Density functional for ternary non-additive hard sphere mixtures.
Schmidt, Matthias
2011-10-19
Based on fundamental measure theory, a Helmholtz free energy density functional for three-component mixtures of hard spheres with general, non-additive interaction distances is constructed. The functional constitutes a generalization of the previously given theory for binary non-additive mixtures. The diagrammatic structure of the spatial integrals in both functionals is of star-like (or tree-like) topology. The ternary diagrams possess a higher degree of complexity than the binary diagrams. Results for partial pair correlation functions, obtained via the Ornstein-Zernike route from the second functional derivatives of the excess free energy functional, agree well with Monte Carlo simulation data. PMID:21946780
Density Fluctuations of Hard-Sphere Fluids in Narrow Confinement
NASA Astrophysics Data System (ADS)
Nygârd, Kim; Sarman, Sten; Hyltegren, Kristin; Chodankar, Shirish; Perret, Edith; Buitenhuis, Johan; van der Veen, J. Friso; Kjellander, Roland
2016-01-01
Spatial confinement induces microscopic ordering of fluids, which in turn alters many of their dynamic and thermodynamic properties. However, the isothermal compressibility has hitherto been largely overlooked in the literature, despite its obvious connection to the underlying microscopic structure and density fluctuations in confined geometries. Here, we address this issue by probing density profiles and structure factors of hard-sphere fluids in various narrow slits, using x-ray scattering from colloid-filled nanofluidic containers and integral-equation-based statistical mechanics at the level of pair distributions for inhomogeneous fluids. Most importantly, we demonstrate that density fluctuations and isothermal compressibilities in confined fluids can be obtained experimentally from the long-wavelength limit of the structure factor, providing a formally exact and experimentally accessible connection between microscopic structure and macroscopic, thermodynamic properties. Our approach will thus, for example, allow direct experimental verification of theoretically predicted enhanced density fluctuations in liquids near solvophobic interfaces.
Density Functional Approximation for Non-Hard Sphere Fluids Subjected to External Fields
NASA Astrophysics Data System (ADS)
Zhou, Shiqi
A theoretical way is proposed, by which any hard sphere density functional approximation (DFA) can be applied to non-hard sphere fluids for the calculation of density profile in the framework of density functional theory (DFT). Used as examples, the present formalism is combined respectively with two recently proposed hard sphere DFAs to predict the density profile of Lennard-Jones (LJ) fluid, hard core square well (SW) fluid and penetrable potenial fluid subjected to diverse external fields. Extensive comparison between theoretical predictions and corresponding simulation results shows that the present theoretical way, when combined with an accurate hard sphere DFA, can perform well for calculating the density profile of the non-uniform fluids of the above mentioned potentials. Concretely speaking, for LJ and hard core SW fluid, even a less accurate FEDFA is sufficient, while for extreme potential such as the penetrable potenial, a more accurate adjustable parameter free version of LTDFA is needed to combine with the present theoretical way to predict density profile satisfactorily. The advantage of the proposed theoretical way is that the resultant DFA is applicable to both subcritical and supercritical temperature cases, thereby overcoming the disadvantages of previous two categories of DFT approach.
Equilibrium Sampling of Hard Spheres up to the Jamming Density and Beyond
NASA Astrophysics Data System (ADS)
Berthier, Ludovic; Coslovich, Daniele; Ninarello, Andrea; Ozawa, Misaki
2016-06-01
We implement and optimize a particle-swap Monte Carlo algorithm that allows us to thermalize a polydisperse system of hard spheres up to unprecedentedly large volume fractions, where previous algorithms and experiments fail to equilibrate. We show that no glass singularity intervenes before the jamming density, which we independently determine through two distinct nonequilibrium protocols. We demonstrate that equilibrium fluid and nonequilibrium jammed states can have the same density, showing that the jamming transition cannot be the end point of the fluid branch.
Equilibrium Sampling of Hard Spheres up to the Jamming Density and Beyond.
Berthier, Ludovic; Coslovich, Daniele; Ninarello, Andrea; Ozawa, Misaki
2016-06-10
We implement and optimize a particle-swap Monte Carlo algorithm that allows us to thermalize a polydisperse system of hard spheres up to unprecedentedly large volume fractions, where previous algorithms and experiments fail to equilibrate. We show that no glass singularity intervenes before the jamming density, which we independently determine through two distinct nonequilibrium protocols. We demonstrate that equilibrium fluid and nonequilibrium jammed states can have the same density, showing that the jamming transition cannot be the end point of the fluid branch. PMID:27341260
Density-functional theory of elastic moduli: Hard-sphere and Lennard-Jones crystals
NASA Astrophysics Data System (ADS)
Jarić, Marko V.; Mohanty, Udayan
1988-03-01
We propose a density-functional method for calculating elastic moduli of crystalline solids. The method is based on the second-order Ramakrishnan-Yussouff (RY) expansion of the variational grand-canonical potential around a uniform liquid state. The densities of the strained and unstrained crystal are represented as sums of narrow Gaussians. We express the crystal moduli in terms of the liquid structure factor its first and second derivatives evaluated at the reciprocal-lattice points of the crystal. We evaluate the elastic moduli for fcc hard-sphere and Lennard-Jones crystals using the Percus-Yevick and computer-simulation liquid structure factors, respectively. An indirect comparison with available experimental and theoretical values shows that although our calculated moduli are accurate to an order of magnitude, higher-order terms in the RY expansion might be significant. We find important contributions from density equilibration within the strained unit cell.
Shells of charge: a density functional theory for charged hard spheres
NASA Astrophysics Data System (ADS)
Roth, Roland; Gillespie, Dirk
2016-06-01
A functional for the electrostatic excess free-energy for charged, hard sphere fluids is proposed. The functional is derived from two complementary, but equivalent, interpretations of the mean spherical approximation (MSA). The first combines fundamental measure theory (FMT) from hard-core interactions with the idea that MSA can be interpreted in terms of the interaction spherical shells of charge. This formulation gives the free-energy density as a function of weighted densities. When all the ions have the same size, the functional adopts an FMT-like form. The second in effect ‘functionalizes’ the derivation of MSA; that is, it generalizes the MSA as a functional-based version of MSA (fMSA). This formulation defines the free-energy density as a function of a position-dependent MSA screening parameter and the weighted densities of the FMT approach. This FMT/fMSA functional is shown to give accurate density profiles, as compared to Monte Carlo simulations, under a wide range of ion concentrations, size asymmetries, and valences.
Shells of charge: a density functional theory for charged hard spheres.
Roth, Roland; Gillespie, Dirk
2016-06-22
A functional for the electrostatic excess free-energy for charged, hard sphere fluids is proposed. The functional is derived from two complementary, but equivalent, interpretations of the mean spherical approximation (MSA). The first combines fundamental measure theory (FMT) from hard-core interactions with the idea that MSA can be interpreted in terms of the interaction spherical shells of charge. This formulation gives the free-energy density as a function of weighted densities. When all the ions have the same size, the functional adopts an FMT-like form. The second in effect 'functionalizes' the derivation of MSA; that is, it generalizes the MSA as a functional-based version of MSA (fMSA). This formulation defines the free-energy density as a function of a position-dependent MSA screening parameter and the weighted densities of the FMT approach. This FMT/fMSA functional is shown to give accurate density profiles, as compared to Monte Carlo simulations, under a wide range of ion concentrations, size asymmetries, and valences. PMID:27116385
Communication: Dynamical density functional theory for dense suspensions of colloidal hard spheres
NASA Astrophysics Data System (ADS)
Stopper, Daniel; Roth, Roland; Hansen-Goos, Hendrik
2015-11-01
We study structural relaxation of colloidal hard spheres undergoing Brownian motion using dynamical density functional theory. Contrary to the partial linearization route [D. Stopper et al., Phys. Rev. E 92, 022151 (2015)] which amounts to using different free energy functionals for the self and distinct part of the van Hove function G(r, t), we put forward a unified description employing a single functional for both components. To this end, interactions within the self part are removed via the zero-dimensional limit of the functional with a quenched self component. In addition, we make use of a theoretical result for the long-time mobility in hard-sphere suspensions, which we adapt to the inhomogeneous fluid. Our results for G(r, t) are in excellent agreement with numerical simulations even in the dense liquid phase. In particular, our theory accurately yields the crossover from free diffusion at short times to the slower long-time diffusion in a crowded environment.
Free Energy Calculations of Crystalline Hard Sphere Complexes Using Density Functional Theory
Gunawardana, K. G.S.H.; Song, Xueyu
2014-12-22
Recently developed fundamental measure density functional theory (FMT) is used to study binary hard sphere (HS) complexes in crystalline phases. By comparing the excess free energy, pressure and phase diagram, we show that the fundamental measure functional yields good agreements to the available simulation results of AB, AB_{2} and AB_{13} crystals. Additionally, we use this functional to study the HS models of five binary crystals, Cu_{5}Zr(C15_{b}), Cu_{51}Zr_{14}(β), Cu_{10}Zr_{7}(φ), CuZr(B2) and CuZr_{2} (C11_{b}), which are observed in the Cu-Zr system. The FMT functional gives well behaved minimum for most of the hard sphere crystal complexes in the two dimensional Gaussian space, namely a crystalline phase. However, the current version of FMT functional (white Bear) fails to give a stable minimum for the structure Cu_{10}Zr_{7}(φ). We argue that the observed solid phases for the HS models of the Cu-Zr system are true thermodynamic stable phases and can be used as a reference system in perturbation calculations.
Free Energy Calculations of Crystalline Hard Sphere Complexes Using Density Functional Theory
Gunawardana, K. G.S.H.; Song, Xueyu
2014-12-22
Recently developed fundamental measure density functional theory (FMT) is used to study binary hard sphere (HS) complexes in crystalline phases. By comparing the excess free energy, pressure and phase diagram, we show that the fundamental measure functional yields good agreements to the available simulation results of AB, AB2 and AB13 crystals. Additionally, we use this functional to study the HS models of five binary crystals, Cu5Zr(C15b), Cu51Zr14(β), Cu10Zr7(φ), CuZr(B2) and CuZr2 (C11b), which are observed in the Cu-Zr system. The FMT functional gives well behaved minimum for most of the hard sphere crystal complexes in the two dimensional Gaussian space,more » namely a crystalline phase. However, the current version of FMT functional (white Bear) fails to give a stable minimum for the structure Cu10Zr7(φ). We argue that the observed solid phases for the HS models of the Cu-Zr system are true thermodynamic stable phases and can be used as a reference system in perturbation calculations.« less
How to Extend the Bridge Density Functional Approximation to the Confined Non-hard Sphere Fluid
NASA Astrophysics Data System (ADS)
Zhou, Shi-qi
2006-08-01
A theoretical method was proposed to extend a bridge density functional approximation (BDFA) for the non-uniform hard sphere fluid to the non-uniform Lennard-Jones (LJ) fluid. The DFT approach for LJ fluid is simple, quantitatively accurate in a wide range of coexistence phase and external field parameters. Especially, the DFT approach only needs a second order direct correlation function (DCF) of the coexistence bulk fluid as input, and is therefore applicable to the subcritical temperature region. The present theoretical method can be regarded as a non-uniform counterpart of the thermodynamic perturbation theory, in which it is not at the level of the free energy but at the level of the second order DCF.
Hard sphere packings within cylinders.
Fu, Lin; Steinhardt, William; Zhao, Hao; Socolar, Joshua E S; Charbonneau, Patrick
2016-02-23
Arrangements of identical hard spheres confined to a cylinder with hard walls have been used to model experimental systems, such as fullerenes in nanotubes and colloidal wire assembly. Finding the densest configurations, called close packings, of hard spheres of diameter σ in a cylinder of diameter D is a purely geometric problem that grows increasingly complex as D/σ increases, and little is thus known about the regime for D > 2.873σ. In this work, we extend the identification of close packings up to D = 4.00σ by adapting Torquato-Jiao's adaptive-shrinking-cell formulation and sequential-linear-programming (SLP) technique. We identify 17 new structures, almost all of them chiral. Beyond D ≈ 2.85σ, most of the structures consist of an outer shell and an inner core that compete for being close packed. In some cases, the shell adopts its own maximum density configuration, and the stacking of core spheres within it is quasiperiodic. In other cases, an interplay between the two components is observed, which may result in simple periodic structures. In yet other cases, the very distinction between the core and shell vanishes, resulting in more exotic packing geometries, including some that are three-dimensional extensions of structures obtained from packing hard disks in a circle. PMID:26843132
NASA Astrophysics Data System (ADS)
Stopper, Daniel; Marolt, Kevin; Roth, Roland; Hansen-Goos, Hendrik
2015-08-01
We study the dynamics of colloidal suspensions of hard spheres that are subject to Brownian motion in the overdamped limit. We obtain the time evolution of the self- and distinct parts of the van Hove function by means of dynamical density functional theory. The free-energy model for the hard-sphere fluid that we use is the very accurate White Bear II version of Rosenfeld's fundamental measure theory. However, in order to remove interactions within the self-part of the van Hove function, a nontrivial modification has to be applied to the free-energy functional. We compare our theoretical results with data that we obtain from dynamical Monte Carlo simulations, and we find that the latter are well described by our approach even for colloid packing fractions as large as 40%.
Stopper, Daniel; Marolt, Kevin; Roth, Roland; Hansen-Goos, Hendrik
2015-08-01
We study the dynamics of colloidal suspensions of hard spheres that are subject to Brownian motion in the overdamped limit. We obtain the time evolution of the self- and distinct parts of the van Hove function by means of dynamical density functional theory. The free-energy model for the hard-sphere fluid that we use is the very accurate White Bear II version of Rosenfeld's fundamental measure theory. However, in order to remove interactions within the self-part of the van Hove function, a nontrivial modification has to be applied to the free-energy functional. We compare our theoretical results with data that we obtain from dynamical Monte Carlo simulations, and we find that the latter are well described by our approach even for colloid packing fractions as large as 40%. PMID:26382387
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
Segregation of Fluidized Binary Hard-Sphere Systems Under Gravity
NASA Astrophysics Data System (ADS)
Kim, Soon-Chul
We have derived an analytic expression for the contact value of the local density of binary hard-sphere systems under gravity. We have obtained the crossover conditions for the Brazil-nut type segregation of binary hard-sphere mixtures and binary hard-sphere chain mixtures from the segregation criterion, where the segregation occurs when the density (or the pressure) of the small spheres at the bottom is higher than that of the large spheres, or vice versa. For the binary hard-sphere chain mixtures, the crossover condition for the segregation depends on the number of monomers composed of hard-sphere chains as well as the mass and the diameter of each species. The fundamental-measure theories (FMTs) and local density approximation (LDA) are employed to examine the crossover condition for the segregation of the gravity-induced hard-sphere mixtures. The calculated results show that the LDA does not explain the density oscillation near the bottom, whereas the modified fundamental-measure theory (MFMT) compares with molecular dynamics simulations.
Demixing in binary mixtures of apolar and dipolar hard spheres
NASA Astrophysics Data System (ADS)
Almarza, N. G.; Lomba, E.; Martín, C.; Gallardo, A.
2008-12-01
We study the demixing transition of mixtures of equal size hard spheres and dipolar hard spheres using computer simulation and integral equation theories. Calculations are carried out at constant pressure, and it is found that there is a strong correlation between the total density and the composition. The critical temperature and the critical total density are found to increase with pressure. The critical mole fraction of the dipolar component on the contrary decreases as pressure is augmented. These qualitative trends are reproduced by the theoretical approaches that on the other hand overestimate by far the value of the critical temperature. Interestingly, the critical parameters for the liquid-vapor equilibrium extrapolated from the mixture results in the limit of vanishing neutral hard sphere concentration agree rather well with recent estimates based on the extrapolation of charged hard dumbbell phase equilibria when dumbbell elongation shrinks to zero [G. Ganzenmüller and P. J. Camp, J. Chem. Phys. 126, 191104 (2007)].
Computational polymer physics: Hard-sphere chain in solvent systems
NASA Astrophysics Data System (ADS)
Gautam, Avinash; Gavazzi, Daniel; Taylor, Mark
2009-10-01
In this work we present results for chain conformation in two simple chain-in-solvent systems constructed from hard-sphere monomers of diameter D. The first system consists of a flexible chain of fused hard spheres (i.e., bond length L=D) in a monomeric hard-sphere solvent. The second system consists of a flexible tangent hard-sphere chain (L=D) in a dimeric hard-sphere solvent with L=D. These systems are studied using Monte Carlo simulations which employ both single-site crankshaft and multi-site pivot moves to sample the configuration space of the chain. We report chain structure, in terms of site-site probability functions, as a function of solvent density. In all cases, increasing solvent density leads to an overall compression of the chain. At high solvent density the chain conformation is closely coupled to the local solvent structure and we speculate that incommensurate structures may lead to interesting conformational transitions.
Geometrical characterization of hard-sphere systems.
Richard, P; Oger, L; Troadec, J P; Gervois, A
1999-10-01
By using molecular dynamics simulations on a large number of hard spheres and the Voronoï tessellation we characterize hard-sphere systems geometrically at any packing fraction eta along the different branches of the phase diagram. Crystallization of disordered packings occurs only for a small range of packing fraction. For the other packing fractions the system behaves as either a fluid (stable or metastable) or a glass. We have studied the evolution of the statistics of the Voronoï tessellation during crystallization and characterized the apparition of order by an order parameter (Q(6)) built from spherical harmonics. PMID:11970312
Sesé, Luis M; Bailey, Lorna E
2007-04-28
The structural features of the quantum hard-sphere system in the region of the fluid-face-centered-cubic-solid transition, for reduced number densities 0.45
Glass transition of dense fluids of hard and compressible spheres.
Berthier, Ludovic; Witten, Thomas A
2009-08-01
We use computer simulations to study the glass transition of dense fluids made of polydisperse repulsive spheres. For hard particles, we vary the volume fraction, phi , and use compressible particles to explore finite temperatures, T>0 . In the hard sphere limit, our dynamic data show evidence of an avoided mode-coupling singularity near phi(MCT) is approximately 0.592; they are consistent with a divergence of equilibrium relaxation times occurring at phi(0) is approximately 0.635, but they leave open the existence of a finite temperature singularity for compressible spheres at volume fraction phi>phi(0). Using direct measurements and a scaling procedure, we estimate the equilibrium equation of state for the hard sphere metastable fluid up to phi(0), where pressure remains finite, suggesting that phi(0) corresponds to an ideal glass transition. We use nonequilibrium protocols to explore glassy states above phi(0) and establish the existence of multiple equations of state for the unequilibrated glass of hard spheres, all diverging at different densities in the range phi in [0.642, 0.664]. Glassiness thus results in the existence of a continuum of densities where jamming transitions can occur. PMID:19792128
Thermodynamic properties of non-conformal soft-sphere fluids with effective hard-sphere diameters.
Rodríguez-López, Tonalli; del Río, Fernando
2012-01-28
In this work we study a set of soft-sphere systems characterised by a well-defined variation of their softness. These systems represent an extension of the repulsive Lennard-Jones potential widely used in statistical mechanics of fluids. This type of soft spheres is of interest because they represent quite accurately the effective intermolecular repulsion in fluid substances and also because they exhibit interesting properties. The thermodynamics of the soft-sphere fluids is obtained via an effective hard-sphere diameter approach that leads to a compact and accurate equation of state. The virial coefficients of soft spheres are shown to follow quite simple relationships that are incorporated into the equation of state. The approach followed exhibits the rescaling of the density that produces a unique equation for all systems and temperatures. The scaling is carried through to the level of the structure of the fluids. PMID:22158949
Prediction of binary hard-sphere crystal structures.
Filion, Laura; Dijkstra, Marjolein
2009-04-01
We present a method based on a combination of a genetic algorithm and Monte Carlo simulations to predict close-packed crystal structures in hard-core systems. We employ this method to predict the binary crystal structures in a mixture of large and small hard spheres with various stoichiometries and diameter ratios between 0.4 and 0.84. In addition to known binary hard-sphere crystal structures similar to NaCl and AlB2, we predict additional crystal structures with the symmetry of CrB, gammaCuTi, alphaIrV, HgBr2, AuTe2, Ag2Se, and various structures for which an atomic analog was not found. In order to determine the crystal structures at infinite pressures, we calculate the maximum packing density as a function of size ratio for the crystal structures predicted by our GA using a simulated annealing approach. PMID:19518387
Aging dynamics of colloidal hard sphere glasses.
Martinez, V A; Bryant, G; van Megen, W
2010-09-21
We report the results of dynamic light scattering measurements of the coherent intermediate scattering function (ISF) of glasses of colloidal hard spheres for several volume fractions and a range of scattering vectors around the primary peak of the static structure factor. The ISF shows a clear crossover from an initial fast decay to a slower nonstationary decay. Aging is quantified in several different ways. However, regardless of the method chosen, the perfect "aged" glass is approached in a power law fashion. In particular the coupling between the fast and slow decays, as measured by the degree of stretching of the ISF at the crossover, also decreases algebraically with waiting time. The nonstationarity of this coupling implies that even the fastest detectable processes are themselves nonstationary. PMID:20866156
Dynamics of heterogeneous hard spheres in a file
NASA Astrophysics Data System (ADS)
Flomenbom, Ophir
2010-09-01
Normal dynamics in a quasi-one-dimensional channel of length L (→∞) of N hard spheres are analyzed. The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W˜D-γ for small D , where 0≤γ<1 . The initial spheres’ density ρ is nonuniform and scales with the distance (from the origin) l as ρ˜l-α , 0≤α≤1 . An approximation for the N -particle PDF for this problem is derived. From this solution, scaling law analysis and numerical simulations, we show here that the mean square displacement for a particle in such a system obeys ⟨r2⟩˜t(1-γ)/(2c-γ) , where c=1/(1+α) . The PDF of the tagged particle is Gaussian in position. Generalizations of these results are considered.
NASA Astrophysics Data System (ADS)
Oyarzún, Bernardo; van Westen, Thijs; Vlugt, Thijs J. H.
2013-05-01
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.
Non-hard sphere thermodynamic perturbation theory
NASA Astrophysics Data System (ADS)
Zhou, Shiqi
2011-08-01
A non-hard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the non-HS perturbation scheme in a coupling parameter expansion (CPE) thermodynamic perturbation framework. NVT-Monte Carlo simulation is carried out for a generalized Lennard-Jones (LJ) 2n-n potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the non-HS CPE 3rd-order thermodynamic perturbation theory (TPT) and give a comparison between the non-HS CPE 3rd-order TPT and other theoretical approaches. It is indicated that the non-HS CPE 3rd-order TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)-equation of state and is at least comparable to several currently the most accurate Ornstein-Zernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of fex - ref, chiefly decide the quality of the non-HS CPE TPT. Considering that the non-HS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamic perturbation framework is amenable to high-order truncation, the non-HS CPE 3rd-order or higher order TPT will be more promising once the above-mentioned three technological advances are established.
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.
Dendritic Growth of Hard-Sphere Crystals. Experiment 34
NASA Technical Reports Server (NTRS)
Russel, W. B.; Chaikin, P. M.; Zhu, Ji-Xiang; Meyer, W. V.; Rogers, R.
1998-01-01
Recent observations of the disorder-order transition for colloidal hard spheres under microgravity revealed dendritic crystallites roughly 1-2 mm in size for samples in the coexistence region of the phase diagram. Order-of-magnitude estimates rationalize the absence of large or dendritic crystals under normal gravity and their stability to annealing in microgravity. A linear stability analysis of the Ackerson and Schaetzel model for crystallization of hard spheres establishes the domain of instability for diffusion-limited growth at small supersaturations. The relationship between hard-sphere and molecular crystal growth is established and exploited to relate the predicted linear instability to the well-developed dendrites observed.
Scaled particle theory for hard sphere pairs. I. Mathematical structure.
Stillinger, Frank H; Debenedetti, Pablo G; Chatterjee, Swaroop
2006-11-28
We develop an extension of the original Reiss-Frisch-Lebowitz scaled particle theory that can serve as a predictive method for the hard sphere pair correlation function g(r). The reversible cavity creation work is analyzed both for a single spherical cavity of arbitrary size, as well as for a pair of identical such spherical cavities with variable center-to-center separation. These quantities lead directly to a prediction of g(r). Smooth connection conditions have been identified between the small-cavity situation where the work can be exactly and completely expressed in terms of g(r), and the large-cavity regime where macroscopic properties become relevant. Closure conditions emerge which produce a nonlinear integral equation that must be satisfied by the pair correlation function. This integral equation has a structure which straightforwardly generates a solution that is a power series in density. The results of this series replicate the exact second and third virial coefficients for the hard sphere system via the contact value of the pair correlation function. The predicted fourth virial coefficient is approximately 0.6% lower than the known exact value. Detailed numerical analysis of the nonlinear integral equation has been deferred to the subsequent paper. PMID:17144712
Scaled particle theory for hard sphere pairs. I. Mathematical structure
NASA Astrophysics Data System (ADS)
Stillinger, Frank H.; Debenedetti, Pablo G.; Chatterjee, Swaroop
2006-11-01
We develop an extension of the original Reiss-Frisch-Lebowitz scaled particle theory that can serve as a predictive method for the hard sphere pair correlation function g(r ). The reversible cavity creation work is analyzed both for a single spherical cavity of arbitrary size, as well as for a pair of identical such spherical cavities with variable center-to-center separation. These quantities lead directly to a prediction of g(r ). Smooth connection conditions have been identified between the small-cavity situation where the work can be exactly and completely expressed in terms of g(r ), and the large-cavity regime where macroscopic properties become relevant. Closure conditions emerge which produce a nonlinear integral equation that must be satisfied by the pair correlation function. This integral equation has a structure which straightforwardly generates a solution that is a power series in density. The results of this series replicate the exact second and third virial coefficients for the hard sphere system via the contact value of the pair correlation function. The predicted fourth virial coefficient is approximately 0.6% lower than the known exact value. Detailed numerical analysis of the nonlinear integral equation has been deferred to the subsequent paper.
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
Freezing, melting and the glass transition in a suspension of hard spheres
NASA Astrophysics Data System (ADS)
van Megen, W.
2002-08-01
When a suspension of hard spheres traverses the freezing volume fraction we find discontinuous changes in the character of the tagged particle density. In particular, the velocity auto-correlation function develops a negative algebraic decay and the fluctuations become subject to interruption. From these, and the exponent of the algebraic growth of the non-Gaussian parameter, the difference in mode of relaxation of the density fluctuations between the stable and metastable colloidal fluids can be quantified. A diagrammatic scheme is proposed that reconciles the dynamics of phase transitions observed in hard-sphere colloids.
Local order variations in confined hard-sphere fluids
NASA Astrophysics Data System (ADS)
Nygârd, Kim; Sarman, Sten; Kjellander, Roland
2013-10-01
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.
Depletion effects in smectic phases of hard-rod-hard-sphere mixtures.
Martínez-Ratón, Y; Cinacchi, G; Velasco, E; Mederos, L
2006-10-01
It is known that when hard spheres are added to a pure system of hard rods the stability of the smectic phase may be greatly enhanced, and that this effect can be rationalised in terms of depletion forces. In the present paper we first study the effect of orientational order on depletion forces in this particular binary system, comparing our results with those obtained adopting the usual approximation of considering the rods parallel and their orientations frozen. We consider mixtures with rods of different aspect ratios and spheres of different diameters, and we treat them within Onsager theory. Our results indicate that depletion effects, and consequently smectic stability, decrease significantly as a result of orientational disorder in the smectic phase when compared with corresponding data based on the frozen-orientation approximation. These results are discussed in terms of the tau parameter, which has been proposed as a convenient measure of depletion strength. We present closed expressions for tau, and show that it is intimately connected with the depletion potential. We then analyse the effect of particle geometry by comparing results pertaining to systems of parallel rods of different shapes (spherocylinders, cylinders and parallelepipeds). We finally provide results based on the Zwanzig approximation of a fundamental-measure density-functional theory applied to mixtures of parallelepipeds and cubes of different sizes. In this case, we show that the tau parameter exhibits a linear asymptotic behaviour in the limit of large values of the hard-rod aspect ratio, in conformity with Onsager theory, as well as in the limit of large values of the ratio of rod breadth to cube side length, d, in contrast to Onsager approximation, which predicts tau approximately d (3). Based on both this result and the Percus-Yevick approximation for the direct correlation function for a hard-sphere binary mixture in the same limit of infinite asymmetry, we speculate that, for
Solano-Altamirano, J M; Goldman, Saul
2015-12-01
We determined the total system elastic Helmholtz free energy, under the constraints of constant temperature and volume, for systems comprised of one or more perfectly bonded hard spherical inclusions (i.e. "hard spheres") embedded in a finite spherical elastic solid. Dirichlet boundary conditions were applied both at the surface(s) of the hard spheres, and at the outer surface of the elastic solid. The boundary conditions at the surface of the spheres were used to describe the rigid displacements of the spheres, relative to their initial location(s) in the unstressed initial state. These displacements, together with the initial positions, provided the final shape of the strained elastic solid. The boundary conditions at the outer surface of the elastic medium were used to ensure constancy of the system volume. We determined the strain and stress tensors numerically, using a method that combines the Neuber-Papkovich spherical harmonic decomposition, the Schwartz alternating method, and Least-squares for determining the spherical harmonic expansion coefficients. The total system elastic Helmholtz free energy was determined by numerically integrating the elastic Helmholtz free energy density over the volume of the elastic solid, either by a quadrature, or a Monte Carlo method, or both. Depending on the initial position of the hard sphere(s) (or equivalently, the shape of the un-deformed stress-free elastic solid), and the displacements, either stationary or non-stationary Helmholtz free energy minima were found. The non-stationary minima, which involved the hard spheres nearly in contact with one another, corresponded to lower Helmholtz free energies, than did the stationary minima, for which the hard spheres were further away from one another. PMID:26701708
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
Rowlinson’s concept of an effective hard sphere diameter
Henderson, Douglas
2010-01-01
Attention is drawn to John Rowlinson’s idea that the repulsive portion of the intermolecular interaction may be replaced by a temperature-dependent hard sphere diameter. It is this approximation that made the development of perturbation theory possible for realistic fluids whose intermolecular interactions have a steep, but finite, repulsion at short separations. PMID:20953320
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.
Transport properties of highly asymmetric hard-sphere mixtures.
Bannerman, Marcus N; Lue, Leo
2009-04-28
The static and dynamic properties of binary mixtures of hard spheres with a diameter ratio of sigma(B)/sigma(A)=0.1 and a mass ratio of m(B)/m(A)=0.001 are investigated using event driven molecular dynamics. The contact values of the pair correlation functions are found to compare favorably with recently proposed theoretical expressions. The transport coefficients of the mixture, determined from simulation, are compared to the predictions of the revised Enskog theory using both a third-order Sonine expansion and direct simulation Monte Carlo. Overall, the Enskog theory provides a fairly good description of the simulation data, with the exception of systems at the smallest mole fraction of larger spheres (x(A)=0.01) examined. A "fines effect" was observed at higher packing fractions, where adding smaller spheres to a system of large spheres decreases the viscosity of the mixture; this effect is not captured by the Enskog theory. PMID:19405594
Transport properties of highly asymmetric hard-sphere mixtures
NASA Astrophysics Data System (ADS)
Bannerman, Marcus N.; Lue, Leo
2009-04-01
The static and dynamic properties of binary mixtures of hard spheres with a diameter ratio of σB/σA=0.1 and a mass ratio of mB/mA=0.001 are investigated using event driven molecular dynamics. The contact values of the pair correlation functions are found to compare favorably with recently proposed theoretical expressions. The transport coefficients of the mixture, determined from simulation, are compared to the predictions of the revised Enskog theory using both a third-order Sonine expansion and direct simulation Monte Carlo. Overall, the Enskog theory provides a fairly good description of the simulation data, with the exception of systems at the smallest mole fraction of larger spheres (xA=0.01) examined. A "fines effect" was observed at higher packing fractions, where adding smaller spheres to a system of large spheres decreases the viscosity of the mixture; this effect is not captured by the Enskog theory.
Clustering and gelation of hard spheres induced by the Pickering effect.
Fortini, Andrea
2012-04-01
A mixture of hard-sphere particles and model emulsion droplets is studied with a Brownian dynamics simulation. We find that the addition of nonwetting emulsion droplets to a suspension of pure hard spheres can lead to both gas-liquid and fluid-solid phase separations. Furthermore, we find a stable fluid of hard-sphere clusters. The stability is due to the saturation of the attraction that occurs when the surface of the droplets is completely covered with colloidal particles. At larger emulsion droplet densities a percolation transition is observed. The resulting networks of colloidal particles show dynamical and mechanical properties typical of a colloidal gel. The results of the model are in good qualitative agreement with recent experimental findings [E. Koos and N. Willenbacher, Science 331, 897 (2011)] in a mixture of colloidal particles and two immiscible fluids. PMID:22680411
Topological lifetimes of polydisperse colloidal hard spheres at a wall
NASA Astrophysics Data System (ADS)
Dullens, Roel P. A.; Kegel, Willem K.
2005-01-01
Confocal scanning laser microscopy was used to study the behavior of dense suspensions of model colloidal hard spheres at a single wall. Due to the slight polydispersity, our system shows a reentrant melting transition at high densities involving a hexatic structure [R. P. A. Dullens and W. K. Kegel, Phys. Rev. Lett 92, 195702 (2004)]. The reentrant melting transition is accompanied by an increase in the mean-squared displacement. The correlation between structure and dynamics was quantitatively analyzed on a single-particle level. In particular, the topological lifetime, being the average time that a particle spends having the same coordination number, is determined for all coordination numbers and as a function of volume fraction. The defective (non-sixfold-coordinated) particles exhibit shorter lifetimes than sixfold-coordinated particles, indicating that the mobility of the system is larger at or close to defective particles. The lifetime itself is a strong function of volume fraction. In particular, the global behavior of the mean-squared displacement is proportional to the hopping frequency (the inverse of the lifetime), showing that particles changing their coordination number contribute most to the local mobility.
Velocity and energy distributions in microcanonical ensembles of hard spheres.
Scalas, Enrico; Gabriel, Adrian T; Martin, Edgar; Germano, Guido
2015-08-01
In a microcanonical ensemble (constant NVE, hard reflecting walls) and in a molecular dynamics ensemble (constant NVEPG, periodic boundary conditions) with a number N of smooth elastic hard spheres in a d-dimensional volume V having a total energy E, a total momentum P, and an overall center of mass position G, the individual velocity components, velocity moduli, and energies have transformed beta distributions with different arguments and shape parameters depending on d, N, E, the boundary conditions, and possible symmetries in the initial conditions. This can be shown marginalizing the joint distribution of individual energies, which is a symmetric Dirichlet distribution. In the thermodynamic limit the beta distributions converge to gamma distributions with different arguments and shape or scale parameters, corresponding respectively to the Gaussian, i.e., Maxwell-Boltzmann, Maxwell, and Boltzmann or Boltzmann-Gibbs distribution. These analytical results agree with molecular dynamics and Monte Carlo simulations with different numbers of hard disks or spheres and hard reflecting walls or periodic boundary conditions. The agreement is perfect with our Monte Carlo algorithm, which acts only on velocities independently of positions with the collision versor sampled uniformly on a unit half sphere in d dimensions, while slight deviations appear with our molecular dynamics simulations for the smallest values of N. PMID:26382376
Velocity and energy distributions in microcanonical ensembles of hard spheres
NASA Astrophysics Data System (ADS)
Scalas, Enrico; Gabriel, Adrian T.; Martin, Edgar; Germano, Guido
2015-08-01
In a microcanonical ensemble (constant N V E , hard reflecting walls) and in a molecular dynamics ensemble (constant N V E PG , periodic boundary conditions) with a number N of smooth elastic hard spheres in a d -dimensional volume V having a total energy E , a total momentum P , and an overall center of mass position G , the individual velocity components, velocity moduli, and energies have transformed beta distributions with different arguments and shape parameters depending on d , N , E , the boundary conditions, and possible symmetries in the initial conditions. This can be shown marginalizing the joint distribution of individual energies, which is a symmetric Dirichlet distribution. In the thermodynamic limit the beta distributions converge to gamma distributions with different arguments and shape or scale parameters, corresponding respectively to the Gaussian, i.e., Maxwell-Boltzmann, Maxwell, and Boltzmann or Boltzmann-Gibbs distribution. These analytical results agree with molecular dynamics and Monte Carlo simulations with different numbers of hard disks or spheres and hard reflecting walls or periodic boundary conditions. The agreement is perfect with our Monte Carlo algorithm, which acts only on velocities independently of positions with the collision versor sampled uniformly on a unit half sphere in d dimensions, while slight deviations appear with our molecular dynamics simulations for the smallest values of N .
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
Self-consistent phonon theory of the crystallization and elasticity of attractive hard spheres.
Shin, Homin; Schweizer, Kenneth S
2013-02-28
We propose an Einstein-solid, self-consistent phonon theory for the crystal phase of hard spheres that interact via short-range attractions. The approach is first tested against the known behavior of hard spheres, and then applied to homogeneous particles that interact via short-range square well attractions and the Baxter adhesive hard sphere model. Given the crystal symmetry, packing fraction, and strength and range of attractive interactions, an effective harmonic potential experienced by a particle confined to its Wigner-Seitz cell and corresponding mean square vibrational amplitude are self-consistently calculated. The crystal free energy is then computed and, using separate information about the fluid phase free energy, phase diagrams constructed, including a first-order solid-solid phase transition and its associated critical point. The simple theory qualitatively captures all the many distinctive features of the phase diagram (critical and triple point, crystal-fluid re-entrancy, low-density coexistence curve) as a function of attraction range, and overall is in good semi-quantitative agreement with simulation. Knowledge of the particle localization length allows the crystal shear modulus to be estimated based on elementary ideas. Excellent predictions are obtained for the hard sphere crystal. Expanded and condensed face-centered cubic crystals are found to have qualitatively different elastic responses to varying attraction strength or temperature. As temperature increases, the expanded entropic solid stiffens, while the energy-controlled, fully-bonded dense solid softens. PMID:23464163
Monte Carlo methods: Application to hydrogen gas and hard spheres
NASA Astrophysics Data System (ADS)
Dewing, Mark Douglas
2001-08-01
Quantum Monte Carlo (QMC) methods are among the most accurate for computing ground state properties of quantum systems. The two major types of QMC we use are Variational Monte Carlo (VMC), which evaluates integrals arising from the variational principle, and Diffusion Monte Carlo (DMC), which stochastically projects to the ground state from a trial wave function. These methods are applied to a system of boson hard spheres to get exact, infinite system size results for the ground state at several densities. The kinds of problems that can be simulated with Monte Carlo methods are expanded through the development of new algorithms for combining a QMC simulation with a classical Monte Carlo simulation, which we call Coupled Electronic-Ionic Monte Carlo (CEIMC). The new CEIMC method is applied to a system of molecular hydrogen at temperatures ranging from 2800K to 4500K and densities from 0.25 to 0.46 g/cm3. VMC requires optimizing a parameterized wave function to find the minimum energy. We examine several techniques for optimizing VMC wave functions, focusing on the ability to optimize parameters appearing in the Slater determinant. Classical Monte Carlo simulations use an empirical interatomic potential to compute equilibrium properties of various states of matter. The CEIMC method replaces the empirical potential with a QMC calculation of the electronic energy. This is similar in spirit to the Car-Parrinello technique, which uses Density Functional Theory for the electrons and molecular dynamics for the nuclei. The challenges in constructing an efficient CEIMC simulation center mostly around the noisy results generated from the QMC computations of the electronic energy. We introduce two complementary techniques, one for tolerating the noise and the other for reducing it. The penalty method modifies the Metropolis acceptance ratio to tolerate noise without introducing a bias in the simulation of the nuclei. For reducing the noise, we introduce the two-sided energy
Using compressibility factor as a predictor of confined hard-sphere fluid dynamics.
Mittal, Jeetain
2009-10-22
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 ( approximately 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
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
Simple liquids’ quasiuniversality and the hard-sphere paradigm
NASA Astrophysics Data System (ADS)
Dyre, Jeppe C.
2016-08-01
This topical review discusses the quasiuniversality of simple liquids’ structure and dynamics and two possible justifications of it. The traditional one is based on the van der Waals picture of liquids in which the hard-sphere system reflects the basic physics. An alternative explanation argues that all quasiuniversal liquids to a good approximation conform to the same equation of motion, referring to the exponentially repulsive pair-potential system as the basic reference system. The paper, which is aimed at non-experts, ends by listing a number of open problems in the field.
Simple liquids' quasiuniversality and the hard-sphere paradigm.
Dyre, Jeppe C
2016-08-17
This topical review discusses the quasiuniversality of simple liquids' structure and dynamics and two possible justifications of it. The traditional one is based on the van der Waals picture of liquids in which the hard-sphere system reflects the basic physics. An alternative explanation argues that all quasiuniversal liquids to a good approximation conform to the same equation of motion, referring to the exponentially repulsive pair-potential system as the basic reference system. The paper, which is aimed at non-experts, ends by listing a number of open problems in the field. PMID:27345623
New closed virial equation of state for hard-sphere fluids.
Tian, Jianxiang; Gui, Yuanxing; Mulero, Angel
2010-10-28
A new closed virial equation of state of hard-sphere fluids is proposed which reproduces the calculated or estimated values of the first 16 virial coefficients and at the same time gives very good accuracy when compared with computer simulation data for the compressibility factor over the entire fluid range, as well as having a pole at the correct closest packing density. PMID:20883000
Hoppe, Travis
2013-01-01
We compute the singular value decomposition of the radial distribution function for hard sphere, and square well solutions. We find that decomposes into a small set of basis vectors allowing for an extremely accurate representation at all interpolated densities and potential strengths. In addition, we find that the coefficient vectors describing the magnitude of each basis vector are well described by a low-order polynomial. We provide a program to calculate in this compact representation for the investigated parameter range. PMID:24143174
Thermodynamics of dipolar hard spheres with low-to-intermediate coupling constants.
Elfimova, Ekaterina A; Ivanov, Alexey O; Camp, Philip J
2012-08-01
The thermodynamic properties of the dipolar hard-sphere fluid are studied using theory and simulation. A new theory is derived using a convenient mathematical approximation for the Helmholtz free energy relative to that for the hard-sphere fluid. The approximation is designed to give the correct low-density virial expansion. New theoretical and numerical results for the fourth virial coefficient are given. Predictions of thermodynamic functions for dipolar coupling constants λ=1 and 2 show excellent agreement with simulation results, even at the highest value of the particle volume fraction φ. For higher values of λ, there are deviations at high volume fractions, but the correct low-density behavior is retained. The theory is compared critically against the established thermodynamic perturbation theory; it gives significant improvements at low densities and is more convenient in terms of the required numerics. Dipolar hard spheres provide a basic model for ferrofluids, and the theory is accurate for typical experimental parameters λ
Thermodynamic perturbation theory for fused hard-sphere and hard-disk chain fluids
Zhou, Y.; Hall, C.K.; Stell, G.
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}.
Compact Collision Kernels for Hard Sphere and Coulomb Cross Sections; Fokker-Planck Coefficients
Chang Yongbin; Shizgal, Bernie D.
2008-12-31
A compact collision kernel is derived for both hard sphere and Coulomb cross sections. The difference between hard sphere interaction and Coulomb interaction is characterized by a parameter {eta}. With this compact collision kernel, the calculation of Fokker-Planck coefficients can be done for both the Coulomb and hard sphere interactions. The results for arbitrary order Fokker-Planck coefficients are greatly simplified. An alternate form for the Coulomb logarithm is derived with concern to the temperature relaxation in a binary plasma.
Astillero, Antonio; Santos, Andrés
2005-09-01
In the preceding paper, we have conjectured that the main transport properties of a dilute gas of inelastic hard spheres (IHSs) can be satisfactorily captured by an equivalent gas of elastic hard spheres (EHSs), provided that the latter are under the action of an effective drag force and their collision rate is reduced by a factor (1+alpha)/2 (where alpha is the constant coefficient of normal restitution). In this paper we test the above expectation in a paradigmatic nonequilibrium state, namely, the simple or uniform shear flow, by performing Monte Carlo computer simulations of the Boltzmann equation for both classes of dissipative gases with a dissipation range 0.5 < or = alpha < or = 0.95 and two values of the imposed shear rate a. It is observed that the evolution toward the steady state proceeds in two stages: a short kinetic stage (strongly dependent on the initial preparation of the system) followed by a slower hydrodynamic regime that becomes increasingly less dependent on the initial state. Once conveniently scaled, the intrinsic quantities in the hydrodynamic regime depend on time, at a given value of alpha, only through the reduced shear rate a*(t) is proportional to a/square root(T(t)), until a steady state, independent of the imposed shear rate and of the initial preparation, is reached. The distortion of the steady-state velocity distribution from the local equilibrium state is measured by the shear stress, the normal stress differences, the cooling rate, the fourth and sixth cumulants, and the shape of the distribution itself. In particular, the simulation results seem to be consistent with an exponential overpopulation of the high-velocity tail. These properties are common to both the IHS and EHS systems. In addition, the EHS results are in general hardly distinguishable from the IHS ones if alpha approximately > 0.7, so that the distinct signature of the IHS gas (higher anisotropy and overpopulation) only manifests itself at relatively high
NASA Astrophysics Data System (ADS)
Hanifpour, M.; Francois, N.; Robins, V.; Kingston, A.; Vaez Allaei, S. M.; Saadatfar, M.
2015-06-01
Here we present an experimental and numerical investigation on the grain-scale geometrical and mechanical properties of partially crystallized structures made of macroscopic frictional grains. Crystallization is inevitable in arrangements of monosized hard spheres with packing densities exceeding Bernal's limiting density ϕBernal≈0.64 . We study packings of monosized hard spheres whose density spans over a wide range (0.59 <ϕ <0.72 ) . These experiments harness x-ray computed tomography, three-dimensional image analysis, and numerical simulations to access precisely the geometry and the 3D structure of internal forces within the sphere packings. We show that clear geometrical transitions coincide with modifications of the mechanical backbone of the packing both at the grain and global scale. Notably, two transitions are identified at ϕBernal≈0.64 and ϕc≈0.68 . These results provide insights on how geometrical and mechanical features at the grain scale conspire to yield partially crystallized structures that are mechanically stable.
Hanifpour, M; Francois, N; Robins, V; Kingston, A; Allaei, S M Vaez; Saadatfar, M
2015-06-01
Here we present an experimental and numerical investigation on the grain-scale geometrical and mechanical properties of partially crystallized structures made of macroscopic frictional grains. Crystallization is inevitable in arrangements of monosized hard spheres with packing densities exceeding Bernal's limiting density ϕ(Bernal)≈0.64. We study packings of monosized hard spheres whose density spans over a wide range (0.59<ϕ<0.72). These experiments harness x-ray computed tomography, three-dimensional image analysis, and numerical simulations to access precisely the geometry and the 3D structure of internal forces within the sphere packings. We show that clear geometrical transitions coincide with modifications of the mechanical backbone of the packing both at the grain and global scale. Notably, two transitions are identified at ϕ(Bernal)≈0.64 and ϕ(c)≈0.68. These results provide insights on how geometrical and mechanical features at the grain scale conspire to yield partially crystallized structures that are mechanically stable. PMID:26172700
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
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 ϕJ 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 ϕJ 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
NASA Astrophysics Data System (ADS)
Henderson, D.; Plischke, M.
1987-04-01
Starting from well-known relations for the derivatives of the radial distribution functions of a mixture of fluids, and allowing the diameter of one particle to become exceedingly large, three sum rules for a fluid with density inhomogeneities are obtained. None of these sum rules are new. However, the relation between the Lovett-Mou-Buff-Wertheim and the Born-Green hierarchy of equations seems not well known. The accuracy of a recent parametrization of the pair correlation of hard spheres near a hard wall and of the solutions of the Percus-Yevick and hypernetted-chain equation for this same function are examined by determination of how well these functions satisfy these sum rules and the accuracy of their surface tension, calculated from the sum rule of Triezenberg and Zwanzig. Generally speaking, the Percus-Yevick theory gives the best results and the hypernetted-chain approximation gives the worst results with the parametrization being intermediate.
