Density Functional Theory for Baxter's Sticky Hard Spheres in Confinement Hendrik Hansen-Goos,1
Wettlaufer, John S.
Density Functional Theory for Baxter's Sticky Hard Spheres in Confinement Hendrik Hansen-Goos,1 recently been shown that a free energy for Baxter's sticky hard-sphere fluid is uniquely defined within the framework of fundamental measure theory (FMT) for the inhomogeneous hard-sphere fluid, provided
Song, Xueyu
Fundamental-measure density functional theory study of the crystal-melt interface of the hard used to study the hard-sphere crystal-melt interface in the framework of the fundamental measure cost is still quite de- manding. For the hard sphere system, it was found that the anisotropy
NASA Astrophysics Data System (ADS)
Velasco, E.; Mederos, L.; Navascues, G.
We extend the well-known free-volume approach to describe the thermodynamic properties and density distribution of crystalline phases of hard hypersphere systems. Despite its extreme simplicity the approach yields results which are in quantitative agreement with simulation data. The theory can, in particular, describe the properties of the body-centred cubic phase of hard spheres, for which density-functional approaches provide unphysical results, allowing for the application of perturbation theory to situations where, as is the case in some colloidal systems, the body-centred cubic is one of the most interesting phases. The theory is also tested by applying it to systems of hard discs.
The radial distribution function for a fluid of hard spheres at high densities
Eduardo Waisman
1973-01-01
A radial distribution function for hard spheres is obtained, which improves at high densities on the Percus-Yevick function. This is achieved by solving the mean spherical integral equation for a Yukawa form, adjusted to satisfy the Carnahan-Starling equation of state. The solution to the related problem of the mean spherical model approximation for a model fluid which interacts via the
Mode expansion for the density profile of crystal-fluid interfaces: Hard spheres as a test case
M. Oettel
2012-03-16
We present a technique for analyzing the full three-dimensional density profiles of a planar crystal-fluid interface in terms of density modes. These density modes can also be related to crystallinity order parameter profiles which are used in coarse-grained, phase field type models of the statics and dynamics of crystal-fluid interfaces and are an alternative to crystallinity order parameters extracted from simulations using local crystallinity criteria. We illustrate our results for the hard sphere system using finely-resolved, three-dimensional density profiles from density functional theory of fundamental measure type.
Mode expansion for the density profiles of crystal-fluid interfaces: hard spheres as a test case.
Oettel, M
2012-11-21
We present a technique for analyzing the full three-dimensional density profiles of planar crystal-fluid interfaces in terms of density modes. These density modes can also be related to crystallinity order parameter profiles which are used in coarse-grained, phase field type models of the statics and dynamics of crystal-fluid interfaces and are an alternative to crystallinity order parameters extracted from simulations using local crystallinity criteria. We illustrate our results for the hard sphere system using finely resolved, three-dimensional density profiles from a density functional theory of fundamental measure type. PMID:23114279
Collision statistics in sheared inelastic hard spheres.
Bannerman, Marcus N; Green, Thomas E; Grassia, Paul; Lue, Leo
2009-04-01
The dynamics of sheared inelastic-hard-sphere systems is studied using nonequilibrium molecular-dynamics simulations and direct simulation Monte Carlo. In the molecular-dynamics simulations Lees-Edwards boundary conditions are used to impose the shear. The dimensions of the simulation box are chosen to ensure that the systems are homogeneous and that the shear is applied uniformly. Various system properties are monitored, including the one-particle velocity distribution, granular temperature, stress tensor, collision rates, and time between collisions. The one-particle velocity distribution is found to agree reasonably well with an anisotropic Gaussian distribution, with only a slight overpopulation of the high-velocity tails. The velocity distribution is strongly anisotropic, especially at lower densities and lower values of the coefficient of restitution, with the largest variance in the direction of shear. The density dependence of the compressibility factor of the sheared inelastic-hard-sphere system is quite similar to that of elastic-hard-sphere fluids. As the systems become more inelastic, the glancing collisions begin to dominate over more direct, head-on collisions. Examination of the distribution of the times between collisions indicates that the collisions experienced by the particles are strongly correlated in the highly inelastic systems. A comparison of the simulation data is made with direct Monte Carlo simulation of the Enskog equation. Results of the kinetic model of Montanero [J. Fluid Mech. 389, 391 (1999)] based on the Enskog equation are also included. In general, good agreement is found for high-density, weakly inelastic systems. PMID:19518225
Wen-Sheng Xu; Zhao-Yan Sun; Li-Jia An
2011-06-10
We report a molecular dynamics study of crystallization in highly asymmetric binary hard-sphere mixtures, in which the large spheres can form a crystal phase while the small ones remain disordered during the crystallization process of the large spheres. By taking advantage of assisting crystal nucleation with a patterned substrate, direct evidence is presented that there is a close link between the diffusive redistribution of the small spheres and the crystal formation of the large spheres. Although the addition of a second component with large size disparity will not alter the crystal structure formed by the large spheres, the density profile of the small spheres displays corresponding changes at different crystallization stages and closely relates to the crystal growth, suggesting possible effect of small spheres on the crystallization kinetics.
Amorphous packings of hard spheres in large space dimension
G. Parisi; F. Zamponi
2006-01-25
In a recent paper (cond-mat/0506445) we derived an expression for the replicated free energy of a liquid of hard spheres based on the HNC free energy functional. An approximate equation of state for the glass and an estimate of the random close packing density were obtained in d=3. Here we show that the HNC approximation is not needed: the same expression can be obtained from the full diagrammatic expansion of the replicated free energy. Then, we consider the asymptotics of this expression when the space dimension d is very large. In this limit, the entropy of the hard sphere liquid has been computed exactly. Using this solution, we derive asymptotic expressions for the glass transition density and for the random close packing density for hard spheres in large space dimension.
Theory of asymmetric nonadditive binary hard-sphere mixtures.
Roth, R; Evans, R; Louis, A A
2001-11-01
It is shown that the formal procedure of integrating out the degrees of freedom of the small spheres in a binary hard-sphere mixture works equally well for nonadditive as it does for additive mixtures. For highly asymmetric mixtures (small size ratios) the resulting effective Hamiltonian of the one-component fluid of big spheres, which consists of an infinite number of many-body interactions, should be accurately approximated by truncating after the term describing the effective pair interaction. Using a density functional treatment developed originally for additive hard-sphere mixtures the zero, one, and two-body contribution to the effective Hamiltonian are determined. It is demonstrated that even small degrees of positive or negative nonadditivity have significant effect on the shape of the depletion potential. The second virial coefficient B2, corresponding to the effective pair interaction between two big spheres, is found to be a sensitive measure of the effects of nonadditivity. The variation of B2 with the density of the small spheres shows significantly different behavior for additive, slightly positive and slightly negative nonadditive mixtures. Possible repercussions of these results for the phase behavior of binary hard-sphere mixtures are discussed and it is suggested that measurements of B2 might provide a means of determining the degree of nonadditivity in real colloidal mixtures. PMID:11735911
Song, Xueyu
-sphere and Lennard-Jones mixtures Vadim B. Warshavsky and Xueyu Songa Ames Laboratory and Department of Chemistry theory the free energies of solid and liquid Lennard-Jones LJ mixtures are obtained from correlation of the HS systems was used in the WCA perturbation theory to calcu- late the free energies of the Lennard-Jones
Hard spheres on the gyroid surface
Dotera, Tomonari; Kimoto, Masakiyo; Matsuzawa, Junichi
2012-01-01
We find that 48/64 hard spheres per unit cell on the gyroid minimal surface are entropically self-organized. Striking evidence is obtained in terms of the acceptance ratio of Monte Carlo moves and order parameters. The regular tessellations of the spheres can be viewed as hyperbolic tilings on the Poincaré disc with a negative Gaussian curvature, one of which is, equivalently, the arrangement of angels and devils in Escher's Circle Limit IV. PMID:24098841
Most stable structure for hard spheres.
Koch, Hans; Radin, Charles; Sadun, Lorenzo
2005-07-01
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. PMID:16090135
First derivative of the hard-sphere radial distribution function at contact
David M Heyes; Michael Cass; Arkadiusz C Bra?ka; Hisashi Okumura
2006-01-01
Molecular dynamics simulations have been carried out of the radial distribution function of the hard sphere fluid for a range of densities in the equilibrium fluid and just into the metastable region. The first derivative of the hard-sphere radial distribution function at contact was computed and its density dependence fitted to a simple analytic form. Comparisons were made with semi-empirical
Time correlation functions of hard sphere and soft sphere fluids.
Bra?ka, A C; Heyes, D M
2004-02-01
We explore the transition between soft particle fluids of increasing steepness to the hard sphere limit. We analyze the analytic forms of the time correlation functions used in determining transport coefficients in Green-Kubo formulas for fluids composed of particles interacting through a repulsive r(-n) potential. We focus on the steeply repulsive n--> infinity limit where the potential tends to the hard sphere interaction. Dufty [Mol. Phys. 100, 2331 (2002)] developed a theoretical framework that can be used to characterize the transition from a steeply repulsive continuous potential toward the hard sphere potential for the shear stress time correlation function. This function was shown to consist of a rapidly decaying contribution (which is singular in the steeply repulsive limit) and a slowly decaying nonsingular part which can be reasonably well represented by Enskog's prediction on times of order and in excess of the mean collision time. We extend this treatment to the bulk viscosity and thermal conductivity. We focus on the bulk viscosity (pressure) correlation function as it is purely singular for hard spheres, and has no kinetic or cross term contributions in this limit. There is no relaxation of this correlation function on the mean collision or Enskog time scale for hard spheres. We show that it is not possible to represent the steeply repulsive behavior of this function entirely in terms of a sech function, i.e., C(B)(t)=sech(a(n)t/tau(n)), where a(n) is a numerical factor, t is time, and tau(n) is a relaxation time proportional to n(-1). An additional singular function, which we call w(t), is required to obtain the correct short-time behavior of C(B)(t) and the Enskog value for the bulk viscosity. With this additional function, the value of a(n) in the n--> infinity limit is a(n)=square root of 2 which is consistent with the second moment of the time expansion of the time correlation function. We compute this function for large n and extrapolate it to n--> infinity, determining one possible analytic form. The shear stress correlation function also gives a(n)=square root of 2 in the hard sphere limit for the singular part when the sech and w functions are used. This function has a nonsingular component, even in the hard sphere limit. We explore various forms for the crossover function X(t/tau(n)) introduced by Dufty, which weights the limiting singular and nonsingular contributions to C(S)(t) particularly at intermediate times. The qualitative behavior for the heat flux time correlation function (used to obtain the thermal conductivity) is much the same as the shear case. The w(t) derived by several self-consistent extrapolations appears, within the simulation statistics, to be the same for the bulk and shear viscosity, and for the thermal conductivity cases. PMID:14995434
Conformal Solution Theory: Hard-Sphere Mixtures
Douglas Henderson; Peter J. Leonard
1971-01-01
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.
Radial distribution function for hard spheres
S. Bravo Yuste; A. Santos
1991-01-01
The radial distribution function g(r) provided by the solution of the Percus-Yevick (PY) equation for hard spheres is rederived in terms of the simplest Padé approximant of a function defined in the Laplace space that is consistent with the following physical requirements: g(r) is continuous for r>1, the isothermal compressibility is finite, and the zeroth- and first-order coefficients in the
Hard-sphere-like dynamics in a non-hard-sphere liquid.
Scopigno, T; Di Leonardo, R; Comez, L; Baron, A Q R; Fioretto, D; Ruocco, G
2005-04-22
The collective dynamics of liquid gallium close to the melting point has been studied using inelastic x-ray scattering to probe length scales smaller than the size of the first coordination shell. Although the structural properties of this partially covalent liquid strongly deviate from a simple hard-sphere model, the dynamics, as reflected in the quasielastic scattering, are beautifully described within the framework of the extended heat mode approximation of Enskog's kinetic theory, analytically derived for a hard-sphere system. The present work demonstrates, therefore, the applicability of Enskog's theory beyond simple liquids. PMID:15904154
Equation of state of the hard-sphere crystal
NASA Astrophysics Data System (ADS)
Rascón, C.; Mederos, L.; Navascués, G.
1996-06-01
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 free energy density functional [Phys. Rev. A 31, 2672 (1985)]. They are in excellent agreement with simulation results over the physical range of densities up to almost close packing. We also include the comparison with the results obtained by two other functional approaches, which are also excellent.
Multiple Glasses in Asymmetric Binary Hard Spheres
Th. Voigtmann
2010-10-03
Multiple distinct glass states occur in binary hard-sphere mixtures with constituents of very disparate sizes according to the mode-coupling theory of the glass transition (MCT), distinguished by considering whether small particles remain mobile or not, and whether small particles contribute significantly to perturb the big-particle structure or not. In the idealized glass, the four different glasses are separated by sharp transitions that give rise to higher-order transition phenomena involving logarithmic decay laws, and to anomalous power-law-like diffusion. The phenomena are argued to be expected generally in glass-forming mixtures.
Hard sphere dynamics for normal and granular fluids.
Dufty, James W; Baskaran, Aparna
2005-06-01
A fluid of N smooth, hard spheres is considered as a model for normal (elastic collision) and granular (inelastic collision) fluids. The potential energy is discontinuous for hard spheres so that the pairwise forces are singular and the usual forms of Newtonian and Hamiltonian mechanics do not apply. Nevertheless, particle trajectories in the N particle phase space are well defined and the generators for these trajectories can be identified. The first part of this presentation is a review of the generators for the dynamics of observables and probability densities. The new results presented in the second part refer to applications of these generators to the Liouville dynamics for granular fluids. A set of eigenvalues and eigenfunctions of the generator for this Liouville dynamics system is identified in a special stationary representation. This provides a class of exact solutions to the Liouville equation that are closely related to hydrodynamics for granular fluids. PMID:15980307
Simulation of the binary hard-sphere crystal/melt interface
Davidchack, Ruslan L.; Laird, Brian Bostian
1996-12-01
We report results of molecular-dynamics simulations on a planar binary hard-sphere disordered facecentered-cubic [100] crystal/melt interface. From the analysis of the single-particle density and diffusion profiles for the separate components...
Wettlaufer, John S.
2011-01-01
THE JOURNAL OF CHEMICAL PHYSICS 134, 014506 (2011) A fundamental measure theory for the sticky hard; published online 6 January 2011) We construct a density functional theory (DFT) for the sticky hard sphere (SHS) fluid which, like Rosenfeld's fundamental measure theory (FMT) for the hard sphere fluid [Y
Viscosity, hard sphere diameter and interionic potential for liquid lead
Boyer, Edmond
L-347 Viscosity, hard sphere diameter and interionic potential for liquid lead G. Chaussemy The Macedo-Litovitz equation for a hard sphere liquid provides a satisfactory model for the viscosity of lead and molecular dynamics. The activation energy for viscosity (0.07 eV) is similar to the height of the interionic
Phase diagram of the hard-sphere/attractive-Yukawa system
NASA Astrophysics Data System (ADS)
Mederos, L.; Navascués, G.
1994-12-01
A density functional approximation is used to study the phase diagram of a hard sphere-attractive Yukawa system. We pay special attention to the dependence of the liquid phase stability on the range of the attractive tail. When this is sufficiently short-ranged, the liquid phase is not present in the phase diagram. The transition to the usual behavior with a phase diagram showing vapor, liquid, and solid phases takes place for a value of the range of the attractive part which is in reasonable agreement with recent Monte Carlo simulations and theoretical results.
Sciortino, Francesco
-density behaviour of dipolar hard- sphere (DHS) particles, i.e., hard spheres with dipoles embedded in their centre. We aim at de- scribing the DHS fluid in terms of a network of chains and rings (the fundamental and a liquid phase. Simulation studies of systems which have the dipo- lar hard sphere (DHS) fluid
Self-diffusion in liquid gallium and hard sphere model
NASA Astrophysics Data System (ADS)
Blagoveshchenskii, Nikolay; Novikov, Arkady; Puchkov, Alexander; Savostin, Vadim; Sobolev, Oleg
2015-01-01
Incoherent and coherent components of quasielastic neutron scattering have been studied in the temperature range of T = 313 K - 793 K aiming to explore the applicability limits of the hard-sphere approach for the microscopic dynamics of liquid gallium, which is usually considered as a non-hard-sphere system. It was found that the non-hard-sphere effects come into play at the distances shorter than the average interatomic distance. The longer range diffusive dynamics of liquid Ga is dominated by the repulsive forces between the atoms.
Interfacial free energy of a hard-sphere fluid in contact with curved hard surfaces
Laird, Brian Bostian; Hunter, Allie; Davidchack, Ruslan L.
2012-12-20
Using molecular-dynamics simulation, we have calculated the interfacial free energy ? between a hard-sphere fluid and hard spherical and cylindrical colloidal particles, as functions of the particle radius R and the fluid ...
Eckert, Thomas; Richtering, Walter
2008-09-28
The colloidal phase behavior, structure factors, short-time collective diffusion coefficients, and hydrodynamic interactions of concentrated poly(N-isopropylacryamide) (PNiPAM) microgels in dimethylformamide suspensions were measured with simultaneous static and dynamic three-dimensional cross-correlated light scattering. The data are interpreted through comparison with hard sphere theory. The fluid-crystal transition and the static structure factors can be described consistently by the hard sphere approximation. On the other hand, collective diffusion and hydrodynamic interaction cannot be described satisfactorily by the hard sphere model. The microgel structure is different from hard spheres, as the cross-link density decreases with the distance from the particle center leading to a "fuzzy" particle surface with dangling polymer chains. These seem to affect the hydrodynamic interaction much more as compared to direct thermodynamic interaction. PMID:19045060
Depletion effects in smectic phases of hard-rod-hard-sphere mixtures
NASA Astrophysics Data System (ADS)
Mart?nez-Ratón, Y.; Cinacchi, G.; Velasco, E.; Mederos, L.
2006-10-01
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.
Revisit of interfacial free energy of the hard sphere system near hard wall
Mingcheng Yang; Hongru Ma
2008-06-23
We propose a simple Monte Carlo method to calculate the interfacial free energy between the substrate and the material. Using this method we investigate the interfacial free energys of the hard sphere fluid and solid phases near a smooth hard wall. According to the obtained interfacial free energys of the coexisting fluid and solid phases and the Young equation we are able to determine the contact angle with high accuracy, cos$\\theta$ = 1:010(31), which indicates that a smooth hard wall can be wetted completely by the hard sphere crystal at the interface between the wall and the hard sphere fluid.
Diffusion and structure of a quasi-one-dimensional hard-sphere fluid
NASA Astrophysics Data System (ADS)
Lin, Binhua; Lee, Ji Hwan; Cui, Bianxiao
2001-03-01
We report the results of an experimental study of a quasi-one-dimensional hard-sphere fluid. The system consists of uncharged Si colloidal spheres confined in long, uncorrelated 1D-channels whose narrow width forbids mutual passage of spheres along the channel. By tracking the trajectories of the spheres using digital video microscopy, we studied the diffusion and structure of the system as a function of the density of the fluid. Our results show that the behavior of the spheres in self-diffusion is changed gradually from Fickian to non-Fickian near the onset of the collision between the spheres, indicating the correlation between the collision of the hard-spheres and the change in diffusion mechanism. At high density, the self-part of the van Hove function of the system is no longer a Gaussian distribution but a Poisson distribution which can be interpreted using a hydrodynamic analysis for effective wall-drag effect. The pair distribution function of the system can be explained by an analytical expression for a 1D hard-sphere fluid [1]. [1] Y. Rosenfeld, M. Schmidt, H. Lowen and P. Tarazona, Phys. Rev. E 55, 4245 (1997).
Experiments with Hard, Soft, and Hydrodynamically Interacting Spheres
Maarten Arnold Rutgers
1995-01-01
This thesis presents research on colloidal suspensions of nearly identical spheres and shows that some very interesting phenomena take place while the inter-particle interactions are simple in nature. The work is divided into three areas which explore aspects of hydrodynamic and hard core and electrostatic repulsive interactions. In chapter two hard core interactions are singled out, as we verify the
Inhomogeneous quasistationary state of dense fluids of inelastic hard spheres.
Fouxon, Itzhak
2014-05-01
We study closed dense collections of freely cooling hard spheres that collide inelastically with constant coefficient of normal restitution. We find inhomogeneous states (ISs) where the density profile is spatially nonuniform but constant in time. The states are exact solutions of nonlinear partial differential equations that describe the coupled distributions of density and temperature valid when inelastic losses of energy per collision are small. The derivation is performed without modeling the equations' coefficients that are unknown in the dense limit (such as the equation of state) using only their scaling form specific for hard spheres. Thus the IS is the exact state of this dense many-body system. It captures a fundamental property of inelastic collections of particles: the possibility of preserving nonuniform temperature via the interplay of inelastic cooling and heat conduction that generalizes previous results. We perform numerical simulations to demonstrate that arbitrary initial state evolves to the IS in the limit of long times where the container has the geometry of the channel. The evolution is like a gas-liquid transition. The liquid condenses in a vanishing part of the total volume but takes most of the mass of the system. However, the gaseous phase, which mass grows only logarithmically with the system size, is relevant because its fast particles carry most of the energy of the system. Remarkably, the system self-organizes to dissipate no energy: The inelastic decay of energy is a power law [1+t/t(c)](-2), where t(c) diverges in the thermodynamic limit. This is reinforced by observing that for supercritical systems the IS coincide in most of the space with the steady states of granular systems heated at one of the walls. We discuss the relation of our results to the recently proposed finite-time singularity in other container's geometries. PMID:25353790
Phonon contribution to the entropy of hard-sphere crystals
NASA Astrophysics Data System (ADS)
Elser, Veit
2014-05-01
Comparing the entropies of hard spheres in the limit of close packing, for different stacking sequences of the hexagonal layers, has been a challenge because the differences are so small. Here we present a method based on a "sticky-sphere" model by which the system interpolates between hard spheres in one limit and a harmonic crystal in the other. For the fcc and hcp stackings we have calculated the entropy difference in the harmonic (sticky) limit, as well as the differences in the free energy change upon removing the stickiness in the model. The former, or phonon entropy, accounts for most of the entropy difference. Our value for the net entropy difference, ?s =0.001164(8)kB per sphere, is in excellent agreement with the best previous estimate by Mau and Huse [Phys. Rev. E 59, 4396 (1999), 10.1103/PhysRevE.59.4396].
Transport coefficients for the hard-sphere granular fluid.
Baskaran, Aparna; Dufty, James W; Brey, J Javier
2008-03-01
In the preceding paper, linear response methods have been applied to obtain formally exact expressions for the parameters of Navier-Stokes order hydrodynamics. The analysis there is general, applying to both normal and granular fluids with a wide range of collision rules. Those results are specialized here to the case of smooth, inelastic, hard spheres with constant coefficient of normal restitution, for further elaboration. Explicit expressions for the cooling rate, pressure, and transport coefficients are given and compared with the corresponding expressions for a system of elastic hard spheres. The scope of the results for further analytical explorations and possible numerical evaluation is discussed. PMID:18517374
A generalized hard-sphere model for Monte Carlo simulation
NASA Technical Reports Server (NTRS)
Hassan, H. A.; Hash, David B.
1993-01-01
A new molecular model, called the generalized hard-sphere, or GHS model, is introduced. This model contains, as a special case, the variable hard-sphere model of Bird (1981) and is capable of reproducing all of the analytic viscosity coefficients available in the literature that are derived for a variety of interaction potentials incorporating attraction and repulsion. In addition, a new procedure for determining interaction potentials in a gas mixture is outlined. Expressions needed for implementing the new model in the direct simulation Monte Carlo methods are derived. This development makes it possible to employ interaction models that have the same level of complexity as used in Navier-Stokes calculations.
Structure of ternary additive hard-sphere fluid mixtures
NASA Astrophysics Data System (ADS)
Malijevský, Alexander; Malijevský, Anatol; Yuste, Santos B.; Santos, Andrés; López de Haro, Mariano
2002-12-01
Monte Carlo simulations on the structural properties of ternary fluid mixtures of additive hard spheres are reported. The results are compared with those obtained from a recent analytical approximation [S. B. Yuste, A. Santos, and M. López de Haro, J. Chem. Phys. 108, 3683 (1998)] to the radial distribution functions of hard-sphere mixtures and with the results derived from the solution of the Ornstein-Zernike integral equation with both the Martynov-Sarkisov and the Percus-Yevick closures. Very good agreement between the results of the first two approaches and simulation is observed, with a noticeable improvement over the Percus-Yevick predictions especially near contact.
Depletion effects in smectic phases of hard-rod-hard-sphere mixtures.
Martínez-Ratón, Y; Cinacchi, G; Velasco, E; Mederos, L
2006-10-01
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 tau parameter, which has been proposed as a convenient measure of depletion strength. We present closed expressions for tau, 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 tau 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 tau approximately d (3). 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 tau parameter should be of order unity as d tends to infinity. PMID:17171313
NASA Astrophysics Data System (ADS)
Hanifpour, M.; Francois, N.; Robins, V.; Kingston, A.; Vaez Allaei, S. M.; Saadatfar, M.
2015-06-01
Here we present an experimental and numerical investigation on the grain-scale geometrical and mechanical properties of partially crystallized structures made of macroscopic frictional grains. Crystallization is inevitable in arrangements of monosized hard spheres with packing densities exceeding Bernal's limiting density ?Bernal?0.64 . We study packings of monosized hard spheres whose density spans over a wide range (0.59 sphere packings. We show that clear geometrical transitions coincide with modifications of the mechanical backbone of the packing both at the grain and global scale. Notably, two transitions are identified at ?Bernal?0.64 and ?c?0.68 . These results provide insights on how geometrical and mechanical features at the grain scale conspire to yield partially crystallized structures that are mechanically stable.
NASA Astrophysics Data System (ADS)
Jing, Zhicheng; Karato, Shun-ichiro
2012-05-01
Density of ultramafic silicate melts was determined using the sink/float technique at high pressures. Seven melt compositions were studied, among which three were dry compositions with different Mg#'s (molar MgO/(MgO + FeO) × 100) and the other four were hydrous compositions synthesized by adding 2-7 wt.% H2O to the anhydrous ones. Experimental conditions range from 9 to 15 GPa and from 2173 to 2473 K. The sinking and floatation of density markers were observed for all melt compositions. Melt density data were analyzed by applying the Birch-Murnaghan equation of state and a newly developed equation of state for silicate melts based on the model of hard sphere mixtures. The presence of water can significantly reduce the density of melts due to its small molecular mass. On the other hand, water makes hydrous silicate melts more compressible than anhydrous melts and therefore the effect of H2O on melt density is less significant at high pressures. The density of hydrous melts was then calculated as a function of H2O content at the conditions of the bottom of the upper mantle, and was compared with the density of the dominant upper mantle minerals. Results show that the conditions for a negatively buoyant melt that coexists with a pyrolite mantle atop the 410 km discontinuity are marginally satisfied if H2O is the only volatile component to facilitate melting, but such conditions will be satisfied by a broader range of conditions when other heavier volatile elements (C, K, etc.) are also present.
Jing, Zhicheng; Karato, Shun-ichiro (Yale); (UC)
2012-04-20
Density of ultramafic silicate melts was determined using the sink/float technique at high pressures. Seven melt compositions were studied, among which three were dry compositions with different Mg's (molar MgO/(MgO + FeO) x 100) and the other four were hydrous compositions synthesized by adding 2-7 wt.% H{sub 2}O to the anhydrous ones. Experimental conditions range from 9 to 15 GPa and from 2173 to 2473 K. The sinking and floatation of density markers were observed for all melt compositions. Melt density data were analyzed by applying the Birch-Murnaghan equation of state and a newly developed equation of state for silicate melts based on the model of hard sphere mixtures. The presence of water can significantly reduce the density of melts due to its small molecular mass. On the other hand, water makes hydrous silicate melts more compressible than anhydrous melts and therefore the effect of H{sub 2}O on melt density is less significant at high pressures. The density of hydrous melts was then calculated as a function of H{sub 2}O content at the conditions of the bottom of the upper mantle, and was compared with the density of the dominant upper mantle minerals. Results show that the conditions for a negatively buoyant melt that coexists with a pyrolite mantle atop the 410 km discontinuity are marginally satisfied if H{sub 2}O is the only volatile component to facilitate melting, but such conditions will be satisfied by a broader range of conditions when other heavier volatile elements (C, K, etc.) are also present.
Extended hard-sphere model and collisions of cohesive particles.
Kosinski, Pawel; Hoffmann, Alex C
2011-09-01
In two earlier papers the present authors modified a standard hard-sphere particle-wall and particle-particle collision model to account for the presence of adhesive or cohesive interaction between the colliding particles: the problem is of importance for modeling particle-fluid flow using the Lagrangian approach. This technique, which involves a direct numerical simulation of such flows, is gaining increasing popularity for simulating, e.g., dust transport, flows of nanofluids and grains in planetary rings. The main objective of the previous papers was to formally extend the impulse-based hard-sphere model, while suggestions for quantifications of the adhesive or cohesive interaction were made. This present paper gives an improved quantification of the adhesive and cohesive interactions for use in the extended hard-sphere model for cases where the surfaces of the colliding bodies are "dry," e.g., there is no liquid-bridge formation between the colliding bodies. This quantification is based on the Johnson-Kendall-Roberts (JKR) analysis of collision dynamics but includes, in addition, dissipative forces using a soft-sphere modeling technique. In this way the cohesive impulse, required for the hard-sphere model, is calculated together with other parameters, namely the collision duration and the restitution coefficient. Finally a dimensional analysis technique is applied to fit an analytical expression to the results for the cohesive impulse that can be used in the extended hard-sphere model. At the end of the paper we show some simulation results in order to illustrate the model. PMID:22060357
Extended hard-sphere model and collisions of cohesive particles
NASA Astrophysics Data System (ADS)
Kosinski, Pawel; Hoffmann, Alex C.
2011-09-01
In two earlier papers the present authors modified a standard hard-sphere particle-wall and particle-particle collision model to account for the presence of adhesive or cohesive interaction between the colliding particles: the problem is of importance for modeling particle-fluid flow using the Lagrangian approach. This technique, which involves a direct numerical simulation of such flows, is gaining increasing popularity for simulating, e.g., dust transport, flows of nanofluids and grains in planetary rings. The main objective of the previous papers was to formally extend the impulse-based hard-sphere model, while suggestions for quantifications of the adhesive or cohesive interaction were made. This present paper gives an improved quantification of the adhesive and cohesive interactions for use in the extended hard-sphere model for cases where the surfaces of the colliding bodies are “dry,” e.g., there is no liquid-bridge formation between the colliding bodies. This quantification is based on the Johnson-Kendall-Roberts (JKR) analysis of collision dynamics but includes, in addition, dissipative forces using a soft-sphere modeling technique. In this way the cohesive impulse, required for the hard-sphere model, is calculated together with other parameters, namely the collision duration and the restitution coefficient. Finally a dimensional analysis technique is applied to fit an analytical expression to the results for the cohesive impulse that can be used in the extended hard-sphere model. At the end of the paper we show some simulation results in order to illustrate the model.
NASA Astrophysics Data System (ADS)
Hansen-Goos, Hendrik; Mortazavifar, Mostafa; Oettel, Martin; Roth, Roland
2015-05-01
Based on Santos' general solution for the scaled-particle differential equation [Phys. Rev. E 86, 040102(R) (2012), 10.1103/PhysRevE.86.040102], we construct a free-energy functional for the hard-sphere system. The functional is obtained by a suitable generalization and extension of the set of scaled-particle variables using the weighted densities from Rosenfeld's fundamental measure theory for the hard-sphere mixture [Phys. Rev. Lett. 63, 980 (1989), 10.1103/PhysRevLett.63.980]. While our general result applies to the hard-sphere mixture, we specify remaining degrees of freedom by requiring the functional to comply with known properties of the pure hard-sphere system. Both for mixtures and pure systems, the functional can be systematically extended following the lines of our derivation. We test the resulting functionals regarding their behavior upon dimensional reduction of the fluid as well as their ability to accurately describe the hard-sphere crystal and the liquid-solid transition.
Hard-sphere radial distribution function from the residual chemical potential
Tomás Boublík
2006-01-01
A method of determining the radial distribution function on the basis of expressions for the residual chemical potential of hard spheres and of the infinitely diluted mixture of a hard dumbbell (originated from overlapping of two spheres) in hard spheres is revised. The enlarged hard dumbbell (instead of the standard one used in our previous study [T. Boublík, Molec. Phys.
NASA Astrophysics Data System (ADS)
Santos, A.; Yuste, S. B.; López de Haro, M.
The composition-independent virial coefficients of a d-dimensional binary mixture of (additive) hard hyperspheres following from a recent proposal for the equation of state of the mixture (SANTOS, A., YUSTE, S. B., and LÓPEZ DE HARO, M., 1999, Molec. Phys., 96 , 1) are examined. Good agreement between theoretical estimates and available exact or numerical results is found for d = 2, 3, 4 and 5, except for mixtures whose components are very disparate in size. A slight modification that remedies this deficiency is introduced and the resummation of the associated virial series is carried out, leading to a new proposal for the equation of state. The case of binary hard sphere mixtures (d = 3) is analysed in some detail.
Physics of Hard Spheres Experiment: Significant and Quantitative Findings Made
NASA Technical Reports Server (NTRS)
Doherty, Michael P.
2000-01-01
Direct examination of atomic interactions is difficult. One powerful approach to visualizing atomic interactions is to study near-index-matched colloidal dispersions of microscopic plastic spheres, which can be probed by visible light. Such spheres interact through hydrodynamic and Brownian forces, but they feel no direct force before an infinite repulsion at contact. Through the microgravity flight of the Physics of Hard Spheres Experiment (PHaSE), researchers have sought a more complete understanding of the entropically driven disorder-order transition in hard-sphere colloidal dispersions. The experiment was conceived by Professors Paul M. Chaikin and William B. Russel of Princeton University. Microgravity was required because, on Earth, index-matched colloidal dispersions often cannot be density matched, resulting in significant settling over the crystallization period. This settling makes them a poor model of the equilibrium atomic system, where the effect of gravity is truly negligible. For this purpose, a customized light-scattering instrument was designed, built, and flown by the NASA Glenn Research Center at Lewis Field on the space shuttle (shuttle missions STS 83 and STS 94). This instrument performed both static and dynamic light scattering, with sample oscillation for determining rheological properties. Scattered light from a 532- nm laser was recorded either by a 10-bit charge-coupled discharge (CCD) camera from a concentric screen covering angles of 0 to 60 or by sensitive avalanche photodiode detectors, which convert the photons into binary data from which two correlators compute autocorrelation functions. The sample cell was driven by a direct-current servomotor to allow sinusoidal oscillation for the measurement of rheological properties. Significant microgravity research findings include the observation of beautiful dendritic crystals, the crystallization of a "glassy phase" sample in microgravity that did not crystallize for over 1 year in 1g (Earth's gravity), and the emergence of face-centered-cubic (FCC) crystals late in the coarsening process (as small crystallites lost particles to the slow ripening of large crystallites). Significant quantitative findings from the microgravity experiments have been developed describing complex interactions among crystallites during the growth process, as concentration fields overlap in the surrounding disordered phase. Time-resolved Bragg scattering under microgravity captures one effect of these interactions quite conclusively for the sample at a volume fraction of 0.528. From the earliest time until the sample is almost fully crystalline, the size and overall crystallinity grow monotonically, but the number of crystallites per unit volume (number density) falls. Apparently nucleation is slower than the loss of crystallites because of the transfer of particles from small to large crystals. Thus, coarsening occurs simultaneously with growth, rather than following the completion of nucleation and growth as is generally assumed. In the same sample, an interesting signature appears in the apparent number density of crystallites and the volume fraction within the crystallites shortly before full crystallinity is reached. A brief upturn in both indicates the creation of more domains of the size of the average crystallite simultaneous with the compression of the crystallites. Only the emergence of dendritic arms offers a reasonable explanation. The arms would be "seen" by the light scattering as separate domains whose smaller radii of curvature would compress the interior phase. In fiscal year 1999, numerous papers, a doctoral dissertation, and the PHaSE final report were produced. Although this flight project has been completed, plans are in place for a follow-on colloid experiment by Chaikin and Russel that employs a light microscope within Glenn's Fluids and Combustion Facility on the International Space Station. PHaSE is providing us with a deeper understanding of the nure of phase transitions. The knowledge derived has added to the understandin
The nematic-isotropic phase transition in semiflexible fused hard-sphere chain fluids
NASA Astrophysics Data System (ADS)
Jaffer, K. M.; Opps, S. B.; Sullivan, D. E.; Nickel, B. G.; Mederos, L.
2001-02-01
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.
The nematic-isotropic phase transition in semiflexible fused hard-sphere chain fluids
NASA Astrophysics Data System (ADS)
Jaffer, K. M.; Opps, S. B.; Sullivan, D. E.; Nickel, B. G.; Mederos, L.
2001-03-01
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.
A molecular theory for the freezing of hard spheres
A. D. J. Haymet
1983-01-01
Using statisical mechanics and a series of well-defined approximations we present a calculation of the equilibrium liquid to solid transition for hard spheres. No computer simulation results are used. The transition is located from structural information about the liquid using a first-principles order parameter theory of freezing. The order parameters are the coefficients of a Fourier expansion of the spatially
On the relaxation of single hard-sphere gases
1990-01-01
The nonlinear Boltzmann equation is solved to examine the Maxwellization of a spatially uniform hard-sphere gas using the Laguerre moment method. The computations are carried out for two different classes of initial conditions. Emphasis is layed on the characteristic times for the relaxation of the distribution function toward the equilibrium. As a result, in the thermal energy range the relaxation
Contact values for disparate-size hard-sphere mixtures
Andres Santos; Santos B. Yuste; Mariano Lopez de Haro; Morad Alawneh; Douglas Henderson
2009-01-01
A universality ansatz for the contact values of a multicomponent mixture of additive hard spheres is used to propose new formulae for the case of disparate-size binary mixtures. A comparison with simulation data and with a recent proposal by Alawneh and Henderson for binary mixtures shows reasonably good agreement with the predictions for the contact values of the large-large radial
Experiments with Hard, Soft, and Hydrodynamically Interacting Spheres
NASA Astrophysics Data System (ADS)
Rutgers, Maarten Arnold
1995-01-01
This thesis presents research on colloidal suspensions of nearly identical spheres and shows that some very interesting phenomena take place while the inter-particle interactions are simple in nature. The work is divided into three areas which explore aspects of hydrodynamic and hard core and electrostatic repulsive interactions. In chapter two hard core interactions are singled out, as we verify the prediction of a remarkable first order phase transition from a disordered fluid of spheres to a long range ordered solid. We accurately measured the full equation of state of a sediment of sub micrometer hard spheres using an X-ray densitometry technique. The measurements prove the existence of hard sphere behavior in a real system with unprecedented accuracy and prove our method a new and accurate probe of colloidal interactions. Chapter three is concerned with the settling state preceding the equilibrium sediments described above. This problem of many-body hydrodynamic interactions at near zero Reynolds number has proven elusive to the extent that even the most rudimentary macroscopic quantities, such as the mean settling velocity < v> , have only been calculated (with limited success) for dilute suspensions of spheres. We created a steady state fluidized suspension of colloidal spheres in which we deliberately controlled particle dynamics and positions by altering their interactions. The measurements are the first to quantitatively confirm calculations for flow through periodic lattices and have introduced a novel way to measure the effects of suspension microstructure and concentration on the average sedimentation rate. The final chapter concentrates on the microscopic, and often locally collective, motions of settling non-Brownian hard spheres. Of interest here were recent measurements of anomalously large sedimentation velocity fluctuations and again the need for observations of the suspension microstructure, whose lack has lead to theoretical speculations on the possibility of infinite sedimentation velocity variances. From digital particle imaging velocimetry on dilute fluidized beds we have found no evidence of a diverging velocity variance, but did observe strong spatial velocity correlations out to 50 particle diameters. The latter discovery should have a significant impact on redirecting theoretical efforts concerning dilute sedimentation.
Model energy landscapes of low-temperature fluids: Dipolar hard spheres Dmitry V. Matyushov*
Matyushov, Dmitry
Model energy landscapes of low-temperature fluids: Dipolar hard spheres Dmitry V. Matyushov* Center of dipolar hard spheres. The entire excitation profile of the liquid, from the high-temperature liquid hard spheres loses stability close to the point of ideal-glass transition transforming via a first
Hard-sphere melting and crystallization with event-chain Monte Carlo
Isobe, Masaharu
2015-01-01
We simulate crystallization and melting with local Monte Carlo (LMC), event-chain Monte Carlo (ECMC), and with event-driven molecular dynamics (EDMD) in systems with up to one million three-dimensional hard spheres. We illustrate that our implementations of the three algorithms rigorously coincide in their equilibrium properties. We then study nucleation in the NVE ensemble from the fcc crystal into the homogeneous liquid phase and from the liquid into the homogeneous crystal. ECMC and EDMD both approach equilibrium orders of magnitude faster than LMC. ECMC is also notably faster than EDMD, especially for the equilibration into a crystal from a disordered initial condition at high density. ECMC can be trivially implemented for hard-sphere and for soft-sphere potentials, and we suggest possible applications of this algorithm for studying jamming and the physics of glasses, as well as disordered systems.
Eisenberg, E; Baram, A
2007-04-01
For a large class of repulsive interaction models, the Mayer cluster integrals can be transformed into a tridiagonal real symmetric matrix R(mn), whose elements converge to two constants with 1/n(2) correction. We find exact expressions in terms of these correction terms for the two critical exponents describing the density near the two singular termination points of the fluid phase. We apply the method to the hard-spheres model and find that the metastable fluid phase terminates at rho(t) = 0.751[5]. The density near the transition is given by rho(t)-rho approximately (z(t) - z)(sigma'), where the critical exponent is predicted to be sigma' = 0.0877[25]. Interestingly, the termination density is close to the observed glass transition; thus, the above critical behavior is expected to be associated with the onset of glassy behavior in hard spheres. PMID:17389362
Contact values for disparate-size hard-sphere mixtures
Santos, A; de Haro, M López; Alawneh, M; Henderson, D
2009-01-01
A universality ansatz for the contact values of a multicomponent mixture of additive hard spheres is used to propose new formulae for the case of disparate-size binary mixtures. A comparison with simulation data and with a recent proposal by Alawneh and Henderson for binary mixtures shows reasonably good agreement with the predictions for the contact values of the large-large radial distribution functions. A discussion on the usefulness and limitations of the new proposals is also presented.
Contact values for disparate-size hard-sphere mixtures
A. Santos; S. B. Yuste; M. López de Haro; M. Alawneh; D. Henderson
2009-05-22
A universality ansatz for the contact values of a multicomponent mixture of additive hard spheres is used to propose new formulae for the case of disparate-size binary mixtures. A comparison with simulation data and with a recent proposal by Alawneh and Henderson for binary mixtures shows reasonably good agreement with the predictions for the contact values of the large-large radial distribution functions. A discussion on the usefulness and limitations of the new proposals is also presented.
Microstructure evolution and rheological responses of hard sphere suspensions
Jae-Hyun So; Seung-Man Yang; Jae Chun Hyun
2001-01-01
In the present study, the microstructural transitions of concentrated ‘hard-sphere’ suspensions under a simple shear flow were investigated by measuring the shear viscosity and flow-induced dichroism. Monodisperse silica particles of two different sizes, 260 and 545nm in diameter, were prepared by the so-called modified Stöber method. The monodisperse particles were coated with 3-(trimethoxysilyl)propyl methacrylate (MPTS) to enhance the dispersion stability
Self-consistent phonon theory of the crystallization and elasticity of attractive hard spheres
NASA Astrophysics Data System (ADS)
Shin, Homin; Schweizer, Kenneth S.
2013-02-01
We propose an Einstein-solid, self-consistent phonon theory for the crystal phase of hard spheres that interact via short-range attractions. The approach is first tested against the known behavior of hard spheres, and then applied to homogeneous particles that interact via short-range square well attractions and the Baxter adhesive hard sphere model. Given the crystal symmetry, packing fraction, and strength and range of attractive interactions, an effective harmonic potential experienced by a particle confined to its Wigner-Seitz cell and corresponding mean square vibrational amplitude are self-consistently calculated. The crystal free energy is then computed and, using separate information about the fluid phase free energy, phase diagrams constructed, including a first-order solid-solid phase transition and its associated critical point. The simple theory qualitatively captures all the many distinctive features of the phase diagram (critical and triple point, crystal-fluid re-entrancy, low-density coexistence curve) as a function of attraction range, and overall is in good semi-quantitative agreement with simulation. Knowledge of the particle localization length allows the crystal shear modulus to be estimated based on elementary ideas. Excellent predictions are obtained for the hard sphere crystal. Expanded and condensed face-centered cubic crystals are found to have qualitatively different elastic responses to varying attraction strength or temperature. As temperature increases, the expanded entropic solid stiffens, while the energy-controlled, fully-bonded dense solid softens.
Self-consistent phonon theory of the crystallization and elasticity of attractive hard spheres.
Shin, Homin; Schweizer, Kenneth S
2013-02-28
We propose an Einstein-solid, self-consistent phonon theory for the crystal phase of hard spheres that interact via short-range attractions. The approach is first tested against the known behavior of hard spheres, and then applied to homogeneous particles that interact via short-range square well attractions and the Baxter adhesive hard sphere model. Given the crystal symmetry, packing fraction, and strength and range of attractive interactions, an effective harmonic potential experienced by a particle confined to its Wigner-Seitz cell and corresponding mean square vibrational amplitude are self-consistently calculated. The crystal free energy is then computed and, using separate information about the fluid phase free energy, phase diagrams constructed, including a first-order solid-solid phase transition and its associated critical point. The simple theory qualitatively captures all the many distinctive features of the phase diagram (critical and triple point, crystal-fluid re-entrancy, low-density coexistence curve) as a function of attraction range, and overall is in good semi-quantitative agreement with simulation. Knowledge of the particle localization length allows the crystal shear modulus to be estimated based on elementary ideas. Excellent predictions are obtained for the hard sphere crystal. Expanded and condensed face-centered cubic crystals are found to have qualitatively different elastic responses to varying attraction strength or temperature. As temperature increases, the expanded entropic solid stiffens, while the energy-controlled, fully-bonded dense solid softens. PMID:23464163
Chen, Wei-Ren [ORNL
2010-01-01
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 algo- rithm for many-body systems, two liquid models are considered, including hard sphere uids 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 PY integral equation theory is resorted to compute 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 uids in the future. Furthermore, we nd 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.
Leonid V. Yelash; Thomas Kraska; Ulrich K. Deiters
1999-01-01
Two new hard-sphere equations are proposed which, in combination with a van der Waals attraction term, lead to a biquadratic, respectively a cubic, equation of state. The new equations show the correct limiting behavior at low as well as at high densities; their poles are close to the physical packing fraction of hard spheres. Both equations of state were extended
Force distribution affects vibrational properties in hard-sphere glasses
DeGiuli, Eric; Lerner, Edan; Brito, Carolina; Wyart, Matthieu
2014-01-01
We theoretically and numerically study the elastic properties of hard-sphere glasses and provide a real-space description of their mechanical stability. In contrast to repulsive particles at zero temperature, we argue that the presence of certain pairs of particles interacting with a small force f soften elastic properties. This softening affects the exponents characterizing elasticity at high pressure, leading to experimentally testable predictions. Denoting ?(f)?f?e, the force distribution of such pairs and ?c the packing fraction at which pressure diverges, we predict that (i) the density of states has a low-frequency peak at a scale ?*, rising up to it as D(?)??2+a, and decaying above ?* as D(?)???a where a=(1??e)/(3+?e) and ? is the frequency, (ii) shear modulus and mean-squared displacement are inversely proportional with ??R2??1/??(?c??)?, where ?=2?2/(3+?e), and (iii) continuum elasticity breaks down on a scale ?c?1/?z?(?c??)?b, where b=(1+?e)/(6+2?e) and ?z=z?2d, where z is the coordination and d the spatial dimension. We numerically test (i) and provide data supporting that ?e?0.41 in our bidisperse system, independently of system preparation in two and three dimensions, leading to ??1.41, a?0.17, and b?0.21. Our results for the mean-square displacement are consistent with a recent exact replica computation for d=?, whereas some observations differ, as rationalized by the present approach. PMID:25406326
Using compressibility factor as a predictor of confined hard-sphere fluid dynamics
Mittal, Jeetain
2009-01-01
We study the correlations between the diffusivity (or viscosity) and the compressibility factor of bulk hard-sphere fluid as predicted by the ultralocal limit of the barrier hopping theory. Our specific aim is to determine if these correlations observed in the bulk equilibrium hard-sphere fluid can be used to predict the self-diffusivity of fluid confined between a slit-pore or a rectangular channel. In this work, we consider a single-component and a binary mixture of hard spheres. To represent confining walls, we use purely reflecting hard walls and interacting square-well walls. Our results clearly show that the correspondence between the diffusivity and the compressibility factor can be used along with the knowledge of the confined fluid's compressibility factor to predict its diffusivity with quantitative accuracy. Our analysis also suggests that a simple measure, the average fluid density, can be an accurate predictor of confined fluid diffusivity for very tight confinements (? 2-3 particle diameters wide) at low to intermediate density conditions. Together, these results provide further support for the idea that one can use robust connections between thermodynamic and dynamic quantities to predict dynamics of confined fluids from their thermodynamics. PMID:19702285
Maiti, Moumita; Lakshminarayanan, Arun; Sastry, Srikanth
2013-01-01
The implementation of a method for the exact evaluation of the volume and surface area of cavities and free volumes in polydisperse sphere packings is described. The generalization of an algorithm for Voronoi tessellation by Tanemura et al. is presented, employing the radical plane construction, as a part of the method. We employ this method to calculate the equation of state for monodisperse and polydisperse hard-sphere fluids, crystals, and for the metastable amorphous branch up to random close packing or jamming densities. We compute the distribution of free volumes, and compare with previous results employing a heuristic definition of free volume. We show the efficacy of the method for analyzing protein structure, by computing various quantities such as the distribution of sizes of buried cavities and pockets, the scaling of solvent accessible area to the corresponding occupied volume, the composition of residues lining cavities, etc. PMID:23355091
Douglas Henderson; Andrij Trokhymchuk; Leslie V. Woodcock; Kwong-Yu Chan
2005-01-01
The Henderson and Chan (HC) formulae for the contact values of the radial distribution functions (RDFs) of a highly asymmetric hard sphere mixture are reconsidered in light of a recent formula of Roth, Evans and Dietrich for the RDF of a pair of exceedingly large spheres at zero concentration in a solvent of small hard spheres. Two modifications of the
Sphere drag tests in the variable density wind tunnel
NASA Technical Reports Server (NTRS)
Jacobs, Eastman N
1929-01-01
The air forces on a twenty-centimeter sphere were measured after it had been rebuilt as an open throat type. The results from tests made at widely different densities and airspeeds and also on a smaller sphere are given.
