Related papers: Ratner's property and mixing for special flows ove…
In the turbulent boundary layer of multicomponent fluid mixtures, the species-specific mass flux is determined by the combination of turbulent-diffusiophoretic diffusion and diffusion due to gradients in supplementary fields (e.g.…
We consider the inverse mean curvature flow in smooth Riemannian manifolds of the form $([R_{0},\infty)\times S^n,\bar{g})$ with metric $\bar{g}=dr^2+{\vartheta}^2(r){\sigma}$ and non-positive radial sectional curvature. We prove, that for…
In the present work we consider the behavior of the geodesic flow on the unit tangent bundle of the 2-torus $T^2$ for an arbitrary Riemannian metric. A natural non-negative quantity which measures the complexity of the geodesic flow is the…
The Ratner property, a quantitative form of divergence of nearby trajectories, is a central feature in the study of parabolic homogeneous flows. Discovered by Marina Ratner and used in her 1980th seminal works on horocycle flows, it pushed…
In this paper we introduce the branched $\alpha$-flows on closed surfaces with Euler characteristic \(\chi \leq 0\). Based on the strict convexity of the branched $\alpha$-potentials, we establish the long time existence and convergence of…
A simplified model for the stationary, axisymmetric structure of magnetized winds with a polytropic equation of state is presented. The shape of the magnetic surfaces is assumed to be known (conical in this paper) within the fast…
We introduce a dynamical energy functional on compact ancient asymptotically Ricci-flat Ricci flows with modest decay using limits of conjugate heat flows. This functional satisfies a steady Ricci breather-type rigidity and provides an…
In this paper, we firstly establish an Interpolating curvature invariance between the well known nonnegative and 2-non-negative curvature invariant along the Ricci flow. Then a related strong maximum principle for the $(\lambda_1,…
We show existence of smooth, weakly mixing reparametrizations of some linear flows on $\mathbb{T}^2$ for which all orbits sampled at prime times are dense.
Hamiltonian flows on compact surfaces are characterized, and the topological invariants of such flows with finitely many singular points are constructed from the viewpoints of integrable systems, fluid mechanics, and dynamical systems.…
Current-voltage measurements of type-II superconductors are described by a coarse-grained model of superconducting vortex dynamics. We find that the power spectra of the voltage fluctuations, and the noise power, are related to the large…
We review a number a recent advances in the study of two-dimensional statistical models with strong geometrical constraints. These include folding problems of regular and random lattices as well as the famous meander problem of enumerating…
The paper is devoted to generic translation flows corresponding to Abelian differentials with one zero of order two on flat surfaces of genus two. These flows are weakly mixing by the Avila-Forni theorem. Our main result gives first…
We show that a flow or a semiflow with a weaker reparametrized form of gluing orbit property is either minimal or of positive topological entropy.
We study the topological entropy of the magnetic flow on a closed riemannian surface. We prove that if the magnetic flow has a non-hyperbolic closed orbit in some energy set T^cM= E^{-1}(c), then there exists an exact $…
We investigate the behavior of flows, including turbulent flows, driven by a horizontal body-force and subject to a vertical magnetic field, with the following question in mind: for very strong applied magnetic field, is the flow mostly…
It is possible to define mixing properties for subshifts according to the intensity which allows to concatenate two rectangular blocks. We study the interplay between this intensity and computational properties. In particular we prove that…
We consider flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are treated with Neumann type flow conditions, and a…
We consider the compressible Euler system for ideal gas flow in the absence of any forces except the internal thermodynamic pressure. In this setting, and in dimensions higher 1, it is known that wave-focusing can drive Euler solutions to…
This paper investigates the nonlinear dynamics of Newton's problem of minimal resistance in radial fields. We move beyond classical translational symmetry to analyze two non-equilibrium scenarios: a scale-invariant free expansion and an…