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1

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

SciTech Connect

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

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

1994-10-01

2

Freezing of binary hard-sphere mixtures into disordered crystals: a density functional approach  

Microsoft Academic Search

The density functional theory of freezing is extended to the crystallisation of multicomponent systems into substitutional solid solutions. The formalism is applied to the case of binary mixtures of hard spheres. As the ratio of diameters alpha = sigma 1\\/ sigma 2 is lowered, the fluid-solid phase diagram evolves from a spindle shape (1> alpha >0.94) into an azeotropic diagram

J. L. Barrat; M. Baus; J. P. Hansen

1987-01-01

3

Thermodynamic Properties of Hard-Sphere Fluid under Confined Condition Based on Bridge Density Function  

NASA Astrophysics Data System (ADS)

Based on the functional integral procedure, a recently proposed bridge density function [J. Chem. Phys. 112 (2000) 8079] is developed to calculate global thermodynamic properties of non-uniform fluids. The resulting surface tension of a hard wall-hard sphere interface as a function of the bulk hard sphere fluid density is in good agreement with the available simulation data. The proposed numerical procedure from the approximation of non-uniform first-order direct correlation function to a non-uniform system with excess Helmholtz free energy is of fundamental importance for phase behaviour under the confined condition due to the fact that many available simple approximations in classical density functional theory are for non-uniform first-order direct correlation function.

Zhou, Shi-Qi

2003-12-01

4

Thermodynamic self-consistency for hard spheres at low density  

SciTech Connect

We consider the conditions on the triplet-distribution function g/sup( //sup 3/)/sup /, and the pair-distribution g/sup( //sup 2/)/sup /, sufficient that thermodynamic quantities calculated from g/sup( //sup 2/)/sup / be state functions. We show that g/sup( //sup 3/)/sup / cannot be, even to first order in density, equivalent to the Kirkwood superposition approximation. We obtain a g/sup( //sup 3/)/sup / that does yield a thermodynamically self-consistent g/sup( //sup 2/)/sup /, to second order in density. We show that this g/sup( //sup 2/)/sup / differs little from the exact g/sup( //sup 2/)/sup /, at that order. We also examine the low-density behavior of a partially self-consistent closure in which angular correlations appear explicitly. The latter closure is found to describe three-particle correlations well when two of the particles are in contact. A principal conclusion which follows from these studies is that the criterion of thermodynamic self-consistency is useful as a constraint in constructing closures, although it does not in itself determine a closure.

Siders, P.; Kozak, J.J.

1985-05-01

5

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

PubMed

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

6

Hard Sphere Gas Model  

NSDL National Science Digital Library

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

Christian, Wolfgang

2008-07-06

7

Thermodynamic properties of polydisperse hard spheres  

Microsoft Academic Search

The virial expansion of a polydisperse system of hard spheres has been studied. The virial coefficients are shown to be a function of the total number density and the first three moments of the diameter distribution. The small number of moment variables identified is used to construct a simple but physically reasonable model of a polydisperse hard sphere crystal. Analytical

Paul Bartlett

1999-01-01

8

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

Microsoft Academic Search

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

Konstantin V. Tretiakov; Krzysztof W. Wojciechowski

2005-01-01

9

Fundamental measure density functional theory studies on the freezing of binary hard-sphere and Lennard-Jones mixtures  

SciTech Connect

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

Warshavsky, Vadim B.; Song, Xueyu

2008-07-18

10

Phase Transitions in a Mixture of Hard-Sphere Dipoles and Neutral Hard Spheres  

NASA Astrophysics Data System (ADS)

Using the reference hypernetted chain (RHNC) integral equation theory and a rigorous stability analysis method, we investigate the phase behavior of a mixture of hard-sphere dipoles and neutral hard spheres based on the correlations of the homogeneous isotropic phase. Lowering the temperature down to the points where the RHNC equations fail to have a solution, several fluctuations strongly increase. At low densities our results indicate the onset of chain formation, which is similar with the pure DHS system. At high densities, the results indicate the appearance of isotropic-to-ferroelectric transitions (small neutral hard spheres concentrations) and demixing transitions (large neutral hard spheres concentrations).

Li, Li; Li, Liang-Sheng; Chen, Xiao-Song

2009-09-01

11

Evaluating the accuracy of a density functional theory of polymer solutions with additive hard sphere diameters  

NASA Astrophysics Data System (ADS)

We assess the accuracy of a density functional theory for athermal polymer solutions, consisting of solvent particles with a smaller radius than that of the monomers. The monomer and solvent density profiles in a slit bound by hard, flat, and inert surfaces are compared with those obtained by a Metropolis Monte Carlo simulation. At the relatively high density at which the comparison is performed, there are considerable packing effects at the walls. The density functional theory introduces a simple weight function to describe nonlocal correlations in the fluid. A recent study of surface forces in polymer solutions used a different weighting scheme to that proposed in this article, leading to less accurate results. The implications of the conclusions of that study are discussed.

Forsman, Jan; Woodward, Clifford E.

2004-01-01

12

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

PubMed

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

Odriozola, Gerardo; Berthier, Ludovic

2011-02-01

13

Exact theory of dense amorphous hard spheres in high dimension. II. The high density regime and the Gardner transition.  

PubMed

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

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

2013-10-24

14

Structure of penetrable sphere fluids and mixtures near a slit hard wall: a modified bridge density functional approximation.  

PubMed

The modified density functional theory, which is based both on the bridge density functional and the contact value theorem, has been proposed for the structural properties of penetrable sphere fluids and their mixtures near a slit hard wall. The Verlet-modified bridge function proposed by Choudhury and Ghosh [J. Chem. Phys. 119, 4827 (2003)] for one-component system has been extended for fluid mixtures. The radial distribution functions obtained from the Verlet-modified bridge function are in excellent agreement with computer simulations over a wide range of density and temperature and better than those obtained from the standard integral theories including the Percus-Yevick and hypernetted-chain closures. The calculated particle density distributions confined in a slit pore are also found to be reasonably good compared to the simulation data. Even for high density systems the accuracy of the hypernetted-chain and the mean-field approximation functionals increase with increasing temperature. However, the agreement between theory and simulation slightly deteriorates in the systems of low temperature. PMID:19814564

Kim, Soon-Chul; Seong, Baek-Seok; Suh, Soong-Hyuck

2009-10-01

15

Structure of penetrable sphere fluids and mixtures near a slit hard wall: A modified bridge density functional approximation  

NASA Astrophysics Data System (ADS)

The modified density functional theory, which is based both on the bridge density functional and the contact value theorem, has been proposed for the structural properties of penetrable sphere fluids and their mixtures near a slit hard wall. The Verlet-modified bridge function proposed by Choudhury and Ghosh [J. Chem. Phys. 119, 4827 (2003)] for one-component system has been extended for fluid mixtures. The radial distribution functions obtained from the Verlet-modified bridge function are in excellent agreement with computer simulations over a wide range of density and temperature and better than those obtained from the standard integral theories including the Percus-Yevick and hypernetted-chain closures. The calculated particle density distributions confined in a slit pore are also found to be reasonably good compared to the simulation data. Even for high density systems the accuracy of the hypernetted-chain and the mean-field approximation functionals increase with increasing temperature. However, the agreement between theory and simulation slightly deteriorates in the systems of low temperature.

Kim, Soon-Chul; Seong, Baek-Seok; Suh, Soong-Hyuck

2009-10-01

16

Closure-based perturbative density-functional theory of hard-sphere freezing: properties of the bridge functional.  

PubMed

The study of freezing using perturbative classical density-functional theory is revisited, using a bridge functional approach to resum all terms beyond second order in the free energy expansion. More precisely, the first-order direct correlation function of the solid phase is written as a functional expansion about the homogeneous liquid phase, and the sum of all higher-order terms is represented as a functional of the second-order term. Information about the shape and uniqueness of this bridge functional for the case of hard spheres is obtained via an inversion procedure that employs Monte Carlo fluid-solid coexistence data from the literature. The parametric plots obtained from the inversion procedure show very little scatter in certain regions, suggesting a unique functional dependence, but large scatter in other regions. The scatter is related to the anisotropy of the solid lattice at the particle scale. Interestingly, the thermodynamic properties of the phase transition are quite insensitive to the regions where the scatter is large, and several simple closures (i.e., analytical forms of the bridge function) reproduce exactly the liquid-solid coexistence densities and Lindemann parameter from simulation. The form of these closures is significantly different from the usual closures employed in liquid-state integral equation theory. PMID:19905064

Verma, Anurag; Ford, David M

2009-09-01

17

Hard-sphere fluid in infinite dimensions  

NASA Technical Reports Server (NTRS)

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

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

1987-01-01

18

Transport coefficients of hard sphere fluids  

NASA Astrophysics Data System (ADS)

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

Sigurgeirsson, H.; Heyes, D. M.

19

Multidensity integral-equation theory for short diblock hard-sphere-sticky-hard-sphere chains.  

PubMed

The multidensity Ornstein-Zernike integral equation theory is applied to study a simple model of hard sphere/sticky hard sphere diblock chains. The multidensity integral equation formalism has been successfully used to model the equilibrium structure and thermodynamic properties of homonuclear chains and shorter dimer fluids; to our knowledge it has not been applied to model diblock chains. In this work, a diblock chain fluids is represented by an m-component equal molar mixture of hard spheres with species 1,2,...,mh and sticky hard spheres with species mh+1,mh+2,...,m. Each spherical particle has two attractive sites A and B except species 1 and m, which have only one site per particle. In the limit of complete association, this mixture yields a system of monodisperse diblock chains. A general solution of this model is obtained in the Percus-Yevick, Polymer Percus-Yevick and ideal chain approximations. Both structural and thermodynamic properties of this model are investigated. From this study, a microphase separation is predicted for relatively short diblock symmetric and asymmetric chains. This microphase separation is enhanced at lower temperature and higher density. When chain length increases, the phase transition changes from a microphase level to a macrophase level. The size of microdomain structure is found to be dependent on total chain length, relative ratio of block lengths, temperature, and density. PMID:20481746

Wu, Ning; Chiew, Y C

2010-04-01

20

The equation of state of flexible chains of tangent hard spheres at high-density region from simulation and thermodynamic perturbation theory.  

PubMed

Radial and triplet correlation functions of the reference hard sphere system are determined at several solid densities by canonical Monte Carlo (MC) simulations. These customized data are used to extend the second order thermodynamic perturbation theory (TPT) to the solid phase of flexible hard chain systems. In order to test the accuracy of the TPT equation of state (EOS) for hard chains, MC simulations are carried out for systems of chain length 4 to 15. Several simulations are performed in the isobaric-isothermal ensemble to obtain the high-density EOS of hard chains in the fluid and solid phases. To determine solid-fluid equilibrium (SFE), Helmholtz free energies of solid crystals at a reference density are determined in a series of canonical MC simulations. As the chain length increases, asymptotic behaviors are observed in the coexistence pressure and densities of fluid and solid phases. It is found that the accuracy of TPT for EOS and SFE in systems of hard chains greatly improves by extending it to second order. PMID:23320717

Alavi, Farzad; Feyzi, Farzaneh

2013-01-14

21

Local structure in hard-sphere chain-molecule fluids  

NASA Astrophysics Data System (ADS)

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

Wasti, Sambid; Taylor, Mark

2011-10-01

22

Local structure in hard-sphere chain-molecule fluids  

NASA Astrophysics Data System (ADS)

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

Wasti, Sambid; Taylor, Mark

2012-04-01

23

Heterogeneous shear in hard sphere glasses.  

PubMed

There is growing evidence that the flow of driven amorphous solids is not homogeneous, even if the macroscopic stress is constant across the system. Via event-driven molecular dynamics simulations of a hard sphere glass, we provide the first direct evidence for a correlation between the fluctuations of the local volume fraction and the fluctuations of the local shear rate. Higher shear rates do preferentially occur at regions of lower density and vice versa. The temporal behavior of fluctuations is governed by a characteristic time scale, which, when measured in units of strain, is independent of shear rate in the investigated range. Interestingly, the correlation volume is also roughly constant for the same range of shear rates. A possible connection between these two observations is discussed. PMID:22463672

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

2012-03-01

24

Equation of State and Integral Equation Theory for Hard Sphere and Hard-Sphere Chain Fluids  

Microsoft Academic Search

The development of an accurate equation of state based on molecular thermodynamics for simple and complex fluids is important to chemical process design. In this dissertation we study the thermodynamic and intermolecular structural properties of hard sphere and hard-sphere chain fluids. These are theoretically challenging problems, the solution of which are useful for perturbation theory of more realistic potential models.

Jaeeon Chang

1994-01-01

25

Hard spheres on the gyroid surface  

PubMed Central

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

26

A replica approach to glassy hard spheres  

NASA Astrophysics Data System (ADS)

Hard spheres have been used to model many different systems in condensed matter. Amorphous packings have attracted a lot of interest as theoretical models for glasses. We will review here a theory of amorphous packings, and more generally glassy states, of hard spheres that is based on the replica method: this theory gives predictions on the structure and thermodynamics of these states. Replica theory relies on approximations and certain assumptions that will be elucidated in this paper. The aim of this paper is to identify a class of amorphous packings that might be described using equilibrium statistical mechanics, that is, in a static framework. These packings will be defined as the infinite pressure limit of glassy states of hard spheres.

Parisi, Giorgio; Zamponi, Francesco

2009-03-01

27

Crystallization of hard-sphere colloids in microgravity  

Microsoft Academic Search

The structure of, and transitions between, liquids, crystals and glasses have commonly been studied with the hard-sphere model, in which the atoms are modelled as spheres that interact only through an infinite repulsion on contact. Suspensions of uniform colloidal polymer particles are good approximations to hard spheres, and so provide an experimental model system for investigating hard-sphere phases. They display

Jixiang Zhu; Min Li; R. Rogers; W. Meyer; R. H. Ottewill; W. B. Russel; P. M. Chaikin

1997-01-01

28

Computational study of the melting-freezing transition in the quantum hard-sphere system for intermediate densities. II. Structural features  

NASA Astrophysics Data System (ADS)

The structural features of the quantum hard-sphere system in the region of the fluid-face-centered-cubic-solid transition, for reduced number densities 0.45hard spheres has been performed, and some interesting differences between the classical and quantum melting-freezing transition are observed.

Sesé, Luis M.; Bailey, Lorna E.

2007-04-01

29

Computational study of the melting-freezing transition in the quantum hard-sphere system for intermediate densities. II. Structural features.  

PubMed

The structural features of the quantum hard-sphere system in the region of the fluid-face-centered-cubic-solid transition, for reduced number densities 0.45hard spheres has been performed, and some interesting differences between the classical and quantum melting-freezing transition are observed. PMID:17477616

Sesé, Luis M; Bailey, Lorna E

2007-04-28

30

EQUATION OF STATE OF THE HARD-SPHERE CRYSTAL  

Microsoft Academic Search

A new approach to the averaged two-particle distribution function of a crystalline phase is presented. It includes an indirect check of the merit of the Gaussian approximation for the local density and a new way to inferring values of the thermodynamic variables from simulation data. The equa- tion of state and the compressibility of the hard-sphere FCC crystal is computed

C. Rascon; L. Mederos; G. Navascues

31

Equation of state of the hard-sphere crystal  

Microsoft Academic Search

An approach to the averaged two-particle distribution function of a crystalline phase is presented. It includes an indirect check of the merit of the Gaussian approximation for the local density and a way to infer values of the thermodynamic variables from simulation data. The equation of state and the compressibility of the hard-sphere fcc crystal is computed from the Tarazona

C. Rascón; L. Mederos; G. Navascués

1996-01-01

32

Most stable structure for hard spheres  

Microsoft Academic Search

The hard sphere model is known to show a liquid-solid phase transition, with the solid expected to be either face centered cubic or hexagonal close packed. The differences in free energy of the two structures are very small and various attempts have been made to determine which structure is the more stable. We contrast the different approaches and extend one.

Hans Koch; Charles Radin; Lorenzo Sadun

2005-01-01

33

Computational study of the melting-freezing transition in the quantum hard-sphere system for intermediate densities. I. Thermodynamic results.  

PubMed

The points where the fluid-solid (face-centered-cubic) transition takes place in the quantum hard-sphere system, for reduced densities 0.85>rhoN*>0.5 (reduced de Broglie wavelengths lambdaB*densities are arranged along a straight line rhoFCC*=rho(rhoF*), a behavior which at least holds even for lambdaB*<2, as revealed by completing the present analysis with data available in the literature. PMID:17477615

Sesé, Luis M

2007-04-28

34

Fundamental measure theory for hard-sphere mixtures: a review.  

PubMed

Hard-sphere systems are one of the fundamental model systems of statistical physics and represent an important reference system for molecular or colloidal systems with soft repulsive or attractive interactions in addition to hard-core repulsion at short distances. Density functional theory for classical systems, as one of the core theoretical approaches of statistical physics of fluids and solids, has to be able to treat such an important system successfully and accurately. Fundamental measure theory is up to date the most successful and most accurate density functional theory for hard-sphere mixtures. Since its introduction fundamental measure theory has been applied to many problems, tested against computer simulations, and further developed in many respects. The literature on fundamental measure theory is already large and is growing fast. This review aims to provide a starting point for readers new to fundamental measure theory and an overview of important developments. PMID:21389360

Roth, Roland

2010-02-17

35

Conformal Solution Theory: Hard-Sphere Mixtures  

Microsoft Academic Search

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

Douglas Henderson; Peter J. Leonard

1971-01-01

36

The Crystallization of Hard Spheres in Three Dimensions Due to Gravity  

NASA Astrophysics Data System (ADS)

When a collection of hard spheres is cooled down in the presence of gravity, there is a critical temperature, T_c, at which particles in the bottom layer reach a maximum packing density. When the system is cooled further below T_c, a fraction of the hard spheres forms a solid-like regime from the bottom whose translational modes are frozen. Based on the Enskog theory of hard spheres, we investigate this phenomena for a three dimensional system of hard spheres, where we determine Tc as a function of the control parameters such as the mass and diameter of the hard sphere, and the initial layer thickness. Event-Driven(ED) simulation results show that the fraction of condensed particles is given by 1-T/T_c, as predicted by the theory. Further, we also find an excellent agreement between the Enskog density profile and the average density profile obtained by ED in the fluid region.

Hotchkiss, Justin; Quinn, Paul V.

2002-03-01

37

Evolution of Correlation Functions in the Hard Sphere Dynamics  

NASA Astrophysics Data System (ADS)

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

Simonella, Sergio

2014-01-01

38

Evolution of Correlation Functions in the Hard Sphere Dynamics  

NASA Astrophysics Data System (ADS)

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

Simonella, Sergio

2014-06-01

39

Second virial coefficients of dipolar hard spheres  

NASA Astrophysics Data System (ADS)

An asymptotic formula is reported for the second virial coefficient B2 of a dipolar hard-sphere (DHS) fluid, in zero external field, for strongly coupled dipolar interactions. This simple formula, together with the one for the weak-coupling B2, provides an accurate prediction of the second virial coefficient for a wide range of dipole moments, including those that are experimentally accessible in magnetite ferrofluids. The weak-coupling B2 also yields an estimate of the magnetic moment minimally needed for isotropic gas-liquid phase-separation, if any, in the DHS fluid.

Philipse, Albert P.; Kuipers, Bonny W. M.

2010-08-01

40

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

41

A generalized hard-sphere model for Monte Carlo simulation  

Microsoft Academic Search

A new molecular model, called the generalized hard-sphere, or GHS model, is introduced. This model contains, as a special case, the variable hard-sphere model of Bird (1981) and is capable of reproducing all of the analytic viscosity coefficients available in the literature that are derived for a variety of interaction potentials incorporating attraction and repulsion. In addition, a new procedure

H. A. Hassan; David B. Hash

1993-01-01

42

Dendritic Growth of Hard Sphere Colloidal Crystals in Microgravity  

Microsoft Academic Search

We have observed the dendritic growth of colloidal crystals in the coexistence region of the hard sphere phase diagram. The system is an index matched suspension of 0.518 mu PMMA spheres (with short polymer coating of PSHA) in a decaline\\/tetraline mixture. Samples with effective hard sphere volume fractions between 0.5 and 0.54 form phase separated liquid and solid regions under

P. M. Chaikin; Jixiang Zhu; Min Li; W. R. Russel; R. Rogers; W. Meyers

1996-01-01

43

Quantum-hard-sphere system equations of state revisited  

SciTech Connect

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)] [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)] [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)] [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)] [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)] [Theoretical Division, University of California, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

1996-10-01

44

A polydisperse hard sphere model for interatomic correlations in multi-component metallic melts  

NASA Astrophysics Data System (ADS)

We propose a polydisperse hard sphere model for numerical calculation of the analytic radial distribution function of multi-component atomic liquids. The vibrational part of atomic thermal motion in liquids is modeled by the effective density profile of polydisperse hard spheres. We applied an orthogonal polynomial technique for the solution of a system of Ornstein-Zernike equations using the hard sphere Percus-Yevick analytic expression for the direct correlation functions. The partial radial distribution functions were calculated for the case of a binary liquid where the size distribution of the components is specified by Schultz distributions.

Yakibchuk, P. M.; Volkov, O. V.; Vakarchuk, S. O.

2009-12-01

45

Non-hard sphere thermodynamic perturbation theory.  

PubMed

A non-hard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the non-HS perturbation scheme in a coupling parameter expansion (CPE) thermodynamic perturbation framework. NVT-Monte Carlo simulation is carried out for a generalized Lennard-Jones (LJ) 2n-n potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the non-HS CPE 3rd-order thermodynamic perturbation theory (TPT) and give a comparison between the non-HS CPE 3rd-order TPT and other theoretical approaches. It is indicated that the non-HS CPE 3rd-order TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)-equation of state and is at least comparable to several currently the most accurate Ornstein-Zernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of f(ex-ref), chiefly decide the quality of the non-HS CPE TPT. Considering that the non-HS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamic perturbation framework is amenable to high-order truncation, the non-HS CPE 3rd-order or higher order TPT will be more promising once the above-mentioned three technological advances are established. PMID:21861552

Zhou, Shiqi

2011-08-21

46

Solid-Fluid Coexistence in Binary Hard Sphere Mixtures by Semigrand Monte Carlo Simulation  

Microsoft Academic Search

We report on Monte Carlo simulations of binary mixtures of single-occupancy hard spheres, which were conducted to evaluate coexistence with the fluid phase. The simulations were performed in a semigrand ensemble in which the temperature, pressure, total number of spheres, and fugacity fraction are independent variables, while the mixture composition and density fluctuates, and thus are averaged. Using the pure

David A. Kofke

1991-01-01

47

Dynamics of hard sphere colloidal dispersions  

NASA Technical Reports Server (NTRS)

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

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

1994-01-01

48

Shear induced diffusion in hard sphere glasses  

NASA Astrophysics Data System (ADS)

The response of dense hard sphere suspensions is examined during the application of steady and non-linear oscillatory shear using Brownian Dynamics (BD) simulations and experimental Light Scattering echo coupled with rheology. At rest, volume fractions around the glass transition exhibit long or infinite relaxation times. However, non-linear shear induces out of cage motions of comparable time scale to the applied rates. We found two distinct regimes in terms of stresses and dynamic response under shear. One regime for lower rates or frequencies of oscillation, governed by Brownian activated diffusion, and a second for higher rates related to shear activated diffusion. A linear dependence with rate was found for the diffusivity in the high rate regime, mirroring the viscous loss due to shear activated particle rearrangements, while diffusivities in the Brownian activated regime showed a power law exponent of less than unity. The exponent was found to increase with volume fraction. For applied rates inducing diffusivities above the in-cage diffusivity at rest, we find a time window of super-diffusive behavior, between the short time (in-cage) and long time (out-of cage) diffusivities under shear, a signature of a dynamic breaking and reforming of the cage.

Koumakis, Nick; Petekidis, George; Brady, John

2012-02-01

49

Velocity of sound in a dense, hard-sphere Bose liquid  

Microsoft Academic Search

The collective approach is used to calculate the velocity of sound in a dense system of bosons interacting via a two-body hard-sphere potential. The calculation is carried out with a hard-sphere potential that is equivalent to the real potential between 4He atoms over the density range of liquid 4He. The agreement between the calculated and experimental results is good over

Moshe Schwartz

1979-01-01

50

Classical growth of hard-sphere colloidal crystals  

NASA Astrophysics Data System (ADS)

The classical theory of nucleation and growth of crystals is examined for concentrated suspensions of hard-sphere colloidal particles. The work of Russel is modified, extended, and evaluated, explicitly. Specifically, the Wilson-Frenkel growth law is modified to include the Gibbs-Thomson effect and is evaluated numerically. The results demonstrate that there is a critical nucleus radius below which crystal nuclei will not grow. A kinetic coefficient determines the maximum growth velocity possible. For large values of this coefficient, quenches to densities above the melting density show interface limited growth with the crystal radius increasing linearly with time. For quenches into the coexistence region the growth is diffusion limited, with the crystal radius increasing as the square root of elapsed time. Smaller values of the kinetic coefficient produce long lived transients which evidence quasi-power-law growth behavior with exponents between one half and unity. The smaller kinetic coefficients also lead to larger crystal compression. Crystal compression and nonclassical exponents have been observed in recent experiments. The theory is compared to data from small angle scattering studies of nucleation and growth in suspensions of hard colloidal spheres. The experimental nucleation rate is much larger than the theoretically predicted value as the freezing point is approached but shows better agreement near the melting point. The crystal growth with time is described reasonably well by the theory and suggests that the experiments are observing long lived transient rather than asymptotic growth behavior. (c) 1995 The American Physical Society

Ackerson, Bruce J.; Schätzel, Klaus

1995-12-01

51

Dendritic Growth of Hard-Sphere Crystals. Experiment 34  

NASA Technical Reports Server (NTRS)

Recent observations of the disorder-order transition for colloidal hard spheres under microgravity revealed dendritic crystallites roughly 1-2 mm in size for samples in the coexistence region of the phase diagram. Order-of-magnitude estimates rationalize the absence of large or dendritic crystals under normal gravity and their stability to annealing in microgravity. A linear stability analysis of the Ackerson and Schaetzel model for crystallization of hard spheres establishes the domain of instability for diffusion-limited growth at small supersaturations. The relationship between hard-sphere and molecular crystal growth is established and exploited to relate the predicted linear instability to the well-developed dendrites observed.

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

1998-01-01

52

Depletion effects in smectic phases of hard-rod-hard-sphere mixtures  

NASA Astrophysics Data System (ADS)

It is known that when hard spheres are added to a pure system of hard rods the stability of the smectic phase may be greatly enhanced, and that this effect can be rationalised in terms of depletion forces. In the present paper we first study the effect of orientational order on depletion forces in this particular binary system, comparing our results with those obtained adopting the usual approximation of considering the rods parallel and their orientations frozen. We consider mixtures with rods of different aspect ratios and spheres of different diameters, and we treat them within Onsager theory. Our results indicate that depletion effects, and consequently smectic stability, decrease significantly as a result of orientational disorder in the smectic phase when compared with corresponding data based on the frozen-orientation approximation. These results are discussed in terms of the ? parameter, which has been proposed as a convenient measure of depletion strength. We present closed expressions for ?, and show that it is intimately connected with the depletion potential. We then analyse the effect of particle geometry by comparing results pertaining to systems of parallel rods of different shapes (spherocylinders, cylinders and parallelepipeds). We finally provide results based on the Zwanzig approximation of a fundamental-measure density-functional theory applied to mixtures of parallelepipeds and cubes of different sizes. In this case, we show that the ? parameter exhibits a linear asymptotic behaviour in the limit of large values of the hard-rod aspect ratio, in conformity with Onsager theory, as well as in the limit of large values of the ratio of rod breadth to cube side length, d, in contrast to Onsager approximation, which predicts ? ˜ d3. Based on both this result and the Percus-Yevick approximation for the direct correlation function for a hard-sphere binary mixture in the same limit of infinite asymmetry, we speculate that, for spherocylinders and spheres, the ? parameter should be of order unity as d tends to infinity.

