TBA

• Hisao Hayakawa (Yukawa Institute for Theoretical Physics)

Mean-field theory of vibrational density of states of jammed packing

• Harukuni Ikeda (Yukawa Institute for Theoretical Physics)

Several mean-field theories predict that the Hessian matrix of amorphous solids converges to the Wishart matrix in the limit of large spatial dimensions. Motivated by these results, we calculate here the density of states of random packing of harmonic spheres by mapping the Hessian of the original system to the Wishart matrix. We compare our result with that of previous numerical simulations of harmonic spheres in several spatial dimensions d=3, 5, and 9. For small pressure (near jamming), we find a good agreement even in d=3, and obtain better agreements in larger d, suggesting that the approximation becomes exact in the limit of large spatial dimension.

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• Kota Noto (Yukawa Institute for Theoretical Physics)

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• Satoshi Takada (Tokyo University of Agriculture and Technology)

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• Michio Otsuki (Shimane University)

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• Ryudo Suzuki (Kyoto University)

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• Kuniyasu Saitoh (Kyoto Sangyo University)

From flowing to static: statistics of elasto-plastic transitions

• Stefan Luding (Twente)

How do soft granular materials (or dense amorphous systems) respond to externally applied deformations at different rates – from fast to slow to very slow – and for different system sizes? This long-standing question was intensively studied for shear deformation modes, but only more recently also for isotropic deformations, like compression-decompression cycles [1,2]. For moderate strain rates, in the solid-like state, above jamming [3,4,5], the system appears to evolve more or less smoothly in time/strain, whereas for slow enough deformations, the material flips intermittently between the elastic, reversible base-state and plastic, dynamic “events”. Only during the latter events the micro-structure changes, it re-arranges, irreversibly. The reversible base state involves both affine and non-affine deformations, while the events are purely non-affine. Besides their phenomenology and statistical properties, in particular, the system size and rate dependence [6] of the events is studied, providing reference data, to be compared in future to experiments on model materials like hydrogel particles using modern techniques. Finally, perspectives and relations to real materials in application are to be addressed. Figure 1 displays the affine, non-affine, and total displacement fields, where in the center of the event (much larger localized displacements) the particles are highlighted. Figure 2 displays the kinetic to potential energy ratio during compression from below jamming to above, for various different system sizes and strain-rates. The zoom-in in Fig. 2 (right) allows to observe isolated events (for slow enough compression rate) and their exponential decay of granular temperature (dynamic cooling) relaxing towards the steady, smooth, elastic situation between events. The larger the system size, the more events occur, overlapping in time (strain) if the compression rate is too fast. References [1] K. Taghizadeh, S. Luding, R. Basak, L. Kondic, Understanding slow compression of frictional granular particles under slow compression by network analysis, Soft Matter (submitted 2023) [2] S. Luding, K. Taghizadeh, C. Cheng, L. Kondic, Understanding slow compression and decompression of frictionless soft granular matter by network analysis, Soft Matter 18, 1868 (2022) [3] S. Luding, Granular matter: so much for the jamming point, Nature Physics 12, 531-532, 2016 [4] N. Kumar, S. Luding, Memory of jamming -- multiscale models for soft and granular matter, Granular Matter 18, 58, 2016 [5] S. Luding, Y. Jiang, and M. Liu, Un-jamming due to energetic instability: statics to dynamics, Granular Matter 23, 80, 2021 [6] S. Luding, How does static granular matter re-arrange for different isotropic strain rate?, in Powders & Grains 2021 – EPJ Web of Conferences (2021), Vol. 249, p. 10001 [7] S. Luding, Elastic-plastic intermittent re-arrangements of frictionless, soft granular matter under very slow isotropic deformations, Frontiers Physics 11, 1211394, 2023

TBA

• Takeshi Kawasaki (Osaka University)

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• Balazs Fuvesi

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• Roxana Saghafian Larijani (Twente)