors intermediate between the solid and the metastable branches. It can be obtained from either Monte Carlo simulations alone or a combination of Monte Carlo and molecular dynamics calculations. An analysis of the intermediate scattering

Guang-Wen Wu; Richard J. Sadus

2004-01-01

57

Dynamic equivalences in the hard-sphere dynamic universality class

NASA Astrophysics Data System (ADS)

We perform systematic simulation experiments on model systems with soft-sphere repulsive interactions to test the predicted dynamic equivalence between soft-sphere liquids with similar static structure. For this we compare the simulated dynamics (mean squared displacement, intermediate scattering function, ?-relaxation time, etc.) of different soft-sphere systems, between them and with the hard-sphere liquid. We then show that the referred dynamic equivalence does not depend on the (Newtonian or Brownian) nature of the microscopic laws of motion of the constituent particles, and hence, applies independently to colloidal and to atomic simple liquids. Finally, we verify another more recently proposed dynamic equivalence, this time between the long-time dynamics of an atomic liquid and its corresponding Brownian fluid (i.e., the Brownian system with the same interaction potential).

López-Flores, Leticia; Ruíz-Estrada, Honorina; Chávez-Páez, Martín; Medina-Noyola, Magdaleno

2013-10-01

58

Bond-orientational analysis of hard-disk and hard-sphere structures

NASA Astrophysics Data System (ADS)

We report the bond-orientational analysis results for the thermodynamic, random, and homogeneously sheared inelastic structures of hard-disks and hard-spheres. The thermodynamic structures show a sharp rise in the order across the freezing transition. The random structures show the absence of crystallization. The homogeneously sheared structures get ordered at a packing fraction higher than the thermodynamic freezing packing fraction, due to the suppression of crystal nucleation. On shear ordering, strings of close-packed hard-disks in two dimensions and close-packed layers of hard-spheres in three dimensions, oriented along the velocity direction, slide past each other. Such a flow creates a considerable amount of fourfold order in two dimensions and body-centered-tetragonal (bct) structure in three dimensions. These transitions are the flow analogs of the martensitic transformations occurring in metals due to the stresses induced by a rapid quench. In hard-disk structures, using the bond-orientational analysis we show the presence of fourfold order. In sheared inelastic hard-sphere structures, even though the global bond-orientational analysis shows that the system is highly ordered, a third-order rotational invariant analysis shows that only about 40% of the spheres have face-centered-cubic (fcc) order, even in the dense and near-elastic limits, clearly indicating the coexistence of multiple crystalline orders. When layers of close-packed spheres slide past each other, in addition to the bct structure, the hexagonal-close-packed (hcp) structure is formed due to the random stacking faults. Using the Honeycutt-Andersen pair analysis and an analysis based on the 14-faceted polyhedra having six quadrilateral and eight hexagonal faces, we show the presence of bct and hcp signatures in shear ordered inelastic hard-spheres. Thus, our analysis shows that the dense sheared inelastic hard-spheres have a mixture of fcc, bct, and hcp structures.

Senthil Kumar, V.; Kumaran, V.

2006-05-01

59

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

NASA Astrophysics Data System (ADS)

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

Wang, Zhao; Liu, Longcheng

2012-09-01

60

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 regular (or periodic, e.g., face-centered-cubic) close-packing density usually associated with a crystalline branch. Improved fluid branches are constructed based upon exact, field-theoretic perturbation-theory low-density expansions for many-boson and many-fermion systems, extrapolated to intermediate densities via Pade and other approximants, but whose ultimate density is irregular or random closest close-packing as suggested in studies of a classical system of hard spheres. Results show substantially improved agreement with the best available Green-function Monte Carlo and diffusion Monte Carlo simulations for bosons, as well as with ladder, variational Fermi hypernetted chain, and so-called L-expansion data for two-component fermions.

Solis, M. A. [Department of Physics, Washington University, St. Louis, Missouri 63130 (United States); Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Apartado Postal 20-364, 01000 Mexico, D.F. (Mexico); Llano, M. de [Instituto de Investigaciones en Materiales, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-360, 04510 Mexico, D.F. (Mexico) and Consortium of the Americas for Interdisciplinary Science, University of New Mexico, Albuquerque, New Mexico 87131 (United States); Clark, J. W. [Department of Physics, Washington University, St. Louis, Missouri 63130 (United States); Baker, George A. Jr. [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

2007-09-15

61

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

62

Reversible and irreversible deformation in hard-sphere colloidal glasses

NASA Astrophysics Data System (ADS)

Colloidal glass provides a unique experimental system with which to study the structure, defects, and dynamics of amorphous materials. We report experiments on 1.55-?m-diameter, hard-sphere silica colloidal glasses under conditions of uniform shear. We deform the samples to maximum strains ranging from 0.5% to 10% at various strain rates, and then reverse the deformation so that the net bulk strain is zero at the end of the experiment. We use confocal microscopy to follow the 3D, real-time trajectories of roughly 50,000 particles over the course of an experiment. In this way, we probe the elastic, anelastic, and plastic response of the system, with particular emphasis on the specific, local mechanisms of deformation. We directly observe yield as the onset of local, irreversible deformation. In both sheared and unsheared (quiescent) samples, we observe thermally-activated clusters of particles that behave as Eshelby inclusions, undergoing highly localized plastic strain that couples elastically to the surrounding material. We identify and characterize these regions as they develop in the glass, with particular focus on density-related properties including the Voronoi volume and free volume.

Jensen, Katharine; Nakamura, Nobutomo; Weitz, David; Spaepen, Frans

2013-03-01

63

Effective interaction between hard sphere colloidal particles in a polymerizing Yukawa solvent

The effective interaction between colloidal hard sphere particles in a Yukawa solvent that can polymerize with the formation of chains and rings is studied and compared with the corresponding results for colloidal hard sphere particles in a solvent of polymerizing hard spheres. The attractive nature of the polymerizing Yukawa solvent particles induces significant changes in the effective interactions between the

R. H. Gee; D. Henderson; A. Kovalenko

1999-01-01

64

Complex Oscillatory Yielding of Model Hard-Sphere Glasses

NASA Astrophysics Data System (ADS)

The yielding behavior of hard sphere glasses under large-amplitude oscillatory shear has been studied by probing the interplay of Brownian motion and shear-induced diffusion at varying oscillation frequencies. Stress, structure and dynamics are followed by experimental rheology and Browian dynamics simulations. Brownian-motion-assisted cage escape dominates at low frequencies while escape through shear-induced collisions at high ones, both related with a yielding peak in G''. At intermediate frequencies a novel, for hard sphere glasses, double peak in G'' is revealed reflecting both mechanisms. At high frequencies and strain amplitudes a persistent structural anisotropy causes a stress drop within the cycle after strain reversal, while higher stress harmonics are minimized at certain strain amplitudes indicating an apparent harmonic response.

Koumakis, N.; Brady, J. F.; Petekidis, G.

2013-04-01

65

An asymptotically consistent approximant method with application to soft- and hard-sphere fluids

NASA Astrophysics Data System (ADS)

A modified Padé approximant is used to construct an equation of state, which has the same large-density asymptotic behavior as the model fluid being described, while still retaining the low-density behavior of the virial equation of state (virial series). Within this framework, all sequences of rational functions that are analytic in the physical domain converge to the correct behavior at the same rate, eliminating the ambiguity of choosing the correct form of Padé approximant. The method is applied to fluids composed of ``soft'' spherical particles with separation distance r interacting through an inverse-power pair potential, ? = ?(?/r)n, where ? and ? are model parameters and n is the ``hardness'' of the spheres. For n < 9, the approximants provide a significant improvement over the 8-term virial series, when compared against molecular simulation data. For n >= 9, both the approximants and the 8-term virial series give an accurate description of the fluid behavior, when compared with simulation data. When taking the limit as n --> ?, an equation of state for hard spheres is obtained, which is closer to simulation data than the 10-term virial series for hard spheres, and is comparable in accuracy to other recently proposed equations of state. By applying a least square fit to the approximants, we obtain a general and accurate soft-sphere equation of state as a function of n, valid over the full range of density in the fluid phase.

Barlow, N. S.; Schultz, A. J.; Weinstein, S. J.; Kofke, D. A.

2012-11-01

66

NASA Astrophysics Data System (ADS)

We investigate Monte Carlo simulation strategies for determining the effective (``depletion'') potential between a pair of hard spheres immersed in a dense sea of much smaller hard spheres. Two routes to the depletion potential are considered. The first is based on estimates of the insertion probability of one big sphere in the presence of the other; we describe and compare three such methods. The second route exploits collective (cluster) updating to sample the depletion potential as a function of the separation of the big particles; we describe two such methods. For both routes, we find that the sampling efficiency at high densities of small particles can be enhanced considerably by exploiting ``geometrical shortcuts'' that focus the computational effort on a subset of small particles. All the methods we describe are readily extendable to particles interacting via arbitrary potentials.

Ashton, D. J.; Sánchez-Gil, V.; Wilding, N. B.

2013-10-01

67

Ferromagnetic transition of a two-component Fermi gas of hard spheres

NASA Astrophysics Data System (ADS)

We use microscopic many-body theory to analyze the problem of itinerant ferromagnetism in a repulsive atomic Fermi gas of hard spheres. Using simple arguments we show that the available theoretical predictions for the onset of the ferromagnetic transition predict a transition point at a density (kFa˜1) that is too large to be compatible with the universal low-density expansion of the energy. We present variational calculations for the hard-sphere Fermi gas, in the framework of Fermi hypernetted chain theory, that shift the transition to higher densities (kFa˜1.8). Backflow correlations, which are mainly active in the unpolarized system, are essential for this shift.

Arias de Saavedra, F.; Mazzanti, F.; Boronat, J.; Polls, A.

2012-03-01

68

For a large class of repulsive interaction models, the Mayer cluster integrals can be transformed into a tridiagonal real symmetric matrix R(mn), whose elements converge to two constants with 1/n(2) correction. We find exact expressions in terms of these correction terms for the two critical exponents describing the density near the two singular termination points of the fluid phase. We apply the method to the hard-spheres model and find that the metastable fluid phase terminates at rho(t) = 0.751[5]. The density near the transition is given by rho(t)-rho approximately (z(t) - z)(sigma'), where the critical exponent is predicted to be sigma' = 0.0877[25]. Interestingly, the termination density is close to the observed glass transition; thus, the above critical behavior is expected to be associated with the onset of glassy behavior in hard spheres. PMID:17389362

Eisenberg, E; Baram, A

2007-03-26

69

Passive and active microrheology of hard-sphere colloids.

We performed passive and active microrheology using probe particles in a bath of well-characterized, model hard-sphere colloids in the fluid state over the whole range of volume fractions below the glass transition. The probe and bath particles have nearly the same size. Passive tracking of probe particles yields short-time self-diffusion coefficients. Comparison with literature data demonstrates that the interaction between probe and bath particles is hard-sphere-like. The short-time diffusivities yield one set of microviscosities as a function of volume fraction, which agrees with previous macrorheological measurements of the high-frequency viscosity of hard-sphere colloids. Using optical tweezers, we measure the force on a trapped probe particle as the rest of the sample is translated at constant velocity. This yields a second set of microviscosities at high Péclet numbers. These agree with previous macrorheological measurements of the high-shear viscosity of similar colloids, at shear-rates below the onset of shear-thickening. PMID:19673070

Wilson, L G; Harrison, A W; Schofield, A B; Arlt, J; Poon, W C K

2009-03-26

70

NASA Astrophysics Data System (ADS)

The density profiles of a dimerizing fluid near a crystalline surface are investigated. The model of the bulk fluid is that proposed by Stell and Zhou, which is a generalization of Wertheim's model for dimerization. The formation of dimers results from the interaction between the intracore attractive sites. The fluid-solid interaction consists of two terms. The non-associative term is that proposed by Steele. The directional associative fluid-solid atom interaction is chosen to have a Gaussian form. This provides bonding of the bulk fluid particles with the solid atoms. The solid substrate is assumed to be the graphite basal plane. The density profiles are studied by using the associative singlet Percus-Yevick approximation. When the distance from the surface is greater than the dimer length, the effect of crystalline symmetry is not apparent. The second adlayer tends to disappear when association is present. The relative importance of various positions in the surface unit cell tends to be less when the size of the fluid atom is larger. The dimers prefer to be oriented parallel to the surface but are tilted from the surface plane when bonded to the carbon atoms. Only a small fraction of non-associatively adsorbed dimers have a near-normal orientation.

Kovalenko, Andriy

71

First derivative of the hard-sphere radial distribution function at contact.

Molecular dynamics simulations have been carried out of the radial distribution function of the hard sphere fluid for a range of densities in the equilibrium fluid and just into the metastable region. The first derivative of the hard-sphere radial distribution function at contact was computed and its density dependence fitted to a simple analytic form. Comparisons were made with semi-empirical formulae from the literature, and of these the formula proposed by Tao et al (1992 Phys. Rev. A 46 8007) was found to be in best agreement with the simulation data, although it slightly underestimates the derivative at the higher packing fractions in excess of about 0.45. Close to contact, within a few per cent of the particle diameter, the radial distribution function can be represented well by a second order polynomial. An exponential function, which has some useful analytic features, can also be applied in this region. PMID:21690868

Heyes, David M; Cass, Michael; Bra?ka, Arkadiusz C; Okumura, Hisashi

2006-07-25

72

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

Maiti, Moumita; Lakshminarayanan, Arun; Sastry, Srikanth

2013-01-28

73

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.

Hoppe, Travis

2013-01-01

74

Highly cross-linked polystyrene microgel colloids dispersed in an index and density matching solvent provide a system with hard-sphere-like interactions, where gravity effects are effectively minimized. They are a suitable target for time-resolved observations of solidification in purely repulsive systems. We have investigated the crystallization kinetics at increasing undercooling using time resolved light scattering. Crystallization starts always with the formation of

Sara Iacopini; Thomas Palberg; Hans Joachim Schöpe

2009-01-01

75

A study of the pair and triplet structures of the quantum hard-sphere Yukawa fluid.

The pair and triplet structures of the quantum hard-sphere Yukawa fluid, evaluated for equilateral and isosceles correlations in both the r and the k spaces for a range of conditions and with a particular focus on a region where the onset of increasing number fluctuations takes place (for densities 0.4

Sesé, Luis M

2009-02-21

76

Dynamic-light-scattering study of glasses of hard colloidal spheres

Dynamic light scattering is applied to the glass phase of nonaqueous suspensions of sterically stabilized colloidal spheres. The short-ranged steric repulsion ensures that the particle interactions are close to hard sphere. This is supported by the observation that the equilibrium phase behavior of these suspensions agrees with that predicted for the hard-sphere atomic system. We verify a model for a

W. van Megen; S. M. Underwood

1993-01-01

77

Two methods are presented for the correlation and prediction of the viscosities and thermal conductivities of refrigerants R11, R12, R22, R32, R124, R125, R134a, R141b, and R152 and their mixtures. The first (termed RHS1) is a modified rough-hard-sphere method based on the smooth hard-sphere correlations of Assael et al. The method requires two or three parameters for characterizing each refrigerant but is able to correlate transport properties over wide ranges of pressure and temperature. The second method (RHS2) is also a modified rough-hard-sphere method, but based on an effective hard-sphere diameter for Lennard-Jones (LJ) fluids. The LJ parameters and the effective hard-sphere diameter required in this method are determined from a knowledge of the density-temperature behavior of the fluid at saturation. Comparisons with the rough-hard-sphere method of Assael and co-workers (RHS3) are shown. They also show that the RHS2 method can be used to correlate as well as predict the transport properties of refrigerants.

Teja, A.S.; King, R.K.; Sun, T.F. [Georgia Inst. of Tech., Atlanta, GA (United States). School of Chemical Engineering; Smith, R.L. Jr. [Tohoku Univ., Sendai (Japan). Dept. of Chemical Engineering

1999-01-01

78

Nonequilibrium thermodynamics in sheared hard-sphere materials.

We combine the shear-transformation-zone (STZ) theory of amorphous plasticity with Edwards' statistical theory of granular materials to describe shear flow in a disordered system of thermalized hard spheres. The equations of motion for this system are developed within a statistical thermodynamic framework analogous to that which has been used in the analysis of molecular glasses. For hard spheres, the system volume V replaces the internal energy U as a function of entropy S in conventional statistical mechanics. In place of the effective temperature, the compactivity X=?V/?S characterizes the internal state of disorder. We derive the STZ equations of motion for a granular material accordingly, and predict the strain rate as a function of the ratio of the shear stress to the pressure for different values of a dimensionless, temperature-like variable near a jamming transition. We use a simplified version of our theory to interpret numerical simulations by Haxton, Schmiedeberg, and Liu, and in this way are able to obtain useful insights about internal rate factors and relations between jamming and glass transitions. PMID:23005087

Lieou, Charles K C; Langer, J S

2012-06-19

79

Crystallization and dynamical arrest of attractive hard spheres.

Crystallization of hard spheres interacting with a square well potential was investigated by numerical simulations using so-called Brownian cluster dynamics. The phase diagram was determined over a broad range of volume fractions. The crystallization rate was studied as a function of the interaction strength expressed in terms of the second virial coefficient. For volume fractions below about 0.3 the rate was found to increase abruptly with increasing attraction at the binodal of the metastable liquid-liquid phase separation. The rate increased until a maximum was reached after which it decreased with a power law dependence on the second virial coefficient. Above a critical percolation concentration, a transient system spanning network of connected particles was formed. Crystals were formed initially as part of the network, but eventually crystallization led to the breakup of the network. The lifetime of the transient gels increased very rapidly over a small range of interaction energies. Weak attraction destabilized the so-called repulsive crystals formed in pure hard sphere systems and shifted the coexistence line to higher volume fractions. Stronger attraction led to the formation of a denser, so-called attractive, crystalline phase. Nucleation of attractive crystals in the repulsive crystalline phase was observed close to the transition. PMID:19222281

Babu, Sujin; Gimel, Jean-Christophe; Nicolai, Taco

2009-02-14

80

Branching points in the low-temperature dipolar hard sphere fluid

NASA Astrophysics Data System (ADS)

In this contribution, we investigate the low-temperature, low-density behaviour of dipolar hard-sphere (DHS) particles, i.e., hard spheres with dipoles embedded in their centre. We aim at describing the DHS fluid in terms of a network of chains and rings (the fundamental clusters) held together by branching points (defects) of different nature. We first introduce a systematic way of classifying inter-cluster connections according to their topology, and then employ this classification to analyse the geometric and thermodynamic properties of each class of defects, as extracted from state-of-the-art equilibrium Monte Carlo simulations. By computing the average density and energetic cost of each defect class, we find that the relevant contribution to inter-cluster interactions is indeed provided by (rare) three-way junctions and by four-way junctions arising from parallel or anti-parallel locally linear aggregates. All other (numerous) defects are either intra-cluster or associated to low cluster-cluster interaction energies, suggesting that these defects do not play a significant part in the thermodynamic description of the self-assembly processes of dipolar hard spheres.

Rovigatti, Lorenzo; Kantorovich, Sofia; Ivanov, Alexey O.; Tavares, José Maria; Sciortino, Francesco

2013-10-01

81

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

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

Chang Yongbin; Shizgal, Bernie D. [Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1 (Canada)

2008-12-31

82

NASA Astrophysics Data System (ADS)

In a previous article (Baeyens and Verschelde in J. Math. Phys. 36:201, 1995), an improved approach to the scaled particle theory of Reiss et al. was presented. We used a generalized series expansion of the contact correlation function G( y, r). Truncating it after the third term, we obtained a Padé-like expression for the compressibility factor of the system. That expression contains two parameters which we were able to calculate, not only for the fluid state, but also for the known glassy states (Baeyens and Verschelde in Z. Phys. B 102:255, 1997). The resulting equations of state are in good agreement with the simulation data. Yet in the case of the hard sphere crystal our improved scaled particle theory fails, which is one of the reasons why an extension of it is desirable. In this paper the above mentioned expansion of G( y, r) will once more be generalized. Truncation after the sixth term leads to a simple but acceptable equation of state for the hard sphere fcc-crystal. It reproduces the free energies, the compressibility factors and the pressure of freezing and melting to within 0.3, 5, and 0.6 percent respectively.

Baeyens, Bruno

2011-12-01

83

Voronoi neighbor statistics of homogeneously sheared inelastic hard disks and hard spheres

NASA Astrophysics Data System (ADS)

In this work we extend our earlier Voronoi neighbor analysis [J. Chem. Phys. 123, 074502 (2005)] to homogeneously sheared inelastic hard-particle structures, the simplest model for rapid granular matter. The pair distribution function is partitioned into the nth neighbor coordination number (Cn) , and the nth neighbor position distribution [fn(r)] . The distribution of the number of Voronoi faces (Pn) is also considered since C1 is its mean. We report the Cn and Pn for the homogeneously sheared inelastic hard-disk and hard-sphere structures. These statistics are sensitive to shear ordering transition, the nonequilibrium analogue of the freezing transition. In the near-elastic limit, the sheared fluid statistics approach that of the thermodynamic fluid. On shear ordering, due to the onset of order, the Cn for sheared structures approach that of the thermodynamic solid phase. The suppression of nucleation by the homogeneous shear is evident in these statistics. As inelasticity increases, the shear ordering packing fraction increases. Due to the topological instability of the isotropically perturbed face-centered cubic lattice, polyhedra with faces 12 to 18, with a mean at 14, coexist even in the regular close packed limit for the thermodynamic hard-sphere solid. In shear ordered inelastic hard-sphere structures there is a high incidence of 14-faceted polyhedra and a consequent depletion of polyhedra with faces 12, 13, 15-18, due to the formation of body-centered-tetragonal (bct) structures. These bct structures leave a body-centered-cubic-like signature in the Cn and Pn data. On shear ordering, close-packed layers slide past each other. However, with a velocity-dependent coefficient of restitution, at a critical shear rate these layers get disordered or amorphized. We find that the critical shear rate for amorphization is inversely proportional to the particle diameter, as compared to the inverse square scaling observed in dense colloidal suspensions.

Senthil Kumar, V.; Kumaran, V.

2006-05-01

84

In the preceding paper, we have conjectured that the main transport properties of a dilute gas of inelastic hard spheres (IHSs) can be satisfactorily captured by an equivalent gas of elastic hard spheres (EHSs), provided that the latter are under the action of an effective drag force and their collision rate is reduced by a factor (1+alpha)/2 (where alpha is the constant coefficient of normal restitution). In this paper we test the above expectation in a paradigmatic nonequilibrium state, namely, the simple or uniform shear flow, by performing Monte Carlo computer simulations of the Boltzmann equation for both classes of dissipative gases with a dissipation range 0.5 < or = alpha < or = 0.95 and two values of the imposed shear rate a. It is observed that the evolution toward the steady state proceeds in two stages: a short kinetic stage (strongly dependent on the initial preparation of the system) followed by a slower hydrodynamic regime that becomes increasingly less dependent on the initial state. Once conveniently scaled, the intrinsic quantities in the hydrodynamic regime depend on time, at a given value of alpha, only through the reduced shear rate a*(t) is proportional to a/square root(T(t)), until a steady state, independent of the imposed shear rate and of the initial preparation, is reached. The distortion of the steady-state velocity distribution from the local equilibrium state is measured by the shear stress, the normal stress differences, the cooling rate, the fourth and sixth cumulants, and the shape of the distribution itself. In particular, the simulation results seem to be consistent with an exponential overpopulation of the high-velocity tail. These properties are common to both the IHS and EHS systems. In addition, the EHS results are in general hardly distinguishable from the IHS ones if alpha approximately > 0.7, so that the distinct signature of the IHS gas (higher anisotropy and overpopulation) only manifests itself at relatively high dissipations. PMID:16241428

Astillero, Antonio; Santos, Andrés

2005-09-30

85

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

2000-03-01

86

Collisional statistics of the hard-sphere gas.

We investigate the probability distribution functions of the free flight time and of the number of collisions in a hard-sphere gas at equilibrium. At variance with naive expectation, the latter quantity does not follow Poissonian statistics, even in the dilute limit, which is the focus of the present analysis. The corresponding deviations are addressed both numerically and analytically. In writing an equation for the generating function of the cumulants of the number of collisions, we came across a perfect mapping between our problem and a previously introduced model: the probabilistic ballistic annihilation process [Coppex, Phys. Rev. E 69, 11303 (2004)]. We exploit this analogy to construct a Monte Carlo-like algorithm able to investigate the asymptotically large time behavior of the collisional statistics within a reasonable computational time. In addition, our predictions are compared with the results of molecular dynamics simulations and the direct simulation Monte Carlo technique. An excellent agreement is reported. PMID:18517588

Visco, Paolo; van Wijland, Frédéric; Trizac, Emmanuel

2008-04-18

87

Hard-sphere crystallization gets rarer with increasing dimension.

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

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

2009-12-08

88

The kinetics of crystallization and vitrification in colloidal hard spheres

NASA Astrophysics Data System (ADS)

We investigated the process of vitrification and crystallization in a model system of colloidal particles with a hard sphere (HS) like interaction. To analyze the similarities and differences of these two kinds of solidification processes we used two different kinds of experiments. The solidification kinetics was measured using time resolved static light scattering. By using a special dynamic light scattering setup we were able to track the change of the dynamic properties during the solidification process in great detail. By performing further analysis we confirm that solidification of a HS colloidal model system is mediated by precursors. In crystallization these objects convert into highly ordered crystals whereas in the case of vitrification this conversion is blocked and the system is locked in the metastable precursor state.

Franke, Markus; Golde, Sebastian; Schöpe, Hans Joachim

2013-02-01

89

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

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

Zhao, Nanrong; Sugiyama, Masaru; Ruggeri, Tommaso

2008-08-01

90

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

NASA Astrophysics Data System (ADS)

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

Zhao, Nanrong; Sugiyama, Masaru; Ruggeri, Tommaso

2008-08-01

91

We evaluate the effect of interaction strength on the condensate distribution and condensate fraction of hard sphere bosons in an external trapping potential. Quantum Monte-Carlo methods are used to obtain the dependence of the T=0 ground state properties on the hard sphere radius and the number of particles. Condensate properties are then obtained through direct diagonalization of the one body

Jonathan L. Dubois; Henry R. Glyde

2002-01-01

92

Dense Random Packing of Hard Spheres as a Structural Model for Non-Crystalline Metallic Solids.

National Technical Information Service (NTIS)

The pair distribution function for dense random packing of hard spheres is very similar to that observed for non-crystalline Ni-P alloys. The hard sphere model distribution function has a split second peak; this splitting is a characteristic structural fe...

G. S. Cargill

1969-01-01

93

Clusterization in Two-Dimensional System of Hard Spheres

NASA Astrophysics Data System (ADS)

A clusterization process in two-dimensional system of granular hard disks is investigated by two novel numerical methods: the nearest neighbourhood density and the anti-percolation function. The tendency of the band like structures in the clustered state is recognized to be driven by two factors: the stretching forces at the junction of two clusters (or two parts of one cluster) with different kinetic energies and the density fluctuations, which act as a seed for the empty ponds (voids free of particles). Moreover, the examples (and animations) of the collision of two clusters and the breakup of the granular band are presented.

Chrzanowska, A.; Traczuk, G.; Fornal, P.

2008-01-01

94

Anisotropic spheres with variable energy density in general relativity

Interior solutions of Einstein field equations for anisotropic spheres with variable energy density are obtained. The solutions for uniform energy density [10] and for radial pressure equal to zero [11] are particular cases of the present solution. With this solution we are also able to discuss an anisotropic gas sphere. Physically it explains larger red-shifts of different quasi-stellar objects. The

M. K. Gokhroo; A. L. Mehra

1994-01-01

95

We investigate the value of the correlation function of an inhomogeneous hard-sphere fluid at contact. This quantity plays a critical role in statistical associating fluid theory, which is the basis of a number of recently developed classical density functionals. We define two averaged values for the correlation function at contact and derive formulas for each of them from the White Bear version of the fundamental measure theory functional, using an assumption of thermodynamic consistency. We test these formulas, as well as two existing formulas, against Monte Carlo simulations and find excellent agreement between the Monte Carlo data and one of our averaged correlation functions. PMID:23367925

Schulte, Jeff B; Kreitzberg, Patrick A; Haglund, Chris V; Roundy, David

2012-12-28

96

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

NASA Astrophysics Data System (ADS)

In this paper we investigate the solubility of a hard-sphere gas in a solvent modeled as an associating lattice gas. The solution phase diagram for solute at 5% is compared with the phase diagram of the original solute free model. Model properties are investigated both through Monte Carlo simulations and a cluster approximation. The model solubility is computed via simulations and is 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, in accordance with the literature on continuous realistic models and on the ``cavity'' picture.

Szortyka, Marcia M.; Girardi, Mauricio; Henriques, Vera B.; Barbosa, Marcia C.

2012-08-01

97

We compute the singular value decomposition of the radial distribution function [Formula: see text] for hard sphere, and square well solutions. We find that [Formula: see text] 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 [Formula: see text] in this compact representation for the investigated parameter range. PMID:24143174

Hoppe, Travis

2013-10-15

98

Class of consistent fundamental-measure free energies for hard-sphere mixtures.

