14,679 research outputs found
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
- …