Computer simulation of solid-liquid coexistence in binary hard sphere mixtures
NASA Astrophysics Data System (ADS)
Kranendonk, W. G. T.; Frenkel, D.
We present the results of a computer simulation study of the solid-liquid coexistence of a binary hard sphere mixture for diameter ratios in the range 0·85 ? ?a ? 1>·00. For the solid phase we only consider substitutionally disordered FCC and HCP crystals. For 0·9425 < ? < 1·00 we find a solid-liquid coexistence curve of the 'spindle' type. For ? = 0·9425 this becomes an azeotropic and for ? = 0·875 a eutectic diagram. We compare these results with the predictions of the density functional theory of Barrat, Baus and Hansen. We observe that the density functional theory accurately predicts the point where the spindle diagram transforms into an azeotrope. However, the density functional theory differs from the simulation results on a number of counts. The greatest differences between computer simulations and theory are that the changeover from an azeotropic to a eutectic diagram is found to occur at ? = 0·875, rather than at the predicted value of ? = 0·92, that the density difference between the solid and the liquid at liquid-solid coexistence is found to have a minimum as a function of the mole fraction of the large spheres, while density functional theory predicts a maximum, and finally that the solubility of large spheres in a solid mixture of small spheres is much larger than predicted.
Entropic forces in binary hard sphere mixtures: Theory and simulation Ronald Dickmana)
Attard, Phil
Entropic forces in binary hard sphere mixtures: Theory and simulation Ronald Dickmana) Department hard-sphere mixtures with diameter ratios of 5 and 10 , to determine the entropic force between 1 a macrosphere and a hard wall, and 2 a pair of macrospheres. The microsphere background fluid at volume
Assembly of vorticity-aligned hard-sphere colloidal strings in a simple shear flow
Dinner, Aaron
Assembly of vorticity-aligned hard-sphere colloidal strings in a simple shear flow Xiang Chenga,1 in the simple case of hard-sphere colloidal particles under shear, there are conflicting predictions about of these nonequilibrium phases are much less understood relative to their equilibrium counterparts (79). Sheared hard
Equation of state of nonadditive d-dimensional hard-sphere mixtures
NASA Astrophysics Data System (ADS)
Santos, A.; López de Haro, M.; Yuste, S. B.
2005-01-01
An equation of state for a multicomponent mixture of nonadditive hard spheres in d dimensions is proposed. It yields a rather simple density dependence and constitutes a natural extension of the equation of state for additive hard spheres proposed by us [A. Santos, S. B. Yuste, and M. López de Haro, Mol. Phys. 96, 1 (1999)]. The proposal relies on the known exact second and third virial coefficients and requires as input the compressibility factor of the one-component system. A comparison is carried out both with another recent theoretical proposal based on a similar philosophy and with the available exact results and simulation data in d=1, 2, and 3. Good general agreement with the reported values of the virial coefficients and of the compressibility factor of binary mixtures is observed, especially for high asymmetries and/or positive nonadditivities.
Compact Collision Kernels for Hard Sphere and Coulomb Cross Sections; Fokker-Planck Coefficients
Chang Yongbin; Shizgal, Bernie D. [Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1 (Canada)
2008-12-31
A compact collision kernel is derived for both hard sphere and Coulomb cross sections. The difference between hard sphere interaction and Coulomb interaction is characterized by a parameter {eta}. With this compact collision kernel, the calculation of Fokker-Planck coefficients can be done for both the Coulomb and hard sphere interactions. The results for arbitrary order Fokker-Planck coefficients are greatly simplified. An alternate form for the Coulomb logarithm is derived with concern to the temperature relaxation in a binary plasma.
Universal Features of Collective Interactions in Hard-Sphere Systems at Higher Volume Fractions
M. Tokuyama; Y. Terada; H. Yamazaki; I. Oppenheim
2004-01-01
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
Dual falling sphere determination of density and transition flow parameter
NASA Technical Reports Server (NTRS)
Karr, G. R.
1974-01-01
A new approach to the analysis of falling sphere drag data is described in which the data from two trajectories through the same region of the atmosphere are analyzed simultaneously. The analysis provides important aerodynamic information which is used to obtain an improved value of atmospheric density. The technique is applied to a set of falling sphere data in which a sphere transition-flow parameter and atmospheric density results are obtained in the 80-120 km region from published data for falling spheres over Kwajalein. Another set of data for a falling sphere test over Wallops Island is also analyzed with comparable results.
Astillero, Antonio; Santos, Andrés
2005-09-01
In the preceding paper, we have conjectured that the main transport properties of a dilute gas of inelastic hard spheres (IHSs) can be satisfactorily captured by an equivalent gas of elastic hard spheres (EHSs), provided that the latter are under the action of an effective drag force and their collision rate is reduced by a factor (1+alpha)/2 (where alpha is the constant coefficient of normal restitution). In this paper we test the above expectation in a paradigmatic nonequilibrium state, namely, the simple or uniform shear flow, by performing Monte Carlo computer simulations of the Boltzmann equation for both classes of dissipative gases with a dissipation range 0.5 < or = alpha < or = 0.95 and two values of the imposed shear rate a. It is observed that the evolution toward the steady state proceeds in two stages: a short kinetic stage (strongly dependent on the initial preparation of the system) followed by a slower hydrodynamic regime that becomes increasingly less dependent on the initial state. Once conveniently scaled, the intrinsic quantities in the hydrodynamic regime depend on time, at a given value of alpha, only through the reduced shear rate a*(t) is proportional to a/square root(T(t)), until a steady state, independent of the imposed shear rate and of the initial preparation, is reached. The distortion of the steady-state velocity distribution from the local equilibrium state is measured by the shear stress, the normal stress differences, the cooling rate, the fourth and sixth cumulants, and the shape of the distribution itself. In particular, the simulation results seem to be consistent with an exponential overpopulation of the high-velocity tail. These properties are common to both the IHS and EHS systems. In addition, the EHS results are in general hardly distinguishable from the IHS ones if alpha approximately > 0.7, so that the distinct signature of the IHS gas (higher anisotropy and overpopulation) only manifests itself at relatively high dissipations. PMID:16241428
Phase transition induced by a shock wave in hard-sphere and hard-disk systems.
Zhao, Nanrong; Sugiyama, Masaru; Ruggeri, Tommaso
2008-08-01
Dynamic phase transition induced by a shock wave in hard-sphere and hard-disk systems is studied on the basis of the system of Euler equations with caloric and thermal equations of state. First, Rankine-Hugoniot conditions are analyzed. The quantitative classification of Hugoniot types in terms of the thermodynamic quantities of the unperturbed state (the state before a shock wave) and the shock strength is made. Especially Hugoniot in typical two possible cases (P-1 and P-2) of the phase transition is analyzed in detail. In the case P-1 the phase transition occurs between a metastable liquid state and a stable solid state, and in the case P-2 the phase transition occurs through coexistence states, when the shock strength changes. Second, the admissibility of the two cases is discussed from a viewpoint of the recent mathematical theory of shock waves, and a rule with the use of the maximum entropy production rate is proposed as the rule for selecting the most probable one among the possible cases, that is, the most suitable constitutive equation that predicts the most probable shock wave. According to the rule, the constitutive equation in the case P-2 is the most promising one in the dynamic phase transition. It is emphasized that hard-sphere and hard-disk systems are suitable reference systems for studying shock wave phenomena including the shock-induced phase transition in more realistic condensed matters. PMID:18698913
Nested sampling for materials: The case of hard spheres
NASA Astrophysics Data System (ADS)
Pártay, Lívia B.; Bartók, Albert P.; Csányi, Gábor
2014-02-01
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.
Nested sampling for materials: the case of hard spheres.
Pártay, Lívia B; Bartók, Albert P; Csányi, Gábor
2014-02-01
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. PMID:25353467
Hard-sphere crystallization gets rarer with increasing dimension
NASA Astrophysics Data System (ADS)
van Meel, J. A.; Charbonneau, B.; Fortini, A.; Charbonneau, P.
2009-12-01
We recently found that crystallization of monodisperse hard spheres from the bulk fluid faces a much higher free-energy barrier in four than in three dimensions at equivalent supersaturation, due to the increased geometrical frustration between the simplex-based fluid order and the crystal [J. A. van Meel, D. Frenkel, and P. Charbonneau, Phys. Rev. E 79, 030201(R) (2009)]. Here, we analyze the microscopic contributions to the fluid-crystal interfacial free energy to understand how the barrier to crystallization changes with dimension. We find the barrier to grow with dimension and we identify the role of polydispersity in preventing crystal formation. The increased fluid stability allows us to study the jamming behavior in four, five, and six dimensions and to compare our observations with two recent theories [C. Song, P. Wang, and H. A. Makse, Nature (London) 453, 629 (2008); G. Parisi and F. Zamponi, Rev. Mod. Phys. (to be published)].
Singh, Jayant K.
to use the hard cylindrical wall with hard-sphere model out of many candi- date models due to itsCharacterization of fluid-solid phase transition of hard-sphere fluids in cylindrical pore via;Characterization of fluid-solid phase transition of hard-sphere fluids in cylindrical pore via molecular dynamics
A new approach to the equation of state of silicate melts: An application of the theory of hard melts based on the hard sphere mixture model of a liquid. We assign a hard sphere for each cation. The effective size of a hard sphere for each component in silicate melts is determined. The temperature
Dimensional interpolation of hard sphere virial coefficients John G. Loeser and Zheng Zhen
Kais, Sabre
Dimensional interpolation of hard sphere virial coefficients John G. Loeser and Zheng Zhen expansion.We report hard disk virial coefficientsthrough B,, and hard spherevalues through B,,,; the maximum,we explorea similar approachfor the vir- ial coefficientsof a hard-spherefluid. The virial expansion
Albert S. Kim; Yuewei Liu
2008-01-01
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,
Single file and normal dual mode diffusion in highly confined hard sphere mixtures under flow.
Spiteri, Raymond J.
the dual-mode diffusion regime of binary and tertiary mixtures of hard spheres confined in narrowSingle file and normal dual mode diffusion in highly confined hard sphere mixtures under flow and below their passing thresholds still exhibit behaviors consistent with normal and single-file diffusion
Ignacio Urrutia; Gabriela Castelletti
2014-09-29
This paper presents a modified grand canonical ensemble which provides a new simple and efficient scheme to study few-body fluid-like inhomogeneous systems under confinement. The new formalism is implemented to investigate the exact thermodynamic properties of a hard sphere (HS) fluid-like system with up to three particles confined in a spherical cavity. In addition, the partition function of this system was used to analyze the surface thermodynamic properties of the many-HS system and to derive the exact curvature dependence of both the surface tension and adsorption in powers of the density. The expressions for the surface tension and the adsorption were also obtained for the many- HS system outside of a fixed hard spherical object. We used these results to derive the dependence of the fluid-substrate Tolman length up to first order in density.
Solid-to-solid isostructural transition in the hard sphere/attractive Yukawa system
NASA Astrophysics Data System (ADS)
Rascón, C.; Mederos, L.; Navascués, G.
1995-12-01
A thermodynamically consistent density functional-perturbation theory is used to study the isostructural solid-to-solid transition which takes place in the hard sphere/attractive Yukawa system when the Yukawa tail is sufficiently short ranged. A comparison with results for the square well potential allows us to study the effect of the attractive potential form on the solid-solid transition. Reasonable agreement with simulations is found for the main transition properties as well as for the phase diagram evolution with the range of the attractive potential.
Granular mixtures modeled as elastic hard spheres subject to a drag force.
Vega Reyes, Francisco; Garzó, Vicente; Santos, Andrés
2007-06-01
Granular gaseous mixtures under rapid flow conditions are usually modeled as a multicomponent system of smooth inelastic hard disks (two dimensions) or spheres (three dimensions) with constant coefficients of normal restitution alpha{ij}. In the low density regime an adequate framework is provided by the set of coupled inelastic Boltzmann equations. Due to the intricacy of the inelastic Boltzmann collision operator, in this paper we propose a simpler model of elastic hard disks or spheres subject to the action of an effective drag force, which mimics the effect of dissipation present in the original granular gas. For each collision term ij, the model has two parameters: a dimensionless factor beta{ij} modifying the collision rate of the elastic hard spheres, and the drag coefficient zeta{ij}. Both parameters are determined by requiring that the model reproduces the collisional transfers of momentum and energy of the true inelastic Boltzmann operator, yielding beta{ij}=(1+alpha{ij})2 and zeta{ij} proportional, variant1-alpha{ij}/{2}, where the proportionality constant is a function of the partial densities, velocities, and temperatures of species i and j. The Navier-Stokes transport coefficients for a binary mixture are obtained from the model by application of the Chapman-Enskog method. The three coefficients associated with the mass flux are the same as those obtained from the inelastic Boltzmann equation, while the remaining four transport coefficients show a general good agreement, especially in the case of the thermal conductivity. The discrepancies between both descriptions are seen to be similar to those found for monocomponent gases. Finally, the approximate decomposition of the inelastic Boltzmann collision operator is exploited to construct a model kinetic equation for granular mixtures as a direct extension of a known kinetic model for elastic collisions. PMID:17677254
A continuum hard-sphere model of protein adsorption
NASA Astrophysics Data System (ADS)
Finch, Craig; Clarke, Thomas; Hickman, James J.
2013-07-01
Protein adsorption plays a significant role in biological phenomena such as cell-surface interactions and the coagulation of blood. Two-dimensional random sequential adsorption (RSA) models are widely used to model the adsorption of proteins on solid surfaces. Continuum equations have been developed so that the results of RSA simulations can be used to predict the kinetics of adsorption. Recently, Brownian dynamics simulations have become popular for modeling protein adsorption. In this work a continuum model was developed to allow the results from a Brownian dynamics simulation to be used as the boundary condition in a computational fluid dynamics (CFD) simulation. Brownian dynamics simulations were used to model the diffusive transport of hard-sphere particles in a liquid and the adsorption of the particles onto a solid surface. The configuration of the adsorbed particles was analyzed to quantify the chemical potential near the surface, which was found to be a function of the distance from the surface and the fractional surface coverage. The near-surface chemical potential was used to derive a continuum model of adsorption that incorporates the results from the Brownian dynamics simulations. The equations of the continuum model were discretized and coupled to a CFD simulation of diffusive transport to the surface. The kinetics of adsorption predicted by the continuum model closely matched the results from the Brownian dynamics simulation. This new model allows the results from mesoscale simulations to be incorporated into micro- or macro-scale CFD transport simulations of protein adsorption in practical devices.
A CONTINUUM HARD-SPHERE MODEL OF PROTEIN ADSORPTION
Finch, Craig; Clarke, Thomas; Hickman, James J.
2012-01-01
Protein adsorption plays a significant role in biological phenomena such as cell-surface interactions and the coagulation of blood. Two-dimensional random sequential adsorption (RSA) models are widely used to model the adsorption of proteins on solid surfaces. Continuum equations have been developed so that the results of RSA simulations can be used to predict the kinetics of adsorption. Recently, Brownian dynamics simulations have become popular for modeling protein adsorption. In this work a continuum model was developed to allow the results from a Brownian dynamics simulation to be used as the boundary condition in a computational fluid dynamics (CFD) simulation. Brownian dynamics simulations were used to model the diffusive transport of hard-sphere particles in a liquid and the adsorption of the particles onto a solid surface. The configuration of the adsorbed particles was analyzed to quantify the chemical potential near the surface, which was found to be a function of the distance from the surface and the fractional surface coverage. The near-surface chemical potential was used to derive a continuum model of adsorption that incorporates the results from the Brownian dynamics simulations. The equations of the continuum model were discretized and coupled to a CFD simulation of diffusive transport to the surface. The kinetics of adsorption predicted by the continuum model closely matched the results from the Brownian dynamics simulation. This new model allows the results from mesoscale simulations to be incorporated into micro- or macro-scale CFD transport simulations of protein adsorption in practical devices. PMID:23729843
A CONTINUUM HARD-SPHERE MODEL OF PROTEIN ADSORPTION.
Finch, Craig; Clarke, Thomas; Hickman, James J
2013-07-01
Protein adsorption plays a significant role in biological phenomena such as cell-surface interactions and the coagulation of blood. Two-dimensional random sequential adsorption (RSA) models are widely used to model the adsorption of proteins on solid surfaces. Continuum equations have been developed so that the results of RSA simulations can be used to predict the kinetics of adsorption. Recently, Brownian dynamics simulations have become popular for modeling protein adsorption. In this work a continuum model was developed to allow the results from a Brownian dynamics simulation to be used as the boundary condition in a computational fluid dynamics (CFD) simulation. Brownian dynamics simulations were used to model the diffusive transport of hard-sphere particles in a liquid and the adsorption of the particles onto a solid surface. The configuration of the adsorbed particles was analyzed to quantify the chemical potential near the surface, which was found to be a function of the distance from the surface and the fractional surface coverage. The near-surface chemical potential was used to derive a continuum model of adsorption that incorporates the results from the Brownian dynamics simulations. The equations of the continuum model were discretized and coupled to a CFD simulation of diffusive transport to the surface. The kinetics of adsorption predicted by the continuum model closely matched the results from the Brownian dynamics simulation. This new model allows the results from mesoscale simulations to be incorporated into micro- or macro-scale CFD transport simulations of protein adsorption in practical devices. PMID:23729843
Avalanches mediate crystallization in a hard-sphere glass
Sanz, Eduardo; Valeriani, Chantal; Zaccarelli, Emanuela; Poon, Wilson C. K.; Cates, Michael E.; Pusey, Peter N.
2014-01-01
By molecular-dynamics simulations, we have studied the devitrification (or crystallization) of aged hard-sphere glasses. First, we find that the dynamics of the particles are intermittent: Quiescent periods, when the particles simply “rattle” in their nearest-neighbor cages, are interrupted by abrupt “avalanches,” where a subset of particles undergo large rearrangements. Second, we find that crystallization is associated with these avalanches but that the connection is not straightforward. The amount of crystal in the system increases during an avalanche, but most of the particles that become crystalline are different from those involved in the avalanche. Third, the occurrence of the avalanches is a largely stochastic process. Randomizing the velocities of the particles at any time during the simulation leads to a different subsequent series of avalanches. The spatial distribution of avalanching particles appears random, although correlations are found among avalanche initiation events. By contrast, we find that crystallization tends to take place in regions that already show incipient local order. PMID:24306932
Avalanches mediate crystallization in a hard-sphere glass
Eduardo Sanz; Chantal Valeriani; Emanuela Zaccarelli; Wilson C K Poon; Michael E Cates; Peter N Pusey
2014-04-02
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.
Avalanches mediate crystallization in a hard-sphere glass.
Sanz, Eduardo; Valeriani, Chantal; Zaccarelli, Emanuela; Poon, Wilson C K; Cates, Michael E; Pusey, Peter N
2014-01-01
By molecular-dynamics simulations, we have studied the devitrification (or crystallization) of aged hard-sphere glasses. First, we find that the dynamics of the particles are intermittent: Quiescent periods, when the particles simply "rattle" in their nearest-neighbor cages, are interrupted by abrupt "avalanches," where a subset of particles undergo large rearrangements. Second, we find that crystallization is associated with these avalanches but that the connection is not straightforward. The amount of crystal in the system increases during an avalanche, but most of the particles that become crystalline are different from those involved in the avalanche. Third, the occurrence of the avalanches is a largely stochastic process. Randomizing the velocities of the particles at any time during the simulation leads to a different subsequent series of avalanches. The spatial distribution of avalanching particles appears random, although correlations are found among avalanche initiation events. By contrast, we find that crystallization tends to take place in regions that already show incipient local order. PMID:24306932
Dynamics in dense hard-sphere colloidal suspensions.
Orsi, Davide; Fluerasu, Andrei; Moussaïd, Abdellatif; Zontone, Federico; Cristofolini, Luigi; Madsen, Anders
2012-01-01
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 A 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. 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. 77, 771 (1996)]. We discuss our results in view of previous experimental attempts to validate this scaling law [L. Lurio et al., Phys. Rev. Lett. 84, 785 (2000)]. PMID:22400568
Song, Xueyu
Anisotropic Interfacial Free Energies of the Hard-Sphere Crystal-Melt Interfaces Yan Mu, Andrew the free energies of the fcc crystal-melt interfaces for the hard-sphere system as a function of crystal > 110 > 111 for the hard-sphere system, similar to the results of the Lennard-Jones system. I
Structure and anomalous solubility for hard spheres in an associating lattice gas model
Barbosa, Marcia C. B.
Structure and anomalous solubility for hard spheres in an associating lattice gas model Marcia M://jcp.aip.org/about/rights_and_permissions #12;THE JOURNAL OF CHEMICAL PHYSICS 137, 064905 (2012) Structure and anomalous solubility for hard July 2012; published online 13 August 2012) In this paper we investigate the solubility of a hard
Short-time diffusion in concentrated bidisperse hard-sphere suspensions
NASA Astrophysics Data System (ADS)
Wang, Mu; Heinen, Marco; Brady, John F.
2015-02-01
Diffusion in bidisperse Brownian hard-sphere suspensions is studied by Stokesian Dynamics (SD) computer simulations and a semi-analytical theoretical scheme for colloidal short-time dynamics, based on Beenakker and Mazur's method [Physica A 120, 388-410 (1983); 126, 349-370 (1984)]. Two species of hard spheres are suspended in an overdamped viscous solvent that mediates the salient hydrodynamic interactions among all particles. In a comprehensive parameter scan that covers various packing fractions and suspension compositions, we employ numerically accurate SD simulations to compute the initial diffusive relaxation of density modulations at the Brownian time scale, quantified by the partial hydrodynamic functions. A revised version of Beenakker and Mazur's ??-scheme for monodisperse suspensions is found to exhibit surprisingly good accuracy, when simple rescaling laws are invoked in its application to mixtures. The so-modified ?? scheme predicts hydrodynamic functions in very good agreement with our SD simulation results, for all densities from the very dilute limit up to packing fractions as high as 40%.
Hardness and softness in density functional theory
José Gázquez
The fundamental equations to describe the change from one ground-state to another, in the framework of density functional theory, are used to analyze a set of hardness and softness functions that are hierarchized as non-local, local and global quantities. Through these definitions it is shown that under conditions of constant chemical potential, the interaction between two chemical systems evolves towards
Dynamics in dense hard-sphere colloidal suspensions
NASA Astrophysics Data System (ADS)
Orsi, Davide; Fluerasu, Andrei; Moussaïd, Abdellatif; Zontone, Federico; Cristofolini, Luigi; Madsen, Anders
2012-01-01
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)].
Singh, Jayant K.
of many candi- date models due to its theoretical tractability and repulsive hard-core-oriented natureCharacterization of fluid-solid phase transition of hard-sphere fluids in cylindrical pore via 2009 Equation of state and structure of hard-sphere fluids confined in a cylindrical hard pore were
Scattering functions of core-shell-structured hard spheres with Schulz-distributed radii.
Nayeri, M; Zackrisson, M; Bergenholtz, J
2009-06-18
The scattering intensity of polydisperse systems of core-shell and layered hard spheres is considered. The Percus-Yevick solution for the partial structure factors is cast in a form suitable for numerical and analytical treatment. Closed-form, analytical expressions are given for an effective hard-sphere model of the scattering intensity of particles with an internal layered structure and a size polydispersity governed by a Schulz distribution. A similar model for polydisperse hard spheres of core-shell structure but with a monodisperse shell thickness is also presented. The models are tested against small-angle X-ray scattering experiments on a hard-sphere-like microemulsion system. PMID:19462945
One and two point micro-rheology of hard sphere suspensions
Harrison, Andrew William
2011-11-23
The material that is covered in this thesis concerns the calibration and application of a set of optical tweezers to be used for one- and two-point micro-rheology experiments on hard sphere colloidal suspensions. The ...
Transport coefficients of a granular gas of inelastic rough hard spheres
NASA Astrophysics Data System (ADS)
Kremer, Gilberto M.; Santos, Andrés; Garzó, Vicente
2014-08-01
The Boltzmann equation for inelastic and rough hard spheres is considered as a model of a dilute granular gas. In this model, the collisions are characterized by constant coefficients of normal and tangential restitution, and hence the translational and rotational degrees of freedom are coupled. A normal solution to the Boltzmann equation is obtained by means of the Chapman-Enskog method for states near the homogeneous cooling state. The analysis is carried out to first order in the spatial gradients of the number density, the flow velocity, and the granular temperature. The constitutive equations for the momentum and heat fluxes and for the cooling rate are derived, and the associated transport coefficients are expressed in terms of the solutions of linear integral equations. For practical purposes, a first Sonine approximation is used to obtain explicit expressions of the transport coefficients as nonlinear functions of both coefficients of restitution and the moment of inertia. Known results for purely smooth inelastic spheres and perfectly elastic and rough spheres are recovered in the appropriate limits.
Direct simulation of diatomic gases using the generalized hard sphere model
NASA Technical Reports Server (NTRS)
Hash, D. B.; Hassan, H. A.
1993-01-01
The generalized hard sphere model which incorporates the effects of attraction and repulsion is used to predict flow measurements in tests involving extremely low freestream temperatures. For the two cases considered, a Mach 26 nitrogen shock and a Mach 20 nitrogen flow over a flat place, only rotational excitation is deemed important, and appropriate modifications for the Borgnakke-Larsen procedure are developed. In general, for the cases considered, the present model performed better than the variable hard sphere model.
Inter-particle correlations in a hard-sphere colloidal suspension with polymer additives
Schofield, Andrew B.
of solvent penetration into the polymer brush grafted on to the PMMA spheres to prevent aggregationInter-particle correlations in a hard-sphere colloidal suspension with polymer additives particles or extended polymer chains. Maximization of the entropy of the smaller particles leads
Path integral Monte Carlo study of quantum-hard sphere solids
NASA Astrophysics Data System (ADS)
Sesé, Luis M.
2013-07-01
A path integral study of the fcc, hcp, and bcc quantum hard-sphere solids is presented. Ranges of densities within the interval of reduced de Broglie wavelengths 0.2 ? ? _B^* ? 0.8 have been analyzed using Monte Carlo simulations with Cao-Berne propagator. Energies, pressures, and structural quantities (pair radial correlation functions, centroid structure factors, and Steinhardt order parameters) have been computed. Also, applications of the Einstein crystal technique [L. M. Sesé, J. Chem. Phys. 126, 164508 (2007)] have been made to compute the free energies of the fcc and hcp solids. Some technical points related to the latter technique are discussed, and it is shown that these calculations produce consistent results with increasing sample sizes. The fluid-solid (fcc and hcp) equilibria have been studied, thus completing prior work by this author on the fluid-fcc equilibrium. Within the accuracy attained no significant differences between the relative stabilities of the fcc and hcp lattices have been detected. The bcc case stands apart from the other two lattices, as the simulations lead either to irregular lattices (two types) that keep some traces of bcc-memory, or to spontaneous transitions to hcp-like lattices. The latter transitions make manifestly clear the potential repercussions that the quantum hard-sphere behavior can have on solid-solid equilibria at low temperatures in real systems (e.g., helium).
Phase behavior of binary hard-sphere mixtures from perturbation theory.
Velasco, E; Navascués, G; Mederos, L
1999-09-01
Using a first-order perturbation theory, we have studied the phase diagram of a binary mixture of hard spheres for different values of the size ratio. Recent models for the two-body depletion potential between large spheres are used to take into account the role of the small spheres. The theory predicts a complex phase diagram including a fluid-solid transition at high packing fraction of small spheres, metastability of fluid-fluid demixing, an isostructural solid-solid transition at high packing fraction of the large spheres for sufficiently small values of the size ratio q of the spheres, and the tendency to sticky-sphere behavior in the limit q-->0. The agreement with recent simulation results is quite good. We also show that this phenomenology was already implicit in the pioneering work of Asakura and Oosawa. PMID:11970123
Phase behavior of binary hard-sphere mixtures from perturbation theory
NASA Astrophysics Data System (ADS)
Velasco, E.; Navascués, G.; Mederos, L.
1999-09-01
Using a first-order perturbation theory, we have studied the phase diagram of a binary mixture of hard spheres for different values of the size ratio. Recent models for the two-body depletion potential between large spheres are used to take into account the role of the small spheres. The theory predicts a complex phase diagram including a fluid-solid transition at high packing fraction of small spheres, metastability of fluid-fluid demixing, an isostructural solid-solid transition at high packing fraction of the large spheres for sufficiently small values of the size ratio q of the spheres, and the tendency to sticky-sphere behavior in the limit q-->0. The agreement with recent simulation results is quite good. We also show that this phenomenology was already implicit in the pioneering work of Asakura and Oosawa.
Stochastic Hard-Sphere Dynamics for Hydrodynamics of Non-Ideal Fluids
Donev, A; Alder, B J; Garcia, A L
2008-02-26
A novel stochastic fluid model is proposed with a nonideal structure factor consistent with compressibility, and adjustable transport coefficients. This stochastic hard-sphere dynamics (SHSD) algorithm is a modification of the direct simulation Monte Carlo algorithm and has several computational advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD results in an equation of state and a pair correlation function identical to that of a deterministic Hamiltonian system of penetrable spheres interacting with linear core pair potentials. The fluctuating hydrodynamic behavior of the SHSD fluid is verified for the Brownian motion of a nanoparticle suspended in a compressible solvent.
The nematic-isotropic phase transition in semiflexible fused hard-sphere chain fluids
Sullivan, Donald E.
,a) S. B. Opps,b) D. E. Sullivan,c) and B. G. Nickel Department of Physics and Guelph-Waterloo Physics is equivalent to that of a binary mixture of hard spheres and hard diatomic molecules. It is assumed
Schofield, Jeremy
Multiple-point and multiple-time correlation functions in a hard-sphere fluid Ramses van Zon densities. Multiple-point and multiple-time correlation functions of the densities of conserved variables important contributions to both the multiple point and multiple-time correlation functions on all time
Role of bond orientational order in the crystallization of hard spheres
NASA Astrophysics Data System (ADS)
Russo, John; Tanaka, Hajime
2013-02-01
With computer simulations of the hard sphere model, we examine in detail the microscopic pathway connecting the metastable melt to the emergence of crystalline clusters. In particular we will show that the nucleation of the solid phase does not follow a two-step mechanism, where crystals form inside dense precursor regions. On the contrary, we will show that nucleation is driven by fluctuations of orientational order, and not by the density fluctuations. By considering the development of the pair-excess entropy inside crystalline nuclei, we confirm that orientational order precedes positional order. These results are at odd with the idea of a two-step nucleation mechanism for fluids without a metastable liquid-liquid phase separation. Our study suggests the pivotal role of bond orientational ordering in triggering crystal nucleation.
Hard sphere-like glass transition in eye lens ?-crystallin solutions.
Foffi, Giuseppe; Savin, Gabriela; Bucciarelli, Saskia; Dorsaz, Nicolas; Thurston, George M; Stradner, Anna; Schurtenberger, Peter
2014-11-25
We study the equilibrium liquid structure and dynamics of dilute and concentrated bovine eye lens ?-crystallin solutions, using small-angle X-ray scattering, static and dynamic light scattering, viscometry, molecular dynamics simulations, and mode-coupling theory. We find that a polydisperse Percus-Yevick hard-sphere liquid-structure model accurately reproduces both static light scattering data and small-angle X-ray scattering liquid structure data from ?-crystallin solutions over an extended range of protein concentrations up to 290 mg/mL or 49% vol fraction and up to ca. 330 mg/mL for static light scattering. The measured dynamic light scattering and viscosity properties are also consistent with those of hard-sphere colloids and show power laws characteristic of an approach toward a glass transition at ?-crystallin volume fractions near 58%. Dynamic light scattering at a volume fraction beyond the glass transition indicates formation of an arrested state. We further perform event-driven molecular dynamics simulations of polydisperse hard-sphere systems and use mode-coupling theory to compare the measured dynamic power laws with those of hard-sphere models. The static and dynamic data, simulations, and analysis show that aqueous eye lens ?-crystallin solutions exhibit a glass transition at high concentrations that is similar to those found in hard-sphere colloidal systems. The ?-crystallin glass transition could have implications for the molecular basis of presbyopia and the kinetics of molecular change during cataractogenesis. PMID:25385638
Hard sphere-like glass transition in eye lens ?-crystallin solutions
Savin, Gabriela; Bucciarelli, Saskia; Dorsaz, Nicolas; Thurston, George M.; Stradner, Anna; Schurtenberger, Peter
2014-01-01
We study the equilibrium liquid structure and dynamics of dilute and concentrated bovine eye lens ?-crystallin solutions, using small-angle X-ray scattering, static and dynamic light scattering, viscometry, molecular dynamics simulations, and mode-coupling theory. We find that a polydisperse Percus–Yevick hard-sphere liquid-structure model accurately reproduces both static light scattering data and small-angle X-ray scattering liquid structure data from ?-crystallin solutions over an extended range of protein concentrations up to 290 mg/mL or 49% vol fraction and up to ca. 330 mg/mL for static light scattering. The measured dynamic light scattering and viscosity properties are also consistent with those of hard-sphere colloids and show power laws characteristic of an approach toward a glass transition at ?-crystallin volume fractions near 58%. Dynamic light scattering at a volume fraction beyond the glass transition indicates formation of an arrested state. We further perform event-driven molecular dynamics simulations of polydisperse hard-sphere systems and use mode-coupling theory to compare the measured dynamic power laws with those of hard-sphere models. The static and dynamic data, simulations, and analysis show that aqueous eye lens ?-crystallin solutions exhibit a glass transition at high concentrations that is similar to those found in hard-sphere colloidal systems. The ?-crystallin glass transition could have implications for the molecular basis of presbyopia and the kinetics of molecular change during cataractogenesis. PMID:25385638
Michio Tokuyama; Hiroyuki Yamazaki; Yayoi Terada
2003-01-01
We investigate how universal the collective behavior, due to the many-body interactions in polydisperse hard-sphere systems, is at higher volume fractions. We perform two types of computer simulations, a Brownian-dynamics simulation on colloidal suspensions of hard spheres, where the hydrodynamic interactions between particles are neglected, and a molecular-dynamic simulation on atomic systems of hard spheres. Thus, we show that the
Mean properties and free energy of a few hard spheres confined in a spherical cavity.
Urrutia, I; Pastorino, C
2014-09-28
We use analytical calculations and event-driven molecular dynamics simulations to study a small number of hard sphere particles in a spherical cavity. The cavity is also taken as the thermal bath so that the system thermalizes by collisions with the wall. In that way, these systems of two, three, and four particles, are considered in the canonical ensemble. We characterize various mean and thermal properties for a wide range of number densities. We study the density profiles, the components of the local pressure tensor, the interface tension, and the adsorption at the wall. This spans from the ideal gas limit at low densities to the high-packing limit in which there are significant regions of the cavity for which the particles have no access, due the conjunction of excluded volume and confinement. The contact density and the pressure on the wall are obtained by simulations and compared to exact analytical results. We also obtain the excess free energy for N = 4, by using a simulated-assisted approach in which we combine simulation results with the knowledge of the exact partition function for two and three particles in a spherical cavity. PMID:25273472
Mean properties and Free Energy of a few hard spheres confined in a spherical cavity
Ignacio Urrutia; Claudio Pastorino
2014-09-29
We use analytical calculations and event-driven molecular dynamics simulations to study a small number of hard sphere particles in a spherical cavity. The cavity is taken also as the thermal bath so that the system thermalizes by collisions with the wall. In that way, these systems of two, three and four particles, are considered in the canonical ensemble. We characterize various mean and thermal properties for a wide range of number densities. We study the density profiles, the components of the local pressure tensor, the interface tension, and the adsorption at the wall. This spans from the ideal gas limit at low densities to the high-packing limit in which there are significant regions of the cavity for which the particles have no access, due the conjunction of excluded volume and confinement. The contact density and the pressure on the wall are obtained by simulations and compared to exact analytical results. We also obtain the excess free energy for N=4, by using a simulated-assisted approach in which we combine simulation results with the knowledge of the exact partition function for two and three particles in a spherical cavity.
Geometrical characteristics of the enlarged fused hard sphere models of simple molecules.
Boublík, Tomas
2005-10-20
The enlarged fused hard sphere model represents a compromise between fused hard sphere- and hard convex body models of repulsive interactions of nonspherical molecules. Geometric functionals of the enlarged fused hard sphere models, i.e., the hard body volume, surface area, and "mean radius" for 25 molecules of the linear and approximately planar shapes (cycloalkanes and aromatic compounds), neopentane and cyclohexane were determined from the bond lengths and bond angles and expressed in the dimensionless form. The hard sphere diameters, first approximated by the values found from the correlation of the second virial coefficients, were then adjusted to heats of vaporization of the studied compounds. Parameters of nonsphericity and molar volumes, evaluated from these characteristics, are compared with parameters of modern semiempirical equations of state (BACK, BACKONE, SAFT). The calculated geometric quantities for a series of compounds make it possible to improve methods of determining the characteristic parameters of the modern semiempirical equations of state, as well as those from the perturbation approaches. PMID:16853511
Phase behavior of polymer mixtures with nonadditive hard-sphere potential
A. O. Malakhov; V. V. Volkov
2007-01-01
The phase behavior of a binary mixture of homopolymers in which macromolecules are composed of tangent hard spheres was studied.\\u000a The interaction of unlike units is characterized by the contact distance (1\\/2)(?A + ?B)(1 + ?), where ?\\u000a i\\u000a is the diameter of the ith sphere (unit) and ? is the nonadditivity parameter. The effect of nonadditivity was taken into
Kernels of the linear Boltzmann equation for spherical particles and rough hard sphere particles
NASA Astrophysics Data System (ADS)
Khurana, Saheba; Thachuk, Mark
2013-10-01
Kernels for the collision integral of the linear Boltzmann equation are presented for several cases. First, a rigorous and complete derivation of the velocity kernel for spherical particles is given, along with reductions to the smooth, rigid sphere case. This combines and extends various derivations for this kernel which have appeared previously in the literature. In addition, the analogous kernel is derived for the rough hard sphere model, for which a dependence upon both velocity and angular velocity is required. This model can account for exchange between translational and rotational degrees of freedom. Finally, an approximation to the exact rough hard sphere kernel is presented which averages over the rotational degrees of freedom in the system. This results in a kernel depending only upon velocities which retains a memory of the exchange with rotational states. This kernel tends towards the smooth hard sphere kernel in the limit when translational-rotational energy exchange is attenuated. Comparisons are made between the smooth and approximate rough hard sphere kernels, including their dependence upon velocity and their eigenvalues.
Kernels of the linear Boltzmann equation for spherical particles and rough hard sphere particles.
Khurana, Saheba; Thachuk, Mark
2013-10-28
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
Stochastic interactions of two Brownian hard spheres in the presence of depletants
Karzar-Jeddi, Mehdi; Fan, Tai-Hsi, E-mail: thfan@engr.uconn.edu [Department of Mechanical Engineering, University of Connecticut, Storrs, Connecticut 06269-3139 (United States); Tuinier, Remco [Van't Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute, Department of Chemistry, Utrecht University, Padualaan 8, 3584 CH, Utrecht (Netherlands); DSM ChemTech R and D, P.O. Box 18, 6160 MD Geleen (Netherlands); Taniguchi, Takashi [Graduate School of Engineering, Kyoto University Katsura Campus, Nishikyo-ku, Kyoto 615-8510 (Japan)
2014-06-07
A quantitative analysis is presented for the stochastic interactions of a pair of Brownian hard spheres in non-adsorbing polymer solutions. The hard spheres are hypothetically trapped by optical tweezers and allowed for random motion near the trapped positions. The investigation focuses on the long-time correlated Brownian motion. The mobility tensor altered by the polymer depletion effect is computed by the boundary integral method, and the corresponding random displacement is determined by the fluctuation-dissipation theorem. From our computations it follows that the presence of depletion layers around the hard spheres has a significant effect on the hydrodynamic interactions and particle dynamics as compared to pure solvent and uniform polymer solution cases. The probability distribution functions of random walks of the two interacting hard spheres that are trapped clearly shift due to the polymer depletion effect. The results show that the reduction of the viscosity in the depletion layers around the spheres and the entropic force due to the overlapping of depletion zones have a significant influence on the correlated Brownian interactions.
Stochastic interactions of two Brownian hard spheres in the presence of depletants.
Karzar-Jeddi, Mehdi; Tuinier, Remco; Taniguchi, Takashi; Fan, Tai-Hsi
2014-06-01
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
Chaudhari, Mangesh I.; Holleran, Sinead A.; Ashbaugh, Henry S.; Pratt, Lawrence R.
2013-01-01
The osmotic second virial coefficients, B2, for atomic-sized hard spheres in water are attractive (B2 < 0) and become more attractive with increasing temperature (?B2/?T < 0) in the temperature range 300 K ? T ? 360 K. Thus, these hydrophobic interactions are attractive and endothermic at moderate temperatures. Hydrophobic interactions between atomic-sized hard spheres in water are more attractive than predicted by the available statistical mechanical theory. These results constitute an initial step toward detailed molecular theory of additional intermolecular interaction features, specifically, attractive interactions associated with hydrophobic solutes. PMID:24297918
Gel transition in adhesive hard-sphere colloidal dispersions: the role of gravitational effects.
Kim, Jung Min; Fang, Jun; Eberle, Aaron P R; Castañeda-Priego, Ramón; Wagner, Norman J
2013-05-17
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 Pe(g), which is a function of particle size, volume fraction, and gravitational acceleration. Through a systematic variation of the parameters, we observe the critical Pe(g) of ? 0.01 can predict the stability of gels composed of adhesive hard spheres. PMID:25167458
NASA Astrophysics Data System (ADS)
Ogarko, Vitaliy; Luding, Stefan
2013-03-01
Polydisperse hard sphere mixtures have equilibrium properties which essentially depend on the number density and a reduced number K of moments of the size distribution function. Such systems are equivalent to other systems with different size distributions if the K moments are matched. In particular, a small number s of components, such that 2 s - 1 = K is sufficient to mimic systems with continuous size distributions. For most of the fluid phase K = 3 moments (s = 2 components) are enough to define an equivalent system, while in the glassy states one needs K = 5 moments (s = 3 components) to achieve good agreement between the polydisperse and its maximally-equivalent tridisperse system. With K = 5 matched moments they are also close in number- and volume-fractions of rattlers. Finally, also the jamming density of maximally-equivalent jammed packings is very close, where the tiny differences can be explained by the distribution of rattlers. Polydisperse hard sphere mixtures have equilibrium properties which essentially depend on the number density and a reduced number K of moments of the size distribution function. Such systems are equivalent to other systems with different size distributions if the K moments are matched. In particular, a small number s of components, such that 2 s - 1 = K is sufficient to mimic systems with continuous size distributions. For most of the fluid phase K = 3 moments (s = 2 components) are enough to define an equivalent system, while in the glassy states one needs K = 5 moments (s = 3 components) to achieve good agreement between the polydisperse and its maximally-equivalent tridisperse system. With K = 5 matched moments they are also close in number- and volume-fractions of rattlers. Finally, also the jamming density of maximally-equivalent jammed packings is very close, where the tiny differences can be explained by the distribution of rattlers. This research is supported by the Dutch Technology Foundation STW, which is the applied science division of NWO, and the Technology Programme of the Ministry of Economic Affairs, project Nr. STW-MUST 10120.
Enhancement of Crystallization of Hard Spheres by Gravity: Monte Carlo Simulation
Shin-ichiro Yanagiya; Atsushi Mori; Yoshihisa Suzuki; Yasuo Miyoshi; Masashi Kasuga; Tsutomu Sawada; Kensaku Ito; Tetsuo Inoue
2005-01-01
We present the effects of gravity on the growth of a hard-sphere (HS) crystal as determined by Monte Carlo simulations. HSs were confined between hard walls at the top (z=Lz) and the bottom (z=0) of the system with a periodic boundary condition in the horizontal direction. After preparing a melt state as an initial state, the gravity was suddenly switched
W. van Megen
2006-01-01
Mean-squared displacements (MSDs) of colloidal fluids of hard spheres are analyzed in terms of a random walk, an analysis which assumes that the process of structural relaxation among the particles can be described in terms of thermally driven memoryless encounters. For the colloidal fluid in thermodynamic equilibrium the magnitude of the stretching of the MSD is able to be reconciled
On the evolution of the empirical measure for the Hard-Sphere dynamics
Mario Pulvirenti; Sergio Simonella
2015-04-13
We prove that the evolution of marginals associated to the empirical measure of a finite system of hard spheres is driven by the BBGKY hierarchical expansion. The usual hierarchy of equations for $L^1$ measures is obtained as a corollary. We discuss the ambiguities arising in the corresponding notion of microscopic series solution to the Boltzmann-Enskog equation.
One and Two-Fluid van der Waals Theories of Liquid Mixtures, I. Hard Sphere Mixtures
Douglas Henderson; Peter J. Leonard
1970-01-01
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.
The potential energy landscape and inherent dynamics of a hard-sphere fluid
Qingqing Ma; Richard M. Stratt
2014-08-13
Hard-sphere models exhibit many of the same kinds of supercooled-liquid behavior as more realistic models of liquids, but the highly non-analytic character of their potentials makes it a challenge to think of that behavior in potential-energy-landscape terms. We show here that it is possible to calculate an important topological property of hard-sphere landscapes, the geodesic pathways through those landscapes, and to do so without artificially coarse-graining or softening the potential. We show, moreover, that the rapid growth of the lengths of those pathways with increasing packing fraction quantitatively predicts the precipitous decline in diffusion constants in a glass-forming hard-sphere mixture model. The geodesic paths themselves can be considered as defining the intrinsic dynamics of hard spheres, so it is also revealing to find that they (and therefore the features of the underlying potential-energy landscape) correctly predict the occurrence of dynamic heterogeneity and non-zero values of the non-Gaussian parameter. The success of these landscape predictions for the dynamics of such a singular model emphasizes that there is more to potential energy landscapes than is revealed by looking at the minima and saddle points.
Note: equation of state and the freezing point in the hard-sphere model.
Robles, Miguel; López de Haro, Mariano; Santos, Andrés
2014-04-01
The merits of different analytical equations of state for the hard-sphere system with respect to the recently computed high-accuracy value of the freezing-point packing fraction are assessed. It is found that the Carnahan-Starling-Kolafa and the branch-point approximant equations of state yield the best performance. PMID:24712819
Potential energy landscape and inherent dynamics of a hard-sphere fluid
NASA Astrophysics Data System (ADS)
Ma, Qingqing; Stratt, Richard M.
