Algebraic conformal quantum field theory in perspective

Conformal quantum field theory is reviewed in the perspective of Axiomatic, notably Algebraic QFT. This theory is particularly developped in two spacetime dimensions, where many rigorous constructions are possible, as well as some complete classifications. The structural insights, analytical methods and constructive tools are expected to be useful also for four-dimensional QFT.Comment: Review paper, 40 pages. v2: minor changes and references added, so as to match published versio

Visualization of Tensor Fields in Mechanics

Tensors are used to describe complex physical processes in many applications. Examples include the distribution of stresses in technical materials, acting forces during seismic events, or remodeling of biological tissues. While tensors encode such complex information mathematically precisely, the semantic interpretation of a tensor is challenging. Visualization can be beneficial here and is frequently used by domain experts. Typical strategies include the use of glyphs, color plots, lines, and isosurfaces. However, data complexity is nowadays accompanied by the sheer amount of data produced by large-scale simulations and adds another level of obstruction between user and data. Given the limitations of traditional methods, and the extra cognitive effort of simple methods, more advanced tensor field visualization approaches have been the focus of this work. This survey aims to provide an overview of recent research results with a strong application-oriented focus, targeting applications based on continuum mechanics, namely the fields of structural, bio-, and geomechanics. As such, the survey is complementing and extending previously published surveys. Its utility is twofold: (i) It serves as basis for the visualization community to get an overview of recent visualization techniques. (ii) It emphasizes and explains the necessity for further research for visualizations in this context

Computational characterization and prediction of metal-organic framework properties

In this introductory review, we give an overview of the computational chemistry methods commonly used in the field of metal-organic frameworks (MOFs), to describe or predict the structures themselves and characterize their various properties, either at the quantum chemical level or through classical molecular simulation. We discuss the methods for the prediction of crystal structures, geometrical properties and large-scale screening of hypothetical MOFs, as well as their thermal and mechanical properties. A separate section deals with the simulation of adsorption of fluids and fluid mixtures in MOFs

A Planning-and-Exploring Approach to Extreme-Mechanics Force Fields

Extreme mechanical processes such as strong lattice distortion and bond breakage during fracture are ubiquitous in nature and engineering, which often lead to catastrophic failure of structures. However, understanding the nucleation and growth of cracks is challenged by their multiscale characteristics spanning from atomic-level structures at the crack tip to the structural features where the load is applied. Molecular simulations offer an important tool to resolve the progressive microstructural changes at crack fronts and are widely used to explore processes therein, such as mechanical energy dissipation, crack path selection, and dynamic instabilities (e.g., kinking, branching). Empirical force fields developed based on local descriptors based on atomic positions and the bond orders do not yield satisfying predictions of fracture, even for the nonlinear, anisotropic stress-strain relations and the energy densities of edges. High-fidelity force fields thus should include the tensorial nature of strain and the energetics of rare events during fracture, which, unfortunately, have not been taken into account in both the state-of-the-art empirical and machine-learning force fields. Based on data generated by first-principles calculations, we develop a neural network-based force field for fracture, NN-F$^3$, by combining pre-sampling of the space of strain states and active-learning techniques to explore the transition states at critical bonding distances. The capability of NN-F$^3$ is demonstrated by studying the rupture of h-BN and twisted bilayer graphene as model problems. The simulation results confirm recent experimental findings and highlight the necessity to include the knowledge of electronic structures from first-principles calculations in predicting extreme mechanical processes

Recent Mathematical Developments in Quantum Field Theory

This workshop has focused on three areas in mathematical quantum field theory and their interrelations: 1) conformal field theory, 2) constructions of interacting models of quantum field theory by various methods, and 3) several approaches studying the interplay of quantum field theory and gravity

Generalized liquid crystals: giant fluctuations and the vestigial chiral order of II, OO and TT matter

The physics of nematic liquid crystals has been subject of intensive research since the late 19th century. However, because of the limitations of chemistry the focus has been centered around uni- and biaxial nematics associated with constituents bearing a $D_{\infty h}$ or $D_{2h}$ symmetry respectively. In view of general symmetries, however, these are singularly special since nematic order can in principle involve any point group symmetry. Given the progress in tailoring nano particles with particular shapes and interactions, this vast family of "generalized nematics" might become accessible in the laboratory. Little is known since the order parameter theories associated with the highly symmetric point groups are remarkably complicated, involving tensor order parameters of high rank. Here we show that the generic features of the statistical physics of such systems can be studied in a highly flexible and efficient fashion using a mathematical tool borrowed from high energy physics: discrete non-Abelian gauge theory. Explicitly, we construct a family of lattice gauge models encapsulating nematic ordering of general three dimensional point group symmetries. We find that the most symmetrical "generalized nematics" are subjected to thermal fluctuations of unprecedented severity. As a result, novel forms of fluctuation phenomena become possible. In particular, we demonstrate that a vestigial phase carrying no more than chiral order becomes ubiquitous departing from high point group symmetry chiral building blocks, such as $I$, $O$ and $T$ symmetric matter.Comment: 14 pages, 5 figures; published versio

Recent mathematical developments in quantum field theory

This workshop has focused on three areas in mathematical quantum field theory and their interrelations: 1) conformal field theory, 2) constructions of interacting models of quantum field theory by various methods, and 3) several approaches studying the interplay of quantum field theory and gravit