Local Berry curvature signatures in dichroic angle-resolved photoelectron spectroscopy from two-dimensional materials

Topologically nontrivial two-dimensional materials hold great promise for next-generation optoelectronic applications. However, measuring the Hall or spin-Hall response is often a challenge and practically limited to the ground state. An experimental technique for tracing the topological character in a differential fashion would provide useful insights. In this work, we show that circular dichroism angle-resolved photoelectron spectroscopy provides a powerful tool that can resolve the topological and quantum-geometrical character in momentum space. In particular, we investigate how to map out the signatures of the momentum-resolved Berry curvature in two-dimensional materials by exploiting its intimate connection to the orbital polarization. A spin-resolved detection of the photoelectrons allows one to extend the approach to spin-Chern insulators. The present proposal can be extended to address topological properties in materials out of equilibrium in a time-resolved fashion.

Michael Selwyn Longuet-Higgins. 8 December 1925—26 February 2016

Michael Longuet-Higgins was a geometer and applied mathematician who made notable contributions to geophysics and physical oceanography, particularly to the theory of oceanic microseism and to the dynamics of finite amplitude, sharp-crested wind-generated surface waves. The latter led to his pioneering studies on breaking waves. On a much larger scale, he showed how ocean waves produce currents around islands in the ocean. He considered wider aspects of the physics of waves, including wave-driven transport of sand along beaches, and the electrical effects of tidal streams. He also contributed to subjects of a geometrical character such as the growth of quasi-crystals, the assembly of protein sheaths in viruses, to chains of circle themes and to a wide variety of other topics. He was an extraordinary applied mathematician, using the simplest forms of mathematics to demonstrate and discover highly complex nonlinear phenomena. In particular, he often thought of problems involving water waves using his unique knowledge of geometry and then tested his theories by experiment. Along with Brooke Benjamin FRS, Sir James Lighthill FRS, Walter Munk FRS, John Miles and Andrei Monin, Michael Longuet-Higgins stands out as one of the towering figures of theoretical fluid dynamics in the twentieth century. His contributions will have a continuing influence on our attempts to understand better the processes that influence the oceans.

ELKO and Dirac spinors seen from torsion

In this paper, the recently-introduced ELKO and the well-known Dirac spinor fields will be compared. However, instead of comparing them under the point of view of their algebraic properties or their dynamical features, we will proceed by investigating the analogies and similarities in terms of their geometrical character viewed from the perspective of torsion. The paper will be concluded by sketching some consequences for the application to cosmology and particle physics.

Bifurcation in calculus of variations with constraints

We describe a variational problem on a domain of a plane under a constraint of geometrical character. We provide sufficient and necessary conditions for the existence of bifurcation points. The problem in 2 coordinate form, corresponds to a quasilinear elliptic boundary value problem. The problem provides a physical model for several applications referring to continuum media and membranes.

Study on Image Retrieval Method Based on Color and Location

In content-based image retrieval technology,color has been widely used as a kind of important image visual information.Compared with the geometrical character of image, color has certain stability and strong robustness to zoom, parallel move and rotate.Currently there are a lot of image retrieval technologies which own their own limitations.This paper puts forward an image retrieval method based on color and location,which is available for mobile platform.This paper adopts a histogram method in color characteristics and uses block color method to solve the color space distribution.Combined with the location-based service(LBS),this method can effectively improve the performance of image retrieval on the mobile platform.

INITIAL SHIP DESIGN USING A PEARSON CORRELATION COEFFICIENT AND ARTIFICIAL INTELLIGENCE TECHNIQUES

In this paper we analyzed correlation between geometrical character and resistance, and effective horse power by using Pearson correlation coefficient which is one of the data mining methods. Also we made input data to ship's geometrical character which has strong correlation with output data. We calculated effective horse power and resistance by using Neuro-Fuzzy system. To verify the calculation, 9 of 11 container ships' data were improved as data of Neuro-Fuzzy system and the others were improved as verification data. After analyzing rate of error between existing data and calculation data, we concluded that calculation data have sound agreement with existing data.

On boundary estimation

We consider the problem of estimating the boundary of a compact set S ⊂ ℝ d from a random sample of points taken from S. We use the Devroye-Wise estimator which is a union of balls centred at the sample points with a common radius (the smoothing parameter in this problem). A universal consistency result, with respect to the Hausdorff metric, is proved and convergence rates are also obtained under broad intuitive conditions of a geometrical character. In particular, a shape condition on S, which we call expandability, plays an important role in our results. The simple structure of the considered estimator presents some practical advantages (for example, the computational identification of the boundary is very easy) and makes this problem quite close to some basic issues in stochastic geometry.

On boundary estimation

We consider the problem of estimating the boundary of a compact set S ⊂ ℝd from a random sample of points taken from S. We use the Devroye-Wise estimator which is a union of balls centred at the sample points with a common radius (the smoothing parameter in this problem). A universal consistency result, with respect to the Hausdorff metric, is proved and convergence rates are also obtained under broad intuitive conditions of a geometrical character. In particular, a shape condition on S, which we call expandability, plays an important role in our results. The simple structure of the considered estimator presents some practical advantages (for example, the computational identification of the boundary is very easy) and makes this problem quite close to some basic issues in stochastic geometry.