linkedin post 2021-04-11 04:30:30

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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
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linkedin post 2021-04-11 04:32:15

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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
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linkedin post 2021-04-11 04:35:09

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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
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linkedin post 2021-04-11 04:37:40

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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
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linkedin post 2021-04-11 04:40:26

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KEPLER PACKING. “Trapped surfaces form late in the collapse process, only when a certain threshold density is reached, analogous to the critical packing fraction required for jammed states in granular matter. In Fig. 2, untrapped and trapped surfaces are shown, with volume expansion of constant-time (spacelike hypersurface) slices of flat Minkowski spacetime, and volume con- traction occurring for a gravitationally collapsing body.” https://lnkd.in/dusKMKM View in LinkedIn
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linkedin post 2021-04-11 04:43:10

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THE NUMBER LINKAGE. “It is clear that if the shear, twist and Ricci tensor vanish, the geodesic congruence is convergent, i.e., θ(τ) < 0 at every τ for θ(0) < 0. This is the case of spontaneous jamming, and is independent of any assumed symmetries of spacetime, spherical or otherwise.” https://lnkd.in/dusKMKM View in LinkedIn
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linkedin post 2021-04-11 04:45:53

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THE ANALOGY. “On the other hand, for initially unjammed states with θ(0) = 0, but with non-vanishing shear, while the rotation still vanishes, there is still convergence θ(τ ) < 0, corresponding to shear jamming in granular matter, provided, we use the Einstein equation " "Rμν = (8πG/c4)(Tμν−(1/2)gμνT) (where T ≡ gμνTμν) with non-negative energy density Tμνnμnν ≥ 0. The presence of an external stress-energy tensor exacerbates jamming, if the analogy holds.” https://lnkd.in/dusKMKM View in LinkedIn
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linkedin post 2021-04-11 04:48:48

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SO ENDS this first of two weekends focused on a fearlessly imaginative essay linking William Blake’s grain of sand not just to the world, but to black holes, relativity and the very fabric of the universe, spacetime. It should be an Exemplar for students in the tradition of Darwin’s excavating earthworms, photonic crystals in beetle wings, and peacock feather Iridescence. Looking is not enough, but observing keenly with a primed mind is how science is built. https://lnkd.in/dusKMKM View in LinkedIn
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