Related papers: Strongly Rigid Flows
By using direct numerical simulations (DNS) at unprecedented resolution we study turbulence under rotation in the presence of simultaneous direct and inverse cascades. The accumulation of energy at large scale leads to the formation of…
We prove long-time existence of the Ricci flow starting from complete manifolds with bounded curvature and scale-invariant integral curvature sufficiently pinched with respect to the inverse of its Sobolev constant. Moreover, if the…
The theory of flows was used as a crucial tool in the recent proof by Margolis, Rhodes and Schilling that Krohn-Rhodes complexity is decidable. In this paper we begin a systematic study of aperiodic flows. We give the foundations of the…
Following the findings in \cite{wangsawijaya2020}, we re-examine the turbulent boundary layers developing over surfaces with spanwise heterogeneous roughness of various roughness wavelengths $0.32 \leq S/\overline{\delta} \leq 3.63$, where…
We present the hydrodynamic theory of active XY spins coupled with flow fields, for systems both having and or lacking number conservation in two dimensions (2D). For the latter, with strong activity or nonequilibrium drive, the system can…
This article grew out of the urge to realize explicit examples of solutions for the Ricci flow as families of isometrically embedded submanifolds, together with its Gromov-Hausdorff collapses. To this aim, we consider the Ricci flow of…
We introduce and study the notion of relative rigidity for pairs $(X,\JJ)$ where 1) $X$ is a hyperbolic metric space and $\JJ$ a collection of quasiconvex sets 2) $X$ is a relatively hyperbolic group and $\JJ$ the collection of parabolics…
Our first purpose is to study the stability of linear flows on real, connected, compact, semisimple Lie groups. After, we study and classify periodic orbits of linear and invariant flows. In particular, we obtain a version of…
Unipotent flows are well-behaved dynamical systems. In particular, Marina Ratner has shown that the closure of every orbit for such a flow is of a nice algebraic (or geometric) form. After presenting some consequences of this important…
We consider the motion of a two-dimensional body of arbitrary shape in a planar irrotational, incompressible fluid with a given amount of circulation around the body. We derive the equations of motion for this system by performing…
In this paper, we investigate the embeddings for topological flows. We prove an embedding theorem for discrete topological system. Our results apply to suspension flows via constant function, and for this case we show an embedding theorem…
Dense suspensions of self-propelled bacteria and related active fluids exhibit spontaneous flow generation, vortex formation, and spatiotemporally chaotic dynamics despite operating at vanishingly small Reynolds numbers. These phenomena,…
We consider a class of 2d $\sigma$-models on products of group spaces that provide new examples of a close connection between integrability and stability under the RG flow. We first study the integrable $G \times G$ model derived from the…
This work deals with a number of questions relative to the discrete and continuous adjoint fields associated with the compressible Euler equations and classical aerodynamic functions. The consistency of the discrete adjoint equations with…
We develop a geometric flow framework to investigate two classical shape functionals: the torsional rigidity and the first Dirichlet eigenvalue of the Laplacian. First, by constructing novel deformation paths governed by height-stretching…
Generative modeling seeks to uncover the underlying factors that give rise to observed data that can often be modeled as the natural symmetries that manifest themselves through invariances and equivariances to certain transformation laws.…
More serious works on 2D2C, 2D3C, 2C2Dcw1C3D, 3D3C, rotating turbulence, thin-layer flows, quasi-static magnetohydrodynamics (QSMHD), and all that are wanted, but we report timely here some studies on locally and globally 2C2Dcw1C3D flows,…
We consider the gravity-driven flow of a perfect dielectric, viscous, thin liquid film, wetting a flat substrate inclined at a non-zero angle to the horizontal. The dynamics of the thin film is influenced by an electric field which is set…
Rheological properties of dense flows of hard particles are singular as one approaches the jamming threshold where flow ceases, both for aerial granular flows dominated by inertia, and for over-damped suspensions. Concomitantly, the…
We investigate a steady flow of compressible fluid with inflow boundary condition on the density and slip boundary conditions on the velocity in a square domain in $\mathbf{R^2}$. We show existence of a strong solution $(v,\rho) \in…