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

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

Intensification of liquid mixing and local turbulence using a fractal injector with staggered conformation

Two self-similar, tree-like injectors of the same fractal dimension are compared, demonstrating that other geometric parameters besides dimension play a crucial role in determining mixing performance. In one injector, when viewed from the top, the conformation of branches is eclipsed; in the other one, it is staggered. The flow field and the fractal injector induced mixing performance are investigated through computational fluid dynamics (CFD) simulations. The finite rate/eddy dissipation model (FR/EDM) is modified for fast liquid-phase reactions involving local micromixing. Under the same operating conditions, flow field uniformity and micromixing are improved when a staggered fractal injector is used. This is because of enhanced jet entrainment and local turbulence around the spatially distributed nozzles. Compared with a traditional double-ring sparger, a larger reaction region volume and lower micromixing time are obtained with fractal injectors. Local turbulence around the spatially distributed nozzles in fractal injectors improves reaction efficiency

Variable-Based Fault Localization via Enhanced Decision Tree

Fault localization, aiming at localizing the root cause of the bug under repair, has been a longstanding research topic. Although many approaches have been proposed in the last decades, most of the existing studies work at coarse-grained statement or method levels with very limited insights about how to repair the bug (granularity problem), but few studies target the finer-grained fault localization. In this paper, we target the granularity problem and propose a novel finer-grained variable-level fault localization technique. Specifically, we design a program-dependency-enhanced decision tree model to boost the identification of fault-relevant variables via discriminating failed and passed test cases based on the variable values. To evaluate the effectiveness of our approach, we have implemented it in a tool called VARDT and conducted an extensive study over the Defects4J benchmark. The results show that VARDT outperforms the state-of-the-art fault localization approaches with at least 247.8% improvements in terms of bugs located at Top-1, and the average improvements are 330.5%. Besides, to investigate whether our finer-grained fault localization result can further improve the effectiveness of downstream APR techniques, we have adapted VARDT to the application of patch filtering, where VARDT outperforms the state-of-the-art PATCH-SIM by filtering 26.0% more incorrect patches. The results demonstrate the effectiveness of our approach and it also provides a new way of thinking for improving automatic program repair techniques

Biomass derived oligosaccharides for potential leather tanning

The global demand for renewable and affordable feedstocks, combined with the worldwide targets for reducing carbon emissions, is the driving force behind a breakthrough in resource revolution and GreenTech innovations..