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      Topology of the force network in the jamming transition of an isotropically compressed granular packing

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      Physical Review E
      American Physical Society (APS)

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          Jamming is not just cool any more

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            Characterization of complex networks: A survey of measurements

            Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements. Important related issues covered in this work comprise the representation of the evolution of complex networks in terms of trajectories in several measurement spaces, the analysis of the correlations between some of the most traditional measurements, perturbation analysis, as well as the use of multivariate statistics for feature selection and network classification. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the proper application and interpretation of measurements.
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              Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder

              We have studied how 2- and 3- dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and applied stress. For each configuration, there is a unique jamming threshold, \(\phi_c\), at which particles can no longer avoid each other and the bulk and shear moduli simultaneously become non-zero. The distribution of \(\phi_c\) values becomes narrower as the system size increases, so that essentially all configurations jam at the same \(\phi\) in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close-packing. In fact, our results provide a well-defined meaning for "random close-packing" in terms of the fraction of all phase space with inherent structures that jam. The jamming threshold, Point J, occurring at zero temperature and applied stress and at the random close-packing density, has properties reminiscent of an ordinary critical point. As Point J is approached from higher packing fractions, power-law scaling is found for many quantities. Moreover, near Point J, certain quantities no longer self-average, suggesting the existence of a length scale that diverges at J. However, Point J also differs from an ordinary critical point: the scaling exponents do not depend on dimension but do depend on the interparticle potential. Finally, as Point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes. All of these results suggest that Point J may control behavior in its vicinity-perhaps even at the glass transition.
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                Author and article information

                Journal
                PLEEE8
                Physical Review E
                Phys. Rev. E
                American Physical Society (APS)
                1539-3755
                1550-2376
                April 2010
                April 14 2010
                : 81
                : 4
                Article
                10.1103/PhysRevE.81.041302
                e3e3b819-db20-4cb4-a3fd-2363039a2ff7
                © 2010

                http://link.aps.org/licenses/aps-default-license

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