Isostaticity at Frictional Jamming

Amorphous packings of frictionless, spherical particles are isostatic at jamming onset, with the number of constraints (contacts) equal to the number of degrees of freedom. Their structural and mechanical properties are controlled by the interparticle contact network. In contrast, amorphous packings of frictional particles are typically hyperstatic at jamming onset. We perform extensive numerical simulations in two dimensions of the geometrical asperity (GA) model for static friction, to further investigate the role of isostaticity. In the GA model, interparticle forces are obtained by summing up purely repulsive central forces between periodically spaced circular asperities on contacting grains. We compare the packing fraction, contact number, mobilization distribution, and vibrational density of states using the GA model to those generated using the Cundall-Strack (CS) approach. We find that static packings of frictional disks obtained from the GA model are mechanically stable and isostatic when we consider interactions between asperities on contacting particles. The crossover in the structural and mechanical properties of static packings from frictionless to frictional behavior as a function of the static friction coefficient coincides with a change in the type of interparticle contacts and the disappearance of a peak in the density of vibrational modes for the GA model. These results emphasize that mesoscale features of the model for static friction play an important role in determining the properties of granular packings.Comment: 4.5 pages, 5 figures, http://prl.aps.org/covers/110/1

Bending crystals: Emergence of fractal dislocation structures

We provide a minimal continuum model for mesoscale plasticity, explaining the cellular dislocation structures observed in deformed crystals. Our dislocation density tensor evolves from random, smooth initial conditions to form self-similar structures strikingly similar to those seen experimentally - reproducing both the fractal morphologies and some features of the scaling of cell sizes and misorientations analyzed experimentally. Our model provides a framework for understanding emergent dislocation structures on the mesoscale, a bridge across a computationally demanding mesoscale gap in the multiscale modeling program, and a new example of self-similar structure formation in non-equilibrium systems.Comment: 4 pages, 4 figures, 5 movies (They can be found at http://www.lassp.cornell.edu/sethna/Plasticity/SelfSimilarity.html .) In press at Phys. Rev. Let

Topological phases and topological entropy of two-dimensional systems with finite correlation length

We elucidate the topological features of the entanglement entropy of a region in two dimensional quantum systems in a topological phase with a finite correlation length $\xi$. Firstly, we suggest that simpler reduced quantities, related to the von Neumann entropy, could be defined to compute the topological entropy. We use our methods to compute the entanglement entropy for the ground state wave function of a quantum eight-vertex model in its topological phase, and show that a finite correlation length adds corrections of the same order as the topological entropy which come from sharp features of the boundary of the region under study. We also calculate the topological entropy for the ground state of the quantum dimer model on a triangular lattice by using a mapping to a loop model. The topological entropy of the state is determined by loop configurations with a non-trivial winding number around the region under study. Finally, we consider extensions of the Kitaev wave function, which incorporate the effects of electric and magnetic charge fluctuations, and use it to investigate the stability of the topological phase by calculating the topological entropy.Comment: 17 pages, 4 figures, published versio

Fractional Chern insulator on a triangular lattice of strongly correlated t2gt_{2g} electrons

We discuss the low-energy limit of three-orbital Kondo-lattice and Hubbard models describing $t_{2g}$ orbitals on a triangular lattice near half-filling. We analyze how very flat bands with non-trivial topological character, a Chern number C=1, arise both in the limit of infinite on-site interactions as well as in more realistic regimes. Exact diagonalization is then used to investigate fractional filling of an effective one-band spinless-fermion model including nearest-neighbor interaction $V$; it reveals signatures of fractional Chern insulators (FCIs) for several filling fractions. In addition to indications based on energies, e.g. flux insertion and fractional statistics of quasiholes, Chern numbers are obtained. It is shown that FCIs are robust against disorder in the underlying magnetic texture that defines the topological character of the band. We also investigate competition between FCI states and a charge density wave (CDW) and discuss particle-hole asymmetry as well as Fermi-surface nesting. FCI states turn out to be rather robust and do not require very flat bands, but can also arise when filling or an absence of Fermi-surface nesting disfavor the competing CDW. Nevertheless, very flat bands allow FCI states to be induced by weaker interactions than those needed for more dispersive bands.Comment: 14 pages, 13 figure

Gravitational Lensing as Signal and Noise in Lyman-alpha Forest Measurements

In Lyman-alpha forest measurements it is generally assumed that quasars are mere background light sources which are uncorrelated with the forest. Gravitational lensing of the quasars violates this assumption. This effect leads to a measurement bias, but more interestingly it provides a valuable signal. The lensing signal can be extracted by correlating quasar magnitudes with the flux power spectrum and with the flux decrement. These correlations will be challenging to measure but their detection provides a direct measure of how features in the Lyman-alpha forest trace the underlying mass density field. Observing them will test the fundamental hypothesis that fluctuations in the forest are predominantly driven by fluctuations in mass, rather than in the ionizing background, helium reionization or winds. We discuss ways to disentangle the lensing signal from other sources of such correlations, including dust, continuum and background residuals. The lensing-induced measurement bias arises from sample selection: one preferentially collects spectra of magnified quasars which are behind overdense regions. This measurement bias is ~0.1-1% for the flux power spectrum, optical depth and the flux probability distribution. Since the effect is systematic, quantities such as the amplitude of the flux power spectrum averaged across scales should be interpreted with care.Comment: 22 pages, 8 figures; v2: references added, discussion expanded, matches PRD accepted versio

A comparison of high-latitude ionospheric propagation predictions from Advanced Prophet 4.0 with measured data

Progress in computers during the past two decades has sparked the development of many useful high frequency (HF) ionospheric propagation prediction codes. The high-latitude (polar) ionosphere still remains as the most difficult propagation region to predict. A 'Non centric database of collected high-latitude signal and noise measurements was obtained during 1988 and 1989 by the University of Leicester, UK The Advanced Prophet 4.0 HF Ionospheric Propagation Prediction Code was exercised and compared to a portion of the 'Non centric database, for a transmitter at Clyde River, Canada and a receiver at Leicester, U.K. The Prophet predictions were better during winter months than during summer months. Overall, 70% of the signal strength data from Prophet 4.0 were between -20 dB and +20 dB error, compared to the measured data.http://archive.org/details/acomparisonofhig1094527587Lieutenant, Hellenic NavyApproved for public release; distribution is unlimited