2014-10-01
Hard-sphere models exhibit many of the same kinds of supercooled-liquid behavior as more realistic models of liquids, but the highly nonanalytic character of their potentials makes it a challenge to think of that behavior in potential energy landscape terms. We show here that it is possible to calculate an important topological property of hard-sphere landscapes, the geodesic pathways through those landscapes, and to do so without artificially coarse-graining or softening the potential. We show, moreover, that the rapid growth of the lengths of those pathways with increasing packing fraction quantitatively predicts the precipitous decline in diffusion constants in a glass-forming hard-sphere mixture model. The geodesic paths themselves can be considered as defining the intrinsic dynamics of hard spheres, so it is also revealing to find that they (and therefore the features of the underlying potential energy landscape) correctly predict the occurrence of dynamic heterogeneity and nonzero values of the non-Gaussian parameter. The success of these landscape predictions for the dynamics of such a singular model emphasizes that there is more to potential energy landscapes than is revealed by looking at the minima and saddle points.
Note: Equation of state and the freezing point in the hard-sphere model
NASA Astrophysics Data System (ADS)
Robles, Miguel; López de Haro, Mariano; Santos, Andrés
2014-04-01
The merits of different analytical equations of state for the hard-sphere system with respect to the recently computed high-accuracy value of the freezing-point packing fraction are assessed. It is found that the Carnahan-Starling-Kolafa and the branch-point approximant equations of state yield the best performance.
RESEARCH ARTICLE Contact values for disparate-size hard-sphere mixtures
Andres Santos; Santos B. Yuste; Mariano Lopez de Haro; Morad Alawneh; Douglas Henderson
A universality ansatz for the contact values of a multicomponent mixture of additive hard spheres is used to propose new formulae for the case of disparate-size binary mixtures. A comparison with simulation data and with a recent proposal by Alawneh and Henderson for binary mixtures shows reasonably good agreement with the predictions for the contact values of the large-large radial
Experimental studies on the rheology of hard-sphere suspensions near the glass transition
Louise. Marshall; Charles F. Zukoski
1990-01-01
We have investigated the rheological behavior of sterically stabilized colloidal silica particles of three different sizes at volume fractions above 0.5. Despite a small surface charge, which elevated the intrinsic viscosity from the Einstein value of 2.5, the particles were found to behave essentially as hard spheres in the concentrated suspensions and to have properties highly reminiscent of molecular glasses.
Analytical representation of the Percus-Yevick hard-sphere radial distribution function
W. R. Smith; D. Henderson
1970-01-01
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.
S. Labík; A. Malijevský
1983-01-01
An algorithm that utilizes the advantage of a machine language and integer arithmetic is proposed for the Monte Carlo simulations of the radial distribution function of fluid hard spheres. The influence of integer arithmetic upon the accuracy of results is discussed. The method can be easily adapted for more complicated potentials.
Hard-Sphere Model Applied to the Solubility of Gases in Low-Boiling Liquids
L. A. K. Staveley
1970-01-01
The hard-sphere model for fluids has been applied by Snider and Herrington to the calculation of the excess thermodynamic functions of binary liquid mixtures and also to the problem of the solubility of gases in liquids. While remarkably successful in the first case, it appeared to fail rather badly when applied to gas solubility. It is shown that this apparent
Hypersonic acoustic excitations in binary colloidal crystals: Big versus small hard sphere control
Schofield, Andrew B.
Hypersonic acoustic excitations in binary colloidal crystals: Big versus small hard sphere control January 2007 The phononic band structure of two binary colloidal crystals, at hypersonic frequencies of light photonic crystals 2 and sound at hypersonic frequencies.3 The propa- gation of phonons
NASA Astrophysics Data System (ADS)
Ashton, Douglas J.; Wilding, Nigel B.; Roth, Roland; Evans, Robert
2011-12-01
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
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 ?(s)(r). 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 ?(s)(r). 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, ?(s)(r) = 0.35. These discrepancies are, however, small compared to those between simulation and the much poorer predictions of the Derjaguin approximation at this ?(s)(r). 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 B(2) as a function of ?(s)(r). 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. PMID:22304069
Radial distribution function of a hard-sphere solid
J. M. Kincaid; J. J. Weis
1977-01-01
New Monte Carlo estimates of the radial distribution function of a hardsphere solid are given, along with a simple analytic approximation for that function. The approximation is useful over a wider range of densities than that developed earlier by one of us.
The microstructures of cold dense systems as informed by hard sphere models and optimal packings
NASA Astrophysics Data System (ADS)
Hopkins, Adam Bayne
Sphere packings, or arrangements of "billiard balls" of various sizes that never overlap, are especially informative and broadly applicable models. In particular, a hard sphere model describes the important foundational case where potential energy due to attractive and repulsive forces is not present, meaning that entropy dominates the system's free energy. Sphere packings have been widely employed in chemistry, materials science, physics and biology to model a vast range of materials including concrete, rocket fuel, proteins, liquids and solid metals, to name but a few. Despite their richness and broad applicability, many questions about fundamental sphere packings remain unanswered. For example, what are the densest packings of identical three-dimensional spheres within certain defined containers? What are the densest packings of binary spheres (spheres of two different sizes) in three-dimensional Euclidean space R3 ? The answers to these two questions are important in condensed matter physics and solid-state chemistry. The former is important to the theory of nucleation in supercooled liquids and the latter in terms of studying the structure and stability of atomic and molecular alloys. The answers to both questions are useful when studying the targeted self-assembly of colloidal nanostructures. In this dissertation, putatively optimal answers to both of these questions are provided, and the applications of these findings are discussed. The methods developed to provide these answers, novel algorithms combining sequential linear and nonlinear programming techniques with targeted stochastic searches of conguration space, are also discussed. In addition, connections between the realizability of pair correlation functions and optimal sphere packings are studied, and mathematical proofs are presented concerning the characteristics of both locally and globally maximally dense structures in arbitrary dimension d. Finally, surprising and unexpected findings are presented concerning structural signatures inherent to nonequilibrium glassy states of matter, as modeled using a prototypical glass of 1,000,000 identical spheres.
Simulating asymmetric colloidal mixture with adhesive hard sphere model.
Jamnik, A
2008-06-21
Monte Carlo simulation and Percus-Yevick (PY) theory are used to investigate the structural properties of a two-component system of the Baxter adhesive fluids with the size asymmetry of the particles of both components mimicking an asymmetric binary colloidal mixture. The radial distribution functions for all possible species pairs, g(11)(r), g(22)(r), and g(12)(r), exhibit discontinuities at the interparticle distances corresponding to certain combinations of n and m values (n and m being integers) in the sum nsigma(1)+msigma(2) (sigma(1) and sigma(2) being the hard-core diameters of individual components) as a consequence of the impulse character of 1-1, 2-2, and 1-2 attractive interactions. In contrast to the PY theory, which predicts the delta function peaks in the shape of g(ij)(r) only at the distances which are the multiple of the molecular sizes corresponding to different linear structures of successively connected particles, the simulation results reveal additional peaks at intermediate distances originating from the formation of rigid clusters of various geometries. PMID:18570507
Disorder and excess modes in hard-sphere colloidal systems
NASA Astrophysics Data System (ADS)
Zargar, R.; Russo, J.; Schall, P.; Tanaka, H.; Bonn, D.
2014-11-01
The anomalous thermodynamic properties of glasses remain incompletely understood, notably the anomalous peak in the heat capacity at low temperatures; it is believed to be due to an excess of low-frequency vibrational modes and a manifestation of the structural disorder in these systems. We study the thermodynamics and vibrational dynamics of colloidal glasses and (defected) crystals. The experimental determination of the vibrational density of states allows us to directly observe a strong enhancement of low-frequency modes. Using a novel method (Zargar R. et al., Phys. Rev. Lett. 110 (2013) 258301) to determine the free energy, we also determine the entropy and the specific heat experimentally. It follows that the emergence of the excess modes and high values of the specific heat are directly related and are specific to the glass: even for solids containing a very large amount of defects, both the low-frequency density of states and the specific heat are significantly smaller than for the glass.
Thermodynamic consistency of the hard-sphere solid distribution function
NASA Astrophysics Data System (ADS)
Rascón, C.; Mederos, L.; Navascués, G.
1996-12-01
A discussion about the role of the two-particle density function in the fundamental equation of the compressibility is presented. The thermodynamic inconsistency found by different authors between the compressibility obtained from the equation of state and that from the compressibility equation, in both cases using simulation data, is clarified. A new parameterization for the solid radial distribution function, which includes properly the compressibility effects, is proposed.
NASA Astrophysics Data System (ADS)
Virrueta, A.; Gaines, J.; O'Hern, C. S.; Regan, L.
2015-03-01
Current research in the O'Hern and Regan laboratories focuses on the development of hard-sphere models with stereochemical constraints for protein structure prediction as an alternative to molecular dynamics methods that utilize knowledge-based corrections in their force-fields. Beginning with simple hydrophobic dipeptides like valine, leucine, and isoleucine, we have shown that our model is able to reproduce the side-chain dihedral angle distributions derived from sets of high-resolution protein crystal structures. However, methionine remains an exception - our model yields a chi-3 side-chain dihedral angle distribution that is relatively uniform from 60 to 300 degrees, while the observed distribution displays peaks at 60, 180, and 300 degrees. Our goal is to resolve this discrepancy by considering clashes with neighboring residues, and averaging the reduced distribution of allowable methionine structures taken from a set of crystallized proteins. We will also re-evaluate the electron density maps from which these protein structures are derived to ensure that the methionines and their local environments are correctly modeled. This work will ultimately serve as a tool for computing side-chain entropy and protein stability. A. V. is supported by an NSF Graduate Research Fellowship and a Ford Foundation Fellowship. J. G. is supported by NIH training Grant NIH-5T15LM007056-28.
Energy production rates in fluid mixtures of inelastic rough hard spheres
Andrés Santos; Gilberto M. Kremer; Vicente Garzó
2010-07-16
The aim of this work is to explore the combined effect of polydispersity and roughness on the partial energy production rates and on the total cooling rate of a granular fluid mixture. We consider a mixture of inelastic rough hard spheres of different number densities, masses, diameters, moments of inertia, and mutual coefficients of normal and tangential restitution. Starting from the first equation of the BBGKY hierarchy, the collisional energy production rates associated with the translational and rotational temperatures ($T_i^\\text{tr}$ and $T_i^\\text{rot}$) are expressed in terms of two-body average values. Next, those average values are estimated by assuming a velocity distribution function based on maximum-entropy arguments, allowing us to express the energy production rates and the total cooling rate in terms of the partial temperatures and the parameters of the mixture. Finally, the results are applied to the homogeneous cooling state of a binary mixture and the influence of inelasticity and roughness on the temperature ratios $T_1^\\text{tr}/T_1^\\text{rot}$, $T_2^\\text{tr}/T_1^\\text{tr}$, and $T_2^\\text{rot}/T_1^\\text{rot}$ is analyzed.
NASA Astrophysics Data System (ADS)
Thorneywork, Alice L.; Roth, Roland; Aarts, Dirk G. A. L.; Dullens, Roel P. A.
2014-04-01
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
2014-04-28
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
Extension of the hard-sphere particle-wall collision model to account for particle deposition.
Kosinski, Pawel; Hoffmann, Alex C
2009-06-01
Numerical simulations of flows of fluids with granular materials using the Eulerian-Lagrangian approach involve the problem of modeling of collisions: both between the particles and particles with walls. One of the most popular techniques is the hard-sphere model. This model, however, has a major drawback in that it does not take into account cohesive or adhesive forces. In this paper we develop an extension to a well-known hard-sphere model for modeling particle-wall interactions, making it possible to account for adhesion. The model is able to account for virtually any physical interaction, such as van der Waals forces or liquid bridging. In this paper we focus on the derivation of the new model and we show some computational results. PMID:19658496
Nature of the divergence in low shear viscosity of colloidal hard-sphere dispersions
NASA Astrophysics Data System (ADS)
Cheng, Zhengdong; Zhu, Jixiang; Chaikin, Paul M.; Phan, See-Eng; Russel, William B.
2002-04-01
Measurements of the low-shear viscosity ?o with a Zimm-Crothers viscometer for dispersions of colloidal hard spheres are reported as a function of volume fraction ? up to 0.56. Nonequilibrium theories based on solutions to the two-particle Smoluchoski equation or ideal mode coupling approximations do not capture the divergence. However, the nonhydrodynamic contribution to the relative viscosity ??o is correlated over a wide range of volume fractions by the Doolittle and Adam-Gibbs equations, indicating an exponential divergence at ?m=0.625+/-0.015. The data extend the previously proposed master curve, providing a test for improved theories for the many-body thermodynamic and hydrodynamic interactions that determine the viscosity of hard-sphere dispersions.
On the radial distribution function of a hard-sphere fluid
M. Lopez de Haro; A. Santos; S. B. Yuste
2006-04-17
Two related approaches, one fairly recent [A. Trokhymchuk et al., J. Chem. Phys. 123, 024501 (2005)] and the other one introduced fifteen years ago [S. B. Yuste and A. Santos, Phys. Rev. A 43, 5418 (1991)], for the derivation of analytical forms of the radial distribution function of a fluid of hard spheres are compared. While they share similar starting philosophy, the first one involves the determination of eleven parameters while the second is a simple extension of the solution of the Percus-Yevick equation. It is found that the {second} approach has a better global accuracy and the further asset of counting already with a successful generalization to mixtures of hard spheres and other related systems.
Nature of the divergence in low shear viscosity of colloidal hard-sphere dispersions.
Cheng, Zhengdong; Zhu, Jixiang; Chaikin, Paul M; Phan, See-Eng; Russel, William B
2002-04-01
Measurements of the low-shear viscosity eta(o) with a Zimm-Crothers viscometer for dispersions of colloidal hard spheres are reported as a function of volume fraction phi up to 0.56. Nonequilibrium theories based on solutions to the two-particle Smoluchoski equation or ideal mode coupling approximations do not capture the divergence. However, the nonhydrodynamic contribution to the relative viscosity Deltaeta(o) is correlated over a wide range of volume fractions by the Doolittle and Adam-Gibbs equations, indicating an exponential divergence at phi(m)=0.625+/-0.015. The data extend the previously proposed master curve, providing a test for improved theories for the many-body thermodynamic and hydrodynamic interactions that determine the viscosity of hard-sphere dispersions. PMID:12005822
Physics of Hard Spheres Experiment (PhaSE) or "Making Jello in Space"
NASA Technical Reports Server (NTRS)
Ling, Jerri S.; Doherty, Michael P.
1998-01-01
The Physics of Hard Spheres Experiment (PHaSE) is a highly successful experiment that flew aboard two shuttle missions to study the transitions involved in the formation of jellolike colloidal crystals in a microgravity environment. A colloidal suspension, or colloid, consists of fine particles, often having complex interactions, suspended in a liquid. Paint, ink, and milk are examples of colloids found in everyday life. In low Earth orbit, the effective force of gravity is thousands of times less than at the Earth's surface. This provides researchers a way to conduct experiments that cannot be adequately performed in an Earth-gravity environment. In microgravity, colloidal particles freely interact without the complications of settling that occur in normal gravity on Earth. If the particle interactions within these colloidal suspensions could be predicted and accurately modeled, they could provide the key to understanding fundamental problems in condensed matter physics and could help make possible the development of wonderful new "designer" materials. Industries that make semiconductors, electro-optics, ceramics, and composites are just a few that may benefit from this knowledge. Atomic interactions determine the physical properties (e.g., weight, color, and hardness) of ordinary matter. PHaSE uses colloidal suspensions of microscopic solid plastic spheres to model the behavior of atomic interactions. When uniformly sized hard spheres suspended in a fluid reach a certain concentration (volume fraction), the particle-fluid mixture changes from a disordered fluid state, in which the spheres are randomly organized, to an ordered "crystalline" state, in which they are structured periodically. The thermal energy of the spheres causes them to form ordered arrays, analogous to crystals. Seven of the eight PHaSE samples ranged in volume fraction from 0.483 to 0.624 to cover the range of interest, while one sample, having a concentration of 0.019, was included for instrument calibration.
The anisotropic hard-sphere crystal-melt interfacial free energy from fluctuations
Davidchack, Ruslan L.; Morris, James R.; Laird, Brian Bostian
2006-09-05
. Phys. 118, 7651 #1;2003#2;. 14D. Y. Sun, M. Asta, and J. J. Hoyt, Phys. Rev. B 69, 174103 #1;2004#2;. nergy of hard-sphere crystal-melt interface obtained Ref. 15 Ref. 16 This work 0.573#1;5#2; 0.62#1;2#2; 0.559#1;17#2; 0.09#1;4#2; 0.056 0.072#1;9#2; 0...
NASA Astrophysics Data System (ADS)
van Megen, W.
2006-01-01
Mean-squared displacements (MSDs) of colloidal fluids of hard spheres are analyzed in terms of a random walk, an analysis which assumes that the process of structural relaxation among the particles can be described in terms of thermally driven memoryless encounters. For the colloidal fluid in thermodynamic equilibrium the magnitude of the stretching of the MSD is able to be reconciled by a bias in the walk. This description fails for the under-cooled colloidal fluid.
Growth of hard-sphere models with two different sizes: Can a quasicrystal result\\?
NASA Astrophysics Data System (ADS)
Minchau, B.; Szeto, K. Y.; Villain, J.
1987-05-01
We define a growth model analogous to the Eden model, but with two types of atoms interacting through hard-sphere potentials. In some two-dimensional cases, these models generate structures which are neither periodic nor quasiperiodic, but have a characteristic topology that distinguishes them from glasses. This topology is analogous to that of Penrose lattices. Locally, the structure is of the Hendricks-Teller type: alternation of strips of fat and skinny Penrose rhombi.
Crystallization and phase-separation in non-additive binary hard-sphere mixtures
A. A. Louis; R. Finken; J. P. Hansen
1999-11-23
We calculate for the first time the full phase-diagram of an asymmetric non-additive hard-sphere mixture. The non-additivity strongly affects the crystallization and the fluid-fluid phase-separation. The global topology of the phase-diagram is controlled by an effective size-ratio y_{eff}, while the fluid-solid coexistence scales with the depth of the effective potential well.
On fluid-solid direct coexistence simulations: The pseudo-hard sphere model
NASA Astrophysics Data System (ADS)
Espinosa, Jorge R.; Sanz, Eduardo; Valeriani, Chantal; Vega, Carlos
2013-10-01
We investigate methodological issues concerning the direct coexistence method, an increasingly popular approach to evaluate the solid-fluid coexistence by means of computer simulations. The first issue is the impact of the simulation ensemble on the results. We compare the NpT ensemble (easy to use but approximate) with the NpzT ensemble (rigorous but more difficult to handle). Our work shows that both ensembles yield similar results for large systems (>5000 particles). Another issue, which is usually disregarded, is the stochastic character of a direct coexistence simulation. Here, we assess the impact of stochasticity in the determination of the coexistence point. We demonstrate that the error generated by stochasticity is much larger than that caused by the use of the NpT ensemble, and can be minimized by simply increasing the system size. To perform this study we use the pseudo hard-sphere model recently proposed by Jover et al. [J. Chem. Phys. 137, 144505 (2012)], and obtain a coexistence pressure of p* = 11.65(1), quite similar to that of hard spheres (only about 0.6% higher). Therefore, we conclude that this model can be reliably used to investigate the physics of hard spheres in phenomena like crystal nucleation.
On fluid-solid direct coexistence simulations: the pseudo-hard sphere model.
Espinosa, Jorge R; Sanz, Eduardo; Valeriani, Chantal; Vega, Carlos
2013-10-14
We investigate methodological issues concerning the direct coexistence method, an increasingly popular approach to evaluate the solid-fluid coexistence by means of computer simulations. The first issue is the impact of the simulation ensemble on the results. We compare the NpT ensemble (easy to use but approximate) with the NpzT ensemble (rigorous but more difficult to handle). Our work shows that both ensembles yield similar results for large systems (>5000 particles). Another issue, which is usually disregarded, is the stochastic character of a direct coexistence simulation. Here, we assess the impact of stochasticity in the determination of the coexistence point. We demonstrate that the error generated by stochasticity is much larger than that caused by the use of the NpT ensemble, and can be minimized by simply increasing the system size. To perform this study we use the pseudo hard-sphere model recently proposed by Jover et al. [J. Chem. Phys. 137, 144505 (2012)], and obtain a coexistence pressure of p? = 11.65(1), quite similar to that of hard spheres (only about 0.6% higher). Therefore, we conclude that this model can be reliably used to investigate the physics of hard spheres in phenomena like crystal nucleation. PMID:24116630
Equation of state of the hard-disk fluid on a sphere from Percus–Yevick equation
S. V. Lishchuk
2006-01-01
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.
fascinating 3 . The bulk phase diagram of monodisperse hard spheres has been verified ex- perimentally . Such templates are struc- tural patterns at the bottom of the container that act as crys- tallization seed
J. Largo; J. R. Solana
2000-01-01
An analytical expression for the first coordination cell of the radial distribution function (RDF) of the hard-sphere fluid is derived. It is based on a series expansion of the analytical expression of the Percus–Yevick solution of the RDF of the hard-sphere fluid derived by Chang and Sandler [J. Chang, S.I. Sandler, Mol. Phys. 81 (1994) 745.]. The expansion is carried
Hopkins, Paul; Schmidt, Matthias
2010-08-18
Using a fundamental measure density functional theory we investigate both bulk and inhomogeneous systems of the binary non-additive hard sphere model. For sufficiently large (positive) non-additivity the mixture phase separates into two fluid phases with different compositions. We calculate bulk fluid-fluid coexistence curves for a range of size ratios and non-additivity parameters and find that they compare well to simulation results from the literature. Using the Ornstein-Zernike equation, we investigate the asymptotic, [Formula: see text], decay of the partial pair correlation functions, g(ij)(r). At low densities a structural crossover occurs in the asymptotic decay between two different damped oscillatory modes with different wavelengths corresponding to the two intra-species hard-core diameters. On approaching the fluid-fluid critical point there is a Fisher-Widom crossover from exponentially damped oscillatory to monotonic asymptotic decay. Using the density functional we calculate the density profiles for the planar free fluid-fluid interface between coexisting fluid phases. We show that the type of asymptotic decay of g(ij)(r) not only determines the asymptotic decay of the interface profiles, but is also relevant for intermediate and even short-ranged behaviour. We also determine the surface tension of the free fluid interface, finding that it increases with non-additivity, and that on approaching the critical point mean-field scaling holds. PMID:21386490
The Physics of Hard Spheres Experiment on MSL-1: Required Measurements and Instrument Performance
NASA Technical Reports Server (NTRS)
Doherty, Michael P.; Lant, Christian T.; Ling, Jerri S.
1998-01-01
The Physics of HArd Spheres Experiment (PHaSE), one of NASA Lewis Research Center's first major light scattering experiments for microgravity research on complex fluids, flew on board the Space Shuttle's Microgravity Science Laboratory (MSL-1) in 1997. Using colloidal systems of various concentrations of micron-sized plastic spheres in a refractive index-matching fluid as test samples, illuminated by laser light during and after crystallization, investigations were conducted to measure the nucleation and growth rate of colloidal crystals as well as the structure, rheology, and dynamics of the equilibrium crystal. Together, these measurements support an enhanced understanding of the nature of the liquid-to-solid transition. Achievement of the science objectives required an accurate experimental determination of eight fundamental properties for the hard sphere colloidal samples. The instrument design met almost all of the original measurement requirements, but with compromise on the number of samples on which data were taken. The instrument performs 2-D Bragg and low angle scattering from 0.4 deg. to 60 deg., dynamic and single-channel static scattering from 10 deg. to 170 deg., rheology using fiber optics, and white light imaging of the sample. As a result, PHaSE provided a timely microgravity demonstration of critical light scattering measurement techniques and hardware concepts, while generating data already showing promise of interesting new scientific findings in the field of condensed matter physics.
Impact of microstructure on the effective diffusivity in random packings of hard spheres
NASA Astrophysics Data System (ADS)
Liasneuski, H.; Hlushkou, D.; Khirevich, S.; Höltzel, A.; Tallarek, U.; Torquato, S.
2014-07-01
We present results of computer simulations of the effective diffusion coefficient in bulk random packings of hard monosized spheres with solid volume fraction between 0.54 (random-loose packing) and 0.634 (maximally random jammed). Six types of sphere packings were generated with different protocols and parameters resulting in a systematically varied degree of microstructural heterogeneity. The packing morphology is qualitatively characterized by statistical analyses of Voronoi cells obtained from spatial tessellation of the packing space. Diffusive transport of point-like tracers in the pore space of the packings was simulated with a random-walking particle-tracking technique. Our results indicate that the effective transport characteristics of the random sphere packings are not fully defined from the solid volume fraction but also depend on the packing microstructure. For the first time, we compared (i) the values of the effective diffusion coefficient Deff simulated in packings with different morphologies, and (ii) the corresponding values of Deff obtained from an approximate analytical formula involving the three-point microstructural parameter ?2. This analysis reveals that this approximation involving ?2 clearly reflects key morphological specificity of individual sphere packings and provides a sufficiently accurate estimate of the effective diffusion coefficient.
An autonomous phase-boundary detection technique for colloidal hard sphere suspension experiments.
McDowell, Mark; Gray, Elizabeth; Rogers, Richard B
2006-04-01
Colloidal suspensions of monodisperse spheres are used as physical models of thermodynamic phase transitions and as precursors to photonic band gap materials. Current techniques for identifying the phase boundaries involve manually identifying the phase transitions, which is very tedious and time-consuming. In addition, 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. We have developed an intelligent machine vision technique that automatically identifies colloidal phase boundaries. The technique utilizes intelligent image processing algorithms 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 wherein regions of interest are distinguished from the background by differing patterns of motion over time. PMID:16586491
On the definition of an ideal amorphous solid of uniform hard spheres
NASA Astrophysics Data System (ADS)
To, Long-Thang; Daley, Daryl J.; Stachurski, Zbigniew H.
2006-08-01
Perfection of structure is defined firstly by the definition of imperfections that may occur in that structure, and secondly by the strict requirement of absence of those imperfections. An ideal amorphous solid is a geometrical structure with perfectly random (as distinct from disordered) packing of spheres/atoms. This is achieved by requiring all spheres to be in fixed positions (no rattlers) and the packing to obey certain statistical rules (without exceptions). The random configurations of local clusters are described by the mathematics of self-avoiding random walks, and the distribution of mutual contacts (coordination numbers) is described by combinatorics developed in connection with an earlier work on the structure of liquids. Flaws in the structure are defined. An ideal amorphous solid, based on packing of identical spheres and without any flaws, appears to have packing density close to approximately 0.61. Flaws which form clusters with close packing configurations (fcc and hcp) have the effect of increasing the packing density, whereas other type of flaws, i.e., loose spheres or vacancies will inevitably decrease the packing density. This relationship is revealed by analysis of recently published experimental packings and computer simulations. In that sense, the ideal amorphous solid described here is entirely new and original.
Saitow, Ken-ichi; Sasaki, Jungo
2005-03-01
The short-range structure of supercritical methanol (CH(3)OH) is investigated by measuring the spontaneous Raman spectra of the C-O stretching mode. The spectra are obtained at a reduced temperature, T(r)=T/T(c)=1.02 (522.9 K), which permits the neat fluid to be studied isothermally as a function of density. As the density increases, the spectral peaks shift toward the lower energy side and the spectra broaden. In the supercritical region, the amount of shifting shows nonlinear density dependence and the width becomes anomalously large. We use the perturbed hard-sphere model to analyze these density dependencies along the vibrational coordinate. The amount of shifting is decomposed into attractive and repulsive components, and the changes in attractive and repulsive energies are evaluated as functions of density and packing fraction, both of which are continuously varied by a factor of 120. Here we show that the shift amount consists principally of the attractive component at all densities, since the attractive energy is about eight times the repulsive energy. The density dependence of the widths is analyzed by calculating homogeneous and inhomogeneous widths as a function of density. The results show that, although vibrational dephasing and density inhomogeneity contribute similarly to the width at low and middle densities, at high density the main contributor turns out to be the vibrational dephasing. We estimate the local density enhancements of supercritical CH(3)OH as function of bulk density by two methods. The results of these analyses show common features, and both the estimated local density enhancements of CH(3)OH are considerably larger than the local density enhancements of simple fluids, i.e., those having nonhydrogen bonding. It is revealed that the local density of supercritical CH(3)OH is 40%-60% greater than the local densities of the simple fluids. We also estimate the local density fluctuation using the obtained values of attractive shift, inhomogeneous width, and local density. The density fluctuation in the vicinity of a vibrating molecule is compared to the fluctuation of bulk density, which is obtained from the thermodynamic calculation. PMID:15836327
Phase separation of binary nonadditive hard sphere fluid mixture confined in random porous media
NASA Astrophysics Data System (ADS)
Chen, W.
2013-10-01
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.
Phase separation of binary nonadditive hard sphere fluid mixture confined in random porous media.
Chen, W
2013-10-21
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
Crystal-liquid interfacial free energy of hard spheres via a thermodynamic integration scheme
NASA Astrophysics Data System (ADS)
Benjamin, Ronald; Horbach, Jürgen
2015-03-01
The hard-sphere crystal-liquid interfacial free energy ?cl is determined from molecular dynamics simulations using a thermodynamic integration (TI) scheme. The advantage of this TI scheme compared to previous methods is to successfully circumvent hysteresis effects due to the movement of the crystal-liquid interface. This is accomplished by the use of extremely-short-range and impenetrable Gaussian flat walls that prevent the drift of the interface while imposing a negligible free-energy penalty. We find that it is crucial to analyze finite-size effects in order to obtain reliable estimates of ?cl in the thermodynamic limit.
Crystal-liquid interfacial free energy of hard spheres via a thermodynamic integration scheme.
Benjamin, Ronald; Horbach, Jürgen
2015-03-01
The hard-sphere crystal-liquid interfacial free energy ?cl is determined from molecular dynamics simulations using a thermodynamic integration (TI) scheme. The advantage of this TI scheme compared to previous methods is to successfully circumvent hysteresis effects due to the movement of the crystal-liquid interface. This is accomplished by the use of extremely-short-range and impenetrable Gaussian flat walls that prevent the drift of the interface while imposing a negligible free-energy penalty. We find that it is crucial to analyze finite-size effects in order to obtain reliable estimates of ?cl in the thermodynamic limit. PMID:25871126
Isotropic-nematic phase equilibria of hard-sphere chain fluids—Pure components and binary mixtures
NASA Astrophysics Data System (ADS)
Oyarzún, Bernardo; van Westen, Thijs; Vlugt, Thijs J. H.
2015-02-01
The isotropic-nematic phase equilibria of linear hard-sphere chains and binary mixtures of them are obtained from Monte Carlo simulations. In addition, the infinite dilution solubility of hard spheres in the coexisting isotropic and nematic phases is determined. Phase equilibria calculations are performed in an expanded formulation of the Gibbs ensemble. This method allows us to carry out an extensive simulation study on the phase equilibria of pure linear chains with a length of 7 to 20 beads (7-mer to 20-mer), and binary mixtures of an 8-mer with a 14-, a 16-, and a 19-mer. The effect of molecular flexibility on the isotropic-nematic phase equilibria is assessed on the 8-mer+19-mer mixture by allowing one and two fully flexible beads at the end of the longest molecule. Results for binary mixtures are compared with the theoretical predictions of van Westen et al. [J. Chem. Phys. 140, 034504 (2014)]. Excellent agreement between theory and simulations is observed. The infinite dilution solubility of hard spheres in the hard-sphere fluids is obtained by the Widom test-particle insertion method. As in our previous work, on pure linear hard-sphere chains [B. Oyarzún, T. van Westen, and T. J. H. Vlugt, J. Chem. Phys. 138, 204905 (2013)], a linear relationship between relative infinite dilution solubility (relative to that of hard spheres in a hard-sphere fluid) and packing fraction is found. It is observed that binary mixtures greatly increase the solubility difference between coexisting isotropic and nematic phases compared to pure components.
NASA Astrophysics Data System (ADS)
Lomba, E.; Alvarez, M.; Lee, L. L.; Almarza, N. G.
1996-03-01
We have tested the capabilities of a new self-consistent integral equation, closely connected with Verlet's modified closure, for the study of fluid-fluid phase separation in symmetric non-additive hard-sphere mixtures. New expressions to evaluate the chemical potential of mixtures are presented and play a key role in the construction of the phase diagram. The new integral equation, which implements consistency between virial and fluctuation theorem routes to the isothermal compressibility, together with chemical potential and virial pressure consistency via the Gibbs-Duhem relation, yields a phase diagram which especially at high densities agrees remarkably well with the new semi-Grand Ensemble Monte Carlo simulation data also presented in this work. Deviations close to the critical point can be understood as a consequence of the inability to enforce virial-fluctuation consistency in the neighborhood of the spinodal decomposition curve.
F. Weysser; A. M. Puertas; M. Fuchs; Th. Voigtmann
2010-10-15
We analyze the slow, glassy structural relaxation as measured through collective and tagged-particle density correlation functions obtained from Brownian dynamics simulations for a polydisperse system of quasi-hard spheres in the framework of the mode-coupling theory of the glass transition (MCT). Asymptotic analyses show good agreement for the collective dynamics when polydispersity effects are taken into account in a multi-component calculation, but qualitative disagreement at small $q$ when the system is treated as effectively monodisperse. The origin of the different small-$q$ behaviour is attributed to the interplay between interdiffusion processes and structural relaxation. Numerical solutions of the MCT equations are obtained taking properly binned partial static structure factors from the simulations as input. Accounting for a shift in the critical density, the collective density correlation functions are well described by the theory at all densities investigated in the simulations, with quantitative agreement best around the maxima of the static structure factor, and worst around its minima. A parameter-free comparison of the tagged-particle dynamics however reveals large quantiative errors for small wave numbers that are connected to the well-known decoupling of self-diffusion from structural relaxation and to dynamical heterogeneities. While deviations from MCT behaviour are clearly seen in the tagged-particle quantities for densities close to and on the liquid side of the MCT glass transition, no such deviations are seen in the collective dynamics.
Physics of Hard Sphere Experiment: Scattering, Rheology and Microscopy Study of Colloidal Particles
NASA Technical Reports Server (NTRS)
Cheng, Z.-D.; Zhu, J.; Phan, S.-E.; Russel, W. B.; Chaikin, P. M.; Meyer, W. V.
2002-01-01
The Physics of Hard Sphere Experiment has two incarnations: the first as a scattering and rheology experiment on STS-83 and STS-94 and the second as a microscopy experiment to be performed in the future on LMM on the space station. Here we describe some of the quantitative and qualitative results from previous flights on the dynamics of crystallization in microgravity and especially the observed interaction of growing crystallites in the coexistance regime. To clarify rheological measurements we also present ground based experiments on the low shear rate viscosity and diffusion coefficient of several hard sphere experiments at high volume fraction. We also show how these experiments will be performed with confocal microscopy and laser tweezers in our lab and as preparation for the phAse II experiments on LMM. One of the main aims of the microscopy study will be the control of colloidal samples using an array of applied fields with an eye toward colloidal architectures. Temperature gradients, electric field gradients, laser tweezers and a variety of switchable imposed surface patterns are used toward this control.
System of elastic hard spheres which mimics the transport properties of a granular gas.
Santos, Andrés; Astillero, Antonio
2005-09-01
The prototype model of a fluidized granular system is a gas of inelastic hard spheres (IHS) with a constant coefficient of normal restitution alpha. Using a kinetic theory description we investigate the two basic ingredients that a model of elastic hard spheres (EHS) must have in order to mimic the most relevant transport properties of the underlying IHS gas. First, the EHS gas is assumed to be subject to the action of an effective drag force with a friction constant equal to half the cooling rate of the IHS gas, the latter being evaluated in the local equilibrium approximation for simplicity. Second, the collision rate of the EHS gas is reduced by a factor (1/2)(1+alpha), relative to that of the IHS gas. Comparison between the respective Navier-Stokes transport coefficients shows that the EHS model reproduces almost perfectly the self-diffusion coefficient and reasonably well the two transport coefficients defining the heat flux, the shear viscosity being reproduced within a deviation less than 14% (for alpha > or = 0.5). Moreover, the EHS model is seen to agree with the fundamental collision integrals of inelastic mixtures and dense gases. The approximate equivalence between IHS and EHS is used to propose kinetic models for inelastic collisions as simple extensions of known kinetic models for elastic collisions. PMID:16241427
NASA Astrophysics Data System (ADS)
Wagner, Norman; Cwalina, Colin
2015-03-01
Reversible shear thickening is common in concentrated dispersions of Brownian hard-spheres at high shear rates. We confirm the existence of a well-defined colloidal shear-thickened state through experimental measurements of the shear stress and the first and second normal stress differences in the shear-thickened state as a function of the particle volume fraction for a model dispersion of near hard-spheres. The shear stress and normal stress differences are observed to grow linearly with the shear rate in the shear-thickened state and both normal stress differences are observed to be negative. Our experimental results show the shear-thickened state of colloidal dispersions can be described by three material properties--the shear viscosity and first and second normal stress difference coefficients--that are a function of the volume fraction. All three material properties are found to diverge with a power law scaling with the approach to maximum packing,which is found to be 0.54 +/- 0.01. We find the magnitude of the relative shear viscosity is greater than the magnitude of the dimensionless second normal stress difference, which is greater than the magnitude of the dimensionless first normal stress difference. These results are consistent with theoretical predictions for shear thickening by hydrocluster formation and quantitatively comparable to Stokesian Dynamics simulations. We further postulate and show that these material properties are consistent with those measured for non-Brownian suspensions.
Critical endpoint and analytical phase diagram of attractive hard-core Yukawa spheres.
Tuinier, Remco; Fleer, Gerard J
2006-10-19
We analytically calculate the gas-liquid critical endpoint (cep) for hard spheres with a Yukawa attraction. This cep is a boundary condition for the existence of a liquid. We use an analytical Helmholtz energy expression for the attractive Yukawa (hard) spheres based on the first-order mean spherical approximation to the attractive Yukawa potential by Tang and Lu (J. Chem. Phys. 1993, 99, 9828). This theory and our analytical simplification of it predict the gas-liquid and fluid-solid phase behavior, as found from computer simulations, very accurately as long as the range 1/kappa of attraction is not too short. We find that the cep is situated at kappasigma approximately 6 and at a contact potential around 2 kT. It follows that a liquid state is only possible when the attraction range is longer than (1/6) of the particle diameter sigma, and the attraction strength is smaller than 2 kT. The liquid region does not span more than 0.6 kT in strength, and there is also a relatively narrow window for the attraction range. PMID:17034241
Simulation of a Solid-Solid Transition in Confined Colloidal Hard Spheres
NASA Astrophysics Data System (ADS)
Qi, Weikai; Peng, Yi; Han, Yilong; Bowles, Richard; Dijkstra, Marjolein
2015-03-01
Recent experiments on a system of colloidal particles confined between two flat plates showed a two-stage nucleation process involving the transition of a solid, consisting of n +1 crystalline layers with a square symmetry (n +1 s-phase), to another solid consisting of n triangular layers (n t-phase), via an intermediate metastable liquid droplet. Using event-driven molecular dynamics and Monte Carlo simulations, we study the 5s --> 4t solid-solid transition in colloidal hard spheres confined between two planar hard walls. The 5s solid initially melts, forming a liquid droplet, within which the 4t solid nucleates. Calculations of the free-energy landscape confirm that the optimal kinetic pathway is a two-stage nucleation process with a critical nucleus consisting of liquid-like and t-solid-like particles. In addition, we find that the t-solid-like cluster nucleates near the planar hard walls, and contains both face-centered-cubic and hexagonal-close-packed ordered particles. Current Address: Dept. Chemistry, University of Saskatchewan, Canada.
Sokolowski; Rzysko; Pizio
1999-10-01
We consider a slit-like pore filled with a disordered hard-sphere matrix. The diameter of matrix species is chosen almost equal to the pore width. Another hard-sphere fluid species, of smaller diameter, enters, at a given chemical potential, into this confined quenched microporous medium. The model is similar to the experimental setup; see G. Cruz de Leon et al. Phys. Rev. Lett. 81, 1122 (1998). The model is solved by using the inhomogeneous replica Ornstein-Zernike equations with Percus-Yevick approximation. We discuss the effective interactions between species in a confined medium on the chemical potential and matrix microporosity. Copyright 1999 Academic Press. PMID:10489311
Lamperski, Stanis?aw; Sosnowska, Joanna; Bhuiyan, Lutful Bari; Henderson, Douglas
2014-01-01
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. PMID:24410234
NASA Astrophysics Data System (ADS)
Lamperski, Stanis?aw; Sosnowska, Joanna; Bhuiyan, Lutful Bari; Henderson, Douglas
2014-01-01
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.
Continuous model for bosonic hard spheres in quasi-one-dimensional optical lattices
NASA Astrophysics Data System (ADS)
Carbonell-Coronado, C.; De Soto, F.; Gordillo, M. C.
2013-06-01
By means of diffusion Monte Carlo calculations, we investigated the quantum phase transition between a superfluid and a Mott insulator for a system of hard-sphere bosons in a quasi-one-dimensional optical lattice. For this continuous Hamiltonian, we studied how the stability limits of the Mott phase changed with the optical lattice depth and the transverse confinement width. A comparison of these results to those of a one-dimensional homogeneous Bose-Hubbard model indicates that this last model describes accurately the phase diagram only in the limit of deep lattices. For shallow ones, our results are comparable to those of the sine-Gordon model in its limit of application. We provide an estimate of the critical parameters when none of those models are realistic descriptions of a quasi-one-dimensional optical lattice.
Equation of state of sticky-hard-sphere fluids in the chemical-potential route.
Rohrmann, René D; Santos, Andrés
2014-04-01
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
Towards a general definition of gelation for adhesive hard-sphere dispersions
Néstor E. Valadez-Pérez; Yun Liu; Aaron P. R. Eberle; Norman J. Wagner; Ramón Castañeda-Priego
2013-06-25
One major goal in condensed matter physics is identifying the physical mechanisms that lead to arrested states of matter, especially gels and glasses. The complex nature and microscopic details of each particular system are relevant. However, from both scientific and technological viewpoints, a general, consistent and unified definition is of paramount importance. Through Monte Carlo computer simulations of states identified in experiments, we demonstrate that adhesive hard-sphere dispersions are the result of rigidity percolation with average number of bonds, $$, equals to 2.4. This corresponds to an established mechanism leading to phase transitions in network-forming materials. Our findings connect the concept of critical gel formation in colloidal suspensions with short-range attractive interactions to the universal concept of rigidity percolation. Furthermore, the bond, angular and local distributions along the gelation line are explicitly studied in order to determine the topology of the structure of the critical gel state.
"Sticky" hard spheres: equation of state, phase diagram, and metastable gels.
Buzzaccaro, Stefano; Rusconi, Roberto; Piazza, Roberto
2007-08-31
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. PMID:17931041
On the Born-Green-Yvon equation and triplet distributions for hard spheres
NASA Astrophysics Data System (ADS)
Taylor, Mark P.; Lipson, J. E. G.
1992-09-01
The Born-Green-Yvon integral equation for hard spheres is studied using two closures which provide improvements to the traditional Kirkwood superposition approximation (KSA). These rigorous corrections to the KSA arise from a diagrammatic expansion of the triplet potential of mean force which can be carried out in terms of either the Mayer f-function or the total correlation function h. While the short-ranged f-bond corrections improve the calculated pair distribution function at contact, they otherwise distort this function and thus give very poor compressibility results. The long-ranged h-bond corrections are found to give overall improvement to the pair distribution function and, in particular, give nearly the correct phase of this function. Furthermore, the triplet distribution function computed with the second-order h-bond correction is found to be reasonably close to Monte Carlo results.
Apparent wall slip in non-Brownian hard-sphere suspensions.
Korhonen, Marko; Mohtaschemi, Mikael; Puisto, Antti; Illa, Xavier; Alava, Mikko J
2015-05-01
We analyze apparent wall slip, the reduction of particle concentration near the wall, in hard-sphere suspensions at concentrations well below the jamming limit utilizing a continuum level diffusion model. The approach extends a constitutive equation proposed earlier with two additional potentials describing the effects of gravitation and wall-particle repulsion. We find that although both mechanisms are shear independent by nature, due to the shear-rate-dependent counter-balancing particle migration fluxes, the resulting net effect is non-linearly shear dependent, causing larger slip at small shear rates. In effect, this shows up in the classically measured flow curves as a mild shear thickening regime at the transition from small to intermediate shear rates. PMID:25998170
NASA Astrophysics Data System (ADS)
Donev, Aleksandar; Torquato, Salvatore; Stillinger, Frank H.
2005-01-01
We study the approach to jamming in hard-sphere packings and, in particular, the pair correlation function g2(r) around contact, both theoretically and computationally. Our computational data unambiguously separate the narrowing ? -function contribution to g2 due to emerging interparticle contacts from the background contribution due to near contacts. The data also show with unprecedented accuracy that disordered hard-sphere packings are strictly isostatic: i.e., the number of exact contacts in the jamming limit is exactly equal to the number of degrees of freedom, once rattlers are removed. For such isostatic packings, we derive a theoretical connection between the probability distribution of interparticle forces Pf(f) , which we measure computationally, and the contact contribution to g2 . We verify this relation for computationally generated isostatic packings that are representative of the maximally random jammed state. We clearly observe a maximum in Pf and a nonzero probability of zero force, shedding light on long-standing questions in the granular-media literature. We computationally observe an unusual power-law divergence in the near-contact contribution to g2 , persistent even in the jamming limit, with exponent -0.4 clearly distinguishable from previously proposed inverse-square-root divergence. Additionally, we present high-quality numerical data on the two discontinuities in the split-second peak of g2 and use a shared-neighbor analysis of the graph representing the contact network to study the local particle clusters responsible for the peculiar features. Finally, we present the computational data on the contact contribution to g2 for vacancy-diluted fcc crystal packings and also investigate partially crystallized packings along the transition from maximally disordered to fully ordered packings. We find that the contact network remains isostatic even when ordering is present. Unlike previous studies, we find that ordering has a significant impact on the shape of Pf for small forces.
Fast decay of the velocity autocorrelation function in dense shear flow of inelastic hard spheres
Ashish V. Orpe; V. Kumaran; K. Anki Reddy; Arshad Kudrolli
2008-11-18
We find in complementary experiments and event driven simulations of sheared inelastic hard spheres that the velocity autocorrelation function $\\psi(t)$ decays much faster than $t^{-3/2}$ obtained for a fluid of elastic spheres at equilibrium. Particle displacements are measured in experiments inside a gravity driven flow sheared by a rough wall. The average packing fraction obtained in the experiments is 0.59, and the packing fraction in the simulations is varied between 0.5 and 0.59. The motion is observed to be diffusive over long times except in experiments where there is layering of particles parallel to boundaries, and diffusion is inhibited between layers. Regardless, a rapid decay of $\\psi(t)$ is observed, indicating that this is a feature of the sheared dissipative fluid, and is independent of the details of the relative particle arrangements. An important implication of our study is that the non-analytic contribution to the shear stress may not be present in a sheared inelastic fluid, leading to a wider range of applicability of kinetic theory approaches to dense granular matter.
Goldman, Daniel I.
Signatures of Glass Formation in a Fluidized Bed of Hard Spheres Daniel I. Goldman* and Harry L motion and thus the loss of fluidization. Microscopic motion persists in this state, but the bed can be jammed by application of a small increase in flow rate. Thus a fluidized bed can serve as a test system
The complete T-->V,R energy conversion in three-body collisions within the hard sphere model.
Azriel, Vladimir M; Rusin, Lev Yu; Sevryuk, Mikhail B
2005-02-15
It is shown that in hard sphere (impulsive) collisions of atoms with diatomic molecules, complete conversion of the collision energy into the internal energy of the diatomic partner is possible for any number of impacts between the elastic balls representing the particles. The corresponding collision geometries and relations between the masses of the particles are described in detail. PMID:15743247
Stéphane Mischler; Clément Mouhot
2006-01-01
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
Combining off-lattice Monte Carlo and cellular automata for the simulation of hard-sphere systems.
Pazzona, Federico G; Demontis, Pierfranco; Suffritti, Giuseppe B
2014-08-01
In the present work we show how the update rule of a diffusive cellular automaton with mutual exclusion can be exploited in off-lattice Monte Carlo simulations of hard spheres to obtain a synchronous Monte Carlo sampling that satisfies the detailed balance principle. PMID:25215851
D. Viduna; W. R. Smith
2002-01-01
New and very accurate formulae for additive binary hard sphere (HS) mixture radial distribution functions (RDFs) at contact are proposed in a simple analytical form. Using the virial theorem, the formulae also provide a new HS mixture equation of state (EOS). The new RDF formulae are the most accurate currently available. The new EOS is of comparable accuracy with that
P. J. Leonard; D. Henderson; J. A. Barker
1971-01-01
A formulation is given which permits the rapid mechanical computation of the three radial distribution functions gij(r) of a binary hard-sphere mixture to any distance r, in the Percus-Yevick (P-Y) approximation. The consistency of the P-Y equation of state obtained by various methods is discussed.
