Density Functional Theory and Freezing of Hard Spheres, Beyond the Percus-Yevick Approximation
M. Moradi; A. Razeghizadeh
2007-01-01
The density functional theory for the freezing hard spheres is studied. We use a variety of the hard sphere direct correlation functions (DCFs) such as the one introduced by Roth et al. [J. Phys. Condens. Matter 14, 12063 (2002)]; we call it RELK DCF, a new hard sphere DCF developed here by a combination of the RELK and the Percus-Yevick
Ott, Albrecht
Density functional theory for colloidal mixtures of hard platelets, rods, and spheres Ansgar, hard needles, and hard platelets; both the needles and platelets are taken to be of vanishing thickness the correct second virial expansion of the excess free-energy functional. The case of sphere-platelet overlap
Alexander, F.J.; Garcia, A.L.; Alder, B.J.
1994-10-01
The direct simulation Monte Carlo method is modified with a post-collision displacement in order to obtain the hard sphere equation of state. This leads to consistent thermodynamic and transport properties in the low density regime. At higher densities, when the enhanced collision rate according to kinetic theory is introduced, the exact hard sphere equation of state is recovered. and the transport coefficients are comparable to those of the Enskog theory. The computational advantages of this scheme over hard sphere molecular dynamics are that it is significantly faster at low and moderate densities and that it is readily parallelizable.
Density functional theory for colloidal mixtures of hard platelets, rods, and spheres
Ansgar Esztermann; Hendrik Reich; Matthias Schmidt
2005-11-18
A geometry-based density functional theory is presented for mixtures of hard spheres, hard needles and hard platelets; both the needles and the platelets are taken to be of vanishing thickness. Geometrical weight functions that are characteristic for each species are given and it is shown how convolutions of pairs of weight functions recover each Mayer bond of the ternary mixture and hence ensure the correct second virial expansion of the excess free energy functional. The case of sphere-platelet overlap relies on the same approximation as does Rosenfeld's functional for strictly two-dimensional hard disks. We explicitly control contributions to the excess free energy that are of third order in density. Analytic expressions relevant for the application of the theory to states with planar translational and cylindrical rotational symmetry, e.g. to describe behavior at planar smooth walls, are given. For binary sphere-platelet mixtures, in the appropriate limit of small platelet densities, the theory differs from that used in a recent treatment [L. Harnau and S. Dietrich, Phys. Rev. E 71, 011504 (2004)]. As a test case of our approach we consider the isotropic-nematic bulk transition of pure hard platelets, which we find to be weakly first order, with values for the coexistence densities and the nematic order parameter that compare well with simulation results.
Hard sphere mixtures near a hard wall
JERZY P. NOWORYTA; DOUGLAS HENDERSON; STEFAN SOKO?OWSKI; KWONG-YU CHAN
1998-01-01
Hard spheres with ratios of diameters of 3:5 and 1:3 and at various densities are studied by means of grand canonical ensemble (GCE) simulations, first- and second-order Percus—Yevick theory, scaled particle theory (SPT) and density functional theory (DFT). Generally, but not always, the density profiles of the first-order Percus—Yevick (PY1) theory results are smaller at contact than the GCE simulation
M. Plischke; D. Henderson
1986-01-01
Solutions for the pair correlation function and density profile of a system of hard spheres near a hard wall are obtained by using the Percus-Yevick and hypernetted chain approximations, generalized for inhomogeneous fluids. The Percus-Yevick (PY) results are similar in accuracy to those obtained for the bulk fluid. The PY pair correlation function is generally too small near contact but
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.
M. Oettel; S. Goerig; A. Haertel; H. Loewen; M. Radu; T. Schilling
2010-09-03
We perform a comparative study of the free energies and the density distributions in hard sphere crystals using Monte Carlo simulations and density functional theory (employing Fundamental Measure functionals). Using a recently introduced technique (Schilling and Schmid, J. Chem. Phys 131, 231102 (2009)) we obtain crystal free energies to a high precision. The free energies from Fundamental Measure theory are in good agreement with the simulation results and demonstrate the applicability of these functionals to the treatment of other problems involving crystallization. The agreement between FMT and simulations on the level of the free energies is also reflected in the density distributions around single lattice sites. Overall, the peak widths and anisotropy signs for different lattice directions agree, however, it is found that Fundamental Measure theory gives slightly narrower peaks with more anisotropy than seen in the simulations. Among the three types of Fundamental Measure functionals studied, only the White Bear II functional (Hansen-Goos and Roth, J. Phys.: Condens. Matter 18, 8413 (2006)) exhibits sensible results for the equilibrium vacancy concentration and a physical behavior of the chemical potential in crystals constrained by a fixed vacancy concentration.
NASA Astrophysics Data System (ADS)
Oettel, M.; Görig, S.; Härtel, A.; Löwen, H.; Radu, M.; Schilling, T.
2010-11-01
We perform a comparative study of the free energies and the density distributions in hard-sphere crystals using Monte Carlo simulations and density functional theory (employing Fundamental Measure functionals). Using a recently introduced technique [T. Schilling and F. Schmid, J. Chem. Phys. 131, 231102 (2009)10.1063/1.3274951] we obtain crystal free energies to a high precision. The free energies from fundamental measure theory are in good agreement with the simulation results and demonstrate the applicability of these functionals to the treatment of other problems involving crystallization. The agreement between fundamental measure theory and simulations on the level of the free energies is also reflected in the density distributions around single lattice sites. Overall, the peak widths and anisotropy signs for different lattice directions agree, however, it is found that fundamental measure theory gives slightly narrower peaks with more anisotropy than seen in the simulations. Among the three types of fundamental measure functionals studied, only the White Bear II functional [H. Hansen-Goos and R. Roth, J. Phys.: Condens. Matter 18, 8413 (2006)10.1088/0953-8984/18/37/002] exhibits sensible results for the equilibrium vacancy concentration and a physical behavior of the chemical potential in crystals constrained by a fixed vacancy concentration.
NASA Astrophysics Data System (ADS)
Avazpour, A.; Avazpour, L.
2010-12-01
This article applies the density functional theory to confined liquid crystals, comprised of ellipsoidal shaped particles interacting through the hard Gaussian overlap (HGO) potential. The extended restricted orientation model proposed by Moradi and co-workers [J. Phys.: Condens. Matter 17, 5625 (2005)] is used to study the surface anchoring. The excess free energy is calculated as a functional expansion of density around a reference homogeneous fluid. The pair direct correlation function (DCF) of a homogeneous HGO fluid is approximated, based on the optimized sum of Percus-Yevick and Roth DCF for hard spheres; the anisotropy introduced by means of the closest approach parameter, the expression proposed by Marko [Physica B 392, 242 (2007)] for DCF of HGO, and hard ellipsoids were used. In this study we extend an our previous work [Phys. Rev. E 72, 061706 (2005)] on the anchoring behavior of hard particle liquid crystal model, by studying the effect of changing the particle-substrate contact function instead of hard needle-wall potentials. We use the two particle-surface potentials: the HGO-sphere and the HGO-surface potentials. The average number density and order parameter profiles of a confined HGO fluid are obtained using the two particle-wall potentials. For bulk isotropic liquid, the results are in agreement with the Monte Carlo simulation of Barmes and Cleaver [Phys. Rev. E 71, 021705 (2005)]. Also, for the bulk nematic phase, the theory gives the correct density profile and order parameter between the walls.
T. Antal; P. L. Krapivsky; S. Redner
2008-05-25
We investigate the collision cascade that is generated by a single moving incident particle on a static hard-sphere gas. We argue that the number of moving particles at time t grows as t^{xi} and the number collisions up to time t grows as t^{eta}, with xi=2d/(d+2) and eta=2(d+1)/(d+2) and d the spatial dimension. These growth laws are the same as those from a hydrodynamic theory for the shock wave emanating from an explosion. Our predictions are verified by molecular dynamics simulations in d=1 and 2. For a particle incident on a static gas in a half-space, the resulting backsplatter ultimately contains almost all the initial energy.
Odriozola, Gerardo; Berthier, Ludovic
2011-02-01
We use replica exchange Monte Carlo simulations to measure the equilibrium equation of state of the disordered fluid state for a binary hard sphere mixture up to very large densities where standard Monte Carlo simulations do not easily reach thermal equilibrium. For the moderate system sizes we use (up to N = 100), we find no sign of a pressure discontinuity near the location of dynamic glass singularities extrapolated using either algebraic or simple exponential divergences, suggesting they do not correspond to genuine thermodynamic glass transitions. Several scenarios are proposed for the fate of the fluid state in the thermodynamic limit. PMID:21303135
Ordering of hard spheres inside hard cylindrical pores.
Durán-Olivencia, F J; Gordillo, M C
2009-06-01
Isothermal-isobaric simulations on the ordering behavior of hard spheres upon confinement are presented. The radii of the confining cylinders go from 1.1 to 2 in units of the diameters of the hard spheres adsorbed. In all the range of pressures considered the spheres were located in concentric layers, as many as the radius of the hard cylinder would permit. When the pressure increases, the hard spheres go from being loosely arranged to the formation of ordered structures. This change is marked in all cases by a distinct break in the density of spheres in a narrow pressure range. When the tube radius is smaller than 1.5, the high-pressure ordering is determined by the number of coplanar spheres you can have within a circle of radius equal to that of the confining tube. For wider tubes, the change upon compression is determined by the formation of defected two-dimensional triangular lattices wrapped to fit inside the particular cylinder we are considering. PMID:19658477
Verma, Anurag; Ford, David M
2009-09-01
The study of freezing using perturbative classical density-functional theory is revisited, using a bridge functional approach to resum all terms beyond second order in the free energy expansion. More precisely, the first-order direct correlation function of the solid phase is written as a functional expansion about the homogeneous liquid phase, and the sum of all higher-order terms is represented as a functional of the second-order term. Information about the shape and uniqueness of this bridge functional for the case of hard spheres is obtained via an inversion procedure that employs Monte Carlo fluid-solid coexistence data from the literature. The parametric plots obtained from the inversion procedure show very little scatter in certain regions, suggesting a unique functional dependence, but large scatter in other regions. The scatter is related to the anisotropy of the solid lattice at the particle scale. Interestingly, the thermodynamic properties of the phase transition are quite insensitive to the regions where the scatter is large, and several simple closures (i.e., analytical forms of the bridge function) reproduce exactly the liquid-solid coexistence densities and Lindemann parameter from simulation. The form of these closures is significantly different from the usual closures employed in liquid-state integral equation theory. PMID:19905064
P. V. Giaquinta; G. Giunta; G. Malescio
1991-01-01
Using an integral-equation approach based upon an approximation for the tail function, the equilibrium properties of a system of hard spheres are studied with special concern for the behavior in the region of close packing. The closure adopted is such that full, internal consistency is ensured in the thermodynamics of the model with respect to both the two zero-separation theorems
Brian B. Laird
1992-01-01
The isothermal elastic constants for the face-centered-cubic (fcc) and body-centered-cubic (bcc) hard-sphere crystal are calculated for a range of densities using the modified weighted-density functional of Denton and Ashcroft [Phys. Rev. A 39, 4701 (1989)]. The fcc elastic constants are shown to be in excellent agreement with the computer simulation data and to represent a significant improvement over the predictions
Effects of polydispersity on hard sphere crystals
See-Eng Phan; William B. Russel; Jixiang Zhu; Paul M. Chaikin
1998-01-01
We use simple models and molecular dynamics simulations to determine the effects of polydispersity delta on the equation of state for hard sphere crystals. Experiments show that the osmotic pressure for poly-(methyl methacrylate) (PMMA) spheres with a poly-(12-hydroxy stearic acid) (PHSA) layer with a 5% polydispersity exceeds the value expected for hard spheres as the volume fraction phi increases, particularly
Effects of polydispersity on hard sphere crystals
See-Eng Phan; William B. Russel; Jixiang Zhu; Paul M. Chaikin
1998-01-01
We use simple models and molecular dynamics simulations to determine the effects of polydispersity ? on the equation of state for hard sphere crystals. Experiments show that the osmotic pressure for poly-(methyl methacrylate) (PMMA) spheres with a poly-(12-hydroxy stearic acid) (PHSA) layer with a 5% polydispersity exceeds the value expected for hard spheres as the volume fraction ? increases, particularly
Depletion potential in colloidal mixtures of hard spheres and platelets
L. Harnau; S. Dietrich
2004-01-21
The depletion potential between two hard spheres in a solvent of thin hard disclike platelets is investigated by using either the Derjaguin approximation or density functional theory. Particular attention is paid to the density dependence of the depletion potential. A second-order virial approximation is applied, which yields nearly exact results for the bulk properties of the hard-platelet fluid at densities two times smaller than the density of the isotropic fluid at isotropic-nematic phase coexistence. As the platelet density increases, the attractive primary minimum of the depletion potential deepens and an additional small repulsive barrier at larger sphere separations develops. Upon decreasing the ratio of the radius of the spheres and the platelets, the primary minimum diminishes and the position of the small repulsive barrier shifts to smaller values of the sphere separation.
Collision statistics in sheared inelastic hard spheres
Marcus N. Bannerman; Thomas E. Green; Paul Grassia; Leo Lue
2009-03-24
The dynamics of sheared inelastic-hard-sphere systems are studied using non-equilibrium 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 more direct, head-on collisions. Examination of the distribution of the time 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 DSMC simulation of the Enskog equation. Results of the kinetic model of Montanero et al. {[}Montanero et al., 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.
Shape Deformation of Vesicles Containing Hard Spheres
NASA Astrophysics Data System (ADS)
Itoga, Hibiki; Morikawa, Ryota; Miyakawa, Takeshi; Yamada, Hironao; Natsume, Yuno; Ueta, Tsuyoshi; Takasu, Masako
Vesicles containing charged colloids show peculiar shape deformation under certain conditions. However, its physical mechanism is not clear. We have performed Monte Carlo simulation for a model of closed triangulated membrane and encapsulated hard spheres. We analyzed vesicular shapes and encapsulated hard spheres by using diffusion coefficient, change of area difference and volume, and the radial distribution of hard spheres from the membrane. The discussion of our results can be used as the foundation for understanding of the complex behavior of vesicles containing colloids.
Hard-sphere fluids in very narrow cylindrical pores
NASA Astrophysics Data System (ADS)
Mon, K. K.; Percus, J. K.
2000-02-01
Properties of fluids in narrow pores have been studied extensively in recent years. In this paper, we study the pore radius dependence of hard-sphere fluids in very narrow cylindrical pores via Monte Carlo simulations to explore the crossover from strictly one-dimensional to quasi-one-dimensional fluids. Our study shows that this crossover is not simple. We observe, for constant pressure, an unexpected but interesting nonmonotonic variation of density and compressibility as the pore radius is varied near the value of one hard-sphere diameter (?hs). These results are related to the onset of configurations with two or more nearest-neighbor hard spheres across the diameter of the cylindrical pore.
Pair distribution function for fluid hard spheres
R. O. Watts; D. Henderson
1969-01-01
The pair distribution function of a system of fluid hard spheres is calculated by means of a simple generalization of the Percus-Yevick theory. A relation between the pair distribution function and the direct correlation function which leads to self-consistent results from the pressure and compressibility equations of state and which is similar, but not identical, to a proposal of Rowlinson,
Regularized 13 moment equations for hard spheres
NASA Astrophysics Data System (ADS)
Struchtrup, Henning; Torrilhon, Manuel
2012-11-01
The regularized 13 moment equations (R13) of rarefied gas dynamics for a monatomic hard sphere gas in the linear regime are presented. The equations are based on an extended Grad-type moment system, which was systematically reduced by means of the Order of Magnitude Method [Struchtrup, Phys. Fluids 16(11), 3921-3934 (2004)]. The linear Burnett and super-Burnett equations are derived from Chapman-Enskog expansion of the R13 equations. While the Burnett coefficients agree with literature values, this seems to be the first time that super-Burnett coefficients are computed for a hard sphere gas. The equations are considered for stability, and dispersion and damping of sound waves. Boundary conditions are given, and solutions of simple boundary value problems are briefly discussed.
Defects in hard-sphere colloidal crystals
NASA Astrophysics Data System (ADS)
Persson Gulda, Maria Christina Margareta
Colloidal crystals of 1.55 microm diameter silica particles were grown on {100} and flat templates by sedimentation and centrifugation. The particles interact as hard spheres. The vacancies and divacancies in these crystals are not in equilibrium, since no movement of single vacancies is observed. The lack of mobility is consistent with the extrapolation of earlier simulations at lower densities. The volume of relaxation of the vacancy has a plausible value for these densities as the volume of formation is approaching the volume in a close-packed crystal. The volume of relaxation for the divacancy is smaller than that of two vacancies, so that the association of two vacancies into a divacancy requires extra volume, and hence extra entropy. The mean square displacement of the nearest neighbors of the vacancies is an order of magnitude larger than that of the nearest neighbors of particles. The mobility of the divacancies is consistent with the extrapolation of older simulations and is similar to that associated with the annihilation of the vacancy-interstitial pair. The volume of motion of the divacancies is DeltaVm = 0.19Vo (Vo: close-packed volume) and the entropy of motion is DeltaSm = 0.49kBT. Dislocation-twin boundary interactions can be observed by introducing strain via a misfit template. The dislocations formed are Shockley partials. When a dislocation goes through the boundary, two more dislocations are created: a reflected dislocation and one left at the boundary, both with the same magnitude Burgers vector. The dislocations relieve a total of about a third of the misfit strain. The remaining strain is sufficiently large to move the dislocation up to the boundary and close to sufficient to move the dislocation through the boundary. A small amount to extra strain energy is needed to cause nucleation of the two additional dislocations after a waiting time.
Effects of polydispersity on hard sphere crystals
NASA Astrophysics Data System (ADS)
Phan, See-Eng; Russel, William B.; Zhu, Jixiang; Chaikin, Paul M.
1998-06-01
We use simple models and molecular dynamics simulations to determine the effects of polydispersity ? on the equation of state for hard sphere crystals. Experiments show that the osmotic pressure for poly-(methyl methacrylate) (PMMA) spheres with a poly-(12-hydroxy stearic acid) (PHSA) layer with a 5% polydispersity exceeds the value expected for hard spheres as the volume fraction ? increases, particularly for ?>0.60. Mean field theory predicts a higher osmotic pressure with increasing polydispersity, but the effects are only significant for ?>0.10. Molecular dynamics simulations with ?=0.05 bound the equation of state between a metastable disordered upper limit and a crystalline organized polydisperse (possibly) lower limit. The pressure for the PMMA-PHSA spheres lies close to the organized polydisperse limit, indicating a preference for a crystalline ordered arrangement where smaller particles surround larger ones. Thus, the higher osmotic pressure seen in the equation of state of PMMA-PHSA spheres is a direct effect of polydispersity, manifest as a pronounced reduction in the crystalline close packed volume fraction from ?max(FCC, ?=0)=0.7404 to ?max(FCC, ?=0.1)=0.665. The random close packing ?max(RCP) is almost independent of polydispersity. This leads to a crossing of values of ?max(FCC) and ?max(RCP) and hence a possible terminal polydispersity of 0.12±0.01, consistent with other simulations, theories, and experiments. Since our results do not include size fractionation of the liquid and solid, the exact meaning of this crossing is unclear and its agreement with previously reported terminal polydispersities may be coincidental.
Chemical potential of hard-sphere fluids by Monte Carlo methods
D. J. Adams
1974-01-01
The ‘potential distribution’ expressions derived by Widom for the pressure and chemical potential of a fluid are developed for the special case of a hard-sphere fluid. The exact equations produced are closely related to those used in Scaled Particle Theory. They have been used to determine the chemical potential of hard-sphere fluids over the reduced density range 0·1 ? ??
Derivative of the hard-sphere radial distribution function at contact
Tao, F.; Song, Y.; Mason, E.A. (Department of Chemistry and Division of Engineering, Brown University, Providence, Rhode Island 02912 (United States))
1992-12-15
A simple and accurate formula for the first derivative of the hard-sphere radial distribution function at contact as a function of density is proposed, suggested by the solution of the Percus-Yevick equation for a fluid of hard spheres.
Haptic Search for Hard and Soft Spheres
van Polanen, Vonne; Bergmann Tiest, Wouter M.; Kappers, Astrid M. L.
2012-01-01
In this study the saliency of hardness and softness were investigated in an active haptic search task. Two experiments were performed to explore these properties in different contexts. In Experiment 1, blindfolded participants had to grasp a bundle of spheres and determine the presence of a hard target among soft distractors or vice versa. If the difference in compliance between target and distractors was small, reaction times increased with the number of items for both features; a serial strategy was found to be used. When the difference in compliance was large, the reaction times were independent of the number of items, indicating a parallel strategy. In Experiment 2, blindfolded participants pressed their hand on a display filled with hard and soft items. In the search for a soft target, increasing reaction times with the number of items were found, but the location of target and distractors appeared to have a large influence on the search difficulty. In the search for a hard target, reaction times did not depend on the number of items. In sum, this showed that both hardness and softness are salient features. PMID:23056197
Fluid--fluid phase separations in nonadditive hard sphere mixtures
Jung, J.; Jhon, M.S. (Center for Molecular Science and Department of Chemistry, Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)); Ree, F.H. (University of California, Lawrence Livermore National Laboratory, Livermore, California 94551 (United States))
1995-01-15
We investigated the phase stability of a system of nonadditive hard sphere (NAHS) mixtures with equal diameters, [ital d], between like species and an unequal collision diameter, [ital d](1+[alpha]), between unlike species. It is based on an analytic equation of state (EOS) which refines an earlier expression [J. Chem. Phys. [bold 100], 9064 (1994)] within the mixed fluid phase range. The new EOS gives a reliable representation of Monte Carlo EOS data over a wide range of density, composition, and nonadditivity parameters ([alpha]). Comparisons with available computer simulations show that the new EOS predicts satisfactory phase boundaries and the critical density line. It is superior to results derived from integral equations (the Percus--Yevick, the Martynov--Sarkisov, and the modified Martynov--Sarkisov) and analytic theories (the MIX1 model, the van der Waals one-fluid model, and the scaled particle theory). The present study shows that, unless [alpha] exceeds 0.026, the fluid phase will remain fully miscible up to the freezing point of pure hard spheres. We have also investigated structural aspects of the phase stability by Monte Carlo computations. The radial distribution functions, the local mole fraction, and coordination numbers for like and unlike pairs of hard spheres exhibit significant number dependencies close to the fluid phase boundary. They provide precursory signals to an impending phase change. Finite systems used in the Monte Carlo sampling limit fluctuations in sizes and shapes of heterogeneous clusters. The observed number dependence simply reflects this fact.
Bulk and wetting phenomena in a colloidal mixture of hard spheres and platelets
L. Harnau; S. Dietrich
2004-08-27
Density functional theory is used to study binary colloidal fluids consisting of hard spheres and thin platelets in their bulk and near a planar hard wall. This system exhibits liquid-liquid coexistence of a phase that is rich in spheres (poor in platelets) and a phase that is poor in spheres (rich in platelets). For the mixture near a planar hard wall, we find that the phase rich in spheres wets the wall completely upon approaching the liquid demixing binodal from the sphere-poor phase, provided the concentration of the platelets is smaller than a threshold value which marks a first-order wetting transition at coexistence. No layering transitions are found in contrast to recent studies on binary mixtures of spheres and non-adsorbing polymers or thin hard rods.
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
Oyarzún, Bernardo; van Westen, Thijs; Vlugt, Thijs J H
2013-05-28
The liquid crystal phase behavior of linear and partially flexible hard-sphere chain fluids and the solubility of hard spheres in hard-sphere chain fluids are studied by constant pressure Monte Carlo simulations. An extensive study on the phase behavior of linear fluids with a length of 7, 8, 9, 10, 11, 12, 13, 14, 15, and 20 beads is carried out. The phase behavior of partially flexible fluids with a total length of 8, 10, 14, and 15 beads and with different lengths for the linear part is also determined. A precise description of the reduced pressure and of the packing fraction change at the isotropic-nematic coexistence was achieved by performing long simulation runs. For linear fluids, a maximum in the isotropic to nematic packing fraction change is observed for a chain length of 15 beads. The infinite dilution solubility of hard spheres in linear and partially flexible hard-sphere chain fluids is calculated by the Widom test-particle insertion method. To identify the effect of chain connectivity and molecular anisotropy on free volume, solubility is expressed relative to that of hard spheres in a hard sphere fluid at same packing fraction as relative Henry's law constants. A linear relationship between relative Henry's law constants and packing fraction is observed for all linear fluids. Furthermore, this linearity is independent of liquid crystal ordering and seems to be independent of chain length for linear chains of 10 beads and longer. The same linear relationship was observed for the solubility of hard spheres in nematic forming partially flexible fluids for packing fractions up to a value slightly higher than the nematic packing fraction at the isotropic-nematic coexistence. At higher packing fractions, the small flexibility of these fluids seems to improve solubility in comparison with the linear fluids. PMID:23742514
Thermodynamic and rheological properties of hard sphere dispersions
See-Eng Phan
1998-01-01
We investigate the thermodynamic and rheological properties of hard sphere dispersions with colloidal poly-(methyl methacrylate) particles grafted with a layer of poly-(12-hydroxy stearic acid) (PMMA-PHSA). These spheres are index-matched in a mixture of tetralin and decalin and the absorption of tetralin into the PMMA core is determined with light scattering. The effective hard sphere volume fraction is set by the
Tunable long range forces mediated by self-propelled colloidal hard spheres.
Ni, Ran; Cohen Stuart, Martien A; Bolhuis, Peter G
2015-01-01
Using Brownian dynamics simulations, we systematically study the effective interaction between two parallel hard walls in a 2D suspension of self-propelled (active) colloidal hard spheres, and we find that the effective force between two hard walls can be tuned from a long range repulsion into a long range attraction by changing the density of active particles. At relatively high densities, the active hard spheres can form a dynamic crystalline bridge, which induces a strong oscillating long range dynamic wetting repulsion between the walls. With decreasing density, the dynamic bridge gradually breaks, and an intriguing long range dynamic depletion attraction arises. A similar effect occurs in a quasi-2D suspension of self-propelled colloidal hard spheres by changing the height of the confinement. Our results open up new possibilities to manipulate the motion and assembly of microscopic objects by using active matter. PMID:25615510
Tunable long range forces mediated by self-propelled colloidal hard spheres
Ran Ni; Martien A. Cohen Stuart; Peter G. Bolhuis
2014-12-11
Using Brownian dynamics simulations, we systematically study the effective interaction between two parallel hard walls in a 2D suspension of self-propelled (active) colloidal hard spheres, and we find that the effective force between two hard walls can be tuned from a long range repulsion into a long range attraction by changing the density of active particles. At relatively high densities, the active hard spheres can form a dynamic crystalline bridge, which induces a strong oscillating long range dynamic wetting repulsion between the walls. With decreasing density, the dynamic bridge gradually breaks, and an intriguing long range dynamic depletion attraction arises. A similar effect occurs in a quasi-2D suspension of self-propelled colloidal hard spheres by changing the height of the confinement. Our results open up new possibilities to manipulate the motion and assembly of microscopic objects by using active matter.
Tunable Long Range Forces Mediated by Self-Propelled Colloidal Hard Spheres
NASA Astrophysics Data System (ADS)
Ni, Ran; Cohen Stuart, Martien A.; Bolhuis, Peter G.
2015-01-01
Using Brownian dynamics simulations, we systematically study the effective interaction between two parallel hard walls in a 2D suspension of self-propelled (active) colloidal hard spheres, and we find that the effective force between two hard walls can be tuned from a long range repulsion into a long range attraction by changing the density of active particles. At relatively high densities, the active hard spheres can form a dynamic crystalline bridge, which induces a strong oscillating long range dynamic wetting repulsion between the walls. With decreasing density, the dynamic bridge gradually breaks, and an intriguing long range dynamic depletion attraction arises. A similar effect occurs in a quasi-2D suspension of self-propelled colloidal hard spheres by changing the height of the confinement. Our results open up new possibilities to manipulate the motion and assembly of microscopic objects by using active matter.
Equations of state for hard-sphere fluids
Zhou, Y.; Stell, G.
1988-11-01
Equations of state and contact values of hard-sphere radial distribution functions (rdf's) which are given by a linear combination of the Percus-Yevick and scaled-particle virial expressions are considered. In the one-component case the mixing coefficient /theta/(/eta/)is, in general a function of the volume fraction /eta/. In mixtures the coefficient /theta/(/eta//sub i/, d/sub i/), in general, depends upon the volume fraction /eta//sub i/ and diameter d/sub i/ of each species, i and j. For the contact values Y/sub ij/ of the rdf's, the mixing coefficients /Theta//sub ij/(/eta//sub k/) also depend on species i and j. Density expansions for the exact /theta/ for the one-component hard-sphere fluid are obtained and compared with several approximations made in earlier works and in the authors own work, as well as with simulation. For a mixture, it turns out that one cannot obtain the exact fourth virial coefficient by using a linear combination of the Percus-Yevick and scaled-particle virial expression for Y/sub ij/ unless one allows /Theta//sub ij/ to depend on mole fractions x/sub i/ even at the zeroth order of its density expansion. They also find that /Theta//sub ij/ must depend on particle species i and j in order to satisfy the exact limits obtained earlier by Sung and Stell. A new equation of state for the binary hard-sphere mixture which satisfies all the exact limits they have considered is suggested.
Hard-sphere fluid: new exact results with applications
Zhou, Y.; Stell, G.
1988-09-01
A theorem for convolution integrals is proved and then applied to extend the second zero-separation theorem to the bridge function b(r) and direct-correlation tail functions d(r). This theorem allows us to exactly relate deltab(r)/deltar and deltad(r)/deltar at r = 0 for the hard-sphere fluid to the contact values of the radial distribution function g(r) at r = sigma/sup +/. From this we obtain immediately the exact values of deltab(r)/deltar and deltad(r)/deltar at r = 0 through second order in number density rho. Using our results to compare the exact and Percus-Yevick (PY) bridge function, we find that they differ significantly. After obtaining the bridge function and tail function and their derivatives at r = 0 and r = sigma through, we suggest new approximations for b(0) and d(0) as well as an analytical integral-equation theory to improve the PY approximation in the pure hard-sphere fluid. The major deficiency of that approximation has been its poor assessment of the cavity function inside the hard-core region. Our theory remedies this defect is a way that yields a y(r) that is self-consistent with respect to the virial and compressibility relations and also the two zero-separation relations involving y(r) and its spatial derivative at r = 0.
Hard-sphere solids near close packing: Testing theories for crystallization
Benito Groh; Bela Mulder
2000-01-01
The freezing transition of hard spheres has been well described by various versions of density-functional theory (DFT). These theories should possess the close-packed crystal as a special limit, which represents an extreme testing ground for the quality of such liquid-state based theories. We therefore study the predictions of DFT for the structure and thermodynamics of the hard-sphere crystal in this
Dynamics of hard sphere colloidal dispersions
NASA Technical Reports Server (NTRS)
Zhu, J. X.; Chaikin, Paul M.; Phan, S.-E.; Russel, W. B.
1994-01-01
Our objective is to perform on homogeneous, fully equilibrated dispersions the full set of experiments characterizing the transition from fluid to solid and the properties of the crystalline and glassy solid. These include measurements quantifying the nucleation and growth of crystallites, the structure of the initial fluid and the fully crystalline solid, and Brownian motion of particles within the crystal, and the elasticity of the crystal and the glass. Experiments are being built and tested for ideal microgravity environment. Here we describe the ground based effort, which exploits a fluidized bed to create a homogeneous, steady dispersion for the studies. The differences between the microgravity environment and the fluidized bed is gauged by the Peclet number Pe, which measures the rate of convection/sedimentation relative to Brownian motion. We have designed our experiment to accomplish three types of measurements on hard sphere suspensions in a fluidized bed: the static scattering intensity as a function of angle to determine the structure factor, the temporal autocorrelation function at all scattering angles to probe the dynamics, and the amplitude of the response to an oscillatory forcing to deduce the low frequency viscoelasticity. Thus the scattering instrument and the colloidal dispersion were chosen such as that the important features of each physical property lie within the detectable range for each measurement.
alpha-Relaxation processes in binary hard-sphere mixtures.
Foffi, G; Götze, W; Sciortino, F; Tartaglia, P; Voigtmann, Th
2004-01-01
Molecular-dynamics simulations are presented for two correlation functions formed with the partial density fluctuations of binary hard-sphere mixtures in order to explore the effects of mixing on the evolution of glassy dynamics upon compressing the liquid into high-density states. Partial-density-fluctuation correlation functions for the two species are reported. Results for the alpha-relaxation process are quantified by parameters for the strength, stretching, and time scale, where the latter varies over almost four orders of magnitude upon compression. The parameters exhibit an appreciable dependence on the wave vector, and this dependence is different for the correlation function referring to the smaller and that for the larger species. These features are shown to be in semiquantitative agreement with those calculated within the mode-coupling theory for ideal liquid-glass transitions. PMID:14995626
Multiple reentrant glass transitions in confined hard-sphere glasses
S. Mandal; S. Lang; M. Gross; M. Oettel; D. Raabe; T. Franosch; F. Varnik
2014-06-20
Glass forming liquids exhibit a rich phenomenology upon confinement. This is often related to the effects arising from wall-fluid interactions. Here we focus on the interesting limit where the separation of the confining walls becomes of the order of a few particle diameters. For a moderately polydisperse, densely packed hard-sphere fluid confined between two smooth hard walls, we show via event-driven molecular dynamics simulations the emergence of a multiple reentrant glass transition scenario upon a variation of the wall separation. Using thermodynamic relations, this reentrant phenomenon is shown to persist also under constant chemical potential. This allows straightforward experimental investigation and opens the way to a variety of applications in micro- and nanotechnology, where channel dimensions are comparable to the size of the contained particles. The results are in-line with theoretical predictions obtained by a combination of density functional theory and the mode-coupling theory of the glass transition.
Multiple reentrant glass transitions in confined hard-sphere glasses
NASA Astrophysics Data System (ADS)
Mandal, Suvendu; Lang, Simon; Gross, Markus; Oettel, Martin; Raabe, Dierk; Franosch, Thomas; Varnik, Fathollah
2014-07-01
Glass-forming liquids exhibit a rich phenomenology upon confinement. This is often related to the effects arising from wall-fluid interactions. Here we focus on the interesting limit where the separation of the confining walls becomes of the order of a few particle diameters. For a moderately polydisperse, densely packed hard-sphere fluid confined between two smooth hard walls, we show via event-driven molecular dynamics simulations the emergence of a multiple reentrant glass transition scenario upon a variation of the wall separation. Using thermodynamic relations, this reentrant phenomenon is shown to persist also under constant chemical potential. This allows straightforward experimental investigation and opens the way to a variety of applications in micro- and nanotechnology, where channel dimensions are comparable to the size of the contained particles. The results are in line with theoretical predictions obtained by a combination of density functional theory and the mode-coupling theory of the glass transition.
Multiple reentrant glass transitions in confined hard-sphere glasses.
Mandal, Suvendu; Lang, Simon; Gross, Markus; Oettel, Martin; Raabe, Dierk; Franosch, Thomas; Varnik, Fathollah
2014-01-01
Glass-forming liquids exhibit a rich phenomenology upon confinement. This is often related to the effects arising from wall-fluid interactions. Here we focus on the interesting limit where the separation of the confining walls becomes of the order of a few particle diameters. For a moderately polydisperse, densely packed hard-sphere fluid confined between two smooth hard walls, we show via event-driven molecular dynamics simulations the emergence of a multiple reentrant glass transition scenario upon a variation of the wall separation. Using thermodynamic relations, this reentrant phenomenon is shown to persist also under constant chemical potential. This allows straightforward experimental investigation and opens the way to a variety of applications in micro- and nanotechnology, where channel dimensions are comparable to the size of the contained particles. The results are in line with theoretical predictions obtained by a combination of density functional theory and the mode-coupling theory of the glass transition. PMID:25033741
Clustering and percolation in dipolar hard-sphere fluids
NASA Astrophysics Data System (ADS)
Laría, Daniel; Vericat, Fernando
1991-02-01
Clustering and continuum percolation in dipolar fluids are studied through Monte Carlo simulation and connectedness theory with an emphasis on the effect of the dipole-dipole interactions on the size and shape of the clusters and on the threshold percolation density. Two simple models for the dipolar fluid are considered: (i) a system of hard spheres with an embedded point dipole and (ii) a related system of hard spheres in which the dipole-dipole forces are replaced by an angular-averaged dipolar potential. A first-order perturbation theory (for the first model) and the connectedness version of the Percus-Yevick integral equation (for the second one) are used to describe clustering and percolation, and their results are compared with the corresponding Monte Carlo data. Our results show that clusters become larger in size and acquire a stronger mean dipolar moment when the particles' dipolar moments are increased. Far from the percolation transition, the clusters are nonspherical, the eccentricity being favored by the energetics of dipolar orientation. Furthermore, they reveal that larger dipolar strengths imply smaller percolation densities.
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.
Quantum-mechanical third virial coefficient of a hard-sphere gas at high temperature
B. Jancovici; S. P. Merkuriev
1975-01-01
The third virial coefficient B3 of a gas of hard spheres, of diameter a and mass m, has been expanded in powers of lambdaa, where lambda is the thermal wavelength (2pik T)12 (ℏ=m=1). B3 can be expressed in terms of integrals on all configurations of the quantum-statistical-mechanical probability density of the configurations of a three-sphere system. This probability density is
Stochastic model of a dense spinless hard-sphere gas
L. M. Morato; G. Galilei
1991-01-01
Summary The motion of a spinless quantum particle subjected to random hard-sphere scatterings is studied in the framework of stochastic\\u000a mechanics. The result is applied to the case of a generic particle of a dense spinless hard-sphere gas leading to a description\\u000a that displays the competition between the thermal and the quantum noise. Finally, the model is discussed in connection with
Nearly logarithmic decay in the colloidal hard-sphere system.
Sperl, M
2005-06-01
Nearly logarithmic decay is identified in the data for the mean-squared displacement of the colloidal hard-sphere system at the liquid-glass transition [W. van Megen, Phys. Rev. E 58, 6073 (1998)]. The solutions of the mode-coupling theory for the microscopic equations of motion fit the experimental data well. Based on these equations, the nearly logarithmic decay is explained as the equivalent of a beta-peak phenomenon, a manifestation of the critical relaxation when the coupling between of the probe variable and the density fluctuations is strong. In an asymptotic expansion, a Cole-Cole formula including corrections is derived from the microscopic equations of motion, which describes the experimental data for three decades in time. PMID:16089713
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
Steady Shear Viscosities of Two Hard Sphere Colloidal Dispersions
Zhengdong Cheng; Paul M. Chaikin; See-Eng Phan; William B. Russel; Jixiang Zhu
1996-01-01
Though hard spheres have the simplest inter-particle potential, the many body hydrodynamic interactions are complex and the rheological properties of dispersions are not fully understood in the concentrated regime. We studied two model systems: colloidal poly-(Methyl Methacrylate) spheres with a grafted layer of poly-(12-hydroxy stearic acid) (PMMA\\/PHSA) and spherical Silica particles (PST-5, Nissan Chemical Industries, Ltd, Tokyo, Japan). Steady shear
Investigating hard sphere interactions through spin echo scattering angle measurement
NASA Astrophysics Data System (ADS)
Washington, Adam
Spin Echo Scattering Angle Measurement (SESAME) allows neutron scattering instruments to perform real space measurements on large micron scale samples by encoding the scattering angle into the neutron's spin state via Larmor precession. I have built a SESAME instrument at the Low Energy Neutron Source. I have also assisted in the construction of a modular SESAME instrument on the ASTERIX beamline at Los Alamos National lab. The ability to tune these instruments has been proved mathematically and optimized and automated experimentally. Practical limits of the SESAME technique with respect to polarization analyzers, neutron spectra, Larmor elements, and data analysis were investigated. The SESAME technique was used to examine the interaction of hard spheres under depletion. Poly(methyl methacrylate) spheres suspended in decalin had previously been studied as a hard sphere solution. The interparticle correlations between the spheres were found to match the Percus-Yevick closure, as had been previously seen in dynamical light scattering experiments. To expand beyond pure hard spheres, 900kDa polystyrene was added to the solution in concentrations of less than 1% by mass. The steric effects of the polystyrene were expected to produce a short-range, attractive, "sticky" potential. Experiment showed, however, that the "sticky" potential was not a stable state and that the spheres would eventually form long range aggregates.
Steady Shear Viscosities of Two Hard Sphere Colloidal Dispersions
NASA Astrophysics Data System (ADS)
Cheng, Zhengdong; Chaikin, Paul M.; Phan, See-Eng; Russel, William B.; Zhu, Jixiang
1996-03-01
Though hard spheres have the simplest inter-particle potential, the many body hydrodynamic interactions are complex and the rheological properties of dispersions are not fully understood in the concentrated regime. We studied two model systems: colloidal poly-(Methyl Methacrylate) spheres with a grafted layer of poly-(12-hydroxy stearic acid) (PMMA/PHSA) and spherical Silica particles (PST-5, Nissan Chemical Industries, Ltd, Tokyo, Japan). Steady shear viscosities were measured by a Zimm viscometer. The high shear relative viscosity of the dispersions compares well with other hard sphere systems, but the low shear relative viscosity of PMMA/PHSA dispersions is ? / ? 0 = 50 at ? = 0.5 , higher than ? / ? 0 = 22 for other hard sphere systems, consistent with recently published data (Phys. Rev. Lett. 75(1995)958). Bare Silica spheres are used to clarify the effect of the grafted layer. With the silica spheres, volume fraction can be determined independent of intrinsic viscosity measurements; also, higher concentrated dispersions can be made.