Hard-sphere kinetic models for inert and reactive mixtures.
Polewczak, Jacek
2016-10-19
I consider stochastic variants of a simple reacting sphere (SRS) kinetic model (Xystris and Dahler 1978 J. Chem. Phys. 68 387-401, Qin and Dahler 1995 J. Chem. Phys. 103 725-50, Dahler and Qin 2003 J. Chem. Phys. 118 8396-404) for dense reacting mixtures. In contrast to the line-of-center models of chemical reactive models, in the SRS kinetic model, the microscopic reversibility (detailed balance) can be easily shown to be satisfied, and thus all mathematical aspects of the model can be fully justified. In the SRS model, the molecules behave as if they were single mass points with two internal states. Collisions may alter the internal states of the molecules, and this occurs when the kinetic energy associated with the reactive motion exceeds the activation energy. Reactive and non-reactive collision events are considered to be hard sphere-like. I consider a four component mixture A, B, A (*), B (*), in which the chemical reactions are of the type [Formula: see text], with A (*) and B (*) being distinct species from A and B. This work extends the joined works with George Stell to the kinetic models of dense inert and reactive mixtures. The idea of introducing smearing-type effect in the collisional process results in a new class of stochastic kinetic models for both inert and reactive mixtures. In this paper the important new mathematical properties of such systems of kinetic equations are proven. The new results for stochastic revised Enskog system for inert mixtures are also provided. PMID:27545341
Simple and accurate theory for strong shock waves in a dense hard-sphere fluid.
Montanero, J M; López de Haro, M; Santos, A; Garzó, V
1999-12-01
Following an earlier work by Holian et al. [Phys. Rev. E 47, R24 (1993)] for a dilute gas, we present a theory for strong shock waves in a hard-sphere fluid described by the Enskog equation. The idea is to use the Navier-Stokes hydrodynamic equations but taking the temperature in the direction of shock propagation rather than the actual temperature in the computation of the transport coefficients. In general, for finite densities, this theory agrees much better with Monte Carlo simulations than the Navier-Stokes and (linear) Burnett theories, in contrast to the well-known superiority of the Burnett theory for dilute gases. PMID:11970718
Jamming transition and inherent structures of hard spheres and disks.
Ozawa, Misaki; Kuroiwa, Takeshi; Ikeda, Atsushi; Miyazaki, Kunimasa
2012-11-16
Recent studies show that volume fractions φ(J) at the jamming transition of frictionless hard spheres and disks are not uniquely determined but exist over a continuous range. Motivated by this observation, we numerically investigate the dependence of φ(J) on the initial configurations of the parent fluid equilibrated at a volume fraction φ(eq), before compressing to generate a jammed packing. We find that φ(J) remains constant when φ(eq) is small but sharply increases as φ(eq) exceeds the dynamic transition point which the mode-coupling theory predicts. We carefully analyze configurational properties of both jammed packings and parent fluids and find that, while all jammed packings remain isostatic, the increase of φ(J) is accompanied with subtle but distinct changes of local orders, a static length scale, and an exponent of the finite-size scaling. These results are consistent with the scenario of the random first-order transition theory of the glass transition. PMID:23215507
NASA Astrophysics Data System (ADS)
Wang, Lin; An, Xizhong; Wang, Defeng; Qian, Quan
2016-01-01
Quantitative characterization on the topological and metrical properties of radical subunits (polyhedra) for two new ternary hard sphere crystals was studied. These two ideal crystalline structures are numerically constructed by filling small and medium spheres into interstices (corresponding to regular tetrahedral and octahedral pores) of perfect face centered cubic (FCC) and hexagonal close packed (HCP) crystals formed by the packing of large spheres. Topological properties such as face number, edge number, vertex number of each radical polyhedron (RP), edge number of each RP face and metrical properties such as volume, surface area, total perimeter and pore volume of each RP, area and perimeter of each RP face were analyzed and compared. The results show that even though the overall packing densities for FCC and HCP ternary crystals are the same, different characteristics of radical polyhedra for corresponding spheres in these two crystals can be identified. That is, in the former structure RPs are more symmetric than those in the latter; the orientations of corresponding RP in the latter are twice as many as that in the former. Moreover, RP topological and metrical properties in the HCP ternary crystal are much more complicated than those in the FCC ternary crystal. These differences imply the structure and property differences of these two ternary crystals. Analyses of RPs provide intensive understanding of pores in the structure.
Klatt, Michael A; Torquato, Salvatore
2016-08-01
In the first paper of this series, we introduced Voronoi correlation functions to characterize the structure of maximally random jammed (MRJ) sphere packings across length scales. In the present paper, we determine a variety of different correlation functions that arise in rigorous expressions for the effective physical properties of MRJ sphere packings and compare them to the corresponding statistical descriptors for overlapping spheres and equilibrium hard-sphere systems. Such structural descriptors arise in rigorous bounds and formulas for effective transport properties, diffusion and reactions constants, elastic moduli, and electromagnetic characteristics. First, we calculate the two-point, surface-void, and surface-surface correlation functions, for which we derive explicit analytical formulas for finite hard-sphere packings. We show analytically how the contact Dirac delta function contribution to the pair correlation function g_{2}(r) for MRJ packings translates into distinct functional behaviors of these two-point correlation functions that do not arise in the other two models examined here. Then we show how the spectral density distinguishes the MRJ packings from the other disordered systems in that the spectral density vanishes in the limit of infinite wavelengths; i.e., these packings are hyperuniform, which means that density fluctuations on large length scales are anomalously suppressed. Moreover, for all model systems, we study and compute exclusion probabilities and pore size distributions, as well as local density fluctuations. We conjecture that for general disordered hard-sphere packings, a central limit theorem holds for the number of points within an spherical observation window. Our analysis links problems of interest in material science, chemistry, physics, and mathematics. In the third paper of this series, we will evaluate bounds and estimates of a host of different physical properties of the MRJ sphere packings that are based on the
NASA Astrophysics Data System (ADS)
Wu, Liang; Malijevský, Alexandr; Jackson, George; Müller, Erich A.; Avendaño, Carlos
2015-07-01
We study the structure and fluid-phase behaviour of binary mixtures of hard spheres (HSs) and hard spherocylinders (HSCs) in isotropic and nematic states using the NPnAT ensemble Monte Carlo (MC) approach in which the normal component of the pressure tensor is fixed in a system confined between two hard walls. The method allows one to estimate the location of the isotropic-nematic phase transition and to observe the asymmetry in the composition between the coexisting phases, with the expected enhancement of the HSC concentration in the nematic phase. This is in stark contrast with the previously reported MC simulations where a conventional isotropic NPT ensemble was used. We further compare the simulation results with the theoretical predictions of two analytic theories that extend the original Parsons-Lee theory using the one-fluid and the many-fluid approximations [Malijevský et al., J. Chem. Phys. 129, 144504 (2008)]. In the one-fluid version of the theory, the properties of the mixture are related to an effective one-component HS system, while in the many-fluid theory, the components of the mixtures are represented as separate effective HS particles. The comparison reveals that both the one- and the many-fluid approaches provide a reasonably accurate quantitative description of the mixture including the predictions of the isotropic-nematic phase boundary and degree of orientational order of the HSC-HS mixture.
PREPARATION OF HIGH-DENSITY THORIUM OXIDE SPHERES
McNees, R.A. Jr.; Taylor, A.J.
1963-12-31
A method of preparing high-density thorium oxide spheres for use in pellet beds in nuclear reactors is presented. Sinterable thorium oxide is first converted to free-flowing granules by means such as compression into a compact and comminution of the compact. The granules are then compressed into cubes having a density of 5.0 to 5.3 grams per cubic centimeter. The cubes are tumbled to form spheres by attrition, and the spheres are then fired at 1250 to 1350 deg C. The fired spheres are then polished and fired at a temperature above 1650 deg C to obtain high density. Spherical pellets produced by this method are highly resistant to mechanical attrition hy water. (AEC)
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.
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.
Paricaud, P.
2015-07-28
A simple modification of the Boublík-Mansoori-Carnahan-Starling-Leland equation of state is proposed for an application to the metastable disordered region. The new model has a positive pole at the jamming limit and can accurately describe the molecular simulation data of pure hard in the stable fluid region and along the metastable branch. The new model has also been applied to binary mixtures hard spheres, and an excellent description of the fluid and metastable branches can be obtained by adjusting the jamming packing fraction. The new model for hard sphere mixtures can be used as the repulsive term of equations of state for real fluids. In this case, the modified equations of state give very similar predictions of thermodynamic properties as the original models, and one can remove the multiple liquid density roots observed for some versions of the Statistical Associating Fluid Theory (SAFT) at low temperature without any modification of the dispersion term.
Phase behavior of binary hard-sphere mixtures from perturbation theory.
Velasco, E; Navascués, G; Mederos, L
1999-09-01
Using a first-order perturbation theory, we have studied the phase diagram of a binary mixture of hard spheres for different values of the size ratio. Recent models for the two-body depletion potential between large spheres are used to take into account the role of the small spheres. The theory predicts a complex phase diagram including a fluid-solid transition at high packing fraction of small spheres, metastability of fluid-fluid demixing, an isostructural solid-solid transition at high packing fraction of the large spheres for sufficiently small values of the size ratio q of the spheres, and the tendency to sticky-sphere behavior in the limit q-->0. The agreement with recent simulation results is quite good. We also show that this phenomenology was already implicit in the pioneering work of Asakura and Oosawa. PMID:11970123
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.
Costa, L.A.; Zhou, Y.; Hall, C.K.; Carra, S.
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.
Variational Monte Carlo study of soliton excitations in hard-sphere Bose gases
NASA Astrophysics Data System (ADS)
Rota, R.; Giorgini, S.
2015-10-01
By using a full many-body approach, we calculate the excitation energy, the effective mass, and the density profile of soliton states in a three-dimensional Bose gas of hard spheres at zero temperature. The many-body wave function used to describe the soliton contains a one-body term, derived from the solution of the Gross-Pitaevskii equation, and a two-body Jastrow term, which accounts for the repulsive correlations between atoms. We optimize the parameters in the many-body wave function via a variational Monte Carlo procedure, calculating the grand-canonical energy and the canonical momentum of the system in a moving reference frame where the soliton is stationary. As the density of the gas is increased, significant deviations from the mean-field predictions are found for the excitation energy and the density profile of both dark and gray solitons. In particular, the soliton effective mass m* and the mass m Δ N of missing particles in the region of the density depression are smaller than the result from the Gross-Pitaevskii equation, their ratio, however, being well reproduced by this theory up to large values of the gas parameter. We also calculate the profile of the condensate density around the soliton notch, finding good agreement with the prediction of the local-density approximation.
Jamming II: Edwards’ statistical mechanics of random packings of hard spheres
NASA Astrophysics Data System (ADS)
Wang, Ping; Song, Chaoming; Jin, Yuliang; Makse, Hernán A.
2011-02-01
The problem of finding the most efficient way to pack spheres has an illustrious history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal in the 1960s. This problem finds applications spanning from the mathematician’s pencil, the processing of granular materials, the jamming and glass transitions, all the way to fruit packing in every grocery. There are presently numerous experiments showing that the loosest way to pack spheres gives a density of ∼55% (named random loose packing, RLP) while filling all the loose voids results in a maximum density of ∼63%-64% (named random close packing, RCP). While those values seem robustly true, to this date there is no well-accepted physical explanation or theoretical prediction for them. Here we develop a common framework for understanding the random packings of monodisperse hard spheres whose limits can be interpreted as the experimentally observed RLP and RCP. The reason for these limits arises from a statistical picture of jammed states in which the RCP can be interpreted as the ground state of the ensemble of jammed matter with zero compactivity, while the RLP arises in the infinite compactivity limit. We combine an extended statistical mechanics approach ‘a la Edwards’ (where the role traditionally played by the energy and temperature in thermal systems is substituted by the volume and compactivity) with a constraint on mechanical stability imposed by the isostatic condition. We show how such approaches can bring results that can be compared to experiments and allow for an exploitation of the statistical mechanics framework. The key result is the use of a relation between the local Voronoi volumes of the constituent grains (denoted the volume function) and the number of neighbors in contact that permits us to simply combine the two approaches to develop a theory of volume fluctuations in jammed matter. Ultimately, our results lead to a phase diagram that
Hard-sphere fluid adsorbed in an annular wedge: The depletion force of hard-body colloidal physics
NASA Astrophysics Data System (ADS)
Herring, A. R.; Henderson, J. R.
2007-01-01
Many important issues of colloidal physics can be expressed in the context of inhomogeneous fluid phenomena. When two large colloids approach one another in solvent, they interact at least partly by the response of the solvent to finding itself adsorbed in the annular wedge formed between the two colloids. At shortest range, this fluid mediated interaction is known as the depletion force/interaction because solvent is squeezed out of the wedge when the colloids approach closer than the diameter of a solvent molecule. An equivalent situation arises when a single colloid approaches a substrate/wall. Accurate treatment of this interaction is essential for any theory developed to model the phase diagrams of homogeneous and inhomogeneous colloidal systems. The aim of our paper is a test of whether or not we possess sufficient knowledge of statistical mechanics that can be trusted when applied to systems of large size asymmetry and the depletion force in particular. When the colloid particles are much larger than a solvent diameter, the depletion force is dominated by the effective two-body interaction experienced by a pair of solvated colloids. This low concentration limit of the depletion force has therefore received considerable attention. One route, which can be rigorously based on statistical mechanical sum rules, leads to an analytic result for the depletion force when evaluated by a key theoretical tool of colloidal science known as the Derjaguin approximation. A rival approach has been based on the assumption that modern density functional theories (DFT) can be trusted for systems of large size asymmetry. Unfortunately, these two theoretical predictions differ qualitatively for hard sphere models, as soon as the solvent density is higher than about 2/3 that at freezing. Recent theoretical attempts to understand this dramatic disagreement have led to the proposal that the Derjaguin and DFT routes represent opposite limiting behavior, for very large size asymmetry
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.
Relaxation rates in the Maxwellian collision model and its variable hard sphere surrogate
NASA Astrophysics Data System (ADS)
Rubinstein, Robert
2015-08-01
The variable hard sphere and related models have proven to be accurate and computationally convenient replacements for the inverse power law model of classical kinetic theory in direct simulation Monte Carlo calculations. We attempt to provide theoretical support for this remarkable success by comparing the relaxation rates in the linearized Boltzmann equation for the Maxwellian collision model with those of its variable hard sphere surrogate. The comparison demonstrates that the linearized collision operator with variable hard sphere interactions can accurately approximate the linearized collision operator with Maxwellian inverse power law interactions under well-defined and broadly applicable conditions. Extensions of the analysis to the general inverse power law model and to more realistic intermolecular potentials are briefly discussed.
Stochastic interactions of two Brownian hard spheres in the presence of depletants
Karzar-Jeddi, Mehdi; Fan, Tai-Hsi; Tuinier, Remco; Taniguchi, Takashi
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 (ΔB2/ΔT < 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
Equilibrium distribution of hard-sphere systems and revised Enskog theory
NASA Astrophysics Data System (ADS)
van Beijeren, H.
1983-10-01
A revised Enskog theory (RET) is shown to lead to a correct equilibrium distribution in hard-sphere systems in a stationary external potential, while the standard Enskog theory (SET) does not. Attention is given to the s-component hard-sphere mixture with constant external potential acting on particles of a particular species. The different definition of the pair correlation function at a contact point of two different species used in RET is demonstrated to be consistent with equilibrium statistical mechanics, whereas the definition chosen for the contact point in SET is not.
Note: equation of state and the freezing point in the hard-sphere model.
Robles, Miguel; López de Haro, Mariano; Santos, Andrés
2014-04-01
The merits of different analytical equations of state for the hard-sphere system with respect to the recently computed high-accuracy value of the freezing-point packing fraction are assessed. It is found that the Carnahan-Starling-Kolafa and the branch-point approximant equations of state yield the best performance. PMID:24712819
Brandani, V.; Prausnitz, J. M.
1982-01-01
This paper is the second of three describing a two-fluid theory of binary liquid mixtures. The general theory presented in the preceding paper is used to derive a model for calculating thermodynamic properties of hard-sphere mixtures. Calculations indicate that desirable boundary conditions are satisfied. PMID:16593220
NASA Astrophysics Data System (ADS)
Ogarko, Vitaliy; Luding, Stefan
2013-03-01
Polydisperse hard sphere mixtures have equilibrium properties which essentially depend on the number density and a reduced number K of moments of the size distribution function. Such systems are equivalent to other systems with different size distributions if the K moments are matched. In particular, a small number s of components, such that 2 s - 1 = K is sufficient to mimic systems with continuous size distributions. For most of the fluid phase K = 3 moments (s = 2 components) are enough to define an equivalent system, while in the glassy states one needs K = 5 moments (s = 3 components) to achieve good agreement between the polydisperse and its maximally-equivalent tridisperse system. With K = 5 matched moments they are also close in number- and volume-fractions of rattlers. Finally, also the jamming density of maximally-equivalent jammed packings is very close, where the tiny differences can be explained by the distribution of rattlers. This research is supported by the Dutch Technology Foundation STW, which is the applied science division of NWO, and the Technology Programme of the Ministry of Economic Affairs, project Nr. STW-MUST 10120.
Radial distribution function for hard spheres in fractal dimensions: A heuristic approximation
NASA Astrophysics Data System (ADS)
Santos, Andrés; de Haro, Mariano López
2016-06-01
Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension d (1 ≤d ≤3 ) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for a fractal dimension [M. Heinen et al., Phys. Rev. Lett. 115, 097801 (2015), 10.1103/PhysRevLett.115.097801], a good agreement being observed.
Hard sphere-like glass transition in eye lens α-crystallin solutions
Savin, Gabriela; Bucciarelli, Saskia; Dorsaz, Nicolas; Thurston, George M.; Stradner, Anna; Schurtenberger, Peter
2014-01-01
We study the equilibrium liquid structure and dynamics of dilute and concentrated bovine eye lens α-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 α-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 α-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 α-crystallin solutions exhibit a glass transition at high concentrations that is similar to those found in hard-sphere colloidal systems. The α-crystallin glass transition could have implications for the molecular basis of presbyopia and the kinetics of molecular change during cataractogenesis. PMID:25385638
Hynninen, Antti-Pekka; Dijkstra, Marjolein
2005-04-01
Phase diagrams of hard and soft spheres with a fixed dipole moment are determined by calculating the Helmholtz free energy using simulations. The pair potential is given by a dipole-dipole interaction plus a hard-core and a repulsive Yukawa potential for soft spheres. Our system models colloids in an external electric or magnetic field, with hard spheres corresponding to uncharged and soft spheres to charged colloids. The phase diagram of dipolar hard spheres shows fluid, face-centered-cubic (fcc), hexagonal-close-packed (hcp), and body-centered-tetragonal (bct) phases. The phase diagram of dipolar soft spheres exhibits, in addition to the above mentioned phases, a body-centered-orthorhombic (bco) phase, and it agrees well with the experimental phase diagram [Nature (London) 421, 513 (2003)]. Our results show that bulk hcp, bct, and bco crystals can be realized experimentally by applying an external field. PMID:15904046
NASA Astrophysics Data System (ADS)
Reiss, Howard; Manzanares, José A.
2016-09-01
Using several theoretical toolsldots (i) the nucleation theorem, (ii) an equivalent cavity, (iii) the reversible work of adding a cavity to an open hard sphere system, and (iv) the theory of "stability"... the authors estimated the density at which the hard sphere freezing transition occurs. No direct involvement of the equilibrium solid phase is involved. The reduced density \\uppi a^3ρ _f/6 (where a is the hard sphere diameter and ρ _f is the actual density at which freezing occurs) is found to be 0.4937 while the value obtained by computer simulation is 0.494. The agreement is good, but the new method still contains some approximation. However, the approximation is based on the idea that at a density just below ρ _f the fluid adopts a distorted structure resembling the solid, but different enough so that long-range order vanishes. Initial loss of stability may not be involved in every fluid-solid transition, but it may be an early step in the hard sphere and related systems.
NASA Astrophysics Data System (ADS)
Virrueta, A.; Gaines, J.; O'Hern, C. S.; Regan, L.
2015-03-01
Current research in the O'Hern and Regan laboratories focuses on the development of hard-sphere models with stereochemical constraints for protein structure prediction as an alternative to molecular dynamics methods that utilize knowledge-based corrections in their force-fields. Beginning with simple hydrophobic dipeptides like valine, leucine, and isoleucine, we have shown that our model is able to reproduce the side-chain dihedral angle distributions derived from sets of high-resolution protein crystal structures. However, methionine remains an exception - our model yields a chi-3 side-chain dihedral angle distribution that is relatively uniform from 60 to 300 degrees, while the observed distribution displays peaks at 60, 180, and 300 degrees. Our goal is to resolve this discrepancy by considering clashes with neighboring residues, and averaging the reduced distribution of allowable methionine structures taken from a set of crystallized proteins. We will also re-evaluate the electron density maps from which these protein structures are derived to ensure that the methionines and their local environments are correctly modeled. This work will ultimately serve as a tool for computing side-chain entropy and protein stability. A. V. is supported by an NSF Graduate Research Fellowship and a Ford Foundation Fellowship. J. G. is supported by NIH training Grant NIH-5T15LM007056-28.
Mendoza, Carlos I; Santamaría-Holek, I
2009-01-28
We propose a simple and general model accounting for the dependence of the viscosity of a hard sphere suspension at arbitrary volume fractions. The model constitutes a continuum-medium description based on a recursive-differential method where correlations between the spheres are introduced through an effective volume fraction. In contrast to other differential methods, the introduction of the effective volume fraction as the integration variable implicitly considers interactions between the spheres of the same recursive stage. The final expression for the viscosity scales with this effective volume fraction, which allows constructing a master curve that contains all the experimental situations considered. The agreement of our expression for the viscosity with experiments at low- and high-shear rates and in the high-frequency limit is remarkable for all volume fractions. PMID:19191410
Thorneywork, Alice L; Roth, Roland; Aarts, Dirk G A L; Dullens, Roel P A
2014-04-28
Two-dimensional hard disks are a fundamentally important many-body model system in classical statistical mechanics. Despite their significance, a comprehensive experimental data set for two-dimensional single component and binary hard disks is lacking. Here, we present a direct comparison between the full set of radial distribution functions and the contact values of a two-dimensional binary colloidal hard sphere model system and those calculated using fundamental measure theory. We find excellent quantitative agreement between our experimental data and theoretical predictions for both single component and binary hard disk systems. Our results provide a unique and fully quantitative mapping between experiments and theory, which is crucial in establishing the fundamental link between structure and dynamics in simple liquids and glass forming systems. PMID:24784245
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
Newman, Hugh D; Yethiraj, Anand
2015-01-01
In this work, we use structure and dynamics in sedimentation equilibrium, in the presence of gravity, to examine, via confocal microscopy, a Brownian colloidal system in the presence of an external electric field. The zero field equation of state (EOS) is hard sphere without any re-scaling of particle size, and the hydrodynamic corrections to the long-time self-diffusion coefficient are quantitatively consistent with the expected value for hard spheres. Care is taken to ensure that both the dimensionless gravitational energy, which is equivalent to a Peclet number Peg, and dipolar strength Λ are of order unity. In the presence of an external electric field, anisotropic chain-chain clusters form; this cluster formation manifests itself with the appearance of a plateau in the diffusion coefficient when the dimensionless dipolar strength Λ ~ 1. The structure and dynamics of this chain-chain cluster state is examined for a monodisperse system for two particle sizes. PMID:26323363
The Dynamics of Disorder-Order Transition in Hard Sphere Colloidal Dispersions
NASA Technical Reports Server (NTRS)
Chaikin, Paul M.; Zhu, Jixiang; Cheng, Zhengdong; Phan, See-Eng; Russel, William B.; Lant, Christian T.; Doherty, Michael P.; Meyer, William V.; Rogers, Richard; Cannell, D. S.; Ottewill, R. H.
1998-01-01
The Physics of Hard Spheres Experiment (PHaSE) seeks a complete understanding of the entropically driven disorder-order transition in hard sphere colloidal dispersions. The light scattering instrument designed for flight collects Bragg and low angle light scattering in the forward direction via a CCD camera and performs conventional static and dynamic light scattering at 10-160 deg. through fiber optic cables. Here we report on the kinetics of nucleation and growth extracted from time-resolved Bragg images and measurements of the elastic modulus of crystalline phases obtained by monitoring resonant responses to sinusoidal forcing through dynamic light scattering. Preliminary analysis of the former indicates a significant difference from measurements on the ground, while the latter confirms nicely laboratory experiments with the same instrument and predictions from computer simulations.
The structural origin of the hard-sphere glass transition in granular packing
Xia, Chengjie; Li, Jindong; Cao, Yixin; Kou, Binquan; Xiao, Xianghui; Fezzaa, Kamel; Xiao, Tiqiao; Wang, Yujie
2015-09-28
Glass transition is accompanied by a rapid growth of the structural relaxation time and a concomitant decrease of configurational entropy. It remains unclear whether the transition has a thermodynamic origin, and whether the dynamic arrest is associated with the growth of a certain static order. Using granular packing as a model hard-sphere glass, we show the glass transition as a thermodynamic phase transition with a ‘hidden’ polytetrahedral order. This polytetrahedral order is spatially correlated with the slow dynamics. It is geometrically frustrated and has a peculiar fractal dimension. Additionally, as the packing fraction increases, its growth follows an entropy-driven nucleationmore » process, similar to that of the random first-order transition theory. In conclusion, our study essentially identifies a long-sought-after structural glass order in hard-sphere glasses.« less
The structural origin of the hard-sphere glass transition in granular packing
Xia, Chengjie; Li, Jindong; Cao, Yixin; Kou, Binquan; Xiao, Xianghui; Fezzaa, Kamel; Xiao, Tiqiao; Wang, Yujie
2015-09-28
Glass transition is accompanied by a rapid growth of the structural relaxation time and a concomitant decrease of configurational entropy. It remains unclear whether the transition has a thermodynamic origin, and whether the dynamic arrest is associated with the growth of a certain static order. Using granular packing as a model hard-sphere glass, we show the glass transition as a thermodynamic phase transition with a ‘hidden’ polytetrahedral order. This polytetrahedral order is spatially correlated with the slow dynamics. It is geometrically frustrated and has a peculiar fractal dimension. Additionally, as the packing fraction increases, its growth follows an entropy-driven nucleation process, similar to that of the random first-order transition theory. In conclusion, our study essentially identifies a long-sought-after structural glass order in hard-sphere glasses.
The structural origin of the hard-sphere glass transition in granular packing
Xia, Chengjie; Li, Jindong; Cao, Yixin; Kou, Binquan; Xiao, Xianghui; Fezzaa, Kamel; Xiao, Tiqiao; Wang, Yujie
2015-01-01
Glass transition is accompanied by a rapid growth of the structural relaxation time and a concomitant decrease of configurational entropy. It remains unclear whether the transition has a thermodynamic origin, and whether the dynamic arrest is associated with the growth of a certain static order. Using granular packing as a model hard-sphere glass, we show the glass transition as a thermodynamic phase transition with a ‘hidden' polytetrahedral order. This polytetrahedral order is spatially correlated with the slow dynamics. It is geometrically frustrated and has a peculiar fractal dimension. Additionally, as the packing fraction increases, its growth follows an entropy-driven nucleation process, similar to that of the random first-order transition theory. Our study essentially identifies a long-sought-after structural glass order in hard-sphere glasses. PMID:26412008
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.
Newman, Hugh D.; Yethiraj, Anand
2015-01-01
In this work, we use structure and dynamics in sedimentation equilibrium, in the presence of gravity, to examine, via confocal microscopy, a Brownian colloidal system in the presence of an external electric field. The zero field equation of state (EOS) is hard sphere without any re-scaling of particle size, and the hydrodynamic corrections to the long-time self-diffusion coefficient are quantitatively consistent with the expected value for hard spheres. Care is taken to ensure that both the dimensionless gravitational energy, which is equivalent to a Peclet number Peg, and dipolar strength Λ are of order unity. In the presence of an external electric field, anisotropic chain-chain clusters form; this cluster formation manifests itself with the appearance of a plateau in the diffusion coefficient when the dimensionless dipolar strength Λ ~ 1. The structure and dynamics of this chain-chain cluster state is examined for a monodisperse system for two particle sizes. PMID:26323363
López de Haro, Mariano; Tejero, Carlos F; Santos, Andrés
2013-04-28
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. PMID:23635104
The structural origin of the hard-sphere glass transition in granular packing
NASA Astrophysics Data System (ADS)
Xia, Chengjie; Li, Jindong; Cao, Yixin; Kou, Binquan; Xiao, Xianghui; Fezzaa, Kamel; Xiao, Tiqiao; Wang, Yujie
2015-09-01
Glass transition is accompanied by a rapid growth of the structural relaxation time and a concomitant decrease of configurational entropy. It remains unclear whether the transition has a thermodynamic origin, and whether the dynamic arrest is associated with the growth of a certain static order. Using granular packing as a model hard-sphere glass, we show the glass transition as a thermodynamic phase transition with a `hidden' polytetrahedral order. This polytetrahedral order is spatially correlated with the slow dynamics. It is geometrically frustrated and has a peculiar fractal dimension. Additionally, as the packing fraction increases, its growth follows an entropy-driven nucleation process, similar to that of the random first-order transition theory. Our study essentially identifies a long-sought-after structural glass order in hard-sphere glasses.
The structural origin of the hard-sphere glass transition in granular packing.
Xia, Chengjie; Li, Jindong; Cao, Yixin; Kou, Binquan; Xiao, Xianghui; Fezzaa, Kamel; Xiao, Tiqiao; Wang, Yujie
2015-01-01
Glass transition is accompanied by a rapid growth of the structural relaxation time and a concomitant decrease of configurational entropy. It remains unclear whether the transition has a thermodynamic origin, and whether the dynamic arrest is associated with the growth of a certain static order. Using granular packing as a model hard-sphere glass, we show the glass transition as a thermodynamic phase transition with a 'hidden' polytetrahedral order. This polytetrahedral order is spatially correlated with the slow dynamics. It is geometrically frustrated and has a peculiar fractal dimension. Additionally, as the packing fraction increases, its growth follows an entropy-driven nucleation process, similar to that of the random first-order transition theory. Our study essentially identifies a long-sought-after structural glass order in hard-sphere glasses. PMID:26412008
Parallelized event chain algorithm for dense hard sphere and polymer systems
Kampmann, Tobias A. Boltz, Horst-Holger; Kierfeld, Jan
2015-01-15
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.
Radial distribution function of penetrable sphere fluids to the second order in density
NASA Astrophysics Data System (ADS)
Santos, Andrés; Malijevský, Alexandr
2007-02-01
The simplest bounded potential is that of penetrable spheres, which takes a positive finite value γ if the two spheres are overlapped, being zero otherwise. In this paper we derive the cavity function to second order in density and the fourth virial coefficient as functions of T*≡kBT/γ (where kB is the Boltzmann constant and T is the temperature) for penetrable sphere fluids. The expressions are exact, except for the function represented by an elementary diagram inside the core, which is approximated by a polynomial form in excellent agreement with accurate results obtained by Monte Carlo integration. Comparison with the hypernetted-chain (HNC) and Percus-Yevick (PY) theories shows that the latter is better than the former for T*≲1 only. However, even at zero temperature (hard sphere limit), the PY solution is not accurate inside the overlapping region, where no practical cancellation of the neglected diagrams takes place. The exact fourth virial coefficient is positive for T*≲0.73 , reaches a minimum negative value at T*≈1.1 , and then goes to zero from below as 1/T*4 for high temperatures. These features are captured qualitatively, but not quantitatively, by the HNC and PY predictions. In addition, in both theories the compressibility route is the best one for T*≲0.7 , while the virial route is preferable if T*≳0.7 .
Tracking three-phase coexistences in binary mixtures of hard plates and spheres
NASA Astrophysics Data System (ADS)
Aliabadi, Roohollah; Moradi, Mahmood; Varga, Szabolcs
2016-02-01
The stability of demixing phase transition in binary mixtures of hard plates (with thickness L and diameter D) and hard spheres (with diameter σ) is studied by means of Parsons-Lee theory. The isotropic-isotropic demixing, which is found in mixtures of large spheres and small plates, is very likely to be pre-empted by crystallization. In contrast, the nematic-nematic demixing, which is obtained in mixtures of large plates and small spheres, can be stabilized at low diameter ratios (σ/D) and aspect ratios (L/D). At intermediate values of σ/D, where the sizes of the components are similar, neither the isotropic-isotropic nor the nematic-nematic demixing can be stabilized, but a very strong fractionation takes place between a plate rich nematic and a sphere rich isotropic phases. Our results show that the excluded volume interactions are capable alone to explain the experimental observation of the nematic-nematic demixing, but they fail in the description of isotropic-isotropic one [M. Chen et al., Soft Matter 11, 5775 (2015)].
NASA Astrophysics Data System (ADS)
Hoang, Hai; Galliero, Guillaume
2013-12-01
This work aims at providing a tractable approach to model the local shear viscosity of strongly inhomogeneous dense fluids composed of spherical molecules, in which the density variations occur on molecular distance. The proposed scheme, which relies on the local density average model, has been applied to the quasi-hard-sphere, the Week-Chandler-Andersen and the Lennard-Jones fluids. A weight function has been developed to deal with the hard-sphere fluid given the specificities of momentum exchange. To extend the approach to the smoothly repulsive potential, we have taken into account that the non-local contributions to the viscosity due to the interactions of particles separated by a given distance are temperature dependent. Then, using a simple perturbation scheme, the approach is extended to the Lennard-Jones fluids. It is shown that the viscosity profiles of inhomogeneous dense fluids deduced from this approach are consistent with those directly computed by non-equilibrium molecular dynamics simulations.
NASA Astrophysics Data System (ADS)
Urrutia, Ignacio
2014-12-01
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 < β < 2π. It enables a unified approach to both wedges and edges.
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 < β < 2π. It enables a unified approach to both wedges and edges.
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 < β < 2π. It enables a unified approach to both wedges and edges. PMID:25554179
Scaled Particle Theory for Multicomponent Hard Sphere Fluids Confined in Random Porous Media.
Chen, W; Zhao, S L; Holovko, M; Chen, X S; Dong, W
2016-06-23
The formulation of scaled particle theory (SPT) is presented for a quite general model of fluids confined in a random porous media, i.e., a multicomponent hard sphere (HS) fluid in a multicomponent hard sphere or a multicomponent overlapping hard sphere (OHS) matrix. The analytical expressions for pressure, Helmholtz free energy, and chemical potential are derived. The thermodynamic consistency of the proposed theory is established. Moreover, we show that there is an isomorphism between the SPT for a multicomponent system and that for a one-component system. Results from grand canonical ensemble Monte Carlo simulations are also presented for a binary HS mixture in a one-component HS or a one-component OHS matrix. The accuracy of various variants derived from the basic SPT formulation is appraised against the simulation results. Scaled particle theory, initially formulated for a bulk HS fluid, has not only provided an analytical tool for calculating thermodynamic properties of HS fluid but also helped to gain very useful insight for elaborating other theoretical approaches such as the fundamental measure theory (FMT). We expect that the general SPT for multicomponent systems developed in this work can contribute to the study of confined fluids in a similar way. PMID:27294670
NASA Astrophysics Data System (ADS)
Parisi, Giorgio
In a hard spheres systems particles cannot overlap. Increasing the density we reach a point where most of the particles are blocked and the density cannot be increased any more: this is the jamming point. The jamming point separates the phase, where all the constraint can be satisfied, from an unsatifiable phase, where spheres do have to overlap. A scaling theory of the behavior around the jamming critical point has been formulated and a few critical exponents have been introduced. The exponents are apparently super-universal, as far as they do seem to be independent from the space dimensions. The mean field version of the model (i.e. the infinite dimensions limit) has been solved analytically using broken replica symmetry techniques and the computed critical exponents have been found in a remarkable agreement with three-dimensional and two-dimensional numerical results and experiments. The theory predicts in hard spheres (in glasses) a new transition (the Gardener transition) from the replica symmetric phase to the replica broken phase at high density (at low temperature), in agreement with simulations on hard sphere systems. I will briefly discuss the possible consequences of this new picture on the very low temperature behavior of glasses in the quantum regime.
Radial distribution function for hard spheres in fractal dimensions: A heuristic approximation.
Santos, Andrés; de Haro, Mariano López
2016-06-01
Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension d (1≤d≤3) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for a fractal dimension [M. Heinen et al., Phys. Rev. Lett. 115, 097801 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.097801], a good agreement being observed. PMID:27415227
Equations of state of freely jointed hard-sphere chain fluids: Theory
Stell, G.; Lin, C.; Kalyuzhnyi, Y.V.
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 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.
Long-range weight functions in fundamental measure theory of the non-uniform hard-sphere fluid.
Hansen-Goos, Hendrik
2016-06-22
We introduce long-range weight functions to the framework of fundamental measure theory (FMT) of the non-uniform, single-component hard-sphere fluid. While the range of the usual weight functions is equal to the hard-sphere radius R, the modified weight functions have range 3R. Based on the augmented FMT, we calculate the radial distribution function g(r) up to second order in the density within Percus' test particle theory. Consistency of the compressibility and virial routes on this level allows us to determine the free parameter γ of the theory. As a side result, we obtain a value for the fourth virial coefficient B 4 which deviates by only 0.01% from the exact result. The augmented FMT is tested for the dense fluid by comparing results for g(r) calculated via the test particle route to existing results from molecular dynamics simulations. The agreement at large distances (r > 6R) is significantly improved when the FMT with long-range weight functions is used. In order to improve agreement close to contact (r = 2R) we construct a free energy which is based on the accurate Carnahan-Starling equation of state, rather than the Percus-Yevick compressibility equation underlying standard FMT. PMID:27115721
Jiang, Hao; Adidharma, Hertanto
2014-11-07
The thermodynamic modeling of flexible charged hard-sphere chains representing polyampholyte or polyelectrolyte molecules in solution is considered. The excess Helmholtz energy and osmotic coefficients of solutions containing short polyampholyte and the osmotic coefficients of solutions containing short polyelectrolytes are determined by performing canonical and isobaric-isothermal Monte Carlo simulations. A new equation of state based on the thermodynamic perturbation theory is also proposed for flexible charged hard-sphere chains. For the modeling of such chains, the use of solely the structure information of monomer fluid for calculating the chain contribution is found to be insufficient and more detailed structure information must therefore be considered. Two approaches, i.e., the dimer and dimer-monomer approaches, are explored to obtain the contribution of the chain formation to the Helmholtz energy. By comparing with the simulation results, the equation of state with either the dimer or dimer-monomer approach accurately predicts the excess Helmholtz energy and osmotic coefficients of polyampholyte and polyelectrolyte solutions except at very low density. It also well captures the effect of temperature on the thermodynamic properties of these solutions.
Mirigian, Stephen; Schweizer, Kenneth
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.
NASA Astrophysics Data System (ADS)
Mirigian, Stephen; Schweizer, Kenneth S.
2014-05-01
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.
Long-range weight functions in fundamental measure theory of the non-uniform hard-sphere fluid
NASA Astrophysics Data System (ADS)
Hansen-Goos, Hendrik
2016-06-01
We introduce long-range weight functions to the framework of fundamental measure theory (FMT) of the non-uniform, single-component hard-sphere fluid. While the range of the usual weight functions is equal to the hard-sphere radius R, the modified weight functions have range 3R. Based on the augmented FMT, we calculate the radial distribution function g(r) up to second order in the density within Percus’ test particle theory. Consistency of the compressibility and virial routes on this level allows us to determine the free parameter γ of the theory. As a side result, we obtain a value for the fourth virial coefficient B 4 which deviates by only 0.01% from the exact result. The augmented FMT is tested for the dense fluid by comparing results for g(r) calculated via the test particle route to existing results from molecular dynamics simulations. The agreement at large distances (r > 6R) is significantly improved when the FMT with long-range weight functions is used. In order to improve agreement close to contact (r = 2R) we construct a free energy which is based on the accurate Carnahan–Starling equation of state, rather than the Percus–Yevick compressibility equation underlying standard FMT.
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.
Edison, John R; Dasgupta, Tonnishtha; Dijkstra, Marjolein
2016-08-01
We study the phase behaviour of a binary mixture of colloidal hard spheres and freely jointed chains of beads using Monte Carlo simulations. Recently Panagiotopoulos and co-workers predicted [Nat. Commun. 5, 4472 (2014)] that the hexagonal close packed (HCP) structure of hard spheres can be stabilized in such a mixture due to the interplay between polymer and the void structure in the crystal phase. Their predictions were based on estimates of the free-energy penalty for adding a single hard polymer chain in the HCP and the competing face centered cubic (FCC) phase. Here we calculate the phase diagram using free-energy calculations of the full binary mixture and find a broad fluid-solid coexistence region and a metastable gas-liquid coexistence region. For the colloid-monomer size ratio considered in this work, we find that the HCP phase is only stable in a small window at relatively high polymer reservoir packing fractions, where the coexisting HCP phase is nearly close packed. Additionally we investigate the structure and dynamic behaviour of these mixtures. PMID:27497577
NASA Astrophysics Data System (ADS)
Edison, John R.; Dasgupta, Tonnishtha; Dijkstra, Marjolein
2016-08-01
We study the phase behaviour of a binary mixture of colloidal hard spheres and freely jointed chains of beads using Monte Carlo simulations. Recently Panagiotopoulos and co-workers predicted [Nat. Commun. 5, 4472 (2014)] that the hexagonal close packed (HCP) structure of hard spheres can be stabilized in such a mixture due to the interplay between polymer and the void structure in the crystal phase. Their predictions were based on estimates of the free-energy penalty for adding a single hard polymer chain in the HCP and the competing face centered cubic (FCC) phase. Here we calculate the phase diagram using free-energy calculations of the full binary mixture and find a broad fluid-solid coexistence region and a metastable gas-liquid coexistence region. For the colloid-monomer size ratio considered in this work, we find that the HCP phase is only stable in a small window at relatively high polymer reservoir packing fractions, where the coexisting HCP phase is nearly close packed. Additionally we investigate the structure and dynamic behaviour of these mixtures.
Yan, Zhenyu; Buldyrev, Sergey V; Giovambattista, Nicolas; Debenedetti, Pablo G; Stanley, H Eugene
2006-05-01
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< or =lambda<6/7. As in water, the regions where these anomalies occur are nested domes in the (T, p) or (T, P) planes , with the thermodynamic anomaly dome contained entirely within the dynamic anomaly dome. We calculate translational and orientational order parameters (t and Q6), and project equilibrium state points onto the (t, Q6) plane, or order map. The order map evolves from waterlike behavior to hard-sphere-like behavior upon varying lambda between 4/7 and 6/7. Thus, we traverse the range of liquid behavior encompassed by hard spheres (lanbda=1) and waterlike (lambda approximately 4/7) with a family 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< or=lambda< or=1, waterlike structural anomalies (i.e., decrease in both t and Q6 upon compression and strictly correlated T and Q6 in the anomalous region) occur only around lambda=4/7. Waterlike anomalies in structure, dynamics and thermodynamics arise solely due to the existence of two length scales, with their ratio lambda being the single control parameter, orientation-dependent interactions being absent by design. PMID:16802925
The role of bond tangency and bond gap in hard sphere crystallization of chains.
Karayiannis, Nikos Ch; Foteinopoulou, Katerina; Laso, Manuel
2015-03-01
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 [σ, σ + dl], where σ 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
Glass-transition properties of Yukawa potentials: from charged point particles to hard spheres.
Yazdi, Anoosheh; Ivlev, Alexei; Khrapak, Sergey; Thomas, Hubertus; Morfill, Gregor E; Löwen, Hartmut; Wysocki, Adam; Sperl, Matthias
2014-06-01
The glass transition is investigated in three dimensions for single and double Yukawa potentials for the full range of control parameters. For vanishing screening parameter, the limit of the one-component plasma is obtained; for large screening parameters and high coupling strengths, the glass-transition properties cross over to the hard-sphere system. Between the two limits, the entire transition diagram can be described by analytical functions. Unlike other potentials, the glass-transition and melting lines for Yukawa potentials are found to follow shifted but otherwise identical curves in control-parameter space. PMID:25019902
NASA Astrophysics Data System (ADS)
Gámez, Francisco; Acemel, Rafael D.; Cuetos, Alejandro
2013-10-01
Parsons-Lee approach is formulated for the isotropic-nematic transition in a binary mixture of oblate hard spherocylinders and hard spheres. Results for the phase coexistence and for the equation of state in both phases for fluids with different relative size and composition ranges are presented. The predicted behaviour is in agreement with Monte Carlo simulations in a qualitative fashion. The study serves to provide a rational view of how to control key aspects of the behaviour of these binary nematogenic colloidal systems. This behaviour can be tuned with an appropriate choice of the relative size and molar fractions of the depleting particles. In general, the mixture of discotic and spherical particles is stable against demixing up to very high packing fractions. We explore in detail the narrow geometrical range where demixing is predicted to be possible in the isotropic phase. The influence of molecular crowding effects on the stability of the mixture when spherical molecules are added to a system of discotic colloids is also studied.
NASA Astrophysics Data System (ADS)
Michailidou, V. N.; Swan, J. W.; Brady, J. F.; Petekidis, G.
2013-10-01
Evanescent wave dynamic light scattering and Stokesian dynamics simulations were employed to study the dynamics of hard-sphere colloidal particles near a hard wall in concentrated suspensions. The evanescent wave averaged short-time diffusion coefficients were determined from experimental correlation functions over a range of scattering wave vectors and penetration depths. Stokesian dynamics simulations performed for similar conditions allow a direct comparison of both the short-time self- and collective diffusivity. As seen earlier [V. N. Michailidou, G. Petekidis, J. W. Swan, and J. F. Brady, Phys. Rev. Lett. 102, 068302 (2009)] while the near wall dynamics in the dilute regime slow down compared to the free bulk diffusion, the reduction is negligible at higher volume fractions due to an interplay between the particle-wall and particle-particle hydrodynamic interactions. Here, we provide a comprehensive comparison between experiments and simulations and discuss the interplay of particle-wall and particle-particle hydrodynamics in the self- and cooperative dynamics determined at different scattering wave vectors and penetration depths.
Hard-sphere behavior in the dynamics of all mono-atomic liquids at the de Gennes minimum
NASA Astrophysics Data System (ADS)
Montfrooij, Wouter
2016-08-01
We show that the position of the de Gennes minimum in scattering spectra, where the dynamics of liquids shows down, is given by a hard-sphere expression for a range of mono-atomic liquids that crystallize in a close packed structure. This expression relates the position of the minimum to the number density of the liquid, without any adjustable or unknown parameters. We argue that this implies that a liquid can be viewed as a close packed structure of the cages that represent the confinement of atoms by their neighbors. We further show that some metals deviate from this expression, namely those metals that crystallize in a structure that is not close packed. Our expression should prove very useful in identifying what liquids to study in inelastic scattering experiments given that deviations from normal fluid behavior can already be predicted based on the peak position of the static structure factor.
Physics of Hard Sphere Experiment: Scattering, Rheology and Microscopy Study of Colloidal Particles
NASA Technical Reports Server (NTRS)
Cheng, Z.-D.; Zhu, J.; Phan, S.-E.; Russel, W. B.; Chaikin, P. M.; Meyer, W. V.