Weeks, Eric R.
Gravity-Induced Aging in Glasses of Colloidal Hard Spheres Nikoleta B. Simeonova and Willem K) The influence of gravity on the long-time behavior of the mean squared displacement in glasses of polydisperse present, for the first time, a significant influence of gravity on the mean squared displacements
New exact relations for the many-cavity distribution function of non-uniform hard-sphere systems
NASA Astrophysics Data System (ADS)
Rascón, C.; Navascués, G.; Mederos, L.
New exact relations for the many-cavity distribution function y(n)(1, …, n) of a non-uniform hard-sphere system are derived. Some of these relations have been used previously without guarantee of their validity. They are of interest in perturbation theories of non-uniform classical systems and, in particular, in the theory of freezing of classical liquids.
Hardness of FeB4: density functional theory investigation.
Zhang, Miao; Lu, Mingchun; Du, Yonghui; Gao, Lili; Lu, Cheng; Liu, Hanyu
2014-05-01
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
Jammed lattice sphere packings
NASA Astrophysics Data System (ADS)
Kallus, Yoav; Marcotte, Étienne; Torquato, Salvatore
2013-12-01
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.
Jammed lattice sphere packings.
Kallus, Yoav; Marcotte, Étienne; Torquato, Salvatore
2013-12-01
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
Estimate of snow density knowing grain and share hardness
NASA Astrophysics Data System (ADS)
Valt, Mauro; Cianfarra, Paola; Cagnati, Anselmo; Chiambretti, Igor; Moro, Daniele
2010-05-01
Alpine avalanche warning services produces, weekly, snow profiles. Usually such profiles are made in horizontal snow fields, homogenously distributed by altitude and climatic micro-areas. Such profile allows grain shape, dimension and hardness (hand test) identification. Horizontal coring of each layer allows snow density identification. Such data allows the avalanche hazard evaluation and an estimation of the Snow Water Equivalent (SWE). Nevertheless the measurement of snow density, by coring, of very thin layers (less than 5 cm of thickness) is very difficult and are usually not measured by snow technicians. To bypass such problems a statistical analysis was performed to assign density values also to layers which cannot be measured. This system allows, knowing each layer thickness and its density, to correctly estimate SWE. This paper presents typical snow density values for snow hardness values and grain types for the Eastern Italian Alps. The study is based onto 2500 snow profiles with 17000 sampled snow layers from the Dolomites and Venetian Prealps (Eastern Alps). The table of typical snow density values for each grain type is used by YETI Software which elaborate snow profiles and automatically evaluate SWE. This method allows a better use of Avalanche Warning Services datasets for SWE estimation and local evaluation of SWE yearly trends for each snow field.
Arseni Goussev; J. R. Dorfman
2006-07-18
We consider the time evolution of a wave packet representing a quantum particle moving in a geometrically open billiard that consists of a number of fixed hard-disk or hard-sphere scatterers. Using the technique of multiple collision expansions we provide a first-principle analytical calculation of the time-dependent autocorrelation function for the wave packet in the high-energy diffraction regime, in which the particle's de Broglie wave length, while being small compared to the size of the scatterers, is large enough to prevent the formation of geometric shadow over distances of the order of the particle's free flight path. The hard-disk or hard-sphere scattering system must be sufficiently dilute in order for this high-energy diffraction regime to be achievable. Apart from the overall exponential decay, the autocorrelation function exhibits a generally complicated sequence of relatively strong peaks corresponding to partial revivals of the wave packet. Both the exponential decay (or escape) rate and the revival peak structure are predominantly determined by the underlying classical dynamics. A relation between the escape rate, and the Lyapunov exponents and Kolmogorov-Sinai entropy of the counterpart classical system, previously known for hard-disk billiards, is strengthened by generalization to three spatial dimensions. The results of the quantum mechanical calculation of the time-dependent autocorrelation function agree with predictions of the semiclassical periodic orbit theory.
Yi Liu; Jerzy Blawzdziewicz; Bogdan Cichocki; Jan K. G. Dhont; Maciej Lisicki; Eligiusz Wajnryb; Yuan-N. Young; Peter R. Lang
2015-07-02
In this article we report on a study of the near-wall dynamics of suspended colloidal hard spheres over a broad range of volume fractions. We present a thorough comparison of experimental data with predictions based on a virial approximation and simulation results. We find that the virial approach describes the experimental data reasonably well up to a volume fraction of $\\phi=0.25$ which provides us with a fast and non-costly tool for the analysis and prediction of Evanescent Wave DLS data. Based on this we propose a new method to assess the near-wall self-diffusion at elevated density. Here, we qualitatively confirm earlier results [Michailidou et al., Phys. Rev. Lett., 2009, 102, 068302], which indicate that many-particle hydrodynamic interactions are diminished by the presence of the wall at increasing volume fractions as compared to bulk dynamics. Beyond this finding we show that this diminishment is different for the particle motion normal and parallel to the wall.
NASA Astrophysics Data System (ADS)
Elfimova, Ekaterina A.; Karavaeva, Tatyana E.; Ivanov, Alexey O.
2014-12-01
A method for calculation of the free energy of dipolar hard spheres under the presence of an applied magnetic field is presented. The method is based on the virial expansion in terms of density as well as the dipolar coupling constant ?, and it uses diagram technique. The formulas and the diagrams, needed to calculate the second B2 and third B3 virial coefficients, are derived up to the order of ˜?3, and compared to the zero-field case. The formula for B2 is the same as in the zero-field case; the formula for B3, however, is different in an applied field, and a derivation is presented. This is a surprising result which is not emphasized in standard texts, but which has been noticed before in the virial expansion for flexible molecules (Caracciolo et al., 2006; Caracciolo et al., 2008). To verify the correctness of the obtained formulas, B2 and B3 were calculated within the accuracy of ?2, which were applied to initial magnetic susceptibility. The obtained expression fully coincides with the well-known theories (Morozov and Lebedev, 1990; Huke and Lücke, 2000; Ivanov and Kuznetsova, 2001), which used different methods to calculate the initial magnetic susceptibility.
The vanishing limit of the square-well fluid: the adhesive hard-sphere model as a reference system.
Largo, J; Miller, M A; Sciortino, F
2008-04-01
We report a simulation study of the gas-liquid critical point for the square-well potential, for values of well width delta as small as 0.005 times the particle diameter sigma. For small delta, the reduced second virial coefficient at the critical point B2*c is found to depend linearly on delta. The observed weak linear dependence is not sufficient to produce any significant observable effect if the critical temperature Tc is estimated via a constant B2*c assumption, due to the highly nonlinear transformation between B2*c and Tc. This explains the previously observed validity of the law of corresponding states. The critical density rho c is also found to be constant when measured in units of the cube of the average distance between two bonded particles (1+0.5 delta)sigma. The possibility of describing the delta-->0 dependence with precise functional forms provides improved accurate estimates of the critical parameters of the adhesive hard-sphere model. PMID:18397083
The power of simple hard-sphere models in protein structure prediction
NASA Astrophysics Data System (ADS)
Regan, Lynne
2012-02-01
There are several force-fields that are currently used to describe the potential energy of biological macromolecules such as proteins. These typically include many parameters, derived from a combination of statistical, experimental sources. These work on average to describe a protein, but the large number of parameters moves this description further away from a true physical understanding than is desirable. Our approach is to investigate to what extent simple hard sphere models can be used to model and predict the behavior of different aspects of protein structure. We present the results of specific calculations. The distributions of the side-chain dihedral angle chi1 of Val and Thr in proteins of known structure show distinctive features: Val side chains predominantly adopt dihedral angle, chi1, of 180, whereas Thr side chains typically adopt a dihedral angle, chi1, of 60 or 300. Several hypotheses have been proposed to explain these differences, including inter-residue steric clashes and hydrogen-bonding interactions. In contrast, we show that the observed side-chain dihedral angle distributions for both Val and Thr can be explained using only local steric interactions in a dipeptide mimetic. Our results emphasize the power of a simple physics-based approaches and their importance for future advances in protein engineering and design.
Assembly of vorticity-aligned hard-sphere colloidal strings in a simple shear flow
Cheng, Xiang; Xu, Xinliang; Rice, Stuart A.; Dinner, Aaron R.; Cohen, Itai
2012-01-01
Colloidal suspensions self-assemble into equilibrium structures ranging from face- and body-centered cubic crystals to binary ionic crystals, and even kagome lattices. When driven out of equilibrium by hydrodynamic interactions, even more diverse structures can be accessed. However, mechanisms underlying out-of-equilibrium assembly are much less understood, though such processes are clearly relevant in many natural and industrial systems. Even in the simple case of hard-sphere colloidal particles under shear, there are conflicting predictions about whether particles link up into string-like structures along the shear flow direction. Here, using confocal microscopy, we measure the shear-induced suspension structure. Surprisingly, rather than flow-aligned strings, we observe log-rolling strings of particles normal to the plane of shear. By employing Stokesian dynamics simulations, we address the mechanism leading to this out-of-equilibrium structure and show that it emerges from a delicate balance between hydrodynamic and interparticle interactions. These results demonstrate a method for assembling large-scale particle structures using shear flows. PMID:22198839
Experimental studies on the rheology of hard-sphere suspensions near the glass transition
Marshall, L.; Zukoski, C.F. IV (Univ. of Illinois, Urbana (USA))
1990-02-08
We have investigated the rheological behavior of sterically stabilized colloidal silica particles of three different sizes at volume fractions above 0.5. Despite a small surface charge, which elevated the intrinsic viscosity from the Einstein value of 2.5, the particles were found to behave essentially as hard spheres in the concentrated suspensions and to have properties highly reminiscent of molecular glasses. The zero shear rate viscosity, characteristic of disordered suspensions and present at all volume fractions, diverges as {phi} {yields} 0.6 and is well-described by the Doolittle equation for glassy flow. For suspensions with a relative zero shear rate viscosity greater than 5 {times} 10{sub 2}, shear thickening was observed. Characteristic time scales for particle rearrangement determined from critical shear rates for shear thinning and shear thickening were found to follow trends predicted for molecular glasses. A transition from a liquid like linear relaxation response to glassy stretched exponential behavior was observed as volume fraction was increased. The onset of the glassy relaxation response, indicative of nondecaying correlations, occurred near a volume fraction of 0.52.
Shock-induced phase transition in systems of hard spheres with internal degrees of freedom.
Taniguchi, Shigeru; Mentrelli, Andrea; Zhao, Nanrong; Ruggeri, Tommaso; Sugiyama, Masaru
2010-06-01
Shock waves and shock-induced phase transitions are theoretically and numerically studied on the basis of the system of Euler equations with caloric and thermal equations of state for a system of hard spheres with internal degrees of freedom. First, by choosing the unperturbed state (the state before the shock wave) in the liquid phase, the Rankine-Hugoniot conditions are studied and their solutions are classified on the basis of the phase of the perturbed state (the state after the shock wave), being a shock-induced phase transition possible under certain conditions. With this regard, the important role of the internal degrees of freedom is shown explicitly. Second, the admissibility (stability) of shock waves is studied by means of the results obtained by Liu in the theory of hyperbolic systems. It is shown that another type of instability of a shock wave can exist even though the perturbed state is thermodynamically stable. Numerical calculations have been performed in order to confirm the theoretical results in the case of admissible shocks and to obtain the actual evolution of the wave profiles in the case of inadmissible shocks (shock splitting phenomena). PMID:20866522
Monte Carlo simulation of growth of hard-sphere crystals on a square pattern
Atsushi Mori
2010-11-01
Monte Carlo simulations of the colloidal epitaxy of hard spheres (HSs) on a square pattern have been performed. This is an extension of previous simulations; we observed a shrinking intrinsic stacking fault running in an oblique direction through the glide of a Shockley partial dislocation terminating its lower end in fcc (001) stacking [Mori et al., Molec. Phys. 105 (2007) 1377], which was an answer to a question why the defect in colloidal crystals reduced by gravity [Zhu et al., Nature 387 (1997) 883]. We have resolved one of shortcomings of the previous simulations; the driving force for fcc (001) stacking, which was stress from a small periodic boundary simulation box, has been replaced with the stress from a pattern on the bottom. We have observed disappearance of stacking fault in this realizable condition. Sinking of the center of gravity has been smooth and of a single relaxation mode under the condition that the gravitational energy mgd is slightly less than the thermal energy kT. In the snapshots tetrahedral structures have appeared often, suggesting formation of staking fault tetrahedra.
NASA Astrophysics Data System (ADS)
Lechman, Jeremy; Pierce, Flint
2012-02-01
Diffusive transport is a ubiquitous process that is typically understood in terms of a classical random walk of non-interacting particles. Here we present the results for a model of hard-sphere colloids in a Newtonian incompressible solvent at various volume fractions below the ordering transition (˜50%). We numerically simulate the colloidal systems via Fast Lubrication Dynamics -- a Brownian Dynamics approach with corrected mean-field hydrodynamic interactions. Colloid-colloid interactions are also included so that we effectively solve a system of interacting Langevin equations. The results of the simulations are analyzed in terms of the diffusion coefficient as a function of time with the early and late time diffusion coefficients comparing well with experimental results. An interpretation of the full time dependent behavior of the diffusion coefficient and mean-squared displacement is given in terms of a continuous time random walk. Therefore, the deterministic, continuum diffusion equation which arises from the discrete, interacting random walkers is presented. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Cavity averages for hard spheres in the presence of polydispersity and incomplete data
Michael Schindler; A. C. Maggs
2015-06-16
We develop a cavity-based method which allows to extract thermodynamic properties from position information in hard-sphere/disk systems. So far, there are 'available-volume' and 'free-volume' methods. We add a third one, which we call 'available-volume-after-takeout', and which is shown to be mathematically equivalent to the others. In applications, where data sets are finite, all three methods show limitations, and they do this in different parameter ranges. We illustrate the principal equivalence and the limitations on data from molecular dynamics -- In particular, we test robustness against missing data. We have in mind experimental limitations where there is a small polydispersity, say 4% in the particle radii, but individual radii cannot be determined. We observe that, depending on the used method, the errors in such a situation are easily 100% for the pressure and 10kT for the chemical potentials. Our work is meant as guideline to the experimentalist for choosing the right one of the three methods, in order to keep the outcome of experimental data analysis meaningful.
NASA Astrophysics Data System (ADS)
Oshima, Hiraku; Kinoshita, Masahiro
2015-04-01
In earlier works, we showed that the entropic effect originating from the translational displacement of water molecules plays the pivotal role in protein folding and denaturation. The two different solvent models, hard-sphere solvent and model water, were employed in theoretical methods wherein the entropic effect was treated as an essential factor. However, there were similarities and differences in the results obtained from the two solvent models. In the present work, to unveil the physical origins of the similarities and differences, we simultaneously consider structural transition, cold denaturation, and pressure denaturation for the same protein by employing the two solvent models and considering three different thermodynamic states for each solvent model. The solvent-entropy change upon protein folding/unfolding is decomposed into the protein-solvent pair (PA) and many-body (MB) correlation components using the integral equation theories. Each component is further decomposed into the excluded-volume (EV) and solvent-accessible surface (SAS) terms by applying the morphometric approach. The four physically insightful constituents, (PA, EV), (PA, SAS), (MB, EV), and (MB, SAS), are thus obtained. Moreover, (MB, SAS) is discussed by dividing it into two factors. This all-inclusive investigation leads to the following results: (1) the protein-water many-body correlation always plays critical roles in a variety of folding/unfolding processes; (2) the hard-sphere solvent model fails when it does not correctly reproduce the protein-water many-body correlation; (3) the hard-sphere solvent model becomes problematic when the dependence of the many-body correlation on the solvent number density and temperature is essential: it is not quite suited to studies on cold and pressure denaturating of a protein; (4) when the temperature and solvent number density are limited to the ambient values, the hard-sphere solvent model is usually successful; and (5) even at the ambient values, however, the many-body correlation plays significant roles in the ?-sheet formation and argument of relative stabilities of very similar structures of a protein. These results are argued in detail with respect to the four physically insightful constituents and the two factors mentioned above. The relevance to the absence or presence of hydrogen-bonding properties in the solvent is also discussed in detail.
bubbling of almost-harmonic maps between 2-spheres at points of zero energy density
Mitchener, Paul
bubbling of almost-harmonic maps between 2-spheres at points of zero energy density Peter Topping depending on whether or not bubbles develop at points in the domain at which the energy density of the body harmonic u. Since the harmonic maps occur in families, the energy E is degenerate near each critical point
D. J. Rader; M. A. Gallis; J. R. Torczynski; W. Wagner
2006-01-01
The convergence behavior of the direct simulation Monte Carlo (DSMC) method is systematically investigated for near-continuum, one-dimensional Fourier flow. An argon-like, hard-sphere gas is confined between two parallel, fully accommodating, motionless walls of unequal temperature. The simulations are performed using four variations based on Bird's DSMC algorithm that differ in the ordering of the move, collide, and sample operations. The
D. J. Rader; M. A. Gallis; J. R. Torczynski; W. Wagner
2006-01-01
The convergence behavior of the direct simulation Monte Carlo (DSMC) method is systematically investigated for near-continuum, one-dimensional Fourier flow. An argon-like, hard-sphere gas is confined between two parallel, fully accommodating, motionless walls of unequal temperature. The simulations are performed using four variations based on Bird’s DSMC algorithm that differ in the ordering of the move, collide, and sample operations. The
Zhou, Alice Qinhua; O'Hern, Corey S; Regan, Lynne
2014-10-01
The side-chain dihedral angle distributions of all amino acids have been measured from myriad high-resolution protein crystal structures. However, we do not yet know the dominant interactions that determine these distributions. Here, we explore to what extent the defining features of the side-chain dihedral angle distributions of different amino acids can be captured by a simple physical model. We find that a hard-sphere model for a dipeptide mimetic that includes only steric interactions plus stereochemical constraints is able to recapitulate the key features of the back-bone dependent observed amino acid side-chain dihedral angle distributions of Ser, Cys, Thr, Val, Ile, Leu, Phe, Tyr, and Trp. We find that for certain amino acids, performing the calculations with the amino acid of interest in the central position of a short ?-helical segment improves the match between the predicted and observed distributions. We also identify the atomic interactions that give rise to the differences between the predicted distributions for the hard-sphere model of the dipeptide and that of the ?-helical segment. Finally, we point out a case where the hard-sphere plus stereochemical constraint model is insufficient to recapitulate the observed side-chain dihedral angle distribution, namely the distribution P(?(3)) for Met. PMID:24912976
Malijevský, Alexandr; Jackson, George; Varga, Szabolcs
2008-10-14
The extension of Onsager's second-virial theory [L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949)] for the orientational ordering of hard rods to mixtures of nonspherical hard bodies with finite length-to-breadth ratios is examined using the decoupling approximations of Parsons [Phys. Rev. A 19, 1225 (1979)] and Lee [J. Chem. Phys. 86, 6567 (1987); 89, 7036 (1988)]. Invariably the extension of the Parsons-Lee (PL) theory to mixtures has in the past involved a van der Waals one-fluid treatment in which the properties of the mixture are approximated by those of a reference one-component hard-sphere fluid with an effective diameter which depends on the composition of the mixture and the molecular parameters of the various components; commonly this is achieved by equating the molecular volumes of the effective hard sphere and of the components in the mixture and is referred to as the PL theory of mixtures. It is well known that a one-fluid treatment is not the most appropriate for the description of the thermodynamic properties of isotropic fluids, and inadequacies are often rectified with a many-fluid (MF) theory. Here, we examine MF theories which are developed from the virial theorem and the virial expansion of the Helmholtz free energy of anisotropic fluid mixtures. The use of the decoupling approximation of the pair distribution function at the level of a multicomponent hard-sphere reference system leads to our MF Parsons (MFP) theory of anisotropic mixtures. Alternatively the mapping of the virial coefficients of the hard-body mixtures onto those of equivalent hard-sphere systems leads to our MF Lee (MFL) theory. The description of the isotropic-nematic phase behavior of binary mixtures of hard Gaussian overlap particles is used to assess the adequacy of the four different theories, namely, the original second-virial theory of Onsager, the usual PL one-fluid theory, and the MF theories based on the Lee (MFL) and Parsons (MFP) approaches. A comparison with the simulation data for the mixtures studied by Zhou et al. [J. Chem. Phys. 120, 1832 (2004)] suggests that the Parsons MF description (MFP) provides the most accurate representation of the properties of the isotropic-nematic ordering transition and density (pressure) dependence of the order parameters. PMID:19045155
Density-functional theory of inhomogeneous systems of hard spherocylinders
Velasco; Mederos; Sullivan
2000-09-01
The smectic-A phase boundaries of a hard-spherocylinder fluid are calculated using a density-functional theory based on one proposed earlier by Somoza and Tarazona [Phys. Rev. A 41, 965 (1990)]. Our calculations do not employ the translation-rotation decoupling approximation used in previous density-functional theories. The calculated phase boundaries agree well with computer simulation results up to aspect ratios L/D approximately 5 and are in better agreement with the simulations than are previous theories. We generalize the model fluid by including long-range interactions with quadrupolar orientational symmetry, which are taken into account by mean-field approximation. For sufficiently large strength, these interactions produce a smectic-C phase, which undergoes either a continuous or weakly first-order transition to the smectic-A phase. The theory and numerical methods discussed here can be applied to the analysis of interfacial phenomena. PMID:11088887
Density-functional theory of inhomogeneous systems of hard spherocylinders
NASA Astrophysics Data System (ADS)
Velasco, E.; Mederos, L.; Sullivan, D. E.
2000-09-01
The smectic-A phase boundaries of a hard-spherocylinder fluid are calculated using a density-functional theory based on one proposed earlier by Somoza and Tarazona [Phys. Rev. A 41, 965 (1990)]. Our calculations do not employ the translation-rotation decoupling approximation used in previous density-functional theories. The calculated phase boundaries agree well with computer simulation results up to aspect ratios L/D~5 and are in better agreement with the simulations than are previous theories. We generalize the model fluid by including long-range interactions with quadrupolar orientational symmetry, which are taken into account by mean-field approximation. For sufficiently large strength, these interactions produce a smectic-C phase, which undergoes either a continuous or weakly first-order transition to the smectic-A phase. The theory and numerical methods discussed here can be applied to the analysis of interfacial phenomena.
Nguyen, Minh Tho
Density Functional Approach to Regiochemistry, Activation Energy, and Hardness Profile in 1Ven, Celestijnenlaan 200F, B-3001 LeuVen, Belgium ReceiVed: January 29, 1998 The principle of hard and soft acids that the transition state with higher hardness is associated with lower activation energy. The hardness profile has
Amokrane, S; Ayadim, A; Malherbe, J G
2005-11-01
A simple modification of the reference hypernetted chain (RHNC) closure of the multicomponent Ornstein-Zernike equations with bridge functions taken from Rosenfeld's hard-sphere bridge functional is proposed. Its main effect is to remedy the major limitation of the RHNC closure in the case of highly asymmetric mixtures--the wide domain of packing fractions in which it has no solution. The modified closure is also much faster, while being of similar complexity. This is achieved with a limited loss of accuracy, mainly for the contact value of the big sphere correlation functions. Comparison with simulation shows that inside the RHNC no-solution domain, it provides a good description of the structure, while being clearly superior to all the other closures used so far to study highly asymmetric mixtures. The generic nature of this closure and its good accuracy combined with a reduced no-solution domain open up the possibility to study the phase diagram of complex fluids beyond the hard-sphere model. PMID:16375547
bubbling of almost-harmonic maps between 2-spheres at points of zero energy density *
Mitchener, Paul
bubbling of almost-harmonic maps between 2-spheres at points of zero energy the energy density of the body map is zero. We also see that this translates i* *nto different behaviour be- haviour depending on whether or not bubbles develop at points in the domai* *n at which
Ayadim, A; Amokrane, S
2006-08-01
Fluid-fluid binodals of binary hard-sphere mixtures are computed from the recently proposed fundamental measure functional-mean spherical approximation closure of the two-component Ornstein-Zernike equation. The results, especially in the dense fluid region that was not accessible by previous theoretical methods, are compared with the corresponding ones for the one-component fluid of big spheres with effective potential obtained from the same closure. The general trends are those expected for hard-sphere potentials but small difference are detectable. The overall agreement found validates the equivalence of the two descriptions for size ratios R = 8.5 or greater. PMID:17025392
G. Jacucci; E. Omerti
1983-01-01
The two body contribution to the radial distribution function of quantum hard spheres is calculated using the Monte Carlo method based on path integrals. Hard core boundary conditions are taken into account by means of an ‘‘image’’ approximation obtaining accurate numerical results.
NASA Astrophysics Data System (ADS)
Wolf, Aaron S.; Asimow, Paul D.; Stevenson, David J.
2015-08-01
We develop a new model to understand and predict the behavior of oxide and silicate melts at extreme temperatures and pressures, including deep mantle conditions like those in the early Earth magma ocean. The Coordinated Hard Sphere Mixture (CHaSM) is based on an extension of the hard sphere mixture model, accounting for the range of coordination states available to each cation in the liquid. By utilizing approximate analytic expressions for the hard sphere model, this method is capable of predicting complex liquid structure and thermodynamics while remaining computationally efficient, requiring only minutes of calculation time on standard desktop computers. This modeling framework is applied to the MgO system, where model parameters are trained on a collection of crystal polymorphs, producing realistic predictions of coordination evolution and the equation of state of MgO melt over a wide range of pressures and temperatures. We find that the typical coordination number of the Mg cation evolves continuously upward from 5.25 at 0 GPa to 8.5 at 250 GPa. The results produced by CHaSM are evaluated by comparison with predictions from published first-principles molecular dynamics calculations, indicating that CHaSM is accurately capturing the dominant physics controlling the behavior of oxide melts at high pressure. Finally, we present a simple quantitative model to explain the universality of the increasing Grüneisen parameter trend for liquids, which directly reflects their progressive evolution toward more compact solid-like structures upon compression. This general behavior is opposite that of solid materials, and produces steep adiabatic thermal profiles for silicate melts, thus playing a crucial role in magma ocean evolution.
Schaefer, B.; Lambert, S.M.; Song, Y.; Prausnitz, J.M.
1994-10-01
Goal of this work is the extension of a Perturbed-Hard-Sphere-Chain equation of state (PHSC EOS) to systems containing strong polar components. Three different types of association models (ten Brinke/Karasz, SAFI, modified Veytsman) were used to calculate the contribution of specific interactions like hydrogen bonding to thermodynamic quantities. Pure component parameters obtained from regression of temperature dependent density and vapor pressure data allow the prediction of VLE and LLE data. The results of simple fluids and polymer solutions were compared with experimental data. The SAFT and the modified Veytsman extension give similar results for pure fluids and mixtures with components of similar segment size. Differences increase with increasing difference of segment size.
Boda, Dezs?; Henderson, Douglas; Eisenberg, Bob; Gillespie, Dirk
2011-01-01
In the implicit solvent models of electrolytes (such as the primitive model (PM)), the ions are modeled as point charges in the centers of spheres (hard spheres in the case of the PM). The surfaces of the spheres are not polarizable which makes these models appropriate to use in computer simulations of electrolyte systems where these ions do not leave their host dielectrics. The same assumption makes them inappropriate in simulations where these ions cross dielectric boundaries because the interaction energy of the point charge with the polarization charge induced on the dielectric boundary diverges. In this paper, we propose a procedure to treat the passage of such ions through dielectric interfaces with an interpolation method. Inspired by the “bubble ion” model (in which the ion's surface is polarizable), we define a space-dependent effective dielectric coefficient, ? eff (r), for the ion that overlaps with the dielectric boundary. Then, we replace the “bubble ion” with a point charge that has an effective charge q?? eff (r) and remove the portion of the dielectric boundary where the ion overlaps with it. We implement the interpolation procedure using the induced charge computation method [D. Boda, D. Gillespie, W. Nonner, D. Henderson, and B. Eisenberg, Phys. Rev. E 69, 046702 (2004)]. We analyze the various energy terms using a spherical ion passing through an infinite flat dielectric boundary as an example. PMID:21842924
Laura Filion; Michiel Hermes; Ran Ni; Marjolein Dijkstra
2010-06-15
Over the last number of years several simulation methods have been introduced to study rare events such as nucleation. In this paper we examine the crystal nucleation rate of hard spheres using three such numerical techniques: molecular dynamics, forward flux sampling and a Bennett-Chandler type theory where the nucleation barrier is determined using umbrella sampling simulations. The resulting nucleation rates are compared with the experimental rates of Harland and Van Megen [J. L. Harland and W. van Megen, Phys. Rev. E 55, 3054 (1997)], Sinn et al. [C. Sinn et al., Prog. Colloid Polym. Sci. 118, 266 (2001)] and Schatzel and Ackerson [K. Schatzel and B.J. Ackerson, Phys. Rev. E, 48, 3766 (1993)] and the predicted rates for monodisperse and 5% polydisperse hard spheres of Auer and Frenkel [S. Auer and D. Frenkel, Nature 409, 1020 (2001)]. When the rates are examined in long-time diffusion units, we find agreement between all the theoretically predicted nucleation rates, however, the experimental results display a markedly different behaviour for low supersaturation. Additionally, we examined the pre-critical nuclei arising in the molecular dynamics, forward flux sampling, and umbrella sampling simulations. The structure of the nuclei appear independent of the simulation method, and in all cases, the nuclei contain on average significantly more face-centered-cubic ordered particles than hexagonal-close-packed ordered particles.
NASA Astrophysics Data System (ADS)
Rota, R.; Tramonto, F.; Galli, D. E.; Giorgini, S.
2014-08-01
We obtain ab-initio estimations of the dynamic structure factor, S(q,?), of Bose gases at zero temperature. More precisely, we use the Genetic Inversion via Falsification of Theories (GIFT) algorithm to perform analytic continuations of imaginary time correlation functions computed via an exact Path Integral projector method. Using the hard-sphere potential to model the two-body interactions between the atoms, we compute S(q,?) changing the gas parameter from the dilute regime (na3 = 10-4) up to the density corresponding to superfluid 4He at equilibrium (na3 = 0.2138). With increasing density, we observe the emergence of a broad multiphonon contribution accompanying the quasiparticle peak and a crossover of the dispersion of elementary excitations from a Bogoliubov-like spectrum to a phonon-maxon- roton curve. Apart from the low wave vector region, for na3 = 0.2138 the energy-momentum dispersion relation and the static density response function, ?(q), turns out to be in good agreement with the superfluid 4He experimental data at equilibrium density.
Equilibrium Phase Behavior of Polydisperse Hard Spheres Moreno Fasolo* and Peter Sollich
Sollich, Peter
experimentally, using, e.g., colloidal latex particles steri- cally stabilized by a polymer coating [1]. Hard new phe- nomena. First, it is intuitively clear [9] that significant diameter polydispersity should
Nanopatterned ferroelectrics for ultrahigh density rad-hard nonvolatile memories.
Brennecka, Geoffrey L.; Stevens, Jeffrey; Scrymgeour, David; Gin, Aaron V.; Tuttle, Bruce Andrew
2010-09-01
Radiation hard nonvolatile random access memory (NVRAM) is a crucial component for DOE and DOD surveillance and defense applications. NVRAMs based upon ferroelectric materials (also known as FERAMs) are proven to work in radiation-rich environments and inherently require less power than many other NVRAM technologies. However, fabrication and integration challenges have led to state-of-the-art FERAMs still being fabricated using a 130nm process while competing phase-change memory (PRAM) has been demonstrated with a 20nm process. Use of block copolymer lithography is a promising approach to patterning at the sub-32nm scale, but is currently limited to self-assembly directly on Si or SiO{sub 2} layers. Successful integration of ferroelectrics with discrete and addressable features of {approx}15-20nm would represent a 100-fold improvement in areal memory density and would enable more highly integrated electronic devices required for systems advances. Towards this end, we have developed a technique that allows us to carry out block copolymer self-assembly directly on a huge variety of different materials and have investigated the fabrication, integration, and characterization of electroceramic materials - primarily focused on solution-derived ferroelectrics - with discrete features of {approx}20nm and below. Significant challenges remain before such techniques will be capable of fabricating fully integrated NVRAM devices, but the tools developed for this effort are already finding broader use. This report introduces the nanopatterned NVRAM device concept as a mechanism for motivating the subsequent studies, but the bulk of the document will focus on the platform and technology development.
Mikko Haataja; László Gránásy; Hartmut Löwen
2010-01-01
Herein we provide a brief summary of the background, events and results\\/outcome of the CECAM workshop 'Classical density functional theory methods in soft and hard matter held in Lausanne between October 21 and October 23 2009, which brought together two largely separately working communities, both of whom employ classical density functional techniques: the soft-matter community and the theoretical materials science
A linear programming algorithm to test for jamming in hard-sphere packings
Aleksandar Donev; Salvatore Torquato; Frank H. Stillinger; Robert Connelly
2004-01-01
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
Diffusion in concentrated micellar and hard sphere solutions S. Walrand, L. Belloni and M. Drifford
Boyer, Edmond
of the mutual diffusion coefficient Dm at large volume fraction arises from the many-body hydrodynamic volume fraction 03A6 the hydrodynamic interactions are essentially dominated by uncharged hard. On the other hand, the hydrodynamic interactions are much more difficult to account for, except for dilute
Atsushi Mori; Yoshihisa Suzuki; Shin-ichiro Yanagiya; Tsutomu Sawada; Kensaku Ito
2007-05-13
Disappearance of a stacking fault in the hard-sphere crystal under gravity, such as reported by Zhu et al. [Nature 387 (1997) 883], has successfully been demonstrated by Monte Carlo simulations. We previously found that a less ordered (or defective) crystal formed above a bottom ordered crystal under stepwise controlled gravity [Mori et al. J. Chem. Phys. 124 (2006) 174507]. A defect in the upper defective region has been identified with a stacking fault for the (001) growth. We have looked at the shrinking of a stacking fault mediated by the motion of the Shockley partial dislocation; the Shockley partial dislocation terminating the lower end of the stacking fault glides. In addition, the presence of crystal strain, which cooperates with gravity to reduce stacking faults, has been observed.
NASA Astrophysics Data System (ADS)
Li, Da; Xu, Hong
2015-10-01
The bulk modulus of hard sphere solids has been computed directly by constant pressure Monte-Carlo simulations, using the histogram of the volume fluctuations. In considering first the one-component system, we show that the method is accurate in a large range of pressures, including high-pressure regime. The method is then applied to a polydisperse solid with relatively low polydispersity index. For illustrative purpose, we took a three-component mixture with symmetric size-distribution, and we studied the solid phase (fcc crystal) of this system. Our results show that the equation of state is very sensitive to the polydispersity. Furthermore, in the high-pressure region, where no (accurate) analytical fit for the equation of state exists, our simulations are able to predict the bulk modulus of such systems.
NASA Astrophysics Data System (ADS)
Zhou, Alice; O'Hern, Corey; Regan, Lynne
2013-03-01
We seek to dramatically improve computational protein design using minimal models that include only the dominant physical interactions. By modeling proteins with hard-sphere interactions and stereochemical constraints, we are able to explain the side-chain dihedral angle distributions for Leu, Ile, and other hydrophobic residues that are observed in protein crystal structures. We also consider inter-residue interactions on the distribution of side-chain dihedral angles for residues in the hydrophobic core of T4 lysozyme. We calculate the energetic and entropic contributions to the free energy differences between wildtype T4 lysozyme and several mutants involving Leu to Ala substitutions. We find a strong correlation between the entropy difference and the decrease in the melting temperature of the mutatants. These results emphasize that considering both entropy and enthalpy is crucial for obtaining a quantitative understanding of protein stability. We seek to dramatically improve computational protein design using minimal models that include only the dominant physical interactions. By modeling proteins with hard-sphere interactions and stereochemical constraints, we are able to explain the side-chain dihedral angle distributions for Leu, Ile, and other hydrophobic residues that are observed in protein crystal structures. We also consider inter-residue interactions on the distribution of side-chain dihedral angles for residues in the hydrophobic core of T4 lysozyme. We calculate the energetic and entropic contributions to the free energy differences between wildtype T4 lysozyme and several mutants involving Leu to Ala substitutions. We find a strong correlation between the entropy difference and the decrease in the melting temperature of the mutatants. These results emphasize that considering both entropy and enthalpy is crucial for obtaining a quantitative understanding of protein stability. NSF DMR-1006537 and PHY-1019147, the Raymond and Beverly Sackler Institute for Biological, Physical and Engineering Sciences, and Howard Hughes Medical Institute International Research Fellowship
Largo, Julio; Wilding, Nigel B
2006-03-01
We report a Monte Carlo simulation study of the properties of highly asymmetric binary hard-sphere mixtures. This system is treated within an effective fluid approximation in which the large particles interact through a depletion potential [R. Roth, Phys. Rev. E 62 5360 (2000)] designed to capture the effects of a virtual sea of small particles. We generalize this depletion potential to include the effects of explicit size dispersity in the large particles and consider the case in which the particle diameters are distributed according to a Schulz form having a degree of polydispersity 14%. The resulting alteration (with respect to the monodisperse limit) of the metastable fluid-fluid critical point parameters is determined for two values of the ratio of the diameters of the small and large particles: q(triple bond)sigma(s)/(-)sigma(b)=0.1 and q=0.05. We find that the inclusion of polydispersity moves the critical point to lower reservoir volume fractions of the small particles and high volume fractions of the large ones. The estimated critical point parameters are found to be in good agreement with those predicted by a generalized corresponding states argument which provides a link to the known critical adhesion parameter of the adhesive hard-sphere model. Finite-size scaling estimates of the cluster percolation line in the one phase fluid region indicate that inclusion of polydispersity moves the critical point deeper into the percolating regime. This suggests that phase separation is more likely to be preempted by dynamical arrest in polydisperse systems. PMID:16605606
A. Santos; S. B. Yuste; M. Lopez de Haro
2002-07-01
The contact values $g_{ij}(\\sigma_{ij})$ of the radial distribution functions of a $d$-dimensional mixture of (additive) hard spheres are considered. A `universality' assumption is put forward, according to which $g_{ij}(\\sigma_{ij})=G(\\eta, z_{ij})$, where $G$ is a common function for all the mixtures of the same dimensionality, regardless of the number of components, $\\eta$ is the packing fraction of the mixture, and $z_{ij}$ is a dimensionless parameter that depends on the size distribution and the diameters of spheres $i$ and $j$. For $d=3$, this universality assumption holds for the contact values of the Percus--Yevick approximation, the Scaled Particle Theory, and, consequently, the Boublik--Grundke--Henderson--Lee--Levesque approximation. Known exact consistency conditions are used to express $G(\\eta,0)$, $G(\\eta,1)$, and $G(\\eta,2)$ in terms of the radial distribution at contact of the one-component system. Two specific proposals consistent with the above conditions (a quadratic form and a rational form) are made for the $z$-dependence of $G(\\eta,z)$. For one-dimensional systems, the proposals for the contact values reduce to the exact result. Good agreement between the predictions of the proposals and available numerical results is found for $d=2$, 3, 4, and 5.
Washington, A L; Li, X; Schofield, A B; Hong, K; Fitzsimmons, M R; Dalgliesh, R; Pynn, R
2014-05-01
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
Numerical simulations of granular dynamics: I. Hard-sphere discrete element method and tests
NASA Astrophysics Data System (ADS)
Richardson, Derek C.; Walsh, Kevin J.; Murdoch, Naomi; Michel, Patrick
2011-03-01
We present a new particle-based (discrete element) numerical method for the simulation of granular dynamics, with application to motions of particles on small solar system body and planetary surfaces. The method employs the parallel N-body tree code pkdgrav to search for collisions and compute particle trajectories. Collisions are treated as instantaneous point-contact events between rigid spheres. Particle confinement is achieved by combining arbitrary combinations of four provided wall primitives, namely infinite plane, finite disk, infinite cylinder, and finite cylinder, and degenerate cases of these. Various wall movements, including translation, oscillation, and rotation, are supported. We provide full derivations of collision prediction and resolution equations for all geometries and motions. Several tests of the method are described, including a model granular “atmosphere” that achieves correct energy equipartition, and a series of tumbler simulations that show the expected transition from tumbling to centrifuging as a function of rotation rate.
D. Viduna; W. R. Smith
2002-01-01
An exact formula is derived relating the contact value of the solute-solvent radial distribution function for an additive binary hard-sphere (HS) mixture at infinite dilution, g 1 ? 2 ( d 12 ), to the mixture equation of state (EOS) (1 denotes the solvent and 2 denotes the solute). This result can also be considered to be a consistency condition
Sergio Simonella; Herbert Spohn
2015-01-28
Review of From Newton to Boltzmann: Hard Spheres and Short-range Potentials, by Isabelle Gallagher, Laure Saint-Raymond and Benjamin Texier, European Mathematical Society, Z\\"urich, 2014, xi+135 pp., ISBN 978-3- 03719-129-3.
NASA Technical Reports Server (NTRS)
Woo, Myeung-Jouh; Greber, Isaac
1995-01-01
Molecular dynamics simulation is used to study the piston driven shock wave at Mach 1.5, 3, and 10. A shock tube, whose shape is a circular cylinder, is filled with hard sphere molecules having a Maxwellian thermal velocity distribution and zero mean velocity. The piston moves and a shock wave is generated. All collisions are specular, including those between the molecules and the computational boundaries, so that the shock development is entirely causal, with no imposed statistics. The structure of the generated shock is examined in detail, and the wave speed; profiles of density, velocity, and temperature; and shock thickness are determined. The results are compared with published results of other methods, especially the direct simulation Monte-Carlo method. Property profiles are similar to those generated by direct simulation Monte-Carlo method. The shock wave thicknesses are smaller than the direct simulation Monte-Carlo results, but larger than those of the other methods. Simulation of a shock wave, which is one-dimensional, is a severe test of the molecular dynamics method, which is always three-dimensional. A major challenge of the thesis is to examine the capability of the molecular dynamics methods by choosing a difficult task.
The Power of Hard-Sphere Models: Explaining Side-Chain Dihedral Angle Distributions of Thr and Val
Zhou, Alice Qinhua; O'Hern, Corey S.; Regan, Lynne
2012-01-01
The energy functions used to predict protein structures typically include both molecular-mechanics and knowledge-based terms. In contrast, our approach is to develop robust physics- and geometry-based methods. Here, we investigate to what extent simple hard-sphere models can be used to predict side-chain conformations. The distributions of the side-chain dihedral angle ?1 of Val and Thr in proteins of known structure show distinctive features: Val side chains predominantly adopt ?1 = 180°, whereas Thr side chains typically adopt ?1 = 60° and 300° (i.e., ?1 = ±60° or g? and g+ configurations). Several hypotheses have been proposed to explain these differences, including interresidue steric clashes and hydrogen-bonding interactions. In contrast, we show that the observed side-chain dihedral angle distributions for both Val and Thr can be explained using only local steric interactions in a dipeptide mimetic. Our results emphasize the power of simple physical approaches and their importance for future advances in protein engineering and design. PMID:22677388
NASA Astrophysics Data System (ADS)
Icardi, Matteo; Asinari, Pietro; Marchisio, Daniele; Izquierdo, Salvador; Fox, Rodney
2011-11-01
Recently the Quadrature Method of Moments (QMOM) has been extended to solve several kinetic equations, in particular for gas-particle flows and rarefied gases. This method is usually coupled with simplified linear models for particle collisions. In this work QMOM is tested as a closure for the dynamics of high-order moments with a more realistic collision model namely the hard-spheres model in the Homogeneous Isotropic Boltzmann Equation. The behavior of QMOM far away and approaching the equilibrium is studied. Results are compared to other techniques such as the Lattice-Boltzmann (LBM) and the Grad's expansion (GM) methods. Comparison with a more accurate and computationally expensive model, based on the Discrete Velocity Method (DVM), is also carried out. Our results show that QMOM describes very well the evolution when it is far away from equilibrium, without the drawbacks of the GM and LBM or the computational costs of DVM but it is not able to accurately reproduce the equilibrium and the dynamics close to it. Corrections to cure this behavior are proposed and tested.
NASA Astrophysics Data System (ADS)
Icardi, M.; Asinari, P.; Marchisio, D. L.; Izquierdo, S.; Fox, R. O.
2012-08-01
Recently the Quadrature Method of Moments (QMOM) has been extended to solve several kinetic equations, in particular for gas-particle flows and rarefied gases in which the non-equilibrium effects can be important. In this work QMOM is tested as a closure for the dynamics of the Homogeneous Isotropic Boltzmann Equation (HIBE) with a realistic description for particle collisions, namely the hard-sphere model. The behaviour of QMOM far away and approaching the equilibrium is studied. Results are compared to other techniques such as the Grad's moment method (GM) and the off-Lattice Boltzmann Method (oLBM). Comparison with a more accurate and computationally expensive approach, based on the Discrete Velocity Method (DVM), is also carried out. Our results show that QMOM describes very well the evolution when it is far away from equilibrium, without the drawbacks of the GM and oLBM or the computational costs of DVM, but it is not able to accurately reproduce equilibrium and the dynamics close to it. Static and dynamic corrections to cure this behaviour are here proposed and tested.
A. S. de Wijn
2010-03-30
In the study of chaotic behaviour of systems of many hard spheres, Lyapunov exponents of small absolute value exhibit interesting characteristics leading to speculations about connections to non-equilibrium statistical mechanics. Analytical approaches to these exponents so far can be divided into two groups, macroscopically oriented approaches, using kinetic theory or hydrodynamics, and more microscopically oriented random-matrix approaches in quasi-one-dimensional systems. In this paper, I present an approach using random matrices and weak disorder expansion in an arbitrary number of dimensions. Correlations between subsequent collisions of a particle are taken into account. It is shown that the results are identical to those of a previous approach based on an extended Enskog-equation. I conclude that each approach has its merits, and provides different insights into the approximations made, which include the Sto{\\ss}zahlansatz, the continuum limit, and the long-wavelength approximation. The comparison also gives insight into possible connections between Lyapunov exponents and fluctuations.
Kinetic Theory of Response Functions for the Hard Sphere Granular Fluid
Aparna Baskaran; James W. Dufty; J. Javier Brey
2007-08-05
The response functions for small spatial perturbations of a homogeneous granular fluid have been described recently. In appropriate dimensionless variables, they have the form of stationary state time correlation functions. Here, these functions are expressed in terms of reduced single particle functions that are expected to obey a linear kinetic equation. The functional assumption required for such a kinetic equation, and a Markov approximation for its implementation are discussed. If, in addition, static velocity correlations are neglected, a granular fluid version of the linearized Enskog kinetic theory is obtained. The derivation makes no a priori limitation on the density, space and time scale, nor degree of inelasticity. As an illustration, recently derived Helfand and Green-Kubo expressions for the Navier-Stokes order transport coefficients are evaluated with this kinetic theory. The results are in agreement with those obtained from the Chapman-Enskog solution to the nonlinear Enskog kinetic equation.
The equilibrium states of A 1- x B 1+ x binary alloys in the hard-sphere and pair-binding model
NASA Astrophysics Data System (ADS)
Kistanov, A. A.; Iskandarov, A. M.; Dmitriev, S. V.
2012-03-01
The equilibrium ordering states of A 1- x B 1+ x alloys are investigated analytically and by computer simulation with the hard-sphere and pair-binding model. The alloy energies are calculated for the case where an excess of the B component forms a solid solution or precipitates as pure phase particles. Criteria for pair-binding energies are obtained that define the type of the resulting alloy. The analytical results are presented for an alloy of arbitrary dimensionality and for any number of coordination spheres involved in interatomic interactions. Illustrating examples are given for B2 and L10 superstructures and for a two-dimensional square lattice in view of the atomic interaction in the first two coordination spheres.
Yu. T. Pavlyukhin
2007-01-01
A liquid with the interaction potential of hard spheres plus a square-well is analyzed using the Monte-Carlo technique. Numerical\\u000a results for the perturbation theory series over a square-well potential are obtained in the form of the Barker and Henderson\\u000a discrete representation. Approximating expressions for the correction to a liquid radial distribution function in the second\\u000a order of perturbation theory are
NASA Astrophysics Data System (ADS)
Rader, D. J.; Gallis, M. A.; Torczynski, J. R.; Wagner, W.
2006-07-01
The convergence behavior of the direct simulation Monte Carlo (DSMC) method is systematically investigated for near-continuum, one-dimensional Fourier flow. An argon-like, hard-sphere gas is confined between two parallel, fully accommodating, motionless walls of unequal temperature. The simulations are performed using four variations based on Bird's DSMC algorithm that differ in the ordering of the move, collide, and sample operations. The primary convergence metric studied is the ratio of the DSMC-calculated bulk thermal conductivity to the infinite-approximation Chapman-Enskog (CE) theoretical value, although temperature and heat flux are also considered. Ensemble, temporal, and spatial averaging are used to reduce statistical errors to levels that are small compared to the discretization errors from the time step (?t), the cell size (?x), and the number of computational particles per cell (Nc). The errors from these three parameters are determined using over 700 individual cases selected from the ranges 0.05
Co-pelletization of sewage sludge and biomass: the density and hardness of pellet.