In fundamental-measure theories the bulk excess free-energy density of a hard-sphere fluid mixture is assumed to depend on the partial number densities {?(i)} only through the four scaled-particle-theory variables {?(?)}, i.e., ?({?(i)})??({?(?)}). By imposing consistency conditions, it is proven here that such a dependence must necessarily have the form ?({?(?)})=-?(0)ln(1-?(3))+?(y)?(1)?(2)/(1-?(3)), where y??(2)(2)/12??(1)(1-?(3)) is a scaled variable and ?(y) is an arbitrary dimensionless scaling function which can be determined from the free-energy density of the one-component system. Extension to the inhomogeneous case is achieved by standard replacements of the variables {?(?)} by the fundamental-measure (scalar, vector, and tensor) weighted densities {n(?)(r)}. Comparison with computer simulations shows the superiority of this bulk free energy over the White Bear one. PMID:23214514

Santos, Andrés

2012-10-05

99

NASA Astrophysics Data System (ADS)

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

Kern, Jesse; Laird, Brian

2013-03-01

100

Properties of the path-integral quantum hard-sphere fluid in k space

NASA Astrophysics Data System (ADS)

The properties of quantum fluids in Fourier space, as the system response functions to weak external fields, are analyzed taking the quantum hard-sphere fluid as a probe. This serves to clarify the physical meaning of the different radial correlation functions that can be defined in a path-integral quantum fluid, since these functions are the r-space counterparts of the response functions. The basic feature of the external field relevant to this discussion is connected with its localizing/nonlocalizing effect on the quantum particles composing the fluid (i.e., a localizing field causes the collapse of the particle thermal packet). Fields that localize the quantum particles reveal the so-called instantaneous quantities (e.g., the conventional static structure factor), which are related with the diagonal elements of the density matrix. Fields that do not localize the quantum particles show the so-called linear response quantities, which are related to the diagonal and the off-diagonal density matrix elements. To perform this study the path-integral formalism is considered from the functional analysis approach. Given that the Gaussian Feynman-Hibbs effective potential picture is known to represent well many structural features of the quantum hard-sphere fluid, the parallel study of the response functions within this picture is also presented. In particular, the latter picture provides an accurate Ornstein-Zernike scheme that can be used for numerical calculations of response functions over a wide range of conditions, and also gives fine estimates for quantities difficult to compute with the path integral. Results for the quantum hard-sphere fluid obtained within the latter scheme are reported, tests of consistency are given, and the possibility of approximating the instantaneous response function by means of the coherent part of the linear response function is assessed.

Sesé, Luis M.

2002-05-01

101

Granular mixtures modeled as elastic hard spheres subject to a drag force

NASA Astrophysics Data System (ADS)

Granular gaseous mixtures under rapid flow conditions are usually modeled as a multicomponent system of smooth inelastic hard disks (two dimensions) or spheres (three dimensions) with constant coefficients of normal restitution ?ij . In the low density regime an adequate framework is provided by the set of coupled inelastic Boltzmann equations. Due to the intricacy of the inelastic Boltzmann collision operator, in this paper we propose a simpler model of elastic hard disks or spheres subject to the action of an effective drag force, which mimics the effect of dissipation present in the original granular gas. For each collision term ij , the model has two parameters: a dimensionless factor ?ij modifying the collision rate of the elastic hard spheres, and the drag coefficient ?ij . Both parameters are determined by requiring that the model reproduces the collisional transfers of momentum and energy of the true inelastic Boltzmann operator, yielding ?ij=(1+?ij)/2 and ?ij?1-?ij2 , where the proportionality constant is a function of the partial densities, velocities, and temperatures of species i and j . The Navier-Stokes transport coefficients for a binary mixture are obtained from the model by application of the Chapman-Enskog method. The three coefficients associated with the mass flux are the same as those obtained from the inelastic Boltzmann equation, while the remaining four transport coefficients show a general good agreement, especially in the case of the thermal conductivity. The discrepancies between both descriptions are seen to be similar to those found for monocomponent gases. Finally, the approximate decomposition of the inelastic Boltzmann collision operator is exploited to construct a model kinetic equation for granular mixtures as a direct extension of a known kinetic model for elastic collisions.

Vega Reyes, Francisco; Garzó, Vicente; Santos, Andrés

2007-06-01

102

Granular mixtures modeled as elastic hard spheres subject to a drag force.

Granular gaseous mixtures under rapid flow conditions are usually modeled as a multicomponent system of smooth inelastic hard disks (two dimensions) or spheres (three dimensions) with constant coefficients of normal restitution alpha{ij}. In the low density regime an adequate framework is provided by the set of coupled inelastic Boltzmann equations. Due to the intricacy of the inelastic Boltzmann collision operator, in this paper we propose a simpler model of elastic hard disks or spheres subject to the action of an effective drag force, which mimics the effect of dissipation present in the original granular gas. For each collision term ij, the model has two parameters: a dimensionless factor beta{ij} modifying the collision rate of the elastic hard spheres, and the drag coefficient zeta{ij}. Both parameters are determined by requiring that the model reproduces the collisional transfers of momentum and energy of the true inelastic Boltzmann operator, yielding beta{ij}=(1+alpha{ij})2 and zeta{ij} proportional, variant1-alpha{ij}/{2}, where the proportionality constant is a function of the partial densities, velocities, and temperatures of species i and j. The Navier-Stokes transport coefficients for a binary mixture are obtained from the model by application of the Chapman-Enskog method. The three coefficients associated with the mass flux are the same as those obtained from the inelastic Boltzmann equation, while the remaining four transport coefficients show a general good agreement, especially in the case of the thermal conductivity. The discrepancies between both descriptions are seen to be similar to those found for monocomponent gases. Finally, the approximate decomposition of the inelastic Boltzmann collision operator is exploited to construct a model kinetic equation for granular mixtures as a direct extension of a known kinetic model for elastic collisions. PMID:17677254

Vega Reyes, Francisco; Garzó, Vicente; Santos, Andrés

2007-06-26

103

Voronoi cell volume distribution and configurational entropy of hard-spheres

NASA Astrophysics Data System (ADS)

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

Senthil Kumar, V.; Kumaran, V.

2005-09-01

104

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

National Technical Information Service (NTIS)

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...

J. S. Ling M. P. Doherty

1998-01-01

105

National Technical Information Service (NTIS)

Calculations of the thermodynamic properties and pair distribution function of a one-component classical fluid of charged hard spheres in a uniform neutralizing background are reported and compared with Monte Carlo results of Hansen and Weis. Thermodynami...

Z. Badirkhan G. Pastore M. P. Tosi

1991-01-01

106

Settling and fluidization of non Brownian hard spheres in a viscous liquid

NASA Astrophysics Data System (ADS)

A mean field approach is used to estimate the energy dissipation during the homogeneous sedimentation or the particulate fluidization of non Brownian hard spheres in a concentrated suspension of infinite extent. Depending on inertial screening and the range of the hydrodynamic interactions, the effective buoyancy force is determined either from the average suspension density in a Stokes flow or from the fluid density in the turbulent flow regime. An energy balance then yields a settling or fluidization law depending on the particle Reynolds number in reasonable agreement with the Richardson and Zaki correlation and recent experimental results for particle settling or fluidization. We further estimate the energy dissipation in the turbulent boundary layers around the particles to precise the Reynolds number dependence of the hindered settling function in the intermediate flow regime.

Snabre, P.; Mills, P.

2000-02-01

107

Phase transition, equation of state, and limiting shear viscosities of hard sphere dispersions

NASA Astrophysics Data System (ADS)

Despite an interparticle potential consisting of only an infinite repulsion at contact, the thermodynamics and dynamics of concentrated dispersions of hard spheres are not yet fully understood. Colloidal poly-(methyl methacrylate) spheres with a grafted layer of poly-(12-hydroxy stearic acid) (PMMA-PHSA) comprise a common model for investigating structural, dynamic, and rheological properties. These highly monodisperse spheres can be index matched in nonaqueous solvents, reducing van der Waals forces and allowing characterization via light scattering. In this work, we test the behavior of these dispersions against expectations for hard spheres through observations of the phase behavior, x-ray densitometry of equilibrium sediments, and Zimm viscometry. We set the effective hard sphere volume fraction by the disorder-order transition, thereby accounting for the polymer layer, any swelling due to the solvent, and polydispersity. The melting transition then occurs close to the expected value and 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 even after accounting for polydispersity. 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, e.g., a relative viscosity of 45+/-3 at ?=0.50 rather than 24. Our low shear viscosities are consistent with other PMMA-PHSA data after rescaling for both the polymer layer thickness and polydispersity, and may represent the true hard sphere curve. We anticipate that the equation of state for the crystal deviates due to polycrystallinity or a direct effect of polydispersity.

Phan, See-Eng; Russel, William B.; Cheng, Zhengdong; Zhu, Jixiang; Chaikin, Paul M.; Dunsmuir, John H.; Ottewill, Ronald H.

1996-12-01

108

Experimental Phase Diagram of a Binary Colloidal Hard-Sphere Mixture with a Large Size Ratio

We determined the phase diagram of a binary hard-sphere dispersion with size ratio 9.3. Phase separation into a fluid and a crystal of large spheres is observed. The fluid-solid binodal is determined by measurements of compositions of coexisting phases. The results agree qualitatively with recent theories, although the latter strongly overestimate the depletion activity of the smaller spheres. By fluorescent

A. Imhof; J. K. G. Dhont

1995-01-01

109

Phase transition, equation of state, and limiting shear viscosities of hard sphere dispersions

Despite an interparticle potential consisting of only an infinite repulsion at contact, the thermodynamics and dynamics of concentrated dispersions of hard spheres are not yet fully understood. Colloidal poly-(methyl methacrylate) spheres with a grafted layer of poly-(12-hydroxy stearic acid) (PMMA-PHSA) comprise a common model for investigating structural, dynamic, and rheological properties. These highly monodisperse spheres can be index matched in

See-Eng Phan; William B. Russel; Zhengdong Cheng; Jixiang Zhu; Paul M. Chaikin; John H. Dunsmuir; Ronald H. Ottewill

1996-01-01

110

Shapes of Delaunay Simplexes and Structural Analysis of Hard Sphere Packings

In this chapter we apply a computational geometry technique to investigate the structure of packings of hard spheres. The\\u000a hard sphere model is the base for understanding the structure of many physical matters: liquids, solids, colloids and granular\\u000a materials. The structure analysis is based on the concept of the Voronoi Diagram (Voronoi-Delaunay tessellation), which is\\u000a well known in mathematics and

Alexey V. Anikeenko; Marina L. Gavrilova; Nikolai N. Medvedev

2008-01-01

111

The usefulness of the hard-sphere model in characterizing polydispersity in concentrated colloidal solutions is stressed. A recently derived equation for (??i\\/??j)? is used to give a simpler route for application to light scattering and sedimentation in multicomponent and polydisperse systems. Some light-scattering intensity calculations are performed for a log-normal distribution of hard-sphere diameters. Special attention is given to the contribution

A. Vrij

1982-01-01

112

Path integral Monte Carlo study of quantum-hard sphere solids.

A path integral study of the fcc, hcp, and bcc quantum hard-sphere solids is presented. Ranges of densities within the interval of reduced de Broglie wavelengths 0.2??B(*)?0.8 have been analyzed using Monte Carlo simulations with Cao-Berne propagator. Energies, pressures, and structural quantities (pair radial correlation functions, centroid structure factors, and Steinhardt order parameters) have been computed. Also, applications of the Einstein crystal technique [L. M. Sese?, J. Chem. Phys. 126, 164508 (2007)] have been made to compute the free energies of the fcc and hcp solids. Some technical points related to the latter technique are discussed, and it is shown that these calculations produce consistent results with increasing sample sizes. The fluid-solid (fcc and hcp) equilibria have been studied, thus completing prior work by this author on the fluid-fcc equilibrium. Within the accuracy attained no significant differences between the relative stabilities of the fcc and hcp lattices have been detected. The bcc case stands apart from the other two lattices, as the simulations lead either to irregular lattices (two types) that keep some traces of bcc-memory, or to spontaneous transitions to hcp-like lattices. The latter transitions make manifestly clear the potential repercussions that the quantum hard-sphere behavior can have on solid-solid equilibria at low temperatures in real systems (e.g., helium). PMID:23901988

Sesé, Luis M

2013-07-28

113

Interaction energy and force for a pair of colloidal particles in a bidisperse hard-sphere solvent

A convenient approximation is proposed for the correlation function of a pair of large hard-sphere particles in a bidisperse or binary hard-sphere mixture. This approximation is based on the solution of the Ornstein–Zernike\\/Percus–Yevick integral equations for a hard-sphere mixture. From this result, we obtain the potential of mean force and interaction force for a pair of colloidal spheres in a

D. Henderson; A. D. Trokhymchuk; D. T. Wasan

2004-01-01

114

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

115

Thermodynamics of d-dimensional hard sphere fluids confined to micropores.

We derive an analytical expression of the second virial coefficient of d-dimensional hard sphere fluids confined to slit pores by applying Speedy and Reiss' interpretation of cavity space. We confirm that this coefficient is identical to the one obtained from the Mayer cluster expansion up to second order with respect to fugacity. The key step of both approaches is to evaluate either the surface area or the volume of the d-dimensional exclusion sphere confined to a slit pore. We, further, present an analytical form of thermodynamic functions such as entropy and pressure tensor as a function of the size of the slit pore. Molecular dynamics simulations are performed for d = 2 and d = 3, and the results are compared with analytically obtained equations of state. They agree satisfactorily in the low density regime, and, for given density, the agreement of the results becomes excellent as the width of the slit pore gets smaller, because the higher order virial coefficients become unimportant. PMID:21428627

Kim, Hyungjun; Goddard, William A; Han, Kyeong Hwan; Kim, Changho; Lee, Eok Kyun; Talkner, Peter; Hänggi, Peter

2011-03-21

116

Thermodynamics of d-dimensional hard sphere fluids confined to micropores

NASA Astrophysics Data System (ADS)

We derive an analytical expression of the second virial coefficient of d-dimensional hard sphere fluids confined to slit pores by applying Speedy and Reiss' interpretation of cavity space. We confirm that this coefficient is identical to the one obtained from the Mayer cluster expansion up to second order with respect to fugacity. The key step of both approaches is to evaluate either the surface area or the volume of the d-dimensional exclusion sphere confined to a slit pore. We, further, present an analytical form of thermodynamic functions such as entropy and pressure tensor as a function of the size of the slit pore. Molecular dynamics simulations are performed for d = 2 and d = 3, and the results are compared with analytically obtained equations of state. They agree satisfactorily in the low density regime, and, for given density, the agreement of the results becomes excellent as the width of the slit pore gets smaller, because the higher order virial coefficients become unimportant.

Kim, Hyungjun; Goddard, William A.; Han, Kyeong Hwan; Kim, Changho; Lee, Eok Kyun; Talkner, Peter; Hänggi, Peter

2011-03-01

117

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

NASA Astrophysics Data System (ADS)

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

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

2011-02-01

118

Energy and Structure of Hard-Sphere Bose Gases in three and two dimensions

NASA Astrophysics Data System (ADS)

The energy and structure of dilute gases of hard spheres in three dimensions is discussed, together with some aspects of the corresponding 2D systems. A variational approach in the framework of the Hypernetted Chain Equations (HNC) is used starting from a Jastrow wavefunction that is optimized to produce the best two--body correlation factor with the appropriate long range. Relevant quantities describing static properties of the system are studied as a function of the gas parameter $x=\\rho a^d$ where $\\rho$, $a$ and $d$ are the density, $s$--wave scattering length of the potential and dimensionality of the space, respectively. The occurrence of a maximum in the radial distribution function and in the momentum distribution is a natural effect of the correlations when $x$ increases. Some aspects of the asymptotic behavior of the functions characterizing the structure of the systems are also investigated.

Mazzanti, F.; Polls, A.; Fabrocini, A.

2005-02-01

119

Role of bond orientational order in the crystallization of hard spheres

NASA Astrophysics Data System (ADS)

With computer simulations of the hard sphere model, we examine in detail the microscopic pathway connecting the metastable melt to the emergence of crystalline clusters. In particular we will show that the nucleation of the solid phase does not follow a two-step mechanism, where crystals form inside dense precursor regions. On the contrary, we will show that nucleation is driven by fluctuations of orientational order, and not by the density fluctuations. By considering the development of the pair-excess entropy inside crystalline nuclei, we confirm that orientational order precedes positional order. These results are at odd with the idea of a two-step nucleation mechanism for fluids without a metastable liquid-liquid phase separation. Our study suggests the pivotal role of bond orientational ordering in triggering crystal nucleation.

Russo, John; Tanaka, Hajime

2013-02-01

120

Structural and thermodynamic properties of freely-jointed hard-sphere rings and chains

In this paper, we employ the product-reactant Ornstein-Zernike approach (PROZA) developed by the authors to investigate the structural and thermodynamic properties of freely-jointed hard-sphere ring fluids. Using an Mxm component sticky two-point (S2P) model and specifying an appropriate association rule between various species, the associating monomers will form M rings with each ring composed of m beads in the complete-association limit. Applying the PROZA to such a Hamiltonian and considering the limit of complete association, we are able to derive analytical expressions for the average monomer-monomer radial distribution function (RDF) as well as its intermolecular and intramolecular contributions and a closed form of the compressibility pressure. To test the theory, we also perform Monte Carlo simulations for the freely-jointed hard-sphere ring model over a wide range of densities and ring sizes. Compared to the simulation results, we find that the predictions of the PROZA for the compressibility factor of flexible ring melts are quantitatively accurate and the average monomer-monomer RDF g(r) is in excellent agreement with the simulation data over a wide range of densities that includes the polymer-melt regime. Based upon such a comparison as well as theoretical considerations, we conclude that ring-size independence of g(r) is a quantitatively accurate approximation and also that the g(r) of rings will be a good approximation for melts of long chains. Finally, we find that we must go beyond our PROZA framework in order to accurately obtain the separate intramolecular and intermolecular parts of g(r), for which we give a quantitatively satisfactory recipe. (c) 2000 American Institute of Physics.

Lin, C.-T [Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794-3400 (United States); Stell, G. [Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794-3400 (United States); Kalyuzhnyi, Yu. V. [Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794-3400 (United States); Institute for Condensed Matter Physics, Svientsitskoho 1, 290011 Lviv, (Ukraine)

2000-02-08

121

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

NASA Astrophysics Data System (ADS)

Using molecular dynamics simulations, we calculate fluctuations and responses for steadily sheared hard spheres over a wide range of packing fractions ? and shear strain rates ??, 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 Teff that is equal to or larger than the kinetic temperature Tkin. We find a crossover in the relationship between the relaxation time ? and the the nondimensionalized effective temperature Teff/p?3, where p is the pressure and ? is the sphere diameter. In the solid response regime, the behavior at a fixed packing fraction satisfies ????exp(-cp?3/Teff), where c depends weakly on ?, 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 Teff/p?3 as it depends on Tkin/p?3 in equilibrium. This regime includes both near-equilibrium conditions where Teff?Tkin and far-from-equilibrium conditions where Teff?Tkin. We discuss the implications of our results for systems with soft repulsive interactions.

Haxton, Thomas K.

2012-01-01

122

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

123

Tracer diffusion in hard sphere fluids from molecular to hydrodynamic regimes.

Molecular dynamics is employed to investigate tracer diffusion in hard sphere fluids. Reduced densities (rho*=rhosigma(3), sigma is the diameter of bath fluid particles) ranging from 0.02 to 0.52 and tracers ranging in diameter from 0.125sigma to 16sigma are considered. Finite-size effects are found to pose a significant problem and can lead to seriously underestimated tracer diffusion constants even in systems that are very large by simulation standards. It is shown that this can be overcome by applying a simple extrapolation formula that is linear in the reciprocal cell length L(-1), allowing us to obtain infinite-volume estimates of the diffusion constant for all tracer sizes. For higher densities, the range of tracer diameters considered spans diffusion behavior from molecular to hydrodynamic regimes. In the hydrodynamic limit our extrapolated results are clearly consistent with the theoretically expected slip boundary conditions, whereas the underestimated values obtained without extrapolation could easily be interpreted as approaching the stick limit. It is shown that simply adding the Enskog and hydrodynamic contributions gives a reasonable qualitative description of the diffusion behavior but tends to overestimate the diffusion constant. We propose another expression that fits the simulation results for all densities and tracer diameters. PMID:17144710

Sokolovskii, R O; Thachuk, M; Patey, G N

2006-11-28

124

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

2008-05-23

125

NASA Astrophysics Data System (ADS)

A comparison of compressional properties of silicate solids, glasses, and liquids reveals the following fundamental differences: (1) Liquids have much smaller bulk moduli than solids and glasses and the bulk moduli of various silicate melts have a narrow range of values; (2) Liquids do not follow the Birch's law of corresponding state as opposed to solids and glasses; (3) The Grüneisen parameter increases with increasing pressure for liquids but decreases for solids; (4) The radial distribution functions of liquids show that the interatomic distances in liquids do not change upon compression as much as solids do. The last observation indicates that the compression of silicate melts occurs mostly through the geometrical arrangement of various units whose sizes do not change much with compression, i.e., the entropic mechanism of compression plays a dominant role over the internal energy contribution. All of the other three observations listed above can be explained by this point of view. In order to account for the role of the entropic contribution, we propose a new equation of state for multi-component silicate melts based on the hard sphere mixture model of a liquid. We assign a hard sphere for each cation species that moves in the liquid freely except for the volume occupied by other spheres. The geometrical arrangement of these spheres gives the entropic contribution to compression, while the Columbic attraction between all ions provides the internal energy contribution to compression. We calibrate the equation of state using the experimental data on room-pressure density and room-pressure bulk modulus of liquids. The effective size of a hard sphere for each component in silicate melts is determined. The temperature and volume dependencies of sphere diameters are also included in the model in order to explain the experimental data especially the melt density data at high pressures. All compressional properties of a silicate melt can be calculated using the calibrated sphere diameters. This equation of state provides a unified explanation for most of compressional behaviors of silicate melts and the experimental observations cited above including the uniformly small bulk moduli of silicate melts as well as the pressure dependence of Grüneisen parameters. With additional data to better constrain the key parameters, this equation of state will serve as a first step toward the unified equation of state for silicate melts.

Jing, Zhicheng; Karato, Shun-ichiro

2011-11-01

126

Theoretical problems in the crystallization of hard sphere colloidal particles

In this paper we demonstrate the utility of density functional theories in providing unified descriptions of two problems associated with colloidal crystallization. The first problem involves crystallization in a fixed volume. The result is a time dependent pressure and, hence, density. This process is further complicated during growth by the presence of a depletion zone in advance of the growing

Robert Wild; Peter Harrowell

2000-01-01

127

The radial distribution function and the structure factor of dipolar hard spheres

The structure of a ferrocolloid suspension is studied theoretically. The system is modeled as a fluid of dipolar hard spheres, for which the zero-field radial distribution function and the structure factor are determined. The radial distribution function is calculated on the basis of a power-series expansion in terms of the ferroparticle concentration, retaining terms of up to the second order.

E. Elfimova; A. Ivanov

2008-01-01

128

We have investigated the structural change of dipolar hard sphere fluid while we change the dipole from an idealised point dipole (pDHS fluid) to a physically more realistic extended dipole (eDHS fluid) by increasing the distance d of the two point charges ±q while keeping the dipole moment ? = qd fixed. We discuss our results on the basis of

Monika Valisko; Tibor Varga; Andras Baczoni; Dezso Boda

2010-01-01

129

Monte Carlo simulation of growth of hard-sphere crystals on a square pattern

Monte Carlo simulations of the colloidal epitaxy of hard spheres (HSs) on a square pattern have been performed. This is an extension of previous simulations; we observed a shrinking intrinsic stacking fault running in an oblique direction through the glide of a Shockley partial dislocation terminating its lower end in fcc (001) stacking [A. Mori, Y. Suzuki, S.i. Yanagiya, T.

Atsushi Mori

2011-01-01

130

Fluid fluid and fluid solid phase separation in nonadditive asymmetric binary hard-sphere mixtures

Very asymmetric mixtures of hard spheres naturally arise in the modellization of colloidal dispersions. Effective potentials have emerged as a powerful tool for describing these systems and have often been employed to extract the phase diagram in both the additive and nonadditive cases. However, most theoretical investigations have been carried out by means of mean-field-like approaches, so their quantitative accuracy

F. Lo Verso; D. Pini; L. Reatto

2005-01-01

131

Signatures of Glass Formation in a Fluidized Bed of Hard Spheres

We demonstrate that a fluidized bed of hard spheres during defluidization displays properties associated with formation of a glass. The final state is rate dependent, and as this state is approached, the bed exhibits heterogeneity with increasing time and length scales. The formation of a glass results in the arrest of macroscopic particle motion and thus the loss of fluidization.

Daniel I. Goldman; Harry L. Swinney

2006-01-01

132

Statistical Thermodynamics of a Dipole Hard Sphere Liquid. Hindered Rotation Model

Approximate analytical expressions are obtained using the hindered molecular rotation model to describe the thermodynamic properties of a model polar liquid of dipolar hard spheres; the results are in good agreement with the available computer simulation data. A polar liquid is represented as a macromolecular knot of particles bonded by dipole forces. The resulting formulas correspond to the first and

G. B. Litinskii

2004-01-01

133

The explicit expression of the fugacity for hard-sphere Bose and Fermi gases

In this paper, we calculate the explicit expression for the fugacity for three-dimensional hard-sphere Bose and Fermi gases from their equations of state in isochoric and isobaric processes, respectively, based on the mathematical result of the boundary problem of an analytic function -- the homogeneous Riemann-Hilbert problem.

Wu-Sheng Dai; Mi Xie

2009-01-01

134

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

135

NASA Astrophysics Data System (ADS)

The development of a new Monte Carlo scheme is provided -- the Reduced Monte Carlo Scheme (RMCS). The term ``reduced'' is used because only a small number of particles (n) is needed in the simulation for accurate calculation of material properties. Ie., n >˜ 10. The fundamental ensemble used as basis for the scheme is the canonical ensemble. The power and efficiency of RMCS is demonstrated by reproducing well known results for the statistical thermodynamic properties of ideal quantum systems (Fermi and Bose cases) and the classical hard sphere system at all densities.

Edgal, Uduzei

2010-03-01

136

Simulating asymmetric colloidal mixture with adhesive hard sphere model

NASA Astrophysics Data System (ADS)

Monte Carlo simulation and Percus-Yevick (PY) theory are used to investigate the structural properties of a two-component system of the Baxter adhesive fluids with the size asymmetry of the particles of both components mimicking an asymmetric binary colloidal mixture. The radial distribution functions for all possible species pairs, g11(r), g22(r), and g12(r), exhibit discontinuities at the interparticle distances corresponding to certain combinations of n and m values (n and m being integers) in the sum n?1+m?2 (?1 and ?2 being the hard-core diameters of individual components) as a consequence of the impulse character of 1-1, 2-2, and 1-2 attractive interactions. In contrast to the PY theory, which predicts the delta function peaks in the shape of gij(r) only at the distances which are the multiple of the molecular sizes corresponding to different linear structures of successively connected particles, the simulation results reveal additional peaks at intermediate distances originating from the formation of rigid clusters of various geometries.

Jamnik, A.

2008-06-01

137

NASA Astrophysics Data System (ADS)

Asymmetric binary mixtures of hard-spheres exhibit several interesting thermodynamic phenomena, such as multiple kinds of glassy states. When the degrees of freedom of the small spheres are integrated out from the description, their effects are incorporated into an effective pair interaction between large spheres known as the depletion potential. The latter has been widely used to study both the phase behavior and dynamic arrest of the big particles. Depletion forces can be accounted for by a contraction of the description in the multicomponent Ornstein-Zernike equation [R. Castan~eda-Priego, A. Rodríguez-López, and J. M. Méndez-Alcaraz, Phys. Rev. E 73, 051404 (2006)]. Within this theoretical scheme, an approximation for the difference between the effective and bare bridge functions is needed. In the limit of infinite dilution, this difference is irrelevant and the typical Asakura-Osawa depletion potential is recovered. At higher particle concentrations, however, this difference becomes important, especially where the shell of first neighbors is formed, and, as shown here, cannot be simply neglected. In this work, we use a variant of the Verlet expression for the bridge functions to highlight their importance in the calculation of the depletion potential at high densities and close to the spinodal decomposition. We demonstrate that the modified Verlet closure predicts demixing in binary mixtures of hard spheres for different size ratios and compare its predictions with both liquid state and density functional theories, computer simulations, and experiments. We also show that it provides accurate correlation functions even near the thermodynamic instability; this is explicitly corroborated with results of molecular dynamics simulations of the whole mixture. Particularly, our findings point toward a possible universal behavior of the depletion potential around the spinodal line.

López-Sánchez, Erik; Estrada-Álvarez, César D.; Pérez-Ángel, Gabriel; Méndez-Alcaraz, José Miguel; González-Mozuelos, Pedro; Castañeda-Priego, Ramón

2013-09-01

138

Dynamic-light-scattering study of glasses of hard colloidal spheres

Dynamic light scattering is applied to the glass phase of nonaqueous suspensions of sterically stabilized colloidal spheres. The short-ranged steric repulsion ensures that the particle interactions are close to hard sphere. This is supported by the observation that the equilibrium phase behavior of these suspensions agrees with that predicted for the hard-sphere atomic system. We verify a model for a nonergodic medium, which assumes that the particles are localized during an experiment and which allows the intermediate scattering function to be calculated from a single measurement of the time-averaged intensity autocorrelation function. Intermediate scattering functions are obtained for several concentrations over a range of wave vectors around the main diffraction peak. The measured nonergodicity parameters are in good agreement with the predictions of mode-coupling theory for the hard-sphere glass. The comparison involves no adjustable parameters. At long times the intermediate scattering functions can be scaled to a single curve for over 2.5 decades in time. This, combined with the results that the nonergodicity parameters and critical amplitudes required for the scaling are in quantitative agreement with mode-coupling theory, provides a convincing verification of the predicted factorization property of the [beta] process in the glass phase.

van Megen, W.; Underwood, S.M. (Department of Applied Physics, Royal Melbourne Institute of Technology, Melbourne, Victoria 3000 (Australia))

1993-01-01

139

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

140

In this study, a new cubic hard sphere equation of state (EOS) was developed from standard classical thermodynamics. The new\\u000a equation is applied to calculate properties of fluids and vapor-liquid phase equilibrium calculations. The derived equation\\u000a is a simplified expression of the hard sphere equation which yields satisfactory agreement with the molecular simulation of\\u000a hard molecule data. The EOS is

S. Hajipour; M. Edalat

2008-01-01

141

The screened Coulomb (Yukawa) charged hard sphere binary fluid

NASA Astrophysics Data System (ADS)

The screened Coulomb (Yukawa) restricted primitive model (Y RPM) of a binary fluid is treated within the one-pole generalized mean-spherical approximation (GMSA). Fluid phase behaviour and structure are compared with the corresponding results for the unscreened Coulombic RPM. Screening increases the critical density and temperature above the values for the RPM and decreases the width of the liquid-gas coexistence curves. The asymptotics of pairwise correlation functions and the genesis of disorder lines in the phase diagram are discussed. These lines are where the ultimate decay of total density or concentration (charge) correlations crosses over from monotonic to oscillatory. The location of the disorder lines is strongly dependent on the range of the Yukawa potentials. We show that very shortrange interionic potentials (Yukawa models) can give rise to correlation functions which are difficult to distinguish (at all interionic separations) from those obtained for the long-range Coulombic case for structurally equivalent thermodynamic states, reinforcing the idea that pronounced charge ordering is not unique to Coulombic interactions but can occur whenever the interaction potential between different species (AB) is strongly attractive and the potentials between identical species (AA and BB) are repulsive. Although the GMSA generally improves upon the MSA, we show that it leads to artificial peaks (not found in simulation) for correlations g(r)between identical ionic species at separations r close to ionic contract when the density is high and the temperature is low. This failing, which occurs for both the RPM and Y RPM, reflects the sensitivity of g(r) near contact to approximations.ii

Leote de Carvalho, R. J. F.; Evans, R.

