Related papers: Universal Mixers in All Dimensions
We consider the questions of efficient mixing and un-mixing by incompressible flows which satisfy periodic, no-flow, or no-slip boundary conditions on a square. Under the uniform-in-time constraint $\|\nabla u(\cdot,t)\|_p\leq 1$ we show…
We consider the question of exponential mixing for random dynamical systems on arbitrary compact manifolds without boundary. We put forward a robust, dynamics-based framework that allows us to construct space-time smooth, uniformly bounded…
The problem of incompressible fluid mixing arises in numerous engineering applications and has been well-studied over the years, yet many open questions remain. This paper aims to address the question "what do efficient flow fields for…
We consider a model for mixing binary viscous fluids under an incompressible flow. We proof the impossibility of perfect mixing in finite time for flows with finite viscous dissipation. As measures of mixedness we consider a…
In this survey, we address mixing from the point of view of partial differential equations, motivated by applications that arise in fluid dynamics. We give an account of optimal mixing, loss of regularity for transport equations, enhanced…
In these lecture notes, we provide an introduction to the theory of mixing for incompressible flows from a PDE perspective. We discuss both the Lagrangian (ODE) and Eulerian (PDE, continuity equation) viewpoints, and introduce suitable…
Mixing by incompressible flows is a ubiquitous yet incompletely understood phenomenon in fluid dynamics. While previous studies have focused on optimal mixing rates, the question of its genericity, i.e., whether mixing occurs for typical…
We prove the existence of a large class of global-in-time expanding solutions to vacuum free boundary compressible Euler flows without relying on the existence of an underlying finite-dimensional family of special affine solutions of the…
Optimizing the energy efficiency of driving processes provides valuable insights into the underlying physics and is of crucial importance for numerous applications, from biological processes to the design of machines and robots. Knowledge…
We introduce a general-purpose method for optimising the mixing rate of advective fluid flows. An existing velocity field is perturbed in a $C^1$ neighborhood to maximize the mixing rate for flows generated by velocity fields in this…
Microscopic flows are almost universally linear, laminar and stationary because Reynolds number, $Re$, is usually very small. That impedes mixing in micro-fluidic devices, which sometimes limits their performance. Here we show that truly…
Irreversible aggregation is an archetypal example of a system driven far from equilibrium by sources and sinks of a conserved quantity (mass). The source is a steady input of monomers and the evaporation of colliding particles with a small…
Turbulent flows, ubiquitous in nature and engineering, comprise fluctuations over a wide range of spatial and temporal scales. While flows with fluctuations in thermodynamic variables are much more common, much less is known about these…
In the context of the long-standing issue of mixing in infinite ergodic theory, we introduce the idea of mixing for observables possessing an infinite-volume average. The idea is borrowed from statistical mechanics and appears to be…
We study the problem of the optimal mixing of a passive scalar under the action of an incompressible flow in two space dimensions. The scalar solves the continuity equation with a divergence-free velocity field, which satisfies a bound in…
In this paper, we extend our study of mass transport in multicomponent isothermal fluids to the incompressible case. For a mixture, incompressibility is defined as the independence of average volume on pressure, and a weighted sum of the…
The universality of the directed polymer model and the analogous KPZ equation is supported by numerical simulations using non-Gaussian random probability distributions in two, three and four dimensions. It is shown that although in the…
Majority of theoretical results regarding turbulent mixing are based on the model of ideal flows with zero correlation time. We discuss the reasons why such results may fail for real flows and develop a scheme which makes it possible to…
Despite the flexibility and popularity of mixture models, their associated parameter spaces are often difficult to represent due to fundamental identification problems. This paper looks at a novel way of representing such a space for…
We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…