Jiang, Longbo; Liang, Jie; Yuan, Xingzhong; Li, Hui; Li, Changzhu; Xiao, Zhihua; Huang, Huajun; Wang, Hou; Zeng, Guangming
2014-08-01
In the present study, the effects of process parameters on pellet properties were investigated for the co-pelletization of sludge and biomass materials. The relaxed pellet density and Meyer hardness of pellets were identified. Scanning electron microscopy, FT-IR spectra and chemical analysis were conducted to investigate the mechanisms of inter-particular adhesion bonding. Thermogravimetric analysis was applied to investigate the combustion characteristics. Results showed that the pellet density was increased with the parameters increasing, such as pressure, sludge ratio and temperature. High hardness pellets could be obtained at low pressure, temperature and biomass size. The optimal moisture content for co-pelletization was 10-15%. Moreover, the addition of sludge can reduce the diversity of pellet hardness caused by the heterogeneity of biomass. Increasing ratio of sludge in the pellet would slow down the release of volatile. Synergistic effects of protein and lignin can be the mechanism in the co-pelletization of sludge and biomass. PMID:24935004
Drude-type conductivity of charged sphere colloidal crystals: Density and temperature dependence
NASA Astrophysics Data System (ADS)
Medebach, Martin; Jordán, Raquel Chuliá; Reiber, Holger; Schöpe, Hans-Joachim; Biehl, Ralf; Evers, Martin; Hessinger, Dirk; Olah, Julianna; Palberg, Thomas; Schönberger, Ernest; Wette, Patrick
2005-09-01
We report on extensive measurements in the low-frequency limit of the ac conductivity of colloidal fluids and crystals formed from charged colloidal spheres suspended in de-ionized water. Temperature was varied in a range of 5°Cdensity n between 0.2 and 25?m-3 for the larger, respectively, 2.75 and 210?m-3 for the smaller of two investigated species. At fixed ? the conductivity increased linearly with increasing n without any significant change at the fluid-solid phase boundary. At fixed n it increased with increasing ? and the increase was more pronounced for larger n. Lacking a rigorous electrohydrodynamic treatment for counterion-dominated systems we describe our data with a simple model relating to Drude's theory of metal conductivity. The key parameter is an effectively transported particle charge or valence Z*. All temperature dependencies other than that of Z* were taken from literature. Within experimental resolution Z* was found to be independent of n irrespective of the suspension structure. Interestingly, Z* decreases with temperature in near quantitative agreement with numerical calculations.
Drude-type conductivity of charged sphere colloidal crystals: density and temperature dependence.
Medebach, Martin; Jordán, Raquel Chuliá; Reiber, Holger; Schöpe, Hans-Joachim; Biehl, Ralf; Evers, Martin; Hessinger, Dirk; Olah, Julianna; Palberg, Thomas; Schönberger, Ernest; Wette, Patrick
2005-09-01
We report on extensive measurements in the low-frequency limit of the ac conductivity of colloidal fluids and crystals formed from charged colloidal spheres suspended in de-ionized water. Temperature was varied in a range of 5 degrees C < Theta < 35 degrees C and the particle number density n between 0.2 and 25 microm(-3) for the larger, respectively, 2.75 and 210 microm(-3) for the smaller of two investigated species. At fixed Theta the conductivity increased linearly with increasing n without any significant change at the fluid-solid phase boundary. At fixed n it increased with increasing Theta and the increase was more pronounced for larger n. Lacking a rigorous electrohydrodynamic treatment for counterion-dominated systems we describe our data with a simple model relating to Drude's theory of metal conductivity. The key parameter is an effectively transported particle charge or valence Z(*). All temperature dependencies other than that of Z(*) were taken from literature. Within experimental resolution Z(*) was found to be independent of n irrespective of the suspension structure. Interestingly, Z(*) decreases with temperature in near quantitative agreement with numerical calculations. PMID:16178620
Gaygadzhiev, Zafir; Corredig, Milena; Alexander, Marcela
2008-04-15
Understanding the underlying processes that govern interparticle interactions in colloidal systems is fundamental to predicting changes in their bulk properties. In this paper we discuss the colloidal behavior of casein micelles and protein-stabilized fat globules individually and in a mixture. The colloidal interactions were observed by transmission diffusing wave spectroscopy. The turbidity parameter, l*, and the diffusion coefficients of the samples studied were measured experimentally and compared to the theoretically calculated parameters for a hard-sphere system. The light scattering properties of casein micelles (volume fraction phi = 0.1-0.2) dispersed in milk permeate showed no deviation from the theoretically predicted model. Whey protein isolate (WPI)-stabilized emulsions (phi = 0.025-0.1) prepared either in milk permeate or in 5 mM imidazole buffer at pH 6.8 showed a behavior identical to that of the hard-sphere model. Similarly to the WPI-stabilized fat globules, the sodium caseinate (NaCas)-stabilized emulsions (phi = 0.025-0.1) prepared in milk permeate also showed resemblance to the theory. In contrast, NaCas-stabilized emulsions prepared in 5 mM imidazole buffer exhibited some discrepancy from the theoretically calculated parameters. The deviation from theory is attributed to the enhanced steric stabilization properties of these droplets in a low ionic strength environment. When recombined milks made from concentrated milk and WPI- and NaCas-stabilized droplets prepared in permeate (phi = 0.125-0.2) were studied, the experimental data showed a significant deviation from the theoretical behavior of a hard-sphere model due to mixing of two different species. PMID:18324850
Steel and titanium hollow sphere foams
Hurysz, K.M.; Clark, J.L.; Nagel, A.R.; Lee, K.J.; Cochran, J.K.; Sanders, T.H. Jr. [Georgia Inst. of Tech., Atlanta, GA (United States); Hardwicke, C.U. [General Electric Corp., Schenectady, NY (United States). Physical Metallurgy Lab.
1998-12-31
Metal hollow sphere foams are fabricated by bonding millimeter sized metal alloy hollow spheres at points of contact. The spheres are formed as powder shells from slurries. For stainless steel spheres, the starting powder is a mixture of iron and chromium oxide. Thermal treatment in hydrogen reduces the oxides to Fe/Cr alloys with less than 2% porosity in sphere walls. The nominal composition is close to that of 405 stainless. Carburization in CO/CO{sub 2} atmosphere followed by heat treatment produces foams of either 410 or 420 type stainless steels depending on carbon content. Compressive stress-strain behavior was measured on point contact bonded stainless foams both before and after carburization. Hardness measurements on steel sphere walls were used to estimate the yield strength. Relative strengths of the foams were positioned between open and closed cell models. This was encouraging because bonding in the foams was less than optimum and the hollow sphere walls contained defects. As processing improves, strengths should increase. To produce titanium alloy spheres, the starting powder is titanium alloy hydride. Thermal treatment in an inert atmosphere decomposes the hydride and sinters the titanium powder in the sphere walls to greater than 96% relative density. Both titanium and Ti-6V-4V spheres and foams have been produced. Oxygen contents are a concern for titanium compositions and processing is being altered to reduce oxygen levels to increase ductility.
NASA Technical Reports Server (NTRS)
Lubken, F.-J.; Hillert, W.; Lehmacher, G.; Von Zahn, U.; Bittner, M.; Offermann, D.; Schmidlin, F. J.; Hauchecorne, A.; Mourier, M.; Czechowsky, P.
1994-01-01
During the course of the DYnamics Adapted Network for the Atmosphere (DYANA) campaign in early 1990, various techniques to measure densities and temperatures from the ground up to the lower thermosphere were employed. Some of these measurements were performed near simultaneously (maximum allowed time difference: 1 h) and at the same location, and therefore offered the unique chance of intercomparison of different techniques. In this study, we will report on intercomparisons of data from ground-based instruments (Rayleigh- and sodium-lidar), balloon-borne methods (datasondes and radiosondes) and rocket-borne techniques (falling spheres and ionization gauges). The main result is that there is good agreement between the various measurements when considering the error bars. Only occasionally did we notice small but systematic differences (e.g. for the datasondes above 65 km). The most extensive intercomparison was possible between the Rayleigh lidar and the falling sphere technique, both employed in Biscarrosse (44 deg N, 1 deg W). Concerning densities, excellent agreement was found below 63 km: the mean of the deviations is less than 1% and the root mean square (RMS) is approximately 3%. Systematic differences of the order of 5% were noticed around 67 km and above 80 km. The former can be accounted for by an instrumental effect of the falling sphere (Ma = 1 transition; Ma = Mach number), whereas the latter is tentatively explained by the presence of Mie scatterers in the upper mesosphere. Concerning temperatures, the agreement is excellent between 35 and 65 km: the mean of the deviations is less than +/- 3 K and the variability is +/- 5 K. The two systematic density differences mentioned above also affect the temperatures: between 65 and 80 km, the Rayleigh lidar temperatures are systematically lower than the falling sphere values by approximately 5 K.
Howard, David M; Kearfott, Kimberlee J; Wilderman, Scott J; Dewaraja, Yuni K
2011-10-01
High computational requirements restrict the use of Monte Carlo algorithms for dose estimation in a clinical setting, despite the fact that they are considered more accurate than traditional methods. The goal of this study was to compare mean tumor absorbed dose estimates using the unit density sphere model incorporated in OLINDA with previously reported dose estimates from Monte Carlo simulations using the dose planning method (DPMMC) particle transport algorithm. The dataset (57 tumors, 19 lymphoma patients who underwent SPECT/CT imaging during I-131 radioimmunotherapy) included tumors of varying size, shape, and contrast. OLINDA calculations were first carried out using the baseline tumor volume and residence time from SPECT/CT imaging during 6 days post-tracer and 8 days post-therapy. Next, the OLINDA calculation was split over multiple time periods and summed to get the total dose, which accounted for the changes in tumor size. Results from the second calculation were compared with results determined by coupling SPECT/CT images with DPM Monte Carlo algorithms. Results from the OLINDA calculation accounting for changes in tumor size were almost always higher (median 22%, range -1%-68%) than the results from OLINDA using the baseline tumor volume because of tumor shrinkage. There was good agreement (median -5%, range -13%-2%) between the OLINDA results and the self-dose component from Monte Carlo calculations, indicating that tumor shape effects are a minor source of error when using the sphere model. However, because the sphere model ignores cross-irradiation, the OLINDA calculation significantly underestimated (median 14%, range 2%-31%) the total tumor absorbed dose compared with Monte Carlo. These results show that when the quantity of interest is the mean tumor absorbed dose, the unit density sphere model is a practical alternative to Monte Carlo for some applications. For applications requiring higher accuracy, computer-intensive Monte Carlo calculation is needed. PMID:21939358
Howard, David M.; Kearfott, Kimberlee J.; Wilderman, Scott J.
2011-01-01
Abstract High computational requirements restrict the use of Monte Carlo algorithms for dose estimation in a clinical setting, despite the fact that they are considered more accurate than traditional methods. The goal of this study was to compare mean tumor absorbed dose estimates using the unit density sphere model incorporated in OLINDA with previously reported dose estimates from Monte Carlo simulations using the dose planning method (DPMMC) particle transport algorithm. The dataset (57 tumors, 19 lymphoma patients who underwent SPECT/CT imaging during I-131 radioimmunotherapy) included tumors of varying size, shape, and contrast. OLINDA calculations were first carried out using the baseline tumor volume and residence time from SPECT/CT imaging during 6 days post-tracer and 8 days post-therapy. Next, the OLINDA calculation was split over multiple time periods and summed to get the total dose, which accounted for the changes in tumor size. Results from the second calculation were compared with results determined by coupling SPECT/CT images with DPM Monte Carlo algorithms. Results from the OLINDA calculation accounting for changes in tumor size were almost always higher (median 22%, range ?1%–68%) than the results from OLINDA using the baseline tumor volume because of tumor shrinkage. There was good agreement (median ?5%, range ?13%–2%) between the OLINDA results and the self-dose component from Monte Carlo calculations, indicating that tumor shape effects are a minor source of error when using the sphere model. However, because the sphere model ignores cross-irradiation, the OLINDA calculation significantly underestimated (median 14%, range 2%–31%) the total tumor absorbed dose compared with Monte Carlo. These results show that when the quantity of interest is the mean tumor absorbed dose, the unit density sphere model is a practical alternative to Monte Carlo for some applications. For applications requiring higher accuracy, computer-intensive Monte Carlo calculation is needed. PMID:21939358
Large attractive depletion interactions in soft repulsive-sphere binary mixtures
NASA Astrophysics Data System (ADS)
Cinacchi, Giorgio; Martínez-Ratón, Yuri; Mederos, Luis; Navascués, Guillermo; Tani, Alessandro; Velasco, Enrique
2007-12-01
We consider binary mixtures of soft repulsive spherical particles and calculate the depletion interaction between two big spheres mediated by the fluid of small spheres, using different theoretical and simulation methods. The validity of the theoretical approach, a virial expansion in terms of the density of the small spheres, is checked against simulation results. Attention is given to the approach toward the hard-sphere limit and to the effect of density and temperature on the strength of the depletion potential. Our results indicate, surprisingly, that even a modest degree of softness in the pair potential governing the direct interactions between the particles may lead to a significantly more attractive total effective potential for the big spheres than in the hard-sphere case. This might lead to significant differences in phase behavior, structure, and dynamics of a binary mixture of soft repulsive spheres. In particular, a perturbative scheme is applied to predict the phase diagram of an effective system of big spheres interacting via depletion forces for a size ratio of small and big spheres of 0.2; this diagram includes the usual fluid-solid transition but, in the soft-sphere case, the metastable fluid-fluid transition, which is probably absent in hard-sphere mixtures, is close to being stable with respect to direct fluid-solid coexistence. From these results, the interesting possibility arises that, for sufficiently soft repulsive particles, this phase transition could become stable. Possible implications for the phase behavior of real colloidal dispersions are discussed.
Sujin Babu; Jean Christophe Gimel; Taco Nicolai; C. De Michele
2007-11-02
Hard spheres interacting through a square-well potential were simulated using two different methods: Brownian Cluster Dynamics (BCD) and Event Driven Brownian Dynamics (EDBD). The structure of the equilibrium states obtained by both methods were compared and found to be almost the identical. Self diffusion coefficients ($D$) were determined as a function of the interaction strength. The same values were found using BCD or EDBD. Contrary the EDBD, BCD allows one to study the effect of bond rigidity and hydrodynamic interaction within the clusters. When the bonds are flexible the effect of attraction on $D$ is relatively weak compared to systems with rigid bonds. $D$ increases first with increasing attraction strength, and then decreases for stronger interaction. Introducing intra-cluster hydrodynamic interaction weakly increases $D$ for a given interaction strength. Introducing bond rigidity causes a strong decrease of $D$ which no longer shows a maximum as function of the attraction strength.
V. A. Martinez; J. H. J Thijssen; F. Zontone; W. van Megen; G. Bryant
2010-08-12
Intermediate Scattering Functions (ISF's) are measured for colloidal hard sphere systems using both Dynamic Light Scattering (DLS) and X-ray Photon Correlation Spectroscopy (XPCS). We compare the techniques, and discuss the advantages and disadvantages of each. Both techniques agree in the overlapping range of scattering vectors. We investigate the scaling behaviour found by Segre and Pusey [1] but challenged by Lurio et al. [2]. We observe a scaling behaviour over several decades in time but not in the long time regime. Moreover, we do not observe long time diffusive regimes at scattering vectors away from the peak of the structure factor and so question the existence of a long time diffusion coefficients at these scattering vectors.
Atsushi Mori; Yoshihisa Suzuki
2014-06-30
In this paper, we have successfully identified the triangular-shaped defect structures with stacking fault tetrahedra. These structure often appeared in hard-sphere (HS) crystals grown on a square pattern under gravity. We have, so far, performed Monte Carlo simulations of the HS crystals under gravity. Single stacking faults as observed previously in the HS crystals grown on a flat wall were not seen in the case of square template. Instead, defect structures with triangular appearance in $xz$- and $yz$- projections were appreciable. We have identified them by looking layer by layer. Those structures are surrounded by stacking faults along face-centered cubic (fcc) {111}. Also, we see isolated vacancies and vacancy-interstitial pairs, and we have found octahedral structures surrounded by stacking faults along fcc {111}.
NASA Astrophysics Data System (ADS)
Li, Hui-ning; Dai, Hong-xing; He, Hong; Tong Au, Chak
2007-12-01
Using magnesium nitrate as Mg source and regularly packed polymethyl methacrylate (PMMA) spheres were synthesized via a combined strategy of emulsifier-free emulsion polymerization and water floating technique as hard template, we fabricated ordered nanoporous magnesium oxide. The synthesized PMMA and MgO samples were characterized by N2 adsorption-desorption, X-ray diffraction, high-resolution scanning electron microscopy, transmission electron microscopy, and selected area electron diffraction. It was observed that the synthesized PMMA spheres possessed a uniform diameter of approximately 284 nm and were in a highly ordered array, and the MgO generated by using the PMMA-templating method exhibited polycrystallinity with three-dimensionally ordered pores. BET surface area of the synthesized MgO sample is 100.7 m2/g, pore volume is 0.46 cm3/g, wall thickness is 4-24 nm, and pore sizes are in the range of 10-120 nm. Such a 3D high-surface-area nanoporous strongly basic MgO is useful in the applications of catalyst supports and acidic gas adsorbents.
Density-functional study of the nematic-isotropic interface of hard spherocylinders.
Velasco, E; Mederos, L; Sullivan, D E
2002-08-01
The Somoza-Tarazona density-functional theory is applied to the isotropic-nematic interface of hard spherocylinders with length (L)-to-diameter (D) ratios in the range L/D=5-20. Properties such as the density and orientational order-parameter profiles and the variation of interfacial tension with bulk nematic tilt angle agree qualitatively with results of previous studies at larger values of L/D using both computer simulation and the Onsager second-virial approximation. The minimum interfacial tension is obtained at a tilt angle of 90 degrees. For values of L/D approximately 5, it is found that the Onsager approximation predicts a spurious minimum in the interfacial tension at small tilt angles. PMID:12241197
Density-functional study of the nematic-isotropic interface of hard spherocylinders
NASA Astrophysics Data System (ADS)
Velasco, E.; Mederos, L.; Sullivan, D. E.
2002-08-01
The Somoza-Tarazona density-functional theory is applied to the isotropic-nematic interface of hard spherocylinders with length (L)-to-diameter (D) ratios in the range L/D=5-20. Properties such as the density and orientational order-parameter profiles and the variation of interfacial tension with bulk nematic tilt angle agree qualitatively with results of previous studies at larger values of L/D using both computer simulation and the Onsager second-virial approximation. The minimum interfacial tension is obtained at a tilt angle of 90°. For values of L/D~5, it is found that the Onsager approximation predicts a spurious minimum in the interfacial tension at small tilt angles.
NASA Astrophysics Data System (ADS)
Fish, C. S.; Larsen, M. F.; Pfaff, R. F., Jr.; Fullmer, R.; Swenson, C.; Martineau, R.; Sanderson, W.; Pilinski, M.
2014-12-01
We outline the development, test, calibration, and results from the first flights of a new rigid falling sphere probe which were launched in the summers of 2011 and 2013 as part of the NASA Daytime Dynamo sounding rocket campaign at Wallops Island, Virginia. Using highly sensitive accelerometers in conjunction with GPS data, the new rigid falling sphere probe provides a new means to detect the neutral wind, density, and temperature measurements, primarily below approximately 130 km. Initial results will be shown and the accuracy of this technique will be assessed. The maturing of the falling sphere technique provides a possible complement to the well-established vapor trail technique.
NASA Astrophysics Data System (ADS)
Haataja, Mikko; Gránásy, László; Löwen, Hartmut
2010-08-01
Herein we provide a brief summary of the background, events and results/outcome of the CECAM workshop 'Classical density functional theory methods in soft and hard matter held in Lausanne between October 21 and October 23 2009, which brought together two largely separately working communities, both of whom employ classical density functional techniques: the soft-matter community and the theoretical materials science community with interests in phase transformations and evolving microstructures in engineering materials. After outlining the motivation for the workshop, we first provide a brief overview of the articles submitted by the invited speakers for this special issue of Journal of Physics: Condensed Matter, followed by a collection of outstanding problems identified and discussed during the workshop. 1. Introduction Classical density functional theory (DFT) is a theoretical framework, which has been extensively employed in the past to study inhomogeneous complex fluids (CF) [1-4] and freezing transitions for simple fluids, amongst other things. Furthermore, classical DFT has been extended to include dynamics of the density field, thereby opening a new avenue to study phase transformation kinetics in colloidal systems via dynamical DFT (DDFT) [5]. While DDFT is highly accurate, the computations are numerically rather demanding, and cannot easily access the mesoscopic temporal and spatial scales where diffusional instabilities lead to complex solidification morphologies. Adaptation of more efficient numerical methods would extend the domain of DDFT towards this regime of particular interest to materials scientists. In recent years, DFT has re-emerged in the form of the so-called 'phase-field crystal' (PFC) method for solid-state systems [6, 7], and it has been successfully employed to study a broad variety of interesting materials phenomena in both atomic and colloidal systems, including elastic and plastic deformations, grain growth, thin film growth, solid-liquid interface properties, glassy dynamics, nucleation and growth, and diffusive phase transformations at the nano- and mesoscales [8-16]. The appealing feature of DDFT (as applied to solid-state systems) is that it automatically incorporates diffusive dynamics with atomic scale spatial resolution, and it naturally incorporates multiple components, elastic strains, dislocations, free surfaces, and multiple crystalline orientations; all of these features are critical in modeling the behavior of solid-state systems. Similarities between the problems of interest to the two communities and the complementary nature of the methods they apply suggest that a direct interaction between them should be highly beneficial for both parties. Here we summarize some of the discussions during a three-day CECAM workshop in Lausanne (21-23 October 2009) which was organized in order to bring together researchers from the complex fluids and materials science communities and to foster the exchange of ideas between these two communities. During the course of the workshop, several open problems relevant to both fields (DFT and PFC) were identified, including developing better microscopically-informed density functionals, incorporating stochastic fluctuations, and accounting for hydrodynamic interactions. The goal of this special issue is to highlight recent progress in DFT and PFC approaches, and discuss key outstanding problems for future work. The rest of this introductory paper is organized as follows. In section 2, we give a brief overview of the current research topics addressed in this special issue. Then, in section 3, we present a collection of outstanding problems, which have been identified as important for further developments of the two fields and intensely debated at the CECAM workshop. Finally, we close the paper with a few concluding remarks. 2. Research topics addressed in this special issue This special issue consists of research papers that cover a broad range of interesting subjects, about a half of which are related to the theoretical materials science community and
NASA Technical Reports Server (NTRS)
Nemeth, Noel
2013-01-01
Models that predict the failure probability of monolithic glass and ceramic components under multiaxial loading have been developed by authors such as Batdorf, Evans, and Matsuo. These "unit-sphere" failure models assume that the strength-controlling flaws are randomly oriented, noninteracting planar microcracks of specified geometry but of variable size. This report develops a formulation to describe the probability density distribution of the orientation of critical strength-controlling flaws that results from an applied load. This distribution is a function of the multiaxial stress state, the shear sensitivity of the flaws, the Weibull modulus, and the strength anisotropy. Examples are provided showing the predicted response on the unit sphere for various stress states for isotropic and transversely isotropic (anisotropic) materials--including the most probable orientation of critical flaws for offset uniaxial loads with strength anisotropy. The author anticipates that this information could be used to determine anisotropic stiffness degradation or anisotropic damage evolution for individual brittle (or quasi-brittle) composite material constituents within finite element or micromechanics-based software
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
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.
NASA Astrophysics Data System (ADS)
Sakhel, Asaad R.; Dubois, Jonathan L.; Sakhel, Roger R.
2010-04-01
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.
NASA Astrophysics Data System (ADS)
Virrueta, Alejandro; Zhou, Alice; O'Hern, Corey; Regan, Lynne
2014-03-01
Molecular dynamics methods have significantly advanced the understanding of protein folding and stability. However, current force-fields cannot accurately calculate and rank the stability of modified or de novo proteins. One possible reason is that current force-fields use knowledge-based corrections that improve dihedral angle sampling, but do not satisfy the stereochemical constraints for amino acids. I propose the use of simple hard-sphere models for amino acids with stereochemical constraints taken from high-resolution protein crystal structures. This model can enable a correct consideration of the entropy of side-chain rotations, and may be sufficient to predict the effects of single residue mutations in the hydrophobic cores of staphylococcal nuclease and T4 lysozyme on stability changes. I will computationally count the total number of allowed side-chain conformations ? and calculate the associated entropy, S = kBln(?) , before and after each mutation. I will then rank the stability of the mutated cores based on my computed entropy changes, and compare my results with structural and thermodynamic data published by the Stites and Matthews groups. If successful, this project will provide a novel framework for the evaluation of entropic protein stabilities, and serve as a possible tool for computational protein design.
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
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.}
Bulk fluid phase behaviour of colloidal platelet-sphere and platelet-polymer mixtures
Daniel de las Heras; Matthias Schmidt
2012-10-09
Using a geometry-based fundamental measure density functional theory, we calculate bulk fluid phase diagrams of colloidal mixtures of vanishingly thin hard circular platelets and hard spheres. We find isotropic-nematic phase separation with strong broadening of the biphasic region upon increasing the pressure. In mixtures with large size ratio of platelet and sphere diameter, there is also demixing between two nematic phases with differing platelet concentrations. We formulate a fundamental-measure density functional for mixtures of colloidal platelets and freely overlapping spheres, which represent ideal polymers, and use it to obtain phase diagrams. We find that for low platelet-polymer size ratio in addition to isotropic-nematic and nematic-nematic phase coexistence, platelet-polymer mixtures also display isotropic-isotropic demixing. In contrast, we do not find isotropic-isotropic demixing in hard core platelet-sphere mixtures for the size ratios considered.
Wang Jianfeng; Li Ran; Xu Tao; Li Yan; Liu Zengqian; Huang Lu; Hua Nengbin; Zhang Tao [Key Laboratory of Aerospace Materials and Performance (Ministry of Education), School of Materials Science and Engineering, Beihang University, Beijing 100191 (China); Xiao Ruijuan [Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Li Gong [Stat Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004 (China); Li Yanchun [BSRF, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100039 (China)
2011-10-10
An incompressible Co{sub 54}Ta{sub 11}B{sub 35} bulk metallic glass (BMG) was investigated using in situ high-pressure synchrotron diffraction and nanoindendation. The elastic constants were deduced from the experiments based on the isotropic model. The Vickers hardness was measured to be 17.1 GPa. The elastic moduli and hardness are the highest values known in BMGs. The theoretically calculated elastic properties by density-functional study were well consistent with experimental measurements. The analysis of charge density and bonding character indicates the covalent character of Co-B and B-B bonds, underlying the unusually high elastic modulus and hardness in this material.
THE FIRST HARD X-RAY POWER SPECTRAL DENSITY FUNCTIONS OF ACTIVE GALACTIC NUCLEUS
Shimizu, T. Taro; Mushotzky, Richard F., E-mail: tshimizu@astro.umd.edu [Department of Astronomy, University of Maryland, College Park, MD 20742 (United States)
2013-06-10
We present results of our power spectral density (PSD) analysis of 30 active galactic nuclei (AGNs) using the 58 month light curves from Swift's Burst Alert Telescope (BAT) in the 14-150 keV band. PSDs were fit using a Monte Carlo based algorithm to take into account windowing effects and measurement error. All but one source were found to be fit very well using an unbroken power law with a slope of {approx} - 1, consistent at low frequencies with previous studies in the 2-10 keV band, with no evidence of a break in the PSD. For five of the highest signal-to-noise ratio sources, we tested the energy dependence of the PSD and found no significant difference in the PSD at different energies. Unlike previous studies of X-ray variability in AGNs, we do not find any significant correlations between the hard X-ray variability and different properties of the AGN including luminosity and black hole mass. The lack of break frequencies and correlations seem to indicate that AGNs are similar to the high state of Galactic black holes.
Dependence of hardness and stiffness on density of Ta{sub 2}O{sub 5} and TiO{sub 2} layers
Baker, S.P. [Max-Planck-Inst. fuer Metallforschung, Stuttgart (Germany); Ottermann, C.R.; Bange, K. [Schott Glaswerke R and D, Mainz (Germany); Laube, M.; Rauch, F. [Univ. Frankfurt (Germany). Inst. fuer Kernphysik
1997-05-01
Highly refractive amorphous TiO{sub 2} and Ta{sub 2}O{sub 5} films with thicknesses between 270 and 514 nm were deposited on fused silica glass substrates by reactive evaporation and reactive ion plating. Density, hardness, and stiffness were investigated as a function of deposition process. The films were examined using Rutherford backscattering spectroscopy and were found to have densities between 72 and 100% of those of the corresponding bulk oxides. Nanoindentation studies indicated a strong correlation between density and both hardness and elastic stiffness of the oxide film materials. Hardness and modulus both varied by more than 40% over this density range.
Brambrink, E; Wei, H G; Barbrel, B; Audebert, P; Benuzzi-Mounaix, A; Boehly, T; Endo, T; Gregory, C D; Kimura, T; Kodama, R; Ozaki, N; Park, H-S; Koenig, M
2009-11-01
We present the application of short-pulse laser-driven hard x rays (>40 keV) for the direct density measurement of iron compressed by a laser-driven shock. By using an on-shot calibration of the spectral absorption, we are able to obtain line densities with 5%-10% precision, although the x-ray source is not monochromatic. We also discuss possibilities for increasing the precision, which would be an improvement for equation of state measurements. PMID:20365083
Large attractive depletion interactions in soft repulsive-sphere binary mixtures.
Cinacchi, Giorgio; Martínez-Ratón, Yuri; Mederos, Luis; Navascués, Guillermo; Tani, Alessandro; Velasco, Enrique
2007-12-01
We consider binary mixtures of soft repulsive spherical particles and calculate the depletion interaction between two big spheres mediated by the fluid of small spheres, using different theoretical and simulation methods. The validity of the theoretical approach, a virial expansion in terms of the density of the small spheres, is checked against simulation results. Attention is given to the approach toward the hard-sphere limit and to the effect of density and temperature on the strength of the depletion potential. Our results indicate, surprisingly, that even a modest degree of softness in the pair potential governing the direct interactions between the particles may lead to a significantly more attractive total effective potential for the big spheres than in the hard-sphere case. This might lead to significant differences in phase behavior, structure, and dynamics of a binary mixture of soft repulsive spheres. In particular, a perturbative scheme is applied to predict the phase diagram of an effective system of big spheres interacting via depletion forces for a size ratio of small and big spheres of 0.2; this diagram includes the usual fluid-solid transition but, in the soft-sphere case, the metastable fluid-fluid transition, which is probably absent in hard-sphere mixtures, is close to being stable with respect to direct fluid-solid coexistence. From these results, the interesting possibility arises that, for sufficiently soft repulsive particles, this phase transition could become stable. Possible implications for the phase behavior of real colloidal dispersions are discussed. PMID:18067358
A Classical Density-Functional Theory for Describing Water Interfaces
Jessica Hughes; Eric Krebs; David Roundy
2012-08-31
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 (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.
Characterization of maximally random jammed sphere packings: Voronoi correlation functions
NASA Astrophysics Data System (ADS)
Klatt, Michael A.; Torquato, Salvatore
2014-11-01
We characterize the structure of maximally random jammed (MRJ) sphere packings by computing the Minkowski functionals (volume, surface area, and integrated mean curvature) of their associated Voronoi cells. The probability distribution functions of these functionals of Voronoi cells in MRJ sphere packings are qualitatively similar to those of an equilibrium hard-sphere liquid and partly even to the uncorrelated Poisson point process, implying that such local statistics are relatively structurally insensitive. This is not surprising because the Minkowski functionals of a single Voronoi cell incorporate only local information and are insensitive to global structural information. To improve upon this, we introduce descriptors that incorporate nonlocal information via the correlation functions of the Minkowski functionals of two cells at a given distance as well as certain cell-cell probability density functions. We evaluate these higher-order functions for our MRJ packings as well as equilibrium hard spheres and the Poisson point process. It is shown that these Minkowski correlation and density functions contain visibly more information than the corresponding standard pair-correlation functions. We find strong anticorrelations in the Voronoi volumes for the hyperuniform MRJ packings, consistent with previous findings for other pair correlations [A. Donev et al., Phys. Rev. Lett. 95, 090604 (2005), 10.1103/PhysRevLett.95.090604], indicating that large-scale volume fluctuations are suppressed by accompanying large Voronoi cells with small cells, and vice versa. In contrast to the aforementioned local Voronoi statistics, the correlation functions of the Voronoi cells qualitatively distinguish the structure of MRJ sphere packings (prototypical glasses) from that of not only the Poisson point process but also the correlated equilibrium hard-sphere liquids. Moreover, while we did not find any perfect icosahedra (the locally densest possible structure in which a central sphere contacts 12 neighbors) in the MRJ packings, a preliminary Voronoi topology analysis indicates the presence of strongly distorted icosahedra.
Characterization of maximally random jammed sphere packings: Voronoi correlation functions
Michael Andreas Klatt; Salvatore Torquato
2015-01-03
We characterize the structure of maximally random jammed (MRJ) sphere packings by computing the Minkowski functionals (volume, surface area, and integrated mean curvature) of their associated Voronoi cells. The probability distribution functions of these functionals of Voronoi cells in MRJ sphere packings are qualitatively similar to those of an equilibrium hard-sphere liquid and partly even to the uncorrelated Poisson point process, implying that such local statistics are relatively structurally insensitive. This is not surprising because the Minkowski functionals of a single Voronoi cell incorporate only local information and are insensitive to global structural information. To improve upon this, we introduce descriptors that incorporate nonlocal information via the correlation functions of the Minkowski functionals of two cells at a given distance as well as certain cell-cell probability density functions. We evaluate these higher-order functions for our MRJ packings as well as equilibrium hard spheres and the Poisson point process. We find strong anticorrelations in the Voronoi volumes for the hyperuniform MRJ packings, consistent with previous findings for other pair correlations [A. Donev et al., Phys. Rev. Lett. 95, 090604 (2005)], indicating that large-scale volume fluctuations are suppressed by accompanying large Voronoi cells with small cells, and vice versa. In contrast to the aforementioned local Voronoi statistics, the correlation functions of the Voronoi cells qualitatively distinguish the structure of MRJ sphere packings (prototypical glasses) from that of the correlated equilibrium hard-sphere liquids. Moreover, while we did not find any perfect icosahedra (the locally densest possible structure in which a central sphere contacts 12 neighbors) in the MRJ packings, a preliminary Voronoi topology analysis indicates the presence of strongly distorted icosahedra.
NASA Technical Reports Server (NTRS)
Wang, Taylor G. (Inventor); Elleman, Daniel D. (Inventor); Lee, Mark C. (Inventor); Kendall, Jr., James M. (Inventor)
1989-01-01
The improved, heterogeneous catalysts are in the form of gas-impervious, hollow, thin-walled spheres (10) suitably formed of a shell (12) of metal such as aluminum having a cavity (14) containing a gas at a pressure greater than atmospheric pressure. The wall material may be, itself, catalytic or the catalyst can be coated onto the sphere as a layer (16), suitably platinum or iron, which may be further coated with a layer (18) of activator or promoter. The density of the spheres (30) can be uniformly controlled to a preselected value within .+-.10 percent of the density of the fluid reactant such that the spheres either remain suspended or slowly fall or rise through the liquid reactant.
NASA Technical Reports Server (NTRS)
Wang, Taylor G. (Inventor); Elleman, Daniel D. (Inventor); Lee, Mark C. (Inventor); Kendall, Jr., James M. (Inventor)
1986-01-01
The improved, heterogeneous catalysts are in the form of gas-impervious, hollow, thin-walled spheres (10) suitably formed of a shell (12) of metal such as aluminum having a cavity (14) containing a gas at a pressure greater than atmospheric pressure. The wall material may be, itself, catalytic or the catalyst can be coated onto the sphere as a layer (16), suitably platinum or iron, which may be further coated with a layer (18) of activator or promoter. The density of the spheres (30) can be uniformly controlled to a preselected value within .+-.10 percent of the density of the fluid reactant such that the spheres either remain suspended or slowly fall or rise through the liquid reactant.
Catalytic, hollow, refractory spheres
NASA Technical Reports Server (NTRS)
Wang, Taylor G. (Inventor); Elleman, Daniel D. (Inventor); Lee, Mark C. (Inventor); Kendall, Jr., James M. (Inventor)
1987-01-01
Improved, heterogeneous, refractory catalysts are in the form of gas-impervious, hollow, thin-walled spheres (10) suitable formed of a shell (12) of refractory such as alumina having a cavity (14) containing a gas at a pressure greater than atmospheric pressure. The wall material may be itself catalytic or a catalytically active material coated onto the sphere as a layer (16), suitably platinum or iron, which may be further coated with a layer (18) of activator or promoter. The density of the spheres (30) can be uniformly controlled to a preselected value within .+-.10 percent of the density of the fluid reactant such that the spheres either remain suspended or slowly fall or rise through the liquid reactant.
Walker, Peter; Purdin, Susan
2004-06-01
This paper tells the story of the initiation and first year of Sphere. It traces the history of how the project was started and its relationship to other major events of that time, principally the multi-donor Rwanda evaluation. The paper describes how the basic structure of the Sphere standards was agreed upon and discusses why some sectors were eventually left out of the standards. Tensions and public disagreements between the agencies that created Sphere are discussed, along with the manner in which the chosen working processes contributed to the successful publication of the Sphere standards. We show how the process of policy formulation, which led up to the publication of the first edition of the Sphere standards, was as dependent upon the ability of the project team to work opportunistically as it was upon the application of agency principles. Finally the paper reflects upon the success of Sphere and lessons that can be learned from this early Sphere process. PMID:15186358
NASA Astrophysics Data System (ADS)
Guo, Yufei; Whitehead, M. A.
1989-03-01
The first through fourth derivatives of the statistical total energy in the generalized exchange local-spin-density-functional (LSD-GX) theory with respect to the occupation number are given, and used to calculate electronegativities, hardnesses, first and second ionization potentials, and electron affinities for some atoms. The effects of the Coulomb correlation and relaxation correction on the calculations of ionization potentials and electron affinities are discussed. Comparing the results with experiment, it is shown that the Gazquez and Ortiz relaxation model in the LSD-GX scheme [Gazquez and Ortiz, J. Chem. Phys. 81, 2741 (1984)] is a powerful method for calculating the first and second ionization potentials of atoms, but not for calculating electron affinities, since correlation is more important than relaxation in the calculation of the electron affinity.
Bulk phase behaviour of binary hard platelet mixtures from density functional theory
Jonathan Phillips; Matthias Schmidt
2010-01-29
We investigate isotropic-isotropic, isotropic-nematic and nematic-nematic phase coexistence in binary mixtures of circular platelets with vanishing thickness, continuous rotational degrees of freedom and radial size ratios $\\lambda$ up to 5. A fundamental measure density functional theory, previously used for the one-component model, is proposed and results are compared against those from Onsager theory as a benchmark. For $\\lambda \\leq 1.7$ the system displays isotropic-nematic phase coexistence with a widening of the biphasic region for increasing values of $\\lambda$. For size ratios $\\lambda \\geq 2$, we find demixing into two nematic states becomes stable and an isotropic-nematic-nematic triple point can occur. Fundamental measure theory gives a smaller isotropic-nematic biphasic region than Onsager theory and locates the transition at lower densities. Furthermore, nematic-nematic demixing occurs over a larger range of compositions at a given value of $\\lambda$ than found in Onsager theory. Both theories predict the same topologies of the phase diagrams. The partial nematic order parameters vary strongly with composition and indicate that the larger particles are more strongly ordered than the smaller particles.
Improved association in a classical density functional theory for water
NASA Astrophysics Data System (ADS)
Krebs, Eric J.; Schulte, Jeff B.; Roundy, David
2014-03-01
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.
Walker, Cassandra K; Ford, Rebecca; Muñoz-Amatriaín, María; Panozzo, Joe F
2013-10-01
Using a barley mapping population, 'Vlamingh' × 'Buloke' (V × B), whole grain analyses were undertaken for physical seed traits and malting quality. Grain density and size were predicted by digital image analysis (DIA), while malt extract and protein content were predicted using near infrared (NIR) analysis. Validation of DIA and NIR algorithms confirmed that data for QTL analysis was highly correlated (R (2) > 0.82), with high RPD values (the ratio of the standard error of prediction to the standard deviation, 2.31-9.06). Endosperm hardness was measured on this mapping population using the single kernel characterisation system. Grain density and endosperm hardness were significantly inter-correlated in all three environments (r > 0.22, P < 0.001); however, other grain components were found to interact with the traits. QTL for these traits were also found on different genomic regions, for example, grain density QTLs were found on chromosomes 2H and 6H, whereas endosperm hardness QTLs were found on 1H, 5H, and 7H. In this study, the majority of the genomic regions associated with grain texture were also coincident with QTLs for grain size, yield, flowering date and/or plant development genes. This study highlights the complexity of genomic regions associated with the variation of endosperm hardness and grain density, and their relationships with grain size traits, agronomic-related traits, and plant development loci. PMID:23884598
Schmidt, Matthias
Bulk phase behavior of binary hard platelet mixtures from density functional theory Jonathan of circular platelets with vanishing thickness, continuous rotational degrees of freedom, and radial size.20.Jj I. INTRODUCTION There is a wide range of colloidal particles with platelet- like shape, including
NSDL National Science Digital Library
2010-12-02
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.
Numerical simulation of a sphere moving down an incline with identical spheres placed equally apart
Ling, Chi-Hai; Jan, Chyan-Deng; Chen, Cheng-lung; Shen, Hsieh Wen
1992-01-01
This paper describes a numerical study of an elastic sphere moving down an incline with a string of identical spheres placed equally apart. Two momentum equations and a moment equation formulated for the moving sphere are solved numerically for the instantaneous velocity of the moving sphere on an incline with different angles of inclination. Input parameters for numerical simulation include the properties of the sphere (the radius, density, Poison's ratio, and Young's Modulus of elasticity), the coefficient of friction between the spheres, and a damping coefficient of the spheres during collision.
Random sphere packing lattices
NASA Astrophysics Data System (ADS)
Kallus, Yoav
2015-03-01
Bravais lattices have always been an important special case of the high-dimensional sphere packing problem, but from the statistical mechanics and random packing perspectives, they have not been studied much until recently. I will discuss the statistical mechanical phenomena exhibited by a system of one sphere under periodic boundary conditions, where the only degrees of freedom are the unit cell parameters. Equilibrium behavior includes a ``crystallization'' transition, but most of the interest comes from studying non-equilibrium behavior: glass transition, random packing, and hysteresis. The random-packed lattices exhibit surprising properties, including a density remarkably higher than amorphous random packing and a quasicontact divergence.
NASA Technical Reports Server (NTRS)
Schmidlin, F. J.; Michel, W. R.
1985-01-01
Analysis of inflatable sphere measurements obtained during the Energy Budget and MAP/WINE campaigns led to questions concerning the precision of the MPS-36 radar used for tracking the spheres; the compatibility of the sphere program with the MPS-36 radar tracking data; and the oversmoothing of derived parameters at high altitudes. Simulations, with winds having sinusoidal vertical wavelengths, were done with the sphere program (HIROBIN) to determine the resolving capability of various filters. It is concluded that given a precision radar and a perfectly performing sphere, the HIROBIN filters can be adjusted to provide small-scale perturbation information to 70 km (i.e., sinusoidal wavelengths of 2 km). It is recommended that the HIROBIN program be modified to enable it to use a variable length filter, that adjusts to fall velocity and accelerations to provide wind data with small perturbations.
NSDL National Science Digital Library
WPSU
2010-04-09
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.
Hard body amphiphiles at a hard wall JOSEPH M. BRADER1y
Ott, Albrecht
Hard body amphiphiles at a hard wall JOSEPH M. BRADER1y , CHRISTIAN VON FERBER2 and MATTHIAS 2003) We investigate the structure of amphiphilic molecules exposed to a substrate that is modelled by a hard wall. Our simple model amphiphiles consist of a hard sphere head group to which a vanishingly thin
NASA Astrophysics Data System (ADS)
Haque, Najmul; Andersen, Jens O.; Mustafa, Munshi G.; Strickland, Michael; Su, Nan
2014-03-01
We present results of a three-loop hard-thermal-loop perturbation theory calculation of the thermodynamical potential of a finite temperature and baryon chemical potential system of quarks and gluons. We compare the resulting pressure and diagonal quark susceptibilities with available lattice data. We find reasonable agreement between our analytic results and lattice data at both zero and finite chemical potential.
Exciting hard spheres P. L. Krapivsky,2
Antal, Tibor
an explosion. Our predictions are verified by molecular dynamics simulations in d=1 and 2. For a particle that move on straight-line constant-velocity trajectories and that are interrupted by elastic collisions Dynamics, Harvard University, Cambridge, Massachusetts 02138, USA 2 Center for Polymer Studies & Department
T. Semba
2001-01-01
This paper proposes a method of designing a multi-rate servo controller for a hard disk drive that operates at a higher sampling frequency than the position error signal. It is desirable to increase the servo performance without increasing the capacity overhead caused by the tracking information on a disk. A zero-interpolator is introduced as an up-sampling scheme to convert the
NSDL National Science Digital Library
Miss Witcher
2011-10-06
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! ...
Kahk, J M; Poll, C G; Oropeza, F E; Ablett, J M; Céolin, D; Rueff, J-P; Agrestini, S; Utsumi, Y; Tsuei, K D; Liao, Y F; Borgatti, F; Panaccione, G; Regoutz, A; Egdell, R G; Morgan, B J; Scanlon, D O; Payne, D J
2014-03-21
The electronic structure of IrO2 has been investigated using hard x-ray photoelectron spectroscopy and density-functional theory. Excellent agreement is observed between theory and experiment. We show that the electronic structure of IrO2 involves crystal field splitting of the iridium 5d orbitals in a distorted octahedral field. The behavior of IrO2 closely follows the theoretical predictions of Goodenough for conductive rutile-structured oxides [J. B. Goodenough, J. Solid State Chem. 3, 490 (1971). PMID:24702416
Generating perfect fluid spheres in general relativity
Boonserm, Petarpa; Visser, Matt; Weinfurtner, Silke [School of Mathematics, Statistics, and Computer Science, Victoria University of Wellington, PO Box 600, Wellington (New Zealand)
2005-06-15
Ever since Karl Schwarzschild's 1916 discovery of the spacetime geometry describing the interior of a particular idealized general relativistic star--a static spherically symmetric blob of fluid with position-independent density--the general relativity community has continued to devote considerable time and energy to understanding the general-relativistic static perfect fluid sphere. Over the last 90 years a tangle of specific perfect fluid spheres has been discovered, with most of these specific examples seemingly independent from each other. To bring some order to this collection, in this article we develop several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. These transformation theorems sometimes lead to unexpected connections between previously known perfect fluid spheres, sometimes lead to new previously unknown perfect fluid spheres, and in general can be used to develop a systematic way of classifying the set of all perfect fluid spheres.
NASA Astrophysics Data System (ADS)
Shoockron, Joseph
1989-06-01
This work deals with the analysis and calculation of the critical angle for the ricochet of a sphere off water. The critical angle is defined as the maximum incidence angle of a sphere over water which enables it to ricochet. This work presents the development and calculation of the forces acting on the sphere during its entry into the water. Since the critical angle is very sensitive to the hydrodynamic forces, the accurate development and calculation of these forces has been emphasized in some previous methods. There is a simple empirical formula for calculation of the critical angle, which is theta(sub c) = 18 deg/square root of zeta, where theta(sub c) is the critical angle and zeta is the ratio between the density of the sphere and the density of the water. Likewise, there are works which give a theoretical basis to the above-mentioned formula. This formula does not depend on the incidence velocity of the sphere or on the sphere radius, these being parameters that affect the critical angle. In this work it is verified that the critical angle depends on these added parameters, in the form of the F(sub r) number, where F(sub r) = V(exp 2)/Rg.
NSDL National Science Digital Library
Mr. Hansen
2010-10-26
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 ...
