Related papers: Conformal invariance in two-dimensional turbulence

Spontaneous emergence of periodic oscillations due to self-organization is ubiquitous in turbulent flows. The emergence of such oscillatory instabilities in turbulent fluid mechanical systems is often studied in different system-specific…

Fitting percolation into the conformal field theory framework requires showing that connection probabilities have a conformally invariant scaling limit. For critical site percolation on the triangular lattice, we prove that the probability…

Is there really such a thing as weak turbulence? Here we analyze turbulence of weakly interacting waves using the tools of information theory. It offers a unique perspective for comparing thermal equilibrium and turbulence: the mutual…

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…

We suggest a new focus for turbulence studies -- multi-mode correlations -- which reveal the hitherto hidden nature of turbulent state. We apply this approach to shell models describing basic properties of turbulence. The family of such…

The geometrical structure is among the most fundamental ingredients in understanding complex systems. Is there any systematic approach in defining structures quantitatively, rather than illustratively? If yes, what are the basic principles…

Governing equations for two-dimensional inviscid free-surface flows with constant vorticity over arbitrary non-uniform bottom profile are presented in exact and compact form using conformal variables. An efficient and very accurate…

As the variety of systems displaying scale invariant characteristics are matched only by their number, it is becoming increasingly important to understand their fundamental and universal elements. Much work has attempted to apply 2nd order…

We use multiscale-multispace correlations and Fourier transform techniques, to study some intermittent random field properties, which escape analysis by structure function scaling. These properties are parametrized in terms of a set of…

Recent remarkable progress in computing power and numerical analysis is enabling us to fill a gap in the dynamical systems approach to turbulence. One of the significant advances in this respect has been the numerical discovery of simple…

The significance of small-scale forcing of particles on the carrier two-dimensional turbulent flow has been shown to influence the spectral scaling properties of the carrier fluid. We investigate possible consequences of such two-way…

We study a classical spin model (more precisely a class of models) with O(N) symmetry that can be viewed as a simplified $D$ dimensional lattice model. It is equivalent to a non-translationinvariant one dimensional model and contains the…

We investigate the problem of the superuniversality of the phase transition between different quantum Hall plateaus. We construct a set of models which give a qualitative description of this transition in a pure system of interacting…

We discuss a certain class of two-dimensional quantum systems which exhibit conventional order and topological order, as well as two-dimensional quantum critical points separating these phases. All of the ground-state equal-time correlators…

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 first summarize briefly several properties concerning the dynamics of two-dimensional (2D) turbulence, with an emphasis on the inverse cascade of energy to the largest accessible scale of the system. In order to study a similar…

In low dimensions, conformal anomaly has profound influence on the critical behavior of random surfaces with extrinsic curvature rigidity $1/\a$. We illustrate this by making a small $D$ expansion of rigid random surfaces, where a…

We study examples where conformal invariance implies rational critical indices, triviality of the underlying quantum field theory and emergence of hypergeometric functions as solutions of the field equations.

The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…

Confinement can significantly alter fluid properties, offering potential for specific technological applications. However, achieving precise control over the structural complexity of confined fluids and soft matter remains challenging, as…