Mart?nez-Ratón, Y.; Cinacchi, G.; Velasco, E.; Mederos, L.

2006-10-01

53

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

54

A generalized hard-sphere model for Monte Carlo simulation  

Microsoft Academic Search

A new molecular model, called the generalized hard-sphere, or GHS model, is introduced. This model contains, as a special case, the variable hard-sphere (VHS) model of Bird [RarefiedGasDynamics, edited by S. S. Fisher (AIAA, New York, 1981), Part 1, p. 239] and is capable of reproducing all of the analytic viscosity coefficients available in the literature that are derived for

H. A. Hassana; David B. Hashb

1993-01-01

55

Distribution Functions of a Hard-Sphere Fermi Gas  

Microsoft Academic Search

The singlet and pair distribution functions of a Fermi gas are evaluated for low temperatures. It is assumed that the particles interact with a hard-sphere potential and have an arbitrary spin, and the evaluation is made to first order in the hard-sphere diameter. The binary-kernel method developed by Siegert, Lee, and Yang is used and the cluster-expansion theory given recently

A. Isihara; Arun K. Gupta

1967-01-01

56

Radial Distribution Function of a Hard-Sphere Fluid  

Microsoft Academic Search

A hard-sphere fluid (8788 particles) is modeled by the Monte Carlo method for 41 occupation coefficients in the range of ? = 0.10-0.50 (step 0.01). The radial distribution functions were determined at 512 points in an interval of up to five hard sphere radii. In this interval, the number of analyzed particle pairs was from 1.8 · 109 to 9.0·

Yu. T. Pavlyukhin

2000-01-01

57

Stochastic model of a dense spinless hard-sphere gas  

Microsoft Academic Search

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

L. M. Morato; G. Galilei

1991-01-01

58

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

PubMed

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

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

2006-11-28

59

Scalar fundamental measure theory for hard spheres in three dimensions: application to hydrophobic solvation.  

PubMed

Hard-sphere mixtures provide one a solvable reference system that can be used to improve the density functional theory of realistic molecular fluids. We show how the Kierlik-Rosinberg's scalar version of the fundamental measure density functional theory of hard spheres [E. Kierlik and M. L. Rosinberg, Phys. Rev. A 42, 3382 (1990)], which presents computational advantages with respect to the original Rosenfeld's vectorial formulation or its extensions, can be implemented and minimized in three dimensions to describe fluid mixtures in complex environments. This implementation is used as a basis for defining a molecular density functional theory of water around molecular hydrophobic solutes of arbitrary shape. PMID:22830691

Levesque, Maximilien; Vuilleumier, Rodolphe; Borgis, Daniel

2012-07-21

60

Nearly logarithmic decay in the colloidal hard-sphere system.  

PubMed

Nearly logarithmic decay is identified in the data for the mean-squared displacement of the colloidal hard-sphere system at the liquid-glass transition [W. van Megen, Phys. Rev. E 58, 6073 (1998)]. The solutions of the mode-coupling theory for the microscopic equations of motion fit the experimental data well. Based on these equations, the nearly logarithmic decay is explained as the equivalent of a beta-peak phenomenon, a manifestation of the critical relaxation when the coupling between of the probe variable and the density fluctuations is strong. In an asymptotic expansion, a Cole-Cole formula including corrections is derived from the microscopic equations of motion, which describes the experimental data for three decades in time. PMID:16089713

Sperl, M

2005-06-01

61

Inhomogeneous quasistationary state of dense fluids of inelastic hard spheres  

NASA Astrophysics Data System (ADS)

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

Fouxon, Itzhak

2014-05-01

62

Structural precursor to freezing in the hard-disk and hard-sphere systems  

NASA Astrophysics Data System (ADS)

We show that the simplest model fluids in two and three dimensions, namely, the hard-disk and hard-sphere fluids, exhibit a structural precursor to the freezing transition, which manifests itself as a shoulder in the second peak of the radial distribution function. This feature is not present in the radial distribution function of the low-density fluid. Close examination of the two-dimensional fluid configurations in the vicinity of the freezing transition reveals that the shoulder corresponds to the formation of a distinct structural motif, identifiable as a four-particle hexagonally close-packed arrangement. As the dense fluid approaches the freezing transition, the ordered arrangements form large embryonic domains, commensurate with those seen in the crystal at the melting point. Contrary to the notion that the split second peak is a signature of the amorphous solid, our results support the idea that it is a precursor to the development of long-range order.

Truskett, Thomas M.; Torquato, Salvatore; Sastry, Srikanth; Debenedetti, Pablo G.; Stillinger, Frank H.

1998-09-01

63

Investigating hard sphere interactions through spin echo scattering angle measurement  

NASA Astrophysics Data System (ADS)

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

Washington, Adam

64

A generalized hard-sphere model for Monte Carlo simulation  

NASA Technical Reports Server (NTRS)

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

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

1993-01-01

65

Local order variations in confined hard-sphere fluids.  

PubMed

Pair distributions of fluids confined between two surfaces at close distance are of fundamental importance for a variety of physical, chemical, and biological phenomena, such as interactions between macromolecules in solution, surface forces, and diffusion in narrow pores. However, in contrast to bulk fluids, properties of inhomogeneous fluids are seldom studied at the pair-distribution level. Motivated by recent experimental advances in determining anisotropic structure factors of confined fluids, we analyze theoretically the underlying anisotropic pair distributions of the archetypical hard-sphere fluid confined between two parallel hard surfaces using first-principles statistical mechanics of inhomogeneous fluids. For this purpose, we introduce an experimentally accessible ensemble-averaged local density correlation function and study its behavior as a function of confining slit width. Upon increasing the distance between the confining surfaces, we observe an alternating sequence of strongly anisotropic versus more isotropic local order. The latter is due to packing frustration of the spherical particles. This observation highlights the importance of studying inhomogeneous fluids at the pair-distribution level. PMID:24182058

Nygård, Kim; Sarman, Sten; Kjellander, Roland

2013-10-28

66

Event-driven Langevin simulations of hard spheres  

NASA Astrophysics Data System (ADS)

The blossoming of interest in colloids and nanoparticles has given renewed impulse to the study of hard-body systems. In particular, hard spheres have become a real test system for theories and experiments. It is therefore necessary to study the complex dynamics of such systems in presence of a solvent; disregarding hydrodynamic interactions, the simplest model is the Langevin equation. Unfortunately, standard algorithms for the numerical integration of the Langevin equation require that interactions are slowly varying during an integration time step. This is not the case for hard-body systems, where there is no clear-cut distinction between the correlation time of the noise and the time scale of the interactions. Starting first from a splitting of the Fokker-Plank operator associated with the Langevin dynamics, and then from an approximation of the two-body Green's function, we introduce and test two algorithms for the simulation of the Langevin dynamics of hard spheres.

Scala, A.

2012-08-01

67

Physics of Hard Spheres Experiment: Significant and Quantitative Findings Made  

NASA Technical Reports Server (NTRS)

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

Doherty, Michael P.

2000-01-01

68

Structure factor of a one-dimensional shouldered hard-sphere fluid  

Microsoft Academic Search

We present an exact description of how the structure factor of a one-dimensional shouldered hard-sphere systems depends on the shoulder height and width of the potential, and the number density. The applicability of these results to liquid-metal systems is discussed.

John M. Kincaid; George Stell

1978-01-01

69

Three-Particle Collision Integrals for a Gas of Hard Spheres  

Microsoft Academic Search

In order to predict the first density corrections to the transport coefficients of gases, it is necessary to evaluate collision integrals which account for the correlations in the position and velocity variables of three molecules. These correlations are both of a statistical and dynamical nature. For a gas of hard spheres the statistical correlations reduce to excluded volume effects and

J. V. Sengers; M. H. Ernst; D. T. Gillespie

1972-01-01

70

Time scales for transitions between free-energy minima of a dense hard-sphere system  

Microsoft Academic Search

Time scales associated with activated transitions between glassy metastable states of a free-energy functional appropriate for a dense hard-sphere system are calculated by using a new Monte Carlo method for the local density variables. In particular, we calculate the time the system, initially placed in a shallow glassy minimum of the free energy, spends in the neighborhood of this minimum

Chandan Dasgupta; Oriol T. Valls

1996-01-01

71

Bose condensation in dilute gas of hard spheres with attraction  

NASA Astrophysics Data System (ADS)

Critical temperature is calculated for Bose-Einstein condensation of hard spheres with attraction using the path-integral Monte Carlo (PIMC) method and finite-size scaling. It is demonstrated that the scattering length is not the only parameter which the critical temperature depends on. It is also shown that Bose condensation may be observed in the case of negative scattering length.

Bronin, S. Y.; Zelener, B. V.; Klyarfeld, A. B.; Filinov, V. S.

2013-09-01

72

Variable hard-sphere model for gas mixture  

Microsoft Academic Search

The variable hard-sphere model of Bird, which is used in simulating molecular collisions in pure gas, is extended so that it is applicable to the collisions in gas mixture. The constant in the model is determined from the coefficient of diffusion.

Kenichi Nanbu

1990-01-01

73

Dielectric properties of a mixture of dipolar hard spheres  

Microsoft Academic Search

A theory for the dielectric constant, ?, of a fluid mixture of dipolar hard spheres is formulated by generalizing the methods developed by Ramshaw and Wertheim for the pure fluid case. The resulting expression for ? depends on the pair distribution functions, g??(r1, ?1, r2, ?2) for a dipolar mixture. Due to the unavailability of exact representations for these dipolar

Ben Freasier; Norman Hamer; Dennis Isbister

1979-01-01

74

Clustering and gelation of hard spheres induced by the Pickering effect  

NASA Astrophysics Data System (ADS)

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, ScienceSCIEAS0036-807510.1126/science.1199243 331, 897 (2011)] in a mixture of colloidal particles and two immiscible fluids.

Fortini, Andrea

2012-04-01

75

Solidification of a colloidal hard sphere like model system approaching and crossing the glass transition.  

PubMed

We investigated the process of vitrification and crystallization in a model system of colloidal hard spheres. The kinetics of the solidification process was measured using time resolved static light scattering, while the time evolution of the dynamic properties was determined using time resolved dynamic light scattering. By performing further analysis we confirm that solidification of hard sphere colloids is mediated by precursors. Analyzing the dynamic properties we can show that the long time dynamics and thus the shear rigidity of the metastable melt is highly correlated with the number density of solid clusters (precursors) nucleated. In crystallization these objects convert into highly ordered crystals whereas in the case of vitrification this conversion is blocked and the system is (temporarily) locked in the metastable precursor state. From the early stages of solidification one cannot clearly conclude whether the melt will crystallize or vitrify. Furthermore our data suggests that colloidal hard sphere glasses can crystallize via homogeneous nucleation. PMID:24926966

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

2014-08-01

76

Calculation of inhomogeneous-fluid cluster expansions with application to the hard-sphere/hard-wall system  

NASA Astrophysics Data System (ADS)

We examine the suitability of cluster expansion methods for the description of inhomogeneous fluids. In particular, we apply these methods to characterize the density profile, surface tension, and excess adsorption for a hard-sphere fluid near a hard wall. Coefficients for these series up to seventh order are evaluated by the Mayer-sampling Monte Carlo method. Comparison of the series to Monte Carlo simulations of these systems finds very good agreement up to bulk densities approaching the freezing point. This work indicates that knowledge of surface cluster integrals of inhomogeneous systems can be at least as useful as the bulk-phase virial expansions.

Yang, Jung Ho; Schultz, Andrew J.; Errington, Jeffrey R.; Kofke, David A.

2013-04-01

77

Calculation of inhomogeneous-fluid cluster expansions with application to the hard-sphere?hard-wall system.  

PubMed

We examine the suitability of cluster expansion methods for the description of inhomogeneous fluids. In particular, we apply these methods to characterize the density profile, surface tension, and excess adsorption for a hard-sphere fluid near a hard wall. Coefficients for these series up to seventh order are evaluated by the Mayer-sampling Monte Carlo method. Comparison of the series to Monte Carlo simulations of these systems finds very good agreement up to bulk densities approaching the freezing point. This work indicates that knowledge of surface cluster integrals of inhomogeneous systems can be at least as useful as the bulk-phase virial expansions. PMID:23574251

Yang, Jung Ho; Schultz, Andrew J; Errington, Jeffrey R; Kofke, David A

2013-04-01

78

The nematic-isotropic phase transition in semiflexible fused hard-sphere chain fluids  

NASA Astrophysics Data System (ADS)

A density-functional theory of the isotropic-nematic phase transition in both rigid and semiflexible hard-sphere chain fluids is described. The theory is based on an exact analytical evaluation of the excluded volume and second virial coefficient ( B2 ) for rigid chain molecules, which demonstrates that ( B2 ) in these cases is equivalent to that of a binary mixture of hard spheres and hard diatomic molecules. It is assumed that the same binary-mixture representation applies to semiflexible chains, while scaled particle theory is used to obtain the properties of the fluid at arbitrary densities. The result s of the theory are in very good agreement with Monte Carlo (MC) simulation data for rigid tangent hard-sphere chains, but in lesser agreement with available MC studies of rigid fused hard-sphere chains. We find that there is reasonable agreement between the theory and MC data for semiflexible tangent chains, which improves with increasing chain length. The behavior predicted by the theory for semiflexible chains is contrasted with that given by the Khokhlov and Semenov theory of nematic ordering of wormlike polymer chains.

Jaffer, K. M.; Opps, S. B.; Sullivan, D. E.; Nickel, B. G.; Mederos, L.

2001-03-01

79

The nematic-isotropic phase transition in semiflexible fused hard-sphere chain fluids  

NASA Astrophysics Data System (ADS)

A density-functional theory of the isotropic-nematic phase transition in both rigid and semiflexible hard-sphere chain fluids is described. The theory is based on an exact analytical evaluation of the excluded volume and second virial coefficient B2 for rigid chain molecules, which demonstrates that B2 in these cases is equivalent to that of a binary mixture of hard spheres and hard diatomic molecules. It is assumed that the same binary-mixture representation applies to semiflexible chains, while scaled particle theory is used to obtain the properties of the fluid at arbitrary densities. The results of the theory are in very good agreement with Monte Carlo (MC) simulation data for rigid tangent hard-sphere chains, but in lesser agreement with available MC studies of rigid fused hard-sphere chains. We find that there is reasonable agreement between the theory and MC data for semiflexible tangent chains, which improves with increasing chain length. The behavior predicted by the theory for semiflexible chains is contrasted with that given by the Khokhlov and Semenov theory of nematic ordering of wormlike polymer chains.

Jaffer, K. M.; Opps, S. B.; Sullivan, D. E.; Nickel, B. G.; Mederos, L.

2001-02-01

80

Depletion effects in smectic phases of hard rod--hard sphere mixtures  

Microsoft Academic Search

It is known that when hard spheres are added to a pure system of hard rods the stability of the smectic phase may be greatly enhanced, and that this effect can be rationalised in terms of depletion forces. In the present paper we first study the effect of orientational order on depletion forces in this particular binary system, comparing our

Yuri Martinez-Raton; Giorgio Cinacchi; Enrique Velasco; Luis Mederos

2007-01-01

81

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

PubMed

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 Padé 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. PMID:17930217

Solís, M A; de Llano, M; Clark, J W; Baker, George A

2007-09-01

82

Improved quantum hard-sphere ground-state equations of state  

SciTech Connect

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

83

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

84

Nonuniversality of density and disorder in jammed sphere packings  

NASA Astrophysics Data System (ADS)

We show for the first time that collectively jammed disordered packings of three-dimensional monodisperse frictionless hard spheres can be produced and tuned using a novel numerical protocol with packing density ? as low as 0.6. This is well below the value of 0.64 associated with the maximally random jammed state and entirely unrelated to the ill-defined ``random loose packing'' state density. Specifically, collectively jammed packings are generated with a very narrow distribution centered at any density ? over a wide density range ??(0.6,0.740 48...) with variable disorder. Our results support the view that there is no universal jamming point that is distinguishable based on the packing density and frequency of occurrence. Our jammed packings are mapped onto a density-order-metric plane, which provides a broader characterization of packings than density alone. Other packing characteristics, such as the pair correlation function, average contact number, and fraction of rattlers are quantified and discussed.

Jiao, Yang; Stillinger, Frank H.; Torquato, Salvatore

2011-01-01

85

Multiplepoint and multiple-time correlation functions in a hard-sphere fluid  

Microsoft Academic Search

A recent mode-coupling theory of higher-order correlation functions is tested on a simple hard-sphere fluid system at intermediate densities. Multiple-point and multiple-time correlation functions of the densities of conserved variables are calculated in the hydrodynamic limit and compared to results obtained from event-based molecular dynamics simulations. It is demonstrated that the mode-coupling theory results are in excellent agreement with the

Ramses van Zon; Jeremy Schofield

2002-01-01

86

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

87

Higher Order Chapman-Enskog Expansion for Dilute Hard Spheres  

NASA Astrophysics Data System (ADS)

The matrix elements corresponding to the collision term in the Boltzmann equation for dilute hard spheres were calculated with a computer algebra system and the fast Fourier transform, and utilized to solve the 10th-order Chapman-Enskog (CE) expansion for a steady heat-transfer problem. The solution of the CE expansion was examined using the results of the direct simulation Monte Carlo method and was shown to be a good approximation in the region of moderate Knudsen number.

Fushiki, M.

2006-01-01

88

Irreducible Cluster Integrals of Hard-Sphere Gases. II  

Microsoft Academic Search

It is shown that a class of irreducible clusters of hard-sphere gases can be evaluated by a multiple-series method by changing the integration variable from position vectors to bond vectors and from bond vectors to face vectors using bond—face transformation. The class includes graphs which were intractable so far, for example, Nos. 9 and 10 clusters of the fifth virial

J. E. Kilpatrick; Shigetoshi Katsura

1966-01-01

89

Nearly logarithmic decay in the colloidal hard-sphere system  

Microsoft Academic Search

Nearly logarithmic decay is identified in the data for the mean-squared displacement of the colloidal hard-sphere system at the liquid-glass transition [W. van Megen , Phys. Rev. E 58, 6073 (1998)]. The solutions of the mode-coupling theory for the microscopic equations of motion fit the experimental data well. Based on these equations, the nearly logarithmic decay is explained as the

Matthias Sperl

2005-01-01

90

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

Microsoft Academic Search

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

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

2006-01-01

91

Mean-field theory of hard sphere glasses and jamming  

NASA Astrophysics Data System (ADS)

Hard spheres are ubiquitous in condensed matter: they have been used as models for liquids, crystals, colloidal systems, granular systems, and powders. Packings of hard spheres are of even wider interest as they are related to important problems in information theory, such as digitalization of signals, error correcting codes, and optimization problems. In three dimensions the densest packing of identical hard spheres has been proven to be the fcc lattice, and it is conjectured that the closest packing is ordered (a regular lattice, e.g., a crystal) in low enough dimension. Still, amorphous packings have attracted much interest because for polydisperse colloids and granular materials the crystalline state is not obtained in experiments for kinetic reasons. A theory of amorphous packings, and more generally glassy states, of hard spheres is reviewed here, that is based on the replica method: this theory gives predictions on the structure and thermodynamics of these states. In dimensions between two and six these predictions can be successfully compared with numerical simulations. The limit of large dimension is also discussed where an exact solution is possible. Some of the results presented here were published, but others are original: in particular, an improved discussion of the large dimension limit and new results on the correlation function and the contact force distribution in three dimensions. The main assumptions that are beyond the theory presented are clarified and, in particular, the relation between static computation and the dynamical procedures used to construct amorphous packings. There remain many weak points in the theory that should be better investigated.

Parisi, Giorgio; Zamponi, Francesco

2010-01-01

92

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

93

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

PubMed

A modified Pade? 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 Pade? 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. PMID:23205976

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

2012-11-28

94

Monte Carlo methods for estimating depletion potentials in highly size-asymmetrical hard sphere mixtures  

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

95

Replica exchange Monte Carlo applied to hard spheres.  

PubMed

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

Odriozola, Gerardo

2009-10-14

96

Depletion effects in smectic phases of hard-rod-hard-sphere mixtures  

Microsoft Academic Search

.  It is known that when hard spheres are added to a pure system of hard rods the stability of the smectic phase may be greatly\\u000a enhanced, and that this effect can be rationalised in terms of depletion forces. In the present paper we first study the effect\\u000a of orientational order on depletion forces in this particular binary system, comparing our

Y. Martinez-Ratón; Giorgio Cinacchi; Enrique Velasco; Luis Mederos

2006-01-01

97

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

PubMed Central

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

Mittal, Jeetain

2009-01-01

98

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

PubMed

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

2013-01-01

99

A numerical calculation of the excitation of helium II based on the hard-sphere model  

Microsoft Academic Search

In this letter we would like to report some numerical computations of a hard-sphere Boson system at liquid helium density. These computations are based on an exact iteration process from non-local field operators and with the core diameter taken as 2.1 Å. The Hamiltonian includes only the repulsive hardcore taken into consideration via the algebra for these field operators developed

K. W. Wong; Y. H. Huang

1969-01-01

100

High-order virial coefficients and equation of state for hard sphere and hard disk systems.  

PubMed

A very simple and accurate approach is proposed to predict the high-order virial coefficients of hard spheres and hard disks. In the approach, the nth virial coefficient B(n) is expressed as the sum of n(D-1) and a remainder, where D is the spatial dimension of the system. When n > or = 3, the remainders of the virials can be accurately expressed with Padé-type functions of n. The maximum deviations of predicted B(5)-B(10) for the two systems are only 0.0209%-0.0044% and 0.0390%-0.0525%, respectively, which are much better than the numerous existing approaches. The virial equation based on the predicted virials diverges when packing fraction eta = 1. With the predicted virials, the compressibility factors of hard sphere system can be predicted very accurately in the whole stable fluid region, and those in the metastable fluid region can also be well predicted up to eta = 0.545. The compressibility factors of hard disk fluid can be predicted very accurately up to eta = 0.63. The simulated B(7) and B(10) for hard spheres are found to be inconsistent with the other known virials and therefore they are modified as 53.2467 and 105.042, respectively. PMID:19830321

Hu, Jiawen; Yu, Yang-Xin

2009-11-01

101

Electrical resistivity of liquid lanthanides using charge hard sphere system  

NASA Astrophysics Data System (ADS)

In the present paper, we have studied electrical resistivity (?) of liquid lanthanides. To describe the structural information, the structure factor S(q) due to the charged hard sphere (CHS) reference systems is used along with our newly constructed model potential. To see the influence of exchange and correlation effect on the electrical resistivity (?) have used different local field correction functions like Hartree (H), Sarkar et al (S) and Taylor (T). Lastly we conclude that the proper choice of the model potential along with local field correction function plays a vital role to the study of the electrical resistivity (?).

Sonvane, Y. A.; Thakor, P. B.; Jani, A. R.

2013-06-01

102

Correlation and prediction of the transport properties of refrigerants using two modified rough hard-sphere models  

SciTech Connect

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] [Georgia Inst. of Tech., Atlanta, GA (United States). School of Chemical Engineering; Smith, R.L. Jr. [Tohoku Univ., Sendai (Japan). Dept. of Chemical Engineering] [Tohoku Univ., Sendai (Japan). Dept. of Chemical Engineering

1999-01-01

103

A Monte Carlo study of the freezing transition of hard spheres  

NASA Astrophysics Data System (ADS)

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

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

2011-08-01

104

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

PubMed

A simulation method for fluid-solid transitions, which is based on a modification of the constrained cell model of Hoover and Ree, is developed and tested on a system of hard spheres. In the fully occupied constrained cell model, each particle is confined in its own Wigner-Seitz cell. Constant-pressure simulations of the constrained cell model for a system of hard spheres indicate a point of mechanical instability at a density which is about 64% of the density at the close packed limit. Below that point, the solid is mechanically unstable since without the confinement imposed by the cell walls it will disintegrate to a disordered, fluid-like phase. Hoover and Ree proposed a modified cell model by introducing an external field of variable strength. High values of the external field variable favor configurations with one particle per cell and thus stabilize the solid phase. In this work, the modified cell model of a hard-sphere system is simulated under constant-pressure conditions using tempering and histogram reweighting techniques. The simulations indicate that as the strength of the field is reduced, the transition from the solid to the fluid phase is continuous below the mechanical instability point and discontinuous above. The fluid-solid transition of the hard-sphere system is determined by analyzing the field-induced fluid-solid transition of the modified cell model in the limit in which the external field vanishes. The coexistence pressure and densities are obtained through finite-size scaling techniques and are in good accord with previous estimates. PMID:21795778

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

2011-08-17

105

Nonequilibrium thermodynamics in sheared hard-sphere materials.  

PubMed

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

2012-06-01

106

Branching points in the low-temperature dipolar hard sphere fluid.  

PubMed

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. PMID:24116579

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

2013-10-01

107

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

108

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

NASA Astrophysics Data System (ADS)

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

Kirkpatrick, T. R.

1985-11-01

109

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

NASA Astrophysics Data System (ADS)

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

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

2014-04-01

110

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

PubMed

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

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

2014-04-01

111

Nested sampling for materials: The case of hard spheres  

NASA Astrophysics Data System (ADS)

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

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

2014-02-01

112

Mean Spherical Model Integral Equation for Charged Hard Spheres. II. Results.  

National Technical Information Service (NTIS)

The authors continue their investigation of the solution of the mean spherical model integral equation for systems of charged hard spheres and charged hard sheets (in one dimension). The paper contains explicit expressions for the structure functions and ...

E. Waisman J. L. Lebowitz

1971-01-01

113

Mean Spherical Model Integral Equation for Charged Hard Spheres. I. Method of Solution.  

National Technical Information Service (NTIS)

The thermodynamic properties and radial distribution function of a 'primitive model electrolyte' are calculated in the Mean Spherical Model (MSM) approximation. The system considered is formally described as a classical fluid of charged hard spheres (hard...

E. Waisman J. L. Lebowitz

1971-01-01

114

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

PubMed

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

115

Critical flux of hard sphere suspensions in crossflow filtration: Hydrodynamic force bias Monte Carlo simulations  

Microsoft Academic Search

A Monte Carlo method is developed for crossflow membrane filtration to determine the critical flux of hard sphere suspensions. Brownian and shear-induced diffusion are incorporated into an effective hydrodynamic force exerted on the hard spheres in a concentrated shear flow. Effects of shear rate and particle size on the critical flux are investigated using hydrodynamic force bias Monte Carlo simulations,

Albert S. Kim; Yuewei Liu

2008-01-01

116

Anisotropic spheres with variable energy density in general relativity  

Microsoft Academic Search

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

117

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

PubMed

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

Baranau, Vasili; Tallarek, Ulrich

2014-06-01

118

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

NASA Astrophysics Data System (ADS)

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

Tessarotto, Massimo; Cremaschini, Claudio

2014-05-01

119

Simple and accurate theory for strong shock waves in a dense hard-sphere fluid  

NASA Astrophysics Data System (ADS)

Following an earlier work by Holian et al. [Phys. Rev. E 47, R24 (1993)] for a dilute gas, we present a theory for strong shock waves in a hard-sphere fluid described by the Enskog equation. The idea is to use the Navier-Stokes hydrodynamic equations but taking the temperature in the direction of shock propagation rather than the actual temperature in the computation of the transport coefficients. In general, for finite densities, this theory agrees much better with Monte Carlo simulations than the Navier-Stokes and (linear) Burnett theories, in contrast to the well-known superiority of the Burnett theory for dilute gases.