Prediction of a Structural Transition in the Hard Disk Fluid
Jaroslaw Piasecki; Piotr Szymczak; John J. Kozak
2010-09-16
Starting from the second equilibrium equation in the BBGKY hierarchy under the Kirkwood superposition closure, we implement a new method for studying the asymptotic decay of correlations in the hard disk fluid in the high density regime. From our analysis and complementary numerical studies, we find that exponentially damped oscillations can occur only up to a packing fraction {\\eta}*~0.718, a value which is in substantial agreement with the packing fraction, {\\eta}~0.723, believed to characterize the transition from the ordered solid phase to a dense fluid phase, as inferred from Mak's Monte Carlo simulations [Phys. Rev. E 73, 065104 (2006)]. We next show that the same method of analysis predicts that exponential damping of oscillations in the hard sphere fluid becomes impossible when \\lambda = 4n\\pi {\\sigma}^3 [1 + H(1)]>/- 34.81, where H(1) is the contact value of the correlation function, n is the number density and {\\sigma} is the sphere diameter, in exact agreement with the condition, \\lambda >/- 34.8, first reported in a numerical study of the Kirkwood equation by Kirkwood et al. [J. Chem. Phys. 18, 1040 (1950)]. Finally, we show that our method confirms the absence of any structural transition in hard rods for the entire range of densities below close packing.
Thermodynamics and gelation of dimerizing adhesive spheres
Weist, A.O.; Glandt, E.D. (Department of Chemical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6393 (United States))
1992-09-15
Wertheim's dual density formalism is applied to study the thermodynamics and gelation behavior of dimerizing adhesive spheres. Both the thermodynamic results (critical points and site--site correlation functions) and connectivity results (gelation threshold and site--site connectedness functions) are determined for mixtures of dumbbells and spheres as a function of the fraction {ital x}{sub 1} of spheres forming dumbbells, the bond length, and the degree of adhesiveness.
Enumerating rigid sphere packings
Miranda C. Holmes-Cerfon
2015-05-08
Packing problems, which ask how to arrange a collection of objects in space to meet certain criteria, are important in a great many physical and biological systems, where geometrical arrangements at small scales control behaviour at larger ones. In many systems there is no single, optimal packing that dominates, but rather one must understand the entire set of possible packings. As a step in this direction we enumerate rigid clusters of identical hard spheres for $n\\leq 14$, and clusters with the maximum number of contacts for $n\\leq 19$. A rigid cluster is one that cannot be continuously deformed while maintaining all contacts. This is a nonlinear notion that arises naturally because such clusters are the metastable states when the spheres interact with a short-range potential, as is the case in many nano- or micro-scale systems. We expect these lists are nearly complete, except for a small number of highly singular clusters (linearly floppy but nonlinearly rigid.) The data contains some major geometrical surprises, such as the prevalence of hypostatic clusters: those with less than the $3n-6$ contacts generically necessary for rigidity. We discuss these and several other unusual clusters, whose geometries may shed insight into physical mechanisms, pose mathematical and computational problems, or bring inspiration for designing new materials.
NSDL National Science Digital Library
Mrs. Petersen
2013-10-28
Students will explain the concept of and be able to calculate density based on given volumes and masses. Throughout today's assignment, you will need to calculate density. You can find a density calculator at this site. Make sure that you enter the correct units. For most of the problems, grams and cubic centimeters will lead you to the correct answer: Density Calculator What is Density? Visit the following website to answer questions ...
Berenstein, David; Lashof-Regas, Robin
2015-01-01
We construct various exact analytical solutions of the $SO(3)$ BMN matrix model that correspond to rotating fuzzy spheres and rotating fuzzy tori.These are also solutions of Yang Mills theory compactified on a sphere times time and they are also translationally invariant solutions of the $\\mathcal{N} = 1^*$ field theory with a non-trivial charge density. The solutions we construct have a $\\mathbb{Z}_N$ symmetry, where $N$ is the rank of the matrices. After an appropriate ansatz, we reduce the problem to solving a set of polynomial equations in $2N$ real variables. These equations have a discrete set of solutions for each value of the angular momentum. We study the phase structure of the solutions for various values of $N$. Also the continuum limit where $N\\to \\infty$, where the problem reduces to finding periodic solutions of a set of coupled differential equations. We also study the topology change transition from the sphere to the torus.
David Berenstein; Eric Dzienkowski; Robin Lashof-Regas
2015-06-15
We construct various exact analytical solutions of the $SO(3)$ BMN matrix model that correspond to rotating fuzzy spheres and rotating fuzzy tori.These are also solutions of Yang Mills theory compactified on a sphere times time and they are also translationally invariant solutions of the $\\mathcal{N} = 1^*$ field theory with a non-trivial charge density. The solutions we construct have a $\\mathbb{Z}_N$ symmetry, where $N$ is the rank of the matrices. After an appropriate ansatz, we reduce the problem to solving a set of polynomial equations in $2N$ real variables. These equations have a discrete set of solutions for each value of the angular momentum. We study the phase structure of the solutions for various values of $N$. Also the continuum limit where $N\\to \\infty$, where the problem reduces to finding periodic solutions of a set of coupled differential equations. We also study the topology change transition from the sphere to the torus.
Sound scattering from two concentric fluid spheres
Jared McNew; Roberto Lavarello; William D. O'Brien
2009-01-01
The solution to the problem of plane wave and point source scattering by two concentric fluid spheres is derived. The effect of differences in sound speed, density, and absorption coefficient is taken into account. The scattered field is then found in the limit as the outer sphere becomes an infinitely thin shell and compared to the solution for a single
Specific surface area of overlapping spheres in the presence of obstructions
NASA Astrophysics Data System (ADS)
Jenkins, D. R.
2013-02-01
This study considers the random placement of uniform sized spheres, which may overlap, in the presence of another set of randomly placed (hard) spheres, which do not overlap. The overlapping spheres do not intersect the hard spheres. It is shown that the specific surface area of the collection of overlapping spheres is affected by the hard spheres, such that there is a minimum in the specific surface area as a function of the relative size of the two sets of spheres. The occurrence of the minimum is explained in terms of the break-up of pore connectivity. The configuration can be considered to be a simple model of the structure of a porous composite material. In particular, the overlapping particles represent voids while the hard particles represent fillers. Example materials are pervious concrete, metallurgical coke, ice cream, and polymer composites. We also show how the material properties of such composites are affected by the void structure.
NASA Astrophysics Data System (ADS)
Kahk, J. M.; Poll, C. G.; Oropeza, F. E.; Ablett, J. M.; Céolin, D.; Rueff, J.-P.; Agrestini, S.; Utsumi, Y.; Tsuei, K. D.; Liao, Y. F.; Borgatti, F.; Panaccione, G.; Regoutz, A.; Egdell, R. G.; Morgan, B. J.; Scanlon, D. O.; Payne, D. J.
2014-03-01
The electronic structure of IrO2 has been investigated using hard x-ray photoelectron spectroscopy and density-functional theory. Excellent agreement is observed between theory and experiment. We show that the electronic structure of IrO2 involves crystal field splitting of the iridium 5d orbitals in a distorted octahedral field. The behavior of IrO2 closely follows the theoretical predictions of Goodenough for conductive rutile-structured oxides [J. B. Goodenough, J. Solid State Chem. 3, 490 (1971)]. Strong satellites associated with the core lines are ascribed to final state screening effects. A simple plasmon model for the satellites applicable to many other metallic oxides appears to be not valid for IrO2.
Casimir forces between spheres
James Babington
2009-11-13
We discuss the calculation of Casimir forces between a collection of $N$-dielectric spheres. This is done by evaluating directly the force on a sphere constructed from a stress tensor, rather than an interaction energy. Two and three body forces between the spheres are evaluated for setups of two and three sphere systems respectively. An approximate large-$N$ limit is also obtained for the functional dependence on the number of spheres.
Konishi, Junko; Watari, Fumio; Kawamoto, Chiharu; Sano, Hidehiko
2003-08-15
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
Feng, Gaoming; Liu, Bo; Song, Zhitang; Lv, Shilong; Wu, Liangcai; Feng, Songlin; Chen, Bomy
2009-02-01
Being able to pattern and etch chalcogenide materials in nanometer scale is essential for the integration of high density chalcogenide random access memory. We investigated dry etching methods for the patterning of Ge1Sb2Te4 films in CHF3/O2 gas mixture using reactive-ion etching system. The gas species CHF3/O2 can reach good etched features with smooth sidewall and a taper angle of 86 degrees. The nanosized Ge1Sb2Te4 patterns were defined by electron-beam lithography using hydrogen silsesquioxane as negative type e-beam resist. A hard mask of TiN, to which the selectivity of Ge1Sb2Te4 is as high as 12, was chosen for employing a CHF3/O2 gas mixture for Ge1Sb2Te4 etching. The Ge1Sb2Te4 line with width of 170 nm could be successfully obtained with good profiles and uniformity using these optimized patterning conditions, which could be very helpful for fabricating high density chalcogenide random access memory based on Ge1Sb2Te4. PMID:19441562
Equilibrium and nonequilibrium dynamics of soft sphere fluids.
Ding, Yajun; Mittal, Jeetain
2015-07-14
We use computer simulations to test the freezing-point scaling relationship between equilibrium transport coefficients (self-diffusivity, viscosity) and thermodynamic parameters for soft sphere fluids. The fluid particles interact via the inverse-power potential (IPP), and the particle softness is changed by modifying the exponent of the distance-dependent potential term. In the case of IPP fluids, density and temperature are not independent variables and can be combined to obtain a coupling parameter to define the thermodynamic state of the system. We find that the rescaled coupling parameter, based on its value at the freezing point, can approximately collapse the diffusivity and viscosity data for IPP fluids over a wide range of particle softness. Even though the collapse is far from perfect, the freezing-point scaling relationship provides a convenient and effective way to compare the structure and dynamics of fluid systems with different particle softness. We further show that an alternate scaling relationship based on two-body excess entropy can provide an almost perfect collapse of the diffusivity and viscosity data below the freezing transition. Next, we perform nonequilibrium molecular dynamics simulations to calculate the shear-dependent viscosity and to identify the distinct role of particle softness in underlying structural changes associated with rheological properties. Qualitatively, we find a similar shear-thinning behavior for IPP fluids with different particle softness, though softer particles exhibit stronger shear-thinning tendency. By investigating the distance and angle-dependent pair correlation functions in these systems, we find different structural features in the case of IPP fluids with hard-sphere like and softer particle interactions. Interestingly, shear-thinning in hard-sphere like fluids is accompanied by enhanced translational order, whereas softer fluids exhibit loss of order with shear. Our results provide a systematic evaluation of the role of particle softness in equilibrium and nonequilibrium transport properties and their underlying connection with thermodynamic and structural properties. PMID:26052921
Local thermodynamic mapping for effective liquid density-functional theory
NASA Technical Reports Server (NTRS)
Kyrlidis, Agathagelos; Brown, Robert A.
1992-01-01
The structural-mapping approximation introduced by Lutsko and Baus (1990) in the generalized effective-liquid approximation is extended to include a local thermodynamic mapping based on a spatially dependent effective density for approximating the solid phase in terms of the uniform liquid. This latter approximation, called the local generalized effective-liquid approximation (LGELA) yields excellent predictions for the free energy of hard-sphere solids and for the conditions of coexistence of a hard-sphere fcc solid with a liquid. Moreover, the predicted free energy remains single valued for calculations with more loosely packed crystalline structures, such as the diamond lattice. The spatial dependence of the weighted density makes the LGELA useful in the study of inhomogeneous solids.
NSDL National Science Digital Library
Targeting a middle and high school population, this web page has an introduction to the concept of density. It is an appendix of a larger site called, MathMol (Mathematics and Molecules), designed as an introduction to molecular modeling.
Free energy density functional for adsorption of fluids in nanopores.
Zhou, Shiqi
2010-11-16
A classical free energy density functional, which is isomorphic to a usual effective hard sphere model + mean field approximation for tail contribution, is proposed for treatment of real fluids in inhomogeneous states. In the framework of the classical density functional theory (DFT), the present functional is applied to two representative model fluids, namely, a Lennard-Jones fluid and a hard core attractive Yukawa fluid, subject to influence of various external fields. A comprehensive comparison with simulation results and a detailed analysis show that the present functional holds simultaneously all of the desirable properties inherent in an excellent functional, such as high accuracy, computational simplicity, consistency with a hard wall sum rule, nonrecourse to use of adjustable parameter(s) and weighted densities, reproduction of bulk second-order direct correlation function (DCF) in bulk limit, and applicability to subcritical fluid phenomena. PMID:20954714
Thermodynamic properties and entropy scaling law for diffusivity in soft spheres
NASA Astrophysics Data System (ADS)
Pieprzyk, S.; Heyes, D. M.; Bra?ka, A. C.
2014-07-01
The purely repulsive soft-sphere system, where the interaction potential is inversely proportional to the pair separation raised to the power n, is considered. The Laplace transform technique is used to derive its thermodynamic properties in terms of the potential energy and its density derivative obtained from molecular dynamics simulations. The derived expressions provide an analytic framework with which to explore soft-sphere thermodynamics across the whole softness-density fluid domain. The trends in the isochoric and isobaric heat capacity, thermal expansion coefficient, isothermal and adiabatic bulk moduli, Grüneisen parameter, isothermal pressure, and the Joule-Thomson coefficient as a function of fluid density and potential softness are described using these formulas supplemented by the simulation-derived equation of state. At low densities a minimum in the isobaric heat capacity with density is found, which is a new feature for a purely repulsive pair interaction. The hard-sphere and n =3 limits are obtained, and the low density limit specified analytically for any n is discussed. The softness dependence of calculated quantities indicates freezing criteria based on features of the radial distribution function or derived functions of it are not expected to be universal. A new and accurate formula linking the self-diffusion coefficient to the excess entropy for the entire fluid softness-density domain is proposed, which incorporates the kinetic theory solution for the low density limit and an entropy-dependent function in an exponential form. The thermodynamic properties (or their derivatives), structural quantities, and diffusion coefficient indicate that three regions specified by a convex, concave, and intermediate density dependence can be expected as a function of n, with a narrow transition region within the range 5
Thermodynamic properties and entropy scaling law for diffusivity in soft spheres.
Pieprzyk, S; Heyes, D M; Bra?ka, A C
2014-07-01
The purely repulsive soft-sphere system, where the interaction potential is inversely proportional to the pair separation raised to the power n, is considered. The Laplace transform technique is used to derive its thermodynamic properties in terms of the potential energy and its density derivative obtained from molecular dynamics simulations. The derived expressions provide an analytic framework with which to explore soft-sphere thermodynamics across the whole softness-density fluid domain. The trends in the isochoric and isobaric heat capacity, thermal expansion coefficient, isothermal and adiabatic bulk moduli, Grüneisen parameter, isothermal pressure, and the Joule-Thomson coefficient as a function of fluid density and potential softness are described using these formulas supplemented by the simulation-derived equation of state. At low densities a minimum in the isobaric heat capacity with density is found, which is a new feature for a purely repulsive pair interaction. The hard-sphere and n = 3 limits are obtained, and the low density limit specified analytically for any n is discussed. The softness dependence of calculated quantities indicates freezing criteria based on features of the radial distribution function or derived functions of it are not expected to be universal. A new and accurate formula linking the self-diffusion coefficient to the excess entropy for the entire fluid softness-density domain is proposed, which incorporates the kinetic theory solution for the low density limit and an entropy-dependent function in an exponential form. The thermodynamic properties (or their derivatives), structural quantities, and diffusion coefficient indicate that three regions specified by a convex, concave, and intermediate density dependence can be expected as a function of n, with a narrow transition region within the range 5 < n < 8. PMID:25122250
Banchio, Adolfo J; Nägele, Gerhard
2008-03-14
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. PMID:18345924
Maximum Chemical and Physical Hardness
Ralph G. Pearson
1999-01-01
Density functional theory (DFT) is briefly reviewed, especially concepts such as the electronic chemical potential and the hardness of the electron density function. There is much evidence, and a mathematical proof, that this chemical hardness is a maximum for an equilibrium system. The proof is based on a combination of statistical mechanics, the fluctuation-dissipation theorem, and correlation functions. In MO
Catalytic, hollow, refractory spheres, conversions with them
NASA Technical Reports Server (NTRS)
Wang, Taylor G. (Inventor); Elleman, Daniel D. (Inventor); Lee, Mark C. (Inventor); Kendall, Jr., James M. (Inventor)
1989-01-01
Improved, heterogeneous, refractory catalysts are in the form of gas-impervious, hollow, thin-walled spheres (10) suitable formed of a shell (12) of refractory such as alumina having a cavity (14) containing a gas at a pressure greater than atmospheric pressure. The wall material may be itself catalytic or a catalytically active material coated onto the sphere as a layer (16), suitably platinum or iron, which may be further coated with a layer (18) of activator or promoter. The density of the spheres (30) can be uniformly controlled to a preselected value within .+-.10 percent of the density of the fluid reactant such that the spheres either remain suspended or slowly fall or rise through the liquid reactant.
Phase behaviour of polarizable colloidal hard rods in an external electric field: A simulation study
NASA Astrophysics Data System (ADS)
Troppenz, Thomas; Filion, Laura; van Roij, René; Dijkstra, Marjolein
2014-10-01
We present a double-charge model for the interaction between parallel polarizable hard spherocylinders subject to an external electric field. Using Monte Carlo simulations and free-energy calculations, we predict the phase behaviour for this model as a function of the density and electric field strength, at a fixed length-to-diameter ratio L/D = 5. The resulting phase diagram contains, in addition to the well-known nematic, smectic A, ABC crystal, and columnar phases, a smectic C phase, and a low temperature crystal X phase. We also find a string fluid at low densities and field strengths, resembling results found for dipolar spheres.
Troppenz, Thomas; Filion, Laura; van Roij, René; Dijkstra, Marjolein
2014-10-21
We present a double-charge model for the interaction between parallel polarizable hard spherocylinders subject to an external electric field. Using Monte Carlo simulations and free-energy calculations, we predict the phase behaviour for this model as a function of the density and electric field strength, at a fixed length-to-diameter ratio L/D = 5. The resulting phase diagram contains, in addition to the well-known nematic, smectic A, ABC crystal, and columnar phases, a smectic C phase, and a low temperature crystal X phase. We also find a string fluid at low densities and field strengths, resembling results found for dipolar spheres. PMID:25338909
Ken-ichi Amano; Kota Hashimoto; Ryosuke Sawazumi
2015-05-21
We suggest a transform theory for calculating a density distribution of small colloids around a large colloid from a force curve between the two-large colloids. The main idea (calculation process) is that the force curve between the two-large colloids is converted into the pressure on the surface element of the large colloid. This conversion is different from the celebrated Derjaguin approximation. A numerical matrix calculation is performed in the conversion to calculate it more precisely. Subsequently, the pressure on the surface element is transformed into the density distribution of the small colloids around the large colloid by using a transform theory for surface force apparatus proposed by Amano. In this letter, the whole process of the transformation is explained in detail.
Amano, Ken-ichi; Sawazumi, Ryosuke
2015-01-01
We suggest a transform theory for calculating a density distribution of small colloids around a large colloid from a force curve between the two-large colloids. The main idea (calculation process) is that the force curve between the two-large colloids is converted into the pressure on the surface element of the large colloid. This conversion is different from the celebrated Derjaguin approximation. A numerical matrix calculation is performed in the conversion to calculate it more precisely. Subsequently, the pressure on the surface element is transformed into the density distribution of the small colloids around the large colloid by using a transform theory for surface force apparatus proposed by Amano. In this letter, the whole process of the transformation is explained in detail.
Density functional theory for carbon dioxide crystal
Chang, Yiwen; Mi, Jianguo, E-mail: mijg@mail.buct.edu.cn; Zhong, Chongli [State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029 (China)
2014-05-28
We present a density functional approach to describe the solid?liquid phase transition, interfacial and crystal structure, and properties of polyatomic CO{sub 2}. Unlike previous phase field crystal model or density functional theory, which are derived from the second order direct correlation function, the present density functional approach is based on the fundamental measure theory for hard-sphere repulsion in solid. More importantly, the contributions of enthalpic interactions due to the dispersive attractions and of entropic interactions arising from the molecular architecture are integrated in the density functional model. Using the theoretical model, the predicted liquid and solid densities of CO{sub 2} at equilibrium triple point are in good agreement with the experimental values. Based on the structure of crystal-liquid interfaces in different planes, the corresponding interfacial tensions are predicted. Their respective accuracies need to be tested.
Chaney, A; Stern, A
2015-01-01
We show that fuzzy spheres are solutions of ${\\it Lorentzian}$ IKKT matrix models. The commutative limit of these solutions corresponds to a sphere embedded in Minkowski space. This `sphere' has several novel features. The induced metric does not agree with the standard metric on the sphere, and moreover, it does not have a fixed signature. The curvature computed from the induced metric is not constant, has singularities at fixed latitudes (not corresponding to the poles) and is negative. The fuzzy sphere solutions serve as toy models of closed noncommutative cosmologies where big bang/crunch singularities appear only after taking the commutative limit. Perturbations are made about the solutions, and are shown to yield a scalar field theory on the sphere in the commutative limit. The scalar field can become tachyonic for a range of the parameters of the theory.
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.
Sound scattering from two concentric fluid spheres (L).
McNew, Jared; Lavarello, Roberto; O'Brien, William D
2007-11-01
The solution to the problem of plane wave and point source scattering by two concentric fluid spheres is derived. The effect of differences in sound speed, density, and absorption coefficient is taken into account. The scattered field is then found in the limit as the outer sphere becomes an infinitely thin shell and compared to the solution for a single fluid sphere for verification. A simulation is then performed using the concentric fluid sphere solution as an approximation to the human head and compared to the solution of a single fluid sphere with the properties of either bone or water. The solutions were found to be similar outside of the spheres but differ significantly inside the spheres. PMID:21743603
ERIC Educational Resources Information Center
Szekely, George
2011-01-01
This article describes an art lesson that allows students to set up and collect sphere canvases. Spheres move art away from a rectangular canvas into a dimension that requires new planning and painting. From balls to many other spherical canvases that bounce, roll, float and fly, art experiences are envisioned by students. Even if adults recognize…
B. F. Myers; F. C. Montgomery; R. N. Morris
1993-01-01
The equivalent sphere model, which is widely used in calculating the release of fission gases from nuclear fuel, is idealized. The model is based on the diffusion of fission products in and their escape from a homogeneous sphere of fuel; the fission products are generated at a constant rate and undergo radiodecay. The fuel is assumed to be a set
Jim McGuigan
2005-01-01
Media research that uses the concept of a public sphere in order to measure distortion against its ideal standard of dialogic democracy tends to concentrate upon the cognitive aspects of news and either ignores or disdains affective communications. Jurgen Habermas’s original formulation distinguished between the literary and the political public spheres. While everyday news was a feature of the political
Periodically oscillating plasma sphere
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
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.
Fuel Fabrication for Surrogate Sphere-Pac Rodlet
Del Cul
2005-01-01
Sphere-pac fuel consists of a blend of spheres of two or three different size fractions contained in a fuel rod. The smear density of the sphere-pac fuel column can be adjusted to the values obtained for light-water reactor (LWR) pellets (91-95%) by using three size fractions, and to values typical of the fast-reactor oxide fuel column (â85%) by using two
NASA Astrophysics Data System (ADS)
Koiller, J.; Ehlers, K.
2007-04-01
“Rubber” coated bodies rolling over a surface satisfy a no-twist condition in addition to the no slip condition satisfied by “marble” coated bodies [1]. Rubber rolling has an interesting differential geometric appeal because the geodesic curvatures of the curves on the surfaces at corresponding points are equal. The associated distribution in the 5 dimensional configuration space has 2 3 5 growth (these distributions were first studied by Cartan; he showed that the maximal symmetries occurs for rubber rolling of spheres with 3:1 diameters ratio and materialize the exceptional group G 2). The 2 3 5 nonholonomic geometries are classified in a companion paper [2] via Cartan’s equivalence method [3]. Rubber rolling of a convex body over a sphere defines a generalized Chaplygin system [4 8] with SO(3) symmetry group, total space Q = SO(3) × S 2 and base S 2, that can be reduced to an almost Hamiltonian system in T* S 2 with a non-closed 2-form ?NH. In this paper we present some basic results on the sphere-sphere problem: a dynamically asymmetric but balanced sphere of radius b (unequal moments of inertia I j but with center of gravity at the geometric center), rubber rolling over another sphere of radius a. In this example ?NH is conformally symplectic [9]: the reduced system becomes Hamiltonian after a coordinate dependent change of time. In particular there is an invariant measure, whose density is the determinant of the reduced Legendre transform, to the power p = 1/2( b/a - 1). Using sphero-conical coordinates we verify the result by Borisov and Mamaev [10] that the system is integrable for p = -1/2 (ball over a plane). They have found another integrable case [11] corresponding to p = -3/2 (rolling ball with twice the radius of a fixed internal ball). Strikingly, a different set of sphero-conical coordinates separates the Hamiltonian in this case. No other integrable cases with different I j are known.
MAGNETISM AND EFFECTIVE ELECTROMAGNETIC PARAMETERS FROM DIELECTRIC SPHERES
Mojahedi, Mohammad
MAGNETISM AND EFFECTIVE ELECTROMAGNETIC PARAMETERS FROM DIELECTRIC SPHERES Mark S. Wheeler, J, composition, size, and volume density of the spheres. A fundamental resonant magnetic response is found when in metamaterials has stimulated many studies on how to design particular electromagnetic re- sponses of composite
A Simplified Theory of Liquid-Solid Transitions. III HardCore Transitions
Hazime Mori; Shiro Isa; Hisao Okamoto; Hiroshi Furukawa
1972-01-01
The hard-sphere transition predicted by computer experiments is theoretically studied with the aid of the expandable-lattice theory of liquid-solid transitions developed in previous two papers. The freezing and melting points are thus given in the mean energy approximation by P\\/kT_rho_c = 2.3577, rho_f\\/rho_c = 0.6819, rho_m\\/rho_c = 0.9053, where rho_c is the closest-packed density &surd;{2}\\/r_0^3, r_0 being the core diameter.{
Daphne Klotsa; Kyle A. Baldwin; Richard J. A. Hill; Roger M. Bowley; Michael R. Swift
2015-01-21
We describe experiments and simulations demonstrating the propulsion of a neutrally-buoyant swimmer that consists of a pair of spheres attached by a spring, placed in a vibrating fluid. The vibration of the fluid induces relative motion of the spheres which, for sufficiently large amplitudes, can lead to motion of the center of mass of the two spheres. We find that the swimming speed obtained from both experiment and simulation agree and collapse onto a single curve if plotted as a function of the streaming Reynolds number, suggesting that the propulsion is related to streaming flows. There appears to be a critical onset value of the streaming Reynolds number for swimming to occur. The mechanism for swimming is traced to a jet of fluid generated by the relative motion of the spheres.
Amphiphilic hard body mixtures Matthias Schmidt and Christian von Ferber
Ott, Albrecht
Amphiphilic hard body mixtures Matthias Schmidt and Christian von Ferber Institut fu¨r Theoretische Received 16 June 2001; published 29 October 2001 In order to study ternary amphiphilic mixtures, we and amphiphilic particles, where the hydrophilic head is modeled as a hard sphere and the hydrophobic tail
New free energy density functional and application to core-softened fluid.
Zhou, Shiqi
2010-05-21
A new free energy density functional is advanced for general nonhard sphere potentials characterized by a repulsive core with a singular point at zero separation. The present functional is characterized by several features. (i) It does not involve with dividing the potentials into hard-sphere-like contribution and tail contribution in sharp contrast with usual effective hard sphere model+mean field approximation for tail contribution. (ii) It has no recourse to the use of weighted density and is computationally modest; it also does not resort to an equation of state and/or an excess Helmholtz free energy of bulk fluid over a range of density as input. Consequently, all of input information can be obtained by numerical solution of a bulk Ornstein-Zernike integral equation theory (OZ IET). Correspondingly, despite the use of bulk second-order direct correlation function (DCF) as input, the functional is applicable to the subcritical region. (iii) There is no any adjustable parameter associated with the present functional, and an effective hard sphere diameter entering the functional can be determined self-consistently and analytically once the input information, i.e., the second-order DCF and pressure of the coexistence bulk fluid, are obtained by the OZ IET. The present functional is applied to a core-softened fluid subject to varying external fields, and the density distributions predicted by the present functional are more self-consistent with available simulation results than a previous third-order+second-order perturbation density functional theory. PMID:20499956
Complex Ordering of Soft Spheres in Block Polymer Melts
NASA Astrophysics Data System (ADS)
Lee, Sangwoo; Zhang, Jingwen; Bates, Frank S.
2014-03-01
Hard sphere systems, such as low-z metallic elements and colloids, generally form densely packed crystalline states with BCC, FCC and HCP symmetry. In contrast, a certain self-assembling soft materials including block polymers, surfactants, and dendrimers have the capacity to order into more open crystalline structures. Recently, we have identified five discrete sphere-packing symmetries in poly(styrene- b-isoprene- b-styrene- b-ethylene oxide) (SISO) tetrablock terpolymers: BCC, Frank-Kasper ?-phase, dodecagonal quasicrystal (DQC), Pm 3 n(A15), and non-close-packed hexagonal (sHEX). Some of these packing symmetries have been documented in certain heavy metals and organic dendrimers, and interestingly Landau theory anticipated a similar set of non-close-packed symmetries more than three decades ago. This talk will draw analogies between the ordering of spheres in soft and hard materials. Present address: Rensselaser polytechnic institute, 110 8th st., Tory, NY 12180.
Freezing of parallel hard cubes with rounded edges.
Marechal, Matthieu; Zimmermann, Urs; Löwen, Hartmut
2012-04-14
The freezing transition in a classical three-dimensional system of rounded hard cubes with fixed, equal orientations is studied by computer simulation and fundamental-measure density functional theory. By switching the rounding parameter s from zero to one, one can smoothly interpolate between cubes with sharp edges and hard spheres. The equilibrium phase diagram of rounded parallel hard cubes is computed as a function of their volume fraction and the rounding parameter s. The second order freezing transition known for oriented cubes at s = 0 is found to be persistent up to s = 0.65. The fluid freezes into a simple-cubic crystal which exhibits a large vacancy concentration. Upon a further increase of s, the continuous freezing is replaced by a first-order transition into either a sheared simple cubic lattice or a deformed face-centered cubic lattice with two possible unit cells: body-centered orthorhombic or base-centered monoclinic. In principle, a system of parallel cubes could be realized in experiments on colloids using advanced synthesis techniques and a combination of external fields. PMID:22502532
A heuristic radial distribution function for hard disks
S. Bravo Yuste; A. Santos
1993-01-01
We propose a model radial distribution function for hard disks that is interpolated between the Percus–Yevick distribution functions for hard rods and hard spheres. The model contains a mixing parameter and two scaling parameters, which are determined by imposing self-consistency with an extension to d=2 of the Carnahan–Starling equation of state. Comparison with computer simulation is carried out.
Beatty; R. E. R. L. Norman; K. J. Notz
1979-01-01
Recent interest in proliferation-resistant fuel cycles for light-water reactors has focused attention on spiked plutonium and Â²Â³Â³U-Th fuels, requiring remote refabrication. The gel-sphere-pac process for fabricating metal-clad fuel elements has drawn special attention because it involves fewer steps. Gel-sphere-pac fabrication technology involves two major areas: the preparation of fuel spheres of high density and loading these spheres into rods in
ERIC Educational Resources Information Center
Kolata, Gina
1985-01-01
To determine how hard it is for computers to solve problems, researchers have classified groups of problems (polynomial hierarchy) according to how much time they seem to require for their solutions. A difficult and complex proof is offered which shows that a combinatorial approach (using Boolean circuits) may resolve the problem. (JN)
Self diffusion of reversibly aggregating spheres
Sujin Babu; Jean Christophe Gimel; Taco Nicolai
2007-05-10
Reversible diffusion limited cluster aggregation of hard spheres with rigid bonds was simulated and the self diffusion coefficient was determined for equilibrated systems. The effect of increasing attraction strength was determined for systems at different volume fractions and different interaction ranges. It was found that the slowing down of the diffusion coefficient due to crowding is decoupled from that due to cluster formation. The diffusion coefficient could be calculated from the cluster size distribution and became zero only at infinite attraction strength when permanent gels are formed. It is concluded that so-called attractive glasses are not formed at finite interaction strength.
Sheinberg, Haskell (Los Alamos, NM)
1986-01-01
A composition of matter having a Rockwell A hardness of at least 85 is formed from a precursor mixture comprising between 3 and 10 weight percent boron carbide and the remainder a metal mixture comprising from 70 to 90 percent tungsten or molybdenum, with the remainder of the metal mixture comprising nickel and iron or a mixture thereof. The composition has a relatively low density of between 7 to 14 g/cc. The precursor is preferably hot pressed to yield a composition having greater than 100% of theoretical density.
Sheinberg, H.
1983-07-26
A composition of matter having a Rockwell A hardness of at least 85 is formed from a precursor mixture comprising between 3 and 10 wt % boron carbide and the remainder a metal mixture comprising from 70 to 90% tungsten or molybdenum, with the remainder of the metal mixture comprising nickel and iron or a mixture thereof. The composition has a relatively low density of between 7 and 14 g/cc. The precursor is preferably hot pressed to yield a composition having greater than 100% of theoretical density.
Equation of state and sound velocity of a hadronic gas with a hard-core interaction
NASA Astrophysics Data System (ADS)
Satarov, L. M.; Bugaev, K. A.; Mishustin, I. N.
2015-05-01
Thermodynamic properties of hot and dense hadronic systems with a hard-sphere interaction are calculated in the Boltzmann approximation. Two parametrizations of pressure as a function of density are considered: the first one, used in the excluded-volume model and the second one, suggested earlier by Carnahan and Starling. The results are given for one-component systems containing only nucleons or pions, as well as for chemically equilibrated mixtures of different hadronic species. It is shown that the Carnahan-Starling approach can be used in a much broader range of hadronic densities as compared to the excluded-volume model. In this case the superluminal sound velocities appear only at very high densities, in the region where the deconfinement effects should be already important.
NASA Astrophysics Data System (ADS)
Xia, Xiang-Gen; Zhang, Lei
1996-10-01
In this paper, Malvar wavelets defined on a unit sphere are introduced. They are constructed by using a similar technique of constructing 2D Malvar wavelets, where one dimension (theta) is periodic on (0, 2(pi) ) and the other dimension (phi) is not periodic on (0, (pi) ).
Boles, Michael A; Talapin, Dmitri V
2015-04-01
This work analyzes the role of hydrocarbon ligands in the self-assembly of nanocrystal (NC) superlattices. Typical NCs, composed of an inorganic core of radius R and a layer of capping ligands with length L, can be described as soft spheres with softness parameter L/R. Using particle tracking measurements of transmission electron microscopy images, we find that close-packed NCs, like their hard-sphere counterparts, fill space at approximately 74% density independent of softness. We uncover deformability of the ligand capping layer that leads to variable effective NC size in response to the coordination environment. This effect plays an important role in the packing of particles in binary nanocrystal superlattices (BNSLs). Measurements on BNSLs composed of NCs of varying softness in several coordination geometries indicate that NCs deform to produce dense BNSLs that would otherwise be low-density arrangements if the particles remained spherical. Consequently, rationalizing the mixing of two NC species during BNSL self-assembly need not employ complex energetic interactions. We summarize our analysis in a set of packing rules. These findings contribute to a general understanding of entropic effects during crystallization of deformable objects (e.g., nanoparticles, micelles, globular proteins) that can adapt their shape to the local coordination environment. PMID:25773648
Kinetic Theory and Hydrodynamics for a Low Density Gas
James W. Dufty
2001-09-12
Many features of real granular fluids under rapid flow are exhibited as well by a system of smooth hard spheres with inelastic collisions. For such a system, it is tempting to apply standard methods of kinetic theory and hydrodynamics to calculate properties of interest. The domain of validity for such methods is a priori uncertain due to the inelasticity, but recent systematic studies continue to support the utility of kinetic theory and hydrodynamics as both qualitative and quantitative descriptions for many physical states. The basis for kinetic theory and hydrodynamic descriptions is discussed briefly for the special case of a low density gas.
Characterization of Polymers Covalently Bound to Hard Spheres
NASA Astrophysics Data System (ADS)
Huber, Dale L.; Seery, Thomas A. P.
1997-03-01
We have synthesized poly(hexylisocyanate) with a range of molecular weights, from initiators that are covelently bound to gold nanoparticles. These systems are soluble in a range of organic solvents so that we are able to utilize solution techniques (NMR and dynamic light scattering) to characterize our synthetic products. The particles provide a synthetic testing ground for future preparation of thin films. These heterogeneous, nanoscale materials have been studied in the solid state by TEM, XPS, WAXS and thermal analysis. Isocyanates have been chosen as a model stiff polymer; the effect of crowding at the curved interface between the polymer and the gold nanoparticle on chain configuration will be considered.
Axiomatic foundations of entropic theorems for hard-sphere systems
NASA Astrophysics Data System (ADS)
Tessarotto, Massimo; Cremaschini, Claudio
2015-05-01
Following the recent establishment of an exact kinetic theory describing the statistical behavior of the Boltzmann-Sinai Classical Dynamical System and realized by the Master kinetic equation, in this paper the problem is posed of the construction of related appropriate entropic theorems. The same equation is proved to warrant, in particular, an exact constant H-theorem, referred to here as Master constant H-theorem, which holds for the 1-body ( i.e., kinetic) Boltzmann-Shannon entropy. The relationship with the customary Boltzmann H-theorem holding for the Boltzmann equation and the physical origin of the related phenomenon of macroscopic irreversibility are investigated.
Crystallization of Hard-Sphere Glasses E. Zaccarelli,1
Zaccarelli, Emanuela
of fabricating SWCNT intraconnects at high yield; sharp electrode tips were used as seed catalysts thus) Schematic diagram of our CNT FET. Co was deposited as a catalyst on top of Ti electrode to initiate CNT
NASA Astrophysics Data System (ADS)
Feng, Xuan; Yang, Ling; Liu, Yingliang
2010-11-01
TiO 2 hollow spheres have been prepared by hydrothermal method using carbon spheres as hard templates based on template-directed deposition and calcination in order to remove templates. The morphology and structure of samples were systematically characterized by using various techniques, including XRD, zeta analyzer, SEM, TEM, DRS and FTIR. In this approach, the anatase phase was retained for temperatures up to 900 °C. Moreover, negative charged titania is deposited onto the negative charged surface of carbon spheres, which is proved by nanoparticle size analyzer. Therefore, a possible formation mechanism of TiO 2 hollow spheres was proposed. TiO 2 hollow spheres calcined at 550 °C exhibited the superior photocatalytic activity for the degradation of Rhodamine B, 2.9 times greater than that of Degussa P25. Furthermore, thermal stability of TiO 2 hollow spheres was examined. Fortunately, we found that hollow structures could still be visible distinctly after calcining at 900 °C.
Krogh, M.; Painter, J.; Hansen, C.
1996-10-01
Sphere rendering is an important method for visualizing molecular dynamics data. This paper presents a parallel algorithm that is almost 90 times faster than current graphics workstations. To render extremely large data sets and large images, the algorithm uses the MIMD features of the supercomputers to divide up the data, render independent partial images, and then finally composite the multiple partial images using an optimal method. The algorithm and performance results are presented for the CM-5 and the M.
Superintegrable systems on sphere
A. V. Borisov; I. S. Mamaev
2005-01-01
We consider various generalizations of the Kepler problem to three-dimensional sphere $S^3$, a compact space of constant curvature. These generalizations include, among other things, addition of a spherical analog of the magnetic monopole (the Poincar\\\\'e--Appell system) and addition of a more complicated field, which itself is a generalization of the MICZ-system. The mentioned systems are integrable -- in fact, superintegrable.
Depletion effects in a mixture of hard and attractive colloids.
Lajovic, A; Tomsic, M; Jamnik, A
2009-03-14
Monte Carlo simulation and theory were used to study the potential of mean force (PMF) between a pair of big colloidal (solute) particles suspended in a sea of smaller particles (solvent) interacting via Baxter's sticky hard sphere (SHS) potential. Simulation results were obtained by applying a special simulation technique developed for sampling the hard sphere collision force, while the theoretical predictions were calculated from the analytic solution of the Percus-Yevick/Ornstein-Zernike integral equation for spatial correlations in a two-component mixture at vanishing solute concentration. Both theory and simulation revealed oscillations of the solute-solute PMF with a period equal to the diameter of the solvent molecules. Further, the attractive PMF between solute particles in the SHS fluid decays slower than in a hard sphere solvent. Upon increasing the strength of attraction (stickiness) between the molecules of solvent, these oscillations gradually disappear, the PMF becoming long ranged and attractive at all separations. PMID:19292517
Molecular-Scale Density Oscillations in Water Adjacent to a Mica Surface
Cheng, L.; Fenter, P.; Nagy, K. L.; Schlegel, M. L.; Sturchio, N. C.
2001-10-08
High-resolution specular x-ray reflectivity of the mica(001)-water interface under ambient conditions reveals oscillations in water oxygen density in the surface-normal direction, giving evidence of interfacial water ordering. The spacings between neighboring water layers in the near-surface, strongly oscillatory region are 2.5(2)--2.7(2){angstrom}, approximately the size of the water molecule. The density oscillations extend to about 10{angstrom} above the surface and do not strictly maintain a solvent-size periodicity as that in interfacial liquid metal and hard-sphere molecular liquids. We interpret this oscillatory density profile of the interfacial water as due to the ''hard-wall'' effect of the molecularly smooth mica surface.
NASA Astrophysics Data System (ADS)
Liu, You-Lin; Shi, Cheng-Xiang; Xu, Xue-Yan; Sun, Ping-Chuan; Chen, Tie-Hong
2015-06-01
Using hierarchically mesoporous silica spheres as a hard template and methyl violet as carbon and nitrogen source, nitrogen-doped hierarchically porous carbon spheres (N-HCS) are successfully prepared via a nanocasting method. The nitrogen-doped carbon spheres obtained after carbonization at 1000 °C (N-HCS-1000) exhibit a hierarchically micro-meso-macroporous structure with a relatively high surface area (BET) of 1413 m2 g-1 and a notably large pore volume of 2.96 cm3 g-1. In an oxygen reduction reaction (ORR) in alkaline media, the N-HCS-1000 material exhibits excellent activity with high current density, and its onset potential is notably close to that of the commercial Pt/C catalyst. The efficient catalytic activity of this catalyst could be attributed to the high electrical conductivity of the nitrogen-doped carbon matrix as well as the hierarchically porous framework. This catalyst also exhibits better methanol crossover resistance and higher stability than the commercial Pt/C catalyst.
Random packing of spheres in Menger sponge
NASA Astrophysics Data System (ADS)
Cie?la, Micha?; Barbasz, Jakub
2013-06-01
Random packing of spheres inside fractal collectors of dimension 2 < d < 3 is studied numerically using Random Sequential Adsorption (RSA) algorithm. The paper focuses mainly on the measurement of random packing saturation limit. Additionally, scaling properties of density autocorrelations in the obtained packing are analyzed. The RSA kinetics coefficients are also measured. Obtained results allow to test phenomenological relation between random packing saturation density and collector dimension. Additionally, performed simulations together with previously obtained results confirm that, in general, the known dimensional relations are obeyed by systems having non-integer dimension, at least for d < 3.
Conformally flat anisotropic spheres in general relativity
Herrera, L; Ospina, J F; Fuenmayor, E
2001-01-01
The condition for the vanishing of the Weyl tensor is integrated in the spherically symmetric case. Then, the resulting expression is used to find new, conformally flat, interior solutions to Einstein equations for locally anisotropic fluids. The slow evolution of these models is contrasted with the evolution of models with similar energy density or radial pressure distribution but non-vanishing Weyl tensor, thereby bringing out the different role played by the Weyl tensor, the local anisotropy of pressure and the inhomogeneity of the energy density in the collapse of relativistic spheres.
NASA Astrophysics Data System (ADS)
Leibundgut, B.; Beuzit, J.-L.; Gibson, N.; Girard, J.; Kasper, M.; Kerber, F.; Lundin, L.; Mawet, D.; McClure, M.; Milli, J.; Petr-Gotzens, M.; Siebenmorgen, R.; van den Ancker, M.; Wahhaj, Z.
2015-03-01
Science Verification (SV) for the latest instrument to arrive on Paranal, the high-contrast and spectro-polarimetric extreme adaptive optics instrument SPHERE, is described. The process through which the SV proposals were solicited and evaluated is briefly outlined; the resulting observations took place in December 2014 and February 2015. A wide range of targets was observed, ranging from the Solar System, young stars with planets and discs, circumstellar environments of evolved stars to a galaxy nucleus. Some of the first results are previewed.
Krogh, M.; Hansen, C.; Painter, J. [Los Alamos National Lab., NM (United States); de Verdiere, G.C. [CEA Centre d`Etudes de Limeil, 94 - Villeneuve-Saint-Georges (France)
1995-05-01
Sphere rendering is an important method for visualizing molecular dynamics data. This paper presents a parallel divide-and-conquer algorithm that is almost 90 times faster than current graphics workstations. To render extremely large data sets and large images, the algorithm uses the MIMD features of the supercomputers to divide up the data, render independent partial images, and then finally composite the multiple partial images using an optimal method. The algorithm and performance results are presented for the CM-5 and the T3D.
Magnetic spheres in microwave cavities
NASA Astrophysics Data System (ADS)
Zare Rameshti, Babak; Cao, Yunshan; Bauer, Gerrit E. W.
2015-06-01
We apply Mie scattering theory to study the interaction of magnetic spheres with microwaves in cavities beyond the magnetostatic and rotating wave approximations. We demonstrate that both strong and ultrastrong coupling can be realized for stand alone magnetic spheres made from yttrium iron garnet (YIG), acting as an efficient microwave antenna. The eigenmodes of YIG spheres with radii of the order mm display distinct higher angular momentum character that has been observed in experiments.
DSMC simulation and experimental validation of shock interaction in hypersonic low density flow.
Xiao, Hong; Shang, Yuhe; Wu, Di
2014-01-01
Direct simulation Monte Carlo (DSMC) of shock interaction in hypersonic low density flow is developed. Three collision molecular models, including hard sphere (HS), variable hard sphere (VHS), and variable soft sphere (VSS), are employed in the DSMC study. The simulations of double-cone and Edney's type IV hypersonic shock interactions in low density flow are performed. Comparisons between DSMC and experimental data are conducted. Investigation of the double-cone hypersonic flow shows that three collision molecular models can predict the trend of pressure coefficient and the Stanton number. HS model shows the best agreement between DSMC simulation and experiment among three collision molecular models. Also, it shows that the agreement between DSMC and experiment is generally good for HS and VHS models in Edney's type IV shock interaction. However, it fails in the VSS model. Both double-cone and Edney's type IV shock interaction simulations show that the DSMC errors depend on the Knudsen number and the models employed for intermolecular interaction. With the increase in the Knudsen number, the DSMC error is decreased. The error is the smallest in HS compared with those in the VHS and VSS models. When the Knudsen number is in the level of 10(-4), the DSMC errors, for pressure coefficient, the Stanton number, and the scale of interaction region, are controlled within 10%. PMID:24672360
DSMC Simulation and Experimental Validation of Shock Interaction in Hypersonic Low Density Flow
2014-01-01
Direct simulation Monte Carlo (DSMC) of shock interaction in hypersonic low density flow is developed. Three collision molecular models, including hard sphere (HS), variable hard sphere (VHS), and variable soft sphere (VSS), are employed in the DSMC study. The simulations of double-cone and Edney's type IV hypersonic shock interactions in low density flow are performed. Comparisons between DSMC and experimental data are conducted. Investigation of the double-cone hypersonic flow shows that three collision molecular models can predict the trend of pressure coefficient and the Stanton number. HS model shows the best agreement between DSMC simulation and experiment among three collision molecular models. Also, it shows that the agreement between DSMC and experiment is generally good for HS and VHS models in Edney's type IV shock interaction. However, it fails in the VSS model. Both double-cone and Edney's type IV shock interaction simulations show that the DSMC errors depend on the Knudsen number and the models employed for intermolecular interaction. With the increase in the Knudsen number, the DSMC error is decreased. The error is the smallest in HS compared with those in the VHS and VSS models. When the Knudsen number is in the level of 10?4, the DSMC errors, for pressure coefficient, the Stanton number, and the scale of interaction region, are controlled within 10%. PMID:24672360
Abradable dual-density ceramic turbine seal system
NASA Technical Reports Server (NTRS)
Clingman, D. L.; Schechter, B.; Cross, K. R.; Cavanagh, J. R.
1981-01-01
A plasma sprayed dual density ceramic abradable seal system for direct application to the HPT seal shroud of small gas turbine engines. The system concept is based on the thermal barrier coating and depends upon an additional layer of modified density ceramic material adjacent to the gas flow path to provide the desired abradability. This is achieved by codeposition of inert fillers with yttria stabilized zirconia (YSZ) to interrupt the continuity of the zirconia struture. The investigation of a variety of candidate fillers, with hardness values as low as 2 on Moh's scale, led to the conclusion that solid filler materials in combination with a YSZ matrix, regardless of their hardness values, have a propensity for compacting rather than shearing as originally expected. The observed compaction is accompanied by high energy dissipation in the rub interaction, usually resulting in the adhesive transfer of blade material to the stationary seal member. Two YSZ based coating systems which incorported hollow alumino silicate spheres as density reducing agents were surveyed over the entire range of compositions from 100 percent filler to 100 percent YSZ. Abradability and erosion characteristics were determined, hardness and permeability characterized, and engine experience acquired with several system configurations.
