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

Statistical Physics of Design

A key challenge in complex design problems that permeate science and engineering is the need to balance design objectives for specific design elements or subsystems with global system objectives. Global objectives give rise to competing design pressures, whose effects can be difficult to trace in subsystem design. Here, using examples from arrangement problems, we show that the systems-level application of statistical physics principles, which we term "systems physics", provides a detailed characterization of subsystem design in terms of the concepts of stress and strain from materials physics. We analyze instances of routing problems in naval architectures, and show that systems physics provides a direct means of classifying architecture types, and quantifying trade-offs between subsystem- and overall performance. Our approach generalizes straightforwardly to design problems in a wide range of other disciplines that require concrete understanding of how the pressure to meet overall design objectives drives the outcomes for component subsystems.Comment: 9 RevTeX pages, 7 figure

Understanding shape entropy through local dense packing

Entropy drives the phase behavior of colloids ranging from dense suspensions of hard spheres or rods to dilute suspensions of hard spheres and depletants. Entropic ordering of anisotropic shapes into complex crystals, liquid crystals, and even quasicrystals has been demonstrated recently in computer simulations and experiments. The ordering of shapes appears to arise from the emergence of directional entropic forces (DEFs) that align neighboring particles, but these forces have been neither rigorously defined nor quantified in generic systems. Here, we show quantitatively that shape drives the phase behavior of systems of anisotropic particles upon crowding through DEFs. We define DEFs in generic systems, and compute them for several hard particle systems. We show that they are on the order of a few kT at the onset of ordering, placing DEFs on par with traditional depletion, van der Waals, and other intrinsic interactions. In experimental systems with these other interactions, we provide direct quantitative evidence that entropic effects of shape also contribute to self-assembly. We use DEFs to draw a distinction between self-assembly and packing behavior. We show that the mechanism that generates directional entropic forces is the maximization of entropy by optimizing local particle packing. We show that this mechanism occurs in a wide class of systems, and we treat, in a unified way, the entropy-driven phase behavior of arbitrary shapes incorporating the well-known works of Kirkwood, Onsager, and Asakura and Oosawa.Comment: v3: 9+10 revtex pages, 10 figures, minor changes, changed title to match journal versio

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