2002-01-01
The Physics of Hard Sphere Experiment has two incarnations: the first as a scattering and rheology experiment on STS-83 and STS-94 and the second as a microscopy experiment to be performed in the future on LMM on the space station. Here we describe some of the quantitative and qualitative results from previous flights on the dynamics of crystallization in microgravity and especially the observed interaction of growing crystallites in the coexistance regime. To clarify rheological measurements we also present ground based experiments on the low shear rate viscosity and diffusion coefficient of several hard sphere experiments at high volume fraction. We also show how these experiments will be performed with confocal microscopy and laser tweezers in our lab and as preparation for the phAse II experiments on LMM. One of the main aims of the microscopy study will be the control of colloidal samples using an array of applied fields with an eye toward colloidal architectures. Temperature gradients, electric field gradients, laser tweezers and a variety of switchable imposed surface patterns are used toward this control.
NASA Astrophysics Data System (ADS)
Gazzillo, Domenico; Giacometti, Achille; Fantoni, Riccardo; Sollich, Peter
2006-11-01
We investigate the dependence of the stickiness parameters tij=1/(12τij) —where the τij are the conventional Baxter parameters—on the solute diameters σi and σj 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,σi,σj) can be approximated by essentially the same expression, i.e., a simple polynomial in the variable σiσj/σij2 , with coefficients depending on the temperature T , or—for depletion interactions—on the packing fraction η0 of the depletant particles.
Sedov, I A; Magsumov, T I
2015-07-16
Thermodynamic solvation properties of mixtures of water with tetrahydrofuran at 298 K are studied. The Gibbs free energies and enthalpies of solvation of n-octane and toluene are determined experimentally. For molecular dynamics simulations of the binary solvent, we have modified a TraPPE-UA model for tetrahydrofuran and combined it with the SPC/E potential for water. The excess thermodynamic functions of neon, xenon, and hard spheres with two different radii are calculated using the particle insertion method. Simulated and real systems share the same characteristic trends for the thermodynamic functions. A maximum is present on dependencies of the enthalpy of solvation from the composition of solvent at 70-90 mol % water, making it higher than in both of the cosolvents. It is caused by a high enthalpy of cavity formation in the mixtures rich with water due to solvent reorganization around the cavity, which is shown by calculation of the enthalpy of solvation of hard spheres. Addition of relatively small amounts of tetrahydrofuran to water effectively suppresses the hydrophobic effect, leading to a quick increase of both the entropy and enthalpy of cavity formation and solvation of low polar molecules. PMID:26115405
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 βɛ = 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].
NASA Astrophysics Data System (ADS)
Hopkins, Paul; Fortini, Andrea; Archer, Andrew J.; Schmidt, Matthias
2010-12-01
We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the "self " component having only one particle, the "distinct" component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components. We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy, and arrested dynamics at high densities.
Hopkins, Paul; Fortini, Andrea; Archer, Andrew J; Schmidt, Matthias
2010-12-14
We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the "self " component having only one particle, the "distinct" component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components. We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy, and arrested dynamics at high densities. PMID:21171689
NASA Astrophysics Data System (ADS)
de las Heras, Daniel; Varga, Szabolcs; Vesely, Franz J.
2011-06-01
We present the phase diagram of a system of mesogenic top-shaped molecules based on the Parsons-Lee density functional theory and Monte Carlo simulation. The molecules are modeled as a hard spherocylinder with a hard sphere embedded in its center. The stability of five different phases is studied, namely, isotropic, nematic, smectic A, smectic C, and columnar phases. The positionally ordered phases are investigated only for the case of parallel alignment. It is found that the central spherical unit destabilizes the nematic with respect to the isotropic phase, while increasing the length of the cylinder has the opposite effect. Also, the central hard sphere has a strong destabilizing effect on the smectic A phase, due the inefficient packing of the molecules into layers. For large hard sphere units the smectic A phase is completely replaced by a smectic C structure. The columnar phase is first stabilized with increasing diameter of the central unit, but for very large hard sphere units it becomes less stable again. The density functional results are in good agreement with the simulations.
Rovibrationally Inelastic Atom-Molecule Collision Cross Sections from a Hard Sphere Model
NASA Astrophysics Data System (ADS)
Lashner, Jacob; Stewart, Brian
2016-05-01
Hard-shell models have long been used to elucidate the principal features of molecular energy transfer and exchange reaction in the A + BC system. Nevertheless, no three-dimensional hard-shell calculation of inelastic collision cross sections has been reported. This work aims to fill that void. A particular motivation comes from our experimental results, which show the importance of equatorial impacts in the vibrational excitation process. Working with the simple hard-sphere model, we incorporated secondary impacts, defined as those in which A strikes C after striking B. Such collisions are important in systems such as Li2 - X, in which vibrational energy transfer occurs principally through side impacts. We discuss the complexity this adds to the model and present fully three-dimensional cross sections for rovibrational excitation of an initially stationary molecule in the homonuclear A + B2 system, examining the cross section as a function of the masses and radii of the atoms. We show how the features in the cross section evolve as these parameters are varied and calculate the contribution of secondary (near-equatorial) impacts to the dynamics. We compare with recent measurements in our laboratory and with the results of quasiclassical trajectories.
Nonclassical Nucleation in a Solid-Solid Transition of Confined Hard Spheres
NASA Astrophysics Data System (ADS)
Qi, Weikai; Peng, Yi; Han, Yilong; Bowles, Richard K.; Dijkstra, Marjolein
2015-10-01
A solid-solid phase transition of colloidal hard spheres confined between two planar hard walls is studied using a combination of molecular dynamics and Monte Carlo simulation. The transition from a solid consisting of five crystalline layers with square symmetry (5 □ ) to a solid consisting of four layers with triangular symmetry (4 △ ) is shown to occur through a nonclassical nucleation mechanism that involves the initial formation of a precritical liquid cluster, within which the cluster of the stable 4 △ phase grows. Free-energy calculations show that the transition occurs in one step, crossing a single free-energy barrier, and that the critical nucleus consists of a small 4 △ solid cluster wetted by a metastable liquid. In addition, the liquid cluster and the solid cluster are shown to grow at the planar hard walls. We also find that the critical nucleus size increases with supersaturation, which is at odds with classical nucleation theory. The △-solid-like cluster is shown to contain both face-centered-cubic and hexagonal-close-packed ordered particles.
Correlation between dynamical and structural heterogeneities in colloidal hard-sphere suspensions
NASA Astrophysics Data System (ADS)
Golde, Sebastian; Palberg, Thomas; Schöpe, Hans Joachim
2016-07-01
Dynamical and structural heterogeneities have long been thought to play a key role in a unified picture of solidification in view of the two competitive processes of crystallization and vitrification. Here, we study these heterogeneities by means of a combination of dynamic and static light-scattering techniques applied to the simplest model system exhibiting crystallization and vitrification: the colloidal hard-sphere system. Our method enables us to quantify and correlate the temporal evolution of the amount of ordered clusters (precursors) and the amount of slow particles. Our analysis shows that their temporal evolutions are closely related and that there is an intimate link between structural and dynamic heterogeneities, crystal nucleation and the non-crystallization transition.
Creep and aging of hard-sphere glasses under constant stress
NASA Astrophysics Data System (ADS)
Ballesta, P.; Petekidis, G.
2016-04-01
We investigate the aging behavior of glassy suspensions of nearly hard-sphere colloids submitted to a constant shear stress. For low stresses, below the yield stress, the system is subject to creep motion. As the sample ages, the shear rate exhibits a power-law decrease with time with exponents that depend on the sample age. We use a combination of rheological experiments with time-resolved photon correlation spectroscopy to investigate the time evolution of the sample dynamics under shear on various time and length scales. Long-time light-scattering experiments reveal the occurrence of microscopic rearrangement events that are linked with the macroscopic strain deformation of the sample. Dynamic time sweep experiments indicate that while the internal microscopic dynamics slow down continuously with waiting time, the storage and loss moduli are almost constant after a fast, weak decrease, resembling the behavior of quenched systems with partially frozen-in stresses.
Hlushak, Stepan
2015-09-28
An analytical expression for the Laplace transform of the radial distribution function of a mixture of hard-sphere chains of arbitrary segment size and chain length is used to rigorously formulate the first-order Barker-Henderson perturbation theory for the contribution of the segment-segment dispersive interactions into thermodynamics of the Lennard-Jones chain mixtures. Based on this approximation, a simple variant of the statistical associating fluid theory is proposed and used to predict properties of several mixtures of chains of different lengths and segment sizes. The theory treats the dispersive interactions more rigorously than the conventional theories and provides means for more accurate description of dispersive interactions in the mixtures of highly asymmetric components.
Equation of state of sticky-hard-sphere fluids in the chemical-potential route.
Rohrmann, René D; Santos, Andrés
2014-04-01
The coupling-parameter method, whereby an extra particle is progressively coupled to the rest of the particles, is applied to the sticky-hard-sphere fluid to obtain its equation of state in the so-called chemical-potential route (μ route). As a consistency test, the results for one-dimensional sticky particles are shown to be exact. Results corresponding to the three-dimensional case (Baxter's model) are derived within the Percus-Yevick approximation by using different prescriptions for the dependence of the interaction potential of the extra particle on the coupling parameter. The critical point and the coexistence curve of the gas-liquid phase transition are obtained in the μ route and compared with predictions from other thermodynamics routes and from computer simulations. The results show that the μ route yields a general better description than the virial, energy, compressibility, and zero-separation routes. PMID:24827207
Apparent wall slip in non-Brownian hard-sphere suspensions.
Korhonen, Marko; Mohtaschemi, Mikael; Puisto, Antti; Illa, Xavier; Alava, Mikko J
2015-05-01
We analyze apparent wall slip, the reduction of particle concentration near the wall, in hard-sphere suspensions at concentrations well below the jamming limit utilizing a continuum level diffusion model. The approach extends a constitutive equation proposed earlier with two additional potentials describing the effects of gravitation and wall-particle repulsion. We find that although both mechanisms are shear independent by nature, due to the shear-rate-dependent counter-balancing particle migration fluxes, the resulting net effect is non-linearly shear dependent, causing larger slip at small shear rates. In effect, this shows up in the classically measured flow curves as a mild shear thickening regime at the transition from small to intermediate shear rates. PMID:25998170
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
Upper bound on the Edwards entropy in frictional monodisperse hard-sphere packings.
Baranau, Vasili; Zhao, Song-Chuan; Scheel, Mario; Tallarek, Ulrich; Schröter, Matthias
2016-05-01
We extend the Widom particle insertion method [B. Widom, J. Chem. Phys., 1963, 39, 2808-2812] to determine an upper bound sub on the Edwards entropy in frictional hard-sphere packings. sub corresponds to the logarithm of the number of mechanically stable configurations for a given volume fraction and boundary conditions. To accomplish this, we extend the method for estimating the particle insertion probability through the pore-size distribution in frictionless packings [V. Baranau, et al., Soft Matter, 2013, 9, 3361-3372] to the case of frictional particles. We use computer-generated and experimentally obtained three-dimensional sphere packings with volume fractions φ in the range 0.551-0.65. We find that sub has a maximum in the vicinity of the Random Loose Packing Limit φRLP = 0.55 and decreases then monotonically with increasing φ to reach a minimum at φ = 0.65. Further on, sub does not distinguish between real mechanical stability and packings in close proximity to mechanical stable configurations. The probability to find a given number of contacts for a particle inserted in a large enough pore does not depend on φ, but it decreases strongly with the contact number. PMID:27020114
Fluids density functional theory studies of supramolecular polymers at a hard surface
NASA Astrophysics Data System (ADS)
McGarrity, E. S.; Thijssen, J. M.; Besseling, N. A. M.
2010-08-01
We have applied a fluids density functional theory based on that of Yu and Wu [J. Chem. Phys. 116, 7094 (2002)] to treat reversible supramolecular polymers near a hard surface. This approach combines a hard-sphere fluids density functional theory with the first-order thermodynamic perturbation theory of Wertheim. The supramolecular polymers are represented in the theory by hard-spheres with two associating sites. We explore the effects of the bonding scheme, monomer concentration, and association energy upon the equilibrium chain sizes and the depletion lengths. This study is performed on simple systems containing two-site monomers and binary mixtures of two-site monomers combined with end stopper monomers which have only a single association site. Our model has correct behavior in the dilute and overlap regimes and the bulk results can be easily connected to simpler random-flight models. We find that there is a nonmonotonic behavior of the depletion length of the polymers as a function of concentration and that this depletion length can be controlled through the concentration of end stoppers. These results are applicable to the study of colloidal dispersions in supramolecular polymer solutions.
Thorneywork, Alice L; Rozas, Roberto E; Dullens, Roel P A; Horbach, Jürgen
2015-12-31
We compare experimental results from a quasi-two-dimensional colloidal hard sphere fluid to a Monte Carlo simulation of hard disks with small particle displacements. The experimental short-time self-diffusion coefficient D(S) scaled by the diffusion coefficient at infinite dilution, D(0), strongly depends on the area fraction, pointing to significant hydrodynamic interactions at short times in the experiment, which are absent in the simulation. In contrast, the area fraction dependence of the experimental long-time self-diffusion coefficient D(L)/D(0) is in quantitative agreement with D(L)/D(0) obtained from the simulation. This indicates that the reduction in the particle mobility at short times due to hydrodynamic interactions does not lead to a proportional reduction in the long-time self-diffusion coefficient. Furthermore, the quantitative agreement between experiment and simulation at long times indicates that hydrodynamic interactions effectively do not affect the dependence of D(L)/D(0) on the area fraction. In light of this, we discuss the link between structure and long-time self-diffusion in terms of a configurational excess entropy and do not find a simple exponential relation between these quantities for all fluid area fractions. PMID:26765032
NASA Astrophysics Data System (ADS)
Thorneywork, Alice L.; Rozas, Roberto E.; Dullens, Roel P. A.; Horbach, Jürgen
2015-12-01
We compare experimental results from a quasi-two-dimensional colloidal hard sphere fluid to a Monte Carlo simulation of hard disks with small particle displacements. The experimental short-time self-diffusion coefficient DS scaled by the diffusion coefficient at infinite dilution, D0, strongly depends on the area fraction, pointing to significant hydrodynamic interactions at short times in the experiment, which are absent in the simulation. In contrast, the area fraction dependence of the experimental long-time self-diffusion coefficient DL/D0 is in quantitative agreement with DL/D0 obtained from the simulation. This indicates that the reduction in the particle mobility at short times due to hydrodynamic interactions does not lead to a proportional reduction in the long-time self-diffusion coefficient. Furthermore, the quantitative agreement between experiment and simulation at long times indicates that hydrodynamic interactions effectively do not affect the dependence of DL/D0 on the area fraction. In light of this, we discuss the link between structure and long-time self-diffusion in terms of a configurational excess entropy and do not find a simple exponential relation between these quantities for all fluid area fractions.
Tensorial density functional theory for non-spherical hard-body fluids.
Hansen-Goos, Hendrik; Mecke, Klaus
2010-09-15
In a recent publication (Hansen-Goos and Mecke 2009 Phys. Rev. Lett. 102 018302) we constructed a free energy functional for the inhomogeneous hard-body fluid, which reduces to Rosenfeld's fundamental measure theory (Rosenfeld 1989 Phys. Rev. Lett. 63 980) when applied to hard spheres. The new functional is able to yield the isotropic-nematic transition for the hard-spherocylinder fluid in contrast to Rosenfeld's fundamental measure theory for non-spherical particles (Rosenfeld 1994 Phys. Rev. E 50 R3318). The description of inhomogeneous isotropic fluids is also improved when compared with data from Monte Carlo simulations for hard spherocylinders in contact with a planar hard wall. However, the new functional for the inhomogeneous fluid in general does not comply with the exact second order virial expansion. We introduced the ζ correction in order to minimize the deviation from Onsager's exact result in the isotropic bulk fluid. In this article we give a detailed account of the construction of the new functional. An extension of the ζ correction makes the latter better suited for non-isotropic particle distributions. The extended ζ correction is shown to improve the description of the isotropic-nematic bulk phase diagram while it has little effect on the results for the isotropic but inhomogeneous hard-spherocylinder fluid. We argue that the gain from using higher order tensorial weighted densities in the theory is likely to be inferior to the associated increase in complexity. PMID:21386523
Härtel, A; Löwen, H
2010-03-17
The recently developed fundamental measure density functional theory (Hansen-Goos and Mecke 2009 Phys. Rev. Lett. 102 018302) for an inhomogeneous anisotropic hard body fluid is used as a basic ingredient in treating the Brownian dynamics of hard spherocylinders. After discussing the relevance of a free parameter in the fundamental measure density functional for the isotropic-nematic transition in equilibrium, we discuss the equilibrium phase behaviour of hard spherocylinders in a static external potential which couples only to the orientations. For external potentials favouring rod orientations along the poles of the unit sphere, there is a well-known paranematic-nematic transition which ceases to exist above a threshold of the strength V(0) of the external potential. However, when orientations along the equator are more favoured, in the plane of the potential energy V(0) and density, there is a phase transition from paranematic to nematic for any strength, which becomes second order above a critical threshold of V(0). The full equilibrium phase diagram in the V(0)-density plane is computed for a fixed rod aspect ratio of 5. For the equatorial cases, strength V(0) is then oscillating in time and dynamical density functional theory is used to compute the evolution of the orientational distribution. A subtle resonance for increasing oscillation frequencies is detected if the oscillating V(0) crosses the paranematic-nematic phase transition. PMID:21389446
NASA Astrophysics Data System (ADS)
McBride, Carl; Vega, Carlos
2002-12-01
A study of a rigid fully flexible fused hard sphere model [C. McBride, C. Vega, and L. G. MacDowell, Phys. Rev. E 64, 011703 (2001)] is extended to the smectic and solid branches of the phase diagram. Computer simulations have been performed for a completely rigid model composed of 15 fused hard spheres (15+0), a model of 15 fused hard spheres of which 2 monomers at one end of the model form a flexible tail (13+2), and a model consisting of 15 fused hard spheres with 5 monomers forming a flexible tail (10+5). For the 15+0 model the phase sequence isotropic-nematic-smectic A-columnar is found on compression, and the sequence solid-smectic A-nematic-isotropic on expansion. For the 13+2 model the phase sequence isotropic-nematic-smectic C is found on compression, and the sequence solid-smectic A-nematic-isotropic on expansion. For the 10+5 model the phase sequence isotropic-glass is found on compression. The expansion runs displayed the phase sequence solid-smectic A-isotropic. The introduction of flexibility was seen to stabilize the smectic A phase at the expense of the nematic phase.
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)
NASA Astrophysics Data System (ADS)
Qiao, Yu; Liu, Xuejiao; Chen, Minxin; Lu, Benzhuo
2016-04-01
The hard sphere repulsion among ions can be considered in the Poisson-Nernst-Planck (PNP) equations by combining the fundamental measure theory (FMT). To reduce the nonlocal computational complexity in 3D simulation of biological systems, a local approximation of FMT is derived, which forms a local hard sphere PNP (LHSPNP) model. In the derivation, the excess chemical potential from hard sphere repulsion is obtained with the FMT and has six integration components. For the integrands and weighted densities in each component, Taylor expansions are performed and the lowest order approximations are taken, which result in the final local hard sphere (LHS) excess chemical potential with four components. By plugging the LHS excess chemical potential into the ionic flux expression in the Nernst-Planck equation, the three dimensional LHSPNP is obtained. It is interestingly found that the essential part of free energy term of the previous size modified model (Borukhov et al. in Phys Rev Lett 79:435-438, 1997; Kilic et al. in Phys Rev E 75:021502, 2007; Lu and Zhou in Biophys J 100:2475-2485, 2011; Liu and Eisenberg in J Chem Phys 141:22D532, 2014) has a very similar form to one term of the LHS model, but LHSPNP has more additional terms accounting for size effects. Equation of state for one component homogeneous fluid is studied for the local hard sphere approximation of FMT and is proved to be exact for the first two virial coefficients, while the previous size modified model only presents the first virial coefficient accurately. To investigate the effects of LHS model and the competitions among different counterion species, numerical experiments are performed for the traditional PNP model, the LHSPNP model, the previous size modified PNP (SMPNP) model and the Monte Carlo simulation. It's observed that in steady state the LHSPNP results are quite different from the PNP results, but are close to the SMPNP results under a wide range of boundary conditions. Besides, in both
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.
Low-shear Viscosity and Diffusion of Hard-sphere Dispersion at High Concentration
NASA Astrophysics Data System (ADS)
Cheng, Zhengdong; Chaikin, P. M.; Phan, See-Eng; Zhu, Jixiang; Russel, W. B.
1997-03-01
We are interested in the rheology of hard-sphere dispersion at high concentration, especially the asymptotic behavior near the glass transition, which is the ideal place to test various theories.(J.F. Brady, J. Chem. phys. 99(1993)567) (M. Tokuyama and I. Oppenheim, Phys. Rev. E. 50(1994)R16) The dispersion studied is silica in Ethylene glycol/Glycerol/NaCl. Low-shear viscosity is measured by a Zimm viscometer. The data are consistent with recent PMMA measurement at low concentration(P.N. Segreet. al.), Phys. Rev. Lett. 75(1995)958; 76(1996)585 (See-eng Phan et. al.), Phys. rev. E., to be published., and at high concentration (metastable state) are better described by the Doolittle equation as in earlier experiments (L. Marshall, C.F. Zukoski IV, J. Phys. Chem. 94(1990)1164) (L.V. Woodcock, C.A. Angell, Phys. Rev. Lett. 47(1981)1129)). No theory yet gives a complete interpretion of the data. Dynamic light scattering (ensemble averaged) is used to measure self diffusion.
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.
Cavity averages for hard spheres in the presence of polydispersity and incomplete data.
Schindler, Michael; Maggs, A C
2015-09-01
We develop a cavity-based method which allows to extract thermodynamic properties from position information in hard-sphere/disk systems. So far, there are available-volume and free-volume methods. We add a third one, which we call available volume after take-out, and which is shown to be mathematically equivalent to the others. In applications, where data sets are finite, all three methods show limitations, and they do this in different parameter ranges. We illustrate the principal equivalence and the limitations on data from molecular dynamics: In particular, we test robustness against missing data. We have in mind experimental limitations where there is a small polydispersity, say 4% in the particle radii, but individual radii cannot be determined. We observe that, depending on the used method, the errors in such a situation are easily 100% for the pressure and 10kT for the chemical potentials. Our work is meant as guideline to the experimentalists for choosing the right one of the three methods, in order to keep the outcome of experimental data analysis meaningful. PMID:26359237
Crystal nucleation in the hard-sphere system revisited: a critical test of theoretical approaches.
Tóth, Gyula I; Gránásy, László
2009-04-16
The hard-sphere system is the best known fluid that crystallizes: the solid-liquid interfacial free energy, the equations of state, and the height of the nucleation barrier are known accurately, offering a unique possibility for a quantitative validation of nucleation theories. A recent significant downward revision of the interfacial free energy from approximately 0.61kT/sigma(2) to (0.56 +/- 0.02)kT/sigma(2) [Davidchack, R.; Morris, J. R.; Laird, B. B. J. Chem. Phys. 2006, 125, 094710] necessitates a re-evaluation of theoretical approaches to crystal nucleation. This has been carried out for the droplet model of the classical nucleation theory (CNT), the self-consistent classical theory (SCCT), a phenomenological diffuse interface theory (DIT), and single- and two-field variants of the phase field theory that rely on either the usual double-well and interpolation functions (PFT/S1 and PFT/S2, respectively) or on a Ginzburg-Landau expanded free energy that reflects the crystal symmetries (PFT/GL1 and PFT/GL2). We find that the PFT/GL1, PFT/GL2, and DIT models predict fairly accurately the height of the nucleation barrier known from Monte Carlo simulations in the volume fraction range of 0.52 < varphi < 0.54, whereas the CNT, SCCT, PFT/S1, and PFT/S2 models underestimate it significantly. PMID:19320450
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 λ, 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 ˜λ3, 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 λ2, 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.
Liu, Yi; Bławzdziewicz, Jerzy; Cichocki, Bogdan; Dhont, Jan K G; Lisicki, Maciej; Wajnryb, Eligiusz; Young, Y-N; Lang, Peter R
2015-10-01
In this article we report on a study of the near-wall dynamics of suspended colloidal hard spheres over a broad range of volume fractions. We present a thorough comparison of experimental data with predictions based on a virial approximation and simulation results. We find that the virial approach describes the experimental data reasonably well up to a volume fraction of ϕ≈ 0.25 which provides us with a fast and non-costly tool for the analysis and prediction of evanescent wave DLS data. Based on this we propose a new method to assess the near-wall self-diffusion at elevated density. Here, we qualitatively confirm earlier results [Michailidou, et al., Phys. Rev. Lett., 2009, 102, 068302], which indicate that many-particle hydrodynamic interactions are diminished by the presence of the wall at increasing volume fractions as compared to bulk dynamics. Beyond this finding we show that this diminishment is different for the particle motion normal and parallel to the wall. PMID:26264420
Combined temperature and density series for fluid-phase properties. I. Square-well spheres
Elliott, J. Richard; Schultz, Andrew J.; Kofke, David A.
2015-09-21
Cluster integrals are evaluated for the coefficients of the combined temperature- and density-expansion of pressure: Z = 1 + B{sub 2}(β) η + B{sub 3}(β) η{sup 2} + B{sub 4}(β) η{sup 3} + ⋯, where Z is the compressibility factor, η is the packing fraction, and the B{sub i}(β) coefficients are expanded as a power series in reciprocal temperature, β, about β = 0. The methodology is demonstrated for square-well spheres with λ = [1.2-2.0], where λ is the well diameter relative to the hard core. For this model, the B{sub i} coefficients can be expressed in closed form as a function of β, and we develop appropriate expressions for i = 2-6; these expressions facilitate derivation of the coefficients of the β series. Expanding the B{sub i} coefficients in β provides a correspondence between the power series in density (typically called the virial series) and the power series in β (typically called thermodynamic perturbation theory, TPT). The coefficients of the β series result in expressions for the Helmholtz energy that can be compared to recent computations of TPT coefficients to fourth order in β. These comparisons show good agreement at first order in β, suggesting that the virial series converges for this term. Discrepancies for higher-order terms suggest that convergence of the density series depends on the order in β. With selection of an appropriate approximant, the treatment of Helmholtz energy that is second order in β appears to be stable and convergent at least to the critical density, but higher-order coefficients are needed to determine how far this behavior extends into the liquid.
Combined temperature and density series for fluid-phase properties. I. Square-well spheres.
Elliott, J Richard; Schultz, Andrew J; Kofke, David A
2015-09-21
Cluster integrals are evaluated for the coefficients of the combined temperature- and density-expansion of pressure: Z = 1 + B2(β) η + B3(β) η(2) + B4(β) η(3) + ⋯, where Z is the compressibility factor, η is the packing fraction, and the B(i)(β) coefficients are expanded as a power series in reciprocal temperature, β, about β = 0. The methodology is demonstrated for square-well spheres with λ = [1.2-2.0], where λ is the well diameter relative to the hard core. For this model, the B(i) coefficients can be expressed in closed form as a function of β, and we develop appropriate expressions for i = 2-6; these expressions facilitate derivation of the coefficients of the β series. Expanding the B(i) coefficients in β provides a correspondence between the power series in density (typically called the virial series) and the power series in β (typically called thermodynamic perturbation theory, TPT). The coefficients of the β series result in expressions for the Helmholtz energy that can be compared to recent computations of TPT coefficients to fourth order in β. These comparisons show good agreement at first order in β, suggesting that the virial series converges for this term. Discrepancies for higher-order terms suggest that convergence of the density series depends on the order in β. With selection of an appropriate approximant, the treatment of Helmholtz energy that is second order in β appears to be stable and convergent at least to the critical density, but higher-order coefficients are needed to determine how far this behavior extends into the liquid. PMID:26395690
Combined temperature and density series for fluid-phase properties. I. Square-well spheres
NASA Astrophysics Data System (ADS)
Elliott, J. Richard; Schultz, Andrew J.; Kofke, David A.
2015-09-01
Cluster integrals are evaluated for the coefficients of the combined temperature- and density-expansion of pressure: Z = 1 + B2(β) η + B3(β) η2 + B4(β) η3 + ⋯, where Z is the compressibility factor, η is the packing fraction, and the Bi(β) coefficients are expanded as a power series in reciprocal temperature, β, about β = 0. The methodology is demonstrated for square-well spheres with λ = [1.2-2.0], where λ is the well diameter relative to the hard core. For this model, the Bi coefficients can be expressed in closed form as a function of β, and we develop appropriate expressions for i = 2-6; these expressions facilitate derivation of the coefficients of the β series. Expanding the Bi coefficients in β provides a correspondence between the power series in density (typically called the virial series) and the power series in β (typically called thermodynamic perturbation theory, TPT). The coefficients of the β series result in expressions for the Helmholtz energy that can be compared to recent computations of TPT coefficients to fourth order in β. These comparisons show good agreement at first order in β, suggesting that the virial series converges for this term. Discrepancies for higher-order terms suggest that convergence of the density series depends on the order in β. With selection of an appropriate approximant, the treatment of Helmholtz energy that is second order in β appears to be stable and convergent at least to the critical density, but higher-order coefficients are needed to determine how far this behavior extends into the liquid.
Kalyuzhnyi, Y.V. |; Lin, C.; Stell, G.
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.}
Hayashi, Tomohiko; Oshima, Hiraku; Harano, Yuichi; Kinoshita, Masahiro
2016-09-01
For neutral hard-sphere solutes, we compare the reduced density profile of water around a solute g(r), solvation free energy μ, energy U, and entropy S under the isochoric condition predicted by the two theories: dielectrically consistent reference interaction site model (DRISM) and angle-dependent integral equation (ADIE) theories. A molecular model for water pertinent to each theory is adopted. The hypernetted-chain (HNC) closure is employed in the ADIE theory, and the HNC and Kovalenko-Hirata (K-H) closures are tested in the DRISM theory. We also calculate g(r), U, S, and μ of the same solute in a hard-sphere solvent whose molecular diameter and number density are set at those of water, in which case the radial-symmetric integral equation (RSIE) theory is employed. The dependences of μ, U, and S on the excluded volume and solvent-accessible surface area are analyzed using the morphometric approach (MA). The results from the ADIE theory are in by far better agreement with those from computer simulations available for g(r), U, and μ. For the DRISM theory, g(r) in the vicinity of the solute is quite high and becomes progressively higher as the solute diameter d U increases. By contrast, for the ADIE theory, it is much lower and becomes further lower as d U increases. Due to unphysically positive U and significantly larger |S|, μ from the DRISM theory becomes too high. It is interesting that μ, U, and S from the K-H closure are worse than those from the HNC closure. Overall, the results from the DRISM theory with a molecular model for water are quite similar to those from the RSIE theory with the hard-sphere solvent. Based on the results of the MA analysis, we comparatively discuss the different theoretical methods for cases where they are applied to studies on the solvation of a protein. PMID:27366886
NASA Astrophysics Data System (ADS)
Hayashi, Tomohiko; Oshima, Hiraku; Harano, Yuichi; Kinoshita, Masahiro
2016-09-01
For neutral hard-sphere solutes, we compare the reduced density profile of water around a solute g(r), solvation free energy μ, energy U, and entropy S under the isochoric condition predicted by the two theories: dielectrically consistent reference interaction site model (DRISM) and angle-dependent integral equation (ADIE) theories. A molecular model for water pertinent to each theory is adopted. The hypernetted-chain (HNC) closure is employed in the ADIE theory, and the HNC and Kovalenko–Hirata (K–H) closures are tested in the DRISM theory. We also calculate g(r), U, S, and μ of the same solute in a hard-sphere solvent whose molecular diameter and number density are set at those of water, in which case the radial-symmetric integral equation (RSIE) theory is employed. The dependences of μ, U, and S on the excluded volume and solvent-accessible surface area are analyzed using the morphometric approach (MA). The results from the ADIE theory are in by far better agreement with those from computer simulations available for g(r), U, and μ. For the DRISM theory, g(r) in the vicinity of the solute is quite high and becomes progressively higher as the solute diameter d U increases. By contrast, for the ADIE theory, it is much lower and becomes further lower as d U increases. Due to unphysically positive U and significantly larger |S|, μ from the DRISM theory becomes too high. It is interesting that μ, U, and S from the K–H closure are worse than those from the HNC closure. Overall, the results from the DRISM theory with a molecular model for water are quite similar to those from the RSIE theory with the hard-sphere solvent. Based on the results of the MA analysis, we comparatively discuss the different theoretical methods for cases where they are applied to studies on the solvation of a protein.
NASA Astrophysics Data System (ADS)
Oshima, Hiraku; Kinoshita, Masahiro
2015-04-01
In earlier works, we showed that the entropic effect originating from the translational displacement of water molecules plays the pivotal role in protein folding and denaturation. The two different solvent models, hard-sphere solvent and model water, were employed in theoretical methods wherein the entropic effect was treated as an essential factor. However, there were similarities and differences in the results obtained from the two solvent models. In the present work, to unveil the physical origins of the similarities and differences, we simultaneously consider structural transition, cold denaturation, and pressure denaturation for the same protein by employing the two solvent models and considering three different thermodynamic states for each solvent model. The solvent-entropy change upon protein folding/unfolding is decomposed into the protein-solvent pair (PA) and many-body (MB) correlation components using the integral equation theories. Each component is further decomposed into the excluded-volume (EV) and solvent-accessible surface (SAS) terms by applying the morphometric approach. The four physically insightful constituents, (PA, EV), (PA, SAS), (MB, EV), and (MB, SAS), are thus obtained. Moreover, (MB, SAS) is discussed by dividing it into two factors. This all-inclusive investigation leads to the following results: (1) the protein-water many-body correlation always plays critical roles in a variety of folding/unfolding processes; (2) the hard-sphere solvent model fails when it does not correctly reproduce the protein-water many-body correlation; (3) the hard-sphere solvent model becomes problematic when the dependence of the many-body correlation on the solvent number density and temperature is essential: it is not quite suited to studies on cold and pressure denaturating of a protein; (4) when the temperature and solvent number density are limited to the ambient values, the hard-sphere solvent model is usually successful; and (5) even at the ambient
Oshima, Hiraku; Kinoshita, Masahiro
2015-04-14
In earlier works, we showed that the entropic effect originating from the translational displacement of water molecules plays the pivotal role in protein folding and denaturation. The two different solvent models, hard-sphere solvent and model water, were employed in theoretical methods wherein the entropic effect was treated as an essential factor. However, there were similarities and differences in the results obtained from the two solvent models. In the present work, to unveil the physical origins of the similarities and differences, we simultaneously consider structural transition, cold denaturation, and pressure denaturation for the same protein by employing the two solvent models and considering three different thermodynamic states for each solvent model. The solvent-entropy change upon protein folding/unfolding is decomposed into the protein-solvent pair (PA) and many-body (MB) correlation components using the integral equation theories. Each component is further decomposed into the excluded-volume (EV) and solvent-accessible surface (SAS) terms by applying the morphometric approach. The four physically insightful constituents, (PA, EV), (PA, SAS), (MB, EV), and (MB, SAS), are thus obtained. Moreover, (MB, SAS) is discussed by dividing it into two factors. This all-inclusive investigation leads to the following results: (1) the protein-water many-body correlation always plays critical roles in a variety of folding/unfolding processes; (2) the hard-sphere solvent model fails when it does not correctly reproduce the protein-water many-body correlation; (3) the hard-sphere solvent model becomes problematic when the dependence of the many-body correlation on the solvent number density and temperature is essential: it is not quite suited to studies on cold and pressure denaturating of a protein; (4) when the temperature and solvent number density are limited to the ambient values, the hard-sphere solvent model is usually successful; and (5) even at the ambient
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 α, 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 α≳0.8 that do not demix, R(c) decreases strongly with Δϕ(J), as R(c)∼exp(-1/Δϕ(J)(2)), where Δϕ(J) is the difference between the average packing fraction of the amorphous packings and random crystal structures at R(c). Systems with α≲0.8 partially demix, which promotes crystallization, but we still find a strong correlation between R(c) and Δϕ(J). We show that known metal-metal BMGs occur in the regions of the α 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 α to increase packing efficiency, while maximizing α to prevent demixing. PMID:25314450
Trokhymchuk; Orozco; Pizio; Vlachy
1998-11-15
The thermodynamics of a two-component fluid with a hard core interaction and screened Coulomb (Yukawa) interaction between particles, similar to the primitive model of an electrolyte solution, adsorbed in a disordered matrix of hard spheres, is studied by using replica Ornstein-Zernike integral equations and the mean spherical approximation (MSA). The gas-liquid transition is localized. The coexistence curve is investigated dependent on the range of interaction between fluid species, on matrix density, and on fluid-matrix attraction. We have observed shrinking of the coexistence envelope with increasing matrix density. The critical temperature of adsorbed mixture decreases with increasing matrix density. The critical density is less affected; however, it also decreases slightly. The critical temperature is sensitive to the fluid species-matrix attraction and depends nonmonotonously on their strength. For a given matrix microporosity, it increases slightly and then decreases with augmenting strength of fluid-matrix attraction. The critical density is less affected by this attraction. However, it decreases for the model with a sufficiently long-range tail of fluid-matrix attraction. Copyright 1998 Academic Press. PMID:9792783
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
Density-functional theory of inhomogeneous systems of hard spherocylinders
Velasco; Mederos; Sullivan
2000-09-01
The smectic-A phase boundaries of a hard-spherocylinder fluid are calculated using a density-functional theory based on one proposed earlier by Somoza and Tarazona [Phys. Rev. A 41, 965 (1990)]. Our calculations do not employ the translation-rotation decoupling approximation used in previous density-functional theories. The calculated phase boundaries agree well with computer simulation results up to aspect ratios L/D approximately 5 and are in better agreement with the simulations than are previous theories. We generalize the model fluid by including long-range interactions with quadrupolar orientational symmetry, which are taken into account by mean-field approximation. For sufficiently large strength, these interactions produce a smectic-C phase, which undergoes either a continuous or weakly first-order transition to the smectic-A phase. The theory and numerical methods discussed here can be applied to the analysis of interfacial phenomena. PMID:11088887
Bending rigidity and higher-order curvature terms for the hard-sphere fluid near a curved wall.
Urrutia, Ignacio
2014-03-01
In this work I derive analytic expressions for the curvature-dependent fluid-substrate surface tension of a hard-sphere fluid on a hard curved wall. In the first step, the curvature thermodynamic properties are found as truncated power series in the activity in terms of the exactly known second- and third-order cluster integrals of the hard-sphere fluid near spherical and cylindrical walls. These results are then expressed as packing fraction power series and transformed to different reference regions, which is equivalent to considering different positions of the dividing surface. Based on the truncated series it is shown that the bending rigidity of the system is non-null and that higher-order terms in the curvature also exist. In the second step, approximate analytic expressions for the surface tension, the Tolman length, the bending rigidity, and the Gaussian rigidity as functions of the packing fraction are found by considering the known terms of the series expansion complemented with a simple fitting approach. It is found that the obtained formulas accurately describe the curvature thermodynamic properties of the system; further, they are more accurate than any previously published expressions. PMID:24730805
NASA Astrophysics Data System (ADS)
Wolf, Aaron S.; Asimow, Paul D.; Stevenson, David J.
2015-08-01
We develop a new model to understand and predict the behavior of oxide and silicate melts at extreme temperatures and pressures, including deep mantle conditions like those in the early Earth magma ocean. The Coordinated Hard Sphere Mixture (CHaSM) is based on an extension of the hard sphere mixture model, accounting for the range of coordination states available to each cation in the liquid. By utilizing approximate analytic expressions for the hard sphere model, this method is capable of predicting complex liquid structure and thermodynamics while remaining computationally efficient, requiring only minutes of calculation time on standard desktop computers. This modeling framework is applied to the MgO system, where model parameters are trained on a collection of crystal polymorphs, producing realistic predictions of coordination evolution and the equation of state of MgO melt over a wide range of pressures and temperatures. We find that the typical coordination number of the Mg cation evolves continuously upward from 5.25 at 0 GPa to 8.5 at 250 GPa. The results produced by CHaSM are evaluated by comparison with predictions from published first-principles molecular dynamics calculations, indicating that CHaSM is accurately capturing the dominant physics controlling the behavior of oxide melts at high pressure. Finally, we present a simple quantitative model to explain the universality of the increasing Grüneisen parameter trend for liquids, which directly reflects their progressive evolution toward more compact solid-like structures upon compression. This general behavior is opposite that of solid materials, and produces steep adiabatic thermal profiles for silicate melts, thus playing a crucial role in magma ocean evolution.
NASA Astrophysics Data System (ADS)
Zhou, Yaoqi; Stell, George
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.
Hard-sphere dispersions: Small-wave-vector structure-factor measurements in a linear shear flow
NASA Astrophysics Data System (ADS)
Ackerson, Bruce J.; van der Werff, Jos; de Kruif, C. G.
1988-06-01
Small-scattering-wave-vector structure-factor measurements have been made for model hard-sphere suspensions undergoing a steady linear shear flow. The samples are comprised of sterically stabilized silica particles in cyclohexane and have been well characterized previously by rheological, light scattering, and neutron scattering measurements. These combined measurements provide a strict test of recent theories of microscopic order in suspensions undergoing shear and suggest a picture which unifies several intuitive notions about suspensions undergoing shear flow: distortion of the pair correlation function, clustering, layering, and nonequilibrium phase transitions.
NASA Astrophysics Data System (ADS)
Cai, Zhenning; Torrilhon, Manuel
2015-08-01
A sequence of approximate linear collision models for hard-sphere and inverse-power-law gases is introduced. These models are obtained by expanding the linearized Boltzmann collision operator into series, and a practical algorithm is proposed for evaluating the coefficients in the series. The sequence is proven to be convergent to the linearized Boltzmann operator, and it established a connection between the Shakhov model and the linearized collision model. The convergence is demonstrated by solving the spatially homogeneous Boltzmann equation. By observing the magnitudes of the coefficients, simpler models are developed through removing small entries in the coefficient matrices.
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
Baranau, Vasili; Tallarek, Ulrich
2016-06-01
We estimate the excess chemical potential Δμ and excess entropy per particle Δs of computer-generated, monodisperse and polydisperse, frictionless hard-sphere fluids. For this purpose, we utilize the Widom particle insertion method, which for hard-sphere systems relates Δμ to the probability to successfully (without intersections) insert a particle into a system. This insertion probability is evaluated directly for each configuration of hard spheres by extrapolating to infinity the pore radii (nearest-surface) distribution and integrating its tail. The estimates of Δμ and Δs are compared to (and comply well with) predictions from the Boublík-Mansoori-Carnahan-Starling-Leland equation of state. For polydisperse spheres, we employ log-normal particle radii distributions with polydispersities δ = 0.1, 0.2, and 0.3. PMID:27276959
Disordered strictly jammed binary sphere packings attain an anomalously large range of densities
NASA Astrophysics Data System (ADS)
Hopkins, Adam B.; Stillinger, Frank H.; Torquato, Salvatore
2013-08-01
Previous attempts to simulate disordered binary sphere packings have been limited in producing mechanically stable, isostatic packings across a broad spectrum of packing fractions. Here we report that disordered strictly jammed binary packings (packings that remain mechanically stable under general shear deformations and compressions) can be produced with an anomalously large range of average packing fractions 0.634≤ϕ≤0.829 for small to large sphere radius ratios α restricted to α≥0.100. Surprisingly, this range of average packing fractions is obtained for packings containing a subset of spheres (called the backbone) that are exactly strictly jammed, exactly isostatic, and also generated from random initial conditions. Additionally, the average packing fractions of these packings at certain α and small sphere relative number concentrations x approach those of the corresponding densest known ordered packings. These findings suggest for entropic reasons that these high-density disordered packings should be good glass formers and that they may be easy to prepare experimentally. We also identify an unusual feature of the packing fraction of jammed backbones (packings with rattlers excluded). The backbone packing fraction is about 0.624 over the majority of the α-x plane, even when large numbers of small spheres are present in the backbone. Over the (relatively small) area of the α-x plane where the backbone is not roughly constant, we find that backbone packing fractions range from about 0.606 to 0.829, with the volume of rattler spheres comprising between 1.6% and 26.9% of total sphere volume. To generate isostatic strictly jammed packings, we use an implementation of the Torquato-Jiao sequential linear programming algorithm [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.82.061302 82, 061302 (2010)], which is an efficient producer of inherent structures (mechanically stable configurations at the local maxima in the density landscape). The identification and
Mills, P; Snabre, P
2009-11-01
We consider the steady shear flow of a homogeneous and dense assembly of hard spheres suspended in a Newtonian viscous fluid. In a first part, a mean-field approach based on geometric arguments is used to determine the viscous dissipation in a dense isotropic suspension of smooth hard spheres and the hydrodynamic contribution to the suspension viscosity. In a second part, we consider the coexistence of transient solid clusters coupled to regions with free flowing particles near the jamming transition. The fraction of particles in transient clusters is derived through the Landau-Ginzburg concepts for first-order phase transition with an order parameter corresponding to the proportion of "solid" contacts. A state equation for the fraction of particle-accessible volume is introduced to derive the average normal stresses and a constitutive law that relates the total shear stress to the shear rate. The analytical expression of the average normal stresses well accounts for numerical or experimental evaluation of the particle pressure and non-equilibrium osmotic pressure in a dense sheared suspension. Both the friction level between particles and the suspension dilatancy are shown to determine the singularity of the apparent shear viscosity and the flow stability near the jamming transition. The model further predicts a Newtonian behavior for a concentrated suspension of neutrally buoyant particles and no shear thinning behavior in relation with the shear liquefaction of transient solid clusters. PMID:19856003
NASA Astrophysics Data System (ADS)
Filion, L.; Hermes, M.; Ni, R.; Dijkstra, M.
2010-12-01
Over the last number of years several simulation methods have been introduced to study rare events such as nucleation. In this paper we examine the crystal nucleation rate of hard spheres using three such numerical techniques: molecular dynamics, forward flux sampling, and a Bennett-Chandler-type theory where the nucleation barrier is determined using umbrella sampling simulations. The resulting nucleation rates are compared with the experimental rates of Harland and van Megen [Phys. Rev. E 55, 3054 (1997)], Sinn et al. [Prog. Colloid Polym. Sci. 118, 266 (2001)], Schätzel and Ackerson [Phys. Rev. E 48, 3766 (1993)], and the predicted rates for monodisperse and 5% polydisperse hard spheres of Auer and Frenkel [Nature 409, 1020 (2001)]. When the rates are examined in units of the long-time diffusion coefficient, we find agreement between all the theoretically predicted nucleation rates, however, the experimental results display a markedly different behavior for low supersaturation. Additionally, we examined the precritical nuclei arising in the molecular dynamics, forward flux sampling, and umbrella sampling simulations. The structure of the nuclei appears independent of the simulation method, and in all cases, the nuclei contains on average significantly more face-centered-cubic ordered particles than hexagonal-close-packed ordered particles.
