Stability of Soft Quasicrystals in a Coupled-Mode Swift-Hohenberg Model for Three-Component Systems

In this article, we discuss the stability of soft quasicrystalline phases in a coupled-mode Swift-Hohenberg model for three-component systems, where the characteristic length scales are governed by the positive-definite gradient terms. Classic two-mode approximation method and direct numerical minimization are applied to the model. In the latter approach, we apply the projection method to deal with the potentially quasiperiodic ground states. A variable cell method of optimizing the shape and size of higher-dimensional periodic cell is developed to minimize the free energy with respect to the order parameters. Based on the developed numerical methods, we rediscover decagonal and dodecagonal quasicrystalline phases, and find diverse periodic phases and complex modulated phases. Furthermore, phase diagrams are obtained in various phase spaces by comparing the free energies of different candidate structures. It does show not only the important roles of system parameters, but also the effect of optimizing computational domain. In particular, the optimization of computational cell allows us to capture the ground states and phase behavior with higher fidelity. We also make some discussions on our results and show the potential of applying our numerical methods to a larger class of mean-field free energy functionals.Comment: 26 pages, 13 figures; accepted by Communications in Computational Physic

Detection and visualisation of climate trends in China

Research on climate trends in China has been carried out within a co-operation of the Justus Liebig Universities Department of Geography and Zentrum für internationale Entwicklungs- und Umweltforschung (ZEU) and the Nanjing Institute of Geography and Limnology (CAS). First results were introduced by BECKER et al. 2003 a, b who worked on precipitation trend analyses in the Yangtze River Catchment. In the meanwhile, the National Climatic Centre of China (NCCC) kindly provided climatic data in China within the framework of this co-operation. Financial support from the CAS Key project KZCX3-SW-331 and the NSFC project 40271112 enabled the data acquisition. The analysis of both, precipitation and temperature data for the whole of China from 1951- 2002 can be carried out now. A shorter version of the precipitation trend observation will soon be published in Theoretical and Applied Climatology (GEMMER et al. 2003, accepted for publication/in print). Results of the temperature trend research have not been published yet. They will be submitted to an international Journal when further statistical approaches with regard to daily temperature data are processed. The discussion paper in hand will make the actual results accessible for further research groups in Germany. --

Feature Augmentation via Nonparametrics and Selection (FANS) in High Dimensional Classification

We propose a high dimensional classification method that involves nonparametric feature augmentation. Knowing that marginal density ratios are the most powerful univariate classifiers, we use the ratio estimates to transform the original feature measurements. Subsequently, penalized logistic regression is invoked, taking as input the newly transformed or augmented features. This procedure trains models equipped with local complexity and global simplicity, thereby avoiding the curse of dimensionality while creating a flexible nonlinear decision boundary. The resulting method is called Feature Augmentation via Nonparametrics and Selection (FANS). We motivate FANS by generalizing the Naive Bayes model, writing the log ratio of joint densities as a linear combination of those of marginal densities. It is related to generalized additive models, but has better interpretability and computability. Risk bounds are developed for FANS. In numerical analysis, FANS is compared with competing methods, so as to provide a guideline on its best application domain. Real data analysis demonstrates that FANS performs very competitively on benchmark email spam and gene expression data sets. Moreover, FANS is implemented by an extremely fast algorithm through parallel computing.Comment: 30 pages, 2 figure

Stability of Two-Dimensional Soft Quasicrystals

The relative stability of two-dimensional soft quasicrystals is examined using a recently developed projection method which provides a unified numerical framework to compute the free energy of periodic crystal and quasicrystals. Accurate free energies of numerous ordered phases, including dodecagonal, decagonal and octagonal quasicrystals, are obtained for a simple model, i.e. the Lifshitz-Petrich free energy functional, of soft quasicrystals with two length-scales. The availability of the free energy allows us to construct phase diagrams of the system, demonstrating that, for the Lifshitz-Petrich model, the dodecagonal and decagonal quasicrystals can become stable phases, whereas the octagonal quasicrystal stays as a metastable phase.Comment: 11 pages, 7 figure

Investigation of a scale-up manufacturing approach for nanostructures by using a nanoscale multi-tip diamond tool

Increasing interest in commercializing functional nanostructured devices heightens the need for cost-effective manufacturing approaches for nanostructures. This paper presents an investigation of a scale-up manufacturing approach for nanostructures through diamond turning using a nanoscale multi-tip diamond tool (four tip tool with tip width of 150 nm) fabricated by focused ion beam (FIB). The manufacturing capacity of this new technique is evaluated through a series of cutting trials on copper substrates under different cutting conditions (depth of cut 100–500 nm, spindle speed 12–120 rpm). The machined surface roughness and nanostructure patterns are measured by using a white light interferometer and a scanning electron microscope, respectively. Results show that the form accuracy and integrity of the machined nanostructures were degraded with the increase of the depth of cut and the cutting speed. The burr and the structure damage are two major machining defects. High precision nano-grooves (form error of bottom width < 6.7 %) was achieved when a small depth of cut of 100 nm was used (spindle speed = 12 rpm). Initial tool wear was found at both the clearance cutting edge and the side edges of tool tips after a cutting distance of 2.5 km. Moreover, the nanometric cutting process was emulated by molecular dynamic (MD) simulations. The research findings obtained from MD simulation reveal the underlying mechanism for machining defects and the initialization of tool wear observed in experiments