We present results on a meso-scale model for amorphous matter in athermal, quasi-static (a-AQS), steady state shear flow. In particular, we perform a careful analysis of the scaling with the lateral system size, L, of: i) statistics of individual relaxation events in terms of stress relaxation, S, and individual event mean-squared displacement, M , and the subsequent load increments, ∆γ, required to initiate the next event; ii) static properties of the system encoded by x = σy − σ, the distance of local stress values from threshold; and iii) long-time correlations and the emergence of diffusive behavior. For the event statistics, we find that the distribution of S is similar to, but distinct from, the distribution of M . The exponents governing the scaling properties of P (S) completely determine the exponent α governing the finite size scaling of the load increment required to trigger the next event ∆γ ∼ L −α . P (M ) is analogous to but distinct from P (S). We find a strong correlation between S and M for any particular event, with S ∼ M q with q ≈ 0.65. This new exponent, q, completely determines the scaling exponents for P (M ) given those for P (S). For the distribution of local thresholds, we find P (x) is analytic at x = 0, and has a value P (x)| x=0 = p0 which scales with lateral system length as p0 ∼ L −a 1 . In our model, by construction, the minimum, xmin, of x in any particular configuration is precisely equal to ∆γ, and, also by construction, S = ∆γ . Extreme value statistics arguments lead to a scaling relation between the exponents governing P (x) and those governing P (S). Finally, we study the long-time correlations via single-particle tracer statistics. At short times, the displacement distributions are strongly non-Gaussian and consistent with exponentials as observed at short times in other driven and thermal glassy systems. At long times, a diffusive behavior emerges where the distributions become Gaussian. The value of the diffusion coefficient is completely determined by ∆γ and the scaling properties of P (M ) (in particular from M ) rather than directly from P (S) as one might have naively guessed. Our results: i) further define the a-AQS universality class with the identification of new scaling exponents unrelated to old ones, ii) help clarify the relation between avalanches of stress relaxation and longtime diffusive behavior, iii) help clarify the relation between local threshold distributions and event statistics and iv) should be important for any future work on the broad class of systems which fall into this universality class including amorphous alloys, glassy polymers, compressed granular matter, and soft glasses like foams, emulsions, and pastes. arXiv:1905.07388v1 [cond-mat.soft]

A mesoscopic model of amorphous plasticity is discussed in the context of depinning models. After embedding in a d + 1 dimensional space, where the accumulated plastic strain lives along the additional dimension, the gradual plastic deformation of amorphous media can be regarded as the motion of an elastic manifold in a disordered landscape. While the associated depinning transition leads to scaling properties, the quadrupolar Eshelby interactions at play in amorphous plasticity induce specific additional features like shear-banding and weak ergodicity break-down. The latters are shown to be controlled by the existence of soft modes of the elastic interaction, the consequence of which is discussed in the context of depinning.

We present results on tagged particle diffusion in a meso-scale lattice model for sheared amorphous material in athermal quasi-static conditions. We find a short time diffusive regime and a long time diffusive regime whose diffusion coefficients depend on system size in dramatically different ways. At short time, we find that the diffusion coefficient, D, scales roughly linearly with system length, D ∼ L 1.05 . This short time behavior is consistent with particle-based simulations. The longtime diffusion coefficient scales like D ∼ L 1.6 , close to previous studies which found D ∼ L 1.5 . Furthermore, we show that the near-field details of the interaction kernel do not affect the short time behavior, but qualitatively and dramatically affect the long time behavior, potentially causing a saturation of the mean-squared displacement at long times. Our finding of a D ∼ L 1.05 short time scaling resolves a long standing puzzle about the disagreement between the diffusion coefficient measured in particle-based models and meso-scale lattice models of amorphous plasticity.Over the past few decades, the notion of local shear transformations has been used to describe and explain the plastic flow of amorphous solids [1,2]. A class of mesocopic lattice models is built on this picture [3][4][5][6][7][8][9][10][11][12][13][14][15], (see Nicolas et al. [16] for a recent review). In these lattice models, the system is partitioned into local regions, and any one of them may undergo a yielding event if loaded beyond some threshold. These models are designed to operate at a mesoscopic scale; slightly coarser than the particles, but not at a macroscopic scale where continuum thermodynamical models describe phenomena such as persistent shear localization [2,17,18].Avalanches of local shear transformations are observed in both particle-scale [19][20][21][22] and meso-scale models [5,6,14,15,23,24] during slow steady shear. The cascades are caused by the elastically mediated redistribution of stress after a local yielding event [1,7,25]. The result is a broad spectrum of bursts of plastic activity [26] and fractal patterns of accumulated plasticity [27]. Similar avalanching behavior is observed in many different dynamically critical systems [28][29][30][31][32][33].Despite the quantitative agreement in the spectrum of avalanche sizes and the qualitative agreement in the spatial correlations in the plastic strain [4], one major discrepancy between particulate and mesoscale models has remained. It involves the diffusion coefficient, D, of the motion of tagged particles. Lemaître and Caroli [34] argued that the spatial correlations in the plastic strain field should give rise to a dependence of D on the system length, L. In quasi-static simulations of a Lennard-Jones glass, Maloney and Robbins [35] showed that D ∼ L out to L ≈ 1000 particles. In a lattice model, Martens et. al.[8], found a very different scaling with system length for the diffusion coefficient, D ∼ L 1.5 . Nicolas and co-workers then [10] showed that including the effect...