Local order variations in confined hard-sphere fluids.
Nygård, Kim; Sarman, Sten; Kjellander, Roland
2013-10-28
Pair distributions of fluids confined between two surfaces at close distance are of fundamental importance for a variety of physical, chemical, and biological phenomena, such as interactions between macromolecules in solution, surface forces, and diffusion in narrow pores. However, in contrast to bulk fluids, properties of inhomogeneous fluids are seldom studied at the pair-distribution level. Motivated by recent experimental advances in determining anisotropic structure factors of confined fluids, we analyze theoretically the underlying anisotropic pair distributions of the archetypical hard-sphere fluid confined between two parallel hard surfaces using first-principles statistical mechanics of inhomogeneous fluids. For this purpose, we introduce an experimentally accessible ensemble-averaged local density correlation function and study its behavior as a function of confining slit width. Upon increasing the distance between the confining surfaces, we observe an alternating sequence of strongly anisotropic versus more isotropic local order. The latter is due to packing frustration of the spherical particles. This observation highlights the importance of studying inhomogeneous fluids at the pair-distribution level. PMID:24182058
Free volume distribution of nearly jammed hard sphere packings
NASA Astrophysics Data System (ADS)
Maiti, Moumita; Sastry, Srikanth
2014-07-01
We calculate the free volume distributions of nearly jammed packings of monodisperse and bidisperse hard sphere configurations. These distributions differ qualitatively from those of the fluid, displaying a power law tail at large free volumes, which constitutes a distinct signature of nearly jammed configurations, persisting for moderate degrees of decompression. We reproduce and explain the observed distribution by considering the pair correlation function within the first coordination shell for jammed hard sphere configurations. We analyze features of the equation of state near jamming, and discuss the significance of observed asphericities of the free volumes to the equation of state.
Free volume distribution of nearly jammed hard sphere packings
Moumita Maiti; Srikanth Sastry
2014-07-25
We calculate the free volume distributions of nearly jammed packings of monodisperse and bidisperse hard sphere configurations. These distributions differ qualitatively from those of the fluid, displaying a power law tail at large free volumes, which constitutes a distinct signature of nearly jammed configurations, persisting for moderate degrees of decompression. We reproduce and explain the observed distribution by considering the pair correlation function within the first coordination shell for jammed hard sphere configurations. We analyze features of the equation of state near jamming, and discuss the significance of observed asphericities of the free volumes to the equation of state.
Free volume distribution of nearly jammed hard sphere packings.
Maiti, Moumita; Sastry, Srikanth
2014-07-28
We calculate the free volume distributions of nearly jammed packings of monodisperse and bidisperse hard sphere configurations. These distributions differ qualitatively from those of the fluid, displaying a power law tail at large free volumes, which constitutes a distinct signature of nearly jammed configurations, persisting for moderate degrees of decompression. We reproduce and explain the observed distribution by considering the pair correlation function within the first coordination shell for jammed hard sphere configurations. We analyze features of the equation of state near jamming, and discuss the significance of observed asphericities of the free volumes to the equation of state. PMID:25084929
Packing Confined Hard Spheres Denser with Adaptive Prism Phases
Erdal C. O?uz; Matthieu Marechal; Fernando Ramiro-Manzano; Isabelle Rodriguez; René Messina; Francisco J. Meseguer; Hartmut Löwen
2012-11-27
We show that hard spheres confined between two parallel hard plates pack denser with periodic adaptive prismatic structures which are composed of alternating prisms of spheres. The internal structure of the prisms adapts to the slit height which results in close packings for a range of plate separations, just above the distance where three intersecting square layers fit exactly between the plates. The adaptive prism phases are also observed in real-space experiments on confined sterically stabilized colloids and in Monte Carlo simulations at finite pressure.
A Dense Packing of Hard Spheres with Five-fold Symmetry
B. G. Bagley
1965-01-01
SUPPOSE a plane of hard spheres is constructed such that the spheres form concentric pentagons with an odd number of balls per pentagon side. A second plane of hard spheres is now constructed such that the spheres form concentric pentagons with an even number of spheres per pentagon side. If this second plane is placed in intimate contact with the
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.
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.
R. Castillo; J. Orozco
1993-01-01
The present paper explores the ability of the effective diameter hard sphere theory to estimate the transport properties of a fluid made up of particles interacting through the Gaussian overlap model. This method relies on the assumption that at high densities the behaviour of a fluid is dominated by harsh repulsive forces. Hence, the properties of the fluid can be
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
Yang, Jung Ho; Schultz, Andrew J; Errington, Jeffrey R; Kofke, David A
2013-04-01
We examine the suitability of cluster expansion methods for the description of inhomogeneous fluids. In particular, we apply these methods to characterize the density profile, surface tension, and excess adsorption for a hard-sphere fluid near a hard wall. Coefficients for these series up to seventh order are evaluated by the Mayer-sampling Monte Carlo method. Comparison of the series to Monte Carlo simulations of these systems finds very good agreement up to bulk densities approaching the freezing point. This work indicates that knowledge of surface cluster integrals of inhomogeneous systems can be at least as useful as the bulk-phase virial expansions. PMID:23574251
Hard sphere correlation functions in the Percus-Yevick approximation
J. W. Perram
1975-01-01
A reformulation of the Ornstein-Zernike equation permits rapid and simple numerical calculation of the total correlation functions for single and multi-component systems of hard spheres. Such correlation functions permit the application of sophisticated statistical mechanical perturbation theories to more complicated systems than has been possible heretofore.
Probing the evolution and morphology of hard carbon spheres
Pol, Vilas G.; Wen, Jianguo; Lau, Kah Chun; Callear, Samantha; Bowron, Daniel T.; Lin, Chi-Kai; Deshmukh, Sanket A.; Sankaranarayanan, Subramanian; Curtiss, Larry A.; David, William; Miller, Dean J.; Thackeray, Michael M.
2014-03-01
Monodispersed hard carbon spheres can be synthesized quickly and reproducibly by autogenic reactions of hydrocarbon precursors, notably polyethylene (including plastic waste), at high temperature and pressure. The carbon microparticles formed by this reaction have a unique spherical architecture, with a dominant internal nanometer layered motif, and they exhibit diamond-like hardness and electrochemical properties similar to graphite. In the present study, in-situ monitoring by X-ray diffraction along with electron microscopy, Raman spectroscopy, neutron pair-distribution function analysis, and computational modeling has been used to elucidate the morphology and evolution of the carbon spheres that form from the autogenic reaction of polyethylene at high temperature and pressure. A mechanism is proposed on how polyethylene evolves from a linear chain-based material to a layered carbon motif. Heating the spheres to 2400-2800 °C under inert conditions increases their graphitic character, particularly at the surface, which enhances their electrochemical and tribological properties.
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.
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.
Comparison of structure and transport properties of concentrated hard and soft sphere fluids
Erik Lange; Jose B. Caballero; Antonio M. Puertas; Matthias Fuchs
2009-01-16
Using Newtonian and Brownian dynamics simulations, the structural and transport properties of hard and soft spheres have been studied. The soft spheres were modeled using inverse power potentials ($V\\sim r^{-n}$, with $1/n$ the potential softness). Although the pressure, diffusion coefficient and viscosity depend at constant density on the particle softness up to extremely high values of $n$, we show that scaling the density with the freezing point for every system effectively collapses these parameters for $n\\geq 18$ (including hard spheres), for large densities. At the freezing points, the long range structure of all systems is identical, when the distance is measured in units of the interparticle distance, but differences appear at short distances (due to the different shape of the interaction potential). This translates into differences at short times in the velocity and stress autocorrelation functions, although they concur to give the same value of the corresponding transport coefficient (for the same density to freezing ratio); the microscopic dynamics also affects the short time behaviour of the correlation functions and absolute values of the transport coefficients, but the same scaling with the freezing density works for Newtonian or Brownian dynamics. For hard spheres, the short time behaviour of the stress autocorrelation function has been studied in detail, confirming quantitatively the theoretical forms derived for it.
Dynamic equivalences in the hard-sphere dynamic universality class
NASA Astrophysics Data System (ADS)
López-Flores, Leticia; Ruíz-Estrada, Honorina; Chávez-Páez, Martín; Medina-Noyola, Magdaleno
2013-10-01
We perform systematic simulation experiments on model systems with soft-sphere repulsive interactions to test the predicted dynamic equivalence between soft-sphere liquids with similar static structure. For this we compare the simulated dynamics (mean squared displacement, intermediate scattering function, ?-relaxation time, etc.) of different soft-sphere systems, between them and with the hard-sphere liquid. We then show that the referred dynamic equivalence does not depend on the (Newtonian or Brownian) nature of the microscopic laws of motion of the constituent particles, and hence, applies independently to colloidal and to atomic simple liquids. Finally, we verify another more recently proposed dynamic equivalence, this time between the long-time dynamics of an atomic liquid and its corresponding Brownian fluid (i.e., the Brownian system with the same interaction potential).
Hugh D. Newman; Anand Yethiraj
2014-12-10
Hard-sphere colloids are simple conceptually, yet density-matched micron-scale colloidal hard-sphere systems for real-space microscopy are difficult to obtain in the laboratory. Colloids with a dipolar interaction are complex, with angle-dependent attractions or repulsions, and there remain unanswered questions: whether the gas-liquid transition exists, and why there is a low-density networking-forming "void" phase. In this work, we vary the electric field and measure density profiles of Brownian dipolar colloids in sedimentation equilibrium. At zero field, the equation of state matches the hard-sphere equation of state. When there is an electric field parallel to gravity, the clusters of chains form from the bottom substrate, and expand the colloidal sediment; the second virial coefficient obtained from the apparent equation of state is larger than the hard-sphere value. Additional information about the spatial distribution of hydrodynamic sizes, obtained from "sedimentation-diffusion" profiles, also shows the effects of clustering. For micron-scale dipolar colloids in gravity, clustering begins at the surface: the resulting registry between dipoles can enhance repulsions, and lead to less compact structures.
Self-assembly in colloidal hard-sphere systems
NASA Astrophysics Data System (ADS)
Filion, L. C.
2011-01-01
In this thesis, we examine the phase behaviour and nucleation in a variety of hard-sphere systems. In Chapter 1 we present a short introduction and describe some of the simulation techniques used in this thesis. One of the main difficulties in predicting the phase behaviour in colloidal, atomic and nanoparticle systems is in determining the stable crystalline phases. To address this problem, in Chapters 2 and 4 we present two different methods for predicting possible crystal phases. In Chapter 2, we apply a genetic algorithm to binary hard-sphere mixtures and use it to predict the best-packed structures for this system. In Chapter 4 we present a novel method based on Monte Carlo simulations to predict possible crystalline structures for a variety of models. When the possible phases are known, full free-energy calculations can be used to predict the phase diagrams. This is the focus of Chapters 3 and 5. In Chapter 3, we examine the phase behaviour for binary hard-sphere mixtures with size ratios of the large and small spheres between 0.74 and 0.85. Between size ratios 0.76 and 0.84 we find regions where the binary Laves phases are stable, in addition to monodisperse face-centered-cubic (FCC) crystals of the large and small spheres and a binary liquid. For size ratios 0.74 and 0.85 we find only the monodisperse FCC crystals and the binary liquid. In Chapter 5 we examine the phase behaviour of binary hard-sphere mixtures with size ratios between 0.3 and 0.42. In this range, we find an interstitial solid solution (ISS) to be stable, as well as FCC crystals of the small and large spheres, and a binary fluid. The ISS phase consists of an FCC crystal of the large particles with some of the octahedral holes filled by smaller particles. We show that this filling fraction can be tuned from 0 to 100%. Additionally, we examine the diffusive properties of the small particles in the ISS for size ratio 0.3. In contrast to most systems, we find a region where the diffusion increases as a function of the packing fraction. Finally, in Chapters 6, 7, and 8 we examine nucleation in colloidal systems. In Chapter 6, we examine the crystal nucleation for hard spheres using a variety of simulation techniques, namely, umbrella sampling (US), forward flux sampling (FFS), and molecular dynamics (MD). We compare the resulting nucleation rates with previous experimental and simulated rates. and find agreement between all the theoretically predicted nucleation rates. However, the experimental results display a markedly different behaviour for low supersaturation. In Chapter 7, we examine in more detail the FFS technique, in particular, the effect measurement error has on the resulting nucleation rates. In Chapter 8, we examine the crystal nucleation of the Weeks-Chandler-Andersen (WCA) model with ?? = 40 using Brownian dynamics, US and FFS. This WCA potential is softer than the hard-sphere potential, but is frequently used to approximate hard spheres. Our predicted nucleation rates for this potential are in agreement with those found for hard spheres.
Thermodynamic and rheological properties of hard sphere dispersions
NASA Astrophysics Data System (ADS)
Phan, See-Eng
1998-09-01
We investigate the thermodynamic and rheological properties of hard sphere dispersions with colloidal poly-(methyl methacrylate) particles grafted with a layer of poly-(12-hydroxy stearic acid) (PMMA-PHSA). These spheres are index-matched in a mixture of tetralin and decalin and the absorption of tetralin into the PMMA core is determined with light scattering. The effective hard sphere volume fraction is set by the disorder-order transition, thereby accounting for the polymer layer, any swelling due to the solvent, and polydispersity. The equation of state for the fluid phase, extracted from the equilibrium sediment with x-ray densitometry, conforms to the Carnahan-Starling equation. However, the osmotic pressure of the crystalline phase lies slightly above that calculated for a single FCC crystal. Likewise the high shear viscosity of the fluid compares well with other hard sphere dispersions, but the low shear viscosity for PMMA-PHSA hard spheres exceeds those for polystyrene and silica hard spheres. Our low shear viscosities are consistent with other PMMA-PHSA data after rescaling for both the polymer layer thickness and polydispersity. We use simple models and molecular dynamics simulations to determine that the higher osmotic pressure in the crystalline phase is a direct effect of polydispersity. Polydispersity appears to lower the crystalline close packed volume fraction. The random close packing is almost independent of polydispersity. We measure the high frequency shear modulus and dynamic viscosity for our PMMA-PHSA crystals by detecting the resonant response to oscillatory forcing with a novel dynamic light scattering scheme. The resonant response for colloidal crystals formed in normal and microgravity environments were similar, indicating that the bulk rheological properties are unaffected within experimental error by differing crystal structure and crystallite size. Our high frequency shear modulus seem reasonable, lying close to predictions for the static modulus of hard sphere crystals, whereas our high frequency dynamic viscosity seem high, exceeding measurements on the high frequency dynamic viscosity for metastable fluids. The measurements are in the linear regime for the shear modulus but may not be for the dynamic viscosity, which may explain our anomalously high dynamic viscosity.
Calculation of high-order virial coefficients with applications to hard and soft spheres.
Wheatley, Richard J
2013-05-17
A virial expansion of fluid pressure in powers of the density can be used to calculate a wealth of thermodynamic information, but the Nth virial coefficient, which multiplies the Nth power of the density in the expansion, becomes rapidly more complicated with increasing N. This Letter shows that the Nth virial coefficient can be calculated using a method that scales exponentially with N in computer time and memory. This is orders of magnitude more efficient than any existing method for large N, and the method is simple and general. New results are presented for N = 11 and 12 for hard spheres, and N = 9 and 10 for soft spheres. PMID:25167391
Reversible and irreversible deformation in hard-sphere colloidal glasses
NASA Astrophysics Data System (ADS)
Jensen, Katharine; Nakamura, Nobutomo; Weitz, David; Spaepen, Frans
2013-03-01
Colloidal glass provides a unique experimental system with which to study the structure, defects, and dynamics of amorphous materials. We report experiments on 1.55-?m-diameter, hard-sphere silica colloidal glasses under conditions of uniform shear. We deform the samples to maximum strains ranging from 0.5% to 10% at various strain rates, and then reverse the deformation so that the net bulk strain is zero at the end of the experiment. We use confocal microscopy to follow the 3D, real-time trajectories of roughly 50,000 particles over the course of an experiment. In this way, we probe the elastic, anelastic, and plastic response of the system, with particular emphasis on the specific, local mechanisms of deformation. We directly observe yield as the onset of local, irreversible deformation. In both sheared and unsheared (quiescent) samples, we observe thermally-activated clusters of particles that behave as Eshelby inclusions, undergoing highly localized plastic strain that couples elastically to the surrounding material. We identify and characterize these regions as they develop in the glass, with particular focus on density-related properties including the Voronoi volume and free volume.
Complex Oscillatory Yielding of Model Hard-Sphere Glasses
NASA Astrophysics Data System (ADS)
Koumakis, N.; Brady, J. F.; Petekidis, G.
2013-04-01
The yielding behavior of hard sphere glasses under large-amplitude oscillatory shear has been studied by probing the interplay of Brownian motion and shear-induced diffusion at varying oscillation frequencies. Stress, structure and dynamics are followed by experimental rheology and Browian dynamics simulations. Brownian-motion-assisted cage escape dominates at low frequencies while escape through shear-induced collisions at high ones, both related with a yielding peak in G''. At intermediate frequencies a novel, for hard sphere glasses, double peak in G'' is revealed reflecting both mechanisms. At high frequencies and strain amplitudes a persistent structural anisotropy causes a stress drop within the cycle after strain reversal, while higher stress harmonics are minimized at certain strain amplitudes indicating an apparent harmonic response.
Mean field theory of hard sphere glasses and jamming
Giorgio Parisi; Francesco Zamponi
2010-03-16
Hard spheres are ubiquitous in condensed matter: they have been used as models for liquids, crystals, colloidal systems, granular systems, and powders. Packings of hard spheres are of even wider interest, as they are related to important problems in information theory, such as digitalization of signals, error correcting codes, and optimization problems. In three dimensions the densest packing of identical hard spheres has been proven to be the FCC lattice, and it is conjectured that the closest packing is ordered (a regular lattice, e.g, a crystal) in low enough dimension. Still, amorphous packings have attracted a lot of interest, because for polydisperse colloids and granular materials the crystalline state is not obtained in experiments for kinetic reasons. We review here a theory of amorphous packings, and more generally glassy states, of hard spheres that is based on the replica method: this theory gives predictions on the structure and thermodynamics of these states. In dimensions between two and six these predictions can be successfully compared with numerical simulations. We will also discuss the limit of large dimension where an exact solution is possible. Some of the results we present here have been already published, but others are original: in particular we improved the discussion of the large dimension limit and we obtained new results on the correlation function and the contact force distribution in three dimensions. We also try here to clarify the main assumptions that are beyond our theory and in particular the relation between our static computation and the dynamical procedures used to construct amorphous packings.
On the jamming phase diagram for frictionless hard-sphere packings.
Baranau, Vasili; Tallarek, Ulrich
2014-10-21
We computer-generated monodisperse and polydisperse frictionless hard-sphere packings of 10(4) particles with log-normal particle diameter distributions in a wide range of packing densities ? (for monodisperse packings ? = 0.46-0.72). We equilibrated these packings and searched for their inherent structures, which for hard spheres we refer to as closest jammed configurations. We found that the closest jamming densities ?(J) for equilibrated packings with initial densities ? ? 0.52 are located near the random close packing limit ?(RCP); the available phase space is dominated by basins of attraction that we associate with liquid. ?(RCP) depends on the polydispersity and is ? 0.64 for monodisperse packings. For ? > 0.52, ?(J) increases with ?; the available phase space is dominated by basins of attraction that we associate with glass. When ? reaches the ideal glass transition density ?(g), ?(J) reaches the ideal glass density (the glass close packing limit) ?(GCP), so that the available phase space is dominated at ?(g) by the basin of attraction of the ideal glass. For packings with sphere diameter standard deviation ? = 0.1, ?(GCP) ? 0.655 and ?(g) ? 0.59. For monodisperse and slightly polydisperse packings, crystallization is superimposed on these processes: it starts at the melting transition density ?(m) and ends at the crystallization offset density ?(off). For monodisperse packings, ?(m) ? 0.54 and ?(off) ? 0.61. We verified that the results for polydisperse packings are independent of the generation protocol for ? ? ?(g). PMID:25155116
Replica exchange Monte Carlo applied to hard spheres.
Odriozola, Gerardo
2009-10-14
In this work a replica exchange Monte Carlo scheme which considers an extended isobaric-isothermal ensemble with respect to pressure is applied to study hard spheres (HSs). The idea behind the proposal is expanding volume instead of increasing temperature to let crowded systems characterized by dominant repulsive interactions to unblock, and so, to produce sampling from disjoint configurations. The method produces, in a single parallel run, the complete HS equation of state. Thus, the first order fluid-solid transition is captured. The obtained results well agree with previous calculations. This approach seems particularly useful to treat purely entropy-driven systems such as hard body and nonadditive hard mixtures, where temperature plays a trivial role. PMID:19831433
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
Second-order Percus-Yevick theory for a confined hard-sphere fluid
Douglas Henderson; Stefan Sokolowski; Darsh Wasan
1997-01-01
A fluid of hard spheres confined between two hard walls and in equilibrium with a bulk hard-sphere fluid is studied using\\u000a a second-order Percus-Yevick approximation. We refer to this approximation as second-order because the correlations that are\\u000a calculated depend upon the position of two hard spheres in the confined fluid. However, because the correlation functions\\u000a depend upon the positions of
Geometrical Frustration: A Study of 4d Hard Spheres
J. A. van Meel; D. Frenkel; P. Charbonneau
2008-11-25
The smallest maximum kissing-number Voronoi polyhedron of 3d spheres is the icosahedron and the tetrahedron is the smallest volume that can show up in Delaunay tessalation. No periodic lattice is consistent with either and hence these dense packings are geometrically frustrated. Because icosahedra can be assembled from almost perfect tetrahedra, the terms "icosahedral" and "polytetrahedral" packing are often used interchangeably, which leaves the true origin of geometric frustration unclear. Here we report a computational study of freezing of 4d hard spheres, where the densest Voronoi cluster is compatible with the symmetry of the densest crystal, while polytetrahedral order is not. We observe that, under otherwise comparable conditions, crystal nucleation in 4d is less facile than in 3d. This suggest that it is the geometrical frustration of polytetrahedral structures that inhibits crystallization.
Percus-Yevick results for a binary mixture of hard spheres with non-additive diameters
J. H. Nixon; M. Silbert
1984-01-01
We have carried out extensive calculations, within the Percus-Yevick approximation, for a binary mixture of hard spheres with negative departures from additivity in their hard sphere diameters. The results presented in this work are restricted to the case of equal size spheres at equimolar composition. We have calculated the virial equation of state and show that the more negative the
A. Astillero; A. Santos
2005-08-30
In the preceding paper (cond-mat/0405252), we have conjectured that the main transport properties of a dilute gas of inelastic hard spheres (IHS) can be satisfactorily captured by an equivalent gas of elastic hard spheres (EHS), 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 $0.5\\leq \\alpha\\leq 0.95$ and two values of the imposed shear rate $a$. 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. The EHS results are in general hardly distinguishable from the IHS ones if $\\alpha\\gtrsim 0.7$, so that the distinct signature of the IHS gas (higher anisotropy and overpopulation) only manifests itself at relatively high dissipations
The Boltzmann-Grad Limit of a Hard Sphere System: Analysis of the Correlation Error
Mario Pulvirenti; Sergio Simonella
2014-05-19
We present a quantitative analysis of the Boltzmann-Grad (low-density) limit of a hard sphere system. We introduce and study a set of functions (correlation errors) measuring the deviations in time from the statistical independence of particles (propagation of chaos). In the context of the BBGKY hierarchy, a correlation error of order $k$ measures the event where $k$ tagged particles are connected by a chain of interactions preventing the factorization. We prove that, provided $k$ is not too large, such an error flows to zero with the hard spheres diameter $\\varepsilon$, for short times, as $\\varepsilon^{\\gamma k}$, for some $\\gamma>0$. This requires a new analysis of many-recollision events, and improves previous estimates of high order correlation functions.
D. B. Miracle; Peter Harrowell
2009-01-01
Insight into the efficient filling of space in systems of binary spheres is explored using bipyramids consisting of 3<=n<=8 tetrahedra sharing a common pair of spheres. Compact packings are sought in bipyramids consisting of larger hard spheres of unit radius and smaller hard spheres of radius 0.001<=R=0.9473 and for 0.8493>=R>=0.7434. A topological instability eliminates compact packings for R<=0.1547. Pentagonal bipyramids
Percus-Yevick theory for the system of hard spheres with a square-well attraction
I. Nezbeda
1977-01-01
Analytic solution of the Percus-Yevick equation for the system of hard spheres with a square-well attraction is proposed provided the range of attraction,?, is much smaller than the hard sphere diameter. It is shown that for? close to zero the system exhibits the first-order phase transition similar to that found for sticky hard spheres; for attraction ranges greater than a
Thermodynamic perturbation theory for fused hard-sphere and hard-disk chain fluids
Zhou, Y.; Hall, C.K. [Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina 27695-7905 (United States)] [Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina 27695-7905 (United States); Stell, G. [Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794-3400 (United States)] [Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794-3400 (United States)
1995-08-15
We find that first-order thermodynamic perturbation theory (TPT1) which incorporates the reference monomer fluid used in the generalized Flory--{ital AB} (GF--{ital AB}) theory yields an equation of state for fused hard-sphere (FHS) chain fluids that has accuracy comparable to the GF--{ital AB} and GF--dimer--{ital AC} theories. The new TPT1 equation of state is significantly more accurate than other extensions of the TPT1 theory to FHS chain fluids. The TPT1 is also extended to two-dimensional fused hard-disk chain fluids. For the fused hard-disk dimer fluid, the extended TPT1 equation of state is found to be more accurate than the Boublik hard-disk dimer equation of state. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
Thermodynamic perturbation theory for fused hard-sphere and hard-disk chain fluids
NASA Astrophysics Data System (ADS)
Zhou, Yaoqi; Hall, Carol K.; Stell, George
1995-08-01
We find that first-order thermodynamic perturbation theory (TPT1) which incorporates the reference monomer fluid used in the generalized Flory-AB (GF-AB) theory yields an equation of state for fused hard-sphere (FHS) chain fluids that has accuracy comparable to the GF-AB and GF-dimer-AC theories. The new TPT1 equation of state is significantly more accurate than other extensions of the TPT1 theory to FHS chain fluids. The TPT1 is also extended to two-dimensional fused hard-disk chain fluids. For the fused hard-disk dimer fluid, the extended TPT1 equation of state is found to be more accurate than the Boublík hard-disk dimer equation of state.
ESTIMATING THE DENSITY OF DRY SNOW LAYERS FROM HARDNESS, AND HARDNESS FROM DENSITY
Jamieson, Bruce
ESTIMATING THE DENSITY OF DRY SNOW LAYERS FROM HARDNESS, AND HARDNESS FROM DENSITY Daehyun Kim 1 and hardness of dry snow layers for common grain types. These relations have been widely used to estimate), and to estimate the hardness of layers in snowpack evolution models. Since 2000, the database of snow layers has
NASA Astrophysics Data System (ADS)
Baeyens, Bruno
2011-12-01
In a previous article (Baeyens and Verschelde in J. Math. Phys. 36:201, 1995), an improved approach to the scaled particle theory of Reiss et al. was presented. We used a generalized series expansion of the contact correlation function G( y, r). Truncating it after the third term, we obtained a Padé-like expression for the compressibility factor of the system. That expression contains two parameters which we were able to calculate, not only for the fluid state, but also for the known glassy states (Baeyens and Verschelde in Z. Phys. B 102:255, 1997). The resulting equations of state are in good agreement with the simulation data. Yet in the case of the hard sphere crystal our improved scaled particle theory fails, which is one of the reasons why an extension of it is desirable. In this paper the above mentioned expansion of G( y, r) will once more be generalized. Truncation after the sixth term leads to a simple but acceptable equation of state for the hard sphere fcc-crystal. It reproduces the free energies, the compressibility factors and the pressure of freezing and melting to within 0.3, 5, and 0.6 percent respectively.
NASA Astrophysics Data System (ADS)
Sellitto, M.; Zamponi, F.
2013-12-01
We study, via the replica method of disordered systems, the packing problem of hard-spheres with a square-well attractive potential when the space dimensionality, d, becomes infinitely large. The phase diagram of the system exhibits reentrancy of the liquid-glass transition line, two distinct glass states and a glass-to-glass transition, much similar to what has been previously obtained by Mode-Coupling Theory, numerical simulations and experiments. The presence of the phase reentrance implies that for a suitable choice of the intensity and attraction range, high-density sphere packings more compact than the one corresponding to pure hard-spheres can be constructed in polynomial time in the number of particles (at fixed, large d) for packing fractions phiv <= 6.5d2-d. Although our derivation is not a formal mathematical proof, we believe it meets the standards of rigor of theoretical physics, and at this level of rigor it provides a small improvement of the lower bound on the sphere packing problem.
Simple effective rule to estimate the jamming packing fraction of polydisperse hard spheres.
Santos, Andrés; Yuste, Santos B; López de Haro, Mariano; Odriozola, Gerardo; Ogarko, Vitaliy
2014-04-01
A recent proposal in which the equation of state of a polydisperse hard-sphere mixture is mapped onto that of the one-component fluid is extrapolated beyond the freezing point to estimate the jamming packing fraction ?J of the polydisperse system as a simple function of M1M3/M22, where Mk is the kth moment of the size distribution. An analysis of experimental and simulation data of ?J for a large number of different mixtures shows a remarkable general agreement with the theoretical estimate. To give extra support to the procedure, simulation data for seventeen mixtures in the high-density region are used to infer the equation of state of the pure hard-sphere system in the metastable region. An excellent collapse of the inferred curves up to the glass transition and a significant narrowing of the different out-of-equilibrium glass branches all the way to jamming are observed. Thus, the present approach provides an extremely simple criterion to unify in a common framework and to give coherence to data coming from very different polydisperse hard-sphere mixtures. PMID:24827171
Binary hard-sphere crystals with the cesium chloride structure
NASA Astrophysics Data System (ADS)
Schofield, A. B.
2001-11-01
The possibility of binary hard-sphere colloids crystallizing with the cesium chloride (CsCl) structure was examined experimentally using poly (methyl methacrylate) particles dispersed in organic solvents. Towards this end, two dispersions were prepared that contained particles with a radius ratio ?=RB/RA, where A refers to the large particles and B the small, of 0.736. This is close to the optimum ratio of 0.732 at which this structure is predicted to form as determined by space-filling calculations. The phases found within the binary mixture were examined using laser light crystallography and scanning electromicroscopy, and some were shown to have the CsCl structure. Over a period of time some of the CsCl crystals disappeared indicating that they were metastable and that this structure may not be the most enduring phase at this size ratio.
Geometric interpretation of pre-vitrification in hard sphere liquids
Carolina Brito; Matthieu Wyart
2009-06-04
We derive a microscopic criterion for the stability of hard sphere configurations, and we show empirically that this criterion is marginally satisfied in the glass. This observation supports a geometric interpretation for the initial rapid rise of viscosity with packing fraction, or pre-vitrification. It also implies that barely stable soft modes characterize the glass structure, whose spatial extension is estimated. We show that both the short-term dynamics and activation processes occur mostly along those soft modes, and we study some implications of these observations. This article synthesizes new and previous results [C. Brito and M. Wyart, Euro. Phys. Letters, {\\bf 76}, 149-155, (2006) and C. Brito and M. Wyart, J. Stat. Mech., L08003 (2007) ] in a unified view.
Geometric interpretation of previtrification in hard sphere liquids.
Brito, Carolina; Wyart, Matthieu
2009-07-14
We derive a microscopic criterion for the stability of hard sphere configurations and we show empirically that this criterion is marginally satisfied in the glass. This observation supports a geometric interpretation for the initial rapid rise in viscosity with packing fraction or previtrification. It also implies that barely stable soft modes characterize the glass structure, whose spatial extension is estimated. We show that both the short-term dynamics and activation processes occur mostly along those soft modes and we study some implications of these observations. This article synthesizes new and previous results [C. Brito and M. Wyart, Europhys. Lett. 76, 149 (2006); C. Brito and M. Wyart, J. Stat. Mech.: Theory Exp. 2007, L08003] in a unified view. PMID:19604001
Detecting Phase Boundaries in Hard-Sphere Suspensions
NASA Technical Reports Server (NTRS)
McDowell, Mark; Rogers, Richard B.; Gray, Elizabeth
2009-01-01
A special image-data-processing technique has been developed for use in experiments that involve observation, via optical microscopes equipped with electronic cameras, of moving boundaries between the colloidal-solid and colloidal-liquid phases of colloidal suspensions of monodisperse hard spheres. During an experiment, it is necessary to adjust the position of a microscope to keep the phase boundary within view. A boundary typically moves at a speed of the order of microns per hour. Because an experiment can last days or even weeks, it is impractical to require human intervention to keep the phase boundary in view. The present image-data-processing technique yields results within a computation time short enough to enable generation of automated-microscope-positioning commands to track the moving phase boundary
Glass transition of hard spheres in high dimensions.
Schmid, Bernhard; Schilling, Rolf
2010-04-01
We have investigated analytically and numerically the liquid-glass transition of hard spheres for dimensions d-->infinity in the framework of mode-coupling theory. The numerical results for the critical collective and self-nonergodicity parameters fc(k;d) and fc(s)(k;d) exhibit non-Gaussian k dependence even up to d=800.fc(s)(k;d) and fc(k;d) differ for k approximately d1/2, but become identical on a scale k approximately d, which is proven analytically. The critical packing fraction phic(d) approximately d(2)2(-d) is above the corresponding Kauzmann packing fraction phiK(d) derived by a small cage expansion. Its quadratic pre-exponential factor is different from the linear one found earlier. The numerical values for the exponent parameter and therefore the critical exponents a and b depend on d, even for the largest values of d. PMID:20481726
Percus-Yevick theory of correlation functions and nucleation effects in the sticky hard-sphere model
P. T. Cummings; J. W. Perram; E. R. Smith
1976-01-01
We use the Percus-Yevick approximation to study indirect correlation functions in the sticky hard-sphere model introduced by Baxter. The model has a critical point below which there is a liquid gas transition. We illustrate the changes in the structure of the correlation function as the density increases on the critical isotherm and on supercritical and subcritical isotherms. We also examine
Stefan Sokolowski; Marek Kosmulski
1978-01-01
The first three virial coefficients of a new type in the density expansion of the adsorption isotherm for hard spheres in contact with a wall with a soft surface layer are calculated. The results are compared with those for hard spheres in contact with a hard wall.
NASA Astrophysics Data System (ADS)
Amos, Michael D.; Jackson, George
1992-03-01
The bonded hard-sphere (BHS) approach originally developed for diatomic and triatomic molecules is generalized to hard-sphere polyatomic models which are formed by bonding together their constituent hard spheres. The thermodynamic properties of the polyatomic fluid are obtained from the known properties of a corresponding multicomponent mixture of different sized hard spheres with bonding sites. In the limit of complete bonding, hard-sphere polyatomic molecules are formed. As well as the general expressions for polyatomic molecules and their mixtures, the equation of state of hard-sphere chain molecules, which are simple models of homologous series such as the alkanes, perfluoroalkanes, etc., is presented. More specifically, the chain molecules are formed from two different types of hard spheres 1 and 2. Spheres of type 1 make up the backbone of the chain and, in this case, would represent the carbon atoms; spheres of type 2 represent the substituents, i.e., the hydrogen or fluorine atoms. Although the BHS theory is only strictly valid for molecules of tangent spheres, the theory can also be applied to fused hard-sphere (FHS) molecules with overlapping spheres. The latter are more realistic models of actual molecules. In the spirit of the semiempirical scaled particle theories (SPT), the properties of the FHS molecule can be related to those of an equivalent BHS molecule of tangent spheres with the same parameter of nonsphericity, ?. When dealing with large polyatomic molecules, ? does not need to be calculated numerically as is the case with the usual SPT approach. As an approximation one may use the analytical values of ? for the diatomic segments making up the molecule. This simple approach turns out to be quite successful. The BHS equation of state has been compared with ``exact'' computer simulation data for homonuclear and heteronuclear FHS systems of diatomics, linear and nonlinear triatomics, and tetrahedral pentatomics, as well as mixtures of FHS molecules. Good agreement is found for all of these systems. In general, the BHS approach is more rigorous and easier to extend to larger polyatomic molecules and their mixtures than SPT.
Exact solution of the Percus-Yevick integral equation for collapsing hard spheres
I. Klebanov; P. Gritsay; N. Ginchitskii
2006-01-01
By Wertheim-method the exact solution of the Percus-Yevick integral equation for a system of particles with the repulsive step potential interacting (collapsing hard spheres) is obtained. On the basis of this solution the state equation for the repulsive step potential is built and determined, that the Percus-Yevick equation does not show phase transition for collapsing hard spheres.
Random-close packing limits for monodisperse and polydisperse hard spheres.
Baranau, Vasili; Tallarek, Ulrich
2014-06-01
We investigate how the densities of inherent structures, which we refer to as the closest jammed configurations, are distributed for packings of 10(4) frictionless hard spheres. A computational algorithm is introduced to generate closest jammed configurations and determine corresponding densities. Closest jamming densities for monodisperse packings generated with high compression rates using Lubachevsky-Stillinger and force-biased algorithms are distributed in a narrow density range from ? = 0.634-0.636 to ?? 0.64; closest jamming densities for monodisperse packings generated with low compression rates converge to ?? 0.65 and grow rapidly when crystallization starts with very low compression rates. We interpret ?? 0.64 as the random-close packing (RCP) limit and ?? 0.65 as a lower bound of the glass close packing (GCP) limit, whereas ? = 0.634-0.636 is attributed to another characteristic (lowest typical, LT) density ?LT. The three characteristic densities ?LT, ?RCP, and ?GCP are determined for polydisperse packings with log-normal sphere radii distributions. PMID:24723008
Ornstein-Zernike equations and simulation results for hard-sphere fluids adsorbed in porous media
Lomba, E.; Given, J.A.; Stell, G. (Department of Chemistry, State Univeristy of New York at Stony Brook, Stony Brook, New York 11794-3400 (United States)); Weis, J.J.; Levesque, D. (Laboratoire de Physique Theorique et Hautes Energies, Batiment 211, Universite de Paris-Sud, 91405 Orsay CEDEX (France))
1993-07-01
In this paper we solve the replica Ornstein-Zernike (ROZ) equations in the hypernetted-chain (HNC), Percus-Yevick (PY), and reference Percus-Yevick (RPY) approximations for partly quenched systems. The ROZ equations, which apply to the general class of partly quenched systems, are here applied to a class of models for porous media. These models involve two species of particles: an annealed or equilibrated species, which is used to model the fluid phase, and a quenched or frozen species, whose excluded-volume interactions constitute the matrix in which the fluid is adsorbed. We study two models for the quenched species of particles: a hard-sphere matrix, for which the fluid-fluid, matrix-matrix, and matrix-fluid sphere diameters [sigma][sub 11], [sigma][sub 00], and [sigma][sub 01] are additive, and a matrix of randomly overlapping particles (which still interact with the fluid particle as hard spheres) that gives a random'' matrix with interconnected pore structure. For the random-matrix case we study a ratio [sigma][sub 01]/[sigma][sub 11] of 2.5, which is a demanding one for the theories. The HNC and RPY results represent significant improvements over the PY result when compared with the Monte Carlo simulations we have generated for this study, with the HNC result yielding the best results overall among those studied. A phenomenological percolating-fluid approximation is also found to be of comparable accuracy to the HNC results over a significant range of matrix and fluid densities. In the hard-sphere matrix case, the RPY is the best of the theories that we have considered.
Paho Lurie-Gregg; Jeff B. Schulte; David Roundy
2014-09-24
We introduce an approximation for the pair distribution function of the inhomogeneous hard sphere fluid. Our approximation makes use of our recently published averaged pair distribution function at contact which has been shown to accurately reproduce the averaged pair distribution function at contact for inhomogeneous density distributions. This approach achieves greater computational efficiency than previous approaches by enabling the use of exclusively fixed-kernel convolutions and thus allowing an implementation using fast Fourier transforms. We compare results for our pair distribution approximation with two previously published works and Monte-Carlo simulation, showing favorable results.
A new integral equation for the radial distribution function of a hard sphere fluid
Wehner, M.F.; Wolfer, W.G.
1986-02-01
Based on a proposal by Shinomoto, a new integral equation is derived for the radial distribution function of a hard-sphere fluid using mainly geometric arguments. This integral equation is solved by a perturbation expansion in the density of the fluid, and the results obtained are compared with those from molecular dynamics simulations and from the Born-Green-Yvon (BGY) and Percus-Yevick (PY) theories. The present theory provides results for the radial distribution function which are intermediate in accuracy between those obtained from the BGY and from the PY theories.
