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Register a new userGenerating dense packings of hard spheres by soft interaction design
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Packing spheres efficiently in large dimension $d$ is a particularly difficult optimization problem. In this paper we add an isotropic interaction potential to the pure hard-core repulsion, and show that one can tune it in order to maximize a lower bound on packing density. Our results suggest that exponentially many (in the number of particles) distinct disordered sphere packings can be effectively constructed by this method, up to a packing fraction close to $7, d, 2^{-d}$. The latter is determined by solving the inverse problem of maximizing the dynamical glass transition over the space of the interaction potentials. Our method crucially exploits a recent exact formulation of the thermodynamics and the dynamics of simple liquids in infinite dimension.
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We consider a class of random block matrix models in $d$ dimensions, $d ge 1$, motivated by the study of the vibrational density of states (DOS) of soft spheres near the isostatic point. The contact networks of average degree $Z = z_0 + zeta$ are represented by random $z_0$-regular graphs (only the circle graph in $d=1$ with $z_0=2$) to which Erdos-Renyi graphs having a small average degree $zeta$ are superimposed. In the case $d=1$, for $zeta$ small the shifted Kesten-McKay DOS with parameter $Z$ is a mean-field solution for the DOS. Numerical simulations in the $z_0=2$ model, which is the $k=1$ Newman-Watts small-world model, and in the $z_0=3$ model lead us to conjecture that for $zeta to 0$ the cumulative function of the DOS converges uniformly to that of the shifted Kesten-McKay DOS, in an interval $[0, omega_0]$, with $omega_0 < sqrt{z_0-1} + 1$. For $2 le d le 4$, we introduce a cutoff parameter $K_d le 0.5$ modeling sphere repulsion. The case $K_d=0$ is the random elastic network case, with the DOS close to the Marchenko-Pastur DOS with parameter $t=frac{Z}{d}$. For $K_d$ large the DOS is close for small $omega$ to the shifted Kesten-McKay DOS with parameter $t=frac{Z}{d}$; in the isostatic case the DOS has around $omega=0$ the expected plateau. The boson peak frequency in $d=3$ with $K_3$ large is close to the one found in molecular dynamics simulations for $Z=7$ and $8$.
We extend our theory of amorphous packings of hard spheres to binary mixtures and more generally to multicomponent systems. The theory is based on the assumption that amorphous packings produced by typical experimental or numerical protocols can be identified with the infinite pressure limit of long lived metastable glassy states. We test this assumption against numerical and experimental data and show that the theory correctly reproduces the variation with mixture composition of structural observables, such as the total packing fraction and the partial coordination numbers.
In this paper we numerically investigate the influence of dissipation during particle collisions in an homogeneous turbulent velocity field by coupling a discrete element method to a Lattice-Boltzmann simulation with spectral forcing. We show that even at moderate particle volume fractions the influence of dissipative collisions is important. We also investigate the transition from a regime where the turbulent velocity field significantly influences the spatial distribution of particles to a regime where the distribution is mainly influenced by particle collisions.
Sound attenuation in low temperature amorphous solids originates from their disordered structure. However, its detailed mechanism is still being debated. Here we analyze sound attenuation starting directly from the microscopic equations of motion. We derive an exact expression for the zero-temperature sound damping coefficient and verify that it agrees with results of earlier sound attenuation simulations. The small wavevector analysis of this expression shows that sound attenuation is primarily determined by the non-affine displacements contribution to the wave propagation coefficient coming from the frequency shell of the sound wave.
We show that soft spheres interacting with a linear ramp potential when overcompressed beyond the jamming point fall in an amorphous solid phase which is critical, mechanically marginally stable and share many features with the jamming point itself. In the whole phase, the relevant local minima of the potential energy landscape display an isostatic contact network of perfectly touching spheres whose statistics is controlled by an infinite lengthscale. Excitations around such energy minima are non-linear, system spanning, and characterized by a set of non-trivial critical exponents. We perform numerical simulations to measure their values and show that, while they coincide, within numerical precision, with the critical exponents appearing at jamming, the nature of the corresponding excitations is richer. Therefore, linear soft spheres appear as a novel class of finite dimensional systems that self-organize into new, critical, marginally stable, states.
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