Related papers: Resonant forms at zero for dissipative Anosov flow…
Differentially rotating, "advection-dominated" accretion flows are considered in which the heat generated by viscous dissipation is retained in the fluid. The equations of time-dependent quasi-spherical accretion are solved in a simplified…
In this study we consider the stability and transitions for the Poiseuille flow of a second grade fluid which is a model for non-Newtonian fluids. We restrict our attention to flows in an infinite pipe with circular cross section that are…
We define and study the foliated centralizer: the group of $C^\infty$ centralizer elements of the lift of an Anosov system on a non-compact manifold which additionally preserve the stable and unstable foliations. When the Anosov system is…
We study the turbulent square duct flow of dense suspensions of neutrally-buoyant spherical particles. Direct numerical simulations (DNS) are performed in the range of volume fractions $\phi=0-0.2$, using the immersed boundary method (IBM)…
For a surface semiflow that is a suspension of a \( C^{1+\alpha} \) expanding Markov interval map, we prove that, under the assumptions that the roof function is Lipschitz continuous and not cohomologous to a locally constant function, the…
We show that any topologically transitive codimension-one Anosov flow on a closed manifold is topologically equivalent to a smooth Anosov flow that preserves a smooth volume. By a classical theorem due to Verjovsky, any higher dimensional…
We propose a new second-order asymptotic-preserving (AP) dual formulation finite-volume (DF-FV) method for the thermal rotating shallow water (TRSW) equations. The TRSW system models geophysical flows characterized by horizontal…
In a neighborhood of a hyperbolic periodic orbit of a volume-preserving flow on a manifold of dimension 3, we define and show the existence of a normal form for the generator of the flow that encodes the dynamics. If the flow is a contact…
We study both the local and global existence of a gradient flow of the Sinai-Ruelle-Bowen entropy functional on a Hilbert manifold of expanding maps of a circle equipped with a Sobolev norm in the tangent space of the manifold. We show…
This paper discusses the effect of rotation on the boundary layer in high Reynolds number flow over a ridge using a numerical method based on stabilised finite elements that captures steady solutions up to Reynolds number of order $10^6$.…
This study investigates the dynamics of incompressible fluid flows through quaternionic variables integrated within Sobolev-Besov spaces. Traditional mathematical models for fluid dynamics often employ Sobolev spaces to analyze the…
In this work we develop a new criterion for the existence of topological horseshoes for surface homeomorphisms in the isotopy class of the identity. Based on our previous work on forcing theory, this new criterion is purely topological and…
Let $M$ be a closed $3$-dimensional Riemann manifold and let $3\le r\le \infty$. We prove that there exists an open dense subset in the space of $C^r$ volume-preserving Anosov flows on $M$ such that all the flows in it are exponentially…
We consider a smooth Anosov diffeomorphism with a smooth dynamical foliation. We show upper bounds on the essential spectral radius of its transfer operator acting on anisotropic Sobolev spaces. (Such bounds are related to the essential…
We have used nanoelectromechanical resonators to probe superfluid $^4$He at different temperature regimes, spanning over four orders of magnitude in damping. These regimes are characterized by the mechanisms which provide the dominant…
We prove that in a $C^1$-open and $C^k$-dense set of some classes of $C^k$ Anosov flows all Lyapunov exponents have multiplicity 1 with respect to appropriate measures. The classes are geodesic flows with equilibrium states of…
We characterize, using commuting zero-flux homologies, those volume-preserving vector fields on a $3$-manifold that are steady solutions of the Euler equations for some Riemannian metric. This result extends Sullivan's homological…
In this article we obtain a simple topological and dynamical systems condition which is necessary and sufficient for an arbitrary pseudo-Anosov flow in a closed, hyperbolic three manifold to be quasigeodesic. Quasigeodesic means that orbits…
Despite its homotopical stability, new relevant dynamics appear in the isotopy class of a pseudo-Anosov homeomorphism. We study these new dynamics by identifying homotopically equivalent orbits, obtaining a more complete description of the…
We prove a local trace formula for Anosov flows. It relates Pollicott--Ruelle resonances to the periods of closed orbits. As an application, we show that the counting function for resonances in a sufficiently wide strip cannot have a…