相关论文: Dynamics and Rigidity through the Lens of Circles

Over times shorter than that required for relaxation of enthalpy, a liquid can exhibit striking heterogeneities. The picture of these heterogeneities is complex with transient patches of rigidity, irregular yet persistent, intersected by…

We describe recent work that extends some of the measure and topological rigidity results in dynamical systems from situations homogeneous under a Lie group to quite general manifolds.

Circle packings are arrangement of circles satisfying specified tangency requirements. Many problems about packing of circles and spheres occur in nature particularly in material design and protein structure. Surprisingly, little is known…

The dynamics of fluids is a long standing challenge that remained as an unsolved problem for centuries. Understanding its main features, chaos and turbulence, is likely to provide an understanding of the principles and non-linear dynamics…

Understanding how topological constraints affect the dynamics of polymers in solution is at the basis of any polymer theory and it is particularly needed for melts of rings. These polymers fold as crumpled and space-filling objects and,…

Dynamic heterogeneity is now recognised as a central aspect of structural relaxation in disordered materials with slow dynamics, and was the focus of intense research in the last decade. Here we describe how initial, indirect observations…

This article discusses two recent works by the author, one with Brown and Hurtado on Zimmer's conjecture and one with Bader, Miller and Stover on totally geodesic submanifolds of real and complex hyperbolic manifolds. The main purpose of…

Dynamical heterogeneities have been introduced in the context of the glass transition of molecular liquids and the lengthscale associated with them has been argued to be at the origin of the observed quasi-universal behaviour of glassy…

We give some results about the dynamics of a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. Our main results concern (1) singularities and (2) the dynamics in…

A central question in dynamics is whether the topology of a system determines its geometry. This is known as rigidity. Under mild topological conditions rigidity holds for many classical cases, including: Kleinian groups, circle…

We show how dynamical heterogeneities in glass forming systems emerge as a consequence of the existence of dynamical constraints, and we offer an interpretation of the glass transition as an entropy crisis in trajectory space (space-time)…

Amorphous solids are mechanically rigid while possessing a disordered structure similar to that of dense liquids. Recent research indicates that dynamical heterogeneity, spatio-temporal fluctuations in local dynamical behavior, might help…

The existence of heterogeneity in the dynamics of supercooled liquids is believed to be one of the hallmarks of the glass transition. Intense research has been carried out in the past to understand the origin of this heterogeneity in…

The origin of the dramatic changes in the behavior of liquids as they approach their vitreous state - increases of many orders of magnitude in transport properties and dynamic time scales - is a major unsolved problem in condensed matter.…

Dynamic heterogeneity in glass-formers has been related to their static structure using the concept of dynamic propensity. We re-examine this relationship by analyzing dynamical fluctuations in two atomistic glass-formers and two…

A complete description of dynamics of compact locally homogeneous universes is given, which, in particular, includes explicit calculations of Teichm\"uller deformations and careful counting of dynamical degrees of freedom. We regard each of…

Despite the use of glasses for thousands of years, the nature of the glass transition is still mysterious. On approaching the glass transition, the growth of dynamic heterogeneity has long been thought to play a key role in explaining the…

We review a theoretical perspective of the dynamics of glass forming liquids and the glass transition. It is a perspective we have developed with our collaborators during this decade. It is based upon the structure of trajectory space. This…

This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description…

By using fluid-kinetic simulations of confined and concentrated emulsion droplets, we investigate the nature of space non-homogeneity in soft-glassy dynamics and provide quantitative measurements of the statistical features of plastic…