142

The isotropic-nematic phase transition of tangent hard-sphere chain fluids--pure components.

An extension of Onsager's second virial theory is developed to describe the isotropic-nematic phase transition of tangent hard-sphere chain fluids. Flexibility is introduced by the rod-coil model. The effect of chain-flexibility on the second virial coefficient is described using an accurate, analytical approximation for the orientation-dependent pair-excluded volume. The use of this approximation allows for an analytical treatment of intramolecular flexibility by using a single pure-component parameter. Two approaches to approximate the effect of the higher virial coefficients are considered, i.e., the Vega-Lago rescaling and Scaled Particle Theory (SPT). The Onsager trial function is employed to describe the orientational distribution function. Theoretical predictions for the equation of state and orientational order parameter are tested against the results from Monte Carlo (MC) simulations. For linear chains of length 9 and longer, theoretical results are in excellent agreement with MC data. For smaller chain lengths, small errors introduced by the approximation of the higher virial coefficients become apparent, leading to a small under- and overestimation of the pressure and density difference at the phase transition, respectively. For rod-coil fluids of reasonable rigidity, a quantitative comparison between theory and MC simulations is obtained. For more flexible chains, however, both the Vega-Lago rescaling and SPT lead to a small underestimation of the location of the phase transition. PMID:23883045

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

2013-07-21

143

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

144

Layering, freezing, and re-entrant melting of hard spheres in soft confinement

NASA Astrophysics Data System (ADS)

Confinement can have a dramatic effect on the behavior of all sorts of particulate systems, and it therefore is an important phenomenon in many different areas of physics and technology. Here, we investigate the role played by the softness of the confining potential. Using grand canonical Monte Carlo simulations, we determine the phase diagram of three-dimensional hard spheres that in one dimension are constrained to a plane by a harmonic potential. The phase behavior depends strongly on the density and on the stiffness of the harmonic confinement. While we find the familiar sequence of confined hexagonal and square-symmetric packings, we do not observe any of the usual intervening ordered phases. Instead, the system phase separates under strong confinement, or forms a layered re-entrant liquid phase under weaker confinement. It is plausible that this behavior is due to the larger positional freedom in a soft confining potential and to the contribution that the confinement energy makes to the total free energy. The fact that specific structures can be induced or suppressed by simply changing the confinement conditions (e.g., in a dielectrophoretic trap) is important for applications that involve self-assembled structures of colloidal particles.

Curk, Tine; de Hoogh, Anouk; Martinez-Veracoechea, Francisco J.; Eiser, Erika; Frenkel, Daan; Dobnikar, Jure; Leunissen, Mirjam E.

2012-02-01

145

Layering, freezing, and re-entrant melting of hard spheres in soft confinement.

Confinement can have a dramatic effect on the behavior of all sorts of particulate systems, and it therefore is an important phenomenon in many different areas of physics and technology. Here, we investigate the role played by the softness of the confining potential. Using grand canonical Monte Carlo simulations, we determine the phase diagram of three-dimensional hard spheres that in one dimension are constrained to a plane by a harmonic potential. The phase behavior depends strongly on the density and on the stiffness of the harmonic confinement. While we find the familiar sequence of confined hexagonal and square-symmetric packings, we do not observe any of the usual intervening ordered phases. Instead, the system phase separates under strong confinement, or forms a layered re-entrant liquid phase under weaker confinement. It is plausible that this behavior is due to the larger positional freedom in a soft confining potential and to the contribution that the confinement energy makes to the total free energy. The fact that specific structures can be induced or suppressed by simply changing the confinement conditions (e.g., in a dielectrophoretic trap) is important for applications that involve self-assembled structures of colloidal particles. PMID:22463214

Curk, Tine; de Hoogh, Anouk; Martinez-Veracoechea, Francisco J; Eiser, Erika; Frenkel, Daan; Dobnikar, Jure; Leunissen, Mirjam E

2012-02-21

146

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

NASA Astrophysics Data System (ADS)

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.

Leocmach, Mathieu; Russo, John; Tanaka, Hajime

2013-03-01

147

Regularized 13 moment equations for hard sphere molecules: Linear bulk equations

NASA Astrophysics Data System (ADS)

The regularized 13 moment equations of rarefied gas dynamics are derived for a monatomic hard sphere gas in the linear regime. The equations are based on an extended Grad-type moment system, which is systematically reduced by means of the Order of Magnitude Method [H. Struchtrup, ``Stable transport equations for rarefied gases at high orders in the Knudsen number,'' Phys. Fluids 16(11), 3921-3934 (2004)]. Chapman-Enskog expansion of the final equations yields the linear Burnett and super-Burnett equations. While the Burnett coefficients agree with literature values, this seems to be the first time that super-Burnett coefficients are computed for a hard sphere gas. As a first test of the equations the dispersion and damping of sound waves is considered.

Struchtrup, Henning; Torrilhon, Manuel

2013-05-01

148

Chemical-potential route: a hidden Percus-Yevick equation of state for hard spheres.

The chemical potential of a hard-sphere fluid can be expressed in terms of the contact value of the radial distribution function of a solute particle with a diameter varying from zero to that of the solvent particles. Exploiting the explicit knowledge of such a contact value within the Percus-Yevick theory, and using standard thermodynamic relations, a hitherto unknown Percus-Yevick equation of state, p/?k(B)T = -(9/?) ln(1-?)-(16-31?)/2(1-?)(2), is unveiled. This equation of state turns out to be better than the one obtained from the conventional virial route. Interpolations between the chemical-potential and compressibility routes are shown to be more accurate than the widely used Carnahan-Starling equation of state. The extension to polydisperse hard-sphere systems is also presented. PMID:23005929

Santos, Andrés

2012-09-17

149

Chemical-Potential Route: A Hidden Percus-Yevick Equation of State for Hard Spheres

NASA Astrophysics Data System (ADS)

The chemical potential of a hard-sphere fluid can be expressed in terms of the contact value of the radial distribution function of a solute particle with a diameter varying from zero to that of the solvent particles. Exploiting the explicit knowledge of such a contact value within the Percus-Yevick theory, and using standard thermodynamic relations, a hitherto unknown Percus-Yevick equation of state, p/?kBT=-(9/?)ln?(1-?)-(16-31?)/2(1-?)2, is unveiled. This equation of state turns out to be better than the one obtained from the conventional virial route. Interpolations between the chemical-potential and compressibility routes are shown to be more accurate than the widely used Carnahan-Starling equation of state. The extension to polydisperse hard-sphere systems is also presented.

Santos, Andrés

2012-09-01

150

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 on 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 expresses 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 reversible work, the pressure on the wall, the pressure in the homogeneous region, the wall-fluid surface tension, the line tension, and other similar properties. PMID:20849174

Urrutia, Ignacio

2010-09-14

151

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

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

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

2009-08-14

152

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

153

NASA Astrophysics Data System (ADS)

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

van Megen, W.

2006-01-01

154

Motions in binary mixtures of hard colloidal spheres: Melting of the glass

Dynamic light-scattering experiments are performed on binary mixtures of hard-sphere-like colloidal suspensions with a size ratio of 0.6. The optical properties of the particles are such that the relative contrast of the two species is very sensitive to temperature, a feature that is exploited to obtain the three partial coherent intermediate scattering functions. The glass transition is identified by the

S. R. Williams; W. van Megen

2001-01-01

155

Connecting structural relaxation with the low frequency modes in a hard-sphere colloidal glass.

Structural relaxation in hard-sphere colloidal glasses has been studied using confocal microscopy. The motion of individual particles is followed over long time scales to detect the rearranging regions in the system. We have used normal mode analysis to understand the origin of the rearranging regions. The low-frequency modes, obtained over short time scales, show strong spatial correlation with the rearrangements that happen on long time scales. PMID:22107681

Ghosh, Antina; Chikkadi, Vijayakumar; Schall, Peter; Bonn, Daniel

2011-10-27

156

Monte Carlo simulation of growth of hard-sphere crystals on a square pattern

Monte Carlo simulations of the colloidal epitaxy of hard spheres (HSs) on a\\u000asquare pattern have been performed. This is an extension of previous\\u000asimulations; we observed a shrinking intrinsic stacking fault running in an\\u000aoblique direction through the glide of a Shockley partial dislocation\\u000aterminating its lower end in fcc (001) stacking [Mori et al., Molec. Phys. 105\\u000a(2007)

Atsushi Mori

2010-01-01

157

Jastrow wave function for condensed phases of Bose particles: Hard-sphere system

By a Monte Carlo variational calculation, it is shown that the description of the ground-state properties of a hard-sphere Bose system is improved if the Jastrow wave function contains a correlation structure at distances intermediate between the first and the second shell of neighbors. We relate these correlations to the zero-point motion of rotons. We predict that the oscillations of

C. de Michelis; G. Masserini; L. Reatto

1978-01-01

158

On fluid-solid direct coexistence simulations: The pseudo-hard sphere model

NASA Astrophysics Data System (ADS)

We investigate methodological issues concerning the direct coexistence method, an increasingly popular approach to evaluate the solid-fluid coexistence by means of computer simulations. The first issue is the impact of the simulation ensemble on the results. We compare the NpT ensemble (easy to use but approximate) with the NpzT ensemble (rigorous but more difficult to handle). Our work shows that both ensembles yield similar results for large systems (>5000 particles). Another issue, which is usually disregarded, is the stochastic character of a direct coexistence simulation. Here, we assess the impact of stochasticity in the determination of the coexistence point. We demonstrate that the error generated by stochasticity is much larger than that caused by the use of the NpT ensemble, and can be minimized by simply increasing the system size. To perform this study we use the pseudo hard-sphere model recently proposed by Jover et al. [J. Chem. Phys. 137, 144505 (2012)], and obtain a coexistence pressure of p* = 11.65(1), quite similar to that of hard spheres (only about 0.6% higher). Therefore, we conclude that this model can be reliably used to investigate the physics of hard spheres in phenomena like crystal nucleation.

Espinosa, Jorge R.; Sanz, Eduardo; Valeriani, Chantal; Vega, Carlos

2013-10-01

159

On fluid-solid direct coexistence simulations: The pseudo-hard sphere model.

We investigate methodological issues concerning the direct coexistence method, an increasingly popular approach to evaluate the solid-fluid coexistence by means of computer simulations. The first issue is the impact of the simulation ensemble on the results. We compare the NpT ensemble (easy to use but approximate) with the NpzT ensemble (rigorous but more difficult to handle). Our work shows that both ensembles yield similar results for large systems (>5000 particles). Another issue, which is usually disregarded, is the stochastic character of a direct coexistence simulation. Here, we assess the impact of stochasticity in the determination of the coexistence point. We demonstrate that the error generated by stochasticity is much larger than that caused by the use of the NpT ensemble, and can be minimized by simply increasing the system size. To perform this study we use the pseudo hard-sphere model recently proposed by Jover et al. [J. Chem. Phys. 137, 144505 (2012)], and obtain a coexistence pressure of p? = 11.65(1), quite similar to that of hard spheres (only about 0.6% higher). Therefore, we conclude that this model can be reliably used to investigate the physics of hard spheres in phenomena like crystal nucleation. PMID:24116630

Espinosa, Jorge R; Sanz, Eduardo; Valeriani, Chantal; Vega, Carlos

2013-10-14

160

Kitset hollow spheres: The combination of twin polymerization with hard templates makes hollow carbon spheres (HCSs) with tailored properties easily accessible. The thickness and pore texture of the HCS shells and also the diameter of the spherical cavity can be varied. The application potential of synthesized HCS is substantiated by an excellent cycling stability of lithium-sulfur batteries. PMID:23620268

Böttger-Hiller, Falko; Kempe, Patrick; Cox, Gerhard; Panchenko, Alexander; Janssen, Nicole; Petzold, Albrecht; Thurn-Albrecht, Thomas; Borchardt, Lars; Rose, Marcus; Kaskel, Stefan; Georgi, Colin; Lang, Heinrich; Spange, Stefan

2013-04-25

161

Phase diagrams of mixtures of colloidal hard spheres with hard discs are calculated by means of the free-volume theory. The free-volume fraction available to the discs is determined from scaled-particle theory. The calculations show that depletion induced phase separation should occur at low disc concentrations in systems now experimentally available. The gas–liquid equilibrium of the spheres becomes stable at comparable

S. M. Oversteegen; H. N. W. Lekkerkerker

2004-01-01

162

Phase diagrams of mixtures of colloidal hard spheres with hard discs are calculated by means of the free-volume theory. The free-volume fraction available to the discs is determined from scaled-particle theory. The calculations show that depletion induced phase separation should occur at low disc concentrations in systems now experimentally available. The gas-liquid equilibrium of the spheres becomes stable at comparable

S. M. Oversteegen; H. N. W. Lekkerkerker

2004-01-01

163

Phase diagrams of mixtures of colloidal hard spheres with hard discs are calculated by means of the free-volume theory. The free-volume fraction available to the discs is determined from scaled-particle theory. The calculations show that depletion induced phase separation should occur at low disc concentrations in systems now experimentally available. The gas-liquid equilibrium of the spheres becomes stable at comparable

S. M. Oversteegen; H. N. W. Lekkerkerker

164

NASA Astrophysics Data System (ADS)

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

Wu, Guang-Wen; Sadus, Richard J.

2004-12-01

165

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

M. Iwamatsu

1989-01-01

166

A first-order phase transition at the random close packing of hard spheres

Randomly packing spheres of equal size into a container consistently results in a static configuration with a density of ˜64%. The ubiquity of random close packing (RCP) rather than the optimal crystalline array at 74% begs the question of the physical law behind this empirically deduced state. Indeed, there is no signature of any macroscopic quantity with a discontinuity associated

Hernan Makse; Yuliang Jin

2010-01-01

167

A first-order phase transition defines the random close packing of hard spheres

Randomly packing spheres of equal size into a container consistently results in a static configuration with a density of ?64%. The ubiquity of random close packing (RCP) rather than the optimal crystalline array at 74% begs the question of the physical law behind this empirically deduced state. Indeed, there is no signature of any macroscopic quantity with a discontinuity associated

Yuliang Jin; Hernán A. Makse

2010-01-01

168

NASA Astrophysics Data System (ADS)

Although in the case of polymer solutions the existence of hydrodynamic screening was theoretically established some time ago, use of the same methods for suspensions of hard spheres thus far have failed to produce similar results. In this work we reconsider this problem. Using superposition of topological and London-style qualitative arguments we prove the existence of screening in hard sphere suspensions. Even though some of these arguments were employed initially for treatments of superconductivity and superfluidity, we find analogs of these phenomena in non-traditional settings such as in colloidal suspensions, turbulence, magnetohydrodynamics, etc. In particular, in suspensions, we demonstrate that the hydrodynamic screening is an exact analog of Meissner effect in superconductors. The extent of screening depends on the volume fraction of hard spheres. The zero volume fraction limit corresponds to the normal state. The case of finite volume fractions-to the mixed state typical for superconductors of the second kind with such a state becoming fully “superconducting” at the critical volume fraction ? for which the (zero frequency) relative viscosity ?(relative) diverges. Brady and, independently, Bicerano et al using scaling-type arguments predicted that for ? close to ? the viscosity ?(relative) behaves as C()-2 with C being some constant. Their prediction is well supported by experimental data. In this work we explain such a behavior of viscosity in terms of a topological-type transition which, mathematically can be made isomorphic to the more familiar Bose-Einstein condensation transition. Because of this, the results and methods of this work are not limited to suspensions. In the concluding section we describe other applications ranging from turbulence and magnetohydrodynamics to high temperature superconductors and QCD, etc.

Ballard, Ethan E.; Kholodenko, Arkady L.

2009-08-01

169

On the influence of a patterned substrate on crystallization in suspensions of hard spheres

NASA Astrophysics Data System (ADS)

We present a computer simulation study on crystal nucleation and growth in supersaturated suspensions of mono-disperse hard spheres induced by a triangular lattice substrate. The main result is that compressed substrates are wet by the crystalline phase (the crystalline phase directly appears without any induction time), while for stretched substrates we observe heterogeneous nucleation. The shapes of the nucleated crystallites fluctuate strongly. In the case of homogeneous nucleation amorphous precursors have been observed [T. Schilling et al., Phys. Rev. Lett. 105(2), 025701 (2010)]. For heterogeneous nucleation we do not find such precursors. The fluid is directly transformed into highly ordered crystallites.

Dorosz, Sven; Schilling, Tanja

2012-01-01

170

Phase separation of binary nonadditive hard sphere fluid mixture confined in random porous media

NASA Astrophysics Data System (ADS)

I analyze the fluid-fluid phase separation of nonadditive hard sphere fluid mixture absorbed in random porous media. An equation of state is derived by using the perturbation theory to this complex system with quenched disorders. The results of this theory are in good agreement with those obtained from semi-grand canonical ensemble Monte Carlo simulations. The contact value of the fluid-fluid radial distribution functions of the reference which is the key point of the perturbation process is derived as well, the comparison against Monte Carlo simulations shows that it has an excellent accuracy.

Chen, W.

2013-10-01

171

Signatures of glass formation in a fluidized bed of hard spheres.

We demonstrate that a fluidized bed of hard spheres during defluidization displays properties associated with formation of a glass. The final state is rate dependent, and as this state is approached, the bed exhibits heterogeneity with increasing time and length scales. The formation of a glass results in the arrest of macroscopic particle motion and thus the loss of fluidization. Microscopic motion persists in this state, but the bed can be jammed by application of a small increase in flow rate. Thus a fluidized bed can serve as a test system for studies of glass formation and jamming. PMID:16712096

Goldman, Daniel I; Swinney, Harry L

2006-04-14

172

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

NASA Astrophysics Data System (ADS)

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

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

2010-07-01

173

NASA Astrophysics Data System (ADS)

The short-range structure of supercritical methanol (CH3OH) is investigated by measuring the spontaneous Raman spectra of the C-O stretching mode. The spectra are obtained at a reduced temperature, Tr=T/Tc=1.02 (522.9 K), which permits the neat fluid to be studied isothermally as a function of density. As the density increases, the spectral peaks shift toward the lower energy side and the spectra broaden. In the supercritical region, the amount of shifting shows nonlinear density dependence and the width becomes anomalously large. We use the perturbed hard-sphere model to analyze these density dependencies along the vibrational coordinate. The amount of shifting is decomposed into attractive and repulsive components, and the changes in attractive and repulsive energies are evaluated as functions of density and packing fraction, both of which are continuously varied by a factor of 120. Here we show that the shift amount consists principally of the attractive component at all densities, since the attractive energy is about eight times the repulsive energy. The density dependence of the widths is analyzed by calculating homogeneous and inhomogeneous widths as a function of density. The results show that, although vibrational dephasing and density inhomogeneity contribute similarly to the width at low and middle densities, at high density the main contributor turns out to be the vibrational dephasing. We estimate the local density enhancements of supercritical CH3OH as function of bulk density by two methods. The results of these analyses show common features, and both the estimated local density enhancements of CH3OH are considerably larger than the local density enhancements of simple fluids, i.e., those having nonhydrogen bonding. It is revealed that the local density of supercritical CH3OH is 40%-60% greater than the local densities of the simple fluids. We also estimate the local density fluctuation using the obtained values of attractive shift, inhomogeneous width, and local density. The density fluctuation in the vicinity of a vibrating molecule is compared to the fluctuation of bulk density, which is obtained from the thermodynamic calculation.

Saitow, Ken-Ichi; Sasaki, Jungo

2005-03-01

174

Minimal energy packings and collapse of sticky tangent hard-sphere polymers.

We enumerate all minimal energy packings (MEPs) for small single linear and ring polymers composed of spherical monomers with contact attractions and hard-core repulsions and compare them to corresponding results for monomer packings. We define and identify "dividing surfaces" in polymer packings, which reduce the number of arrangements that satisfy hard-sphere and covalent-bond constraints. Compared to monomer MEPs, polymer MEPs favor intermediate structural symmetry. We also examine the packing-preparation dependence for longer single chains using molecular dynamics simulations. For slow temperature quenches, chains form crystallites with close-packed cores. As the quench rate increases, the core size decreases and the exterior becomes more disordered. By examining the contact number, we connect the suppression of crystallization to the onset of isostaticity in disordered packings. PMID:20868016

Hoy, Robert S; O'Hern, Corey S

2010-08-05

175

NASA Astrophysics Data System (ADS)

We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the ``self '' component having only one particle, the ``distinct'' component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components. We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy, and arrested dynamics at high densities.

Hopkins, Paul; Fortini, Andrea; Archer, Andrew J.; Schmidt, Matthias

2010-12-01

176

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

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

Punnathanam, S; Monson, P A

2006-07-14

177

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

NASA Astrophysics Data System (ADS)

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

Punnathanam, S.; Monson, P. A.

2006-07-01

178

The Percus-Yevick approximation for repulsive hard spheres with surface adhesion

NASA Astrophysics Data System (ADS)

We have adapted Baxter's sticky hard sphere (SHS) model so that it more adequately describes systems where the interparticle potential well is preceded by an energy barrier. In the original model the particles interact via a pair potential with a narrow attractive region next to a repulsive core. Colloidal particles, however, often exhibit long range repulsion whereas they do attract each other at shorter ranges. This motivated our effort to extend the model. It is shown that the Percus-Yevick equation can also be solved analytically for this particular potential, provided that the regions of attraction and repulsion are sufficiently small. It is found that the structure functions of both models are identical. The new feature of the repulsive sticky hard sphere (RSHS) model is that the fraction of aggregated particles may increase with temperature, a phenomenon which is experimentally observed in such systems. Structure functions from small angle X-ray studies on water/AOT/iso-octane microemulsions can be fit to those predicted by the RSHS model. The thus obtained binding enthalpy is comparable with earlier determinations from dielectric studies.

Koper, G. J. M.; Bedeaux, D.

1992-09-01

179

Free energy barriers for homogeneous crystal nucleation in a eutectic system of binary hard spheres.

In this study, the free energy barriers for homogeneous crystal nucleation in a system that exhibits a eutectic point are computed using Monte Carlo simulations. The system studied is a binary hard sphere mixture with a diameter ratio of 0.85 between the smaller and larger hard spheres. The simulations of crystal nucleation are performed for the entire range of fluid compositions. The free energy barrier is found to be the highest near the eutectic point and is nearly five times that for the pure fluid, which slows down the nucleation rate by a factor of 10(-31). These free energy barriers are some of highest ever computed using simulations. For most of the conditions studied, the composition of the critical nucleus corresponds to either one of the two thermodynamically stable solid phases. However, near the eutectic point, the nucleation barrier is lowest for the formation of the metastable random hexagonal closed packed (rhcp) solid phase with composition lying in the two-phase region of the phase diagram. The fluid to solid phase transition is hypothesized to proceed via formation of a metastable rhcp phase followed by a phase separation into respective stable fcc solid phases. PMID:23656140

Ganagalla, Srinivasa Rao; Punnathanam, Sudeep N

2013-05-01

180

Glass Transition and Re-entrant Melting in a Polydisperse Hard-Sphere Fluid

NASA Astrophysics Data System (ADS)

Extensive molecular dynamics simulations are performed for a hard-sphere fluid at 6% polydispersity. The simulation results are then analyzed based on the mean-field theory proposed recently by Tokuyama (Physica A 364, 23-62 (2006)). The phase diagram and the dynamic behavior are investigated fully in each phase. It is then found that as the volume fraction ? is increased, a supercooled liquid phase appears at the supercooled point ?? (~= 0.5524) and a transition from supercooled liquid to crystal then occurs at the melting volume fraction ?m(1) (~= 0.5625). As ? is further increased, a transition from crystal to supercooled liquid (re-entrant melting) is also observed at the second melting volume fraction ?m(2) (~= 0.5770) within a waiting time tw = 7 × 104t0, where t0 is a time for a particle to move over a distance of a particle radius with an average velocity. The glass transition is thus predicted to occur at the glass transition volume fraction ?g (~= 0.6005). The various aspects obtained in our study is quite similar to those in the experiment for the suspension of hard spheres, including the logarithmic growth of the mean-square displacement in fast-? stage, the non-singular behavior of the long-time self-diffusion coefficient, and the non divergence of any characteristic times, such as the ?- and ?-relaxation times.

Tokuyama, Michio; Terada, Yayoi

2006-05-01

181

In this paper we examine the phase behavior of the Weeks-Chandler-Andersen (WCA) potential with ?? = 40. Crystal nucleation in this model system was recently studied by Kawasaki and Tanaka [Proc. Natl. Acad. Sci. U.S.A. 107, 14036 (2010)], who argued that the computed nucleation rates agree well with experiment, a finding that contradicted earlier simulation results. Here we report an extensive numerical study of crystallization in the WCA model, using three totally different techniques (Brownian dynamics, umbrella sampling, and forward flux sampling). We find that all simulations yield essentially the same nucleation rates. However, these rates differ significantly from the values reported by Kawasaki and Tanaka and hence we argue that the huge discrepancy in nucleation rates between simulation and experiment persists. When we map the WCA model onto a hard-sphere system, we find good agreement between the present simulation results and those that had been obtained for hard spheres [L. Filion, M. Hermes, R. Ni, and M. Dijkstra, J. Chem. Phys. 133, 244115 (2010); S. Auer and D. Frenkel, Nature 409, 1020 (2001)]. PMID:21476768

Filion, L; Ni, R; Frenkel, D; Dijkstra, M

2011-04-01

182

NASA Astrophysics Data System (ADS)

We present a continuous pseudo-hard-sphere potential based on a cut-and-shifted Mie (generalized Lennard-Jones) potential with exponents (50, 49). Using this potential one can mimic the volumetric, structural, and dynamic properties of the discontinuous hard-sphere potential over the whole fluid range. The continuous pseudo potential has the advantage that it may be incorporated directly into off-the-shelf molecular-dynamics code, allowing the user to capitalise on existing hardware and software advances. Simulation results for the compressibility factor of the fluid and solid phases of our pseudo hard spheres are presented and compared both to the Carnahan-Starling equation of state of the fluid and published data, the differences being indistinguishable within simulation uncertainty. The specific form of the potential is employed to simulate flexible chains formed from these pseudo hard spheres at contact (pearl-necklace model) for mc = 4, 5, 7, 8, 16, 20, 100, 201, and 500 monomer segments. The compressibility factor of the chains per unit of monomer, mc, approaches a limiting value at reasonably small values, mc < 50, as predicted by Wertheim's first order thermodynamic perturbation theory. Simulation results are also presented for highly asymmetric mixtures of pseudo hard spheres, with diameter ratios of 3:1, 5:1, 20:1 over the whole composition range.

Jover, J.; Haslam, A. J.; Galindo, A.; Jackson, G.; Müller, E. A.

2012-10-01

183

Density functional theory for molecular orientation of hard rod fluids in hard slits

A density functional theory (DFT) is used to investigate molecular orientation of hard rod fluids in a hard slit. The DFT approach combines a modified fundamental measure theory (MFMT) for excluded-volume effect with the first order thermodynamics perturbation theory for chain connectivity. In the DFT approach, the intra-molecular bonding orientation function is introduced. We consider the effects of molecular length

Da-Peng Cao; Li-Sheng Cheng; Wen-Chuan Wang

2007-01-01

184

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

2013-06-20

185

Roles of icosahedral and crystal-like order in the hard spheres glass transition

NASA Astrophysics Data System (ADS)

A link between structural ordering and slow dynamics has recently attracted much attention from the context of the origin of glassy slow dynamics. Candidates for such structural order are icosahedral, exotic amorphous and crystal-like. Each type of order is linked to a different scenario of glass transition. Here we experimentally access local structural order in polydisperse hard spheres by particle-level confocal microscopy. We identify the key structures as icosahedral and FCC-like order, both statistically associated with slow particles. However, when approaching the glass transition, the icosahedral order does not grow in size, whereas crystal-like order grows. It is the latter that governs the dynamics and is linked to dynamic heterogeneity. This questions the direct role of the local icosahedral ordering in glassy slow dynamics and suggests that the growing length scale of structural order is essential for the slowing down of dynamics and the non-local cooperativity in particle motion.

Leocmach, Mathieu; Tanaka, Hajime

2012-07-01

186

Particle characterization using multiple scattering decorrelation methods: Hard-sphere model system

NASA Astrophysics Data System (ADS)

Applying static light scattering experiments, we characterize colloidal particles that are used as model hard-sphere systems in experiments investigating their crystallization kinetics. The particles comprise of a compact core of poly(methyl methacrylate) and short polymer hairs grafted onto the surface. We use a contrast variation procedure to determine the refractive index variation within the particles and observe that one component of the binary mixture used as a solvent penetrates the particles and masks completely the small polymer hairs. Making use of the determined refractive index variation, we obtain the average particle radius and its polydispersity from measurements of the particle form factor close to its minimae. The scattered intensity has been corrected carefully for multiple scattering contributions applying dynamic light scattering measurements with multiple scattering decorrelation. We obtain a mean particle radius of R¯=435+/-4 nm and a polydispersity of ?=2.5%, a resolution that has not been achieved with light scattering experiments before.

Heymann, Andreas; Sinn, Christian; Palberg, Thomas

2000-07-01

187

Transport properties of dense dissipative hard-sphere fluids for arbitrary energy loss models.