NASA Astrophysics Data System (ADS)
Kern, Jesse; Laird, Brian
2013-03-01
The interfacial free energy, ?, of fluids at surfaces is a parameter that is central to a number of technologically important phenomena, such as wetting, nucleation and the stability and self assembly of colloidal particles in solution. In recent years, our group has developed techniques to determine ? from atomistic simulation. In this work, we apply one of these methods, Gibbs-Cahn Integration, to determine ? for a model two-component (binary) mixture of hard spheres. Molecular dynamics simulation is used to characterize a hard-sphere fluid mixture in a slit-pore confined geometry as packing fraction, mole fraction, and diameter ratio are varied. We find that recent theoretical predictions from the White Bear II classical density functional theory [Roth et al., J. Phys.: Condens. Matter, 18, 8413, (2006)] agree well with our computational results We also observe that, for this model system, the preferential adsorption of one particle species over the other contributes negligibly to the interfacial free energy at modest diameter ratios.
Granular mixtures modeled as elastic hard spheres subject to a drag force
NASA Astrophysics Data System (ADS)
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 ?ij . In the low density regime an adequate framework is provided by the set of coupled inelastic Boltzmann equations. Due to the intricacy of the inelastic Boltzmann collision operator, in this paper we propose a simpler model of elastic hard disks or spheres subject to the action of an effective drag force, which mimics the effect of dissipation present in the original granular gas. For each collision term ij , the model has two parameters: a dimensionless factor ?ij modifying the collision rate of the elastic hard spheres, and the drag coefficient ?ij . Both parameters are determined by requiring that the model reproduces the collisional transfers of momentum and energy of the true inelastic Boltzmann operator, yielding ?ij=(1+?ij)/2 and ?ij?1-?ij2 , where the proportionality constant is a function of the partial densities, velocities, and temperatures of species i and j . The Navier-Stokes transport coefficients for a binary mixture are obtained from the model by application of the Chapman-Enskog method. The three coefficients associated with the mass flux are the same as those obtained from the inelastic Boltzmann equation, while the remaining four transport coefficients show a general good agreement, especially in the case of the thermal conductivity. The discrepancies between both descriptions are seen to be similar to those found for monocomponent gases. Finally, the approximate decomposition of the inelastic Boltzmann collision operator is exploited to construct a model kinetic equation for granular mixtures as a direct extension of a known kinetic model for elastic collisions.
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.
Short-time diffusion in concentrated bidisperse hard-sphere suspensions.
Wang, Mu; Heinen, Marco; Brady, John F
2015-02-14
Diffusion in bidisperse Brownian hard-sphere suspensions is studied by Stokesian Dynamics (SD) computer simulations and a semi-analytical theoretical scheme for colloidal short-time dynamics, based on Beenakker and Mazur's method [Physica A 120, 388-410 (1983); 126, 349-370 (1984)]. Two species of hard spheres are suspended in an overdamped viscous solvent that mediates the salient hydrodynamic interactions among all particles. In a comprehensive parameter scan that covers various packing fractions and suspension compositions, we employ numerically accurate SD simulations to compute the initial diffusive relaxation of density modulations at the Brownian time scale, quantified by the partial hydrodynamic functions. A revised version of Beenakker and Mazur's ??-scheme for monodisperse suspensions is found to exhibit surprisingly good accuracy, when simple rescaling laws are invoked in its application to mixtures. The so-modified ?? scheme predicts hydrodynamic functions in very good agreement with our SD simulation results, for all densities from the very dilute limit up to packing fractions as high as 40%. PMID:25681941
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%.
Rice, S.A.; Cerjan, C.; Bagchi, B.
1985-04-01
It is conjectured that the hard sphere system has several distinct solid phases, all but one of which are metastable. The bifurcation theory analysis of freezing is extended to the description of the transition between a supercooled liquid and a disordered solid by defining a restricted phase space for the disordered solid. This approach leads to the prediction of a first order transition between a supercooled hard sphere fluid and a disordered metastable hard sphere solid. The results of the calculation are in qualitative agreement with the results of Woodcock's molecular dynamics computer simulations.
Swarn Lata Singh; Atul S. Bharadwaj; Yashwant Singh
2011-01-31
A free-energy functional that contains both the symmetry conserved and symmetry broken parts of the direct pair correlation function has been used to investigate the freezing of a system of hard spheres into crystalline and amorphous structures. The freezing parameters for fluid-crystal transition have been found to be in very good agreement with the results found from simulations. We considered amorphous structures found from the molecular dynamics simulations at packing fractions $\\eta$ lower than the glass close packing fraction $\\eta_{J}$ and investigated their stability compared to that of a homogeneous fluid. The existence of free-energy minimum corresponding to a density distribution of overlapping Gaussians centered around an amorphous lattice depicts the deeply supercooled state with a heterogeneous density profile.
Effective-interaction approach to the Fermi hard-sphere system
NASA Astrophysics Data System (ADS)
Mecca, Angela; Lovato, Alessandro; Benhar, Omar; Polls, Artur
2015-03-01
The formalism based on correlated basis functions and the cluster-expansion technique has been recently employed to derive an effective interaction from a realistic nuclear Hamiltonian. To gauge the reliability of this scheme, we perform a systematic comparison between the results of its application to the Fermi hard-sphere system and the predictions obtained from low-density expansions, as well as from other many-body techniques. The analysis of a variety of properties, including the ground-state energy, the effective mass, and the momentum distribution, shows that the effective-interaction approach is quite accurate, thus suggesting that it may be employed to achieve a consistent description of the structure and dynamics of nuclear matter in the density region relevant to astrophysical applications.
Radial distribution functions of non-additive hard sphere mixtures via Percus' test particle route
NASA Astrophysics Data System (ADS)
Hopkins, Paul; Schmidt, Matthias
2011-08-01
Using fundamental density functional theory we calculate the partial radial distribution functions, gij(r), of a binary non-additive hard sphere mixture using either Percus' test particle approach or inversion of the analytic structure factor obtained via the Ornstein-Zernike route. We find good agreement between the theoretical results and Monte Carlo simulation data for both positive and moderate negative non-additivities. We investigate the asymptotic, r\\to \\infty , decay of the gij(r) and show that this agrees with the analytic analysis of the contributions to the partial structure factors in the plane of complex wavevectors. We find the test particle density profiles to be free of unphysical artefacts, contrary to earlier reports.
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
Low-noise Monte Carlo simulation of the variable hard sphere gas
Radtke, Gregg A.
We present an efficient particle simulation method for the Boltzmann transport equation based on the low-variance deviational simulation Monte Carlo approach to the variable-hard-sphere gas. The proposed method exhibits ...
Hard-Sphere Fluids with Chemical Self-Potentials
Kiessling, Michael K -H
2009-01-01
Existence, uniqueness and stability of solutions is studied for a set of nonlinear fixed point equations which define self-consistent hydrostatic equilibria of a classical continuum fluid that is confined inside a container and in contact with either a heat and a matter reservoir, or just a heat reservoir. The local thermodynamics is furnished by the statistical mechanics of a system of hard balls, in the approximation of Carnahan-Starling. The fluid's local chemical potential per particle at is the sum of the matter reservoir's contribution and a self contribution which is computed by convoluting the fluid density distribution with a van der Waals, a Yukawa, or a Newton kernel. We prove the existence of a grand canonical phase transition, and a petit canonical phase transition which is embedded in the former.
Hard-Sphere Fluids with Chemical Self-Potentials
Michael K. -H. Kiessling; Jerome K. Percus
2010-01-23
Existence, uniqueness and stability of solutions is studied for a set of nonlinear fixed point equations which define self-consistent hydrostatic equilibria of a classical continuum fluid that is confined inside a container and in contact with either a heat and a matter reservoir, or just a heat reservoir. The local thermodynamics is furnished by the statistical mechanics of a system of hard balls, in the approximation of Carnahan-Starling. The fluid's local chemical potential per particle at is the sum of the matter reservoir's contribution and a self contribution which is computed by convoluting the fluid density distribution with a van der Waals, a Yukawa, or a Newton kernel. We prove the existence of a grand canonical phase transition, and a petit canonical phase transition which is embedded in the former.
Phase transition, equation of state, and limiting shear viscosities of hard sphere dispersions
NASA Astrophysics Data System (ADS)
Phan, See-Eng; Russel, William B.; Cheng, Zhengdong; Zhu, Jixiang; Chaikin, Paul M.; Dunsmuir, John H.; Ottewill, Ronald H.
1996-12-01
Despite an interparticle potential consisting of only an infinite repulsion at contact, the thermodynamics and dynamics of concentrated dispersions of hard spheres are not yet fully understood. Colloidal poly-(methyl methacrylate) spheres with a grafted layer of poly-(12-hydroxy stearic acid) (PMMA-PHSA) comprise a common model for investigating structural, dynamic, and rheological properties. These highly monodisperse spheres can be index matched in nonaqueous solvents, reducing van der Waals forces and allowing characterization via light scattering. In this work, we test the behavior of these dispersions against expectations for hard spheres through observations of the phase behavior, x-ray densitometry of equilibrium sediments, and Zimm viscometry. We set the effective hard sphere volume fraction by the disorder-order transition, thereby accounting for the polymer layer, any swelling due to the solvent, and polydispersity. The melting transition then occurs close to the expected value and the equation of state for the fluid phase, extracted from the equilibrium sediment with x-ray densitometry, conforms to the Carnahan-Starling equation. However, the osmotic pressure of the crystalline phase lies slightly above that calculated for a single fcc crystal even after accounting for polydispersity. Likewise the high shear viscosity of the fluid compares well with other hard sphere dispersions, but the low shear viscosity for PMMA-PHSA hard spheres exceeds those for polystyrene and silica hard spheres, e.g., a relative viscosity of 45+/-3 at ?=0.50 rather than 24. Our low shear viscosities are consistent with other PMMA-PHSA data after rescaling for both the polymer layer thickness and polydispersity, and may represent the true hard sphere curve. We anticipate that the equation of state for the crystal deviates due to polycrystallinity or a direct effect of polydispersity.
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.
Phase transition, equation of state, and limiting shear viscosities of hard sphere dispersions
See-Eng Phan; William B. Russel; Zhengdong Cheng; Jixiang Zhu; Paul M. Chaikin; John H. Dunsmuir; Ronald H. Ottewill
1996-01-01
Despite an interparticle potential consisting of only an infinite repulsion at contact, the thermodynamics and dynamics of concentrated dispersions of hard spheres are not yet fully understood. Colloidal poly-(methyl methacrylate) spheres with a grafted layer of poly-(12-hydroxy stearic acid) (PMMA-PHSA) comprise a common model for investigating structural, dynamic, and rheological properties. These highly monodisperse spheres can be index matched in
Solubilities of Solutes in Ionic Liquids from a SimplePerturbed-Hard-Sphere Theory
Qin, Yuan; Prausnitz, John M.
2005-09-20
In recent years, several publications have provided solubilities of ordinary gases and liquids in ionic liquids. This work reports an initial attempt to correlate the experimental data using a perturbed-hard-sphere theory; the perturbation is based on well-known molecular physics when the solution is considered as a dielectric continuum. For this correlation, the most important input parameters are hard-sphere diameters of the solute and of the cation and anion that constitute the ionic liquid. In addition, the correlation uses the solvent density and the solute's polarizability and dipole and quadrupole moments, if any. Dispersion-energy parameters are obtained from global correlation of solubility data. Results are given for twenty solutes in several ionic liquids at normal temperatures; in addition, some results are given for gases in two molten salts at very high temperatures. Because the theory used here is much simplified, and because experimental uncertainties (especially for gaseous solutes) are often large, the accuracy of the correlation presented here is not high; in general, predicted solubilities (Henry's constants) agree with experiment to within roughly {+-} 70%. As more reliable experimental data become available, modifications in the characterizing parameters are likely to improve accuracy. Nevertheless, even in its present form, the correlation may be useful for solvent screening in engineering design.
NASA Astrophysics Data System (ADS)
Costa, Lorenza A.; Zhou, Yaoqi; Hall, Carol K.; Carrà, Sergio
1995-04-01
We report Monte Carlo simulation results for the bulk pressure of fused-hard-sphere (FHS) chain fluids with bond-length-to-bead-diameter ratios ? 0.4 at chain lengths n=4, 8 and 16. We also report density profiles for FHS chain fluids at a hard wall. The results for the compressibility factor are compared to results from extensions of the Generalized Flory (GF) and Generalized Flory Dimer (GFD) theories proposed by Yethiraj et al. and by us. Our new GF theory, GF-AB, significantly improves the prediction of the bulk pressure of fused-hard-sphere chains over the GFD theories proposed by Yethiraj et al. and by us although the GFD theories give slightly better low-density results. The GFD-A theory, the GFD-B theory and the new theories (GF-AB, GFD-AB, and GFD-AC) satisfy the exact zero-bonding-length limit. All theories considered recover the GF or GFD theories at the tangent hard-sphere chain limit.
Costa, L.A.; Zhou, Y.; Hall, C.K. [Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina 27695-7905 (United States)] [Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina 27695-7905 (United States); Carra, S. [Dipartimento di Chimica Fisica Applicata, Politecnico di Milano, Via Mancinelli 7, 20131 Milano (Italy)] [Dipartimento di Chimica Fisica Applicata, Politecnico di Milano, Via Mancinelli 7, 20131 Milano (Italy)
1995-04-15
We report Monte Carlo simulation results for the bulk pressure of fused-hard-sphere (FHS) chain fluids with bond-length-to-bead-diameter ratios {approx} 0.4 at chain lengths {ital n}=4, 8 and 16. We also report density profiles for FHS chain fluids at a hard wall. The results for the compressibility factor are compared to results from extensions of the Generalized Flory (GF) and Generalized Flory Dimer (GFD) theories proposed by Yethiraj {ital et} {ital al}. and by us. Our new GF theory, GF-AB, significantly improves the prediction of the bulk pressure of fused-hard-sphere chains over the GFD theories proposed by Yethiraj {ital et} {ital al}. and by us although the GFD theories give slightly better low-density results. The GFD-A theory, the GFD-B theory and the new theories (GF-AB, GFD-AB, and GFD-AC) satisfy the exact zero-bonding-length limit. All theories considered recover the GF or GFD theories at the tangent hard-sphere chain limit.
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
Inhomogeneous quasi-stationary state of dense fluid of inelastic hard spheres
Itzhak Fouxon
2014-02-13
We study closed dense collections of hard spheres that collide inelastically with constant coefficient of normal restitution. We find inhomogeneous states (IS) where the density profile is spatially non-uniform but constant in time. The states are exact solutions of non-linear partial differential equations that describe the coupled distributions of density and temperature when inelastic losses of energy per collision are small. The derivation is performed without modelling the equations' coefficients that are unknown in the dense limit (such as the equation of state), using only their scaling form specific for hard spheres. The IS is exact non-linear state of this many-body system. It captures a fundamental property of inelastic collections of particles: the possibility of preserving non-uniform temperature via the interplay of inelastic cooling and heat conduction, generalizing previous results in the dilute case. We perform numerical simulations to demonstrate that arbitrary initial state evolves to the IS in the limit of long times where the container has the geometry of the channel. The evolution is like gas-liquid transition. The liquid condenses in a vanishing part of the total volume but takes most of the mass of the system. However, the gaseous phase, which mass grows only logarithmically with the system size, is relevant because its fast particles carry most of the energy of the system. Remarkably, the system self-organizes to dissipate no energy: the inelastic decay of energy is a power-law $[1+t/t_c]^{-2}$ where $t_c$ diverges in the thermodynamic limit. This behavior is caused by unusual spatial distribution of particles: on approach to one of the container's walls the density grows inversely with the distance. We discuss the relation of our results to the recently proposed finite-time singularity in other container's geometries.
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.
Hard-sphere fluids with chemical self-potentials
NASA Astrophysics Data System (ADS)
Kiessling, M. K.-H.; Percus, J. K.
2010-01-01
The existence, uniqueness, and stability of solutions are studied for a set of nonlinear fixed point equations which define self-consistent hydrostatic equilibria of a classical continuum fluid that is confined inside a container ?¯?R3 and in contact with either a heat and a matter reservoir, or just a heat reservoir. The local thermodynamics is furnished by the statistical mechanics of a system of hard balls, in the approximation of Carnahan-Starling. The fluid's local chemical potential per particle at r ?? is the sum of the matter reservoir's contribution and a self-contribution -(V??)(r), where ? is the fluid density function and V a non-negative linear combination of the Newton kernel VN(|r|)=-|r|-1, the Yukawa kernel VY(|r|)=-|r|-1e-?|r|, and a van der Waals kernel VW(|r|)=-(1+?2|r|2)-3. The fixed point equations involving the Yukawa and Newton kernels are equivalent to semilinear elliptic partial differential equations (PDEs) of second order with a nonlinear, nonlocal boundary condition. We prove the existence of a grand canonical phase transition and of a petit canonical phase transition which is embedded in the former. The proofs suggest that, except for boundary layers, the grand canonical transition is of the type "all gas?all liquid" while the petit canonical one is of the type "all vapor?liquid drop with vapor atmosphere." The latter proof, in particular, suggests the existence of solutions with interface structure which compromise between the all-liquid and all-gas density solutions.
Energy and Structure of Hard-Sphere Bose Gases in three and two dimensions
NASA Astrophysics Data System (ADS)
Mazzanti, F.; Polls, A.; Fabrocini, A.
2005-02-01
The energy and structure of dilute gases of hard spheres in three dimensions is discussed, together with some aspects of the corresponding 2D systems. A variational approach in the framework of the Hypernetted Chain Equations (HNC) is used starting from a Jastrow wavefunction that is optimized to produce the best two--body correlation factor with the appropriate long range. Relevant quantities describing static properties of the system are studied as a function of the gas parameter $x=\\rho a^d$ where $\\rho$, $a$ and $d$ are the density, $s$--wave scattering length of the potential and dimensionality of the space, respectively. The occurrence of a maximum in the radial distribution function and in the momentum distribution is a natural effect of the correlations when $x$ increases. Some aspects of the asymptotic behavior of the functions characterizing the structure of the systems are also investigated.
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
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.
Ratio of effective temperature to pressure controls the mobility of sheared hard spheres
Thomas K. Haxton
2011-10-28
Using molecular dynamics simulation, we calculate fluctuations and response for steadily sheared hard spheres over a wide range of packing fractions $\\phi$ and shear strain rates $\\gamma$, using two different methods to dissipate energy. To a good approximation, shear stress and density fluctuations are related to their associated response functions by a single effective temperature $T_{eff}$ that is equal to or larger than the kinetic temperature $T_{kin}$. We find a crossover in the relationship between the relaxation time $\\tau$ and the the nondimensionalized effective temperature $T_{eff}/p\\sigma^3$, where $p$ is the pressure and $\\sigma$ is the sphere diameter. In the solid response regime, the behavior at fixed packing fraction satisfies $\\tau\\gamma\\propto \\exp(-cp\\sigma^3/T_{eff})$, where $c$ depends weakly on $\\phi$, suggesting that the average local yield strain is controlled by the effective temperature in a way that is consistent with shear transformation zone theory. In the fluid response regime, the relaxation time depends on $T_{eff}/p\\sigma^3$ as it depends on $T_{kin}/p\\sigma^3$ in equilibrium. This regime includes both near-equilibrium conditions where $T_{eff} ~ T_{kin}$ and far-from-equilibrium conditions where $T_{eff} \
A Thermodynamically-Consistent Non-Ideal Stochastic Hard-Sphere Fluid
Donev, A; Alder, B J; Garcia, A L
2009-08-03
A grid-free variant of the Direct Simulation Monte Carlo (DSMC) method is proposed, named the Isotropic DSMC (I-DSMC) method, that is suitable for simulating collision-dominated dense fluid flows. The I-DSMC algorithm eliminates all grid artifacts from the traditional DSMC algorithm and is Galilean invariant and microscopically isotropic. The stochastic collision rules in I-DSMC are modified to introduce a non-ideal structure factor that gives consistent compressibility, as first proposed in [Phys. Rev. Lett. 101:075902 (2008)]. The resulting Stochastic Hard Sphere Dynamics (SHSD) fluid is empirically shown to be thermodynamically identical to a deterministic Hamiltonian system of penetrable spheres interacting with a linear core pair potential, well-described by the hypernetted chain (HNC) approximation. We develop a kinetic theory for the SHSD fluid to obtain estimates for the transport coefficients that are in excellent agreement with particle simulations over a wide range of densities and collision rates. The fluctuating hydrodynamic behavior of the SHSD fluid is verified by comparing its dynamic structure factor against theory based on the Landau-Lifshitz Navier-Stokes equations. We also study the Brownian motion of a nano-particle suspended in an SHSD fluid and find a long-time power-law tail in its velocity autocorrelation function consistent with hydrodynamic theory and molecular dynamics calculations.
Ratio of effective temperature to pressure controls the mobility of sheared hard spheres
NASA Astrophysics Data System (ADS)
Haxton, Thomas K.
2012-01-01
Using molecular dynamics simulations, we calculate fluctuations and responses for steadily sheared hard spheres over a wide range of packing fractions ? and shear strain rates ??, using two different methods to dissipate energy. To a good approximation, shear stress and density fluctuations are related to their associated response functions by a single effective temperature Teff that is equal to or larger than the kinetic temperature Tkin. We find a crossover in the relationship between the relaxation time ? and the the nondimensionalized effective temperature Teff/p?3, where p is the pressure and ? is the sphere diameter. In the solid response regime, the behavior at a fixed packing fraction satisfies ????exp(-cp?3/Teff), where c depends weakly on ?, suggesting that the average local yield strain is controlled by the effective temperature in a way that is consistent with shear transformation zone theory. In the fluid response regime, the relaxation time depends on Teff/p?3 as it depends on Tkin/p?3 in equilibrium. This regime includes both near-equilibrium conditions where Teff?Tkin and far-from-equilibrium conditions where Teff?Tkin. We discuss the implications of our results for systems with soft repulsive interactions.
Quantum-Mechanical Equation of State of a Hard-Sphere Gas at High Temperature. II
B. Jancovici
1969-01-01
As the continuation of a preceding paper, an expansion for the quantum-mechanical free energy F of a hard-sphere gas at high temperature is extended up to the second order in the thermal wavelength lambda=(2piℏ2mkT)12. To reach this order, one must study the three-body problem in a lowest-order approximation, in which adjacent sphere surfaces can be regarded as parallel planes. Coefficients
Moments of the Percus-Yevick hard-sphere correlation function
N. E. Berger; V. Twersky
1990-01-01
A simple recursive relation is derived for the momentsMn,n=1, 2,..., of the Percus-Yevick correlation functionh(r) for identical hard spheres. TheMn are rational functions of the volume fractionw occupied by the spheres; the first ten are given explicitly, and a single-term asymptotic form is obtained to suffice for the rest. Applications of theMn(w) include testing different approximations forh by numerical integration
T1 process and dynamics in glass-forming hard-sphere liquids.
Zhou, Yuxing; Milner, Scott T
2015-03-18
To study the relationship between dynamics and structure in a glass-forming liquid, we introduce a purely geometric criterion for locally mobile particles in a dense hard-sphere fluid: namely, "T1-active" particles, which can gain or lose at least one Voronoi neighbor by moving within their free volume with other particles fixed. We obtain geometrical and dynamical properties for monodisperse hard-sphere fluids with 0.40 < ? < 0.64 using a "crystal-avoiding" MD simulation that effectively suppresses crystallization without altering the dynamics. We find that the fraction of T1-active particles vanishes at random close packing, while the percolation threshold of T1-inactive particles is essentially identical to the commonly identified hard-sphere glass transition, ?g ? 0.585. PMID:25693721
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.
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.
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
Mixtures of Hard Ellipsoids and Spheres: Stability of the Nematic Phase
Carlos E. Alvarez; Martial Mazars
2014-05-09
The stability of liquid crystal phases in presence of small amount of non-mesogenic impurities is of general interest for a large spectrum of technological applications and in the theories of binary mixtures. Starting from the known phase diagram of the hard ellipsoids systems, we propose a simple model and method to explore the stability of the nematic phase in presence of small impurities represented by hard spheres. The study is performed in the isobaric ensemble with Monte Carlo simulations.
Fluid spheres of uniform density in general relativity
Ponce de Leon, J.
1986-01-01
A number of exact solutions for spherically symmetric nonstatic fluids of uniform density, surrounded by empty space, are derived and investigated. Solutions that represent expanding and contracting spheres, which tend asymptotically to static configurations described by the Schwarzschild interior solution ( rho = const), are obtained In some cases the motion of contraction or expansion is reversed, while in other cases there is no bouncing at all. Oscillating solutions are presented.
A New Bound on the Local Density of Sphere Packings
Douglas J. Muder
1993-01-01
It is shown that a packing of unit spheres in three-dimensional Euclidean space can have density at most 0.773055..., and\\u000a that a Voronoi polyhedron defined by such a packing must have volume at least 5.41848... These bounds are superior to the\\u000a best bounds previously published [5] (0.77836 and 5.382, respectively), but are inferior to the tight bounds of 0.7404...\\u000a and
Demixing and confinement of non-additive hard-sphere mixtures in slit pores.
Almarza, N G; Martín, C; Lomba, E; Bores, C
2015-01-01
Using Monte Carlo simulation, we study the influence of geometric confinement on demixing for a series of symmetric non-additive hard spheres mixtures confined in slit pores. We consider both a wide range of positive non-additivities and a series of pore widths, ranging from the pure two dimensional limit to a large pore width where results are close to the bulk three dimensional case. Critical parameters are extracted by means of finite size analysis. As a general trend, we find that for this particular case in which demixing is induced by volume effects, the critical demixing densities (and pressures) increase due to confinement between neutral walls, following the expected behavior for phase equilibria of systems confined by pure repulsive walls: i.e., confinement generally enhances miscibility. However, a non-monotonous dependence of the critical pressure and density with pore size is found for small non-additivities. In this latter case, it turns out that an otherwise stable bulk mixture can be unexpectedly forced to demix by simple geometric confinement when the pore width decreases down to approximately one and a half molecular diameters. PMID:25573573
Demixing and confinement of non-additive hard-sphere mixtures in slit pores
NASA Astrophysics Data System (ADS)
Almarza, N. G.; Martín, C.; Lomba, E.; Bores, C.
2015-01-01
Using Monte Carlo simulation, we study the influence of geometric confinement on demixing for a series of symmetric non-additive hard spheres mixtures confined in slit pores. We consider both a wide range of positive non-additivities and a series of pore widths, ranging from the pure two dimensional limit to a large pore width where results are close to the bulk three dimensional case. Critical parameters are extracted by means of finite size analysis. As a general trend, we find that for this particular case in which demixing is induced by volume effects, the critical demixing densities (and pressures) increase due to confinement between neutral walls, following the expected behavior for phase equilibria of systems confined by pure repulsive walls: i.e., confinement generally enhances miscibility. However, a non-monotonous dependence of the critical pressure and density with pore size is found for small non-additivities. In this latter case, it turns out that an otherwise stable bulk mixture can be unexpectedly forced to demix by simple geometric confinement when the pore width decreases down to approximately one and a half molecular diameters.
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.
A comprehensive approach to an equation of state for hard spheres and Lennard Jones fluids
S. B. Khasare
2011-01-01
We present a simple method of obtaining various equations of state for hard sphere fluid in a simple unifying way. We will guess equations of state by using suitable axiomatic functional forms (n = 1, 2, 3, 4, 5) for surface tension Smn(r), r >= d\\/2 with intermolecular separation r as a variable, where m is an arbitrary real number
Extension of the hard-sphere particle-wall collision model to account for particle deposition
Pawel Kosinski; Alex C. Hoffmann
2009-01-01
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
Cooling process for inelastic Boltzmann equations for hard spheres, Part I: The Cauchy problem
Mischler, Stéphane
. Mischler1 , C. Mouhot2 and M. Rodriguez Ricard3 November 16, 2004 Abstract We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate) non-concentration estimates in Orlicz spaces, from which we deduce weak stability and existence
A generalized mixing rule for hard-sphere equations of state of Percus–Yevick type
Mohammad K. Khoshkbarchi; Juan H. Vera
1998-01-01
An analogical approach has been used to extend to mixtures the radial distribution function of Percus–Yevick type of equations of state for hard spheres. The proposed approach follows the same formalism employed by Mansoori et al. to extend to mixtures the Carnahan–Starling equation of state. The generality of the proposed method permits to extend to mixtures equations of state with
EXACT SOLUTION OF THE PERCUS-YEVICK INTEGRAL EQUATION FOR HARD SPHERES
M. Wertheim
1963-01-01
ABS>The equation of state and the pair distribution for the Percus-; Yevick integral equation for the radiai distribution function of a classical ; fluid are obtained in closed form for the prototype of interacting hard spheres. ; (D.C.W.);
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.
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.
A perturbation theory and simulations of the dipole solvation thermodynamics: Dipolar hard spheres
Matyushov, Dmitry
A perturbation theory and simulations of the dipole solvation thermodynamics: Dipolar hard spheres of the thermodynamic perturbation theory is used to calculate the solvation chemical potential of a dipolar solute testing the performance of the PadeÂ´ perturbation theory against simulations, ii understanding
Potential energy landscape and inherent dynamics of a hard-sphere fluid.
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. PMID:25375501
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.
Weeks, Eric R.
Equivalence of Glass Transition and Colloidal Glass Transition in the Hard-Sphere Limit Ning Xu,1 that the slowing of the dynamics in simulations of several model glass-forming liquids is equivalent to the hard-sphere glass transition in the low-pressure limit. In this limit, we find universal behavior of the relaxation
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.
Equation of state for hard-sphere fluid in restricted geometry.
Kamenetskiy, I E; Mon, K K; Percus, J K
2004-10-15
Many practical applications require the knowledge of the equation of state of fluids in restricted geometry. We study a hard-sphere fluid at equilibrium in a narrow cylindrical pore with hard walls for pore radii R<((square root 3)+2)/4 (in units of the hard sphere diameter). In this case each particle can interact only with its nearest neighbors, which makes possible the use of analytical methods to study the thermodynamics of the system. Using a transfer operator formalism and expanding in low- and high-pressure regions, we can obtain a simple analytical equation of state for almost all ranges of pressure. The results agree with Monte Carlo simulations. Additionally, it is shown that a convenient analytical representation can be chosen to accurately describe the equation of state within the error of the Monte Carlo simulation. PMID:15473806
Equation of state for hard-sphere fluid in restricted geometry
NASA Astrophysics Data System (ADS)
Kamenetskiy, I. E.; Mon, K. K.; Percus, J. K.
2004-10-01
Many practical applications require the knowledge of the equation of state of fluids in restricted geometry. We study a hard-sphere fluid at equilibrium in a narrow cylindrical pore with hard walls for pore radii R<(?3 +2)/4 (in units of the hard sphere diameter). In this case each particle can interact only with its nearest neighbors, which makes possible the use of analytical methods to study the thermodynamics of the system. Using a transfer operator formalism and expanding in low- and high-pressure regions, we can obtain a simple analytical equation of state for almost all ranges of pressure. The results agree with Monte Carlo simulations. Additionally, it is shown that a convenient analytical representation can be chosen to accurately describe the equation of state within the error of the Monte Carlo simulation.
Rolling friction for hard cylinder and sphere on viscoelastic solid.
Persson, B N J
2010-12-01
We calculate the friction force acting on a hard cylinder or spherical ball rolling on a flat surface of a viscoelastic solid. The rolling-friction coefficient depends non-linearly on the normal load and the rolling velocity. For a cylinder rolling on a viscoelastic solid characterized by a single relaxation time Hunter has obtained an exact result for the rolling friction, and our result is in very good agreement with his result for this limiting case. The theoretical results are also in good agreement with experiments of Greenwood and Tabor. We suggest that measurements of rolling friction over a wide range of rolling velocities and temperatures may constitute a useful way to determine the viscoelastic modulus of rubber-like materials. PMID:21107881
Polydispersity and Optimal Relaxation in the Hard Sphere Fluid
NASA Astrophysics Data System (ADS)
Barbier, Matthieu; Trizac, Emmanuel
2014-03-01
We consider the mass heterogeneity in a gas of polydisperse hard particles as a key to optimizing a dynamical property: the kinetic relaxation rate. Using the framework of the Boltzmann equation, we study the long time approach of a perturbed velocity distribution toward the equilibrium Maxwellian solution. We work out the cases of discrete as well as continuous distributions of masses, as found in dilute fluids of mesoscopic particles such as granular matter and colloids. On the basis of analytical and numerical evidence, we formulate a dynamical equipartition principle that leads to the result that no such continuous dispersion in fact minimizes the relaxation time, as the global optimum is characterized by a finite number of species. This optimal mixture is found to depend on the dimension of space, ranging from five species for to a single one for . The role of the collisional kernel is also discussed, and extensions to dissipative systems are shown to be possible.
Rolling friction for hard cylinder and sphere on viscoelastic solid
B. N. J. Persson
2010-08-26
We calculate the friction force acting on a hard cylinder or spherical ball rolling on a flat surface of a viscoelastic solid. The rolling friction coefficient depends non-linearly on the normal load and the rolling velocity. For a cylinder rolling on a viscoelastic solid characterized by a single relaxation time Hunter has obtained an exact result for the rolling friction, and our result is in very good agreement with his result for this limiting case. The theoretical results are also in good agreement with experiments of Greenwood and Tabor. We suggest that measurements of rolling friction over a wide range of rolling velocities and temperatures may constitute an useful way to determine the viscoelastic modulus of rubber-like materials.
López-Sánchez, Erik; Estrada-Álvarez, César D; Pérez-Ángel, Gabriel; Méndez-Alcaraz, José Miguel; González-Mozuelos, Pedro; Castañeda-Priego, Ramón
2013-09-14
Asymmetric binary mixtures of hard-spheres exhibit several interesting thermodynamic phenomena, such as multiple kinds of glassy states. When the degrees of freedom of the small spheres are integrated out from the description, their effects are incorporated into an effective pair interaction between large spheres known as the depletion potential. The latter has been widely used to study both the phase behavior and dynamic arrest of the big particles. Depletion forces can be accounted for by a contraction of the description in the multicomponent Ornstein-Zernike equation [R. Castañeda-Priego, A. Rodríguez-López, and J. M. Méndez-Alcaraz, Phys. Rev. E 73, 051404 (2006)]. Within this theoretical scheme, an approximation for the difference between the effective and bare bridge functions is needed. In the limit of infinite dilution, this difference is irrelevant and the typical Asakura-Osawa depletion potential is recovered. At higher particle concentrations, however, this difference becomes important, especially where the shell of first neighbors is formed, and, as shown here, cannot be simply neglected. In this work, we use a variant of the Verlet expression for the bridge functions to highlight their importance in the calculation of the depletion potential at high densities and close to the spinodal decomposition. We demonstrate that the modified Verlet closure predicts demixing in binary mixtures of hard spheres for different size ratios and compare its predictions with both liquid state and density functional theories, computer simulations, and experiments. We also show that it provides accurate correlation functions even near the thermodynamic instability; this is explicitly corroborated with results of molecular dynamics simulations of the whole mixture. Particularly, our findings point toward a possible universal behavior of the depletion potential around the spinodal line. PMID:24050366
NASA Astrophysics Data System (ADS)
López-Sánchez, Erik; Estrada-Álvarez, César D.; Pérez-Ángel, Gabriel; Méndez-Alcaraz, José Miguel; González-Mozuelos, Pedro; Castañeda-Priego, Ramón
2013-09-01
Asymmetric binary mixtures of hard-spheres exhibit several interesting thermodynamic phenomena, such as multiple kinds of glassy states. When the degrees of freedom of the small spheres are integrated out from the description, their effects are incorporated into an effective pair interaction between large spheres known as the depletion potential. The latter has been widely used to study both the phase behavior and dynamic arrest of the big particles. Depletion forces can be accounted for by a contraction of the description in the multicomponent Ornstein-Zernike equation [R. Castañeda-Priego, A. Rodríguez-López, and J. M. Méndez-Alcaraz, Phys. Rev. E 73, 051404 (2006)], 10.1103/PhysRevE.73.051404. Within this theoretical scheme, an approximation for the difference between the effective and bare bridge functions is needed. In the limit of infinite dilution, this difference is irrelevant and the typical Asakura-Osawa depletion potential is recovered. At higher particle concentrations, however, this difference becomes important, especially where the shell of first neighbors is formed, and, as shown here, cannot be simply neglected. In this work, we use a variant of the Verlet expression for the bridge functions to highlight their importance in the calculation of the depletion potential at high densities and close to the spinodal decomposition. We demonstrate that the modified Verlet closure predicts demixing in binary mixtures of hard spheres for different size ratios and compare its predictions with both liquid state and density functional theories, computer simulations, and experiments. We also show that it provides accurate correlation functions even near the thermodynamic instability; this is explicitly corroborated with results of molecular dynamics simulations of the whole mixture. Particularly, our findings point toward a possible universal behavior of the depletion potential around the spinodal line.
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.
The isotropic-nematic phase transition of tangent hard-sphere chain fluids--pure components.
van Westen, Thijs; Oyarzún, Bernardo; Vlugt, Thijs J H; Gross, Joachim
2013-07-21
An extension of Onsager's second virial theory is developed to describe the isotropic-nematic phase transition of tangent hard-sphere chain fluids. Flexibility is introduced by the rod-coil model. The effect of chain-flexibility on the second virial coefficient is described using an accurate, analytical approximation for the orientation-dependent pair-excluded volume. The use of this approximation allows for an analytical treatment of intramolecular flexibility by using a single pure-component parameter. Two approaches to approximate the effect of the higher virial coefficients are considered, i.e., the Vega-Lago rescaling and Scaled Particle Theory (SPT). The Onsager trial function is employed to describe the orientational distribution function. Theoretical predictions for the equation of state and orientational order parameter are tested against the results from Monte Carlo (MC) simulations. For linear chains of length 9 and longer, theoretical results are in excellent agreement with MC data. For smaller chain lengths, small errors introduced by the approximation of the higher virial coefficients become apparent, leading to a small under- and overestimation of the pressure and density difference at the phase transition, respectively. For rod-coil fluids of reasonable rigidity, a quantitative comparison between theory and MC simulations is obtained. For more flexible chains, however, both the Vega-Lago rescaling and SPT lead to a small underestimation of the location of the phase transition. PMID:23883045
The kinetic coefficient of hard-sphere crystal-melt interfaces from molecular-dynamics simulations
NASA Astrophysics Data System (ADS)
Amini, Majeed; Laird, Brian
2006-03-01
The kinetic coefficient for a crystal melt interface, ?, is the ratio of the interface growth velocity to the undercooling (TM- T), where TM is the melting point. In this work we determine the kinetic coeffiecient for the hard-sphere system by analyzing capillary fluctuations in interface position using molecular dynamics (MD) simulation [Hoyt et al, Mat. Sci. Eng. R 41, 121-163 (2003)]. We report the kinetic coefficient for the three interfaces: (100), (110), and (111). Our results for ?100, ?110, and ?111 are 1.15(4) (kB/(m TM))^1/2, 0.85(6) (kB/(m TM))^1/2, and 0.57(8) (kB/(m TM))^1/2, respectively, which gives the relation ?100> ?110> ?111. This ordering is consistent with the recent results of MD simulations for a variety of metals. The anisotropy ratios ?100/?110, and ?100/?111 are 1.35(11), and 2.0(3), respectively. We compare our results to those of classical density functional theory (DFT) of [Mikheev and Chernov, J. Cryst. Growth 112, 591-596 (1991)].
Theory of molecular crowding in Brownian hard-sphere liquids
NASA Astrophysics Data System (ADS)
Zaccone, Alessio; Terentjev, Eugene M.
2012-06-01
We derive an analytical pair potential of mean force for Brownian molecules in the liquid state. Our approach accounts for many-particle correlations of crowding particles of the liquid and for diffusive transport across the spatially modulated local density of crowders in the dense environment. Focusing on the limit of equal-size particles, we show that this diffusive transport leads to additional density- and structure-dependent terms in the interaction potential and to a much stronger attraction (by a factor of ?4 at average volume fraction of crowders ?0=0.25) than in the standard depletion interaction where the diffusive effects are neglected. As an illustration of the theory, we use it to study the size of a polymer chain in a solution of inert crowders. Even in the case of an athermal background solvent, when a classical chain should be fully swollen, we find a sharp coil-globule transition of the ideal chain collapsing at a critical value of the crowder volume fraction ?c?0.145.
Urrutia, Ignacio
2014-12-28
This work is devoted to analyze the relation between the thermodynamic properties of a confined fluid and the shape of its confining vessel. Recently, new insights in this topic were found through the study of cluster integrals for inhomogeneous fluids that revealed the dependence on the vessel shape of the low density behavior of the system. Here, the statistical mechanics and thermodynamics of fluids confined in wedges or by edges is revisited, focusing on their cluster integrals. In particular, the well known hard sphere fluid, which was not studied in this framework so far, is analyzed under confinement and its thermodynamic properties are analytically studied up to order two in the density. Furthermore, the analysis is extended to the confinement produced by a corrugated wall. These results rely on the obtained analytic expression for the second cluster integral of the confined hard sphere system as a function of the opening dihedral angle 0 < ? < 2?. It enables a unified approach to both wedges and edges. PMID:25554179
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.
