相关论文: On H\"{o}lder solutions to the spiral winding prob…

We define winding numbers of regular closed curves on surfaces with a nice euclidean or hyperbolic geometry. We prove that two regular closed curves are regularly homotopic if and only if they are freely homotopic and have the same winding…

Interface dynamics in two-dimensional systems with a maximal number of conservation laws gives an accurate theoretical model for many physical processes, from the hydrodynamics of immiscible, viscous flows (zero surface-tension limit of…

Here we study a class of second-order nonautonomous differential equations, and the corresponding planar and spatial systems, from the point of view of fractal geometry. The fractal oscillatority of solutions at infinity is measured by…

The process of a stationary range formation in the wind-wave spectrum is investigated numerically. The evolution equation for the two-dimensional wind-wave spectrum is numerically solved by using an exact calculation of the Hasselmann…

Gaseous rotating razor-thin discs are a testing ground for theories of spiral structure that try to explain appearance and diversity of disc galaxy patterns. These patterns are believed to arise spontaneously under the action of…

From a database of direct numerical simulations of homogeneous and isotropic turbulence, generated in periodic boxes of various sizes, we extract the spherically symmetric part of moments of velocity increments and first verify the…

Recently, Stull [18], [17] resolved a long-standing open problem posed by Lutz, on whether the set of effective Hausdorff dimensions of points on a straight line in $\mathbb{R}^2$ -- the effective dimension spectrum of the line -- contains…

In this paper, applying a canonical system with field rotation parameters and using geometric properties of the spirals filling the interior and exterior domains of limit cycles, we solve first the problem on the maximum number of limit…

Sommerfeld paradox roughly says that mathematically Couette linear shear is linearly stable for all Reynolds number, but experimentally arbitrarily small perturbations can induce the transition from the linear shear to turbulence when the…

Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed…

The regularity of refinable functions has been investigated deeply in the past 25 years using Fourier analysis, wavelet analysis, restricted and joint spectral radii techniques. However the shift-invariance of the underlying regular setting…

In this thesis, we are concerned with the dynamics of spiral wave solutions to Reaction-Diffsion systems of equations, and how they behave when subject to symmetry breaking perturbations. We present an asymptotic theory of the study of…

We present results on stripe formation in the Swift-Hohenberg equation with a directional quenching term. Stripes are "grown" in the wake of a moving parameter step line, and we analyze how the orientation of stripes changes depending on…

In this paper we develop methods to extend the minimal hypersurface approach to positive scalar curvature problems to all dimensions. This includes a proof of the positive mass theorem in all dimensions without a spin assumption. It also…

We study compressible turbulent flow in a circular pipe, at computationally high Reynolds number. Classical related issues are addressed and discussed in light of the DNS data, including validity of compressibility transformations,…

The defect of a complex Hadamard matrix $H$ is an upper bound for the dimension of a continuous Hadamard orbit stemming from $H$. We provide a new interpretation of the defect as the dimension of the center subspace of a gradient flow and…

The main purpose of this paper is twofold. We first want to analyze in details the meaningful geometric aspect of the method introduced in the previous paper [12], concerning regularity of families of irreducible, nodal "curves" on a…

We are concerned with supersonic vortex sheets for the Euler equations of compressible inviscid fluids in two space dimensions. For the problem with constant coefficients, in [10] the authors have derived a pseudo-differential equation…

This paper presents a detailed regularity analysis of anisotropic wavelet frames and subdivision. In the univariate setting, the smoothness of wavelet frames and subdivision is well understood by means of the matrix approach. In the…

We study non-supersymmetric solutions of five dimensional N=2 supergravity theories coupled to an arbitrary number of abelian vector multiplets. The solutions constructed can be considered as deformations of known supersymmetric black hole…