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

Geometric Properties of the 2-D Peskin Problem

The 2-D Peskin problem describes a 1-D closed elastic string immersed and moving in a 2-D Stokes flow that is induced by its own elastic force. The geometric shape of the string and its internal stretching configuration evolve in a coupled way, and they combined govern the dynamics of the system. In this paper, we show that certain geometric quantities of the moving string satisfy extremum principles and decay estimates. As a result, we can prove that the 2-D Peskin problem admits a unique global solution when the initial data satisfies a medium-size geometric condition on the string shape, while no assumption on the size of stretching is needed

Boosting Commit Classification with Contrastive Learning

Commit Classification (CC) is an important task in software maintenance, which helps software developers classify code changes into different types according to their nature and purpose. It allows developers to understand better how their development efforts are progressing, identify areas where they need improvement, and make informed decisions about when and how to release new software versions. However, existing models need lots of manually labeled data for fine-tuning processes, and ignore sentence-level semantic information, which is often essential for discovering the difference between diverse commits. Therefore, it is still challenging to solve CC in fewshot scenario. To solve the above problems, we propose a contrastive learning-based commit classification framework. Firstly, we generate $K$ sentences and pseudo-labels according to the labels of the dataset, which aims to enhance the dataset. Secondly, we randomly group the augmented data $N$ times to compare their similarity with the positive $T_p^{|C|}$ and negative $T_n^{|C|}$ samples. We utilize individual pretrained sentence transformers (ST)s to efficiently obtain the sentence-level embeddings from different features respectively. Finally, we adopt the cosine similarity function to limit the distribution of vectors, similar vectors are more adjacent. The light fine-tuned model is then applied to the label prediction of incoming commits. Extensive experiments on two open available datasets demonstrate that our framework can solve the CC problem simply but effectively in fewshot scenarios, while achieving state-of-the-art(SOTA) performance and improving the adaptability of the model without requiring a large number of training samples for fine-tuning. The code, data, and trained models are available at https://github.com/AppleMax1992/CommitFit