We present an analytic scheme to connect the fragility and viscoelasticity of metallic glasses to the effective ion-ion interaction in the metal. This is achieved by an approximation of the short-range repulsive part of the interaction, combined with nonaffine lattice dynamics to obtain analytical expressions for the shear modulus, viscosity, and fragility in terms of the ion-ion interaction. By fitting the theoretical model to experimental data, we are able to link the steepness of the interionic repulsion to the Thomas-Fermi screened Coulomb repulsion and to the Born-Mayer valence electron overlap repulsion for various alloys. The result is a simple closed-form expression for the fragility of the supercooled liquid metal in terms of few crucial atomic-scale interaction and anharmonicity parameters. In particular, a linear relationship is found between the fragility and the energy scales of both the screened Coulomb and the electron overlap repulsions. This relationship opens up opportunities to fabricate alloys with tailored thermoelasticity and fragility by rationally tuning the chemical composition of the alloy according to general principles. The analysis presented here brings a new way of looking at the link between the outer shell electronic structure of metals and metalloids and the viscoelasticity and fragility thereof. Understanding the mechanism which governs the emergence of mechanical stability at the glass transition of supercooled metallic liquids (1) calls for deeper insights into the connection between the fragility index and the interatomic interaction. As previous work suggested (2-4), mechanical stability in amorphous solids is crucially linked to the repulsive part of the interatomic interaction potential. However, no consensus has been reached on whether interatomic repulsion softness correlates with strong glasses (5) or with fragile glasses (6). We derive an analytical closedform relation between the fragility index of metallic glass formers and the short-ranged repulsive part of the interatomic interaction given by pseudopotential theory. This fundamental relation is obtained from a one-parameter theory fit to experimental rheological data of supercooled metallic melts. Resorting to this combination of theory and experiments, it is established that interatomic repulsion softness in metals goes along with strong glasses and low fragility. Surprisingly, given the difference in energy scale of many orders of magnitude and the nature of the microscopic interaction, this finding is in full agreement with the correlation observed experimentally for soft colloidal glasses by Mattsson, Weitz, and coworkers (5). Finally, we establish a quantitative link between our analysis and the theory of shear transformation zones to estimate the size of the cooperatively rearranging regions in good agreement with the findings in ref. 7. Shear Modulus of GlassesThe starting point for linking the shear modulus and the atomic connectivity analytically is the theoretical framework of nonaffine elastic response ...

A sparse random block matrix model suggested by the Hessian matrix used in the study of elastic vibrational modes of amorphous solids is presented and analyzed. By evaluating some moments, benchmarked against numerics, differences in the eigenvalue spectrum of this model in different limits of space dimension d, and for arbitrary values of the lattice coordination number Z, are shown and discussed. As a function of these two parameters (and their ratio Z/d), the most studied models in random matrix theory (Erdos-Renyi graphs, effective medium, and replicas) can be reproduced in the various limits of block dimensionality d. Remarkably, the Marchenko-Pastur spectral density (which is recovered by replica calculations for the Laplacian matrix) is reproduced exactly in the limit of infinite size of the blocks, or d→∞, which clarifies the physical meaning of space dimension in these models. We feel that the approximate results for d=3 provided by our method may have many potential applications in the future, from the vibrational spectrum of glasses and elastic networks to wave localization, disordered conductors, random resistor networks, and random walks.

The molecular machinery of life is largely created via self-organisation of individual molecules into functional assemblies. Minimal coarse-grained models, where a whole macromolecule is represented by a small number of particles, can be of great value in identifying the main driving forces behind self-organisation in cell biology. Such models can incorporate data from both molecular and continuum scales, and their results can be directly compared to experiments. Here we review the state of the art of models for studying the formation and biological function of macromolecular assemblies in cells. We outline the key ingredients of each model and their main findings. We illustrate the contribution of this class of simulations to identifying the physical mechanisms behind life and diseases, and discuss their future developments. IntroductionSelf-assembly of individual molecules into large-scale functional structures generates the molecular machinery of life [1]. Such processes underlie the formation of cell membranes, protein filaments and networks, and drive the formation of three-dimensional genome structures. Many of these assemblies, such as protein filaments and lattices, also function as efficient nanomachines that enable cells to sense, move, divide, and transport materials in and out of the cell [2]. To sustain life, the formation of macromolecular assemblies needs to *