Low Velocity Sphere Impact of a Soda Lime Silicate Glass
Wereszczak, Andrew A [ORNL; Fox, Ethan E [ORNL; Morrissey, Timothy G [ORNL; Vuono, Daniel J [ORNL
2011-10-01
This report summarizes TARDEC-sponsored work at Oak Ridge National Laboratory (ORNL) during the FY11 involving low velocity (< 30 m/s or < 65 mph) ball impact testing of Starphire soda lime silicate glass. The intent was to better understand low velocity impact response in the Starphire for sphere densities that bracketed that of rock. Five sphere materials were used: borosilicate glass, soda-lime silicate glass, steel, silicon nitride, and alumina. A gas gun was fabricated to produce controlled velocity delivery of the spheres against Starphire tile targets. Minimum impact velocities to initiate fracture in the Starphire were measured and interpreted in context to the kinetic energy of impact and the elastic property mismatch between the any of the five sphere-Starphire-target combinations. The primary observations from this low velocity (< 30 m/s or < 65 mph) testing were: (1) Frictional effects contribute to fracture initiation. (2) Spheres with a lower elastic modulus require less force to initiate fracture in the Starphire than spheres with a higher elastic modulus. (3) Contact-induced fracture did not initiate in the Starphire SLS for impact kinetic energies < 150 mJ. Fracture sometimes initiated or kinetic energies between {approx} 150-1100 mJ; however, it tended to occur when lower elastic modulus spheres were impacting it. Contact-induced fracture would always occur for impact energies > 1100 mJ. (4) The force necessary to initiate contact-induced fracture is higher under dynamic or impact conditions than it is under quasi-static indentation conditions. (5) Among the five used sphere materials, silicon nitride was the closest match to 'rock' in terms of both density and (probably) elastic modulus.
RADIATION PROTECTION KEYWORDS: equivalent sphere
Lin, Zi-wei
RADIATION PROTECTION KEYWORDS: equivalent sphere model, space radiation, organ dose IMPROVEMENT OF THE EQUIVALENT SPHERE MODEL FOR SPACE RADIATION ENVIRONMENTS Z. W. LIN East Carolina University, Department Accepted for Publication January 21, 2009 In space radiation calculations it is often useful to calculate
Jason D. Mcewen; Michael P. Hobson; Anthony N. Lasenby
2008-01-01
We derive optimal filters on the sphere in the context of detecting compact objects embedded in a stochastic background process. The matched filter and the scale adaptiv e filter are derived on the sphere in the most general setting, allowing for directional template profiles and filters. The p erfor- mance and relative merits of the two optimal filters are discu
Superintegrable systems on sphere
A. V. Borisov; I. S. Mamaev
2005-04-07
We consider various generalizations of the Kepler problem to three-dimensional sphere $S^3$, a compact space of constant curvature. These generalizations include, among other things, addition of a spherical analog of the magnetic monopole (the Poincar\\'e--Appell system) and addition of a more complicated field, which itself is a generalization of the MICZ-system. The mentioned systems are integrable -- in fact, superintegrable. The latter is due to the vector integral, which is analogous to the Laplace--Runge--Lenz vector. We offer a classification of the motions and consider a trajectory isomorphism between planar and spatial motions. The presented results can be easily extended to Lobachevsky space $L^3$.
Perturbation density functional theory for nonuniform fluid mixture based on Lagrangian theorem
NASA Astrophysics Data System (ADS)
Zhou, Shiqi
2004-02-01
First order direct correlation function (DCF) of non-uniform fluid mixture was expanded around the bulk fluid mixture, the expansion was truncated at the lowest order and made formally exact by making use of functional counterpart of Lagrangian theorem of differential calculus. The concrete procedure involves the specification of the non-uniform component i-component j pair second order DCF by their respective uniform counterpart with appropriate weighted packing fraction and weighted concentration as their arguments. As an example, the truncated expansion was incorporated into the density functional theory (DFT) formalism to predict the density profile of binary hard sphere fluid near a structureless hard wall. Good agreement between theoretical predictions and simulation data demonstrates the reliable accuracy of the present approach.
Casimir Forces in Multi-Sphere Configurations
James Babington; Stefan Scheel
2010-05-06
We calculate the Casimir force on an isolated dielectric sphere in an ensemble of $N$ spheres due to multiple mutual interactions of the collection of spheres. In particular we consider dielectric spheres immersed in some other background dielectric. As an example, the Casimir force between two and three spheres at zero and finite temperature is evaluated. For a very large number of spheres, we consider a large-$N$ scaling limit of the Casimir force.
The nature of the glass and gel transitions in sticky spheres
C. Patrick Royall; Stephen R. Williams; Hajime Tanaka
2014-09-18
Glasses and gels are the two dynamically arrested, disordered states of matter. Despite their importance, their similarities and differences remain elusive, especially at high density. We identify dynamical and structural signatures which distinguish the gel and glass transitions in a colloidal model system of hard and "sticky" spheres. Gelation is induced by crossing the gas-liquid phase-separation line and the resulting rapid densification of the colloid-rich phase leads to a sharp change in dynamics and local structure. Thus, we find that gelation is first-order-like and can occur at much higher densities than previously thought: far from being low-density networks, gels have a clear "thermodynamic" definition which nevertheless leads to a non-equilibrium state with a distinct local structure characteristic of a rapidly quenched glass. In contrast, approaching the glass transition, the dynamics slow continuously accompanied by the emergence of local five-fold symmetric structure. Our findings provide a general thermodynamic, kinetic, and structural basis upon which to distinguish gelation from vitrification.
Medasani, Bharat; Ovanesyan, Zaven; Thomas, Dennis G.; Sushko, Maria L.; Marucho, Marcelo
2014-01-01
In this article, we present a classical density functional theory for electrical double layers of spherical macroions that extends the capabilities of conventional approaches by accounting for electrostatic ion correlations, size asymmetry, and excluded volume effects. The approach is based on a recent approximation introduced by Hansen-Goos and Roth for the hard sphere excess free energy of inhomogeneous fluids [J. Chem. Phys. 124, 154506 (2006); Hansen-Goos and Roth, J. Phys.: Condens. Matter 18, 8413 (2006)]. It accounts for the proper and efficient description of the effects of ionic asymmetry and solvent excluded volume, especially at high ion concentrations and size asymmetry ratios including those observed in experimental studies. Additionally, we utilize a leading functional Taylor expansion approximation of the ion density profiles. In addition, we use the mean spherical approximation for multi-component charged hard sphere fluids to account for the electrostatic ion correlation effects. These approximations are implemented in our theoretical formulation into a suitable decomposition of the excess free energy which plays a key role in capturing the complex interplay between charge correlations and excluded volume effects. We perform Monte Carlo simulations in various scenarios to validate the proposed approach, obtaining a good compromise between accuracy and computational cost. We use the proposed computational approach to study the effects of ion size, ion size asymmetry, and solvent excluded volume on the ion profiles, integrated charge, mean electrostatic potential, and ionic coordination number around spherical macroions in various electrolyte mixtures. Our results show that both solvent hard sphere diameter and density play a dominant role in the distribution of ions around spherical macroions, mainly for experimental water molarity and size values where the counterion distribution is characterized by a tight binding to the macroion, similar to that predicted by the Stern model. PMID:24880304
Benmei, Chen
» BOOKSHELF Hard Disk Drive Servo Systems, 2nd edition by B.M. CHEN, T.H. LEE, K. PENG, and V- widths ever higher as higher frequency disturbances become relevant. THE BOOK Hard Disk Drive Servo I of Hard Disk Drive Servo Systems briefly discusses the history of hard drive control and the disk
Collective excitations in an infinite set of aligned spheres
NASA Astrophysics Data System (ADS)
Aizpurua, J.; Rivacoba, A.; Zabala, N.; García de Abajo, F. J.
1998-05-01
We present here electron energy loss spectra (EELS) calculations for an infinite set of aligned dielectric spheres as a first approximation to calculations in a more complex periodic array with small computer cost. The boundary charge method is analytically developed for such a system with use of local dielectric theory. A convenient distribution of surface charge densities at the spherical interfaces, selfconsistently interacting with each other as well as with the external field created by the incoming electron, can provide a solution of the surface collective modes. Energy loss spectra in the valence range (a few eV) are obtained for trajectories parallel and perpendicular to the axis of the aligned spheres and the nature of the excitations is studied by analysing the charge density distribution induced at the spheres,
The Lorentz forces on an electrically conducting sphere in an alternating magnetic field
Udaya B. Sathuvalli; Yildiz Bayazitoglu
1996-01-01
A method to calculate the Lorentz force on an electrically conducting sphere placed in an arbitrary sinusoidally varying magnetic field is developed. The crux of this method lies in expressing the external magnetic held and the eddy current density in the sphere in terms of a “source function” of the current sources and a “skin depth dependent function”. The general
Marcia M. Szortyka; Maurício Girardi; Vera B. Henriques; Marcia C. Barbosa
2012-05-09
In this paper we investigate the solubility of a hard - sphere gas in a solvent modeled as an associating lattice gas (ALG). The solution phase diagram for solute at 5% is compared with the phase diagram of the original solute free model. Model properties are investigated thr ough Monte Carlo simulations and a cluster approximation. The model solubility is computed via simulations and shown to exhibit a minimum as a function of temperature. The line of minimum solubility (TmS) coincides with the line of maximum density (TMD) for different solvent chemical potentials.
Rebound and jet formation of a fluid-filled sphere
NASA Astrophysics Data System (ADS)
Killian, Taylor W.; Klaus, Robert A.; Truscott, Tadd T.
2012-12-01
This study investigates the impact dynamics of hollow elastic spheres partially filled with fluid. Unlike an empty sphere, the internal fluid mitigates some of the rebound through an impulse driven exchange of energy wherein the fluid forms a jet inside the sphere. Surprisingly, this occurs on the second rebound or when the free surface is initially perturbed. Images gathered through experimentation show that the fluid reacts more quickly to the impact than the sphere, which decouples the two masses (fluid and sphere), imparts energy to the fluid, and removes rebound energy from the sphere. The experimental results are analyzed in terms of acceleration, momentum and an energy method suggesting an optimal fill volume in the neighborhood of 30%. While the characteristics of the fluid (i.e., density, viscosity, etc.) affect the fluid motion (i.e., type and size of jet formation), the rebound characteristics remain similar for a given fluid volume independent of fluid type. Implications of this work are a potential use of similar passive damping systems in sports technology and marine engineering.
NASA Technical Reports Server (NTRS)
Luers, J. K.
1978-01-01
Instrumentation was developed for the high altitude inflatable sphere to measure its skin temperature, acceleration and internal pressure. The sphere without instrumentation has routinely been used over the past 10 years to provide measurements of winds, density, temperature and pressure between 100 Km and 30 Km altitude. With the miniaturized instrumentation package onboard, the system offers the potential for providing meteorological information as well as a better understanding of sphere performance and dynamics during its descent. Of the six launches of instrumented spheres only one provided telemetry data. However, many of the objectives of the program were achieved.
Microscopic investigations of homogeneous nucleation in charged sphere suspensions
Patrick Wette; Hans Joachim Schöpe; Thomas Palberg
2005-01-01
We studied the homogeneous nucleation kinetics of an aqueous suspension of charged colloidal spheres under de-ionized conditions. Samples of equilibrium crystalline structure were shear molten and the metastable melt left to solidify after cessation of shear. At low particle number densities n, corresponding to low metastability of the melt, nucleation was monitored directly via video microscopy. We determined the nucleation
Frontal Impact of Rolling Spheres.
ERIC Educational Resources Information Center
Domenech, A.; Casasus, E.
1991-01-01
A model of the inelastic collision between two spheres rolling along a horizontal track is presented, taking into account the effects of frictional forces at impact. This experiment makes possible direct estimates of the coefficients of restitution and friction. (Author)
Statistical characterization of the forces on spheres in an upflow of air
R. P. Ojha; A. R. Abate; D. J. Durian
2004-11-09
The dynamics of a sphere fluidized in a nearly-levitating upflow of air were previously found to be identical to those of a Brownian particle in a two-dimensional harmonic trap, consistent with a Langevin equation [Ojha {\\it et al.}, Nature {\\bf 427}, 521 (2004)]. The random forcing, the drag, and the trapping potential represent different aspects of the interaction of the sphere with the air flow. In this paper we vary the experimental conditions for a single sphere, and report on how the force terms in the Langevin equation scale with air flow speed, sphere radius, sphere density, and system size. We also report on the effective interaction potential between two spheres in an upflow of air.
Viscosity, entropy and the viscosity to entropy density ratio; how perfect is a nucleonic fluid?
Aram Z. Mekjian
2010-09-29
The viscosity of hadronic matter is studied using a classical evaluation of the scattering angle and a quantum mechanical discussion based on phase shifts from a potential. Semi classical limits of the quantum theory are presented. A hard sphere and an attractive square well potential step are each considered as well as the combined effects of both. The lowest classical value of the viscosity for an attractive potential is shown to be a hard sphere limit. The high wave number-short wavelength limits of the quantum result have scaling laws associated with it for both the viscosity and entropy. These scaling laws are similar to the Fraunhoher diffraction increase for the hard sphere geometric cross section. Specific examples for nuclear collisions are given. The importance of the nuclear tensor force and hard core is mentioned. The viscosity (eta), entropy density (s) and eta/s ratio are calculated for a gas of dilute neutrons in the unitary limit of large scattering length. Away from the unitary limit, the ratio of the interaction radius or the scattering length to the interparticle spacing introduces a variable y besides the fugacity z. The isothermal compressibility is shown to impose important constraints. The results for eta/s are compared to the AdS/CFT string theory minimum of (1/4Pi)hbar/kb to see how close a nucleonic gas is to being a perfect fluid. The eta/s ~1hbar/kb for a neutron gas in its unitary limit. The eta/s 3hbar/kb treating the nuclear scattering as billiard ball collisions. The minimum eta/s for a neutron gas occurs in regions of negative isothermal compressibility and high fugacity where higher virial terms are important. In a neutron-proton system higher virial terms are associated with a liquid-gas phase transition and critical opalescent phenomena.The type of flow-laminar,vortex, turbulent- is investigated.
Image current inclusion in the permeable sphere
D. V. Redzic; S. S. Redzic
2006-01-01
An interesting property of the magnetostatic image theory for a superconducting sphere in the field of a static circular current loop with its axis radial to the sphere is pointed out: the magnetic field outside the superconducting sphere remains unchanged if the superconductor is replaced by a permeable sphere with an embedded current loop which coincides with the image current
Excluded volume effects in compressed polymer brushes: A density functional theory
NASA Astrophysics Data System (ADS)
Chen, Cangyi; Tang, Ping; Qiu, Feng; Shi, An-Chang
2015-03-01
A classical density functional theory (DFT) is applied to investigate the behavior of compressed polymer brushes composed of hard-sphere chains. The excluded volume interactions among the chain segments are explicitly treated. Two compression systems are used to study the behavior of brush-wall and brush-brush interactions. For the brush-brush systems, an obvious interpenetration zone has been observed. The extent of the interpenetration depends strongly on the grafting density. Furthermore, the repulsive force between the brush and wall or between the two brushes has been obtained as a function of the compression distance. Compared to the prediction of the analytic self-consistent field theory, such force increases more rapidly in the brush-wall compression with high polymer grafting densities or at higher compressions. In the brush-brush compression system, the interpenetration between the two compressed brushes creates a "softer" interaction. The influence of hard-sphere solvents on the behavior of compressed brushes is also discussed.
Excluded volume effects in compressed polymer brushes: A density functional theory.
Chen, Cangyi; Tang, Ping; Qiu, Feng; Shi, An-Chang
2015-03-28
A classical density functional theory (DFT) is applied to investigate the behavior of compressed polymer brushes composed of hard-sphere chains. The excluded volume interactions among the chain segments are explicitly treated. Two compression systems are used to study the behavior of brush-wall and brush-brush interactions. For the brush-brush systems, an obvious interpenetration zone has been observed. The extent of the interpenetration depends strongly on the grafting density. Furthermore, the repulsive force between the brush and wall or between the two brushes has been obtained as a function of the compression distance. Compared to the prediction of the analytic self-consistent field theory, such force increases more rapidly in the brush-wall compression with high polymer grafting densities or at higher compressions. In the brush-brush compression system, the interpenetration between the two compressed brushes creates a "softer" interaction. The influence of hard-sphere solvents on the behavior of compressed brushes is also discussed. PMID:25833606
Baryonic sphere: A spherical domain wall carrying baryon number
NASA Astrophysics Data System (ADS)
Gudnason, Sven Bjarke; Nitta, Muneto
2014-01-01
We construct a spherical domain wall which has baryon charge distributed on a sphere of finite radius in a Skyrme model with a sixth-order derivative term and a modified mass term. Its distribution of energy density likewise takes the form of a sphere. In order to localize the domain wall at a finite radius we need a negative coefficient in front of the Skyrme term and a positive coefficient of the sixth order derivative term to stabilize the soliton. Increasing the pion mass pronounces the shell-like structure of the configuration.
Dense sphere packings from optimized correlation functions Adam B. Hopkins and Frank H. Stillinger
Stillinger, Frank
arrangements of a set finite or infinite of nonoverlapping objects in a space of given dimension 13 . Often in three dimensions, / 18 0.7405 and 0.64, the approxi- mate fraction associated with maximally random function defined below of a "random" packing. Random packings of three-dimensional hard spheres have been
Collective diffusion of charged spheres in the presence of hydrodynamic interaction
U. Genz; R. Klein
1991-01-01
The short-time behavior of the scattering intensity, which can be measured by dynamic light scattering, is investigated theoretically. We consider a monodisperse system of charged hard spheres and study the combined effects of electrostatic repulsion and hydrodynamic interactions. The electrostatic repulsion determines the static properties, which are calculated from the thermodynamically consistent Rogers-Young scheme. For comparison, some results obtained within
Chandler, H. [ed.
1999-07-01
This basic book provides a comprehensive overview of hardness testing, including the various methods and equipment used, testing applications, and the selection of testing methods. The revised and updated second edition features expanded information on microhardness testing, specialized hardness tests; and hardness testing standards. Contents include: introduction to hardness testing; brinell testing; rockwell hardness testing; vickers hardness testing; microhardness testing; scleroscope and leeb hardness testing; hardness testing applications; and selection of hardness testing methods.
Wear of hard materials by hard particles
Hawk, Jeffrey A.
2003-10-01
Hard materials, such as WC-Co, boron carbide, titanium diboride and composite carbide made up of Mo2C and WC, have been tested in abrasion and erosion conditions. These hard materials showed negligible wear in abrasion against SiC particles and erosion using Al2O3 particles. The WC-Co materials have the highest wear rate of these hard materials and a very different material removal mechanism. Wear mechanisms for these materials were different for each material with the overall wear rate controlled by binder composition and content and material grain size.
Ferminoic Casimir effect between spheres
Teo, L P
2015-01-01
We consider the Casimir interaction between two spheres corresponding to massless Dirac fields with MIT-bag boundary conditions. Using operator approach, we derive the TGTG-formula for the Casimir interaction energy between the two spheres. A byproduct is the explicit formula for the translation matrix that relates the fermionic spherical waves in different coordinate systems. In the large separation limit, it is found that the order of the Casimir interaction energy is $L^{-5}$, where $L$ is the separation between the centers of the spheres. This order is intermediate between that of two Dirichlet spheres (of order $L^{-3}$) and two Neumann spheres (of order $L^{-7}$). In the small separation limit, we derive analytically the asymptotic expansion of the Casimir interaction energy up to the next-to-leading order term. The leading term agrees with the proximity force approximation. The result for the next-to-leading order term is compared to the corresponding results for scalar fields and electromagnetic field...
Ferminoic Casimir effect between spheres
NASA Astrophysics Data System (ADS)
Teo, L. P.
2015-04-01
We consider the Casimir interaction between two spheres corresponding to massless Dirac fields with MIT-bag boundary conditions. Using operator approach, we derive the TGTG formula for the Casimir interaction energy between the two spheres. A byproduct is the explicit formula for the translation matrix that relates the fermionic spherical waves in different coordinate systems. In the large separation limit, it is found that the order of the Casimir interaction energy is L-5 , where L is the separation between the centers of the spheres. This order is intermediate between that of two Dirichlet spheres (of order L-3 ) and two Neumann spheres (of order L-7 ). In the small separation limit, we derive analytically the asymptotic expansion of the Casimir interaction energy up to the next-to-leading order term. The leading term agrees with the proximity force approximation. The result for the next-to-leading order term is compared to the corresponding results for scalar fields and electromagnetic fields.
Ferminoic Casimir effect between spheres
L. P. Teo
2015-03-27
We consider the Casimir interaction between two spheres corresponding to massless Dirac fields with MIT-bag boundary conditions. Using operator approach, we derive the TGTG-formula for the Casimir interaction energy between the two spheres. A byproduct is the explicit formula for the translation matrix that relates the fermionic spherical waves in different coordinate systems. In the large separation limit, it is found that the order of the Casimir interaction energy is $L^{-5}$, where $L$ is the separation between the centers of the spheres. This order is intermediate between that of two Dirichlet spheres (of order $L^{-3}$) and two Neumann spheres (of order $L^{-7}$). In the small separation limit, we derive analytically the asymptotic expansion of the Casimir interaction energy up to the next-to-leading order term. The leading term agrees with the proximity force approximation. The result for the next-to-leading order term is compared to the corresponding results for scalar fields and electromagnetic fields.
Hyperuniformity of self-assembled soft colloidal spheres
NASA Astrophysics Data System (ADS)
Bretz, Coline
2015-03-01
Hyperuniformity characterizes a state of matter for which density fluctuations vanish on large scales. Hyperuniform materials are of technological importance as they exhibit interesting photonic properties. We have shown that such materials can be obtained by assembling spheres into a disordered jammed 2D- packing. To this end, we use a binary mixture of large and small Poly(NIPAM) particles confined between two cover slips. These soft spheres have been chosen for their temperature-sensitive properties. We can locally increase or decrease the volume fraction occupied by the spheres by finely tuning the temperature. By applying various temperature patterns, we are studying the spatial arrangements of the microgels and characterizing their hyperuniform properties through reconstruction and detection algorithms. CNRS-Rhodia-UPenn UMI 3254, Bristol, PA 19007-3624, USA
Combustion of a Polymer (PMMA) Sphere in Microgravity
NASA Technical Reports Server (NTRS)
Yang, Jiann C.; Hamins, Anthony; Donnelly, Michelle K.
1999-01-01
A series of low gravity, aircraft-based, experiments was conducted to investigate the combustion of supported thermoplastic polymer spheres under varying ambient conditions. The three types of thermoplastic investigated were polymethylmethacrylate (PMMA), polypropylene (PP). and polystyrene (PS). Spheres with diameters ranging from 2 mm to 6.35 mm were tested. The total initial pressure varied from 0.05 MPa to 0. 15 MPa whereas the ambient oxygen concentration varied from 19 % to 30 % (by volume). The ignition system consisted of a pair of retractable energized coils. Two CCD cameras recorded the burning histories of the spheres. The video sequences revealed a number of dynamic events including bubbling and sputtering, as well as soot shell formation and break-up during combustion of the spheres at reduced gravity. The ejection of combusting material from the burning spheres represents a fire hazard that must be considered at reduced gravity. The ejection process was found to be sensitive to polymer type. All average burning rates were measured to increase with initial sphere diameter and oxygen concentration, whereas the initial pressure had little effect. The three thermoplastic types exhibited different burning characteristics. For the same initial conditions, the burning rate of PP was slower than PMMA, whereas the burning rate of PS was comparable to PMMA. The transient diameter of the burning thermoplastic exhibited two distinct periods: an initial period (enduring approximately half of the total burn duration) when the diameter remained approximately constant, and a final period when the square of the diameter linearly decreased with time. A simple homogeneous two-phase model was developed to understand the changing diameter of the burning sphere. Its value is based on a competition between diameter reduction due to mass loss from burning and sputtering, and diameter expansion due to the processes of swelling (density decrease with heating) and bubble growth. The model relies on empirical parameters for input, such as the burning rate and the duration of the initial and final burning periods.
ORSPHERE: CRITICAL, BARE, HEU(93.2)-METAL SPHERE
Margaret A. Marshall
2013-09-01
In the early 1970’s Dr. John T. Mihalczo (team leader), J.J. Lynn, and J.R. Taylor performed experiments at the Oak Ridge Critical Experiments Facility (ORCEF) with highly enriched uranium (HEU) metal (called Oak Ridge Alloy or ORALLOY) in an attempt to recreate GODIVA I results with greater accuracy than those performed at Los Alamos National Laboratory in the 1950’s (HEU-MET-FAST-001). The purpose of the Oak Ridge ORALLOY Sphere (ORSphere) experiments was to estimate the unreflected and unmoderated critical mass of an idealized sphere of uranium metal corrected to a density, purity, and enrichment such that it could be compared with the GODIVA I experiments. “The very accurate description of this sphere, as assembled, establishes it as an ideal benchmark for calculational methods and cross-section data files.” (Reference 1) While performing the ORSphere experiments care was taken to accurately document component dimensions (±0. 0001 in. for non-spherical parts), masses (±0.01 g), and material data The experiment was also set up to minimize the amount of structural material in the sphere proximity. A three part sphere was initially assembled with an average radius of 3.4665 in. and was then machined down to an average radius of 3.4420 in. (3.4425 in. nominal). These two spherical configurations were evaluated and judged to be acceptable benchmark experiments; however, the two experiments are highly correlated.
Mixtures of ions and amphiphilic molecules in slit-like pores: A density functional approach.
Pizio, O; R?ysko, W; Soko?owski, S; Soko?owska, Z
2015-04-28
We investigate microscopic structure and thermodynamic properties of a mixture that contains amphiphilic molecules and charged hard spheres confined in slit-like pores with uncharged hard walls. The model and the density functional approach are the same as described in details in our previous work [Pizio et al., J. Chem. Phys. 140, 174706 (2014)]. Our principal focus is in exploring the effects brought by the presence of ions on the structure of confined amphiphilic particles. We have found that for some cases of anisotropic interactions, the change of the structure of confined fluids occurs via the first-order transitions. Moreover, if anions and cations are attracted by different hemispheres of amphiphiles, a charge at the walls appears at the zero value of the wall electrostatic potential. For a given thermodynamic state, this charge is an oscillating function of the pore width. PMID:25933780
Wang, Hui; Wu, Ping, E-mail: zjuwuping@njnu.edu.cn; Shi, Huimin; Lou, Feijian; Tang, Yawen; Zhou, Tongge; Zhou, Yiming, E-mail: zhouyiming@njnu.edu.cn; Lu, Tianhong
2014-07-01
Highlights: • In situ magnesiothermic reduction route for the formation of porous Si@C spheres. • Unique microstructural characteristics of both porous sphere and carbon matrix. • Enhanced anodic performance in term of cycling stability for lithium-ion batteries. - Abstract: A novel type of porous Si–C micro/nano-hybrids, i.e., porous Si spheres encapsulated in carbon shells (porous Si@C spheres), has been constructed through the pyrolysis of polyvinylidene fluoride (PVDF) and subsequent magnesiothermic reduction methodology by using SiO{sub 2} spheres as precursors. The as-synthesized porous Si@C spheres have been applied as anode materials for lithium-ion batteries (LIBs), and exhibit enhanced anodic performance in term of cycling stability compared with bare Si spheres. For example, the porous Si@C spheres are able to exhibit a high reversible capacity of 900.0 mA h g{sup ?1} after 20 cycles at a current density of 0.05 C (1 C = 4200 mA g{sup ?1}), which is much higher than that of bare Si spheres (430.7 mA h g{sup ?1})
Fuel Fabrication for Surrogate Sphere-Pac Rodlet
Del Cul, G.D.
2005-07-19
Sphere-pac fuel consists of a blend of spheres of two or three different size fractions contained in a fuel rod. The smear density of the sphere-pac fuel column can be adjusted to the values obtained for light-water reactor (LWR) pellets (91-95%) by using three size fractions, and to values typical of the fast-reactor oxide fuel column ({approx}85%) by using two size fractions. For optimum binary packing, the diameters of the two sphere fractions must differ by at least a factor of 7 (ref. 3). Blending of spheres with smaller-diameter ratios results in difficult blending, nonuniform loading, and lower packing fractions. A mixture of about 70 vol% coarse spheres and 30 vol% fine spheres is needed to obtain high packing fractions. The limiting smear density for binary packing is 86%, with about 82% achieved in practice. Ternary packing provides greater smear densities, with theoretical values ranging from 93 to 95%. Sphere-pac technology was developed in the 1960-1990 period for thermal and fast spectrum reactors of nearly all types (U-Th and U-Pu fuel cycles, oxide and carbide fuels), but development of this technology was most strongly motivated by the need for remote fabrication in the thorium fuel cycle. The application to LWR fuels as part of the DOE Fuel Performance Improvement Program did not result in commercial deployment for a number of reasons, but the relatively low production cost of existing UO{sub 2} pellet fuel is probably the most important factor. In the case of transmutation fuels, however, sphere-pac technology has the potential to be a lower-cost alternative while also offering great flexibility in tailoring the fuel elements to match the exact requirements of any particular reactor core at any given time in the cycle. In fact, the blend of spheres can be adjusted to offer a different composition for each fuel pin or group of pins in a given fuel element. Moreover, it can even provide a vertical gradient of composition in a single fuel pin. For minor-actinide-bearing fuels, the sphere-pac form is likely to accept the large helium release from {sup 241}Am transmutation with less difficulty than pellet forms and is especially well suited to remote fabrication as a dustless fuel form that requires a minimum number of mechanical operations. The sphere-pac (and vi-pac) fuel forms are being explored for use as a plutonium-burning fuel by the European Community, the Russian Federation, and Japan. Sphere-pac technology supports flexibility in the design and fabrication of fuels. For example, the blend composition can be any combination of fissile, fertile, transmutation, and inert components. Since the blend of spheres can be used to fill any geometric form, nonconventional fuel geometries (e.g., annular fuels rods, or annular pellets with the central region filled with spheres) are readily fabricated using sphere-pac loading methods. A project, sponsored by the U.S. Department of Energy Advanced Fuel Cycle Initiative (AFCI), has been initiated at Oak Ridge National Laboratory (ORNL) with the objective of conducting the research and development necessary to evaluate sphere-pac fuel for transmutation in thermal and fast-spectrum reactors. This AFCI work is unique in that it targets minor actinide transmutation and explores the use of a resin-loading technology for the fabrication of the remote-handled minor actinide fraction. While there are extensive data on sphere-pac fuel performance for both thermal-spectrum and fast-spectrum reactors, there are few data with respect to their use as a transmutation fuel. The sphere-pac fuels developed will be tested as part of the AFCI LWR-2 irradiations. This report provides a review of development efforts related to the fabrication of a sphere-pac rodlet containing surrogate fuel materials. The eventual goal of this activity is to develop a robust process that can be used to fabricate fuels or targets containing americium. The report also provides a review of the materials, methods, and techniques to be used in the fabrication of the surrogate fuel rodlet that will also b
Molecular density functional theory for water with liquid-gas coexistence and correct pressure
NASA Astrophysics Data System (ADS)
Jeanmairet, Guillaume; Levesque, Maximilien; Sergiievskyi, Volodymyr; Borgis, Daniel
2015-04-01
The solvation of hydrophobic solutes in water is special because liquid and gas are almost at coexistence. In the common hypernetted chain approximation to integral equations, or equivalently in the homogenous reference fluid of molecular density functional theory, coexistence is not taken into account. Hydration structures and energies of nanometer-scale hydrophobic solutes are thus incorrect. In this article, we propose a bridge functional that corrects this thermodynamic inconsistency by introducing a metastable gas phase for the homogeneous solvent. We show how this can be done by a third order expansion of the functional around the bulk liquid density that imposes the right pressure and the correct second order derivatives. Although this theory is not limited to water, we apply it to study hydrophobic solvation in water at room temperature and pressure and compare the results to all-atom simulations. The solvation free energy of small molecular solutes like n-alkanes and hard sphere solutes whose radii range from angstroms to nanometers is now in quantitative agreement with reference all atom simulations. The macroscopic liquid-gas surface tension predicted by the theory is comparable to experiments. This theory gives an alternative to the empirical hard sphere bridge correction used so far by several authors.
Rotational Relaxation of Rough Spheres
B. Widom
1960-01-01
A theory of rotational relaxation of spherical top molecules in an inert gas is given, under the assumption that the molecules and atoms collide as rough spheres. Some general aspects of relaxation theory are first discussed and a theorem is presented which, under some circumstances, allows the problem to be greatly simplified. The rotational relaxation problem is then solved both
Tessellating the Sphere with Regular Polygons
ERIC Educational Resources Information Center
Soto-Johnson, Hortensia; Bechthold, Dawn
2004-01-01
Tessellations in the Euclidean plane and regular polygons that tessellate the sphere are reviewed. The regular polygons that can possibly tesellate the sphere are spherical triangles, squares and pentagons.
Crystalline assembly of hard polyhedra via directional entropic forces
NASA Astrophysics Data System (ADS)
Damasceno, Pablo F.; Engel, Michael; Glotzer, Sharon C.
2012-02-01
Entropic forces are effective forces that result from a system's statistical tendency to increase its entropy. Hard rods and disks spontaneously align and can assemble into layers and columns if those structures increase the configurational space available to the particles. Hard spheres, cubes and even tetrahedra order for the same reason. Here we extend those findings by showing that hard polyhedra can self-assemble into a variety of complex phases, most of them never before reported in systems of single-component hard particles. The role of shape and directional entropic forces in stabilizing these structures will be discussed. Our results suggest new possibilities for self-assembling complex target structures from colloidal building blocks. [4pt] [1] Damasceno, PF; Engel, M; Glotzer, SC. arXiv:1109.1323v1
NSDL National Science Digital Library
2007-12-20
Hardness is probably a concept you are well familiar with. You already know that certain materials are harder than others; in fact, you prove it everyday when you chew your food and your teeth don’t break (because your teeth are harder than the foods you chew). Hardness can be defined as a material's ability to resist a change in shape. Modern hardness testers take a well-defined shape and press it into a material with a certain force, observing the indent it leaves in the material when it is removed. In this lesson, you will be performing hardness testing on different bars of chocolate.
Iwamoto, Takashi; Mackenzie, J.D. [Univ. of California, Los Angeles, CA (United States). Dept. of Materials Science and Engineering
1994-12-31
Organically modified silicates (ormosils) of high hardness were prepared by the reactions of tetraethoxysilane (TEOS) and polydimethylsiloxane (PDMS) aided by ultrasonic irradiation. The mechanisms leading to the hard ormosil formation were investigated by liquid state {sup 29}Si NMR spectroscopy. PDMS chains were found to be broken into shorter chains and/or 4-membered siloxane rings during the reaction and finally, all PDMS chains were chemically incorporated as short chains into silica networks. Vickers hardnesses of the hard ormosils were measured and compared with those of the hardest transparent plastics. Whereas the hardest transparent plastics have Vickers hardness values of less than 25 kg/mm{sup 2}, the hard ormosils have Vickers hardnesses tip to higher than 150 kg/mm{sup 2}. A theoretical model was developed for the calculation of Vickers hardnesses of the hard ormosils and agreed well with experimental results. Predictions based on this theory indicate that even harder ormosils can be made when Al{sub 2}O{sub 3}, ZrO{sub 2} and TiO{sub 2} are substituted for SiO{sub 2}. Results based on these new ormosils are also presented.
Kinetic Theory for Binary Granular Mixtures at Low-Density
Vicente Garzo
2007-04-10
Many features of granular media can be modelled as a fluid of hard spheres with {\\em inelastic} collisions. Under rapid flow conditions, the macroscopic behavior of grains can be described through hydrodynamic equations. At low-density, a fundamental basis for the derivation of the hydrodynamic equations and explicit expressions for the transport coefficients appearing in them is provided by the Boltzmann kinetic theory conveniently modified to account for inelastic binary collisions. The goal of this chapter is to give an overview of the recent advances made for binary granular gases by using kinetic theory tools. Some of the results presented here cover aspects such as transport properties, energy nonequipartition, instabilities, segregation or mixing, non-Newtonian behavior, .... In addition, comparison of the analytical results with those obtained from Monte Carlo and molecular dynamics simulations is also carried out, showing the reliability of kinetic theory to describe granular flows even for strong dissipation.
The viscosity of suspensions of rigid spheres
R. Roscoe
1952-01-01
An explanation is given of the dependence of the relative viscosity on the size distribution of the suspended spheres, an effect recently observed by Ward and Whitmore.(1) It is shown theoretically that if the spheres are of very diverse sizes, the relative viscosity is (1 - c)-2.5 for all values of the volume concentration c. For spheres of equal size,
Vacuum energies on spheres and in cubes
J. S. Dowker
2011-06-18
The vacuum energy of a conformally coupled scalar field on the d-dimensional sphere is calculated. On even spheres it is zero and on odd spheres it oscillates in sign. Results for the d-torus and d-cube are also given.
Higher complements of combinatorial sphere arrangements Higher complements of
Berger, Clemens
Higher complements of combinatorial sphere arrangements Higher complements of combinatorial sphere¨uck, October 8, 2009 Nice, October 15, 2009 #12;Higher complements of combinatorial sphere arrangements 1 complements of combinatorial sphere arrangements Hyperplane arrangements A (central) hyperplane arrangement
Implementation of Hard Real-Time Embedded Control Systems
Matjaz Colnaric; Domen Verber; Roman Gumzej; Wolfgang A. Halang
1998-01-01
Although the domain of hard real-time systems has been thoroughly elaborated in the academic sphere, embedded computer control\\u000a systems — being an important component in mechatronic designs — are seldom dealt with consistently. Often, off-the-shelf computer\\u000a systems are used, with no guarantee that they will be able to meet the requirements specified. In this paper, a design for\\u000a embedded control
Torquato, Salvatore
an approximate low-density expansion of(T * derived here for interpenetrable-sphere models, reveals throughout a matrix (e.g., dispersions,2 sandstones,4,5 sintered materials,4 and unglazed ceramics4) for any by some parameter A whose value varies between zero (in the case where the sphere centers are randomly cen
Session: Hard Rock Penetration
Tennyson, George P. Jr.; Dunn, James C.; Drumheller, Douglas S.; Glowka, David A.; Lysne, Peter
1992-01-01
This session at the Geothermal Energy Program Review X: Geothermal Energy and the Utility Market consisted of five presentations: ''Hard Rock Penetration - Summary'' by George P. Tennyson, Jr.; ''Overview - Hard Rock Penetration'' by James C. Dunn; ''An Overview of Acoustic Telemetry'' by Douglas S. Drumheller; ''Lost Circulation Technology Development Status'' by David A. Glowka; ''Downhole Memory-Logging Tools'' by Peter Lysne.
Stojmenovic, Ivan
1! CSI3131 Topics CPU Memory Hard Drive Peripherals Computing Systems OS Overview StructureDeadlocks M em ory M anagem ent Basic Memory Managermtn Virtual Memory Storage and I/O File Systems Hard Drive Management Swap I/O Management 2 Module 7: Memory Management Reading: Chapter 8 § To provide a detailed
Self-diffusion of spheres in a concentrated suspension
C. W. J. Beenakker; P. Mazur
1983-01-01
We calculate the concentration-dependence of the short-time self-diffusion coefficient Ds for spherical particles in suspension. Our analysis is valid up to high densities and fully takes into account the many-body hydrodynamic interactions between an arbitrary number of spheres. The importance of these many-body interactions can be inferred from our calculation of the second virial coefficient of Ds.
Cugell, D W
1992-06-01
Hard metal is a mixture of tungsten carbide and cobalt, to which small amounts of other metals may be added. It is widely used for industrial purposes whenever extreme hardness and high temperature resistance are needed, such as for cutting tools, oil well drilling bits, and jet engine exhaust ports. Cobalt is the component of hard metal that can be a health hazard. Respiratory diseases occur in workers exposed to cobalt--either in the production of hard metal, from machining hard metal parts, or from other sources. Adverse pulmonary reactions include asthma, hypersensitivity pneumonitis, and interstitial fibrosis. A peculiar, almost unique form of lung fibrosis, giant cell interstitial pneumonia, is closely linked with cobalt exposure. PMID:1511554
Archaic artifacts resembling celestial spheres
NASA Astrophysics Data System (ADS)
Dimitrakoudis, S.; Papaspyrou, P.; Petoussis, V.; Moussas, X.
We present several bronze artifacts from the Archaic Age in Greece (750-480 BC) that resemble celestial spheres or forms of other astronomical significance. They are studied in the context of the Dark Age transition from Mycenaean Age astronomical themes to the philosophical and practical revival of astronomy in the Classical Age with its plethora of astronomical devices. These artifacts, mostly votive in nature are spherical in shape and appear in a variety of forms their most striking characteristic being the depiction of meridians and/or an equator. Most of those artifacts come from Thessaly, and more specifically from the temple of Itonia Athena at Philia, a religious center of pan-Hellenic significance. Celestial spheres, similar in form to the small artifacts presented in this study, could be used to measure latitudes, or estimate the time at a known place, and were thus very useful in navigation.
Instabilities in Very Young Neutron Stars: Density
NSDL National Science Digital Library
Pamela ONeil
1994-02-12
This simulation shows the first 20 milliseconds in the life of a neutron star which is formed in a Type II supernova. After an initial collapse phase, the neutron star becomes unstable to convection. The resulting convective motions destroy the spherical symmetry of the star and rapidly mix the inner regions. In addition, the neutrino flux from the neutron star will be non-spherical and will be significantly enhanced by the convective motions. This may have major implications for the Type II supernova mechanism. The calculation was performed using the Piecewise-Parabolic Method for hydrodynamics. The computational grid contained 300 zones in radius and 200 zones in angle. The inner 200 zones in radius were uniformly spaced, ranging from the inner boundary at 25 km to 175 km. The outer 100 zones were non-uniformly spaced and stretched to 2000 km. Only the inner 200 zones are plotted. The inner boundary was treated as a hard sphere. At the outer boundary, zero gradients for all the variables were assumed. Periodic boundary conditions were used along the sides of the grid. The following sequence shows the density evolution for 20 milliseconds after the shock stalls. The density is plotted on a log scale. Values range from 10^9 gm-cm^3 at the outer boundary to 1.4 x 10^12 gm-cm^3 at the inner boundary.
Mesoporous carbon spheres with controlled porosity for high-performance lithium-sulfur batteries
NASA Astrophysics Data System (ADS)
Wang, Dexian; Fu, Aiping; Li, Hongliang; Wang, Yiqian; Guo, Peizhi; Liu, Jingquan; Zhao, Xiu Song
2015-07-01
Mesoporous carbon (MC) spheres with hierarchical pores, controlled pore volume and high specific surface areas have been prepared by a mass-producible spray drying assisted template method using sodium alginate as carbon precursor and commercial colloidal silica particles as hard template. The resulting MC spheres, possessing hierarchical pores in the range of 3-30 nm, are employed as conductive matrices for the preparation of cathode materials for lithium-sulfur batteries. A high pressure induced one-step impregnation of elemental sulfur into the pore of the MC spheres has been exploited. The electrochemical performances of sulfur-impregnated MC spheres (S-MC) derived from MC spheres with different pore volume and specific surface area but with the same sulfur loading ratio of 60 wt% (S-MC-X-60) have been investigated in details. The S-MC-4-60 composite cathode material displayed a high initial discharge capacity of 1388 mAhg-1 and a good cycling stability of 857 mAhg-1 after 100 cycles at 0.2C, and shows also excellent rate capability of 864 mAhg-1 at 2C. More importantly, the sulfur loading content in MC-4 spheres can reach as high as 80%, and it still can deliver a capacity of 569 mAhg-1 after 100 cycles at 0.2C.
Radiation Hard AlGaN Detectors and Imager
None
2012-05-01
Radiation hardness of AlGaN photodiodes was tested using a 65 MeV proton beam with a total proton fluence of 3x10{sup 12} protons/cm{sup 2}. AlGaN Deep UV Photodiode have extremely high radiation hardness. These new devices have mission critical applications in high energy density physics (HEDP) and space explorations. These new devices satisfy radiation hardness requirements by NIF. NSTec is developing next generation AlGaN optoelectronics and imagers.
low-density particles include spheres with silicate cores and organic mantles, carbonaceous spheres,
Napp, Nils
observations, depending on the (currently unknown) wavelength dependence of the extinction cross sections (Table 1). The need for internal consistency leaves us with a twofold conclusion: If large interstellar with astronomical observations (45). By contrast, if large interstellar dust particles have low den- sities, which
STATISTICAL ANALYSIS ON HIGH-DIMENSIONAL SPHERES AND SHAPE SPACES1
Ian L. Dryden
2003-01-01
We consider the statistical analysis of data on high-dimensional spheres and shape spaces. The work is of particular relevance to ap- plications where high-dimensional data are available—a commonly encountered situation in many disciplines. First the uniform measure on the infinite-dimensional sphere is reviewed, together with connec- tions with Wiener measure. We then discuss densities of Gaussian measures with respect to
Thermal plasma deposition of nanophase hard coatings
J. Heberlein; O. Postel; S. Girshick; P. McMurry; W. Gerberich; D. Iordanoglou; F. Di Fonzo; D. Neumann; A. Gidwani; M. Fan; N. Tymiak
2001-01-01
Thermal plasmas offer several specific advantages for the generation of hard coatings. In particular, the high energy density of the thermal plasma allows higher precursor flow rates and a wider choice of precursors. Expansion of the plasma into a low pressure chamber offers the additional advantages that improved control over the chemistry can be achieved or that nanosize particles can
Ionic density distributions near the charged colloids: Spherical electric double layers
Kim, Eun-Young; Kim, Soon-Chul, E-mail: sckim@andong.ac.kr [Department of Physics, Andong National University, Andong 760-749 (Korea, Republic of)] [Department of Physics, Andong National University, Andong 760-749 (Korea, Republic of)
2013-11-21
We have studied the structure of the spherical electric double layers on charged colloids by a density functional perturbation theory, which is based both on the modified fundamental-measure theory for the hard spheres and on the one-particle direct correlation functional (DCF) for the electronic residual contribution. The contribution of one-particle DCF has been approximated as the functional integration of the second-order correlation function of the ionic fluids in a bulk phase. The calculated result is in very good agreement with the computer simulations for the ionic density distributions and the zeta potentials over a wide range of macroion sizes and electrolyte concentrations, and compares with the results of Yu et al. [J. Chem. Phys. 120, 7223 (2004)] and modified Poisson-Boltzmann approximation [L. B. Bhuiyan and C. W. Outhwaite, Condens. Matter Phys. 8, 287 (2005)]. The present theory is able to provide interesting insights about the charge inversion phenomena occurring at the interface.
Analysis of data on the densities of liquid rare-earth metals from thermodynamic parameters
Kiselev, A.I.; Kononenko, V.I.
1987-05-01
Calculations have been performed on the pseudopotential parameters and packing coefficients in hard-sphere reference system for rare-earth metals near their melting points on the basis of minimum Helmholz free energy if the calculated and observed values for the resistivity agree. The results have been used in calculating the thermodynamic parameters in the liquid state. Theory is in satisfactory agreement with experiment. A method is proposed for analyzing measurements on the temperature coefficient of the density, where there are sometimes substantial differences in the data. Calculated values for the thermodynamic parameters have been used in examining the reliability of the data on the temperature coefficients of density for rare-earth metals; recommendations are made.
Self-assembly of amphiphilic Janus particles at planar walls: A density functional study
Gerald Rosenthal; Sabine H. L. Klapp
2010-12-06
We investigate the structure formation of amphiphilic molecules at planar walls using density functional theory. The molecules are modeled as (hard) spheres composed of a hydrophilic and hydrophobic part. The orientation of the resulting Janus-particles is described as a vector representing an internal degree of freedom. Our density functional approach involves Fundamental Measure Theory combined with a mean-field approximation for the anisotropic interaction. Considering neutral, hydrophilic and hydrophobic walls, we study the adsorption of the particles, focussing on the competition between the surface field and interact ion-induced ordering phenomena. Finally, we consider systems confined between two planar walls. It is shown that the anisotropic Janus interaction yields pronounced frustration effects at low temperatures.
ERIC Educational Resources Information Center
Stocker, H. Robert; Hilton, Thomas S. E.
