Recent theoretical advances offer an exact, first-principle theory of jamming criticality in infinite dimension as well as universal scaling relations between critical exponents in all dimensions. For packings of frictionless spheres near the jamming
transition, these advances predict that nontrivial power-law exponents characterize the critical distribution of (i) small inter-particle gaps and (ii) weak contact forces, both of which are crucial for mechanical stability. The scaling of the inter-particle gaps is known to be constant in all spatial dimensions $d$ -- including the physically relevant $d=2$ and 3, but the value of the weak force exponent remains the object of debate and confusion. Here, we resolve this ambiguity by numerical simulations. We construct isostatic jammed packings with extremely high accuracy, and introduce a simple criterion to separate the contribution of particles that give rise to localized buckling excitations, i.e., bucklers, from the others. This analysis reveals the remarkable dimensional robustness of mean-field marginality and its associated criticality.
We characterize and analyze rotational torsional oscillations developing in a large-eddy magnetohydrodynamical simulation of solar convection (Ghizaru, Charbonneau, and Smolarkiewicz, Astrophys. J. Lett., 715, L133 (2010); Racine et al., Astrophys. J
., 735, 46 (2011)) producing an axisymmetric large-scale magnetic field undergoing periodic polarity reversals. Motivated by the many solar-like features exhibited by these oscillations, we carry out an analysis of the large-scale zonal dynamics. We demonstrate that simulated torsional oscillations are not driven primarily by the periodically-varying large-scale magnetic torque, as one might have expected, but rather via the magnetic modulation of angular-momentum transport by the large-scale meridional flow. This result is confirmed by a straightforward energy analysis. We also detect a fairly sharp transition in rotational dynamics taking place as one moves from the base of the convecting layers to the base of the thin tachocline-like shear layer formed in the stably stratified fluid layers immediately below. We conclude by discussing the implications of our analyses with regards to the mechanism of amplitude saturation in the global dynamo operating in the simulation, and speculate on the possible precursor value of torsional oscillations for the forecast of solar cycle characteristics.
There exists a variety of theories of the glass transition and many more numerical models. But because the models need built-in complexity to prevent crystallization, comparisons with theory can be difficult. We study the dynamics of a deeply supersa
turated emph{monodisperse} four-dimensional (4D) hard-sphere fluid, which has no such complexity, but whose strong intrinsic geometrical frustration inhibits crystallization, even when deeply supersaturated. As an application, we compare its behavior to the mode-coupling theory (MCT) of glass formation. We find MCT to describe this system better than any other structural glass formers in lower dimensions. The reduction in dynamical heterogeneity in 4D suggested by a milder violation of the Stokes-Einstein relation could explain the agreement. These results are consistent with a mean-field scenario of the glass transition.
The smallest maximum kissing-number Voronoi polyhedron of 3d spheres is the icosahedron and the tetrahedron is the smallest volume that can show up in Delaunay tessalation. No periodic lattice is consistent with either and hence these dense packings
are geometrically frustrated. Because icosahedra can be assembled from almost perfect tetrahedra, the terms icosahedral and polytetrahedral packing are often used interchangeably, which leaves the true origin of geometric frustration unclear. Here we report a computational study of freezing of 4d hard spheres, where the densest Voronoi cluster is compatible with the symmetry of the densest crystal, while polytetrahedral order is not. We observe that, under otherwise comparable conditions, crystal nucleation in 4d is less facile than in 3d. This suggest that it is the geometrical frustration of polytetrahedral structures that inhibits crystallization.
