Topological Insulators by Topology Optimization

An acoustic topological insulator (TI) is synthesized using topology optimization, a free material inverse design method. The TI appears spontaneously from the optimization process without imposing requirements on the existence of pseudo spin-1/2 states at the TI interface edge, or the Chern number of the topological phases. The resulting TI is passive; consisting of acoustically hard members placed in an air background and has an operational bandwidth of $\approx$12.5\% showing high transmission. Further analysis demonstrates confinement of more than 99\% of the total field intensity in the TI within at most six lattice constants from the TI interface. The proposed design hereby outperforms a reference from recent literature regarding energy transmission, field confinement and operational bandwidth.Comment: 6 pages, 5 figure

Designing Photonic Topological Insulators with Quantum-Spin-Hall Edge States using Topology Optimization

Designing photonic topological insulators is highly non-trivial because it requires inversion of band symmetries around the band gap, which was so far done using intuition combined with meticulous trial and error. Here we take a completely different approach: we consider the design of photonic topological insulators as an inverse design problem and use topology optimization to maximize the transmission through an edge mode with a sharp bend. Two design domains composed of two different, but initially identical, C$_\text{6v}$-symmetric unit cells define the geometrical design problem. Remarkably, the optimization results in a photonic topological insulator reminiscent of the shrink-and-grow approach to quantum-spin-Hall photonic topological insulators but with notable differences in the topology of the crystal as well as qualitatively different band structures and with significantly improved performance as gauged by the band-gap sizes, which are at least 50 \% larger than previous designs. Furthermore, we find a directional beta factor exceeding 99 \%, and very low losses for sharp bends. Our approach allows for the introduction of fabrication limitations by design and opens an avenue towards designing PTIs with hitherto unexplored symmetry constraints.Comment: 7 pages, 5 figure

Inverse design in photonics by topology optimization: tutorial

Topology optimization methods for inverse design of nano-photonic systems have recently become extremely popular and are presented in various forms and under various names. Approaches comprise gradient and non-gradient based algorithms combined with more or less systematic ways to improve convergence, discreteness of solutions and satisfaction of manufacturing constraints. We here provide a tutorial for the systematic and efficient design of nano-photonic structures by Topology Optimization (TopOpt). The implementation is based on the advanced and systematic approaches developed in TopOpt for structural optimization during the last three decades. The tutorial presents a step-by-step guide for deriving the continuous constrained optimization problem forming the foundation of the Topology Optimization method, using a cylindrical metalens design problem as an example. It demonstrates the effect and necessity of applying a number of auxiliary tools in the design process in order to ensure good numerical modelling practice and to achieve physically realisable designs. Application examples also include an optical demultiplexer.Comment: 8 figures, 19 page

A Century of Psychology as Science

This reissued edition (originally published by McGraw-Hill in 1985) of A Century of Psychology as Science comprehensively assesses the accomplishments, status, and prospects of psychology at the end of its first century as a science, while offering a new postscript. The forty-three contributors are among psychology\u27s foremost authorities. Among the fields addressed are sensory processes and perception, learning, motivation, emotion, cognition, development, personality, and social psychology.https://scholarship.richmond.edu/bookshelf/1168/thumbnail.jp

Maximizing the quality factor to mode volume ratio for ultra-small photonic crystal cavities

Small manufacturing-tolerant photonic crystal cavities are systematically designed using topology optimization to enhance the ratio between quality factor and mode volume, Q/V. For relaxed manufacturing tolerance, a cavity with bow-tie shape is obtained which confines light beyond the diffraction limit into a deep-subwavelength volume. Imposition of a small manufacturing tolerance still results in efficient designs, however, with diffraction-limited confinement. Inspired by numerical results, an elliptic ring grating cavity concept is extracted via geometric fitting. Numerical evaluations demonstrate that for small sizes, topology-optimized cavities enhance the Q/V-ratio by up to two orders of magnitude relative to standard L1 cavities and more than one order of magnitude relative to shape-optimized L1 cavities. An increase in cavity size can enhance the Q/V-ratio by an increase of the Q-factor without significant increase of V. Comparison between optimized and reference cavities illustrates that significant reduction of V requires big topological changes in the cavity

Phase separation in the vicinity of "quantum critical" doping concentration: implications for high temperature superconductors