Montanero, J. M.; López de Haro, M.; Santos, A.; Garzó, V.

1999-12-01

120

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

PubMed

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

2012-10-01

121

Avalanches mediate crystallization in a hard-sphere glass.  

PubMed

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

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

2014-01-01

122

Avalanches mediate crystallization in a hard-sphere glass  

PubMed Central

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

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

2014-01-01

123

Crystallization time scales for polydisperse hard-sphere fluids  

NASA Astrophysics Data System (ADS)

We study the evolution of crystallization in dense mono- and polydisperse hard sphere fluids, initially quenched to an amorphous configuration. We use as signatures of crystallization both the decay of the reduced pressure Z and the increase in the local and global orientational order parameters Q¯6. For a given realization of the crystallization process these parameters show sudden changes, both large and small, separated by long periods of quiescence. However, averaging over a large number of realizations, a well-defined scenario for their evolution appears. We find an initial fast relaxation to a disordered state, followed by a period of slow variation, associated to the presence of nucleation events, followed by a fast change, composed of the growth of a few crystals with different orientations, and a final and slow coarsening in a domain-growth process. No clear scaling for this whole process was found. We also find that the transition to an stable glassy fluid is quite sharp as the polydispersity is increased, showing a probable first-order phase transition behavior. A well-defined boundary between crystallizing and permanently amorphous fluids should exist, at least for a region in packing fractions. We looked for segregation at large values of polydispersity, but no effects of this type were found.

Vargas, M. Cristina; Pérez-Ángel, Gabriel

2013-04-01

124

Even hard-sphere colloidal suspensions display fickian yet non-gaussian diffusion.  

PubMed

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

Guan, Juan; Wang, Bo; Granick, Steve

2014-04-22

125

Dynamic light scattering measurements in the activated regime of dense colloidal hard spheres  

NASA Astrophysics Data System (ADS)

We use dynamic light scattering and numerical simulations to study the approach to equilibrium and the equilibrium dynamics of systems of colloidal hard spheres over a broad range of densities, from dilute systems up to very concentrated suspensions undergoing glassy dynamics. We discuss several experimental issues (sedimentation, thermal control, non-equilibrium ageing effects, dynamic heterogeneity) arising when very large relaxation times are measured. When analyzed over more than seven decades in time, we find that the equilibrium relaxation time, ??, of our system is described by the algebraic divergence predicted by mode-coupling theory over a window of about three decades. At higher density, ?? increases exponentially with distance to a critical volume fraction phiv0, which is much larger than the mode-coupling singularity. This is reminiscent of the behavior of molecular glass-formers in the activated regime. We compare these results to previous work, carefully discussing crystallization and size polydispersity effects. Our results suggest the absence of a genuine algebraic divergence of ?? in colloidal hard spheres.

El Masri, D.; Brambilla, G.; Pierno, M.; Petekidis, G.; Schofield, A. B.; Berthier, L.; Cipelletti, L.

2009-07-01

126

Dynamics in dense hard-sphere colloidal suspensions  

NASA Astrophysics Data System (ADS)

The dynamic behavior of a hard-sphere colloidal suspension was studied by x-ray photon correlation spectroscopy and small-angle x-ray scattering over a wide range of particle volume fractions. The short-time mobility of the particles was found to be smaller than that of free particles even at relatively low concentrations, showing the importance of indirect hydrodynamic interactions. Hydrodynamic functions were derived from the data, and for moderate particle volume fractions (?? 0.40) there is good agreement with earlier many-body theory calculations by Beenakker and Mazur [Physica A0378-437110.1016/0378-4371(84)90206-1 120, 349 (1984)]. Important discrepancies appear at higher concentrations, above ?? 0.40, where the hydrodynamic effects are overestimated by the Beenakker-Mazur theory, but predicted accurately by an accelerated Stokesian dynamics algorithm developed by Banchio and Brady [J. Chem. Phys.0021-960610.1063/1.1571819 118, 10323 (2003)]. For the relaxation rates, good agreement was also found between the experimental data and a scaling form predicted by the mode coupling theory. In the high concentration range, with the fluid suspensions approaching the glass transition, the long-time diffusion coefficient was compared with the short-time collective diffusion coefficient to verify a scaling relation previously proposed by Segrè and Pusey [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.77.771 77, 771 (1996)]. We discuss our results in view of previous experimental attempts to validate this scaling law [L. Lurio , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.84.785 84, 785 (2000)].

Orsi, Davide; Fluerasu, Andrei; Moussaïd, Abdellatif; Zontone, Federico; Cristofolini, Luigi; Madsen, Anders

2012-01-01

127

A Monte Carlo algorithm for computing spin echo small angle neutron scattering correlation functions in real space: Hard sphere liquids.  

PubMed

A Monte Carlo algorithm is developed to compute the autocorrelation function of liquids and the corresponding spatial correlation function from spin echo small angle neutron scattering (SESANS) spectra. The accuracy of the simulation algorithm is tested with isolated hard spheres and single dumbbells consisting of two hard spheres separated by a given distance. The simulation results accurately reproduce the exact expressions of these two models. To further test the algorithm for many-body systems, two liquid models are considered including hard sphere fluids and hard spheres with an attractive tail. The many-particle Monte Carlo simulation is carried out to obtain the ensemble average of these correlation functions. Meanwhile, the Percus-Yevic (PY) integral equation theory is resorted to compute the autocorrelation function and SESANS spatial correlation function for a density that the PY theory is reasonably applicable. The agreement between simulation and theory indicates that the algorithm is quite robust and can be extended to more complex fluids in the future. Furthermore, we find that the SESANS spatial correlation function is highly sensitive to the interaction potential between particles, which may serve as a useful tool to explore particle interactions in a liquid. PMID:20113065

Shew, Chwen-Yang; Chen, Wei-Ren

2010-01-28

128

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

National Technical Information Service (NTIS)

Perturbative variational calculations of thermodynamic and structural properties of liquid metals, based on the use of ab initio and highly reliable nonlocal pseudopotentials for the electron-ion interactions and of the fluid of charged hard spheres as re...

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

1990-01-01

129

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

130

Thermodynamic pressures for hard spheres and closed-virial equation-of-state.  

PubMed

Hard-sphere molecular dynamics (MD) simulation results, with six-figure accuracy in the thermodynamic equilibrium pressure, are reported and used to test a closed-virial equation-of-state. This latest equation, with no adjustable parameters except known virial coefficients, is comparable in accuracy both to Padé approximants, and to numerical parameterizations of MD data. There is no evidence of nonconvergence at stable fluid densities. The virial pressure begins to deviate significantly from the thermodynamic fluid pressure at or near the freezing density, suggesting that the passage from stable fluid to metastable fluid is associated with a higher-order phase transition; an observation consistent with some previous experimental results. Revised parameters for the crystal equation-of-state [R. J. Speedy, J. Phys.: Condens. Matter 10, 4387 (1998)] are also reported. PMID:20192307

Bannerman, Marcus N; Lue, Leo; Woodcock, Leslie V

2010-02-28

131

The rheology of hard sphere suspensions at arbitrary volume fractions: An improved differential viscosity model  

Microsoft Academic Search

We propose a simple and general model accounting for the dependence of the viscosity of a hard sphere suspension at arbitrary volume fractions. The model constitutes a continuum-medium description based on a recursive-differential method where correlations between the spheres are introduced through an effective volume fraction. In contrast to other differential methods, the introduction of the effective volume fraction as

Carlos I. Mendoza; I. Santamaría-Holek

2009-01-01

132

Direct simulation of diatomic gases using the generalized hard sphere model  

NASA Technical Reports Server (NTRS)

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

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

1993-01-01

133

A Monte Carlo study of the freezing transition of hard spheres  

Microsoft Academic Search

A simulation method for fluid-solid transitions, which is based on a modification of the constrained cell model of Hoover and Ree, is developed and tested on a system of hard spheres. In the fully occupied constrained cell model, each particle is confined in its own Wigner-Seitz cell. Constant-pressure simulations of the constrained cell model for a system of hard spheres

Michael Nayhouse; Ankur M. Amlani; G. Orkoulas

2011-01-01

134

Simulation of the chemical potential and the cavity free energy of dense hard-sphere fluids  

Microsoft Academic Search

The chemical potential of dense hard-sphere fluids, and also the work of cavity formation, are simulated directly by a force-balance Monte Carlo technique. Here the coupling between a solute and the solvent varies in the presence of an external field. For a hard-sphere fluid the variable is the cavity diameter, and the scaled particle theory proves sufficient for the applied

Phil Attard

1993-01-01

135

Hard-sphere perturbation theory for a model of liquid Ga  

NASA Astrophysics Data System (ADS)

Investigating thermodynamic properties of a model for liquid Ga, we have extended the application of the hard-sphere (HS) perturbation theory to an interatomic pair potential that possesses a soft repulsive core and a long-range oscillatory part. The model is interesting for displaying a discontinuous jump on the main-peak position of the radial distribution function at some critical density. At densities less than this critical value, the effective HS diameter of the model, estimated by the variational HS perturbation theory, has a substantial reduction with increasing density. Thus, the density dependence of the packing fraction of the HS reference fluid has an anomalous behavior, with a negative slope, within a density region below the critical density. By adding a correction term originally proposed by Mon to remedy the inherent deficiency of the HS perturbation theory, the extended Mansoori-Canfield/Rasaiah-Stell theory [J. Chem. Phys. 120, 4844 (2004)] very accurately predicts the Helmholtz free energy and entropy of the model, including an excess entropy anomaly. Almost occurring in the same density region, the excess entropy anomaly is found to be associated with the anomalous packing faction of the HS fluid.

Tsai, K. H.; Wu, Ten-Ming

2008-07-01

136

Hard-sphere perturbation theory for a model of liquid Ga.  

PubMed

Investigating thermodynamic properties of a model for liquid Ga, we have extended the application of the hard-sphere (HS) perturbation theory to an interatomic pair potential that possesses a soft repulsive core and a long-range oscillatory part. The model is interesting for displaying a discontinuous jump on the main-peak position of the radial distribution function at some critical density. At densities less than this critical value, the effective HS diameter of the model, estimated by the variational HS perturbation theory, has a substantial reduction with increasing density. Thus, the density dependence of the packing fraction of the HS reference fluid has an anomalous behavior, with a negative slope, within a density region below the critical density. By adding a correction term originally proposed by Mon to remedy the inherent deficiency of the HS perturbation theory, the extended Mansoori-Canfield/Rasaiah-Stell theory [J. Chem. Phys. 120, 4844 (2004)] very accurately predicts the Helmholtz free energy and entropy of the model, including an excess entropy anomaly. Almost occurring in the same density region, the excess entropy anomaly is found to be associated with the anomalous packing faction of the HS fluid. PMID:18624534

Tsai, K H; Wu, Ten-Ming

2008-07-14

137

Two hard spheres in a pore: Exact statistical mechanics for different shaped cavities  

Microsoft Academic Search

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

Ignacio Urrutia; Investigaciones Científicas; Energía Atómica; San Martín

2010-01-01

138

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

139

Dynamic Simulations of Hard-Sphere Suspensions Under Steady Shear  

Microsoft Academic Search

We have studied the flow of suspensions of solid spheres under steady shear using a newly developed flow simulator. For the first time, the complicated interplay between hydrodynamic interactions and solids' variable configuration under flow conditions in which large departures from equilibrium configurations occur can be simulated in full 3D. For volume fractions up to 35%, viscosities have been obtained

J. M. V. A. Koelman; P. J. Hoogerbrugge

1993-01-01

140

Packing of crystalline structures of binary hard spheres: An analytical approach and application to amorphization  

NASA Astrophysics Data System (ADS)

The geometrical stability of the three lattices of the cubic crystal system, viz. face-centered cubic (fcc), body-centered cubic (bcc), and simple cubic (sc), consisting of bimodal discrete hard spheres, and the transition to amorphous packing is studied. First, the random close packing (rcp) fraction of binary mixtures of amorphously packed spheres is recapitulated. Next, the packing of a binary mixture of hard spheres in randomly disordered cubic structures is analyzed, resulting in original analytical expressions for the unit cell volume and the packing fraction, and which are also valid for the other five crystal systems. The bimodal fcc lattice parameter appears to be in close agreement with empirical hard sphere data from literature, and this parameter could be used to distinguish the size mismatch effect from all other effects in distorted binary lattices of materials. Here, as a first model application, bimodal amorphous and crystalline fcc/bcc packing fractions are combined, yielding the optimum packing configuration, which depends on mixture composition and diameter ratio only. Maps of the closest packing mode are established and applied to colloidal mixtures of polydisperse spheres and to binary alloys of bcc, fcc, and hcp metals. The extensive comparison between the analytical expressions derived here and the published numerical and empirical data yields good agreement. Hence, it is seen that basic space-filling theories on “simple” noninteracting hard spheres are a valuable tool for the study of crystalline materials.

Brouwers, H. J. H.

2007-10-01

141

Evaporation from or condensation onto a sphere: Numerical analysis of the Boltzmann equation for hard-sphere molecules  

Microsoft Academic Search

A steady weak evaporation from or condensation onto a spherical condensed phase in its vapor gas is investigated, mainly numerically, on the basis of the Boltzmann equation for hard-sphere molecules. The numerical method is the combination of the hybrid-difference-scheme method, which can describe the discontinuity of the velocity distribution function in the gas, and the numerical kernel method [1]. The

M. Wakabayashi

1998-01-01

142

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

143

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

SciTech Connect

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

144

On the relation between virial coefficients and the close-packing of hard disks and hard spheres.  

PubMed

The question of whether the known virial coefficients are enough to determine the packing fraction ?(?) at which the fluid equation of state of a hard-sphere fluid diverges is addressed. It is found that the information derived from the direct Pade? approximants to the compressibility factor constructed with the virial coefficients is inconclusive. An alternative approach is proposed which makes use of the same virial coefficients and of the equation of state in a form where the packing fraction is explicitly given as a function of the pressure. The results of this approach both for hard-disk and hard-sphere fluids, which can straightforwardly accommodate higher virial coefficients when available, lends support to the conjecture that ?(?) is equal to the maximum packing fraction corresponding to an ordered crystalline structure. PMID:21361546

Maestre, Miguel Angel G; Santos, Andrés; Robles, Miguel; de Haro, Mariano López

2011-02-28

145

A mean-field hard-spheres model of glass  

Microsoft Academic Search

We present a model of spheres moving in a high-dimensional compact space. We relate it to a mixed matrix model with a O.N\\/ invariant model plus a P. N\\/invariant perturbation. We then study the low pressure regime by performing a diagrammatic expansion of this matrix model. Finally, we show the results from numerical simulations and we present evidence for a

L F Cugliandoloy; Piazzale A Moro

1996-01-01

146

The effect of surface friction on the rheology of hard-sphere colloids  

Microsoft Academic Search

Intuition plus experimental evidence indicate that an essential, but missing, ingredient from all previous theoretical and\\u000a simulation models of experimental idealised hard-sphere monodisperse suspensions is surface friction. The modelling of real, i.e., rough, spheres requires\\u000a at least one additional system parameter, to account for contact rotational friction, in thedimensional analysis leading to\\u000a corresponding states scaling laws.\\u000a \\u000a Idealised latex particles with

J. Castle; A. Farid; L. Woodcock

147

Binary mixture of nonadditive hard spheres adsorbed in a slit pore: a study of the population inversion by the integral equations theory.  

PubMed

The structure of a binary mixture of nonadditive hard spheres confined in a slit pore is studied by the integral equations method in which the confining medium acts as a giant particle at infinite dilution. The adsorption/desorption curves are studied as a function of the composition and density, when the homogeneous bulk mixture is near the demixing instability. The Ornstein-Zernike integral equations are solved with the reference functional approximation closure in which the bridge functions are derived from Rosenfeld's hard sphere functional for additive hard sphere. To study the high composition asymmetry regime in which a population inversion occurs, we developed an approximate closure that overcomes the no solution problem of the integral equation. By comparison with simulation data, this method is shown to be sufficiently accurate for predicting the threshold density for the population inversion. The predictions of simpler closure relations are briefly examined. PMID:21090779

Ayadim, A; Amokrane, S

2010-12-23

148

Universal Features of Collective Interactions in Hard-Sphere Systems at Higher Volume Fractions  

NASA Astrophysics Data System (ADS)

In order to investigate the universal features of collective behavior due to the many-body interactions, we perform two types of computer simulations on hard-sphere systems, a Brownian-dynamics simulation on polydisperse suspensions of hard spheres, where the hydrodymamic interactions between particles are neglected, and a molecular-dynamics simulation on atomic systems of hard spheres. Thus, we show that the long-time self-diffusion coefficient in atomic systems has the same form as that derived theoretically by Tokuyama and Oppenheim (TO) for the monodisperse suspension by taking into account the many-body hydrodynamic interactions, except that the singular point is now replaced by a new one. We also show that the difference between two coefficients in both systems can be well explained by the short-time self-diffusion coefficient derived theoretically for a wide range of volume fractions.

Tokuyama, M.; Terada, Y.; Yamazaki, H.; Oppenheim, I.

2004-04-01

149

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

PubMed

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

Fantoni, Riccardo; Santos, Andrés

2014-06-28

150

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

PubMed

A quantitative analysis is presented for the stochastic interactions of a pair of Brownian hard spheres in non-adsorbing polymer solutions. The hard spheres are hypothetically trapped by optical tweezers and allowed for random motion near the trapped positions. The investigation focuses on the long-time correlated Brownian motion. The mobility tensor altered by the polymer depletion effect is computed by the boundary integral method, and the corresponding random displacement is determined by the fluctuation-dissipation theorem. From our computations it follows that the presence of depletion layers around the hard spheres has a significant effect on the hydrodynamic interactions and particle dynamics as compared to pure solvent and uniform polymer solution cases. The probability distribution functions of random walks of the two interacting hard spheres that are trapped clearly shift due to the polymer depletion effect. The results show that the reduction of the viscosity in the depletion layers around the spheres and the entropic force due to the overlapping of depletion zones have a significant influence on the correlated Brownian interactions. PMID:24908040

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

2014-06-01

151

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

NASA Astrophysics Data System (ADS)

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

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

2014-06-01

152

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

PubMed

Kernels for the collision integral of the linear Boltzmann equation are presented for several cases. First, a rigorous and complete derivation of the velocity kernel for spherical particles is given, along with reductions to the smooth, rigid sphere case. This combines and extends various derivations for this kernel which have appeared previously in the literature. In addition, the analogous kernel is derived for the rough hard sphere model, for which a dependence upon both velocity and angular velocity is required. This model can account for exchange between translational and rotational degrees of freedom. Finally, an approximation to the exact rough hard sphere kernel is presented which averages over the rotational degrees of freedom in the system. This results in a kernel depending only upon velocities which retains a memory of the exchange with rotational states. This kernel tends towards the smooth hard sphere kernel in the limit when translational-rotational energy exchange is attenuated. Comparisons are made between the smooth and approximate rough hard sphere kernels, including their dependence upon velocity and their eigenvalues. PMID:24182019

Khurana, Saheba; Thachuk, Mark

2013-10-28

153

Isoperimetric problems on the sphere and on surfaces with density  

Microsoft Academic Search

We discuss partitions of the sphere and other ellipsoids into equal areas and isoperimetric problems on surfaces with density. We prove that the least-perimeter partition of any ellipsoid into two equal areas is by division along the shortest equator. We extend the work of C. Quinn, 2007, and give a new sufficient condition for a perimeter- minimizing partition of S2

Max Engelstein; Anthony Marcuccio; Quinn Maurmann; Taryn Pritchard

154

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

PubMed Central

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

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

2013-01-01

155

Gel Transition in Adhesive Hard-Sphere Colloidal Dispersions: The Role of Gravitational Effects  

NASA Astrophysics Data System (ADS)

The role of gravity in gelation of adhesive hard spheres is studied and a critical criterion developed for homogeneous gelation within the gas-liquid binodal. We hypothesize that gelation by Brownian diffusion competes with phase separation enhanced by gravitational settling. This competition is characterized by the gravitational Péclet number Peg, which is a function of particle size, volume fraction, and gravitational acceleration. Through a systematic variation of the parameters, we observe the critical Peg of ˜0.01 can predict the stability of gels composed of adhesive hard spheres.

Kim, Jung Min; Fang, Jun; Eberle, Aaron P. R.; Castañeda-Priego, Ramón; Wagner, Norman J.

2013-05-01

156

The probability density function of the multiplication factor due to small, random displacements of fissile spheres  

Microsoft Academic Search

An analytical expression is obtained for the probability density function of the multiplication factor of an array of spheres when each sphere is displaced in a random fashion from its initial position. Two cases are considered: (1) spheres in an infinite background medium in which the total cross section in spheres and medium is the same, and (2) spheres in

M. M. R. Williams

2003-01-01

157

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

Microsoft Academic Search

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

Douglas Henderson; Peter J. Leonard

1970-01-01

158

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

National Technical Information Service (NTIS)

The evaluation of thermodynamic properties of liquid alkali metals is re-examined in the approach based on the Gibbs-Bogoliubov inequality and using the fluid of charged hard spheres in the mean spherical approximation as reference system, with a view to ...

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

1989-01-01

159

Molecular Dynamics Simulation of a Piston Driven Shock Wave in a Hard Sphere Gas.  

National Technical Information Service (NTIS)

Molecular dynamics simulation is used to study the piston driven shock wave at Mach 1.5, 3, and 10. A shock tube, whose shape is a circular cylinder, is filled with hard sphere molecules having a Maxwellian thermal velocity distribution and zero mean velo...

M. Woo I. Greber

1995-01-01

160

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

Microsoft Academic Search

We present and validate a variance reduced deviational particle method for simulating the Boltzmann transport equation for the variable hard sphere (VHS) collision operator. In comparison with the direct simulation Monte Carlo (DSMC) method, the proposed method is more suitable for simulating transport in regimes where the departure from equilibrium is small, such as dilute gas flows in small-scale devices

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

2011-01-01

161

Direct simulation of diatomic gases using the generalized hard sphere model  

Microsoft Academic Search

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

D. B. Hash; H. A. Hassan

1993-01-01

162

Enskog-Landau kinetic equation. Calculation of the transport coefficients for charged hard spheres  

Microsoft Academic Search

Using the charged hard sphere model as an example, the dense one-component plasma is considered. For this model, the Enskog-Landau kinetic equation is obtained and its normal solution is found using the Chapman-Enskog method. Transport coefficients are obtained numerically and analytically which are then compared with the experimental data available.

A. E. Kobryn; V. G. Morozov; I. P. Omelyan; M. V. Tokarchuk

1996-01-01

163

A comprehensive approach to an equation of state for hard spheres and Lennard Jones fluids  

Microsoft Academic Search

We present a simple method of obtaining various equations of state for hard sphere fluid in a simple unifying way. We will guess equations of state by using suitable axiomatic functional forms (n = 1, 2, 3, 4, 5) for surface tension Smn(r), r >= d\\/2 with intermolecular separation r as a variable, where m is an arbitrary real number

S. B. Khasare

2011-01-01

164

Large-amplitude jumps and non-Gaussian dynamics in highly concentrated hard sphere fluids  

Microsoft Academic Search

Our microscopic stochastic nonlinear Langevin equation theory of activated dynamics has been employed to study the real-space van Hove function of dense hard sphere fluids and suspensions. At very short times, the van Hove function is a narrow Gaussian. At sufficiently high volume fractions, such that the entropic barrier to relaxation is greater than the thermal energy, its functional form

Erica J. Saltzman; Kenneth S. Schweizer

2008-01-01

165

Analytical representation of the Percus-Yevick hard-sphere radial distribution function  

Microsoft Academic Search

Explicit analytical expressions, written in terms of complex variables and suitable for rapid computer evaluation, are presented for the Percus-Yevick hard-sphere radial distribution function, g(R), for R ˇ- 5sigma. Some effects of truncating g(R) to unity past R = 5 sigma are discussed.

W. R. Smith; D. Henderson

1970-01-01

166

Direct simulation of diatomic gases using the generalized hard sphere model  

Microsoft Academic Search

The generalized hard sphere model that incorporates the effects of attraction and repulsion is examined. First, the model is used to study simple adiabatic heat baths. Then, it is used to predict flow measurements in tests involving extremely low freestream temperatures. For the two cases considered, a Mach 26 nitrogen shock and a Mach 20 nitrogen flow over a flat

D. B. Hash; James N. Moss; H. A. Hassan

1994-01-01

167

Cooling Process for Inelastic Boltzmann Equations for Hard Spheres, Part I: The Cauchy Problem  

Microsoft Academic Search

We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitution coefficients depending on the kinetic energy and the relative velocity as well as the sticky particles model. We prove (local in time) non-concentration estimates in Orlicz spaces, from which we deduce weak

Stéphane Mischler; Clément Mouhot; Mariano Rodriguez Ricard

2006-01-01

168

Integral equation theory of hard sphere liquids on two-dimensional cylindrical surfaces  

Microsoft Academic Search

An integral equation theory has been developed to elucidate the structure of hard sphere liquids on the two dimensional (2D) surface of a cylinder. The 2D cylindrical coordinate breaks the spherical symmetry. Hence, the pair correlation function is reformulated as a function of two variables to account for particles packing along and around the cylinder. Both Percus–Yevick (PY) and Hypernetted

Takafumi Iwaki; Chwen-Yang Shew; Godfrey Gumbs

2006-01-01

169

Cooling process for inelastic Boltzmann equations for hard spheres, Part I: The Cauchy problem  

Microsoft Academic Search

We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitution coefficients depending on the kinetic energy and the relative velocity as well as the sticky particles model. We prove (local in time) non-concentration estimates in Orlicz spaces, from which we deduce weak

S. Mischler; C. Mouhot; M. Rodriguez Ricard

2004-01-01

170

The orientational pair correlation functions in a dense hard sphere fluid at long times  

Microsoft Academic Search

The two-particle contribution to the potential part of the stress tensor autocorrelation function of a dense hard sphere fluid is studied. It is shown that the long-time decay is given as the solution of a diffusion equation for the relative particle in a potential of mean force. The diffusion constant needed in order to accurately reproduce molecular dynamics results is

Jan A. Leegwater; Henk van Beijeren

1989-01-01

171

Note: Equation of state and the freezing point in the hard-sphere model  

NASA Astrophysics Data System (ADS)

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

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

2014-04-01

172

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

PubMed

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

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

2014-04-01

173

Flow heterogeneity and correlations in a sheared hard sphere glass: Insight from computer simulations  

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

174

Mesophase formation in a system of top-shaped hard molecules: Density functional theory and Monte Carlo simulation  

Microsoft Academic Search

We present the phase diagram of a system of mesogenic top-shaped molecules based on the Parsons-Lee density functional theory and Monte Carlo simulation. The molecules are modeled as a hard spherocylinder with a hard sphere embedded in its center. The stability of five different phases is studied, namely, isotropic, nematic, smectic A, smectic C, and columnar phases. The positionally ordered

Daniel de las Heras; Szabolcs Varga; Franz J. Vesely

2011-01-01

175

Polydispersity and Optimal Relaxation in the Hard Sphere Fluid  

NASA Astrophysics Data System (ADS)

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

Barbier, Matthieu; Trizac, Emmanuel

2014-03-01

176

Numerical analysis of a uniform flow of a rarefied gas past a sphere on the basis of the Boltzmann equation for hard-sphere molecules  

Microsoft Academic Search

A slow uniform flow of a rarefied gas past a sphere is investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules and the diffuse reflection condition. With the aid of a similarity solution, the Boltzmann equation is reduced to two simultaneous integrodifferential equations with three independent variables, which are solved numerically. The collision integral is computed efficiently

Shigeru Takata; Yoshio Sone; Kazuo Aoki

1993-01-01

177

Depletion potentials in highly size-asymmetric binary hard-sphere mixtures: Comparison of simulation results with theory  

NASA Astrophysics Data System (ADS)

We report a detailed study, using state-of-the-art simulation and theoretical methods, of the effective (depletion) potential between a pair of big hard spheres immersed in a reservoir of much smaller hard spheres, the size disparity being measured by the ratio of diameters q??s/?b. Small particles are treated grand canonically, their influence being parameterized in terms of their packing fraction in the reservoir ?sr. Two Monte Carlo simulation schemes—the geometrical cluster algorithm, and staged particle insertion—are deployed to obtain accurate depletion potentials for a number of combinations of q?0.1 and ?sr. After applying corrections for simulation finite-size effects, the depletion potentials are compared with the prediction of new density functional theory (DFT) calculations based on the insertion trick using the Rosenfeld functional and several subsequent modifications. While agreement between the DFT and simulation is generally good, significant discrepancies are evident at the largest reservoir packing fraction accessible to our simulation methods, namely, ?sr=0.35. These discrepancies are, however, small compared to those between simulation and the much poorer predictions of the Derjaguin approximation at this ?sr. The recently proposed morphometric approximation performs better than Derjaguin but is somewhat poorer than DFT for the size ratios and small-sphere packing fractions that we consider. The effective potentials from simulation, DFT, and the morphometric approximation were used to compute the second virial coefficient B2 as a function of ?sr. Comparison of the results enables an assessment of the extent to which DFT can be expected to correctly predict the propensity toward fluid-fluid phase separation in additive binary hard-sphere mixtures with q?0.1. In all, the new simulation results provide a fully quantitative benchmark for assessing the relative accuracy of theoretical approaches for calculating depletion potentials in highly size-asymmetric mixtures.

