Related papers: Instabilities of shear layers
This note is an expository account of the theory of staggered sheaves, based on a series of lectures given by the author at RIMS (Kyoto) in October 2008.
In this paper we extend the recent theory of shear-localization in 2-dimensional amorphous solids to 3-D. In 2-D the fundamental instability of shear-localization is related to the appearance of a line of displacement quadrupoles, that…
Dynamical instabilities in fluid mechanics are responsible of a variety of important common phenomena, such as waves on the sea surface or Taylor vorteces in Couette flow. In granular media dynamical instabilities has just begun to be…
This article accompanies the submission of a fluid dynamics video (entry V032) of inertial particle entrainment in a shearless mixing layer for the Gallery of Fluid Motion of the 64th Annual Meeting of the American Physical Society,…
In this set of lectures I review recent developments in string theory emphasizing their non-perturbative aspects and their recently discovered duality symmetries. The goal of the lectures is to make the recent exciting developments in…
This Ph.D. thesis is divided in two parts. The first one concerns the equilibrium properties of glassy systems. Some aspects of the phenomenology of glasses and of theories attempting to describe them are reviewed in chapter 1. A study of…
Under shear, a system of particles changes its contact network and becomes unstable as it transitions between mechanically stable states. For hard spheres at zero pressure, contact breaking events necessarily generate an instability, but…
Informal lecture notes with examples on sheaf theory and the derived category of sheaves; sheaves and Morse theory; perverse sheaves, and some applications to representation theory. Added Oct 2021: cellular perverse sheaves. Proofs are…
This is the draft of lecture notes for Phd students in Sichuan University. In this notes we expand Li-Ruan's paper with much more detailed explanations and calculations.
We introduce applied shear as a method to control viscous fingering by smoothing the interface between miscible fluids. In the viscous fingering instability, a less viscous fluid displaces a more viscous one through the formation of…
Considering a granular fluid of inelastic smooth hard spheres we discuss the conditions delineating the rheological regimes comprising Newtonian, Bagnoldian, shear thinning, and shear thickening behavior. Developing a kinetic theory, valid…
In these lecture notes we give an introduction to Bridgeland stability conditions on smooth complex projective varieties with a particular focus on the case of surfaces. This includes basic definitions of stability conditions on derived…
This is a series of remedial lectures on open and unoriented strings for the heterotic string generation. The particular focus is on the interesting features that arise under T-duality---D-branes and orientifolds. The final lecture…
These lectures start with the mean field theory for a symmetric binary fluid mixture, addressing interfacial tension, the stress tensor, and the equations of motion (Model H). We then consider the phase separation kinetics of such a…
This is the first part of the lecture notes that grew out of the special course given during the 2021-2022 academic year. In these lecture notes we present an approach to the fundamental structures of differential geometry that uses the…
This is an invited commentary on "Geometrically incompatible confinement of solids", B. Davidovitch, Y. Sun and G. M. Grason (PNAS, doi:10.1073/pnas.1815507116 , arxiv:1809.06919).
This is a lecture notes for a mini-course in Department of Mathematics, Ghent University, 14 Mar.-25 Mar. 2023.
We consider a shear layer of a kind not previously studied to our knowledge. Contrary to the classical free shear layer, the width of the shear zone does not vary in the streamwise direction but rather exhibits a lateral variation. Based on…
We study networks of coupled bistable elastic elements, recently proposed as a model for crumpled thin sheets. The networks are poised on the verge of a localized instability, and the model allows unique access to both local and global…
This note surveys some classical results and recent developments on the interplay between lower curvature bounds and the isoperimetric problem. It is based on mini-courses given at the European Doctorate School of Differential Geometry…