NASA Astrophysics Data System (ADS)
Zhou, Shiqi
2011-12-01
Thermodynamic and structural properties of liquids are of fundamental interest in physics, chemistry, and biology, and perturbation approach has been fundamental to liquid theoretical approaches since the dawn of modern statistical mechanics and remains so to this day. Although thermodynamic perturbation theory (TPT) is widely used in the chemical physics community, one of the most popular versions of the TPT, i.e. Zwanzig (Zwanzig, R. W. J. Chem. Phys. 1954, 22, 1420-1426) 1st-order high temperature series expansion (HTSE) TPT and its 2nd-order counterpart under a macroscopic compressibility approximation of Barker-Henderson (Barker, J. A.; Henderson, D. J. Chem. Phys. 1967, 47, 2856-2861), have some serious shortcomings: (i) the nth-order term of the HTSE is involved with reference fluid distribution functions of order up to 2n, and the higher-order terms hence progressively become more complicated and numerically inaccessible; (ii) the performance of the HTSE rapidly deteriorates and the calculated results become even qualitatively incorrect as the temperature of interest decreases. This account deals with the developments that we have made over the last five years or so to advance a coupling parameter series expansion (CPSE) and a non hard sphere (HS) perturbation strategy that has scored some of its greatest successes in overcoming the above-mentioned difficulties. In this account (i) we expatiate on implementation details of our schemes: how input information indispensable to high-order truncation of the CPSE in both the HS and non HS perturbation schemes is calculated by an Ornstein-Zernike integral equation theory; how high-order thermodynamic quantities, such as critical parameters and excess constant volume heat capacity, are extracted from the resulting excess Helmholtz free energy with irregular and inevitable numerical errors; how to select reference potential in the non HS perturbation scheme. (ii) We give a quantitative analysis on why convergence
NASA Astrophysics Data System (ADS)
Wolf, A. S.; Asimow, P. D.; Stevenson, D. J.
2015-12-01
Recent first-principles calculations (e.g. Stixrude, 2009; de Koker, 2013), shock-wave experiments (Mosenfelder, 2009), and diamond-anvil cell investigations (Sanloup, 2013) indicate that silicate melts undergo complex structural evolution at high pressure. The observed increase in cation-coordination (e.g. Karki, 2006; 2007) induces higher compressibilities and lower adiabatic thermal gradients in melts as compared with their solid counterparts. These properties are crucial for understanding the evolution of impact-generated magma oceans, which are dominated by the poorly understood behavior of silicates at mantle pressures and temperatures (e.g. Stixrude et al. 2009). Probing these conditions is difficult for both theory and experiment, especially given the large compositional space (MgO-SiO2-FeO-Al2O3-etc). We develop a new model to understand and predict the behavior of oxide and silicate melts at extreme P-T conditions (Wolf et al., 2015). The Coordinated Hard Sphere Mixture (CHaSM) extends the Hard Sphere mixture model, accounting for the range of coordination states for each cation in the liquid. Using approximate analytic expressions for the hard sphere model, this fast statistical method compliments classical and first-principles methods, providing accurate thermodynamic and structural property predictions for melts. This framework is applied to the MgO system, where model parameters are trained on a collection of crystal polymorphs, producing realistic predictions of coordination evolution and the equation of state of MgO melt over a wide P-T range. Typical Mg-coordination numbers are predicted to evolve continuously from 5.25 (0 GPa) to 8.5 (250 GPa), comparing favorably with first-principles Molecular Dynamics (MD) simulations. We begin extending the model to a simplified mantle chemistry using empirical potentials (generally accurate over moderate pressure ranges, <~30 GPa), yielding predictions rooted in statistical representations of melt structure
Dynamics of Disorder-Order Transitions in Hard Sphere Colloidal Dispersions in micro-g
NASA Technical Reports Server (NTRS)
Zhu, J. X.; Li, M.; Phan, S. E.; Russel, W. B.; Chaikin, Paul M.; Rogers, Rick; Meyers, W.
1996-01-01
We performed a series of experiments on 0.518 millimeter PMMA spheres suspended in an index matching mixture of decalin and tetralin the microgravity environment provided by the Shuttle Columbia on mission STS-73. The samples ranged in concentration from 0.49 to 0.62. volume fraction (phi) of spheres, which covers the range in which liquid, coexistence, solid and glass phases are expected from Earth bound experiments. Light scattering was used to probe the static structure, and the particle dynamics. Digital and 35 mm photos provided information on the morphology of the crystals. In general, the crystallites grew considerably larger (roughly an order of magnitude larger) than the same samples with identical treatment in 1 g. The dynamic light scattering shows the typical short time diffusion and long time caging effects found in 1 g. The surprises that were encountered in microgravity include the preponderance of random hexagonal close packed (RHCP) structures and the complete absence of the expected face centered cubic (FCC) structure, existence of large dendritic crystals floating in the coexistence samples (where liquid and solid phases coexist) and the rapid crystallization of samples which exist only in glass phase under the influence of one g. These results suggest that colloidal crystal growth is profoundly effected by gravity in yet unrecognized ways. We suspect that the RCHP structure is related to the nonequilibrium growth that is evident from the presence of dendrites. An analysis of the dendritic growth instabilities is presented within the framework of the Ackerson-Schatzel equation.
Uniform electron gases. III. Low-density gases on three-dimensional spheres
Agboola, Davids; Knol, Anneke L.; Gill, Peter M. W. Loos, Pierre-François
2015-08-28
By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of Cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGF centers are found by solving the Thomson problem (i.e., the minimum-energy arrangement of n point charges) on the 3-sphere for various values of n. We have found 11 special values of n whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids — the hyper-tetrahedron (n = 5), the hyper-octahedron (n = 8), and the 24-cell (n = 24) — and a fourth is a highly symmetric structure (n = 13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy.
Uniform electron gases. III. Low-density gases on three-dimensional spheres
NASA Astrophysics Data System (ADS)
Agboola, Davids; Knol, Anneke L.; Gill, Peter M. W.; Loos, Pierre-François
2015-08-01
By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of Cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGF centers are found by solving the Thomson problem (i.e., the minimum-energy arrangement of n point charges) on the 3-sphere for various values of n. We have found 11 special values of n whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids — the hyper-tetrahedron (n = 5), the hyper-octahedron (n = 8), and the 24-cell (n = 24) — and a fourth is a highly symmetric structure (n = 13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy.
Finite-size effects in the microscopic structure of a hard-sphere fluid in a narrow cylindrical pore
NASA Astrophysics Data System (ADS)
Román, F. L.; White, J. A.; González, A.; Velasco, S.
2006-04-01
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.
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.
Diffuse interface analysis of crystal nucleation in hard-sphere liquid
NASA Astrophysics Data System (ADS)
Gránásy, László; Pusztai, Tamás
2002-12-01
We show that the increase of the interface free energy with deviation from equilibrium seen in recent Monte Carlo simulations [S. Auer and D. Frenkel, Nature (London) 413, 711 (2001)] can be recovered if the molecular scale diffuseness of the crystal-liquid interface is considered. We compare two models, Gránásy's phenomenological diffuse interface theory, and a density functional theory that relies on the type of Ginzburg-Landau expansion for fcc nucleation, that Shih et al. introduced for bcc crystal. It is shown that, in the range of Monte Carlo simulations, the nucleation rate of the stable fcc phase is by several orders of magnitude higher than for the metastable bcc phase, seen to nucleate first in other fcc systems. The nucleation barrier that the diffuse interface theories predict for small deviations from equilibrium is in far better agreement with the simulations than the classical droplet model. The behavior expected at high densities is model dependent. Gránásy's phenomenological diffuse interface theory indicates a spinodal point close to glass transition, while a nonsingular behavior is predicted by the density functional theory with constant Ginzburg-Landau coefficients. Remarkably, a minimum of the nucleation barrier, similar to the one seen in polydisperse systems, occurs if the known density dependence of the Ginzburg-Landau coefficients is considered.
Funakoshi, Ken-ichi; Nozawa, Akifumi
2012-10-01
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. PMID:23126783
Funakoshi, Ken-ichi; Nozawa, Akifumi
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.
Santos, Andres
2011-05-20
The Boltzmann collision operator for a dilute granular gas of inelastic rough hard spheres is much more intricate than its counterpart for inelastic smooth spheres. Now the one-body distribution function depends not only on the translational velocity v of the center of mass but also on the angular velocity {omega} of the particle. Moreover, the collision rules couple v and {omega}, involving not only the coefficient of normal restitution {alpha} but also the coefficient of tangential restitution {beta}. The aim of this paper is to propose an extension to inelastic rough particles of a Bhatnagar-Gross-Krook-like kinetic model previously proposed for inelastic smooth particles. The Boltzmann collision operator is replaced by the sum of three terms representing: (i) the relaxation to a two-temperature local equilibrium distribution, (ii) the action of a nonconservative drag force F proportional to v-u(u being the flow velocity), and (iii) the action of a nonconservative torque M equal to a linear combination of {omega} and {Omega}({Omega} being the mean angular velocity). The three coefficients in F and M are fixed to reproduce the Boltzmann collisional rates of change of {Omega} and of the two granular temperatures (translational and rotational). A simpler version of the model is also constructed in the form of two coupled kinetic equations for the translational and rotational velocity distributions. The kinetic model is applied to the simple shear flow steady state and the combined influence of {alpha} and {beta} on the shear and normal stresses and on the translational velocity distribution function is analyzed.
Equations of state of freely jointed hard-sphere chain fluids: Numerical results
Stell, G.; Lin, C.; Kalyuzhnyi, Y.V.
1999-03-01
We continue our series of studies in which the equations of state (EOS) are derived based on the product-reactant Ornstein{endash}Zernike approach (PROZA) and first-order thermodynamic perturbation theory (TPT1). These include two compressibility EOS, two virial EOS, and one TPT1 EOS (TPT1-D) that uses the structural information of the dimer fluid as input. In this study, we carry out the numerical implementation for these five EOS and compare their numerical results as well as those obtained from Attard{close_quote}s EOS and GF-D (generalized Flory-dimer) EOS with computer simulation results for the corresponding chain models over a wide range of densities and chain length. The comparison shows that our compressibility EOS, GF-D, and TPT1-D are in quantitative agreement with simulation results, and TPT1-D is the best among various EOS according to its average absolute deviation (AAD). On the basis of a comparison of limited data, our virial EOS appears to be superior to the predictions of Attard{close_quote}s approximate virial EOS and the approximate virial EOS derived by Schweizer and Curro in the context of the PRISM approach; all of them are only qualitatively accurate. The degree of accuracy predicted by our compressibility EOS is comparable to that of GF-D EOS, and both of them overestimate the compressibility factor at low densities and underestimate it at high densities. The compressibility factor of a polydisperse homonuclear chain system is also investigated in this work via our compressibility EOS; the numerical results are identical to those of a monodisperse system with the same chain length. {copyright} {ital 1999 American Institute of Physics.}
NASA Astrophysics Data System (ADS)
Zhou, Alice; O'Hern, Corey; Regan, Lynne
2013-03-01
We seek to dramatically improve computational protein design using minimal models that include only the dominant physical interactions. By modeling proteins with hard-sphere interactions and stereochemical constraints, we are able to explain the side-chain dihedral angle distributions for Leu, Ile, and other hydrophobic residues that are observed in protein crystal structures. We also consider inter-residue interactions on the distribution of side-chain dihedral angles for residues in the hydrophobic core of T4 lysozyme. We calculate the energetic and entropic contributions to the free energy differences between wildtype T4 lysozyme and several mutants involving Leu to Ala substitutions. We find a strong correlation between the entropy difference and the decrease in the melting temperature of the mutatants. These results emphasize that considering both entropy and enthalpy is crucial for obtaining a quantitative understanding of protein stability. NSF DMR-1006537 and PHY-1019147, the Raymond and Beverly Sackler Institute for Biological, Physical and Engineering Sciences, and Howard Hughes Medical Institute International Research Fellowship
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
NASA Astrophysics Data System (ADS)
Haataja, Mikko; Gránásy, László; Löwen, Hartmut
2010-08-01
evolving microstructures in spatially extended system with atomic scale spatial resolution over diffusive time scales, DFT provides both its theoretical underpinning and (hopefully) the means to construct microscopically more quantitative density functionals for use in engineering materials. Outstanding issues within the PFC and DFT approaches, discussed next, will provide further opportunities for interactions between the PFC and DFT communities. 3. Important open issues and exciting avenues for further research In the following we summarize some of the exciting topics for future research, which were discussed during the CECAM workshop. They concern both fundamental problems and applications, all within the framework of DFT and PFC. Addressing these issues will provide a framework for future work in these two overlapping fields. (a) How to construct a reliable density functional (DF) for soft repulsions? Most of the recent developments in classical density functional theory were focussed on hard-sphere-like interactions in the framework of fundamental-measure-theory (FMT) [30-33]. While this approach can be extended to additive and nonadditive mixtures [34, 35] and to non-spherical hard objects [36, 37], it is much more difficult to include soft-core interactions, such as inverse-power-law pair-potentials. There have been attempts to include those, mainly using the Ramakrishnan-Yussouff [38] or the weighted-density [39-41] approximation, or other modifications (see e.g., [42, 43]), but the accuracy of these functionals are inferior to that of FMT for hard spheres. Clearly the FMT of Rosenfeld needs an extension for the hard-core Coulomb system. A complementary approach is to start from a density functional for hard orientable objects [36] and to integrate out the orientational degrees of freedom. This would lead to a softened effective repulsion between spherical objects. We mention finally that in the extreme limit of ultrasoft pair potentials, which are penetrable, the
NASA Technical Reports Server (NTRS)
Zhu, Ji-Xiang; Chaikin, P. M.; Li, Min; Russel, W. B.; Ottewill, R. H.; Rogers, R.; Meyer, W. V.
1998-01-01
Classical hard spheres have long served as a paradigm for our understanding of the structure of liquids, crystals, and glasses and the transitions between these phases. Ground-based experiments have demonstrated that suspensions of uniform polymer colloids are near-ideal physical realizations of hard spheres. However, gravity appears to play a significant and unexpected role in the formation and structure of these colloidal crystals. In the microgravity environment of the Space Shuttle, crystals grow purely via random stacking of hexagonal close-packed planes, lacking any of the face-centered cubic (FCC) component evident in crystals grown in 1 g beyond melting and allowed some time to settle. Gravity also masks 33-539 the natural growth instabilities of the hard sphere crystals which exhibit striking dendritic arms when grown in microgravity. Finally, high volume fraction "glass" samples which fail to crystallize after more than a year in 1 g begin nucleation after several days and fully crystallize in less than 2 weeks on the Space Shuttle.
Drude-type conductivity of charged sphere colloidal crystals: density and temperature dependence.
Medebach, Martin; Jordán, Raquel Chuliá; Reiber, Holger; Schöpe, Hans-Joachim; Biehl, Ralf; Evers, Martin; Hessinger, Dirk; Olah, Julianna; Palberg, Thomas; Schönberger, Ernest; Wette, Patrick
2005-09-01
We report on extensive measurements in the low-frequency limit of the ac conductivity of colloidal fluids and crystals formed from charged colloidal spheres suspended in de-ionized water. Temperature was varied in a range of 5 degrees C < Theta < 35 degrees C and the particle number density n between 0.2 and 25 microm(-3) for the larger, respectively, 2.75 and 210 microm(-3) for the smaller of two investigated species. At fixed Theta the conductivity increased linearly with increasing n without any significant change at the fluid-solid phase boundary. At fixed n it increased with increasing Theta and the increase was more pronounced for larger n. Lacking a rigorous electrohydrodynamic treatment for counterion-dominated systems we describe our data with a simple model relating to Drude's theory of metal conductivity. The key parameter is an effectively transported particle charge or valence Z(*). All temperature dependencies other than that of Z(*) were taken from literature. Within experimental resolution Z(*) was found to be independent of n irrespective of the suspension structure. Interestingly, Z(*) decreases with temperature in near quantitative agreement with numerical calculations. PMID:16178620
Hsu, Wei-Hung; Masim, Frances Camille P; Porta, Matteo; Nguyen, Mai Thanh; Yonezawa, Tetsu; Balčytis, Armandas; Wang, Xuewen; Rosa, Lorenzo; Juodkazis, Saulius; Hatanaka, Koji
2016-09-01
Femtosecond laser-induced hard X-ray generation in air from a 100-µm-thick solution film of distilled water or Au nano-sphere suspension was carried out by using a newly-developed automatic positioning system with 1-µm precision. By positioning the solution film for the highest X-ray intensity, the optimum position shifted upstream as the laser power increased due to breakdown. Optimized positioning allowed us to control X-ray intensity with high fidelity. X-ray generation from Au nano-sphere suspension and distilled water showed different power scaling. Linear and nonlinear absorption mechanism are analyzed together with numerical modeling of light delivery. PMID:27607607
Effect of gamma irradiation on high temperature hardness of low-density polyethylene
NASA Astrophysics Data System (ADS)
Chen, Pei-Yun; Yang, Fuqian; Lee, Sanboh
2015-11-01
Gamma irradiation can cause the change of microstructure and molecular structure of polymer, resulting in the change of mechanical properties of polymers. Using the hardness measurement, the effect of gamma irradiation on the high temperature hardness of low-density polyethylene (LDPE) was investigated. The gamma irradiation caused the increase in the melting point, the enthalpy of fusion, and the portion of crystallinity of LDPE. The Vickers hardness of the irradiated LDPE increases with increasing the irradiation dose, annealing temperature, and annealing time. The activation energy for the rate process controlling the reaction between defects linearly decreases with the irradiation dose. The process controlling the hardness evolution in LDPE is endothermic because LDPE is semi-crystalline.
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.
NASA Astrophysics Data System (ADS)
Virrueta, Alejandro; O'Hern, Corey; Regan, Lynne
Methionine (Met) is a versatile amino acid found frequently both in protein cores and at protein-protein interfaces. Thus, a complete description of the structure of Met is tantamount to a fundamental understanding of protein structure and design. In previous work, we showed that our hard-sphere dipeptide model is able to recapitulate the side chain dihedral angle distributions observed in high-resolution protein crystal structures for the 8 amino acids we have studied to date: Val, Thr, Ser, Leu, Ile, Cys, Tyr, and Phe. Using the same approach, we can predict the observed Met side chain dihedral angle distributions P (χ1) and P (χ2) , but not P (χ3) . In this manuscript, we investigate the possible origins of the discrepancy and identify the minimal additions to the hard-sphere dipeptide model necessary to quantitatively predict P (χ3) of Met. We find that applying a Lennard-Jones potential with weak attraction between hydrogen atoms is sufficient to achieve predictions that match the observed χ3 side chain dihedral angle probability distributions for Met, Nle, and Mse without negatively affecting our results for the 8 previously studied amino acids. A. V. is supported by an NSF Graduate Research Fellowship and a Ford Foundation Fellowship.
NASA Technical Reports Server (NTRS)
Lubken, F.-J.; Hillert, W.; Lehmacher, G.; Von Zahn, U.; Bittner, M.; Offermann, D.; Schmidlin, F. J.; Hauchecorne, A.; Mourier, M.; Czechowsky, P.
1994-01-01
During the course of the DYnamics Adapted Network for the Atmosphere (DYANA) campaign in early 1990, various techniques to measure densities and temperatures from the ground up to the lower thermosphere were employed. Some of these measurements were performed near simultaneously (maximum allowed time difference: 1 h) and at the same location, and therefore offered the unique chance of intercomparison of different techniques. In this study, we will report on intercomparisons of data from ground-based instruments (Rayleigh- and sodium-lidar), balloon-borne methods (datasondes and radiosondes) and rocket-borne techniques (falling spheres and ionization gauges). The main result is that there is good agreement between the various measurements when considering the error bars. Only occasionally did we notice small but systematic differences (e.g. for the datasondes above 65 km). The most extensive intercomparison was possible between the Rayleigh lidar and the falling sphere technique, both employed in Biscarrosse (44 deg N, 1 deg W). Concerning densities, excellent agreement was found below 63 km: the mean of the deviations is less than 1% and the root mean square (RMS) is approximately 3%. Systematic differences of the order of 5% were noticed around 67 km and above 80 km. The former can be accounted for by an instrumental effect of the falling sphere (Ma = 1 transition; Ma = Mach number), whereas the latter is tentatively explained by the presence of Mie scatterers in the upper mesosphere. Concerning temperatures, the agreement is excellent between 35 and 65 km: the mean of the deviations is less than +/- 3 K and the variability is +/- 5 K. The two systematic density differences mentioned above also affect the temperatures: between 65 and 80 km, the Rayleigh lidar temperatures are systematically lower than the falling sphere values by approximately 5 K.
Steel and titanium hollow sphere foams
Hurysz, K.M.; Clark, J.L.; Nagel, A.R.; Lee, K.J.; Cochran, J.K.; Sanders, T.H. Jr.; Hardwicke, C.U.
1998-12-31
Metal hollow sphere foams are fabricated by bonding millimeter sized metal alloy hollow spheres at points of contact. The spheres are formed as powder shells from slurries. For stainless steel spheres, the starting powder is a mixture of iron and chromium oxide. Thermal treatment in hydrogen reduces the oxides to Fe/Cr alloys with less than 2% porosity in sphere walls. The nominal composition is close to that of 405 stainless. Carburization in CO/CO{sub 2} atmosphere followed by heat treatment produces foams of either 410 or 420 type stainless steels depending on carbon content. Compressive stress-strain behavior was measured on point contact bonded stainless foams both before and after carburization. Hardness measurements on steel sphere walls were used to estimate the yield strength. Relative strengths of the foams were positioned between open and closed cell models. This was encouraging because bonding in the foams was less than optimum and the hollow sphere walls contained defects. As processing improves, strengths should increase. To produce titanium alloy spheres, the starting powder is titanium alloy hydride. Thermal treatment in an inert atmosphere decomposes the hydride and sinters the titanium powder in the sphere walls to greater than 96% relative density. Both titanium and Ti-6V-4V spheres and foams have been produced. Oxygen contents are a concern for titanium compositions and processing is being altered to reduce oxygen levels to increase ductility.
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
Hardness of FeB{sub 4}: Density functional theory investigation
Zhang, Miao; Du, Yonghui; Gao, Lili; Lu, Mingchun; Lu, Cheng; Liu, Hanyu
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.
The high density phase of the k-NN hard core lattice gas model
NASA Astrophysics Data System (ADS)
Nath, Trisha; Rajesh, R.
2016-07-01
The k-NN hard core lattice gas model on a square lattice, in which the first k next nearest neighbor sites of a particle are excluded from being occupied by another particle, is the lattice version of the hard disc model in two dimensional continuum. It has been conjectured that the lattice model, like its continuum counterpart, will show multiple entropy-driven transitions with increasing density if the high density phase has columnar or striped order. Here, we determine the nature of the phase at full packing for k up to 820 302 . We show that there are only eighteen values of k, all less than k = 4134, that show columnar order, while the others show solid-like sublattice order.
High-density ferroelectric recording using a hard disk drive-type data storage system
NASA Astrophysics Data System (ADS)
Aoki, Tomonori; Hiranaga, Yoshiomi; Cho, Yasuo
2016-05-01
Ferroelectric probe data storage has been proposed as a novel data storage method in which bits are recorded based on the polarization directions of individual domains. These bits are subsequently read by scanning nonlinear dielectric microscopy. The domain walls of typical ferroelectric materials are quite thin: often only several times the lattice constant, which is advantageous for high-density data storage. In this work, high-density read/write (R/W) demonstrations were conducted using a hard disk drive-type test system, and the writing of bit arrays with a recording density of 3.4 Tbit/in.2 was achieved. Additionally, a series of writing and reading operations was successfully demonstrated at a density of 1 Tbit/in.2. Favorable characteristics of ferroelectric recording media for use with the proposed method are discussed in the latter part of this paper.
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.
The column density distribution of hard X-ray radio galaxies
NASA Astrophysics Data System (ADS)
Panessa, F.; Bassani, L.; Landi, R.; Bazzano, A.; Dallacasa, D.; La Franca, F.; Malizia, A.; Venturi, T.; Ubertini, P.
2016-09-01
In order to investigate the role of absorption in active galactic nuclei (AGN) with jets, we have studied the column density distribution of a hard X-ray selected sample of radio galaxies, derived from the INTEGRAL/Imager on Board the Integral Satellite (IBIS) and Swift/The Burst Alert Telescope (BAT) AGN catalogues (˜7-10 per cent of the total AGN population). The 64 radio galaxies have a typical FR II radio morphology and are characterized by high 20-100 keV luminosities (from 1042 to 1046 erg s-1) and high Eddington ratios (log LBol/LEdd typically larger than ˜0.01). The observed fraction of absorbed AGN (NH > 1022 cm-2) is around 40 per cent among the total sample, and ˜75 per cent among type 2 AGN. The majority of obscured AGN are narrow-line objects, while unobscured AGN are broad-line objects, obeying to the zeroth-order predictions of unified models. A significant anti-correlation between the radio core dominance parameter and the X-ray column density is found. The observed fraction of Compton thick AGN is ˜2-3 per cent, in comparison with the 5-7 per cent found in radio-quiet hard X-ray selected AGN. We have estimated the absorption and Compton thick fractions in a hard X-ray sample containing both radio galaxies and non-radio galaxies and therefore affected by the same selection biases. No statistical significant difference was found in the absorption properties of radio galaxies and non-radio galaxies sample. In particular, the Compton thick objects are likely missing in both samples and the fraction of obscured radio galaxies appears to decrease with luminosity as observed in hard X-ray non-radio galaxies.
Encircling the dark: constraining dark energy via cosmic density in spheres
NASA Astrophysics Data System (ADS)
Codis, S.; Pichon, C.; Bernardeau, F.; Uhlemann, C.; Prunet, S.
2016-05-01
The recently published analytic probability density function for the mildly non-linear cosmic density field within spherical cells is used to build a simple but accurate maximum likelihood estimate for the redshift evolution of the variance of the density, which, as expected, is shown to have smaller relative error than the sample variance. This estimator provides a competitive probe for the equation of state of dark energy, reaching a few percent accuracy on wp and wa for a Euclid-like survey. The corresponding likelihood function can take into account the configuration of the cells via their relative separations. A code to compute one-cell density probability density functions for arbitrary initial power spectrum, top-hat smoothing and various spherical collapse dynamics is made available online so as to provide straightforward means of testing the effect of alternative dark energy models and initial power-spectra on the low-redshift matter distribution.
Encircling the dark: constraining dark energy via cosmic density in spheres
NASA Astrophysics Data System (ADS)
Codis, S.; Pichon, C.; Bernardeau, F.; Uhlemann, C.; Prunet, S.
2016-08-01
The recently published analytic probability density function for the mildly non-linear cosmic density field within spherical cells is used to build a simple but accurate maximum likelihood estimate for the redshift evolution of the variance of the density, which, as expected, is shown to have smaller relative error than the sample variance. This estimator provides a competitive probe for the equation of state of dark energy, reaching a few per cent accuracy on wp and wa for a Euclid-like survey. The corresponding likelihood function can take into account the configuration of the cells via their relative separations. A code to compute one-cell-density probability density functions for arbitrary initial power spectrum, top-hat smoothing and various spherical-collapse dynamics is made available online, so as to provide straightforward means of testing the effect of alternative dark energy models and initial power spectra on the low-redshift matter distribution.
Hu, Yougen; Zhao, Tao; Zhu, Pengli; Zhu, Yu; Liang, Xianwen; Sun, Rong; Wong, Ching-Ping
2016-09-01
Silver nanoparticles (AgNPs) were deposited onto the monodispersed carboxylic polystyrene (CPS) spheres by an improved in situ reduction method. The size and coverage density of the AgNPs on the surface of CPS spheres could be easily tailored by tuning the concentrations of carboxylic functional groups and silver precursor. The morphologies and structures of the resulting CPS/Ag hybrid particles were studied by scanning electron microscopy (SEM), transmission electron microscopy (TEM), X-ray diffraction (XRD), UV-Vis-NIR spectrometer and X-ray photoelectron spectroscopy (XPS), etc. The surface enhanced Raman scattering (SERS) performances of the resulting uniform CPS/Ag hybrid particles were investigated using 4-aminobenzenethiol (4-ABT) as the probe molecule. The optimized CPS/Ag hybrid particles show high enhancement factor (EF) of 2.71×10(7) , low limit of detection (LOD) of 10(-10) m and good reproducibility with relative standard deviation (RSD) of 9.64 %. The good SERS improvement properties demonstrate these hybrid particles could be employed as simple and effective substrates in the SERS spectroscopy. PMID:27511618
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
Boss, Alan P.; Keiser, Sandra A.
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.
Significance of gluon density at soft and hard processes at LHC
NASA Astrophysics Data System (ADS)
Grinyuk, A. A.; Lipatov, A. V.; Lykasov, G. I.
2015-11-01
We study the role of the non-perturbative input to the transverse momentum dependent (TMD) gluon density in hard processes at the LHC. We derive the TMD gluon distribution from the fit of the inclusive hadron spectra measured at low transverse momenta in pp collisions at the LHC and demonstrate that the best description of these spectra for larger hadron transverse momenta can be achieved by matching the derived TMD gluon distribution with the exact solution of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation obtained at small transverse momenta outside the saturation region. A special attention is put to the phenomenological applications of presented TMD parton densities to some LHC processes, which are sensitive to the quark and gluon content of a proton.
Density-functional study of the nematic-isotropic interface of hard spherocylinders.
Velasco, E; Mederos, L; Sullivan, D E
2002-08-01
The Somoza-Tarazona density-functional theory is applied to the isotropic-nematic interface of hard spherocylinders with length (L)-to-diameter (D) ratios in the range L/D=5-20. Properties such as the density and orientational order-parameter profiles and the variation of interfacial tension with bulk nematic tilt angle agree qualitatively with results of previous studies at larger values of L/D using both computer simulation and the Onsager second-virial approximation. The minimum interfacial tension is obtained at a tilt angle of 90 degrees. For values of L/D approximately 5, it is found that the Onsager approximation predicts a spurious minimum in the interfacial tension at small tilt angles. PMID:12241197
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
Expansion-free evolving spheres must have inhomogeneous energy density distributions
Herrera, L.; Le Denmat, G.; Santos, N. O.
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.
Size and Fiber Density Controlled Synthesis of Fibrous Nanosilica Spheres (KCC-1)
Bayal, Nisha; Singh, Baljeet; Singh, Rustam; Polshettiwar, Vivek
2016-01-01
We report a facile protocol for the synthesis of fibrous nano-silica (KCC-1) with controllable size and fiber density. In this work, we have shown that the particle size, fiber density, surface area and pore volume of KCC-1 can be effectively controlled and tuned by changing various reaction parameters, such as the concentrations of urea, CTAB, 1-pentanol, reaction time, temperature, solvent ratio, and even outside stirring time. For the first time, we were able to control the particle size ranging from as small as 170 nm to as large as 1120 nm. We were also able to control the fiber density from low to medium to very dense, which consequently allowed the tuning of the pore volume. We were able to achieve a pore volume of 2.18 cm3/g, which is the highest reported for such a fibrous material. Notably we were even able to increase the surface area up to 1244 m2/g, nearly double the previously reported surface area of KCC-1. Thus, one can now synthesize KCC-1 with various degrees of size, surface area, pore volume, and fiber density. PMID:27118152
Size and Fiber Density Controlled Synthesis of Fibrous Nanosilica Spheres (KCC-1)
NASA Astrophysics Data System (ADS)
Bayal, Nisha; Singh, Baljeet; Singh, Rustam; Polshettiwar, Vivek
2016-04-01
We report a facile protocol for the synthesis of fibrous nano-silica (KCC-1) with controllable size and fiber density. In this work, we have shown that the particle size, fiber density, surface area and pore volume of KCC-1 can be effectively controlled and tuned by changing various reaction parameters, such as the concentrations of urea, CTAB, 1-pentanol, reaction time, temperature, solvent ratio, and even outside stirring time. For the first time, we were able to control the particle size ranging from as small as 170 nm to as large as 1120 nm. We were also able to control the fiber density from low to medium to very dense, which consequently allowed the tuning of the pore volume. We were able to achieve a pore volume of 2.18 cm3/g, which is the highest reported for such a fibrous material. Notably we were even able to increase the surface area up to 1244 m2/g, nearly double the previously reported surface area of KCC-1. Thus, one can now synthesize KCC-1 with various degrees of size, surface area, pore volume, and fiber density.
NASA Astrophysics Data System (ADS)
van Westen, Thijs; Vlugt, Thijs J. H.; Gross, Joachim
2012-07-01
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 (γ), where γ 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)], 10.1080/00268979500102391.
NASA Astrophysics Data System (ADS)
Hansen-Goos, Hendrik
2016-04-01
We derive an analytical equation of state for the hard-sphere fluid that is within 0.01% of computer simulations for the whole range of the stable fluid phase. In contrast, the commonly used Carnahan-Starling equation of state deviates by up to 0.3% from simulations. The derivation uses the functional form of the isothermal compressibility from the Percus-Yevick closure of the Ornstein-Zernike relation as a starting point. Two additional degrees of freedom are introduced, which are constrained by requiring the equation of state to (i) recover the exact fourth virial coefficient B4 and (ii) involve only integer coefficients on the level of the ideal gas, while providing best possible agreement with the numerical result for B5. Virial coefficients B6 to B10 obtained from the equation of state are within 0.5% of numerical computations, and coefficients B11 and B12 are within the error of numerical results. We conjecture that even higher virial coefficients are reliably predicted.
NASA Astrophysics Data System (ADS)
Virrueta, Alejandro; Zhou, Alice; O'Hern, Corey; Regan, Lynne
2014-03-01
Molecular dynamics methods have significantly advanced the understanding of protein folding and stability. However, current force-fields cannot accurately calculate and rank the stability of modified or de novo proteins. One possible reason is that current force-fields use knowledge-based corrections that improve dihedral angle sampling, but do not satisfy the stereochemical constraints for amino acids. I propose the use of simple hard-sphere models for amino acids with stereochemical constraints taken from high-resolution protein crystal structures. This model can enable a correct consideration of the entropy of side-chain rotations, and may be sufficient to predict the effects of single residue mutations in the hydrophobic cores of staphylococcal nuclease and T4 lysozyme on stability changes. I will computationally count the total number of allowed side-chain conformations Ω and calculate the associated entropy, S = kBln(Ω) , before and after each mutation. I will then rank the stability of the mutated cores based on my computed entropy changes, and compare my results with structural and thermodynamic data published by the Stites and Matthews groups. If successful, this project will provide a novel framework for the evaluation of entropic protein stabilities, and serve as a possible tool for computational protein design.
Hansen-Goos, Hendrik
2016-04-28
We derive an analytical equation of state for the hard-sphere fluid that is within 0.01% of computer simulations for the whole range of the stable fluid phase. In contrast, the commonly used Carnahan-Starling equation of state deviates by up to 0.3% from simulations. The derivation uses the functional form of the isothermal compressibility from the Percus-Yevick closure of the Ornstein-Zernike relation as a starting point. Two additional degrees of freedom are introduced, which are constrained by requiring the equation of state to (i) recover the exact fourth virial coefficient B4 and (ii) involve only integer coefficients on the level of the ideal gas, while providing best possible agreement with the numerical result for B5. Virial coefficients B6 to B10 obtained from the equation of state are within 0.5% of numerical computations, and coefficients B11 and B12 are within the error of numerical results. We conjecture that even higher virial coefficients are reliably predicted. PMID:27131556
Ferracane, J L; Ferracane, L L; Braga, R R
2003-07-15
Additives that provide stress relief may be incorporated into dental composites to reduce contraction stress (CS). This study attempted to test the hypothesis that conventional fillers could be replaced by high-density polyethylene (HDPE) spheres in hybrid and nanofill composites to reduce CS, but with minimal effect on mechanical properties. Nanofill and hybrid composites were made from a Bis-GMA/TEGDMA resin having either all silica nanofiller or 75 wt.% strontium glass + 5 wt.% silica and replacing some of the nanofiller or the glass with 0%, 5% (hybrid only), 10% or 20 wt.% HDPE. The surface of the HDPE was either left untreated or had a reactive gas surface treatment (RGST). Contraction stress (CS) was monitored for 10 min in a tensilometer (n = 5) after light curing for 60 s at 390 mW/cm(2). Other specimens (n = 5) were light cured 40 s from two sides in a light-curing unit and aged 1 d in water before testing fracture toughness (K(Ic)), flexure strength (FS), and modulus (E). Results were analyzed by ANOVA with Tukey's multiple comparison test at p < 0.05. There was no difference between composites with RGST and untreated HDPE except for FS-10% HDPE hybrid (RGST higher). An increased level of HDPE reduced contraction stress for both types of composites. Flexure strength, modulus (hybrid only), and fracture toughness were also reduced as the concentration of HDPE increased. SEM showed evidence for HDPE debonding and plastic deformation during fracture of the hybrid composites. In conclusion, the addition of HDPE spheres reduces contraction stress in composites, either through stress relief or a reduction in elastic modulus. PMID:12808590
Improved Contact X-Ray Microradiographic Method to Measure Mineral Density of Hard Dental Tissues.
Schmuck, B D; Carey, C M
2010-03-01
Contact X-ray microradiography is the current gold standard for measuring mineral densities of partially demineralized tooth specimens. The X-ray sensitive film specified in the last J Res NIST publication on the subject is no longer commercially available. OBJECTIVES: Develop a new microradiographic method by identifying a commercially available film with greater than 3000 lines per millimeter resolution, which is sensitive to X rays, and develop correct film processing for X-ray microradiographic application. METHODS: A holographic film was identified as a potential replacement film. Proper exposure was determined utilizing a thick nickel plate to create test-strips. Film development was bracketed around manufacturer suggestions. Film linearity was determined with aluminum step-wedges. Microradiographs of 100 µm thick tooth sections, before and after acidic challenges, were a final test for film. Magnified images were captured with a digital microscope camera with 0.305 micrometers per pixel resolution. RESULTS: The appropriate film exposure was 30 minutes at 80 kV(p) and 3 mA with a development time of 2 minutes. Step-wedge experiments show the system to be linear in terms of pixel intensities with respect to x-ray attenuation for normalized pixel intensity values that are 10% to 90% of full scale (r(2) = 0.997) which encompasses the full exposure region of tooth tissue. Enamel sections were analyzed and show distinctive differences between erosion and demineralization. The image capture device resolution of 0.305 micrometers per pixel limits the system resolution. CONCLUSION: Use of the identified holographic film when combined with the described processing modifications has resulted in an improved X-ray microradiographic method for the measurement of mineral density of dental hard tissues. The method described can be further improved by using a higher resolution digitization system. The method is appropriate for quantitatively measuring changes in mineral
THE FIRST HARD X-RAY POWER SPECTRAL DENSITY FUNCTIONS OF ACTIVE GALACTIC NUCLEUS
Shimizu, T. Taro; Mushotzky, Richard F.
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.
Wang Jianfeng; Li Ran; Xu Tao; Li Yan; Liu Zengqian; Huang Lu; Hua Nengbin; Zhang Tao; Xiao Ruijuan; Li Gong; Li Yanchun
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.
Ates, C.; Moseley, Ch.; Ziegler, K.
2005-06-15
The characteristic oscillations of the density-density correlation function and the resulting structure factor are studied for a hard-core Bose gas in a one-dimensional lattice. Their wavelength diverges as the system undergoes a continuous transition from an incommensurate to a Mott insulating phase. The transition is associated with a unit static structure factor and a vanishing sound velocity. The qualitative picture is unchanged when a weak confining potential is applied to the system.
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.
Brambrink, E; Wei, H G; Barbrel, B; Audebert, P; Benuzzi-Mounaix, A; Boehly, T; Endo, T; Gregory, C D; Kimura, T; Kodama, R; Ozaki, N; Park, H-S; Koenig, M
2009-11-01
We present the application of short-pulse laser-driven hard x rays (>40 keV) for the direct density measurement of iron compressed by a laser-driven shock. By using an on-shot calibration of the spectral absorption, we are able to obtain line densities with 5%-10% precision, although the x-ray source is not monochromatic. We also discuss possibilities for increasing the precision, which would be an improvement for equation of state measurements. PMID:20365083
Large attractive depletion interactions in soft repulsive-sphere binary mixtures.
Cinacchi, Giorgio; Martínez-Ratón, Yuri; Mederos, Luis; Navascués, Guillermo; Tani, Alessandro; Velasco, Enrique
2007-12-01
We consider binary mixtures of soft repulsive spherical particles and calculate the depletion interaction between two big spheres mediated by the fluid of small spheres, using different theoretical and simulation methods. The validity of the theoretical approach, a virial expansion in terms of the density of the small spheres, is checked against simulation results. Attention is given to the approach toward the hard-sphere limit and to the effect of density and temperature on the strength of the depletion potential. Our results indicate, surprisingly, that even a modest degree of softness in the pair potential governing the direct interactions between the particles may lead to a significantly more attractive total effective potential for the big spheres than in the hard-sphere case. This might lead to significant differences in phase behavior, structure, and dynamics of a binary mixture of soft repulsive spheres. In particular, a perturbative scheme is applied to predict the phase diagram of an effective system of big spheres interacting via depletion forces for a size ratio of small and big spheres of 0.2; this diagram includes the usual fluid-solid transition but, in the soft-sphere case, the metastable fluid-fluid transition, which is probably absent in hard-sphere mixtures, is close to being stable with respect to direct fluid-solid coexistence. From these results, the interesting possibility arises that, for sufficiently soft repulsive particles, this phase transition could become stable. Possible implications for the phase behavior of real colloidal dispersions are discussed. PMID:18067358
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
NASA Astrophysics Data System (ADS)
Grinyuk, A. A.; Lipatov, A. V.; Lykasov, G. I.; Zotov, N. P.
2016-01-01
We study the role of the nonperturbative input to the transverse momentum dependent (TMD) gluon density in hard processes at the LHC. We derive the input TMD gluon distribution at a low scale μ02˜1 GeV2 from a fit of inclusive hadron spectra measured at low transverse momenta in p p collisions at the LHC and demonstrate that the best description of these spectra for larger hadron transverse momenta can be achieved by matching the derived TMD gluon distribution with the exact solution of the Balitsky-Fadin-Kuraev-Lipatov equation obtained at low x and small gluon transverse momenta outside the saturation region. Then, we extend the input TMD gluon density to higher μ2 numerically using the Catani-Ciafoloni-Fiorani-Marchesini gluon evolution equation. Special attention is paid to phenomenological applications of the obtained TMD gluon density to some LHC processes, which are sensitive to the gluon content of a proton.
Pinter, Balazs; Nagels, Nick; Herrebout, Wouter A; De Proft, Frank
2013-01-01
Halogen bonds between the trifluoromethyl halides CF(3)Cl, CF(3)Br and CF(3)I, and dimethyl ether, dimethyl sulfide, trimethylamine and trimethyl phosphine were investigated using Pearson's hard and soft acids and bases (HSAB) concept with conceptual DFT reactivity indices, the Ziegler-Rauk-type energy-decomposition analysis, the natural orbital for chemical valence (NOCV) framework and the non-covalent interaction (NCI) index. It is found that the relative importance of electrostatic and orbital (charge transfer) interactions varies as a function of both the donor and acceptor molecules. Hard and soft interactions were distinguished and characterised by atomic charges, electrophilicity and local softness indices. Dual-descriptor plots indicate an orbital σ hole on the halogen similar to the electrostatic σ hole manifested in the molecular electrostatic potential. The predicted high halogen-bond-acceptor affinity of N-heterocyclic carbenes was evidenced in the highest complexation energy for the hitherto unknown CF(3) I·NHC complex. The dominant NOCV orbital represents an electron-density deformation according to a n→σ*-type interaction. The characteristic signal found in the reduced density gradient versus electron-density diagram corresponds to the non-covalent interaction between contact atoms in the NCI plots, which is the manifestation of halogen bonding within the NCI theory. The unexpected C-X bond strengthening observed in several cases was rationalised within the molecular orbital framework. PMID:23169478
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.
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.
NASA Technical Reports Server (NTRS)
Wang, Taylor G. (Inventor); Elleman, Daniel D. (Inventor); Lee, Mark C. (Inventor); Kendall, Jr., James M. (Inventor)
1986-01-01
The improved, heterogeneous catalysts are in the form of gas-impervious, hollow, thin-walled spheres (10) suitably formed of a shell (12) of metal such as aluminum having a cavity (14) containing a gas at a pressure greater than atmospheric pressure. The wall material may be, itself, catalytic or the catalyst can be coated onto the sphere as a layer (16), suitably platinum or iron, which may be further coated with a layer (18) of activator or promoter. The density of the spheres (30) can be uniformly controlled to a preselected value within .+-.10 percent of the density of the fluid reactant such that the spheres either remain suspended or slowly fall or rise through the liquid reactant.
Catalytic, hollow, refractory spheres
NASA Technical Reports Server (NTRS)
Wang, Taylor G. (Inventor); Elleman, Daniel D. (Inventor); Lee, Mark C. (Inventor); Kendall, Jr., James M. (Inventor)
1987-01-01
Improved, heterogeneous, refractory catalysts are in the form of gas-impervious, hollow, thin-walled spheres (10) suitable formed of a shell (12) of refractory such as alumina having a cavity (14) containing a gas at a pressure greater than atmospheric pressure. The wall material may be itself catalytic or a catalytically active material coated onto the sphere as a layer (16), suitably platinum or iron, which may be further coated with a layer (18) of activator or promoter. The density of the spheres (30) can be uniformly controlled to a preselected value within .+-.10 percent of the density of the fluid reactant such that the spheres either remain suspended or slowly fall or rise through the liquid reactant.
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.
Colloidal rod-sphere mixtures: fluid-fluid interfaces and the Onsager limit.
Brader, Joseph M; Esztermann, Ansgar; Schmidt, Matthias
2002-09-01
Using a geometry-based density functional theory we investigate the free interface between demixed bulk fluid phases of a colloidal mixture of hard spheres and vanishingly thin needles. Results are presented for the spatial and orientational density distributions of the particles, as well as for the interface tension. Density profiles display oscillations on the sphere-rich side of the interface provided the sphere liquid phase is on the oscillatory side of the Fisher-Widom line in the bulk phase diagram. Needles tend to align parallel (perpendicular) to the interface on the needle-rich (sphere-rich) side displaying biaxial (uniaxial) order. Furthermore, we generalize the theory to the Onsager limit for interacting rods, and give explicit expressions for the functional in simple geometries. PMID:12366111
NASA Technical Reports Server (NTRS)
Huebner, W. F.; Keady, J. J.
1984-01-01
Energy-independent first-flight transport kernels are evaluated for a spherical region with an R(-2) density distribution. The uncollided angular-flux distribution is obtained and integrated for a source distribution that is proportional to the density to give the uncollided emitted particle flux and current density. These are useful for the calculation of mass, energy, and momentum carried away by fast particles born in the medium. The data are relevant to estimate escape from weakly bound atmospheres such as comet comae, dilute circumstellar envelopes, and some unconfined laboratory plasmas.
Band structures and charge densities of KCl, NaF, and LiF obtained by the intersecting-spheres model
NASA Astrophysics Data System (ADS)
Antoci, S.; Mihich, L.
1980-01-01
The self-consistent electronic structures of KCl, NaF, and LiF have been calculated by the intersecting-spheres model and the results were compared with band structures calculated by other methods using the approximation of the exchange potential adopted by us. While for KCl close agreement was found between the augmented-plane-wave non-muffin-tin results by De Cicco and the intersecting-spheres-model (ISM) band structure, in the case of LiF differences of even 2.5 eV were found between conduction bands calculated by the ISM and the corresponding levels determined by linear-combination-of-atomic-orbitals (LCAO) methods. This disagreement seems to be imputable to a lack of convergence occurring in the LCAO calculations. The Fourier components of the charge densities (scattering factors) were determined using the Kohn-Sham-Gáspár form of the exchange potential. The agreement of the calculated scattering factors with experiment is not much worse than that obtained by Hartree-Fock calculations.
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.
NASA Technical Reports Server (NTRS)
Reed, W. B.
1972-01-01
The sphere launcher was designed to eject a 200 lb, 15 in. diameter sphere from a space vehicle or missile, at a velocity of 58 ft/sec without imparting excessive lateral loads to the vehicle. This launching is accomplished with the vehicle operating in vacuum conditions and under a 9 g acceleration. Two principal elements are used: a high thrust, short burn time rocket motor and two snubbers for reducing the lateral loads to acceptable limits.
NASA Astrophysics Data System (ADS)
Pastore, G.; Bernu, B.; Hansen, J. P.; Hiwatari, Y.