The revised Enskog approximation for a fluid of hard spheres which lose energy upon collision is discussed for the case that the energy is lost from the normal component of the velocity at collision but is otherwise arbitrary. Granular fluids with a velocity-dependent coefficient of restitution are an important special case covered by this model. A normal solution to the Enskog equation is developed using the Chapman-Enskog expansion. The lowest order solution describes the general homogeneous cooling state and a generating function formalism is introduced for the determination of the distribution function. The first order solution, evaluated in the lowest Sonine approximation, provides estimates for the transport coefficients for the Navier-Stokes hydrodynamic description. All calculations are performed in an arbitrary number of dimensions. PMID:16196555

Lutsko, James F

2005-08-26

188

The Fokker-Planck equation governing the evolution of the distribution function of a massive Brownian hard sphere suspended in a fluid of much lighter spheres is derived from the exact hierarchy of kinetic equations for the total system via a multiple-time-scale analysis akin to a uniform expansion in powers of the square root of the mass ratio. The derivation leads to an exact expression for the friction coefficient which naturally splits into an Enskog contribution and a dynamical correction. The latter, which accounts for correlated collisions events, reduces to the integral of a time-displaced correlation function of dynamical variables linked to the collisional transfer of momentum between the infinitively heavy (i.e., immobile) Brownian sphere and the fluid particles.

Bocquet, L.; Piasecki, J.; Hansen, J.P. [Ecole Normale Superieure de Lyon (France)

1994-07-01

189

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

NASA Astrophysics Data System (ADS)

We find in complementary experiments and event-driven simulations of sheared inelastic hard spheres that the velocity autocorrelation function ?(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 ?(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.

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

2008-12-01

190

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

2012-01-08

191

Dipolar sticky hard spheres within the Percus-Yevick approximation plus orientational linearization.

We consider a strongly idealized model for polar fluids, which consists of spherical particles, having, in addition to a hard-core repulsion, a "surface dipolar" interaction, acting only when particles are exactly at contact. A fully analytic solution of the molecular Orstein-Zernike equation is found for this potential, within the Percus-Yevick approximation complemented by a linearization of the angular dependence on molecular orientations (Percus-Yevick closure with orientational linearization). Numerical results are also presented in a detailed analysis about the local orientational structure. From the pair correlation function g(1,2), we first derive the best orientations of a test particle which explores the space around an arbitrary reference molecule. Then some local and global order parameters, related to the polarization induced by the reference particle, are also calculated. The local structure of this model with only short-ranged anisotropic interactions turns out to be, at least within the chosen approximation, qualitatively different from that of hard spheres with fully long-ranged dipolar potentials. PMID:20649341

Gazzillo, Domenico

2010-07-21

192

Dipolar sticky hard spheres within the Percus-Yevick approximation plus orientational linearization

NASA Astrophysics Data System (ADS)

We consider a strongly idealized model for polar fluids, which consists of spherical particles, having, in addition to a hard-core repulsion, a ``surface dipolar'' interaction, acting only when particles are exactly at contact. A fully analytic solution of the molecular Orstein-Zernike equation is found for this potential, within the Percus-Yevick approximation complemented by a linearization of the angular dependence on molecular orientations (Percus-Yevick closure with orientational linearization). Numerical results are also presented in a detailed analysis about the local orientational structure. From the pair correlation function g(1,2), we first derive the best orientations of a test particle which explores the space around an arbitrary reference molecule. Then some local and global order parameters, related to the polarization induced by the reference particle, are also calculated. The local structure of this model with only short-ranged anisotropic interactions turns out to be, at least within the chosen approximation, qualitatively different from that of hard spheres with fully long-ranged dipolar potentials.

Gazzillo, Domenico

2010-07-01

193

We present a confocal microscopy study of 1.55mum monodisperse silica hard spheres as they sediment and crystallize at the bottom wall of a container. If the particles sediment onto a feature less flat wall, the two bottom layers crystallize simultaneously and layerwise growth follows. If the wall is replaced by a hexagonal template, only layerwise growth occurs. Our results complement

I. B. Ramsteiner; K. E. Jensen; D. A. Weitz; F. Spaepen

2009-01-01

194

The volume and surface area of a fused hard-sphere molecule can be calculated by the usual formula relating the union of a number of sets to their intersections. In principle, this formula includes intersections of all orders; however, we show that, by making use of the properties of certain types of double, triple, quadruple and quintuple intersection, all terms of

K. D. Gibson; H. A. Scheraga

1987-01-01

195

Suppression of the local density of states in a medium made of randomly arranged dielectric spheres

NASA Astrophysics Data System (ADS)

Light propagation in a medium made of densely packed dielectric spheres is investigated by using a rigorous diffraction theory. It is shown that a substantial suppression of the local density of states occurs in spectral domains where the single constituents exhibit Mie resonances. The local density of states decreases exponentially at the pertinent frequencies with a linearly increasing spatial extension of the aggregated spheres. It is shown that a self-sustaining random arrangement of core-shell spheres shows the same fundamental characteristics. Such approach offers a path toward easy to fabricate photonic materials with omnidirectional gaps that may find use in various applications.

Rockstuhl, Carsten; Lederer, Falk

2009-04-01

196

The friction coefficient {gamma} exerted by a hard-sphere fluid on an infinitely massive Brownian sphere is calculated for several size ratios {Sigma}/{sigma} where {Sigma} and {sigma} are the diameters of the Brownian and fluid spheres, respectively. The exact microscopic expression derived in part I of this work from kinetic theory is transformed and shown to be proportional to the time integral of the autocorrelation function of the momentum transferred from the fluid to the Brownian sphere during instantaneous collisions. Three different methods are described to extract the friction coefficient from molecular dynamics simulations carried out on finite systems. The three independent methods lead to estimates of {gamma} which agree within statistical errors (typically 5%). The results are compared to the predictions of Enskog theory and of the hydrodynamic Stokes law. The former breaks down as the size ratio and/or the packing fraction of the fluid increase. Somewhat surprisingly, Stokes` law is found to hold with stick boundary conditions, in the range 1 {le} {Sigma}/{sigma} {le} 4.5 explored in the present simulations, with a hydrodynamic diameter d={Sigma}. The analysis of the molecular dynamics data on the basis of Stokes` law with slip boundary conditions is less conclusive, although the right trend is found as {Sigma}/{sigma} increases.

Bocquet, L.; Hansen, J.P.; Piasecki, J. [Ecole Normale Superieure de Lyon (France)

1994-07-01

197

NASA Astrophysics Data System (ADS)

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

Sesé, Luis M.

2012-06-01

198

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

NASA Astrophysics Data System (ADS)

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

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

2010-06-01

199

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

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

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

2010-06-16

200

Thermodynamic and structural properties of the path-integral quantum hard-sphere fluid

NASA Astrophysics Data System (ADS)

An extensive study of the path-integral quantum hard-sphere fluid far from exchange is presented. The results cover the calculation of mechanical, thermal, r-space and k-space pair properties. Path-integral Monte Carlo simulations involving the Cao-Berne's propagator provide the internal energies and pair radial distribution functions (instantaneous, linear response, and necklace center of mass). For the sake of comparison, Barker's and Jaccuci-Omerti's image propagators are also applied at several state points. To obtain k-space properties use of the Gaussian Feynman-Hibbs picture for representing quantum systems is made. This picture is known to yield two Ornstein-Zernike equations; one for true quantum particles (linear response) and the other for the centers of mass of quantum particles. Direct correlation functions and static structure factors are obtained via Baxter's partition complemented with Dixon-Hutchinson's variational procedure. Wherever possible, the present results are compared with semiclassical (Yoon-Scheraga's) and path-integral (Runge-Chester's) data available in the literature. The limits of validity of the Gaussian Feynman-Hibbs picture in this context are also established.

Sesé, Luis M.

1998-06-01

201

Structure of hard-sphere fluid and precursor structures to crystallization

NASA Astrophysics Data System (ADS)

The structural origin of the commonly observed split second peak of the radial distribution function of a supercooled or glassy liquid is examined in this work using the hard-sphere fluid as an example. A novel approach to the analysis of the microscopic structure of a fluid is described, which permits the decomposition of both the radial distribution function and bond-angle distribution function of a system of particles into contributions from a small number of ring structures. The method uses a modified shortest-path definition of rings appropriate to the analysis of the medium-range structure of dense systems. It is shown that the split peak is an indicator of the emergence of precursor structures to crystal formation. The origin of the split peak provides a structural link between fluid and crystalline phases and our results suggest that it is neither a structural feature peculiar to glassy phases nor a smooth structural continuation of the stable-fluid phase. This structural feature of simple glassy systems is more appropriately described as a signifier of the frustration of emerging crystalline order in a fluid.

O'Malley, Brendan; Snook, Ian

2005-08-01

202

Single file and normal dual mode diffusion in highly confined hard sphere mixtures under flow.

We use Monte Carlo simulations to study the dual-mode diffusion regime of binary and tertiary mixtures of hard spheres confined in narrow cylindrical pores under the influence of an imposed flow. The flow is introduced to the dynamics by adding a small bias directed along the long axis of the pore to the random displacement of each Monte Carlo move. As a result, the motion of the particles in all the components is dominated by a drift velocity that causes the mean squared displacements to increase quadratically in the long time limit. However, an analysis of the mean squared displacements at intermediate time scales shows that components of the mixture above and below their passing thresholds still exhibit behaviors consistent with normal and single-file diffusion, respectively. The difference between the mean squared displacements of the various components is shown to go though a maximum, suggesting there may be an optimal pore diameter for the separation of mixtures exhibiting dual-mode diffusion. PMID:22979868

Wanasundara, Surajith N; Spiteri, Raymond J; Bowles, Richard K

2012-09-14

203

Experimental studies on the rheology of hard-sphere suspensions near the glass transition

We have investigated the rheological behavior of sterically stabilized colloidal silica particles of three different sizes at volume fractions above 0.5. Despite a small surface charge, which elevated the intrinsic viscosity from the Einstein value of 2.5, the particles were found to behave essentially as hard spheres in the concentrated suspensions and to have properties highly reminiscent of molecular glasses. The zero shear rate viscosity, characteristic of disordered suspensions and present at all volume fractions, diverges as {phi} {yields} 0.6 and is well-described by the Doolittle equation for glassy flow. For suspensions with a relative zero shear rate viscosity greater than 5 {times} 10{sub 2}, shear thickening was observed. Characteristic time scales for particle rearrangement determined from critical shear rates for shear thinning and shear thickening were found to follow trends predicted for molecular glasses. A transition from a liquid like linear relaxation response to glassy stretched exponential behavior was observed as volume fraction was increased. The onset of the glassy relaxation response, indicative of nondecaying correlations, occurred near a volume fraction of 0.52.

Marshall, L.; Zukoski, C.F. IV (Univ. of Illinois, Urbana (USA))

1990-02-08

204

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

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

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

2011-12-23

205

Doubled heterogeneous crystal nucleation in sediments of hard sphere binary-mass mixtures.

Crystallization during the sedimentation process of a binary colloidal hard spheres mixture is explored by Brownian dynamics computer simulations. The two species are different in buoyant mass but have the same interaction diameter. Starting from a completely mixed system in a finite container, gravity is suddenly turned on, and the crystallization process in the sample is monitored. If the Peclet numbers of the two species are both not too large, crystalline layers are formed at the bottom of the cell. The composition of lighter particles in the sedimented crystal is non-monotonic in the altitude: it is first increasing, then decreasing, and then increasing again. If one Peclet number is large and the other is small, we observe the occurrence of a doubled heterogeneous crystal nucleation process. First, crystalline layers are formed at the bottom container wall which are separated from an amorphous sediment. At the amorphous-fluid interface, a secondary crystal nucleation of layers is identified. This doubled heterogeneous nucleation can be verified in real-space experiments on colloidal mixtures. PMID:21992290

Löwen, Hartmut; Allahyarov, Elshad

2011-10-01

206

Microscopic theories of the structure and glassy dynamics of ultra-dense hard sphere fluids

NASA Astrophysics Data System (ADS)

We construct a new thermodynamically self-consistent integral equation theory (IET) for the equilibrium metastable fluid structure of monodisperse hard spheres that incorporates key features of the jamming transition. A two Yukawa generalized mean spherical IET closure for the direct correlation function tail is employed to model the distinctive short and long range contributions for highly compressed fluids. The exact behavior of the contact value of the radial distribution function (RDF) and isothermal compressibility are enforced, as well as an approximate theory for the RDF contact derivative. Comparison of the theoretical results for the real and Fourier space structure with nonequilibrium jammed simulations reveals many similarities, but also differences as expected. The new structural theory is used as input into the nonlinear Langevin equation (NLE) theory of activated single particle dynamics to study the alpha relaxation time, and good agreement with recent experiments and simulations is found. We demonstrate it is crucial to accurately describe the very high wave vector Fourier space to reliably extract the dynamical predictions of NLE theory, and structural precursors of jamming play an important role in determining entropic barriers.

Jadrich, Ryan; Schweizer, Kenneth

2013-03-01

207

Measuring Depletion Interactions between Isolated Pairs of Hard-Sphere Colloidal Particles

We trap pairs of 1.07 mum polystyrene spheres on a line by rapidly scanning a high power optical tweezer along the line. For sufficiently high scan frequency, the spheres should diffuse freely along the line, while being strongly confined in the transverse directions. We measure the spheres' pair interaction vs. separation by measuring their dynamics with digital video microscopy. The

J. C. Crocker; A. D. Dinsmore; D. Weitz; A. G. Yodh

1997-01-01

208

NASA Astrophysics Data System (ADS)

The quantum features in liquid nitrogen at T = 66 K are studied. Quantum Monte Carlo runs have been performed using different one-centre interaction potentials and strategies. Hard-sphere, Lennard-Jones and quantum effective potential (Feynman-Hibbs, Wigner-Kirkwood) models are the basic ingredients for carrying out calculations, which are classical, semiclassical and of path-integral nature. Relevant thermodynamic and structural data are presented. The results show how the magnitude of hard-sphere quantum effect is dramatically reduced in using smooth potentials. The Wigner-Kirkwood fluid is, the closest to the 'exact' path-integral fluid compared with other effective potential models. The results obtained from path-integral MC account for the available experimental information.

Sesé, Luis M.

209

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

210

We formulate and apply a non-replica equilibrium theory for the fluid-glass transition, glass thermodynamic properties, and jamming of hard spheres in three and all higher spatial dimensions. Numerical predictions for the zero complexity glass transition and jamming packing fractions, and a "densest" equilibrium glass, are made. The equilibrium glass equation of state is regarded as the practical continuation of its fluid analog up to jamming. The analysis provides a possible resolution to the inability of any fluid virial series re-summation based equation of state to capture jamming at a reasonable volume fraction. The numerical results are quantitatively compared with various simulation data for equilibrium hard sphere glasses in 3 to 12 dimensions. Although there are uncertainties in this comparison, the predicted zero complexity or configurational entropy and corresponding jamming packing fractions do agree well with two characteristic packing fractions deduced from the dynamic simulation data. The similarities and differences of our approach compared to the replica approach are discussed. The high dimensional scaling of the equilibrium glass transition and jamming volume fractions are also derived. The developments in this paper serve as input to Paper II [R. Jadrich and K. S. Schweizer, J. Chem. Phys. 139, 054502 (2013)] that constructs a self-consistent integral equation theory of the 3-dimensional hard sphere pair structure, in real and Fourier space, in the metastable regime up to jamming. The latter is employed as input to a microscopic dynamical theory of single particle activated barrier hopping. PMID:23927264

Jadrich, Ryan; Schweizer, Kenneth S

2013-08-01

211

Kernel Approach to Estimation of the Sphere Radius Density in Wicksell's Corpuscle Problem.

National Technical Information Service (NTIS)

The estimation of the probability density function of the radii of spheres in a medium, given the radii of their profiles in a random slice, known as Wicksell's corpuscle problem is considered. An estimator related to the classical kernel density estimato...

A. J. Vanes A. W. Hoogendoorn

1988-01-01

212

Hardness of T-carbon: Density functional theory calculations

NASA Astrophysics Data System (ADS)

We reconsider and interpret the mechanical properties of the recently proposed allotrope of carbon, T-carbon [Sheng , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.106.155703 106, 155703 (2011)], using density functional theory in combination with different empirical hardness models. In contrast with the early estimation based on Gao 's model, which attributes to T-carbon a high Vickers hardness of 61 GPa comparable to that of superhard cubic boron nitride (c-BN), we find that T-carbon is not a superhard material, since its Vickers hardness does not exceed 10 GPa. Besides providing clear evidence for the absence of superhardness in T-carbon, we discuss the physical reasons behind the failure of Gao 's and Šimu?nek and Vacká?'s (SV) models in predicting the hardness of T-carbon, residing in their improper treatment of the highly anisotropic distribution of quasi-sp3-like C-C hybrids. A possible remedy for the Gao and SV models based on the concept of the superatom is suggested, which indeed yields a Vickers hardness of about 8 GPa.

Chen, Xing-Qiu; Niu, Haiyang; Franchini, Cesare; Li, Dianzhong; Li, Yiyi

2011-09-01

213

Colloidal particles dispersed in a non-polar solvent are modeled by a binary mixture of large spheres in a “solvent” of small\\u000a spheres using the liquid state model of adhesive hard sphere mixtures. The discrete nature of the solvent molecules is explicitly\\u000a taken into account. Solvation forces can be described fairly well using both solvent-solvent and solvent-solute interactions.\\u000a By increasing the

M. Penders; A. Vrij

214

Tropical Air Density Below 80 Km from Hypersonic Sphere Measurements.

National Technical Information Service (NTIS)

The measurement of air density at strato-mesopheric altitudes above Kwajalein, Marshall Islands, is part of a continuing study of the behavior of the upper atmosphere in the central tropical Pacific. This note presents some recent results and summarizes t...

J. E. Salah

1969-01-01

215

Absolute Electron Density Measurements in Turbulent Hypersonic Sphere Wakes with Langmuir Probes.

National Technical Information Service (NTIS)

Measurements were carried out in the ballistic range facilities at DREV of the absolute electron density levels in the wakes of 2.7 inch diameter spheres flown at 14,500 feet/second in air atmospheres at 10 torr. The experimental technique involved the us...

D. Heckman L. Sevigny A. Emond

1973-01-01

216

NASA Astrophysics Data System (ADS)

The aim of the paper is the presentation of results obtained by the direct numerical solution of the Boltzmann equation in the case of a binary mixture of hard sphere gases. The system of two coupled Boltzmann equations is solved by a technique combining finite differences with the Monte Carlo evaluation of the Boltzmann collision integrals. It is shown how the technique proposed by Aristov and Tcheremissine (1980) for a single gas can be extended to a mixture. The resulting algorithm can be very well vectorized. The results of a few test calculations on the vector computer CRAY-XMP 48 are presented.

Frezzotti, Aldo; Pavani, Raffaella

1989-09-01

217

We investigate the existence of a fluid–fluid phase separation in binary mixtures of equal-size hard spheres with positively nonadditive diameters [i.e., d11=d22?d, d12=(1+?)d with ?>0]. An integral-equation approach is used to evaluate both thermodynamics and structure of many symmetric (equal to equimolar) mixtures (with ?=0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 1) and some asymmetric cases. We present the results obtained

Domenico Gazzillo; S. Marta

1991-01-01

218

Goal of this work is the extension of a Perturbed-Hard-Sphere-Chain equation of state (PHSC EOS) to systems containing strong polar components. Three different types of association models (ten Brinke/Karasz, SAFI, modified Veytsman) were used to calculate the contribution of specific interactions like hydrogen bonding to thermodynamic quantities. Pure component parameters obtained from regression of temperature dependent density and vapor pressure data allow the prediction of VLE and LLE data. The results of simple fluids and polymer solutions were compared with experimental data. The SAFT and the modified Veytsman extension give similar results for pure fluids and mixtures with components of similar segment size. Differences increase with increasing difference of segment size.

Schaefer, B.; Lambert, S.M.; Song, Y.; Prausnitz, J.M.

1994-10-01

219

NASA Astrophysics Data System (ADS)

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

Jing, Z.; Karato, S.

2009-12-01

220

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

221

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

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

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

2013-08-30

222

NASA Astrophysics Data System (ADS)

Love's classical (1911) linear elastic model for the tidal amplitude of a self-gravitating body assumes that prior to application of the external tidal potential the body is uniform in density and elastic parameters. Numerical evaluations of the solution to Love's governing equations reveal portions of parameter space for which infinitesimal tide raisers can raise tides of arbitrary height (Hurford et. al. this conference). However, a homogeneously dense sphere is a rather non-physical initial condition for tidal deformations. Here we consider a more physically relevant model, that of a continuous density profile which varies with radius. We also allow for the radially varying elastic parameters. We show that the singularities observed in the homogeneous case persist. We assume the density, rigidity and/or Lamè constant are of the form of a polynomial in the normalized radius. The solution to the equations governing the tidal deformation of a radially varying sphere depends only on the effective gravitational rigidity, ? g R / ? , and the ratio of rigidity to Lamé constant, ? / ? . As the magnitude of the radial density variation is increased, the locations of the singularities are displaced in parameter space. Through study of the change in singularity location as the profiles of density, rigidity and compressibility are varied, we can investigate the forces dominating the occurrence of the singular type behavior: Self-gravitation is the force driving the large amplitude tidal deformations. To elucidate the effect further, we developed a non-linear elastic formulation of the self-gravitational collapse of a homogeneous sphere, which reveals material parameter values for which the sphere is unstable. The singularities that we mapped represent the effects of these instabilities in self-gravitation.

Frey, S. E.; Hurford, T.; Greenberg, R.

2005-05-01

223

The erosion of metals by the normal impingement of hard solid spheres

Results of experiments are presented which show that single hardened steel spheres (8 mm in diameter) travelling at velocities in the range 50-400 m s-1 can remove material when they strike mild steel targets at normal impingement. Impacts were photographed using a high-speed camera at microsecond framing rates. The results are interesting since some erosion theories predict zero material removal

D. R. Andrews; J. E. Field

1982-01-01

224

Previous applications of scaled particle theory have been limited to the calculation of thermodynamic properties of fluids rather than structure. In the present paper, the theory is expanded so that it is capable of yielding the radial distribution function. The method is first illustrated by applying it to one- dimensional fluids of hard rods where, as in other theories, the

H. Reiss; R. V. Casberg

1974-01-01

225

A linear programming algorithm to test for jamming in hard-sphere packings

Jamming in hard-particle packings has been the subject of considerable interest in recent years. In a paper by Torquato and Stillinger [J. Phys. Chem. B 105 (2001)], a classification scheme of jammed packings into hierarchical categories of locally, collectively and strictly jammed configurations has been proposed. They suggest that these jamming categories can be tested using numerical algorithms that analyze

Aleksandar Donev; Salvatore Torquato; Frank H. Stillinger; Robert Connelly

2004-01-01

226

The analytical solution of the associative mean spherical approximation (AMSA) for a Yukawa dimerizing multicomponent hard-sphere fluid is derived. The general multi-Yukawa case is discussed. The simpler one-Yukawa case with factorizable coefficients is explicitly solved. As in the previously discussed electrolyte case the solution of the AMSA reduces to the solution of only one nonlinear algebraic equation for the scaling parameter {gamma}{sup B}. The analytical results for the AMSA closure is illustrated by numerical examples and computer simulation for the one-component one-Yukawa dimerizing fluid. Good agreement between theoretical and computer simulation results was found for both the thermodynamic properties and the structure of the system. (c) 2000 American Institute of Physics.

Kalyuzhnyi, Yu. V. [Institute for Condensed Matter Physics, Svientsitskoho 1, 290011 Lviv, (Ukraine); Blum, L. [Department of Physics, University of Puerto Rico, Rio Piedras, Puerto Rico 00931 (Puerto Rico); Rescic, J. [Faculty of Chemistry and Chemical Technology, University of Ljubljana, 1001 Ljubljana, (Slovenia); Stell, G. [Department of Chemistry, State University of New York at Stony Brook, New York 11794-3400 (United States)

2000-07-15

227

NASA Astrophysics Data System (ADS)

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

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

2013-03-01

228

The shear properties of Brownian, rigid spheres consisting of sterically stabilized, crosslinked polymethylmethacrylate (PMMA) particles were studied in suspension. Three different volume fractions were used to carry out this study. The suspensions' elastic-like and viscous-like components of the shear stress were measured by a recently developed technique utilizing cessation of steady shear. The elastic-like viscosity component, or the amount of stress retained at the instant of cessation divided by the shear rate, due to Brownian and possible interparticle forces, decreased in magnitude over the entire range of shear rates used (shear thinning). The decay of the elastic-like stress with time after cessation of flow was also analysed and found to fit a power law relation. The viscous-like component, or the amount of stress lost at the instant of cessation divided by the shear rate, is related to hydrodynamic interactions between and drag on particles and remained essentially constant with shear rate. These data are the first of this kind gathered for a model hard sphere system (i.e., mechanical means) and agrees well with results of Bender and Wagner (J. Colloid Interface Sci. 172, 171 (1995) who used an optical technique. PMID:9245312

Kaffashi; O'Brien; Mackay; Underwood

1997-03-01

229

NASA Astrophysics Data System (ADS)

We used video microscopy and particle tracking to study the dynamics of confined hard-sphere suspensions. Our fluids consisted of 1.1-?m-diameter silica spheres suspended at volume fractions of 0.33--0.42 in water-dimethyl sulfoxide. Suspensions were confined in a quasiparallel geometry between two glass surfaces. First, as the separation distance (H) is decreased from 18 to 1 particle diameter, a transition takes place from a subdiffusive behavior (as in bulk) at large H, to completely caged particle dynamics at small H. These changes are accompanied by a strong decrease in the amplitude of the mean-square displacement (MSD) in the horizontal plane parallel to the confining surfaces. In contrast, the global volume fraction essentially remains constant when H is decreased. Second, measuring the MSD as a function of distance from the confining walls, we found that the MSD is not spatially uniform but smaller close to the walls.. Although confinement also induces local variations in volume fraction, the spatial variations in MSD can be attributed only partially to this effect. The changes in MSD are predominantly a direct effect of the confining surfaces. Hence, both the wall roughness and the separation distance (H) influence the dynamics in confined geometries.

Eral, Burak; van den Ende, Dirk; Duits, Michel; Mugele, Frieder

2011-11-01

230

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

231

Dipolar sticky hard spheres within the Percus-Yevick approximation plus orientational linearization

We consider a strongly idealized model for polar fluids, which consists of spherical particles, having, in addition to a hard-core repulsion, a ``surface dipolar'' interaction, acting only when particles are exactly at contact. A fully analytic solution of the molecular Orstein-Zernike equation is found for this potential, within the Percus-Yevick approximation complemented by a linearization of the angular dependence on

Domenico Gazzillo

2010-01-01

232

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

Santos, Andres [Departamento de Fisica, Universidad de Extremadura, E-06071 Badajoz (Spain)

2011-05-20

233

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

234

NASA Astrophysics Data System (ADS)

Despite the lack of attractive interaction potentials in hard-sphere (HS) colloidal dispersions, a colloid immersed in a solvent of smaller hard-spheres may still experience a net force toward a surface due to imbalanced collisions. Consequently, depletion forces may be utilized to control self-assembly of colloidal structures on various surfaces or control aggregation of colloidal dispersions. To begin to better understand the ability of depletion forces to generate colloidal structures, guide colloidal motion, and control aggregation, accurate theoretical descriptions of depletion forces are necessary. Here, we discuss models of HS colloidal dispersions based on the ideas of Scaled Particle Theory (SPT) to provide methods of computing both HS thermophysical properties and depletion forces in HS fluids. We begin by introducing a new SPT interpolation that accurately provides many HS fluid properties, including the surface tension. We then further develop the inhomogeneous SPT (I-SPT) that describes cavities grown near a planar surface that confines a HS fluid, thereby providing a complete description of cavities near a planar surface, i.e., cavities that are centered at any position relative to the wall. The surface thermodynamics of HS cavities are then reexamined using a Gibbs dividing surface analysis, which produces thermodynamic expressions related to, among other things, the line tension of a HS cavity. Subsequently, we utilize I-SPT to compute the HS line tension and explore its behavior for different cavity locations. Using the accurate description of HS surface thermodynamics from SPT and I-SPT, we then construct a geometric model of depletion forces that is generalizable to many different surface structures and is based on different thermodynamic approximations. Versions of the geometric model based on HS surface thermodynamics (including the line tension) are demonstrated to be highly accurate, though simpler versions based on ideal gas arguments are often sufficient and more easily implemented for complex surfaces. Finally, using the geometric model, we perform stochastic simulations of HS colloids to investigate the dynamics of depletion interactions. The combination of the geometric model and stochastic simulations serves as an engineering tool, allowing one to design surfaces and examine their suitability for controlling colloidal dispersions.

Siderius, Daniel William

235

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

236

The static fluctuation approximation (SFA) is applied to compute the thermodynamic properties of a trapped two-dimensional (2D) interacting hard-sphere (HS) Bose gas in the weakly and strongly interacting regime. A mean-field approach involving a variational wave function is used to compute the mean-field energy as a function of temperature for each harmonic oscillator (HO) state plugged into the SFA technique. In the variational approach, a parameter {alpha} is introduced into the harmonic oscillator wave function in order to take into account the changes in the width when the repulsive interactions between the bosons are increased. In the weakly interacting regime, below the critical temperature, the total energy of all HO states (evaluated by our model) matches the noninteracting result very well. However, beyond the critical temperature, we 'fit' our energies to the classical limit for 2D bosons in a trap by using a suitably proposed weighting function. We compare our results to earlier results of mean-field theory. Further, we evaluate the density matrix arising from correlations between the HO orbitals.

