Related papers: Regularity theory for $2$-dimensional almost minim…

We study a novel class of Renormalization Group flows which connect multicritical versions of the two-dimensional Yang-Lee edge singularity described by the conformal minimal models M(2,2n+3). The absence in these models of an order…

We consider a collection of self-driven apolar particles on a substrate that organize into an active nematic phase at sufficiently high density or low noise. Using the dynamical renormalization group, we systematically study the 2d…

We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold. This extends the classical notion of asymptotic directions usually defined on smooth submanifolds. We…

We investigate the quasi two-dimensional Taylor-Couette system in the regime where the radius ratio is close to unity - a transitional regime between three and two dimensions. By systematically increasing the Reynolds number we observe a…

The last half century of research into the structure, dynamics, and thermodynamics of simple liquids has revealed a number of approximate universalities. This paper argues that simple liquids' reduced-coordinate constant-potential-energy…

The purpose of this paper is to study the validity of Stokes' Theorem for singular submanifolds and differential forms with singularities in Euclidean space. The results are presented in the context of Lebesgue Integration, but their proofs…

We consider $L^2$ minimizing geodesics along the group of volume preserving maps $SDiff(D)$ of a given 3-dimensional domain $D$. The corresponding curves describe the motion of an ideal incompressible fluid inside $D$ and are (formally)…

We give simple examples of weakly coupled or free quantum mechanical systems that exhibit scale invariance with an anomalous dimension for a conserved current. In these models scaling as an exact symmetry only emerges in a large N limit,…

Geometric singular perturbation theory provides a powerful mathematical framework for the analysis of 'stationary' multiple time-scale systems which possess a critical manifold, i.e. a smooth manifold of steady states for the limiting fast…

We present a rigorous reassessment of chaotic behavior in two-dimensional autonomous systems with singular or nonsmooth dynamics. For the Cummings-Dixon-Kaus (CDK) model, we show that blow-up regularization restores smoothness and renders…

Two-dimensional topological field theories possessing a non-abelian current symmetry are constructed. The topological conformal algebra of these models is analysed. It differs from the one obtained by twisting the $N=2$ superconformal…

I consider superconducting condensates which become incompressible in the infinite gap limit. Classical 2D incompressible fluids possess the dynamical symmetry of area-preserving diffeomorphisms. I show that the corresponding infinite…

In the context of incompressible fluids, the observation that turbulent singular structures fail to be space filling is known as ``intermittency'' and it has strong experimental foundations. Consequently, as first pointed out by Landau,…

Quasi-two-dimensional fluids can be generated by confining a fluid between two parallel walls with narrow separation. Such fluids exhibit an inhomogeneous structure perpendicular to the walls due to the loss of translational symmetry.…

Consider an $m$-dimensional area minimizing mod$(2Q)$ current $T$, with $Q\in\mathbb{N}$, inside a sufficiently regular Riemannian manifold of dimension $m + 1$. We show that the set of singular density-$Q$ points with a flat tangent cone…

In [15], Jean Taylor has proved a regularity theorem away from boundary for Almgren almost minimal sets of dimension two in $\mathbb{R}^{3}$. It is quite important for understanding the soap films and the solutions of Plateau's problem away…

This paper reports several new classes of weakly unstable recurrent solutions of the 2+1-dimensional Euler equation on a square domain with periodic boundary conditions. These solutions have a number of remarkable properties which…

We give a new, simpler proof of the main approximation theorem for area minimizing current contained in Almgren's Big regularity paper. Our proof relies on a new estimate concerning the higher integrability of the quantity called here the…

Quantum systems with multiple degenerate classical harmonic minima exhibit new non-perturbative phenomena which are not present for the double-well and periodic potentials. The simplest characteristic example of this family is the…

The conditions in which meridional recirculations appear in swirling flows above a fixed wall are analysed. In the classical Bodew\"adt problem, where the swirl tends towards an aysmptotic value away from the wall, the well-known "tea-cup…