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.
Extension of the hard-sphere particle-wall collision model to account for particle deposition
NASA Astrophysics Data System (ADS)
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.
Regularized 13 moment equations for hard sphere molecules: Linear bulk equations
NASA Astrophysics Data System (ADS)
Struchtrup, Henning; Torrilhon, Manuel
2013-05-01
The regularized 13 moment equations of rarefied gas dynamics are derived for a monatomic hard sphere gas in the linear regime. The equations are based on an extended Grad-type moment system, which is systematically reduced by means of the Order of Magnitude Method [H. Struchtrup, "Stable transport equations for rarefied gases at high orders in the Knudsen number," Phys. Fluids 16(11), 3921-3934 (2004)], 10.1063/1.1782751. Chapman-Enskog expansion of the final equations yields the linear Burnett and super-Burnett equations. While the Burnett coefficients agree with literature values, this seems to be the first time that super-Burnett coefficients are computed for a hard sphere gas. As a first test of the equations the dispersion and damping of sound waves is considered.
Parallelized event chain algorithm for dense hard sphere and polymer systems
NASA Astrophysics Data System (ADS)
Kampmann, Tobias A.; Boltz, Horst-Holger; Kierfeld, Jan
2015-01-01
We combine parallelization and cluster Monte Carlo for hard sphere systems and present a parallelized event chain algorithm for the hard disk system in two dimensions. For parallelization we use a spatial partitioning approach into simulation cells. We find that it is crucial for correctness to ensure detailed balance on the level of Monte Carlo sweeps by drawing the starting sphere of event chains within each simulation cell with replacement. We analyze the performance gains for the parallelized event chain and find a criterion for an optimal degree of parallelization. Because of the cluster nature of event chain moves massive parallelization will not be optimal. Finally, we discuss first applications of the event chain algorithm to dense polymer systems, i.e., bundle-forming solutions of attractive semiflexible polymers.
NASA Astrophysics Data System (ADS)
López de Haro, Mariano; Tejero, Carlos F.; Santos, Andrés
2013-04-01
The problem of demixing in a binary fluid mixture of highly asymmetric additive hard spheres is revisited. A comparison is presented between the results derived previously using truncated virial expansions for three finite size ratios with those that one obtains with the same approach in the extreme case in which one of the components consists of point particles. Since this latter system is known not to exhibit fluid-fluid segregation, the similarity observed for the behavior of the critical constants arising in the truncated series in all instances, while not being conclusive, may cast serious doubts as to the actual existence of a demixing fluid-fluid transition in disparate-sized binary additive hard-sphere mixtures.
An equation of state for fused hard-sphere polyatomic molecules
NASA Astrophysics Data System (ADS)
Phan, S.; Kierlik, E.; Rosinberg, M. L.
1994-11-01
An equation of state for a fluid of fused hard sphere (FHS) molecules is developed based on an interpolation scheme which relates the free energy per particle to that of a fluid of tangent hard sphere (THS) molecules at the same packing fraction. Use of Wertheim's TPT1 (first order thermodynamic perturbation theory) equation for this latter quantity yields an analytical expression for the compressibility factor for any shape of the FHS molecule. Predictions are in good agreement with the simulation results for rigid homonuclear and heteronuclear diatomics, linear and nonlinear triatomics, and tetrahedral pentatomics. For purely repulsive models of n-alkane chains, it is found that the accuracy of the theory deteriorates with increasing chain length. The interpolation procedure is also generalized to the case of chemical association.
Stability of LS and LS2 crystal structures in binary mixtures of hard and charged spheres.
Hynninen, A-P; Filion, L; Dijkstra, M
2009-08-14
We study by computer simulations the stability of various crystal structures in a binary mixture of large and small spheres interacting either with a hard sphere or a screened-Coulomb potential. In the case of hard-core systems, we consider structures that have atomic prototypes CrB, gammaCuTi, alphaIrV, HgBr2, AuTe2, Ag2Se and the Laves phases (MgCu2, MgNi2, and MgZn2) as well as a structure with space group symmetry 74. By utilizing Monte Carlo simulations to calculate Gibbs free energies, we determine composition versus pressure and constant volume phase diagrams for diameter ratios of q=0.74, 0.76, 0.8, 0.82, 0.84, and 0.85 for the small and large spheres. For diameter ratios 0.76 < or = q < or = 0.84, we find the Laves phases to be stable with respect to the other crystal structures that we considered and the fluid mixture. By extrapolating to the thermodynamic limit, we show that the MgZn2 structure is the most stable one of the Laves structures. We also calculate phase diagrams for equally and oppositely charged spheres for size ratio of 0.73 taking into consideration the Laves phases and CsCl. In the case of equally charged spheres, we find a pocket of stable Laves phases, while in the case of oppositely charged spheres, Laves phases are found to be metastable with respect to the CsCl and fluid phases. PMID:19691406
Stability of LS and LS2 crystal structures in binary mixtures of hard and charged spheres
NASA Astrophysics Data System (ADS)
Hynninen, A.-P.; Filion, L.; Dijkstra, M.
2009-08-01
We study by computer simulations the stability of various crystal structures in a binary mixture of large and small spheres interacting either with a hard sphere or a screened-Coulomb potential. In the case of hard-core systems, we consider structures that have atomic prototypes CrB, ?CuTi, ?IrV, HgBr2, AuTe2, Ag2Se and the Laves phases (MgCu2, MgNi2, and MgZn2) as well as a structure with space group symmetry 74. By utilizing Monte Carlo simulations to calculate Gibbs free energies, we determine composition versus pressure and constant volume phase diagrams for diameter ratios of q =0.74, 0.76, 0.8, 0.82, 0.84, and 0.85 for the small and large spheres. For diameter ratios 0.76?q?0.84, we find the Laves phases to be stable with respect to the other crystal structures that we considered and the fluid mixture. By extrapolating to the thermodynamic limit, we show that the MgZn2 structure is the most stable one of the Laves structures. We also calculate phase diagrams for equally and oppositely charged spheres for size ratio of 0.73 taking into consideration the Laves phases and CsCl. In the case of equally charged spheres, we find a pocket of stable Laves phases, while in the case of oppositely charged spheres, Laves phases are found to be metastable with respect to the CsCl and fluid phases.
Energy and structure of dilute hard- and soft-sphere gases
NASA Astrophysics Data System (ADS)
Mazzanti, F.; Polls, A.; Fabrocini, A.
2003-06-01
The energy and structure of dilute hard- and soft-sphere Bose gases are systematically studied in the framework of several many-body approaches, such as the variational correlated theory, the Bogoliubov model, and the uniform limit approximation, valid in the weak-interaction regime. When possible, the results are compared with the exact diffusion Monte Carlo ones. Jastrow-type correlation provides a good description of the systems, both hard- and soft-spheres, if the hypernetted chain energy functional is freely minimized and the resulting Euler equation is solved. The study of the soft-sphere potentials confirms the appearance of a dependence of the energy on the shape of the potential at gas paremeter values of x˜0.001. For quantities other than the energy, such as the radial distribution functions and the momentum distributions, the dependence appears at any value of x. The occurrence of a maximum in the radial distribution function, in the momentum distribution, and in the excitation spectrum is a natural effect of the correlations when x increases. The asymptotic behaviors of the functions characterizing the structure of the systems are also investigated. The uniform limit approach is very easy to implement and provides a good description of the soft-sphere gas. Its reliability improves when the interaction weakens.
Energy and structure of dilute hard- and soft-sphere gases
Mazzanti, F. [Departament d'Electronica, Enginyeria i Arquitectura La Salle, Pg. Bonanova 8, Universitat Ramon Llull, E-08022 Barcelona (Spain); Polls, A. [Departament d'Estructura i Constituents de la Materia, Diagonal 645, Universitat de Barcelona, E-08028 Barcelona (Spain); Fabrocini, A. [Dipartimento di Fisica 'E. Fermi', Universita di Pisa, and INFN, Sezione di Pisa, Via Buonarroti, 2, I-56100 Pisa (Italy)
2003-06-01
The energy and structure of dilute hard- and soft-sphere Bose gases are systematically studied in the framework of several many-body approaches, such as the variational correlated theory, the Bogoliubov model, and the uniform limit approximation, valid in the weak-interaction regime. When possible, the results are compared with the exact diffusion Monte Carlo ones. Jastrow-type correlation provides a good description of the systems, both hard- and soft-spheres, if the hypernetted chain energy functional is freely minimized and the resulting Euler equation is solved. The study of the soft-sphere potentials confirms the appearance of a dependence of the energy on the shape of the potential at gas paremeter values of x{approx}0.001. For quantities other than the energy, such as the radial distribution functions and the momentum distributions, the dependence appears at any value of x. The occurrence of a maximum in the radial distribution function, in the momentum distribution, and in the excitation spectrum is a natural effect of the correlations when x increases. The asymptotic behaviors of the functions characterizing the structure of the systems are also investigated. The uniform limit approach is very easy to implement and provides a good description of the soft-sphere gas. Its reliability improves when the interaction weakens.
Distribution functions of multi-component fluid mixtures of hard spheres
E. W. Grundke; D. Henderson
1972-01-01
A simple algorithm for obtaining accurate pair distribution functions gij of hard-sphere mixtures is proposed. This generalizes the pure-fluid procedure of Verlet and Weis for improving the Percus-Yevick distribution functions. Two theorems are proved concerning the distribution functions yij=exp (uij\\/kT)gij, and an approximation for these functions is proposed. Finally, a method for computing direct correlation functions, given the pair distribution
Percus-Yevick integral-equation theory for athermal hard-sphere chains
Yee C. Chiew
1990-01-01
A theoretical method for the modelling of athermal freely jointed tangent hard-sphere chain fluids, of fixed length r, is developed based on a ‘particle-particle’ description of the chain system. This approach is based on the Percus-Yevick (PY) theory in the context of the particle-particle Ornstein-Zernike integral equation subject to some imposed connectivity constraints. Analytical expressions for the compressibility equations of
Analytic solution of Percus-Yevick equation for fluid of hard spheres
I. Nezbeda
1974-01-01
A new method of analytic solution of the Percus-Yevick equation for the radial distribution functiong(r) of hard-sphere fluid is proposed. The original non-linear integral equation is reduced to non-homogeneous linear integral equation of Volterra's type of the second order. The kernel of this new equation has a polynomial form which allows to find analytic expression forg(r) itself without using the
Estimation of the free energy of hard-sphere crystals via a free-volume approach
Sang Kyu Kwak; Yong-Jin Yoon; Jong-Min Lee
2011-01-01
The free energies of the face-centred (FCC) and base-centred cubic (BCC) hard-sphere (HS) crystals have been estimated via the free-volume approach. We present two free-volume equations for the FCC and BCC HS crystals, which are different from those predicted by Velasco et al. [Langmuir 14(19) (1998), 5652–5655], and the equations exhibit more accuracy than Velasco et al.'s equations. The limitation
Estimation of the free energy of hard-sphere crystals via a free-volume approach
Sang Kyu Kwak; Yong-Jin Yoon; Jong-Min Lee
2012-01-01
The free energies of the face-centred (FCC) and base-centred cubic (BCC) hard-sphere (HS) crystals have been estimated via the free-volume approach. We present two free-volume equations for the FCC and BCC HS crystals, which are different from those predicted by Velasco et al. [Langmuir 14(19) (1998), 5652–5655], and the equations exhibit more accuracy than Velasco et al.'s equations. The limitation
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
Mahdi Zaeifi Yamchi; Richard K. Bowles
2014-09-16
We use a series of molecular dynamics simulations, and analytical theory, to demonstrate that a system of hard spheres confined to a narrow cylindrical channel exhibits a continuous phase transition from an isotropic fluid at low densities, to an orientationally ordered, but translationally disordered, helical fluid at high densities. The ordered fluid phase contains small sections of helix separated by topological defects that change the direction of the twist, altering the local chirailty. The defects break up the translational order, but the fluid develops long range orientational order. An analysis of the particle packings show that the length separation between defects controls the geometrical properties of the helical sections, including the orientation, and that pairs of defects experience a weak, but long range attraction resulting from entropic free volumes effects. These collective long range interactions overcome the restrictions on quasi-one-dimensional transitions, even though the particle-particle interaction is short ranged.
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.
Paul Hopkins; Matthias Schmidt
2010-07-29
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, r->infinity, decay of the partial pair correlation functions, g_ij(r). At low densities there occurs a structural crossover 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 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.
Mirigian, Stephen [University of Illinois, Urbana-Champaign] [University of Illinois, Urbana-Champaign; Schweizer, Kenneth [University of Illinois] [University of Illinois
2014-01-01
We generalize the force-level nonlinear Langevin equation theory of single particle hopping to include collective effects associated with long range elastic distortion of the liquid. The activated alpha relaxation event is of a mixed spatial character, involving two distinct, but inter-related, local and collective barriers. There are no divergences at volume fractions below jamming or temperatures above zero Kelvin. The ideas are first developed and implemented analytically and numerically in the context of hard sphere fluids. In an intermediate volume fraction crossover regime, the local cage process is dominant in a manner consistent with an apparent Arrhenius behavior. The super-Arrhenius collective barrier is more strongly dependent on volume fraction, dominates the highly viscous regime, and is well described by a nonsingular law below jamming. The increase of the collective barrier is determined by the amplitude of thermal density fluctuations, dynamic shear modulus or transient localization length, and a growing microscopic jump length. Alpha relaxation time calculations are in good agreement with recent experiments and simulations on dense fluids and suspensions of hard spheres. Comparisons of the theory with elastic models and entropy crisis ideas are explored. The present work provides a foundation for constructing a quasi-universal, fit-parameter-free theory for relaxation in thermal molecular liquids over 14 orders of magnitude in time.
Gupta, R.B.; Prausnitz, J.M. [Univ. of California, Berkeley, CA (United States). Dept. of Chemical Engineering] [Univ. of California, Berkeley, CA (United States). Dept. of Chemical Engineering; [Lawrence Berkeley Lab., CA (United States). Chemical Sciences Div.
1996-04-01
Vapor-liquid equilibria (VLE) for solvent-polymer mixtures at modest pressures are obtained from a perturbed hard-sphere-chain equation of state. This equation of state is the sum of a hard-sphere-chain term as the reference system and a van der Waals attractive term as the perturbation. The reference equation follows from the Percus-Yevick integral theory coupled with chain connectivity as described by Chiew. The effect of specific interactions, such as hydrogen bonding, is introduced through the proposal of Veytsman based on the statistical distribution of hydrogen bonds between donor and acceptor sites suggested by molecular structure. Calculated and observed vapor-liquid equilibria are presented for nonpolar, polar, and hydrogen-bonding solvent + homopolymer systems. Pure-component parameters (number of segments per molecule, segment-segment energy, and segment diameter) are obtained from pure-component properties: liquid density and vapor pressure data for normal fluids and pressure-volume-temperature data for polymers. A binary energy interaction parameter must be obtained from limited VLE data for each binary system; this parameter appears to be independent of temperature and composition over a useful range. Theoretical correlations and predictions are in good agreement with experiment.
Equations of state of freely jointed hard-sphere chain fluids: Theory
Stell, G.; Lin, C. [Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794-3400 (United States)] [Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794-3400 (United States); Kalyuzhnyi, Y.V. [Institute for Condensed Matter Physics, Svientsitskoho 1, 290011 Lviv (Ukraine)] [Institute for Condensed Matter Physics, Svientsitskoho 1, 290011 Lviv (Ukraine)
1999-03-01
Using the analytical solution of a multidensity integral equation solved in our previous papers [J. Chem. Phys. {bold 108}, 6513, 6525 (1998)], we derive two compressibility and two virial equations of state (EOS) for freely jointed hard-sphere chain fluids on the basis of the approximations defined by the polymer Percus{endash}Yevick (PPY) closure and of the PPY ideal-chain closure for the integral equations. We also extend a version of first-order thermodynamic perturbation theory to polymers, using a dimer fluid as the reference system, to treat mixtures of heteronuclear chain fluids and polymer solutions; the structural information of the dimer fluid is obtained from the PPY ideal-chain approximation in the complete-association limit. The attractive forces between monomers of chain molecules are treated using simple perturbation theory. We find that the compressibility EOS derived on the basis of the PPY approximation subject to the chain-connectivity condition reduces to the compressibility EOS based upon the PPY ideal-chain approximation in the complete-association limit, which is also equivalent to the EOS derived by Chiew [Mol. Phys. {bold 70}, 129 (1990)] and to the EOS derived by Kalyuzhnyi and Cummings [J. Chem. Phys. {bold 105}, 2011 (1996)]. On the other hand, the virial EOS derived on the basis of the PPY ideal-chain approximation coincides with Attard{close_quote}s virial EOS [J. Chem. Phys. {bold 102}, 5411 (1995)] only in the zero-density limit. The advantages in numerical implementation of the EOS presented in this work are also discussed, but a full quantitative assessment of our results and a detailed numerical comparison among them are made in a companion paper, as is comparison with available simulation results. {copyright} {ital 1999 American Institute of Physics.}
The distribution of forces affects vibrational properties in hard sphere glasses
E. DeGiuli; E. Lerner; C. Brito; M. Wyart
2014-08-08
We study theoretically and numerically 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 $P(f)\\sim f^{\\theta_e}$ the force distribution of such pairs and $\\phi_c$ the packing fraction at which pressure diverges, we predict that (i) the density of states has a low-frequency peak at a scale $\\omega^*$, rising up to it as $D(\\omega) \\sim \\omega^{2+a}$, and decaying above $\\omega^*$ as $D(\\omega)\\sim \\omega^{-a}$ where $a=(1-\\theta_e)/(3+\\theta_e)$ and $\\omega$ is the frequency, (ii) shear modulus and mean-squared displacement are inversely proportional with $\\langle \\delta R^2\\rangle\\sim1/\\mu\\sim (\\phi_c-\\phi)^{\\kappa} $ where $\\kappa=2-2/(3+\\theta_e)$, and (iii) continuum elasticity breaks down on a scale $\\ell_c \\sim1/\\sqrt{\\delta z}\\sim (\\phi_c-\\phi)^{-b}$ where $b=(1+\\theta_e)/(6+2\\theta_e)$ and $\\delta z=z-2d$, where $z$ is the coordination and $d$ the spatial dimension. We numerically test (i) and provide data supporting that $\\theta_e\\approx 0.41$ in our bi-disperse system, independently of system preparation in two and three dimensions, leading to $\\kappa\\approx1.41$, $a \\approx 0.17$, and $b\\approx 0.21$. Our results for the mean-square displacement are consistent with a recent exact replica computation for $d=\\infty$, whereas some observations differ, as rationalized by the present approach.
Bounds for Local Density of Sphere Packings and the Kepler Conjecture
Jeffrey C. Lagarias
2002-01-01
This paper formalizes the local density inequality approach to getting upper bounds for sphere packing densities in Rn. This approach was first suggested by L. Fejes-Toth in 1954 as a method to prove the Kepler conjecture that the densest packing of unit spheres in R3 has density ? p18, which is attained by the \\
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.
Constitutive relations for granular fluid of smooth inelastic hard spheres, to Burnett order
NASA Astrophysics Data System (ADS)
Gupta, Vinay; Alam, Meheboob
2011-03-01
In the framework of kinetic theory for dilute granular gases, we have generalized the work of Sela & Goldhirsch (1998) by including body force (gravity) term in the Boltzmann equation. In order to derive the constitutive relations for flows of smooth inelastic hard spheres in three dimensions, the Boltzmann equation is perturbatively solved by performing generalized Chapman-Enskog (double expansion) in two small parameters, the Knudsen number and the degree of inelasticity. We have derived the constitutive relations till Burnett order (up to second order in small parameters). In this talk I would like to present the methodology for obtaining the constitutive relations.[4pt] Ref: Sela, N. & Goldhirsch, I. 1998 Hydrodynamic equations for rapid flows of smooth inelastic spheres, to Burnett order. J. Fluid Mech. 361, 41--74.
An Automatic Phase-Change Detection Technique for Colloidal Hard Sphere Suspensions
NASA Technical Reports Server (NTRS)
McDowell, Mark; Gray, Elizabeth; Rogers, Richard B.
2005-01-01
Colloidal suspensions of monodisperse spheres are used as physical models of thermodynamic phase transitions and as precursors to photonic band gap materials. However, current image analysis techniques are not able to distinguish between densely packed phases within conventional microscope images, which are mainly characterized by degrees of randomness or order with similar grayscale value properties. Current techniques for identifying the phase boundaries involve manually identifying the phase transitions, which is very tedious and time consuming. We have developed an intelligent machine vision technique that automatically identifies colloidal phase boundaries. The algorithm utilizes intelligent image processing techniques that accurately identify and track phase changes vertically or horizontally for a sequence of colloidal hard sphere suspension images. This technique is readily adaptable to any imaging application where regions of interest are distinguished from the background by differing patterns of motion over time.
The role of bond tangency and bond gap in hard sphere crystallization of chains.
Karayiannis, Nikos Ch; Foteinopoulou, Katerina; Laso, Manuel
2015-02-18
We report results from Monte Carlo simulations on dense packings of linear, freely-jointed chains of hard spheres of uniform size. In contrast to our past studies where bonded spheres along the chain backbone were tangent, in the present work a finite tolerance in the bond is allowed. Bond lengths are allowed to fluctuate in the interval [?, ? + dl], where ? is the sphere diameter. We find that bond tolerance affects the phase behaviour of hard-sphere chains, especially in the close vicinity of the melting transition. First, a critical dl(crit) exists marking the threshold for crystallization, whose value decreases with increasing volume fraction. Second, bond gaps enhance the onset of phase transition by accelerating crystal nucleation and growth. Finally, bond tolerance has an effect on crystal morphologies: in the tangent limit the majority of structures correspond to stack-faulted random hexagonal close packing (rhcp). However, as bond tolerance increases a wealth of diverse structures can be observed: from single fcc (or hcp) crystallites to random hcp/fcc stackings with multiple directions. By extending the simulations over trillions of MC steps (10(12)) we are able to observe crystal-crystal transitions and perfection even for entangled polymer chains in accordance to the Ostwald's rule of stages in crystal polymorphism. Through simple geometric arguments we explain how the presence of rigid or flexible constraints affects crystallization in general atomic and particulate systems. Based on the present results, it can be concluded that proper tuning of bond gaps and of the connectivity network can be a controlling factor for the phase behaviour of model, polymer-based colloidal and granular systems. PMID:25594158
Perturbation approach for equation of state for hard-sphere and Lennard–Jones pure fluids
S B KHASARE; M S DESHPANDE
2011-01-01
In this paper we have established the equation of state (EOS) for liquids. The EOS was established for hard-sphere (HS) fluid\\u000a along with Lennard–Jones (LJ) fluid incorporating perturbation techniques. The calculations are based on suitable axiomatic\\u000a functional forms for surface tension S\\u000a \\u000a m\\u000a (r), r???d\\/2 with intermolecular separation r, as a variable, and m is an arbitrary real number (pole).
Quantum-Mechanical Equation of State of a Hard-Sphere Gas at High Temperature
B. Jancovici
1969-01-01
The quantum-mechanical free energy F of a hard-sphere gas at high temperature is a series in powers of the thermal wavelength lambda=(2piℏ2mkT)12 the coefficients of this series can be expressed in terms of the classical correlation functions. The result to first order is FNk T=F(0)Nk T+pi2 g2(a)a2rholambda, where F( 0) is the classical free energy, N the total number of
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.
Playing with Marbles: Structural and Thermodynamic Properties of Hard-Sphere Systems
Andrés Santos
2013-10-21
These lecture notes present an overview of equilibrium statistical mechanics of classical fluids, with special applications to the structural and thermodynamic properties of systems made of particles interacting via the hard-sphere potential or closely related model potentials. The exact statistical-mechanical properties of one-dimensional systems, the issue of thermodynamic (in)consistency among different routes in the context of several approximate theories, and the construction of analytical or semi-analytical approximations for the structural properties are also addressed.
Playing with Marbles: Structural and Thermodynamic Properties of Hard-Sphere Systems
Santos, Andrés
2013-01-01
These lecture notes present an overview of equilibrium statistical mechanics of classical fluids, with special applications to the structural and thermodynamic properties of systems made of particles interacting via the hard-sphere potential or closely related model potentials. The exact statistical-mechanical properties of one-dimensional systems, the issue of thermodynamic (in)consistency among different routes in the context of several approximate theories, and the construction of analytical or semi-analytical approximations for the structural properties are also addressed.
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.
Isotropic-nematic phase equilibria of hard-sphere chain fluids-Pure components and binary mixtures.
Oyarzún, Bernardo; van Westen, Thijs; Vlugt, Thijs J H
2015-02-14
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. PMID:25681939
Gazzillo, Domenico; Giacometti, Achille; Fantoni, Riccardo; Sollich, Peter
2006-11-01
We investigate the dependence of the stickiness parameters tij=1/(12tauij)--where the tauij are the conventional Baxter parameters--on the solute diameters sigmai and sigmaj in multicomponent sticky hard sphere (SHS) models for fluid mixtures of mesoscopic neutral particles. A variety of simple but realistic interaction potentials, utilized in the literature to model short-ranged attractions present in real solutions of colloids or reverse micelles, is reviewed. We consider: (i) van der Waals attractions, (ii) hard-sphere-depletion forces, (iii) polymer-coated colloids, and (iv) solvation effects (in particular hydrophobic bonding and attractions between reverse micelles of water-in-oil microemulsions). We map each of these potentials onto an equivalent SHS model by requiring the equality of the second virial coefficients. The main finding is that, for most of the potentials considered, the size-dependence of tij(T,sigmai,sigmaj) can be approximated by essentially the same expression, i.e., a simple polynomial in the variable sigmaisigmaj/sigmaij2, with coefficients depending on the temperature T, or--for depletion interactions--on the packing fraction eta0 of the depletant particles. PMID:17279909
NASA Astrophysics Data System (ADS)
Filion, L.; Ni, R.; Frenkel, D.; Dijkstra, M.
2011-04-01
In this paper we examine the phase behavior of the Weeks-Chandler-Andersen (WCA) potential with ?? = 40. Crystal nucleation in this model system was recently studied by Kawasaki and Tanaka [Proc. Natl. Acad. Sci. U.S.A. 107, 14036 (2010)], 10.1021/pr100656u, who argued that the computed nucleation rates agree well with experiment, a finding that contradicted earlier simulation results. Here we report an extensive numerical study of crystallization in the WCA model, using three totally different techniques (Brownian dynamics, umbrella sampling, and forward flux sampling). We find that all simulations yield essentially the same nucleation rates. However, these rates differ significantly from the values reported by Kawasaki and Tanaka and hence we argue that the huge discrepancy in nucleation rates between simulation and experiment persists. When we map the WCA model onto a hard-sphere system, we find good agreement between the present simulation results and those that had been obtained for hard spheres [L. Filion, M. Hermes, R. Ni, and M. Dijkstra, J. Chem. Phys. 133, 244115 (2010), 10.1063/1.3506838; S. Auer and D. Frenkel, Nature 409, 1020 (2001), 10.1038/35059035].
Small-angle neutron scattering of concentrated adhesive-hard-sphere dispersions
Duits, M.H.G.; Vrij, A.; de Kruif, C.G. (Univ. of Utrecht (Netherlands)); May, R.P. (Institut Laue Langevin, Grenoble (France))
1991-01-01
Small-angle neutron-scattering experiments were performed on concentrated dispersions of sterically stabilized silica particles dispersed in benzene, where the particles show an effective attraction on lowering the temperature. In this study, the system was cooled down from 52 C, where almost-hard-sphere behavior is observed, to just above the phase transition temperature at 33 C in seven steps. At each temperature, scattered intensities were measured at four volume fractions up to 0.28. The constancy of the particle form factor allowed data analysis at the level of structure factors. Experimental data were fitted with model calculations using the Percus-Yevick solution for Baxter's adhesive hard-sphere potential, taking the particle size polydispersity into account. A quite satisfactory model description of the experimental structure factors could be obtained. At lower temperatures and higher volume fractions, the fits are even quantitative. The obtained stickiness parameter is directly related to sample temperature, and it does not depend on volume fraction. These observations confirm the model of a short-ranged attraction between the particles, with a well depth governed by enthalpic and entropic contributions to the chain-chain and chain-solvent interactions.
System of elastic hard spheres which mimics the transport properties of a granular gas
Andres Santos; Antonio Astillero
2005-08-30
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 $(1+\\alpha)/2$, 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 $\\alpha\\geq 0.5$). 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
Free energy barriers for homogeneous crystal nucleation in a eutectic system of binary hard spheres.
Ganagalla, Srinivasa Rao; Punnathanam, Sudeep N
2013-05-01
In this study, the free energy barriers for homogeneous crystal nucleation in a system that exhibits a eutectic point are computed using Monte Carlo simulations. The system studied is a binary hard sphere mixture with a diameter ratio of 0.85 between the smaller and larger hard spheres. The simulations of crystal nucleation are performed for the entire range of fluid compositions. The free energy barrier is found to be the highest near the eutectic point and is nearly five times that for the pure fluid, which slows down the nucleation rate by a factor of 10(-31). These free energy barriers are some of highest ever computed using simulations. For most of the conditions studied, the composition of the critical nucleus corresponds to either one of the two thermodynamically stable solid phases. However, near the eutectic point, the nucleation barrier is lowest for the formation of the metastable random hexagonal closed packed (rhcp) solid phase with composition lying in the two-phase region of the phase diagram. The fluid to solid phase transition is hypothesized to proceed via formation of a metastable rhcp phase followed by a phase separation into respective stable fcc solid phases. PMID:23656140
NASA Astrophysics Data System (ADS)
Jover, J.; Haslam, A. J.; Galindo, A.; Jackson, G.; Müller, E. A.
2012-10-01
We present a continuous pseudo-hard-sphere potential based on a cut-and-shifted Mie (generalized Lennard-Jones) potential with exponents (50, 49). Using this potential one can mimic the volumetric, structural, and dynamic properties of the discontinuous hard-sphere potential over the whole fluid range. The continuous pseudo potential has the advantage that it may be incorporated directly into off-the-shelf molecular-dynamics code, allowing the user to capitalise on existing hardware and software advances. Simulation results for the compressibility factor of the fluid and solid phases of our pseudo hard spheres are presented and compared both to the Carnahan-Starling equation of state of the fluid and published data, the differences being indistinguishable within simulation uncertainty. The specific form of the potential is employed to simulate flexible chains formed from these pseudo hard spheres at contact (pearl-necklace model) for mc = 4, 5, 7, 8, 16, 20, 100, 201, and 500 monomer segments. The compressibility factor of the chains per unit of monomer, mc, approaches a limiting value at reasonably small values, mc < 50, as predicted by Wertheim's first order thermodynamic perturbation theory. Simulation results are also presented for highly asymmetric mixtures of pseudo hard spheres, with diameter ratios of 3:1, 5:1, 20:1 over the whole composition range.
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.
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
Direct measurement of the free energy of aging hard sphere colloidal glasses.
Zargar, Rojman; Nienhuis, Bernard; Schall, Peter; Bonn, Daniel
2013-06-21
The nature of the glass transition is one of the most important unsolved problems in condensed matter physics. The difference between glasses and liquids is believed to be caused by very large free energy barriers for particle rearrangements; however, so far it has not been possible to confirm this experimentally. We provide the first quantitative determination of the free energy for an aging hard sphere colloidal glass. The determination of the free energy allows for a number of new insights in the glass transition, notably the quantification of the strong spatial and temporal heterogeneity in the free energy. A study of the local minima of the free energy reveals that the observed variations are directly related to the rearrangements of the particles. Our main finding is that the probability of particle rearrangements shows a power law dependence on the free energy changes associated with the rearrangements similar to the Gutenberg-Richter law in seismology. PMID:23829762
Yielding of Hard-Sphere Glasses during Start-Up Shear
NASA Astrophysics Data System (ADS)
Koumakis, N.; Laurati, M.; Egelhaaf, S. U.; Brady, J. F.; Petekidis, G.
2012-03-01
Concentrated hard-sphere suspensions and glasses are investigated with rheometry, confocal microscopy, and Brownian dynamics simulations during start-up shear, providing a link between microstructure, dynamics, and rheology. The microstructural anisotropy is manifested in the extension axis where the maximum of the pair-distribution function exhibits a minimum at the stress overshoot. The interplay between Brownian relaxation and shear advection as well as the available free volume determine the structural anisotropy and the magnitude of the stress overshoot. Shear-induced cage deformation induces local constriction, reducing in-cage diffusion. Finally, a superdiffusive response at the steady state, with a minimum of the time-dependent effective diffusivity, reflects a continuous cage breakup and reformation.
Single-particle fluctuations and directional correlations in driven hard-sphere glasses
NASA Astrophysics Data System (ADS)
Mandal, Suvendu; Chikkadi, Vijaykumar; Nienhuis, Bernard; Raabe, Dierk; Schall, Peter; Varnik, Fathollah
2013-08-01
Via event-driven molecular dynamics simulations and experiments, we study the packing-fraction and shear-rate dependence of single-particle fluctuations and dynamic correlations in hard-sphere glasses under shear. At packing fractions above the glass transition, correlations increase as shear rate decreases: the exponential tail in the distribution of single-particle jumps broadens and dynamic four-point correlations increase. Interestingly, however, upon decreasing the packing fraction, a broadening of the exponential tail is also observed, while dynamic heterogeneity is shown to decrease. An explanation for this behavior is proposed in terms of a competition between shear and thermal fluctuations. Building upon our previous studies [Chikkadi , Europhys. Lett.EULEEJ0295-507510.1209/0295-5075/100/56001 100, 56001 (2012)], we further address the issue of anisotropy of the dynamic correlations.
Single-particle fluctuations and directional correlations in driven hard-sphere glasses.
Mandal, Suvendu; Chikkadi, Vijaykumar; Nienhuis, Bernard; Raabe, Dierk; Schall, Peter; Varnik, Fathollah
2013-08-01
Via event-driven molecular dynamics simulations and experiments, we study the packing-fraction and shear-rate dependence of single-particle fluctuations and dynamic correlations in hard-sphere glasses under shear. At packing fractions above the glass transition, correlations increase as shear rate decreases: the exponential tail in the distribution of single-particle jumps broadens and dynamic four-point correlations increase. Interestingly, however, upon decreasing the packing fraction, a broadening of the exponential tail is also observed, while dynamic heterogeneity is shown to decrease. An explanation for this behavior is proposed in terms of a competition between shear and thermal fluctuations. Building upon our previous studies [Chikkadi et al., Europhys. Lett. 100, 56001 (2012)], we further address the issue of anisotropy of the dynamic correlations. PMID:24032797
Cooling process for inelastic Boltzmann equations for hard spheres, Part I: The Cauchy problem
Stéphane Mischler; Clément Mouhot; Mariano Rodriguez Ricard
2006-07-21
We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitution coefficients depending on the kinetic energy and the relative velocity as well as the sticky particles model. We prove (local in time) non-concentration estimates in Orlicz spaces, from which we deduce weak stability and existence theorem. Strong stability together with uniqueness and instantaneous appearance of exponential moments are proved under additional smoothness assumption on the initial datum, for a restricted class of collision rates. Concerning the long-time behaviour, we give conditions for the cooling process to occur or not in finite time.
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.
Disordered Solids without Well-Defined Transverse Phonons: The Nature of Hard-Sphere Glasses
NASA Astrophysics Data System (ADS)
Wang, Xipeng; Zheng, Wen; Wang, Lijin; Xu, Ning
2015-01-01
We probe the Ioffe-Regel limits of glasses with repulsions near the zero-temperature jamming transition by calculating the dynamical structure factors. The Ioffe-Regel limit (frequency) is reached when the phonon wavelength is comparable to the mean free path, beyond which phonons are no longer well defined. At zero temperature, the transverse Ioffe-Regel frequency vanishes at the jamming transition with a diverging length, but the longitudinal one does not, which excludes the existence of a diverging length associated with the longitudinal excitations. At low temperatures, the transverse and longitudinal Ioffe-Regel frequencies approach zero at the jamminglike transition and glass transition, respectively. As a consequence, glasses between the glass transition and the jamminglike transition, which are hard-sphere glasses in the low temperature limit, can only carry well-defined longitudinal phonons and have an opposite pressure dependence of the ratio of the shear modulus to the bulk modulus from glasses beyond the jamminglike transition.
NASA Astrophysics Data System (ADS)
Bocquet, Lydéric; Piasecki, Jaroslaw; Hansen, Jean-Pierre
1994-07-01
The Fokker-Planck equation governing the evolution of the distribution function of a massive Brownian hard sphere suspended in a fluid of much lighter spheres is derived from the exact hierarchy of kinetic equations for the total system via a multiple-time-scale analysis akin to a uniform expansion in powers of the square root of the mass ratio. The derivation leads to an exact expression for the friction coefficient which naturally splits into an Enskog contribution and a dynamical correction. The latter, which accounts for correlated collisions events, reduces to the integral of a time-displaced correlation function of dynamical variables linked to the collisional transfer of momentum between the infinitively heavy (i.e., immobile) Brownian sphere and the fluid particles.
Homogeneous Free Cooling State in Binary Granular Fluids of Inelastic Rough Hard Spheres
NASA Astrophysics Data System (ADS)
Santos, Andrés
2011-05-01
In a recent paper [A. Santos, G. M. Kremer, and V. Garzó, Prog. Theor. Phys. Suppl. 184, 31-48 (2010)] the collisional energy production rates associated with the translational and rotational granular temperatures in a granular fluid mixture of inelastic rough hard spheres have been derived. In the present paper the energy production rates are explicitly decomposed into equipartition rates (tending to make all the temperatures equal) plus genuine cooling rates (reflecting the collisional dissipation of energy). Next the homogeneous free cooling state of a binary mixture is analyzed, with special emphasis on the quasi-smooth limit. A previously reported singular behavior (according to which a vanishingly small amount of roughness has a finite effect, with respect to the perfectly smooth case, on the asymptotic long-time translational/translational temperature ratio) is further elaborated. Moreover, the study of the time evolution of the temperature ratios shows that this dramatic influence of roughness already appears in the transient regime for times comparable to the relaxation time of perfectly smooth spheres.
Fluctuations, structure factor and polytetrahedra in random packings of sticky hard spheres
NASA Astrophysics Data System (ADS)
Blétry, M.; Blétry, J.
2015-03-01
Sequentially-built random sphere-packings have been numerically studied in the packing fraction interval $0.329 < \\gamma < 0.586$. For that purpose fast running geometrical algorithms have been designed in order to build about 300 aggregates, containing $10^6$ spheres each one, which allowed a careful study of the local fluctuations and an improved accuracy in the calculations of the pair distribution $P(r)$ and structure factors $S(Q)$ of the aggregates. Among various parameters (Voronoi tessellation, contact coordination number distribution,...), fluctuations were quantitatively evaluated by the direct evaluation of the fluctuations of the local sphere number density, which appears to follow a power law. The FWHM of the Voronoi cells volume shows a regular variation over the whole packing fraction range. Dirac peaks appear on the pair correlation function as the packing fraction of the aggregates decreases, indicating the growth of larger and larger polytetrahedra, which manifest in two ways on the structure factor, at low and large $Q$values. These low PF aggregates have a composite structure made of regular polytetrahedra embedded in a more disordered matrix. Incidentally, the irregularity index of the building tetrahedron appears as a better parameter than the packing fraction to describe various features of the aggregates structure.
ERIC Educational Resources Information Center
Duer, W. C.; And Others
1977-01-01
Discusses comparisons of packing densities derived from known molar volume data of liquids and solutions. Suggests further studies for using assemblies of spheres as models for simple liquids and solutions. (MLH)
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
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.
T. Arisawa; T. Arai; I. Yokoyama
1999-01-01
In this paper we have attempted to estimate the pair and triplet correlation entropies (S(2) and S(3)) of the hard sphere fluid using the Percus–Yevick approximation. The pair correlation entropies are computed from the pair correlation functions, while the triplet correlation entropies are estimated by the structure factors with the help of an analytical formula for evaluation of a change
NASA Astrophysics Data System (ADS)
Tokuyama, Michio; Yamazaki, Hiroyuki; Terada, Yayoi
2003-10-01
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 long-time self-diffusion coefficients DSL in both systems become singular as DSL( ?)?(1- ?/ ?c) 2 because of the collective interactions due to the many-body collision processes, where ? is a particle volume fraction and ?c?0.586 for 6% polydispersity. Although DSL exhibits the same singular behavior as that obtained theoretically for the monodisperse suspension with the hydrodynamic interactions, no liquid-glass transition is found because even the polydisperse hard-sphere systems crystallize without the hydrodynamic interactions for all ? above the melting volume fraction, which is lower than ?c.
