Abstract:
1. Introduction 2. Molecular dynamics simulation of amorphous carbon structures 3. Atomistic simulation of the bombardment process during the BEN phase of diamond CVD 4. Growth of amorphous silicon 5. One-dimensional hopping in disordered organic solids

Abstract:
We use machine learning methods on local structure to identify flow defects - or regions susceptible to rearrangement - in jammed and glassy systems. We apply this method successfully to two disparate systems: a two dimensional experimental realization of a granular pillar under compression, and a Lennard-Jones glass in both two and three dimensions above and below its glass transition temperature. We also identify characteristics of flow defects that differentiate them from the rest of the sample. Our results show it is possible to discern subtle structural features responsible for heterogeneous dynamics observed across a broad range of disordered materials.

Abstract:
Disordered solids exhibit unusual properties of their vibrational states and thermal conductivities. Recent progresses have well established the concept of "elastic heterogeneity", i.e., disordered materials show spatially inhomogeneous elastic moduli. In this study, by using molecular-dynamics simulations, we gradually introduce "disorder" into a numerical system to control its modulus heterogeneity. The system starts from a perfect crystalline state, progressively transforms into an increasingly disordered crystalline state, and finally undergoes structural amorphisation. We monitor independently the elastic heterogeneity, the vibrational states, and the thermal conductivity across this transition, and show that the heterogeneity in elastic moduli is well correlated to vibrational and thermal anomalies of the disordered system.

Abstract:
Shear transformations (i.e., localised rearrangements of particles resulting in the shear deformation of a small region of the sample) are the building blocks of mesoscale models for the flow of disordered solids. In order to compute the time-dependent response of the solid material to such a shear transformation, with a proper account of elastic heterogeneity and shear wave propagation, we propose and implement a very simple Finite-Element (FE) -based method. Molecular Dynamics (MD) simulations of a binary Lennard-Jones glass are used as a benchmark for comparison, and information about the microscopic viscosity and the local elastic constants is directly extracted from the MD system and used as input in FE. We find very good agreement between FE and MD regarding the temporal evolution of the disorder-averaged displacement field induced by a shear transformation, which turns out to coincide with the response of a uniform elastic medium. However, fluctuations are relatively large, and their magnitude is satisfactorily captured by the FE simulations of an elastically heterogeneous system. Besides, accounting for elastic anisotropy on the mesoscale is not crucial in this respect. The proposed method thus paves the way for models of the rheology of amorphous solids which are both computationally efficient and realistic, in that structural disorder and inertial effects are accounted for.

Abstract:
Due to the peculiar non-fermi liquid of one dimensional systems, disorder has particularly strong effects. We show that such systems belong to the more general class of disordered quantum solids. We discuss the physics of such disordered interacting systems and the methods that allows to treat them. In addition to, by now standard renormalization group methods, We explain how a simple variational approach allows to treat these problems even in case when the RG fails. We discuss various physical realizations of such disordered quantum solids both in one and higher dimensions (Wigner crystal, Bose glass). We investigate in details the interesting example of a disordered Mott insulator and argue that intermediate disorder can lead to a novel phase, the Mott glass, intermediate between a Mott and and Anderson insulator.

Abstract:
Spatial heterogeneity in the elastic properties of soft random solids is investigated via a two-pronged approach. First, a nonlocal phenomenological model for the elastic free energy is examined. This features a quenched random kernel, which induces randomness in the residual stress and Lame coefficients. Second, a semi-microscopic model network is explored using replica statistical mechanics. The Goldstone fluctuations of the semi-microscopic model are shown to reproduce the phenomenological model, and via this correspondence the statistical properties of the residual stress and Lame coefficients are inferred. Correlations involving the residual stress are found to be long-ranged and governed by a universal parameter that also gives the mean shear modulus.

Abstract:
The low temperature universal properties in disordered and amorphous solids are considered. We introduce a model that includes two types of two level systems (TLSs), which, based on their local symmetry, interact weakly or strongly with the phonon field. This accounts well for the experimental results, and addresses some long-standing questions: the nature of the TLSs; the smallness and universality of the phonon attenuation, and the energy scale of $3$K below which universality is observed. Our model describes disordered lattices; we also discuss its application to amorphous solids.

Abstract:
We propose a simple route to evaluate the static structure, in terms of average coordination, of completely disordered solids with spherical constituents, from ca. 55% volume fraction up to random close packing, in the absence of structural heterogeneities. Based on the current understanding, according to which the structure-determining interaction in amorphous solids is the hard-core repulsion while weaker, longer-range interactions are mere perturbations, the model yields the average coordination in the solid as a result of a hyperquenching process where the instantaneous structure of the precursor liquid snapshot is distorted to the same degree required to quench the hard-sphere liquid into the isostatic jammed state at 64% volume fraction. The characteristic length of distortion turns out to be about 3% of the particle diameter. Extrapolating to lower volume fractions, this is thus the quenching route leading to the most spatially homogeneous states. Thus the model can be usefully employed to quantitatively assess the degree of structural inhomogeneity in amorphous solids. When spatial inhomogeneity is small, as for very dense systems, the model can be used to evaluate coordination-dependent macroscopic properties (e.g. the elastic moduli) as shown in parallel works.

Abstract:
Using finite difference time domain and band structure computer simulations, we show that it is possible to construct optical cavities and waveguide architectures in hyperuniform disordered photonic solids that are unattainable in photonic crystals. The cavity modes can be classified according to the symmetry (monopole, dipole, quadrupole,etc.) of the confined electromagnetic wave pattern. Owing to the isotropy of the band gaps characteristic of hyperuniform disordered solids, high-quality waveguides with freeform geometries (e.g., arbitrary bending angles) can be constructed that have no analogue in periodic or quasiperiodic solids. These capabilities have implications for many photonic applications.

Abstract:
The fact that a disordered material is not constrained in its properties in the same way as a crystal presents significant and yet largely untapped potential for novel material design. However, unlike their crystalline counterparts, disordered solids are not well understood. 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 an idealized system of frictionless athermal soft spheres that, when compressed, undergoes 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 necessary for 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 "contact nonlinearities." We then investigate the critical nature of the transition, focusing on diverging length scales and finite-size effects. Next, we argue that jamming plays the same role for disordered solids as the perfect crystal plays for crystalline solids. Not only can it be considered an idealized starting point for understanding disordered materials, but it can even influence systems that have a relatively high amount of crystalline order. The behavior of solids can thus be thought of as existing on a spectrum, with the perfect crystal and the jamming transition at opposing ends. Finally, we introduce a new principle 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 and provides a great deal of flexibility in designing materials with unique, textured and tunable properties.