Sakhel, Asaad R. [Al-Balqa Applied University, Faculty of Engineering Technology, Amman 11134 (Jordan); Qashou, Saleem I. [Department of Physics, Faculty of Science and Information Technology, Zarqa Private University, Zarqa 13132 (Jordan); Sakhel, Roger R. [Department of Basic Sciences, Faculty of Information Technology, Al-Isra University, Amman 11622 (Jordan); Ghassib, Humam B. [Department of Physics, University of Jordan, Amman (Jordan)

2010-12-15

237

Face-centered cubic single crystals of ?=1.55 ?m diameter hard-sphere silica colloidal particles were prepared by sedimentation onto (100) and (110) oriented templates. The crystals had a wide interface with the overlaying liquid that was parallel to the template. The location of the interface was determined by confocal microscopic location of the particles, followed by identification of the crystalline and liquid phases by a bond-orientation order parameter. Fluctuations in the height of the interface about its average position were recorded for several hundred configurations. The interfacial stiffness ? was determined from the slope of the inverse squared Fourier components of the height profile vs the square of the wave number, according to the continuum capillary fluctuation method. The offset of the fit from the origin could quantitatively be accounted for by gravitational damping of the fluctuations. For the (100) interface, ?=(1.3±0.3)k(B)T/?(2); for the (110) interface, ?=(1.0±0.2)k(B)T/?(2). The interfacial stiffness of both interfaces was found to be isotropic in the plane. This is surprising for the (110), where crystallography predicts twofold symmetry. Sedimentation onto a (111) template yielded a randomly stacked hexagonal crystal with isotropic ?=0.66k(B)T/?(2). This value, however, is less reliable than the two others due to imperfections in the crystal. PMID:21230283

Ramsteiner, I B; Weitz, D A; Spaepen, F

2010-10-20

238

NASA Astrophysics Data System (ADS)

Recently the Quadrature Method of Moments (QMOM) has been extended to solve several kinetic equations, in particular for gas--particle flows and rarefied gases. This method is usually coupled with simplified linear models for particle collisions. In this work QMOM is tested as a closure for the dynamics of high--order moments with a more realistic collision model namely the hard--spheres model in the Homogeneous Isotropic Boltzmann Equation. The behavior of QMOM far away and approaching the equilibrium is studied. Results are compared to other techniques such as the Lattice--Boltzmann (LBM) and the Grad's expansion (GM) methods. Comparison with a more accurate and computationally expensive model, based on the Discrete Velocity Method (DVM), is also carried out. Our results show that QMOM describes very well the evolution when it is far away from equilibrium, without the drawbacks of the GM and LBM or the computational costs of DVM but it is not able to accurately reproduce the equilibrium and the dynamics close to it. Corrections to cure this behavior are proposed and tested.

Icardi, Matteo; Asinari, Pietro; Marchisio, Daniele; Izquierdo, Salvador; Fox, Rodney

2011-11-01

239

Ultimate enhancement of the local density of electromagnetic states outside an absorbing sphere

NASA Astrophysics Data System (ADS)

The local density of states (LDOS) of the electromagnetic field on the surface of an absorbing dielectric microsphere at frequencies of the whispering-gallery modes (WGMs) is evaluated using the dyadic Green tensors of the electric and magnetic fields. In the calculation, the morphology-dependent resonances in the frequency dependence of the Mie coefficients are described analytically in terms of the resonant frequency and the partial quality factors which allow for light radiation and absorption. The Purcell factor of LDOS enhancement by WGMs is calculated to be proportional to the product of the quality factor and the squared ratio of the light wavelength to the sphere diameter. The ultimate values of the electric-field LDOS enhancement are estimated to be of the order of 107 for a fused-silica microsphere in air. The efficiency of radiation of the resonant spontaneous emission from electric dipoles located near the surface outside of a sphere is determined. The characteristics of a dielectric microsphere are compared with those of other cavities.

Datsyuk, Vitaly V.

2007-04-01

240

Packing Densities and Simulated Tempering for Hard Core Gibbs Point Processes

Monotonicity and convergence properties of the intensity of hard core Gibbs point processes are investigated and compared to the closest packing density. For such processes simulated tempering is shown to be an ecien t alternative to commonly used Markov chain Monte Carlo algorithms. Various spatial characteristics of the pure hard core process are studied based on samples obtained with the

S. Mase; J. Møller; D. Stoyan; R. P. Waagepetersen; G. Döge

2001-01-01

241

Packing Densities and Simulated Tempering for Hard Core Gibbs Point Processes

Monotonicity and convergence properties of the intensity of hard core Gibbs point processes are investigated and compared to the closest packing density. For such processes simulated tempering is shown to be an efficient alternative to commonly used Markov chain Monte Carlo algorithms. Various spatial characteristics of the pure hard core process are studied based on samples obtained with the simulated

S. Mase; J. Møller; D. Stoyan; R. P. Waagepetersen; G. Döge

2001-01-01

242

Brownian trajectory simulation methods are employed to fully establish the non-Gaussian fluctuation effects predicted by our nonlinear Langevin equation theory of single particle activated dynamics in glassy hard-sphere fluids. The consequences of stochastic mobility fluctuations associated with the space-time complexities of the transient localization and barrier hopping processes have been determined. The incoherent dynamic structure factor was computed for a range of wave vectors and becomes of an increasingly non-Gaussian form for volume fractions beyond the (naive) ideal mode coupling theory (MCT) transition. The non-Gaussian parameter (NGP) amplitude increases markedly with volume fraction and is well described by a power law in the maximum restoring force of the nonequilibrium free energy profile. The time scale associated with the NGP peak becomes much smaller than the alpha relaxation time for systems characterized by significant entropic barriers. An alternate non-Gaussian parameter that probes the long time alpha relaxation process displays a different shape, peak intensity, and time scale of its maximum. However, a strong correspondence between the classic and alternate NGP amplitudes is predicted which suggests a deep connection between the early and final stages of cage escape. Strong space-time decoupling emerges at high volume fractions as indicated by a nondiffusive wave vector dependence of the relaxation time and growth of the translation-relaxation decoupling parameter. Displacement distributions exhibit non-Gaussian behavior at intermediate times, evolving into a strongly bimodal form with slow and fast subpopulations at high volume fractions. Qualitative and semiquantitative comparisons of the theoretical results with colloid experiments, ideal MCT, and multiple simulation studies are presented. PMID:17280071

Saltzman, Erica J; Schweizer, Kenneth S

2006-12-12

243

NASA Astrophysics Data System (ADS)

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

Yiantsios, Stergios G.

2006-05-01

244

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

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

2010-01-01

245

NASA Astrophysics Data System (ADS)

We study binary, ternary and polydisperse mixtures of hard particle fuids as models for granular matter, colloids and other soft matter. Size ratios between 1 and 100 are studied for different size distributions. Simulation results are compared with previously found analytical equations of state by looking at the compressibility factor, Z, and agreement is found with much better than 1% deviation in the fluid regime. A slightly improved empirical correction to Z is proposed. When the density is further increased, the behavior of Z changes and there is a close relationship between many-component mixtures and their two- and three-component equivalents (where our contribution is to define the term ``equivalent''). We determine the size ratios for which the liquid-solid transition exhibits crystalline, amorphous or mixed system structure. Near the jamming density, Z is independent of the size distribution and follows a -1 power law as function of the difference from the jamming density. In this limit, Z depends only on one free parameter, the jamming density itself, as reported for several different size distributions with a wide range of widths.

Ogarko, Vitaliy; Luding, Stefan

2012-02-01

246

A Review of Sphere Drag Coefficients Applicable to Atmospheric Density Sensing.

National Technical Information Service (NTIS)

A comprehensive search has been performed on the drag coefficient of spheres in the Reynolds number range from 50 to 50,000 and for Mach numbers up to 5. This Reynolds-Mach number range corresponds to the range of interest in the falling sphere technique ...

M. V. Krumins

1972-01-01

247

Drude-type conductivity of charged sphere colloidal crystals: density and temperature dependence.

We report on extensive measurements in the low-frequency limit of the ac conductivity of colloidal fluids and crystals formed from charged colloidal spheres suspended in de-ionized water. Temperature was varied in a range of 5 degrees C < Theta < 35 degrees C and the particle number density n between 0.2 and 25 microm(-3) for the larger, respectively, 2.75 and 210 microm(-3) for the smaller of two investigated species. At fixed Theta the conductivity increased linearly with increasing n without any significant change at the fluid-solid phase boundary. At fixed n it increased with increasing Theta and the increase was more pronounced for larger n. Lacking a rigorous electrohydrodynamic treatment for counterion-dominated systems we describe our data with a simple model relating to Drude's theory of metal conductivity. The key parameter is an effectively transported particle charge or valence Z(*). All temperature dependencies other than that of Z(*) were taken from literature. Within experimental resolution Z(*) was found to be independent of n irrespective of the suspension structure. Interestingly, Z(*) decreases with temperature in near quantitative agreement with numerical calculations. PMID:16178620

Medebach, Martin; Jordán, Raquel Chuliá; Reiber, Holger; Schöpe, Hans-Joachim; Biehl, Ralf; Evers, Martin; Hessinger, Dirk; Olah, Julianna; Palberg, Thomas; Schönberger, Ernest; Wette, Patrick

2005-09-01

248

Packing Densities and Simulated Tempering for Hard Core Gibbs Point Processes

: Monotonicity and convergence properties of the intensity of hard core Gibbs pointprocesses are investigated and compared to the closest packing density. For such processessimulated tempering is shown to be an e#cient alternative to commonly used Markov chainMonte Carlo algorithms. Various spatial characteristics of the pure hard core process arestudied based on samples obtained with the simulated tempering algorithm.Keywords: closest

S. Mase; J. Møller; D. Stoyan; R. p. Waagepetersen; G. Döge

2000-01-01

249

NASA Astrophysics Data System (ADS)

Monte Carlo results are reported for three liquid states of a model consisting of two species (anions and cations) of charged hard spheres of equal diameter, which interact with a screened Coulomb potential. Results of the mean spherical approximation, the truncated ?2 approximation, and the EXP approximation are compared with the MC results. Numerical and theoretical relationships between this model and the restricted primitive model (RPM) are established. The effect of the methodological errors involved in MC simulations of the RPM is studied by comparing the MC radial distribution functions (rdf's) for the RPM with the rdf's obtained from a perturbation theory, using the screened Coulomb system as the reference system.

Larsen, B.; Rogde, S. A.

1980-02-01

250

Density measurements with relative uncertainty of 1×10-7 have been made on a highly polished 1-kg single crystal silicon sphere with out-of-roundness <40 nm. Roundness was profiled using a 2-D Talyrond machine and 3-D profiles were produced. The diameter was obtained using optical interferometry for a series of breadth measurements at carefully selected points and by combining them with roundness data.

Michael J. Kenny; Achim J. Leistner; Christopher J. Walsh; Kitty Fen; Walter J. Giardini; Leszek S. Wielunski; Roger P. Netterfield; Bradley R. Ward

2001-01-01

251

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

252

A high density perturbation expansion for the hard square lattice gas

NASA Astrophysics Data System (ADS)

We develop a high density perturbation expansion about the columnar ordered state in the hard square lattice gas (particles on a square lattice with next nearest neighbour exclusion). The high z expansion for this model has singular terms of the type 1/z, where is the fugacity associated with each particle. We develop a technique to systematically evaluate each term in this 1/zseries.

Ramola, Kabir; Dhar, Deepak

2012-06-01

253

The shear properties of Brownian, rigid spheres consisting of sterically stabilized, crosslinked polymethylmethacrylate (PMMA) particles were studied in suspension. Three different volume fractions were used to carry out this study. The suspensions’ elastic-like and viscous-like components of the shear stress were measured by a recently developed technique utilizing cessation of steady shear. The elastic-like viscosity component, or the amount of

Babak Kaffashi; Vincent T. O'Brien; Michael E. Mackay; Sylvia M. Underwood

1997-01-01

254

Interacting hard rods on a lattice: distribution of microstates and density functionals.

We derive exact density functionals for systems of hard rods with first-neighbor interactions of arbitrary shape but limited range on a one-dimensional lattice. The size of all rods is the same integer unit of the lattice constant. The derivation, constructed from conditional probabilities in a Markov chain approach, yields the exact joint probability distribution for the positions of the rods as a functional of their density profile. For contact interaction ("sticky core model") between rods, we give a lattice fundamental measure form of the density functional and present explicit results for contact correlators, entropy, free energy, and chemical potential. Our treatment includes inhomogeneous couplings and external potentials. PMID:23927249

Bakhti, Benaoumeur; Müller, Gerhard; Maass, Philipp

2013-08-01

255

Large attractive depletion interactions in soft repulsive-sphere binary mixtures

NASA Astrophysics Data System (ADS)

We consider binary mixtures of soft repulsive spherical particles and calculate the depletion interaction between two big spheres mediated by the fluid of small spheres, using different theoretical and simulation methods. The validity of the theoretical approach, a virial expansion in terms of the density of the small spheres, is checked against simulation results. Attention is given to the approach toward the hard-sphere limit and to the effect of density and temperature on the strength of the depletion potential. Our results indicate, surprisingly, that even a modest degree of softness in the pair potential governing the direct interactions between the particles may lead to a significantly more attractive total effective potential for the big spheres than in the hard-sphere case. This might lead to significant differences in phase behavior, structure, and dynamics of a binary mixture of soft repulsive spheres. In particular, a perturbative scheme is applied to predict the phase diagram of an effective system of big spheres interacting via depletion forces for a size ratio of small and big spheres of 0.2; this diagram includes the usual fluid-solid transition but, in the soft-sphere case, the metastable fluid-fluid transition, which is probably absent in hard-sphere mixtures, is close to being stable with respect to direct fluid-solid coexistence. From these results, the interesting possibility arises that, for sufficiently soft repulsive particles, this phase transition could become stable. Possible implications for the phase behavior of real colloidal dispersions are discussed.

Cinacchi, Giorgio; Martínez-Ratón, Yuri; Mederos, Luis; Navascués, Guillermo; Tani, Alessandro; Velasco, Enrique

2007-12-01

256

NASA Astrophysics Data System (ADS)

Intermediate scattering functions are measured for colloidal hard sphere systems using both dynamic light scattering and x-ray photon correlation spectroscopy. We compare the techniques, and discuss the advantages and disadvantages of each. Both techniques agree in the overlapping range of scattering vectors. We investigate the scaling behavior found by Segré and Pusey [Phys. Rev. Lett. 77, 771 (1996)] but challenged by Lurio et al. [Phys. Rev. Lett. 84, 785 (2000)]. We observe a scaling behavior over several decades in time but not in the long-time regime. Moreover, we do not observe long-time diffusive regimes at scattering vectors away from the peak of the structure factor and so question the existence of long-time diffusion coefficients at these scattering vectors.

Martinez, V. A.; Thijssen, J. H. J.; Zontone, F.; van Megen, W.; Bryant, G.

2011-02-01

257

NASA Astrophysics Data System (ADS)

The velocity autocorrelation function is derived from the mean-squared displacement measured on a colloidal suspension of particles with hard-sphere-like interactions. It decays to zero from below and follows a stretched exponential function of delay time for the thermodynamically stable suspension. For the metastable suspension a power-law decay emerges. The results are discussed in terms of the classical Lorentz gas and the model that describes diffusion confined to one dimension. With the aid of these models, the experimental results provide a characterization of the dynamical heterogeneities which are observed microscopically, and an explanation for the enhanced resistance to flow and diffusion usually found in undercooled fluids upon approaching the glass transition.

van Megen, W.; Bryant, G.

2007-08-01

258

Density profiles of chemically reacting hard spheres near a large hard sphere, mimicking a colloid, are studied by means of Percus-Yevick approximation. The model of Cummings and Stell is used for a bulk fluid. We investigate the dependence of the profiles on the curvature of the surface, the bulk density, and the degree of association.

Orest Pizio; Douglas Henderson; Stefan Sokolowski

1995-01-01

259

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

260

Effect of light energy density on conversion degree and hardness of dual-cured resin cement.

This study evaluated the effect of different light energy densities on conversion degree (CD) and Knoop hardness number (KHN) of RelyX ARC (RLX) resin cement. After manipulation according to the manufacturer's instructions, RLX was inserted into a rubber mold (0.8 mm x 5 mm) and covered with a Mylar strip. The tip of the light-curing unit (LCU) was positioned in contact with the Mylar surface. Quartz-tungsten-halogen (QTH) and light-emitting diode (LED) LCUs with light densities of 10, 20 and 30 J/cm2 were used to light-cure the specimens. After light curing, the specimens were stored dry in lightproof containers at 37 degrees C. After 24 hours, the CD was analyzed by FT-Raman and, after an additional 24-hours, samples were submitted to Knoop hardness testing. The data of the CD (%) and KHN were submitted to two-way ANOVA and the Tukey's test (alpha = 0.05). QTH and LED were effective light curing units. For QTH, there were no differences among the light energy densities for CD or KHN. For LED, there was a significant reduction in CD with the light energy density set at 10 J/cm2. KHN was not influenced by the light-curing unit and by its light energy density. PMID:20166419

Komori, Paula Carolina de Paiva; de Paula, Andréia Bolzan; Martin, Airton Abr?o; Tango, Rubens Nisie; Sinhoreti, Mario Alexandre Coelho; Correr-Sobrinho, Lourenço

261

The preparation of ultraporous polymer resins using a straightforward hard-templating synthesis is presented. Self-assembly of silica nanospheres into densely packed glasses allows an easy preparation of templates. Polydivinylbenzene resins with surface areas of up to 1000 m(2) g(-1) are synthesized as a model system and porosity analysis reveals bimodal porosity (spherical mesopores and micropores within the pore walls). The prepared systems can be further functionalized without loss of porosity as demonstrated by sulfonation. Because of their large pore sizes (13-28 nm), they are efficient adsorbents also for large molecules. Finally, the systems can also be used as model systems for the study of the pore drying and collapse process, which is of crucial importance for any application of mesoporous polymers. PMID:22351298

Wilke, Antje; Weber, Jens

2012-02-21

262

Hard x-ray radiography for density measurement in shock compressed matter

In this letter we report on the direct density measurement in a shock compressed aluminum target using hard x-ray radiography. Experimental data employing a molybdenum K{alpha} source at 17.5 keV, generated with a short pulse laser are presented. High spatial resolution was obtained thanks to a new design for the backlighter geometry. Density values deduced from radiography are compared to predictions from hydrodynamic simulations, which have been calibrated in order to reproduce shock velocities measured from a rear-side self-emission diagnostic. Our results reveal the great potential of this technique as a diagnostic tool for direct density measurements in dense high-Z opaque materials.

Ravasio, A.; Koenig, M.; Benuzzi-Mounaix, A.; Ozaki, N.; Loupias, B.; Vinci, T. [Laboratoire pour l'Utilisation de Lasers Intenses, UMR7605, CNRS-CEA-Universite Paris VI -Ecole Polytechnique, 91128 Palaiseau Cedex (France); Le Pape, S.; Park, H. S.; Patel, P.; Mackinnon, A. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States); Cecchetti, C.; Borghesi, M. [School of Mathematics and Physics, Queens University of Belfast, Belfast BT7 INN (United Kingdom); Schiavi, A. [Department of Energetics, University of Rome 'La Sapienza', Via A Scarpa 14-16, I-00161 Rome (Italy); Batani, D.; Dezulian, R. [Dipartimento di Fisica G. Occhialini, Universita di Milano-Bicocca, Piazza Della Scienze 3, 20126 Milano (Italy); Boehly, T. [Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14627 (United States); Henry, E. [Departement de conception et realisation des experiences (DECRE), CEA-DIF, BP 12, 91680 Bruyeres-le-Chatel (France); Notley, M.; Bandyopadhyay, S.; Clarke, R. [CCLRC, Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX (United Kingdom)

2008-06-15

263

The sedimentation equilibrium of a colloidal suspension modeled as a collection of adhesive hard-sphere particles confined in a planar slit pore is studied by using a density functional approach with a newly developed approximation in which the repulsive part of the adhesive hard-sphere interaction potential is treated within weighted density functional theory while the attractive part is evaluated by a

Niharendu Choudhury; Swapan K. Ghosh

2002-01-01

264

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

265

NASA Astrophysics Data System (ADS)

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

Boss, Alan P.; Keiser, Sandra A.

2013-02-01

266

High-density plasma etching of CoFeSiB magnetic films with hard mask

High-density plasma etching of amorphous CoFeSiB magnetic films was carried out in a Cl2\\/Ar and Cl2\\/O2\\/Ar gas mixes. In a Cl2\\/Ar gas, as the Cl2 concentration increased, the etch rate of CoFeSiB films decreased, and etch residues decreased but the etch slope was slanted. However, in Cl2\\/O2\\/Ar gas mix, the etch characteristics of CoFeSiB films with TiN hard mask was

Jang Woo Lee; Su Ryun Min; Tae Wan Kim; Chee Won Chung

2006-01-01

267

The effect of strongly repulsive interactions on the tunneling amplitude of hard-sphere (HS) bosons confined in a simple cubic optical lattice plus tight external harmonic confinement in continuous space is investigated. The quantum variational Monte Carlo (VMC) and the variational path integral (VPI) Monte Carlo techniques are used at zero temperature. The effects of the lattice spacing on the tunneling amplitude are also considered. The occupancies of the lattice sites as a function of the repulsion between the bosons are further revealed. Our chief result is that for a small number of bosons (N=8) the overlap of the wave functions in neighboring wells practically does not change with an increase of the repulsive interactions and changes only minimally for a larger number of particles (N=40). The tunneling amplitude rises with a reduction in the lattice spacing. In addition, the occupancy of the center of the trap decreases in favor of a rise in the occupancy of the lattice sites at the edges of the trap with increasing HS repulsion. Further, it was found that the energy per particle at certain optical-lattice barrier heights is insensitive to the number of particles and variations in the HS diameter of the bosons. In order to support our results, we compare the VMC results with corresponding VPI results.

Sakhel, Asaad R. [Al-Balqa Applied University, Faculty of Engineering Technology, Basic Sciences Department, Amman 11134 (Jordan); Dubois, Jonathan L. [Lawrence Livermore National Laboratory, 7000 East Ave, L-415, Livermore California 94550 (United States); Sakhel, Roger R. [Department of Basic Sciences, Faculty of Science and Information Technology, Al-Isra University, Amman 11622 (Jordan)

2010-04-15

268

Structure, Density and Velocity Fluctuations in Quasi2D non-Brownian Suspensions of Spheres

Non-brownian sedimenting suspensions exhibit density and velocity fluctuations. We have performed experiments on a quasi-2D counter-flow stabilized suspension of 2000 spherical particles, namely a liquid-solid fluidized bed in a Hele-Shaw cell. This 2D suspension displays a uniform concentration but the particle radial distribution function and the fluctuations of the particle number in a sub-volume of the suspension suggest that the

Florence Rouyer; Daniel Lhuillier; Jérôme Martin; Dominique Salin

1999-01-01

269

Non-Brownian sedimenting suspensions exhibit density and velocity fluctuations. We have performed experiments on a quasi-two-dimensional counter-flow stabilized suspension of 2000 spherical particles, namely a liquid-solid fluidized bed in a Hele-Shaw cell. This two-dimensional suspension displays a uniform concentration but the particle radial distribution function and the fluctuations of the particle number in a subvolume of the suspension suggest that the

F. Rouyer; D. Lhuillier; J. Martin; D. Salin

2000-01-01

270

Interactions between colloidal particles in polymer solutions: A density functional theory study

We present a density functional theory study of colloidal interactions in a concentrated polymer solution. The colloids are modeled as hard spheres and polymers are modeled as freely jointed tangent hard sphere chains. Our theoretical results for the polymer-mediated mean force between two dilute colloids are compared with recent simulation data for this model. Theory is shown to be in

N. Patel; S. A. Egorov

2004-01-01

271

Melting of polydisperse hard disks

NASA Astrophysics Data System (ADS)

The melting of a polydisperse hard-disk system is investigated by Monte Carlo simulations in the semigrand canonical ensemble. This is done in the context of possible continuous melting by a dislocation-unbinding mechanism, as an extension of the two-dimensional hard-disk melting problem. We find that while there is pronounced fractionation in polydispersity, the apparent density-polydispersity gap does not increase in width, contrary to 3D polydisperse hard spheres. The point where the Young’s modulus is low enough for the dislocation unbinding to occur moves with the apparent melting point, but stays within the density gap, just like for the monodisperse hard-disk system. Additionally, we find that throughout the accessible polydispersity range, the bound dislocation-pair concentration is high enough to affect the dislocation-unbinding melting as predicted by Kosterlitz, Thouless, Halperin, Nelson, and Young.

Pronk, Sander; Frenkel, Daan

2004-06-01

272

Reducing Head-Gimbal-Assembly Windage for High-Track-Density Hard Disk Drives

NASA Astrophysics Data System (ADS)

The windage of a head gimbal assembly (HGA) is the flow-induced vibration affecting head slider positioning in the off-track direction. Reducing the windage is important for increasing the track density of hard disk drives (HDDs). To develop HGAs with a windage smaller than that of conventional HGAs, we examined the characteristics of HGA windage. We used a 12-mm (from the swage hole center to the dimple) HGA that had a maximum windage peak at 11 kHz. We put it in a spin stand and in a HDD and measured its windage with a laser Doppler vibrometer. The windage amplitude correlated well with the mean airflow velocity in the HDD (measured with a laser Doppler anemometer). Windage amplitude was also affected by fluctuation of the airflow velocity. Our results show that HGA windage can be reduced by increasing the distances between the rotating disk and the cover and the base.

Nakamura, Shigeo; Hirono, Yoshiyuki; Aduma, Ryohei; Takahashi, Haruhide; Hagiya, Shinobu; Wakatsuki, Kousaku; Saegusa, Shozo

273

From Spheres to Ellipsoids: The Story of the Density of States

NASA Astrophysics Data System (ADS)

Packings of frictionless ellipsoids have not only captured the imagination of the public, but also bring up a number of fundamental issues regarding the properties of jammed media. For instance, the average contact number Z of such packings at jamming varies continuously between the spherical isostatic value Ziso=6 and the value Ziso=10 for ellipsoids of revolution if the ellipticity ?-1 is turned on. Here we study the vibrational spectra of soft ellipsoids both as a function of density and ?. Our spectra show a two-band structure. For small aspect ratios there is first a rotational band, then a gap and then a second band of translational character. As we increase the aspect ratio, the gap closes and the remaining band has a mixed character. We discuss various surprising features of the spectrum in detail and show how the changes in the gap are related with the change of Z with ?.

Zeravcic, Zorana; Xu, Ning; Nagel, Sidney R.; Liu, Andrea J.

2009-03-01

274

Three responses of rainbow trout (Salmo gairdneri), common carp (Cyprinus carpio), and fathead minnows (Pimephales promelas) to the anesthetic MS-222 (tricaine methanesulfonate) were identified: induction times to total loss of equilibrium decreased with increasing temperatures; resistance to MS-222 increased with increasing water hardness; and resistance to the drug increased when the density of test fish was increased from 0.3 to

J. R. Sylvester; L. E. Holland

1982-01-01

275

The hydrodynamic problem of a thermonuclear explosion in a sphere of normal-density liquid deuterium was solved (Institute for Physics and Power Engineering, Obninsk) in 1952-1954 in the framework of the Soviet Atomic Project. The principal result was that the explosion shockwave in deuterium strongly decayed because of radiation energy loss and nonlocal energy release by fast neutrons. At that time,

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

2009-01-01

276

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

277

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

278

Experimental study of heat transfer in a critical point of sphere in hypersonic low-density flow

In an experimental study of heat transfer at the critical point of a sphere the possibility is confirmed of using underexpanded nozzles in hypersonic wind tunnels for radiation of the flow about the models over a wide range of Reynolds numbers. Experiments were carried out in a hypersonic shock tube with numbers M32.

V. N. Gusev; Y. V. Nikoskii

1975-01-01

279

Unusual order in squeezed repulsive spheres

NASA Astrophysics Data System (ADS)

The soft spheres that we have been using for years to study jamming into disordered packings can make a range of surprising ordered structures at higher densities. Monodisperse repulsive harmonic disks in two dimensions form, apart form the triangular lattice everyone would expect, a square lattice and various non-bravais lattices that can be described as a triangular lattice with a basis. The latter class includes the honeycomb structure, a chiral structure, and a structure which is best described as a tiling of pentagons and triangles. The appearance of these structures, some of which have not been previously reported, is surprising because the potential between the disks only very weakly violates the condition of complete monotonicity which has been conjectured to guarantee the triangular lattice to be the ground state structure. I will discuss how these structures come about, how they are related to tiny periodic packings of hard spheres and in what ways the resulting structures might be useful.

Ellenbroek, Wouter G.

2013-03-01

280

We present a comprehensive study of the equilibrium pair structure in fluids of nonoverlapping spheres interacting by a repulsive Yukawa-like pair potential, with special focus on suspensions of charged colloidal particles. The accuracy of several integral equation schemes for the static structure factor, S(q), and radial distribution function, g(r), is investigated in comparison to computer simulation results and static light scattering data on charge-stabilized silica spheres. In particular, we show that an improved version of the so-called penetrating-background corrected rescaled mean spherical approximation (PB-RMSA) by Snook and Hayter [Langmuir 8, 2880 (1992)], referred to as the modified PB-RMSA (MPB-RMSA), gives pair structure functions which are in general in very good agreement with Monte Carlo simulations and results from the accurate but nonanalytical and therefore computationally more expensive Rogers-Young integral equation scheme. The MPB-RMSA preserves the analytic simplicity of the standard rescaled mean spherical (RMSA) solution. The combination of high accuracy and fast evaluation makes the MPB-RMSA ideally suited for extensive parameter scans and experimental data evaluation, and for providing the static input to dynamic theories. We discuss the results of extensive parameter scans probing the concentration scaling of the pair structure of strongly correlated Yukawa particles, and we determine the liquid-solid coexistence line using the Hansen-Verlet freezing rule. PMID:21280773

Heinen, Marco; Holmqvist, Peter; Banchio, Adolfo J; Nägele, Gerhard

2011-01-28

281

Small-angle neutron scattering (SANS) data for the tri-n-butyl phosphate (TBP)-n-dodecane, HNO{sub 3}-UO{sub 2}(NO{sub 3}){sub 2} solvent extraction system have been interpreted using the Baxter model for hard spheres with surface adhesion. The increase in the scattering intensity in the low Q range observed when increasing amounts of HNO{sub 3} or UO{sub 2}(NO{sub 3}){sub 2} are transferred into the organic phase has been interpreted as arising from interactions between solute particles. The SANS data have been reproduced using a 12--16 {angstrom} diameter of the hard sphere, d{sub hs}, and a 5.6k{sub B}T-7.1k{sub B}T stickiness parameter, {tau}{sup -1}. When in contact with an aqueous phase, TBP in n-dodecane forms small reverse micelles containing three TBP molecules. Upon extraction of water, HNO{sub 3}, and UO{sub 2}(NO{sub 3}){sub 2}, the swollen micelles interact through attractive forces between their polar cores with a potential energy of about 2k{sub B}T and an effective Hamaker constant of about 4k{sub B}T. The intermicellar attraction, under suitable conditions, leads to third-phase formation. Upon phase splitting, most of the solutes in the original organic phase (water, TBP, HNO{sub 3}, and UO{sub 2}(NO{sub 3}){sub 2}) separate in a continuous phase containing interspersed layers of n-dodecane.