Ashton, Douglas J.; Wilding, Nigel B.; Roth, Roland; Evans, Robert

2011-12-01

178

An improved perturbed hard-sphere equation of state  

Microsoft Academic Search

The Carnahan–Starling–Patel–Teja (CSPT) equation of state was revisited to improve the fitting accuracy of vapour–liquid equilibrium data of pure fluid substances. By setting the pseudo-critical compressibility factor and the correction coefficient in the attractive parameter as the temperature-dependent variables, the fitting accuracies of the vapour pressures and the saturated liquid-phase densities from the new CSPT increased significantly compared with the

Guang-Wen Wu; Jonathan Ennis-King; Lincoln Paterson

2009-01-01

179

Demixing transition, structure, and depletion forces in binary mixtures of hard-spheres: The role of bridge functions  

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

180

Demixing transition, structure, and depletion forces in binary mixtures of hard-spheres: the role of bridge functions.  

PubMed

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. Castañeda-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. PMID:24050366

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

2013-09-14

181

Theory of molecular crowding in Brownian hard-sphere liquids  

NASA Astrophysics Data System (ADS)

We derive an analytical pair potential of mean force for Brownian molecules in the liquid state. Our approach accounts for many-particle correlations of crowding particles of the liquid and for diffusive transport across the spatially modulated local density of crowders in the dense environment. Focusing on the limit of equal-size particles, we show that this diffusive transport leads to additional density- and structure-dependent terms in the interaction potential and to a much stronger attraction (by a factor of ?4 at average volume fraction of crowders ?0=0.25) than in the standard depletion interaction where the diffusive effects are neglected. As an illustration of the theory, we use it to study the size of a polymer chain in a solution of inert crowders. Even in the case of an athermal background solvent, when a classical chain should be fully swollen, we find a sharp coil-globule transition of the ideal chain collapsing at a critical value of the crowder volume fraction ?c?0.145.

Zaccone, Alessio; Terentjev, Eugene M.

2012-06-01

182

On the asymptotic properties of a hard sphere fluid.  

PubMed

An analysis of the expected divergences in thermodynamic properties at the close-pack density (eta(cp) = pi square root(2)/6) along with the known virial coefficients up to 10th order suggests a weak logarithmic singularity in the excess fluid entropy. The corresponding equation of state (EOS) also possesses a singularity at eta(cp). The new EOS accurately describes extant molecular dynamics data up to the fluid-solid transition (eta approximately 0.494) with differences of less than 1 part per thousand. This accuracy is maintained into the metastable fluid regime up to eta approximately 0.52. In terms of accuracy, the new EOS is no better than Pade approximants, but the new EOS, unlike the Pade approximants, diverges at eta(cp). In addition, a new order parameter is defined that enables all system configurations to be classified as either disordered or ordered. Monte Carlo simulations are used to determine this order parameter in the metastable fluid range. Using this new order parameter, evidence is presented to support a thermodynamic glass transition at eta approximately 0.54. With respect to this transition, congruence is found with the traditional ideas espoused by Gibbs and DiMarzio and Adam and Gibbs. It is the rapid disappearance of disordered (random) configurations with increasing density that drives the glass transition and slows the dynamics. PMID:19921954

Sanchez, Isaac C; Lee, Jang S

2009-11-26

183

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

NASA Astrophysics Data System (ADS)

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

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

2010-05-01

184

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

PubMed

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

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

2010-05-01

185

Path-integral ground state and superfluid hydrodynamics of a bosonic gas of hard spheres  

NASA Astrophysics Data System (ADS)

We study a bosonic gas of hard spheres by using the exact zero-temperature path-integral ground-state (PIGS) Monte Carlo method and the equations of superfluid hydrodynamics. The PIGS method is implemented to calculate for the bulk system the energy per particle and the condensate fraction through a large range of the gas parameter na3 (with n the number density and a the s-wave scattering length), going from the dilute gas into the solid phase. The Maxwell construction is then adopted to determine the freezing at na3=0.264±0.003 and the melting at na3=0.290±0.003. In the liquid phase, where the condensate fraction is finite, the equations of superfluid hydrodynamics, based on the PIGS equation of state, are used to find other relevant quantities as a function of the gas parameter: the chemical potential, the pressure, and the sound velocity. In addition, within Feynman's approximation, from the PIGS static structure factor we determine the full excitation spectrum, which displays a maxon-roton behavior when the gas parameter is close to the freezing value. Finally, the equations of superfluid hydrodynamics with the PIGS equation of state are solved for the bosonic system under axially symmetric harmonic confinement obtaining its collective breathing modes.

Rossi, Maurizio; Salasnich, Luca

2013-11-01

186

Communication: Radial distribution functions in a two-dimensional binary colloidal hard sphere system  

NASA Astrophysics Data System (ADS)

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

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

2014-04-01

187

Communication: Radial distribution functions in a two-dimensional binary colloidal hard sphere system.  

PubMed

Two-dimensional hard disks are a fundamentally important many-body model system in classical statistical mechanics. Despite their significance, a comprehensive experimental data set for two-dimensional single component and binary hard disks is lacking. Here, we present a direct comparison between the full set of radial distribution functions and the contact values of a two-dimensional binary colloidal hard sphere model system and those calculated using fundamental measure theory. We find excellent quantitative agreement between our experimental data and theoretical predictions for both single component and binary hard disk systems. Our results provide a unique and fully quantitative mapping between experiments and theory, which is crucial in establishing the fundamental link between structure and dynamics in simple liquids and glass forming systems. PMID:24784245

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

2014-04-28

188

Solvation interactions in colloidal dispersions using the adhesive hard sphere model  

NASA Astrophysics Data System (ADS)

Colloidal particles dispersed in a liquid are modelled by a binary mixture of large spheres in a “solvent” of small spheres; so the discrete nature of the solvent molecules is explicitly taken into account. It is shown in the Percus-Yevick approximation that, following the adhesive hard sphere model, the effective repulsion between the large particles decreases by increasing the stickness between the solvent molecules (simulation of a “poor” solvent). The isothermal osmotic compressibility goes to infinity when the adhesive strength between the solvent becomes very high and phase separation may occur. By increasing the stickness between the solvent and large solute particles the effective repulsion between the solute particles increases, which can be interpreted as a better solvation of the particles.

Penders, M. H. G. M.; Vrij, A.

1991-05-01

189

The rheology of hard sphere suspensions at arbitrary volume fractions: An improved differential viscosity model.  

PubMed

We propose a simple and general model accounting for the dependence of the viscosity of a hard sphere suspension at arbitrary volume fractions. The model constitutes a continuum-medium description based on a recursive-differential method where correlations between the spheres are introduced through an effective volume fraction. In contrast to other differential methods, the introduction of the effective volume fraction as the integration variable implicitly considers interactions between the spheres of the same recursive stage. The final expression for the viscosity scales with this effective volume fraction, which allows constructing a master curve that contains all the experimental situations considered. The agreement of our expression for the viscosity with experiments at low- and high-shear rates and in the high-frequency limit is remarkable for all volume fractions. PMID:19191410

Mendoza, Carlos I; Santamaría-Holek, I

2009-01-28

190

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

NASA Technical Reports Server (NTRS)

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

Ling, Jerri S.; Doherty, Michael P.

1998-01-01

191

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

NASA Technical Reports Server (NTRS)

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

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

1998-01-01

192

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

PubMed

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

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

2004-06-01

193

Local shear viscosity of strongly inhomogeneous dense fluids: from the hard-sphere to the Lennard-Jones fluids.  

PubMed

This work aims at providing a tractable approach to model the local shear viscosity of strongly inhomogeneous dense fluids composed of spherical molecules, in which the density variations occur on molecular distance. The proposed scheme, which relies on the local density average model, has been applied to the quasi-hard-sphere, the Week-Chandler-Andersen and the Lennard-Jones fluids. A weight function has been developed to deal with the hard-sphere fluid given the specificities of momentum exchange. To extend the approach to the smoothly repulsive potential, we have taken into account that the non-local contributions to the viscosity due to the interactions of particles separated by a given distance are temperature dependent. Then, using a simple perturbation scheme, the approach is extended to the Lennard-Jones fluids. It is shown that the viscosity profiles of inhomogeneous dense fluids deduced from this approach are consistent with those directly computed by non-equilibrium molecular dynamics simulations. PMID:24132101

Hoang, Hai; Galliero, Guillaume

2013-12-01

194

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

195

Structure of Some 4f Rare Earth Liquid Metals — A Charged Hard Sphere Approach  

Microsoft Academic Search

A well-established pseodopotential is used to study the structure of some 4f rare earth liquid metals (Ce, Pr, Eu, Gd, Tb, and Yb). The structure factor S(q), pair distribution function g(r), interatomic distance r1, and coordination number n1 are calculated using Charged Hard Sphere (CHS) reference system. To introduce the exchange and correlation effects, the local field correction due to

P. B. Thakor; P. N. Gajjar; A. R. Jani

2006-01-01

196

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

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

197

Linear Hard-Sphere Gas: Variational Eigenvalue Spectra of the Energy Kernel  

Microsoft Academic Search

The relaxation problem for the linear hard-sphere gas is considered using a Rayleigh–Ritz expansion of the energy kernel for transitions in a test-particle\\/heat-bath system at variable mass ratio ?. The basis sets used are the “exact” eigenfunctions for the problem in the Rayleigh limit ? ? 0 and the required expansion matrices can be obtained to order at least 20

M. R. Hoare; C. H. Kaplinsky

1970-01-01

198

Estimation of the free energy of hard-sphere crystals via a free-volume approach  

Microsoft Academic Search

The free energies of the face-centred (FCC) and base-centred cubic (BCC) hard-sphere (HS) crystals have been estimated via the free-volume approach. We present two free-volume equations for the FCC and BCC HS crystals, which are different from those predicted by Velasco et al. [Langmuir 14(19) (1998), 5652–5655], and the equations exhibit more accuracy than Velasco et al.'s equations. The limitation

Sang Kyu Kwak; Yong-Jin Yoon; Jong-Min Lee

2012-01-01

199

Radial distribution function of a hard-sphere fluid for the nearest neighbor surroundings  

Microsoft Academic Search

An expression for RDF as a function of two variables, the distance r and the packing factor ?, was obtained by approximating the results of Monte Carlo simulation of a hard-sphere fluid. The\\u000a mean square accuracy of the expressions presented is about ±0.0002 (1 ? r ? 1.5, 0 ? ? ? 0.5). A continuous extension of RDF to the

Yu. T. Pavlyukhin

2007-01-01

200

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

Microsoft Academic Search

We present an efficient particle simulation method for the Boltzmann transport equation based on the low-variance deviational simulation Monte Carlo approach to the variable-hard-sphere gas. The proposed method exhibits drastically reduced statistical uncertainty for low-signal problems compared to standard particle methods such as the direct simulation Monte Carlo method. We show that by enforcing mass conservation, accurate simulations can be

Gregg A. Radtke; Nicolas G. Hadjiconstantinou; Wolfgang Wagner

2011-01-01

201

Integral equation theory for hard spheres confined on a cylindrical surface: Anisotropic packing entropically driven  

Microsoft Academic Search

The structure of two-dimensional (2D) hard-sphere fluids on a cylindrical surface is investigated by means of the Ornstein-Zernike integral equation with the Percus-Yevick and the hypernetted-chain approximation. The 2D cylindrical coordinate breaks the spherical symmetry. Hence, the pair-correlation function is reformulated as a two-variable function to account for the packing along and around the cylinder. Detailed pair-correlation function calculations based

Takafumi Iwaki; Chwen-Yang Shew; Godfrey Gumbs

2005-01-01

202

A simplified expression for the hard-sphere dimer fluid radial distribution function  

Microsoft Academic Search

Recently, in our laboratory a closed form expression for the correlation function of the hard-sphere dimer fluid obtained\\u000a from Wertheims multidensity Ornstein-Zernike integral equation theory with Percus-Yevick approximation was presented by Kim\\u000a et al. [2001]. However, it is difficult to apply its expression to perturbation theory and vapor-liquid equilibria calculations,\\u000a since it is of very complex form. In this work,

Jichul An; Hwayong Kim

2005-01-01

203

Estimation of the free energy of hard-sphere crystals via a free-volume approach  

Microsoft Academic Search

The free energies of the face-centred (FCC) and base-centred cubic (BCC) hard-sphere (HS) crystals have been estimated via the free-volume approach. We present two free-volume equations for the FCC and BCC HS crystals, which are different from those predicted by Velasco et al. [Langmuir 14(19) (1998), 5652–5655], and the equations exhibit more accuracy than Velasco et al.'s equations. The limitation

Sang Kyu Kwak; Yong-Jin Yoon; Jong-Min Lee

2011-01-01

204

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

Microsoft Academic Search

We discuss the nature of phase transitions in self-gravitating systems both in the microcanonical and in the canonical ensemble. We avoid the divergence of the gravitational potential at short distances by considering the case of self-gravitating fermions and hard-sphere models. Depending on the values of the parameters, three kinds of phase transitions (of zeroth, first, and second order) are evidenced.

Pierre-Henri Chavanis

2002-01-01

205

Group contributions to activity coefficients from the hard sphere expansion corresponding states theory  

NASA Astrophysics Data System (ADS)

A new method has been developed for predicting liquid activity coefficients in ternary mixtures from group contributions. In this method, activity coefficients are obtained from the excess Gibbs free energy of mixing at constant temperature and pressure. In calculating this excess function, the constituent and mixture Gibbs free energies are each represented by an expansion about a pure reference fluid in powers of ratios of hard-sphere diameters and molecular attraction parameters. When the pure component differs from the reference by a single structural group, these ratios represent, respectively, the size contribution and the attraction contribution of this group to the thermodynamic property of the pure fluid. Contributions of intermolecular repulsion to the excess Gibbs free energy are calculated directly from hard-sphere equations of state for the mixture and pure components. The effect of polar contributions calculated by a Padé approximant is also examined. Results indicate that the method developed from the hard-sphere expansion corresponding-states theory is useful for predicting activity coefficients in ternary mixtures when unlike-pair interaction parameters are fitted to binary activity coefficient data. Furthermore, the method shows promise in providing a theoretical basis for applying group contributions to activity coefficients.

Quock, D. E. R.; Leland, T. W.

1986-03-01

206

Equation of state of the hard-disk fluid on a sphere from Percus–Yevick equation  

Microsoft Academic Search

The Percus–Yevick equation is solved numerically for hard disks on a sphere. The effect of curvature of the hosting surface is calculated, and an empirical correction to the equation of state is proposed.

S. V. Lishchuk

2006-01-01

207

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

NASA Astrophysics Data System (ADS)

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

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

2000-01-01

208

An improved differential effective medium model for the viscosity of hard sphere suspensions at arbitrary volume fractions  

Microsoft Academic Search

We propose a simple and general model accounting for the dependence of the viscosity of a hard sphere suspension at arbitrary volume fractions. The model constitutes a continuum-medium description based on a recursive-differential method where correlations between the spheres are introduced through an effective volume fraction. In contrast to other differential methods, the introduction of the effective volume fraction as

Carlos Mendoza; Ivan Santamaria-Holek

2009-01-01

209

Simulation of spatial correlations of impurity ions in solids using configurational entropy and the hard-sphere model  

Microsoft Academic Search

Based on the hard-sphere model, the spatial correlations are considered in a system of impurities with variable valency. In\\u000a a zeroth approximation, the configurational entropy of the spatially correlated system of impurity ions is identified with\\u000a the configurational entropy of a system of hard spheres. The electron mobility limited by scattering on the correlated system\\u000a of impurity ions at finite

V. M. Mikheev

2005-01-01

210

Evaporation and condensation on a plane condensed phase - Numerical analysis of the linearized Boltzmann equation for hard-sphere molecules  

Microsoft Academic Search

The behavior of a semi-infinite expanse of a gas bounded by its plane condensed phase, where evaporation or condensation is taking place, is considered on the basis of the linearized Boltzmann equation for hard-sphere molecules. The half-space boundary-value problem of the linearized Boltzmann equation for hard-sphere molecules is solved numerically by the finite difference method introduced in the temperature jump

Yoshio Sone; Taku Ohwada; Kazuo Aoki

1989-01-01

211

On the Brownian motion of a massive sphere suspended in a hard-sphere fluid. I. Multiple-time-scale analysis and microscopic expression for the friction coefficient  

Microsoft Academic Search

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

Lydéric Bocquet; Jaroslaw Piasecki; Jean-Pierre Hansen

1994-01-01

212

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

NASA Astrophysics Data System (ADS)

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

Mirigian, Stephen; Schweizer, Kenneth S.

2014-05-01

213

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

Microsoft Academic Search

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

214

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

Microsoft Academic Search

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

215

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

Microsoft Academic Search

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; Hernan Makse

2011-01-01

216

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

NASA Technical Reports Server (NTRS)

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

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

2005-01-01

217

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

NASA Astrophysics Data System (ADS)

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

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

2011-07-01

218

Structure of Some 4f Rare Earth Liquid Metals — A Charged Hard Sphere Approach  

NASA Astrophysics Data System (ADS)

A well-established pseodopotential is used to study the structure of some 4f rare earth liquid metals (Ce, Pr, Eu, Gd, Tb, and Yb). The structure factor S(q), pair distribution function g(r), interatomic distance r1, and coordination number n1 are calculated using Charged Hard Sphere (CHS) reference system. To introduce the exchange and correlation effects, the local field correction due to Sarkar et al. (S) is applied. The present investigation is successful in generating the structural information of Ce, Pr, Eu, Gd, Tb, and Yb 4f rare earth liquid metals.

P. B., Thakor; P. N., Gajjar; A. R., Jani

2006-08-01

219

Nonadditive hard-sphere reference system for a perturbative liquid state theory of binary systems  

NASA Astrophysics Data System (ADS)

Here for the first time a Weeks-Chandler-Andersen perturbation theory for binary liquid systems, using nonadditive hard spheres as a reference system for the repulsive parts of the potentials, is presented. The nonadditivity of realistic systems - such as binary metal alloys - can therefore properly be taken into account. Treating nonadditive systems with additive reference systems by introducing additional parameters is no longer necessary, and the parameters are determined uniquely. Including in a subsequent step the attractive forces by means of the optimized random phase approximation, it is found that agreement with other liquid state theories as well as with experimental scattering data is very good, even for extremely nonadditive systems.

Kahl, Gerhard

1990-10-01

220

Equivalence of glass transition and colloidal glass transition in the hard-sphere limit.  

PubMed

We show that the slowing of the dynamics in simulations of several model glass-forming liquids is equivalent to the hard-sphere glass transition in the low-pressure limit. In this limit, we find universal behavior of the relaxation time by collapsing molecular-dynamics data for all systems studied onto a single curve as a function of T/p, the ratio of the temperature to the pressure. At higher pressures, there are deviations from this universal behavior that depend on the interparticle potential, implying that additional physical processes must enter into the dynamics of glass formation. PMID:20366210

Xu, Ning; Haxton, Thomas K; Liu, Andrea J; Nagel, Sidney R

2009-12-11

221

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

222

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

PubMed

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. PMID:24160538

Chen, W

2013-10-21

223

Communication: Structure characterization of hard sphere packings in amorphous and crystalline states.  

PubMed

The channel size distribution in hard sphere systems, based on the local neighbor correlation of four particle positions, is investigated for all volume fractions up to jamming. For each particle, all three particle combinations of neighbors define channels, which are relevant for the concept of caging. The analysis of the channel size distribution is shown to be very useful in distinguishing between gaseous, liquid, partially and fully crystallized, and glassy (random) jammed states. A common microstructural feature of four coplanar particles is observed in crystalline and glassy jammed states, suggesting the presence of "hidden" two-dimensional order in three-dimensional random close packings. PMID:24907982

Ogarko, Vitaliy; Rivas, Nicolas; Luding, Stefan

2014-06-01

224

Perturbation approach for equation of state for hard-sphere and Lennard–Jones pure fluids  

Microsoft Academic Search

In this paper we have established the equation of state (EOS) for liquids. The EOS was established for hard-sphere (HS) fluid\\u000a along with Lennard–Jones (LJ) fluid incorporating perturbation techniques. The calculations are based on suitable axiomatic\\u000a functional forms for surface tension S\\u000a \\u000a m\\u000a (r), r???d\\/2 with intermolecular separation r, as a variable, and m is an arbitrary real number (pole).

S B KHASARE; M S DESHPANDE

2011-01-01

225

Structural properties of liquid lanthanides using charge hard sphere reference system  

NASA Astrophysics Data System (ADS)

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

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

2012-06-01

226

Hard-Sphere Model of Activation Energy Originated in Ion Size: Gate Model  

NASA Astrophysics Data System (ADS)

The gate model is proposed such that a mobile ion happens to hop between adjacent sites only when immobile (gate) ions probabilistically move away to keep an enough space: By taking account of hard-sphere ions vibrating around their stable sites, the transition probability rate \\varGamma is statistical-mechanically evaluated according to the Vineyard method. The obtained \\varGamma is of activation-type where the activation energy increases with the overlap length defined with radii of mobile and immobile ions, and also increases with the gate frequency.

Ishii, Tadao

1992-06-01

227

Minimal Energy Packings and Collapse of Sticky Tangent Hard-Sphere Polymers  

NASA Astrophysics Data System (ADS)

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.

Hoy, Robert S.; O'Hern, Corey S.

2010-08-01

228

Anisotropic diffusion of concentrated hard-sphere colloids near a hard wall studied by evanescent wave dynamic light scattering  

NASA Astrophysics Data System (ADS)

Evanescent wave dynamic light scattering and Stokesian dynamics simulations were employed to study the dynamics of hard-sphere colloidal particles near a hard wall in concentrated suspensions. The evanescent wave averaged short-time diffusion coefficients were determined from experimental correlation functions over a range of scattering wave vectors and penetration depths. Stokesian dynamics simulations performed for similar conditions allow a direct comparison of both the short-time self- and collective diffusivity. As seen earlier [V. N. Michailidou, G. Petekidis, J. W. Swan, and J. F. Brady, Phys. Rev. Lett. 102, 068302 (2009)] while the near wall dynamics in the dilute regime slow down compared to the free bulk diffusion, the reduction is negligible at higher volume fractions due to an interplay between the particle-wall and particle-particle hydrodynamic interactions. Here, we provide a comprehensive comparison between experiments and simulations and discuss the interplay of particle-wall and particle-particle hydrodynamics in the self- and cooperative dynamics determined at different scattering wave vectors and penetration depths.

Michailidou, V. N.; Swan, J. W.; Brady, J. F.; Petekidis, G.

2013-10-01

229

Molecular dynamics calculations of the hard-sphere equation of state  

SciTech Connect

The equation of state of the hard-sphere fluid is studied by a Monte Carlo-molecular dynamics method for volumes ranging from 25 V/sub 0/ to 1.6V/sub 0/, where V/sub 0/ is the close-packed volume, and for systems sizes from 108 to 4000 particles. The N dependence of the equation of state is compared to the theoretical dependence given by Salsburg for the NPT ensemble, after correction for the ensemble difference, in order to obtain estimates for the thermodynamic limit. The observed values of the pressure are compared with both the (3/2) and the (2/3) Pade approximants to the virial series, using Kratky's value for the fifth virial coefficient B/sub 5/ and choosing B/sub 6/ and B/sub 7/ to obtain a least-squares fit. The resulting values of B/sub 6/ and B/sub 7/ lie within the uncertainties of the Ree-Hoover-Kratky Monte Carlo estimates for these virial coefficients. The values of B/sub 8/, B/sub 9/, and B/sub 10/ predicted by our optimal (3/2) approximant are also reported. Finally, the Monte Carlo-molecular dynamics equation of state is compared with a number of analytic number of analytic expressions for the hard-sphere equation of state.

Erpenbeck, J.J.; Wood, W.W.

1984-05-01

230

Multicomponent adhesive hard sphere models and short-ranged attractive interactions in colloidal or micellar solutions.  

PubMed

We investigate the dependence of the stickiness parameters tij=1/(12tauij)--where the tauij are the conventional Baxter parameters--on the solute diameters sigmai and sigmaj in multicomponent sticky hard sphere (SHS) models for fluid mixtures of mesoscopic neutral particles. A variety of simple but realistic interaction potentials, utilized in the literature to model short-ranged attractions present in real solutions of colloids or reverse micelles, is reviewed. We consider: (i) van der Waals attractions, (ii) hard-sphere-depletion forces, (iii) polymer-coated colloids, and (iv) solvation effects (in particular hydrophobic bonding and attractions between reverse micelles of water-in-oil microemulsions). We map each of these potentials onto an equivalent SHS model by requiring the equality of the second virial coefficients. The main finding is that, for most of the potentials considered, the size-dependence of tij(T,sigmai,sigmaj) can be approximated by essentially the same expression, i.e., a simple polynomial in the variable sigmaisigmaj/sigmaij2, with coefficients depending on the temperature T, or--for depletion interactions--on the packing fraction eta0 of the depletant particles. PMID:17279909

Gazzillo, Domenico; Giacometti, Achille; Fantoni, Riccardo; Sollich, Peter

2006-11-01

231

Integral equation theory for hard spheres confined on a cylindrical surface: anisotropic packing entropically driven.  

