We study the geometrically induced cohesion of ensembles of granular "u particles" that mechanically entangle through particle interpenetration. We vary the length-to-width ratio l/w of the u particles and form them into freestanding vertical columns. In a laboratory experiment, we monitor the response of the columns to sinusoidal vibration (with peak acceleration Γ). Column collapse occurs in a characteristic time τ which follows the relation τ∝exp(Γ/Δ). Δ resembles an activation energy and is maximal at intermediate l/w. A simulation reveals that optimal strength results from competition between packing and entanglement.

We study concentrated binary colloidal suspensions, a model system which has a glass transition as the volume fraction φ of particles is increased. We use confocal microscopy to directly observe particle motion within dense samples with φ ranging from 0.4 to 0.7. Our binary mixtures have a particle diameter ratio d S /d L = 1/1.3 and particle number ratio N S /N L = 1.56, which are chosen to inhibit crystallization and enable long-time observations. Near the glass transition we find that particle dynamics are heterogeneous in both space and time. The most mobile particles occur in spatially localized groups. The length scales characterizing these mobile regions grow slightly as the glass transition is approached, with the largest length scales seen being ∼ 4 small particle diameters. We also study temporal fluctuations using the dynamic susceptibility χ 4 , and find that the fluctuations grow as the glass transition is approached. Analysis of both spatial and temporal dynamical heterogeneity show that the smaller species play an important role in facilitating particle rearrangements. The glass transition in our sample occurs at φ g ≈ 0.58, with characteristic signs of aging observed for all samples with φ > φ g .

We have found that the ability of long thin rods to jam into a solidlike state in response to a local perturbation depends upon both the particle aspect ratio and the container size. The dynamic phase diagram in this parameter space reveals a broad transition region separating granular stick-slip and solidlike behavior. In this transition region the pile displays both solid and stick-slip behavior. We measure the force on a small object pulled through the pile, and find the fluctuation spectra to have power law tails with an exponent characteristic of the region. The exponent varies from beta=-2 in the stick-slip region to beta=-1 in the solid region. These values reflect the different origins--granular rearrangements vs dry friction--of the fluctuations. Finally, the packing fraction shows only a slight dependence on container size, but depends on aspect ratio in a manner predicted by mean-field theory and implies an aspect-ratio-independent contact number of =5.25 +/- 0.03.

We investigate the collapse of granular rodpiles as a function of particle (length/diameter) and pile (height/radius) aspect ratio. We find that, for all particle aspect ratios below 24, there exists a critical height H l below which the pile never collapses, maintaining its initial shape as a solid, and a second height Hu above which the pile always collapses. Intermediate heights between H l and Hu collapse with a probability that increases linearly with increasing height. The linear increase in probability is independent of particle length, width, or aspect ratio. When piles collapse, the runoff scales as a piecewise power-law with pile height, with r f ∼H 1.2±0.1 for pile heights belowHc ≈ 0.74 and r f ≈ H 0.6±0.1 for taller piles.

Large-scale internet services aim to remain highly available and responsive in the presence of unexpected failures. Providing this service often requires monitoring and analyzing tens of millions of measurements per second across a large number of systems, and one particularly effective solution is to store and query such measurements in a time series database (TSDB). A key challenge in the design of TSDBs is how to strike the right balance between efficiency, scalability, and reliability. In this paper we introduce Gorilla, Facebook's in-memory TSDB. Our insight is that users of monitoring systems do not place much emphasis on individual data points but rather on aggregate analysis, and recent data points are of much higher value than older points to quickly detect and diagnose the root cause of an ongoing problem. Gorilla optimizes for remaining highly available for writes and reads, even in the face of failures, at the expense of possibly dropping small amounts of data on the write path. To improve query efficiency, we aggressively leverage compression techniques such as delta-of-delta timestamps and XOR'd floating point values to reduce Gorilla's storage footprint by 10x. This allows us to store Gorilla's data in memory, reducing query latency by 73x and improving query throughput by 14x when compared to a traditional database (HBase)-backed time series data. This performance improvement has unlocked new monitoring and debugging tools, such as time series correlation search and more dense visualization tools. Gorilla also gracefully handles failures from a single-node to entire regions with little to no operational overhead.