Chiarizia, R.; Nash, K. L.; Jensen, M. P.; Thiyagarajan, P.; Littrell, K. C.

2003-11-11

282

This thesis consists of two parts: the first part deals with the theory of nonuniform classical fluids and, in particular, with the problem of freezing of classical liquids into crystalline solids. We propose an extended formulation of the Modified Weighted Density Approximation (MWDA) in order to treat the problem of freezing of the classical One Component Plasma (OCP). We call

Christos N. Likos

1993-01-01

283

Compressional properties of silicate liquids including density and bulk modulus at elevated pressures and temperatures (i.e., equation of state) are crucial to our understanding of melting processes such as the generation and differentiation of silicate melts in Earth and hence to explore the geophysical and geochemical consequences of melting. Unlike the solid and gaseous states of a matter for which

Z. Jing; S. Karato

2009-01-01

284

The He3 number density for the gas in an He3 proportional counter was evaluated from a determination of the number of (n,p) reactions detected in a known thermal fluence. Accuracy is 4 percent. The thermal fluence determination, and the analysis of reaction rates for He3 proportional counters in thermal fluences are discussed. It is stressed that the applicability of any

D. J. Thomas; N. Soochak

1988-01-01

285

Al-Li alloys are of particular interest for the aircraft industry, due to their low density and high strength. Precipitation of the alloy results in hardening of the material, which is of great technological importance. During the coarsening stage of Î´â² precipitation the particles have a wide size distribution (polydisperse form). The interparticle interference effect in the small-angle X-ray scattering (SAXS)

C. S. Tsao; T. L. Lin; M. S. Yu

1999-01-01

286

NSDL National Science Digital Library

This animation is a simple model of the apparent motion of the stars in the night sky. Ancient people described the motions as if the stars were all attached to a vast globe, or a Celestial Sphere, centered about the Earth.

Wpsu

2010-04-09

287

NASA Astrophysics Data System (ADS)

The He3 number density for the gas in an He3 proportional counter was evaluated from a determination of the number of (n,p) reactions detected in a known thermal fluence. Accuracy is 4 percent. The thermal fluence determination, and the analysis of reaction rates for He3 proportional counters in thermal fluences are discussed. It is stressed that the applicability of any approximate expressions relating the measured response to the amount of detecting material should be checked. If the detector is fairly opaque to neutrons, the effective temperature of the Maxwellian distribution does need to be known. This is true even for a detector with a 1/v dependence. For such a detector the reaction rate is independent of the shape of the thermal neutron distribution in the limiting case of a thin detector, but this is not true for one where the neutrons have a high probability of being absorbed. The epithermal component of the field needs to be determined since the detector response may be quite different in this energy region. The response of the detector as a function of energy needs to be known over all the relevant neutron energy range. The effects of absorption and scattering in any cladding material around the detecting element must be considered.

Thomas, D. J.; Soochak, N.

1988-07-01

288

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

2013-07-25

289

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

290

By using molecular-dynamics simulations, we determine the jamming phase diagrams at high densities for a bidisperse mixture of soft spheres that interact according to repulsive power-law pair potentials. We observe that the relaxation time varies nonmonotonically as a function of density at constant temperature. Therefore, the jamming phase diagrams contain multiple reentrant glass transitions if temperature and density are used as control parameters. However, if we consider a new formulation of the jamming phase diagrams where temperature over pressure and pressure are employed as control parameters, no nonmonotonic behavior is observed. PMID:23767543

Schmiedeberg, Michael

2013-05-28

291

NASA Astrophysics Data System (ADS)

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

Schmiedeberg, Michael

2013-05-01

292

Polymers as compressible soft spheres

NASA Astrophysics Data System (ADS)

We consider a coarse-grained model in which polymers under good-solvent conditions are represented by soft spheres whose radii, which should be identified with the polymer radii of gyrations, are allowed to fluctuate. The corresponding pair potential depends on the sphere radii. This model is a single-sphere version of the one proposed in Vettorel et al. [Soft Matter 6, 2282 (2010)], and it is sufficiently simple to allow us to determine all potentials accurately from full-monomer simulations of two isolated polymers (zero-density potentials). We find that in the dilute regime (which is the expected validity range of single-sphere coarse-grained models based on zero-density potentials) this model correctly reproduces the density dependence of the radius of gyration. However, for the thermodynamics and the intermolecular structure, the model is largely equivalent to the simpler one in which the sphere radii are fixed to the average value of the radius of gyration and radii-independent potentials are used: for the thermodynamics there is no advantage in considering a fluctuating sphere size.

D'Adamo, Giuseppe; Pelissetto, Andrea; Pierleoni, Carlo

2012-06-01

293

The density of 1,1-dichloro-1-fluoroethane (HCFC 141b)

NASA Astrophysics Data System (ADS)

In this Note we present the density of HCFC 141b, measured between 293.15 and 300.15 K, with an mechanical oscillator densimeter, with an uncertainty of 0.007%. The results are compared with the densities estimated by the reduced hard-sphere-DeSantis equation of state and with the experimental data obtained by several authors.

Sousa, A. T.; Fialho, P. S.; Nieto de Castro, C. A.

1994-03-01

294

Adsorption of fluids on colloidal particles: a density functional approach

Density functional results are presented for adsorption of simple fluids on colloidal particles. Two models of colloidal particles are considered: first a study of adsorption on a large hard sphere, and second the application of the theory to describe adsorption on a large particle interacting via Lennard-Jones type attractive-repulsive forces. In both cases the theoretical predictions are compared with Monte

Douglas Henderson; Stefan Sokolowski; Andzej Patrykiejew

1995-01-01

295

Jammed Ellipsoids Beat Jammed Spheres

NASA Astrophysics Data System (ADS)

We have performed experiments and computer simulations on random packings of ellipsoids. The experiments on M^textregistered Milk Chocolate candies (spheroids with aspect ratio ˜ 1.91:1) indicate a packing fraction 0.68-0.7 considerably higher than that for random sphere packings (0.64). Moreover the number of contacting neighbors is measured as Z ˜ 9.8, close to the isostatic result of twice the number of degrees of freedom f, Z=2f, per particle. For spheres f=3, Z ˜ 6, for ellipsoids of revolution f=5, Z ˜ 10, and for general ellipsoids Z ˜ 12. Simulations, for spheroids support this observation and show a remarkable downward cusp-like behavior for packing fraction vs aspect ratio with a local minimum for spheres. Experiments on general ellipsoids also show high packing fractions and simulations yield orientationally disordered ellipsoid packings up to a density of 0.75, i.e., exceeding even the densest crystal packing of spheres.

Chaikin, Paul; Donev, Aleksandar; Man, Weining; Cisse, Ibrahim; Stillinger, Frank; Torquato, Salvatore

2004-03-01

296

Diffusion-limited reactions in crowded environments: a local density approximation

NASA Astrophysics Data System (ADS)

In the real world, diffusion-limited reactions in chemistry and biology mostly occur in crowded environments, such as macromolecular complex formation in the cell. Despite the paramount importance of such phenomena, theoretical approaches still mainly rely on the Smoluchowski theory, only valid in the infinite dilution limit. In this paper we introduce a novel theoretical framework to describe the encounter rate and the stationary density profiles for encounters between an immobilized target and a fluid of interacting spherical particles, valid in the local density approximation. A comparison with numerical simulations performed for a fluid of hard spheres and square well attractive hard spheres confirms the accuracy of our treatment.

Piazza, F.; Dorsaz, N.; De Michele, C.; De Los Rios, P.; Foffi, G.

2013-09-01

297

Diffusion-limited reactions in crowded environments: a local density approximation.

In the real world, diffusion-limited reactions in chemistry and biology mostly occur in crowded environments, such as macromolecular complex formation in the cell. Despite the paramount importance of such phenomena, theoretical approaches still mainly rely on the Smoluchowski theory, only valid in the infinite dilution limit. In this paper we introduce a novel theoretical framework to describe the encounter rate and the stationary density profiles for encounters between an immobilized target and a fluid of interacting spherical particles, valid in the local density approximation. A comparison with numerical simulations performed for a fluid of hard spheres and square well attractive hard spheres confirms the accuracy of our treatment. PMID:23963402

Piazza, F; Dorsaz, N; De Michele, C; De Los Rios, P; Foffi, G

2013-09-18

298

A series of iron azadithiolate complexes possessing an intramolecular secondary coordination sphere interaction and an ability to reduce HOAc at the potential near the first electron-transfer process are reported. A unique structural feature in which the aza nitrogen has its lone pair point toward the apical carbonyl carbon is observed in [Fe(2)(mu-S(CH(2))(2)NR(CH(2))(2)S)(CO)(6-x)L(x)](2) (R = (n)Pr, x = 0, 1a; R = (i)Pr, x = 0, 1b; R = (n)Pr, L = PPh(3), x = 1, 2; R = (n)Pr, L = P(n)Bu(3), x = 1, 3) as biomimetic models of the active site of Fe-only hydrogenase. The presence of this weak N...C(CO(ap)) interaction provides electronic perturbation at the Fe center. The distance of the N...C(CO(ap)) contact is 3.497 A in 1a. It increases by 0.455 A in 2 when electronic density of the Fe site is slightly enriched by a weak sigma-donating ligand, PPh(3). A longer distance (4.040 A) is observed for the P(n)Bu(3) derivative, 3. This N...C(CO(ap)) distance is thus a dynamic measure of electronic nature of the Fe(2) core. Variation of electronic richness within the Fe(2) moiety among the complexes reflects on their electrochemical response. Reduction of 2 is recorded at the potential of -2.17 V, which is 270 mV more negative than that of 1. Complex 3 requires additional 150 mV for the same reduction. Such cathodic shift results from CO substitution by phosphines. Electrocatalytic hydrogen production from HOAc by both kinds of complexes (all-CO and phosphine-substituted species) requires the potential close to that for reduction of the parent molecules in the absence of acids. The catalytic mechanism of 1a is proposed to involve proton uptake at the Fe(0)Fe(I) redox level instead of the Fe(0)Fe(0) level. This result is the first observation among the all-CO complexes with respect to electrocatalysis of HOAc. PMID:20557034

Liu, Yu-Chiao; Tu, Ling-Kuang; Yen, Tao-Hung; Lee, Gene-Hsiang; Yang, Shu-Ting; Chiang, Ming-Hsi

2010-07-19

299

NSDL National Science Digital Library

This Spheres of Eudoxus model simulates the system devised by the Ancient Greek astronomer Eudoxus to model the motion of the planets. The model consists of four nested concentric spheres. The axis of each sphere is attached to the surface of the next sphere out. The planet itself is located on the surface of the innermost sphere. The outermost sphere rotates with the daily (apparent) rotation of the stars. The Spheres Frame shows the four spheres of the model. The axis of the inner (red) sphere can be tilted relative to that of the middle (blue) sphere using a slider to adjust the angle. The red sphere automatically rotates with angular velocity +1.0 (in arbitrary units). The angular velocities of the blue and green spheres can be adjusted using sliders. Note that the axis of the blue sphere is attached to the equator of the green sphere. This is a crucial part of Eudoxus' model. The equator of the green sphere is in the plane of the ecliptic. The outermost (white) sphere is essentially the Celestial Sphere containing the fixed stars (or at least it rotates about the same axis and at the same rate as the Celestial Sphere). The Sky View Frame shows the motion of the planet (relative to the stars) as seen from the earth, which sits at the center of the concentric spheres in the model. By tilting the red sphere relative to the blue sphere, setting the angular velocity of the blue sphere opposite that of the red sphere, and giving the green sphere a sufficiently small angular speed, Eudoxus was able to qualitatively reproduce the observed retrograde motion of the planets using this model.

Timberlake, Todd

2011-05-18

300

Advanced Processing of Hollow Sphere Foams.

National Technical Information Service (NTIS)

Closed-cell metallic foams were fabricated by bonding millimeter sized hollow spheres at points of contact. The composition of low density metallic foams with hollow sphere architecture achieved to date includes Ti-6Al- 4V, 400 series stainless steel, and...

T. H. Sanders J. K. Cochran

1999-01-01

301

NASA Astrophysics Data System (ADS)

Two types of Hoganas iron powders—sponge (NC), and highly compressible (SC) were investigated. These specimens were compacted with a pressure of 300, 400, 500, 600, and 700 MPa, before sintering in a production belt-type furnace. Steam treatment of the specimens was at 570 °C for 30 min. The sintered density and as-sintered hardness increase with increasing compaction pressure, and are significantly influenced by the powder structural characteristics. During steam treatment the type of powder and compaction pressure have an important influence on the extent of pore closure and weight gain. The maximum hardness was obtained for the components compacted at a pressure of 500 MPa for both groups of iron powders. Surface pore closure and oxidation resistance of the steam-treated components are improved with increasing compaction pressure.

Wang, Wen-Fung

2007-10-01

302

The water entry of decelerating spheres

NASA Astrophysics Data System (ADS)

We present the results of a combined experimental and theoretical investigation of the vertical impact of low-density spheres on a water surface. Particular attention is given to characterizing the sphere dynamics and the influence of its deceleration on the shape of the resulting air cavity. A theoretical model is developed which yields simple expressions for the pinch-off time and depth, as well as the volume of air entrained by the sphere. Theoretical predictions compare favorably with our experimental observations, and allow us to rationalize the form of water-entry cavities resulting from the impact of buoyant and nearly buoyant spheres.

Aristoff, Jeffrey M.; Truscott, Tadd T.; Techet, Alexandra H.; Bush, John W. M.

2010-03-01

303

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

304

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

305

Random packings of spheres and spherocylinders simulated by mechanical contraction

We introduce a simulation technique for creating dense random packings of hard particles. The technique is particularly suited to handle particles of different shapes. Dense amorphous packings of spheres have been formed, which are consistent with the existing work on random sphere packings. Packings of spherocylinders have also been simulated out to the large aspect ratio of alpha=160.0. Our method

S. R. Williams; A. P. Philipse

2003-01-01

306

A density-functional theory is proposed to describe the density profiles of small ions around an isolated colloidal particle in the framework of the restricted primitive model where the small ions have uniform size and the solvent is represented by a dielectric continuum. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-sphere repulsion and

Yang-Xin Yu; Jianzhong Wu; Guang-Hua Gao

2004-01-01

307

Boron{endash}suboxide-based thin films have been deposited on Si in an electron cyclotron resonance microwave plasma using a radio frequency (rf) magnetron as a source of boron. Variations of the oxygen fraction in the deposition ambient and of the rf bias applied to the substrate were related to film tribology. The best films have hardnesses of {approximately}28GPa and moduli of {approximately}240GPa and were deposited in oxygen fractions {lt}1{percent} at substrate temperatures {lt}350{degree}C. The films contain 4{percent}{endash}15{percent} O and {approximately}15{percent}C, with carbon originating from the sputter target. They are amorphous and have surface roughnesses of {approximately}0.2nm. Boron{endash}oxide films may form a self-generating lubricating layer of B(OH){sub 3} in ambient atmosphere. Compositional depth profiling of these films reveals an oxygen-enriched surface of {approximately}10nm thickness. Initial nanoscratch test results indicate that these films fail at high critical loads and have low friction coefficients relative to other hard coatings. {copyright} {ital 1997 American Vacuum Society.}

Doughty, C.; Gorbatkin, S.M. [Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States); Tsui, T.Y.; Pharr, G.M. [Rice University, Houston, Texas 77005 (United States); Medlin, D.L. [Sandia National Laboratory, Livermore, California 94551 (United States)

1997-09-01

308

A thermodynamic method has been developed based on the density functional theory (DFT) to predict the surface tension of polar and associating fluids by the authors. The Barker–Henderson (BH) perturbation theory and statistical associating fluid theory (SAFT) are used to establish the equation of state (EOS). The hard sphere repulsion, dispersion, chain formation, and dipole–dipole or association interactions are taken

Jiu-Fang Lu; Dong Fu; Jin-Chen Liu; Yi-Gui Li

2002-01-01

309

The effect of the sphered particles on the contraction ratio of porcelain inlay processed by the cold isostatic pressure (CIP) method was investigated. The conventional lathe-cut porcelain powder was crushed to finer particles and the secondary particles with spherical shape by adding binders of acrylic resin, wax, and polyvinyl alcohol, respectively. Porcelain powder was molded as a disc-shaped green body in a refractory model and compressed at 200 MPa by CIP. From this green compact, the sintered porcelain was obtained by only one step of firing. The porcelain discs were then used for the measurements of contraction ratio, scanning microscopic observation, biaxial flexure strength, Vickers hardness, and density. Firing contraction was decreased to about 1% in the sphered particle groups, compared with 7% of the lathe-cut porcelain powder. Although biaxial flexure strength was about 85 MPa, which is lower than the 120 MPa of the control group, and the density was significantly decreased by about 10% from the 2.4 g/cm3 of the control substance, Vickers hardness, which ranged from 531 to 537, showed no significant differences among all of the groups. The CIP method could save labor in the process of making porcelain inlays, and sphered powders could contribute significantly to a decrease in the contraction ratio in the sintering process. PMID:12861607

Konishi, Junko; Watari, Fumio; Kawamoto, Chiharu; Sano, Hidehiko

2003-08-15

310

Fabrication of Hard Glass Plates.

National Technical Information Service (NTIS)

This report describes the fabrication of hard glass for use in ballistic application. The work consisted of establishing optimum composition and process conditions for several different glasses. Properties such as Knoop hardness, density, flexural strengt...

A. Z. Hed M. A. Ali

1974-01-01

311

Microscopic models of hardness

Recent developments in the field of microscopic hardness models have been reviewed. In these models, the theoretical hardness\\u000a is described as a function of the bond density and bond strength. The bond strength may be characterized by energy gap, reference\\u000a potential, electron-holding energy or Gibbs free energy, and different expressions of bond strength may lead to different\\u000a hardness models. In

F. M. Gao; L. H. Gao

2010-01-01

312

NASA Astrophysics Data System (ADS)

Pele's tears are a well known curiosity commonly associated with low viscosity basaltic explosive eruptions. However, these pyroclasts are rarely studied in detail and there is no full explanation for their formation. These intriguing pyroclasts have smooth glassy surfaces, vesiculated interiors, and fluidal morphologies tending towards droplets and then spheres as they decrease in size to <2 mm. We present a detailed characterisation of Pele's tears from the 1959 fire-fountaining eruption of Kilauea Iki involving size and density measurements. Using thin section and SEM analysis we also consider their internal and external morphologies, porosity and bubble size distributions, and surface textures. Finally we consider the mechanisms of magma fragmentation, timescales of relaxation, and cooling rates that are responsible for their formation.

Porritt, L. A.; Quane, S.; Russell, K.

2011-12-01

313

Smooth structures on sphere bundles over spheres

In (I) R. De Sapio gave a classification of smooth structures of a p-sphere bundle over a q-sphere with one cross-section and p < q. In (2) J. Munkres also gave a classification up to concordance of differential structures in the case where the bundle has at least two cross-sections. In (3) R. Schultz gave a classification in the case

Samuel Omoloye Ajala; Akoka Yaba; West Africa

1988-01-01

314

Photon diffusion in a relativistically expanding sphere

NASA Astrophysics Data System (ADS)

A relativistically expanding sphere exists in many explosive astrophysical systems, including gammaray bursts, neutron star mergers, and some supernovae. In this paper we investigate the photon diffusion process in a relativistically expanding sphere, which is important for understanding the energetic and radiative characters of the above mentioned explosive systems. The following contents are discussed in the frame work of special relativity: random walks of photons by scattering with electrons, photospheres, photon diffusion, and the energy flux density emerging from the surface of the expanding sphere. Some of the results are also applicable to the Universe since the Universe is also a spherical expanding system.

Li, Li-Xin

2013-10-01

315

Ordering of hard particles between hard walls

NASA Astrophysics Data System (ADS)

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

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

2001-05-01

316

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

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

2009-02-01

317

Shock waves in dense hard disk fluids

NASA Astrophysics Data System (ADS)

Media composed of colliding hard disks (2D) or hard spheres (3D) serve as good approximations for the collective hydrodynamic description of gases, liquids and granular media. In the present study, the compressible hydrodynamics and shock dynamics are studied for a two-dimensional hard-disk medium at both the continuum and discrete particle level descriptions. For the continuum description, closed form analytical expressions for the inviscid hydrodynamic description, shock Hugoniot, isentropic exponent and shock jump conditions were obtained using the Helfand equation of state. The closed-form analytical solutions permitted us to gain physical insight into the role of the material's density on its compressibility, i.e. how the medium compresses under mechanical loadings and sustains wave motion. Furthermore, the predictions were found in excellent agreement with calculations using the event driven molecular dynamics method involving 30,000 particles over the entire range of compressibility spanning the dilute ideal gas and liquid phases. In all cases, it was found that the energy imparted by the piston motion to the thermalized medium behind the propagating shock was quasi-independent of the medium's packing fraction, with a correction vanishing with increasing shock Mach numbers.

Sirmas, N.; Tudorache, M.; Barahona, J.; Radulescu, M. I.

2012-05-01

318

Technology Transfer Automated Retrieval System (TEKTRAN)

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

319

NSDL National Science Digital Library

Density is a property of materials included in the National Science Education Standards Physical Science Content Standard B. It is a property by which mixtures can be separated but has much more profound applications outside the classroom such as rock formation, severe weather and living systems. But none of these concepts are fully comprehensible without a fundamental conceptual understanding of density.The resources here provide examples designed to help you facilitate student acquisition of a conceptual understanding of density.

University, Staff A.

2008-03-07

320

Free energy density functional for adsorption of fluids in nanopores.

A classical free energy density functional, which is isomorphic to a usual effective hard sphere model + mean field approximation for tail contribution, is proposed for treatment of real fluids in inhomogeneous states. In the framework of the classical density functional theory (DFT), the present functional is applied to two representative model fluids, namely, a Lennard-Jones fluid and a hard core attractive Yukawa fluid, subject to influence of various external fields. A comprehensive comparison with simulation results and a detailed analysis show that the present functional holds simultaneously all of the desirable properties inherent in an excellent functional, such as high accuracy, computational simplicity, consistency with a hard wall sum rule, nonrecourse to use of adjustable parameter(s) and weighted densities, reproduction of bulk second-order direct correlation function (DCF) in bulk limit, and applicability to subcritical fluid phenomena. PMID:20954714

Zhou, Shiqi

2010-10-18

321

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

322

NASA Astrophysics Data System (ADS)

We prove that triangulations of homology spheres in any dimension grow much slower than general triangulations. Our bound states in particular that the number of triangulations of homology spheres in 3 dimensions grows at most like the power 1/3 of the number of general triangulations.

Rivasseau, Vincent

2013-06-01

323

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…

Szekely, George

2011-01-01

324

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

325

NASA Astrophysics Data System (ADS)

We investigated the effect of a magnetic field along a hard in-plane axis Hhard on a current-induced magnetization switching (CIMS) in magnetic tunnel junctions (MTJs). Since Hhard causes the effective field to tilt away from the easy axis, we evaluated the Hhard dependence of two contributing factors in CIMS [the intrinsic critical current density (Jc0) and the thermal stability factor (E/kBT)] as functions of the tilting angle (?H). Both measurements and numerical simulations showed that the presence of Hhard can reduce Jc0 by more than the amount estimated by Slonczewski's polarization function g(?) by an order of magnitude and that E/kBT is independent of ?H. These findings suggest that the effect of Hhard mainly appears in the dynamic properties due to the nonconservative force of the spin-transfer torque based on the Slonczewski's model. A simple stability analysis demonstrated that the tilt of the magnetization direction away from the easy axis caused by the presence of Hhard induces an imbalance between the spin-transfer and damping torques and that applying a current achieves the further tilted stable state. Achievement of this stable state can be interpreted as the suppression of the effect of the effective demagnetization field (Hd*). Therefore the major reduction in Jc0 is due to the suppression of Hd* caused by the presence of Hhard.

Miura, Katsuya; Sugano, Ryoko; Ichimura, Masahiko; Hayakawa, Jun; Ikeda, Shoji; Ohno, Hideo; Maekawa, Sadamichi

2011-11-01

326

The effect of size ratio on the sphere structure factor in colloidal sphere-plate mixtures

NASA Astrophysics Data System (ADS)

Binary mixtures of colloidal particles of sufficiently different sizes or shapes tend to demix at high concentration. Already at low concentration, excluded volume interactions between the two species give rise to structuring effects. Here, a new theoretical description is proposed of the structure of colloidal sphere-plate mixtures, based on a density expansion of the work needed to insert a pair of spheres and a single sphere in a sea of them, in the presence or not of plates. The theory is first validated using computer simulations. The predictions are then compared to experimental observations using silica spheres and gibbsite platelets. Small-angle neutron scattering was used to determine the change of the structure factor of spheres on addition of platelets, under solvent contrast conditions where the platelets were invisible. Theory and experiment agreed very well for a platelet/sphere diameter ratio D/d = 2.2 and reasonably well for D/d = 5. The sphere structure factor increases at low scattering vector Q in the presence of platelets; a weak reduction of the sphere structure factor was predicted at larger Q, and for the system with D/d = 2.2 was indeed observed experimentally. At fixed particle volume fraction, an increase in diameter ratio leads to a large change in structure factor. Systems with a larger diameter ratio also phase separate at lower concentrations.

Cinacchi, G.; Doshi, N.; Prescott, S. W.; Cosgrove, T.; Grillo, I.; Lindner, P.; Phipps, J. S.; Gittins, D.; van Duijneveldt, J. S.

2012-11-01

327

NASA Astrophysics Data System (ADS)

“Rubber” coated bodies rolling over a surface satisfy a no-twist condition in addition to the no slip condition satisfied by “marble” coated bodies [1]. Rubber rolling has an interesting differential geometric appeal because the geodesic curvatures of the curves on the surfaces at corresponding points are equal. The associated distribution in the 5 dimensional configuration space has 2 3 5 growth (these distributions were first studied by Cartan; he showed that the maximal symmetries occurs for rubber rolling of spheres with 3:1 diameters ratio and materialize the exceptional group G 2). The 2 3 5 nonholonomic geometries are classified in a companion paper [2] via Cartan’s equivalence method [3]. Rubber rolling of a convex body over a sphere defines a generalized Chaplygin system [4 8] with SO(3) symmetry group, total space Q = SO(3) × S 2 and base S 2, that can be reduced to an almost Hamiltonian system in T* S 2 with a non-closed 2-form ?NH. In this paper we present some basic results on the sphere-sphere problem: a dynamically asymmetric but balanced sphere of radius b (unequal moments of inertia I j but with center of gravity at the geometric center), rubber rolling over another sphere of radius a. In this example ?NH is conformally symplectic [9]: the reduced system becomes Hamiltonian after a coordinate dependent change of time. In particular there is an invariant measure, whose density is the determinant of the reduced Legendre transform, to the power p = 1/2( b/a - 1). Using sphero-conical coordinates we verify the result by Borisov and Mamaev [10] that the system is integrable for p = -1/2 (ball over a plane). They have found another integrable case [11] corresponding to p = -3/2 (rolling ball with twice the radius of a fixed internal ball). Strikingly, a different set of sphero-conical coordinates separates the Hamiltonian in this case. No other integrable cases with different I j are known.

Koiller, J.; Ehlers, K.

2007-04-01

328

Protocol Dependence in Jammed Particulate Media: Statistics of the Density Landscape

NASA Astrophysics Data System (ADS)

The density at which hard-sphere fluids jam into amorphous solids depends strongly on the compression protocol. Extremely fast quenching protocols bring each initial point in configuration space to the closest basin-maximum on the density landscape. In contrast, slower quench protocols allow the system to relax and explore configuration space. The protocol-dependence of the density, other structural quantities, and mechanical properties depends strongly on statistical features of the landscape. In this talk, I describe calculations of the the basin volumes associated with jammed hard sphere packings, and the critical quench rate &*circ; above which the probabilities for obtaining jammed packings are determined by their basin volumes. Basin volumes are exponentially distributed; thus, for ?> &*circ;, so are jammed packing probabilities. We discuss the implications of this result on the statistical mechanics of jammed systems.

Sampangiraj, Ashwin S.

2011-03-01

329

Mass determination of silicon spheres used for the Avogadro project

Spheres made of a silicon single crystal with a mass of about 1kg are used as density standards and in the context of a project for the determination of the Avogadro constant. The status of the mass determination of such silicon spheres at the PTB is presented. Special facilities and procedures used for the mass determination in air are described.

Michael Borys; Michael Gläser; Michael Mecke

2007-01-01

330

Mesospheric density variability

Several sets of measurements of atmospheric density, temperature and winds in the mesosphere were obtained at Kwajalein Atoll, Marshall Islands, during the period 1976-1978. The measurements were made with inflatable passive spheres and accelerometer instrumented falling spheres. Comparisons of sets of measurements obtained over a period of a few hours frequently show relatively large density variability in one or more

C. R. Philbrick; E. A. Murphy; S. P. Zimmerman; E. T. Fletcher Jr.; R. O. Olsen

1980-01-01

331

Densest binary sphere packings.

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 AlB(2) (hexagonal ?), HgBr(2), and AuTe(2) structures, and to XY(n) 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. E 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 et al., Phys. Rev. Lett. 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. PMID:22463175

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

2012-02-22

332

Quantum Isometries and Noncommutative Spheres

We introduce and study two new examples of noncommutative spheres: the half-liberated sphere, and the free sphere. Together\\u000a with the usual sphere, these two spheres have the property that the corresponding quantum isometry group is “easy”, in the\\u000a representation theory sense. We present as well some general comments on the axiomatization problem, and on the “untwisted”\\u000a and “non-easy” case.

Teodor Banica; Debashish Goswami

2010-01-01

333

Hollow cylindrical fusion targets of 200--300 [mu]m diam and 500--600 [mu]m length, were fabricated and fitted at one end with a metallic ablator plate. The cylinders were then filled with a solution of polyfunctional acrylate monomer, which was subsequently polymerized to a gel using ultraviolet initiated polymerization. Either one or two aluminum spheres of diameter between 10 and 30 [mu]m were placed in the gel at defined locations, before the gel was precipitated to give, on drying by critical point dryer, a foam of the required density (about 100 mg cm[sup [minus]3]). The final targets had the sphere or spheres embedded in the foam at specified locations. Several techniques for placing the spheres were examined and the relative merits of the techniques are discussed.

