Related papers: Multiradial SLE with spiral: resampling property a…
We construct martingale observables for systems of multiple SLE curves by applying screening techniques within the CFT framework recently developed by Kang and Makarov, extended to admit multiple SLEs. We illustrate this approach by…
We have recently identified a new radial migration mechanism resulting from the overlap of spiral and bar resonances in galactic disks. Here we confirm the efficiency of this mechanism in fully self-consistent, Tree-SPH simulations, as well…
Abstract Self-similar, fractal nature of turbulence is discussed in the context of two dimensional turbulence, by considering the fractal structure of the wave-number domain using spirals. In loose analogy with phyllotaxis in plants, each…
We prove large deviation principles (LDPs) for full chordal, radial, and multichordal SLE(0+) curves parameterized by capacity. The rate function is given by the appropriate variant of the Loewner energy. There are two key novelties in the…
Lagrangian properties obtained from a Particle Tracking Velocimetry experiment in a turbulent flow at intermediate Reynolds number are presented. Accurate sampling of particle trajectories is essential in order to obtain the Lagrangian…
Conformally-invariant curves that appear at critical points in two-dimensional statistical mechanics systems, and their fractal geometry have received a lot of attention in recent years. On the one hand, Schramm has invented a new rigorous…
Statistical properties of critical wave functions at the spin quantum Hall transition are studied both numerically and analytically (via mapping onto the classical percolation). It is shown that the index $\eta$ characterizing the decay of…
Random Wavelet Series form a class of random processes with multifractal properties. We give three applications of this construction. First, we synthesize a random function having any given spectrum of singularities satisfying some…
Recently it has been reported that biased range-measurements among neighboring agents in the gradient distance-based formation control can lead to predictable collective motion. In this paper we take advantage of this effect and by…
In this paper we establish several results on approximate controllability of a semilinear wave equation by making use of a single multiplicative control. These results are then applied to discuss the exact controllability properties for the…
Experimentally observed magnetic fields with nanoscale variations are theoretically modeled by a piece-wise constant function with jump discontinuity along a smooth curve, the magnetic edge. Assuming the edge is a closed curve with an axis…
We consider the measure on multiple chordal Schramm-Loewner evolution ($SLE_\kappa$) curves. We establish a derivative estimate and use it to give a direct proof that the partition function is $C^2$ if $\kappa<4$.
We study multifractal properties in time evolution of a single particle subject to repeated measurements. For quantum systems, we consider circuit models consisting of local unitary gates and local projective measurements. For classical…
In this paper we define and prove of the existence of the multi-point Green's function for SLE - a normalized limit of the probability that an $SLE_{\kappa}$ curve passes near to a pair of marked points in the interior of a domain. When…
The paper studies multifractal random measures on the sphere $\mathbb{S}^d$ constructed via multifractal products of random fields. It presents new limit theorems for multifractal products of spherical fields and conditions for the…
We construct a conformally invariant random family of closed curves in the plane by welding of random homeomorphisms of the unit circle. The homeomorphism is constructed using the exponential of $\beta X$ where $X$ is the restriction of the…
We deal with decay and boundedness properties of radial functions belonging to Besov and Lizorkin-Triebel spaces. In detail we investigate the surprising interplay of regularity and decay. Our tools are atomic decompositions in combination…
We compute fully local boundary layer scales in three-dimensional turbulent Rayleigh-Benard convection. These scales are directly connected to the highly intermittent fluctuations of the fluxes of momentum and heat at the isothermal top and…
We give a simplified and complete proof of the convergence of the chordal exploration process in critical FK-Ising percolation to chordal SLE$_\kappa( \kappa-6)$ with $\kappa=16/3$. Our proof follows the classical excursion-construction of…
We consider tunnelling of a non-relativistic particle across a potential barrier. It is shown that the barrier acts as an effective beam splitter which builds up the transmitted pulse from the copies of the initial envelope shifted in the…