相关论文: Visually building Smale flows in S3

We describe transversely oriented foliations of codimension one on closed manifolds that admit simple foliated flows.

Various disordered dense systems such as foams, gels, emulsions and colloidal suspensions, exhibit a jamming transition from a liquid state (they flow) to a solid state below a yield stress. Their structure, thoroughly studied with powerful…

We use the bailout embeddings of three-dimensional volume-preserving maps to study qualitatively the dy- namics of small spherical neutrally buoyant impurities suspended in a time-periodic incompressible fluid flow. The accumulation of…

The study of high dimensional data sets often rely on their low dimensional projections that preserve the local geometry of the original space. While numerous methods have been developed to summarize this space as variations of tree-like…

Scale without conformal symmetry corresponds to an inhomogeneous conservation equation for the virial current sourced by the trace of the energy-momentum tensor. Fluids that are just scale-invariant differ qualitatively from their conformal…

We address scaling in inhomogeneous and anisotropic turbulent flows by decomposing structure functions into their irreducible representation of the SO(3) symmetry group which are designated by $j,m$ indices. Employing simulations of channel…

The JHU turbulence database [1] can be used with a state of the art visualisation tool [2] to generate high quality fluid dynamics videos. In this work we investigate the classical idea that smaller structures in turbulent flows, while…

We here present two simplified models aimed at describing the long-term, irregular behaviours observed in the rheological response of certain complex fluids, such as periodic oscillations or chaotic-like variations. Both models exploit the…

Stochastic geometric mechanics (SGM) is known for its potential utility in quantifying uncertainty in global climate modelling of the Earth's ocean and atmosphere while also preserving the fundamental advective transport properties of ideal…

We give complete classification of C^2-regular and non-degenerate projectively Anosov flows on three dimensional manifolds. More precisely, we prove that such a flow on a connected manifold must be either an Anosov flow or represented as a…

Viscoelastic fluids are a common subclass of rheologically complex materials that are encountered in diverse fields from biology to polymer processing. Often the flows of viscoelastic fluids are unstable in situations where ordinary…

Morse theory relates algebraic topology invariants and the dynamics of the gradient flow of a Morse function, allowing to derive information about one out of the other. In the case of the homology, the construction extends to much more…

Flow-based generative models have highly desirable properties like exact log-likelihood evaluation and exact latent-variable inference, however they are still in their infancy and have not received as much attention as alternative…

We performed numerical simulations of blood flow in arteries with a variable stiffness and cross-section at rest using a finite volume method coupled with a hydrostatic reconstruction of the variables at the interface of each mesh cell. The…

We study planar flows without non-wandering points and prove several properties of these flows in relation with their prolongational relation. The main results of this article are that a planar (regular) wandering flow has no generalized…

Any closed, oriented, hyperbolic three-manifold with nontrivial second homology has many quasigeodesic flows, where quasigeodesic means that flow lines are uniformly efficient in measuring distance in relative homotopy classes. The flows…

Significant advancements have emerged in the theory of asymptotic stability of shear flows in stably stratified fluids. In this comprehensive review, we spotlight these recent developments, with particular emphasis on novel approaches that…

We employ the relationship between contact structures and Beltrami fields derived in part I of this series to construct steady nonsingular solutions to the Euler equations on a Riemannian $S^3$ whose flowlines trace out closed curves of all…

Optical flow, semantic segmentation, and surface normals represent different information modalities, yet together they bring better cues for scene understanding problems. In this paper, we study the influence between the three modalities:…

Three dimensional unsteady flow of fluids in the Lagrangian description is considered as an autonomous dynamical system in four dimensions. The condition for the existence of a symplectic structure on the extended space is the frozen field…