1988-07-01
Using molecular-dynamics (MD) data on a binary-alloy model, we have computed the self (incoherent) -part of the density autocorrelation functions of both species in the supercooled liquid and near the glass transition, over an extensive range of wave numbers. Standard theoretical models of liquid-state theory fail to reproduce the data, while the Chudley-Elliott jump diffusion model yields reasonable results in the glass range. With a suitable scaling of the time axis, the data for different temperatures can be brought onto a single master curve, which is well fitted by a Kohlrausch (``stretched-exponential'') function with a wave-number-dependent exponent.
Piestrup, M.A. ); Moran, M.J. ); Boyers, D.G.; Pincus, C.I. ); Kephart, J.O. ); Gearhart, R.A. ); Maruyama, X.K. )
1991-03-01
In experiments using targets consisting of many thin metal foils, we have demonstrated that a narrow, forward-directed cone of transition radiation in the 8- to 60-keV spectral range can be generated by electron beams with moderate energies (between 100 and 500 MeV). The theory suggests that high-density, moderate-atomic-number metals are the optimum foil materials and that the foil thickness can be chosen to maximize photon production within a desired spectral range. The three targets used in the experiments consisted of 10 foils of 1-{mu}m-thick gold, 40 foils of 8.5-{mu}m stainless steel, and 20 foils of 7.9-{mu}m copper. The efficiency with which hard x rays are generated, and the fact that the requisite electron-beam energies are lower by a factor of 5 to 10, make such a radiation source an attractive alternative to synchrotron radiation for applications such as medical imaging, spectroscopy, and microscopy.
Confined disordered strictly jammed binary sphere packings
NASA Astrophysics Data System (ADS)
Chen, D.; Torquato, S.
2015-12-01
Disordered jammed packings under confinement have received considerably less attention than their bulk counterparts and yet arise in a variety of practical situations. In this work, we study binary sphere packings that are confined between two parallel hard planes and generalize the Torquato-Jiao (TJ) sequential linear programming algorithm [Phys. Rev. E 82, 061302 (2010), 10.1103/PhysRevE.82.061302] to obtain putative maximally random jammed (MRJ) packings that are exactly isostatic with high fidelity over a large range of plane separation distances H , small to large sphere radius ratio α , and small sphere relative concentration x . We find that packing characteristics can be substantially different from their bulk analogs, which is due to what we term "confinement frustration." Rattlers in confined packings are generally more prevalent than those in their bulk counterparts. We observe that packing fraction, rattler fraction, and degree of disorder of MRJ packings generally increase with H , though exceptions exist. Discontinuities in the packing characteristics as H varies in the vicinity of certain values of H are due to associated discontinuous transitions between different jammed states. When the plane separation distance is on the order of two large-sphere diameters or less, the packings exhibit salient two-dimensional features; when the plane separation distance exceeds about 30 large-sphere diameters, the packings approach three-dimensional bulk packings. As the size contrast increases (as α decreases), the rattler fraction dramatically increases due to what we call "size-disparity" frustration. We find that at intermediate α and when x is about 0.5 (50-50 mixture), the disorder of packings is maximized, as measured by an order metric ψ that is based on the number density fluctuations in the direction perpendicular to the hard walls. We also apply the local volume-fraction variance στ2(R ) to characterize confined packings and find that these
Zhang, Kai; Fan, Meng; Liu, Yanhui; Schroers, Jan; Shattuck, Mark D.; O’Hern, Corey S.
2015-11-14
When a liquid is cooled well below its melting temperature at a rate that exceeds the critical cooling rate R{sub c}, the crystalline state is bypassed and a metastable, amorphous glassy state forms instead. R{sub c} (or the corresponding critical casting thickness d{sub c}) characterizes the glass-forming ability (GFA) of each material. While silica is an excellent glass-former with small R{sub c} < 10{sup −2} K/s, pure metals and most alloys are typically poor glass-formers with large R{sub c} > 10{sup 10} K/s. Only in the past thirty years have bulk metallic glasses (BMGs) been identified with R{sub c} approaching that for silica. Recent simulations have shown that simple, hard-sphere models are able to identify the atomic size ratio and number fraction regime where BMGs exist with critical cooling rates more than 13 orders of magnitude smaller than those for pure metals. However, there are a number of other features of interatomic potentials beyond hard-core interactions. How do these other features affect the glass-forming ability of BMGs? In this manuscript, we perform molecular dynamics simulations to determine how variations in the softness and non-additivity of the repulsive core and form of the interatomic pair potential at intermediate distances affect the GFA of binary alloys. These variations in the interatomic pair potential allow us to introduce geometric frustration and change the crystal phases that compete with glass formation. We also investigate the effect of tuning the strength of the many-body interactions from zero to the full embedded atom model on the GFA for pure metals. We then employ the full embedded atom model for binary BMGs and show that hard-core interactions play the dominant role in setting the GFA of alloys, while other features of the interatomic potential only change the GFA by one to two orders of magnitude. Despite their perturbative effect, understanding the detailed form of the intermetallic potential is important for
NASA Astrophysics Data System (ADS)
Zhang, Kai; Fan, Meng; Liu, Yanhui; Schroers, Jan; Shattuck, Mark D.; O'Hern, Corey S.
2015-11-01
When a liquid is cooled well below its melting temperature at a rate that exceeds the critical cooling rate Rc, the crystalline state is bypassed and a metastable, amorphous glassy state forms instead. Rc (or the corresponding critical casting thickness dc) characterizes the glass-forming ability (GFA) of each material. While silica is an excellent glass-former with small Rc < 10-2 K/s, pure metals and most alloys are typically poor glass-formers with large Rc > 1010 K/s. Only in the past thirty years have bulk metallic glasses (BMGs) been identified with Rc approaching that for silica. Recent simulations have shown that simple, hard-sphere models are able to identify the atomic size ratio and number fraction regime where BMGs exist with critical cooling rates more than 13 orders of magnitude smaller than those for pure metals. However, there are a number of other features of interatomic potentials beyond hard-core interactions. How do these other features affect the glass-forming ability of BMGs? In this manuscript, we perform molecular dynamics simulations to determine how variations in the softness and non-additivity of the repulsive core and form of the interatomic pair potential at intermediate distances affect the GFA of binary alloys. These variations in the interatomic pair potential allow us to introduce geometric frustration and change the crystal phases that compete with glass formation. We also investigate the effect of tuning the strength of the many-body interactions from zero to the full embedded atom model on the GFA for pure metals. We then employ the full embedded atom model for binary BMGs and show that hard-core interactions play the dominant role in setting the GFA of alloys, while other features of the interatomic potential only change the GFA by one to two orders of magnitude. Despite their perturbative effect, understanding the detailed form of the intermetallic potential is important for designing BMGs with cm or greater casting thickness.
Zhang, Kai; Fan, Meng; Liu, Yanhui; Schroers, Jan; Shattuck, Mark D; O'Hern, Corey S
2015-11-14
When a liquid is cooled well below its melting temperature at a rate that exceeds the critical cooling rate Rc, the crystalline state is bypassed and a metastable, amorphous glassy state forms instead. Rc (or the corresponding critical casting thickness dc) characterizes the glass-forming ability (GFA) of each material. While silica is an excellent glass-former with small Rc < 10(-2) K/s, pure metals and most alloys are typically poor glass-formers with large Rc > 10(10) K/s. Only in the past thirty years have bulk metallic glasses (BMGs) been identified with Rc approaching that for silica. Recent simulations have shown that simple, hard-sphere models are able to identify the atomic size ratio and number fraction regime where BMGs exist with critical cooling rates more than 13 orders of magnitude smaller than those for pure metals. However, there are a number of other features of interatomic potentials beyond hard-core interactions. How do these other features affect the glass-forming ability of BMGs? In this manuscript, we perform molecular dynamics simulations to determine how variations in the softness and non-additivity of the repulsive core and form of the interatomic pair potential at intermediate distances affect the GFA of binary alloys. These variations in the interatomic pair potential allow us to introduce geometric frustration and change the crystal phases that compete with glass formation. We also investigate the effect of tuning the strength of the many-body interactions from zero to the full embedded atom model on the GFA for pure metals. We then employ the full embedded atom model for binary BMGs and show that hard-core interactions play the dominant role in setting the GFA of alloys, while other features of the interatomic potential only change the GFA by one to two orders of magnitude. Despite their perturbative effect, understanding the detailed form of the intermetallic potential is important for designing BMGs with cm or greater casting
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.
NASA Astrophysics Data System (ADS)
Jin, Chengguo; Huang, Duohui; Shao, Juxiang; Yang, Junsheng; Wan, Minjie; Wang, Fanhou; Cao, Qilong
2016-03-01
MnTeMoO6 crystals have been grown by the top-seeded solution growth method. The hardness, density, specific heat and chemical stability of MnTeMoO6 crystal were measured and analyzed. The actual density of MnTeMoO6 crystals are slightly larger than 5.0g/cm-3. An average Mohs hardness of about 4.5 is presented in MnTeMoO6 crystals, indicating the crystal is easy to cut and polish. The hardness and actual density of MnTeMoO6 crystals increase with the crystal quality, and the crystal with the smallest hardness and actual density has the poorest quality. The specific heat was measured to be 0.41-0.55 Jg-1K-1 over the temperature range of 20-300 {}^{circ}C. The chemical stability measurements indicate that the MnTeMoO6 crystal has an excellent chemical stability and is resistant to diluted hydrochloric acid and diluted nitric acid.
NASA Technical Reports Server (NTRS)
Schmidlin, F. J.; Michel, W. R.
1985-01-01
Analysis of inflatable sphere measurements obtained during the Energy Budget and MAP/WINE campaigns led to questions concerning the precision of the MPS-36 radar used for tracking the spheres; the compatibility of the sphere program with the MPS-36 radar tracking data; and the oversmoothing of derived parameters at high altitudes. Simulations, with winds having sinusoidal vertical wavelengths, were done with the sphere program (HIROBIN) to determine the resolving capability of various filters. It is concluded that given a precision radar and a perfectly performing sphere, the HIROBIN filters can be adjusted to provide small-scale perturbation information to 70 km (i.e., sinusoidal wavelengths of 2 km). It is recommended that the HIROBIN program be modified to enable it to use a variable length filter, that adjusts to fall velocity and accelerations to provide wind data with small perturbations.
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
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.
Free Volume of the Hard Spheres Gas
ERIC Educational Resources Information Center
Shutler, P. M. E.; Martinez, J. C.; Springham, S. V.
2007-01-01
The Enskog factor [chi] plays a central role in the theory of dense gases, quantifying how the finite size of molecules causes many physical quantities, such as the equation of state, the mean free path, and the diffusion coefficient, to deviate from those of an ideal gas. We suggest an intuitive but rigorous derivation of this fact by showing how…
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.
NASA Technical Reports Server (NTRS)
Martinez, Andres; Benavides, Jose Victor; Ormsby, Steve L.; GuarnerosLuna, Ali
2014-01-01
Synchronized Position Hold, Engage, Reorient, Experimental Satellites (SPHERES) are bowling-ball sized satellites that provide a test bed for development and research into multi-body formation flying, multi-spacecraft control algorithms, and free-flying physical and material science investigations. Up to three self-contained free-flying satellites can fly within the cabin of the International Space Station (ISS), performing flight formations, testing of control algorithms or as a platform for investigations requiring this unique free-flying test environment. Each satellite is a self-contained unit with power, propulsion, computers, navigation equipment, and provides physical and electrical connections (via standardized expansion ports) for Principal Investigator (PI) provided hardware and sensors.
Towards composite spheres as building blocks for structured molecules.
Lee, Lloyd L; Pellicane, Giuseppe
2016-10-19
In order to design a flexible molecular model that mimics the chemical moieties of a polyatomic molecule, we propose the 'composite-sphere' model that can assemble the essential elements to produce the structure of the target molecule. This is likened to the polymerization process where monomers assemble to form the polymer. The assemblage is built into the pair interaction potentials which can 'react' (figuratively) with selective pieces into various bonds. In addition, we preserve the spherical symmetries of the individual pair potentials so that the isotropic Ornstein-Zernike equation (OZ) for multi-component mixtures can be used as a theoretical framework. We first test our approach on generating a dumbbell molecule. An equimolar binary mixture of hard spheres and square-well spheres are allowed to react to form a dimer. As the bond length shrinks to zero, we create a site-site model of a Janus-like molecule with a repulsive moiety and an attractive moiety. We employ the zero-separation (ZSEP) closure to solve the OZ equations. The structure and thermodynamic properties are calculated at three isotherms and at several densities and the results are compared with Monte Carlo simulations. The close agreement achieved demonstrates that the ZSEP closure is a reliable theory for this composite-sphere fluid model. PMID:27546819
NASA Astrophysics Data System (ADS)
Shoockron, Joseph
1989-06-01
This work deals with the analysis and calculation of the critical angle for the ricochet of a sphere off water. The critical angle is defined as the maximum incidence angle of a sphere over water which enables it to ricochet. This work presents the development and calculation of the forces acting on the sphere during its entry into the water. Since the critical angle is very sensitive to the hydrodynamic forces, the accurate development and calculation of these forces has been emphasized in some previous methods. There is a simple empirical formula for calculation of the critical angle, which is theta(sub c) = 18 deg/square root of zeta, where theta(sub c) is the critical angle and zeta is the ratio between the density of the sphere and the density of the water. Likewise, there are works which give a theoretical basis to the above-mentioned formula. This formula does not depend on the incidence velocity of the sphere or on the sphere radius, these being parameters that affect the critical angle. In this work it is verified that the critical angle depends on these added parameters, in the form of the F(sub r) number, where F(sub r) = V(exp 2)/Rg.
Nematic-isotropic phase transition in diblock fused-sphere chain fluids
NASA Astrophysics Data System (ADS)
Diplock, R.; Sullivan, D. E.; Jaffer, K. M.; Opps, S. B.
2004-06-01
A density-functional theory for the isotropic-nematic phase transition in fluids of rigid or semiflexible fused hard-sphere chains, developed previously by the authors, is extended to diblock chains each consisting of both a rigid and a flexible part. The theory is compared with recent Monte Carlo simulation results of McBride et al. The theoretical results for the variation of pressure and nematic order parameter with density agree well with the simulation data over density ranges where the simulations find isotropic and nematic phases.
Bending and Gaussian rigidities of confined soft spheres from second-order virial series.
Urrutia, Ignacio
2016-08-01
We use virial series to study the equilibrium properties of confined soft-spheres fluids interacting through the inverse-power potentials. The confinement is induced by hard walls with planar, spherical, and cylindrical shapes. We evaluate analytically the coefficients of order two in density of the wall-fluid surface tension γ and analyze the curvature contributions to the free energy. Emphasis is in bending and Gaussian rigidities, which are found analytically at order two in density. Their contribution to γ(R) and the accuracy of different truncation procedures to the low curvature expansion are discussed. Finally, several universal relations that apply to low-density fluids are analyzed. PMID:27627288
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
Augustin, Arun; Huilgol, Prashant; Udupa, K Rajendra; Bhat K, Udaya
2016-10-01
Copper is a well proven antimicrobial material which can be used in the form of a coating on the touch surfaces. Those coating can offer a good service as touch surface for very long time if only they possess good mechanical properties like scratch resistance and microhardness. In the present work the above mentioned mechanical properties were determined on the electrodeposited copper thin film; deposited on double zincated aluminium. During deposition, current density was varied from 2Adm(-2) to 10Adm(-2), to produce crystallite size in the range of 33.5nm to 66nm. The crystallite size was calculated from the X-ray peak broadening (Scherrer׳s formula) which were later confirmed by TEM micrographs. The scratch hardness and microhardness of the coating were measured and correlated with the crystallite size in the copper coating. Both characteristic values were found to increase with the reduction in crystallite size. Reduced crystallite size (Hall-Petch effect) and preferred growth of copper films along (111) plane play a significant role on the increase in the hardness of the coating. Further, TEM analysis reveals the presence of nano-twins in the film deposited at higher current density, which contributed to a large extent to the sharp increase of coating hardness compared to the mechanism of Hall-Petch effect. The antimicrobial ability of the coated sample has been evaluated against Escherichia coli bacteria and which is compared with that of commercially available bulk copper using the colony count method. 94% of E. coli cells were died after six hours of exposure to the copper coated surface. The morphology of the copper treated cells was studied using SEM. PMID:27450037
Specific surface area of overlapping spheres in the presence of obstructions.
Jenkins, D R
2013-02-21
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. PMID:23445025
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.
On the laser beam cutting of metallic hollow sphere structures
NASA Astrophysics Data System (ADS)
Riegel, H.; Fruhstuck, J.; Merkel, M.; Winkler, R.; Öchsner, A.
2013-02-01
Metal hollow sphere structures (MHSS) represent a group of advanced composite materials. A high geometric reproducibility leads to relatively constant mechanical and physical properties. Therefore MHSS combine the advantages of cellular metals without a big scattering of the material properties. Several joining technologies can be used to assemble single metallic hollow spheres to a interdependent structure like sintering, soldering and adhering. This allows adjusting of variable macroscopic attitudes. A cutting process for MHSS needs to reflect the special characteristic of the composite material. In this paper laser beam cutting is presented as an efficient technology. The small amount of heat being involved during the process results in a small heat affected zone. All investigations were done with MHSS having different macroscopic dimensions (length, width, thickness, joining technology). The experimental work was done by a CO2-laser. The cut depth is governed by the heat input per unit length and the MHSS density. Finite element analysis was used to predict heat flux and temperature level for different geometric parameters of the spheres (diameter, wall thickness). The numerical simulation allows a detailed analysis of the physical process in the zone that is influenced by the laser beam and which can hardly be analysed by measuring technique. The models for the static and transient finite element analysis consider heat conduction and convection.
Konishi, Junko; Watari, Fumio; Kawamoto, Chiharu; Sano, Hidehiko
2003-08-15
The effect of the sphered particles on the contraction ratio of porcelain inlay processed by the cold isostatic pressure (CIP) method was investigated. The conventional lathe-cut porcelain powder was crushed to finer particles and the secondary particles with spherical shape by adding binders of acrylic resin, wax, and polyvinyl alcohol, respectively. Porcelain powder was molded as a disc-shaped green body in a refractory model and compressed at 200 MPa by CIP. From this green compact, the sintered porcelain was obtained by only one step of firing. The porcelain discs were then used for the measurements of contraction ratio, scanning microscopic observation, biaxial flexure strength, Vickers hardness, and density. Firing contraction was decreased to about 1% in the sphered particle groups, compared with 7% of the lathe-cut porcelain powder. Although biaxial flexure strength was about 85 MPa, which is lower than the 120 MPa of the control group, and the density was significantly decreased by about 10% from the 2.4 g/cm3 of the control substance, Vickers hardness, which ranged from 531 to 537, showed no significant differences among all of the groups. The CIP method could save labor in the process of making porcelain inlays, and sphered powders could contribute significantly to a decrease in the contraction ratio in the sintering process. PMID:12861607
Hard convex lens-shaped particles: Densest-known packings and phase behavior
NASA Astrophysics Data System (ADS)
Cinacchi, Giorgio; Torquato, Salvatore
2015-12-01
By using theoretical methods and Monte Carlo simulations, this work investigates dense ordered packings and equilibrium phase behavior (from the low-density isotropic fluid regime to the high-density crystalline solid regime) of monodisperse systems of hard convex lens-shaped particles as defined by the volume common to two intersecting congruent spheres. We show that, while the overall similarity of their shape to that of hard oblate ellipsoids is reflected in a qualitatively similar phase diagram, differences are more pronounced in the high-density crystal phase up to the densest-known packings determined here. In contrast to those non-(Bravais)-lattice two-particle basis crystals that are the densest-known packings of hard (oblate) ellipsoids, hard convex lens-shaped particles pack more densely in two types of degenerate crystalline structures: (i) non-(Bravais)-lattice two-particle basis body-centered-orthorhombic-like crystals and (ii) (Bravais) lattice monoclinic crystals. By stacking at will, regularly or irregularly, laminae of these two crystals, infinitely degenerate, generally non-periodic in the stacking direction, dense packings can be constructed that are consistent with recent organizing principles. While deferring the assessment of which of these dense ordered structures is thermodynamically stable in the high-density crystalline solid regime, the degeneracy of their densest-known packings strongly suggests that colloidal convex lens-shaped particles could be better glass formers than colloidal spheres because of the additional rotational degrees of freedom.
Hard convex lens-shaped particles: Densest-known packings and phase behavior
Cinacchi, Giorgio; Torquato, Salvatore
2015-12-14
By using theoretical methods and Monte Carlo simulations, this work investigates dense ordered packings and equilibrium phase behavior (from the low-density isotropic fluid regime to the high-density crystalline solid regime) of monodisperse systems of hard convex lens-shaped particles as defined by the volume common to two intersecting congruent spheres. We show that, while the overall similarity of their shape to that of hard oblate ellipsoids is reflected in a qualitatively similar phase diagram, differences are more pronounced in the high-density crystal phase up to the densest-known packings determined here. In contrast to those non-(Bravais)-lattice two-particle basis crystals that are the densest-known packings of hard (oblate) ellipsoids, hard convex lens-shaped particles pack more densely in two types of degenerate crystalline structures: (i) non-(Bravais)-lattice two-particle basis body-centered-orthorhombic-like crystals and (ii) (Bravais) lattice monoclinic crystals. By stacking at will, regularly or irregularly, laminae of these two crystals, infinitely degenerate, generally non-periodic in the stacking direction, dense packings can be constructed that are consistent with recent organizing principles. While deferring the assessment of which of these dense ordered structures is thermodynamically stable in the high-density crystalline solid regime, the degeneracy of their densest-known packings strongly suggests that colloidal convex lens-shaped particles could be better glass formers than colloidal spheres because of the additional rotational degrees of freedom.
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 κ = 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.
Rana, Atanu; Dey, Subal; Agrawal, Amita; Dey, Abhishek
2015-10-01
Density functional theory (DFT) calculations are performed on the active site of biotin synthase (BS) to investigate the sulfur transfer from the Fe(2)S(2) cluster to dethiobiotin (DTB). The active site is modeled to include both the 1st and 2nd sphere residues. Molecular orbital theory considerations and calculation on smaller models indicate that only an S atom (not S²⁻) transfer from an oxidized Fe(2)S(2) cluster leads to the formation of biotin from the DTB using two adenosyl radicals generated from S-adenosyl-L-methionine. The calculations on larger protein active site model indicate that a 9-monothiobiotin bound reduced cluster should be an intermediate during the S atom insertion from the Fe(2)S(2) cluster consistent with experimental data. The Arg260 bound to Fe1, being a weaker donor than cysteine bound to Fe(2), determines the geometry and the electronic structure of this intermediate. The formation of this intermediate containing the C9-S bond is estimated to have a ΔG(≠) of 17.1 kcal/mol while its decay by the formation of the 2nd C6-S bond is calculated to have a ΔG(≠) of 29.8 kcal/mol, i.e. the 2nd C-S bond formation is calculated to be the rate determining step in the cycle and it leads to the decay of the Fe(2)S(2) cluster. Significant configuration interaction (CI), present in these transition states, helps lower the barrier of these reactions by ~30-25 kcal/mol relative to a hypothetical outer-sphere reaction. The conserved Phe285 residue near the Fe(2)S(2) active site determines the stereo selectivity at the C6 center of this radical coupling reaction. Reaction mechanism of BS investigated using DFT calculations. Strong CI and the Phe285 residue control the kinetic rate and stereochemistry of the product. PMID:26369537
Technology Transfer Automated Retrieval System (TEKTRAN)
Hard pans, hard layers, or compacted horizons, either surface or subsurface, are universal problems that limit crop production. Hard layers can be caused by traffic or soil genetic properties that result in horizons with high density or cemented soil particles; these horizons have elevated penetrati...
Thermodynamic properties and entropy scaling law for diffusivity in soft spheres
NASA Astrophysics Data System (ADS)
Pieprzyk, S.; Heyes, D. M.; Brańka, 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
The Smart SPHERES space robot (Synchronized Position Hold, Engage, Reorient, Experimental Satellites) equipped with an Android smartphone performs a video survey inside of the International Space S...
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.
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. PMID:25768504
Local thermodynamic mapping for effective liquid density-functional theory
NASA Technical Reports Server (NTRS)
Kyrlidis, Agathagelos; Brown, Robert A.
1992-01-01
The structural-mapping approximation introduced by Lutsko and Baus (1990) in the generalized effective-liquid approximation is extended to include a local thermodynamic mapping based on a spatially dependent effective density for approximating the solid phase in terms of the uniform liquid. This latter approximation, called the local generalized effective-liquid approximation (LGELA) yields excellent predictions for the free energy of hard-sphere solids and for the conditions of coexistence of a hard-sphere fcc solid with a liquid. Moreover, the predicted free energy remains single valued for calculations with more loosely packed crystalline structures, such as the diamond lattice. The spatial dependence of the weighted density makes the LGELA useful in the study of inhomogeneous solids.
ERIC Educational Resources Information Center
Szekely, George
2011-01-01
This article describes an art lesson that allows students to set up and collect sphere canvases. Spheres move art away from a rectangular canvas into a dimension that requires new planning and painting. From balls to many other spherical canvases that bounce, roll, float and fly, art experiences are envisioned by students. Even if adults recognize…
Periodically oscillating plasma sphere
Park, J.; Nebel, R.A.; Stange, S.; Murali, S. Krupakar
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 Astrophysics Data System (ADS)
Chaney, A.; Lu, Lei; Stern, A.
2015-09-01
We show that fuzzy spheres are solutions of Lorentzian Ishibashi-Kawai-Kitazawa-Tsuchiya-type matrix models. The solutions serve as toy models of closed noncommutative cosmologies where big bang/crunch singularities appear only after taking the commutative limit. The commutative limit of these solutions corresponds to a sphere embedded in Minkowski space. This "sphere" has several novel features. The induced metric does not agree with the standard metric on the sphere, and, moreover, it does not have a fixed signature. The curvature computed from the induced metric is not constant, has singularities at fixed latitudes (not corresponding to the poles) and is negative. Perturbations are made about the solutions, and are shown to yield a scalar field theory on the sphere in the commutative limit. The scalar field can become tachyonic for a range of the parameters of the theory.
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.
NASA Astrophysics Data System (ADS)
Shaulov, S. B.; Besshapov, S. P.; Kabanova, N. V.; Sysoeva, T. I.; Antonov, R. A.; Anyuhina, A. M.; Bronvech, E. A.; Chernov, D. V.; Galkin, V. I.; Tkaczyk, W.; Finger, M.; Sonsky, M.
2009-12-01
The expedition carried out in March, 2008 to Lake Baikal became an important stage in the development of the SPHERE experiment. During the expedition the SPHERE-2 installation was hoisted, for the first time, on a tethered balloon, APA, to a height of 700 m over the lake surface covered with ice and snow. A series of test measurements were made. Preliminary results of the data processing are presented. The next plan of the SPHERE experiment is to begin a set of statistics for constructing the CR spectrum in the energy range 10-10 eV.
NASA Public Affairs Officer Kelly Humphries conducts a phone interview with Mark Micire, SPHERES Engineering Manager at Ames Research Center. Questions? Ask us on Twitter @NASA_Johnson and include ...
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.
Density functional theory for carbon dioxide crystal
Chang, Yiwen; Mi, Jianguo Zhong, Chongli
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.
Jets generated by a sphere moving vertically in stratified fluids
NASA Astrophysics Data System (ADS)
Hanazaki, Hideshi; Okino, Shinya; Nakamura, Shota; Akiyama, Shinsaku
2013-11-01
Unsteady development of buoyant jets generated by a sphere moving vertically at constant speeds in stratified fluids is investigated. Initially, the sphere simply drags light upper fluids or isopycnal surfaces as it goes down, as long as the molecular diffusion of density is negligible. In the succeeding period, molecular diffusion of density in the boundary layer on the sphere surface becomes increasingly significant, especially in the lower hemisphere. Then, the density is no longer conserved and a vertical jet starts from the rear/upper stagnation point of the sphere, since the fluid particle of altered but small density tends to go back to its original height. Strength and radius of those jets depend significantly on stratification (Froude number), as well as the Reynolds number and the Schmidt number. These mechanisms are investigated by numerical simulations and measurements by laser induced fluorescence (LIF).
Poisson-Boltzmann thermodynamics of counterions confined by curved hard walls
NASA Astrophysics Data System (ADS)
Šamaj, Ladislav; Trizac, Emmanuel
2016-01-01
We consider a set of identical mobile pointlike charges (counterions) confined to a domain with curved hard walls carrying a uniform fixed surface charge density, the system as a whole being electroneutral. Three domain geometries are considered: a pair of parallel plates, the cylinder, and the sphere. The particle system in thermal equilibrium is assumed to be described by the nonlinear Poisson-Boltzmann theory. While the effectively one-dimensional plates and the two-dimensional cylinder have already been solved, the three-dimensional sphere problem is not integrable. It is shown that the contact density of particles at the charged surface is determined by a first-order Abel differential equation of the second kind which is a counterpart of Enig's equation in the critical theory of gravitation and combustion or explosion. This equation enables us to construct the exact series solutions of the contact density in the regions of small and large surface charge densities. The formalism provides, within the mean-field Poisson-Boltzmann framework, the complete thermodynamics of counterions inside a charged sphere (salt-free system).
Poisson-Boltzmann thermodynamics of counterions confined by curved hard walls.
Šamaj, Ladislav; Trizac, Emmanuel
2016-01-01
We consider a set of identical mobile pointlike charges (counterions) confined to a domain with curved hard walls carrying a uniform fixed surface charge density, the system as a whole being electroneutral. Three domain geometries are considered: a pair of parallel plates, the cylinder, and the sphere. The particle system in thermal equilibrium is assumed to be described by the nonlinear Poisson-Boltzmann theory. While the effectively one-dimensional plates and the two-dimensional cylinder have already been solved, the three-dimensional sphere problem is not integrable. It is shown that the contact density of particles at the charged surface is determined by a first-order Abel differential equation of the second kind which is a counterpart of Enig's equation in the critical theory of gravitation and combustion or explosion. This equation enables us to construct the exact series solutions of the contact density in the regions of small and large surface charge densities. The formalism provides, within the mean-field Poisson-Boltzmann framework, the complete thermodynamics of counterions inside a charged sphere (salt-free system). PMID:26871116
The compression of spheres coated with an aqueous ethylcellulose dispersion.
Miller, R A; Leung, E M; Oates, R J
1999-04-01
Tablets were compressed from commercial samples of Sugar Spheres NF, Sucrose NF, Corn Starch NF, as well as ground spheres and a physical mixture of ground sucrose plus cornstarch. Additional tablets were compressed from spheres that had been coated with a water-soluble cellulosic polymer solution followed by an aqueous ethylcellulose dispersion. Tableting parameters measured "in-die" included work of compression, peak offset time, tablet density, and Young's modulus. Following ejection, tensile strength was determined under diametrical loading. Dissolution of a marker contained in the water-soluble layer was determined for both compressed and uncompressed spheres. Porosities at peak pressure and peak offset times or tensile strength as functions of peak pressure did not differ between tablets compressed from pristine spheres or from ground spheres. Tablets compressed from spheres had higher values for porosity, tensile strength, and peak offset time than those compressed from sucrose or the sucrose: starch mixture. Values for work of compression were higher for tablets compressed from pristine spheres or from starch. This was attributed to the work required for particle deformation and for breaking of the spheres. The greatest elastic recovery during decompression was observed for tablets compressed from pristine spheres or starch. More brittle behavior was observed for tablets compressed from sucrose or the sucrose: starch mixture. Tablets compressed from ground spheres were more brittle than those compressed from the pristine spheres, indicating an effect due to grinding. Most mechanical properties of tablets compressed from the coated spheres were comparable to those of tablets compressed from uncoated spheres. An exception was diametric strain for tablets compressed from spheres coated with the aqueous ethylcellulose dispersion. These values increased since the plasticized ethylcellulose allowed greater distortion of the tablet before failure occurred. The dye
Note: Sound velocity of a soft sphere model near the fluid-solid phase transition.
Khrapak, Sergey A
2016-03-28
The quasilocalized charge approximation is applied to estimate the sound velocity of simple soft sphere fluid with the repulsive inverse-power-law interaction. The obtained results are discussed in the context of the sound velocity of the hard-sphere system and of liquid metals at the melting temperature. PMID:27036483
NASA Astrophysics Data System (ADS)
Alemany, M. M. G.; Rey, C.; Gallego, L. J.
1996-11-01
We present a molecular dynamics study of the collective correlation functions of a hard-core system with an attractive Yukawa tail, for various thermodynamic states in the fluid and liquid regions of the phase diagram. The results are compared with available information for hard spheres. The small-q behavior of the intermediate scattering functions indicates the propagation of sound waves, i.e., phononlike collective excitations, in the hard-core Yukawa system. The upper limit of q for these collective modes is practically independent of the thermodynamic state. The computed transverse current correlation functions show that at liquid densities the hard-core Yukawa system is able to sustain shear wave propagation above a critical q; the upper limit of q for sound waves and the lower limit for shear waves nearly coincide. All of these features are qualitatively similar to those found for hard spheres. However, there are significant quantitative differences, which reflect the influence of the attractive Yukawa tail on the dynamical behavior of the system.
Oil capture from a water surface by a falling sphere
NASA Astrophysics Data System (ADS)
Smolka, Linda; McLaughlin, Clare; Witelski, Thomas
2015-11-01
When a spherical particle is dropped from rest into an oil lens that floats on top of a water surface, a portion of the oil adheres to the sphere. Once the sphere comes to rest at the subsurface, the oil forms a pendant drop that remains attached in equilibrium to the sphere effectively removing oil from the water surface. Best fit solutions of the Laplace equation to experimental profiles are used to investigate the parameter dependence of the radius of curvature and the filling and contact angles at the three-phase contact line of the pendant drop for spheres with different wetting properties, densities and radii. The volume of oil captured by a sphere increases with a sphere's mass and diameter. However, lighter and smaller spheres capture more oil relative to their own volume than do heavier and larger spheres (scaling with the sphere mass ~M - 0 . 544) and are thus more efficient at removing oil from a water surface. The authors wish to acknowledge the support of the National Science Foundation Grant Nos. DMS-0707755 and DMS-0968252.
Human postprandial gastric emptying of 1-3-millimeter spheres.
Meyer, J H; Elashoff, J; Porter-Fink, V; Dressman, J; Amidon, G L
1988-06-01
Microspheres of pancreatin should empty from the stomachs of patients with pancreatic insufficiency as fast as food. The present study was undertaken in 26 healthy subjects to identify the size of spheres that would empty from the stomach with food and to determine whether different meals alter this size. Spheres of predefined sizes were labeled with 113mIn or 99mTc. Using a gamma-camera, we studied the concurrent gastric emptying of spheres labeled with 113mIn and of chicken liver labeled with 99mTc in 100-g, 154-kcal or 420-g, 919-kcal meals, or the concurrent emptying of 1-mm vs. larger spheres. One-millimeter spheres emptied consistently (p less than 0.01, paired t-test) faster than 2.4- or 3.2-mm spheres when ingested together with either the 420- or 100-g meals. Thus, in the 1-3-mm range of diameters, sphere size was a more important determinant of sphere emptying than meal size. Statistical analyses indicated that spheres 1.4 +/- 0.3 mm in diameter with a density of 1 empty at the same rate as 99mTc-liver. Our data indicate some commercially marketed microspheres of pancreatin will empty too slowly to be effective in digestion of food. PMID:3360258
Human postprandial gastric emptying of 1-3-millimeter spheres
Meyer, J.H.; Elashoff, J.; Porter-Fink, V.; Dressman, J.; Amidon, G.L.
1988-06-01
Microspheres of pancreatin should empty from the stomachs of patients with pancreatic insufficiency as fast as food. The present study was undertaken in 26 healthy subjects to identify the size of spheres that would empty from the stomach with food and to determine whether different meals alter this size. Spheres of predefined sizes were labeled with /sup 113m/In or /sup 99m/Tc. Using a gamma-camera, we studied the concurrent gastric emptying of spheres labeled with /sup 113m/In and of chicken liver labeled with /sup 99m/Tc in 100-g, 154-kcal or 420-g, 919-kcal meals, or the concurrent emptying of 1-mm vs. larger spheres. One-millimeter spheres emptied consistently (p less than 0.01, paired t-test) faster than 2.4- or 3.2-mm spheres when ingested together with either the 420- or 100-g meals. Thus, in the 1-3-mm range of diameters, sphere size was a more important determinant of sphere emptying than meal size. Statistical analyses indicated that spheres 1.4 +/- 0.3 mm in diameter with a density of 1 empty at the same rate as /sup 99m/Tc-liver. Our data indicate some commercially marketed microspheres of pancreatin will empty too slowly to be effective in digestion of food.
ERIC Educational Resources Information Center
Kolata, Gina
1985-01-01
To determine how hard it is for computers to solve problems, researchers have classified groups of problems (polynomial hierarchy) according to how much time they seem to require for their solutions. A difficult and complex proof is offered which shows that a combinatorial approach (using Boolean circuits) may resolve the problem. (JN)
Li, Xufan; Chi, Miaofang; Mahurin, Shannon Mark; Liu, Rui; Chuang, Yen -Jun; Dai, Sheng; Pan, Zhengwei
2016-01-18
Hard-sphere-templating method has been widely used to synthesize hollow carbon spheres (HCSs), in which the spheres were firstly coated with a carbon precursor, followed by carbonization and core removal. The obtained HCSs are generally amorphous or weakly graphitized (with the help of graphitization catalysts). In this work, we report on the fabrication of graphitized HCSs and yolk–shell Au@HCS nanostructures using a modified templating method, in which smooth, uniform graphene layers were grown on SiO2 spheres or Au@SiO2 nanoparticles via metal-catalyst-free chemical vapor deposition (CVD) of methane. Furthermore, our work not only provides a new method to fabricate high-quality, graphitized HCSsmore » but also demonstrates a reliable approach to grow quality graphene on oxide surfaces using CVD without the presence of metal catalysts.« less
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)
Claudi, R.; Gratton, R.; Desidera, S.; Maire, A.-L.; Mesa, D.; Turatto, M.; Baruffolo, A.; Cascone, E.; De Caprio, V.; D'Orazi, V.; Fantinel, D.; Giro, E.; Salasnich, B.; Scuderi, S.; Sissa, E.; Beuzit, J.-L.; Mouillet, D.
The Spectro-Polarimetric High-contrast Exoplanet Research (SPHERE) facility mounted at ESO-VLT aims at discovering giant extrasolar planets in the proximity of bright stars and characterising them through spectroscopic and polarimetric observations. SPHERE is a complete system with a core made of an extreme-Adaptive Optics (XAO) turbulence correction, a pupil tracker and NIR and Visible coronagraph devices. At its back end, a differential dual imaging camera (IRDIS) and an integral field spectrograph (IFS) work in the Near Infrared (NIR) (0.95 < lambda < 2.32 μm) while a high resolution polarization camera covers the visible domain (0.6 < lambda < 0.9 μm). The IFS is a low resolution spectrograph (R˜50) that operates in the near IR (0.95< lambda < 1.6 μm), an optimal wavelength range for the detection of planetary features, over a field of view of about 1.7 × 1.7 square arcsecs. From spectra it is possible to reconstruct monochromatic images with high contrast (10-6 at 0.5 arcsec) and high spatial resolution, well inside the star PSF. The commissioning of the instrument ended in October 2014 and ESO has already offered SPHERE to the community. In this paper several results obtained during the commissioning and science verification phase are described.
Myers, B.F.; Montgomery, F.C.; Morris, R.N.
1993-08-01
The equivalent sphere model, which is widely used in calculating the release of fission gases from nuclear fuel, is idealized. The model is based on the diffusion of fission products in and their escape from a homogeneous sphere of fuel; the fission products are generated at a constant rate and undergo radiodecay. The fuel is assumed to be a set of spherical particles with a common radius. The value of the radius is such that the surface-to-volume ratio, S/V, of the set of spherical particles is the same as the S/V of the fuel mass of interest. The release rate depends on the dimensionless quantity {lambda}a{sup 2}/D where {lambda} is the radiodecay constant, a, the equivalent sphere radius and D, the diffusion coefficient. In the limit {lambda}t {much_gt} 1, the steady-state fractional release for isotopes with half-lives less than about 5 d is given by the familiar relation R/B = 3{radical}D/{lambda}a{sup 2} (1). For the spherical particles, S/V = 3/a. However, in important cases, the assumption of a single value of a is inappropriate. Examples of configurations for which multiple values of a are appropriate include powders, hydrolyzed fuel kernels, normally configured HTR fuel particles and perhaps, fuel kernels alone. In the latter case, one can imagine a distribution of values of a whose mean yields the value appropriate for agreement of Eq. (1) with measurement.
NASA Astrophysics Data System (ADS)
Nilson, Robert H.; Griffiths, Stewart K.
2006-10-01
Molecular density profiles and charge distributions determined by density functional theory (DFT) are used in conjunction with the continuum Navier-Stokes equations to compute electro-osmotic flows in nanoscale channels. The ion species of the electrolyte are represented as centrally charged hard spheres, and the solvent is treated as a dense fluid of neutral hard spheres having a uniform dielectric constant. The model explicitly accounts for Lennard-Jones interactions among fluid and wall molecules, hard sphere repulsions, and short range electrical interactions, as well as long range Coulombic interactions. Only the last of these interactions is included in classical Poisson-Boltzmann (PB) modeling of the electric field. Although the proposed DFT approach is quite general, the sample calculations presented here are limited to symmetric monovalent electrolytes. For a prescribed surface charge, this DFT model predicts larger counterion concentrations near charged channel walls, relative to classical PB modeling, and hence smaller concentrations in the channel center. This shifting of counterions toward the walls reduces the effective thickness of the Debye layer and reduces electro-osmotic velocities as compared to classical PB modeling. Zeta potentials and fluid speeds computed by the DFT model are as much as two or three times smaller than corresponding PB results. This disparity generally increases with increasing electrolyte concentration, increasing surface charge density and decreasing channel width. The DFT results are found to be comparable to those obtained by molecular dynamics simulation, but require considerably less computing time.
Ultraviolet characterization of integrating spheres.
Shaw, Ping-Shine; Li, Zhigang; Arp, Uwe; Lykke, Keith R
2007-08-01
We have studied the performance of polytetrafluoroethylene integrating spheres in the ultraviolet (UV) region with wavelengths as short as 200 nm. Two techniques were used for this study; first, the spectral throughput of an integrating sphere irradiated by a deuterium lamp was analyzed by a monochromator. Second, a UV laser beam was directed into an integrating sphere, and spectrally dispersed laser induced fluorescence was studied. Significant absorption and fluorescence features were observed in the UV region and attributed to the contamination in the integrating sphere. We demonstrate that integrating spheres are easily contaminated by environmental pollutants such as polycyclic aromatic hydrocarbons emitted from engine exhaust. Baking of the contaminated integrating sphere can reverse some but not all of the effects caused by contaminants. The implications for using integrating spheres for UV measurement are discussed. PMID:17676122
Ultraviolet characterization of integrating spheres
NASA Astrophysics Data System (ADS)
Shaw, Ping-Shine; Li, Zhigang; Arp, Uwe; Lykke, Keith R.
2007-08-01
We have studied the performance of polytetrafluoroethylene integrating spheres in the ultraviolet (UV) region with wavelengths as short as 200 nm. Two techniques were used for this study; first, the spectral throughput of an integrating sphere irradiated by a deuterium lamp was analyzed by a monochromator. Second, a UV laser beam was directed into an integrating sphere, and spectrally dispersed laser induced fluorescence was studied. Significant absorption and fluorescence features were observed in the UV region and attributed to the contamination in the integrating sphere. We demonstrate that integrating spheres are easily contaminated by environmental pollutants such as polycyclic aromatic hydrocarbons emitted from engine exhaust. Baking of the contaminated integrating sphere can reverse some but not all of the effects caused by contaminants. The implications for using integrating spheres for UV measurement are discussed.
Quantum states of two particles on concentric spheres
NASA Astrophysics Data System (ADS)
Ezra, Gregory S.; Berry, R. Stephen
1983-10-01
The model of two particles on a sphere is extended to two particles on concentric spheres (POCS). The quantum states are found for two electrons, one on a sphere of radius 10 a.u. (simulating the shell n=3 in He) and the other, on spheres of 10, 15, 25, 50, and 100 a.u. The eigenvalues and densities ρ(θ12) exhibit a transition from collective, moleculelike behavior to independent-particle-like behavior with Russell-Saunders coupling. The parallel problem of two particles with electron masses interacting via a repulsive Gaussian potential is also treated and a similar transition from collective to independent-particle behavior found. The principal difference between the two cases is only the region of radius of the larger sphere where the transition occurs.
Sheinberg, Haskell
1986-01-01
A composition of matter having a Rockwell A hardness of at least 85 is formed from a precursor mixture comprising between 3 and 10 weight percent boron carbide and the remainder a metal mixture comprising from 70 to 90 percent tungsten or molybdenum, with the remainder of the metal mixture comprising nickel and iron or a mixture thereof. The composition has a relatively low density of between 7 to 14 g/cc. The precursor is preferably hot pressed to yield a composition having greater than 100% of theoretical density.
Sheinberg, H.
1983-07-26
A composition of matter having a Rockwell A hardness of at least 85 is formed from a precursor mixture comprising between 3 and 10 wt % boron carbide and the remainder a metal mixture comprising from 70 to 90% tungsten or molybdenum, with the remainder of the metal mixture comprising nickel and iron or a mixture thereof. The composition has a relatively low density of between 7 and 14 g/cc. The precursor is preferably hot pressed to yield a composition having greater than 100% of theoretical density.
Porosity and specific surface for interpenetrable-sphere models of two-phase random media
NASA Astrophysics Data System (ADS)
Rikvold, Per Arne; Stell, George
1985-01-01
We derive and numerically evaluate expressions for the porosity (matrix volume fraction) φ 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 ɛ, such that for ɛ=1 they reduce to mutually impenetrable spheres, and for ɛ=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 g2(r1, r2). To find the associated gn(r1,...,rn) for n≳2, which are needed to evaluate φ 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 φ 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 φ vs dimensionless density, and of s vs φ. We also briefly discuss the relations between the results obtained in the two cases. Finally, we consider generalizations of φ and s that define the volume and surface available to a particle of finite size, rather than a point.
Equilibrium configurations of degenerate fluid spheres
Whitman, P.G.
1985-04-01
Equilibrium configurations of degenerate fluid spheres which assume a polytropic form in the ultrahigh-density regime are considered. We show that analytic solutions more general than those of Misner and Zapolsky exist which possess the asymptotic equation of state. Simple expressions are derived which indicate this nature of the fluids in the extreme relativistic limit, and the stability of these interiors is considered in the asymptotic region.
Ellipsoids beat Spheres: Experiments with Candies, Colloids and Crystals
NASA Astrophysics Data System (ADS)
Chaikin, Paul
2006-04-01
How many gumballs fit in the glass sphere of a gumball machine? Scientists have been puzzling over problems like this since the Ancient Greeks. Yet it was only recently proven that the standard way of stacking oranges at a grocery store--with one orange on top of each set of three below--is the densist packing for spheres, with a packing fraction φ˜ 0.74. Random (amorphous) packings of spheres have a lower density, with φ ˜0.64. The density of crystalline and random packings of atoms is intimately related to the melting transition in matter. We have studied the crystal-liquid transition in spherical colloidal systems on earth and in microgravity. The simplest objects to study after spheres are squashed spheres -- ellipsoids. Surprisingly we find that ellipsoids can randomly pack more densely than spheres, up to φ˜0.68 - 0.71 for a shape close to that of M&M's^ Candies, and even approach φ˜0.75 for general ellipsoids. The higher density relates directly to the higher number of neighbors needed to prevent the more asymetric ellipsoid from rotating. We have also found the ellipsoids can be packed in a crystalline array to a density, φ˜.7707 which exceeds the highest previous packing. Our findings provide insights into granular materials, rigidity, crystals and glasses, and they may lead to higher quality ceramic materials.
