General Lin-Maldacena solutions and PWMM Instantons from supergravity

We use the Lin-Maldacena prescription to demonstrate how to find the supergravity solutions dual to arbitrary vacua of the plane wave matrix model and maximally supersymmetric Yang-Mills theory on RxS^2, by solving the auxiliary electrostatics problem. We then apply the technique to study instantons at strong coupling in the matrix model.Comment: 15 pages, 4 figures. Minor correctio

Holographic Non-Fermi Liquids and the Luttinger Theorem

We show that the Luttinger theorem, a robust feature of Fermi liquids, can be violated in non-Fermi liquids. We compute non-Fermi liquid Green functions using duality to black holes and find that the volume of the Fermi surface depends exponentially on the scaling dimension, which is a measure of the coupling. This demonstrates that Luttinger's theorem does not extend to non-Fermi liquids. We comment on possible experimental signatures.Comment: 11 pages, 2 figure

Accelerating the solution of families of shifted linear systems with CUDA

We describe the GPU implementation of shifted or multimass iterative solvers for sparse linear systems of the sort encountered in lattice gauge theory. We provide a generic tool that can be used by those without GPU programming experience to accelerate the simulation of a wide array of theories. We stress genericity, which is important to allow the simulation of candidate theories for new physics at LHC, and for the study of various supersymmetric theories. We find significant speed ups, which we conservatively bound below at at least twelve times, that promise to put a variety of research questions within practical reach.Comment: v2: added referenc

Predicting colloidal crystals from shapes via inverse design and machine learning

A fundamental challenge in materials design is linking building block attributes to crystal structure. Addressing this challenge is particularly difficult for systems that exhibit emergent order, such as entropy-stabilized colloidal crystals. We combine recently developed techniques in inverse design with machine learning to construct a model that correctly classifies the crystals of more than ten thousand polyhedral shapes into 13 different structures with a predictive accuracy of 96% using only two geometric shape measures. With three measures, 98% accuracy is achieved. We test our model on previously reported colloidal crystal structures for 71 symmetric polyhedra and obtain 92% accuracy. Our findings (1) demonstrate that entropic colloidal crystals are controlled by surprisingly few parameters, (2) provide a quantitative model to predict these crystals solely from the geometry of their building blocks, and (3) suggest a prediction paradigm that easily generalizes to other self-assembled materials.Comment: 4 figure

Mapping Disorder in Entropically Ordered Crystals

Systems of hard shapes crystallize due to entropy. How is entropy distributed among translational and rotational microscopic contributions? We answer this question by decomposing thermal fluctuation of crystals of hard hexagons into collective modes, a generalization and quantification of the Onsager picture of hard rod liquid crystals. We show that at densities both near densest packing and near the solid-hexatic melting transition, solids of hard regular hexagons hold most of their entropy in translational degrees of freedom.Comment: 5 REVTeX pages, 3 figure

Robust Design in Systems Physics

Ensuring robust outcomes and designs is a crucial challenge in the engineering of modern integrated systems that are comprised of many heterogeneous subsystems. Coupling among heterogeneous subsystems leads to the complex response of design elements to changes in whole-system specifications. Here, we show that the response of design elements to whole-system specification changes can be characterized, as materials are, using strong/weak and brittle/ductile dichotomies. We find these dichotomies emerge from a mesoscale treatment of early stage design problems that we cast in terms of stress--strain relationships. We illustrate the use of this approach with examples from naval engineering, however our approach is immediately applicable to a broad range of problems in integrated systems design.Comment: 8 ReVTeX pages, 4 figure

Relevance of Packing to Colloidal Self-Assembly

Since the 1920s, packing arguments have been used to rationalize crystal structures in systems ranging from atomic mixtures to colloidal crystals. Packing arguments have recently been applied to complex nanoparticle structures, where they often, but not always, work. We examine when, if ever, packing is a causal mechanism in hard particle approximations of colloidal crystals. We investigate three crystal structures comprised of their ideal packing shapes. We show that, contrary to expectations, the ordering mechanism cannot be packing, even when the thermodynamically self-assembled structure is the same as that of the densest packing. We also show that the best particle shapes for hard particle colloidal crystals in the infinite pressure limit are imperfect versions of the ideal packing shape.Comment: 6 page

Little String Theory from a Double-Scaled Matrix Model

Following Lin and Maldacena, we find exact supergravity solutions dual to a class of vacua of the plane wave matrix model by solving an electrostatics problem. These are asymptotically near-horizon D0-brane solutions with a throat associated with NS5-brane degrees of freedom. We determine the precise limit required to decouple the asymptotic geometry and leave an infinite throat solution found earlier by Lin and Maldacena, dual to Little String Theory on S^5. By matching parameters with the gauge theory, we find that this corresponds to a double scaling limit of the plane wave matrix model in which N \to \infty and the 't Hooft coupling \lambda scales as \ln^4(N), which we speculate allows all terms in the genus expansion to contribute even at infinite N. Thus, the double-scaled matrix quantum mechanics gives a Lagrangian description of Little String Theory on S^5, or equivalently a ten-dimensional string theory with linear dilaton background.Comment: 31 pages, LaTeX, 3 figures. Correction of typos in the appendice

Crossover Behavior in the Packing and Assembly of Multivalent Lock-and-Key Colloids

Emergent behaviors occur in a vast array of systems across many scales, and are of fundamental physical importance because of the intrinsic difficulty in linking microscopic system properties to macroscopic behaviors. Here we study the emergent self-assembly behavior of model systems of recently synthesized families of concave dimpled hard spheres, or lock-and-key colloids. We find that as dimple size increases each family exhibits a crossover from a structure that does not reflect the particle symmetry to one that does and, surprisingly, the point at which this crossover occurs is approximately independent of the particle symmetry. Using a combination of numerical and analytic techniques we study systems at infinite and finite pressure, and find different common control parameters in each limit. Our results suggest there exists a set of experimentally realizable colloidal systems that exhibit complex emergent behaviors that can be traced to a common underlying microscopic control parameter.Comment: V2: 18 pages, 22 figures. Revised text with clarifications, corrections, and additional supporting dat

Shape Driven Solid--Solid Transitions in Colloids

Despite the fundamental importance of solid--solid transitions for metallurgy, ceramics, earth science, reconfigurable materials, and colloidal matter, the details of how materials transform between two solid structures are poorly understood. We introduce a class of {simple} model systems in which the direct control of local order, via colloid shape change, induces solid--solid phase transitions, and characterize how the transitions happen thermodynamically. We find that within a single shape family there are solid--solid transitions that can occur with or without a thermal activation barrier. Our results provide new means for the study of solid--solid phase transitions, and have implications for designing reconfigurable materials.Comment: 8 REVTeX pages, 7 figure