2016/09/30 by Kabir Ramola, Bulbul Chakraborty
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Adhesion, Friction, and Surface Interactions #Classical mechanics #Distribution (mathematics) #Field (mathematics) #Force Microscopy Techniques and Applications #Geometry #Material Dynamics and Properties #Mathematical analysis #Mathematics #Order (exchange) #Physics #Scaling #Scaling law #Statistical physics #Total energy #cond-mat.dis-nn #cond-mat.soft
paper · pdf · doi:10.1103/physrevlett.118.138001
published as Phys. Rev. Lett. 118, 138001 (2017) · 5 pages, 3 figures, +Supplemental Material
openalex publication_date 2017/03/27 · arxiv created 2017/03/28 · arxiv updated 2017/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We develop a scaling theory of the unjamming transition of soft frictionless disks in two dimensions by defining local areas, which can be uniquely assigned to each contact. These serve to define local order parameters, whose distribution exhibits divergences as the unjamming transition is approached. We derive scaling forms for these divergences from a mean-field approach that treats the local areas as noninteracting entities, and demonstrate that these results agree remarkably well with numerical simulations. We find that the asymptotic behavior of the scaling functions arises from the geometrical structure of the packing while the overall scaling with the compression energy depends on the force law. We use the scaling forms of the distributions to determine the scaling of the total grain area AG and the total number of contacts NC.