In polycrystalline materials, grain boundaries are sites of enhanced atomic motion, but the complexity of the atomic structures within a grain boundary network makes it difficult to link the ...structure and atomic dynamics. Here, we use a machine learning technique to establish a connection between local structure and dynamics of these materials. Following previous work on bulk glassy materials, we define a purely structural quantity (softness) that captures the propensity of an atom to rearrange. This approach correctly identifies crystalline regions, stacking faults, and twin boundaries as having low likelihood of atomic rearrangements while finding a large variability within high-energy grain boundaries. As has been found in glasses, the probability that atoms of a given softness will rearrange is nearly Arrhenius. This indicates a well-defined energy barrier as well as a well-defined prefactor for the Arrhenius form for atoms of a given softness. The decrease in the prefactor for low-softness atoms indicates that variations in entropy exhibit a dominant influence on the atomic dynamics in grain boundaries.
Although cell shape can reflect the mechanical and biochemical properties of the cell and its environment, quantification of 3D cell shapes within 3D tissues remains difficult, typically requiring ...digital reconstruction from a stack of 2D images. We investigate a simple alternative technique to extract information about the 3D shapes of cells in a tissue; this technique connects the ensemble of 3D shapes in the tissue with the distribution of 2D shapes observed in independent 2D slices. Using cell vertex model geometries, we find that the distribution of 2D shapes allows clear determination of the mean value of a 3D shape index. We analyze the errors that may arise in practice in the estimation of the mean 3D shape index from 2D imagery and find that typically only a few dozen cells in 2D imagery are required to reduce uncertainty below 2%. Even though we developed the method for isotropic animal tissues, we demonstrate it on an anisotropic plant tissue. This framework could also be naturally extended to estimate additional 3D geometric features and quantify their uncertainty in other materials.
Geometrically imposed force cancellations lead to ultralow friction between rigid incommensurate crystalline asperities. Elastic deformations may avert this cancellation but are difficult to treat ...analytically in finite and three-dimensional systems. We use atomic-scale simulations to show that elasticity affects the friction only after the contact radius a exceeds a characteristic length set by the core width of interfacial dislocations b sub(core). As a increases past b sub(core), the frictional stress for both incommensurate and commensurate surfaces decreases to a constant value. This plateau corresponds to a Peierls stress that drops exponentially with increasing b sub(core) but remains finite.
Modeling interfacial phenomena often requires both a detailed atomistic description of surface interactions and accurate calculations of long-range deformations in the substrate. The latter can be ...efficiently obtained using an elastic Green's function if substrate deformations are small. We present a general formulation for rapidly computing the Green's function for a planar surface given the interatomic interactions, and then coupling the Green's function to explicit atoms. The approach is fast, avoids ghost forces, and is not limited to nearest-neighbor interactions. The full system comprising explicit interfacial atoms and an elastic substrate is described by a single Hamiltonian and interactions in the substrate are treated exactly up to harmonic order. This concurrent multiscale coupling provides simple, seamless elastic boundary conditions for atomistic simulations where near-surface deformations occur, such as nanoindentation, contact, friction, or fracture. Applications to surface relaxation and contact are used to test and illustrate the approach.
We use molecular simulations to study jamming of a crumpled bead-spring model polymer in a finite container and compare to jamming of repulsive spheres. After proper constraint counting, the onset of ...rigidity is seen to occur isostatically as in the case of repulsive spheres. Despite this commonality, the presence of the curved container wall and polymer backbone bonds introduce new mechanical properties. Notably, these include additional bands in the vibrational density of states that reflect the material structure as well as oscillations in local contact number and density near the wall but with lower amplitude for polymers. Polymers have fewer boundary contacts, and this low-density surface layer strongly reduces the global bulk modulus. We further show that bulk-modulus dependence on backbone stiffness can be described by a model of stiffnesses in series and discuss potential experimental and biological applications.
Contact of a spherical tip with a flat elastic substrate is simulated with a Green's-function method that includes atomic structure at the interface while capturing elastic deformation in a ...semi-infinite substrate. The tip and substrate have identical crystal structures with nearest-neighbor spacing d and are aligned in registry. Purely repulsive interactions between surface atoms lead to a local shear strength that is the local pressure times a constant local friction coefficient α. The total friction between tip and substrate is calculated as a function of contact radius a and sphere radius R, with a up to 103d and R up to 4×104d. Three regimes are identified depending on the ratio of a to the core width of edge dislocations in the center of the contact. This ratio is proportional to αa2/Rd. In small contacts, all atoms move coherently and the total friction coefficient μ=α. When the contact radius exceeds the core width, a dislocation nucleates at the edge of the contact and rapidly advances to the center where it annihilates. The friction coefficient falls as μ∼α(αa2/Rd)−2/3. An array of dislocations forms in very large contacts and the friction is determined by the Peierls stress for dislocation motion. The Peierls stress rises with pressure, and μ rises with increasing load.
We use molecular simulations to study jamming of a crumpled bead-spring model polymer in a finite container and compare to jamming of repulsive spheres. After proper constraint counting, the onset of ...rigidity is seen to occur isostatically as in the case of repulsive spheres. Despite this commonality, the presence of the curved container wall and polymer backbone bonds introduce new mechanical properties. Notably, these include additional bands in the vibrational density of states that reflect the material structure as well as oscillations in local contact number and density near the wall but with lower amplitude for polymers. Polymers have fewer boundary contacts, and this low-density surface layer strongly reduces the global bulk modulus. We further show that bulk-modulus dependence on backbone stiffness can be described by a model of stiffnesses in series and discuss potential experimental and biological applications.
Machine learning techniques have been used to quantify the relationship between local structural features and variations in local dynamical activity in disordered glass-forming materials. To date ...these methods have been applied to an array of standard (Arrhenius and super-Arrhenius) glass formers, where work on "soft spots" indicates a connection between the linear vibrational response of a configuration and the energy barriers to non-linear deformations. Here we study the Voronoi model, which takes its inspiration from dense epithelial monolayers and which displays anomalous, sub-Arrhenius scaling of its dynamical relaxation time with decreasing temperature. Despite these differences, we find that the likelihood of rearrangements can vary by several orders of magnitude within the model tissue and extract a local structural quantity, "softness" that accurately predicts the temperature-dependence of the relaxation time. We use an information-theoretic measure to quantify the extent to which softness determines impending topological rearrangements; we find that softness captures nearly all of the information about rearrangements that is obtainable from structure, and that this information is large in the solid phase of the model and decreases rapidly as state variables are varied into the fluid phase.
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