Falconer, J.W.; Nazarov, W. (Department of Chemistry, University of Dundee, Dundee DD1 4HN (United Kingdom)); Horsfield, C.J.; Sutton, D.W.; Rothman, S.D.; Freeman, N.J. (Atomic Weapons Establishment PLC, Aldermaston, Reading RG7 4PR (United Kingdom))

1994-09-01

334

Statistical Properties of the Turbulent Wake Behind Hypervelocity Spheres.

National Technical Information Service (NTIS)

Autocorrelation functions and spectra of the gas density fluctuations have been obtained from microdensitometer tracings of schlieren photographs of the turbulent wakes behind hypervelocity spheres 3/8 in. in diameter traveling with a velocity of about 8 ...

W. G. Clay J. Herrmann R. E. Slattery

1965-01-01

335

NASA Astrophysics Data System (ADS)

A combined experimental and theoretical investigation of the electronic structure of the archetypal oxide heterointerface system LaAlO3 on SrTiO3 is presented. High-resolution, hard x-ray photoemission is used to uncover the occupation of Ti 3d states and the relative energetic alignment—and hence internal electric fields—within the LaAlO3 layer. First, the Ti 2p core-level spectra clearly show occupation of Ti 3d states already for two unit cells of LaAlO3. Second, the LaAlO3 core levels were seen to shift to lower binding energy as the LaAlO3 overlayer thickness, n, was increased, agreeing with the expectations from the canonical electron transfer model for the emergence of conductivity at the interface. However, not only is the energy offset of only ˜300 meV between n=2 (insulating interface) and n=6 (metallic interface) an order of magnitude smaller than the simple expectation, but it is also clearly not the sum of a series of unit-cell-by-unit-cell shifts within the LaAlO3 block. Both of these facts argue against the simple charge-transfer picture involving a cumulative shift of the LaAlO3 valence bands above the SrTiO3 conduction bands, resulting in charge transfer only for n?4. We discuss effects which could frustrate this elegant and simple charge-transfer model, concluding that although it cannot be ruled out, photodoping by the x-ray beam is unlikely to be the cause of the observed behavior. Turning to the theoretical data, our density functional simulations show that the presence of oxygen vacancies at the LaAlO3 surface at the 25% level reverses the direction of the internal field in the LaAlO3. Therefore, taking the experimental and theoretical results together, a consistent picture emerges for real-life samples in which nature does not wait until n=4 and already for n=2 mechanisms other than internal-electric-field-driven electron transfer from idealized LaAlO3 to near-interfacial states in the SrTiO3 substrate are active in heading off the incipient polarization catastrophe that drives the physics in these systems.

Slooten, E.; Zhong, Zhicheng; Molegraaf, H. J. A.; Eerkes, P. D.; de Jong, S.; Massee, F.; van Heumen, E.; Kruize, M. K.; Wenderich, S.; Kleibeuker, J. E.; Gorgoi, M.; Hilgenkamp, H.; Brinkman, A.; Huijben, M.; Rijnders, G.; Blank, D. H. A.; Koster, G.; Kelly, P. J.; Golden, M. S.

2013-02-01

336

Hard Disk Drive Manufacturing Optimization

Rapid increase in demand for high hard disk data storage density is forcing R&D centers and manufacturing companies to focus on continuous improvement of hard disk drive (HDD) performance. Current HDD records data on the magnetic disk or platter by controlling a magnetizing ferromagnetic material directionally. The data are read from the disk using a magnetic head by detecting the

Riadh Zaier; Jamil Abdo

2012-01-01

337

Conceptualizing European Public Spheres

Abstract The development,of post-national democracy,in Europe,depends,on the,development ofan overarching communicative space that functions as a public sphere, viz., a common,room,created by speakers,who,are discussing common,affairs in front of an audience. This is a place where opinions ideally are formed,and changed,according to acommunicative,mode ,or interaction. The point of departure ,is Habermas’ seminal work,on the,public sphere from 1962. The author examines,the aptness of

Erik O. Eriksen

2004-01-01

338

NASA Astrophysics Data System (ADS)

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

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

2012-09-01

339

Are Political Weblogs Public Spheres or Partisan Spheres?

In this paper we argue that political weblogs can be theoretically and pragmatically construed as public spheres, albeit with some technological and sociological limitations. Rethinking the notion of public sphere to include \\

Ravi Vatrapu; Scott Robertson; Wimal Dissanayake

340

The inverse problem for simple classical liquids: a density functional approach

A recently introduced algorithm for solving the inverse problem for simple classical fluids (i.e. the deduction of the interatomic interaction from structural data), which is based on the fundamental-measure free-energy density functional for hard spheres, is analysed in comparison with other methods. In a benchmark test for the Lennard-Jones system near the triple point, it is comparable with about ten

Yaakov Rosenfeld; Gerhard Kahlz

1997-01-01

341

Any topological framework requires the development of a theory of errors of characteristic and appropriate mathematical form. The paper develops a form of theory which appears to be appropriate to measurements of position on a sphere. The primary problems of estimation as applied to the true direction, and the precision of observations, are discussed in the subcases which arise. The

Ronald Fisher

1953-01-01

342

Electromechanical polishing of metal spheres

Equipment has been developed to electromechanically polish metal spheres. Mechanical polishing is accomplished by the action of three cup-shaped laps which rotate against the sphere. An abrasive slurry containing an electrolyte is continuously applied to the sphere and laps. Electrochemical etching is accomplished by applying a positive potential to two of the laps and a negative potential to the third.

N. E. Miller; D. E. Engelhaupt

1979-01-01

343

Electromechanical polishing of metal spheres

Equipment has been developed to electromechanically polish metal spheres. Mechanical polishing is accomplished by the action of three cup-shaped laps which rotate against the sphere. An abrasive slurry containing an electrolyte is continuously applied to the sphere and laps. Electrochemical etching is accomplished by applying a positive potential to two of the laps and a negative potential to the third.

N. E. Miller; D. E. Engelhaupt

1980-01-01

344

Electromechanical polishing of metal spheres

Equipment has been developed to electromechanically polish metal spheres. Mechanical polishing is accomplished by the action of three cup-shaped laps which rotate against the sphere. An abrasive slurry containing an electrolyte is continuously applied to the sphere and laps. Electrochemical etching is accomplished by applying a positive potential to two of the laps and a negative potential to the third.

Miller, N.E.; Engelhaupt, D.E.

1980-04-01

345

New free energy density functional and application to core-softened fluid.

A new free energy density functional is advanced for general nonhard sphere potentials characterized by a repulsive core with a singular point at zero separation. The present functional is characterized by several features. (i) It does not involve with dividing the potentials into hard-sphere-like contribution and tail contribution in sharp contrast with usual effective hard sphere model+mean field approximation for tail contribution. (ii) It has no recourse to the use of weighted density and is computationally modest; it also does not resort to an equation of state and/or an excess Helmholtz free energy of bulk fluid over a range of density as input. Consequently, all of input information can be obtained by numerical solution of a bulk Ornstein-Zernike integral equation theory (OZ IET). Correspondingly, despite the use of bulk second-order direct correlation function (DCF) as input, the functional is applicable to the subcritical region. (iii) There is no any adjustable parameter associated with the present functional, and an effective hard sphere diameter entering the functional can be determined self-consistently and analytically once the input information, i.e., the second-order DCF and pressure of the coexistence bulk fluid, are obtained by the OZ IET. The present functional is applied to a core-softened fluid subject to varying external fields, and the density distributions predicted by the present functional are more self-consistent with available simulation results than a previous third-order+second-order perturbation density functional theory. PMID:20499956

Zhou, Shiqi

2010-05-21

346

Phase behaviour of concentrated suspensions of nearly hard colloidal spheres

Suspensions of spherical colloidal particles in a liquid show a fascinating variety of phase behaviour which can mimic that of simple atomic liquids and solids. `Colloidal fluids'1-4, in which there are significant short-range correlations between the positions of neighbouring particles, and `colloidal crystals'5-7, which have long-range spatial order, have been investigated extensively. We report here a detailed study of the

P. N. Pusey; W. van Megen

1986-01-01

347

This paper takes up the systematic study of the Gottlieb groups Gn+k(Sn) of spheres for k?13 by means of the classical homotopy theory methods. We fully determine the groups Gn+k(Sn) for k?13 except for the 2-primary components in the cases: k=9,n=53;k=11,n=115. In particular, we show [?n,?n2?n+2]=0 if n=2i?7 for i?4.

Marek Golasi?ski; Juno Mukai

2008-01-01

348

H2, O2, NH3 and CH4 in situ post-etching treatments (PET) have been investigated as a solution to prevent the residues formation (TiFx based) on TiN metallic hard mask (MHM) after etching in fluorocarbon based plasmas. The PET impact on the residues growth reduction on the mask and on the porous SiOCH modification is presented and discussed. The compatibility of the

N. Posseme; R. Bouyssou; T. Chevolleau; T. David; V. Arnal; S. Chhun; C. Monget; E. Richard; D. Galpin; J. Guillan; L. Arnaud; D. Roy; M. Guillermet; J. Ramard; O. Joubert; C. Verove

2009-01-01

349

Invasive species often influence existing biocenoses by altering their environment or facilitating the ecology of other species.\\u000a Here we combined stable isotope analysis with quantitative benthic community sampling to investigate temporal variation in\\u000a the influence of biodeposition of organic material (biodeposits) by the zebra mussel (Dreissena polymorpha) on the benthic food web in hard substrate habitats of Lake Constance, Germany.

René Gergs; Jonathan Grey; Karl-Otto Rothhaupt

350

Study of the Unequal Spheres Packing Problem:

NASA Astrophysics Data System (ADS)

We employ the Monte Carlo method to study a constrained optimization problem — packing hard spheres with unequal radii (r2 > r1) into a 3D bounded region and discuss its connection with the Gamma Knife radiosurgery treatment planning. Selection of the best fit solution is based on the Boltzmann factor, e-?E/T, which allows us to search for the global optimal solution. As an illustration we determined the least number (?15) of packed spheres that will occupy the largest volume for three different hypothetical tumor sizes (4115, 10 000 and 36 000 voxels). For the bounded regions and the sizes of the packed spheres that we studied here, the optimal volume packing ratio ranges from 41.3 to 48.7%. From our study, using a lower r2/r1 ratio is more desirable due to the ?15 radiation shots constraint. The optimal volume packing ratio can be obtained within a relative short CPU computing time and could provide a good starting point for the radiosurgery treatment planning.

Li, S. P.; Ng, Ka-Lok

351

Density fluctuations and entropy

A functional for the entropy that is asymptotically correct both in the high- and low-density limits is proposed. The new form is S=S{sup (id)}+S{sup (ln)}+S{sup (r)}+S{sup (c)}, where the term S{sup (c)} depends on the p-body density fluctuations {alpha}{sub p} and has the form S{sup (c)}/k=

Hernando, J. A.; Blum, L.

2000-11-01

352

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

353

A simple weighted-density-functional approach to the structure of inhomogeneous fluids

NASA Astrophysics Data System (ADS)

A simple weighted-density-functional approach is developed for inhomogeneous fluids by approximating the excess free energy density functional by that of the corresponding uniform system evaluated at an effective density. This effective weighted density is obtained by a suitable local averaging procedure of the actual density distribution using a weight function which is evaluated only once at the bulk density, thus being decoupled from the weighted density. This approach does not involve any power series expansion or solution of any nonlinear differential equation at every point and each iteration, as is required in some of the analogous schemes. The new theory is applied to predict the structure of simple classical fluids, interacting with hard sphere, Coulombic as well as Yukawa potentials, under confinement in several geometries. The calculated results on the density profiles are shown to compare quite well with available simulation data.

Patra, Chandra N.; Ghosh, Swapan K.

2002-05-01

354

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

355

Molecular dynamics simulations have been used to compute physical properties of model fluids in which the particles interacted via the soft-sphere pair potential (SSP) phi(r)=epsilon(sigma/r)(n), where epsilon and sigma are the characteristic energy and distance, respectively. The emphasis is on small values of n, tending to the lower theromodynamically allowed bound of 3+. An accurate equation of state for the SSP fluid is obtained, consisting of two terms, and as n-->3+, the compressibility factor, Z tends to Z=B(2)zeta(n/3) for zeta>0, where B(2) is the second virial coefficient, and zeta=piNsigma(3)/6V is a nominal packing fraction for N particles in volume V. A simple formula for the position of the first peak in the radial distribution function in the soft particle limit is proposed and shown to agree with the simulation data. The fluid phase velocity autocorrelation function at fluid-solid coexistence becomes more oscillatory as n decreases. Values for the self-diffusion coefficient D and shear viscosity eta were calculated as a function of n and density, and these were used to estimate the n-dependence of an ideal glass transition. The glass transition shifts relatively further into the solid part of the phase diagram as softness ( approximately 1/n) increases. D decreases by ca. 75% and eta increases by about a factor of 3 along the fluid-solid coexistence line from n=infinity to 3.25. Non-Gaussian behavior was calculated from the particle displacements as a function of particle softness. A screened soft-sphere potential, SSSP, was introduced to explore the effects for small n of the long range part of the potential in relation to the scale of the local structure. The SSSP with suitable analytic form and parameters can give statistically indistinguishable results from the full SSP for the static properties, D and eta. PMID:19947693

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

2009-11-28

356

Manipulating spheres that sink: assembly of micrometer sized glass spheres for optical coupling.

Previous work (Tull, E. J.; Bartlett, P. N.; Ryan, K. R. Langmuir 2007, 14, 7859; Tull, E. J.; Bartlett, P. N. Colloids Surf., A 2008, 327, 71) has demonstrated that, since convective forces have little influence over spheres in unstable sols, many conventional assembly techniques are ineffective for the organization of glassy spheres > or =5 microm in diameter into sparse patterns of interest for optoelectronic device applications. Carefully designed bifunctional substrates are required for both planar and "in cavity" assembly. In the present work, novel selective chemical modification of structured Ta2O5/glass substrates has been used to generate surfaces tailored to the assembly of glass microspheres from aqueous solution. Uniform arrays of 40-60 microm diameter glass spheres have been produced in pits of half-diameter depth, demonstrating the suitability of this technique for fabricating optical devices where light is coupled from a waveguide into the equator of a sphere. Individual aspects of the assembly process have been examined, and their influence over defect densities and the positioning of the assembled spheres is discussed. PMID:19125652

Tull, Elizabeth J; Bartlett, Philip N; Murugan, G Senthil; Wilkinson, James S

2009-02-01

357

Random packing of spheres in Menger sponge

NASA Astrophysics Data System (ADS)

Random packing of spheres inside fractal collectors of dimension 2 < d < 3 is studied numerically using Random Sequential Adsorption (RSA) algorithm. The paper focuses mainly on the measurement of random packing saturation limit. Additionally, scaling properties of density autocorrelations in the obtained packing are analyzed. The RSA kinetics coefficients are also measured. Obtained results allow to test phenomenological relation between random packing saturation density and collector dimension. Additionally, performed simulations together with previously obtained results confirm that, in general, the known dimensional relations are obeyed by systems having non-integer dimension, at least for d < 3.

Cie?la, Micha?; Barbasz, Jakub

2013-06-01

358

Fluid-solid transition in hard hypersphere systems

NASA Astrophysics Data System (ADS)

In this work we present a numerical study, based on molecular dynamics simulations, to estimate the freezing point of hard spheres and hypersphere systems in dimension D = 4, 5, 6, and 7. We have studied the changes of the radial distribution function (RDF) as a function of density in the coexistence region. We started our simulations from crystalline states with densities above the melting point, and moved down to densities in the liquid state below the freezing point. For all the examined dimensions (including D = 3), it was observed that the height of the first minimum of the RDF changes in an almost continuous way around the freezing density and resembles a second order phase transition. With these results we propose a numerical method to estimate the freezing point as a function of the dimension D using numerical fits and semiempirical approaches. We find that the estimated values of the freezing point are very close to the previously reported values from simulations and theoretical approaches up to D = 6, reinforcing the validity of the proposed method. This was also applied to numerical simulations for D = 7 giving new estimations of the freezing point for this dimensionality.

Estrada, C. D.; Robles, M.

2011-01-01

359

The relative Stokes vectors at the detector exit port of a sandblasted and gold-plated integrating sphere are determined for four different polarizations incident on five unique surfaces. The results indicate in all cases that the integrating sphere is a depolarizer. These results validate assumptions used in hard-target calibration methodology for infrared lidars. PMID:20856533

Haner, D A; Menzies, R T

1993-11-20

360

Dynamics in Cu46Zr42Al7Y5 melts: Interplay between packing density and viscosity

NASA Astrophysics Data System (ADS)

We have investigated microscopic dynamics in the bulk glass-forming Cu46Zr42Al7Y5 melts using quasielastic neutron scattering (QENS). Self-correlation functions show a fast ? and a slow ?-relaxation process. ? relaxation exhibits stretching and is independent of momentum transfer and temperature. The melt is characterized by low packing density and high viscosity. The dynamics observed and the critical packing density derived from the QENS data are in good agreement with mode-coupling theory predictions for hard-sphere liquids. However, we can show that viscosity dominates over packing density in determining the atomic dynamics and glass-forming ability of the metallic melt.

Chathoth, S. M.; Damaschke, B.; Embs, J. P.; Samwer, K.

2009-05-01

361

NASA Astrophysics Data System (ADS)

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

2009-07-01

362

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

363

NASA Astrophysics Data System (ADS)

I give some scalar field theory calculations on a d-dimensional lune of arbitrary angle, evaluating, numerically, the effective action which is expressed as a simple quadrature, for conformal coupling. Using this, the entanglement and Rényi entropies are computed. Massive fields are also considered and a renormalization to make the (one-loop) effective action vanish for infinite mass is suggested and used, not entirely successfully. However a universal coefficient is derived from the large mass expansion. From the deformation of the corresponding lune result, I conjecture that the effective action on all odd manifolds with a simple conical singularity has an extremum when the singularity disappears. For the round sphere, I show how to convert the quadrature form of the conformal Laplacian determinant into the more usual sum of Riemann ?-functions (and log?2).

Dowker, J. S.

2013-06-01

364

The Minimum Covering Sphere Problem

The minimum covering sphere problem, with applications in location theory, is that of finding the sphere of smallest radius which encloses a set of points in E^{n<\\/sup>. For a finite set of points, it is shown that the Wolfe dual is equivalent to a particular quadratic programming problem and that converse duality holds. A finite decomposition algorithm, based on the}

D. Jack Elzinga; Donald W. Hearn

1972-01-01

365

Magnetic hollow spheres of low density were prepared by plating Fe3O4 magnetic films on hollow glass spheres using ferrite plating. The complex permeability and permittivity of spheres–wax composites were measured in the range of 2–18GHz. The complex permeability and permittivity increased, and the dielectric and magnetic losses were improved as the volume fraction of the magnetic spheres in the composites

Jing Wei; Jianhua Liu; Songmei Li

2007-01-01

366

On the most general accurate solutions for Buchdahl's fluid spheres

NASA Astrophysics Data System (ADS)

The most general accurate solutions for the Buchdhal fluid sphere were obtained and matched with the Schwarzchild's exterior solution at the pressure free interface. Various parameters of the solutions were so adjusted that the energy density, pressure and temperature were positive and decreasing away from the centre, and the velocity of sound was less than unity throughout the spheroid model. Using this procedure, the maximum mass of the fluid sphere with a surface density of 2 × 1014gm cm-3 was determined to be 3.82M? and 4.57 M? for strong and weak energy conditions respectively. PACS number: 0402, 0402J, 0440D, 95301

Gupta, Y. K.; Jasim, M. K.

367

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

368

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

369

Nematic ordering and defects on the surface of a sphere: A Monte Carlo simulation study

NASA Astrophysics Data System (ADS)

We examine the ordering of hard rods on the surface of a sphere using computer simulations. As predicted by previous theories of thin nematic shells we observe four s=+1/2 defects. However, the predicted tetrahedral symmetry for the defects and the ``baseball'' director configuration is not observed. Instead the four defects are located, on average, on a great circle which splits the sphere into two hemispheres, each of which has a splay dominated director configuration. We argue that this result occurs as the bend elastic constant for hard rods is much larger than the splay elastic constant.

Bates, Martin A.

2008-03-01

370

Oxide Layer Mass Determination at the Silicon Sphere of the Avogadro Project

Within the International Avogadro Project, two spheres of highly enriched 28Si crystals have been produced to perform new determination of Avogadro constant NA. The mass of the oxide layer of the spheres has to be measured as one of the critical tasks. For this purpose, a method consisting of precise thickness measurements and density determinations is proposed and tested. Part

Ingo Busch; Hans-Ulrich Danzebrink; Michael Krumrey; Michael Borys; Horst Bettin

2009-01-01

371

NASA Astrophysics Data System (ADS)

We present an extension of our recently introduced molecular density functional theory of water [G. Jeanmairet et al., J. Phys. Chem. Lett. 4, 619 (2013)] to the solvation of hydrophobic solutes of various sizes, going from angstroms to nanometers. The theory is based on the quadratic expansion of the excess free energy in terms of two classical density fields: the particle density and the multipolar polarization density. Its implementation requires as input a molecular model of water and three measurable bulk properties, namely, the structure factor and the k-dependent longitudinal and transverse dielectric susceptibilities. The fine three-dimensional water structure around small hydrophobic molecules is found to be well reproduced. In contrast, the computed solvation free-energies appear overestimated and do not exhibit the correct qualitative behavior when the hydrophobic solute is grown in size. These shortcomings are corrected, in the spirit of the Lum-Chandler-Weeks theory, by complementing the functional with a truncated hard-sphere functional acting beyond quadratic order in density, and making the resulting functional compatible with the Van-der-Waals theory of liquid-vapor coexistence at long range. Compared to available molecular simulations, the approach yields reasonable solvation structure and free energy of hard or soft spheres of increasing size, with a correct qualitative transition from a volume-driven to a surface-driven regime at the nanometer scale.

Jeanmairet, Guillaume; Levesque, Maximilien; Borgis, Daniel

2013-10-01

372

We present an extension of our recently introduced molecular density functional theory of water [G. Jeanmairet et al., J. Phys. Chem. Lett. 4, 619 (2013)] to the solvation of hydrophobic solutes of various sizes, going from angstroms to nanometers. The theory is based on the quadratic expansion of the excess free energy in terms of two classical density fields: the particle density and the multipolar polarization density. Its implementation requires as input a molecular model of water and three measurable bulk properties, namely, the structure factor and the k-dependent longitudinal and transverse dielectric susceptibilities. The fine three-dimensional water structure around small hydrophobic molecules is found to be well reproduced. In contrast, the computed solvation free-energies appear overestimated and do not exhibit the correct qualitative behavior when the hydrophobic solute is grown in size. These shortcomings are corrected, in the spirit of the Lum-Chandler-Weeks theory, by complementing the functional with a truncated hard-sphere functional acting beyond quadratic order in density, and making the resulting functional compatible with the Van-der-Waals theory of liquid-vapor coexistence at long range. Compared to available molecular simulations, the approach yields reasonable solvation structure and free energy of hard or soft spheres of increasing size, with a correct qualitative transition from a volume-driven to a surface-driven regime at the nanometer scale. PMID:24160494

Jeanmairet, Guillaume; Levesque, Maximilien; Borgis, Daniel

2013-10-21

373

After Hard Drives—What Comes Next?

There are numerous emerging nonvolatile memory technologies, which have been proposed as being capable of replacing hard disk drives (HDDs). In this paper, the prospects for these alternative technologies to displace HDDs in 2020 are analyzed. In order to compare technologies, projections were made of storage density and performance in year 2020 for both hard disks and the alternative technologies,

Mark H. Kryder; Chang Soo Kim

2009-01-01

374

Charged fluid sphere in bimetric general theory of relativity

Static and spherical symmetric solutions of the field equations in the bimetric general theory of gravitation are obtained for perfect and anisotropic charged fluids under the assumption that the physical metric admits a one-parameter group of conformal motion. All solutions are matched to the Reissner-Nordstrom metric and possess positive energy density larger than the stresses, everywhere within the sphere. The

S. P. Kandalkar; S. P. Gawande

2010-01-01

375

Magnetization of small iron-nickel spheres

Magnetic properties of small iron-nickel alloy spheres, having compositions which cover the entire Fe-Ni binary, are presented. The spheres were produced by melting fine wires of appropriate compositions and allowing surface tension forces to form spheres from molten droplets of alloy during initial free fall. Solidification took place before the spheres dropped to the base plate. Continued cooling took place

Peter Wasilewski

1981-01-01

376

Building materials with colloidal spheres

NASA Astrophysics Data System (ADS)

Three-dimensionally ordered composite materials with micrometer-scale periodic features can diffract visible light and, under certain conditions, can act as photonic band gap materials---the optical analogues of electronic semiconductors. Conventional methods for fabricating electronic materials are unsuitable for preparing three-dimensionally ordered structures, but colloidal self-assembly is a promising alternative approach. Monodisperse colloidal spheres are readily synthesized in the micrometer or sub-micrometer size range. The challenge in building materials from these particles lies in organizing the spheres and tailoring the material properties of the resulting composite structure. In the first part of this dissertation, I describe how packings of colloidal spheres can be used as templates to prepare structures that strongly diffract light. The densest arrangement of spheres in three dimensions is the face-centered cubic (FCC) packing, and a suspension of monodisperse colloidal spheres can form an FCC arrangement when concentrated. We use FCC packings of liquid emulsion droplets as templates to produce ordered porous titanium dioxide gels, which have high refractive index contrast and show broad minima in the transmission spectra at visible wavelengths. The emulsion templating method allows us to produce large monolithic porous samples that might be used in a variety of applications. However, we find that ordered templates with different symmetry than the FCC packing are necessary to prepare materials with photonic band gaps. In the second part of the dissertation I discuss how we might coax spherical particles to form crystal structures that differ from the FCC packing. Although the FCC arrangement is the only ordered packing observed in systems of many individual spheres, packings with different symmetries are possible in few-sphere systems. We find that when n colloidal microspheres are attached to the surfaces of liquid emulsion droplets, removing fluid from the droplets leads to packings of spheres that are unique and consistent at each n. These finite sphere packings, which range from sphere doublets, triangles, and tetrahedra to exotic polyhedra, might be used as new types of colloidal building blocks to prepare bulk materials with non-FCC symmetry.

Manoharan, Vinothan N.

377

Local hardness equalization: Exploiting the ambiguity

NASA Astrophysics Data System (ADS)

In the density-functional theory of chemical reactivity, the local hardness is known to be an ambiguous concept. The mathematical structure associated with this problematic situation is elaborated and three common definitions for the local hardness are critically examined: the frontier local hardness [S. K. Ghosh, Chem. Phys. Lett. 172, 77 (1990)], the total local hardness [S. K. Ghosh and M. Berkowitz, J. Chem. Phys. 83, 2976 (1985)], and the unconstrained local hardness [P. W. Ayers and R. G. Parr, J. Am. Chem. Soc. 122, 2010 (2000)]. The frontier local hardness has particularly nice properties: (a) it has smaller norm than most, if not all, other choices of the local hardness and (b) it is ``unbiased'' in an information-theoretic sense. For the ground electronic state of a molecular system, the frontier local hardness is equal to the global hardness. For an electronic system in its ground state, both the chemical potential and the frontier local hardness are equalized. The frontier local hardness equalization principle provides a computational approach for designing reagents with desirable chemical reactivity profiles.

Ayers, Paul W.; Parr, Robert G.

2008-05-01

378

The fluid density distribution within microscopic pores is determined by solving integral equations relating to the local chemical potential to the Van der Waals attractions and hard sphere repulsions of surrounding material. To avoid resolving the density distribution on sub-molecular scales, the governing equations are averaged over zones of molecular size using analytic functions to represent local density variations within each zone. These local density profiles range form singularities to uniform distributions depending on the local variation of the potential field. Sample calculations indicate that this integral approach yields results in very good agreement with those based on traditional density functional theory (DFT), while reducing computing times by factors of 10{sup 3} to 10{sup 4} for one- dimensional geometries.

Nilson, R.H.; Griffiths, S.K. [Sandia National Labs., Livermore, CA (United States)

1997-02-01

379

LETTER TO THE EDITOR: Dimensional crossover and the freezing transition in density functional theory

A modified geometrically based free-energy functional for hard spheres is proposed which gives reliable results even for situations of extreme confinements that reduce the effective dimensionality D. It is accurate for hard spheres between narrow plates (D = 2), inside narrow cylindrical pores (D = 1), and is exact in the 0D limit (a cavity that cannot hold more than

Y. Rosenfeld; M. Schmidt; H. Löwen; P. Tarazona

1996-01-01

380

On the density dependence of the self-diffusion coefficient of interacting Brownian particles

NASA Astrophysics Data System (ADS)

A brief summary is given of our theoretical approach to the statistical description of interacting Brownian particles. For the discussion of particle transport processes on the Smoluchowski level a hierarchy of coupled diffusion-like equations in configuration space for the reduced particle density functions and the corresponding particle flows is derived. Non-equilibrium processes are taken into account by means of linear perturbation theory. Applying the direct correlation force formalism, the hierarchy is cut off by replacing the three-particle density function nabc(r1, r2, r3, t). Here closure relations between the direct correlation force and nab(r1, r2, t) have to be added. Specializing the brownons to hard spheres and neglecting the hydrodynamic interaction, the two-particle density function is evaluated from the well-known equilibrium PY approximation and (as a first step) from the low-density limit of the non-equilibrium closure. Using a linear response theory of particle transport, the self-diffusion coefficient in a one-component hard sphere system of Brownian particles is calculated through a formal non-equilibrium picture based on tracer diffusion.

Sonnenburg, Jörn; Kremp, Dietrich; Sändig, Rainer

381

Phase behavior of hard colloidal platelets using free energy calculations.

