Local origins of volume fraction fluctuations in dense granular materials

Fluctuations of the local volume fraction within granular materials have previously been observed to decrease as the system approaches jamming. We experimentally examine the role of boundary conditions and inter-particle friction $\mu$ on this relationship for a dense granular material of bidisperse particles driven under either constant volume or constant pressure. Using a radical Vorono\"i tessellation, we find the variance of the local volume fraction $\phi$ monotonically decreases as the system becomes more dense, independent of boundary condition and $\mu$. We examine the universality and origins of this trend using experiments and the recent granocentric model \cite{Clusel-2009-GMR,Corwin-2010-MRP}, modified to draw particle locations from an arbitrary distribution ${\cal P}(s)$ of neighbor distances $s$. The mean and variance of the observed ${\cal P}(s)$ are described by a single length scale controlled by $\bar \phi$. Through the granocentric model, we observe that diverse functional forms of ${\cal P}(s)$ all produce the trend of decreasing fluctuations, but only the experimentally-observed ${\cal P}(s)$ provides quantitative agreement with the measured $\phi$ fluctuations. Thus, we find that both ${\cal P}(s)$ and ${\cal P}(\phi)$ encode similar information about the ensemble of observed packings, and are connected to each other by the local granocentric model

Evolution of Network Architecture in a Granular Material Under Compression

As a granular material is compressed, the particles and forces within the system arrange to form complex and heterogeneous collective structures. Force chains are a prime example of such structures, and are thought to constrain bulk properties such as mechanical stability and acoustic transmission. However, capturing and characterizing the evolving nature of the intrinsic inhomogeneity and mesoscale architecture of granular systems can be challenging. A growing body of work has shown that graph theoretic approaches may provide a useful foundation for tackling these problems. Here, we extend the current approaches by utilizing multilayer networks as a framework for directly quantifying the progression of mesoscale architecture in a compressed granular system. We examine a quasi-two-dimensional aggregate of photoelastic disks, subject to biaxial compressions through a series of small, quasistatic steps. Treating particles as network nodes and interparticle forces as network edges, we construct a multilayer network for the system by linking together the series of static force networks that exist at each strain step. We then extract the inherent mesoscale structure from the system by using a generalization of community detection methods to multilayer networks, and we define quantitative measures to characterize the changes in this structure throughout the compression process. We separately consider the network of normal and tangential forces, and find that they display a different progression throughout compression. To test the sensitivity of the network model to particle properties, we examine whether the method can distinguish a subsystem of low-friction particles within a bath of higher-friction particles. We find that this can be achieved by considering the network of tangential forces, and that the community structure is better able to separate the subsystem than a purely local measure of interparticle forces alone. The results discussed throughout this study suggest that these network science techniques may provide a direct way to compare and classify data from systems under different external conditions or with different physical makeup

Photoelastic force measurements in granular materials

Photoelastic techniques are used to make both qualitative and quantitative measurements of the forces within idealized granular materials. The method is based on placing a birefringent granular material between a pair of polarizing filters, so that each region of the material rotates the polarization of light according to the amount of local of stress. In this review paper, we summarize past work using the technique, describe the optics underlying the technique, and illustrate how it can be used to quantitatively determine the vector contact forces between particles in a 2D granular system. We provide a description of software resources available to perform this task, as well as key techniques and resources for building an experimental apparatus

Equilibrating temperature-like variables in jammed granular subsystems

Although jammed granular systems are athermal, several thermodynamic-like descriptions have been proposed which make quantitative predictions about the distribution of volume and stress within a system and provide a corresponding temperature-like variable. We perform experiments with an apparatus designed to generate a large number of independent, jammed, two-dimensional configurations. Each configuration consists of a single layer of photoelastic disks supported by a gentle layer of air. New configurations are generated by alternately dilating and re-compacting the system through a series of boundary displacements. Within each configuration, a bath of particles surrounds a smaller subsystem of particles with a different inter-particle friction coefficient than the bath. The use of photoelastic particles permits us to find all particle positions as well as the vector forces at each inter-particle contact. By comparing the temperature-like quantities in both systems, we find compactivity (conjugate to the volume) does not equilibrate between the systems, while the angoricity (conjugate to the stress) does. Both independent components of the angoricity are linearly dependent on the hydrostatic pressure, in agreement with predictions of the stress ensemble

