相关论文: Topological Constraint Theory and Rigidity of Glas…

Plasticity is inherent to many engineering materials such as metals. While it can degrade the load-carrying capacity of structures via material yielding, it can also protect structures through plastic energy dissipation. To fully harness…

This key-issues review is a plea for a new focus on simpler and more realistic models of glass-forming fluids. It seems to me that we have too often been led astray by sophisticated mathematical models that beautifully capture some of the…

Much of the progress achieved in understanding plasticity and failure in amorphous solids had been achieved using experiments and simulations in which the materials were loaded using strain control. There is paucity of results under stress…

Geometrical stability theory is a powerful set of model-theoretic tools that can lead to structural results on models of a simple first-order theory. Typical results offer a characterization of the groups definable in a model of the theory.…

An analytical framework is proposed to describe the elasticity, viscosity and fragility of metallic glasses in relation to their atomic-level structure and the effective interatomic interaction. The bottom-up approach starts with forming an…

Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…

Adaptive Resonance Theory (ART) is considered as an effective approach for realizing continual learning thanks to its ability to handle the plasticity-stability dilemma. In general, however, the clustering performance of ART-based…

Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…

This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral…

The growing sluggishness of glass-forming liquids is thought to be accompanied by growing structural order. The nature of such order, however, remains hotly debated. A decade ago, point-to-set (PTS) correlation lengths were proposed as…

We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive…

It is often stated that if one is presented with a snapshot of the positions of the molecules of a glass and one of a liquid, one is unable to tell the difference. Here we argue instead that given several such snapshots taken over a…

Just as an explicit parameterisation of system dynamics by state, i.e., a choice of coordinates, can impede the identification of general structure, so it is too with an explicit parameterisation of system dynamics by control. However, such…

The atomic-level structure of bulk metallic glasses is a key determinant of their properties. An accurate representation of amorphous systems in computational studies has traditionally required large supercells that are unfortunately…

Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…

This thesis addresses the theory of topological spaces and the foundations of persistence theory. We will discuss chain complexes and the associated simplicial homology groups, as well as their relationship with singular homology theory.…

In this combined experimental and simulation study, we utilize bond-order topology to quantitatively match particle volume fraction in mechanically uniformly compressed colloidal suspensions with temperature in atomistic simulations. The…

The routine transformation of a liquid, as it is cooled rapidly, resulting in glass formation, is remarkably complex. A theoretical explanation of the dynamics associated with this process has remained one of the major unsolved problems in…

In many areas of applied mathematics, engineering, and social and natural sciences, decentralization of information is a key aspect determining how to approach a problem. In this review article, we study information structures in a…

Due to their excellent optical properties, glasses are used for various applications ranging from smartphone screens to telescopes. Developing compositions with tailored Abbe number (Vd) and refractive index (nd), two crucial optical…