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Oblique Impact of Frictionless Spheres: On the Limitations of Hard Sphere Models for Granular Dynamics  [PDF]
Patric Mueller,Thorsten Poeschel
Physics , 2011,
Abstract: When granular systems are modeled by frictionless hard spheres, particle-particle collisions are considered as instantaneous events. This implies that while the velocities change according to the collision rule, the positions of the particles are the same before and after such an event. We show that depending on the material and system parameters, this assumption may fail. For the case of viscoelastic particles we present a universal condition which allows to assess whether the hard-sphere modeling and, thus, event-driven Molecular Dynamics simulations are justified.
Event Driven Langevin simulations of Hard Spheres  [PDF]
Antonio Scala
Physics , 2011, DOI: 10.1103/PhysRevE.86.026709
Abstract: The blossoming of interest in colloids and nano-particles has given renewed impulse to the study of hard-body systems. In particular, hard spheres have become a real test system for theories and experiments. It is therefore necessary to study the complex dynamics of such systems in presence of a solvent; disregarding hydrodynamic interactions, the simplest model is the Langevin equation. Unfortunately, standard algorithms for the numerical integration of the Langevin equation require that interactions are slowly varying during an integration timestep. This in not the case for hard-body systems, where there is no clearcut between the correlation time of the noise and the timescale of the interactions. Starting first from a splitting of the Fokker-Plank operator associated with the Langevin dynamics, and then from an approximation of the two-body Green's function, we introduce and test two new algorithms for the simulation of the Langevin dynamics of hard-spheres.
Molecular dynamics simulations of crystallization of hard spheres  [PDF]
Igor Volkov,Marek Cieplak,Joel Koplik,Jayanth R. Banavar
Physics , 2002, DOI: 10.1103/PhysRevE.66.061401
Abstract: We have carried out molecular dynamics simulations of the crystallization of hard spheres modelling colloidal systems that are studied in conventional and space-based experiments. We use microscopic probes to investigate the effects of gravitational forces, polydispersity and of bounding walls on the phase structure. The simulations employed an extensive exclusive particle grid method and the type and degree of crystalline order was studied in two independent ways: by the structure factor, as in experiments, and through local rotational invariants. We present quantitative comparisons of the nucleation rates of monodisperse and polydisperse hard sphere systems and benchmark them against experimental results. We show how the presence of bounding walls leads to wall-induced nucleation and rapid crystallization and discuss the role of gravity on the dynamics of crystallization.
Disordered jammed packings of frictionless spheres  [PDF]
Massimo Pica Ciamarra,Antonio Coniglio,Antonio de Candia
Physics , 2010, DOI: 10.1039/C001904F
Abstract: At low volume fraction, disordered arrangements of frictionless spheres are found in un--jammed states unable to support applied stresses, while at high volume fraction they are found in jammed states with mechanical strength. Here we show, focusing on the hard sphere zero pressure limit, that the transition between un-jammed and jammed states does not occur at a single value of the volume fraction, but in a whole volume fraction range. This result is obtained via the direct numerical construction of disordered jammed states with a volume fraction varying between two limits, $0.636$ and $0.646$. We identify these limits with the random loose packing volume fraction $\rl$ and the random close packing volume fraction $\rc$ of frictionless spheres, respectively.
Universality of Jamming Criticality in Overdamped Shear-Driven Frictionless Disks  [PDF]
Daniel V?gberg,Peter Olsson,S. Teitel
Physics , 2013, DOI: 10.1103/PhysRevLett.113.148002
Abstract: We investigate the criticality of the jamming transition for overdamped shear-driven frictionless disks in two dimensions for two different models of energy dissipation: (i) Durian's bubble model with dissipation proportional to the velocity difference of particles in contact, and (ii) Durian's "mean-field" approximation to (i), with dissipation due to the velocity difference between the particle and the average uniform shear flow velocity. By considering velocity correlations, finite-size behavior of pressure, and the pressure analog of viscosity, we argue that these two models share the same critical behavior.