R. Castillo; A. Villaverde; J. Orozco
1991-01-01
We present a critical appraisal of the ability of effective diameter hard sphere theory to predict thermal conductivities and shear and bulk viscosities of fluids interacting through the Lennard-Jones potential. This method relies on the use of the kinetic theory of hard spheres and on state dependent effective diameters given by the equilibrium liquid state theory. Predictions using this method
Tokuyama, Michio; Yamazaki, Hiroyuki; Terada, Yayoi
2003-06-01
A mean-field nonlinear equation for the mean-square displacement, recently proposed by one of the present authors [M. Tokuyama, Phys. Rev. E 62, R5915 (2000); Physica A 289, 57 (2001)], for concentrated, equilibrium suspensions of hard spheres is extended to describe equilibrium atomic systems of hard spheres. The validity of two types of mean-field equations is investigated by two kinds of computer simulations; a Brownian-dynamics simulation on suspensions of hard spheres and a molecular-dynamics simulation on atomic systems of hard spheres. A good agreement between the mean-field equations and simulations is then shown for different volume fractions. The two types of model systems of hard spheres are thus shown to be identical to each other on the study of the liquid-solid transition. However, analyses suggest that a new interaction is indispensable to understand the mechanism for the liquid-glass transition in both systems. PMID:16241280
NASA Astrophysics Data System (ADS)
Tokuyama, Michio; Yamazaki, Hiroyuki; Terada, Yayoi
2003-06-01
A mean-field nonlinear equation for the mean-square displacement, recently proposed by one of the present authors [M. Tokuyama, Phys. Rev. E 62, R5915 (2000); Physica A 289, 57 (2001)], for concentrated, equilibrium suspensions of hard spheres is extended to describe equilibrium atomic systems of hard spheres. The validity of two types of mean-field equations is investigated by two kinds of computer simulations; a Brownian-dynamics simulation on suspensions of hard spheres and a molecular-dynamics simulation on atomic systems of hard spheres. A good agreement between the mean-field equations and simulations is then shown for different volume fractions. The two types of model systems of hard spheres are thus shown to be identical to each other on the study of the liquid-solid transition. However, analyses suggest that a new interaction is indispensable to understand the mechanism for the liquid-glass transition in both systems.
NASA Astrophysics Data System (ADS)
Wolf, A. S.; Asimow, P. D.; Stevenson, D. J.
2013-12-01
Recent first-principles theoretical calculations (Stixrude 2009) and experimental shock-wave investigations (Mosenfelder 2009) indicate that melting perovskite requires significantly less energy than previously thought, supporting the idea of a deep-mantle magma ocean early in Earth's history. The modern-day solid Earth is thus likely the result of crystallization from an early predominantly molten state, a process that is primarily controlled by the poorly understood behavior of silicate melts at extreme pressures and temperatures. Probing liquid thermodynamics at mantle conditions is difficult for both theory and experiment, and further challenges are posed by the large relevant compositional space including at least MgO, SiO2, and FeO. First-principles molecular dynamics has been used with great success to determine the high P-T properties of a small set of fixed composition silicate-oxide liquids including MgO (Karki 2006), SiO2 (Karki 2007), Mg2SiO4 (de Koker 2008), MgSiO3 (Stixrude 2005), and Fe2SiO4 (Ramo 2012). While extremely powerful, this approach has limitations including high computational cost, lower bounds on temperature due to relaxation constraints, as well as restrictions to length scales and time scales that are many orders of magnitude smaller than those relevant to the Earth or experimental methods. As a compliment to accurate first-principles calculations, we have developed the Coordinated HArd Sphere Model (CHASM). We extend the standard hard sphere mixture model, recently applied to silicate liquids by Jing (2011), by accounting for the range of oxygen coordination states available to liquid cations. Utilizing approximate analytic expressions for the hard sphere model, the method can predict complex liquid structure and thermodynamics while remaining computationally efficient. Requiring only minutes on standard desktop computers rather than months on supercomputers, the CHASM approach is well-suited to providing an approximate thermodynamic map of the wide compositional space relevant to early Earth evolution. As a first step on this path, we apply the CHASM formalism to the MgO system. We first demonstrate that the model parameters can be obtained by training on equation of state data for a variety of crystal polymorphs, which discretely sample the continuous range of coordination states available to the liquid; training only on solid data, CHASM thus provides a fully predictive model for oxide liquids. Using the best-fit parameter values, the coordination evolution and equation of state of MgO liquid is determined by free-energy minimization over a wide P-T range. These results are evaluated by favorable comparison with predictions from published first-principles molecular dynamics calculations, indicating that CHASM is accurately capturing the dominant physical mechanism controlling the behavior of high pressure oxide liquids. By combining the CHASM description of MgO liquid with a thermodynamic model for solid MgO periclase, we also compare the MgO melting curve with both first principles computations and shock wave measurements. Future development of the CHASM model will incorporate SiO2, FeO, and Al2O3, providing a simple physical framework that enables both interpretation of experiments and prediction of behavior currently outside our technical or computational capabilities.
Kalyuzhnyi, Y.V. [Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York11794-3400 (United States)] [Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York11794-3400 (United States); [Institute for Condensed Matter, Physics, Svientsitskoho 1, 290011Lviv (Ukraine); Lin, C.; Stell, G. [Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York11794-3400 (United States)] [Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York11794-3400 (United States)
1998-04-01
We continue here our series of studies in which integral-equation theory is developed and used for the monomer-monomer correlation functions in a fluid of multicomponent freely jointed hard-sphere polymers. In this study our approach is based on Wertheim{close_quote}s polymer Percus{endash}Yevick (PPY) theory supplemented by the ideal-chain approximation; it can be regarded as a simplified version of Wertheim{close_quote}s four-density PPY approximation for associating fluids considered in the complete-association limit. The numerical procedure of this simplified theory is much easier than that of the original Wertheim{close_quote}s four-density PPY approximation, but the degree of accuracy is reduced. The theory can also be regarded as an extension of the PPY theory for the homonuclear polymer system proposed by Chang and Sandler [J. Chem. Phys. {bold 102}, 437 (1995)]. Their work is based upon a description of a system of hard-sphere monomers that associate into a polydisperse system of chains of prescribed mean length. Our theory instead directly describes a multicomponent system of associating monomers that form monodisperse chains of prescribed length upon complete association. An analytical solution of the PPY ideal-chain approximation for the general case of a multicomponent mixture of heteronuclear hard-sphere linear chain molecules is given. Its use is illustrated by numerical results for two models of copolymer fluids, a symmetrical diblock copolymer system, and an alternating copolymer system. The comparison with Monte Carlo simulations is given to gauge the accuracy of the theory. We find for the molecules we study here that predictions of our theory for heteronuclear chain systems have the same degree of accuracy as Chang and Sandler{close_quote}s theory for homonuclear chain systems. {copyright} {ital 1998 American Institute of Physics.}
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.
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.
Local shear transformations in deformed and quiescent hard-sphere colloidal glasses
NASA Astrophysics Data System (ADS)
Jensen, K. E.; Weitz, D. A.; Spaepen, F.
2014-10-01
We perform a series of deformation experiments on a monodisperse, hard-sphere colloidal glass while simultaneously following the three-dimensional trajectories of roughly 50000 individual particles with a confocal microscope. In each experiment, we deform the glass in pure shear at a constant strain rate [(1-5)×10-5 s-1] to maximum macroscopic strains (5%-10%) and then reverse the deformation at the same rate to return to zero macroscopic strain. We also measure three-dimensional particle trajectories in an identically prepared quiescent glass in which the macroscopic strain is always zero. We find that shear transformation zones exist and are active in both sheared and quiescent colloidal glasses, revealed by a distinctive fourfold signature in spatial autocorrelations of the local shear strain. With increasing shear, the population of local shear transformations develops more quickly than in a quiescent glass and many of these transformations are irreversible. When the macroscopic strain is reversed, we observe partial elastic recovery, followed by plastic deformation of the opposite sign, required to compensate for the irreversibly transformed regions. The average diameter of the shear transformation zones in both strained and quiescent glasses is slightly more than two particle diameters.
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.
Preparation of PHSA-PMMA stabilizer for model hard sphere systems
NASA Astrophysics Data System (ADS)
Hollingsworth, Andrew; Russel, William; van Kats, Carlos; van Blaaderen, Alfons
2006-03-01
Sterically-stabilized colloidal particles are an excellent model hard-sphere system used by many groups. One of the original stabilizers used for such systems was developed and patented by ICI more than 30 years ago. It consists of a `comb-like' stabilizer of a poly(12-hydroxystearic acid) which is soluble in aliphatic hydrocarbons. These pendant PHSA chains are grafted to an insoluble poly(methyl methacrylate) backbone that strongly adsorbs to polymer particles and thus provides a means of anchoring stabilizer to particle surfaces. Unfortunately, the PHSA-g-PMMA stabilizer is not commercially available. Furthermore, the three-step procedure (Antl, et al. 1986) is generally regarded by non-chemists as technique intensive and time-consuming. We have systematically studied the PHSA-PMMA stabilizer synthesis with the goal of taking the mystery out of the protocol and making the entire synthesis reproducible. Several important details, not published in the literature, will be discussed, along with the analytical results from mass spectroscopy, proton NMR, acid titration and gel permeation chromatography, all of which were used to characterize the polymer and its precursors.
Disappearance of a Stacking Fault in Hard-Sphere Crystals under Gravity
NASA Astrophysics Data System (ADS)
Mori, A.; Suzuki, Y.; Matsuo, S.
In the first part of this paper, a review is given on the mechanismfor the disappearance of an intrinsic stacking fault in a hard-sphere (HS) crystal under gravity, which we recently discovered by Monte Carlo (MC) simulations [A. Mori et al., J. Chem. Phys. 124 (2006), 17450; Mol. Phys. 105 (2007), 1377]. We have observed, in the case of fcc (001) stacking, that the intrinsic stacking fault running along an oblique direction shrunk through the gliding of a Shockley partial dislocation at the lower end of the stacking fault. In order to address the shortcomings and approximations of previous simulations, such as the use of periodic ] boundary condition (PBC) and the fact that the fcc (001) stacking had been realized by the stress from the small PBC box, we present an elastic strain energy calculation for an infinite system and a MC simulation result for HSs in a pyramidal pit under gravity. In particular, the geometry of the latter has already been tested experi mentally [S. Matsuo et al., Appl. Phys. Lett. 82 (2003), 4283]. The advantage of using a pyramidal pit as a template as well as the feasibility of the mechanism we describe is demonstrated.
Microscopic theories of the structure and glassy dynamics of ultra-dense hard sphere fluids
NASA Astrophysics Data System (ADS)
Jadrich, Ryan; Schweizer, Kenneth
2013-03-01
We construct a new thermodynamically self-consistent integral equation theory (IET) for the equilibrium metastable fluid structure of monodisperse hard spheres that incorporates key features of the jamming transition. A two Yukawa generalized mean spherical IET closure for the direct correlation function tail is employed to model the distinctive short and long range contributions for highly compressed fluids. The exact behavior of the contact value of the radial distribution function (RDF) and isothermal compressibility are enforced, as well as an approximate theory for the RDF contact derivative. Comparison of the theoretical results for the real and Fourier space structure with nonequilibrium jammed simulations reveals many similarities, but also differences as expected. The new structural theory is used as input into the nonlinear Langevin equation (NLE) theory of activated single particle dynamics to study the alpha relaxation time, and good agreement with recent experiments and simulations is found. We demonstrate it is crucial to accurately describe the very high wave vector Fourier space to reliably extract the dynamical predictions of NLE theory, and structural precursors of jamming play an important role in determining entropic barriers.
NASA Astrophysics Data System (ADS)
Choi, Yumi; Ree, Taikyue; Ree, Francis H.
1991-11-01
The hard-sphere radial distribution functions, gHS(r/d,?), for the face-centered cubic and hexagonal close-packed phases have been computed by the Monte Carlo method at nine values of the packing fraction, ?[=(?/6)?d3], ranging from 4% below the melting density to 99% of the close-packed density. The Monte Carlo data are used to improve available analytic expressions for gHS(r/d,?). By utilizing the new gHS(r/d,?) in the Henderson and Grundke method [J. Chem. Phys. 63, 601 (1975)], we next derive an expression for yHS(r/d,?) [=gHS(r/d)exp{?VHS(r)}] inside the hard-sphere diameter, d. These expressions are employed in a solid-state perturbation theory [J. Chem. Phys. 84, 4547 (1986)] to compute solid-state and melting properties of the Lennard-Jones and inverse-power potentials. Results are in close agreement with Monte Carlo and lattice-dynamics calculations performed in this and previous work. The new gHS(r/d,?) shows a reasonable thermodynamic consistency as required by the Ornstein-Zernike relation. As an application, we have constructed a high-pressure phase diagram for a truncated Lennard-Jones potential. From this study, we conclude that the new gHS(r/d,?) is an improvement over available expressions and that it is useful for solid-state calculations.
NASA Astrophysics Data System (ADS)
Zykova-Timan, T.; Rozas, R. E.; Horbach, J.; Binder, K.
2009-11-01
Using molecular dynamics (MD) and Monte Carlo (MC) simulations interfacial properties of crystal-fluid interfaces are investigated for the hard sphere system and the one-component metallic system Ni (the latter modeled by a potential of the embedded atom type). Different local order parameters are considered to obtain order parameter profiles for systems where the crystal phase is in coexistence with the fluid phase, separated by interfaces with (100) orientation of the crystal. From these profiles, the mean-squared interfacial width w2 is extracted as a function of system size. We rationalize the prediction of capillary wave theory that w2 diverges logarithmically with the lateral size of the system. We show that one can estimate the interfacial stiffness \\tilde {\\gamma } from the interfacial broadening, obtaining \\tilde {\\gamma }\\approx 0.5 k_{\\mathrm {B}} T/\\sigma^2 for hard spheres and \\tilde {\\gamma }\\approx 0.18~\\mathrm {J~m^{-2}} for Ni.
S. B. Khasare
2012-01-01
The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state (EOS) for a mixture of hard sphere (HS), Lennard—Jones (LJ) fluids. A suitable flexible functional form for the radial distribution function G(R) is assumed for the mixture, with R as a variable. The function G(R) has an
Jung Gun Nam; Kyung Hyun Ahn; Seung Jong Lee; Kyu Hyun
Concentrated hard sphere suspensions often show an interesting nonlinear behavior, called strain stiffening, in which the\\u000a viscosity or modulus starts to increase at critical strain amplitude. Sudden increase of rheological properties is similar\\u000a to shear thickening; however, the particle dynamics in the strain stiffening under oscillatory shear flow does not necessarily\\u000a coincide with the mechanism of shear thickening under step
D. Frenkel; R. J. Vos; C. G. de Kruif; A. Vrij
1986-01-01
We present Monte Carlo (MC) simulations of the structure factors of polydisperse hard-sphere fluids. The simulations were carried out for 108 particles and packing fractions up to ?=0.5. The size distribution of the particles was chosen randomly from a log-normal distribution. The MC results are compared with predictions obtained using Percus–Yevick approximation. It is found that for all but the
Kai Zhang; W. Wendell Smith; Minglei Wang; Yanhui Liu; Jan Schroers; Mark D. Shattuck; Corey S. O'Hern
2014-04-02
We perform molecular dynamics simulations to compress binary hard spheres into jammed packings as a function of the compression rate $R$, size ratio $\\alpha$, and number fraction $x_S$ of small particles to determine the connection between the glass-forming ability (GFA) and packing efficiency in bulk metallic glasses (BMGs). We define the GFA by measuring the critical compression rate $R_c$, below which jammed hard-sphere packings begin to form "random crystal" structures with defects. We find that for systems with $\\alpha \\gtrsim 0.8$ that do not de-mix, $R_c$ decreases strongly with $\\Delta \\phi_J$, as $R_c \\sim \\exp(-1/\\Delta \\phi_J^2)$, where $\\Delta \\phi_J$ is the difference between the average packing fraction of the amorphous packings and random crystal structures at $R_c$. Systems with $\\alpha \\lesssim 0.8$ partially de-mix, which promotes crystallization, but we still find a strong correlation between $R_c$ and $\\Delta \\phi_J$. We show that known metal-metal BMGs occur in the regions of the $\\alpha$ and $x_S$ parameter space with the lowest values of $R_c$ for binary hard spheres. Our results emphasize that maximizing GFA in binary systems involves two competing effects: minimizing $\\alpha$ to increase packing efficiency, while maximizing $\\alpha$ to prevent de-mixing.
NASA Astrophysics Data System (ADS)
Jadrich, Ryan; Schweizer, Kenneth S.
2013-08-01
We formulate and apply a non-replica equilibrium theory for the fluid-glass transition, glass thermodynamic properties, and jamming of hard spheres in three and all higher spatial dimensions. Numerical predictions for the zero complexity glass transition and jamming packing fractions, and a "densest" equilibrium glass, are made. The equilibrium glass equation of state is regarded as the practical continuation of its fluid analog up to jamming. The analysis provides a possible resolution to the inability of any fluid virial series re-summation based equation of state to capture jamming at a reasonable volume fraction. The numerical results are quantitatively compared with various simulation data for equilibrium hard sphere glasses in 3 to 12 dimensions. Although there are uncertainties in this comparison, the predicted zero complexity or configurational entropy and corresponding jamming packing fractions do agree well with two characteristic packing fractions deduced from the dynamic simulation data. The similarities and differences of our approach compared to the replica approach are discussed. The high dimensional scaling of the equilibrium glass transition and jamming volume fractions are also derived. The developments in this paper serve as input to Paper II [R. Jadrich and K. S. Schweizer, J. Chem. Phys. 139, 054502 (2013), 10.1063/1.4816276] that constructs a self-consistent integral equation theory of the 3-dimensional hard sphere pair structure, in real and Fourier space, in the metastable regime up to jamming. The latter is employed as input to a microscopic dynamical theory of single particle activated barrier hopping.
NASA Astrophysics Data System (ADS)
Zhang, Kai; Smith, W. Wendell; Wang, Minglei; Liu, Yanhui; Schroers, Jan; Shattuck, Mark D.; O'Hern, Corey S.
2014-09-01
We perform molecular dynamics simulations to compress binary hard spheres into jammed packings as a function of the compression rate R, size ratio ?, and number fraction xS of small particles to determine the connection between the glass-forming ability (GFA) and packing efficiency in bulk metallic glasses (BMGs). We define the GFA by measuring the critical compression rate Rc, below which jammed hard-sphere packings begin to form "random crystal" structures with defects. We find that for systems with ? ?0.8 that do not demix, Rc decreases strongly with ??J, as Rc˜exp(-1/??J2), where ??J is the difference between the average packing fraction of the amorphous packings and random crystal structures at Rc. Systems with ? ?0.8 partially demix, which promotes crystallization, but we still find a strong correlation between Rc and ??J. We show that known metal-metal BMGs occur in the regions of the ? and xS parameter space with the lowest values of Rc for binary hard spheres. Our results emphasize that maximizing GFA in binary systems involves two competing effects: minimizing ? to increase packing efficiency, while maximizing ? to prevent demixing.
Activated hopping and dynamical fluctuation effects in hard sphere suspensions and fluids.
Saltzman, Erica J; Schweizer, Kenneth S
2006-07-28
Single particle Brownian dynamics simulation methods are employed to establish the full trajectory level predictions of our nonlinear stochastic Langevin equation theory of activated hopping dynamics in glassy hard sphere suspensions and fluids. The consequences of thermal noise driven mobility fluctuations associated with the barrier hopping process are determined for various ensemble-averaged properties and their distributions. The predicted mean square displacements show classic signatures of transient trapping and anomalous diffusion on intermediate time and length scales. A crossover to a stronger volume fraction dependence of the apparent nondiffusive exponent occurs when the entropic barrier is of order the thermal energy. The volume fraction dependences of various mean relaxation times and rates can be fitted by empirical critical power laws with parameters consistent with ideal mode-coupling theory. However, the results of our divergence-free theory are largely a consequence of activated dynamics. The experimentally measurable alpha relaxation time is found to be very similar to the theoretically defined mean reaction time for escape from the barrier-dominated regime. Various measures of decoupling have been studied. For fluid states with small or nonexistent barriers, relaxation times obey a simple log-normal distribution, while for high volume fractions the relaxation time distributions become Poissonian. The product of the self-diffusion constant and mean alpha relaxation time increases roughly as a logarithmic function of the alpha relaxation time. The cage scale incoherent dynamic structure factor exhibits nonexponential decay with a modest degree of stretching. A nearly universal collapse of the different volume fraction results occurs if time is scaled by the mean alpha relaxation time. Hence, time-volume fraction superposition holds quite well, despite the presence of stretching and volume fraction dependent decoupling associated with the stochastic barrier hopping process. The relevance of other origins of dynamic heterogeneity (e.g., mesoscopic domains), and comparison of our results with experiments, simulations, and alternative theories, is discussed. PMID:16942158
Hardness and Density Distributions of Pharmaceutical Tablets Measured by Terahertz Pulsed Imaging
Elliott, James
Hardness and Density Distributions of Pharmaceutical Tablets Measured by Terahertz Pulsed Imaging) as a novel tool to quantify the hard- ness and surface density distribution of pharmaceutical tablets. Good these relate to tablet hardness. Numerical simulations of tablet surface density distribu- tion by finite
NASA Astrophysics Data System (ADS)
Haslam, Andrew J.; Jackson, George; McLeish, Tom C. B.
1999-07-01
Results are presented from our simulation study of flexible, tangent hard-sphere polymer chains, using a Monte Carlo technique with a reptation algorithm. We examine the crossover region from the swollen (dilute) region to the semidilute regime using chains of degree up to N=2000. The (average) chain end-to-end distance is analyzed as a function of the number of chain links, as is a correlation function for the internal separation of segments, expressed in terms of their connectivity. We study the structure of the polymer chains using scattering functions, which are presented in addition to the segment-segment distribution functions from which they are calculated. Not surprisingly, the Flory exponent ? changes gradually from the dilute value of ??0.59 to ?1/2 at high density. We find that for chains of 2000 segments, this transition begins at the very low molecular volume fraction of about 0.1%. An analysis of the correlation function for internal segments provides a similar but more detailed picture, in that the role of the screening length ? becomes explicit. The pair distribution and scattering functions in the swollen, crossover, and melt regions are determined and the scaling behavior is reexamined in the context of these functions. The system considered will form a reference system for subsequent studies in which the model will be broadened to include a network and/or attractive interactions. In this paper we seek first of all to establish that reference, and to relate our work to previous studies in this area of interest. As an important technical point, we also note that the use of an inappropriate random number generator can cause the complete failure of simulations of this type.
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
Sedimentation and Crystallization of Hard-Sphere Colloidal Suspensions: Theory and Experiment
NASA Astrophysics Data System (ADS)
Davis, Kevin Eugene
Sedimentation and ultrafiltration are important processes for removing solids from suspensions. The Kynch theory describes the transient settling of non-colloidal particles forming an incompressible sediment by providing a solution to the convective conservation equation. This solution predicts the evolution of several different regions. Subsequent treatments have accounted for compressibility within the sediment. These modifications, nevertheless, rely entirely on Kynch theory for analytical description, differing only by the assumed boundary condition imposed by the sediment. We present a model of sedimentation for colloidal systems by including a diffusion term in the governing equation. In the regions above the sediment, this term acts as a small perturbation to the Kynch theory. Within the sediment, owing to the high volume fraction, diffusion is comparable to convection. Slow compression to the maximum volume fraction contrasts the incompressibility of the Kynch theory. Application of the method of matched asymptotic expansions to the conservation equation enables us to complete a description of the settling process, in particular, the volume fraction evolution within the sediment. This method is also applied to the related ultrafiltration process. Colloidal dispersions exhibit thermodynamic properties similar to molecular systems, including a hard-sphere disorder -to-order transition, i.e. freezing or crystallization, at particle volume fractions above 0.50. Throughout concentrated suspensions investigators have observed nucleation and growth of small ordered regions. Our dilute suspensions of organophilic silica in cyclohexane depend on settling to concentrate particles. In contrast to the above we observe ordered sediments produced by one-dimensional crystal growth. The slow sedimentation of small particles permits rearrangement into the iridescent ordered structure at the phase boundary. Suspensions with particle sizes of up to 0.34mum easily form fully crystalline sediments as detected by their iridescence and scanning electron micrographs. X-ray attenuation measurements give detailed volume fraction profiles and reveal a volume fraction discontinuity coincident with the observed crystal boundary. This discontinuity propagates at constant velocity separating the coexistence volume fractions 0.53 and 0.60 in the disordered and ordered phases, respectively. Suspensions of 0.43 ?m particles, however, formed amorphous sediments. In this case the sediment accumulated faster than the maximum crystallization rate.
NASA Astrophysics Data System (ADS)
Löwe, Henning; Picard, Ghislain
2014-05-01
Within dense media radiative transfer (DMRT) simulations for microwave modeling of snow, the microstructure is often modeled as a discrete sphere assembly, e.g. sticky hard spheres (SHS). An objective mapping of this simplified microstructural model onto the bicontinuous structure of real snow is however missing. This ambiguity in the structural representation actually hinders a compelling comparison of DMRT with other models, such as the microwave emission model of layered snowpacks (MEMLS) which is formulated in terms of the two-point correlation function for continuous microstructures. To connect the different approaches, we have derived an analytical expression for the two-point correlation function for monodisperse SHS in the Percus-Yevick approximation. The analytical form of the two-point correlation function allows both, the evaluation of the scattering coefficient for SHS in the improved Born approximation for MEMLS, and an objective retrieval of the SHS parameters (sphere diameter and stickiness) from micro-computed tomography for DMRT. The parameter estimation is demonstrated for a comprehensive set of 167 different snow samples by providing stickiness values and comparing estimated sphere diameters to the specific surface area.
Zhou, Y.; Stell, G.
1988-12-01
An exact integral-equation formalism for a system of a binary hard-sphere mixture interacting with a spherical semipermeable vesicle (SPV) and plane semipermeable membrane (SPM) is derived by using the Ornstein--Zernike (OZ)= equation with appropriate closures. The Percus--Yevick (PY) closure or the hypernetted chain (HNC) closure, in which the bulk correlation is obtained by the PY approximation, are considered as examples. We refer to these as the PY/PY and HNC/PY approximations, respectively. The mixture contains solvent particles, which are permeable to the membrane, and solute particles (''protein'' or ''polymer'' particles), which can not pass through the membrane. We develop an exact general formalism for this problem and as an illustration of its use give quantative results for solvent and solute particles modeled as hard spheres of different diameters. An analytical expression for the density ratio in the PY/PY and HNC/PY approximations between two sides of a plane SPM is obtained. Results obtained from these expressions agree very well with results obtained by equating chemical potentials in the region of interest. It turns out that the protein--membrane direct correlation function can be given by a simple analytic expression for the limit of a point solvent in the PY/PY approximation. The osmotic pressure and density profiles for the system containing an ideal spherical SPV or plane SPM in the PY/PY approximation are evaluated. Extension to the nonlocal density-functional closures previously introduced by Blum and Stell is discussed. Finally, we note that certain impenetrable-wall problems previously considered elsewhere can be regarded as semipermeable membrane problems treated via McMillan--Mayer formalism in the continuum--solvent approximation.
Visualization of Induced Strain Fields in Hard Sphere Crystals and Glasses Using Confocal Microscopy
Andrew Hollingsworth; Chistopher Harrison; Matthew Sullivan; Paul Chaikin; William Russel; Andrew Schofield
2001-01-01
Using the optical cross-sectioning capability of a confocal (Nipkow disk) microscope, we have studied the strain response of colloidal crystals and glasses to applied stress. The stress was imposed by the harmonic motion of a larger (10 micron diameter) polystyrene sphere submerged in a colloidal suspension of rhodamine-dyed, 0.92 micron poly(methyl methacrylate) spheres grafted with a layer of poly(12-hydroxy stearic
A new Monte Carlo method to study the fluid-solid phase transition of polydisperse hard spheres
Mingcheng Yang; Hongru Ma
2008-07-04
A new Monte Carlo approach is proposed to investigate the fluid-solid phase transition of the polydisperse system. By using the extended ensemble, a reversible path was constructed to link the monodisperse and corresponding polydisperse system. Once the fluid-solid coexistence point of the monodisperse system is known, the fluid-solid coexistence point of the polydisperse system can be obtained from the simulation. The validity of the method is checked by the simulation of the fluid-solid phase transition of a size-polydisperse hard sphere colloid. The results are in agreement with the previous studies.
NASA Astrophysics Data System (ADS)
Cuetos, Alejandro; Martínez-Haya, Bruno; Lago, Santiago; Rull, Luis F.
2007-06-01
Parsons-Lee and Onsager theories are formulated for the isotropic-nematic transition in a binary mixture of hard rods and hard spheres. Results for the phase coexistence and for the equation of state in both phases for mixtures with different relative sizes and composition are presented. The two theories explain correctly the general behavior observed in experiments and computer simulations for these fluids. In particular, the theory accounts for the destabilization of the nematic phase when spherical or globular macromolecules are added to a system of rodlike colloids, and the entrance of the system into a demixed regime at high volume fractions of the spherical particles. Upon demixing a nematic state rich in rods coexists in equilibrium with an isotropic state much more diluted in the rodlike component. Onsager theory fails on quantitative grounds for aspect ratios of the rodlike molecules smaller than 100, and in the cases where the molar fractions of spheres becomes close to unity. On the contrary, the Parsons-Lee approximation remains accurate down to aspect ratios as small as 5. The spinodal analysis indicates that the isotropic-isotropic and nematic-nematic coexistences become feasible for sufficiently large spheres and long rods, respectively. The latter type of coexistence interferes partially with the isotropic-nematic coexistence regime of interest to the present work. Overall, the study serves to rationalize and control key aspects of the behavior of these binary nematogenic colloidal systems, which can be tuned with an appropriate choice of the relative size and molar fractions of the particles.
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.
Hiroshi Frusawa
2014-04-24
A coarse-grained system of one-dimensional (1D) hard spheres (HSs) is created using the Delaunay tessellation, which enables one to define the quasi-0D state. It is found from comparing the quasi-0D and 1D free energy densities that a frozen state due to the emergence of quasi-0D HSs is thermodynamically more favorable than fluidity with a large-scale heterogeneity above crossover volume fraction of $\\phi_c=e/(1+e)=0.731\\cdots$, at which the total entropy of the 1D state vanishes. The Delaunay-based lattice mapping further provides a similarity between the dense HS system above $\\phi_c$ and the jamming limit in the car parking problem.
Choi, Y.; Ree, T. (Department of Chemistry, Korea Advanced Institute of Science and Technology, P. O. Box 150, Cheongyangni, Seoul (Korea)); Ree, F.H. (University of California, Lawrence Livermore National Laboratory, Livermore, California (USA))
1991-11-15
The hard-sphere radial distribution functions, {ital g}{sub HS}({ital r}/{ital d},{eta}), for the face-centered cubic and hexagonal close-packed phases have been computed by the Monte Carlo method at nine values of the packing fraction, {eta}(=({pi}/6){rho}{ital d}{sup 3}), ranging from 4% below the melting density to 99% of the close-packed density. The Monte Carlo data are used to improve available analytic expressions for {ital g}{sub HS}({ital r}/{ital d},{eta}). By utilizing the new {ital g}{sub HS}({ital r}/{ital d},{eta}) in the Henderson and Grundke method (J. Chem. Phys. {bold 63}, 601 (1975)), we next derive an expression for {ital y}{sub HS}({ital r}/{ital d},{eta}) (={ital g}{sub HS}({ital r}/{ital d})exp{l brace}{beta}{ital V}{sub HS}({ital r}){r brace}) inside the hard-sphere diameter, {ital d}. These expressions are employed in a solid-state perturbation theory (J. Chem. Phys. {bold 84}, 4547 (1986)) to compute solid-state and melting properties of the Lennard-Jones and inverse-power potentials. Results are in close agreement with Monte Carlo and lattice-dynamics calculations performed in this and previous work. The new {ital g}{sub HS}({ital r}/{ital d},{eta}) shows a reasonable thermodynamic consistency as required by the Ornstein--Zernike relation. As an application, we have constructed a high-pressure phase diagram for a truncated Lennard-Jones potential. From this study, we conclude that the new {ital g}{sub HS}({ital r}/{ital d},{eta}) is an improvement over available expressions and that it is useful for solid-state calculations.
Visualization of Induced Strain Fields in Hard Sphere Crystals and Glasses Using Confocal Microscopy
NASA Astrophysics Data System (ADS)
Hollingsworth, Andrew; Harrison, Chistopher; Sullivan, Matthew; Chaikin, Paul; Russel, William; Schofield, Andrew
2001-03-01
Using the optical cross-sectioning capability of a confocal (Nipkow disk) microscope, we have studied the strain response of colloidal crystals and glasses to applied stress. The stress was imposed by the harmonic motion of a larger (10 micron diameter) polystyrene sphere submerged in a colloidal suspension of rhodamine-dyed, 0.92 micron poly(methyl methacrylate) spheres grafted with a layer of poly(12-hydroxy stearic acid). An optical tweezer trap was used to manipulate the larger particle. The positions of the colloidal spheres were tracked to within 10 nanometer accuracy at the symmetry plane in order to determine their response as a function of time and position. Comparison of the strain fields and viscoelastic properties for the glass, liquid and solid will be presented.
NASA Astrophysics Data System (ADS)
Boda, Dezs?; Henderson, Douglas; Eisenberg, Bob; Gillespie, Dirk
2011-08-01
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.
NASA Astrophysics Data System (ADS)
Archer, A. L.; Amos, M. D.; Jackson, G.; McLure, I. A.
1996-01-01
The adequacy of the recently developed bonded hard-sphere (BHS) theory in describing the critical behavior of the homologous series of the alkanes and perfluoroalkanes is examined in this work. A simple united atom model, formed from chains of tangent hard spheres, reproduces the major experimental trends and provides good quantitative agreement for systems with two or more carbon atoms. This simple model cannot, however, reproduce the anomalous behavior of the critical pressure of the alkane series: the values of the critical pressure and temperature for methane are smaller than expected. A more sophisticated distributed-site model, which takes explicit account of the backbone and substituent atoms, reproduces this anomalous behavior. The BHS theory has also been used to predict the upper critical solution temperatures of alkane + perfluoroalkane mixtures. For most systems, the segment-segment parameters are fitted to the butane + perfluorobutane system, although in the case of mixtures containing methane, methane + perfluoromethane parameters must be used. Excellent qualitative agreement with experimental data is seen. This indicates the strength of the BHS approach as a type of group contribution method.
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.
Structure Factor of Semiconductor Liquid Metals using Charged Hard Sphere Reference System
NASA Astrophysics Data System (ADS)
Sonvane, Y. A.; Thakor, P. B.; Kanawade, Sandhya; Gajjar, P. N.; Jani, A. R.
2010-06-01
We have calculated structure factor S(q) of some semiconductor liquid Metals (Si, Ga, Ge, In, Sn, Tl and Bi) using our well established single parametric model potential alongwith Charged Heard Sphere (CHS) reference system. To see the influence of exchange and correlation effect, Taylor local field correlation function is used. From present results, it is seen that excellent agreements between present results and experimental data have been achieved. Lastly we conclude that our model potential successfully produces the data of structure factor for some semiconductor liquid Metals (Si, Ga, Ge, In, Sn, Tl and Bi).
NASA Astrophysics Data System (ADS)
Rainone, Corrado; Urbani, Pierfrancesco; Yoshino, Hajime; Zamponi, Francesco
2015-01-01
We consider the adiabatic evolution of glassy states under external perturbations. The formalism we use is very general. Here we use it for infinite-dimensional hard spheres where an exact analysis is possible. We consider perturbations of the boundary, i.e., compression or (volume preserving) shear strain, and we compute the response of glassy states to such perturbations: pressure and shear stress. We find that both quantities overshoot before the glass state becomes unstable at a spinodal point where it melts into a liquid (or yields). We also estimate the yield stress of the glass. Finally, we study the stability of the glass basins towards breaking into sub-basins, corresponding to a Gardner transition. We find that close to the dynamical transition, glasses undergo a Gardner transition after an infinitesimal perturbation.
Kalyuzhnyi, Yu. V. [Institute for Condensed Matter Physics, Svientsitskoho 1, 290011 Lviv, (Ukraine)] [Institute for Condensed Matter Physics, Svientsitskoho 1, 290011 Lviv, (Ukraine); Blum, L. [Department of Physics, University of Puerto Rico, Rio Piedras, Puerto Rico 00931 (Puerto Rico)] [Department of Physics, University of Puerto Rico, Rio Piedras, Puerto Rico 00931 (Puerto Rico); Rescic, J. [Faculty of Chemistry and Chemical Technology, University of Ljubljana, 1001 Ljubljana, (Slovenia)] [Faculty of Chemistry and Chemical Technology, University of Ljubljana, 1001 Ljubljana, (Slovenia); Stell, G. [Department of Chemistry, State University of New York at Stony Brook, New York 11794-3400 (United States)] [Department of Chemistry, State University of New York at Stony Brook, New York 11794-3400 (United States)
2000-07-15
The analytical solution of the associative mean spherical approximation (AMSA) for a Yukawa dimerizing multicomponent hard-sphere fluid is derived. The general multi-Yukawa case is discussed. The simpler one-Yukawa case with factorizable coefficients is explicitly solved. As in the previously discussed electrolyte case the solution of the AMSA reduces to the solution of only one nonlinear algebraic equation for the scaling parameter {gamma}{sup B}. The analytical results for the AMSA closure is illustrated by numerical examples and computer simulation for the one-component one-Yukawa dimerizing fluid. Good agreement between theoretical and computer simulation results was found for both the thermodynamic properties and the structure of the system. (c) 2000 American Institute of Physics.
Stéphane Mischler; Clément Mouhot
2006-07-21
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 of temperature, as well as the algebraic decay of singularities. The proofs are based on the regularity study of a rescaled problem, with the help of the regularity properties of the gain part of the Boltzmann collision integral, well-known in the elastic case, and which are extended here in the context of granular gases.
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.
Román, F L; White, J A; González, A; Velasco, S
2006-04-21
We examine the microscopic structure of a hard-sphere fluid confined to a small cylindrical pore by means of Monte Carlo simulation. In order to analyze finite-size effects, the simulations are carried out in the framework of different statistical mechanics ensembles. We find that the size effects are specially relevant in the canonical ensemble where noticeable differences are found with the results in the grand canonical ensemble (GCE) and the isothermal isobaric ensemble (IIE) which, in most situations, remain very close to the infinite system results. A customary series expansion in terms of fluctuations of either the number of particles (GCE) or the inverse volume (IIE) allows us to connect with the results of the canonical ensemble. PMID:16674252
Rainone, Corrado; Urbani, Pierfrancesco; Yoshino, Hajime; Zamponi, Francesco
2015-01-01
We consider the adiabatic evolution of glassy states under external perturbations. The formalism we use is very general. Here we use it for infinite-dimensional hard spheres where an exact analysis is possible. We consider perturbations of the boundary, i.e., compression or (volume preserving) shear strain, and we compute the response of glassy states to such perturbations: pressure and shear stress. We find that both quantities overshoot before the glass state becomes unstable at a spinodal point where it melts into a liquid (or yields). We also estimate the yield stress of the glass. Finally, we study the stability of the glass basins towards breaking into sub-basins, corresponding to a Gardner transition. We find that close to the dynamical transition, glasses undergo a Gardner transition after an infinitesimal perturbation. PMID:25615481
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.
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.
Funakoshi, Ken-ichi; Nozawa, Akifumi [Japan Synchrotron Radiation Research Institute, Sayo-cho, Hyogo 679-5198 (Japan)
2012-10-15
We describe a new method for the in situ measurement of the density of a liquid at high pressure and high temperature using the falling-sphere technique. Combining synchrotron radiation X-ray radiography with a large-volume press, the newly developed falling-sphere method enables the determination of the density of a liquid at high pressure and high temperature based on Stokes' flow law. We applied this method to liquid sulfur and successfully obtained the density at pressures up to 9 GPa. Our method could be used for the determination of the densities of other liquid materials at higher static pressures than are currently possible.
Numerical simulations of granular dynamics. I. Hard-sphere discrete element method and tests
Richardson, Derek C; Murdoch, Naomi; Michel, Patrick
2013-01-01
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 ...
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.
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
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.
