Statistics of Conserved Quantities in Mechanically Stable Packings of Frictionless Disks Above Jamming

We numerically simulate mechanically stable packings of soft-core, frictionless, bidisperse disks in two dimensions, above the jamming packing fraction $\phi_J$. For configurations with a fixed isotropic global stress tensor, we compute the averages, variances, and correlations of conserved quantities (stress $\Gamma_{\cal C}$, force-tile area $A_{\cal C}$, Voronoi volume $V_{\cal C}$, number of particles $N_{\cal C}$, and number of small particles $N_{s{\cal C}}$) on compact subclusters of particles ${\cal C}$, as a function of the cluster size and the global system stress. We find several significant differences depending on whether the cluster ${\cal C}$ is defined by a fixed radius $R$ or a fixed number of particles $M$. We comment on the implications of our findings for maximum entropy models of jammed packings.Comment: 11 pages, 19 figure

Improved phase-change characteristics of Zn-doped amorphous Sb₇Te₃ films for high-speed and low-power phase change memory

The superior performance of Zn-doped Sb₇Te₃ films might be favorable for the application in phase change memory. It was found that Zn dopants were able to suppress phase separation and form single stable Sb2Te crystal grain, diminish the grain size, and enhance the amorphous thermal stability of Sb₇Te₃ film. Especially, Zn 30.19(Sb₇Te₃)69.81 film has higher crystallization temperature (∼258 °C), larger crystallization activation energy (∼4.15 eV), better data retention (∼170.6 °C for 10 yr), wider band gap (∼0.73 eV), and higher crystalline resistance. The minimum times for crystallization of Zn 30.19(Sb₇Te₃)69.81 were revealed to be as short as ∼10 ns at a given proper laser power of 70 mW.This work was financially supported by the International Science & Technology Cooperation Program of China (Grant No. 2011DFA12040), the National Program on Key Basic Research Project (973 Program) (Grant No. 2012CB722703), the Natural Science Foundation of China (Grant Nos. 61008041 and 60978058), the CAS Special Grant for Postgraduate Research, Innovation and Practice, the Program for Innovative Research Team of Ningbo city (Grant No. 2009B21007), and sponsored by K. C. Wong Magna Fund in Ningbo University

Statistical properties of disordered jammed packings of frictionless disks

Thesis (Ph. D.)--University of Rochester. Department of Physics and Astronomy, 2015.We numerically simulate mechanically stable packings of soft-core, frictionless particles in two dimensions interacting with a short range contact potential for the purpose of studying the statistical properties in such disordered systems. To avoid crystallization of the particles, we use a mixture of equal numbers of big and small particles. To prepare a mechanically stable packing, we use the Conjugate Gradient Method to minimize the total energy of the system U(r) to its local minimum from randomly initialized particle positions. For our system with Lees-Edwards periodic boundary conditions, U implicitly depends on the box parameters (box length in x, y directions Lx, Ly and the skew ratio γ in the x direction). we define a modified total energy Ũ(r, Lx, Ly, γ) so that when Ũ is brought to its local minimum, not only the net force on each particle vanishes, but the total stress tensor of the system will simultaneously be the desired, isotropic stress tensor. We optimize our program so that an ensemble of configurations consisting of a large number of particles can be efficiently generated. Therefore we can have good accuracy on the statistics of the quantities that we want to measure. We study a set of conserved quantities, in particular the stress ΓC, the Maxwell-Cremona forcer-tile area AC, the Voronoi volume VC, the number of particles NC, and the number of small particles NsC on subclusters of particles C. These subclusters are sampled from non-overlapping clusters embedded in the systems with the fixed isotropic global system stress. We defined our circular subclusters in two ways; (i), clusters with fixed radius R; (ii), clusters with fixed number of particles M. We compute the averages, variances and correlations of the conserved quantities on the clusters. We find significantly different behavior of the conserved quantities for the two cluster ensembles. The cluster ensemble with fixed radius R has important advantages and is therefore selected for the study of stress distribution on clusters with the maximum entropy hypothesis. We then show that the maximum entropy hypothesis can successfully explain the stress distribution on clusters for our system with isotropic total stress. In contrary to the previous claim that the stress alone as a conserved quantity is enough to explain the stress distribution on clusters, we find that an additional conserved quantity, called the Maxwell-Cremona force-tile area, also needs to be taken into consideration. We show that the joint distribution of the stress and force-tile area can be successfully explained by the maximum entropy hypothesis subject to constraints on the average values of the conserved quantities. Finally, we investigate the fluctuation of local packing fraction ϕ(r) to test whether our configurations display the hyperuniformity that has beed claimed to exit exactly at ϕJ. For our configurations with fixed isotropic global stress, generated by a rapid quench protocol, we find that hyperuniformity persists only out to a finite length scale, and that this length scale doesn’t appear to increase as the system stress decreases towards zero, i.e., towards the jamming transition. Our results suggests that the presence of hyperuniformity at jamming may be sensitive to the specific protocol used to constructed the jammed configurations

Pressure distribution and critical exponent in statically jammed and shear-driven frictionless disks

We numerically study the distributions of global pressure that are found in ensembles of statically jammed and quasistatically sheared systems of bidisperse, frictionless disks at fixed packing fraction phi in two dimensions. We use these distributions to address the question of how pressure increases as phi increases above the jamming point phi(J), p similar to |phi - phi(J) |(y). For statically jammed ensembles, our results are consistent with the exponent y being simply related to the power law of the interparticle soft-core interaction. For sheared systems, however, the value of y is consistent with a nontrivial value, as found previously in rheological simulations.Originally published in dissertation in manuscript form.</p

Scale of heterogeneity of forage production and winter foraging by elk and bison

The relationship between fine-scale spatial patterns of forage abundance and the feeding patterns of large ungulates is not well known. We compared these patterns for areas grazed in winter by elk and bison in a sagebrush-grassland landscape in northern Yellowstone National Park. At a fine scale, the spatial distribu-tion of mapped feeding stations in 30 m x 30 m sites was found to be random where there were no large patches devoid of vegetation. In areas similar to the mapped sites, the underlying spatial distribution pattern of biomass was also determined to be random. At a broad scale, forage biomass differed among communities across the northern range but forage quality did not. These results suggest that ungulates are feeding random-ly within forage patches (fine scale) but may select feeding sites based upon forage abundance at broader, landscape scales. Contrary to what has been suggested in other systems, ungulates were not ‘overmatching’ at finer scales. 1