Dualities and non-Abelian mechanics

Dualities are mathematical mappings that reveal unexpected links between apparently unrelated systems or quantities in virtually every branch of physics. Systems that are mapped onto themselves by a duality transformation are called self-dual and they often exhibit remarkable properties, as exemplified by an Ising magnet at the critical point. In this Letter, we unveil the role of dualities in mechanics by considering a family of so-called twisted Kagome lattices. These are reconfigurable structures that can change shape thanks to a collapse mechanism easily illustrated using LEGO. Surprisingly, pairs of distinct configurations along the mechanism exhibit the same spectrum of vibrational modes. We show that this puzzling property arises from the existence of a duality transformation between pairs of configurations on either side of a mechanical critical point. This critical point corresponds to a self-dual structure whose vibrational spectrum is two-fold degenerate over the entire Brillouin zone. The two-fold degeneracy originates from a general version of Kramers theorem that applies to classical waves in addition to quantum systems with fermionic time-reversal invariance. We show that the vibrational modes of the self-dual mechanical systems exhibit non-Abelian geometric phases that affect the semi-classical propagation of wave packets. Our results apply to linear systems beyond mechanics and illustrate how dualities can be harnessed to design metamaterials with anomalous symmetries and non-commuting responses.Comment: See http://home.uchicago.edu/~vitelli/videos.html for Supplementary Movi

Kink-antikink asymmetry and impurity interactions in topological mechanical chains

We study the dynamical response of a diatomic periodic chain of rotors coupled by springs, whose unit cell breaks spatial inversion symmetry. In the continuum description, we derive a nonlinear field theory which admits topological kinks and antikinks as nonlinear excitations but where a topological boundary term breaks the symmetry between the two and energetically favors the kink configuration. Using a cobweb plot, we develop a fixed-point analysis for the kink motion and demonstrate that kinks propagate without the Peierls-Nabarro potential energy barrier typically associated with lattice models. Using continuum elasticity theory, we trace the absence of the Peierls-Nabarro barrier for the kink motion to the topological boundary term which ensures that only the kink configuration, and not the antikink, costs zero potential energy. Further, we study the eigenmodes around the kink and antikink configurations using a tangent stiffness matrix approach appropriate for pre-stressed structures to explicitly show how the usual energy degeneracy between the two no longer holds. We show how the kink-antikink asymmetry also manifests in the way these nonlinear excitations interact with impurities introduced in the chain as disorder in the spring stiffness. Finally, we discuss the effect of impurities in the (bond) spring length and build prototypes based on simple linkages that verify our predictions.Comment: 20 pages, 21 figure

Computational Geometry Teaching Tool

When students are taking Computational Geometry course which covers many geometry algorithms, most of them are difficult to follow because these algorithms are very abstract even if authors draw pictures to illustrate. In order to help students to get a better understanding of these algorithms, we decide to design Computational Geometry Teaching Tool. This tool is a web application that covers 8 geometry algorithms : Graham Scan, Quick Hull, Line Segment Intersection, Dual, Line Arrangement, Voronoi Diagram, Incremental Delaunay Triangulation and Kd Tree. First, this tool is developed by using JavaScript so that users don\u27t need to install any software or package. Furthermore, it breaks down the algorithm and go step by step so that students can move forward and backward on their own pace. Finally, all demos in this tool have same layout so that when students learn how to use the first one, they will know how to use others

"El miedo es una de nuestras emociones primarias" : Entrevista a Mariana Enriquez

Entrevista a Mariana EnriquezInterview with Mariana Enrique

Not a Simple 'Anthropocene' Story in Contemporary China: Unveiling the Entanglement of Chinese Social and Environmental Issues

