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砂のようなマクロな粒子の集団は、熱平衡状態に緩和しない非熱的粒子系と呼ばれ、独特の振る舞いを することが知られている。また、地表が粉体に覆われていることからも分かる通り、その制御は極めて重 要で、薬学、化学工学、機械工学、地球科学等での広範な応用があり、基礎物理の対象としても注目を集 めている。 本研究会は専門誌 Granular Matter の managing editor で粉体物理の世界的コミュニティである AEMMG の president でもある Stefan Luding の来訪を機会に 1 日のミニワークショップを開き、情報 交換を行う予定である。
Stefan Luding (Twente)
池田晴國（基研）
齊藤国靖（京産大）
大槻道夫（島根大）
高田智史（農工大）
川崎猛史（阪大）
瀬戸亮平(Wenzhou Institute, UCAS)=to be confirmed
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.
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