NASA Astrophysics Data System (ADS)
van Westen, Thijs; Vlugt, Thijs J. H.; Gross, Joachim
2014-01-01
An analytical equation of state (EoS) is derived to describe the isotropic (I) and nematic (N) phase of linear- and partially flexible tangent hard-sphere chain fluids and their mixtures. The EoS is based on an extension of Onsager's second virial theory that was developed in our previous work [T. van Westen, B. Oyarzún, T. J. H. Vlugt, and J. Gross, J. Chem. Phys. 139, 034505 (2013)]. Higher virial coefficients are calculated using a Vega-Lago rescaling procedure, which is hereby generalized to mixtures. The EoS is used to study (1) the effect of length bidispersity on the I-N and N-N phase behavior of binary linear tangent hard-sphere chain fluid mixtures, (2) the effect of partial molecular flexibility on the binary phase diagram, and (3) the solubility of hard-sphere solutes in I- and N tangent hard-sphere chain fluids. By changing the length bidispersity, two types of phase diagrams were found. The first type is characterized by an I-N region at low pressure and a N-N demixed region at higher pressure that starts from an I-N-N triphase equilibrium. The second type does not show the I-N-N equilibrium. Instead, the N-N region starts from a lower critical point at a pressure above the I-N region. The results for the I-N region are in excellent agreement with the results from molecular simulations. It is shown that the N-N demixing is driven both by orientational and configurational/excluded volume entropy. By making the chains partially flexible, it is shown that the driving force resulting from the configurational entropy is reduced (due to a less anisotropic pair-excluded volume), resulting in a shift of the N-N demixed region to higher pressure. Compared to linear chains, no topological differences in the phase diagram were found. We show that the solubility of hard-sphere solutes decreases across the I-N phase transition. Furthermore, it is shown that by using a liquid crystal mixture as the solvent, the solubility difference can by maximized by tuning the composition. Theoretical results for the Henry's law constant of the hard-sphere solute are in good agreement with the results from molecular simulation.
van Westen, Thijs; Vlugt, Thijs J H; Gross, Joachim
2014-01-21
An analytical equation of state (EoS) is derived to describe the isotropic (I) and nematic (N) phase of linear- and partially flexible tangent hard-sphere chain fluids and their mixtures. The EoS is based on an extension of Onsager's second virial theory that was developed in our previous work [T. van Westen, B. Oyarzún, T. J. H. Vlugt, and J. Gross, J. Chem. Phys. 139, 034505 (2013)]. Higher virial coefficients are calculated using a Vega-Lago rescaling procedure, which is hereby generalized to mixtures. The EoS is used to study (1) the effect of length bidispersity on the I-N and N-N phase behavior of binary linear tangent hard-sphere chain fluid mixtures, (2) the effect of partial molecular flexibility on the binary phase diagram, and (3) the solubility of hard-sphere solutes in I- and N tangent hard-sphere chain fluids. By changing the length bidispersity, two types of phase diagrams were found. The first type is characterized by an I-N region at low pressure and a N-N demixed region at higher pressure that starts from an I-N-N triphase equilibrium. The second type does not show the I-N-N equilibrium. Instead, the N-N region starts from a lower critical point at a pressure above the I-N region. The results for the I-N region are in excellent agreement with the results from molecular simulations. It is shown that the N-N demixing is driven both by orientational and configurational/excluded volume entropy. By making the chains partially flexible, it is shown that the driving force resulting from the configurational entropy is reduced (due to a less anisotropic pair-excluded volume), resulting in a shift of the N-N demixed region to higher pressure. Compared to linear chains, no topological differences in the phase diagram were found. We show that the solubility of hard-sphere solutes decreases across the I-N phase transition. Furthermore, it is shown that by using a liquid crystal mixture as the solvent, the solubility difference can by maximized by tuning the composition. Theoretical results for the Henry's law constant of the hard-sphere solute are in good agreement with the results from molecular simulation. PMID:25669397
NASA Astrophysics Data System (ADS)
Santos, Andres; Yuste, Santos B.; Lopez de Haro, Mariano
2002-09-01
The contact values gij(sigmaij) 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 gij(sigma]ij)=G([eta,zij), 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 zij=(sigma]i[sigma]j/[sigma]ij)<[sigma]d-1>/<[sigmad> is a dimensionless parameter, n>being the nth moment of the diameter distribution. 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-mentioned 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.
Miguel Robles; Mariano López de Haro; Andrés Santos
2004-01-01
Following the work of Leutheusser [Physica A 127, 667 (1984)], the solution to the Percus-Yevick equation for a seven-dimensional hard-sphere fluid is explicitly found. This allows the derivation of the equation of state for the fluid taking both the virial and the compressibility routes. An analysis of the virial coefficients and the determination of the radius of convergence of the
Chang, J.; Sandler, S.I. [Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 (United States)] [Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 (United States)
1995-08-22
We have extended the Wertheim integral equation theory to mixtures of hard spheres with two attraction sites in order to model homonuclear hard-sphere chain fluids, and then solved these equations with the polymer-Percus--Yevick closure and the ideal chain approximation to obtain the average intermolecular and overall radial distribution functions. We obtain explicit expressions for the contact values of these distribution functions and a set of one-dimensional integral equations from which the distribution functions can be calculated without iteration or numerical Fourier transformation. We compare the resulting predictions for the distribution functions with Monte Carlo simulation results we report here for five selected binary mixtures. It is found that the accuracy of the prediction of the structure is the best for dimer mixtures and declines with increasing chain length and chain-length asymmetry. For the equation of state, we have extended the dimer version of the thermodynamic perturbation theory to the hard-sphere chain mixture by introducing the dimer mixture as an intermediate reference system. The Helmholtz free energy of chain fluids is then expressed in terms of the free energy of the hard-sphere mixture and the contact values of the correlation functions of monomer and dimer mixtures. We compared with the simulation results, the resulting equation of state is found to be the most accurate among existing theories with a relative average error of 1.79% for 4-mer/8-mer mixtures, which is the worst case studied in this work. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
Jin, Howon; Kang, Kyongok; Ahn, Kyung Hyun; Dhont, Jan K G
2014-12-21
Flow-induced instabilities that lead to non-uniform stationary flow profiles have been observed in many different soft-matter systems. Two types of instabilities that lead to banded stationary states have been identified, which are commonly referred to as gradient- and vorticity-banding. The molecular origin of these instabilities is reasonably well understood. A third type of instability that has been proposed phenomenologically [Europhys. Lett., 1986, 2, 129 and Phys. Rev. E, 1995, 52, 4009] is largely unexplored. Essential to this "Shear-gradient Concentration Coupling" (SCC-) instability is a mass flux that is induced by spatial gradients of the shear rate. A possible reason that this instability has essentially been ignored is that the molecular origin of the postulated mass flux is not clear, and no explicit expressions for the shear-rate and concentration dependence of the corresponding transport coefficient exist. It is therefore not yet known what types of flow velocity- and concentration-profiles this instability gives rise to. In this paper, an expression for the transport coefficient corresponding to the shear-gradient induced mass flux is derived in terms of the shear-rate dependent pair-correlation function, and Brownian dynamics simulations for hard-spheres are presented that specify the shear-rate and concentration dependence of the pair-correlation function. This allows to explicitly formulate the coupled advection-diffusion equation and an equation of motion for the suspension flow velocity. The inclusion of a non-local contribution to the stress turns out to be essential to describe the SCC-banding transition. The coupled equations of motion are solved numerically, and flow- and concentration-profiles are discussed. It is shown that the SCC-instability occurs within the glass state at sufficiently small shear rates, leading to a banded flow-profile where one of the bands is non-flowing. PMID:25346243
Comparison of weighted-density-functional theories for inhomogeneous liquids
Kroll, D. M.; Laird, Brian Bostian
1990-10-15
Three recent weighted-density-functional (WDF) theories are critically examined in terms of their ability to describe correctly the structure of a hard-sphere fluid at a hard wall. A new derivation of the Curtin-Ashcroft ...
Clustering and percolation for dimerizing penetrable spheres
Weist, A.O.; Glandt, E.D. (Department of Chemical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania (USA))
1991-12-01
Wertheim's dual density formalism is applied to study the percolation behavior of dimerizing permeable spheres. The model is that of permeable spheres introduced by Blum and Stell as a generalized potential having ideal-gas (randomly centered) spheres as one limit and Percus--Yevick hard spheres as the other. Both thermodynamic results (pressure and site--site pair-correlation functions) and connectivity results (percolation threshold and site--site pair-connectedness functions) are determined for mixtures of dumbbells and spheres as a function of the penetrability factor {epsilon}, the bond length {ital L} and the fraction {ital x}{sub 1} of spheres forming dumbbells. A critical bond length {ital L}=0.553 was found for which the percolation threshold is independent of the amount of dimerization.
Hard scale dependent gluon density, saturation, and forward-forward dijet production at the LHC
NASA Astrophysics Data System (ADS)
Kutak, Krzysztof
2015-02-01
We propose a method to introduce Sudakov effects to the unintegrated gluon density, promoting it to be hard scale dependent. The advantage of the approach is that it guarantees that the gluon density is positive definite and that the Sudakov effects cancel on the integrated level. As a case study, we apply the method to calculate angular correlations and the Rp A ratio for p +p vs p +Pb collision in the production of forward-forward dijets.
Single-crystal silicon MEMS microactuator for high-density hard disk drive
Jianqiang Mou; Shixin Chen; Yi Lu
2001-01-01
A single crystal silicon MEMS microactuator for high density hard disk drives is described in this paper. The microactuator is located between a slider and a suspension, and drives the slider on which a magnetic head is attached. The MEMS actuator is fabricated by improved LISA process. It has an electrically isolated 20:1 (40micrometers thick, 2micrometers width) high aspect ratio
Interacting hard rods on a lattice: distribution of microstates and density functionals.
Bakhti, Benaoumeur; Müller, Gerhard; Maass, Philipp
2013-08-01
We derive exact density functionals for systems of hard rods with first-neighbor interactions of arbitrary shape but limited range on a one-dimensional lattice. The size of all rods is the same integer unit of the lattice constant. The derivation, constructed from conditional probabilities in a Markov chain approach, yields the exact joint probability distribution for the positions of the rods as a functional of their density profile. For contact interaction ("sticky core model") between rods, we give a lattice fundamental measure form of the density functional and present explicit results for contact correlators, entropy, free energy, and chemical potential. Our treatment includes inhomogeneous couplings and external potentials. PMID:23927249
NASA Astrophysics Data System (ADS)
Prasanth, P. S.; Kakkassery, Jose K.; Vijayakumar, R.
2012-04-01
A modified phenomenological model is constructed for the simulation of rarefied flows of polyatomic non-polar gas molecules by the direct simulation Monte Carlo (DSMC) method. This variable hard sphere-based model employs a constant rotational collision number, but all its collisions are inelastic in nature and at the same time the correct macroscopic relaxation rate is maintained. In equilibrium conditions, there is equi-partition of energy between the rotational and translational modes and it satisfies the principle of reciprocity or detailed balancing. The present model is applicable for moderate temperatures at which the molecules are in their vibrational ground state. For verification, the model is applied to the DSMC simulations of the translational and rotational energy distributions in nitrogen gas at equilibrium and the results are compared with their corresponding Maxwellian distributions. Next, the Couette flow, the temperature jump and the Rayleigh flow are simulated; the viscosity and thermal conductivity coefficients of nitrogen are numerically estimated and compared with experimentally measured values. The model is further applied to the simulation of the rotational relaxation of nitrogen through low- and high-Mach-number normal shock waves in a novel way. In all cases, the results are found to be in good agreement with theoretically expected and experimentally observed values. It is concluded that the inelastic collision of polyatomic molecules can be predicted well by employing the constructed variable hard sphere (VHS)-based collision model.
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
Hardness of FeB{sub 4}: Density functional theory investigation
Zhang, Miao; Du, Yonghui; Gao, Lili [Department of Physics, Beihua University, Jilin 132013 (China)] [Department of Physics, Beihua University, Jilin 132013 (China); Lu, Mingchun [Department of Aeronautical Engineering Professional Technology, Jilin Institute of Chemical Technology, Jilin 132102 (China)] [Department of Aeronautical Engineering Professional Technology, Jilin Institute of Chemical Technology, Jilin 132102 (China); Lu, Cheng [Department of Physics, Nanyang Normal University, Nanyang 473061 (China)] [Department of Physics, Nanyang Normal University, Nanyang 473061 (China); Liu, Hanyu, E-mail: hal420@mail.usask.ca [Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5E2 (Canada)] [Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5E2 (Canada)
2014-05-07
A recent experimental study reported the successful synthesis of an orthorhombic FeB{sub 4} with a high hardness of 62(5) GPa [H. Gou et al., Phys. Rev. Lett. 111, 157002 (2013)], which has reignited extensive interests on whether transition-metal borides compounds will become superhard materials. However, it is contradicted with some theoretical studies suggesting transition-metal boron compounds are unlikely to become superhard materials. Here, we examined structural and electronic properties of FeB{sub 4} using density functional theory. The electronic calculations show the good metallicity and covalent Fe–B bonding. Meanwhile, we extensively investigated stress-strain relations of FeB{sub 4} under various tensile and shear loading directions. The calculated weakest tensile and shear stresses are 40 GPa and 25 GPa, respectively. Further simulations (e.g., electron localization function and bond length along the weakest loading direction) on FeB{sub 4} show the weak Fe–B bonding is responsible for this low hardness. Moreover, these results are consistent with the value of Vickers hardness (11.7–32.3 GPa) by employing different empirical hardness models and below the superhardness threshold of 40 GPa. Our current results suggest FeB{sub 4} is a hard material and unlikely to become superhard (>40 GPa)
Effective densities of hard coals as a function of their genetic characteristics
Dobronravov, V.F.
1985-01-01
A quantitative analysis has been made of the change in the effective densities of hard coals as a function of the stage of metamorphism, petrographic composition, and degree of reduction. In the sintering and in the leaning components, this index changes along a curve with a minimum at the medium states of metamorphism. The influence of the petrographic composition is a maximum in the region of fat coals and is the range of 0.04-0.07 g/cm/sup 3/. The influence of the degree of reduction is small and decreases with a rise in rank. A formula is proposed for calculating the effective densities of hard coals from their genetic parameters.
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}.
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.
NASA Astrophysics Data System (ADS)
Sun, Jiu-Xun; Jin, Ke; Cai, Ling-Cang; Wu, Qiang
2014-08-01
The equation of state (EOS) for hard-sphere fluid derived from compressibility routes of Percus-Yevick theory (PYC) is extended. The two parameters are determined by fitting well-known virial coefficients of pure fluid. The extended cubic EOS can be directly extended to multi-component mixtures, merely demanding the EOS of mixtures also is cubic and combining two physical conditions for the radial distribution functions at contact (RDFC) of mixtures. The calculated virial coefficients of pure fluid and predicted compressibility factors and RDFC for both pure fluid and mixtures are excellent as compared with the simulation data. The values of RDFC for mixtures with extremely large size ratio 10 are far better than the BGHLL expressions in literature.
Ferdjallah, M; Bostick, F X; Barr, R E
1996-09-01
Cranial electrotherapy stimulation (CES) has been successfully used for treatment of many psychiatric diseases. Its noninvasive nature is its major advantage over other forms of treatments such as drugs. It is postulated that the low electric current of CES causes the release of neurotransmitters. However, the current pathways have not been extensively investigated. In the following paper, analytical and numerical methods are used to determine the distribution of potential and current density in a four zone concentric spheres model of the human head when excited by two electrodes diametrically opposite to each other. Because of the azimuthal symmetry, which is assumed in this study, a two-dimensional (2-D) finite difference approximation is derived in the spherical grid. The current density distribution is projected around the center of the model, where the thalamus is modeled as a concentric sphere. All dimensions and electrical properties of the model are adapted from clinical data. Results of this simulation indicate that, in contrast to previous beliefs, a small fraction of the CES current does reaches the thalamic area and may facilitate the release of neurotransmitters. PMID:9214809
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.
NASA Technical Reports Server (NTRS)
Miller, C. G., III
1975-01-01
Measured shock shapes are presented for sphere and hemisphere models in helium, air, CF4, C2F6, and CO2 test gases, corresponding to normal-shock density ratios (primary factor governing shock detachment distance of blunt bodies at hypersonic speeds) from 4 to 19. These shock shapes were obtained in three facilities capable of generating the high density ratios experienced during planetary entry at hypersonic conditions; namely, the 6-inch expansion tube, with hypersonic CF4 tunnel, and pilot CF4 Mach 6 tunnel (with CF4 replaced by C2F6). Measured results are compared with several inviscid perfect-gas shock shape predictions, in which an effective ratio of specific heats is used as input, and with real-gas predictions which include effects of a laminar viscous layer and thermochemical nonequilibrium.
Adel Mahamood Hassan; Abdalla Alrashdan; Mohammed T. Hayajneh; Ahmad Turki Mayyas
2009-01-01
The potential of using feed forward backpropagation neural network in prediction of some physical properties and hardness of aluminium–copper\\/silicon carbide composites synthesized by compocasting method has been studied in the present work. Two input vectors were used in the construction of proposed network; namely weight percentage of the copper and volume fraction of the reinforced particles. Density, porosity and hardness
Zhenyu Yan; Sergey V. Buldyrev; Nicolas Giovambattista; Pablo G. Debenedetti; H. Eugene Stanley
2006-01-24
We investigate the equation of state, diffusion coefficient, and structural order of a family of spherically-symmetric potentials consisting of a hard core and a linear repulsive ramp. This generic potential has two characteristic length scales: the hard and soft core diameters. The family of potentials is generated by varying their ratio, $\\lambda$. We find negative thermal expansion (thermodynamic anomaly) and an increase of the diffusion coefficient upon isothermal compression (dynamic anomaly) for $0\\leq\\lambdafamily of tunable spherically-symmetric potentials by simply varying the ratio of hard to soft-core diameters. Although dynamic and thermodynamic anomalies occur almost across the entire range $0\\leq\\lambda\\leq1$, water-like structural anomalies (i.e., decrease in both $t$ and $Q_6$ upon compression and strictly correlated $t$ and $Q_6$ in the anomalous region) occur only around $\\lambda=4/7$. Water-like anomalies in structure, dynamics and thermodynamics arise solely due to the existence of two length scales, orientation-dependent interactions being absent by design.
Generalized Density Functional Theory
A. Khein; N. W. Ashcroft
1997-01-01
Positionally dependent and positionally independent weighted density approximations of classical density functional theories are each shown to represent limits of a more general approach. The resulting flexibility is used to improve on the results obtained for inhomogeneous systems, the hard-sphere crystal being given as an example. Physical limitations of such mappings are inherent and are shown to arise from the
Boss, Alan P.; Keiser, Sandra A., E-mail: boss@dtm.ciw.edu [Department of Terrestrial Magnetism, Carnegie Institution for Science, 5241 Broad Branch Road, NW, Washington, DC 20015-1305 (United States)
2013-02-20
Magnetic fields are important contributors to the dynamics of collapsing molecular cloud cores, and can have a major effect on whether collapse results in a single protostar or fragmentation into a binary or multiple protostar system. New models are presented of the collapse of magnetic cloud cores using the adaptive mesh refinement code Enzo2.0. The code was used to calculate the ideal magnetohydrodynamics (MHD) of initially spherical, uniform density, and rotation clouds with density perturbations, i.e., the Boss and Bodenheimer standard isothermal test case for three-dimensional (3D) hydrodynamics codes. After first verifying that Enzo reproduces the binary fragmentation expected for the non-magnetic test case, a large set of models was computed with varied initial magnetic field strengths and directions with respect to the cloud core axis of rotation (parallel or perpendicular), density perturbation amplitudes, and equations of state. Three significantly different outcomes resulted: (1) contraction without sustained collapse, forming a denser cloud core; (2) collapse to form a single protostar with significant spiral arms; and (3) collapse and fragmentation into binary or multiple protostar systems, with multiple spiral arms. Comparisons are also made with previous MHD calculations of similar clouds with a barotropic equations of state. These results for the collapse of initially uniform density spheres illustrate the central importance of both magnetic field direction and field strength for determining the outcome of dynamic protostellar collapse.
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
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
Expansion-free evolving spheres must have inhomogeneous energy density distributions
Herrera, L. [Escuelade Fisica Facultadde Ciencias, Universidad Central de Venezuela, Caracas (Venezuela, Bolivarian Republic of); Le Denmat, G. [LERMA-PVI, Universite Paris 06, Observatoire de Paris, CNRS, 3 rue Galilee, Ivry sur Seine 94200 (France); Santos, N. O. [LERMA-PVI, Universite Paris 06, Observatoire de Paris, CNRS, 3 rue Galilee, Ivry sur Seine 94200 (France); Laboratorio Nacional de Computacao Cientifica, 25651-070 Petropolis Rio de Janeiro (Brazil)
2009-04-15
In a recent paper a systematic study on shearing expansion-free spherically symmetric distributions was presented. As a particular case of such systems, the Skripkin model was mentioned, which corresponds to a nondissipative perfect fluid with a constant energy density. Here we show that such a model is inconsistent with junction conditions. It is shown that in general for any nondissipative fluid distribution, the expansion-free condition requires the energy density to be inhomogeneous. As an example we consider the case of dust, which allows for a complete integration.
NASA Astrophysics Data System (ADS)
Capitán, José A.; Cuesta, José A.
2007-07-01
In this article we obtain a fundamental measure functional for the model of aligned hard hexagons in the plane. Our aim is not just to provide a functional for an admittedly academic model, but to investigate the structure of fundamental measure theory. A model of aligned hard hexagons has similarities with the hard disk model. Both share “lost cases,” i.e. admit configurations of three particles in which there is pairwise overlap but not triple overlap. These configurations are known to be problematic for fundamental measure functionals, which are not able to capture their contribution correctly. This failure lies in the inability of these functionals to yield a correct low density limit of the third order direct correlation function. Here we derive the functional by projecting aligned hard cubes on the plane x+y+z=0 . The correct dimensional crossover behavior of these functionals permits us to follow this strategy. The functional of aligned hard cubes, however, does not have lost cases, so neither had the resulting functional for aligned hard hexagons. The latter exhibits, in fact, a peculiar structure as compared to the one for hard disks. It depends on a uniparametric family of weighted densities through an additional term not appearing in the functional for hard disks. Apart from studying the freezing of this system, we discuss the implications of the functional structure for further developments of fundamental measure theory.
van Westen, Thijs; Vlugt, Thijs J H; Gross, Joachim
2012-07-28
Onsager-like theories are commonly used to describe the phase behavior of nematic (only orientationally ordered) liquid crystals. A key ingredient in such theories is the orientation-dependent excluded volume of two molecules. Although for hard convex molecular models this is generally known in analytical form, for more realistic molecular models that incorporate intramolecular flexibility, one has to rely on approximations or on computationally expensive Monte Carlo techniques. In this work, we provide a general correlation for the excluded volume of tangent hard-sphere chains of arbitrary chain length and flexibility. The flexibility is introduced by means of the rod-coil model. The resulting correlation is of simple analytical form and accurately covers a wide range of pure component excluded volume data obtained from Monte Carlo simulations of two-chain molecules. The extension to mixtures follows naturally by applying simple combining rules for the parameters involved. The results for mixtures are also in good agreement with data from Monte Carlo simulations. We have expressed the excluded volume as a second order power series in sin?(?), where ? is the angle between the molecular axes. Such a representation is appealing since the solution of the Onsager Helmholtz energy functional usually involves an expansion of the excluded volume in Legendre coefficients. Both for pure components and mixtures, the correlation reduces to an exact expression in the limit of completely linear chains. The expression for mixtures, as derived in this work, is thereby an exact extension of the pure component result of Williamson and Jackson [Mol. Phys. 86, 819-836 (1995)]. PMID:22852654
The statistics of pink noise on a sphere: applications to mantle density anomalies
NASA Astrophysics Data System (ADS)
Hipkin, R. G.
2001-02-01
This paper shows that the power spectrum of the Earth's gravity field is very well modelled by white noise signals originating at just four depths within the Earth. Being able to estimate both the lateral and the radial position of anomalous density gives a new and independent way of imaging mantle structure. The success of a four source-depth model undermines the evidence for the long-held picture that a surface observation of gravity reflects density anomalies distributed indistinguishably at all depths within the Earth, a picture largely based on an inappropriate definition of the power spectrum. All spherical harmonics of gravity observed at the Earth's surface with degree greater than about 60 originate within the lithosphere. Degrees less than 4 come from a poorly constrained source near the core-mantle boundary; all other wavelengths come from sources centred near white noise depths of 315km and between 1100 and 1500km. These depths are maxima: the same statistical model describes sources at a shallower depth but now representing a random process with a finite correlation length. The form of the spectrum requires mantle heterogeneity to increase by about two orders of magnitude between the asthenosphere and the core-mantle boundary. It is suggested that the variance of density inhomogeneities is related to mantle viscosity.
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.
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.}
NASA Astrophysics Data System (ADS)
Grigorov, Martin G.; Weber, Jacques; Vulliermet, Nathalie; Chermette, Henry; Tronchet, Jean M. J.
1998-06-01
In a previous work we have presented a numerical procedure for the calculation of the internal chemical hardness tensor at the molecular orbital resolution level from standard density functional calculations. In this article we describe an improvement of our method using the thermal extensions of density functional theory. Furthermore, new concepts are introduced in the orbitally resolved theory of chemical reactivity. Traditional molecular orbital theories of chemical reactivity are based only on considerations concerning the highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) of molecules, supposed to describe the behavior towards electrophiles, respectively, nucleophiles. By applying our methodology to two test molecular systems, namely water and ferrocene, we show how chemical reactivity can be differentiated against hard and soft electrophiles (acids) and hard and soft nucleophiles (bases). As a by-product of the numerical algorithms being used, a self-consistent method for calculating the molecular chemical potential is also described.
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.
Sun, K.
2011-05-04
This slide show presents: space exploration applications; high energy density physics applications; UV LED and photodiode radiation hardness; UV LED and photodiode space qualification; UV LED AC charge management; and UV LED satellite payload instruments. A UV LED satellite will be launched 2nd half 2012.
The First Hard X-Ray Power Spectral Density Functions of AGN
Shimizu, T Taro
2013-01-01
We present results of our Power Spectral Density (PSD) analysis of 30 AGN using the 58 month light curves from Swift's Burst Alert Telescope (BAT) in the 14-150 keV band. PSDs were fit using a Monte Carlo based algorithm to take into account windowing effects and measurement error. All but one source were found to be fit very well using an unbroken power law with a slope of ~-1, consistent at low frequencies with previous studies in the 2-10 keV band, with no evidence of a break in the PSD. For 5 of the highest S/N 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 AGN, 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 AGN are similar to the high state of Galactic Black Holes.
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.
Monte Carlo simulation of the background correlation function of non-spherical hard body fluids
NASA Astrophysics Data System (ADS)
Labík, Stanislav; Malijevský, Anatol
A new Monte Carlo technique for the calculation of the function y = g exp (?u) is proposed for hard body systems. The method is especially suitable at low and moderate densities and separations below the contact. The y-function was calculated for hard spheres and hard diatomics. For hard spheres surprisingly small deviations from Grundke-Henderson formula were found. For the diatomics at Ls = 0·6 radial slices at four special orientations were determined. The applicability of the proposed method and of the umbrella sampling technique due to Patey and Torrie are compared.
Nguyen, Minh Tho
Ven, Celestijnenlaan 200F, B-3001 LeuVen, Belgium ReceiVed: January 29, 1998 The principle of hard and soft acids and soft acids and bases (HSAB) principle, recently proposed by Gazquez and Mendez.11 The beauty concepts useful for the understanding of chemical reactivity (e.g., electronegativity, hardness, softness
Asit K. Chandra; Minh Tho Nguyen
1998-01-01
that average hardness of the products is higher than that of the reactants for the exchange reactions. In the case of isomeriza- tion reactions, they found that hardness is minimum for the transition state. They also considered polarizability of the system as an index and observed that the condition of minimum polarizability can in general be associated with the maximum
Characterization of maximally random jammed sphere packings: Voronoi correlation functions.
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)PRLTAO0031-900710.1103/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. PMID:25493753
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.
Zhijian Peng; Hezhuo Miao; Longhao Qi; Size Yang; Chizi Liu
2003-01-01
Hard and wear-resistant titanium nitride coatings were deposited by pulsed high energy density plasma technique on cemented carbide cutting tools at ambient temperature. The coating thickness was measured by an optical profiler and surface Auger microprobe. The elemental and phase compositions and distribution of the coatings were determined by Auger microprobe, x-photon electron spectroscope, and X-ray diffractometer. The microstructures of
E. P. Kontar; I. G. Hannah; A. L. MacKinnon
2008-08-25
A novel method of using hard X-rays as a diagnostic for chromospheric density and magnetic structures is developed to infer sub-arcsecond vertical variation of magnetic flux tube size and neutral gas density.Using Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) X-ray data and the newly developed X-ray visibilities forward fitting technique we find the FWHM and centroid positions of hard X-ray sources with sub-arcsecond resolution ($\\sim 0.2"$) for a solar limb flare. We show that the height variations of the chromospheric density and the magnetic flux densities can be found with unprecedented vertical resolution of $\\sim$ 150 km by mapping 18-250 keV X-ray emission of energetic electrons propagating in the loop at chromospheric heights of 400-1500 km. Our observations suggest that the density of the neutral gas is in good agreement with hydrostatic models with a scale height of around $140\\pm 30$ km. FWHM sizes of the X-ray sources decrease with energy suggesting the expansion (fanning out) of magnetic flux tube in the chromosphere with height. The magnetic scale height $B(z)(dB/dz)^{-1}$ is found to be of the order of 300 km and strong horizontal magnetic field is associated with noticeable flux tube expansion at a height of $\\sim$ 900 km.
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.
Density functional theory of single-file classical fluids
NASA Astrophysics Data System (ADS)
Percus, J. K.
An overcomplete density functional formalism is derived to represent the thermal behaviour of confined classical fluids under single-file conditions. Strictly one-dimensional hard rod systems are reanalysed from this viewpoint, and the context is then broadened to encompass hard spheres in cylindrical enclosures. Applications to non-single-file conditions, modulated enclosures, and confined polymers are mentioned.
Sun, K. X.
2011-05-31
This presentation provides an overview of robust, radiation hard AlGaN optoelectronic devices and their applications in space exploration & high energy density physics. Particularly, deep UV LED and deep UV photodiodes are discussed with regard to their applications, radiation hardness and space qualification. AC charge management of UV LED satellite payload instruments, which were to be launched in late 2012, is covered.
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.
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.
Wang, George T.; Li, Qiming
2013-04-23
A method for growing low-dislocation-density material atop a layer of the material with an initially higher dislocation density using a monolayer of spheroidal particles to bend and redirect or directly block vertically propagating threading dislocations, thereby enabling growth and coalescence to form a very-low-dislocation-density surface of the material, and the structures made by this method.
Self-diffusion in isotropic and nematic phases of highly elongated hard particles
NASA Astrophysics Data System (ADS)
Tang, Shuang; Evans, Glenn T.
1993-05-01
Velocity time correlation functions (tcfs) and self-diffusion coefficients have been derived by means of an Enskog kinetic theory for hard ellipsoids in isotropic and in nematic environments. The tcfs, calculated on the basis of kinetic theory, track those calculated by Allen by molecular dynamics simulations and show evidence of two exponential decays which we attribute to the differing rates of diffusion parallel and perpendicular to the ellipsoid principle axes. D/DE the ratio of the molecular dynamics (MD) self-diffusion coefficient to our Enskog estimate has a density dependence characteristic of hard sphere systems when diffusion is perpendicular to the macroscopic director; however, diffusion along the director axis is enhanced and this behavior has no hard sphere analog. In the isotropic phase, D/DE follows the same trend as documented previously by Alder in hard sphere systems.
NASA Astrophysics Data System (ADS)
Fontana, R. E.; Decad, G. M.; Hetzler, S. R.
2015-05-01
Memory storage components, i.e., hard disk drives, tape cartridges, solid state drives using Flash NAND chips, and now optical cartridges using Blu-ray disks, have provided annual increases in memory capacity by decreasing the area of the memory cell associated with the technology of these components. The ability to reduce bit cell sizes is now being limited by nano-technology physics so that in order for component manufacturers to continue to increase component capacity, volumetric enhancements to the storage component are now being introduced. Volumetric enhancements include adding more tape per cartridge, more disk platters per drive, and more layers of memory cells on the silicon NAND substrate or on the optical disk substrate. This paper describes these volumetric strategies, projects density trends at the bit cell level, and projects volumetric trends at the component level in order to forecast future component capacity trends.
M. S. Ripoll; C. F. Tejero
1995-01-01
A simple approximate analytical expression for the direct correlation function of a hard-sphere fluid in D dimensions within the Percus-Yevick equation is proposed. The approximation exactly reproduces the well-known results for D = 1 and D = 3, while for D = 2 it compares well to the numerical results for densities not very close to the freezing density.
Sibug-Aga, Rachel; Laird, Brian Bostian
2004-05-26
by an inverse-twelth power repulsive external potential. For comparison we examine results using three weighted density approximations (WDA), namely those due to Curtin and Ashcroft [Phys. Rev. A 32, 2909 (1985)], Denton and Ashcroft [Phys. Rev. A 39, 426 (1989...
Improved association in a classical density functional theory for water
Krebs, Eric J.; Schulte, Jeff B.; Roundy, David [Department of Physics, Oregon State University, Corvallis, Oregon 97331 (United States)] [Department of Physics, Oregon State University, Corvallis, Oregon 97331 (United States)
2014-03-28
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.
Improved association in a classical density functional theory for water.
Krebs, Eric J; Schulte, Jeff B; Roundy, David
2014-03-28
We present a modification to our recently published statistical associating fluid theory-based classical density functional theory for water. We have recently developed and tested a functional for the averaged radial distribution function at contact of the hard-sphere fluid that is dramatically more accurate at interfaces than earlier approximations. We now incorporate this improved functional into the association term of our free energy functional for water, improving its description of hydrogen bonding. We examine the effect of this improvement by studying two hard solutes (a hard hydrophobic rod and a hard sphere) and a Lennard-Jones approximation of a krypton atom solute. The improved functional leads to a moderate change in the density profile and a large decrease in the number of hydrogen bonds broken in the vicinity of the hard solutes. We find an improvement of the partial radial distribution for a krypton atom in water when compared with experiment. PMID:24697459
NSDL National Science Digital Library
Jensen, Douglas
2005-01-01
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.
Thermodynamics of quantum photon spheres
M. C. Baldiotti; Walace S. Elias; C. Molina; Thiago S. Pereira
2014-11-21
Photon spheres, surfaces where massless particles are confined in closed orbits, are expected to be common astrophysical structures surrounding ultracompact objects. In this paper a semiclassical treatment of a photon sphere is proposed. We consider the quantum Maxwell field and derive its energy spectra. A thermodynamic approach for the quantum photon sphere is developed and explored. Within this treatment, an expression for the spectral energy density of the emitted radiation is presented. Our results suggest that photon spheres, when thermalized with their environment, have nonusual thermodynamic properties, which could lead to distinct observational signatures.
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.
Stoessel, J.P.; Wolynes, P.G.
1989-01-01
With analogy to the ''highly accurate'' summation of cluster diagrams for hard sphere fluids a la Carnahan-Starling, we present a simple, real space free energy density functional for arbitrary potential systems, based on the generalization of the second virial coefficient to inhomogeneous systems which, when applied to hard sphere, soft-sphere, and Lennard-Jones freezing, yield melting characteristics in remarkable agreement with experiment. Implications for the liquid-glass transition in all three potential systems are also presented. 45 refs., 7 figs., 1 tab.
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
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
Behaviour of the self-diffusion coefficient of Kr at low densities
P. Codastefano; M. A. Ricci; V. Zanza
1978-01-01
We report high precision measurements of the self-diffusion coefficient of Kr performed along the isotherm T = 293 K, in the density range 0.03-0.12 g\\/cm3. The first correction term of the expansion of varrhoD in powers of density is obtained and compared with the result for a hard-sphere fluid.
Thomas C. Hales
1998-01-01
This is the fifth in a series of papers giving a proof of the Kepler conjecture, which asserts that the density of a packing of congruent spheres in three dimensions is never greater than $\\\\pi\\/\\\\sqrt{18}\\\\approx 0.74048...$. This is the oldest problem in discrete geometry and is an important part of Hilbert's 18th problem. An example of a packing achieving this
A SAFT-based classical density functional for water
NASA Astrophysics Data System (ADS)
Roundy, David; Hughes, Jessica; Krebs, Eric
2012-02-01
We present a new classical density functional for water based on a combination of Statistical Associating Fluid Theory (SAFT-VR) with the Fundamental Measure Theory (FMT) functional for the hard-sphere fluid. In the homogeneous limit, our functional reduces to the the published optimal SAFT model of Clark et al [1]. By adding a single fitting parameter, we reproduce the bulk surface tension of water within a wide temperature range. We will present results for hydrophobic hard rods and spheres, including the temperature dependence of the hydrophobic interaction. [4pt] [1] G. Clak, A. Haslam, A. Galindo, and G. Jackson, Molecular Physics 104, 3561 (2006).
NASA Astrophysics Data System (ADS)
Sen, Sudeepto; McCoy, John D.; Nath, Shyamal K.; Donley, James P.; Curro, John G.
1995-02-01
Density functional theory is applied to inhomogeneous, rotational isomeric state polymer melts. In particular, a melt of tridecane near a hard wall is investigated, and the variation of polymer-wall correlation functions as a function of packing fraction is of primary interest. In addition to the evaluation of the wall-polymer density profile and the fractional distribution of sites, we use the relation between pressure and contact density to calculate the equation of state of the bulk. Agreement with the generalized Flory dimer equation of state is excellent, and this, in conjunction with our earlier comparison [Sen et al. J. Chem. Phys. 101, 9010 (1994)] with full, multichain simulation, indicates that the density functional theory gives an accurate description of inhomogeneous polymer melts.
NASA Astrophysics Data System (ADS)
Marchuk, Gurii I.; Imshennik, Vladimir S.; Basko, Mikhail M.
2009-03-01
The hydrodynamic problem of a thermonuclear explosion in a sphere of normal-density liquid deuterium was solved (Institute for Physics and Power Engineering, Obninsk) in 1952-1954 in the framework of the Soviet Atomic Project. The principal result was that the explosion shockwave in deuterium strongly decayed because of radiation energy loss and nonlocal energy release by fast neutrons. At that time, this negative result implied in essence that the straightforward approach to creating a thermonuclear weapon was in fact a blind alley. This paper describes a numerical solution to the stated problem, obtained with the modern DEIRA code developed for numerical modeling of inertially confined fusion. Detailed numerical calculations have confirmed the above 'historic' result and shed additional light on the physical causes of the detonation wave decay. The most pernicious factor is the radiation energy loss due to the combined effect of bremsstrahlung and the inverse Compton scattering of the emitted photons on the hot electrons. The impact of energy transfer by fast neutrons — which was already quite adequately accounted for in the above-cited historical work — is less significant. We present a more rigorous (compared to that of the 1950s) study of the role of inverse Compton scattering for which, in particular, an independent analytic estimate is obtained.
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
Hakki, Sema S; SiddikMalkoc; Dundar, Niyazi; Kayis, Seyit Ali; Hakki, Erdogan E; Hamurcu, Mehmet; Baspinar, Nuri; Basoglu, Abdullah; Nielsen, Forrest H; Götz, Werner
2015-01-01
The objective of this study was to determine whether dietary boron (B) affects the strength, density and mineral composition of teeth and mineral density of alveolar bone in rabbits with apparent obesity induced by a high-energy diet. Sixty female, 8-month-old, New Zealand rabbits were randomly assigned for 7 months into five groups as follows: (1) control 1, fed alfalfa hay only (5.91 MJ/kg and 57.5 mg B/kg); (2) control 2, high energy diet (11.76 MJ and 3.88 mg B/kg); (3) B10, high energy diet + 10 mg B gavage/kg body weight/96 h; (4) B30, high energy diet + 30 mg B gavage/kg body weight/96 h; (5) B50, high energy diet + 50 mg B gavage/kg body weight/96 h. Maxillary incisor teeth of the rabbits were evaluated for compression strength, mineral composition, and micro-hardness. Enamel, dentin, cementum and pulp tissue were examined histologically. Mineral densities of the incisor teeth and surrounding alveolar bone were determined by using micro-CT. When compared to controls, the different boron treatments did not significantly affect compression strength, and micro-hardness of the teeth, although the B content of teeth increased in a dose-dependent manner. Compared to control 1, B50 teeth had decreased phosphorus (P) concentrations. Histological examination revealed that teeth structure (shape and thickness of the enamel, dentin, cementum and pulp) was similar in the B-treated and control rabbits. Micro CT evaluation revealed greater alveolar bone mineral density in B10 and B30 groups than in controls. Alveolar bone density of the B50 group was not different than the controls. Although the B treatments did not affect teeth structure, strength, mineral density and micro-hardness, increasing B intake altered the mineral composition of teeth, and, in moderate amounts, had beneficial effects on surrounding alveolar bone. PMID:25468191
Generating perfect fluid spheres in general relativity
NASA Astrophysics Data System (ADS)
Boonserm, Petarpa; Visser, Matt; Weinfurtner, Silke
2005-06-01
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.
C. Doughty; S. M. Gorbatkin; T. Y. Tsui; G. M. Pharr; D. L. Medlin
1997-01-01
Boronâsuboxide-based thin films have been deposited on Si in an electron cyclotron resonance microwave plasma using a radio frequency (rf) magnetron as a source of boron. Variations of the oxygen fraction in the deposition ambient and of the rf bias applied to the substrate were related to film tribology. The best films have hardnesses of â¼28GPa and moduli of â¼240GPa
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
Geometry of Frictionless and Frictional Sphere Packings
Leonardo E. Silbert; Deniz Ertas; Gary S. Grest; Thomas C. Halsey; Dov Levine
2001-11-08
We study static packings of frictionless and frictional spheres in three dimensions, obtained via molecular dynamics simulations, in which we vary particle hardness, friction coefficient, and coefficient of restitution. Although frictionless packings of hard-spheres are always isostatic (with six contacts) regardless of construction history and restitution coefficient, frictional packings achieve a multitude of hyperstatic packings that depend on system parameters and construction history. Instead of immediately dropping to four, the coordination number reduces smoothly from $z=6$ as the friction coefficient $\\mu$ between two particles is increased.