PubMed

The structure of two-dimensional (2D) hard-sphere fluids on a cylindrical surface is investigated by means of the Ornstein-Zernike integral equation with the Percus-Yevick and the hypernetted-chain approximation. The 2D cylindrical coordinate breaks the spherical symmetry. Hence, the pair-correlation function is reformulated as a two-variable function to account for the packing along and around the cylinder. Detailed pair-correlation function calculations based on the two integral equation theories are compared with Monte Carlo simulations. In general, the Percus-Yevick theory is more accurate than the hypernetted-chain theory, but exceptions are observed for smaller cylinders. Moreover, analysis of the angular-dependent contact values shows that particles are preferentially packed anisotropically. The origin of such an anisotropic packing is driven by the entropic effect because the energy of all the possible system configurations of a dense hard-sphere fluid is the same. In addition, the anisotropic packing observed in our model studies serves as a basis for linking the close packing with the morphology of an ordered structure for particles adsorbed onto a cylindrical nanotube. PMID:16392516

Iwaki, Takafumi; Shew, Chwen-Yang; Gumbs, Godfrey

2005-09-22

232

Melting and crystallization of colloidal hard-sphere suspensions under shear  

PubMed Central

Shear-induced melting and crystallization were investigated by confocal microscopy in concentrated colloidal suspensions of hard-sphere-like particles. Both silica and polymethylmethacrylate suspensions were sheared with a constant rate in either a countertranslating parallel plate shear cell or a counterrotating cone-plate shear cell. These instruments make it possible to track particles undergoing shear for extended periods of time in a plane of zero velocity. Although on large scales, the flow profile deviated from linearity, the crystal flowed in an aligned sliding layer structure at low shear rates. Higher shear rates caused the crystal to shear melt, but, contrary to expectations, the transition was not sudden. Instead, although the overall order decreased with shear rate, this was due to an increase in the nucleation of localized domains that temporarily lost and regained their ordered structure. Even at shear rates that were considered to have melted the crystal as a whole, ordered regions kept showing up at times, giving rise to very large fluctuations in 2D bond-orientational order parameters. Low shear rates induced initially disordered suspensions to crystallize. This time, the order parameter increased gradually in time without large fluctuations, indicating that shear-induced crystallization of hard spheres does not proceed via a nucleation and growth mechanism. We conclude that the dynamics of melting and crystallization under shear differ dramatically from their counterparts in quiescent suspensions.

Wu, Yu Ling; Derks, Didi; van Blaaderen, Alfons; Imhof, Arnout

2009-01-01

233

Thermodynamic properties of mixtures of dipolar and quadrupolar hard spheres: Theory and simulation  

SciTech Connect

We report a comprehensive study of the thermodynamic properties (the Helmholtz energy, configurational energy, compressibility factor, and chemical potentials) for mixtures of dipolar hard spheres and quadrupolar hard spheres by computer simulation and from perturbation theory based on the Pade approximation. The dipole moment of dipolar component is fixed at {mu}{sub {ital A}}{sup *2}=3.0 and the quadrupole moment of quadrupolar component is varied up to {ital Q}{sub {ital B}}{sup *2}=3.0. The results show that the Pade approximation gives a good description of the Helmholtz energy and configuration energy of the mixtures, but some discrepancies are found for their derivatives, especially for compressibility factor. In view of very large deviations for the system from simple mixtures, the Pade approximation is rather successful for the system. These results are being used as a reference system in our effort to develop an equation of state for the CaCl{sub 2}--H{sub 2}O system.

Jiang, S.; Pitzer, K.S. [Department of Chemistry and Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720 (United States)] [Department of Chemistry and Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720 (United States)

1995-05-15

234

Mesophase formation in a system of top-shaped hard molecules: density functional theory and Monte Carlo simulation.  

PubMed

We present the phase diagram of a system of mesogenic top-shaped molecules based on the Parsons-Lee density functional theory and Monte Carlo simulation. The molecules are modeled as a hard spherocylinder with a hard sphere embedded in its center. The stability of five different phases is studied, namely, isotropic, nematic, smectic A, smectic C, and columnar phases. The positionally ordered phases are investigated only for the case of parallel alignment. It is found that the central spherical unit destabilizes the nematic with respect to the isotropic phase, while increasing the length of the cylinder has the opposite effect. Also, the central hard sphere has a strong destabilizing effect on the smectic A phase, due the inefficient packing of the molecules into layers. For large hard sphere units the smectic A phase is completely replaced by a smectic C structure. The columnar phase is first stabilized with increasing diameter of the central unit, but for very large hard sphere units it becomes less stable again. The density functional results are in good agreement with the simulations. PMID:21663376

de las Heras, Daniel; Varga, Szabolcs; Vesely, Franz J

2011-06-01

235

Mesophase formation in a system of top-shaped hard molecules: Density functional theory and Monte Carlo simulation  

NASA Astrophysics Data System (ADS)

We present the phase diagram of a system of mesogenic top-shaped molecules based on the Parsons-Lee density functional theory and Monte Carlo simulation. The molecules are modeled as a hard spherocylinder with a hard sphere embedded in its center. The stability of five different phases is studied, namely, isotropic, nematic, smectic A, smectic C, and columnar phases. The positionally ordered phases are investigated only for the case of parallel alignment. It is found that the central spherical unit destabilizes the nematic with respect to the isotropic phase, while increasing the length of the cylinder has the opposite effect. Also, the central hard sphere has a strong destabilizing effect on the smectic A phase, due the inefficient packing of the molecules into layers. For large hard sphere units the smectic A phase is completely replaced by a smectic C structure. The columnar phase is first stabilized with increasing diameter of the central unit, but for very large hard sphere units it becomes less stable again. The density functional results are in good agreement with the simulations.

de Las Heras, Daniel; Varga, Szabolcs; Vesely, Franz J.

2011-06-01

236

Flow past a sphere in density-stratified fluid  

Microsoft Academic Search

Stratified flow past a three-dimensional obstacle such as a sphere has been a long-lasting subject of geophysical, environmental and engineering fluid dynamics. In order to investigate the effect of the stratification on the near wake, in particular, the unsteady vortex formation behind a sphere, numerical simulations of stratified flows past a sphere are conducted. The time-dependent Navier–Stokes equations are solved

Sungsu Lee; Kyung-Soo Yang

2004-01-01

237

Density functional approximation for hard-body liquid crystals  

Microsoft Academic Search

We present a density functional approximation for the free energy of a system of hard bodies with arbitrary shape and orientational distribution. For systems with homogeneous density it reduces to existing treatments, which describe the isotropic liquid and the nematic liquid crystal. The treatment of the inhomogeneous density allows the study of smectic and crystal phases. We applied the approximation

A. M. Somoza; P. Tarazona

1989-01-01

238

Quantum Monte Carlo study of the dynamic structure factor in the gas and crystal phase of hard-sphere bosons  

NASA Astrophysics Data System (ADS)

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

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

2013-12-01

239

Density-functional theory for systems of hard rods  

Microsoft Academic Search

We present a density-functional theory, based on the smoothed density approximation, to study systems of hard rods with full translational and orientational freedom. For hard spherocylinders, we find both the nematic-isotropic and the nematic-smectic-A transition in a wide range of length-to-width ratios (L+D)\\/D. We locate the tricritical point for the nematic-smectic-A transition and also make some predictions about the nematic-smectic-A-smectic-B

A. Poniewierski; R. Holyst

1990-01-01

240

Solvent hard sphere diameter from van der Waals volume A statistical analysis of computed and solubility determined solvent diameters  

Microsoft Academic Search

Hard sphere diameters (dHS) of solvent molecules are useful quantities in evaluating the effect of the solvent by means of scaled particle theory, but they can be obtained only through elaborate experiments. It is shown here that dHS can be conveniently replaced with the diameter of van der Waals equivalence sphere (dV). Deviations were found in such replacements for polar,

Valentin Gogonea; Camelia Bãleanu-Gogonea; Eiji Osawa

1998-01-01

241

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

Microsoft Academic Search

Direct Simulation Monte Carlo (DSMC) modeling of spacecraft engine plume radiance in low earth orbit shows significant errors in plume size and shape. These errors are mainly due to deficiencies in extrapolating low energy (<1 eV) Variable Hard-Sphere (VHS) and Variable Soft-Sphere (VSS) collision models to hyperthermal collision energies (>1 eV) important in plume modeling. The VHS and VSS scattering

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

2008-01-01

242

Size asymmetric hard spheres as a convenient model for the capacitance of the electrical double layer of an ionic liquid  

NASA Astrophysics Data System (ADS)

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

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

2014-01-01

243

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

NASA Astrophysics Data System (ADS)

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

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

2012-06-01

244

Equation of state of sticky-hard-sphere fluids in the chemical-potential route.  

PubMed

The coupling-parameter method, whereby an extra particle is progressively coupled to the rest of the particles, is applied to the sticky-hard-sphere fluid to obtain its equation of state in the so-called chemical-potential route (? route). As a consistency test, the results for one-dimensional sticky particles are shown to be exact. Results corresponding to the three-dimensional case (Baxter's model) are derived within the Percus-Yevick approximation by using different prescriptions for the dependence of the interaction potential of the extra particle on the coupling parameter. The critical point and the coexistence curve of the gas-liquid phase transition are obtained in the ? route and compared with predictions from other thermodynamics routes and from computer simulations. The results show that the ? route yields a general better description than the virial, energy, compressibility, and zero-separation routes. PMID:24827207

Rohrmann, René D; Santos, Andrés

2014-04-01

245

Equation of state of sticky-hard-sphere fluids in the chemical-potential route  

NASA Astrophysics Data System (ADS)

The coupling-parameter method, whereby an extra particle is progressively coupled to the rest of the particles, is applied to the sticky-hard-sphere fluid to obtain its equation of state in the so-called chemical-potential route (? route). As a consistency test, the results for one-dimensional sticky particles are shown to be exact. Results corresponding to the three-dimensional case (Baxter's model) are derived within the Percus-Yevick approximation by using different prescriptions for the dependence of the interaction potential of the extra particle on the coupling parameter. The critical point and the coexistence curve of the gas-liquid phase transition are obtained in the ? route and compared with predictions from other thermodynamics routes and from computer simulations. The results show that the ? route yields a general better description than the virial, energy, compressibility, and zero-separation routes.

Rohrmann, René D.; Santos, Andrés

2014-04-01

246

``Sticky'' Hard Spheres: Equation of State, Phase Diagram, and Metastable Gels  

NASA Astrophysics Data System (ADS)

A large variety of engaging phenomena, ranging from crystallization in protein solutions to the formation of colloidal gels and glasses via depletion forces, stems from the occurrence of very short-ranged attractive forces. From depolarized light scattering measurements of equilibrium sedimentation profiles, we obtain an accurate description of the equation of state and of the phase diagram of colloids where depletion forces are tuned by the addition of a surfactant. For weak depletion, a colloidal fluid fully described by Baxter’s “sticky” hard sphere model coexists with ultradense colloidal crystals. For stronger attractive interactions, kinetically arrested looser gels form, showing an elastic modulus that scales as a power law of the local particle concentration.

Buzzaccaro, Stefano; Rusconi, Roberto; Piazza, Roberto

2007-08-01

247

Edwards' approach to horizontal and vertical segregation in a mixture of hard spheres under gravity  

NASA Astrophysics Data System (ADS)

We study the phenomenon of size segregation, observed in models of vibrated granular mixtures such as powders or sand. This consists of the de-mixing of the different components of the system under shaking. Several mechanisms have been proposed to explain this phenomenon. However, the criteria for predicting segregation in a mixture, an issue of great practical importance, are largely unknown. In the present paper we study a binary hard-sphere mixture under gravity on a three-dimensional lattice using Monte Carlo simulations. The vertical and horizontal segregation observed during the tap dynamics is interpreted in the framework of a statistical mechanics approach to granular media in the manner of Edwards. A phase diagram for the vertical segregation is derived, and compared with the simulation data.

Fierro, Annalisa; Nicodemi, Mario; Coniglio, Antonio

2003-03-01

248

Phase and rheological behavior of high-concentration colloidal hard-sphere and protein dispersions.  

PubMed

Colloidal hard-sphere (HS) particles of narrow-size distribution exhibit crystalline and glassy states beginning at the particle volume fractions phi = 0.494 and phi(G) = 0.58, respectively. Dynamic rheological data on the dispersions were strongly modified to solid-like behavior as phi approached phi(G). In addition, cooperative motion in structural relaxation has been observed microscopically in the colloidal dispersions near the glassy state. Very high viscosities and glassy states were also found in high-concentration dispersions of sodium caseinate and the globular proteins: bovine serum albumin and beta-lactoglobulin. Viscosity models developed for HS dispersions predicted accurately the trends but not the absolute values of protein dispersions. Dispersions of food colloidal particles may be employed in studies, in which volume fraction is the thermodynamic variable, for understanding the relaxation and transport processes related to 1st-order and colloidal glass transitions. PMID:17995655

Loveday, S M; Creamer, L K; Singh, H; Rao, M A

2007-09-01

249

Analytical behavior of the fourth and fifth virial coefficients of a hard-sphere mixture  

NASA Astrophysics Data System (ADS)

This paper focus on the study of the composition-dependent fourth and fifth virial coefficient of a hard-sphere binary mixture, namely, B4(s) and B5(s). On one side, the analytical expression of B4(s) is revised. In particular, I analyzed the composition-independent term B4[1](s) included in B4(s) and found a simplified form of its exact expression, which has the advantage over that previously published of highlighting the geometric properties of this term. On the other side, using a geometrical approach, I found a set of nonanalytic points of B4(s) and B5(s) as functions of s by analyzing each of their composition-independent terms.

Urrutia, Ignacio

2011-12-01

250

Microviscoelasticity of adhesive hard sphere dispersions: Tracer particle microrheology of aqueous Pluronic L64 solutions  

NASA Astrophysics Data System (ADS)

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

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

2009-10-01

251

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

NASA Astrophysics Data System (ADS)

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 remains to be assessed. Here we employ previously determined effective potentials for nonadditive hard-sphere mixtures to study the fluid-fluid phase transition by the hierarchical reference theory (HRT), which is designed to take realistically into account the effects of long-range fluctuations on phase separation. Fluid-solid equilibrium is addressed by supplementing HRT with thermodynamic perturbation theory for the solid phase. We apply this approach both to a potential with adjustable nonadditivity parameter (Louis et al 2000 Phys. Rev. E 61 R1028) and to the Asakura-Oosawa (AO) potential, which represents an extreme case of nonadditivity. Our results for the phase diagram, including modified hypernetted chain (MHNC) calculations, are compared to those of other liquid-state theories and are found to agree nicely with available simulation data. Unlike commonly adopted liquid-state theories, HRT is capable both of getting arbitrarily close to the fluid-fluid critical point, and of giving nontrivial critical exponents. In particular, the fluid-fluid coexistence curve is much flatter than that obtained via perturbation theory, in agreement with a recent finite-size scaling Monte Carlo analysis of the AO model.

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

2005-02-01

252

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

253

Solvent effects in weak electrolytes. I. Effect of a hard sphere solvent on the sticky electrolyte model with L=?  

Microsoft Academic Search

The Ornstein–Zernike (OZ) equations are solved for the sticky electrolyte model (SEM) with a hard sphere solvent using the hypernetted chain (HNC) approximation for the stickiness and the mean spherical (MS) approximation for the electrical interactions. Relations among the coefficients of Baxter’s q functions and the equation for the excess internal energy are given in the MS approximation for L??,

Jayendran C. Rasaiah; Jianjun Zhu; Song Hi Lee

1989-01-01

254

Simple cubic equation of state applied to hard-sphere, Lennard-Jones fluids, simple fluids and solids  

NASA Astrophysics Data System (ADS)

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

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

2013-09-01

255

Exact Solution of the Mean Spherical Model for Fluids of Hard Spheres with Permanent Electric Dipole Moments  

Microsoft Academic Search

The mean spherical model is solved in closed form for a fluid of hard spheres with permanent electric dipole moments. Both the pair distribution function g(12) and the direct correlation function c(12) consist of a spherically symmetric term and two other terms with different dependences on the orientations of the two dipole moments. The spherically symmetric part is the solution

M. S. Wertheim

1971-01-01

256

Liquid-state theory of structure, thermodynamics, and phase separation in suspensions of rod polymers and hard spheres  

Microsoft Academic Search

A new formulation of the polymer reference interaction site model (PRISM) theory for suspensions of hard spheres and rigid rods has been developed. The nonlocal loss of orientational entropy when a rod is near an impenetrable particle is accounted for in a thermodynamically self-consistent manner. In the ideal needle limit, quantitative predictions and qualitative scaling behaviors are determined for the

Y. L. Chen; K. S. Schweizer

2004-01-01

257

Cooling Process for Inelastic Boltzmann Equations for Hard Spheres, Part II: Self-Similar Solutions and Tail Behavior  

Microsoft Academic Search

We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres, in the framework of so-called constant normal restitution coefficients. We prove the existence of self-similar solutions, and we give pointwise estimates on their tail. We also give general estimates on the tail and the regularity of generic solutions. In particular we prove Haff's law on the rate of decay

Stéphane Mischler; Clément Mouhot

2006-01-01

258

Stability, convergence to self-similarity and elastic limit for the Boltzmann equation for inelastic hard spheres  

Microsoft Academic Search

We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres, in the framework of so-called constant normal restitution coefficients? ? (0,1). In the physical regime of a small inelasticity (that is ? ? (??,1) for some constructive ?? > 0) we prove uniqueness of the self-similar profile for given values of the resti- tution coefficient? ? (??,1), the mass

S. Mischler; C. Mouhot

2007-01-01

259

Numerical analysis of the shear flow of a binary mixture of hard-sphere gases over a plane wall  

Microsoft Academic Search

The shear flow of a binary mixture of rarefied gases over a plane wall is investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules with the diffuse reflection boundary condition. This fundamental problem in rarefied gas dynamics is analyzed numerically by a finite-difference method, in which the complicated collision integrals are computed by the extension to the

Shugo Yasuda; Shigeru Takata; Kazuo Aoki

2004-01-01

260

A new simple analytical expression for the average site–site radial distribution function of hard sphere chain fluid  

Microsoft Academic Search

A new simple analytical expression for the first coordination shell (1?x?2) of the average site–site intermolecular radial distribution function (ASSIRDF) of freely jointed tangent hard sphere chain fluid (FJTHSC) is proposed. The proposed expression is a polynomial expansion of packing fraction. The dependence of each polynomial coefficient on the radial coordinate and segment number is described by a polynomial expansion

H. Farrokhpour; M. Sohrabi Mahboub

2011-01-01

261

Structural and thermodynamical properties of charged hard spheres in a mixture with core-softened model solvent  

NASA Astrophysics Data System (ADS)

The canonical Monte Carlo computer simulations and integral equation theory were applied to examine the structural and thermodynamic properties of a mixture of ions and a core-softened fluid molecules. The positive and negative ions forming a +1:-1 salt were modeled as charged hard spheres, immersed in the dielectric medium. It was shown previously that the core-softened fluid under study is characterized by a set of structural, thermodynamic, and dynamic anomalies. The principal objective of this work was to elucidate how the presence of ions alters this behavior. The structural properties of the mixtures are discussed in terms of the pair distribution functions; in addition, the pair contribution to the excess entropy was calculated. Thermodynamic properties are investigated by using the dependencies of energy and compressibility factor on density, composition of the mixture, and reduced temperature. The heat capacity was also evaluated. Our principal findings concern the description of structural anomalies in the mixture, the dependence of the temperature of maximum density on the ionic concentration, and establishing the regions delimiting the structural and thermodynamic anomalies of the model mixture.

Lukši?, Miha; Hribar-Lee, Barbara; Vlachy, Vojko; Pizio, O.

2012-12-01

262

Structural and thermodynamical properties of charged hard spheres in a mixture with core-softened model solvent.  

PubMed

The canonical Monte Carlo computer simulations and integral equation theory were applied to examine the structural and thermodynamic properties of a mixture of ions and a core-softened fluid molecules. The positive and negative ions forming a +1:-1 salt were modeled as charged hard spheres, immersed in the dielectric medium. It was shown previously that the core-softened fluid under study is characterized by a set of structural, thermodynamic, and dynamic anomalies. The principal objective of this work was to elucidate how the presence of ions alters this behavior. The structural properties of the mixtures are discussed in terms of the pair distribution functions; in addition, the pair contribution to the excess entropy was calculated. Thermodynamic properties are investigated by using the dependencies of energy and compressibility factor on density, composition of the mixture, and reduced temperature. The heat capacity was also evaluated. Our principal findings concern the description of structural anomalies in the mixture, the dependence of the temperature of maximum density on the ionic concentration, and establishing the regions delimiting the structural and thermodynamic anomalies of the model mixture. PMID:23277940

Lukši?, Miha; Hribar-Lee, Barbara; Vlachy, Vojko; Pizio, O

2012-12-28

263

Sediments of soft spheres arranged by effective density  

NASA Astrophysics Data System (ADS)

Colloidal sedimentation has been studied for decades from both thermodynamic and dynamic perspectives. In the present work, binary mixtures of colloidal spheres are observed to separate spontaneously into two distinct layers on sedimentation. Both layers have a high volume fraction and contain distinct compositions of particles. Although predicting these compositions using settling dynamics is challenging, here we show that the compositions are readily predicted thermodynamically by minimizing the gravitational energy of the system. As the random packing fraction of a mixture of spheres exceeds that of monodisperse spheres of either type, the mixture produces a denser suspension that forms the bottom phase. Experimentally, the use of charged particles and low-ionic-strength solutions provides interparticle repulsions that keep the packed particles mobile, avoiding a glassy state that would prevent particles from reaching their equilibrium configuration. We extend this work beyond binary systems, showing similar separated layers for a five-component mixture of particles.

Serrano, César González; McDermott, Joseph J.; Velegol, Darrell

2011-09-01

264

Phase behavior and concentration fluctuations in suspensions of hard spheres and nearly ideal polymers  

NASA Astrophysics Data System (ADS)

The phase behavior and concentration fluctuations in suspensions of hard sphere colloids and nonadsorbing polymers under nearly ideal solvent conditions is studied experimentally. A remarkably different qualitative behavior compared to the athermal solvent case is observed for the dependence on polymer/particle size asymmetry of both the gelation and fluid-fluid phase separation boundaries. Near the theta state the effect of increasing the range of depletion attractions leads to a weak monotonic destabilization of the homogeneous phase at high particle volume fractions, with a reversal of the trend at lower volume fractions. In stark contrast to athermal solvent behavior, this nonmonotonic behavior results in multiple ``curve crossings'' of gel and phase separation boundaries as the polymer/particle size ratio is varied. Quantitative comparisons with no adjustable parameter PRISM integral equation theory for the fluid-fluid spinodals and osmotic compressibilities show good qualitative or semiquantitative agreement with all the experimental trends. The differences between good and ideal solvent conditions are largely attributed to changes in the polymer-polymer pair correlation functions due to the enhanced ability of coils to interpenetrate and cluster in theta solvents. Even for ideal solvent conditions the simplifying polymer model and statistical mechanical assumptions adopted by prior classic free volume and related approaches appear to miss fundamental aspects of the experimental behavior, especially for large size asymmetry ratios and/or moderate-to-high colloid volume fractions. The primary error can be identified with the approximation of a polymer chain by a phantom sphere with no conformational degrees of freedom.

Shah, S. A.; Chen, Y. L.; Schweizer, K. S.; Zukoski, C. F.

2003-02-01

265

Jammed lattice sphere packings  

NASA Astrophysics Data System (ADS)

We generate and study an ensemble of isostatic jammed hard-sphere lattices. These lattices are obtained by compression of a periodic system with an adaptive unit cell containing a single sphere until the point of mechanical stability. We present detailed numerical data about the densities, pair correlations, force distributions, and structure factors of such lattices. We show that this model retains many of the crucial structural features of the classical hard-sphere model and propose it as a model for the jamming and glass transitions that enables exploration of much higher dimensions than are usually accessible.

Kallus, Yoav; Marcotte, Étienne; Torquato, Salvatore

2013-12-01

266

Jammed lattice sphere packings.  

PubMed

We generate and study an ensemble of isostatic jammed hard-sphere lattices. These lattices are obtained by compression of a periodic system with an adaptive unit cell containing a single sphere until the point of mechanical stability. We present detailed numerical data about the densities, pair correlations, force distributions, and structure factors of such lattices. We show that this model retains many of the crucial structural features of the classical hard-sphere model and propose it as a model for the jamming and glass transitions that enables exploration of much higher dimensions than are usually accessible. PMID:24483429

Kallus, Yoav; Marcotte, Étienne; Torquato, Salvatore

2013-12-01

267

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

268

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

PubMed

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. PMID:22755584

Sesé, Luis M

2012-06-28

269

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

PubMed

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

2010-06-01

270

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

NASA Astrophysics Data System (ADS)

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

Bomont, Jean-Marc; Bretonnet, Jean-Louis

2014-08-01

271

Self-diffusion of non-interacting hard spheres in particle gels  

NASA Astrophysics Data System (ADS)

Different kinds of particle gels were simulated using a process of random aggregation of hard spheres. The mean square displacement of Brownian spherical tracer particles through these rigid gels was monitored and the average diffusion coefficient, normalized with the free diffusion coefficient (D), was obtained. For each gel structure the effect of the gel volume fraction (phi) and size ratio of the tracer (d) on the relative diffusion coefficient was investigated systematically. The volume fraction that is accessible to the tracers (phia) was determined in each case. D was found to be approximately the same if phia was the same, independent of phi, d and the gel structure. However a different behaviour is found if the tracers can penetrate the strands of the gel. A state diagram of d versus phi is given that shows the critical values (dc, phic) at which all tracers become trapped. Different values are found for different gel structures. The dependence of D on phi/phic is independent of d, while the dependence of D on d/dc is independent of phi.

Gimel, Jean-Christophe; Nicolai, Taco

2011-06-01

272

Crystal-melt interfacial free energy of binary hard spheres from capillary fluctuations  

NASA Astrophysics Data System (ADS)

Using molecular-dynamics simulation coupled with an analysis of equilibrium capillary fluctuations in interfacial position, we compute the magnitude and anisotropy of the interfacial free energy ? for a binary hard-sphere system with a diameter ratio ?=0.9 . This system, in which the fluid mixture coexists with a randomly substituted face-centered-cubic solid solution, is a useful reference model for alloys. Our results show that ? increases with increasing mole fraction of the smaller sized particle when temperature is held constant. However, after rescaling the results to fixed pressure and varying temperature, we find that ? decreases with increased alloying by the smaller particle (corresponding to lower temperatures). Thus, ? is seen to decrease with increasing concentration of the lower melting point solute, consistent with earlier simulations on Ni/Cu and Lennard-Jones mixtures. The anisotropy in ? is such that the inequality ?100>?110>?111 holds for all concentrations studied. Using the classification scheme of Haxhimali , [Nat. Mater. 5, 660 (2006)] we find that the anisotropy in ? is consistent with a predicted ?100? primary dendrite growth direction.

Amini, Majeed; Laird, Brian B.

2008-10-01

273

Low-shear Viscosity and Diffusion of Hard-sphere Dispersion at High Concentration  

NASA Astrophysics Data System (ADS)

We are interested in the rheology of hard-sphere dispersion at high concentration, especially the asymptotic behavior near the glass transition, which is the ideal place to test various theories.(J.F. Brady, J. Chem. phys. 99(1993)567) (M. Tokuyama and I. Oppenheim, Phys. Rev. E. 50(1994)R16) The dispersion studied is silica in Ethylene glycol/Glycerol/NaCl. Low-shear viscosity is measured by a Zimm viscometer. The data are consistent with recent PMMA measurement at low concentration(P.N. Segreet. al.), Phys. Rev. Lett. 75(1995)958; 76(1996)585 (See-eng Phan et. al.), Phys. rev. E., to be published., and at high concentration (metastable state) are better described by the Doolittle equation as in earlier experiments (L. Marshall, C.F. Zukoski IV, J. Phys. Chem. 94(1990)1164) (L.V. Woodcock, C.A. Angell, Phys. Rev. Lett. 47(1981)1129)). No theory yet gives a complete interpretion of the data. Dynamic light scattering (ensemble averaged) is used to measure self diffusion.

Cheng, Zhengdong; Chaikin, P. M.; Phan, See-Eng; Zhu, Jixiang; Russel, W. B.

