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THE PROBLEM. “This dichotomic behaviour is at the heart of difficulties in the extensive ongoing and past assays in theoretical analyses of the laws that govern such materials.” https://lnkd.in/dusKMKM View in LinkedIn

THE ANALYSIS. “Isotropically Jammed states: A simple representative of an isotropically jammed state in a granular substance, in contrast to an unjammed state is depicted in Fig. 1, showing that for the same total number of grains, jamming clearly entails a contraction of the spatial volume.” https://lnkd.in/dusKMKM View in LinkedIn

DUAL STATES. “Thus, in each such alignment direction, these materials behave like a solid, while, in other directions, the material may indeed ‘flow’, akin to a fluid.” (Very quantum description in macroscopic material!) https://lnkd.in/dusKMKM View in LinkedIn

ON CABBAGES AND KINGS. “Recently, an emergent continuum elasticity model, capturing the infrared behaviour of amorphous athermal materials has been proposed, based on a tensor electrostatics version of fracton gauge theory. Such a model emerges naturally from the linearized version of the analogue gravity model proposed here.” https://lnkd.in/dusKMKM View in LinkedIn

GRAIN ALIGNMENT. “Within this paradigm, spatial density fluctuations observed in a granular material like sand, are attributed to force chains - force-ordered alignments of grains which inhibit motion of test-grains along the alignment direction (friction).” https://lnkd.in/dusKMKM View in LinkedIn

COSMIC FILAMENTS. “Density perturbation equations around the ‘background’ geometrical configuration do indeed yield as a solution, a time series of density heterogeneities or filamentary structures corresponding to that observed for granular matter, thus showing unexpected similarities with galactic filaments in structure formation models of relativistic cosmology.” https://lnkd.in/dusKMKM View in LinkedIn

BRIDGING TO SAND. “Trapping is characterized by the horizon radius at which the spatial length (given by the metric) may actually diverge. This spatial distance (within a particular frame) is taken to correspond to the correlation length in the phase transition description of ‘spontaneous’ jamming.” https://lnkd.in/dusKMKM View in LinkedIn

THE BLACK HOLE. “In particular, an isotropically jammed state in granular matter corresponds in the analogue gravity description to the formation of a trapped surface in gravitational collapse, with the envelope of such trapped surfaces being a horizon.” https://lnkd.in/dusKMKM View in LinkedIn

THE CORE ANALOGY. “General Relativity is well-known to be inherently non-linear, and to admit a great many time-dependent solutions (like gravitational collapse solutions) which, from a statistical standpoint correspond to distinctly non-equilibrium processes. In many cases though, constant-time spatial slices do reveal steady state aspects of such solutions.” https://lnkd.in/dusKMKM View in LinkedIn

The most beautiful of all the ancient Greek coins, signed by Kimon. " " https://lnkd.in/dzZypJq View in LinkedIn