A general quantitative measure of the tendency towards phase separation is introduced for systems exhibiting phase transitions or crossovers controlled by charge carrier concentration. This measure is devised for the situations when the quantitative knowledge of various contributions to free energy is incomplete, and is applied to evaluate the chances of electronic phase separation associated with the onset of antiferromagnetic correlations in high-temperature cuprate superconductors. The experimental phenomenology of lanthanum- and yittrium-based cuprates was used as input to this analysis. It is also pointed out that Coulomb repulsion between charge carriers separated by the distances of 1-3 lattice periods strengthens the tendency towards phase separation by accelerating the decay of antiferromagnetic correlations with doping. Overall, the present analysis indicates that cuprates are realistically close to the threshold of phase separation -- nanoscale limited or even macroscopic with charge density varying between adjacent crystal planes

Effective approach to the Nagaoka regime of the two dimensional t-J model

We argue that the t-J model and the recently proposed Ising version of this model give the same physical picture of the Nagaoka regime for J/t << 1. In particular, both models are shown to give compatible results for a single Nagaoka polaron as well as for a Nagaoka bipolaron. When compared to the standard t-J or t-Jz models, the Ising version allows for a numerical analysis on much larger clusters by means of classical Monte Carlo simulations. Taking the advantage of this fact, we study the low doping regime of t-J model for J/t << 1 and show that the ground state exhibits phase separation into hole-rich ferromagnetic and hole-depleted antiferromagnetic regions. This picture holds true up to a threshold concentration of holes, \delta < \delta_t ~ 0.44 \sqrt{J/t}. Analytical calculations show that \delta_t=\sqrt{J/2\pi t}.Comment: 10 pages, 10 figures, revte

The Stokes-Einstein Relation in Supercooled Aqueous Solutions of Glycerol

The diffusion of glycerol molecules decreases with decreasing temperature as its viscosity increases in a manner simply described by the Stokes-Einstein(SE) relation. Approaching the glass transition, this relation breaks down as it does with a number of other pure liquid glass formers. We have measured the diffusion coefficient for binary mixtures of glycerol and water and find that the Stokes-Einstein relation is restored with increasing water concentration. Our comparison with theory suggests that addition of water postpones the formation of frustration domainsComment: 4 Pages and 3 Figure

Force and EMG Comparison between a weight-bearing clinical assessment of hip strength assessment and non-weightbearing tasks

Purpose: Altered hip strength is a risk factor for lower extremity injury but its relationship to biomechanical dysfunction is debated. Hip strength assessment methods are criticized for using unidirectional, non-weight-bearing positions which may not be representative of athletic activity and may affect comparison to biomechanical analysis of athletic tasks. A weight-bearing task may better represent hip muscle function during these movements. The aim of this study was to identify EMG and force differences for a clinical weight-bearing method of hip strength (the squat-hold) to traditional non-weight-bearing maximal voluntary isometric contractions (MVICs) for hip abduction, extension, and external rotation. Methods: Twenty-nine healthy volunteers (23 female, 6 male; 23.3±5.8 years) performed the squat-hold, sidelying abduction, prone extension, and seated hip external rotation MVICs. The squat-hold was performed by exerting a bilateral, maximal force against a rigid strap encircling both knees in a semi-squatted position. Surface electromyography (EMG) recorded peak activation of the gluteus medius (GMed), gluteus maximus (Gmax), and tensor fascia lata (TFL) and a handheld dynamometer simultaneously measured force during all tasks. Peak activation was compared between the squat-hold and each MVIC using paired t-tests. Force was compared across tasks using a one-way ANOVA. Results: Greater force was observed during the squat-hold than the external rotation MVIC, but abduction and extension MVICs yielded greater force than the squat-hold. GMax activation was higher during the squat-hold than the external rotation task. TFL activation was higher during the abduction MVIC than the squat-hold but GMed activation was similar across tasks. Peak GMax activation was similar between the extension MVIC and squat-hold. Conclusions: Squat-hold force may have been reduced due to altered gluteal moment arms, which affected the length-tension relationship. Clinicians should consider the squat-hold as an alternative assessment of external rotation force, but should continue to assess abduction and extension force with MVICs. Researchers should examine positions optimizing length-tension relationships to better relate motor function and movement patterns