1997-03-01

274

Solution of the mean spherical approximation for polydisperse multi-Yukawa hard-sphere fluid mixture using orthogonal polynomial expansions.  

PubMed

The Blum-Hoye [J. Stat. Phys. 19 317 (1978)] solution of the mean spherical approximation for a multicomponent multi-Yukawa hard-sphere fluid is extended to a polydisperse multi-Yukawa hard-sphere fluid. Our extension is based on the application of the orthogonal polynomial expansion method of Lado [Phys. Rev. E 54, 4411 (1996)]. Closed form analytical expressions for the structural and thermodynamic properties of the model are presented. They are given in terms of the parameters that follow directly from the solution. By way of illustration the method of solution is applied to describe the thermodynamic properties of the one- and two-Yukawa versions of the model. PMID:16555903

Kalyuzhnyi, Yurij V; Cummings, Peter T

2006-03-21

275

Solution of the mean spherical approximation for polydisperse multi-Yukawa hard-sphere fluid mixture using orthogonal polynomial expansions  

NASA Astrophysics Data System (ADS)

The Blum-Høye [J. Stat. Phys. 19 317 (1978)] solution of the mean spherical approximation for a multicomponent multi-Yukawa hard-sphere fluid is extended to a polydisperse multi-Yukawa hard-sphere fluid. Our extension is based on the application of the orthogonal polynomial expansion method of Lado [Phys. Rev. E 54, 4411 (1996)]. Closed form analytical expressions for the structural and thermodynamic properties of the model are presented. They are given in terms of the parameters that follow directly from the solution. By way of illustration the method of solution is applied to describe the thermodynamic properties of the one- and two-Yukawa versions of the model.

Kalyuzhnyi, Yurij V.; Cummings, Peter T.

2006-03-01

276

Molecular Dynamics. VI. Free-Path Distributions and Collision Rates for Hard-Sphere and Square-Well Molecules  

Microsoft Academic Search

Free-path distributions and collision rates for systems of hard-sphere and square-well molecules are computed and compared to simple models. Mean free paths for solids and dense fluids are found to be within 2% of those predicted by dividing the kinetic-theory mean free path by the relative probability of two molecules in contact. These mean free paths are much smaller than

T. Einwohner; B. J. Alder

1968-01-01

277

Monte Carlo simulations of the solid-liquid transition in hard spheres and colloid-polymer mixtures  

Microsoft Academic Search

Monte Carlo simulations at constant pressure are performed to study coexistence and interfacial properties of the liquid-solid transition in hard spheres and in colloid-polymer mixtures. The latter system is described as a one-component Asakura-Oosawa (AO) model where the polymer's degrees of freedom are incorporated via an attractive part in the effective potential for the colloid-colloid interactions. For the considered AO

T. Zykova-Timan; J. Horbach; K. Binder

2010-01-01

278

Perturbation and variational approach for the equation of state for hard-sphere and Lennard—Jones fluids  

Microsoft Academic Search

The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state (EOS) for a mixture of hard sphere (HS), Lennard—Jones (LJ) fluids. A suitable flexible functional form for the radial distribution function G(R) is assumed for the mixture, with R as a variable. The function G(R) has an

S. B. Khasare

2012-01-01

279

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

Microsoft Academic Search

We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres, in the framework of so-called constant normal restitution coefficients\\u000a $${\\\\alpha \\\\in [0,1]}$$ . In the physical regime of a small inelasticity (that is $${\\\\alpha \\\\in [\\\\alpha_*,1)}$$ for some constructive $${\\\\alpha_* \\\\in [0,1)}$$) we prove uniqueness of the self-similar profile for given values of the restitution coefficient $${\\\\alpha \\\\in [\\\\alpha_*,1)}$$

Stéphane Mischler; Clément Mouhot

2009-01-01

280

Self-structure factor of hard-sphere gases for arbitrary ratio of bath to test particle masses  

Microsoft Academic Search

The self-structure factor Ss(k,?) for test particles of mass different from the mass of the bath particles is considered. For a dilute hard-sphere gas the self-Enskog kinetic equation is solved to high accuracy for Ss(k,?) by the Gross–Jackson (GJ) modeling procedure. When the variables in the self-Enskog kinetic equation are scaled to customary dimensionless parameters, the peak height and width

Michael J. Lindenfeld

1980-01-01

281

Self-structure factor of hard-sphere gases for arbitrary ratio of bath to test particle masses  

Microsoft Academic Search

The self-structure factor Ss(k,omega) for test particles of mass different from the mass of the bath particles is considered. For a dilute hard-sphere gas the self-Enskog kinetic equation is solved to high accuracy for Ss(k,omega) by the Gross-Jackson (GJ) modeling procedure. When the variables in the self-Enskog kinetic equation are scaled to customary dimensionless parameters, the peak height and width

Michael J. Lindenfeld

1980-01-01

282

“Magic Relation” Between the Structures of Coexisting Phases at a First-Order Phase Transition in a Hard Sphere System  

Microsoft Academic Search

In the statistical geometry of a hard sphere system of any number of dimensions, Vo and So, the so-called available space and the area of the interface between the available and unavailable space, respectively, can be used as surrogates for chemical potential and pressure. It is shown exactly that, if a first-order transition occurs, the relation dVo\\/dSo=-s\\/2D, where s is

Howard Reiss

2000-01-01

283

Probability of fluctuations in the number of the nearest neighbours in a hard-sphere liquid: Probabilities of large deviations  

Microsoft Academic Search

The paper analyzes the physical implications of the result obtained in the work [1] that a random variable — the number of\\u000a the nearest neighbors M\\u000a ? in a fluid consisting of N hard spheres in the Gibbs canonical ensemble — can be expressed as a sum of N independent and similarly distributed random variables. The mean value of a

Yu. T. Pavlyukhin

2010-01-01

284

Hardness of FeB4: density functional theory investigation.  

PubMed

A recent experimental study reported the successful synthesis of an orthorhombic FeB4 with a high hardness of 62(5) GPa [H. Gou et al., Phys. Rev. Lett. 111, 157002 (2013)], which has reignited extensive interests on whether transition-metal borides compounds will become superhard materials. However, it is contradicted with some theoretical studies suggesting transition-metal boron compounds are unlikely to become superhard materials. Here, we examined structural and electronic properties of FeB4 using density functional theory. The electronic calculations show the good metallicity and covalent Fe-B bonding. Meanwhile, we extensively investigated stress-strain relations of FeB4 under various tensile and shear loading directions. The calculated weakest tensile and shear stresses are 40 GPa and 25 GPa, respectively. Further simulations (e.g., electron localization function and bond length along the weakest loading direction) on FeB4 show the weak Fe-B bonding is responsible for this low hardness. Moreover, these results are consistent with the value of Vickers hardness (11.7-32.3 GPa) by employing different empirical hardness models and below the superhardness threshold of 40 GPa. Our current results suggest FeB4 is a hard material and unlikely to become superhard (>40 GPa). PMID:24811644

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

2014-05-01

285

Hardness of FeB4: Density functional theory investigation  

NASA Astrophysics Data System (ADS)

A recent experimental study reported the successful synthesis of an orthorhombic FeB4 with a high hardness of 62(5) GPa [H. Gou et al., Phys. Rev. Lett. 111, 157002 (2013)], which has reignited extensive interests on whether transition-metal borides compounds will become superhard materials. However, it is contradicted with some theoretical studies suggesting transition-metal boron compounds are unlikely to become superhard materials. Here, we examined structural and electronic properties of FeB4 using density functional theory. The electronic calculations show the good metallicity and covalent Fe-B bonding. Meanwhile, we extensively investigated stress-strain relations of FeB4 under various tensile and shear loading directions. The calculated weakest tensile and shear stresses are 40 GPa and 25 GPa, respectively. Further simulations (e.g., electron localization function and bond length along the weakest loading direction) on FeB4 show the weak Fe-B bonding is responsible for this low hardness. Moreover, these results are consistent with the value of Vickers hardness (11.7-32.3 GPa) by employing different empirical hardness models and below the superhardness threshold of 40 GPa. Our current results suggest FeB4 is a hard material and unlikely to become superhard (>40 GPa).

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

2014-05-01

286

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

SciTech Connect

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

287

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

NASA Astrophysics Data System (ADS)

Recent theoretical and experimental results demonstrate a close connection between the super-Tonks-Girardeau (STG) gas and a one-dimensional (1D) hard-sphere Bose (HSB) gas with hard-sphere diameter nearly equal to the 1D scattering length a1D of the STG gas, a highly excited gaslike state with nodes only at interparticle separations |xj?|=xnode?a1D. It is shown herein that when the coupling constant gB in the Lieb-Liniger interaction gB?(xj?) is negative and |x12|?xnode, the STG and HSB wave functions for N=2 particles are not merely similar, but identical; the only difference between the STG and HSB wave functions is that the STG wave function allows a small penetration into the region |x12|hard-sphere diameter ahs=xnode, the HSB wave function vanishes when |x12|2. The STG and HSB wave functions for N=2 are given exactly in terms of a parabolic cylinder function, and for N?2, xnode is given accurately by a simple parabola. The metastability of the STG phase generated by a sudden change of the coupling constant from large positive to large negative values is explained in terms of the very small overlap between the ground state of the Tonks-Girardeau gas and collapsed cluster states.

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

2010-06-01

288

Equilibrium theory of the hard sphere fluid and glasses in the metastable regime up to jamming. I. Thermodynamics.  

PubMed

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

289

Large-amplitude jumps and non-Gaussian dynamics in highly concentrated hard sphere fluids.  

PubMed

Our microscopic stochastic nonlinear Langevin equation theory of activated dynamics has been employed to study the real-space van Hove function of dense hard sphere fluids and suspensions. At very short times, the van Hove function is a narrow Gaussian. At sufficiently high volume fractions, such that the entropic barrier to relaxation is greater than the thermal energy, its functional form evolves with time to include a rapidly decaying component at small displacements and a long-range exponential tail. The "jump" or decay length scale associated with the tail increases with time (or particle root-mean-square displacement) at fixed volume fraction, and with volume fraction at the mean alpha relaxation time. The jump length at the alpha relaxation time is predicted to be proportional to a measure of the decoupling of self-diffusion and structural relaxation. At long times corresponding to mean displacements of order a particle diameter, the volume fraction dependence of the decay length disappears. A good superposition of the exponential tail feature based on the jump length as a scaling variable is predicted at high volume fractions. Overall, the theoretical results are in good accord with recent simulations and experiments. The basic aspects of the theory are also compared with a classic jump model and a dynamically facilitated continuous time random-walk model. Decoupling of the time scales of different parts of the relaxation process predicted by the theory is qualitatively similar to facilitated dynamics models based on the concept of persistence and exchange times if the elementary event is assumed to be associated with transport on a length scale significantly smaller than the particle size. PMID:18643071

Saltzman, Erica J; Schweizer, Kenneth S

2008-05-01

290

Liquid-Vapor Coexistence in the Screened Coulomb (Yukawa) Hard Sphere Binary Mixture in Disordered Porous Media: The Mean Spherical Approximation.  

PubMed

The thermodynamics of a two-component fluid with a hard core interaction and screened Coulomb (Yukawa) interaction between particles, similar to the primitive model of an electrolyte solution, adsorbed in a disordered matrix of hard spheres, is studied by using replica Ornstein-Zernike integral equations and the mean spherical approximation (MSA). The gas-liquid transition is localized. The coexistence curve is investigated dependent on the range of interaction between fluid species, on matrix density, and on fluid-matrix attraction. We have observed shrinking of the coexistence envelope with increasing matrix density. The critical temperature of adsorbed mixture decreases with increasing matrix density. The critical density is less affected; however, it also decreases slightly. The critical temperature is sensitive to the fluid species-matrix attraction and depends nonmonotonously on their strength. For a given matrix microporosity, it increases slightly and then decreases with augmenting strength of fluid-matrix attraction. The critical density is less affected by this attraction. However, it decreases for the model with a sufficiently long-range tail of fluid-matrix attraction. Copyright 1998 Academic Press. PMID:9792783

Trokhymchuk; Orozco; Pizio; Vlachy

1998-11-15

291

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

NASA Astrophysics Data System (ADS)

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

Zhou, Shiqi; Solana, J. R.

2009-11-01

292

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

PubMed

A bridge function approximation is proposed to close the Ornstein-Zernike (OZ) integral equation for fluids with purely repulsive potentials. The performance of the bridge function approximation is then tested by applying the approximation to two kinds of repulsive potentials, namely, the square shoulder potential and the triangle shoulder potential. An extensive comparison between simulation and the OZ approach is performed over a wide density range for the fluid phase and several temperatures. It is found that the agreement between the two routes is excellent for not too low temperatures and satisfactory for extremely low temperatures. Then, this globally trustworthy OZ approach is used to investigate the possible existence or not of a liquid anomaly, i.e., a liquid-liquid phase transition at low temperatures and negative values of the thermal expansion coefficient in certain region of the phase diagram. While the existence of the liquid anomaly in the square shoulder potential has been previously predicted by a traditional first-order thermodynamic perturbation theory (TPT), the present investigation indicates that the liquid-liquid phase transition disappears in the OZ approach, so that its prediction by the first-order TPT is only an artifact originating from the low temperature inadequacy of the first-order TPT. However, the OZ approach indeed predicts negative thermal expansion coefficients. The present bridge function approximation, free of adjustable parameters, is suitable to be used within the context of a recently proposed nonhard sphere perturbation scheme. PMID:19947690

Zhou, Shiqi; Solana, J R

2009-11-28

293

The correlation functions of hard-sphere chain fluids: Comparison of the Wertheim integral equation theory with the Monte Carlo simulation  

SciTech Connect

The correlation functions of homonuclear hard-sphere chain fluids are studied using the Wertheim integral equation theory for associating fluids and the Monte Carlo simulation method. The molecular model used in the simulations is the freely jointed hard-sphere chain with spheres that are tangentially connected. In the Wertheim theory, such a chain molecule is described by sticky hard spheres with two independent attraction sites on the surface of each sphere. The OZ-like equation for this associating fluid is analytically solved using the polymer-PY closure and by imposing a single bonding condition. By equating the mean chain length of this associating hard sphere fluid to the fixed length of the hard-sphere chains used in simulation, we find that the correlation functions for the chain fluids are accurately predicted. From the Wertheim theory we also obtain predictions for the overall correlation functions that include intramolecular correlations. In addition, the results for the average intermolecular correlation functions from the Wertheim theory and from the Chiew theory are compared with simulation results, and the differences between these theories are discussed.

Chang, J.; Sandler, S.I. (Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 (United States))

1995-01-01

294

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

PubMed

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

Mirigian, Stephen; Schweizer, Kenneth S

2014-05-21

295

Structure of spherical electric double layers: A density functional approach  

Microsoft Academic Search

A density functional theory is presented for the structure of spherical electric double layers within the restricted primitive model, where the macroion is considered as a hard sphere having uniform surface charge density, the small ions as charged hard spheres, and the solvent is taken as a dielectric continuum. The theory is partially perturbative as the hard-sphere contribution to the

Teena Goel; Chandra N. Patra

2007-01-01

296

Bending rigidity and higher-order curvature terms for the hard-sphere fluid near a curved wall  

NASA Astrophysics Data System (ADS)

In this work I derive analytic expressions for the curvature-dependent fluid-substrate surface tension of a hard-sphere fluid on a hard curved wall. In the first step, the curvature thermodynamic properties are found as truncated power series in the activity in terms of the exactly known second- and third-order cluster integrals of the hard-sphere fluid near spherical and cylindrical walls. These results are then expressed as packing fraction power series and transformed to different reference regions, which is equivalent to considering different positions of the dividing surface. Based on the truncated series it is shown that the bending rigidity of the system is non-null and that higher-order terms in the curvature also exist. In the second step, approximate analytic expressions for the surface tension, the Tolman length, the bending rigidity, and the Gaussian rigidity as functions of the packing fraction are found by considering the known terms of the series expansion complemented with a simple fitting approach. It is found that the obtained formulas accurately describe the curvature thermodynamic properties of the system; further, they are more accurate than any previously published expressions.

Urrutia, Ignacio

2014-03-01

297

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

NASA Astrophysics Data System (ADS)

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

Henderson Kwong-Yu Chan, Douglas

298

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

PubMed

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

Malijevský, Alexandr; Jackson, George; Varga, Szabolcs

2008-10-14

299

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

SciTech Connect

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

Girardeau, M. D. [College of Optical Sciences, University of Arizona, Tucson, Arizona 85721 (United States); Astrakharchik, G. E. [Departament de Fisica i Enginyeria Nuclear, Campus Nord B4, Universitat Politecnica de Catalunya, E-08034 Barcelona (Spain)

2010-06-15

300

Fourth virial coefficient of additive hard-sphere mixtures in the Percus-Yevick and hypernetted-chain approximations  

NASA Astrophysics Data System (ADS)

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

Beltrán-Heredia, Elena; Santos, Andrés

2014-04-01

301

Emerging quasi-0D states at vanishing total entropy of the 1D hard sphere system: A coarse-grained similarity to the car parking problem  

NASA Astrophysics Data System (ADS)

A coarse-grained system of one-dimensional (1D) hard spheres (HSs) is created using the Delaunay tessellation, which enables one to define the quasi-0D state. It is found from comparing the quasi-0D and 1D free energy densities that a frozen state due to the emergence of quasi-0D HSs is thermodynamically more favorable than fluidity with a large-scale heterogeneity above crossover volume fraction of ?c=e/(1+e)=0.731⋯ , at which the total entropy of the 1D state vanishes. The Delaunay-based lattice mapping further provides a similarity between the dense HS system above ?c and the jamming limit in the car parking problem.

Frusawa, Hiroshi

2014-05-01

302

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

NASA Astrophysics Data System (ADS)

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

303

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

Microsoft Academic Search

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

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

2011-01-01

304

Influence of confinement by smooth and rough walls on particle dynamics in dense hard-sphere suspensions.  

PubMed

We used video microscopy and particle tracking to study the dynamics of confined hard-sphere suspensions. Our fluids consisted of 1.1-microm-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: a millimeter-sized rough sphere and a smooth flat wall. 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. This effect is the strongest near the smooth wall where layering takes place. 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. PMID:20365171

Eral, H B; van den Ende, D; Mugele, F; Duits, M H G

2009-12-01

305

Influence of confinement by smooth and rough walls on particle dynamics in dense hard-sphere suspensions  

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: a millimeter-sized rough sphere and a smooth flat wall. 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. This effect is the strongest near the smooth wall where layering takes place. 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, H. B.; van den Ende, D.; Mugele, F.; Duits, M. H. G.

2009-12-01

306

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

307

Chromospheric density profile in asymmetric hard x-ray footpoints  

NASA Astrophysics Data System (ADS)

Asymmetric hard X-ray (HXR) emission is commonly observed in the two conjugate footpoints of magnetic loops in solar flares. It can be interpreted by the asymmetry of chromospheric density in the legs of an overlaying loop. More flare-produced energetic electrons can be stopped in one denser leg by colliding with ambient plasma, which results in less non-thermal electrons reaching to the chromosphere and thus weaker HXR emission there. Several near-limb flares including M and X class in GOES classification with two distinct RHESSI HXR footpoints are studied to characterize the HXR source size, height dependence of HXR emission energy, and the corresponding chromospheric density profile in the two legs of a flaring loop and in different flare phases. Our preliminary results show that the HXR source with higher energy has smaller size. Moreover, such feature is more obvious for the stronger HXR source in the later flare phase. The density profile shows a clear decreasing tendency with height in the impulsive phase.

Chen, Nai-Hwa; Yang, Ya-Hui; Ip, Wing-Huen; Wang, Jingxu

308

A colloidal model system with an interaction tunable from hard sphere to soft and dipolar  

Microsoft Academic Search

Monodisperse colloidal suspensions of micrometre-sized spheres are playing an increasingly important role as model systems to study, in real space, a variety of phenomena in condensed matter physics-such as glass transitions and crystal nucleation. But to date, no quantitative real-space studies have been performed on crystal melting, or have investigated systems with long-range repulsive potentials. Here we demonstrate a charge-

Anand Yethiraj; Alfons van Blaaderen

2003-01-01

309

Structure Factor of Semiconductor Liquid Metals using Charged Hard Sphere Reference System  

NASA Astrophysics Data System (ADS)

We have calculated structure factor S(q) of some semiconductor liquid Metals (Si, Ga, Ge, In, Sn, Tl and Bi) using our well established single parametric model potential alongwith Charged Heard Sphere (CHS) reference system. To see the influence of exchange and correlation effect, Taylor local field correlation function is used. From present results, it is seen that excellent agreements between present results and experimental data have been achieved. Lastly we conclude that our model potential successfully produces the data of structure factor for some semiconductor liquid Metals (Si, Ga, Ge, In, Sn, Tl and Bi).

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

2010-06-01

310

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

Microsoft Academic Search

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

311

Percolation and critical exponents on randomly close-packed mixtures of hard spheres  

Microsoft Academic Search

This paper reports results for the percolation threshold and the critical exponents on a continuum model based on randomly close-packed mixtures of hard spherical particles. In the model, all the particles are identical in all respects save for their label (A or B). Each particle in the system has a variable number of neighbors that are defined by particle contacts,

W. J. Frith; R. Buscall

1991-01-01

312

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

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

313

Inter-particle correlations in a hard-sphere colloidal suspension with polymer additives investigated by Spin Echo Small Angle Neutron Scattering (SESANS).  

PubMed

Using a neutron scattering technique that measures a statistically-averaged density correlation function in real space rather than the conventional reciprocal-space structure factor, we have measured correlations between poly(methyl-methacrylate) (PMMA) colloidal particles of several sizes suspended in decalin. The new method, called Spin Echo Small Angle Neutron Scattering (SESANS) provides accurate information about particle composition, including the degree of solvent penetration into the polymer brush grafted on to the PMMA spheres to prevent aggregation. It confirms for particles, between 85 nm and 150 nm in radius that inter-particle correlations closely follow the Percus-Yevick hard-sphere model when the colloidal volume-fraction is between 30% and 50% provided the volume-fraction is used as a fitted parameter. No particle aggregation occurs in these systems. When small amounts of polystyrene are added as a depletant to a concentrated suspension of PMMA particles, short-range clustering of the particles occurs and there is an increase in the frequency of near-neighbor contacts. Within a small range of depletant concentration, near-neighbor correlations saturate and large aggregates with power law density correlations are formed. SESANS clearly separates the short- and long-range correlations and shows that, in this case, the power-law correlations are visible for inter-particle distances larger than roughly two particle diameters. In some cases, aggregate sizes are within our measurement window, which can extend out to 16 microns in favorable cases. We discuss the advantages of SESANS for measurements of the structure of concentrated colloidal systems and conclude that the method offers several important advantages. PMID:24695952

Washington, A L; Li, X; Schofield, A B; Hong, K; Fitzsimmons, M R; Dalgliesh, R; Pynn, R

2014-05-01

314

Concentrating colloids with electric field gradients. I. Particle transport and growth mechanism of hard-sphere-like crystals in an electric bottle  

Microsoft Academic Search

This work concerns the use of electric field gradients to manipulate the local particle concentration in a hard-sphere-like suspension. Inside a specially designed ``electric bottle,'' we observed our colloids to collect in the regions of lowest field strength (``negative dielectrophoresis''). This allows for the use of larger field gradients and stronger dielectrophoretic forces than in the original electric bottle design,

Mirjam E. Leunissen; Matthew T. Sullivan; Paul M. Chaikin; Alfons van Blaaderen

2008-01-01

315

Concentrating colloids with electric field gradients. I. Particle transport and growth mechanism of hard-sphere-like crystals in an electric bottle  

Microsoft Academic Search

This work concerns the use of electric field gradients to manipulate the local particle concentration in a hard-sphere-like suspension. Inside a specially designed “electric bottle,” we observed our colloids to collect in the regions of lowest field strength (“negative dielectrophoresis”). This allows for the use of larger field gradients and stronger dielectrophoretic forces than in the original electric bottle design,

Mirjam E. Leunissen; Matthew T. Sullivan; Paul M. Chaikin; Alfons van Blaaderen

2008-01-01

316

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

Microsoft Academic Search

A modified phenomenological model is constructed for the simulation of rarefied flows of polyatomic non-polar gas molecules by the direct simulation Monte Carlo (DSMC) method. This variable hard sphere-based model employs a constant rotational collision number, but all its collisions are inelastic in nature and at the same time the correct macroscopic relaxation rate is maintained. In equilibrium conditions, there

P S Prasanth; Jose K Kakkassery; R Vijayakumar

2012-01-01

317

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

SciTech Connect

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

318

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

NASA Technical Reports Server (NTRS)

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

Woo, Myeung-Jouh; Greber, Isaac

1995-01-01

319

Epitaxial growth of a colloidal hard-sphere hcp crystal and the effects of epitaxial mismatch on crystal structure.  

PubMed

We demonstrate the epitaxial growth of hard-sphere hcp and double hcp crystals using a surface pattern that directly dictates the stacking sequence. A detailed three-dimensional analysis based on real-space measurements is performed on crystal structure as a function of template-crystal mismatch, which demonstrates the possibilities of colloidal epitaxy as a model system for studying the effects of a patterned substrate on crystal structure. Perfect template-induced hcp-crystal growth occurs at an isotropically deformed template. At deformed lattices we observe growth of a non-close-packed superstructure and of a perfect (100)-aligned fcc crystal. Small mismatches lead to increased out-of-plane displacements followed by a structural breakup in "crystal" grains where particle positions in successive layers are strictly periodic and "defect" grains where these positions are displaced with respect to each other. Large mismatches prevent crystallization in the surface layers. The volume fraction was found to vary drastically (up to about 20% ) as a function of template deformation. PMID:15244824

Hoogenboom, J P; van Langen-Suurling, A K; Romijn, J; van Blaaderen, A

2004-05-01

320

CONDENSED MATTER: STRUCTURE, MECHANICAL AND THERMAL PROPERTIES: Prediction and Refinement of High-Order Virial Coefficients for a Hard-Sphere System  

NASA Astrophysics Data System (ADS)

The nth virial coefficient for a hard-sphere system is expressed as the sum of n2 and a remainder. When n >= 3, the remainders of the virials can be accurately expressed with Pade-type functions of n. The maximum deviations are only 0.039-0.053%, which are much better than the existing approaches. By using the predicted virials, the compressibility factors of the hard-sphere system can be predicted very accurately in the whole stable fluid region, and those in the metastable fluid region can also be well predicted up to a packing fraction of 0.545. The simulated B7 and B10 are found to be inconsistent with the other known virials, and thus they are refined to be 53.2467 and 105.042, respectively.