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.
Evans, Paul R; Zhu, Xinhau; Baxter, Paul; McMillen, Mark; McPhillips, John; Morrison, Finlay D; Scott, James F; Pollard, Robert J; Bowman, Robert M; Gregg, J Marty
2007-05-01
We report on the successful fabrication of arrays of switchable nanocapacitors made by harnessing the self-assembly of materials. The structures are composed of arrays of 20-40 nm diameter Pt nanowires, spaced 50-100 nm apart, electrodeposited through nanoporous alumina onto a thin film lower electrode on a silicon wafer. A thin film ferroelectric (both barium titanate (BTO) and lead zirconium titanate (PZT)) has been deposited on top of the nanowire array, followed by the deposition of thin film upper electrodes. The PZT nanocapacitors exhibit hysteresis loops with substantial remnant polarizations, while although the switching performance was inferior, the low-field characteristics of the BTO nanocapacitors show dielectric behavior comparable to conventional thin film heterostructures. While registration is not sufficient for commercial RAM production, this is nevertheless an embryonic form of the highest density hard-wired FRAM capacitor array reported to date and compares favorably with atomic force microscopy read-write densities. PMID:17407362
Doughty, C.; Gorbatkin, S.M. [Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States)] [Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States); Tsui, T.Y.; Pharr, G.M. [Rice University, Houston, Texas 77005 (United States)] [Rice University, Houston, Texas 77005 (United States); Medlin, D.L. [Sandia National Laboratory, Livermore, California 94551 (United States)] [Sandia National Laboratory, Livermore, California 94551 (United States)
1997-09-01
Boron{endash}suboxide-based thin films have been deposited on Si in an electron cyclotron resonance microwave plasma using a radio frequency (rf) magnetron as a source of boron. Variations of the oxygen fraction in the deposition ambient and of the rf bias applied to the substrate were related to film tribology. The best films have hardnesses of {approximately}28GPa and moduli of {approximately}240GPa and were deposited in oxygen fractions {lt}1{percent} at substrate temperatures {lt}350{degree}C. The films contain 4{percent}{endash}15{percent} O and {approximately}15{percent}C, with carbon originating from the sputter target. They are amorphous and have surface roughnesses of {approximately}0.2nm. Boron{endash}oxide films may form a self-generating lubricating layer of B(OH){sub 3} in ambient atmosphere. Compositional depth profiling of these films reveals an oxygen-enriched surface of {approximately}10nm thickness. Initial nanoscratch test results indicate that these films fail at high critical loads and have low friction coefficients relative to other hard coatings. {copyright} {ital 1997 American Vacuum Society.}
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.
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 ...
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.
Density functional theory of freezing: Analysis of crystal density
Laird, Brian Bostian; McCoy, John D.; Haymet, A. D. J.
1987-09-01
with temperature T, volume V, and chemical potential J.L. The particles interact via a potential energy U(rl, ... ,rn ) and feel an external single particle potential ifJ (r). Defining a dimen sionless single particle effective potential by u (r) = pJ.L - pif..." ( • ) For the remainder of this section the following reduced units will be used: reduced radial distance r* = riO', and reduced density p* = pif. The hard-sphere two-particle direct correlation func tion c(r) used in this and earlier calculations is the exact...
NSDL National Science Digital Library
Day, Martha Marie
This web page introduces the concepts of density and buoyancy. The discovery in ancient Greece by Archimedes is described. The densities of various materials are given and temperature effects introduced. Links are provided to news and other resources related to mass density. This is part of the Vision Learning collection of short online modules covering topics in a broad range of science and math topics.
S. V. Nedea; A. J. H. Frijns; A. A. van Steenhoven; A. J. Markvoort; P. A. J. Hilbers
2006-01-01
We study the deviations for the results of the properties of a hard-sphere gas near the walls of a micro\\/nano channel using the hybrid MD–MC simulation method compared to the pure MD and MC results. Our model for the micro channel consists of two parallel infinite plates situated at distance L apart from each other, and of gas molecules confined
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
Patra, Chandra N
2014-11-14
A systematic investigation of the spherical electric double layers with the electrolytes having size as well as charge asymmetry is carried out using density functional theory and Monte Carlo simulations. The system is considered within the primitive model, where the macroion is a structureless hard spherical colloid, the small ions as charged hard spheres of different size, and the solvent is represented as a dielectric continuum. The present theory approximates the hard sphere part of the one particle correlation function using a weighted density approach whereas a perturbation expansion around the uniform fluid is applied to evaluate the ionic contribution. The theory is in quantitative agreement with Monte Carlo simulation for the density and the mean electrostatic potential profiles over a wide range of electrolyte concentrations, surface charge densities, valence of small ions, and macroion sizes. The theory provides distinctive evidence of charge and size correlations within the electrode-electrolyte interface in spherical geometry. PMID:25399154
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.
Ordering of hard particles between hard walls
NASA Astrophysics Data System (ADS)
Chrzanowska, A.; Teixeira, P. I. C.; Ehrentraut, H.; Cleaver, D. J.
2001-05-01
The structure of a fluid of hard Gaussian overlap particles of elongation ? = 5, confined between two hard walls, has been calculated from density-functional theory and Monte Carlo simulations. By using the exact expression for the excluded volume kernel (Velasco E and Mederos L 1998 J. Chem. Phys. 109 2361) and solving the appropriate Euler-Lagrange equation entirely numerically, we have been able to extend our theoretical predictions into the nematic phase, which had up till now remained relatively unexplored due to the high computational cost. Simulation reveals a rich adsorption behaviour with increasing bulk density, which is described semi-quantitatively by the theory without any adjustable parameters.
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.
NASA Astrophysics Data System (ADS)
Yamamoto, Umi; Schweizer, Kenneth
2013-03-01
A microscopic theory for the motion of topologically entangled, non-rotating needles in presence of spatially fixed, hard sphere inclusions has been formulated. Exact two-body dynamical uncrossability constraints are imposed, and an effective Brownian evolution equation at two-needle level is self-consistently constructed. The needle transverse localization length (effective tube diameter) and long-time diffusivity are determined as a function of its length and concentration, the sphere diameter and volume fraction, and needle-sphere liquid pair structure. In contrast to single-component entangled needle liquids, the transverse and longitudinal diffusivity become coupled, and reptation is increasingly suppressed with sphere volume fraction in a manner that depends on the relative sphere-needle size. The slow dynamics also depends on needle concentration, reflecting a competition between inter-needle topological uncrossability constraints and needle-sphere excluded volume interactions. The effective tube diameter is a monotonically decreasing function of the sphere density, consistent with the suppression of polymer translational diffusion. Extension to treat entangled flexible chains, and comparison with recent simulations and experiments, are under study.
Increasing the density melts ultrasoft colloidal glasses
Ludovic Berthier; Angel J. Moreno; Grzegorz Szamel
2010-09-23
We use theory and simulations to investigate the existence of amorphous glassy states in ultrasoft colloids. We combine the hyper-netted chain approximation with mode-coupling theory to study the dynamic phase diagram of soft repulsive spheres interacting with a Hertzian potential, focusing on low temperatures and large densities. At constant temperature, we find that an amorphous glassy state is entered upon compression, as in colloidal hard spheres, but the glass unexpectedly melts when density increases further. We attribute this re-entrant fluid-glass transition to particle softness, and correlate this behaviour to previously reported anomalies in soft systems, thus emphasizing its generality. The predicted fluid-glass-fluid sequence is confirmed numerically.
Largest Lyapunov Exponent for Many Particle Systems at Low Densities
NASA Astrophysics Data System (ADS)
van Zon, R.; van Beijeren, H.; Dellago, Ch.
1998-03-01
The largest Lyapunov exponent ?+ for a dilute gas with short range interactions in equilibrium is studied by a mapping to a clock model, in which every particle carries a watch, with a discrete time that is advanced at collisions. This model has a propagating front solution with a speed that determines ?+, for which we find a density dependence as predicted by Krylov, but with a larger prefactor. Simulations for the clock model and for hard sphere and hard disk systems confirm these results and are in excellent mutual agreement. They show a slow convergence of ?+ with increasing particle number, in good agreement with a prediction by Brunet and Derrida.
Largest Lyapunov Exponent for Many Particle Systems at Low Densities
R. van Zon; H. van Beijeren; Ch. Dellago
1997-10-27
The largest Lyapunov exponent $\\lambda^+$ for a dilute gas with short range interactions in equilibrium is studied by a mapping to a clock model, in which every particle carries a watch, with a discrete time that is advanced at collisions. This model has a propagating front solution with a speed that determines $\\lambda^+$, for which we find a density dependence as predicted by Krylov, but with a larger prefactor. Simulations for the clock model and for hard sphere and hard disk systems confirm these results and are in excellent mutual agreement. They show a slow convergence of $\\lambda^+$ with increasing particle number, in good agreement with a prediction by Brunet and Derrida.
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.
NSDL National Science Digital Library
2008-01-01
This PheT interactive, downloadable simulation allows students toDiscover the relationship between mass, volume and density by weighing and submerging various materials under water. Do objects like aluminum, Styrofoam, and wood float or sink? Can you identify all the mystery objects by weighing them and submerging them underwater to measure their volumes? Sample earning goals, teaching ideas, and translated versions are available.
NASA Astrophysics Data System (ADS)
Sknepnek, Rastko; Henkes, Silke
2015-02-01
We show that coupling to curvature nontrivially affects collective motion in active systems, leading to motion patterns not observed in flat space. Using numerical simulations, we study a model of self-propelled particles with polar alignment and soft repulsion confined to move on the surface of a sphere. We observe a variety of motion patterns with the main hallmarks being polar vortex and circulating band states arising due to the incompatibility between spherical topology and uniform motion—a consequence of the "hairy ball" theorem. We provide a detailed analysis of density, velocity, pressure, and stress profiles in the circulating band state. In addition, we present analytical results for a simplified model of collective motion on the sphere showing that frustration due to curvature leads to stable elastic distortions storing energy in the band.
NASA Astrophysics Data System (ADS)
Fabrocini, A.; Polls, A.
1999-09-01
We study the ground state of a system of Bose hard spheres trapped in an isotropic harmonic potential to investigate the effect of the interatomic correlations and the accuracy of the Gross-Pitaevskii equation. We compare a local-density approximation, based on the energy functional derived from the low-density expansion of the energy of the uniform hard-sphere gas, and a correlated wave-function approach, which explicitly introduces the correlations induced by the potential. Both higher-order terms in the low-density expansion, beyond Gross-Pitaevskii, and explicit dynamical correlations have effects of the order of percent when the number of trapped particles becomes similar to that attained in recent experiments (N~107).
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.
Cavity approach to sphere packing in Hamming space.
Ramezanpour, A; Zecchina, R
2012-02-01
In this paper we study the hard sphere packing problem in the Hamming space by the cavity method. We show that both the replica symmetric and the replica symmetry breaking approximations give maximum rates of packing that are asymptotically the same as the lower bound of Gilbert and Varshamov. Consistently with known numerical results, the replica symmetric equations also suggest a crystalline solution, where for even diameters the spheres are more likely to be found in one of the subspaces (even or odd) of the Hamming space. These crystalline packings can be generated by a recursive algorithm which finds maximum packings in an ultrametric space. Finally, we design a message passing algorithm based on the cavity equations to find dense packings of hard spheres. Known maximum packings are reproduced efficiently in nontrivial ranges of dimensions and number of spheres. PMID:22463152
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.
NASA Technical Reports Server (NTRS)
Benavides, Jose
2014-01-01
SPHERES is a facility of the ISS National Laboratory with three IVA nano-satellites designed and delivered by MIT to research estimation, control, and autonomy algorithms. Since Fall 2010, The SPHERES system is now operationally supported and managed by NASA Ames Research Center (ARC). A SPHERES Program Office was established and is located at NASA Ames Research Center. The SPHERES Program Office coordinates all SPHERES related research and STEM activities on-board the International Space Station (ISS), as well as, current and future payload development. By working aboard ISS under crew supervision, it provides a risk tolerant Test-bed Environment for Distributed Satellite Free-flying Control Algorithms. If anything goes wrong, reset and try again! NASA has made the capability available to other U.S. government agencies, schools, commercial companies and students to expand the pool of ideas for how to test and use these bowling ball-sized droids. For many of the researchers, SPHERES offers the only opportunity to do affordable on-orbit characterization of their technology in the microgravity environment. Future utilization of SPHERES as a facility will grow its capabilities as a platform for science, technology development, and education. XXXX
Modelling anisotropic fluid spheres in general relativity
Petarpa Boonserm; Tritos Ngampitipan; Matt Visser
2015-02-03
We argue that an arbitrary general relativistic anisotropic fluid sphere, (spherically symmetric but with transverse pressure not equal to radial pressure), can nevertheless be successfully modelled by suitable linear combinations of quite ordinary classical matter: an isotropic perfect fluid, a classical electromagnetic field, and a classical (minimally coupled) scalar field. While the most general decomposition is not unique, a preferred minimal decomposition can be constructed that is unique. We show how the classical energy conditions for the anisotropic fluid sphere can be related to energy conditions for the isotropic perfect fluid, electromagnetic field, and scalar field components of the model. Furthermore we show how this decomposition relates to the distribution of electric charge density and scalar charge density throughout the model that is used to mimic the anisotropic fluid sphere. Consequently, we can build physically reasonable matter models for almost any spherically symmetric spacetime.
Modelling anisotropic fluid spheres in general relativity
Boonserm, Petarpa; Visser, Matt
2015-01-01
We argue that an arbitrary general relativistic anisotropic fluid sphere, (spherically symmetric but with transverse pressure not equal to radial pressure), can nevertheless be successfully modelled by suitable linear combinations of quite ordinary classical matter: an isotropic perfect fluid, a classical electromagnetic field, and a classical (minimally coupled) scalar field. While the most general decomposition is not unique, a preferred minimal decomposition can be constructed that is unique. We show how the classical energy conditions for the anisotropic fluid sphere can be related to energy conditions for the isotropic perfect fluid, electromagnetic field, and scalar field components of the model. Furthermore we show how this decomposition relates to the distribution of electric charge density and scalar charge density throughout the model that is used to mimic the anisotropic fluid sphere. Consequently, we can build physically reasonable matter models for almost any spherically symmetric spacetime.
Low Velocity Sphere Impact of a Soda Lime Silicate Glass
Andrew A Wereszczak; Ethan E Fox; Timothy G Morrissey; Daniel J Vuono
2011-01-01
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
Electromagnetically revolving sphere viscometer
NASA Astrophysics Data System (ADS)
Hosoda, Maiko; Sakai, Keiji
2014-12-01
In this paper, we propose a new method of low viscosity measurement, in which the rolling of a probe sphere on the flat solid bottom of a sample cell is driven remotely and the revolution speed of the probe in a sample liquid gives the viscosity measurements. The principle of this method is based on the electromagnetically spinning technique that we developed, and the method is effective especially for viscosity measurements at levels below 100 mPa·s with an accuracy higher than 1%. The probe motion is similar to that in the well-known rolling sphere (ball) method. However, our system enables a steady and continuous measurement of viscosity, which is problematic using the conventional method. We also discuss the limits of the measurable viscosity range common to rolling-sphere-type viscometers by considering the accelerating motion of a probe sphere due to gravity, and we demonstrate the performance of our methods.
Klotsa, Daphne; Hill, Richard J A; Bowley, Roger M; Swift, Michael R
2015-01-01
We describe experiments and simulations demonstrating the propulsion of a neutrally-buoyant swimmer that consists of a pair of spheres attached by a spring, 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.
NASA Astrophysics Data System (ADS)
Sun, Xiaochun
The armillary sphere was perhaps the most important type of astronomical instrument in ancient China. It was first invented by Luoxia Hong in the first century BC. After Han times, the structure of the armillary sphere became increasingly sophisticated by including more and more rings representing various celestial movements as recognized by the Chinese astronomers. By the eighth century, the Chinese armillary sphere consisted of three concentric sets of rings revolving on the south-north polar axis. The relative position of the rings could be adjusted to reflect the precession of the equinoxes and the regression of the Moon's nodes along the ecliptic. To counterbalance the defect caused by too many rings, Guo Shoujing from the late thirteenth century constructed the Simplified Instruments which reorganized the rings of the armillary sphere into separate instruments for measuring equatorial coordinates and horizontal coordinates. The armillary sphere was still preserved because it was a good illustration of celestial movements. A fifteenth-century replica of Guo Shoujing's armillary sphere still exists today.
Electron Flow in Low-Density Argon Gas Including Space-Charge and Elastic Collisions
Charles M. Goldstein
1967-01-01
The characteristics of one-dimensional electron diode with low-pressure argon scattering gas are analyzed by a Monte Carlo method. Experimentally determined differential elastic scattering cross sections, extra-polated to zero energy, are employed. Current-voltage characteristics are compared with those obtained from a hard-sphere collision model. Negative resistance is found for low emission current densities and low pressure as a result of the
Falconer, J.W.; Nazarov, W. (Department of Chemistry, University of Dundee, Dundee DD1 4HN (United Kingdom)); Horsfield, C.J.; Sutton, D.W.; Rothman, S.D.; Freeman, N.J. (Atomic Weapons Establishment PLC, Aldermaston, Reading RG7 4PR (United Kingdom))
1994-09-01
Hollow cylindrical fusion targets of 200--300 [mu]m diam and 500--600 [mu]m length, were fabricated and fitted at one end with a metallic ablator plate. The cylinders were then filled with a solution of polyfunctional acrylate monomer, which was subsequently polymerized to a gel using ultraviolet initiated polymerization. Either one or two aluminum spheres of diameter between 10 and 30 [mu]m were placed in the gel at defined locations, before the gel was precipitated to give, on drying by critical point dryer, a foam of the required density (about 100 mg cm[sup [minus]3]). The final targets had the sphere or spheres embedded in the foam at specified locations. Several techniques for placing the spheres were examined and the relative merits of the techniques are discussed.
Conformally symmetric radiating spheres in general relativity
Esculpi, M.; Herrera, L.
1986-08-01
A method used to study the evolution of radiating anisotropic (principal stresses unequal) spheres is applied to the case in which the space-time (within the sphere) admits a one-parameter group of conformal motions. Two different kind of models are obtained, depending on the equation of state for the stresses. In one case the energy flux density at the boundary of the sphere (the luminosity) should be given as a function of the timelike coordinate in order to integrate the system of equations. In the other case the luminosity is inferred from the equation of state for the stresses. Both models are integrated numerically and their eventual applications to some astrophysical problems are discussed.
NASA Astrophysics Data System (ADS)
Gurin, Péter; Varga, Szabolcs
2013-12-01
The effect of confinement is studied on the local structure of two- and three-dimensional hard-core fluids. The hard disks are confined between two parallel lines, while the hard spheres are in a cylindrical hard pore. In both cases only nearest neighbour interactions are allowed between the particles. The vertical and longitudinal pair correlation functions are determined by means of the exact transfer-matrix method. The vertical pair correlation function indicates that the wall induced packing constraint gives rise to a zigzag (up-down sequence) shaped close packing structure in both two- and three-dimensional systems. The longitudinal pair correlation function shows that both systems transform continuously from a one-dimensional gas-like behaviour to a zigzag solid-like structure with increasing density.
René Gergs; Jonathan Grey; Karl-Otto Rothhaupt
Invasive species often influence existing biocenoses by altering their environment or facilitating the ecology of other species.\\u000a Here we combined stable isotope analysis with quantitative benthic community sampling to investigate temporal variation in\\u000a the influence of biodeposition of organic material (biodeposits) by the zebra mussel (Dreissena polymorpha) on the benthic food web in hard substrate habitats of Lake Constance, Germany.
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.
Amphiphilic hard body mixtures Matthias Schmidt and Christian von Ferber
Ott, Albrecht
Amphiphilic hard body mixtures Matthias Schmidt and Christian von Ferber Institut fuÂ¨r Theoretische Received 16 June 2001; published 29 October 2001 In order to study ternary amphiphilic mixtures, we and amphiphilic particles, where the hydrophilic head is modeled as a hard sphere and the hydrophobic tail
Porosity and specific surface for interpenetrable-sphere models of two-phase random media
Rikvold, P.A.; Stell, G.
1985-01-15
We derive and numerically evaluate expressions for the porosity (matrix volume fraction) phi and the specific surface (interface area per unit volume) s for two specific models of a random two-phase medium in which the medium is considered as a suspension of interpenetrable spheres of radius R, embedded in a uniform matrix. The models and quantities considered have applications to a wide range of problems concerning transport, mechanical, and chemical properties of composite media. Both models contain a continuously variable hardness parameter epsilon-c, such that for epsilon-c = 1 they reduce to mutually impenetrable spheres, and for epsilon-c = 0 they reduce to fully penetrable spheres. The first of these models, the permeable-sphere model, has been defined only in the context of the Percus--Yevick approximation, which yields for it a unique pair distribution function g/sub 2/(r/sub 1/, r/sub 2/). To find the associated g/sub n/(r/sub 1/,...,r/sub n/) for n>2, which are needed to evaluate phi and s we use the generalized superposition approximation. The second model, the concentric-shell model, can be fully defined without recourse to any particular approximation and proves to be isomorphic to the picture described by the scaled-particle theory of Reiss, Frisch, and Lebowitz. In this case we evaluate phi and s in the scaled-particle approximation introduced by those authors to implement the scaled-particle theory. For both models, we present numerical plots of phi vs dimensionless density, and of s vs phi. We also briefly discuss the relations between the results obtained in the two cases.
Entanglement entropy for odd spheres
J. S. Dowker
2010-12-07
It is shown, non--rigorously, that the effective action on a Z_q factored odd spheres (lune) has a vanishing derivative at q=1. This leaves the effective action on the ordinary odd d-sphere as (minus) the value of the entanglement entropy associated with a (d-2)-sphere. Some numbers are given.
Hard sphere fluids in random fiber networks Matthias Schmidta)
Ott, Albrecht
for the partition coefficient agree well with existing data. Â© 2003 American Institute of Physics. DOI: 10 those of the same substance in bulk.1 Among the wide range of disordered adsorbents one particular class20 see Ref. 21 for brief personal recollections . This solution rules the adsorp- tion probability
Simulation of the hard-sphere crystal–melt interface
Davidchack, Ruslan L.; Laird, Brian Bostian
1998-06-01
profile is used to determine the nonuniform coarse-scale bins. ~b! Temperature: The temperature profile is defined as T ~ z!5 m 3kB 1 Lx LyDzr~z! K(i51 Nz vi 2 L , ~5! where v i is the velocity of a particle between z 2Dz/2 and z1Dz/2 at time t , m... in the article. Reuse of AIP content is sub 129.237.46.100 On: Tue,This corresponds to about 0.4 ns for a simple fluid such as argon. The interfacial diagnostics were recorded every 200 cpp. Initially the total pressure in the systems was approxi- mately 11.7k...
Equation of state and sound velocity of hadronic gas with hard-core interaction
L. M. Satarov; K. A. Bugaev; I. N. Mishustin
2014-11-04
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 pions, nucleons and delta resonances. 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 superluminal sound velocities appear only at very high densities, in the region where the deconfinement effects should be already important.
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.
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.
NASA Astrophysics Data System (ADS)
Nor, Mohd. Fazrul Hisyam Mohd.; Othman, Hafidzah; Abidin, Abd. Rashid Zainal
2009-07-01
This paper presents the density measurement of tridecane by using hydrostatic weighing system, which is currently practised in Density Laboratory of National Metrology Laboratory (NML), SIRIM Berhad. This system weighed the crystal sphere while the crystal sphere was immersed in the tridecane. The volume and mass in air of the crystal sphere were calibrated at KRISS, Korea. The uncertainties of volume and mass in air of the crystal sphere were 4 ppm and 0.3 ppm respectively.
Density Fluctuations in an Electrolyte from Generalized Debye-Hückel Theory
Benjamin P. Lee; Michael E. Fisher
1996-01-01
Near-critical thermodynamics in the hard-sphere (1,1) electrolyte is well\\u000adescribed, at a classical level, by Debye-Hueckel (DH) theory with (+,-) ion\\u000apairing and dipolar-pair-ionic-fluid coupling. But DH-based theories do not\\u000aaddress density fluctuations. Here density correlations are obtained by\\u000afunctional differentiation of DH theory generalized to {\\\\it non}-uniform\\u000adensities of various species. The correlation length $\\\\xi$ diverges universally\\u000aat low
NASA Astrophysics Data System (ADS)
Greenwood, J. A.
1997-06-01
Bradley (1932) showed that if two rigid spheres of radii R1 and R2 are placed in contact, they will adhere with a force 2? R? ? , where R is the equivalent radius R1R2/(R1 + R2) and ? ? is the surface energy or 'work of adhesion' (equal to ? 1 + ? 2 - ? 12). Subsequently Johnson et al. (1971) (JKR theory) showed by a Griffith energy argument (assuming that contact over a circle of radius a introduces a surface energy -? a2? ? ) how the Hertz equations for the contact of elastic spheres are modifed by surface energy, and showed that the force needed to separate the spheres is equal to (3/2)? R? ? , which is independent of the elastic modulus and so appears to be universally applicable and therefore to conflict with Bradley's answer. The discrepancy was explained by Tabor (1977), who identified a parameter ? equiv R1/3? ? 2/3/E* 2/3? governing the transition from the Bradley pull-off force 2? R? ? to the JKR value (3/2)? R? ? . Subsequently Muller et al. (1980) performed a complete numerical solution in terms of surface forces rather than surface energy, (combining the Lennard-Jones law of force between surfaces with the elastic equations for a half-space), and confirmed that Tabor's parameter does indeed govern the transition. The numerical solution is repeated more accurately and in greater detail, confirming the results, but showing also that the load-approach curves become S-shaped for values of ? greater than one, leading to jumps into and out of contact. The JKR equations describe the behaviour well for values of ? of 3 or more, but for low values of ? the simple Bradley equation better describes the behaviour under negative loads.
NASA Astrophysics Data System (ADS)
De Nardis, J.; Caux, J.-S.
2014-12-01
We apply the logic of the quench action to give an exact analytical expression for the time evolution of the one-body density matrix after an interaction quench in the Lieb–Liniger model from the ground state of the free theory (BEC state) to the infinitely repulsive regime. In this limit there exists a mapping between the bosonic wavefuntions and the free fermionic ones but this does not help the computation of the one-body density matrix which is sensitive to particle statistics. The final expression, given in terms of the difference of two Fredholm Pfaffians, can be numerically evaluated and is valid in the thermodynamic limit and for all times after the quench.
Samuel A. Eastwood; David M. Paganin; Timothy C. Petersen; Michael J. Morgan
2014-06-03
Caustics are optical phenomena which occur when a family of rays creates an envelope of divergent intensity. Here we show that caustic surfaces also appear when a real or complex field is mapped to its order parameter manifold. We study these structures in the context of spin-1/2 fields, where the order parameter manifold is the Bloch sphere. These generic structures are a manifestation of catastrophe theory and are stable with respect to perturbations. The corresponding field configurations are also stable and represent a new type of topological defect. Equations governing the conditions for their existence and unfolding are derived.
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.
Medial spheres for shape approximation.
Stolpner, Svetlana; Kry, Paul; Siddiqi, Kaleem
2012-06-01
We study the problem of approximating a 3D solid with a union of overlapping spheres. In comparison with a state-of-the-art approach, our method offers more than an order of magnitude speedup and achieves a tighter approximation in terms of volume difference with the original solid while using fewer spheres. The spheres generated by our method are internal and tangent to the solid's boundary, which permits an exact error analysis, fast updates under local feature size preserving deformation, and conservative dilation. We show that our dilated spheres offer superior time and error performance in approximate separation distance tests than the state-of-the-art method for sphere set approximation for the class of (?,?)-fat solids. We envision that our sphere-based approximation will also prove useful for a range of other applications, including shape matching and shape segmentation. PMID:22516653
NASA Astrophysics Data System (ADS)
Gillespie, Dirk
2014-11-01
Classical density functional theory (DFT) of fluids is a fast and efficient theory to compute the structure of the electrical double layer in the primitive model of ions where ions are modeled as charged, hard spheres in a background dielectric. While the hard-core repulsive component of this ion-ion interaction can be accurately computed using well-established DFTs, the electrostatic component is less accurate. Moreover, many electrostatic functionals fail to satisfy a basic theorem, the contact density theorem, that relates the bulk pressure, surface charge, and ion densities at their distances of closest approach for ions in equilibrium at a smooth, hard, planar wall. One popular electrostatic functional that fails to satisfy the contact density theorem is a perturbation approach developed by Kierlik and Rosinberg [Phys. Rev. A 44, 5025 (1991), 10.1103/PhysRevA.44.5025] and Rosenfeld [J. Chem. Phys. 98, 8126 (1993), 10.1063/1.464569], where the full free-energy functional is Taylor-expanded around a bulk (homogeneous) reference fluid. Here, it is shown that this functional fails to satisfy the contact density theorem because it also fails to satisfy the known low-density limit. When the functional is corrected to satisfy this limit, a corrected bulk pressure is derived and it is shown that with this pressure both the contact density theorem and the Gibbs adsorption theorem are satisfied.
Panoramic stereo sphere vision
NASA Astrophysics Data System (ADS)
Feng, Weijia; Zhang, Baofeng; Röning, Juha; Zong, Xiaoning; Yi, Tian
2013-01-01
Conventional stereo vision systems have a small field of view (FOV) which limits their usefulness for certain applications. While panorama vision is able to "see" in all directions of the observation space, scene depth information is missed because of the mapping from 3D reference coordinates to 2D panoramic image. In this paper, we present an innovative vision system which builds by a special combined fish-eye lenses module, and is capable of producing 3D coordinate information from the whole global observation space and acquiring no blind area 360°×360° panoramic image simultaneously just using single vision equipment with one time static shooting. It is called Panoramic Stereo Sphere Vision (PSSV). We proposed the geometric model, mathematic model and parameters calibration method in this paper. Specifically, video surveillance, robotic autonomous navigation, virtual reality, driving assistance, multiple maneuvering target tracking, automatic mapping of environments and attitude estimation are some of the applications which will benefit from PSSV.
Yoshifumi Kimura; Hisashi Okamoto
1987-01-01
The theory of the vortex motion of two-dimensional incompressible inviscid flow on a sphere is presented. Vorticity and stream function, which are related by the Laplace-Beltrami operator, are initially outlined. Green's function of the equation is obtained in which the stream function is expressed as integral form. The equations of motion for two vortex models on a sphere are derived.
NSDL National Science Digital Library
Amber Thibedeau
2012-07-25
This WebQuest is designed for 6th grade students. Students will work individually or in pairs to explore interactive websites and answer the questions on their Task Sheet. This is designed as an introduction to Earth's spheres (Hydrosphere, Atmosphere, Cryosphere, Biosphere, Geosphere) and how these spheres interact to support life on our planet.
Curvelet transform on the sphere
Pierrick Abrial; Jean-luc Starck; Yassir Moudden; Mai K. Nguyen
2005-01-01
Spherical maps occur in a range of applications for instance in geophysics or in astrophysics with the study of the cosmic microwave background (CMB) radiation field, where observations are over the whole sky. Analyzing these images requires specific tools. This paper describes a new multiscale decomposition for data on the sphere, namely the curvelet transform on the sphere. The curvelet
Thermodynamics and phase behavior of a triangle-well model and density-dependent variety
NASA Astrophysics Data System (ADS)
Zhou, Shiqi
2009-01-01
A hard sphere+triangle-well potential is employed to test a recently proposed thermodynamic perturbation theory (TPT) based on a coupling parameter expansion. It is found that the second-order term of the coupling parameter expansion surpasses by far that of a high temperature series expansion under a macroscopic compressibility approximation and several varieties. It is also found that the fifth-order version displays best among all of the numerically accessible versions with dissimilar truncation orders. Particularly, the superiority of the fifth-order TPT from other available liquid state theories is exhibited the most incisively when the temperature of interest obviously falls. We investigate the modification of the phase behavior of the hard sphere+triangle-well fluid resulting from a density dependence imposed on the original potential function. It is shown that (1) the density dependence induces polymorphism of fluid phase, particularly liquid-liquid transition in metastable supercooled region, and (2) along with enhanced decaying of the potential function as a function of bulk density, both the liquid-liquid transition and vapor-liquid transition tend to be situated at the domain of lower temperature, somewhat similar to a previously disclosed thumb rule that the fluid phase transition tends to metastable with respect to the fluid-solid transition as the range of the attraction part of a density-independence potential is sufficiently short compared to the range of the repulsion part of the same density-independence potential.
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.
Epitaxial frustration in deposited packings of rigid disks and spheres
NASA Astrophysics Data System (ADS)
Lubachevsky, Boris D.; Stillinger, Frank H.
2004-10-01
We use numerical simulation to investigate and analyze the way that rigid disks and spheres arrange themselves when compressed next to incommensurate substrates. For disks, a movable set is pressed into a jammed state against an ordered fixed line of larger disks, where the diameter ratio of movable to fixed disks is 0.8. The corresponding diameter ratio for the sphere simulations is 0.7, where the fixed substrate has the structure of a (001) plane of a face-centered cubic array. Results obtained for both disks and spheres exhibit various forms of density-reducing packing frustration next to the incommensurate substrate, including some cases displaying disorder that extends far from the substrate. The disk system calculations strongly suggest that the most efficient (highest-density) packings involve configurations that are periodic in the lateral direction parallel to the substrate, with substantial geometric disruption occurring only near the substrate. Some evidence has also emerged suggesting that for the sphere systems a corresponding structure doubly periodic in the lateral directions would yield the highest packing density; however, all of the sphere simulations completed thus far produced some residual “bulk” disorder not obviously resulting from substrate mismatch. In view of the fact that the cases studied here represent only a small subset of all that eventually deserve attention, we end with discussion of the directions in which first extensions of the present simulations might profitably be pursued.
Ability of nonperturbative density-functional theories to stabilize arbitrary solids
NASA Astrophysics Data System (ADS)
Kyrlidis, Agathagelos; Brown, Robert A.
1991-12-01
The effects of solid structure and interatomic potential are investigated for density-functional theories based on the definition of a weighted or effective density for approximating the solid phase in terms of the uniform liquid. The introduction of solidlike structure to the modified-weighted-density-approximation (MWDA) theory of Denton and Ashcroft [Phys. Rev. A 39, 4701 (1989)] leads to loss of existence of the weighted density for a system of hard spheres. This behavior is more pronounced for loose crystalline structures, such as the diamond lattice. By contrast, the generalized-effective-liquid-approximation theory (GELA) of Lutsko and Baus [Phys. Rev. A 41, 6647 (1990)] always predicts single-valued weighted densities in the cases studied here. The thermodynamic mapping, which is the core of both of the MWDA and GELA approximations, is ineffective for Lennard-Jones fluids, according to a criterion for the relative stability of the solid phase evaluated using liquid-state information.
Preliminary Health Assessment of Cultured Hard Clams,
Florida, University of
Preliminary Health Assessment of Cultured Hard Clams, Mercenaria mercenaria, in Florida Ruth for cultured hard clams in Floridaclams in Florida #12;Health Monitoring Program: SamplingSampling Â· 60 animals Density lease area Indian River Aquaculture Use Zone represent the majority of the clam production Sand
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.
Dyson Spheres around White Dwarfs
Semiz, ?brahim
2015-01-01
A Dyson Sphere is a hypothetical structure that an advanced civilization might build around a star to intercept all of the star's light for its energy needs. One usually thinks of it as a spherical shell about one astronomical unit (AU) in radius, and surrounding a more or less Sun-like star; and might be detectable as an infrared point source. We point out that Dyson Spheres could also be built around white dwarfs. This type would avoid the need for artificial gravity technology, in contrast to the AU-scale Dyson Spheres. In fact, we show that parameters can be found to build Dyson Spheres suitable --temperature- and gravity-wise-- for human habitation. This type would be much harder to detect.
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.
Analysis of principal nested spheres
Jung, Sungkyu; Dryden, Ian L.; Marron, J. S.
2012-01-01
Summary A general framework for a novel non-geodesic decomposition of high-dimensional spheres or high-dimensional shape spaces for planar landmarks is discussed. The decomposition, principal nested spheres, leads to a sequence of submanifolds with decreasing intrinsic dimensions, which can be interpreted as an analogue of principal component analysis. In a number of real datasets, an apparent one-dimensional mode of variation curving through more than one geodesic component is captured in the one-dimensional component of principal nested spheres. While analysis of principal nested spheres provides an intuitive and flexible decomposition of the high-dimensional sphere, an interesting special case of the analysis results in finding principal geodesics, similar to those from previous approaches to manifold principal component analysis. An adaptation of our method to Kendall’s shape space is discussed, and a computational algorithm for fitting principal nested spheres is proposed. The result provides a coordinate system to visualize the data structure and an intuitive summary of principal modes of variation, as exemplified by several datasets. PMID:23843669
NASA Astrophysics Data System (ADS)
Medasani, Bharat; Ovanesyan, Zaven; Thomas, Dennis G.; Sushko, Maria L.; Marucho, Marcelo
2014-05-01
In this article, we present a classical density functional theory for electrical double layers of spherical macroions that extends the capabilities of conventional approaches by accounting for electrostatic ion correlations, size asymmetry, and excluded volume effects. The approach is based on a recent approximation introduced by Hansen-Goos and Roth for the hard sphere excess free energy of inhomogeneous fluids [J. Chem. Phys. 124, 154506 (2006); Hansen-Goos and Roth, J. Phys.: Condens. Matter 18, 8413 (2006)]. It accounts for the proper and efficient description of the effects of ionic asymmetry and solvent excluded volume, especially at high ion concentrations and size asymmetry ratios including those observed in experimental studies. Additionally, we utilize a leading functional Taylor expansion approximation of the ion density profiles. In addition, we use the mean spherical approximation for multi-component charged hard sphere fluids to account for the electrostatic ion correlation effects. These approximations are implemented in our theoretical formulation into a suitable decomposition of the excess free energy which plays a key role in capturing the complex interplay between charge correlations and excluded volume effects. We perform Monte Carlo simulations in various scenarios to validate the proposed approach, obtaining a good compromise between accuracy and computational cost. We use the proposed computational approach to study the effects of ion size, ion size asymmetry, and solvent excluded volume on the ion profiles, integrated charge, mean electrostatic potential, and ionic coordination number around spherical macroions in various electrolyte mixtures. Our results show that both solvent hard sphere diameter and density play a dominant role in the distribution of ions around spherical macroions, mainly for experimental water molarity and size values where the counterion distribution is characterized by a tight binding to the macroion, similar to that predicted by the Stern model.
The gravitomagnetic field of a sphere, Gravity Probe B and the LAGEOS satellites
Jacob Biemond
2012-01-14
The gravitomagnetic field generated by a rotating sphere is usually calculated from the ideal dipole model. However, for a sphere with a homogeneous mass density, this model is not generally valid. Trying to obtain a more accurate value of the gravitomagnetic field inside and outside the sphere, series expansions for this field are presented in this paper. The calculated polar gravitomagnetic field of the sphere and that from the ideal dipole model appear to coincide, but the field in the vicinity of the sphere may deviate. The deduced field within the sphere strongly deviates from the ideal dipole result. As an illustration, the gravitomagnetic precession rate (or frame-dragging effect) of a gyroscope moving in the gravitomagnetic field from a large rotating sphere is calculated. For the Gravity Probe B experiment the result may coincide with the prediction from the ideal dipole model and in fair agreement with observations. In addition, the obtained Lense-Thirring precession rate for the LAGEOS satellites probably coincides with the standard prediction. For both experiments alternative predictions are calculated, when the gravitomagnetic field and the magnetic field from moving charge are equivalent. Theoretical and observational indications for such an equivalence are summarized. The obtained series expansions for the gravitomagnetic field of a sphere can also be applied to the calculation of the magnetic field, generated by a rotating sphere with a homogeneous charge density. Results for this case are also discussed.
Building materials with colloidal spheres
NASA Astrophysics Data System (ADS)
Manoharan, Vinothan N.
Three-dimensionally ordered composite materials with micrometer-scale periodic features can diffract visible light and, under certain conditions, can act as photonic band gap materials---the optical analogues of electronic semiconductors. Conventional methods for fabricating electronic materials are unsuitable for preparing three-dimensionally ordered structures, but colloidal self-assembly is a promising alternative approach. Monodisperse colloidal spheres are readily synthesized in the micrometer or sub-micrometer size range. The challenge in building materials from these particles lies in organizing the spheres and tailoring the material properties of the resulting composite structure. In the first part of this dissertation, I describe how packings of colloidal spheres can be used as templates to prepare structures that strongly diffract light. The densest arrangement of spheres in three dimensions is the face-centered cubic (FCC) packing, and a suspension of monodisperse colloidal spheres can form an FCC arrangement when concentrated. We use FCC packings of liquid emulsion droplets as templates to produce ordered porous titanium dioxide gels, which have high refractive index contrast and show broad minima in the transmission spectra at visible wavelengths. The emulsion templating method allows us to produce large monolithic porous samples that might be used in a variety of applications. However, we find that ordered templates with different symmetry than the FCC packing are necessary to prepare materials with photonic band gaps. In the second part of the dissertation I discuss how we might coax spherical particles to form crystal structures that differ from the FCC packing. Although the FCC arrangement is the only ordered packing observed in systems of many individual spheres, packings with different symmetries are possible in few-sphere systems. We find that when n colloidal microspheres are attached to the surfaces of liquid emulsion droplets, removing fluid from the droplets leads to packings of spheres that are unique and consistent at each n. These finite sphere packings, which range from sphere doublets, triangles, and tetrahedra to exotic polyhedra, might be used as new types of colloidal building blocks to prepare bulk materials with non-FCC symmetry.
