Unearthing the Anticrystal: Criticality in the Linear Response of Disordered Solids

The fact that a disordered material is not constrained in its properties in the same way as a crystalline one presents significant and yet largely untapped potential for novel material design. However, unlike their crystalline counterparts, disordered solids are not well understood. Though currently the focus of intense research, one of the primary obstacles is the lack of a theoretical framework for thinking about disorder and its relation to mechanical properties. To this end, we study a highly idealized system composed of frictionless soft spheres at zero temperature that, when compressed, undergos a jamming phase transition with diverging length scales and clean power-law signatures. This critical point is the cornerstone of a much larger ``jamming scenario that has the potential to provide the essential theoretical foundation that is sorely needed to develop a unified understanding of the mechanics of disordered solids. We begin by showing that jammed sphere packings have a valid linear regime despite the presence of a new class of ``contact nonlinearities, demonstrating that the leading order behavior of such solids can be ascertained by linear response. We then investigate the critical nature of the jamming transition, focusing on two diverging length scales and the importance of finite-size effects. Next, we argue that this jamming transition plays the same role for disordered solids as the idealized perfect crystal plays for crystalline solids. Not only can it be considered an idealized starting point for understanding the properties of disordered materials, but it can even influence systems that have a relatively high amount of crystalline order. As a result, the behavior of solids can be thought of as existing on a spectrum, with the perfect crystal at one end and the jamming transition at the other. Finally, we introduce a new principle for disordered solids wherein the contribution of an individual bond to one global property is independent of its contribution to another. This principle allows the different global responses of a disordered system to be manipulated independently of one another and provides a great deal of flexibility in designing materials with unique, textured and tunable properties

Designing self-assembling kinetics with differentiable statistical physics models

The inverse problem of designing component interactions to target emergent structure is fundamental to numerous applications in biotechnology, materials science, and statistical physics. Equally important is the inverse problem of designing emergent kinetics, but this has received considerably less attention. Using recent advances in automatic differentiation, we show how kinetic pathways can be precisely designed by directly differentiating through statistical physics models, namely free energy calculations and molecular dynamics simulations. We consider two systems that are crucial to our understanding of structural self-assembly: bulk crystallization and small nanoclusters. In each case, we are able to assemble precise dynamical features. Using gradient information, we manipulate interactions among constituent particles to tune the rate at which these systems yield specific structures of interest. Moreover, we use this approach to learn nontrivial features about the high-dimensional design space, allowing us to accurately predict when multiple kinetic features can be simultaneously and independently controlled. These results provide a concrete and generalizable foundation for studying nonstructural self-assembly, including kinetic properties as well as other complex emergent properties, in a vast array of systems

Jurisprudences of jurisdiction: matters of public authority

This essay examines a number of jurisdictional engagements that point to difficulties in joining or separating relations between public authority, jurisprudences of jurisdiction and the writing of jurisprudence

A computational toolbox for the assembly yield of complex and heterogeneous structures

The self-assembly of complex structures from a set of non-identical building blocks is a hallmark of soft matter and biological systems, including protein complexes, colloidal clusters, and DNA-based assemblies. Predicting the dependence of the equilibrium assembly yield on the concentrations and interaction energies of building blocks is highly challenging, owing to the difficulty of computing the entropic contributions to the free energy of the many structures that compete with the ground state configuration. While these calculations yield well known results for spherically symmetric building blocks, they do not hold when the building blocks have internal rotational degrees of freedom. Here we present an approach for solving this problem that works with arbitrary building blocks, including proteins with known structure and complex colloidal building blocks. Our algorithm combines classical statistical mechanics with recently developed computational tools for automatic differentiation. Automatic differentiation allows efficient evaluation of equilibrium averages over configurations that would otherwise be intractable. We demonstrate the validity of our framework by comparison to molecular dynamics simulations of simple examples, and apply it to calculate the yield curves for known protein complexes and for the assembly of colloidal shells