I developed this thesis, that addresses current social issues and environmental issues in contemporary China, in response to the pursuit of economic development and urbanization, before and after the political-ideological reorientation of the Chinese Communist Party led by Deng Xiaoping and his Reform and Openness policy at the end of the 1970s. I explore the cinematic reflection of environmental problems and social issues in three films of Jia Zhangke, a famous sixth-generation director who adopts realistic aesthetic and artistic pursuit in his films. My reflection is accompanied by a critical discourse analysis of newspaper articles from People’s Daily. Through these two methods, I examine the reality of contemporary China through an economic, cultural, political, social and natural lens to shed light on the root causes of various social and environmental issues in contemporary China. Guided by Anthropocene thinking, I engage in a discussion on tensions within human- nature relationships in China. This research introduces a way of understanding the human- nature relationship within the Anthropocene framework by considering elements including the social structure of human society, the social stratification of different social groups, and the ultimate hegemony of powerholders. In this thesis, I argue that proletariats and ordinary Chinese people in contemporary China who struggle with their personal existential crises do not have the social and political power to make changes to their social reality, neither do they have the power to interfere with the decisions of powerholders, where these decisions are influential in causing social changes, changes to Chinese people’s daily life, changes of Chinese natural landscapes and the human-nature relationship in China

Joint Sensing and Communications for Deep Reinforcement Learning-based Beam Management in 6G

User location is a piece of critical information for network management and control. However, location uncertainty is unavoidable in certain settings leading to localization errors. In this paper, we consider the user location uncertainty in the mmWave networks, and investigate joint vision-aided sensing and communications using deep reinforcement learning-based beam management for future 6G networks. In particular, we first extract pixel characteristic-based features from satellite images to improve localization accuracy. Then we propose a UK-medoids based method for user clustering with location uncertainty, and the clustering results are consequently used for the beam management. Finally, we apply the DRL algorithm for intra-beam radio resource allocation. The simulations first show that our proposed vision-aided method can substantially reduce the localization error. The proposed UK-medoids and DRL based scheme (UKM-DRL) is compared with two other schemes: K-means based clustering and DRL based resource allocation (K-DRL) and UK-means based clustering and DRL based resource allocation (UK-DRL). The proposed method has 17.2% higher throughput and 7.7% lower delay than UK-DRL, and more than doubled throughput and 55.8% lower delay than K-DRL

Sampled-Data Control of Singular Systems with Time Delays

This paper is concerned with sampled-data controller design for singular systems with time delay. It is assumed that the sampling periods are arbitrarily varying but bounded. A time-dependent Lyapunov function is proposed, which is positive definite at sampling times but not necessarily positive definite inside the sampling intervals. Combining input delay approach with Lyapunov method, sufficient conditions are derived which guarante that the singular system is regular, impulse free, and exponentially stable. Then, the existence conditions of desired sampled-data controller can be obtained, which are formulated in terms of strict linear matrix inequality. Finally, numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

Hybrid Data-driven Framework for Shale Gas Production Performance Analysis via Game Theory, Machine Learning and Optimization Approaches

A comprehensive and precise analysis of shale gas production performance is crucial for evaluating resource potential, designing field development plan, and making investment decisions. However, quantitative analysis can be challenging because production performance is dominated by a complex interaction among a series of geological and engineering factors. In this study, we propose a hybrid data-driven procedure for analyzing shale gas production performance, which consists of a complete workflow for dominant factor analysis, production forecast, and development optimization. More specifically, game theory and machine learning models are coupled to determine the dominating geological and engineering factors. The Shapley value with definite physical meanings is employed to quantitatively measure the effects of individual factors. A multi-model-fused stacked model is trained for production forecast, on the basis of which derivative-free optimization algorithms are introduced to optimize the development plan. The complete workflow is validated with actual production data collected from the Fuling shale gas field, Sichuan Basin, China. The validation results show that the proposed procedure can draw rigorous conclusions with quantified evidence and thereby provide specific and reliable suggestions for development plan optimization. Comparing with traditional and experience-based approaches, the hybrid data-driven procedure is advanced in terms of both efficiency and accuracy.Comment: 37 pages, 15 figures, 6 table