M. Schmidt; M. Burgis; W. S. B. Dwandaru; G. Leithall; P. Hopkins
2012-12-27
An overview of several recent developments in density functional theory for classical inhomogeneous liquids is given. We show how Levy's constrained search method can be used to derive the variational principle that underlies density functional theory. An advantage of the method is that the Helmholtz free energy as a functional of a trial one-body density is given as an explicit expression, without reference to an external potential as is the case in the standard Mermin-Evans proof by reductio ad absurdum. We show how to generalize the approach in order to express the internal energy as a functional of the one-body density distribution and of the local entropy distribution. Here the local chemical potential and the bulk temperature play the role of Lagrange multipliers in the Euler-Lagrange equations for minimiziation of the functional. As an explicit approximation for the free-energy functional for hard sphere mixtures, the diagrammatic structure of Rosenfeld's fundamental measure density unctional is laid out. Recent extensions, based on the Kierlik-Rosinberg scalar weight functions, to binary and ternary non-additive hard sphere mixtures are described.
Thermoinertial bouncing of a relativistic collapsing sphere: A numerical model
Herrera, L.; Di Prisco, A.; Barreto, W. [Centro de Fisica Teorica y Computacional, Facultad de Ciencias, Universidad Central de Venezuela, Caracas (Venezuela); Centro de Fisica Fundamental, Facultad de Ciencias, Universidad de los Andes, Merida (Venezuela)
2006-01-15
We present a numerical model of a collapsing radiating sphere, whose boundary surface undergoes bouncing due to a decreasing of its inertial mass density (and, as expected from the equivalence principle, also of the 'gravitational' force term) produced by the 'inertial' term of the transport equation. This model exhibits for the first time the consequences of such an effect, and shows that under physically reasonable conditions this decreasing of the gravitational term in the dynamic equation may be large enough as to revert the collapse and produce a bouncing of the boundary surface of the sphere.
Role of bit patterned media in future of hard disk drives
Aravindakshan, Vibin
2007-01-01
The hard disk industry has traditionally stayed competitive by competing on the means of price alone by cutting down aggressively on cost via increase of areal density. Continuing increases in the areal density of hard ...
Integrability vs non-integrability: Hard hexagons and hard squares compared
M. Assis; J. L. Jacobsen; I. Jensen; J-M. Maillard; B. M. McCoy
2014-06-21
In this paper we compare the integrable hard hexagon model with the non-integrable hard squares model by means of partition function roots and transfer matrix eigenvalues. We consider partition functions for toroidal, cylindrical, and free-free boundary conditions up to sizes $40\\times40$ and transfer matrices up to 30 sites. For all boundary conditions the hard squares roots are seen to lie in a bounded area of the complex fugacity plane along with the universal hard core line segment on the negative real fugacity axis. The density of roots on this line segment matches the derivative of the phase difference between the eigenvalues of largest (and equal) moduli and exhibits much greater structure than the corresponding density of hard hexagons. We also study the special point $z=-1$ of hard squares where all eigenvalues have unit modulus, and we give several conjectures for the value at $z=-1$ of the partition functions.
Lawrence R. Dodd; Doros N. Theodorou
1991-01-01
A general algorithm has been developed for the analytical determination of the volume and exposed surface area of a solid body formed by a collection of arbitrarily sized intersecting spheres and delimited by a set of arbitrarily directed planes. The algorithm is useful for analysing molecules represented as fused hard spheres, sections of such molecules, as well as void or
Boyer, Edmond
diameter(5y 6). Those experiments show an increase i n packing fraction f o r mixtures o f spheres. However various alloys, we have measured the packing fraction o f mixture o f s l i g h t l y d i f f e r e n on small samples o f -a\\ the mixture. The procedure was repeated u n t i l the composition was 50 % (number
Skin Stresses in an Inflated Sphere During Impact
NASA Technical Reports Server (NTRS)
Martin, E. Dale
1961-01-01
An analysis is made of the stresses in the skin of an inflated nonstretchable sphere during normal, nonrotating impact with a hard flat surface, assuming infinite modulus of elasticity in the skin and infinite propagation speed of stress waves. The analysis is further applied to the study of the inflated sphere landing vehicle containing a payload suspended at the center. Curves are presented showing the stress distributions during impact for cases corresponding to those calculated in previous reports in which the impact motion and payload landing performance capabilities of the landing vehicle have been studied. It is found, assuming the force from the payload-suspension cords to be distributed continuously on the skin, that is, neglecting stress concentrations,that the skin stresses along a meridian are reduced by the presence of the suspended payload during impact, but that the maximum values of skin stress normal to a meridian are little affected.
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.
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.
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.
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.
Model of hard spheroplatelets near a hard wall
A. Kapanowski; M. Abram
2014-06-16
A system of hard spheroplatelets near an impenetrable wall is studied in the low-density Onsager approximation. Spheroplatelets have optimal shape between rods and plates, and the direct transition from the isotropic to biaxial nematic phase is present. A simple local approximation for the one-particle distribution function is used. Analytical results for the surface tension and the entropy contributions are derived. The density and the order-parameter profiles near the wall are calculated. The preferred orientation of the short molecule axes is perpendicular to the wall. Biaxiality close to the wall can appear only if the phase is biaxial in the bulk.
Helical packings and phase transformations of soft spheres in cylinders
NASA Astrophysics Data System (ADS)
Lohr, M. A.; Alsayed, A. M.; Chen, B. G.; Zhang, Z.; Kamien, R. D.; Yodh, A. G.
2010-04-01
The phase behavior of helical packings of thermoresponsive microspheres inside glass capillaries is studied as a function of the volume fraction. Stable packings with long-range orientational order appear to evolve abruptly to disordered states as the particle volume fraction is reduced, consistent with recent hard-sphere simulations. We quantify this transition using correlations and susceptibilities of the orientational order parameter ?6 . The emergence of coexisting metastable packings, as well as coexisting ordered and disordered states, is also observed. These findings support the notion of phase-transition-like behavior in quasi-one-dimensional systems.
Chiral Structures of Thermoresponsive Soft Spheres in Hollow Cylinders
NASA Astrophysics Data System (ADS)
Lohr, Matthew A.; Alsayed, Ahmed; Zhang, Zexin; Yodh, Arjun G.
2009-03-01
We experimentally observe the formation of closely packed crystalline structures in hollow cylinders. The structures have varying degrees of chiral order. The systems are created from aqueous suspensions of thermoresponsive N-isopropylacrylamide (NIPA) microgel particles packed in micron-diameter glass capillaries. We categorize these structures according to classifications used by Erickson for tubular packings of hard spheres [1]. By varying the temperature-tunable diameter of these particles, the system's volume fraction is changed, permitting observations of the resilience of these structures and their melting transitions. Melting of these thermal crystalline structures is observed. [1] R. O. Erickson, Science 181 (1973) 705-716.
Data compression on the sphere
NASA Astrophysics Data System (ADS)
McEwen, J. D.; Wiaux, Y.; Eyers, D. M.
2011-07-01
Large data-sets defined on the sphere arise in many fields. In particular, recent and forthcoming observations of the anisotropies of the cosmic microwave background (CMB) made on the celestial sphere contain approximately three and fifty mega-pixels respectively. The compression of such data is therefore becoming increasingly important. We develop algorithms to compress data defined on the sphere. A Haar wavelet transform on the sphere is used as an energy compression stage to reduce the entropy of the data, followed by Huffman and run-length encoding stages. Lossless and lossy compression algorithms are developed. We evaluate compression performance on simulated CMB data, Earth topography data and environmental illumination maps used in computer graphics. The CMB data can be compressed to approximately 40% of its original size for essentially no loss to the cosmological information content of the data, and to approximately 20% if a small cosmological information loss is tolerated. For the topographic and illumination data compression ratios of approximately 40:1 can be achieved when a small degradation in quality is allowed. We make our SZIP program that implements these compression algorithms available publicly.
Symmetries of Spheres Siddhartha Gadgil
Gadgil, Siddhartha
the case when n = 3 and T has no fixed points. #12;' & $ % The Poincar´e-Hopf theorem: · Water flowing smoothly on a sphere must be stationary at some point. · This is not so for water flowing on a torus · On the torus, we can find two tangent vector fields of unit length that are perpendicular everywhere
Virial coefficients and equation of state of hard chain molecules
NASA Astrophysics Data System (ADS)
Boublík, Tomáš
2003-10-01
The second, third, and fourth virial coefficients of hard chain molecules with number of segments up to 10 (up to 7 in the case of the fourth one) and the reduced distances L*=1 and 0.5 were determined numerically. For fused hard sphere (FHS) molecules the enlarged fused hard sphere model is introduced which forms a connection to the hard convex geometry and makes it possible to determine the virial coefficients of FHS molecules from the expressions derived for hard convex bodies. Our numerical values of the virial coefficients together with data from literature are used to test the proposed method and to compare its results with values from Wertheim's theory, from its modified version and from the generalized Flory dimer approach. It is found that prediction of the second virial coefficient is very accurate (for L=0.5 the maximum deviation amounts 0.2 percent) and that our values of the third virial coefficient for higher members of the FHS family are superior to those from other considered methods. The model is successfully used to predict geometric characteristics of the hard models of n-butane conformers and to estimate their second virial coefficients. The equation of state of hard prolate spherocylinders in which the nonsphericity parameters of the enlarged FHS model are considered is used to predict the P-V-T behavior of hard dumbbells, hard triatomics, mixture of hard dumbells of different site-site distances, and n-butane taken as a mixture of conformers. In all the cases prediction within error bars is obtained.
Equilibration and aging of dense soft-sphere glass-forming liquids
NASA Astrophysics Data System (ADS)
Sánchez-Díaz, Luis Enrique; Ramírez-González, Pedro; Medina-Noyola, Magdaleno
2013-05-01
The recently developed nonequilibrium extension of the self-consistent generalized Langevin equation theory of irreversible relaxation [Ramírez-González and Medina-Noyola, Phys. Rev. E10.1103/PhysRevE.82.061503 82, 061503 (2010); Ramírez-González and Medina-Noyola, Phys. Rev. E10.1103/PhysRevE.82.061504 82, 061504 (2010)] is applied to the description of the irreversible process of equilibration and aging of a glass-forming soft-sphere liquid that follows a sudden temperature quench, within the constraint that the local mean particle density remains uniform and constant. For these particular conditions, this theory describes the nonequilibrium evolution of the static structure factor S(k;t) and of the dynamic properties, such as the self-intermediate scattering function FS(k,?;t), where ? is the correlation delay time and t is the evolution or waiting time after the quench. Specific predictions are presented for the deepest quench (to zero temperature). The predicted evolution of the ?-relaxation time ??(t) as a function of t allows us to define the equilibration time teq(?), as the time after which ??(t) has attained its equilibrium value ??eq(?). It is predicted that both, teq(?) and ??eq(?), diverge as ???(a), where ?(a) is the hard-sphere dynamic-arrest volume fraction ?(a)(?0.582), thus suggesting that the measurement of equilibrium properties at and above ?(a) is experimentally impossible. The theory also predicts that for fixed finite waiting times t, the plot of ??(t;?) as a function of ? exhibits two regimes, corresponding to samples that have fully equilibrated within this waiting time (???(c)(t)), and to samples for which equilibration is not yet complete (???(c)(t)). The crossover volume fraction ?(c)(t) increases with t but saturates to the value ?(a).
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.
Eddy currents in a conducting sphere
NASA Technical Reports Server (NTRS)
Bergman, John; Hestenes, David
1986-01-01
This report analyzes the eddy current induced in a solid conducting sphere by a sinusoidal current in a circular loop. Analytical expressions for the eddy currents are derived as a power series in the vectorial displacement of the center of the sphere from the axis of the loop. These are used for first order calculations of the power dissipated in the sphere and the force and torque exerted on the sphere by the electromagnetic field of the loop.
Rockwell Hardness Measurement of
Colton, Jonathan S.
960-5 Rockwell Hardness Measurement of Metallic Materials Samuel R. Low NISTrecommended p r a c t i c e g u i d e Special Publication 960-5 #12;i Rockwell Hardness Measurement of Metallic Materials: (202) 512Â2250 Mail: Stop SSOP, Washington, DC 20402-0001 #12;N FOREWORD The Rockwell hardness test
Benmei, Chen
- widths ever higher as higher frequency disturbances become relevant. THE BOOK Hard Disk Drive Servo examples. In chapters 25 of Hard Disk Drive Servo Systems it is easy to forget that one is reading a book about disk drive control rather than a book on general control theory. Hard Disk Drive Servo Systems
Virial series for fluids of hard hyperspheres in odd dimensions
Rene D. Rohrmann; Miguel Robles; Mariano Lopez de Haro; Andres Santos
2008-04-29
A recently derived method [R. D. Rohrmann and A. Santos, Phys. Rev. E. {\\bf 76}, 051202 (2007)] to obtain the exact solution of the Percus-Yevick equation for a fluid of hard spheres in (odd) $d$ dimensions is used to investigate the convergence properties of the resulting virial series. This is done both for the virial and compressibility routes, in which the virial coefficients $B_j$ are expressed in terms of the solution of a set of $(d-1)/2$ coupled algebraic equations which become nonlinear for $d \\geq 5$. Results have been derived up to $d=13$. A confirmation of the alternating character of the series for $d\\geq 5$, due to the existence of a branch point on the negative real axis, is found and the radius of convergence is explicitly determined for each dimension. The resulting scaled density per dimension $2 \\eta^{1/d}$, where $\\eta$ is the packing fraction, is wholly consistent with the limiting value of 1 for $d \\to \\infty$. Finally, the values for $B_j$ predicted by the virial and compressibility routes in the Percus-Yevick approximation are compared with the known exact values [N. Clisby and B. M. McCoy, J. Stat. Phys. {\\bf 122}, 15 (2006)
Preparation and characterization of N-doped visible-light-responsive mesoporous TiO2 hollow spheres
NASA Astrophysics Data System (ADS)
Wu, Qiong; Li, Wei; Wang, Dianping; Liu, Shouxin
2014-04-01
Visible-light-responsive N-doped TiO2 mesoporous hollow spheres were prepared by acid-catalyzed hydrolysis, using carbon spheres obtained by glucose hydrothermal carbonization as a hard template. The spheres were characterized using scanning electron microscopy, transmission electron microscopy, N2 adsorption-desorption isotherms, X-ray diffraction, ultraviolet-visible diffuse reflectance spectroscopy, and X-ray photoelectron spectroscopy. The effects of the N content and calcination temperature on the morphology and photocatalytic activity of TiO2 were investigated. A visible-light response was obtained with TiO2 hollow spheres of diameter 700-850 nm, shell thickness 100 nm, and a bimodal mesoporosity concentrated at 4-6 and 12-14 nm. Phenol degradation of 79.6% was achieved using a catalyst consisting of TiO2 hollow spheres prepared with a Ti:N mass ratio of 1:0.5, and calcined at 600 °C.
González, A; White, J A; Román, F L; Velasco, S
2006-08-14
Two density functional theories, the fundamental measures theory of Rosenfeld [Phys. Rev. Lett. 63, 980 (1989)] and a subsequent approximation by Tarazona [Phys. Rev. Lett. 84, 694 (2000)] are applied to the study of the hard-sphere fluid in two situations: the cylindrical pore and the spherical cavity. The results are compared with those obtained with grand canonical ensemble Monte Carlo simulations. The differences between both theories are evaluated and interpreted in the terms of the dimensional crossover from three to one and zero dimensions. PMID:16942301
Conductance of packed spheres in vacuum
C. K. Chan; C. L. Tien
1973-01-01
An analytical study is presented for the heat transfer through the solid phase of a packed bed of spheres bounded by 2 infinite plane surfaces of different temperatures. The prediction of the conductance is based on the constriction resistance for spheres in contact. Both exact and approximate equations are derived for solid, hollow, and coated spheres and for several reqular
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.
Absolute Calibration Using the MSX Reference Spheres
NASA Astrophysics Data System (ADS)
Price, S. D.; Paxson, C.; Murdock, T. L.
2004-12-01
MSX conducted five absolute calibration experiments against emissive reference spheres between 25 August 1996 and 20 February 1997. The 2 cm diameter, T6061 Al spheres are coated with Martin Black. The thermal properties of the spheres are well known and their emissivities and reflectivities were accurately measured in the laboratory. The spheres were ejected at an elevation angle of 15 degrees above the MSX velocity vector in the orbital plane; the velocities were measured at the time of ejection. The geometric parameters of the spheres at the time of measurement were determined from orbital dynamics. The energy balance equation between the thermal input from the direct Sunlight, Sunlight reflected by the Earth and upwelling Earthshine and the total flux emitted by the sphere is solved to derive the instantaneous temperature of the sphere. The MSX in-band fluxes are then calculated from the blackbody at the temperature of the sphere predicted by the model modified by the wavelength dependent infrared emissivity at the distance of the sphere plus infrared Earthshine and Sunlight reflected by the sphere. The weighted results for the five spheres agree to within the uncertainties with the SPIRIT III responsivities determined from the absolute fluxes for infrared standard stars derived by Cohen et al. The MSX calibration against the reference spheres thus validate the absolute fluxes for the standard stars to <2%.
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,
An efficient algorithm for classical density functional theory in three dimensions: Ionic solutions
Knepley, Matthew G.; Karpeev, Dmitry A.; Davidovits, Seth; Eisenberg, Robert S.; Gillespie, Dirk
2010-01-01
Classical density functional theory (DFT) of fluids is a valuable tool to analyze inhomogeneous fluids. However, few numerical solution algorithms for three-dimensional systems exist. Here we present an efficient numerical scheme for fluids of charged, hard spheres that uses O(N log N) operations and O(N) memory, where N is the number of grid points. This system-size scaling is significant because of the very large N required for three-dimensional systems. The algorithm uses fast Fourier transforms (FFTs) to evaluate the convolutions of the DFT Euler–Lagrange equations and Picard (iterative substitution) iteration with line search to solve the equations. The pros and cons of this FFT?Picard technique are compared to those of alternative solution methods that use real-space integration of the convolutions instead of FFTs and Newton iteration instead of Picard. For the hard-sphere DFT, we use fundamental measure theory. For the electrostatic DFT, we present two algorithms. One is for the “bulk-fluid” functional of Rosenfeld [Y. Rosenfeld, J. Chem. Phys. 98, 8126 (1993)] that uses O(N log N) operations. The other is for the “reference fluid density” (RFD) functional [D. Gillespie et al., J. Phys.: Condens. Matter 14, 12129 (2002)]. This functional is significantly more accurate than the bulk-fluid functional, but the RFD algorithm requires O(N2) operations. PMID:20370108
Boyer, Edmond
particles are hollow glass spheres of mass density pd = 110 kg/m3 and radius rd = (32 Â± 2) Âµm or rd = (22Micro-Sphere Levitation in a Sheath of a Low Pressure Continuous Discharge C. Arnas, M. Mikikian
Dense Inclined Flows of Spheres
NASA Astrophysics Data System (ADS)
Jenkins, James
2006-11-01
We operate in the context of a slightly modified hydrodynamic theory for frictionless spheres and consider deep, dense flows down a bumpy incline. The modification is the introduction of a length other than the diameter in the expression for the rate of collisional dissipation. The idea is that the first influence of the formation of particle chains is felt by the rate of dissipation. The chain length is determined by a simple algebraic balance between the creation and destruction of chains. The resulting theory is used together with the boundary conditions at a bumpy base and a free surface to determine the profiles of volume fraction, mean velocity, and fluctuation energy for steady, fully-developed flows of identical spheres. The profiles exhibit the features seen in numerical simulations. The integration of the energy balance through the depth of the flow result in an improvement of a velocity scaling often employed in the interpretation of physical experiments.
Chen, Zhimin; Chen, Xin; Zheng, Linli; Gang, Tian; Cui, Tieyu; Zhang, Kai; Yang, Bai
2005-05-01
Ag midnanoparticles (midnanoparticles are those particles whose diameters are in the range from 20 to 80 nm) with average size of 30-50 nm and tunable packing densities were formed on the surface of preformed Tollens-soaked silica spheres by a simple and controlled method. The process mainly involved two steps. In the first step the absorption of Ag(NH3)2(+) ions occurred on the silica spheres and in the second step Ag(NH3)2(+) ions on the silica spheres were reduced to Ag midnanoparticles in the presence of glucose solution. The amount of Ag midnanoparticles on the silica spheres could easily be tuned by varying the washing times in the process of preparing the Tollens-soaked silica spheres. The washing process also effectively avoided the reduction of Ag(NH3)2(+) ions and the nucleation of Ag particles in solution and easily produced more uniform Ag midnanoparticles on the silica spheres. Attributing to the uniform Ag midnanoparticles, the Ag midnanoparticle-coated silica spheres show unique optical properties in the UV-vis absorption spectra. The resulting Ag midnanoparticle-coated silica spheres were characterized with transmission electron microscopy, UV-vis-IR recording spectrophotometry, and X-ray photoelectron spectroscopy. PMID:15797407
Collective excitations in soft-sphere fluids.
Bryk, Taras; Gorelli, Federico; Ruocco, Giancarlo; Santoro, Mario; Scopigno, Tullio
2014-10-01
Despite that the thermodynamic distinction between a liquid and the corresponding gas ceases to exist at the critical point, it has been recently shown that reminiscence of gaslike and liquidlike behavior can be identified in the supercritical fluid region, encoded in the behavior of hypersonic waves dispersion. By using a combination of molecular dynamics simulations and calculations within the approach of generalized collective modes, we provide an accurate determination of the dispersion of longitudinal and transverse collective excitations in soft-sphere fluids. Specifically, we address the decreasing rigidity upon density reduction along an isothermal line, showing that the positive sound dispersion, an excess of sound velocity over the hydrodynamic limit typical for dense liquids, displays a nonmonotonic density dependence strictly correlated to that of thermal diffusivity and kinematic viscosity. This allows rationalizing recent observation parting the supercritical state based on the Widom line, i.e., the extension of the coexistence line. Remarkably, we show here that the extremals of transport properties such as thermal diffusivity and kinematic viscosity provide a robust definition for the boundary between liquidlike and gaslike regions, even in those systems without a liquid-gas binodal line. Finally, we discuss these findings in comparison with recent results for Lennard-Jones model fluid and with the notion of the "rigid-nonrigid" fluid separation lines. PMID:25375488
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.
Patrinoiu, Greta; Calderón-Moreno, Jose Maria; Culita, Daniela C. [Illie Murgulescu Institute of Physical Chemistry, Romanian Academy, Splaiul Independentei 202, 060021 Bucharest (Romania); Birjega, Ruxandra [National Institute for Lasers, Plasma and Radiation Physics, P.O. Box Mg—27, Magurele, Bucharest (Romania); Ene, Ramona [Ilie Murgulescu Institute of Physical Chemistry, Romanian Academy, Splaiul Independentei 202, 060021 Bucharest (Romania); Carp, Oana, E-mail: ocarp@icf.ro [Ilie Murgulescu Institute of Physical Chemistry, Romanian Academy, Splaiul Independentei 202, 060021 Bucharest (Romania)
2013-06-15
A green template route for the synthesis of mesoscale solid ZnO spheres was ascertained. The protocol involves a double coating of the carbonaceous spheres with successive layers of zinc-containing species by alternating a non-ultrasound and ultrasound-assisted deposition, followed by calcination treatments. The composites were characterized by FTIR spectroscopy, thermal analysis, scanning electron microscopy while the obtained ZnO spheres by X-ray diffraction, Raman spectroscopy, scanning and transmission electron microscopy, N{sub 2} adsorption–desorption isotherms and photoluminescence investigations. A growth mechanism of the solid spheres is advanced based on these results. While the spheres' diameters and the mean size values of ZnO are independent on deposition order, the surface area and the external porosity are fairly dependent. The photoluminescence measurements showed interesting emission features, with emission bands in the violet to orange region. The spheres present high photocatalytical activity towards the degradation of phenol under UV irradiation, the main reaction being its mineralization. - Graphical abstract: A novel and eco-friendly methodology for the synthesis of mesoscale solid ZnO spheres was developed. The protocol involves a double coating of the starch-derived carbonaceous spheres with successive layers of zinc-containing species by alternating a non-ultrasound and ultrasound-assisted deposition, followed by calcination treatments. - Highlights: • ZnO solid spheres are obtained via a template route using carbonaceous spheres. • Two-step coatings of interchangeable order are used as deposition procedure. • The coating procedure influences the porosity and surface area. • ZnO spheres exhibited interesting visible photoluminescence properties. • Solid spheres showed photocatalytical activity in degradation of phenol.
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.
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.
The structure of quantum spheres
Sheu, Albert J.
2001-04-02
? K ( `2 ( Zn? )) ? B ( `2 ( Zn? )) via the faithful regular representation [R, MR] of C? (Hn) on `2 ( Zn? ) . On the other hand, ˜Gn| ˜Wn consists of (k, x, w) ? ˜Gn with wi =? for some i ? n and hence k = 0. So ˜Gn| ˜Wn = {0} × ˜Hn| ˜Wn and Gn...PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 129, Number 11, Pages 3307–3311 S 0002-9939(01)06042-7 Article electronically published on April 2, 2001 THE STRUCTURE OF QUANTUM SPHERES ALBERT JEU-LIANG SHEU (Communicated by David R. Larson...
Ultralow-Density Cementing Operations
Weldon Harms; David Sutton
1983-01-01
Attempts to improve ultralow-density cement slurries (9 to 12 lbm\\/gal (1078 to 1438 kg\\/cmÂ³)) suitable for oil and gas well cementing have accomplished little except to define a disappointingly low strength\\/density ratio and to confirm the low-density limit for useful compressive strengths. The use of high-strength hollow spheres as a lightweight additive has been under investigation for a number of
Sphere-Pac Evaluation for Transmutation
Icenhour, A.S.
2005-05-19
The U.S. Department of Energy Advanced Fuel Cycle Initiative (AFCI) is sponsoring a project at Oak Ridge National Laboratory with the objective of conducting the research and development necessary to evaluate the use of sphere-pac transmutation fuel. Sphere-pac fuels were studied extensively in the 1960s and 1970s. More recently, this fuel form is being studied internationally as a potential plutonium-burning fuel. For transmutation fuel, sphere-pac fuels have potential advantages over traditional pellet-type fuels. This report provides a review of development efforts related to the preparation of sphere-pac fuels and their irradiation tests. Based on the results of these tests, comparisons with pellet-type fuels are summarized, the advantages and disadvantages of using sphere-pac fuels are highlighted, and sphere-pac options for the AFCI are recommended. The Oak Ridge National Laboratory development activities are also outlined.
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.
Impingement of Water Droplets on a Sphere
NASA Technical Reports Server (NTRS)
Dorsch, Robert G.; Saper, Paul G.; Kadow, Charles F.
1955-01-01
Droplet trajectories about a sphere in ideal fluid flow were calculated. From the calculated droplet trajectories the droplet impingement characteristics of the sphere were determined. Impingement data and equations for determining the collection efficiency, the area, and the distribution of impingement are presented in terms of dimensionless parameters. The range of flight and atmospheric conditions covered in the calculations was extended considerably beyond the range covered by previously reported calculations for the sphere.
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.
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.
NASA Technical Reports Server (NTRS)
Hauser, D. L.; Buras, D. F.; Corbin, J. M.
1987-01-01
Rubber-hardness tester modified for use on rigid polyurethane foam. Provides objective basis for evaluation of improvements in foam manufacturing and inspection. Typical acceptance criterion requires minimum hardness reading of 80 on modified tester. With adequate correlation tests, modified tester used to measure indirectly tensile and compressive strengths of foam.
K. Terashi
2002-07-12
We present Run I results on hard diffraction obtained by the CDF Collaboration in proton-antiproton collisions at the Fermilab Tevatron. They are compared with results from the DESY ep collider HERA and/or theoretical predictions to test factorization in hard diffraction. In addition, the CDF program for diffractive studies in Run II is presented briefly.
Cugell, D.W. (Department of Medicine, Northwestern University Medical School, Chicago, IL (United States))
1992-06-01
Hard metal is a mixture of tungsten carbide and cobalt, to which small amounts of other metals may be added. It is widely used for industrial purposes whenever extreme hardness and high temperature resistance are needed, such as for cutting tools, oil well drilling bits, and jet engine exhaust ports. Cobalt is the component of hard metal that can be a health hazard. Respiratory diseases occur in workers exposed to cobalt--either in the production of hard metal, from machining hard metal parts, or from other sources. Adverse pulmonary reactions include asthma, hypersensitivity pneumonitis, and interstitial fibrosis. A peculiar, almost unique form of lung fibrosis, giant cell interstitial pneumonia, is closely linked with cobalt exposure.66 references.
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.).
Gravitational viscoelastic relaxation of eccentrically nested spheres
NASA Astrophysics Data System (ADS)
Martinec, Zden?k; Wolf, Detlef
1999-07-01
We present a semi-analytical solution to the 2-D forward modelling of viscoelastic relaxation in a heterogeneous model consisting of eccentrically nested spheres. Several numerical methods for 2-D and 3-D viscoelastic relaxation modelling have been applied recently, including finite-element and spectral-finite-difference schemes. The present semi-analytical approach provides a model response against which more general numerical algorithms can be validated. The eccentrically nested sphere solution has been tested by comparing it with the analytical solutions for viscoelastic relaxation in a homogeneous sphere and in two concentrically nested spheres, and good agreement was obtained.
On locally constructible spheres and balls
Bruno Benedetti; Günter M. Ziegler
2011-01-01
Durhuus and Jonsson (1995) introduced the class of “locally constructible” (LC) 3-spheres and showed that there are only exponentially\\u000a many combinatorial types of simplicial LC 3-spheres. Such upper bounds are crucial for the convergence of models for 3D quantum\\u000a gravity.\\u000a \\u000a \\u000a We characterize the LC property for d-spheres (“the sphere minus a facet collapses to a (d?2)-complex”) and for d-balls. In
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
Contact mechanics of rough spheres
NASA Astrophysics Data System (ADS)
Pastewka, Lars; Robbins, Mark
2013-03-01
We use large scale numerical calculations to study the contact mechanics of rough spheres on flat elastic solids. Such geometries are encountered in systems that range from ball bearings to atomic force microscope tips, but the influence of roughness is seldom considered explicitly. Our calculations show that the contact area A grows linearly with load N at small loads and crosses over to Hertzian behavior A N^2/3 at large loads. The total contact stiffness is defined as K = dN/dz where z is the normal displacement of the sphere. It shows power-law K N^? behavior at all loads with an exponent ? that is close to the value of 1/3 expected from Hertzian contact mechanics. The results are discussed in the context of recent theories for flat rough contacts [1] and Greenwood-Williams theory as modified for spherical contacts [2]. [4pt] [1] B.N.J. Persson, J. Chem. Phys. 115, 3840 (2001); S. Hyun, L. Pei, J.-F. Molinari, M.O. Robbins, Phys. Rev. E 70, 026117 (2004); S. Akarapu, T. Sharp, M.O. Robbins, Phys. Rev. Lett. 106, 204301 (2011) [0pt] [2] K.L. Johnson, Contact Mechanics, Cambridge University Press, 1987
Detecting dark energy with wavelets on the sphere
J. D. McEwen
2007-08-29
Dark energy dominates the energy density of our Universe, yet we know very little about its nature and origin. Although strong evidence in support of dark energy is provided by the cosmic microwave background, the relic radiation of the Big Bang, in conjunction with either observations of supernovae or of the large scale structure of the Universe, the verification of dark energy by independent physical phenomena is of considerable interest. We review works that, through a wavelet analysis on the sphere, independently verify the existence of dark energy by detecting the integrated Sachs-Wolfe effect. The effectiveness of a wavelet analysis on the sphere is demonstrated by the highly statistically significant detections of dark energy that are made. Moreover, the detection is used to constrain properties of dark energy. A coherent picture of dark energy is obtained, adding further support to the now well established cosmological concordance model that describes our Universe.
Giera, Brian; Henson, Neil; Kober, Edward M; Shell, M Scott; Squires, Todd M
2015-03-24
We evaluate the accuracy of local-density approximations (LDAs) using explicit molecular dynamics simulations of binary electrolytes comprised of equisized ions in an implicit solvent. The Bikerman LDA, which considers ions to occupy a lattice, poorly captures excluded volume interactions between primitive model ions. Instead, LDAs based on the Carnahan-Starling (CS) hard-sphere equation of state capture simulated values of ideal and excess chemical potential profiles extremely well, as well as the relationship between surface charge density and electrostatic potential. Excellent agreement between the EDL capacitances predicted by CS-LDAs and computed in molecular simulations is found even in systems where ion correlations drive strong density and free charge oscillations within the EDL, despite the inability of LDAs to capture the oscillations in the detailed EDL profiles. PMID:25723189
Ionic density distributions near the charged colloids: Spherical electric double layers
NASA Astrophysics Data System (ADS)
Kim, Eun-Young; Kim, Soon-Chul
2013-11-01
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.
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.
The statistical mechanics of inhomogeneous hard rod mixtures
Vanderlick, T.K.; Davis, H.T. (Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455 (USA)); Percus, J.K. (Courant Institute of Mathematics Sciences and Physics Department, New York University, New York, New York 10012 (USA))
1989-12-01
The exact statistical mechanical solution to the problem of an equilibrium inhomogeneous classical one-dimensional mixture of hard rods is presented. From the solution, thermodynamic properties, density profiles, and correlation functions of hard rod fluids confined to small regions (micropores) can be calculated. The theory is applied to investigate microstructure, pore pressures, and pore adsorption selectivity of micropores in equilibrium with binary hard rod mixtures. A prescription is suggested for generalizing the one-dimensional results to higher dimensions.
How do hard, regular tetrahedra pack?
Michael Engel; Amir Haji-Akbari; Aaron S. Keys; Xiaoyu Zheng; Rolfe G. Petschek; Peter Palffy-Muhoray; Sharon C. Glotzer
2010-01-01
We simulate a system of hard tetrahedra using Monte Carlo simulations and determine the density-pressure equation of state by compressing an initially disordered fluid. Depending on the speed of the compression, the system either jams or spontaneously orders to a quasicrystal. By compressing a crystalline approximant of the quasicrystal, the highest packing fraction we obtain is 0.8503. We show that
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
Hard Constraints in Optimization Under Uncertainty
NASA Technical Reports Server (NTRS)
Crespo, Luis G.; Giesy, Daniel P.; Kenny, Sean P.
2008-01-01
This paper proposes a methodology for the analysis and design of systems subject to parametric uncertainty where design requirements are specified via hard inequality constraints. Hard constraints are those that must be satisfied for all parameter realizations within a given uncertainty model. Uncertainty models given by norm-bounded perturbations from a nominal parameter value, i.e., hyper-spheres, and by sets of independently bounded uncertain variables, i.e., hyper-rectangles, are the focus of this paper. These models, which are also quite practical, allow for a rigorous mathematical treatment within the proposed framework. Hard constraint feasibility is determined by sizing the largest uncertainty set for which the design requirements are satisfied. Analytically verifiable assessments of robustness are attained by comparing this set with the actual uncertainty model. Strategies that enable the comparison of the robustness characteristics of competing design alternatives, the description and approximation of the robust design space, and the systematic search for designs with improved robustness are also proposed. Since the problem formulation is generic and the tools derived only require standard optimization algorithms for their implementation, this methodology is applicable to a broad range of engineering problems.
NASA Astrophysics Data System (ADS)
Zhang, Zewu; Zhou, Yuming; Zhang, Yiwei; Sheng, Xiaoli; Zhou, Shijian; Xiang, Sanming
2013-12-01
TiO2/carbon hollow composite spheres with mesoporous structure were successfully prepared by using a conventional hard template method but without an on-purpose etching process to remove the core material. A possible surface-protected dissolution mechanism was proposed to account for the spontaneous dissolution of the silica core. The thickness of carbon layer could be well controlled by adjusting the concentration of glucose in the hydrothermal reaction. Moreover, the as-prepared TiO2/C hollow spheres had remarkable light absorption in the visible region. As compared with the SiO2@TiO2 solid spheres prepared without the addition of glucose, the TiO2/C hollow spheres exhibited enhanced photocatalytic efficiency for the visible-light photodegradation of Rhodamine B.
Packing densification of binary mixtures of spheres and cubes subjected to 3D mechanical vibrations
NASA Astrophysics Data System (ADS)
An, X. Z.; He, S. S.; Feng, H. D.; Qian, Q.
2015-01-01
Packing densification of binary mixtures of spheres and cubes, which are large cubes/small spheres and large spheres/small cubes packing systems, under 3D vibrations was studied physically. The influences of vibration conditions such as vibration time, frequency, amplitude, vibration intensity, volume fraction of large particles, and container size on the packing densification were systematically analyzed, and the optimal processing parameters were identified. And the proposed analytical model was validated as well. The results show that the influences of each operating parameter on the packing densification of different binary mixtures have similar trends; however, the maximum packing densities and corresponding optimal parameters are different. The good agreement between physical and analytical results proves the effectiveness of the proposed analytical model. The results provide meaningful information and references for the random dense packings of binary mixtures of cubes and spheres both in industry and in scientific research.
NASA Astrophysics Data System (ADS)
Thapar, Vikram; Escobedo, Fernando A.
2014-01-01
The nucleation kinetics of the rotator phase in hard cuboctahedra, truncated octahedra, and rhombic dodecahedra is simulated via a combination of forward flux sampling and umbrella sampling. For comparable degrees of supersaturation, the polyhedra are found to have significantly lower free-energy barriers and faster nucleation rates than hard spheres. This difference primarily stems from localized orientational ordering, which steers polyhedral particles to pack more efficiently. Orientational order hence fosters here the growth of orientationally disordered nuclei.
Reissner-Nordstrom and charged gas spheres
Christian Fronsdal
2007-08-30
The main point of this paper is a suggestion about the proper treatment of the photon gas in a theory of stellar structure and other plasmas. This problem arises in the study of polytropic gas spheres, where we have already introduced some innovations. The main idea, already advanced in the contextof neutral, homogeneous, polytropic stellar models, is to base the theory firmly on a variational principle. Another essential novelty is to let mass distribution extend to infinity, the boundary between bulk and atmosphere being defined by an abrupt change in the polytropic index, triggered by the density. The logical next step in this program is to include the effect of radiation, which is a very significant complication since a full treatment would have to include an account of ionization, thus fieldsrepresenting electrons, ions, photons, gravitons and neutral atoms as well. In way of preparation, we consider models that are charged but homogeneous, involving only gravity, electromagnetism and a single scalar field that represents both the mass and the electric charge; in short, anon-neutral plasma. While this work only represents a stage in the development of a theory of stars, without direct application to physical systems, it does shed some light on the meaning of the Reissner-Nordstrom solution of the modified Einstein-Maxwell equations., with an application to a simple system.
Rastko Sknepnek; Silke Henkes
2014-07-31
Here we show that coupling to curvature has profound effects on collective motion in active systems, leading to patterns not observed in flat space. Biological examples of such active motion in curved environments are numerous: curvature and tissue folding are crucial during gastrulation, epithelial and endothelial cells move on constantly growing, curved crypts and vili in the gut, and the mammalian corneal epithelium grows in a steady-state vortex pattern. On the physics side, droplets coated with actively driven microtubule bundles show active nematic patterns. We study a model of self-propelled particles with polar alignment on a sphere. Hallmarks of these motion patterns are a polar vortex and a circulating band arising due to the incompatibility between spherical topology and uniform motion - a consequence of the hairy ball theorem. We present analytical results showing that frustration due to curvature leads to stable elastic distortions storing energy in the band.
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.
Black carbon measurements using an integrating sphere
R. Hitzenberger; U. Dusek; A. Berner
1996-01-01
An integrating sphere was used to determine the black carbon (BC) content of aerosol filter samples dissolved in chloroform (method originally described by Heintzenberg [1982]). The specific absorption coefficient Ba (equal to absorption per mass) of the samples was also measured using the sphere as an integrating detector for transmitted light. Comparing the Ba of ambient samples taken in Vienna,
Electric dipoles on the Bloch sphere
NASA Astrophysics Data System (ADS)
Vutha, Amar C.
2015-03-01
The time evolution of a two-level quantum mechanical system can be geometrically described using the Bloch sphere. By mapping the Bloch sphere evolution onto the dynamics of oscillating electric dipoles, we provide a physically intuitive link between classical electromagnetism and the electric dipole transitions of atomic and molecular physics.