We discuss the plastic behavior of an amorphous matrix reinforced by hard particles. A mesoscopic depinning-like model accounting for Eshelby elastic interactions is implemented. Only the effect of a plastic disorder is considered. Numerical results show a complex size dependence of the effective flow stress of the amorphous composite. In particular, the departure from the mixing law shows opposite trends associated to the competing effects of the matrix and the reinforcing particles, respectively. The reinforcing mechanisms and their effects on localization are discussed. Plastic strain is shown to gradually concentrate on the weakest band of the system. This correlation of the plastic behavior with the material structure is used to design a simple analytical model. The latter nicely captures reinforcement size effects in (logN/N)(1/2), where N is the linear size of the system, observed numerically. Predictions of the effective flow stress accounting for further logarithmic corrections show a very good agreement with numerical results.

Hepatitis B virus (HBV) is an endemic, chronic virus that leads to 800000 deaths per year. Central to the HBV lifecycle, the viral core has a protein capsid assembled from many copies of a single protein. The capsid protein adopts different (quasi-equivalent) conformations to form icosahedral capsids containing 180 or 240 proteins: T = 3 or T = 4, respectively, in Caspar–Klug nomenclature. HBV capsid assembly has become an important target for recently developed antivirals; nonetheless, the assembly pathways and mechanisms that control HBV dimorphism remain unclear. We describe computer simulations of the HBV assembly, using a coarse-grained model that has parameters learned from all-atom molecular dynamics simulations of a complete HBV capsid and yet is computationally tractable. Dynamical simulations with the resulting model reproduce experimental observations of HBV assembly pathways and products. By constructing Markov state models and employing transition path theory, we identify pathways leading to T = 3, T = 4, and other experimentally observed capsid morphologies. The analysis shows that capsid polymorphism is promoted by the low HBV capsid bending modulus, where the key factors controlling polymorphism are the conformational energy landscape and protein–protein binding affinities.

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We use computational modeling to investigate the assembly thermodynamics of a particle-based model for geometrically frustrated assembly, in which the local packing geometry of subunits is incompatible with uniform, strain-free large-scale assembly. The model considers discrete triangular subunits that drive assembly toward a closed, hexagonal-ordered tubule, but have geometries that locally favor negative Gaussian curvature. We use dynamical Monte Carlo simulations and enhanced sampling methods to compute the free energy landscape and corresponding self-assembly behavior as a function of experimentally accessible parameters that control assembly driving forces and the magnitude of frustration. The results determine the parameter range where finite-temperature self-limiting assembly occurs, in which the equilibrium assembly size distribution is sharply peaked around a welldefined finite size. The simulations also identify two mechanisms by which the system can escape frustration and assemble to unlimited size, and determine the particle-scale properties of subunits that suppress unbounded growth.

The ability to design and synthesize ever more complicated colloidal particles opens the possibility of self-assembling a zoo of complex structures, including those with one or more self-limited length scales. An undesirable feature of systems with self-limited length scales is that thermal fluctuations can lead to the assembly of nearby, off-target states. We investigate strategies for limiting off-target assembly by using multiple types of subunits. Using simulations and energetics calculations, we explore this concept by considering the assembly of tubules built from triangular subunits that bind edge to edge. While in principle, a single type of triangle can assemble into tubules with a monodisperse width distribution, in practice, the finite bending rigidity of the binding sites leads to the formation of off-target structures. To increase the assembly specificity, we introduce tiling rules for assembling tubules from multiple species of triangles. We show that the selectivity of the target structure can be dramatically improved by using multiple species of subunits, and provide a prescription for choosing the minimum number of subunit species required for near-perfect yield. Our approach of increasing the system’s complexity to reduce the accessibility of neighboring structures should be generalizable to other systems beyond the self-assembly of tubules.