相关论文: Exponential mixing of frame flows for convex cocom…
We show that the ergodic, topological and geometric basins coincide for hyperbolic dominated ergodic $cu$-Gibbs states, solving the ``basin problem'' for a wide class of non-uniformly hyperbolic systems. We obtain robust examples of…
A new computational framework for the simulation of turbulent flow through complex objects and along irregular boundaries is presented. This is motivated by the application of metal foams in compact heat-transfer devices, or as catalyst…
We prove logarithm laws for unipotent flows on non-compact finite-volume hyperbolic manifolds. Our method depends on the estimate of norms of certain incomplete Eisenstein series.
We study the geodesic flow of a compact surface without conjugate points and genus greater than one and continuous Green bundles. Identifying each strip of bi-asymptotic geodesics induces an equivalence relation on the unit tangent bundle.…
Motivated by recent experimental advances (Stroock et al. 2002) in microfluidic mixers, we study the passive mixing and flow properties of a patterned microchannel by means of computational fluid dynamics (CFD). Such geometries overcome the…
For a geometrically finite Kleinian group $\Gamma$, the Bowen-Margulis-Sullivan measure is finite and is the unique measure of maximal entropy for the geodesic flow, as shown by Sullivan and Otal-Peign\'e respectively. Moreover, it is…
Mixing in open incompressible flows is studied in a model problem with inhomogeneous passive scalar injection on an inlet boundary. As a measure of the efficiency of stirring, the bulk scalar concentration variance is bounded and the bound…
In this paper, several fundamental facts, especially the existence and uniqueness of an absolutely continuous ergodic measure with an exponential mixing rate, are derived for smooth expanding circle maps. Although the results are classical,…
We develop a technique of multiple scale asymptotic expansions along mean flows and a corresponding notion of weak multiple scale convergence. These are applied to homogenize convection dominated parabolic equations with rapidly…
We prove gradient estimates for hypersurfaces in the hyperbolic space $\mathbb{H}^{n+1},$ expanding by negative powers of a certain class of homogeneous curvature functions. We obtain optimal gradient estimates for hypersurfaces evolving by…
In this paper we introduce a new geometric flow --- the hyperbolic gradient flow for graphs in the $(n+1)$-dimensional Euclidean space $\mathbb{R}^{n+1}$. This kind of flow is new and very natural to understand the geometry of manifolds. We…
Optimal-order uniform-in-time $H^1$-norm error estimates are given for semi- and full discretizations of mean curvature flow of surfaces in arbitrarily high codimension. The proposed and studied numerical method is based on a parabolic…
We investigate the existence, convergence and uniqueness of modified general curvature flow of convex hypersurfaces in hyperbolic space with a prescribed asymptotic boundary.
This paper considers asymptotically hyperbolic manifolds with a finite boundary intersecting the usual infinite boundary -- cornered asymptotically hyperbolic manifolds -- and proves a theorem of Cartan-Hadamard type near infinity for the…
Computing uniformization maps for surfaces has been a challenging problem and has many practical applications. In this paper, we provide a theoretically rigorous algorithm to compute such maps via combinatorial Calabi flow for vertex…
Multiscale metrics such as negative Sobolev norms are effective for quantifying the degree of mixedness of a passive scalar field advected by an incompressible flow in the absence of diffusion. In this paper we introduce a mix norm that is…
We prove exponential decay of correlations for a realistic model of piecewise hyperbolic flows preserving a contact form, in dimension three. This is the first time exponential decay of correlations is proved for continuous-time dynamics…
In this paper, we propose a new volume-preserving flow and show that it performs similarly to the linear general normalizing flow. The idea is to enrich a linear Inverse Autoregressive Flow by introducing multiple lower-triangular matrices…
We establish the existence and uniqueness of some smooth accelerating transonic flows governed by the three dimensional steady compressible Euler equations with an external force in cylinders with arbitrary cross sections, which include…
We study the thermodynamics and non-relativistic hydrodynamics of the holographic fluid on a finite cutoff surface in the Gauss-Bonnet gravity. It is shown that the isentropic flow of the fluid is equivalent to a radial component of…