Two-dimensional Navier--Stokes simulation of deformation and break up of liquid patches

The large deformations and break up of circular 2D liquid patches in a high Reynolds number (Re=1000) gas flow are investigated numerically. The 2D, plane flow Navier--Stokes equations are directly solved with explicit tracking of the interface between the two phases and a new algorithm for surface tension. The numerical method is able to pursue the simulation beyond the breaking or coalescence of droplets. The simulations are able to unveil the intriguing details of the non-linear interplay between the deforming droplets and the vortical structures in the droplet's wake.Comment: 13 pages including 4 postscript figures; Revised version as resubmitted to PRL. Title has change

Polarization transfer in wide-angle Compton scattering and single-pion photoproduction from the proton

Wide-angle exclusive Compton scattering and single-pion photoproduction from the proton have been investigated via measurement of the polarization transfer from a circularly polarized photon beam to the recoil proton. The wide-angle Compton scattering polarization transfer was analyzed at an incident photon energy of 3.7 GeV at a proton scattering angle of θpcm=70°. The longitudinal transfer KLL, measured to be 0.645±0.059±0.048, where the first error is statistical and the second is systematic, has the same sign as predicted for the reaction mechanism in which the photon interacts with a single quark carrying the spin of the proton. However, the observed value is ∼3 times larger than predicted by the generalized-parton-distribution-based calculations, which indicates a significant unknown contribution to the scattering amplitude

JLab Measurement of the 4^4He Charge Form Factor at Large Momentum Transfers

The charge form factor of ^4He has been extracted in the range 29 fm$^{-2}$ $\le Q^2 \le 77$ fm$^{-2}$ from elastic electron scattering, detecting $^4$He nuclei and electrons in coincidence with the High Resolution Spectrometers of the Hall A Facility of Jefferson Lab. The results are in qualitative agreement with realistic meson-nucleon theoretical calculations. The data have uncovered a second diffraction minimum, which was predicted in the $Q^2$ range of this experiment, and rule out conclusively long-standing predictions of dimensional scaling of high-energy amplitudes using quark counting.Comment: 4 pages, 2 figure

A precise extraction of the induced polarization in the 4He(e,e'p)3H reaction

We measured with unprecedented precision the induced polarization Py in 4He(e,e'p)3H at Q^2 = 0.8 (GeV/c)^2 and 1.3 (GeV/c)^2. The induced polarization is indicative of reaction-mechanism effects beyond the impulse approximation. Our results are in agreement with a relativistic distorted-wave impulse approximation calculation but are over-estimated by a calculation with strong charge-exchange effects. Our data are used to constrain the strength of the spin independent charge-exchange term in the latter calculation.Comment: submitted to Physical Review Letter

Polarization Transfer in the 4He(e,e'p)3H Reaction at Q^2 = 0.8 and 1.3 (GeV/c)^2

Proton recoil polarization was measured in the quasielastic 4He(e,e'p)3H reaction at Q^2 = 0.8 (GeV/c)^2 and 1.3 (GeV/c)^2 with unprecedented precision. The polarization-transfer coefficients are found to differ from those of the 1H(e,e' p) reaction, contradicting a relativistic distorted-wave approximation, and favoring either the inclusion of medium-modified proton form factors predicted by the quark-meson coupling model or a spin-dependent charge-exchange final-state interaction. For the first time, the polarization-transfer ratio is studied as a function of the virtuality of the proton

Freight distribution performance indicators for service quality planning in large transportation networks

This paper studies the use of performance indicators in routing problems to estimate how transportation cost is affected by the quality of service offered. The quality of service is assumed to be directly dependent on the size of the time windows. Smaller time windows mean better service. Three performance indicators are introduced. These indicators are calculated directly from the data without the need of a solution method. The introduced indicators are based mainly on a "request compatibility", which describes whether two visits can be scheduled consecutively in a route. Other two indicators are introduced, which get their values from a greedy constructive heuristic. After introducing the indicators, the correlation between indicators and transportation cost is examined. It is concluded that the indicators give a good first estimation on the transportation cost incurred when providing a certain quality of service. These indicators can be calculated easily in one of the first planning steps without the need of a sophisticated solution tool. The contribution of the paper is the introduction of a simple set of performance indicators that can be used to estimate the transportation cost of a routing problem with time window