Uniform shear flow in dissipative gases. Computer simulations of inelastic hard spheres and (frictional) elastic hard spheres  [PDF]
A. Astillero,A. Santos
Physics , 2005, DOI: 10.1103/PhysRevE.72.031309
Abstract: In the preceding paper (cond-mat/0405252), we have conjectured that the main transport properties of a dilute gas of inelastic hard spheres (IHS) can be satisfactorily captured by an equivalent gas of elastic hard spheres (EHS), provided that the latter are under the action of an effective drag force and their collision rate is reduced by a factor $(1+\alpha)/2$ (where $\alpha$ is the constant coefficient of normal restitution). In this paper we test the above expectation in a paradigmatic nonequilibrium state, namely the simple or uniform shear flow, by performing Monte Carlo computer simulations of the Boltzmann equation for both classes of dissipative gases with a dissipation range $0.5\leq \alpha\leq 0.95$ and two values of the imposed shear rate $a$. The distortion of the steady-state velocity distribution from the local equilibrium state is measured by the shear stress, the normal stress differences, the cooling rate, the fourth and sixth cumulants, and the shape of the distribution itself. In particular, the simulation results seem to be consistent with an exponential overpopulation of the high-velocity tail. The EHS results are in general hardly distinguishable from the IHS ones if $\alpha\gtrsim 0.7$, so that the distinct signature of the IHS gas (higher anisotropy and overpopulation) only manifests itself at relatively high dissipations
Plane shear flows of frictionless spheres: Kinetic theory and 3D soft-sphere discrete element method simulations  [PDF]
Dalila Vescovi,Diego Berzi,Patrick Richard,Nicolas Brodu
Physics , 2014, DOI: 10.1063/1.4879267
Abstract: We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different values of the collisional coefficient of restitution. Then, we perform 3D Discrete Element simulations of plane flows of frictionless, inelastic spheres, sheared between walls made bumpy by gluing particles in a regular array, at fixed average volume fraction and distance between the walls. The results of the numerical simulations are used to derive boundary conditions appropriated in the cases of large and small bumpiness. Those boundary conditions are, then, employed to numerically integrate the differential equations of Extended Kinetic Theory, where the breaking of the molecular chaos assumption at volume fraction larger than 0.49 is taken into account in the expression of the dissipation rate. We show that the Extended Kinetic Theory is in very good agreement with the numerical simulations, even for coefficients of restitution as low as 0.50. When the bumpiness is increased, we observe that some of the flowing particles are stuck in the gaps between the wall spheres. As a consequence, the walls are more dissipative than expected, and the flows resemble simple shear flows, i.e., flows of rather constant volume fraction and granular temperature.
Patchy sticky hard spheres: analytical study and Monte Carlo simulations  [PDF]
Riccardo Fantoni,Domenico Gazzillo,Achille Giacometti,Mark A. Miller,Giorgio Pastore
Physics , 2007, DOI: 10.1063/1.2805066
Abstract: We consider a fluid of hard spheres bearing one or two uniform circular adhesive patches, distributed so as not to overlap. Two spheres interact via a ``sticky'' Baxter potential if the line joining the centers of the two spheres intersects a patch on each sphere, and via a hard sphere potential otherwise. We analyze the location of the fluid-fluid transition and of the percolation line as a function of the size of the patch (the fractional coverage of the sphere's surface) and of the number of patches within a virial expansion up to third order and within the first two terms (C0 and C1) of a class of closures Cn hinging on a density expansion of the direct correlation function. We find that the locations of the two lines depend sensitively on both the total adhesive coverage and its distribution. The treatment is almost fully analytical within the chosen approximate theory. We test our findings by means of specialized Monte Carlo (MC) simulations and find the main qualitative features of the critical behaviour to be well captured in spite of the low density perturbative nature of the closure. The introduction of anisotropic attractions into a model suspension of spherical particles is a first step towards a more realistic description of globular proteins in solution.
Monte Carlo simulations of the solid-liquid transition in hard spheres and colloid-polymer mixtures  [PDF]
T. Zykova-Timan,J. Horbach,K. Binder
Physics , 2010, DOI: 10.1063/1.3455504
Abstract: Monte Carlo simulations at constant pressure are performed to study coexistence and interfacial properties of the liquid-solid transition in hard spheres and in colloid-polymer mixtures. The latter system is described as a one-component Asakura-Oosawa (AO) model where the polymer's degrees of freedom are incorporated via an attractive part in the effective potential for the colloid-colloid interactions. For the considered AO model, the polymer reservoir packing fraction is eta_p^r=0.1 and the colloid-polymer size ratio is q=sigma_p/\sigma=0.15 (with sigma_p and sigma the diameter of polymers and colloids, respectively). Inhomogeneous solid-liquid systems are prepared by placing the solid fcc phase in the middle of a rectangular simulation box creating two interfaces with the adjoined bulk liquid. By analyzing the growth of the crystalline region at various pressures and for different system sizes, the coexistence pressure p_co is obtained, yielding p_co=11.576 k_BT/sigma^3 for the hard sphere system and p_co=8.0 k_BT/sigma^3 for the AO model (with k_B the Boltzmann constant and T the temperature). Several order parameters are introduced to distinguish between solid and liquid phases and to describe the interfacial properties. From the capillary-wave broadening of the solid-liquid interface, the interfacial stiffness is obtained for the (100) crystalline plane, giving the values gamma=0.49 k_BT/sigma^2 for the hard-sphere system and gamma=0.95 k_BT/sigma^2 for the AO model.
The van Hove distribution function for Brownian hard spheres: dynamical test particle theory and computer simulations for bulk dynamics  [PDF]
Paul Hopkins,Andrea Fortini,Andrew Archer,Matthias Schmidt
Physics , 2010, DOI: 10.1063/1.3511719
Abstract: 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.
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