Theoretical study of miscibility and glass-forming trends in mixtures of polystyrene spheres
NASA Technical Reports Server (NTRS)
Shih, W.-H.; Stroud, D.
1984-01-01
A theoretical study of glass-forming trends and miscibility in mixtures of polystyrene spheres (polyballs) of different diameters, suspended in an aqueous solution, is presented. The polyballs are assumed to be charged and to interact via a Debye-Hueckel screened Coulomb potential. The Helmholtz free energy is calculated from a variational principle based on the Gibbs-Bogoliubov inequality, in which a mixture of hard spheres of different diameters is chosen as the reference system. It is found that when the charges of the two types of polyballs are sufficiently different, the variationally determined ratio of hard-sphere diameters differs substantially, leading to packing difficulties characteristic of glass formation. The experimentally observed range of glass formation corresponds to a ratio of hard-sphere diameters of 0.8 or less. Calculations of the free energy as a function of concentration indicate that the liquid polyball mixture is stable against the phase separation, even for widely different polyball charges.
Parsons-Lee approach for oblate hard spherocylinders
NASA Astrophysics Data System (ADS)
Gámez, F.; Merkling, P. J.; Lago, S.
2010-07-01
A Parsons-Lee approach for the isotropic-nematic transition and equation of state (EoS) of oblate hard spherocylinders is presented. The expansion of the orientation distribution function in terms of Legendre polynomials along with a closed expression for the mutually excluded volume of hard particles gives accurate values for the EoS. Results presented in this work compare favorably with recent simulation results for oblate hard spherocylinders and cut spheres. The discussion extends to nematic order parameter.
Krogh, M.; Hansen, C.; Painter, J.; de Verdiere, G.C.
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.
Forming MOFs into spheres by use of molecular gastronomy methods.
Spjelkavik, Aud I; Aarti; Divekar, Swapnil; Didriksen, Terje; Blom, Richard
2014-07-14
A novel method utilizing hydrocolloids to prepare nicely shaped spheres of metal-organic frameworks (MOFs) has been developed. Microcrystalline CPO-27-Ni particles are dispersed in either alginate or chitosan solutions, which are added dropwise to solutions containing, respectively, either divalent group 2 cations or base that act as gelling agents. Well-shaped spheres are immediately formed, which can be dried into spheres containing mainly MOF (>95 wt %). The spheronizing procedures have been optimized with respect to maximum specific surface area, shape, and particle density of the final sphere. At optimal conditions, well-shaped 2.5-3.5 mm diameter CPO-27-Ni spheres with weight-specific surface areas <10 % lower than the nonformulated CPO-27-Ni precursor, and having sphere densities in the range 0.8 to 0.9 g cm(-3) and particle crushing strengths above 20 N, can be obtained. The spheres are well suited for use in fixed-bed catalytic or adsorption processes. PMID:24964774
High pressure gas spheres for neutron and photon experiments
NASA Astrophysics Data System (ADS)
Rupp, G.; Petrich, D.; Käppeler, F.; Kaltenbaek, J.; Leugers, B.; Reifarth, R.
2009-09-01
High pressure gas spheres have been designed and successfully used in several nuclear physics experiments on noble gases. The pros and cons of this solution are the simple design and the high reliability versus the fact that the density is limited to 40-60% of liquid or solid gas samples. Originally produced for neutron capture studies at keV energies, the comparably small mass of the gas spheres were an important advantage, which turned out to be of relevance for other applications as well. The construction, performance, and operation of the spheres are described and examples for their use are presented.
Structure of hard-hypersphere fluids in odd dimensions
NASA Astrophysics Data System (ADS)
Rohrmann, René D.; Santos, Andrés
2007-11-01
The structural properties of single component fluids of hard hyperspheres in odd space dimensionalities d are studied with an analytical approximation method that generalizes the rational function approximation earlier introduced in the study of hard-sphere fluids [S. B. Yuste and A. Santos, Phys. Rev. A 43, 5418 (1991)]. The theory makes use of the exact form of the radial distribution function to first order in density and extends it to finite density by assuming a rational form for a function defined in Laplace space, the coefficients being determined by simple physical requirements. Fourier transform in terms of reverse Bessel polynomials constitute the mathematical framework of this approximation, from which an analytical expression for the static structure factor is obtained. In its most elementary form, the method recovers the solution of the Percus-Yevick closure to the Ornstein-Zernike equation for hyperspheres at odd dimensions. The present formalism allows one to go beyond by yielding solutions with thermodynamic consistency between the virial and compressibility routes to any desired equation of state. Excellent agreement with available computer simulation data at d=5 and d=7 is obtained.
Random packing of spheres in Menger sponge
NASA Astrophysics Data System (ADS)
Cieśla, Michał; Barbasz, Jakub
2013-06-01
Random packing of spheres inside fractal collectors of dimension 2 < d < 3 is studied numerically using Random Sequential Adsorption (RSA) algorithm. The paper focuses mainly on the measurement of random packing saturation limit. Additionally, scaling properties of density autocorrelations in the obtained packing are analyzed. The RSA kinetics coefficients are also measured. Obtained results allow to test phenomenological relation between random packing saturation density and collector dimension. Additionally, performed simulations together with previously obtained results confirm that, in general, the known dimensional relations are obeyed by systems having non-integer dimension, at least for d < 3.
Random packing of spheres in Menger sponge.
Cieśla, Michał; Barbasz, Jakub
2013-06-01
Random packing of spheres inside fractal collectors of dimension 2 < d < 3 is studied numerically using Random Sequential Adsorption (RSA) algorithm. The paper focuses mainly on the measurement of random packing saturation limit. Additionally, scaling properties of density autocorrelations in the obtained packing are analyzed. The RSA kinetics coefficients are also measured. Obtained results allow to test phenomenological relation between random packing saturation density and collector dimension. Additionally, performed simulations together with previously obtained results confirm that, in general, the known dimensional relations are obeyed by systems having non-integer dimension, at least for d < 3. PMID:23758392
Experimental Investigation of Mechanical Properties of Metallic Hollow Sphere Structures
NASA Astrophysics Data System (ADS)
Friedl, O.; Motz, C.; Peterlik, H.; Puchegger, S.; Reger, N.; Pippan, R.
2008-02-01
Metallic foam was fabricated from 316L stainless steel spheres, where the bonding of the spheres was achieved by a sintering process. The mechanical behavior of a low-density material (0.3 g/cm3) with 2- and 4-mm sphere diameter and a high-density material (0.6 g/cm3) with 4-mm sphere diameter was investigated in compression and tension. The cell wall material of this hollow sphere structure (HSS) had different morphologies: dense and porous sintered walls were investigated. The cell wall morphology affects the Young’s modulus (stiffness) and the ductility of the HSS material. Defects, such as the cell wall porosity, lower the ductility of the material. Besides the quasi-static measurements, the HSS material was tested with a resonance frequency method (dynamic measurement), to obtain detailed information on the stiffness at different temperatures up to 700 °C. In-situ compression and tension tests were carried out to understand the deformation mechanisms on the scale of the single hollow spheres. The failure mechanisms in the vicinity of the sintering neck of the spheres was investigated. A doubling of the density leads to an increase of the plateau stress and the ultimate tensile stress of the material, whereas the ductility (strain to fracture) depended mainly on the cell wall morphology. Due to the mainly tensile loading of the cell walls in the vicinity of the sinter neck, the ultimate tensile strength doubled for the high-density HSS, in good agreement with theoretical considerations. In compression, the gain in the plateau stress was not as distinctive compared with the theoretical considerations assuming a bending dominated deformation. The influence of structural parameters, such as cell wall morphology, cell wall thickness, and sphere diameter, on the mechanical behavior is discussed.
A simple weighted-density-functional approach to the structure of inhomogeneous fluids
NASA Astrophysics Data System (ADS)
Patra, Chandra N.; Ghosh, Swapan K.
2002-05-01
A simple weighted-density-functional approach is developed for inhomogeneous fluids by approximating the excess free energy density functional by that of the corresponding uniform system evaluated at an effective density. This effective weighted density is obtained by a suitable local averaging procedure of the actual density distribution using a weight function which is evaluated only once at the bulk density, thus being decoupled from the weighted density. This approach does not involve any power series expansion or solution of any nonlinear differential equation at every point and each iteration, as is required in some of the analogous schemes. The new theory is applied to predict the structure of simple classical fluids, interacting with hard sphere, Coulombic as well as Yukawa potentials, under confinement in several geometries. The calculated results on the density profiles are shown to compare quite well with available simulation data.
Determination of meteor flux distribution over the celestial sphere
NASA Technical Reports Server (NTRS)
Andreev, V. V.; Belkovich, O. I.; Filimonova, T. K.; Sidorov, V. V.
1992-01-01
A new method of determination of meteor flux density distribution over the celestial sphere is discussed. The flux density was derived from observations by radar together with measurements of angles of arrival of radio waves reflected from meteor trails. The role of small meteor showers over the sporadic background is shown.
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.
Viscosities and sintering rates of composite packings of spheres
Jagota, A.; Scherer, G.W.
1995-03-01
The effective sintering rates and viscosities of three-dimensional composite packings have been studied using a discrete numerical model. The packings consist of random mixtures of hard and soft spheres of the same size. With increasing substitution of hard particles for soft particles in the packing, the viscosity increases and the sintering rate decreases. This is particularly abrupt at well-defined rigidity thresholds where there is a transition from softlike to hardlike behavior. The site fraction of hard particles at which the transition occurs depends on the nature of the interaction between hard particles. When the contact between hard particles resists all six relative degrees of freedom (relative velocities and spins). the bonded case, the rigidity threshold coincides with the percolation threshold (site fraction {approx}0.32). When the contact between hard particles resists only interpenetration. the sliding case, the threshold occurs at a site fraction of hard particles very close to unity. Results for the variation of effective properties with site fraction of hard particles are presented for these and other cases. These results can also be applied to the study of elastic percolating networks.
NASA Astrophysics Data System (ADS)
Liu, You-Lin; Shi, Cheng-Xiang; Xu, Xue-Yan; Sun, Ping-Chuan; Chen, Tie-Hong
2015-06-01
Using hierarchically mesoporous silica spheres as a hard template and methyl violet as carbon and nitrogen source, nitrogen-doped hierarchically porous carbon spheres (N-HCS) are successfully prepared via a nanocasting method. The nitrogen-doped carbon spheres obtained after carbonization at 1000 °C (N-HCS-1000) exhibit a hierarchically micro-meso-macroporous structure with a relatively high surface area (BET) of 1413 m2 g-1 and a notably large pore volume of 2.96 cm3 g-1. In an oxygen reduction reaction (ORR) in alkaline media, the N-HCS-1000 material exhibits excellent activity with high current density, and its onset potential is notably close to that of the commercial Pt/C catalyst. The efficient catalytic activity of this catalyst could be attributed to the high electrical conductivity of the nitrogen-doped carbon matrix as well as the hierarchically porous framework. This catalyst also exhibits better methanol crossover resistance and higher stability than the commercial Pt/C catalyst.
Dynamical tachyons on fuzzy spheres
Berenstein, David; Trancanelli, Diego
2011-05-15
We study the spectrum of off-diagonal fluctuations between displaced fuzzy spheres in the Berenstein-Maldacena-Nastase plane wave matrix model. The displacement is along the plane of the fuzzy spheres. We find that when two fuzzy spheres intersect at angles, classical tachyons develop and that the spectrum of these modes can be computed analytically. These tachyons can be related to the familiar Nielsen-Olesen instabilities in Yang-Mills theory on a constant magnetic background. Many features of the problem become more apparent when we compare with maximally supersymmetric Yang-Mills theory on a sphere, of which this system is a truncation. We also set up a simple oscillatory trajectory on the displacement between the fuzzy spheres and study the dynamics of the modes as they become tachyonic for part of the oscillations. We speculate on their role regarding the possible thermalization of the system.
Dynamical tachyons on fuzzy spheres
NASA Astrophysics Data System (ADS)
Berenstein, David; Trancanelli, Diego
2011-05-01
We study the spectrum of off-diagonal fluctuations between displaced fuzzy spheres in the Berenstein-Maldacena-Nastase plane wave matrix model. The displacement is along the plane of the fuzzy spheres. We find that when two fuzzy spheres intersect at angles, classical tachyons develop and that the spectrum of these modes can be computed analytically. These tachyons can be related to the familiar Nielsen-Olesen instabilities in Yang-Mills theory on a constant magnetic background. Many features of the problem become more apparent when we compare with maximally supersymmetric Yang-Mills theory on a sphere, of which this system is a truncation. We also set up a simple oscillatory trajectory on the displacement between the fuzzy spheres and study the dynamics of the modes as they become tachyonic for part of the oscillations. We speculate on their role regarding the possible thermalization of the system.
Low Velocity Sphere Impact of a Soda Lime Silicate Glass
Wereszczak, Andrew A; Fox, Ethan E; Morrissey, Timothy G; Vuono, Daniel J
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.
Accurate bulk density determination of irregularly shaped translucent and opaque aerogels
NASA Astrophysics Data System (ADS)
Petkov, M. P.; Jones, S. M.
2016-05-01
We present a volumetric method for accurate determination of bulk density of aerogels, calculated from extrapolated weight of the dry pure solid and volume estimates based on the Archimedes' principle of volume displacement, using packed 100 μm-sized monodispersed glass spheres as a "quasi-fluid" media. Hard particle packing theory is invoked to demonstrate the reproducibility of the apparent density of the quasi-fluid. Accuracy rivaling that of the refractive index method is demonstrated for both translucent and opaque aerogels with different absorptive properties, as well as for aerogels with regular and irregular shapes.
Pan, Jing; Zhong, Li; Li, Ming; Luo, Yuanyuan; Li, Guanghai
2016-01-22
Monodispersed hierarchically structured V2O5 hollow spheres were successfully obtained from orthorhombic VO2 hollow spheres, which are in turn synthesized by a simple template-free microwave-assisted solvothermal method. The structural evolution of VO2 hollow spheres has been studied and explained by a chemically induced self-transformation process. The reaction time and water content in the reaction solution have a great influence on the morphology and phase structure of the resulting products in the solvothermal reaction. The diameter of the VO2 hollow spheres can be regulated simply by changing vanadium ion content in the reaction solution. The VO2 hollow spheres can be transformed into V2O5 hollow spheres with nearly no morphological change by annealing in air. The nanorods composed of V2O5 hollow spheres have an average length of about 70 nm and width of about 19 nm. When used as a cathode material for lithium-ion batteries, the V2O5 hollow spheres display a diameter-dependent electrochemical performance, and the 440 nm hollow spheres show the highest specific discharge capacity of 377.5 mAhg(-1) at a current density of 50 mAg(-1) , and are better than the corresponding solid spheres and nanorod assemblies. PMID:26749240
NASA Astrophysics Data System (ADS)
Chen, Hongyun; Gou, Li
2015-12-01
Nanocrystalline diamond coatings were deposited by MPCVD on the spheres used for a ball bearing. The nanocrystalline coatings with a grain size of 50 nm were confirmed by the surface morphology and composition analysis. The hardness of the coating is 20-40 GPa tested by nanoindentation, which is higher than that of tungsten carbide and silicon nitride substrates. The coating around the sphere observed from the Micro CT images is uniform with a thickness of 12 μm.
Theory of activated dynamics and glass transition of hard colloids in two dimensions.
Zhang, Bo-kai; Li, Hui-shu; Tian, Wen-de; Chen, Kang; Ma, Yu-qiang
2014-03-01
The microscopic nonlinear Langevin equation theory is applied to study the localization and activated hopping of two-dimensional hard disks in the deeply supercooled and glass states. Quantitative comparisons of dynamic characteristic length scales, barrier, and their dependence on the reduced packing fraction are presented between hard-disk and hard-sphere suspensions. The dynamic barrier of hard disks emerges at higher absolute and reduced packing fractions and correspondingly, the crossover size of the dynamic cage which correlates to the Lindemann length for melting is smaller. The localization lengths of both hard disks and spheres decrease exponentially with packing fraction. Larger localization length of hard disks than that of hard spheres is found at the same reduced packing fraction. The relaxation time of hard disks rises dramatically above the reduced packing fraction of 0.88, which leads to lower reduced packing fraction at the kinetic glass transition than that of hard spheres. The present work provides a foundation for the subsequent study of the glass transition of binary or polydisperse mixtures of hard disks, normally adopted in experiments and simulations to avoid crystallization, and further, the rheology and mechanical response of the two-dimensional glassy colloidal systems. PMID:24606367
Science off the Sphere: Bistronauts
International Space Station Expedition 30 astronaut Don Pettit demonstrates physics in space for 'Science off the Sphere.' Through a partnership between NASA and the American Physical Society you c...
Ancient Celestial Spheres from Greece
NASA Astrophysics Data System (ADS)
Dimitrakoudis, S.; Papaspyrou, P.; Petoussis, V.; Moussas, X.
2006-08-01
We present several ancient celestial spheres from the 8th century B.C. found throughout Greece, mainly in Thessaly, at the temple of Itonia Athena, but also in Olympia and other places. These celestial spheres have an axis, equator and several meridians and they have several markings with the symbol of stars (today's symbol for the Sun) $\\odot$. Such instruments could have been used to measure the time, the latitude of a location, or the coordinates of stars.
NASA Astrophysics Data System (ADS)
Chesneau, O.; Schmid, H.-M.; Carbillet, M.; Chiavassa, A.; Abe, L.; Mouillet, D.
2013-05-01
SPHERE, the Spectro-Polarimetric High-contrast Exoplanet REsearch instrument for the VLT is optimized towards reaching the highest contrast in a limited field of view and at short distances from the central star, thanks to an extreme AO system. SPHERE is very well suited to study the close environment of Betelgeuse, and has a strong potential for detecting the ejection activity around this key red supergiant.
High-Sensitivity Measurement of Density by Magnetic Levitation.
Nemiroski, Alex; Kumar, A A; Soh, Siowling; Harburg, Daniel V; Yu, Hai-Dong; Whitesides, George M
2016-03-01
This paper presents methods that use Magnetic Levitation (MagLev) to measure very small differences in density of solid diamagnetic objects suspended in a paramagnetic medium. Previous work in this field has shown that, while it is a convenient method, standard MagLev (i.e., where the direction of magnetization and gravitational force are parallel) cannot resolve differences in density <10(-4) g/cm(3) for macroscopic objects (>mm) because (i) objects close in density prevent each other from reaching an equilibrium height due to hard contact and excluded volume, and (ii) using weaker magnets or reducing the magnetic susceptibility of the medium destabilizes the magnetic trap. The present work investigates the use of weak magnetic gradients parallel to the faces of the magnets as a means of increasing the sensitivity of MagLev without destabilization. Configuring the MagLev device in a rotated state (i.e., where the direction of magnetization and gravitational force are perpendicular) relative to the standard configuration enables simple measurements along the axes with the highest sensitivity to changes in density. Manipulating the distance of separation between the magnets or the lengths of the magnets (along the axis of measurement) enables the sensitivity to be tuned. These modifications enable an improvement in the resolution up to 100-fold over the standard configuration, and measurements with resolution down to 10(-6) g/cm(3). Three examples of characterizing the small differences in density among samples of materials having ostensibly indistinguishable densities-Nylon spheres, PMMA spheres, and drug spheres-demonstrate the applicability of rotated Maglev to measuring the density of small (0.1-1 mm) objects with high sensitivity. This capability will be useful in materials science, separations, and quality control of manufactured objects. PMID:26815205
Rebound and jet formation of a fluid-filled sphere
NASA Astrophysics Data System (ADS)
Killian, Taylor W.; Klaus, Robert A.; Truscott, Tadd T.
2012-12-01
This study investigates the impact dynamics of hollow elastic spheres partially filled with fluid. Unlike an empty sphere, the internal fluid mitigates some of the rebound through an impulse driven exchange of energy wherein the fluid forms a jet inside the sphere. Surprisingly, this occurs on the second rebound or when the free surface is initially perturbed. Images gathered through experimentation show that the fluid reacts more quickly to the impact than the sphere, which decouples the two masses (fluid and sphere), imparts energy to the fluid, and removes rebound energy from the sphere. The experimental results are analyzed in terms of acceleration, momentum and an energy method suggesting an optimal fill volume in the neighborhood of 30%. While the characteristics of the fluid (i.e., density, viscosity, etc.) affect the fluid motion (i.e., type and size of jet formation), the rebound characteristics remain similar for a given fluid volume independent of fluid type. Implications of this work are a potential use of similar passive damping systems in sports technology and marine engineering.
Scattering of sound by a penetrable sphere above a plane boundary
NASA Astrophysics Data System (ADS)
Lui, Wai Keung; Li, Kai Ming
2002-11-01
The problem of acoustic scattering by a penetrable sphere irradiated by a point source is investigated. A theoretical model is developed for the case of scattering by a sphere placed above an acoustically hard and an impedance boundary. The sphere is made of an extended reaction material that is assumed to be acoustically penetrable. The problems are tackled by using the technique of variables separation and appropriate wave field expansions. By adopting an image source method, the solutions can be formulated in form of multiscattering interaction between the sphere and the image sphere near a hard and an impedance boundary. The effect of boundary impedance on the reflected sound fields is incorporated in the numerical model by using the well-known Wely-van der Pol formula. Preliminary indoor measurements are conducted in an anechoic chamber for the characterization of the acoustical properties of the penetrable sphere as well as the impedance boundary. A further set of experimental measurements is carried out to demonstrate the validity of the proposed theoretical models for various receiver locations around the sphere above the impedance boundary. [Work sponsored by the Innovation & Technology Commission, MTR Corp. Ltd., and The Hong Kong Polytechnic University under Project No. ZM07.
ERIC Educational Resources Information Center
Roser, Charles E.; McCluskey, Catherine L.
1998-01-01
Explains how the Canadian soft drink Orbitz can be used for explorations of density in the classroom. The drink has colored spheres suspended throughout that have a density close to that of the liquid. Presents a hands-on activity that can be easily done in two parts. (DDR)
Polar-solvation classical density-functional theory for electrolyte aqueous solutions near a wall
NASA Astrophysics Data System (ADS)
Warshavsky, Vadim; Marucho, Marcelo
2016-04-01
A precise description of the structural and dielectric properties of liquid water is critical to understanding the physicochemical properties of solutes in electrolyte solutions. In this article, a mixture of ionic and dipolar hard spheres is considered to account for water crowding and polarization effects on ionic electrical double layers near a uniformly charged hard wall. As a unique feature, solvent hard spheres carrying a dipole at their centers were used to model water molecules at experimentally known concentration, molecule size, and dipolar moment. The equilibrium ionic and dipole density profiles of this electrolyte aqueous model were calculated using a polar-solvation classical density-functional theory (PSCDFT). These profiles were used to calculate the charge density distribution, water polarization, dielectric permittivity function, and mean electric potential profiles as well as differential capacitance, excess adsorptions, and wall-fluid surface tension. These results were compared with those corresponding to the pure dipolar model and unpolar primitive solvent model of electrolyte aqueous solutions to understand the role that water crowding and polarization effects play on the structural and thermodynamic properties of these systems. Overall, PSCDFT predictions are in agreement with available experimental data.
Polar-solvation classical density-functional theory for electrolyte aqueous solutions near a wall.
Warshavsky, Vadim; Marucho, Marcelo
2016-04-01
A precise description of the structural and dielectric properties of liquid water is critical to understanding the physicochemical properties of solutes in electrolyte solutions. In this article, a mixture of ionic and dipolar hard spheres is considered to account for water crowding and polarization effects on ionic electrical double layers near a uniformly charged hard wall. As a unique feature, solvent hard spheres carrying a dipole at their centers were used to model water molecules at experimentally known concentration, molecule size, and dipolar moment. The equilibrium ionic and dipole density profiles of this electrolyte aqueous model were calculated using a polar-solvation classical density-functional theory (PSCDFT). These profiles were used to calculate the charge density distribution, water polarization, dielectric permittivity function, and mean electric potential profiles as well as differential capacitance, excess adsorptions, and wall-fluid surface tension. These results were compared with those corresponding to the pure dipolar model and unpolar primitive solvent model of electrolyte aqueous solutions to understand the role that water crowding and polarization effects play on the structural and thermodynamic properties of these systems. Overall, PSCDFT predictions are in agreement with available experimental data. PMID:27176352
Nematic ordering and defects on the surface of a sphere: A Monte Carlo simulation study
NASA Astrophysics Data System (ADS)
Bates, Martin A.
2008-03-01
We examine the ordering of hard rods on the surface of a sphere using computer simulations. As predicted by previous theories of thin nematic shells we observe four s =+1/2 defects. However, the predicted tetrahedral symmetry for the defects and the "baseball" director configuration is not observed. Instead the four defects are located, on average, on a great circle which splits the sphere into two hemispheres, each of which has a splay dominated director configuration. We argue that this result occurs as the bend elastic constant for hard rods is much larger than the splay elastic constant.
Porous Ceramic Spheres From Cation Exchange Beads
NASA Technical Reports Server (NTRS)
Dynys, Fred
2005-01-01
This document is a slide presentation that examines the use of a simple templating process to produce hollow ceramic spheres with a pore size of 1 to 10 microns. Using ion exchange process it was determined that the method produces porous ceramic spheres with a unique structure: (i.e., inner sphere surrounded by an outer sphere.)
Random sphere packing model of heterogeneous propellants
NASA Astrophysics Data System (ADS)
Kochevets, Sergei Victorovich
It is well recognized that combustion of heterogeneous propellants is strongly dependent on the propellant morphology. Recent developments in computing systems make it possible to start three-dimensional modeling of heterogeneous propellant combustion. A key component of such large scale computations is a realistic model of industrial propellants which retains the true morphology---a goal never achieved before. The research presented develops the Random Sphere Packing Model of heterogeneous propellants and generates numerical samples of actual industrial propellants. This is done by developing a sphere packing algorithm which randomly packs a large number of spheres with a polydisperse size distribution within a rectangular domain. First, the packing code is developed, optimized for performance, and parallelized using the OpenMP shared memory architecture. Second, the morphology and packing fraction of two simple cases of unimodal and bimodal packs are investigated computationally and analytically. It is shown that both the Loose Random Packing and Dense Random Packing limits are not well defined and the growth rate of the spheres is identified as the key parameter controlling the efficiency of the packing. For a properly chosen growth rate, computational results are found to be in excellent agreement with experimental data. Third, two strategies are developed to define numerical samples of polydisperse heterogeneous propellants: the Deterministic Strategy and the Random Selection Strategy. Using these strategies, numerical samples of industrial propellants are generated. The packing fraction is investigated and it is shown that the experimental values of the packing fraction can be achieved computationally. It is strongly believed that this Random Sphere Packing Model of propellants is a major step forward in the realistic computational modeling of heterogeneous propellant of combustion. In addition, a method of analysis of the morphology of heterogeneous
NASA Astrophysics Data System (ADS)
Jeanmairet, Guillaume; Levesque, Maximilien; Borgis, Daniel
2013-10-01
We present an extension of our recently introduced molecular density functional theory of water [G. Jeanmairet et al., J. Phys. Chem. Lett. 4, 619 (2013)] to the solvation of hydrophobic solutes of various sizes, going from angstroms to nanometers. The theory is based on the quadratic expansion of the excess free energy in terms of two classical density fields: the particle density and the multipolar polarization density. Its implementation requires as input a molecular model of water and three measurable bulk properties, namely, the structure factor and the k-dependent longitudinal and transverse dielectric susceptibilities. The fine three-dimensional water structure around small hydrophobic molecules is found to be well reproduced. In contrast, the computed solvation free-energies appear overestimated and do not exhibit the correct qualitative behavior when the hydrophobic solute is grown in size. These shortcomings are corrected, in the spirit of the Lum-Chandler-Weeks theory, by complementing the functional with a truncated hard-sphere functional acting beyond quadratic order in density, and making the resulting functional compatible with the Van-der-Waals theory of liquid-vapor coexistence at long range. Compared to available molecular simulations, the approach yields reasonable solvation structure and free energy of hard or soft spheres of increasing size, with a correct qualitative transition from a volume-driven to a surface-driven regime at the nanometer scale.
Depletion, melting and reentrant solidification in mixtures of soft and hard colloids.
Marzi, Daniela; Capone, Barbara; Marakis, John; Merola, Maria Consiglia; Truzzolillo, Domenico; Cipelletti, Luca; Moingeon, Firmin; Gauthier, Mario; Vlassopoulos, Dimitris; Likos, Christos N; Camargo, Manuel
2015-11-14
We present extensive experimental and theoretical investigations on the structure, phase behavior, dynamics and rheology of model soft-hard colloidal mixtures realized with large, multiarm star polymers as the soft component and smaller, compact stars as the hard one. The number and length of the arms in star polymers control their softness, whereas the size ratio, the overall density and the composition are additional parameters varied for the mixtures. A coarse-grained theoretical strategy is employed to predict the structure of the systems as well as their ergodicity properties on the basis of mode coupling theory, for comparison with rheological measurements on the samples. We discovered that dynamically arrested star-polymer solutions recover their ergodicity upon addition of colloidal additives. At the same time the system displays demixing instability, and the binodal of the latter meets the glass line in a way that leads, upon addition of a sufficient amount of colloidal particles, to an arrested phase separation and reentrant solidification. We present evidence for a subsequent solid-to-solid transition well within the region of arrested phase separation, attributed to a hard-sphere-mixture type of glass, due to osmotic shrinkage of the stars at high colloidal particle concentrations. We systematically investigated the interplay of star functionality and size ratio with glass melting and demixing, and rationalized our findings by the depletion of the big stars due to the smaller colloids. This new depletion potential in which, contrary to the classic colloid-polymer case, the hard component depletes the soft one, has unique and novel characteristics and allows the calculation of phase diagrams for such mixtures. This work covers a broad range of soft-hard colloidal mixture compositions in which the soft component exceeds the hard one in size and provides general guidelines for controlling the properties of such complex mixtures. PMID:26356800
DSMC Simulation and Experimental Validation of Shock Interaction in Hypersonic Low Density Flow
2014-01-01
Direct simulation Monte Carlo (DSMC) of shock interaction in hypersonic low density flow is developed. Three collision molecular models, including hard sphere (HS), variable hard sphere (VHS), and variable soft sphere (VSS), are employed in the DSMC study. The simulations of double-cone and Edney's type IV hypersonic shock interactions in low density flow are performed. Comparisons between DSMC and experimental data are conducted. Investigation of the double-cone hypersonic flow shows that three collision molecular models can predict the trend of pressure coefficient and the Stanton number. HS model shows the best agreement between DSMC simulation and experiment among three collision molecular models. Also, it shows that the agreement between DSMC and experiment is generally good for HS and VHS models in Edney's type IV shock interaction. However, it fails in the VSS model. Both double-cone and Edney's type IV shock interaction simulations show that the DSMC errors depend on the Knudsen number and the models employed for intermolecular interaction. With the increase in the Knudsen number, the DSMC error is decreased. The error is the smallest in HS compared with those in the VHS and VSS models. When the Knudsen number is in the level of 10−4, the DSMC errors, for pressure coefficient, the Stanton number, and the scale of interaction region, are controlled within 10%. PMID:24672360
DSMC simulation and experimental validation of shock interaction in hypersonic low density flow.
Xiao, Hong; Shang, Yuhe; Wu, Di
2014-01-01
Direct simulation Monte Carlo (DSMC) of shock interaction in hypersonic low density flow is developed. Three collision molecular models, including hard sphere (HS), variable hard sphere (VHS), and variable soft sphere (VSS), are employed in the DSMC study. The simulations of double-cone and Edney's type IV hypersonic shock interactions in low density flow are performed. Comparisons between DSMC and experimental data are conducted. Investigation of the double-cone hypersonic flow shows that three collision molecular models can predict the trend of pressure coefficient and the Stanton number. HS model shows the best agreement between DSMC simulation and experiment among three collision molecular models. Also, it shows that the agreement between DSMC and experiment is generally good for HS and VHS models in Edney's type IV shock interaction. However, it fails in the VSS model. Both double-cone and Edney's type IV shock interaction simulations show that the DSMC errors depend on the Knudsen number and the models employed for intermolecular interaction. With the increase in the Knudsen number, the DSMC error is decreased. The error is the smallest in HS compared with those in the VHS and VSS models. When the Knudsen number is in the level of 10(-4), the DSMC errors, for pressure coefficient, the Stanton number, and the scale of interaction region, are controlled within 10%. PMID:24672360
Process development and fabrication for sphere-pac fuel rods. [PWR; BWR
Welty, R.K.; Campbell, M.H.
1981-06-01
Uranium fuel rods containing sphere-pac fuel have been fabricated for in-reactor tests and demonstrations. A process for the development, qualification, and fabrication of acceptable sphere-pac fuel rods is described. Special equipment to control fuel contamination with moisture or air and the equipment layout needed for rod fabrication is described and tests for assuring the uniformity of the fuel column are discussed. Fuel retainers required for sphere-pac fuel column stability and instrumentation to measure fuel column smear density are described. Results of sphere-pac fuel rod fabrication campaigns are reviewed and recommended improvements for high throughput production are noted.
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.
Atmospheric structure measurements from accelerometer instrumented falling spheres
NASA Astrophysics Data System (ADS)
Philbrick, C. R.; McIsaac, J. P.; Fryklund, D. H.; Buck, R. F.
1981-12-01
A three axis piezoelectric accelerometer, mounted in a 25 cm diameter sphere was used to measure atmospheric density and winds and to obtain a temperature profile in the altitude range from 50 to 150 km. The sphere with its own telemetry system and beacon transponder was released from a rocket at 70 km altitude on the up leg of the flight. The drag acceleration measured by the accelerometer can be used to directly calculate the atmospheric density with a vertical resolution of 100 m. The wind field is calculated, assuming uniform distribution in the horizontal plane between the up and down leg regions, which are 30 km apart. The atmospheric temperature profile is determined by integrating along the density profile, assuming ideal gas law conditions and hydrostatic equilibrium. The profiles obtained from the density, temperature and wind profiles can be used to describe those regions of the atmosphere expected to be statically and dynamically unstable.
Recent progress in hollow sphere-based electrodes for high-performance supercapacitors
NASA Astrophysics Data System (ADS)
Zhao, Yan; Chen, Min; Wu, Limin
2016-08-01
Hollow spheres have drawn much attention in the area of energy storage and conversion, especially in high-performance supercapacitors owing to their well-defined morphologies, uniform size, low density and large surface area. And quite some significant breakthroughs have been made in advanced supercapacitor electrode materials with hollow sphere structures. In this review, we summarize and discuss the synthesis and application of hollow spheres with controllable structure and morphology as electrode materials for supercapacitors. First, we briefly introduce the fabrication strategies of hollow spheres for electrode materials. Then, we discuss in detail the recent advances in various hollow sphere-based electrode materials for supercapacitors, including single-shelled, yolk-shelled, urchin-like, double-shelled, multi-shelled, and mesoporous hollow structure-based symmetric and asymmetric supercapacitor devices. We conclude this review with some perspectives on the future research and development of the hollow sphere-based electrode materials.
Recent progress in hollow sphere-based electrodes for high-performance supercapacitors.
Zhao, Yan; Chen, Min; Wu, Limin
2016-08-26
Hollow spheres have drawn much attention in the area of energy storage and conversion, especially in high-performance supercapacitors owing to their well-defined morphologies, uniform size, low density and large surface area. And quite some significant breakthroughs have been made in advanced supercapacitor electrode materials with hollow sphere structures. In this review, we summarize and discuss the synthesis and application of hollow spheres with controllable structure and morphology as electrode materials for supercapacitors. First, we briefly introduce the fabrication strategies of hollow spheres for electrode materials. Then, we discuss in detail the recent advances in various hollow sphere-based electrode materials for supercapacitors, including single-shelled, yolk-shelled, urchin-like, double-shelled, multi-shelled, and mesoporous hollow structure-based symmetric and asymmetric supercapacitor devices. We conclude this review with some perspectives on the future research and development of the hollow sphere-based electrode materials. PMID:27406974
Cavitation and radicals drive the sonochemical synthesis of functional polymer spheres
NASA Astrophysics Data System (ADS)
Narayanan, Badri; Deshmukh, Sanket A.; Shrestha, Lok Kumar; Ariga, Katsuhiko; Pol, Vilas G.; Sankaranarayanan, Subramanian K. R. S.
2016-07-01
Sonochemical synthesis can lead to a dramatic increase in the kinetics of formation of polymer spheres (templates for carbon spheres) compared to the modified Stöber silica method applied to produce analogous polymer spheres. Reactive molecular dynamics simulations of the sonochemical process indicate a significantly enhanced rate of polymer sphere formation starting from resorcinol and formaldehyde precursors. The associated chemical reaction kinetics enhancement due to sonication is postulated to arise from the localized lowering of atomic densities, localized heating, and generation of radicals due to cavitation collapse in aqueous systems. This dramatic increase in reaction rates translates into enhanced nucleation and growth of the polymer spheres. The results are of broad significance to understanding mechanisms of sonication induced synthesis as well as technologies utilizing polymers spheres.
Thermoinertial bouncing of a relativistic collapsing sphere: A numerical model
Herrera, L.; Di Prisco, A.; Barreto, W.
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.
Theoretical study of the freezing of polystyrene sphere suspensions
NASA Technical Reports Server (NTRS)
Shih, W.-H.; Stroud, D.
1983-01-01
A theoretical study of melting in aqueous suspensions of polystyrene spheres is presented. The Helmholtz free energies of the liquid and solid phase of the suspensions are calculated as functions of sphere number density and electrolyte concentrations. The results tend to show that the freezing curve of such suspensions is that of a conventional classical liquid with repulsive short-range interactions. The interactions can be treated satisfactorily within a slightly modified Debye-Hueckel approximation. The modifications include size correction and a correction for nonlinear screening. The results are confirmed by analogous calculations for the solid phase, and for the line along which liquid and solid free energies are equal.
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.
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
A fundamental measure density functional for fluid and crystal phases of the Asakura–Oosawa model
NASA Astrophysics Data System (ADS)
Mortazavifar, Mostafa; Oettel, Martin
2016-06-01
We investigate a density functional for the Asakura–Oosawa model of colloid-polymer mixtures, describing both fluid and crystal phases. It is derived by linearizing the two-component fundamental-measure hard sphere tensor functional in the second (polymer) component. We discuss the formulation of an effective density functional for colloids only. For small polymer-colloid size ratios the effective, polymer-induced potential between colloids is short-range attractive and of two-body form but we show that the effective density functional is not equivalent to standard mean-field approaches where attractions are taken into account by terms second order in the colloid density. We calculate numerically free energies and phase diagrams in good agreement with available simulations, furthermore we discuss the colloid and polymer distributions in the crystal and determine equilibrium vacancy concentrations. Numerical results reveal a fairly strong sensitivity to the specific type of underlying fundamental measure hard sphere functional which could aid further development of fundamental measure theory.
A fundamental measure density functional for fluid and crystal phases of the Asakura-Oosawa model.
Mortazavifar, Mostafa; Oettel, Martin
2016-06-22
We investigate a density functional for the Asakura-Oosawa model of colloid-polymer mixtures, describing both fluid and crystal phases. It is derived by linearizing the two-component fundamental-measure hard sphere tensor functional in the second (polymer) component. We discuss the formulation of an effective density functional for colloids only. For small polymer-colloid size ratios the effective, polymer-induced potential between colloids is short-range attractive and of two-body form but we show that the effective density functional is not equivalent to standard mean-field approaches where attractions are taken into account by terms second order in the colloid density. We calculate numerically free energies and phase diagrams in good agreement with available simulations, furthermore we discuss the colloid and polymer distributions in the crystal and determine equilibrium vacancy concentrations. Numerical results reveal a fairly strong sensitivity to the specific type of underlying fundamental measure hard sphere functional which could aid further development of fundamental measure theory. PMID:27116650
Laflamme-Sanders, Alexandra; Zhu, Mu
2008-11-01
LAGO is an efficient kernel algorithm designed specifically for the rare target detection problem. However, unlike other kernel algorithms, LAGO cannot be easily used with many domain-specific kernels. We solve this problem by first providing a unified framework for LAGO and clarifying its basic principle, and then applying that principle on the unit sphere instead of in the Euclidean space. PMID:18775643
Simple manipulator for rotating spheres.
Weinstein, B W; Hendricks, C D; Ward, C M; Willenborg, D L
1978-06-01
We describe a simple device for rapidly rotating a small sphere to any orientation for inspection of the surface. The ball is held between two small, flat surfaces and rolls as the surfaces are moved differentially parallel to one another. PMID:18699214
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.
Effect of surface heating on the drag crisis of sphere
NASA Astrophysics Data System (ADS)
Muto, Masaya; Watanabe, Hiroaki; Tsubokura, Makoto
2012-11-01
The characteristics of flow past a heated sphere are investigated at around critical Reynolds number in conditions using three-dimensional numerical simulation in which temperature dependence of fluid properties such as density and viscosity is exactly considered. Boussinesq approximation is no longer applicable due to large temperature difference adopted in this study. And the order of the buoyancy effect becomes relatively small compared to inertia effect in present Reynolds number region. The result shows that drag coefficient of the heated sphere in drag crisis region becomes larger than that of the unheated case and it increases up to the coefficient found in subcritical region. This is because the temperature difference between the sphere and ambient fluid strongly affects the flow separation points, resulting in small recovery of the pressure in the wake and reduction of the temporal fluctuation of the lift force acting on the sphere. These effects are considered to attribute to the temperature dependence of fluid properties in the vicinity of the sphere and effect on the transient of the boundary surface.
Wear of hard materials by hard particles
Hawk, Jeffrey A.
2003-10-01
Hard materials, such as WC-Co, boron carbide, titanium diboride and composite carbide made up of Mo2C and WC, have been tested in abrasion and erosion conditions. These hard materials showed negligible wear in abrasion against SiC particles and erosion using Al2O3 particles. The WC-Co materials have the highest wear rate of these hard materials and a very different material removal mechanism. Wear mechanisms for these materials were different for each material with the overall wear rate controlled by binder composition and content and material grain size.
Medasani, Bharat; Ovanesyan, Zaven; Thomas, Dennis G.; Sushko, Maria L.; Marucho, Marcelo
2014-05-29
In this article we present a classical density functional theory for electrical double layers of spherical macroions that extends the capabilities of conventional approaches by accounting for electrostatic ion correlations, size asymmetry and excluded volume effects. The approach is based on a recent approximation introduced by Hansen-Goos and Roth for the hard sphere excess free energy of inhomogeneous fluids (J. Chem. Phys. 124, 154506). It accounts for the proper and efficient description of the effects of ionic asymmetry and solvent excluded volume, especially at high ion concentrations and size asymmetry ratios including those observed in experimental studies. Additionally, we utilize a leading functional Taylor expansion approximation of the ion density profiles. In addition, we use the Mean Spherical Approximation for multi-component charged hard sphere fluids to account for the electrostatic ion correlation effects. These approximations are implemented in our theoretical formulation into a suitable decomposition of the excess free energy which plays a key role in capturing the complex interplay between charge correlations and excluded volume effects. We perform Monte Carlo simulations in various scenarios to validate the proposed approach, obtaining a good compromise between accuracy and computational cost. We use the proposed computational approach to study the effects of ion size, ion size asymmetry and solvent excluded volume on the ion profiles, integrated charge, mean electrostatic potential, and ionic coordination number around spherical macroions in various electrolyte mixtures. Our results show that both solvent hard sphere diameter and density play a dominant role in the distribution of ions around spherical macroions, mainly for experimental water molarity and size values where the counterion distribution is characterized by a tight binding to the macroion, similar to that predicted by the Stern model.
Medasani, Bharat; Ovanesyan, Zaven; Thomas, Dennis G.; Sushko, Maria L.; Marucho, Marcelo
2014-01-01
In this article, we present a classical density functional theory for electrical double layers of spherical macroions that extends the capabilities of conventional approaches by accounting for electrostatic ion correlations, size asymmetry, and excluded volume effects. The approach is based on a recent approximation introduced by Hansen-Goos and Roth for the hard sphere excess free energy of inhomogeneous fluids [J. Chem. Phys. 124, 154506 (2006); Hansen-Goos and Roth, J. Phys.: Condens. Matter 18, 8413 (2006)]. It accounts for the proper and efficient description of the effects of ionic asymmetry and solvent excluded volume, especially at high ion concentrations and size asymmetry ratios including those observed in experimental studies. Additionally, we utilize a leading functional Taylor expansion approximation of the ion density profiles. In addition, we use the mean spherical approximation for multi-component charged hard sphere fluids to account for the electrostatic ion correlation effects. These approximations are implemented in our theoretical formulation into a suitable decomposition of the excess free energy which plays a key role in capturing the complex interplay between charge correlations and excluded volume effects. We perform Monte Carlo simulations in various scenarios to validate the proposed approach, obtaining a good compromise between accuracy and computational cost. We use the proposed computational approach to study the effects of ion size, ion size asymmetry, and solvent excluded volume on the ion profiles, integrated charge, mean electrostatic potential, and ionic coordination number around spherical macroions in various electrolyte mixtures. Our results show that both solvent hard sphere diameter and density play a dominant role in the distribution of ions around spherical macroions, mainly for experimental water molarity and size values where the counterion distribution is characterized by a tight binding to the macroion, similar to that
Science off the Sphere: Fun with Antibubbles
International Space Station Expedition 30 astronaut Don Pettit injects air bubbles inside a sphere of water to demonstrate physics in space for 'Science off the Sphere.' Through a partnership betwe...
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.
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.
Fuel Fabrication for Surrogate Sphere-Pac Rodlet
Del Cul, G.D.
2005-07-19
Sphere-pac fuel consists of a blend of spheres of two or three different size fractions contained in a fuel rod. The smear density of the sphere-pac fuel column can be adjusted to the values obtained for light-water reactor (LWR) pellets (91-95%) by using three size fractions, and to values typical of the fast-reactor oxide fuel column ({approx}85%) by using two size fractions. For optimum binary packing, the diameters of the two sphere fractions must differ by at least a factor of 7 (ref. 3). Blending of spheres with smaller-diameter ratios results in difficult blending, nonuniform loading, and lower packing fractions. A mixture of about 70 vol% coarse spheres and 30 vol% fine spheres is needed to obtain high packing fractions. The limiting smear density for binary packing is 86%, with about 82% achieved in practice. Ternary packing provides greater smear densities, with theoretical values ranging from 93 to 95%. Sphere-pac technology was developed in the 1960-1990 period for thermal and fast spectrum reactors of nearly all types (U-Th and U-Pu fuel cycles, oxide and carbide fuels), but development of this technology was most strongly motivated by the need for remote fabrication in the thorium fuel cycle. The application to LWR fuels as part of the DOE Fuel Performance Improvement Program did not result in commercial deployment for a number of reasons, but the relatively low production cost of existing UO{sub 2} pellet fuel is probably the most important factor. In the case of transmutation fuels, however, sphere-pac technology has the potential to be a lower-cost alternative while also offering great flexibility in tailoring the fuel elements to match the exact requirements of any particular reactor core at any given time in the cycle. In fact, the blend of spheres can be adjusted to offer a different composition for each fuel pin or group of pins in a given fuel element. Moreover, it can even provide a vertical gradient of composition in a single fuel pin. For
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.