Hu, Jia-Wen; Yu, Yang-Xin

2009-08-01

321

Numerical solution of the HNC equation for fluids of non-spherical particles. An efficient method with application to dipolar hard spheres  

Microsoft Academic Search

An efficient algorithm is developed for solving the HNC and related equations for fluids characterized by non-spherical, angle-dependent pair interactions by choosing the dipolar hard spheres as an example system. The algorithm is a hybrid of the Picard type and Newton-Raphson (NR) methods. We note that the convergence properties are governed mainly by a few leading projections in the rotational-invariant

M. Kinoshita; M. Harada

1991-01-01

322

A test of equivalence of the variable-hard-sphere and inverse-power-law models in the direct-simulation Monte Carlo method  

Microsoft Academic Search

A test of the equivalence of the variable-hard-sphere (VHS) and inverse-power-law (IPL) models in rarefied gas flows is made for the molecular diffusion in a heat-bath gas and the two-dimensional rarefied gas flow around a circular cylinder using the null-collision Monte Carlo method. For the most severe test, the softest practical model corresponding to the Maxwel molecule is chosen. It

Katsuhisa Koura; Hiroaki Matsumoto; Toru Shimada

1991-01-01

323

The effects of Bhatnagar-Gross-Krook, Brownian, and hard-sphere ion-neutral collision models on the incoherent scatter spectrum in the E region  

Microsoft Academic Search

We revisit the theory developed by Hagfors and Brockelman (1971). The purpose of this work is to improve the understanding of variations in the incoherent scatter spectrum in the lower E region of the ionosphere between approximately 85 and 150 km under the assumption of Brownian, Bhatnagar-Gross-Krook, and hard-sphere collisions in the absence of magnetic field influences, for operating frequencies

J. T. Fentzke; M. P. Sulzer; S. A. González

2011-01-01

324

A perturbed hard-sphere-chain equation of state for normal fluids and polymers using the square-well potential of variable width  

Microsoft Academic Search

A perturbed hard-sphere-chain (PHSC) equation of state is developed for normal fluids and polymers, including mixtures. The new PHSC equation of state for pure fluids uses a perturbation term based on the analytic solution by Chang and Sandler to the second-order perturbation theory of Barker and Henderson for the square-well fluid of variable width. The reference equation of state is

Toshiaki Hino; John M. Prausnitz

1997-01-01

325

Numerical analysis of thermal-slip and diffusion-slip flows of a binary mixture of hard-sphere molecular gases  

Microsoft Academic Search

The thermal-slip (thermal-creep) and the diffusion-slip problems for a binary mixture of gases are investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules with the diffuse reflection boundary condition. The problems are analyzed numerically by the finite-difference method incorporated with the numerical kernel method, which was first proposed by Sone, Ohwada, and Aoki [Phys. Fluids A 1,

Shigeru Takata; Shugo Yasuda; Shingo Kosuge; Kazuo Aoki

2003-01-01

326

Validation of an Augmented Lagrangian Algorithm with a Gauss-Newton Hessian Approximation Using a Set of Hard-Spheres Problems  

Microsoft Academic Search

An Augmented Lagrangian algorithm that uses Gauss-Newton approximations of the Hessian at each inner iteration is introduced and tested using a family of Hard-Spheres problems. The Gauss-Newton model convexifies the quadratic approximations of the Augmented Lagrangian function thus increasing the efficiency of the iterative quadratic solver. The resulting method is considerably more efficient than the corresponding algorithm that uses true

Nataša Kreji?; José Mario Martínez; Margarida Mello; Elvio A. Pilotta

2000-01-01

327

Equation of state and liquid-vapor equilibria of one- and two-Yukawa hard-sphere chain fluids: Theory and simulation  

Microsoft Academic Search

The accuracy of several theories for the thermodynamic properties of the Yukawa hard-sphere chain fluid are studied. In particular, we consider the polymer mean spherical approximation (PMSA), the dimer version of thermodynamic perturbation theory (TPTD), and the statistical associating fluid theory for potentials of variable attractive range (SAFT-VR). Since the original version of SAFT-VR for Yukawa fluids is restricted to

Yurij V. Kalyuzhnyi; Clare McCabe; Eric Whitebay; Peter T. Cummings

2004-01-01

328

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

NASA Technical Reports Server (NTRS)

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

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

1998-01-01

329

Influence of Atomic Sphere Radii on the Electron-Positron Momentum Density Calculated for SiC within the LMTO-ASA  

NASA Astrophysics Data System (ADS)

The atomic sphere approximation consists in replacing the Wigner-Seitz polyhedron, containing individual atom, by the sphere of the same volume. In the case of several not equivalent atoms per primitive cell, e.g. for SiC, the radii of atomic spheres, centred at different atoms, are not uniquely determined and should be judiciously chosen. In the present work one studies the effect of choice of atomic sphere radii on the resulting electron band structure and momentum density as well as the electron-positron momentum density. Calculations were performed for SiC within the linear muffin-tin orbital atomic sphere approximation method.

Rubaszek, A.

2006-11-01

330

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

PubMed

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

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

2013-07-01

331

Stability conditions for density functional reactivity theory: an interpretation of the total local hardness.  

PubMed

The second-order Taylor series expansions commonly used in the density functional chemical reactivity theory are used to define local stability conditions for electronic states. Systems which satisfy these conditions are stable to infinitesimal perturbations due to approaching chemical reagents. The basic formalism considered here supersedes previous variational approaches to chemical reactivity theory like the electrophilicity, potentialphilicity, and chargephilicity. The total local hardness emerges naturally in this analysis, and can be clearly interpreted. When the total local hardness is small, the system is relatively insensitive to perturbations. Furthermore, minus the total local hardness is an energetically favorable perturbation of the external potential. PMID:21253639

Ayers, Paul W; Liu, Shubin; Li, Tonglei

2011-03-14

332

Fluid of penetrable spheres: testing the universality of the bridge functional  

PubMed

Penetrable spheres have been the object of recent extensive investigations as a prototype for intermicellar interactions in a solvent, and as representing a class of bounded potentials allowing complete interpenetrability of the particles. Here we compare density-functional and simulation results for the pair-correlation functions in a bulk fluid of penetrable spheres, as a stringent test for the approximation of "universality" of the bridge functional. Considering either a fundamental-measure functional for penetrable spheres or a perturbative treatment using a fundamental-measure hard-sphere functional, we conclude that hard-sphere-type bridge functionals are applicable also for bounded potentials with high penetrability. PMID:11089049

Rosenfeld; Schmidt; Watzlawek; Lowen

2000-10-01

333

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

PubMed

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

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

2014-08-01

334

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

NASA Astrophysics Data System (ADS)

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

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

2012-04-01

335

Structure of electric double layers: A self-consistent weighted-density-functional approach  

Microsoft Academic Search

A self-consistent weighted-density-functional approach is developed for the structure of electric double layer using the restricted primitive model which corresponds to charged hard sphere ions and a continuum solvent. The one-particle correlation function of this inhomogeneous system is evaluated using suitably averaged weighted densities for the short range hard sphere as well as the long range electrical components. The hard-sphere

Chandra N. Patra; Swapan K. Ghosh

2002-01-01

336

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

NASA Technical Reports Server (NTRS)

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

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

1994-01-01

337

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

NASA Astrophysics Data System (ADS)

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.

Bakhti, Benaoumeur; Müller, Gerhard; Maass, Philipp

2013-08-01

338

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

PubMed

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

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

2011-10-01

339

Density-functional approach to smectic order in an aligned hard-rod fluid  

Microsoft Academic Search

The occurrence of smectic order in a system of perfectly aligned hard cylinders is studied with use of a bifurcation analysis of the free-energy functional in the second virial coefficient approximation. This approximation is shown to yield a second-order transition of mean-field type towards a smectic phase. The influence of higher-order terms in the density expansion of the free-energy functional

Bela Mulder

1987-01-01

340

The Effects of BGK, Brownian, and Hard-Sphere Ion-Neutral Collision Models on the Incoherent Scatter Spectrum in the E-region  

NASA Astrophysics Data System (ADS)

We revisit the theory developed by Hagfors and Brockelman [1971]. The purpose of this work is to improve the understanding of variations in the incoherent scatter spectrum in the lower E-region of the ionosphere between approximately 85 - 150 km under the assumption of Brownian [Chandrasekhar, 1943], Bhatnagar-Gross-Krook (BGK) [Bhatnagar et al., 1954], and Hard-Sphere collisions [Chapman and Cowling, 1970] in the absence of magnetic field influences, for operating frequencies representative of the chain of NSF-sponsored incoherent scatter radars (ISRs), which range from 50 MHz - 1290 MHz. Also, we extend the computationally limited examples in Hagfors and Brockelman [1971] as well as demonstrate the feasibility of making the E-region measurements at the Arecibo Observatory (AO) ISR in Puerto Rico (18 N, 67 W). We show that the original non-dimensionalized examples from Hagfors and Brockelman [1971] were representative of spectra at approximately 95 km, 105 km, and 150 km.

Fentzke, J. T.; Sulzer, M. P.; Gonzalez, S. A.

2010-12-01

341

Equation of state and liquid-vapor equilibria of one- and two-Yukawa hard-sphere chain fluids: theory and simulation.  

PubMed

The accuracy of several theories for the thermodynamic properties of the Yukawa hard-sphere chain fluid are studied. In particular, we consider the polymer mean spherical approximation (PMSA), the dimer version of thermodynamic perturbation theory (TPTD), and the statistical associating fluid theory for potentials of variable attractive range (SAFT-VR). Since the original version of SAFT-VR for Yukawa fluids is restricted to the case of one-Yukawa tail, we have extended SAFT-VR to treat chain fluids with two-Yukawa tails. The predictions of these theories are compared with Monte Carlo (MC) simulation data for the pressure and phase behavior of the chain fluid of different length with one- and two-Yukawa tails. We find that overall the PMSA and TPTD give more accurate predictions than SAFT-VR, and that the PMSA is slightly more accurate than TPTD. PMID:15485277

Kalyuzhnyi, Yurij V; McCabe, Clare; Whitebay, Eric; Cummings, Peter T

2004-10-22

342

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

PubMed

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

2010-01-01

343

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

NASA Technical Reports Server (NTRS)

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

Miller, C. G., III

1975-01-01

344

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

NASA Technical Reports Server (NTRS)

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

Nemeth, Noel

2013-01-01

345

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

SciTech Connect

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

Boss, Alan P.; Keiser, Sandra A., E-mail: boss@dtm.ciw.edu [Department of Terrestrial Magnetism, Carnegie Institution for Science, 5241 Broad Branch Road, NW, Washington, DC 20015-1305 (United States)

2013-02-20

346

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

NASA Astrophysics Data System (ADS)

An incompressible Co54Ta11B35 bulk metallic glass (BMG) was investigated using in situ high-pressure synchrotron diffraction and nanoindendation. The elastic constants were deduced from the experiments based on the isotropic model. The Vickers hardness was measured to be 17.1 GPa. The elastic moduli and hardness are the highest values known in BMGs. The theoretically calculated elastic properties by density-functional study were well consistent with experimental measurements. The analysis of charge density and bonding character indicates the covalent character of Co-B and B-B bonds, underlying the unusually high elastic modulus and hardness in this material.

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

2011-10-01

347

An analytical approximation for the orientation-dependent excluded volume of tangent hard sphere chains of arbitrary chain length and flexibility  

NASA Astrophysics Data System (ADS)

Onsager-like theories are commonly used to describe the phase behavior of nematic (only orientationally ordered) liquid crystals. A key ingredient in such theories is the orientation-dependent excluded volume of two molecules. Although for hard convex molecular models this is generally known in analytical form, for more realistic molecular models that incorporate intramolecular flexibility, one has to rely on approximations or on computationally expensive Monte Carlo techniques. In this work, we provide a general correlation for the excluded volume of tangent hard-sphere chains of arbitrary chain length and flexibility. The flexibility is introduced by means of the rod-coil model. The resulting correlation is of simple analytical form and accurately covers a wide range of pure component excluded volume data obtained from Monte Carlo simulations of two-chain molecules. The extension to mixtures follows naturally by applying simple combining rules for the parameters involved. The results for mixtures are also in good agreement with data from Monte Carlo simulations. We have expressed the excluded volume as a second order power series in sin (?), where ? is the angle between the molecular axes. Such a representation is appealing since the solution of the Onsager Helmholtz energy functional usually involves an expansion of the excluded volume in Legendre coefficients. Both for pure components and mixtures, the correlation reduces to an exact expression in the limit of completely linear chains. The expression for mixtures, as derived in this work, is thereby an exact extension of the pure component result of Williamson and Jackson [Mol. Phys. 86, 819-836 (1995)].

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

2012-07-01

348

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

NASA Astrophysics Data System (ADS)

Herein we provide a brief summary of the background, events and results/outcome of the CECAM workshop 'Classical density functional theory methods in soft and hard matter held in Lausanne between October 21 and October 23 2009, which brought together two largely separately working communities, both of whom employ classical density functional techniques: the soft-matter community and the theoretical materials science community with interests in phase transformations and evolving microstructures in engineering materials. After outlining the motivation for the workshop, we first provide a brief overview of the articles submitted by the invited speakers for this special issue of Journal of Physics: Condensed Matter, followed by a collection of outstanding problems identified and discussed during the workshop. 1. Introduction Classical density functional theory (DFT) is a theoretical framework, which has been extensively employed in the past to study inhomogeneous complex fluids (CF) [1-4] and freezing transitions for simple fluids, amongst other things. Furthermore, classical DFT has been extended to include dynamics of the density field, thereby opening a new avenue to study phase transformation kinetics in colloidal systems via dynamical DFT (DDFT) [5]. While DDFT is highly accurate, the computations are numerically rather demanding, and cannot easily access the mesoscopic temporal and spatial scales where diffusional instabilities lead to complex solidification morphologies. Adaptation of more efficient numerical methods would extend the domain of DDFT towards this regime of particular interest to materials scientists. In recent years, DFT has re-emerged in the form of the so-called 'phase-field crystal' (PFC) method for solid-state systems [6, 7], and it has been successfully employed to study a broad variety of interesting materials phenomena in both atomic and colloidal systems, including elastic and plastic deformations, grain growth, thin film growth, solid-liquid interface properties, glassy dynamics, nucleation and growth, and diffusive phase transformations at the nano- and mesoscales [8-16]. The appealing feature of DDFT (as applied to solid-state systems) is that it automatically incorporates diffusive dynamics with atomic scale spatial resolution, and it naturally incorporates multiple components, elastic strains, dislocations, free surfaces, and multiple crystalline orientations; all of these features are critical in modeling the behavior of solid-state systems. Similarities between the problems of interest to the two communities and the complementary nature of the methods they apply suggest that a direct interaction between them should be highly beneficial for both parties. Here we summarize some of the discussions during a three-day CECAM workshop in Lausanne (21-23 October 2009) which was organized in order to bring together researchers from the complex fluids and materials science communities and to foster the exchange of ideas between these two communities. During the course of the workshop, several open problems relevant to both fields (DFT and PFC) were identified, including developing better microscopically-informed density functionals, incorporating stochastic fluctuations, and accounting for hydrodynamic interactions. The goal of this special issue is to highlight recent progress in DFT and PFC approaches, and discuss key outstanding problems for future work. The rest of this introductory paper is organized as follows. In section 2, we give a brief overview of the current research topics addressed in this special issue. Then, in section 3, we present a collection of outstanding problems, which have been identified as important for further developments of the two fields and intensely debated at the CECAM workshop. Finally, we close the paper with a few concluding remarks. 2. Research topics addressed in this special issue This special issue consists of research papers that cover a broad range of interesting subjects, about a half of which are related to the theoretical materials science community and

Haataja, Mikko; Gránásy, László; Löwen, Hartmut

2010-08-01

349

Tunneling of a few strongly repulsive hard-sphere bosons in an optical lattice with tight external harmonic confinement: A quantum Monte Carlo investigation in continuous space  

SciTech Connect

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

350

Solution of the Chandler{endash}Silbey{endash}Ladanyi equation for the multicomponent hard-sphere site{endash}site molecular fluid: Percus{endash}Yevick approximation  

SciTech Connect

The analytical solution of the Chandler{endash}Silbey{endash}Ladanyi Percus{endash}Yevick (CSL-PY) approximation for multicomponent molecular site{endash}site fluids is presented. The molecules are modeled by a collection of an arbitrary number of hard-sphere sites of any size and geometrical arrangement, provided only that all sites are in contact and the bonding distance is equal to the contact distance between the sites of the molecule. Assuming an additional approximation for the intramolecular correlation between the molecular sites not bonded directly the solution is extended to the case of flexible molecules. A closed-form analytical expression for the compressibility equation of state is derived. In the case of the linear flexible chain model polymer system, this equation of state coincides with the equation of state derived earlier [Y. C. Chiew, Mol. Phys. {bold 70}, 129 (1990)]. Comparison of the theory with computer simulation results shows that predictions of the CSL-PY theory for the compressibility pressure of the star polymer system is fairly accurate, while the structural predictions for linear chain {ital n}-mers are quantitatively accurate only for the systems of dimers. {copyright} {ital 1996 American Institute of Physics.}

Kalyuzhnyi, Y.V.; Cummings, P.T. [Department of Chemical Engineering, University of Tennessee, Knoxville, Tennessee 37996-2200 (United States)] [Department of Chemical Engineering, University of Tennessee, Knoxville, Tennessee 37996-2200 (United States); [Chemical Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6268 (United States)

1996-08-01

351

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

PubMed

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

Jadrich, Ryan; Schweizer, Kenneth S

2013-08-01

352

Equilibrium and shear induced nonequilibrium phase behavior of PMMA microgel spheres  

SciTech Connect

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

Paulin, S.E.; Ackerson, B.J. [Oklahoma State Univ., Stillwater, OK (United States). Dept. of Physics] [Oklahoma State Univ., Stillwater, OK (United States). Dept. of Physics; Wolfe, M.S. [E.I du Pont de Nemours and Co., Wilmington, DE (United States)] [E.I du Pont de Nemours and Co., Wilmington, DE (United States)

1996-03-01

353

Expansion-free evolving spheres must have inhomogeneous energy density distributions  

SciTech Connect

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

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

2009-04-15

354

Structure of electric double layers: A simple weighted density functional approach  

Microsoft Academic Search

A simple weighted density functional approach is developed for inhomogeneous ionic fluids and applied to the structure of the electric double layer using the restricted primitive model where the ions are considered to be charged hard spheres of equal diameter. The formalism is nonperturbative with both hard-sphere and electrical contributions to the one-particle correlation function evaluated through a suitably averaged

Chandra N. Patra

1999-01-01

355

Numerical analysis of the shear and thermal creep flows of a rarefied gas over a plane wall on the basis of the linearized Boltzmann equation for hard-sphere molecules  

Microsoft Academic Search

Shear flow and thermal creep flow (flow induced by the temperature gradient along the boundary wall) of a rarefied gas over a plane wall are considered on the basis of the linearized Boltzmann equation for hard-sphere molecules and diffuse reflection boundary condition. These fundamental rarefied gas dynamic problems, typical half-space boundary-value problems of the linearized Boltzmann equation, are analyzed numerically

Taku Ohwada; Yoshio Sone; Kazuo Aoki

1989-01-01

356

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

357

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

358

Hard and wear-resistant titanium nitride coatings for cemented carbide cutting tools by pulsed high energy density plasma  

Microsoft Academic Search

Hard and wear-resistant titanium nitride coatings were deposited by pulsed high energy density plasma technique on cemented carbide cutting tools at ambient temperature. The coating thickness was measured by an optical profiler and surface Auger microprobe. The elemental and phase compositions and distribution of the coatings were determined by Auger microprobe, x-photon electron spectroscope, and X-ray diffractometer. The microstructures of

Zhijian Peng; Hezhuo Miao; Longhao Qi; Size Yang; Chizi Liu

2003-01-01

359

Chromospheric magnetic field and density structure measurements using hard X-rays in a flaring coronal loop  

NASA Astrophysics Data System (ADS)

Aims: A novel method of using hard X-rays as a diagnostic for chromospheric density and magnetic structures is developed to infer sub-arcsecond vertical variation of magnetic flux tube size and neutral gas density. Methods: Using Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) X-ray data and the newly developed X-ray visibilities forward fitting technique we find the FWHM and centroid positions of hard X-ray sources with sub-arcsecond resolution (~0.2'') for a solar limb flare. We show that the height variations of the chromospheric density and the magnetic flux densities can be found with an unprecedented vertical resolution of ~150 km by mapping 18-250 keV X-ray emission of energetic electrons propagating in the loop at chromospheric heights of 400-1500 km. Results: Our observations suggest that the density of the neutral gas is in good agreement with hydrostatic models with a scale height of around 140 ± 30 km. FWHM sizes of the X-ray sources decrease with energy suggesting the expansion (fanning out) of magnetic flux tubes in the chromosphere with height. The magnetic scale height B(z)(dB/dz)-1 is found to be of the order of 300 km and a strong horizontal magnetic field is associated with noticeable flux tube expansion at a height of ~900 km.

Kontar, E. P.; Hannah, I. G.; MacKinnon, A. L.

2008-10-01

360

Weighted-density-functional theory of nonuniform ionic fluids: Application to electric double layers  

Microsoft Academic Search

A weighted-density-functional theory is developed for inhomogeneous ionic fluids and applied to the structure of the electric double layer using the restricted primitive model where the ions are considered to be charged hard spheres of equal diameter. The formalism is nonperturbative with both hard-sphere and electrical contributions to the one-particle correlation function evaluated through a suitably averaged weighted density, the

Chandra N. Patra; Swapan K. Ghosh

1993-01-01

361

Aquaculture-associated factors in QPX disease of hard clams: density and seed source  

Microsoft Academic Search

Quahog Parasite Unknown (QPX), a recently discovered pathogen of hard clams, Mercenaria mercenaria, appears to be most prevalent in clams held in hatchery or nursery tanks or grown to market in culture parks. The persistent link with cultured clams indicated that culture practices might increase the susceptibility of clams to an opportunistic or facultative parasite. We investigated two hypotheses: (1)

Susan E Ford; John N Kraeuter; Robert D Barber; George Mathis

2002-01-01

362

A classical density-functional theory for describing water interfaces.  

PubMed

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

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

2013-01-14

363

Structure of Rigid Hard-Ring Fluids  

NASA Astrophysics Data System (ADS)

Structure of fluids of molecules consisting of rigid rings of hard spheres is studied in two, quasi two, and three dimensions, using Monte Carlo computer simulations in the canonical ensemble. For rings of various size and for a wide range of densities, results are reported for the pair distribution function of the ring centers and for the pair distribution of the ring orientations. For dense fluids in two dimensions, a shoulder, precursor of the freezing transition, is observed in the second peak of the pair distribution function of the ring centers, as previously seen in the simple hard-sphere fluid. In quasi two dimensions, where the centers of the rings are confined to a plane but the rings themselves can wobble out of plane, a liquid crystalline nematic phase is observed at sufficiently high densities. Results are also presented for three dimensions.

Nouri, Mariam; Robert, Marc

2011-03-01

364

Catalytic hollow spheres  

NASA Technical Reports Server (NTRS)

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

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

1986-01-01

365

Catalytic, hollow, refractory spheres  

NASA Technical Reports Server (NTRS)

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

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

1987-01-01

366

Catalytic hollow spheres  

NASA Technical Reports Server (NTRS)

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

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

1989-01-01

367

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

SciTech Connect

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

Sun, K. X.

2011-05-31

368

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

PubMed

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

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

2013-01-01

369

Atomically Smooth Epitaxial Ferroelectric (Piezoelectric) Thin Films for the Development of a Nonvolatile, Ultrahigh Density, Fast, Low Voltage, Radiation-Hard Memory.  

National Technical Information Service (NTIS)

The goal of this research program is to develop atomically smooth, nanostructured, single crystalline, epitaxial complex oxide thin films as the basic building block for a nonvolatile, ultrahigh density, fast, low voltage, radiation-hard memory. Oxide mat...

C. H. Ahn

2003-01-01

370

Scaling of the Space-Time Correlation Function of Particle Currents in a Suspension of Hard-Sphere-Like Particles: Exposing When the Motion of Particles is Brownian  

Microsoft Academic Search

The current correlation function is determined from dynamic light scattering measurements of a suspension of particles with hard spherelike interactions. For suspensions in thermodynamic equilibrium we find scaling of the space and time variables of the current correlation function. This finding supports the notion that the movement of suspended particles can be described in terms of uncorrelated Brownian encounters. However,

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

2009-01-01

371

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

DOEpatents

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

Wang, George T.; Li, Qiming

2013-04-23

372

Thermodynamic scaling and corresponding states for the self-diffusion coefficient of non-conformal soft-sphere fluids.  

PubMed

In this work, we explore transport properties of a special type of repulsive spheres that exhibit remarkable scaling of their thermodynamic properties. In order to accomplish that we propose a new way to derive and express effective hard-sphere diameters for transport properties of simple fluids. The procedure relies on mapping the system's transport properties, in the low density limit, to the hard-sphere fluid. We have chosen 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 and are an accurate representation of the effective repulsive potentials of real systems. The self-diffusion coefficient of the soft-sphere fluids is obtained by equilibrium molecular dynamics. The soft-sphere collision integrals of different systems are shown to follow quite simple relationships between each other. These collision integrals are incorporated, through the definition of the effective hard-sphere diameter, in the resulting equation for the self-diffusion coefficient. The approach followed exhibits a density rescaling that leads to a single master curve for all systems and temperatures. The scaling is carried through to the level of the mean-squared displacement. PMID:23534644

Rodríguez-López, Tonalli; Moreno-Razo, J Antonio; del Río, Fernando

2013-03-21

373

Pair structure of the hard-sphere Yukawa fluid: An improved analytic method versus simulations, Rogers-Young scheme, and experiment  

NASA Astrophysics Data System (ADS)

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.

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

2011-01-01

374

Pair structure of the hard-sphere Yukawa fluid: an improved analytic method versus simulations, Rogers-Young scheme, and experiment.  

PubMed

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

375

Hard core Yukawa fluid with temperature and density dependent interaction: Phase diagram of the AOT/water/decane microemulsion  

NASA Astrophysics Data System (ADS)

A fluid with an interaction potential consisting of a hard core and an attractive Yukawa tail is considered. The strength of the attraction is taken to depend both on density and temperature in order to take into account the state dependence of the effective interaction suggested by the analysis of structural data of several colloidal suspensions, in particular microemulsions of AOT reverse micelles. The thermodynamics of this fluid is investigated starting from the inverse temperature expansion of the free energy in the mean spherical approximation. The temperature and density dependence of the interaction is incorporated in consistent expressions for the pressure, isothermal compressibility, and chemical potential. The phase diagram predicted by this method is in agreement with experimental data on AOT reverse micelles analyzed in the effective one component approach.

Bouaskarne, M.; Amokrane, S.; Regnaut, C.

1999-08-01

376

Application of the Baxter model for hard-spheres with surface adhesion to SANS data for the U(VI) - HNO{sub 3}, TBP-n-dodecane system.  

SciTech Connect

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

377

High density tungsten-nickel-iron-cobalt alloys having improved hardness and method for making same  

Microsoft Academic Search

This patent describes the process of making high density alloy containing about 85 to 98 weight percent tungsten and the balance of the alloy being essentially a binder of nickel, iron and cobalt, and wherein the cobalt is present in an amount within the range of about 5 to 47.5 weight percent of the binder, comprising: blending powders of the

T. W. Penrice; J. Bost

1988-01-01

378

Band structures and charge densities of KCl, NaF, and LiF obtained by the intersecting-spheres model  

NASA Astrophysics Data System (ADS)

The self-consistent electronic structures of KCl, NaF, and LiF have been calculated by the intersecting-spheres model and the results were compared with band structures calculated by other methods using the approximation of the exchange potential adopted by us. While for KCl close agreement was found between the augmented-plane-wave non-muffin-tin results by De Cicco and the intersecting-spheres-model (ISM) band structure, in the case of LiF differences of even 2.5 eV were found between conduction bands calculated by the ISM and the corresponding levels determined by linear-combination-of-atomic-orbitals (LCAO) methods. This disagreement seems to be imputable to a lack of convergence occurring in the LCAO calculations. The Fourier components of the charge densities (scattering factors) were determined using the Kohn-Sham-Gáspár form of the exchange potential. The agreement of the calculated scattering factors with experiment is not much worse than that obtained by Hartree-Fock calculations.

Antoci, S.; Mihich, L.

1980-01-01

379

Classical and quantum hard spherre fluids: Theory and experiment  

SciTech Connect

A comprehensive picture is presented of what can be reconstructed of the equations of state, at all densities, of both classical an quantum hard sphere fluids (the latter in their ground states) just from the first few coefficients which are known of the low-density expansions. Extrapolation techniques, mostly Pade and generalizations thereof, are employed and comparisons with simulation studies are made wherever these are available.

