Triggering one dimensional phase transition with defects at the graphene zigzag edge

One well-known argument about one dimensional(1D) system is that 1D phase transition at finite temperature cannot exist, despite this concept depends on conditions such as range of interaction, external fields and periodicity. Therefore 1D systems usually have random fluctuations with intrinsic domain walls arising which naturally bring disorder during transition. Herein we introduce a real 1D system in which artificially created defects can induce a well-defined 1D phase transition. The dynamics of structural reconstructions at graphene zigzag edges are examined by in situ aberration corrected transmission electron microscopy (ACTEM). Combined with an in-depth analysis by ab-initio simulations and quantum chemical molecular dynamics (QM/MD), the complete defect induced 1D phase transition dynamics at graphene zigzag edge is clearly demonstrated and understood on the atomic scale. Further, following this phase transition scheme, graphene nanoribbons (GNR) with different edge symmetries can be fabricated, and according to our electronic structure and quantum transport calculations, a metal-insulator-semiconductor transition for ultrathin GNRs is proposed.Comment: 6 pages, 4 figure

A fast numerical solver for local barycentric coordinates

The local barycentric coordinates (LBC), proposed in Zhang et al (2014), demonstrate good locality and can be used for local control on function value interpolation and shape deformation. However, it has no closed- form expression and must be computed by solving an optimization problem, which can be time-consuming especially for high-resolution models. In this paper, we propose a new technique to compute LBC efficiently. The new solver is developed based on two key insights. First, we prove that the non-negativity constraints in the original LBC formulation is not necessary, and can be removed without affecting the solution of the optimization problem. Furthermore, the removal of this constraint allows us to reformulate the computation of LBC as a convex constrained optimization for its gradients, followed by a fast integration to recover the coordinate values. The reformulated gradient optimization problem can be solved using ADMM, where each step is trivially parallelizable and does not involve global linear system solving, making it much more scalable and efficient than the original LBC solver. Numerical experiments verify the effectiveness of our technique on a large variety of models

Les Pensées Dialectiques en Politique de Mencius

Le présent article discutera des principales réflexions dialectiques de Mencius en politique, qui pourraient influencer les politiciens de son époque, mais aussi la postérité. Les idées qu’il avait avancées telles que la corrrélation entre la politique et l’économie, la relation entre les actes d’un souverain et ceux de son peuple ou de ses ministres exercent encore une influence profonde sur les dirigeants d’un état d’aujourd’hui

Les pensées Dialectiques en Politique de Confucius

Les pensées dialectiques sur les problèmes politiques, ou les éléments de ces pensées un peu dispersés, nous l’avons montré, existent réellement dans la doctrine politique de  Confucius. Nous avons donc extrait, de ses nombreux entretiens, les principales réflexions dialectiques en politique de ce grand maître, qui avait traité des relations entre les phénomènes politiques apparemment opposés comme la clémence et l’intransigeance et ceux qui n’étaient pas liés en apparence tels que le perfectionnement de soi et l’administration des autres. Ces réflexions témoignent, par un raisonnement dialectique, de la haute sagesse de Confucius sur les problèmes politiques.

Nonmonotone globalization for Anderson acceleration via adaptive regularization

Anderson acceleration (AA) is a popular method for accelerating fixed-point iterations, but may suffer from instability and stagnation. We propose a globalization method for AA to improve stability and achieve unified global and local convergence. Unlike existing AA globalization approaches that rely on safeguarding operations and might hinder fast local convergence, we adopt a nonmonotone trust-region framework and introduce an adaptive quadratic regularization together with a tailored acceptance mechanism. We prove global convergence and show that our algorithm attains the same local convergence as AA under appropriate assumptions. The effectiveness of our method is demonstrated in several numerical experiments