1991-01-01
Suggests strategies that make hard disk organization easy and efficient, such as making, changing, and removing directories; grouping files by subject; naming files effectively; backing up efficiently; and using PATH. (JOW)
Quantum fractals on n-spheres. Clifford Algebra approach
Arkadiusz Jadczyk
2007-05-25
Using the Clifford algebra formalism we extend the quantum jumps algorithm of the Event Enhanced Quantum Theory (EEQT) to convex state figures other than those stemming from convex hulls of complex projective spaces that form the basis for the standard quantum theory. We study quantum jumps on n-dimensional spheres, jumps that are induced by symmetric configurations of non-commuting state monitoring detectors. The detectors cause quantum jumps via geometrically induced conformal maps (Mobius transformations) and realize iterated function systems (IFS) with fractal attractors located on n-dimensional spheres. We also extend the formalism to mixed states, represented by "density matrices". As a numerical illustration we study quantum fractals on the circle, two--sphere (octahedron), and on three-dimensional sphere (hypercube-tesseract, 24 cell, 600 cell,and 120 cell). The invariant measure on the attractor is approximated by the powers of the Markov operator. In the appendices we calculate the Radon-Nikodym derivative of the SO(n+1) invariant measure on S^n under SO(1,n+1) transformations and discuss the Hamilton's "icossian calculus" as well as its application to quaternionic realization of the binary icosahedral group that is at the basis of the 600 cell and its dual, the 120 cell. As a by-product of this work we obtain several Clifford algebraic results, such as a characterization of positive elements in a Clifford algebra Cl(n+1) as generalized Lorentz boosts, and their action as Moebius transformation on n-sphere, and a decomposition of any element of Spin^+(1,n+1) into a boost and a rotation, including the explicit formula for the pullback of the O(n+1) invariant Riemannian metric with respect to the associated Mobius transformation.
Traveling on a Rotating Sphere
NSDL National Science Digital Library
2013-03-04
This lesson applies the science and math of the rotation of a sphere to water and wind movements on Earth. Students are introduced to convection, the Trade Winds and the Coriolis Force. Using an online visualizer, students generate trajectories and then analyze course patterns and latitudinal changes in strength. Note that this is lesson two of five on the Ocean Motion website. Each lesson investigates ocean surface circulation using satellite and model data and can be done independently. See Related URL's for links to the Ocean Motion Website that provide science background information, data resources, teacher material, student guides and a lesson matrix.
Crystalline Phases of Polydisperse Spheres
NASA Astrophysics Data System (ADS)
Sollich, Peter; Wilding, Nigel B.
2010-03-01
We use specialized Monte Carlo simulation methods and moment free energy calculations to provide conclusive evidence that dense polydisperse spheres at equilibrium demix into coexisting fcc phases, with more phases appearing as the spread of diameters increases. We manage to track up to four coexisting phases. Each of these is fractionated: it contains a narrower distribution of particle sizes than is present in the system overall. We also demonstrate that, surprisingly, demixing transitions can be nearly continuous, accompanied by fluctuations in local particle size correlated over many lattice spacings.
The dynamic sphere test problem
Chabaud, Brandon M. [Los Alamos National Laboratory; Brock, Jerry S. [Los Alamos National Laboratory; Smith, Brandon M. [Los Alamos National Laboratory
2012-05-16
In this manuscript we define the dynamic sphere problem as a spherical shell composed of a homogeneous, linearly elastic material. The material exhibits either isotropic or transverse isotropic symmetry. When the problem is formulated in material coordinates, the balance of mass equation is satisfied automatically. Also, the material is assumed to be kept at constant temperature, so the only relevant equation is the equation of motion. The shell has inner radius r{sub i} and outer radius r{sub o}. Initially, the shell is at rest. We assume that the interior of the shell is a void and we apply a time-varying radial stress on the outer surface.
Camera Calibration from Images of Spheres
Hui Zhang; Kwan-yee Kenneth Wong; Guoqiang Zhang
2007-01-01
This paper introduces a novel approach for solving the problem of camera calibration from spheres. By exploiting the relationship between the dual images of spheres and the dual image of the absolute conic (IAC), it is shown that the common pole and polar w.r.t. the conic images of 2 spheres are also the pole and polar w.r.t the IAC. This
Porous Ceramic Spheres from Ion Exchange Resin
NASA Technical Reports Server (NTRS)
Dynys, Fred
2005-01-01
A commercial cation ion exchange resin, cross-linked polystyrene, has been successfully used as a template to fabricate 20 to 50 micron porous ceramic spheres. Ion exchange resins have dual template capabilities. Pore architecture of the ceramic spheres can be altered by changing the template pattern. Templating can be achieved by utilizing the internal porous structure or the external surface of the resin beads. Synthesis methods and chemical/physical characteristics of the ceramic spheres will be reported.
Process for making hollow carbon spheres
Luhrs, Claudia C.; Phillips, Jonathan; Richard, Monique N.; Knapp, Angela Michelle
2013-04-16
A hollow carbon sphere having a carbon shell and an inner core is disclosed. The hollow carbon sphere has a total volume that is equal to a volume of the carbon shell plus an inner free volume within the carbon shell. The inner free volume is at least 25% of the total volume. In some instances, a nominal diameter of the hollow carbon sphere is between 10 and 180 nanometers.
The diffraction of sound by an impedance sphere in the vicinity of a ground surface.
Li, Kai Ming; Lui, Wai Keung; Frommer, Glenn H
2004-01-01
The problem of sound diffraction by an absorbing sphere due to a monopole point source was investigated. The theoretical models were extended to consider the case of sound diffraction by an absorbing sphere with a locally reacting boundary or an extended reaction boundary placed above an outdoor ground surface of finite impedance. The separation of variables techniques and appropriate wave field expansions were used to derive the analytical solutions. By adopting an image method, the solutions could be formulated to account for the multiple scattering of sound between the sphere and its image near a flat acoustically hard or an impedance ground. The effect of ground on the reflected sound fields was incorporated in the theoretical model by employing an approximate analytical solution known as the Weyl-van der Pol formula. An approximation solution was suggested to determine the scattering coefficients from a set of linearly coupled complex equations for an absorbing sphere not too close to the ground. The approximate method substantially reduced the computational time for calculating the sound field. Preliminary measurements were conducted to characterize the acoustical properties of an absorbing sphere made of open cell polyurethane foam. Subsequent experiments were carried out to demonstrate the validity of the proposed theoretical models for various source/receiver configurations around the sphere above an acoustically hard ground and an impedance ground. Satisfactory comparative results were obtained between the theoretical predictions and experimental data. It was found that the theoretical predictions derived from the approximate solution agreed well with the results obtained by using the exact solutions. PMID:14758994
Multicomponent fluids of hard hyperspheres in odd dimensions.
Rohrmann, René D; Santos, Andrés
2011-01-01
Mixtures of hard hyperspheres in odd-space dimensionalities are studied with an analytical approximation method. This technique is based on the so-called rational function approximation and provides a procedure for evaluating equations of state, structure factors, radial distribution functions, and direct correlation functions of additive mixtures of hard hyperspheres with any number of components and in arbitrary odd-dimension space. The method gives the exact solution of the Ornstein-Zernike equation coupled with the Percus-Yevick closure, thus, extending the solution for hard-sphere mixtures [J. L. Lebowitz, Phys. Rev. 133, A895 (1964)] to arbitrary odd dimensions. Explicit evaluations for binary mixtures in five dimensions are performed. The results are compared with computer simulations, and a good agreement is found. PMID:21405686
Can the Equivalent Sphere Model Approximate Organ Doses in Space?
NASA Technical Reports Server (NTRS)
Lin, Zi-Wei
2007-01-01
For space radiation protection it is often useful to calculate dose or dose,equivalent in blood forming organs (BFO). It has been customary to use a 5cm equivalent sphere to. simulate the BFO dose. However, many previous studies have concluded that a 5cm sphere gives very different dose values from the exact BFO values. One study [1] . concludes that a 9 cm sphere is a reasonable approximation for BFO'doses in solar particle event environments. In this study we use a deterministic radiation transport [2] to investigate the reason behind these observations and to extend earlier studies. We take different space radiation environments, including seven galactic cosmic ray environments and six large solar particle events, and calculate the dose and dose equivalent in the skin, eyes and BFO using their thickness distribution functions from the CAM (Computerized Anatomical Man) model [3] The organ doses have been evaluated with a water or aluminum shielding of an areal density from 0 to 20 g/sq cm. We then compare with results from the equivalent sphere model and determine in which cases and at what radius parameters the equivalent sphere model is a reasonable approximation. Furthermore, we address why the equivalent sphere model is not a good approximation in some cases. For solar particle events, we find that the radius parameters for the organ dose equivalent increase significantly with the shielding thickness, and the model works marginally for BFO but is unacceptable for the eye or the skin. For galactic cosmic rays environments, the equivalent sphere model with an organ-specific constant radius parameter works well for the BFO dose equivalent, marginally well for the BFO dose and the dose equivalent of the eye or the skin, but is unacceptable for the dose of the eye or the skin. The ranges of the radius parameters are also being investigated, and the BFO radius parameters are found to be significantly, larger than 5 cm in all cases, consistent with the conclusion of an earlier study [I]. The radius parameters for the dose equivalent in GCR environments are approximately between 10 and I I cm for the BFO, 3.7 to 4.8 cm for the eye, and 3.5 to 5.6 cm for the skin; while the radius parameters are between 10 and 13 cm for the BFO dose.
Magnetic torque on a rotating superconducting sphere
NASA Technical Reports Server (NTRS)
Holdeman, L. B.
1975-01-01
The London theory of superconductivity is used to calculate the torque on a superconducting sphere rotating in a uniform applied magnetic field. The London theory is combined with classical electrodynamics for a calculation of the direct effect of excess charge on a rotating superconducting sphere. Classical electrodynamics, with the assumption of a perfect Meissner effect, is used to calculate the torque on a superconducting sphere rotating in an arbitrary magnetic induction; this macroscopic approach yields results which are correct to first order. Using the same approach, the torque due to a current loop encircling the rotating sphere is calculated.
Waveguide trapping of hollow glass spheres
NASA Astrophysics Data System (ADS)
Singh Ahluwalia, Balpreet; Løvhaugen, Pål.; Gaute Hellesø, Olav
2011-09-01
Microparticles can be trapped and propelled by the evanescent field of optical waveguides. As the evanescent field only stretches 100--200nm from the surface of the waveguide, only the lower caps of the microparticles interact directly with the field. This is taken advantage of by trapping hollow glass spheres on waveguides in the same way as solid glass spheres. For the chosen waveguide, numerical simulations show that hollow microspheres with a shell thickness above 60nm can be stably trapped, while spheres with thinner shells are repelled. The average refractive index of the sphere--field intersection volume is used to explain the result in a qualitative way.
Waveguide trapping of hollow glass spheres.
Ahluwalia, Balpreet Singh; Løvhaugen, Pål; Hellesø, Olav Gaute
2011-09-01
Microparticles can be trapped and propelled by the evanescent field of optical waveguides. As the evanescent field only stretches 100-200?nm from the surface of the waveguide, only the lower caps of the microparticles interact directly with the field. This is taken advantage of by trapping hollow glass spheres on waveguides in the same way as solid glass spheres. For the chosen waveguide, numerical simulations show that hollow microspheres with a shell thickness above 60?nm can be stably trapped, while spheres with thinner shells are repelled. The average refractive index of the sphere-field intersection volume is used to explain the result in a qualitative way. PMID:21886206
Unexpected ricochet of spheres off water
NASA Astrophysics Data System (ADS)
Shlien, D. J.
1994-08-01
A sphere was observed to apparently ricochet off the free surface of water at incident angles as large as 45° while the expected (empirical/analytical) maximum angle to the horizontal for ricochet was 6°. Closer examination of the process revealed that the cavitating sphere penetrated the liquid to depths as great as 35 sphere diameters. Under certain circumstances the sphere was also observed to leave the liquid in a direction close to the incoming direction; that is, the sphere ricocheted backwards! This peculiar behavior was found to be a result of an unintentional spin applied to the sphere upon launching. By crudely modelling the process, the sphere path is qualitatively predicted. It was found that the drag and lift coefficients required to model the trajectory data were several times smaller than those obtained for the non-cavitating case or for the non-spinning case. If more precise sphere trajectory data were available, this experiment could be used to measure the lift and drag coefficients of a spinning and cavitating sphere.
Preparation of thorium-uranium gel spheres
Spence, R.D.; Haas, P.A.
1980-01-01
Ceramic oxide spheres with diameters of 15 to 1500 ..mu..m are being evaluated for fabrication of power reactor fuel rods. (Th,U)O/sub 2/ spheres can be prepared by internal or external chemical gelation of nitrate solutions or oxide sols. Two established external gelation techniques were tested but proved to be unsatisfactory for the intended application. Established internal gelation techniques for UO/sub 2/ spheres were applied with minor modifications to make 75% ThO/sub 2/-25% UO/sub 2/ spheres that sinter to diameters of 200 to 1400 ..mu..m (99% T.D.).
Electromagnetic energy within single-resonance chiral metamaterial spheres.
Arruda, Tiago J; Pinheiro, Felipe A; Martinez, Alexandre S
2013-06-01
We derive an exact expression for the time-averaged electromagnetic (EM) energy inside a chiral dispersive sphere irradiated by a plane wave. The dispersion relations correspond to a chiral metamaterial consisting of uncoupled single-resonance helical resonators. Using a field decomposition scheme and a general expression for the EM energy density in bianisotropic media, we calculate the Lorenz-Mie solution for the internal fields in a medium that is simultaneously magnetic and chiral. We also obtain an explicit analytical relation between the internal EM energy and the absorption cross section. This result is applied to demonstrate that strong chirality leads to an off-resonance field enhancement within weakly absorbing spheres. PMID:24323108
Geometrical frustration in amorphous and partially crystallized packings of spheres.
Francois, N; Saadatfar, M; Cruikshank, R; Sheppard, A
2013-10-01
We study the persistence of a geometrically frustrated local order inside partially crystallized packings of equal-sized spheres. Measurements by x-ray tomography reveal previously unseen grain scale rearrangements occurring inside large three-dimensional packings as they crystallize. Three successive structural transitions are detected by a statistical description of the local volume fluctuations. These compaction regimes are related to the disappearance of densely packed tetrahedral patterns of beads. Amorphous packings of monodisperse spheres are saturated with these tetrahedral clusters at Bernal's limiting density (??64%). But, no periodic lattice can be built upon these patterns; they are geometrically frustrated and are thus condemned to vanish while the crystallization occurs. Remarkably, crystallization-induced grain rearrangements can be interpreted in terms of the evolution of key topological features of these aggregates. PMID:24138272
Poisson denoising on the sphere
NASA Astrophysics Data System (ADS)
Schmitt, J.; Starck, J. L.; Fadili, J.; Grenier, I.; Casandjian, J. M.
2009-08-01
In the scope of the Fermi mission, Poisson noise removal should improve data quality and make source detection easier. This paper presents a method for Poisson data denoising on sphere, called Multi-Scale Variance Stabilizing Transform on Sphere (MS-VSTS). This method is based on a Variance Stabilizing Transform (VST), a transform which aims to stabilize a Poisson data set such that each stabilized sample has an (asymptotically) constant variance. In addition, for the VST used in the method, the transformed data are asymptotically Gaussian. Thus, MS-VSTS consists in decomposing the data into a sparse multi-scale dictionary (wavelets, curvelets, ridgelets...), and then applying a VST on the coefficients in order to get quasi-Gaussian stabilized coefficients. In this present article, the used multi-scale transform is the Isotropic Undecimated Wavelet Transform. Then, hypothesis tests are made to detect significant coefficients, and the denoised image is reconstructed with an iterative method based on Hybrid Steepest Descent (HST). The method is tested on simulated Fermi data.
Euclidean 5-sphere archaic universe
Ignazio Licata; Leonardo Chiatti
2010-04-09
In this work, we examine in depth the cosmological physical aspects of the archaic universe described by Euclidean 5-sphere geometry. (see Int. Jour. of Theor., Phys 2009, 48:1003-1018). We hypothesize that the big bang consisted of a spatially extended nucleation process which took place at the end of a pre-cosmic phase, characterized by the evolution parameter x0. This parameter, which can be considered a quantum precursor of ordinary physical time, is a coordinate of Euclidean 5-sphere metrics. We must now examine what the privileged role of the x0 axis consists in. The big bang is a sort of nucleation of matter and fields by vacuum; to try to understand it we must therefore make some assumptions regarding a pre-cosmic state of matter and energy. The introduction of an evolution parameter such as x0 which can be extended to pre-big bang situations is absolutely necessary if we are to define any pre-cosmic dynamics. A generalized Bekenstein relation is here proposed for archaic Universe. A complete solution to Projective General Relativity (PGR) equations in the De Sitter Universe is provided, so as to establish univocal relations between the scale factor R(tau) and cosmic time tau. In this way, the physics and geometry of the cosmological model are specified completely.
A comprehensive study of the phase diagram of symmetrical hard-core Yukawa mixtures
NASA Astrophysics Data System (ADS)
Caccamo, C.; Costa, D.; Pellicane, G.
1998-09-01
The phase diagrams of hard-core Yukawa mixtures (HCYM), constituted of equal sized hard spheres interacting through an attractive Yukawa tail, are determined by means of Gibbs Ensemble Monte Carlo (GEMC) simulations, Semi-grand Canonical Monte Carlo (SGCMC) simulations, and through the modified hypernetted-chain (MHNC) theory. Freezing lines are obtained according to an approach recently proposed by Giaquinta and co-workers [Physica A 187, 145 (1992); Phys Rev. A 45, 6966 (1992)] in which an analysis of multiparticle contributions to the excess entropy, ?s, is performed, with the determination of the ?s=0 locus. Liquid-vapor coexistence, determined through GEMC simulations, turns out to be favored when the strength ratio ? of unlike to like particle interaction, is close to 1. For lower ?'s, liquid-vapor coexistence is favored at low densities, and liquid-liquid coexistence, determined through SGCMC simulations, at high densities. The liquid-vapor binodal shifts downward in temperature and flattens when ? decreases, with a decrease of the critical temperature. At ?=0.9 a triple point can be identified from the intersection of the freezing line with the binodal line; at ?=0.7, instead, the binodal ends on the line of liquid-liquid (consolute) critical points, the intersection of the two lines thus identifying the "crossover" density and temperature between the two equilibrium regimes which correspond to the critical end point of the mixture. We find that, for not too high densities, consolute equilibrium can be also explored through GEMC simulations; the results for liquid-liquid coexistence obtained through this method and SGCMC simulations compare quite satisfactorily with each other. The trend of the liquid-vapor binodal to disappear for relatively weak unlike interactions is discussed in connection with the disappearance of liquid-vapor equilibrium which occurs in one component hard-core Yukawa fluids characterized by very short ranged attractive forces. The latter behavior has been conjectured to be relevant for the onset of crystallization in protein solutions; the implications of the present results, which are obtained in the context of a two component, albeit rough, modelization of a realistic solution, are discussed. In agreement with similar results obtained by Giaquinta et al., we finally find that the ?s=0 locus not only brings the signature of the freezing transition, but also of structural rearrangements preluding to other phase equilibria; in fact, the ?s=0 line turns out to be coincident to a high accuracy with the line of consolute critical points and with the gas branches of the liquid-vapor binodals.
Laue lens development for hard X-rays (>60 keV)
D. Pellicciotta; F. Frontera; G. Loffredo; A. Pisa; K. Andersen; P. Courtois; B. Hamelin; V. Carassiti; M. Melchiorri; S. Squerzanti
2006-01-01
Results of reflectivity measurements of mosaic crystal samples of Cu (111) are reported. These tests were performed in the context of a feasibility study of a hard X-ray focusing telescope for space astronomy based on mosaic crystals in transmission configuration (Laue lens). The Laue lens assumed has the shape of a sphere segment with radius R equal to 2 times
Stochastic Interactions of Two Brownian Spheres in the Presence of Depletants
NASA Astrophysics Data System (ADS)
Karzar-Jeddi, Mehdi; Tuinier, Remco; Taniguchi, Takashi; Fan, Tai-Hsi
2014-03-01
The pair interactions between hard spheres play an essential role in many processes such as macromolecular crowding, binding, self-assembly of particles, and many chemical and food processes. Here we focus on theoretical analysis of the long-time correlated stochastic motion of two hard spheres in a non-adsorbing polymer solution. The hard spheres are held by hypothetical optical traps. The pair mobility tenser is found using a two-layer approximation with pure solvent in the depletion zone surrounding the particle and uniform polymer solution elsewhere. The resulting mobility computed by the boundary integral analysis is used to define the level of thermal fluctuation. Results show how the mobility and the decay of displacement correlation functions modified by the polymer depletion effect. The attractive osmotic potential increases the auto-correlation of the pair particle motion, while reduces the cross-correlation of the particles. This work gives better understanding of the pair interactions in a suspension of non-adsorbing polymers as an essential step toward many-particle interactions.
Efficient linear programming algorithm to generate the densest lattice sphere packings.
Marcotte, Étienne; Torquato, Salvatore
2013-06-01
Finding the densest sphere packing in d-dimensional Euclidean space R(d) is an outstanding fundamental problem with relevance in many fields, including the ground states of molecular systems, colloidal crystal structures, coding theory, discrete geometry, number theory, and biological systems. Numerically generating the densest sphere packings becomes very challenging in high dimensions due to an exponentially increasing number of possible sphere contacts and sphere configurations, even for the restricted problem of finding the densest lattice sphere packings. In this paper we apply the Torquato-Jiao packing algorithm, which is a method based on solving a sequence of linear programs, to robustly reproduce the densest known lattice sphere packings for dimensions 2 through 19. We show that the TJ algorithm is appreciably more efficient at solving these problems than previously published methods. Indeed, in some dimensions, the former procedure can be as much as three orders of magnitude faster at finding the optimal solutions than earlier ones. We also study the suboptimal local density-maxima solutions (inherent structures or "extreme" lattices) to gain insight about the nature of the topography of the "density" landscape. PMID:23848802
A set of verification test cases for Eiger : plane wave scattering from a sphere.
Jorgenson, Roy Eberhardt; Kotulski, Joseph Daniel
2004-10-01
This report discusses a set of verification test cases for the frequency-domain, boundary-element, electromagnetics code Eiger based on the analytical solution of plane wave scattering from a sphere. Three cases will be considered: when the sphere is made of perfect electric conductor, when the sphere is made of lossless dielectric and when the sphere is made of lossy dielectric. We outline the procedures that must be followed in order to carefully compare the numerical solution to the analytical solution. We define an error criterion and demonstrate convergence behavior for both the analytical and numerical cases. These problems test the code's ability to calculate the surface current density and secondary quantities, such as near fields and far fields.
Phase diagram of hard tetrahedra.
Haji-Akbari, Amir; Engel, Michael; Glotzer, Sharon C
2011-11-21
Advancements in the synthesis of faceted nanoparticles and colloids have spurred interest in the phase behavior of polyhedral shapes. Regular tetrahedra have attracted particular attention because they prefer local symmetries that are incompatible with periodicity. Two dense phases of regular tetrahedra have been reported recently. The densest known tetrahedron packing is achieved in a crystal of triangular bipyramids (dimers) with a packing density of 4000/4671 ? 85.63%. In simulation a dodecagonal quasicrystal is observed; its approximant, with periodic tiling (3.4.3(2).4), can be compressed to a packing fraction of 85.03%. Here, we show that the quasicrystal approximant is more stable than the dimer crystal for packing densities below 84% using Monte Carlo computer simulations and free energy calculations. To carry out the free energy calculations, we use a variation of the Frenkel-Ladd method for anisotropic shapes and thermodynamic integration. The enhanced stability of the approximant can be attributed to a network substructure, which maximizes the free volume (and hence the wiggle room) available to the particles and facilitates correlated motion of particles, which further contributes to entropy and leads to diffusion for packing densities below 65%. The existence of a solid-solid transition between structurally distinct phases not related by symmetry breaking--the approximant and the dimer crystal--is unusual for hard particle systems. PMID:22112060
Phase Diagram of Hard Tetrahedra
Amir Haji-Akbari; Michael Engel; Sharon C. Glotzer
2011-11-22
Advancements in the synthesis of faceted nanoparticles and colloids have spurred interest in the phase behavior of polyhedral shapes. Regular tetrahedra have attracted particular attention because they prefer local symmetries that are incompatible with periodicity. Two dense phases of regular tetrahedra have been reported recently. The densest known tetrahedron packing is achieved in a crystal of triangular bipyramids (dimers) with packing density 4000/4671=85.63%. In simulation a dodecagonal quasicrystal is observed; its approximant, with periodic tiling (3.4.3^2.4), can be compressed to a packing fraction of 85.03%. Here, we show that the quasicrystal approximant is more stable than the dimer crystal for packing densities below 84% using Monte Carlo computer simulations and free energy calculations. To carry out the free energy calculations, we use a variation of the Frenkel-Ladd method for anisotropic shapes and thermodynamic integration. The enhanced stability of the approximant can be attributed to a network substructure, which maximizes the free volume (and hence the 'wiggle room') available to the particles and facilitates correlated motion of particles, which further contributes to entropy and leads to diffusion for packing densities below 65%. The existence of a solid-solid transition between structurally distinct phases not related by symmetry breaking -- the approximant and the dimer crystal-- is unusual for hard particle systems.
Acoustic Scattering from a Sphere Steve Turley
Hart, Gus
Acoustic Scattering from a Sphere Steve Turley November 24, 2006 Contents 1 Introduction 2 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 References 26 List of Figures 1 Dierential cross section for scattering from an acoustically soft sphere of radius 0.1 wavelengths. 13 2 Dierential cross section for scattering from an acoustically soft
MINIMAL DISCRETE ENERGY ON THE SPHERE
E. A. Rakhmanov; E. B. Saff; Y. M. Zhou
We investigate the energy of arrangements of N points on the surface of a sphere in R3, interacting through a power law potential V = r?, ?2 sphere is devised for the purpose of obtaining bounds for the
Wavelets on the Sphere: Implementation and Approximations
Peraire, Jaime
.Vandergheynst@epfl.ch We continue the analysis of the continuous wavelet transform on the 2-sphere, introduced, obtained by a suitable dilation of the mother wavelet. Key Words: continuous wavelet transform, 2-sphere. INTRODUCTION: THE SPHERICAL CONTINUOUS WAVELET TRANSFORM In a previous paper [6], two of us have introduced
New uniform grids on the sphere
D. Rosca
2010-01-01
Aims: A method for constructing new uniform grids on the sphere is given. Methods: We define a bijection in R2, which maps squares onto discs and preserves areas. Then we use this bijection, combined with Lambert azimuthal projection, for lifting uniform grids from the square to the sphere. Results: We can obtain uniform spherical grids that allow a hierarchical data
Level set estimation on the sphere
Alexander Lorbert; Peter J. Ramadge
2010-01-01
We investigate a technique for estimating level sets of functionals on the 2-sphere. The surface of the sphere is finely partitioned using a tree decomposition and a candidate level set is obtained by minimizing a regularized cost on the tree. A cycle spinning scheme, implemented as an ensemble classification method, is developed to decrease the variance of the tree-based estimate.
C{sub 60}: Sphere or polyhedron?
Haddon, R.C. [Bell Labs., Murray Hill, NJ (United States)] [Bell Labs., Murray Hill, NJ (United States)
1997-02-19
In the original publication on the subject, C{sub 60} was depicted with the aid of a soccer ball, but this representation soon gave way to the familiar line drawing of chemical bonds between nucleii. To a large extent the dichotomy in the representation of the fullerenes remains today, and it is the purpose of this paper to pose and address the question that appears in the title. Of course, in reality the answer is well-known, and neither the sphere nor the polyhedron represent C{sub 60}, which like other molecules exists as a collection of nuclei with an associated distribution of electron density. Nevertheless, it is of interest to consider which of these conventional representations is most relevant for the fullerenes and in particular the language most appropriate to the description of the shape of these molecules and the geometry of the carbon atoms. The analysis presented here shows that topology of the molecule is paramount, and hence, C{sub 60} (and the fullerenes) are best modeled as polyhedra. 16 refs., 3 figs.
The periodically oscillating plasma sphere
Nebel, R.A.; Barnes, D.C. [Los Alamos National Lab., NM (United States)
1998-08-01
A new method of operating an inertial electrostatic confinement (IEC) device is proposed, and its performance is evaluated. The scheme involved an oscillating thermal cloud of ions immersed in a bath of electrons that form a harmonic oscillator potential. The scheme is called the periodically oscillating plasma sphere, and it appears to solve many of the problems that may limit other IEC systems to low gain. A set of self-similar solutions to the ion fluid equations is presented, and plasma performance is evaluated. Results indicate that performance enhancement of gridded IEC systems such as the Los Alamos intense neutron source device is possible as well as high-performance operation for low-loss systems such as the Penning trap experiment. Finally, a conceptual idea for a massively modular Penning trap reactor is also presented.
Tandem spheres in hypersonic flow
Laurence, Stuart J [California Institute of Technology, Pasadena] [California Institute of Technology, Pasadena; Deiterding, Ralf [ORNL] [ORNL; Hornung, Hans G [California Institute of Technology, Pasadena] [California Institute of Technology, Pasadena
2009-01-01
The problem of determining the forces acting on a secondary body when it is travelling at some point within the shocked region created by a hypersonic primary body is of interest in such situations as store or stage separation, re-entry of multiple vehicles, and atmospheric meteoroid fragmentation. The current work is concerned with a special case of this problem, namely that in which both bodies are spheres and are stationary with respect to one another. We first present an approximate analytical model of the problem; subsequently, numerical simulations are described and results are compared with those from the analytical model. Finally, results are presented from a series of experiments in the T5 hypervelocity shock tunnel in which a newly-developed force-measurement technique was employed.
Yu, Yang-Xin; Tian, Ai-Wei; Gao, Guang-Hua
2005-06-21
A new method to predict concentration dependence of collective diffusion coefficient of bovine serum albumin (BSA) in aqueous electrolyte solution is developed based on the generalized Stokes-Einstein equation which relates the diffusion coefficient to the osmotic pressure. The concentration dependence of osmotic pressure is evaluated using the solution of the mean spherical approximation for the two-Yukawa model fluid. The two empirical correlations of sedimentation coefficient are tested in this work. One is for a disordered suspension of hard spheres, and another is for an ordered suspension of hard spheres. The concentration dependence of the collective diffusion coefficient of BSA under different solution conditions, such as pH and ionic strength is predicted. From the comparison between the predicted and experimental values we found that the sedimentation coefficient for the disordered suspension of hard spheres is more suitable for the prediction of the collective diffusion coefficients of charged BSA in aqueous electrolyte solution. The theoretical predictions from the hard-core two-Yukawa model coupled with the sedimentation coefficient for a suspension of hard spheres are in good agreement with available experimental data, while the hard sphere model is unable to describe the behavior of diffusion due to its neglect of the double-layer repulsive charge-charge interaction between BSA molecules. PMID:15962025
ERIC Educational Resources Information Center
Mathews, Jay
2009-01-01
In 1994, fresh from a two-year stint with Teach for America, Mike Feinberg and Dave Levin inaugurated the Knowledge Is Power Program (KIPP) in Houston with an enrollment of 49 5th graders. By this Fall, 75 KIPP schools will be up and running, setting children from poor and minority families on a path to college through a combination of hard work,…
Wu, Mingshen
Soft Skills, Hard Science: A Program to Improve Job Placement of STEM Graduates with Disabilities 2013 Women & Science Conference1 Wednesday, May 22, 13 #12;Why focus on soft skills? What comes to mind rated recent grads on same skills Perception Reality 8 Wednesday, May 22, 13 #12;what are soft skills
ERIC Educational Resources Information Center
Kennedy, Mike
1999-01-01
Provides guidelines to help schools maintain hard floors and carpets, including special areas in schools and colleges that need attention and the elements needed to have a successful carpet-maintenance program. The importance of using heavy equipment to lessen time and effort is explained as are the steps maintenance workers can take to make the…
Monodisperse PEGylated Spheres: An Aqueous Colloidal Model System
2014-01-01
Fluorinated core–shell spheres have been synthesized using a novel semibatch emulsion polymerization protocol employing slow feeding of the initiator. The synthesis results in aqueous dispersions of highly monodisperse spheres bearing a well-defined poly(ethylene glycol) graft (PEGylation). Measurements are consistent with the synthesis achieving a high grafting density that moreover consists of a single PEG layer with the polymer significantly elongated beyond its radius of gyration in bulk. The fluorination of the core of the particles confers a low index of refraction such that the particles can be refractive index matched in water through addition of relatively small amounts of a cosolvent, which enables the use of optical and laser-based methods for studies of concentrated systems. The systems exhibit an extreme stability in NaCl solutions, but attractions among particles can be introduced by addition of other salts, in which case aggregation is shown to be reversible. The PEGylated sphere dispersions are expected to be ideally suited as model systems for studies of the effect of PEG-mediated interactions on, for instance, structure, dynamics, phase behavior, and rheology. PMID:24533774
NASA Astrophysics Data System (ADS)
Cheng, Hongbo
2015-01-01
The Casimir energies for plate-sphere system and sphere-sphere systems under PFA in the presence of one extra compactified universal dimension are analyzed. We find that the Casimir energy between a plate and a sphere in the case of sphere-based PFA is divergent. The Casimir energy of plate-sphere system in the case of plate-based PFA is finite and keeps negative. The extra-dimension corrections to the Casimir energy will be more manifest if the sphere is larger or farther away from the plate. It is shown that the negative Casimir energy for two spheres is also associated with the sizes of spheres and extra space. The larger spheres and the longer distance between them make the influence from the additional dimension stronger.
Charged-current reactions in the supernova neutrino-sphere
NASA Astrophysics Data System (ADS)
Rrapaj, Ermal; Holt, J. W.; Bartl, Alexander; Reddy, Sanjay; Schwenk, A.
2015-03-01
We calculate neutrino absorption rates due to charged-current reactions ?e+n ?e-+p and ?¯e+p ?e++n in the outer regions of a newly born neutron star called the neutrino-sphere. To improve on recent work which has shown that nuclear mean fields enhance the ?e cross section and suppress the ?¯e cross section, we employ realistic nucleon-nucleon interactions that fit measured scattering phase shifts. Using these interactions we calculate the momentum-, density-, and temperature-dependent nucleon self-energies in the Hartree-Fock approximation. A potential derived from chiral effective field theory and a pseudopotential constructed to reproduce nucleon-nucleon phase shifts at the mean-field level are used to study the equilibrium proton fraction and charged-current rates. We compare our results to earlier calculations obtained using phenomenological mean-field models and to those obtained in the virial expansion valid at low density and high temperature. In the virial regime our results are consistent with previous calculations, and at higher densities relevant for the neutrino-sphere, ? ?1012 g/cm 3, we find the difference between the ?e and ?¯e absorption rates to be larger than predicted earlier. Our results may have implications for heavy-element nucleosynthesis in supernovae, and for supernova neutrino detection.
Involute, minimal, outer, and increasingly trapped spheres
Hayward, Sean A. [Center for Astrophysics, Shanghai Normal University, 100 Guilin Road, Shanghai 200234 (China)
2010-01-15
Seven different refinements of trapped surfaces are proposed, each intended as potential stability conditions. This article concerns spherical symmetry, but each condition can be generalized. Involute trapped spheres satisfy a similar condition to minimal trapped spheres, which are strictly minimal with respect to the Kodama vector. There is also a weaker version of involute trapped spheres. Outer trapped spheres have positive surface gravity. Increasingly (future, respectively, past) trapped spheres generate spheres which are more trapped in a (future, respectively, past) causal direction, with three types: in any such causal direction, along the dual Kodama vector, and in some such causal direction. Assuming the null energy condition, the seven conditions form a strict hierarchy, in the above order. In static space-times, they reduce to three inequivalent definitions, namely, minimal, outer, and increasingly trapped spheres. For a widely considered class of so-called nice (or nondirty) black holes, minimal trapped and outer trapped become equivalent. Reissner-Nordstroem black holes provide examples of this, and that the increasingly trapped differs. Examples where all three refinements differ are provided by a simple family of dirty black holes parametrized by mass and singularity area.
Ceramic Spheres From Cation Exchange Beads
NASA Technical Reports Server (NTRS)
Dynys, F. W.
2003-01-01
Porous ZrO2 and hollow TiO2 spheres were synthesized from a strong acid cation exchange resin. Spherical cation exchange beads, polystyrene based polymer, were used as a morphological-directing template. Aqueous ion exchange reaction was used to chemically bind (ZrO)(2+) ions to the polystyrene structure. The pyrolysis of the polystyrene at 600 C produces porous ZrO2 spheres with a surface area of 24 sq m/g with a mean sphere size of 42 microns. Hollow TiO2 spheres were synthesized by using the beads as a micro-reactor. A direct surface reaction - between titanium isopropoxide and the resin beads forms a hydrous TiO2 shell around the polystyrene core. The pyrolysis of the polystyrene core at 600 C produces hollow anatase spheres with a surface area of 42 sq m/g with a mean sphere size of 38 microns. The formation of ceramic spheres was studied by XRD, SEM and B.E.T. nitrogen adsorption measurements.
NASA Astrophysics Data System (ADS)
Yang, Guomin; Liu, Longcheng
2015-05-01
Based on the best available knowledge of density functional theory (DFT), the reference-fluid perturbation method is here extended to yield different approaches that well account for the cross correlations between the Columbic interaction and the hard-sphere exclusion in an inhomogeneous ionic hard-sphere fluid. In order to quantitatively evaluate the advantage and disadvantage of different approaches in describing the interfacial properties of electrical double layers, this study makes a systematic comparison against Monte Carlo simulations over a wide range of conditions. The results suggest that the accuracy of the DFT approaches is well correlated to a coupling parameter that describes the coupling strength of electrical double layers by accounting for the steric effect and that can be used to classify the systems into two regimes. In the weak-coupling regime, the approaches based on the bulk-fluid perturbation method are shown to be more accurate than the counterparts based on the reference-fluid perturbation method, whereas they exhibit the opposite behavior in the strong-coupling regime. More importantly, the analysis indicates that, with a suitable choice of the reference fluid, the weighted correlation approximation (WCA) to DFT gives the best account of the coupling effect of the electrostatic-excluded volume correlations. As a result, a piecewise WCA approach can be developed that is robust enough to describe the structural and thermodynamic properties of electrical double layers over both weak- and strong-coupling regimes.
Chen, Xueqian; Chen, Houyang; Liu, Honglai; Hu, Ying
2011-01-28
We propose a free-space density functional theory for polymer adsorption. The derivation within the framework of density functional theory leads to the splitting of the intrinsic free energy into an ideal-gas term and a residual term responsible for the intrinsic energy and the nonbonded interactions between monomers, respectively. A more reasonable treatment is adopted for the residual free energy to count for the monomer-monomer correlation underestimated by the local density approximation. An approach using propagators is proposed to calculate the single-chain partition function and the segment-density distributions, the three adsorption conformations as trains, loops, and tails are further described by propagators. Dirac's bra-ket notation used makes the derivation simpler and provides clearer physical meanings. The theoretical calculations for the adsorption of hard-sphere chains onto a nonadsorbing and an adsorbing hard wall show that the structure of the adsorption layer is strongly affected by the packing effect which has been underestimated by the previous lattice adsorption theory. PMID:21280791
NASA Astrophysics Data System (ADS)
Chen, Xueqian; Chen, Houyang; Liu, Honglai; Hu, Ying
2011-01-01
We propose a free-space density functional theory for polymer adsorption. The derivation within the framework of density functional theory leads to the splitting of the intrinsic free energy into an ideal-gas term and a residual term responsible for the intrinsic energy and the nonbonded interactions between monomers, respectively. A more reasonable treatment is adopted for the residual free energy to count for the monomer-monomer correlation underestimated by the local density approximation. An approach using propagators is proposed to calculate the single-chain partition function and the segment-density distributions, the three adsorption conformations as trains, loops, and tails are further described by propagators. Dirac's bra-ket notation used makes the derivation simpler and provides clearer physical meanings. The theoretical calculations for the adsorption of hard-sphere chains onto a nonadsorbing and an adsorbing hard wall show that the structure of the adsorption layer is strongly affected by the packing effect which has been underestimated by the previous lattice adsorption theory.
Manipulator for rotating and examining small spheres
Weinstein, Berthold W. [Livermore, CA; Willenborg, David L. [Livermore, CA
1980-02-12
A manipulator which provides fast, accurate rotational positioning of a small sphere, such as an inertial confinement fusion target, which allows inspecting of the entire surface of the sphere. The sphere is held between two flat, flexible tips which move equal amounts in opposite directions. This provides rolling of the ball about two orthogonal axes without any overall translation. The manipulator may be controlled, for example, by an x- and y-axis driven controlled by a mini-computer which can be programmed to generate any desired scan pattern.
Manipulator for rotating and examining small spheres
Weinstein, B.W.; Willenborg, D.L.
1980-02-12
A manipulator is disclosed which provides fast, accurate rotational positioning of a small sphere, such as an inertial confinement fusion target, which allows inspecting of the entire surface of the sphere. The sphere is held between two flat, flexible tips which move equal amounts in opposite directions. This provides rolling of the ball about two orthogonal axes without any overall translation. The manipulator may be controlled, for example, by an x- and y-axis driven controlled by a mini-computer which can be programmed to generate any desired scan pattern. 8 figs.
New uniform grids on the sphere
NASA Astrophysics Data System (ADS)
Ro?ca, D.
2010-09-01
Aims: A method for constructing new uniform grids on the sphere is given. Methods: We define a bijection in R2, which maps squares onto discs and preserves areas. Then we use this bijection, combined with Lambert azimuthal projection, for lifting uniform grids from the square to the sphere. Results: We can obtain uniform spherical grids that allow a hierarchical data manipulation and have an isolatitudinal distribution of cells. Compared with HEALPix grids, nowadays the most used in astronomy and astrophysics, our grids have the advantage of allowing easier implementation, and in addition one can move approximating functions from the square to the sphere by a simple technique.
Surface modification and characterization of carbon spheres by grafting polyelectrolyte brushes
NASA Astrophysics Data System (ADS)
Zhang, Qi; Li, Houbin; Zhang, Pan; Liu, Liangliang; He, Yuhang; Wang, Yali
2014-06-01
Modified carbon spheres (CSPBs) were obtained by grafting poly(diallyl dimethyl ammonium chloride) (p-DMDAAC) on the surface of carbon spheres (CSs). It can be viewed as a kind of cation spherical polyelectrolyte brushes (CSPBs), which consist of carbon spheres as core and polyelectrolytes as shell. The method of synthesizing carbon spheres was hydrothermal reaction. Before the polyelectrolyte brushes were grafted, azo initiator [4,4'-Azobis(4-cyanovaleric acyl chloride)] was attached to the carbon spheres' surface through hydroxyl groups. CSPBs were characterized by scanning electron microscope (SEM), Fourier transform infrared spectroscopy (FTIR), gel permeation chromatography (GPC), conductivity meter, and system zeta potential. The results showed that compared with carbon spheres, the conductivity and zeta potential on CSPBs increased from 9.98 to 49.24 ?S/cm and 11.6 to 42.5 mV, respectively, after the polyelectrolyte brushes were grafted. The colloidal stability in water was enhanced, and at the same time, the average diameter of the CSPBs was found to be 173 nm, and the average molecular weight and grafted density of the grafted polyelectrolyte brushes were 780,138 g/mol and 4.026 × 109/nm2, respectively.
Surface modification and characterization of carbon spheres by grafting polyelectrolyte brushes
2014-01-01
Modified carbon spheres (CSPBs) were obtained by grafting poly(diallyl dimethyl ammonium chloride) (p-DMDAAC) on the surface of carbon spheres (CSs). It can be viewed as a kind of cation spherical polyelectrolyte brushes (CSPBs), which consist of carbon spheres as core and polyelectrolytes as shell. The method of synthesizing carbon spheres was hydrothermal reaction. Before the polyelectrolyte brushes were grafted, azo initiator [4,4?-Azobis(4-cyanovaleric acyl chloride)] was attached to the carbon spheres' surface through hydroxyl groups. CSPBs were characterized by scanning electron microscope (SEM), Fourier transform infrared spectroscopy (FTIR), gel permeation chromatography (GPC), conductivity meter, and system zeta potential. The results showed that compared with carbon spheres, the conductivity and zeta potential on CSPBs increased from 9.98 to 49.24 ?S/cm and 11.6 to 42.5 mV, respectively, after the polyelectrolyte brushes were grafted. The colloidal stability in water was enhanced, and at the same time, the average diameter of the CSPBs was found to be 173 nm, and the average molecular weight and grafted density of the grafted polyelectrolyte brushes were 780,138 g/mol and 4.026?×?109/nm2, respectively. PMID:24948900
Mesoporous silica spheres from colloids.
Ho, Jenny; Zhu, Wei; Wang, Huanting; Forde, Gareth M
2007-04-15
A novel method has been developed to synthesize mesoporous silica spheres using commercial silica colloids (SNOWTEX) as precursors and electrolytes (ammonium nitrate and sodium chloride) as destabilizers. Crosslinked polyacrylamide hydrogel was used as a temporary barrier to obtain dispersible spherical mesoporous silica particles. The influences of synthesis conditions including solution composition and calcination temperature on the formation of the mesoporous silica particles were systematically investigated. The structure and morphology of the mesoporous silica particles were characterized via scanning electron microscopy (SEM) and N2 sorption technique. Mesoporous silica particles with particle diameters ranging from 0.5 to 1.6 microm were produced whilst the BET surface area was in the range of 31-123 m2 g-1. Their pore size could be adjusted from 14.1 to 28.8 nm by increasing the starting particle diameter from 20-30 nm up to 70-100 nm. A simple and cost effective method is reported that should open up new opportunities for the synthesis of scalable host materials with controllable structures. PMID:17270199
Mansur, Louis K [ORNL] [ORNL; Bhattacharya, R [UES, Incorporated, Dayton, OH] [UES, Incorporated, Dayton, OH; Blau, Peter Julian [ORNL] [ORNL; Clemons, Art [ORNL] [ORNL; Eberle, Cliff [ORNL] [ORNL; Evans, H B [UES, Incorporated, Dayton, OH] [UES, Incorporated, Dayton, OH; Janke, Christopher James [ORNL] [ORNL; Jolly, Brian C [ORNL] [ORNL; Lee, E H [Consultant, Milpitas, CA] [Consultant, Milpitas, CA; Leonard, Keith J [ORNL] [ORNL; Trejo, Rosa M [ORNL] [ORNL; Rivard, John D [ORNL] [ORNL
2010-01-01
High energy ion beam surface treatments were applied to a selected group of polymers. Of the six materials in the present study, four were thermoplastics (polycarbonate, polyethylene, polyethylene terephthalate, and polystyrene) and two were thermosets (epoxy and polyimide). The particular epoxy evaluated in this work is one of the resins used in formulating fiber reinforced composites for military helicopter blades. Measures of mechanical properties of the near surface regions were obtained by nanoindentation hardness and pin on disk wear. Attempts were also made to measure erosion resistance by particle impact. All materials were hardness tested. Pristine materials were very soft, having values in the range of approximately 0.1 to 0.5 GPa. Ion beam treatment increased hardness by up to 50 times compared to untreated materials. For reference, all materials were hardened to values higher than those typical of stainless steels. Wear tests were carried out on three of the materials, PET, PI and epoxy. On the ion beam treated epoxy no wear could be detected, whereas the untreated material showed significant wear.
On the binding mode of urease active site inhibitors: A density functional study
NASA Astrophysics Data System (ADS)
Leopoldini, M.; Marino, T.; Russo, N.; Toscano, M.
The way with which boric acid, a rapid reversible competitive inhibitor, binds the urease active site was explored at density functional B3LYP level of theory. The catalytic core of the enzyme was simulated by two models of different size. In both cases, amino acid residues belonging to the inner and to the outer coordination spheres of nickel ions were replaced by smaller molecular species. Contrary to the experimental indication that attributes the inhibitory ability of this acid to the lack of a nucleophilic attack by the enzyme to the boron atom, we instead found that another possibility exists based on the presence of a strong covalent sigma bond between boron and urease that we think can be hardly broken to allow any course of the reaction.
Particle sizing in highly turbid dispersions by Photon Density Wave spectroscopy
NASA Astrophysics Data System (ADS)
Bressel, L.; Hass, R.; Reich, O.
2013-09-01
Photon Density Wave (PDW) spectroscopy is presented as a fascinating technology for the independent determination of scattering (??s) and absorption (?a) properties of highly turbid liquid dispersions. The theory is reviewed introducing new expressions for the PDW coefficients kI and k?. Furthermore, two models for dependent scattering, namely the hard sphere model in the Percus-Yevick Approximation (HSPYA) and the Yukawa model in the Mean Spherical Approximation (YMSA), are experimentally examined. On the basis of the HSPYA particle sizing is feasible in dispersions of high ionic strength. It is furthermore shown that in dialyzed dispersions or in technical copolymers with high particle charge only the YMSA allows for correct dilution-free particle sizing.