Baker G.A. Jr.; Gutierrez, G.; DeLlano, M.

1984-04-01

380

Ionization Potential, Electron Affinity, Electronegativity, Hardness, and Electron Excitation Energy: Molecular Properties from Density Functional Theory Orbital Energies  

SciTech Connect

Representative atomic and molecular systems, including various inorganic and organic molecules with covalent and ionic bonds, have been studied by using density functional theory. The calculations were done with the commonly used exchange-correlation functional B3LYP followed by a comprehensive analysis of the calculated highest-occupied and lowest-unoccupied Kohn-Sham orbital (HOMO and LUMO) energies. The basis set dependence of the DFT results shows that the economical 6-31+G* basis set is generally sufficient for calculating the HOMO and LUMO energies (if the calculated LUMO energies are negative) for use in correlating with molecular properties. The directly calculated ionization potential (IP), electron affinity (EA), electronegativity (c), hardness (h), and first electron excitation energy (t) are all in good agreement with the available experimental data. A generally applicable linear correlation relationship exists between the calculated HOMO energies and the experimental/calculated IP's. We have also found satisfactory linear correlation relationships between the calculated LUMO energies and experimental/calculated EA's (for the bound anionic states), between the calculated average HOMO/LUMO energies and c values, between the calculated HOMO-LUMO energy gaps and h values, and between the calculated HOMO-LUMO energy gaps and experimental/calculated first excitation energies. By using these linear correlation relationships, the calculated HOMO and LUMO energies can be employed to semi-quantitatively estimate ionization potential, electron affinity, electronegativity, hardness, and first excitation energy.

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

2003-05-22

381

GENERAL Augmented Kierlik---Rosinberg Fundamental Measure Functional and Extension of Fundamental Measure Functional to Inhomogeneous Non-hard Sphere Fluids  

Microsoft Academic Search

From point of view of weighted density procedure, it is guessed that a Percus-Yevick (PY) compressibility excess free energy density, appearing in the Kierlik---Rosinberg type fundamental measure functional (KR-FMF) and expressed in terms of scaled particle variables, can be substituted by a corresponding expression dictated by a more accurate Mansoori---Carnahan---Starling---Leland (MCSL) equation of state, while retaining the original weighting functions;

Shi-Qi Zhou

2010-01-01

382

The Sphere  

NSDL National Science Digital Library

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

Jensen, Douglas; Reed, Allen

2005-01-01

383

Sphere launcher  

NASA Technical Reports Server (NTRS)

The sphere launcher was designed to eject a 200 lb, 15 in. diameter sphere from a space vehicle or missile, at a velocity of 58 ft/sec without imparting excessive lateral loads to the vehicle. This launching is accomplished with the vehicle operating in vacuum conditions and under a 9 g acceleration. Two principal elements are used: a high thrust, short burn time rocket motor and two snubbers for reducing the lateral loads to acceptable limits.

Reed, W. B.

1972-01-01

384

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

Microsoft Academic Search

During the course of the DYnamics Adapted Network for the Atmosphere (DYANA) campaign in early 1990, various techniques to measure densities and temperatures from the ground up to the lower thermosphere were employed. Some of these measurements were performed near simultaneously (maximum allowed time difference: 1 h) and at the same location, and therefore offered the unique chance of intercomparison

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

1994-01-01

385

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

USGS Publications Warehouse

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

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

1992-01-01

386

Improved association in a classical density functional theory for water  

NASA Astrophysics Data System (ADS)

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

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

2014-03-01

387

Celestial Sphere  

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

388

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

NASA Technical Reports Server (NTRS)

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

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

1985-01-01

389

Condensation transition in polydisperse hard rods.  

PubMed

We study a mass transport model, where spherical particles diffusing on a ring can stochastically exchange volume v, with the constraint of a fixed total volume V= sum(i=1) (N)v(i), N being the total number of particles. The particles, referred to as p-spheres, have a linear size that behaves as v(i) (1/p) and our model thus represents a gas of polydisperse hard rods with variable diameters v(i) (1/p). We show that our model admits a factorized steady state distribution which provides the size distribution that minimizes the free energy of a polydisperse hard-rod system, under the constraints of fixed N and V. Complementary approaches (explicit construction of the steady state distribution on the one hand; density functional theory on the other hand) completely and consistently specify the behavior of the system. A real space condensation transition is shown to take place for p>1; beyond a critical density a macroscopic aggregate is formed and coexists with a critical fluid phase. Our work establishes the bridge between stochastic mass transport approaches and the optimal polydispersity of hard sphere fluids studied in previous articles. PMID:20078144

Evans, M R; Majumdar, S N; Pagonabarraga, I; Trizac, E

2010-01-01

390

Free Volume of the Hard Spheres Gas  

ERIC Educational Resources Information Center

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

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

2007-01-01

391

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

392

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

NASA Astrophysics Data System (ADS)

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

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

2009-03-01

393

A fluid sphere in general relativity  

Microsoft Academic Search

We solve the Einstein field equations for the interior of a static fluid sphere in closed analytic form. The model sphere obtained has a physically reasonable equation of state, and a maximum mass of 2?5 the fluid radius (in geometric units). As the maximum mass is approached the central density and pressure become infinite, while for masses greater than about

Ronald J. Adler

1974-01-01

394

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

395

Microscopic density functional theory for dendrimers.  

PubMed

Density functional theory for a simple model of dendrimers is proposed. The theory is based on fundamental measure theory, which accounts for the hard-sphere repulsion of the segments and on the Wertheim first-order perturbation theory for the correlations due to connectivity. Set of the recurrence formulas for the ideal chain contribution involving simple integrals is derived. By using perturbation theory dispersion forces can be easily included. PMID:19905376

Malijevský, Alexandr

2009-10-01

396

Specific surface area of overlapping spheres in the presence of obstructions  

NASA Astrophysics Data System (ADS)

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

Jenkins, D. R.

2013-02-01

397

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

398

Density!  

NSDL National Science Digital Library

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

Witcher, Miss

2011-10-06

399

On the laser beam cutting of metallic hollow sphere structures  

NASA Astrophysics Data System (ADS)

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

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

2013-02-01

400

Density-functional theory of spherical electric double layers and zeta potentials of colloidal particles in restricted-primitive-model electrolyte solutions  

Microsoft Academic Search

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

401

Effect of sphered particles on the firing contraction of porcelain inlay processed by cold isostatic pressing.  

PubMed

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

402

A nonlocal density functional theory of electric double layer: Symmetric electrolytes  

Microsoft Academic Search

The density functional theory of inhomogeneous classical neutral fluids is extended to study the structure of electric double layer using the restricted primitive model as well as the nonprimitive three-component molecular solvent model. The formalism is based on a weighted density approach where the hard-sphere contributions to the excess free energy density and the one-particle correlation function are evaluated nonperturbatively

Chandra N. Patra; Swapan K. Ghosh

1994-01-01

403

Density  

NSDL National Science Digital Library

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

Hansen, Mr.

2010-10-26

404

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

NASA Astrophysics Data System (ADS)

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

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

2008-08-01

405

Density  

NSDL National Science Digital Library

This page introduces students to the concept of density by presenting its definition, formula, and two blocks representing materials of different densities. Students are given the mass and volume of each block and asked to calculate the density. Their answers are then compared against a table of densities of common objects (air, wood, gold, etc.) and students must determine, using the density of the blocks, which substance makes up each block.

Carpi, Anthony

2003-01-01

406

Topological defects in nematic droplets of hard spherocylinders  

NASA Astrophysics Data System (ADS)

Using computer simulations we investigate the microscopic structure of the singular director field within a nematic droplet. As a theoretical model for nematic liquid crystals we take hard spherocylinders. To induce an overall topological charge, the particles are either confined to a two-dimensional circular cavity with homeotropic boundary or to the surface of a three-dimensional sphere. Both systems exhibit half-integer topological point defects. The isotropic defect core has a radius of the order of one particle length and is surrounded by free-standing density oscillations. The effective interaction between two defects is investigated. All results should be experimentally observable in thin sheets of colloidal liquid crystals.

Dzubiella, Joachim; Schmidt, Matthias; Löwen, Hartmut

2000-10-01

407

Role of inner- and outer-sphere bonding in the sensitization of EuIII-luminescence deciphered by combined analysis of experimental electron density distribution function and photophysical data.  

PubMed

A series of lanthanide adducts with different amounts of 1,10-phenanthroline, chloride ions, and water molecules in the inner and outer coordination spheres are investigated with the aim of relating the chemical bonding patternin the crystals to the luminescence properties of the Eu ion: [LnCl1Phen2(H2O)3]Cl2(H2O) (Ln ) Eu, 1Eu; Gd, 1Gd;Tb, 1Tb), [EuCl2Phen2(H2O)2]Cl1(H2O) (2), and [EuCl2Phen1(H2O)4]Cl1(H2O) (3). The influence of inner- versus outersphere ligands on the Ln-X bond lengths and angles in the structure is examined. A detailed topological analysis of the electron density function derived from the X-ray diffraction data for 1Gd is performed within the frame of the"atoms in molecule" theory for the first time for a lanthanide complex. The chemical bonding pattern is interpreted in terms of net atomic charges, bond energies, and electron transfers from the ligands to the metal ion. A noteworthy finding is that the energy of extended noncovalent interactions occurring in the second coordination sphere (H-bonding and pi-stacking interactions) is comparable to that of Ln-ligand bonds. The luminescence properties of the three Eu adducts are interpreted with the results of electron density distribution function topology. An intraligand charge transfer state is identified, and its contribution in the ligand-to-europium energy transfer process is analyzed.The outcome of this study is that specific interionic interactions which are usually not considered in theoretical calculations or in the interpretation of luminescence properties play an important role in the sensitization of the Eu luminescence. PMID:18950154

Puntus, Lada N; Lyssenko, Konstantin A; Antipin, Mikhail Yu; Bünzli, Jean-Claude G

2008-12-01

408

Catalytic, hollow, refractory spheres, conversions with them  

NASA Technical Reports Server (NTRS)

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

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

1989-01-01

409

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 that yields simple expressions for the pinch-off time and depth. 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; Truscott, Tadd; Techet, Alexandra; Bush, John

2009-11-01

410

Restricted primitive model for electrical double layers: Modified HNC theory of density profiles and Monte Carlo study of differential capacitance  

Microsoft Academic Search

Interfacial properties of an ionic fluid next to a uniformly charged planar wall are studied in the restricted primitive model by both theoretical and Monte Carlo methods. The system is a 1:1 fluid of equisized charged hard spheres in a state appropriate to 1 M aqueous electrolyte solutions. The interfacial density profiles of counterions and coions are evaluated by extending

P. Ballone; G. Pastore; M. P. Tosi

1986-01-01

411

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

412

An implementation friendly low complexity multiplierless LLR generator for soft MIMO sphere decoders  

Microsoft Academic Search

When combined with advanced FEC techniques such as the turbo code and LDPC code, soft-output MIMO sphere decoders significantly outperform hard-output sphere decoders. Hence, algorithms and implementations of soft-output sphere decoders have attracted intensive interest in recent years. Practical soft-output sphere decoder implementations often consist of a list generator and a LLR generator. Most existing implementations focus on the list

Min Li; David Novo; Bruno Bougard; Frederik Naessens; Liesbet Van Der Perre; Francky Catthoor

2008-01-01

413

Short-time transport properties in dense suspensions: From neutral to charge-stabilized colloidal spheres  

NASA Astrophysics Data System (ADS)

We present a detailed study of short-time dynamic properties in concentrated suspensions of charge-stabilized and of neutral colloidal spheres. The particles in many of these systems are subject to significant many-body hydrodynamic interactions. A recently developed accelerated Stokesian dynamics (ASD) simulation method is used to calculate hydrodynamic functions, wave-number-dependent collective diffusion coefficients, self-diffusion and sedimentation coefficients, and high-frequency limiting viscosities. The dynamic properties are discussed in dependence on the particle concentration and salt content. Our ASD simulation results are compared with existing theoretical predictions, notably those of the renormalized density fluctuation expansion method of Beenakker and Mazur [Physica A 126, 349 (1984)], and earlier simulation data on hard spheres. The range of applicability and the accuracy of various theoretical expressions for short-time properties are explored through comparison with the simulation data. We analyze, in particular, the validity of generalized Stokes-Einstein relations relating short-time diffusion properties to the high-frequency limiting viscosity, and we point to the distinctly different behavior of de-ionized charge-stabilized systems in comparison to hard spheres.

Banchio, Adolfo J.; Nägele, Gerhard

2008-03-01

414

Density  

NSDL National Science Digital Library

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

Day, Martha M.

2008-05-26

415

Local thermodynamic mapping for effective liquid density-functional theory  

NASA Technical Reports Server (NTRS)

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

Kyrlidis, Agathagelos; Brown, Robert A.

1992-01-01

416

Earth's Fluid Spheres  

NSDL National Science Digital Library

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

417

Hardness Test  

Microsoft Academic Search

\\u000a The hardness of materials is commonly characterized using indentation techniques. The hardness values depend on the tool employed\\u000a and the measured parameter, for wood, the anisotropy, heterogeneity and hygroscopicity also influence the measurements. In\\u000a this chapter, different methods used for hardness testing of wood are presented. Possible correlations between the different\\u000a hardness figures and other mechanical properties are indicated, in

Mariapaola Riggio; Maurizio Piazza

418

Sphere based fluid systems  

NASA Technical Reports Server (NTRS)

Systems are described for using multiple closely-packed spheres. In one system for passing fluid, a multiplicity of spheres lie within a container, with all of the spheres having the same outside diameter and with the spheres being closely nested in one another to create multiple interstitial passages of a known size and configuration and smooth walls. The container has an inlet and outlet for passing fluid through the interstitial passages formed between the nested spheres. The small interstitial passages can be used to filter out material, especially biological material such as cells in a fluid, where the cells can be easily destroyed if passed across sharp edges. The outer surface of the spheres can contain a material that absorbs a constitutent in the flowing fluid, such as a particular contamination gas, or can contain a catalyst to chemically react the fluid passing therethrough, the use of multiple small spheres assuring a large area of contact of these surfaces of the spheres with the fluid. In a system for storing and releasing a fluid such as hydrogen as a fuel, the spheres can include a hollow shell containing the fluid to be stored, and located within a compressable container that can be compressed to break the shells and release the stored fluid.

Elleman, Daniel D. (Inventor); Wang, Taylor G. (Inventor)

1989-01-01

419

The role of concavo-convex walls of a nanopore on the density profile, adsorption, solvation force, and capillary condensation of confined fluids: A DFT study  

NASA Astrophysics Data System (ADS)

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

Helmi, Abbas; Keshavarzi, Ezat

2014-03-01

420

Statistical mechanics of jammed packings of 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 60's. There are presently numerous experiments showing that randomly packing spheres of equal size into a container consistently results in a static configuration with a density of 0.64. The ubiquity of random close packing (RCP) rather than the equilibrium crystalline array at 0.74 begs a new statistical framework. Here we introduce a general volume ensemble statistical approach for jammed packings of spheres. This approach provides a thermodynamic definition of RCP: RCP can be interpreted as a manifestation of a thermodynamic singularity, which defines it as the "freezing point'' in a first-order phase transition between ordered and disordered packing phases. We generalize the theory to jammed packings of high dimensional and different size spheres. The asymptotic high-dimensional scaling of the RCP density is consistent with that of other approaches, such as replica theory and density functional theory. The theory predicts the density of random close packing and random loose packing (RLP) of polydisperse systems for a given distribution of sphere size. The present mean-field approach may help to treat packing problems of non-spherical particles, and could serve as a starting point to understand the higher-order correlations present in jammed packings.

Jin, Yuliang

421

Balls and Spheres  

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

422

Sphere light field rendering  

Microsoft Academic Search

Light field algorithm is one of the most famous image-based rendering techniques. In this paper, an improved light field algorithm - sphere light field algorithm - is proposed. This new algorithm replaces the parallel planes used in traditional light field algorithms by a triangularly parameterized sphere surface. Comparing to the traditional light field algorithms, this new algorithm achieves a more

Zigang Wang; Zhengrong Liang

2002-01-01

423

Periodically oscillating plasma sphere  

SciTech Connect

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

424

Micrometer-sized nanoporous tin dioxide spheres for gas sensing  

Microsoft Academic Search

We report the synthesis of mesoporous tin dioxide (SnO2) materials with well-defined particle morphology. The products consist of uniform spheres with a diameter of 5?m. The spheres are hierarchically porous with two distinct pore modes of 5.0nm and 52nm, respectively. This special porosity is the result of a synthesis procedure which involves a ‘hard templating’ (nanocasting) process. The product forms

J.-H. Smått; M. Lindén; T. Wagner; C.-D. Kohl; M. Tiemann

2011-01-01

425

Experiment SPHERE status 2008  

NASA Astrophysics Data System (ADS)

The expedition carried out in March, 2008 to Lake Baikal became an important stage in the development of the SPHERE experiment. During the expedition the SPHERE-2 installation was hoisted, for the first time, on a tethered balloon, APA, to a height of 700 m over the lake surface covered with ice and snow. A series of test measurements were made. Preliminary results of the data processing are presented. The next plan of the SPHERE experiment is to begin a set of statistics for constructing the CR spectrum in the energy range 10-10 eV.

Shaulov, S. B.; Besshapov, S. P.; Kabanova, N. V.; Sysoeva, T. I.; Antonov, R. A.; Anyuhina, A. M.; Bronvech, E. A.; Chernov, D. V.; Galkin, V. I.; Tkaczyk, W.; Finger, M.; Sonsky, M.

2009-12-01

426

Density functional theory for carbon dioxide crystal  

NASA Astrophysics Data System (ADS)

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

Chang, Yiwen; Mi, Jianguo; Zhong, Chongli

2014-05-01

427

Density functional theory for carbon dioxide crystal.  

PubMed

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

Chang, Yiwen; Mi, Jianguo; Zhong, Chongli

2014-05-28

428

Spectroscopy of Fluorescein (FITC) dyed colloidal silica spheres  

Microsoft Academic Search

We have measured the absorption spectrum, the emission spectrum, the emission lifetime, and the photostability of fluorescein isothiocyanate (FITC) incorporated inside colloidal silica spheres as a function of the dye concentration in the spheres, while minimizing scattering effects. Six batches of stable, monodisperse particles were synthesized with FITC up to high densities of 0.03 M. At dye concentrations above 0.001

A. Imhof; M. Megens; J. J. Engelberts; Lang de D. T. N; R. Sprik; W. L. Vos

1999-01-01

429

Atmospheric structure measurements from accelerometer instrumented falling spheres  

Microsoft Academic Search

A three axis piezoelectric accelerometer, mounted in a 25 cm diameter sphere was used to measure atmospheric density and winds and to obtain a temperature profile in the altitude range from 50 to 150 km. The sphere with its own telemetry system and beacon transponder was released from a rocket at 70 km altitude on the up leg of the

C. R. Philbrick; J. P. McIsaac; D. H. Fryklund; R. F. Buck

1981-01-01

430

Conducting Spheres in Electrostatic Fields  

Microsoft Academic Search

The problem of finding the resulting electrostatic potential outside a conducting sphere when the sphere is introduced into a known field is usually attacked by placing suitable image charges and dipoles at specially chosen points within the sphere. Thus, for example, to determine the field due to a point charge e outside an earthed conducting sphere, the standard procedure is

F. Chorlton

1965-01-01

431

Massive fluid spheres in general relativity  

Microsoft Academic Search

We present a class of nonsingular analytic solutions of the general-relativistic field equations in isotropic form for a static spherically symmetric material distribution. Within a sphere the outward variation of pressure, density, pressure-density ratio, and the adiabatic sound speed is monotonic decreasing. The solution has been used to construct causal models for neutron stars with a maximum mass ~=4Mcirdot where

D. N. Pant; A. Sah

1985-01-01

432

Dynamics of the Oblique Impact and Ricochet of Nondeforming Spheres Against Thin Plates.  

National Technical Information Service (NTIS)

The dynamics of the impact of hard spheres against mild steel and aluminum alloy plates has been investigated by using an analytical model of impact dynamics to interpret experimental data. The analytical model assumes rigid body response of the sphere to...

M. E. Backman S. A. Finnegan

1976-01-01

433

Sphere light field rendering  

NASA Astrophysics Data System (ADS)

Light field algorithm is one of the most famous image-based rendering techniques. In this paper, an improved light field algorithm - sphere light field algorithm - is proposed. This new algorithm replaces the parallel planes used in traditional light field algorithms by a triangularly parameterized sphere surface. Comparing to the traditional light field algorithms, this new algorithm achieves a more uniform distribution of light slabs in the three dimensional space. This improves the quality of the rendered images. Using the triangular parameterization and subdivision of the whole light field, less calculation and less memory are needed, resulting in improved real-time rendering.

Wang, Zigang; Liang, Zhengrong

2002-05-01

434

Pair correlation functions and density profiles in the primitive model of the electric double layer  

Microsoft Academic Search

In the primitive model of the electric double layer an electrolyte near a charged surface is modeled by an assembly of charged hard spheres in a medium of dielectric constant &egr;. We solve numerically the inhomogeneous Ornstein–Zernike equation for the pair correlation functions in the hypernetted chain and mean spherical approximations together with the Lovett–Mou–Buff–Wertheim equation for the density of

Michael Plischke; Douglas Henderson

1988-01-01

435

Phase behaviour of deionized binary mixtures of charged colloidal spheres  

NASA Astrophysics Data System (ADS)

We review recent work on the phase behaviour of binary charged sphere mixtures as a function of particle concentration and composition. Both size ratios ? and charge ratios ? are varied over a wide range. Unlike the case for hard spheres, the long-ranged Coulomb interaction stabilizes the crystal phase at low particle concentrations and shifts the occurrence of amorphous solids to particle concentrations considerably larger than the freezing concentration. Depending on ? and ?, we observe upper azeotrope, spindle, lower azeotrope and eutectic types of phase diagrams, all known well from metal systems. Most solids are of body centred cubic structure. Occasionally stoichiometric compounds are formed at large particle concentrations. For very low ?, entropic effects dominate and induce a fluid-fluid phase separation. Since for charged spheres the charge ratio ? is also decisive for the type of phase diagram, future experiments with charge variable silica spheres are suggested.

Lorenz, Nina J.; Schöpe, Hans Joachim; Reiber, Holger; Palberg, Thomas; Wette, Patrick; Klassen, Ina; Holland-Moritz, Dirk; Herlach, Dieter; Okubo, Tsuneo

2009-11-01

436

Phase behaviour of deionized binary mixtures of charged colloidal spheres.  

PubMed

We review recent work on the phase behaviour of binary charged sphere mixtures as a function of particle concentration and composition. Both size ratios ? and charge ratios ? are varied over a wide range. Unlike the case for hard spheres, the long-ranged Coulomb interaction stabilizes the crystal phase at low particle concentrations and shifts the occurrence of amorphous solids to particle concentrations considerably larger than the freezing concentration. Depending on ? and ?, we observe upper azeotrope, spindle, lower azeotrope and eutectic types of phase diagrams, all known well from metal systems. Most solids are of body centred cubic structure. Occasionally stoichiometric compounds are formed at large particle concentrations. For very low ?, entropic effects dominate and induce a fluid-fluid phase separation. Since for charged spheres the charge ratio ? is also decisive for the type of phase diagram, future experiments with charge variable silica spheres are suggested. PMID:21715880

Lorenz, Nina J; Schöpe, Hans Joachim; Reiber, Holger; Palberg, Thomas; Wette, Patrick; Klassen, Ina; Holland-Moritz, Dirk; Herlach, Dieter; Okubo, Tsuneo

2009-11-18

437

Dispersion on a Sphere  

Microsoft Academic Search

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

438

Magnetic Sphere Rheometer.  

National Technical Information Service (NTIS)

A magnetic sphere rheometer which is fully controlled by a personal computer has been developed. It is capable of measuring viscosities in the range of 1000 to 5000 Pa (100-5 X 10 to the 7th power cP). It can operate at shear rates between .0001 and .0002...

R. Hilfiker B. Chu J. Shook

1989-01-01

439

Relativistically spinning charged sphere  

NASA Astrophysics Data System (ADS)

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

Lynden-Bell, D.

2004-11-01

440

Pair correlation functions of two- and three-dimensional hard-core fluids confined into narrow pores: exact results from transfer-matrix method.  

PubMed

The effect of confinement is studied on the local structure of two- and three-dimensional hard-core fluids. The hard disks are confined between two parallel lines, while the hard spheres are in a cylindrical hard pore. In both cases only nearest neighbour interactions are allowed between the particles. The vertical and longitudinal pair correlation functions are determined by means of the exact transfer-matrix method. The vertical pair correlation function indicates that the wall induced packing constraint gives rise to a zigzag (up-down sequence) shaped close packing structure in both two- and three-dimensional systems. The longitudinal pair correlation function shows that both systems transform continuously from a one-dimensional gas-like behaviour to a zigzag solid-like structure with increasing density. PMID:24387389

Gurin, Péter; Varga, Szabolcs

2013-12-28

441

Discontinuous Shear Thickening of Frictional Hard-Sphere Suspensions  

NASA Astrophysics Data System (ADS)

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

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

2013-11-01

442

Sedimentation of hard-sphere suspensions at low Reynolds number  

Microsoft Academic Search

Lattice-Boltzmann simulations have been used to investigate low-Reynolds-number settling of monodisperse and polydisperse suspensions. We confirm the discovery that particle velocity fluctuations are strongly suppressed by no-slip walls at the top and bottom of the system, even in regions distant from the boundaries. We also show that a monodisperse suspension develops a strongly anisotropic long-range microstructure during the settling process,

UYEN N GUYEN; ANTHONY J. C. L ADD

2005-01-01

443

Distribution Function of Classical Fluids of Hard Spheres. II  

Microsoft Academic Search

The pair- and triplet-correlation functions g12[? g(r12)] and g123[? g(r12, r13, r23)] are used to make a superposition approximation g123g124g134g234 ? (g12g13g14g23g24g34) to the quadruplet correlation function g1234. Introduction of this approximation into the second equation of the Born–Green–Yvon (BGY) hierarchy makes it possible to truncate the hierarchy. The resulting equations are a pair of simultaneous integro-differential equations involving g12

Francis H. Ree; Yong-Teh Lee; Taikyue Ree

1971-01-01

444

HSE (Hard Sphere Expansion) Conformal Solution Theory Using Variational Methods.  

National Technical Information Service (NTIS)

This report was written to develop theoretically and demonstrate practically a new procedure for computer calculation of thermodynamic properties of liquid and vapor mixtures along with their equilibrium K-values. The new procedure is designed to give imp...

T. W. Leland

1983-01-01

445

Discontinuous shear thickening of frictional hard-sphere suspensions.  

PubMed

Discontinuous shear thickening (DST) observed in many dense athermal suspensions has proven difficult to understand and to reproduce by numerical simulation. By introducing a numerical scheme including both relevant hydrodynamic interactions and granularlike contacts, we show that contact friction is essential for having DST. Above a critical volume fraction, we observe the existence of two states: a low viscosity, contactless (hence, frictionless) state, and a high viscosity frictional shear jammed state. These two states are separated by a critical shear stress, associated with a critical shear rate where DST occurs. The shear jammed state is reminiscent of the jamming phase of granular matter. Continuous shear thickening is seen as a lower volume fraction vestige of the jamming transition. PMID:24313532

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

2013-11-22

446

Freezing of parallel hard cubes with rounded edges  

NASA Astrophysics Data System (ADS)

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