We investigate the phase behavior of a model for colloidal hard platelets and rigid discotic molecules: oblate hard spherocylinders (OHSC). We perform free energy calculations using Monte Carlo simulations to map out the phase diagram as a function of the aspect ratio L?D of the particles. The phase diagram displays a stable isotropic phase, a nematic liquid crystal phase for L?D?0.12, a columnar phase for L?D?0.3, a tilted crystal phase for L?0.45, and an aligned crystal phase for L?D?0.45. We compare the results to the known phase diagram of hard cut spheres. Thin cut spheres are almost cylinder-shaped, while the interactions between real discotic mesogens and colloidal platelets are more consistent with the toroidal rims of the OHSC. Since the shapes of the OHSC and the cut spheres are otherwise similar, the phase diagrams of the two types of particles are quite akin. However, the tilted crystal phase for OHSC, which is of a crystal type that is frequently found in experiments on disklike molecules, has not been found for hard cut spheres. Furthermore, although we have found a cubatic phase, it was shown to be definitely unstable, whereas the stability of the cubatic phase of cut spheres is still disputed. Finally, we also show that the phase boundaries differ significantly from those for cut spheres. These are remarkable consequences of a subtle change in particle shape, which show that for a detailed comparison with the phase behavior of experimental particles, the OHSC should be used as a model particle. PMID:21384979

Marechal, Matthieu; Cuetos, Alejandro; Martínez-Haya, Bruno; Dijkstra, Marjolein

2011-03-01

382

Free and pendular-like rotation: Orientational dynamics in hard ellipsoid fluids

Rotational motions in molecular fluids may exhibit a coherence arising from collision-free propagation or from highly correlated collisions. Information on both of these behaviors are derived from the analysis of orientational and angular momentum relaxation. In the present study, the rotating body is taken to be a hard ellipsoid, immersed in a hard sphere fluid, and its dynamics are analyzed

Shuang Tang; Glenn T. Evans

1995-01-01

383

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

384

Zinc coordination spheres in protein structures.

Zinc metalloproteins are one of the most abundant and structurally diverse proteins in nature. In these proteins, the Zn(II) ion possesses a multifunctional role as it stabilizes the fold of small zinc fingers, catalyzes essential reactions in enzymes of all six classes, or assists in the formation of biological oligomers. Previously, a number of database surveys have been conducted on zinc proteins to gain broader insights into their rich coordination chemistry. However, many of these surveys suffer from severe flaws and misinterpretations or are otherwise limited. To provide a more comprehensive, up-to-date picture on zinc coordination environments in proteins, zinc containing protein structures deposited in the Protein Data Bank (PDB) were analyzed in detail. A statistical analysis in terms of zinc coordinating amino acids, metal-to-ligand bond lengths, coordination number, and structural classification was performed, revealing coordination spheres from classical tetrahedral cysteine/histidine binding sites to more complex binuclear sites with carboxylated lysine residues. According to the results, coordination spheres of hundreds of crystal structures in the PDB could be misinterpreted due to symmetry-related molecules or missing electron densities for ligands. The analysis also revealed increasing average metal-to-ligand bond length as a function of crystallographic resolution, which should be taken into account when interrogating metal ion binding sites. Moreover, one-third of the zinc ions present in crystal structures are artifacts, merely aiding crystal formation and packing with no biological significance. Our analysis provides solid evidence that a minimal stable zinc coordination sphere is made up by four ligands and adopts a tetrahedral coordination geometry. PMID:24059258

Laitaoja, Mikko; Valjakka, Jarkko; Jänis, Janne

2013-09-23

385

Spontaneous Orbiting of Two Spheres Levitated in a Vibrated Liquid

NASA Astrophysics Data System (ADS)

In the absence of gravity, particles can form a suspension in a liquid irrespective of the difference in density between the solid and the liquid. If such a suspension is subjected to vibration, there is relative motion between the particles and the fluid which can lead to self-organization and pattern formation. Here, we describe experiments carried out to investigate the behavior of two identical spheres suspended magnetically in a fluid, mimicking weightless conditions. Under vibration, the spheres mutually attract and, for sufficiently large vibration amplitudes, the spheres are observed to spontaneously orbit each other. The collapse of the experimental data onto a single curve indicates that the instability occurs at a critical value of the streaming Reynolds number. Simulations reproduce the observed behavior qualitatively and quantitatively, and are used to identify the features of the flow that are responsible for this instability.

Pacheco-Martinez, H. A.; Liao, L.; Hill, R. J. A.; Swift, Michael R.; Bowley, R. M.

2013-04-01

386

Instrumentation for Air Density Measurements.

National Technical Information Service (NTIS)

This report details an operational system for measuring air density at altitudes above those investigated by instrumented balloons and below those investigated by orbiting satellites. The system described is a 7-inch, rigid, falling sphere which is ejecte...

C. D. Westlund O. C. Haycock R. L. Smith G. D. Allred

1967-01-01

387

Sphere Juggler: Fast Context Retrieval in Support of Working Spheres

Information workers typically demand the aggregation of multiple information resources related to their activities such as documents, contacts, and emails. Current mechanisms for aggregation of resources lack enough flexibility to collect different kinds of information and offer no support to facilitate their prompt retrieval. This work presents Sphere Juggler, a system that integrates seamlessly with the popular Microsoft Windows interface

Rodrigo Morteo; Víctor M. González; Jesús Favela; Gloria Mark

2004-01-01

388

Exact solution for a static charged gas sphere in general relativity

The problem of finding exact solutions of the Einstein-Maxwell equations for static distributions of a charged sphere has attracted wide attention. A general solution of the Einstein-Maxwell field equations has been obtained for a static charged gas sphere having maximum matter density at the center. The density decreases along the radius and finally becomes zero at the surface of the sphere. Although this research is a modification of the author's earlier work, it provides scientists with a tool for further progress. 13 refs.

Mehra, A.L.; Gokhroo, M.K. (Government College, Ajmer (India))

1993-04-01

389

NASA Astrophysics Data System (ADS)

We present an experimental study of short-time diffusion properties in fluidlike suspensions of monodisperse charge-stabilized silica spheres suspended in dimethylformamide. The static structure factor S(q), the short-time diffusion function D(q), and the hydrodynamic function H(q) have been probed by combining x-ray photon correlation spectroscopy experiments with static small-angle x-ray scattering. Our experiments cover the full liquid-state part of the phase diagram, including de-ionized systems right at the liquid-solid phase boundary. We show that the dynamic data can be consistently described by the renormalized density fluctuation expansion theory of Beenakker and Mazur over a wide range of concentrations and ionic strengths. In accordance with this theory and Stokesian dynamics computer simulations, the measured short-time properties cross over monotonically, with increasing salt content, from the bounding values of salt-free suspensions to those of neutral hard spheres. Moreover, we discuss an upper bound for the hydrodynamic function peak height of fluid systems based on the Hansen-Verlet freezing criterion.

Gapinski, J.; Patkowski, A.; Banchio, A. J.; Buitenhuis, J.; Holmqvist, P.; Lettinga, M. P.; Meier, G.; Nägele, G.

2009-02-01

390

Scaling and aging in the homogeneous cooling state of a granular fluid of hard particles

NASA Astrophysics Data System (ADS)

The presence of the aging phenomenon in the homogeneous cooling state (HCS) of a granular fluid composed of inelastic hard spheres or disks is investigated. As a consequence of the scaling property of the N-particle distribution function, it is obtained that the decay of the normalized two-time correlation functions slows down as the time elapsed since the beginning of the measurement increases. This result is confirmed by molecular dynamics simulations for the particular case of the total energy of the system. The agreement is also quantitative in the low density limit, for which an explicit analytical form of the time correlation function has been derived. Moreover, the reported results provide support for the existence of the HCS as a solution of the N-particle Liouville equation.

Brey, J. J.; Prados, A.; García de Soria, M. I.; Maynar, P.

2007-11-01

391

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

392

Water entry of spinning spheres

The complex hydrodynamics of water entry by a spinning sphere are investigated experimentally for low Froude numbers. Standard billiard balls are shot down at the free surface with controlled spin around one horizontal axis. High-speed digital video sequences reveal unique hydrodynamic phenomena which vary with spin rate and impact velocity. As anticipated, the spinning motion induces a lift force on

TADD T. T RUSCOTT; ALEXANDRA H. T ECHET

2009-01-01

393

Magnetohydrodynamic flow around a sphere

The flow of an incompressible, viscous, electrically conducting fluid past a sphere in an aligned magnetic field is investigated using the finite difference method for Re 100 and 200 and interaction parameter N in the range 0 <= N <= 10 (or 0 <= M <= 100), where M is the Hartmann number defined by M = (2N Re)1\\/2. The

T. V. S. Sekhar; R. Sivakumar; T. V. R. Ravi Kumar

2005-01-01

394

Science off the Sphere: Bistronauts

International Space Station Expedition 30 astronaut Don Pettit demonstrates physics in space for 'Science off the Sphere.' Through a partnership between NASA and the American Physical Society you can participate in Pettit's physics challenge and view future experiments here: http://www.physicscentral.com/sots

Gerald T Wright

2012-02-24

395

What is the longest rope on the unit sphere? Intuition tells us that the answer to this packing problem depends on the rope's thickness. For a countably infinite number of prescribed thickness values we construct and classify all solution curves. The simplest ones are similar to the seamlines of a tennis ball, others exhibit a striking resemblance to Turing patterns

Henryk Gerlach; Heiko von der Mosel

2010-01-01

396

Dipole Excited Unidirectionally Conducting Sphere.

National Technical Information Service (NTIS)

The problem of frequency independent antennas has aroused the interest of many authors in recent years. In this work an attempt is made to solve the problem of a unidirectionally conducting sphere excited by a radial point source. As it is well known, a u...

A. Ishimaru M. A. Gonzalez

1964-01-01

397

NSDL National Science Digital Library

A giant 6-foot diameter sphere uses projectors and computers to display scientific research of our globe. This site contains beautiful and informative videos of hundreds of datasets that have been displayed using the SOS system. Datasets include atmosphere, land, ocean, models, astronomy, and more.

398

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

399

Complex horospherical transform on real sphere

We define a new integral transform on the real sphere which is invariant relative to the orthogonal group and similar to the horospherical Radon transform for the hyperbolic space. This transform involves complex geometry associated with the sphere.

Simon Gindikin; To Francois Treves

2005-01-01

400

Tessellating the Sphere with Regular Polygons

ERIC Educational Resources Information Center

Tessellations in the Euclidean plane and regular polygons that tessellate the sphere are reviewed. The regular polygons that can possibly tesellate the sphere are spherical triangles, squares and pentagons.

Soto-Johnson, Hortensia; Bechthold, Dawn

2004-01-01

401

Jammed Ellipsoids Beat Jammed Spheres

We have performed experiments and computer simulations on random packings of ellipsoids. The experiments on M^textregistered Milk Chocolate candies (spheroids with aspect ratio ˜ 1.91:1) indicate a packing fraction 0.68-0.7 considerably higher than that for random sphere packings (0.64). Moreover the number of contacting neighbors is measured as Z ˜ 9.8, close to the isostatic result of twice the number

Paul Chaikin; Aleksandar Donev; Weining Man; Ibrahim Cisse; Frank Stillinger; Salvatore Torquato

2004-01-01

402

We study the geometry of orientifolds in the SU(2)k WZW model. They correspond to the two inequivalent, orientation-reversing involutions of S3, whose fixed-point sets are: the north and south poles (Script O0), or the equator two-sphere (Script O2). We show how the geometric action of these involutions leads unambiguously to the previously obtained algebraic results for the Klein bottle and

Constantin Bachas; Nicolas Couchoud; Paul Windey

2001-01-01

403

Magnetohydrodynamic flow around a sphere

The flow of an incompressible, viscous, electrically conducting fluid past a sphere in an aligned magnetic field is investigated using the finite difference method for Re 100 and 200 and interaction parameter N in the range 0?N?10 (or 0?M?100), where M is the Hartmann number defined by M=2NRe. The length of the recirculation bubble in the flow reduces monotonically with

T. V. S. Sekhar; R. Sivakumar; T. V. R. Ravi Kumar

2005-01-01

404

Poisson wavelets on the sphere

NASA Astrophysics Data System (ADS)

In this paper we summarize the basic formulas of wavelet analysis with the help of Poisson wavelets on the sphere. These wavelets have the nice property that all basic formulas of wavelet analysis as reproducing kernels, etc. may be expressed simply with the help of higher degree Poisson wavelets. This makes them numerically attractive for applications in geophysical modeling. We do not give any proofs and we refer to "M. Holschneider, I. Iglewska-Nowak, JFAA, 2007", where all proofs are published.

Holschneider, M.

2007-10-01

405

Black hole formation in fuzzy sphere collapse

NASA Astrophysics Data System (ADS)

We study the collapse of a fuzzy sphere, that is a spherical membrane built out of D0-branes, in the Banks-Fischler-Shenker-Susskind model. At weak coupling, as the sphere shrinks, open strings are produced. If the initial radius is large then open string production is not important and the sphere behaves classically. At intermediate initial radius the backreaction from open string production is important but the fuzzy sphere retains its identity. At small initial radius the sphere collapses to form a black hole. The crossover between the later two regimes is smooth and occurs at the correspondence point of Horowitz and Polchinski.

Iizuka, Norihiro; Kabat, Daniel; Roy, Shubho; Sarkar, Debajyoti

2013-08-01

406

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

NASA Astrophysics Data System (ADS)

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.; Donnelly, T. D.; Ditmire, T.

2007-01-01

407

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

408

On the quality of the hardness kernel and the Fukui function to evaluate the global hardness.

An approximated hardness kernel, which includes the second derivative with respect to the density of the kinetic energy, the electron-electron coulomb repulsion, and the exchange density functionals, has been tested for the calculation of the global hardness. The results obtained for a series of 40 cations and neutral systems and 16 anions represent in most cases an improvement of the results obtained using the HOMO-LUMO gap approach and indicate the viability of this approach to evaluate global hardness. In addition, the relevance of the Fukui function approximation and the role of the three components of the hardness kernel in the evaluation of the global hardness have been analyzed. PMID:17186480

Torrent-Sucarrat, Miquel; Salvador, Pedro; Geerlings, Paul; Solà, Miquel

2007-01-30

409

Jammed Ellipsoids Beat Jammed Spheres: Experiments with Candies and Colloids

Packing problems, how densely objects can fill a volume, are among the most ancient and persistent problems in mathematics and science. For equal spheres, it has only recently been proved that the face-centered cubic lattice has the highest possible packing fraction phi˜ 0.74. It is also well-known that the corresponding random (amorphous) jammed packings have phi˜0.64. The density of packings

Paul Chaikin

2005-01-01

410

Dynamics and wake patterns of freely rising and falling spheres at Re = 500

NASA Astrophysics Data System (ADS)

We study the dynamics of spheres rising or falling freely at Re = 500. All falling spheres, whose mass ratio (or relative density) m*, exceeds 1, descended rectilinearly. For rising spheres, there exists a critical value of the mass ratio below which the sphere undergoes large-amplitude oscillations, m*crit = 0.36. This motion occurs in a vertical plane; no helical trajectories are observed. Initial wake visualizations showed that rather than the two alternately signed vortex loops found in the flow past stationary spheres, the wake of a vibrating freely rising sphere comprised four vortex structures per cycle of oscillation. However, due to the small size and high oscillation frequency of the freely rising spheres, the exact nature and formation of these structures remained unclear. Further studies were performed in a towing tank, prescribing the motion of the sphere based on the measured displacement of the rising spheres. We are able to use much larger, slower-moving bodies while matching the Reynolds numbers of the rising spheres. These experiments result in the same vortex pattern, and reveal that the four structures found in the wake of the rising sphere are vortex rings. What previously appeared to be unusually sharp bends in the counter-rotating vortex pairs are very weak loop-shaped structures, delivering a total of six vortical structures per cycle. Immediately preceding these structures, the two vortices in the pair cross over one another, providing a mechanism for the change in sign of the streamwise vortex pair as the body moves from one half cycle to the next.

Horowitz, M.; Williamson, C. H. K.

2007-11-01

411

Tunable photoluminescence in monodisperse silica spheres.

The nanometer-scale luminescent monodisperse silica spheres have been prepared by a water/oil (W/O) microemulsion method and the size of these spheres changed with the different concentrations of 3-aminopropyltriethoxysilane (APTES). The luminescent monodisperse silica spheres at the submicrometer scale have been prepared via Stöber method and the particles size increased with the increase of the amino concentrations. After calcination, all silica spheres do not change obviously in size. The annealed silica spheres contain C impurities and O defects, which resulted in the luminescence of silica spheres. The spheres showed variations in emission due to the different size and the concentration of organosiloxane precursors. Therefore, the emission can be tuned finely via the change of organosiloxane precursor and the size of samples. PMID:20850127

Kong, Deyan; Zhang, Cuimiao; Xu, Zhenhe; Li, Guogang; Hou, Zhiyao; Lin, Jun

2010-08-31

412

Effective medium theory for random media composed of two-layered spheres.

We study the effective index of random media composed of two-layered spheres by using the energy-density coherent potential approximation method. As expected from the Ewald-Oseen extinction theorem, in the long-wavelength limit, the optical properties of a random medium composed of two-layered spheres are identical to those of a random medium composed of the corresponding pure spheres, while in the Mie-scattering region, the single-scattering resonances lead to an overall shift of the effective refractive index with the modified volume fraction. PMID:22048297

Zhang, Hao; Zhu, Pengfei; Xu, Yuchen; Zhu, Heyuan; Xu, Min

2011-11-01

413

Packing fraction of trimodal spheres with small size ratio: An analytical expression

NASA Astrophysics Data System (ADS)

In previous papers analytical expressions were derived and validated for the packing fraction of bimodal hard spheres with small size ratio, applicable to ordered (crystalline) [H. J. H. Brouwers, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.76.041304 76, 041304 (2007);H. J. H. Brouwers, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.78.011303 78, 011303 (2008)] and disordered (random) packings [H. J. H. Brouwers, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.87.032202 87, 032202 (2013)]. In the present paper the underlying statistical approach, based on counting the occurrences of uneven pairs, i.e., the fraction of contacts between unequal spheres, is applied to trimodal discretely sized spheres. The packing of such ternary packings can be described by the same type of closed-form equation as the bimodal case. This equation contains the mean volume of the spheres and of the elementary cluster formed by these spheres; for crystalline arrangements this corresponds to the unit cell volume. The obtained compact analytical expression is compared with empirical packing data concerning random close packing of spheres, taken from the literature, comprising ternary binomial and geometric packings; good agreement is obtained. The presented approach is generalized to ordered and disordered packings of multimodal mixes.

Brouwers, H. J. H.

2013-09-01

414

Density functional theory for crystal-liquid interfaces of Lennard-Jones fluid

NASA Astrophysics Data System (ADS)

A density functional approach is presented to describe the crystal-liquid interfaces and crystal nucleations of Lennard-Jones fluid. Within the theoretical framework, the modified fundamental measure theory is applied to describe the free energy functional of hard sphere repulsion, and the weighted density method based on first order mean spherical approximation is used to describe the free energy contribution arising from the attractive interaction. The liquid-solid equilibria, density profiles within crystal cells and at liquid-solid interfaces, interfacial tensions, nucleation free energy barriers, and critical cluster sizes are calculated for face-centered-cubic and body-centered-cubic nucleus. Some results are in good agreement with available simulation data, indicating that the present model is quantitatively reliable in describing nucleation thermodynamics of Lennard-Jones fluid.

Wang, Xin; Mi, Jianguo; Zhong, Chongli

2013-04-01

415

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)] 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)], 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

416

Crystalline assembly of hard polyhedra via directional entropic forces

NASA Astrophysics Data System (ADS)

Entropic forces are effective forces that result from a system's statistical tendency to increase its entropy. Hard rods and disks spontaneously align and can assemble into layers and columns if those structures increase the configurational space available to the particles. Hard spheres, cubes and even tetrahedra order for the same reason. Here we extend those findings by showing that hard polyhedra can self-assemble into a variety of complex phases, most of them never before reported in systems of single-component hard particles. The role of shape and directional entropic forces in stabilizing these structures will be discussed. Our results suggest new possibilities for self-assembling complex target structures from colloidal building blocks. [4pt] [1] Damasceno, PF; Engel, M; Glotzer, SC. arXiv:1109.1323v1

Damasceno, Pablo F.; Engel, Michael; Glotzer, Sharon C.

2012-02-01

417

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

418

An efficient algorithm for classical density functional theory in three dimensions: Ionic solutions

NASA Astrophysics Data System (ADS)

Classical density functional theory (DFT) of fluids is a valuable tool to analyze inhomogeneous fluids. However, few numerical solution algorithms for three-dimensional systems exist. Here we present an efficient numerical scheme for fluids of charged, hard spheres that uses (N log N) operations and (N) memory, where N is the number of grid points. This system-size scaling is significant because of the very large N required for three-dimensional systems. The algorithm uses fast Fourier transforms (FFTs) to evaluate the convolutions of the DFT Euler-Lagrange equations and Picard (iterative substitution) iteration with line search to solve the equations. The pros and cons of this FFT/Picard technique are compared to those of alternative solution methods that use real-space integration of the convolutions instead of FFTs and Newton iteration instead of Picard. For the hard-sphere DFT, we use fundamental measure theory. For the electrostatic DFT, we present two algorithms. One is for the ``bulk-fluid'' functional of Rosenfeld [Y. Rosenfeld, J. Chem. Phys. 98, 8126 (1993)] that uses (N log N) operations. The other is for the ``reference fluid density'' (RFD) functional [D. Gillespie et al., J. Phys.: Condens. Matter 14, 12129 (2002)]. This functional is significantly more accurate than the bulk-fluid functional, but the RFD algorithm requires (N2) operations.

Knepley, Matthew G.; Karpeev, Dmitry A.; Davidovits, Seth; Eisenberg, Robert S.; Gillespie, Dirk

2010-03-01

419

Floating behavior of hydrophobic glass spheres.

When a hydrophobic solid sphere is floating on water or salt solutions with different concentrations, it is at equilibrium under the impact of gravity, buoyancy force, and curvature force, the component of surface tension in the vertical direction. We have changed the diameters of the spheres and the concentrations of the two selected salts, NaCl and NaNO(3), to study the floating behaviors of these spheres and the contributions of surface tension and buoyancy force to their floatation. Generally speaking, the surface tension plays a more important role than the buoyancy force when the gravity is small, but the buoyancy force plays an identical or a more important role when the spheres are big enough. The wettability of the spheres significantly influences the height below the contact perimeter especially in salt solutions. The theoretical calculation meniscus slope angles at the sphere three-phase contact line are in agreement with experimental results. PMID:19464018

Liu, Xinjie; Wang, Xiaolong; Liang, Yongmin; Zhou, Feng

2009-04-16

420

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

421

Hollow Spheres in Composite Materials and Metallic Hollow Sphere Composites (MHSC)

NASA Astrophysics Data System (ADS)

The newly developed metallic hollow spheres are used in combination with a polymeric matrix for producing metallic hollow-sphere-composites (MSHC), which have been developed for mechanical engineering applications in the “InnoZellMet” project.

Baumeister, Erika; Molitor, Martin

422

Simulation of rotary-drum and repose tests for frictional spheres and rigid sphere clusters.

National Technical Information Service (NTIS)

The effects of rotation rate and interparticle friction on the bulk flow behavior in rotating horizontal cylinders are studied via particle-dynamic simulations. Assemblies of inelastic, frictional spheres and rigid sphere clusters are utilized, and rotati...

O. R. Walton R. L. Braun

1993-01-01

423

Geometrical Frustration in Amorphous and Partially Crystallized Packings of Spheres

NASA Astrophysics Data System (ADS)

We study the persistence of a geometrically frustrated local order inside partially crystallized packings of equal-sized spheres. Measurements by x-ray tomography reveal previously unseen grain scale rearrangements occurring inside large three-dimensional packings as they crystallize. Three successive structural transitions are detected by a statistical description of the local volume fluctuations. These compaction regimes are related to the disappearance of densely packed tetrahedral patterns of beads. Amorphous packings of monodisperse spheres are saturated with these tetrahedral clusters at Bernal’s limiting density (??64%). But, no periodic lattice can be built upon these patterns; they are geometrically frustrated and are thus condemned to vanish while the crystallization occurs. Remarkably, crystallization-induced grain rearrangements can be interpreted in terms of the evolution of key topological features of these aggregates.

Francois, N.; Saadatfar, M.; Cruikshank, R.; Sheppard, A.

2013-10-01

424

Carbon sphere-silica core–shell structured material was prepared in the presence of cetyltrimethylammonium bromide using tetraethyl orthosilicate as precursor of silica by a sol–gel method combined with Stöber method. Carbon sphere cores with an average diameter of 300nm were prepared by the pyrolysis of acetylene. After carbon sphere cores were removed by calcinations, hollow silica spheres with smooth surface and uniform

Xingmei Guo; Xuguang Liu; Bingshe Xu; Tao Dou

2009-01-01

425

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

426

Template synthesis of composite hollow spheres using sulfonated polystyrene hollow spheres

In this paper, we propose a general template synthesis approach towards composite hollow spheres using sulfonated polystyrene gel hollow spheres. The gel hollow spheres are highly crosslinked to well preserve the spherical contour during template synthesis. It is important that the gel shell is infiltrative to many species to allow their further growth therein by specific interaction. The grown materials

Shu-Jiang Ding; Cheng-Liang Zhang; Mu Yang; Xiao-Zhong Qu; Yun-Feng Lu; Zhen-Zhong Yang

2006-01-01

427

Reduced-complexity sphere decoding with dimension-dependent sphere radius design

A modified sphere decoding (SD) scheme is pro- posed for multiple-input multiple-output (MIMO) communica- tion systems in this paper. The conventional SD goes from the lower dimension to the higher dimension to examine whether a lattice point lies inside the sphere of some radius, which remains fixed for all dimensions. Since the sphere radius directly affects the search range and

Ronald Y. Chang; Wei-Ho Chung

2011-01-01

428

The IMGC volume-density standards for the Avogadro constant

Volume-density standards in the form of single-crystal silicon spheres have been introduced and developed at the IMGC. A new sphere of nearly perfect form has been characterized on the basis of a comprehensive set of interferometric, roundness, mass and hydrostatic measurements. From its mass and volume and from the evaluation of the oxide layer and of impurities, a density of

A. Sacconi; A. M. Peuto; M. Mosca; R. Panciera; W. Pasin; S. Pettorruso

1995-01-01

429

Status of the SPHERE experiment

NASA Astrophysics Data System (ADS)

Here is presented the current state of the SPHERE-2 balloon-borne experiment. The detector is elevated up to 1 km above the snow surface and registers the reflected Vavilov-Cherenkov radiation from extensive air showers. This method has good sensitivity to the mass-composition of the primary cosmic rays due to its high resolution near the shower axis. The detector consists of a 1500 mm spherical mirror with a 109 PMT cluster in its focus. The electronics record a signal pulse profile in each PMT. In the last 2 years the detector was upgraded: time resolution of pulse registration was enhanced up to 12.5 ns, channel sensitivity was increased by a factor of 3, a new LED-based relative PMT calibration method was introduced, and new hardware and etc. was installed.

Antonov, R. A.; Beschapov, S. P.; Bonvech, E. A.; Chernov, D. V.; Dzhatdoev, T. A.; Finger, Mir; Finger, M.; Galkin, V. I.; Kabanova, N. N.; Petkun, A. S.; Podgrudkov, D. A.; Roganova, T. M.; Shaulov, S. B.; Sysoeva, T. I.

2013-02-01

430

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

431

Tandem spheres in hypersonic flow

The problem of determining the forces acting on a secondary body when it is travelling at some point within the shocked region created by a hypersonic primary body is of interest in such situations as store or stage separation, re-entry of multiple vehicles, and atmospheric meteoroid fragmentation. The current work is concerned with a special case of this problem, namely that in which both bodies are spheres and are stationary with respect to one another. We first present an approximate analytical model of the problem; subsequently, numerical simulations are described and results are compared with those from the analytical model. Finally, results are presented from a series of experiments in the T5 hypervelocity shock tunnel in which a newly-developed force-measurement technique was employed.

Laurence, Stuart J [California Institute of Technology, Pasadena; Deiterding, Ralf [ORNL; Hornung, Hans G [California Institute of Technology, Pasadena

2009-01-01

432

Efficient linear programming algorithm to generate the densest lattice sphere packings

NASA Astrophysics Data System (ADS)

Finding the densest sphere packing in d-dimensional Euclidean space Rd is an outstanding fundamental problem with relevance in many fields, including the ground states of molecular systems, colloidal crystal structures, coding theory, discrete geometry, number theory, and biological systems. Numerically generating the densest sphere packings becomes very challenging in high dimensions due to an exponentially increasing number of possible sphere contacts and sphere configurations, even for the restricted problem of finding the densest lattice sphere packings. In this paper we apply the Torquato-Jiao packing algorithm, which is a method based on solving a sequence of linear programs, to robustly reproduce the densest known lattice sphere packings for dimensions 2 through 19. We show that the TJ algorithm is appreciably more efficient at solving these problems than previously published methods. Indeed, in some dimensions, the former procedure can be as much as three orders of magnitude faster at finding the optimal solutions than earlier ones. We also study the suboptimal local density-maxima solutions (inherent structures or “extreme” lattices) to gain insight about the nature of the topography of the “density” landscape.

Marcotte, Étienne; Torquato, Salvatore

2013-06-01

433

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

434

MINIMAL DISCRETE ENERGY ON THE SPHERE

We investigate the energy of arrangements of N points on the surface of a sphere in R3, interacting through a power law potential V = r?, ?2 sphere is devised for the purpose of obtaining bounds for the

E. A. Rakhmanov; E. B. Saff; Y. M. Zhou

435

C{sub 60}: Sphere or polyhedron?

In the original publication on the subject, C{sub 60} was depicted with the aid of a soccer ball, but this representation soon gave way to the familiar line drawing of chemical bonds between nucleii. To a large extent the dichotomy in the representation of the fullerenes remains today, and it is the purpose of this paper to pose and address the question that appears in the title. Of course, in reality the answer is well-known, and neither the sphere nor the polyhedron represent C{sub 60}, which like other molecules exists as a collection of nuclei with an associated distribution of electron density. Nevertheless, it is of interest to consider which of these conventional representations is most relevant for the fullerenes and in particular the language most appropriate to the description of the shape of these molecules and the geometry of the carbon atoms. The analysis presented here shows that topology of the molecule is paramount, and hence, C{sub 60} (and the fullerenes) are best modeled as polyhedra. 16 refs., 3 figs.

Haddon, R.C. [Bell Labs., Murray Hill, NJ (United States)

1997-02-19