Wang, Hui; Wu, Ping Shi, Huimin; Lou, Feijian; Tang, Yawen; Zhou, Tongge; Zhou, Yiming Lu, Tianhong
2014-07-01
Highlights: • In situ magnesiothermic reduction route for the formation of porous Si@C spheres. • Unique microstructural characteristics of both porous sphere and carbon matrix. • Enhanced anodic performance in term of cycling stability for lithium-ion batteries. - Abstract: A novel type of porous Si–C micro/nano-hybrids, i.e., porous Si spheres encapsulated in carbon shells (porous Si@C spheres), has been constructed through the pyrolysis of polyvinylidene fluoride (PVDF) and subsequent magnesiothermic reduction methodology by using SiO{sub 2} spheres as precursors. The as-synthesized porous Si@C spheres have been applied as anode materials for lithium-ion batteries (LIBs), and exhibit enhanced anodic performance in term of cycling stability compared with bare Si spheres. For example, the porous Si@C spheres are able to exhibit a high reversible capacity of 900.0 mA h g{sup −1} after 20 cycles at a current density of 0.05 C (1 C = 4200 mA g{sup −1}), which is much higher than that of bare Si spheres (430.7 mA h g{sup −1})
Coating a Sphere With Evaporated Metal
NASA Technical Reports Server (NTRS)
Strayer, D. M.; Jackson, H. W.; Gatewood, J. R.
1986-01-01
In vacuum coating apparatus, metal evaporated onto sphere from small source located some distance away. Sphere held in path of metal vapor while rotated about axis that rocks back and forth. One tilting motion particularly easy to produce is sinusoidal rocking with frequency much lower than rotational frequency. Apparatus developed for coating single-crystal sapphire spheres with niobium.
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.
Archaic artifacts resembling celestial spheres
NASA Astrophysics Data System (ADS)
Dimitrakoudis, S.; Papaspyrou, P.; Petoussis, V.; Moussas, X.
We present several bronze artifacts from the Archaic Age in Greece (750-480 BC) that resemble celestial spheres or forms of other astronomical significance. They are studied in the context of the Dark Age transition from Mycenaean Age astronomical themes to the philosophical and practical revival of astronomy in the Classical Age with its plethora of astronomical devices. These artifacts, mostly votive in nature are spherical in shape and appear in a variety of forms their most striking characteristic being the depiction of meridians and/or an equator. Most of those artifacts come from Thessaly, and more specifically from the temple of Itonia Athena at Philia, a religious center of pan-Hellenic significance. Celestial spheres, similar in form to the small artifacts presented in this study, could be used to measure latitudes, or estimate the time at a known place, and were thus very useful in navigation.
NASA Astrophysics Data System (ADS)
Gazzillo, Domenico; Munaò, Gianmarco; Prestipino, Santi
2016-06-01
We study a pure fluid of heteronuclear sticky Janus dumbbells, considered to be the result of complete chemical association between unlike species in an initially equimolar mixture of hard spheres (species A) and sticky hard spheres (species B) with different diameters. The B spheres are particles whose attractive surface layer is infinitely thin. Wertheim's two-density integral equations are employed to describe the mixture of AB dumbbells together with unbound A and B monomers. After Baxter factorization, these equations are solved analytically within the associative Percus-Yevick approximation. The limit of complete association is taken at the end. The present paper extends to the more general, heteronuclear case of A and B species with size asymmetry a previous study by Wu and Chiew [J. Chem. Phys. 115, 6641 (2001)], which was restricted to dumbbells with equal monomer diameters. Furthermore, the solution for the Baxter factor correlation functions qi j α β ( r ) is determined here in a fully analytic way, since we have been able to find explicit analytic expressions for all the intervening parameters.
Gazzillo, Domenico; Munaò, Gianmarco; Prestipino, Santi
2016-06-21
We study a pure fluid of heteronuclear sticky Janus dumbbells, considered to be the result of complete chemical association between unlike species in an initially equimolar mixture of hard spheres (species A) and sticky hard spheres (species B) with different diameters. The B spheres are particles whose attractive surface layer is infinitely thin. Wertheim's two-density integral equations are employed to describe the mixture of AB dumbbells together with unbound A and B monomers. After Baxter factorization, these equations are solved analytically within the associative Percus-Yevick approximation. The limit of complete association is taken at the end. The present paper extends to the more general, heteronuclear case of A and B species with size asymmetry a previous study by Wu and Chiew [J. Chem. Phys. 115, 6641 (2001)], which was restricted to dumbbells with equal monomer diameters. Furthermore, the solution for the Baxter factor correlation functions qij (αβ)(r) is determined here in a fully analytic way, since we have been able to find explicit analytic expressions for all the intervening parameters. PMID:27334176
Excluded volume effects in compressed polymer brushes: A density functional theory
Chen, Cangyi; Tang, Ping E-mail: fengqiu@fudan.edu.cn; Qiu, Feng E-mail: fengqiu@fudan.edu.cn; Shi, An-Chang
2015-03-28
A classical density functional theory (DFT) is applied to investigate the behavior of compressed polymer brushes composed of hard-sphere chains. The excluded volume interactions among the chain segments are explicitly treated. Two compression systems are used to study the behavior of brush-wall and brush-brush interactions. For the brush-brush systems, an obvious interpenetration zone has been observed. The extent of the interpenetration depends strongly on the grafting density. Furthermore, the repulsive force between the brush and wall or between the two brushes has been obtained as a function of the compression distance. Compared to the prediction of the analytic self-consistent field theory, such force increases more rapidly in the brush-wall compression with high polymer grafting densities or at higher compressions. In the brush-brush compression system, the interpenetration between the two compressed brushes creates a “softer” interaction. The influence of hard-sphere solvents on the behavior of compressed brushes is also discussed.
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.
When do jammed sphere packings have a valid linear regime?
NASA Astrophysics Data System (ADS)
Goodrich, Carl; Liu, Andrea; Nagel, Sidney
2014-03-01
The physics of jamming can be studied in its purest form in packings of soft spheres at zero temperature. One of the successes of this approach is that bulk material properties, such as the elastic moduli or density of normal modes, can be predicted solely from the distance of the system to the jamming transition. Such properties are both defined and measured in the linear-response regime. It is thus tacitly assumed that the harmonic approximation to the local energy landscape can capture the meaningful physics, and it is therefore essential to delineate when this assumption is valid. We will examine the regime of validity of the harmonic approximation in jammed sphere packings as a function of system size and density. We will also discuss the crossover from linear response of the zero-temperature jammed solid to thermal behavior at nonzero temperatures.
The sphere-in-contact model of carbon materials.
Zeinalipour-Yazdi, Constantinos D; Pullman, David P; Catlow, C Richard A
2016-01-01
A sphere-in-contact model is presented that is used to build physical models of carbon materials such as graphite, graphene, carbon nanotubes and fullerene. Unlike other molecular models, these models have correct scale and proportions because the carbon atoms are represented by their atomic radius, in contrast to the more commonly used space-fill models, where carbon atoms are represented by their van der Waals radii. Based on a survey taken among 65 undergraduate chemistry students and 28 PhD/postdoctoral students with a background in molecular modeling, we found misconceptions arising from incorrect visualization of the size and location of the electron density located in carbon materials. Based on analysis of the survey and on a conceptual basis we show that the sphere-in-contact model provides an improved molecular representation of the electron density of carbon materials compared to other molecular models commonly used in science textbooks (i.e., wire-frame, ball-and-stick, space-fill). We therefore suggest that its use in chemistry textbooks along with the ball-and-stick model would significantly enhance the visualization of molecular structures according to their electron density. Graphical Abstract A sphere-in-contact model of C60-fullerene. PMID:26791534
Perturbative Casimir Energies of Spheres
NASA Astrophysics Data System (ADS)
Barton, G.
The Casimir energies of single bodies (as opposed to the interaction between mutually disjoint bodies) have accumulated deceptive folklore which this talk will try to exorcise, by mean of calculations for atomic solids that, though optically dilute, are realistically dispersive. This is easy, because quantum electrodynamics then yields identically the same energy as one gets from the properly retarded interatomic potentials. The problem of regularizing (nominal) divergences turns out to be quite distinct from the appropriate process of renormalization: simply discarding all nominally divergent contributions would prevent one from understanding the physics. Contrary to legend, the pertinent Casimir energies for dielectric spheres are attractive.
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
Tracer diffusion and cluster formation in mixtures of spheres and rotating rods
NASA Astrophysics Data System (ADS)
Kirchhoff, R.; Löwen, H.
2005-12-01
On the basis of Brownian dynamics computer simulation studies, we investigate the structure and dynamics of two-dimensional mixtures of rods driven by an external torque and spheres. First, we show that the tracer long-time diffusion of spheres in a system of rotating rods can be efficiently tuned via the rod density. It behaves non-monotonically for increasing rod density. In particular, the sphere diffusion becomes strongly enhanced across the jamming transition of the rods. Second, we show that rotating rods in a dense suspension of spheres form aggregates of rod clusters which are rotating jointly. The cluster size is in reasonable agreement with the predictions of a simple theory.
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.
Binary hard chain mixtures. I. Generalized Flory equations of state
Wichert, J.M.; Gulati, H.S.; Hall, C.K.
1996-11-01
In this series of two papers we study the thermodynamics of binary hard chain mixtures. Here, a generalized Flory-dimer (GF-D) equation of state is derived for binary hard chain mixtures composed of chains of variable length and segment diameter. Compressibility factors predicted by the GF-D equation of state developed here and by the previously derived generalized Flory equation of state are compared to previous Monte Carlo results for hard monomer/hard chain mixtures, and to new molecular dynamics (MD) hard monomer/hard chain and hard chain/hard chain mixture simulation results. Compared to the MD simulations, the GF-D theory is found to be quite accurate, with an average error of about 3{percent} at liquid-like densities. {copyright} {ital 1996 American Institute of Physics.}
Cugell, D W
1992-06-01
Hard metal is a mixture of tungsten carbide and cobalt, to which small amounts of other metals may be added. It is widely used for industrial purposes whenever extreme hardness and high temperature resistance are needed, such as for cutting tools, oil well drilling bits, and jet engine exhaust ports. Cobalt is the component of hard metal that can be a health hazard. Respiratory diseases occur in workers exposed to cobalt--either in the production of hard metal, from machining hard metal parts, or from other sources. Adverse pulmonary reactions include asthma, hypersensitivity pneumonitis, and interstitial fibrosis. A peculiar, almost unique form of lung fibrosis, giant cell interstitial pneumonia, is closely linked with cobalt exposure. PMID:1511554
Visual attention on the sphere.
Bogdanova, Iva; Bur, Alexandre; Hugli, Heinz
2008-11-01
Human visual system makes an extensive use of visual attention in order to select the most relevant information and speed-up the vision process. Inspired by visual attention, several computer models have been developed and many computer vision applications rely today on such models. However, the actual algorithms are not suitable to omnidirectional images, which contain a significant amount of geometrical distortion. In this paper, we present a novel computational approach that performs in spherical geometry and thus is suitable for omnidirectional images. Following one of the actual models of visual attention, the spherical saliency map is obtained by fusing together intensity, chromatic, and orientation spherical cue conspicuity maps that are themselves obtained through multiscale analysis on the sphere. Finally, the consecutive maxima in the spherical saliency map represent the spots of attention on the sphere. In the experimental part, the proposed method is then compared to the standard one using a synthetic image. Also, we provide examples of spots detection in real omnidirectional scenes which show its advantages. Finally, an experiment illustrates the homogeneity of the detected visual attention in omnidirectional images. PMID:18854253
NASA Astrophysics Data System (ADS)
Duan, Zhipeng; He, Boshu; Duan, Yuanyuan
2015-07-01
Modelling fluid flows past a body is a general problem in science and engineering. Historical sphere drag and heat transfer data are critically examined. The appropriate drag coefficient is proposed to replace the inertia type definition proposed by Newton. It is found that the appropriate drag coefficient is a desirable dimensionless parameter to describe fluid flow physical behavior so that fluid flow problems can be solved in the simple and intuitive manner. The appropriate drag coefficient is presented graphically, and appears more general and reasonable to reflect the fluid flow physical behavior than the traditional century old drag coefficient diagram. Here we present drag and heat transfer experimental results which indicate that there exists a relationship in nature between the sphere drag and heat transfer. The role played by the heat flux has similar nature as the drag. The appropriate drag coefficient can be related to the Nusselt number. This finding opens new possibilities in predicting heat transfer characteristics by drag data. As heat transfer for flow over a body is inherently complex, the proposed simple means may provide an insight into the mechanism of heat transfer for flow past a body.
Duan, Zhipeng; He, Boshu; Duan, Yuanyuan
2015-01-01
Modelling fluid flows past a body is a general problem in science and engineering. Historical sphere drag and heat transfer data are critically examined. The appropriate drag coefficient is proposed to replace the inertia type definition proposed by Newton. It is found that the appropriate drag coefficient is a desirable dimensionless parameter to describe fluid flow physical behavior so that fluid flow problems can be solved in the simple and intuitive manner. The appropriate drag coefficient is presented graphically, and appears more general and reasonable to reflect the fluid flow physical behavior than the traditional century old drag coefficient diagram. Here we present drag and heat transfer experimental results which indicate that there exists a relationship in nature between the sphere drag and heat transfer. The role played by the heat flux has similar nature as the drag. The appropriate drag coefficient can be related to the Nusselt number. This finding opens new possibilities in predicting heat transfer characteristics by drag data. As heat transfer for flow over a body is inherently complex, the proposed simple means may provide an insight into the mechanism of heat transfer for flow past a body. PMID:26189698
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.
Force and torque of an electromagnetically levitated metal sphere
NASA Astrophysics Data System (ADS)
Lohoefer, G.
1993-09-01
The Lorentz force and torque exerted on an electrically conducting sphere exposed to an external, time-varying magnetic field are analytically calculated. The external magnetic field is generated by a set of sinusoidally alternating, but otherwise arbitrary, current density fields of different frequencies and phases. Expressions for the force and torque in a laboratory frame of reference, which is more convenient for application, are also given. Finally, the special cases of rotational and mirror-symmetric external current density fields are treated in more detail.
Mesoporous carbon spheres with controlled porosity for high-performance lithium-sulfur batteries
NASA Astrophysics Data System (ADS)
Wang, Dexian; Fu, Aiping; Li, Hongliang; Wang, Yiqian; Guo, Peizhi; Liu, Jingquan; Zhao, Xiu Song
2015-07-01
Mesoporous carbon (MC) spheres with hierarchical pores, controlled pore volume and high specific surface areas have been prepared by a mass-producible spray drying assisted template method using sodium alginate as carbon precursor and commercial colloidal silica particles as hard template. The resulting MC spheres, possessing hierarchical pores in the range of 3-30 nm, are employed as conductive matrices for the preparation of cathode materials for lithium-sulfur batteries. A high pressure induced one-step impregnation of elemental sulfur into the pore of the MC spheres has been exploited. The electrochemical performances of sulfur-impregnated MC spheres (S-MC) derived from MC spheres with different pore volume and specific surface area but with the same sulfur loading ratio of 60 wt% (S-MC-X-60) have been investigated in details. The S-MC-4-60 composite cathode material displayed a high initial discharge capacity of 1388 mAhg-1 and a good cycling stability of 857 mAhg-1 after 100 cycles at 0.2C, and shows also excellent rate capability of 864 mAhg-1 at 2C. More importantly, the sulfur loading content in MC-4 spheres can reach as high as 80%, and it still can deliver a capacity of 569 mAhg-1 after 100 cycles at 0.2C.
A unified description of the rheology of hard particles
NASA Astrophysics Data System (ADS)
Hermes, Michiel; Guy, Ben; Poon, Wilson
The rheology of suspensions of Brownian, or colloidal, particles (diameter d <~ 1 μ m) differs markedly from that of larger grains (d >~ 50 μ m). Each of these two regimes has been separately studied, but the flow of suspensions with intermediate particle sizes (1 μm <~ d <~ 50 μ m), which occur ubiquitously in applications, remains poorly understood. By measuring the rheology of suspensions of hard spheres with a wide range of sizes, we show experimentally that shear thickening drives the transition from colloidal to granular flow across the intermediate size regime. This insight makes possible a unified description of the (non-inertial) rheology of hard spheres over the full size spectrum. Moreover, we are able to test a new theory of friction-induced shear thickening, showing that our data can be well fitted using expressions derived from it.
Mixtures of ions and amphiphilic molecules in slit-like pores: A density functional approach
Pizio, O.; Rżysko, W. Sokołowski, S.; Sokołowska, Z.
2015-04-28
We investigate microscopic structure and thermodynamic properties of a mixture that contains amphiphilic molecules and charged hard spheres confined in slit-like pores with uncharged hard walls. The model and the density functional approach are the same as described in details in our previous work [Pizio et al., J. Chem. Phys. 140, 174706 (2014)]. Our principal focus is in exploring the effects brought by the presence of ions on the structure of confined amphiphilic particles. We have found that for some cases of anisotropic interactions, the change of the structure of confined fluids occurs via the first-order transitions. Moreover, if anions and cations are attracted by different hemispheres of amphiphiles, a charge at the walls appears at the zero value of the wall electrostatic potential. For a given thermodynamic state, this charge is an oscillating function of the pore width.
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.
Porous Ceramic Spheres from Ion Exchange Resin
NASA Technical Reports Server (NTRS)
Dynys, Fred
2005-01-01
A commercial cation ion exchange resin, cross-linked polystyrene, has been successfully used as a template to fabricate 20 to 50 micron porous ceramic spheres. Ion exchange resins have dual template capabilities. Pore architecture of the ceramic spheres can be altered by changing the template pattern. Templating can be achieved by utilizing the internal porous structure or the external surface of the resin beads. Synthesis methods and chemical/physical characteristics of the ceramic spheres will be reported.
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.
Polarization effects on hard target calibration of lidar systems
NASA Technical Reports Server (NTRS)
Kavaya, Michael J.
1987-01-01
The theory of hard target calibration of lidar backscatter data, including laboratory measurements of the pertinent target reflectance parameters, is extended to include the effects of polarization of the transmitted and received laser radiation. The bidirectional reflectance-distribution function model of reflectance is expanded to a 4 x 4 matrix allowing Mueller matrix and Stokes vector calculus to be employed. Target reflectance parameters for calibration of lidar backscatter data are derived for various lidar system polarization configurations from integrating sphere and monostatic reflectometer measurements. It is found that correct modeling of polarization effects is mandatory for accurate calibration of hard target reflectance parameters and, therefore, for accurate calibration of lidar backscatter data.
Equations of state for many-body systems at high densities
NASA Astrophysics Data System (ADS)
Khan, Imran; Gao, Bo
2004-05-01
For a many-body system at high densities, the equation of state depends not only on the scattering length, but also on further details of the inter-particle potential. For a many-atom system, in particular, its behavior at high densities will depend on the van der Waals interaction. We are exploring the behavior of a many-atom system in this density regime using the variational Monte Carlo method, in combination with the concept of effective potential introduced in a recent work(B. Gao, J. Phys. B 36), 2111 (2003).. As an initial test, we will compare our hard-sphere results with those of Gross-Pitevaskii equation and diffussion Monte Carlo method(D. Blume and C. H. Greene, Phys. Rev. A 63), 063601 (2001)..
Photonic crystals from multiply-coated spheres
NASA Astrophysics Data System (ADS)
Chan, Che Ting
2000-03-01
We show theoretically and experimentally that photonic band gaps can be realized using metal or metal-coated spheres as building blocks. Robust photonic gaps exist in any periodic structure built from such spheres when the filling ratio of the spheres exceeds a threshold, and they are not sensitive to the symmetry or the global long range order, with stacking faults cause almost no degradation. Good agreement between theory and experiment is obtained in the microwave regime. The gaps persist even in a random packing of such spheres. Calculations show that the approach can be scaled up to IR and optical frequencies.
Science off the Sphere: Earth in Infrared
International Space Station Expedition 30 astronaut Don Pettit views cities, agricultural areas and deserts using an infrared camera for 'Science off the Sphere.' Through a partnership between NASA...
Unexpected ricochet of spheres off water
NASA Astrophysics Data System (ADS)
Shlien, D. J.
1994-08-01
A sphere was observed to apparently ricochet off the free surface of water at incident angles as large as 45° while the expected (empirical/analytical) maximum angle to the horizontal for ricochet was 6°. Closer examination of the process revealed that the cavitating sphere penetrated the liquid to depths as great as 35 sphere diameters. Under certain circumstances the sphere was also observed to leave the liquid in a direction close to the incoming direction; that is, the sphere ricocheted backwards! This peculiar behavior was found to be a result of an unintentional spin applied to the sphere upon launching. By crudely modelling the process, the sphere path is qualitatively predicted. It was found that the drag and lift coefficients required to model the trajectory data were several times smaller than those obtained for the non-cavitating case or for the non-spinning case. If more precise sphere trajectory data were available, this experiment could be used to measure the lift and drag coefficients of a spinning and cavitating sphere.
Method for producing small hollow spheres
Hendricks, C.D.
1979-01-09
Method is disclosed for producing small hollow spheres of glass, metal or plastic, wherein the sphere material is mixed with or contains as part of the composition a blowing agent which decomposes at high temperature (T [approx gt] 600 C). As the temperature is quickly raised, the blowing agent decomposes and the resulting gas expands from within, thus forming a hollow sphere of controllable thickness. The thus produced hollow spheres (20 to 10[sup 3] [mu]m) have a variety of application, and are particularly useful in the fabrication of targets for laser implosion such as neutron sources, laser fusion physics studies, and laser initiated fusion power plants. 1 fig.
Method for producing small hollow spheres
Hendricks, Charles D. [Livermore, CA
1979-01-09
Method for producing small hollow spheres of glass, metal or plastic, wherein the sphere material is mixed with or contains as part of the composition a blowing agent which decomposes at high temperature (T .gtorsim. 600.degree. C). As the temperature is quickly raised, the blowing agent decomposes and the resulting gas expands from within, thus forming a hollow sphere of controllable thickness. The thus produced hollow spheres (20 to 10.sup.3 .mu.m) have a variety of application, and are particularly useful in the fabrication of targets for laser implosion such as neutron sources, laser fusion physics studies, and laser initiated fusion power plants.
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.).
Precise algorithm to generate random sequential addition of hard hyperspheres at saturation.
Zhang, G; Torquato, S
2013-11-01
The study of the packing of hard hyperspheres in d-dimensional Euclidean space R^{d} has been a topic of great interest in statistical mechanics and condensed matter theory. While the densest known packings are ordered in sufficiently low dimensions, it has been suggested that in sufficiently large dimensions, the densest packings might be disordered. The random sequential addition (RSA) time-dependent packing process, in which congruent hard hyperspheres are randomly and sequentially placed into a system without interparticle overlap, is a useful packing model to study disorder in high dimensions. Of particular interest is the infinite-time saturation limit in which the available space for another sphere tends to zero. However, the associated saturation density has been determined in all previous investigations by extrapolating the density results for nearly saturated configurations to the saturation limit, which necessarily introduces numerical uncertainties. We have refined an algorithm devised by us [S. Torquato, O. U. Uche, and F. H. Stillinger, Phys. Rev. E 74, 061308 (2006)] to generate RSA packings of identical hyperspheres. The improved algorithm produce such packings that are guaranteed to contain no available space in a large simulation box using finite computational time with heretofore unattained precision and across the widest range of dimensions (2≤d≤8). We have also calculated the packing and covering densities, pair correlation function g(2)(r), and structure factor S(k) of the saturated RSA configurations. As the space dimension increases, we find that pair correlations markedly diminish, consistent with a recently proposed "decorrelation" principle, and the degree of "hyperuniformity" (suppression of infinite-wavelength density fluctuations) increases. We have also calculated the void exclusion probability in order to compute the so-called quantizer error of the RSA packings, which is related to the second moment of inertia of the average
Precise algorithm to generate random sequential addition of hard hyperspheres at saturation
NASA Astrophysics Data System (ADS)
Zhang, G.; Torquato, S.
2013-11-01
The study of the packing of hard hyperspheres in d-dimensional Euclidean space Rd has been a topic of great interest in statistical mechanics and condensed matter theory. While the densest known packings are ordered in sufficiently low dimensions, it has been suggested that in sufficiently large dimensions, the densest packings might be disordered. The random sequential addition (RSA) time-dependent packing process, in which congruent hard hyperspheres are randomly and sequentially placed into a system without interparticle overlap, is a useful packing model to study disorder in high dimensions. Of particular interest is the infinite-time saturation limit in which the available space for another sphere tends to zero. However, the associated saturation density has been determined in all previous investigations by extrapolating the density results for nearly saturated configurations to the saturation limit, which necessarily introduces numerical uncertainties. We have refined an algorithm devised by us [S. Torquato, O. U. Uche, and F. H. Stillinger, Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.74.061308 74, 061308 (2006)] to generate RSA packings of identical hyperspheres. The improved algorithm produce such packings that are guaranteed to contain no available space in a large simulation box using finite computational time with heretofore unattained precision and across the widest range of dimensions (2≤d≤8). We have also calculated the packing and covering densities, pair correlation function g2(r), and structure factor S(k) of the saturated RSA configurations. As the space dimension increases, we find that pair correlations markedly diminish, consistent with a recently proposed “decorrelation” principle, and the degree of “hyperuniformity” (suppression of infinite-wavelength density fluctuations) increases. We have also calculated the void exclusion probability in order to compute the so-called quantizer error of the RSA packings, which is related to the
NASA Astrophysics Data System (ADS)
Perera, Yibran; Gottmann, Jens; Husmann, Andreas; Klotzbuecher, Thomas; Kreutz, Ernst-Wolfgang; Poprawe, Reinhart
2001-06-01
The deposition of different hard ceramics coatings as Al2O3, ZrO2, c-BN and DLC thin films by pulsed laser deposition (PLD) has been of increasing interest as alternative process compared to the latest progress in CVD and PVD deposition. For instance, in pulsed laser deposition, the properties of the resulting thin films are influenced by the composition, ionization state, density, kinetic and excitation energies of the particles of the vapor/plasma. In order to deposit hard ceramics with different properties and applications, various substrates as Pt/Ti/Si multilayer, glass (fused silica), steel, polymethylmethacrylate (PMMA), polycarbonate (PC), Si(100) and Si(111) are used. These thin films are deposited either by excimer laser radiation ((lambda) equals 248 nm) or by CO2 laser radiation ((lambda) equals 10.6 micrometers ). To characterize the structural, optical and mechanical properties of the hard ceramics thin films, different techniques as Raman spectroscopy, ellipsometry, FTIR spectroscopy and nanoindentation are used.
The Intrinsic Beauty of Polytropic Spheres in Reduced Variables
NASA Astrophysics Data System (ADS)
Caimmi, Roberto
The concept of reduced variables is revisited with regard to van der Waals' theory and an application is made to polytropic spheres, where the reduced radial coordinate is ${\\rm red}(r)=r/R=\\xi/\\Xi$, $R$ radius, and the reduced density is ${\\rm red}(\\rho)=\\rho/\\lambda=\\theta^n$, $\\lambda$ central density. Reduced density profiles are plotted for several polytropic indexes within the range, $0\\le n\\le5$, disclosing two noticeable features. First, any point of coordinates, $({\\rm red}(r),{\\rm red}(\\rho))$, $0\\le{\\rm red}(r)\\le1$, $0\\le{\\rm red}(\\rho)\\le1$, belongs to a reduced density profile of the kind considered. Second, sufficiently steep i.e. large $n$ reduced density profiles exhibit an oblique inflection point, where the threshold is found to be located at $n=n_{\\rm th}=0.888715$. Reduced pressure profiles, ${\\rm red}(P)=P/\\varpi=\\theta^{n+1}$, $\\varpi$ central pressure, Lane-Emden fucntions, $\\theta=(\\rho/\\lambda)^{1/n}$, and polytropic curves, ${\\rm red}(P)={\\rm red}(P)({\\rm red}(\\rho))$, are also plotted. The method can be extended to nonspherical polytropes with regard to a selected direction, ${\\rm red}(r)(\\mu)=r(\\mu)/R(\\mu)=\\xi(\\mu)/\\Xi(\\mu)$. The results can be extended to polytropic spheres made of collisionless particles, for polytropic index within a more restricted range, $1/2\\le n\\le5$.
Hollow Spheres in Composite Materials and Metallic Hollow Sphere Composites (MHSC)
NASA Astrophysics Data System (ADS)
Baumeister, Erika; Molitor, Martin
The newly developed metallic hollow spheres are used in combination with a polymeric matrix for producing metallic hollow-sphere-composites (MSHC), which have been developed for mechanical engineering applications in the “InnoZellMet” project.
Molecular density functional theory for water with liquid-gas coexistence and correct pressure
Jeanmairet, Guillaume Levesque, Maximilien; Sergiievskyi, Volodymyr; Borgis, Daniel
2015-04-21
The solvation of hydrophobic solutes in water is special because liquid and gas are almost at coexistence. In the common hypernetted chain approximation to integral equations, or equivalently in the homogenous reference fluid of molecular density functional theory, coexistence is not taken into account. Hydration structures and energies of nanometer-scale hydrophobic solutes are thus incorrect. In this article, we propose a bridge functional that corrects this thermodynamic inconsistency by introducing a metastable gas phase for the homogeneous solvent. We show how this can be done by a third order expansion of the functional around the bulk liquid density that imposes the right pressure and the correct second order derivatives. Although this theory is not limited to water, we apply it to study hydrophobic solvation in water at room temperature and pressure and compare the results to all-atom simulations. The solvation free energy of small molecular solutes like n-alkanes and hard sphere solutes whose radii range from angstroms to nanometers is now in quantitative agreement with reference all atom simulations. The macroscopic liquid-gas surface tension predicted by the theory is comparable to experiments. This theory gives an alternative to the empirical hard sphere bridge correction used so far by several authors.
Can the Equivalent Sphere Model Approximate Organ Doses in Space?
NASA Technical Reports Server (NTRS)
Lin, Zi-Wei
2007-01-01
For space radiation protection it is often useful to calculate dose or dose,equivalent in blood forming organs (BFO). It has been customary to use a 5cm equivalent sphere to. simulate the BFO dose. However, many previous studies have concluded that a 5cm sphere gives very different dose values from the exact BFO values. One study [1] . concludes that a 9 cm sphere is a reasonable approximation for BFO'doses in solar particle event environments. In this study we use a deterministic radiation transport [2] to investigate the reason behind these observations and to extend earlier studies. We take different space radiation environments, including seven galactic cosmic ray environments and six large solar particle events, and calculate the dose and dose equivalent in the skin, eyes and BFO using their thickness distribution functions from the CAM (Computerized Anatomical Man) model [3] The organ doses have been evaluated with a water or aluminum shielding of an areal density from 0 to 20 g/sq cm. We then compare with results from the equivalent sphere model and determine in which cases and at what radius parameters the equivalent sphere model is a reasonable approximation. Furthermore, we address why the equivalent sphere model is not a good approximation in some cases. For solar particle events, we find that the radius parameters for the organ dose equivalent increase significantly with the shielding thickness, and the model works marginally for BFO but is unacceptable for the eye or the skin. For galactic cosmic rays environments, the equivalent sphere model with an organ-specific constant radius parameter works well for the BFO dose equivalent, marginally well for the BFO dose and the dose equivalent of the eye or the skin, but is unacceptable for the dose of the eye or the skin. The ranges of the radius parameters are also being investigated, and the BFO radius parameters are found to be significantly, larger than 5 cm in all cases, consistent with the conclusion of
Tandem spheres in hypersonic flow
Laurence, Stuart J; Deiterding, Ralf; Hornung, Hans G
2009-01-01
The problem of determining the forces acting on a secondary body when it is travelling at some point within the shocked region created by a hypersonic primary body is of interest in such situations as store or stage separation, re-entry of multiple vehicles, and atmospheric meteoroid fragmentation. The current work is concerned with a special case of this problem, namely that in which both bodies are spheres and are stationary with respect to one another. We first present an approximate analytical model of the problem; subsequently, numerical simulations are described and results are compared with those from the analytical model. Finally, results are presented from a series of experiments in the T5 hypervelocity shock tunnel in which a newly-developed force-measurement technique was employed.
ERIC Educational Resources Information Center
Stocker, H. Robert; Hilton, Thomas S. E.
1991-01-01
Suggests strategies that make hard disk organization easy and efficient, such as making, changing, and removing directories; grouping files by subject; naming files effectively; backing up efficiently; and using PATH. (JOW)
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.
The Circle and Sphere as Great Equalizers.
ERIC Educational Resources Information Center
Schwartzman, Steven
1991-01-01
From the equality of the ratios of the surface areas and volumes of a sphere and its circumscribed cylinder, the exploration of theorems relating the ratios of surface areas and volumes of a sphere and other circumscribed solids in three dimensions, and analogous questions relating two-dimensional concepts of perimeter and area is recounted. (MDH)
The "Magical" Sphere: Uncovering the Secret
ERIC Educational Resources Information Center
Petruševski, Vladimir M.; Bukleski, Miha
2006-01-01
A red sphere is seen at the bottom of a sealed glass tube filled with a colorless, transparent liquid. Holding the tube for a short period makes the sphere rise slowly from the bottom until it finally floats on the surface of the liquid. Instructions for preparing the demonstration are given, together with an explanation of the phenomenon. A…
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.
C{sub 60}: Sphere or polyhedron?
Haddon, R.C.
1997-02-19
In the original publication on the subject, C{sub 60} was depicted with the aid of a soccer ball, but this representation soon gave way to the familiar line drawing of chemical bonds between nucleii. To a large extent the dichotomy in the representation of the fullerenes remains today, and it is the purpose of this paper to pose and address the question that appears in the title. Of course, in reality the answer is well-known, and neither the sphere nor the polyhedron represent C{sub 60}, which like other molecules exists as a collection of nuclei with an associated distribution of electron density. Nevertheless, it is of interest to consider which of these conventional representations is most relevant for the fullerenes and in particular the language most appropriate to the description of the shape of these molecules and the geometry of the carbon atoms. The analysis presented here shows that topology of the molecule is paramount, and hence, C{sub 60} (and the fullerenes) are best modeled as polyhedra. 16 refs., 3 figs.
Radiation Hard AlGaN Detectors and Imager
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.
How 'hard' are hard-rock deformations?
NASA Astrophysics Data System (ADS)
van Loon, A. J.
2003-04-01
The study of soft-rock deformations has received increasing attention during the past two decades, and much progress has been made in the understanding of their genesis. It is also recognized now that soft-rock deformations—which show a wide variety in size and shape—occur frequently in sediments deposited in almost all types of environments. In spite of this, deformations occurring in lithified rocks are still relatively rarely attributed to sedimentary or early-diagenetic processes. Particularly faults in hard rocks are still commonly ascribed to tectonics, commonly without a discussion about a possible non-tectonic origin at a stage that the sediments were still unlithified. Misinterpretations of both the sedimentary and the structural history of hard-rock successions may result from the negligence of a possible soft-sediment origin of specific deformations. It is therefore suggested that a re-evaluation of these histories, keeping the present-day knowledge about soft-sediment deformations in mind, may give new insights into the geological history of numerous sedimentary successions in which the deformations have not been studied from both a sedimentological and a structural point of view.
A set of verification test cases for Eiger : plane wave scattering from a sphere.
Jorgenson, Roy Eberhardt; Kotulski, Joseph Daniel
2004-10-01
This report discusses a set of verification test cases for the frequency-domain, boundary-element, electromagnetics code Eiger based on the analytical solution of plane wave scattering from a sphere. Three cases will be considered: when the sphere is made of perfect electric conductor, when the sphere is made of lossless dielectric and when the sphere is made of lossy dielectric. We outline the procedures that must be followed in order to carefully compare the numerical solution to the analytical solution. We define an error criterion and demonstrate convergence behavior for both the analytical and numerical cases. These problems test the code's ability to calculate the surface current density and secondary quantities, such as near fields and far fields.
Micro-mesoporous carbon spheres derived from carrageenan as electrode material for supercapacitors
NASA Astrophysics Data System (ADS)
Fan, Yang; Yang, Xin; Zhu, Bing; Liu, Pei-Fang; Lu, Hai-Ting
2014-12-01
The polysaccharide carrageenan is used as a natural precursor to prepare micro-mesoporous carbon spheres. The carbon spheres were synthesized by hydrothermal carbonization of carrageenan, and subsequent chemical activation by KOH at different temperatures. The obtained micro-mesoporous carbon spheres have high surface area (up to 2502 m2 g-1) and large pore volume (up to 1.43 cm3 g-1). Moreover, the micro- and mesoporosity can be finely tuned be modifying the activation temperatures in the range of 700-900 °C. The carbon spheres activated at 900 °C present high specific capacitance of 230 F g-1 at a current density of 1 A g-1 and good ion transport kinetics. The good capacitive performance can be ascribed to the high specific surface area, well-controlled micro- and mesoporosity and narrow pore size distribution.
Stochastic Interactions of Two Brownian Spheres in the Presence of Depletants
NASA Astrophysics Data System (ADS)
Karzar-Jeddi, Mehdi; Tuinier, Remco; Taniguchi, Takashi; Fan, Tai-Hsi
2014-03-01
The pair interactions between hard spheres play an essential role in many processes such as macromolecular crowding, binding, self-assembly of particles, and many chemical and food processes. Here we focus on theoretical analysis of the long-time correlated stochastic motion of two hard spheres in a non-adsorbing polymer solution. The hard spheres are held by hypothetical optical traps. The pair mobility tenser is found using a two-layer approximation with pure solvent in the depletion zone surrounding the particle and uniform polymer solution elsewhere. The resulting mobility computed by the boundary integral analysis is used to define the level of thermal fluctuation. Results show how the mobility and the decay of displacement correlation functions modified by the polymer depletion effect. The attractive osmotic potential increases the auto-correlation of the pair particle motion, while reduces the cross-correlation of the particles. This work gives better understanding of the pair interactions in a suspension of non-adsorbing polymers as an essential step toward many-particle interactions.
Shape transitions in soft spheres regulated by elasticity
NASA Astrophysics Data System (ADS)
Fogle, Craig; Rowat, Amy; Levine, Alex; Rudnick, Joseph
2014-03-01
Soft core shell structures abound in nature. Examples of these structures, comprised of a thin outer membrane bounding an elastic core, include raisins, gel-filled vesicles, and a variety of membrane-bound organelles in the cell. We study the elasticity-driven morphological transitions of spherical core shell structures when either their surface area is increased or their interior volume is decreased. We demonstrate a transition, which is related to the Euler buckling, from the spherical initial shape to a lower symmetry one. We discuss the dependence of the critical excess surface area (relative to that of a bounding sphere) for buckling, the internal stresses in the core, and the symmetry of the buckled state on the elastic parameters of the system. We compare these predictions to a variety of observed morphological transitions in hard and soft materials, and discuss extensions of this work to growing viscoelastic media.
Impact into Coarse Grained Spheres
NASA Technical Reports Server (NTRS)
Barnouin-Jha, O. S.; Cintala, M.; Crawford, D. A.
2005-01-01
Several experimental studies [1,2,3] indicate that differences in the grain size of the target relative to the projectile could influence the cratering process. Impacts into coarse sand grains of size comparable to the projectile show some discrepancies with existing relationships for crater growth [e.g. 4]. Similarly, targets of ne grained, uniform in diameter glass spheres show differences in crater depth, transient crater diameter, and volume of ejecta excavated as a function of grain size [2,3]. The purpose of this work is to continue investigating how the relative grain size may influence early time coupling between a projectile and target, with implications for subsequent ejecta excavation and crater growth. In previous efforts we used numerical techniques to focus on the propagation of shock waves in coarse, granular media emphasizing the influence of relative grain size on crater growth, ejecta production, cratering efficiency, target strength, and crater shape [5,6,7]. In this study, we use experimental techniques - in part as a reality check for the numerical studies - to report on how coarse grained targets might influence ejecta excavation and crater shape. This body of work possesses important implications for ejecta excavation and cratering efficiency on asteroids that may possess rubble pile-like structures, and on planets that may possess either pre-fractured surfaces or large-scale heterogeneities in shock impedance.
Ceramic Spheres From Cation Exchange Beads
NASA Technical Reports Server (NTRS)
Dynys, F. W.
2003-01-01
Porous ZrO2 and hollow TiO2 spheres were synthesized from a strong acid cation exchange resin. Spherical cation exchange beads, polystyrene based polymer, were used as a morphological-directing template. Aqueous ion exchange reaction was used to chemically bind (ZrO)(2+) ions to the polystyrene structure. The pyrolysis of the polystyrene at 600 C produces porous ZrO2 spheres with a surface area of 24 sq m/g with a mean sphere size of 42 microns. Hollow TiO2 spheres were synthesized by using the beads as a micro-reactor. A direct surface reaction - between titanium isopropoxide and the resin beads forms a hydrous TiO2 shell around the polystyrene core. The pyrolysis of the polystyrene core at 600 C produces hollow anatase spheres with a surface area of 42 sq m/g with a mean sphere size of 38 microns. The formation of ceramic spheres was studied by XRD, SEM and B.E.T. nitrogen adsorption measurements.
Induced differentiation inhibits sphere formation in neuroblastoma.
Craig, Brian T; Rellinger, Eric J; Alvarez, Alexandra L; Dusek, Haley L; Qiao, Jingbo; Chung, Dai H
2016-08-19
Neuroblastoma arises from the neural crest, the precursor cells of the sympathoadrenal axis, and differentiation status is a key prognostic factor used for clinical risk group stratification and treatment strategies. Neuroblastoma tumor-initiating cells have been successfully isolated from patient tumor samples and bone marrow using sphere culture, which is well established to promote growth of neural crest stem cells. However, accurate quantification of sphere-forming frequency of commonly used neuroblastoma cell lines has not been reported. Here, we show that MYCN-amplified neuroblastoma cell lines form spheres more frequently than non-MYCN-amplified cell lines. We also show that sphere formation is directly sensitive to cellular differentiation status. 13-cis-retinoic acid is a clinically used differentiating agent that induces a neuronal phenotype in neuroblastoma cells. Induced differentiation nearly completely blocked sphere formation. Furthermore, sphere formation was specifically FGF-responsive and did not respond to increasing doses of EGF. Taken together, these data suggest that sphere formation is an accurate method of quantifying the stemness phenotype in neuroblastoma. PMID:27297102
Flow around spheres by dissipative particle dynamics
NASA Astrophysics Data System (ADS)
Chen, Shuo; Phan-Thien, Nhan; Khoo, Boo Cheong; Fan, Xi Jun
2006-10-01
The dissipative particle dynamics (DPD) method is used to study the flow behavior past a sphere. The sphere is represented by frozen DPD particles while the surrounding fluids are modeled by simple DPD particles (representing a Newtonian fluid). For the surface of the sphere, the conventional model without special treatment and the model with specular reflection boundary condition proposed by Revenga et al. [Comput. Phys. Commun. 121-122, 309 (1999)] are compared. Various computational domains, in which the sphere is held stationary at the center, are investigated to gage the effects of periodic conditions and walls for Reynolds number (Re)=0.5 and 50. Two types of flow conditions, uniform flow and shear flow are considered, respectively, to study the drag force and torque acting on the stationary sphere. It is found that the calculated drag force imposed on the sphere based on the model with specular reflection is slightly lower than the conventional model without special treatment. With the conventional model the drag force acting on the sphere is in better agreement with experimental correlation obtained by Brown and Lawler [J. Environ. Eng. 129, 222 (2003)] for the case of larger radius up to Re of about 5. The computed torque also approaches the analytical Stokes value when Re <1. For a force-free and torque-free sphere, its motion in the flow is captured by solving the translational and rotational equations of motion. The effects of different DPD parameters (a, γ, and σ) on the drag force and torque are studied. It shows that the dissipative coefficient (γ) mainly affects the drag force and torque, while random and conservative coefficient have little influence on them. Furthermore the settling of a single sphere in square tube is investigated, in which the wall effect is considered. Good agreement is found with the experiments of Miyamura et al. [Int. J. Multiphase Flow 7, 31 (1981)] and lattice-Boltzmann simulation results of Aidun et al. [J. Fluid Mech
Numerical Simulations of Falling Sphere Viscometry Experiments.
NASA Astrophysics Data System (ADS)
O Dwyer, L.; Kellogg, L. H.; Lesher, C. E.
2007-12-01
The falling sphere technique based on Stokes' law is widely used to determine the viscosities of geologically relevant melts at high pressures. Stokes' law is valid when a rigid sphere falls slowly and steadily through a stationary and infinite Newtonian medium of uniform properties. High-pressure falling sphere experiments however, usually involve dropping a dense, refractory sphere through a liquid contained by a cylindrical capsule of finite size. The sphere velocity is influenced by the walls (Faxen correction) and ends of the capsule, and possible convective motion of the fluid. Efforts are made to minimize thermal gradients in laboratory experiments, but small temperature differences within the capsule can lead to convection complicating interpretation. We utilize GALE (Moresi et al., 2003;), a finite element particle-in-cell code, to examine these factors in numerical models of conditions similar to those of high-pressure experiments. Our modeling considers a three- dimensional box or cylinder containing a cluster of particles that represent the dense sphere in laboratory experiments surrounded by low viscosity particles representing the melt. GALE includes buoyancy forces, heat flow, and viscosity variations so our model can be used to assess the effects of the capsule's walls and ends, and the consequences of thermal gradients on the sphere's velocity and trajectory. Comparisons between our numerical simulations and real-time falling sphere experiments involving lower viscosity molten komatiite are made to assess the validity of Stokes' law with the standard Faxen correction included, and formulations considering end effects. The modeling also permits an evaluation of the uncertainties in recovering accurate liquid viscosities from Stokes' law when a dense sphere falls through a convecting low viscosity melt. It also allows us to assess acceleration to a terminal velocity that can provide constraints on melt viscosity in experiments in which the terminal
NASA Astrophysics Data System (ADS)
Cheng, Hongbo
2015-08-01
The Casimir energies for plate-sphere system and sphere-sphere systems under PFA in the presence of one extra compactified universal dimension are analyzed. We find that the Casimir energy between a plate and a sphere in the case of sphere-based PFA is divergent. The Casimir energy of plate-sphere system in the case of plate-based PFA is finite and keeps negative. The extra-dimension corrections to the Casimir energy will be more manifest if the sphere is larger or farther away from the plate. It is shown that the negative Casimir energy for two spheres is also associated with the sizes of spheres and extra space. The larger spheres and the longer distance between them make the influence from the additional dimension stronger.
Gimbel, C B
2000-10-01
A more conservative, less invasive treatment of the carious lesion has intrigued researchers and clinicians for decades. With over 170 million restorations placed worldwide each year, many of which could be treated using a laser, there exists an increasing need for understanding hard tissue laser procedures. An historical review of past scientific and clinical hard research, biophysics, and histology are discussed. A complete review of present applications and procedures along with their capabilities and limitations will give the clinician a better understanding. Clinical case studies, along with guidelines for tooth preparation and hard tissue laser applications and technological advances for diagnosis and treatment will give the clinician a look into the future. PMID:11048281
Monodisperse PEGylated Spheres: An Aqueous Colloidal Model System
2014-01-01
Fluorinated core–shell spheres have been synthesized using a novel semibatch emulsion polymerization protocol employing slow feeding of the initiator. The synthesis results in aqueous dispersions of highly monodisperse spheres bearing a well-defined poly(ethylene glycol) graft (PEGylation). Measurements are consistent with the synthesis achieving a high grafting density that moreover consists of a single PEG layer with the polymer significantly elongated beyond its radius of gyration in bulk. The fluorination of the core of the particles confers a low index of refraction such that the particles can be refractive index matched in water through addition of relatively small amounts of a cosolvent, which enables the use of optical and laser-based methods for studies of concentrated systems. The systems exhibit an extreme stability in NaCl solutions, but attractions among particles can be introduced by addition of other salts, in which case aggregation is shown to be reversible. The PEGylated sphere dispersions are expected to be ideally suited as model systems for studies of the effect of PEG-mediated interactions on, for instance, structure, dynamics, phase behavior, and rheology. PMID:24533774
Stimulus-responsive azobenzene supramolecules: fibers, gels, and hollow spheres.
