Biomimetic spatial and temporal (4D) design and fabrication

We imagine the built environment of the future as a ‘bio-hybrid machine for living in’ that will sense and react to activities within the space in order to provide experiences and services that will elevate quality of life while coexisting seamlessly with humans and the natural environment. The study of Hierarchical design in biological materials has the potential to alter the way designers/ engineers/ crafts-men of the future engage with materials in order to realise such visions. We are ex-ploring this design approach using digital manufacturing technologies such as jac-quard weaving and 3D printing

Properties of the Z(3) Interface in (2+1)-D SU(3) Gauge Theory

A study is made of some properties of this interface in the SU(3) pure gauge theory in 2+1 dimensions. At high temperatures, the interface tension is measured and shows agreement with the perturbative prediction. Near the critical temperature, the behaviour of the interface is examined, and its fluctuations compared to a scalar field theory model.Comment: 4 pages with 4 figures as one uuencoded, gzipped postscript file; presented at Lattice '9

High-Temperature Properties of the Z(3) Interface in (2+1)-D SU(3) Gauge Theory

We study the high-temperature properties of the Z(3) interface which forms between the various ordered phases of pure SU(3) gauge theory above a critical temperature. On a (2+1)-D Euclidean lattice, we perform an accurate measurement of the interface tension, which shows good agreement with the prediction of perturbation theory. We also examine the behaviour of the Debye electric screening mass, and compare this with theoretical predictions.Comment: 10 pages, 3 figures, uuencoded gzipped tar fil

Critical properties of the Z(3) interface in (2+1)-D SU(3) gauge theory

We study the interface between two different Z(3) vacua in the deconfined phase of SU(3) pure gauge theory in 2+1 dimensions just above the critical temperature. In simulations of the Euclidean lattice gauge theory formulation of the system we measure the fluctuations of the interface as the critical temperature is approached and as a function of system size. We show that the intrinsic width of the interface remains small even very close to the critical temperature. Some dynamical exponents which govern the interaction of the interface with our Monte Carlo algorithm are also estimated. We conclude that the Z(3) interface has properties broadly similar to those in many other comparable statistical mechanical systems.Comment: 26 pages, LaTex with 16 postscript figure

Orbital quantization in the high magnetic field state of a charge-density-wave system

A superposition of the Pauli and orbital coupling of a high magnetic field to charge carriers in a charge-density-wave (CDW) system is proposed to give rise to transitions between subphases with quantized values of the CDW wavevector. By contrast to the purely orbital field-induced density-wave effects which require a strongly imperfect nesting of the Fermi surface, the new transitions can occur even if the Fermi surface is well nested at zero field. We suggest that such transitions are observed in the organic metal $\alpha$-(BEDT-TTF)$_2$KHg(SCN)$_4$ under a strongly tilted magnetic field.Comment: 14 pages including 4 figure

Cyclotron effective masses in layered metals

Many layered metals such as quasi-two-dimensional organic molecular crystals show properties consistent with a Fermi liquid description at low temperatures. The effective masses extracted from the temperature dependence of the magnetic oscillations observed in these materials are in the range, m^*_c/m_e \sim 1-7, suggesting that these systems are strongly correlated. However, the ratio m^*_c/m_e contains both the renormalization due to the electron-electron interaction and the periodic potential of the lattice. We show that for any quasi-two-dimensional band structure, the cyclotron mass is proportional to the density of states at the Fermi energy. Due to Luttinger's theorem, this result is also valid in the presence of interactions. We then evaluate m_c for several model band structures for the \beta, \kappa, and \theta families of (BEDT-TTF)_2X, where BEDT-TTF is bis-(ethylenedithia-tetrathiafulvalene) and X is an anion. We find that for \kappa-(BEDT-TTF)_2X, the cyclotron mass of the \beta-orbit, m^{*\beta}_c, is close to 2 m^{*\alpha}_c, where m^{*\alpha}_c is the effective mass of the \alpha- orbit. This result is fairly insensitive to the band structure details. For a wide range of materials we compare values of the cyclotron mass deduced from band structure calculations to values deduced from measurements of magnetic oscillations and the specific heat coefficient.Comment: 12 pages, 3 eps figure

Templates for Convex Cone Problems with Applications to Sparse Signal Recovery

This paper develops a general framework for solving a variety of convex cone problems that frequently arise in signal processing, machine learning, statistics, and other fields. The approach works as follows: first, determine a conic formulation of the problem; second, determine its dual; third, apply smoothing; and fourth, solve using an optimal first-order method. A merit of this approach is its flexibility: for example, all compressed sensing problems can be solved via this approach. These include models with objective functionals such as the total-variation norm, ||Wx||_1 where W is arbitrary, or a combination thereof. In addition, the paper also introduces a number of technical contributions such as a novel continuation scheme, a novel approach for controlling the step size, and some new results showing that the smooth and unsmoothed problems are sometimes formally equivalent. Combined with our framework, these lead to novel, stable and computationally efficient algorithms. For instance, our general implementation is competitive with state-of-the-art methods for solving intensively studied problems such as the LASSO. Further, numerical experiments show that one can solve the Dantzig selector problem, for which no efficient large-scale solvers exist, in a few hundred iterations. Finally, the paper is accompanied with a software release. This software is not a single, monolithic solver; rather, it is a suite of programs and routines designed to serve as building blocks for constructing complete algorithms.Comment: The TFOCS software is available at http://tfocs.stanford.edu This version has updated reference

Macromolecular theory of solvation and structure in mixtures of colloids and polymers

The structural and thermodynamic properties of mixtures of colloidal spheres and non-adsorbing polymer chains are studied within a novel general two-component macromolecular liquid state approach applicable for all size asymmetry ratios. The dilute limits, when one of the components is at infinite dilution but the other concentrated, are presented and compared to field theory and models which replace polymer coils with spheres. Whereas the derived analytical results compare well, qualitatively and quantitatively, with mean-field scaling laws where available, important differences from ``effective sphere'' approaches are found for large polymer sizes or semi-dilute concentrations.Comment: 23 pages, 10 figure