Lee, Sumi; Oh, Seungwhan; Lee, Joosub; Malpani, Yashwardhan; Jung, Young-Sik; Kang, Baotao; Lee, Jin Yong; Ozasa, Kazunari; Isoshima, Takashi; Lee, Sang Yun; Hara, Masahiko; Hashizume, Daisuke; Kim, Jong-Man
2013-05-14
Novel, stimulus-responsive supramolecular structures in the form of fibers, gels, and spheres, derived from an azobenzene-containing benzenetricarboxamide derivative, are described. Self-assembly of tris(4-((E)-phenyldiazenyl)phenyl)benzene-1,3,5-tricarboxamide (Azo-1) in aqueous organic solvent systems results in solvent dependent generation of microfibers (aq DMSO), gels (aq DMF), and hollow spheres (aq THF). The results of a single crystal X-ray diffraction analysis of Azo-1 (crystallized from a mixture of DMSO and H2O) reveal that it possesses supramolecular columnar packing along the b axis. Data obtained from FTIR analysis and density functional theory (DFT) calculation suggest that multiple hydrogen bonding modes exist in the Azo-1 fibers. UV irradiation of the microfibers, formed in aq DMSO, causes complete melting while regeneration of new fibers occurs upon visible light irradiation. In addition to this photoinduced and reversible phase transition, the Azo-1 supramolecules display a reversible, fiber-to-sphere morphological transition upon exposure to pure DMSO or aq THF. The role played by amide hydrogen bonds in the morphological changes occurring in Azo-1 is demonstrated by the behavior of the analogous, ester-containing tris(4-((E)-phenyldiazenyl)phenyl)benzene-1,3,5-tricarboxylate (Azo-2) and by the hydrogen abstraction in the presence of fluoride anions. PMID:23597134
Monodisperse PEGylated spheres: an aqueous colloidal model system.
Ulama, Jeanette; Zackrisson Oskolkova, Malin; Bergenholtz, Johan
2014-03-01
Fluorinated core-shell spheres have been synthesized using a novel semibatch emulsion polymerization protocol employing slow feeding of the initiator. The synthesis results in aqueous dispersions of highly monodisperse spheres bearing a well-defined poly(ethylene glycol) graft (PEGylation). Measurements are consistent with the synthesis achieving a high grafting density that moreover consists of a single PEG layer with the polymer significantly elongated beyond its radius of gyration in bulk. The fluorination of the core of the particles confers a low index of refraction such that the particles can be refractive index matched in water through addition of relatively small amounts of a cosolvent, which enables the use of optical and laser-based methods for studies of concentrated systems. The systems exhibit an extreme stability in NaCl solutions, but attractions among particles can be introduced by addition of other salts, in which case aggregation is shown to be reversible. The PEGylated sphere dispersions are expected to be ideally suited as model systems for studies of the effect of PEG-mediated interactions on, for instance, structure, dynamics, phase behavior, and rheology. PMID:24533774
Integrating Sphere Alkali-Metal Vapor Cells
NASA Astrophysics Data System (ADS)
McGuyer, Bart; Ben-Kish, Amit; Jau, Yuan-Yu; Happer, William
2010-03-01
An integrating sphere is an optical multi-pass cavity that uses diffuse reflection to increase the optical path length. Typically applied in photometry and radiometry, integrating spheres have previously been used to detect trace gases and to cool and trap alkali-metal atoms. Here, we investigate the potential for integrating spheres to enhance optical absorption in optically thin alkali-metal vapor cells. In particular, we consider the importance of dielectric effects due to a glass container for the alkali-metal vapor. Potential applications include miniature atomic clocks and magnetometers, where multi-passing could reduce the operating temperature and power consumption.
Manipulator for rotating and examining small spheres
Weinstein, Berthold W. [Livermore, CA; Willenborg, David L. [Livermore, CA
1980-02-12
A manipulator which provides fast, accurate rotational positioning of a small sphere, such as an inertial confinement fusion target, which allows inspecting of the entire surface of the sphere. The sphere is held between two flat, flexible tips which move equal amounts in opposite directions. This provides rolling of the ball about two orthogonal axes without any overall translation. The manipulator may be controlled, for example, by an x- and y-axis driven controlled by a mini-computer which can be programmed to generate any desired scan pattern.
Manipulator for rotating and examining small spheres
Weinstein, B.W.; Willenborg, D.L.
1980-02-12
A manipulator is disclosed which provides fast, accurate rotational positioning of a small sphere, such as an inertial confinement fusion target, which allows inspecting of the entire surface of the sphere. The sphere is held between two flat, flexible tips which move equal amounts in opposite directions. This provides rolling of the ball about two orthogonal axes without any overall translation. The manipulator may be controlled, for example, by an x- and y-axis driven controlled by a mini-computer which can be programmed to generate any desired scan pattern. 8 figs.
Superelastic carbon spheres under high pressure
NASA Astrophysics Data System (ADS)
Li, Meifen; Guo, Junjie; Xu, Bingshe
2013-03-01
We report a superelastic deformation behavior of carbon spheres by the in situ Raman spectroscopy in a high-pressure diamond anvil cell. The carbon spheres produced by arc discharging in toluene have a mean diameter of 200 nm and an onion-like multilayer graphitic structure. We find that the elastic coefficients, during both the compression and decompression processes, remain a constant up to 10 GPa, indicating a superior high-pressure structural stability. Such superelastic behavior is related to the isotropic and concentric configuration of carbon spheres and provides additional insight into improving the microscopic mechanical properties of small-scale particles.
Multicomponent fluids of hard hyperspheres in odd dimensions
NASA Astrophysics Data System (ADS)
Rohrmann, René D.; Santos, Andrés
2011-01-01
Mixtures of hard hyperspheres in odd-space dimensionalities are studied with an analytical approximation method. This technique is based on the so-called rational function approximation and provides a procedure for evaluating equations of state, structure factors, radial distribution functions, and direct correlation functions of additive mixtures of hard hyperspheres with any number of components and in arbitrary odd-dimension space. The method gives the exact solution of the Ornstein-Zernike equation coupled with the Percus-Yevick closure, thus, extending the solution for hard-sphere mixtures [J. L. Lebowitz, Phys. Rev.PHRVAO0031-899X10.1103/PhysRev.133.A895 133, A895 (1964)] to arbitrary odd dimensions. Explicit evaluations for binary mixtures in five dimensions are performed. The results are compared with computer simulations, and a good agreement is found.
Soft core thermodynamics from self-consistent hard core fluids.
Schöll-Paschinger, Elisabeth; Reiner, Albert
2006-10-28
In an effort to generalize the self-consistent Ornstein-Zernike approximation (SCOZA)-an accurate liquid state theory that has been restricted so far to hard core systems-to arbitrary soft core systems we study a combination of SCOZA with a recently developed perturbation theory. The latter was constructed by Ben-Amotz and Stell [J. Phys. Chem. B 108, 6877 (2004)] as a reformulation of the Weeks-Chandler-Andersen [J. Chem. Phys. 54, 5237 (1971)] perturbation theory directly in terms of an arbitrary hard sphere reference system. We investigate the accuracy of the combined approach for the Lennard-Jones fluid in comparison with simulation data and pure perturbation theory predictions and determine the dependence of the thermodynamic properties and the phase behavior on the choice of the effective hard core diameter of the reference system. PMID:17092101
Detecting the dynamical state of the atmosphere from the orbital decay of the ODERACS spheres
NASA Technical Reports Server (NTRS)
Tan, Arjun
1996-01-01
The orbital decay curve of a satellite having constant cross-sectional area and in circular orbit can furnish valuable information regarding the dynamical state of the atmosphere. It is shown that a rectilinear decay curve having constant downward slope (zero curvature) should indicate that the atmosphere was undergoing compression during that period. A decay curve having concavity upwards (positive curvature) will strongly indicate that the atmosphere was in a contracting phase. A decay curve with downward concavity (negative curvature) may indicate an expanding, a stationary or a contracting atmosphere. This theory, when applied to the orbital decay of the Orbital Debris Radar Calibration Spheres (ODERACS) satellites, indicates that during the period from Day 90 through Day 240 in the year 1994, the atmosphere was very definitely in a compression mode. During this period, ODERACS Sphere 1 faced nearly constant densities while Sphere 6 actually encountered progressively smaller air densities as they descended. The atmospheric scale height as calculated from the orbital data of Spheres 1 and 6 diminished steadily during the same period. It is shown that Spheres 1 and 6 descended faster and slower respectively, than the level of constant air density equal to 5 x 10 kg/m . During a brief period from Day 240 through Day 290, the atmosphere reversed to a strongly expanding mode. Thereafter, the atmosphere reverted back to a compression mode from Day 290 through Day 390, 1994.
Density profiles of atoms in nano-tubes from an analytic method: hydrogen in a cylindrical pore
NASA Astrophysics Data System (ADS)
Boublík, Tomáš
2011-01-01
Knowledge of the structure of simple fluids in nano-tubes constitutes important information in many scientific and technical branches. Computer simulations and density functional theory (DFT) offer accurate but laborious results. We have proposed a simple analytical method to determine the background correlation function on the basis of the residual chemical potentials of a pair of interacting bodies and of the corresponding combined body. These potentials are obtained in terms of geometric quantities. In this paper we dealt with the combination rule for the geometric quantity Q; the harmonic mean rule was proposed and verified at low densities by calculating the third cross-virial coefficient, and by comparing calculated density profiles of the inhomogeneous systems of hard sphere-wall at higher densities. A slight improvement over the previous results were found. Next, we applied our analytic method to realistic systems of a simple molecule in the graphite cylindrical pore. Hydrogen (and carbon monoxide), interacting with carbon of the graphite via the modified LJ potential are considered and the density profile was determined taking into account only the soft-sphere interaction within Weeks-Chandler-Andersen approximation. The considered approach was found to yield a fair description of the realistic simple fluid-cylindrical pore system.
Goddard, B D; Nold, A; Savva, N; Yatsyshin, P; Kalliadasis, S
2013-01-23
Starting from the Kramers equation for the phase-space dynamics of the N-body probability distribution, we derive a dynamical density functional theory (DDFT) for colloidal fluids including the effects of inertia and hydrodynamic interactions (HI). We compare the resulting theory to extensive Langevin dynamics simulations for both hard rod systems and three-dimensional hard sphere systems with radially symmetric external potentials. As well as demonstrating the accuracy of the new DDFT, by comparing with previous DDFTs which neglect inertia, HI, or both, we also scrutinize the significance of including these effects. Close to local equilibrium we derive a continuum equation from the microscopic dynamics which is a generalized Navier-Stokes-like equation with additional non-local terms governing the effects of HI. For the overdamped limit we recover analogues of existing configuration-space DDFTs but with a novel diffusion tensor. PMID:23220969
Separate spheres and indirect benefits
Brock, Dan W
2003-01-01
On any plausible account of the basis for health care resource prioritization, the benefits and costs of different alternative resource uses are relevant considerations in the prioritization process. Consequentialists hold that the maximization of benefits with available resources is the only relevant consideration. Non-consequentialists do not reject the relevance of consequences of benefits and costs, but insist that other considerations, and in particular the distribution of benefits and costs, are morally important as well. Whatever one's particular account of morally justified standards for the prioritization of different health interventions, we must be able to measure those interventions' benefits and costs. There are many theoretical and practical difficulties in that measurement, such as how to weigh extending life against improving health and quality of life as well as how different quality of life improvements should be valued, but they are not my concern here. This paper addresses two related issues in assessing benefits and costs for health resource prioritization. First, should benefits be restricted only to health benefits, or include as well other non health benefits such as economic benefits to employers from reducing the lost work time due to illness of their employees? I shall call this the Separate Spheres problem. Second, should only the direct benefits, such as extending life or reducing disability, and direct costs, such as costs of medical personnel and supplies, of health interventions be counted, or should other indirect benefits and costs be counted as well? I shall call this the Indirect Benefits problem. These two issues can have great importance for a ranking of different health interventions by either a cost/benefit or cost effectiveness analysis (CEA) standard. PMID:12773217
Electrical double layers and differential capacitance in molten salts from density functional theory
Frischknecht, Amalie L.; Halligan, Deaglan O.; Parks, Michael L.
2014-08-05
Classical density functional theory (DFT) is used to calculate the structure of the electrical double layer and the differential capacitance of model molten salts. The DFT is shown to give good qualitative agreement with Monte Carlo simulations in the molten salt regime. The DFT is then applied to three common molten salts, KCl, LiCl, and LiKCl, modeled as charged hard spheres near a planar charged surface. The DFT predicts strong layering of the ions near the surface, with the oscillatory density profiles extending to larger distances for larger electrostatic interactions resulting from either lower temperature or lower dielectric constant. Inmore » conclusion, overall the differential capacitance is found to be bell-shaped, in agreement with recent theories and simulations for ionic liquids and molten salts, but contrary to the results of the classical Gouy-Chapman theory.« less
Electrical double layers and differential capacitance in molten salts from density functional theory
Frischknecht, Amalie L.; Halligan, Deaglan O.; Parks, Michael L.
2014-08-05
Classical density functional theory (DFT) is used to calculate the structure of the electrical double layer and the differential capacitance of model molten salts. The DFT is shown to give good qualitative agreement with Monte Carlo simulations in the molten salt regime. The DFT is then applied to three common molten salts, KCl, LiCl, and LiKCl, modeled as charged hard spheres near a planar charged surface. The DFT predicts strong layering of the ions near the surface, with the oscillatory density profiles extending to larger distances for larger electrostatic interactions resulting from either lower temperature or lower dielectric constant. In conclusion, overall the differential capacitance is found to be bell-shaped, in agreement with recent theories and simulations for ionic liquids and molten salts, but contrary to the results of the classical Gouy-Chapman theory.
Thermodynamics of the low-density excluded-volume hadron gas
NASA Astrophysics Data System (ADS)
Redlich, Krzysztof; Zalewski, Kacper
2016-01-01
We consider the thermodynamics of excluded-volume particles at finite temperature and chemical potential in the low-density approximation. We assume Boltzmann statistics and study the influence of the excluded volume on an ideal gas thermodynamics at the same temperature, pressure, and number of particles. We show that considering the change of the free enthalpy due to the excluded volume, and using the Maxwell identities, one can derive relevant thermodynamic functions and parameters of multicomponent gases. The derivation is quite general, because particles may have different sizes and shapes which can also depend on their momenta. Besides its simplicity and generality, our approach has the advantage of eliminating the transcendental equations occurring in earlier studies. A representative example of the excluded-volume thermodynamics is the single-component gas of hard spheres. For this case, using a virial expansion, the validity limits of the low-density approximation are also discussed.
Giera, Brian; Henson, Neil; Kober, Edward M.; Shell, M. Scott; Squires, Todd M.
2015-02-27
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 is 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.
Giera, Brian; Lawrence Livermore National Lab.; Henson, Neil; Kober, Edward M.; Shell, M. Scott; Squires, Todd M.
2015-02-27
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 is 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 drivemore » strong density and free charge oscillations within the EDL, despite the inability of LDAs to capture the oscillations in the detailed EDL profiles.« less
1500 Gate standard cell compatible radiation hard gate array
Mills, B.D.; Shafer, B.D.; Melancon, E.P.
1984-11-01
The G1500 gate array combines Sandia Labs' 4/3..mu.. CMOS silicon gate radiation hard process with a novel gate isolated standard cell compatible design for quick turnaround time, low cost, and radiation hardness. This device is hard to 5 x 10/sup 5/ rads, utilizes a configuration that provides high packing density, and is supported on both the Daisy and Mentor workstations. This paper describes Sandia Labs' radiation hard 4/3..mu.. process, the G1500's unique design, and the complete design capabilities offered by the workstations.
#4 Simulated Solar Sphere from Data - Interpolated
Rotating solar sphere made from a combination of imagery from the two STEREO spacecraft, together with simultaneous data from the Solar Dynamic Observatory.This movie is made from data taken on Jan...
Science off the Sphere: Lenses and Vortices
International Space Station Expedition 30 astronaut Don Pettit demonstrates physics in space for 'Science off the Sphere.' Through a partnership between NASA and the American Physical Society you c...
Elastic spheres can walk on water
NASA Astrophysics Data System (ADS)
Belden, Jesse; Hurd, Randy C.; Jandron, Michael A.; Bower, Allan F.; Truscott, Tadd T.
2016-02-01
Incited by public fascination and engineering application, water-skipping of rigid stones and spheres has received considerable study. While these objects can be coaxed to ricochet, elastic spheres demonstrate superior water-skipping ability, but little is known about the effect of large material compliance on water impact physics. Here we show that upon water impact, very compliant spheres naturally assume a disk-like geometry and dynamic orientation that are favourable for water-skipping. Experiments and numerical modelling reveal that the initial spherical shape evolves as elastic waves propagate through the material. We find that the skipping dynamics are governed by the wave propagation speed and by the ratio of material shear modulus to hydrodynamic pressure. With these insights, we explain why softer spheres skip more easily than stiffer ones. Our results advance understanding of fluid-elastic body interaction during water impact, which could benefit inflatable craft modelling and, more playfully, design of elastic aquatic toys.
Acoustic levitation of a large solid sphere
NASA Astrophysics Data System (ADS)
Andrade, Marco A. B.; Bernassau, Anne L.; Adamowski, Julio C.
2016-07-01
We demonstrate that acoustic levitation can levitate spherical objects much larger than the acoustic wavelength in air. The acoustic levitation of an expanded polystyrene sphere of 50 mm in diameter, corresponding to 3.6 times the wavelength, is achieved by using three 25 kHz ultrasonic transducers arranged in a tripod fashion. In this configuration, a standing wave is created between the transducers and the sphere. The axial acoustic radiation force generated by each transducer on the sphere was modeled numerically as a function of the distance between the sphere and the transducer. The theoretical acoustic radiation force was verified experimentally in a setup consisting of an electronic scale and an ultrasonic transducer mounted on a motorized linear stage. The comparison between the numerical and experimental acoustic radiation forces presents a good agreement.
Entanglement entropy across a deformed sphere
NASA Astrophysics Data System (ADS)
Mezei, Márk
2015-02-01
I study the entanglement entropy (EE) across a deformed sphere in conformal field theories (CFTs). I show that the sphere (locally) minimizes the universal term in EE among all shapes. In the work of Allais and Mezei [Phys. Rev. D 91, 046002 (2015)] it was derived that the sphere is a local extremum, by showing that the contribution linear in the deformation parameter is absent. In this paper I demonstrate that the quadratic contribution is positive and is controlled by the coefficient of the stress tensor two-point function, CT. Such a minimization result contextualizes the fruitful relation between the EE of a sphere and the number of degrees of freedom in field theory. I work with CFTs with gravitational duals, where all higher curvature couplings are turned on. These couplings parametrize conformal structures in stress tensor n -point functions; hence I show the result for infinitely many CFT examples.
Elastic spheres can walk on water
Belden, Jesse; Hurd, Randy C.; Jandron, Michael A.; Bower, Allan F.; Truscott, Tadd T.
2016-01-01
Incited by public fascination and engineering application, water-skipping of rigid stones and spheres has received considerable study. While these objects can be coaxed to ricochet, elastic spheres demonstrate superior water-skipping ability, but little is known about the effect of large material compliance on water impact physics. Here we show that upon water impact, very compliant spheres naturally assume a disk-like geometry and dynamic orientation that are favourable for water-skipping. Experiments and numerical modelling reveal that the initial spherical shape evolves as elastic waves propagate through the material. We find that the skipping dynamics are governed by the wave propagation speed and by the ratio of material shear modulus to hydrodynamic pressure. With these insights, we explain why softer spheres skip more easily than stiffer ones. Our results advance understanding of fluid-elastic body interaction during water impact, which could benefit inflatable craft modelling and, more playfully, design of elastic aquatic toys. PMID:26842860
Elastic spheres can walk on water.
Belden, Jesse; Hurd, Randy C; Jandron, Michael A; Bower, Allan F; Truscott, Tadd T
2016-01-01
Incited by public fascination and engineering application, water-skipping of rigid stones and spheres has received considerable study. While these objects can be coaxed to ricochet, elastic spheres demonstrate superior water-skipping ability, but little is known about the effect of large material compliance on water impact physics. Here we show that upon water impact, very compliant spheres naturally assume a disk-like geometry and dynamic orientation that are favourable for water-skipping. Experiments and numerical modelling reveal that the initial spherical shape evolves as elastic waves propagate through the material. We find that the skipping dynamics are governed by the wave propagation speed and by the ratio of material shear modulus to hydrodynamic pressure. With these insights, we explain why softer spheres skip more easily than stiffer ones. Our results advance understanding of fluid-elastic body interaction during water impact, which could benefit inflatable craft modelling and, more playfully, design of elastic aquatic toys. PMID:26842860
StenniSphere reopens after Hurricane Katrina
NASA Technical Reports Server (NTRS)
2006-01-01
StenniSphere reopened Jan. 18, 2006, almost five months after Hurricane Katrina damaged the basement of the building that houses the visitor center. Thanks to the staff's careful preparations before the storm, no artifacts or exhibits were harmed.
Science off the Sphere: Knitting Needles
International Space Station Expedition 30 astronaut Don Pettit uses knitting needles and water droplets to demonstrate physics in space for 'Science off the Sphere.' Through a partnership between N...
Science off the Sphere: Thin Film Physics
International Space Station Expedition 30 astronaut Don Pettit demonstrates physics in space for 'Science off the Sphere.' Through a partnership between NASA and the American Physical Society you c...
ERIC Educational Resources Information Center
Sturgeon, Julie
2008-01-01
Acting on information from students who reported seeing a classmate looking at inappropriate material on a school computer, school officials used forensics software to plunge the depths of the PC's hard drive, searching for evidence of improper activity. Images were found in a deleted Internet Explorer cache as well as deleted file space.…
ERIC Educational Resources Information Center
Berry, John N., III
2009-01-01
Roberta Stevens and Kent Oliver are campaigning hard for the presidency of the American Library Association (ALA). Stevens is outreach projects and partnerships officer at the Library of Congress. Oliver is executive director of the Stark County District Library in Canton, Ohio. They have debated, discussed, and posted web sites, Facebook pages,…
ERIC Educational Resources Information Center
Parrino, Frank M.
2003-01-01
Interviews with school board members and administrators produced a list of suggestions for balancing a budget in hard times. Among these are changing calendars and schedules to reduce heating and cooling costs; sharing personnel; rescheduling some extracurricular activities; and forming cooperative agreements with other districts. (MLF)
Berger, E.L.; Collins, J.C.; Soper, D.E.; Sterman, G.
1986-03-01
I discuss events in high energy hadron collisions that contain a hard scattering, in the sense that very heavy quarks or high P/sub T/ jets are produced, yet are diffractive, in the sense that one of the incident hadrons is scattered with only a small energy loss. 8 refs.
Please comply: the water entry of soft spheres
NASA Astrophysics Data System (ADS)
Belden, Jesse; Hurd, Randy; Fanning, Tate; Jandron, Michael; Rekos, John; Bower, Allan; Truscott, Tadd
2015-11-01
The typical phenomena associated with sphere water impact are significantly altered when the sphere material is highly compliant rather than rigid. We describe the water impact physics of homogenous and hollow elastic spheres. The homogeneous spheres undergo large oscillatory deformations throughout entry that carve nested disturbances into the normally smooth air cavity, altering cavity shape and pinch off. Using an analytical model, we relate the maximum sphere deformation to the material properties and impact velocity. This characteristic deformation is used to reconcile the differences between cavities formed by compliant and rigid spheres. In addition to the nested disturbances seen with the homogeneous spheres, we observe azimuthal irregularities on the cavity during water entry of hollow elastic spheres. Based on experiments and finite-element modeling, we suggest that these disturbances are initiated by vibration mode shapes excited in the hollow spheres upon impact. For all sphere types, we compare the forces throughout water entry to the rigid sphere case.
Generation of a buoyant jet by a sphere moving vertically in a stratified fluid
NASA Astrophysics Data System (ADS)
Hanazaki, Hideshi; Shimobata, Keisuke; Yoshikawa, Hiroyasu
2011-11-01
We consider the flow past a sphere moving vertically at a constant speed in salt-stratified fluid. Experiments have shown that vertical jets are generated even if the vertical mean density gradient is not large. At least seven types of wake structures have been found, including a thin jet with a surrounding bell-shaped structure. In this numerical study, we investigate the unsteady generation mechanism of buoyant jets with the focus on the diffusion effects of the density/salt. When a sphere descends in a stratified fluid, the density is initially conserved along the movement of the fluid and the originally horizontal isopycnal surfaces are simply deformed vertically and pulled down by the sphere. As time proceeds, diffusive effects become significant in the density boudary layer on the sphere surface and in the thin jet, and the density is no longer conserved. This violation of conservation would be the origin of the jet which is composed of the fluids which moves up to return to thier original heights.
Approximating spheroid inductive responses using spheres
Smith, J. Torquil; Morrison, H. Frank
2003-12-12
The response of high permeability ({mu}{sub r} {ge} 50) conductive spheroids of moderate aspect ratios (0.25 to 4) to excitation by uniform magnetic fields in the axial or transverse directions is approximated by the response of spheres of appropriate diameters, of the same conductivity and permeability, with magnitude rescaled based on the differing volumes, D.C. magnetizations, and high frequency limit responses of the spheres and modeled spheroids.
Hollow sphere ceramic particles for abradable coatings
Longo, F.N.; Bader, N.F. III; Dorfman, M.R.
1984-05-22
A hollow sphere ceramic flame spray powder is disclosed. The desired constituents are first formed into agglomerated particles in a spray drier. Then the agglomerated particles are introduced into a plasma flame which is adjusted so that the particles collected are substantially hollow. The hollow sphere ceramic particles are suitable for flame spraying a porous and abradable coating. The hollow particles may be selected from the group consisting of zirconium oxide and magnesium zirconate.
Liouville Quantum Gravity on the Riemann Sphere
NASA Astrophysics Data System (ADS)
David, François; Kupiainen, Antti; Rhodes, Rémi; Vargas, Vincent
2016-03-01
In this paper, we rigorously construct Liouville Quantum Field Theory on the Riemann sphere introduced in the 1981 seminal work by Polyakov. We establish some of its fundamental properties like conformal covariance under PSL{_2({C})}-action, Seiberg bounds, KPZ scaling laws, KPZ formula and the Weyl anomaly formula. We also make precise conjectures about the relationship of the theory to scaling limits of random planar maps conformally embedded onto the sphere.
Dynamical density functional theory for colloidal dispersions including hydrodynamic interactions
NASA Astrophysics Data System (ADS)
Rex, M.; Löwen, H.
2009-02-01
A dynamical density functional theory (DDFT) for translational Brownian dynamics is derived which includes hydrodynamic interactions. The theory reduces to the simple Brownian DDFT proposed by Marconi and Tarazona (U. Marini Bettolo Marconi and P. Tarazona, J. Chem. Phys. 110, 8032 (1999); J. Phys.: Condens. Matter 12, A413 (2000)) when hydrodynamic interactions are neglected. The derivation is based on Smoluchowski’s equation for the time evolution of the probability density with pairwise hydrodynamic interactions. The theory is applied to hard-sphere colloids in an oscillating spherical optical trap which switches periodically in time from a stable confining to an unstable potential. Rosenfeld’s fundamental measure theory for the equilibrium density functional is used and hydrodynamics are incorporated on the Rotne-Prager level. The results for the time-dependent density profiles are compared to extensive Brownian dynamics simulations which are performed on the same Rotne-Prager level and excellent agreement is obtained. It is further found that hydrodynamic interactions damp and slow the dynamics of the confined colloid cluster in comparison to the same situation with neglected hydrodynamic interactions.
NASA Astrophysics Data System (ADS)
Zhu, Xingyu; Guan, Zhou; Lin, Jiaping; Cai, Chunhua
2016-07-01
We found that poly(γ-benzyl-L-glutamate)-block-poly(ethylene glycol) (PBLG-b-PEG) rod-coil block copolymers and polystyrene (PS) homopolymers can cooperatively self-assemble into nano-spheres with striped patterns on their surfaces (strip-pattern-spheres) in aqueous solution. With assistance of dissipative particle dynamics simulation, it is discovered that the PS homopolymers form a spherical template core and the PBLG-b-PEG block copolymers assemble into striped patterns on the spherical surface. The hydrophobic PBLG rods are packed orderly in the strips, while the hydrophilic PEG blocks stabilize the strip-pattern-spheres in solution. Defects such as dislocations and disclinations can be observed in the striped patterns. Self-assembling temperature and sphere radius are found to affect defect densities in the striped patterns. A possible mechanism is proposed to illustrate how PBLG-b-PEG and PS cooperatively self-assemble into hierarchical spheres with striped patterns on surfaces.
Inverse Magnus effect on a rotating sphere
NASA Astrophysics Data System (ADS)
Kim, Jooha; Park, Hyungmin; Choi, Haecheon; Yoo, Jung Yul
2011-11-01
In this study, we investigate the flow characteristics of rotating spheres in the subcritical Reynolds number (Re) regime by measuring the drag and lift forces on the sphere and the two-dimensional velocity in the wake. The experiment is conducted in a wind tunnel at Re = 0 . 6 ×105 - 2 . 6 ×105 and the spin ratio (ratio of surface velocity to the free-stream velocity) of 0 (no spin) - 0.5. The drag coefficient on a stationary sphere remains nearly constant at around 0.52. However, the magnitude of lift coefficient is nearly zero at Re < 2 . 0 ×105 , but rapidly increases to 0.3 and then remains constant with further increasing Reynolds number. On the other hand, with rotation, the lift coefficient shows negative values, called inverse Magnus effect, depending on the magnitudes of the Reynolds number and spin ratio. The velocity field measured from a particle image velocimetry (PIV) indicates that non-zero lift coefficient on a stationary sphere at Re > 2 . 0 ×105 results from the asymmetry of separation line, whereas the inverse Magnus effect for the rotating sphere results from the differences in the boundary-layer growth and separation along the upper and lower sphere surfaces. Supported by the WCU, Converging Research Center and Priority Research Centers Program, NRF, MEST, Korea.
Surface modification and characterization of carbon spheres by grafting polyelectrolyte brushes
2014-01-01
Modified carbon spheres (CSPBs) were obtained by grafting poly(diallyl dimethyl ammonium chloride) (p-DMDAAC) on the surface of carbon spheres (CSs). It can be viewed as a kind of cation spherical polyelectrolyte brushes (CSPBs), which consist of carbon spheres as core and polyelectrolytes as shell. The method of synthesizing carbon spheres was hydrothermal reaction. Before the polyelectrolyte brushes were grafted, azo initiator [4,4′-Azobis(4-cyanovaleric acyl chloride)] was attached to the carbon spheres' surface through hydroxyl groups. CSPBs were characterized by scanning electron microscope (SEM), Fourier transform infrared spectroscopy (FTIR), gel permeation chromatography (GPC), conductivity meter, and system zeta potential. The results showed that compared with carbon spheres, the conductivity and zeta potential on CSPBs increased from 9.98 to 49.24 μS/cm and 11.6 to 42.5 mV, respectively, after the polyelectrolyte brushes were grafted. The colloidal stability in water was enhanced, and at the same time, the average diameter of the CSPBs was found to be 173 nm, and the average molecular weight and grafted density of the grafted polyelectrolyte brushes were 780,138 g/mol and 4.026 × 109/nm2, respectively. PMID:24948900
Robinson, E N; McGee, Z A; Kaplan, J; Hammond, M E; Larson, J K; Buchanan, T M; Schoolnik, G K
1984-01-01
In an effort to determine the ultrastructural location of specific macromolecules on the surface of intact microorganisms and in experimentally infected tissues, a new method of rapidly conjugating antibodies to gold spheres via a staphylococcal protein A intermediary has been developed. This new technique provides the excellent density of marking and versatility of sphere size provided by existing gold methods, but decreases preparation time, decreases the chance of bacterial contamination of antibody reagents, and increases specificity of marking. Staphylococcal protein A-coated gold spheres were conjugated with antibodies from rabbits immunized with purified gonococcal pili. The resulting gold-antibody conjugates allowed demonstration of antibody binding to pilus structures of the same gonococcal strain whose pili were used to raise the antibody and demonstration of the lack of antibody recognition of pilus structures on two other gonococcal strains. The failure of gold spheres to attach to isogenic nonpiliated clones of the homologous gonococcus indicated the absence of pilus antigens on the surface of these organisms. The use of a double label--small gold spheres conjugated to anti-pilus antibody and larger gold spheres conjugated to anti-protein I antibody--allowed the simultaneous localization of two gonococcal antigens. Images PMID:6150005
NASA Astrophysics Data System (ADS)
Lumma, D.; Lurio, L. B.; Borthwick, M. A.; Falus, P.; Mochrie, S. G. J.
2000-12-01
X-ray photon correlation spectroscopy and small-angle x-ray scattering measurements are applied to characterize the dynamics and structure of concentrated suspensions of charge-stabilized polystyrene latex spheres dispersed in glycerol, for volume fractions between 2.7% and 52%. The static structures of the suspensions show essentially hard-sphere behavior. The short-time dynamics shows good agreement with predictions for the wave-vector-dependent collective diffusion coefficient, which are based on a hard-sphere model [C. W. J. Beenakker and P. Mazur, Physica A 126, 349 (1984)]. However, the intermediate scattering function is found to violate a scaling behavior found previously for a sterically stabilized hard-sphere suspension [P. N. Segre and P. N. Pusey, Phys. Rev. Lett. 77, 771 (1996)]. Our measurements are parametrized in terms of a viscoelastic model for the intermediate scattering function [W. Hess and R. Klein, Adv. Phys. 32, 173 (1983)]. Within this framework, two relaxation modes are predicted to contribute to the decay of the dynamic structure factor, with mode amplitudes depending on both wave vector and volume fraction. Our measurements indicate that, for particle volume fractions smaller than about 0.30, the intermediate scattering function is well described in terms of single-exponential decays, whereas a double-mode structure becomes apparent for more concentrated systems.
Lumma; Lurio; Borthwick; Falus; Mochrie
2000-12-01
X-ray photon correlation spectroscopy and small-angle x-ray scattering measurements are applied to characterize the dynamics and structure of concentrated suspensions of charge-stabilized polystyrene latex spheres dispersed in glycerol, for volume fractions between 2.7% and 52%. The static structures of the suspensions show essentially hard-sphere behavior. The short-time dynamics shows good agreement with predictions for the wave-vector-dependent collective diffusion coefficient, which are based on a hard-sphere model [C. W. J. Beenakker and P. Mazur, Physica A 126, 349 (1984)]. However, the intermediate scattering function is found to violate a scaling behavior found previously for a sterically stabilized hard-sphere suspension [P. N. Segre and P. N. Pusey, Phys. Rev. Lett. 77, 771 (1996)]. Our measurements are parametrized in terms of a viscoelastic model for the intermediate scattering function [W. Hess and R. Klein, Adv. Phys. 32, 173 (1983)]. Within this framework, two relaxation modes are predicted to contribute to the decay of the dynamic structure factor, with mode amplitudes depending on both wave vector and volume fraction. Our measurements indicate that, for particle volume fractions smaller than about 0.30, the intermediate scattering function is well described in terms of single-exponential decays, whereas a double-mode structure becomes apparent for more concentrated systems. PMID:11138124
ERIC Educational Resources Information Center
McNeil, Michele
2008-01-01
Hard-to-grasp dollar amounts are forcing real cuts in K-12 education at a time when the cost of fueling buses and providing school lunches is increasing and the demands of the federal No Child Left Behind Act still loom larger over states and districts. "One of the real challenges is to continue progress in light of the economy," said Gale Gaines,…
ERIC Educational Resources Information Center
Mathews, Jay
2009-01-01
In 1994, fresh from a two-year stint with Teach for America, Mike Feinberg and Dave Levin inaugurated the Knowledge Is Power Program (KIPP) in Houston with an enrollment of 49 5th graders. By this Fall, 75 KIPP schools will be up and running, setting children from poor and minority families on a path to college through a combination of hard work,…
Terminal energy distribution of blast waves from bursting spheres
NASA Technical Reports Server (NTRS)
Adamczyk, A. A.; Strehlow, R. A.
1977-01-01
The calculation results for the total energy delivered to the surroundings by the burst of an idealized massless sphere containing an ideal gas are presented. The logic development of various formulas for sphere energy is also presented. For all types of sphere bursts the fraction of the total initial energy available in the sphere that is delivered to the surroundings is shown to lie between that delivered for the constant pressure addition of energy to a source region and that delivered by isentropic expansion of the sphere. The relative value of E sub/Q increases at fixed sphere pressure/surrounding pressure as sphere temperature increases because the velocity of sound increases.
The Separate Spheres Model of Gendered Inequality
Miller, Andrea L.; Borgida, Eugene
2016-01-01
Research on role congruity theory and descriptive and prescriptive stereotypes has established that when men and women violate gender stereotypes by crossing spheres, with women pursuing career success and men contributing to domestic labor, they face backlash and economic penalties. Less is known, however, about the types of individuals who are most likely to engage in these forms of discrimination and the types of situations in which this is most likely to occur. We propose that psychological research will benefit from supplementing existing research approaches with an individual differences model of support for separate spheres for men and women. This model allows psychologists to examine individual differences in support for separate spheres as they interact with situational and contextual forces. The separate spheres ideology (SSI) has existed as a cultural idea for many years but has not been operationalized or modeled in social psychology. The Separate Spheres Model presents the SSI as a new psychological construct characterized by individual differences and a motivated system-justifying function, operationalizes the ideology with a new scale measure, and models the ideology as a predictor of some important gendered outcomes in society. As a first step toward developing the Separate Spheres Model, we develop a new measure of individuals’ endorsement of the SSI and demonstrate its reliability, convergent validity, and incremental predictive validity. We provide support for the novel hypotheses that the SSI predicts attitudes regarding workplace flexibility accommodations, income distribution within families between male and female partners, distribution of labor between work and family spheres, and discriminatory workplace behaviors. Finally, we provide experimental support for the hypothesis that the SSI is a motivated, system-justifying ideology. PMID:26800454
The Separate Spheres Model of Gendered Inequality.
Miller, Andrea L; Borgida, Eugene
2016-01-01
Research on role congruity theory and descriptive and prescriptive stereotypes has established that when men and women violate gender stereotypes by crossing spheres, with women pursuing career success and men contributing to domestic labor, they face backlash and economic penalties. Less is known, however, about the types of individuals who are most likely to engage in these forms of discrimination and the types of situations in which this is most likely to occur. We propose that psychological research will benefit from supplementing existing research approaches with an individual differences model of support for separate spheres for men and women. This model allows psychologists to examine individual differences in support for separate spheres as they interact with situational and contextual forces. The separate spheres ideology (SSI) has existed as a cultural idea for many years but has not been operationalized or modeled in social psychology. The Separate Spheres Model presents the SSI as a new psychological construct characterized by individual differences and a motivated system-justifying function, operationalizes the ideology with a new scale measure, and models the ideology as a predictor of some important gendered outcomes in society. As a first step toward developing the Separate Spheres Model, we develop a new measure of individuals' endorsement of the SSI and demonstrate its reliability, convergent validity, and incremental predictive validity. We provide support for the novel hypotheses that the SSI predicts attitudes regarding workplace flexibility accommodations, income distribution within families between male and female partners, distribution of labor between work and family spheres, and discriminatory workplace behaviors. Finally, we provide experimental support for the hypothesis that the SSI is a motivated, system-justifying ideology. PMID:26800454
Yi, Bin; Chen, Xiaohua; Guo, Kaimin; Xu, Longshan; Chen, Chuansheng; Yan, Haimei; Chen, Jianghua
2011-11-15
Research highlights: {yields} CNTs-implanted porous carbon spheres are prepared by using gelatin as soft template. {yields} Homogeneously distributed CNTs form a well-develop network in carbon spheres. {yields} CNTs act as a reinforcing backbone assisting the formation of pore structure. {yields} CNTs improve electrical conductivity and specific capacitance of supercapacitor. -- Abstract: Carbon nanotube-implanted mesoporous carbon spheres were prepared by an easy polymerization-induced colloid aggregation method using gelatin as a soft template. Scanning electron microscopy, transmission electron microscopy and nitrogen adsorption-desorption measurements reveal that the materials are mesoporous carbon spheres, with a diameter of {approx}0.5-1.0 {mu}m, a specific surface area of 284 m{sup 2}/g and average pore size of 3.9 nm. Using the carbon nanotube-implanted mesoporous carbon spheres as electrode material for supercapacitors in an aqueous electrolyte solution, a low equivalent series resistance of 0.83 {Omega} cm{sup 2} and a maximum specific capacitance of 189 F/g with a measured power density of 8.7 kW/kg at energy density of 6.6 Wh/kg are obtained.
Mansur, Louis K; Bhattacharya, R; Blau, Peter Julian; Clemons, Art; Eberle, Cliff; Evans, H B; Janke, Christopher James; Jolly, Brian C; Lee, E H; Leonard, Keith J; Trejo, Rosa M; Rivard, John D
2010-01-01
High energy ion beam surface treatments were applied to a selected group of polymers. Of the six materials in the present study, four were thermoplastics (polycarbonate, polyethylene, polyethylene terephthalate, and polystyrene) and two were thermosets (epoxy and polyimide). The particular epoxy evaluated in this work is one of the resins used in formulating fiber reinforced composites for military helicopter blades. Measures of mechanical properties of the near surface regions were obtained by nanoindentation hardness and pin on disk wear. Attempts were also made to measure erosion resistance by particle impact. All materials were hardness tested. Pristine materials were very soft, having values in the range of approximately 0.1 to 0.5 GPa. Ion beam treatment increased hardness by up to 50 times compared to untreated materials. For reference, all materials were hardened to values higher than those typical of stainless steels. Wear tests were carried out on three of the materials, PET, PI and epoxy. On the ion beam treated epoxy no wear could be detected, whereas the untreated material showed significant wear.
Field application of lightweight, hollow-glass-sphere drilling fluid
1997-11-01
A new class of underbalanced drilling fluids being developed under US Dept. of Energy (US DOE) sponsorship was recently successfully field tested. The fluid uses hollow glass spheres (HGS`s) to decrease the fluid density to less than that of the base mud while maintaining incompressibility. Concentrations of up to 20 vol% were used to decrease the fluid density to 0.8 lbm/gal less than normally used in the field. Potential benefits of using these fluids include higher penetration rates, decreased formation damage, and lost-circulation mitigation. When used in place of aerated fluid, they can eliminate compressor usage and allow the use of mud-pulse measurement-while-drilling tools. These and other recent advances in technology have spurred interest in underbalanced drilling to the highest level in 30 years. Industry-wide surveys indicate that more than 12% of wells drilled in the US in 1997 will intentionally use underbalanced techniques.
Uniform hollow magnetite spheres: Facile synthesis, growth mechanism, and their magnetic properties
Zhou, Xing; Zhao, Guizhe; Liu, Yaqing
2014-11-15
Highlights: • Uniform Fe{sub 3}O{sub 4} hollow spheres with high saturation magnetization were synthesized through a simple solvothermal process. • Without using any hard templates or external magnetic field. • The as-prepared magnetite hollow spheres exhibit a ferromagnetic behavior with high Ms of ca. 85.9 emu/g at room temperature. • The morphology of Fe{sub 3}O{sub 4} with nanoparticles, hollow, and irregular structures could be adjusted by changing the reactive conditions. - Abstract: Hierarchical porous Fe{sub 3}O{sub 4} hollow spheres with high saturation magnetization were synthesized through a simple solvothermal process in ethylene glycol (EG) in the presence of Tetrabutylammonium chloride (TBAC) and urea. By investigating the effect of reaction temperature, time, the amount of urea, and concentration of iron ion on the formation of hollow spheres, it was proposed that the main formation mechanism of hollow spheres is Ostwald ripening process combined with assembly-then-inside-out evacuation process. Additionally, it is found that the morphology of Fe{sub 3}O{sub 4} with nanoparticles, hollow, and irregular structures could be adjusted by changing the above factors. The resulting products were characterized by means of scanning electron microscopy (SEM), transmission electron microscopy (TEM), X-ray powder diffraction (XRD), high resolution transmission electron microscopy (HRTEM), energy dispersive X-ray spectroscopy (EDX), and vibrating sample magnetometer (VSM). The hierarchical porous Fe{sub 3}O{sub 4} hollow spheres exhibited enhanced saturation magnetization as compared with Fe{sub 3}O{sub 4} nanoparticles.
A thermodynamic self-consistent theory of asymmetric hard-core Yukawa mixtures.
Pellicane, Giuseppe; Caccamo, Carlo
2016-10-19
We perform structural and thermodynamic calculations in the framework of the modified hypernetted chain (MHNC) integral equation closure to the Ornstein-Zernike equation for binary mixtures of size-different particles interacting with hard-core Yukawa pair potentials. We use the Percus-Yevick (PY) bridge functions of a binary mixture of hard-sphere (HSM) particles. The hard-sphere diameters of the PY bridge functions of the HSM system are adjusted so to achieve thermodynamic consistency between the virial and compressibility equations of state. We show the benefit of thermodynamic consistency by comparing the MHNC results with the available computer simulation data reported in the literature, and we demonstrate that the self-consistent thermodynamic theory provides a better reproduction of the simulation data over other microscopic theories. PMID:27545096
Ultrasonic characterization of materials hardness
Badidi Bouda A; Benchaala; Alem
2000-03-01
In this paper, an experimental technique has been developed to measure velocities and attenuation of ultrasonic waves through a steel with a variable hardness. A correlation between ultrasonic measurements and steel hardness was investigated. PMID:10829663
SPHERES flight operations testing and execution
NASA Astrophysics Data System (ADS)
Mohan, Swati; Saenz-Otero, Alvar; Nolet, Simon; Miller, David W.; Sell, Steven
2009-10-01
Synchronized Position Hold Engage Reorient Experimental Satellites (SPHERES) is a formation flight testing facility consisting of three satellites operating inside the International Space Station (ISS). The goal is to use the long term microgravity environment of the ISS to mature formation flight and docking algorithms. The operations processes of SPHERES have also matured over the course of the first seven test sessions. This paper describes the evolution of the SPHERES program operations processes from conception to implementation to refinement through flight experience. Modifications to the operations processes were based on experience and feedback from Marshall Space Flight Center Payload Operations Center, USAF Space Test Program office at Johnson Space Center, and the crew of Expedition 13 (first to operate SPHERES on station). Important lessons learned were on aspects such as test session frequency, determination of session success, and contingency operations. This paper describes the tests sessions; then it details the lessons learned, the change in processes, and the impact on the outcome of later test sessions. SPHERES had very successful initial test sessions which allowed for modification and tailoring of the operations processes to streamline the code delivery and to tailor responses based on flight experiences.
Robotics Programming Competition Spheres, Russian Part
NASA Astrophysics Data System (ADS)
Sadovski, Andrei; Kukushkina, Natalia; Biryukova, Natalia
2016-07-01
Spheres" such name was done to Russian part of the Zero Robotics project which is a student competition devoted to programming of SPHERES (SPHERES - Synchronized Position Hold Engage and Reorient Experimental Satellites are the experimental robotics devices which are capable of rotation and translation in all directions, http://ssl.mit.edu/spheres/), which perform different operations on the board of International Space Station. Competition takes place online on http://zerorobotics.mit.edu. The main goal is to develop a program for SPHERES to solve an annual challenge. The end of the tournament is the real competition in microgravity on the board of ISS with a live broadcast. The Russian part of the tournament has only two years history but the problems, organization and specific are useful for the other educational projects especially for the international ones. We introduce the history of the competition, its scientific and educational goals in Russia and describe the participation of Russian teams in 2014 and 2015 tournaments. Also we discuss the organizational problems.