Related papers: Using multiscale norms to quantify mixing and tran…
In the scope of the statistical description of dynamical systems, one of the defining features of chaos is the tendency of a system to lose memory of its initial conditions (more precisely, of the distribution of its initial conditions).…
Mixing-via-shearing is a powerful and versatile method for establishing mixing properties of smooth parabolic flows. In its quantitative form, it provides upper bounds on the decay of correlations for sufficiently smooth observables.…
This article performs a unified convergence analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified analysis is enabled through the…
We show that the natural scaling of measurement for a particular problem defines the most likely probability distribution of observations taken from that measurement scale. Our approach extends the method of maximum entropy to use…
The statistics of a passive scalar randomly emitted from a point source is investigated analytically. Our attention has been focused on the two-point equal-time scalar correlation function. The latter is indeed easily related to the…
Multivariate normal mixtures provide a flexible method of fitting high-dimensional data. It is shown that their topography, in the sense of their key features as a density, can be analyzed rigorously in lower dimensions by use of a…
Asymptotic homogenisation is considered for problems with integral constraints imposed on a slowly-varying microstructure; an insulator with an array of perfectly dielectric inclusions of slowly varying size serves as a paradigm. Although…
The mixing of binary fluids by stirrers is a commonplace procedure in many industrial and natural settings, and mixing efficiency directly translates into more homogeneous final products, more enriched compounds, and often substantial…
Mixing of a passive scalar in the peripheral region close to a wall is investigated by means of accurate direct numerical simulations of both a three-dimensional Couette channel flow at low Reynolds numbers and a two-dimensional synthetic…
Methods for quantifying mixing in microfluidics have varied largely in the past, and various indices have been employed to represent the extent of mixing. Mixing between two or more colored liquids is usually quantified using simple…
Many porous media are mixtures of inert and reactive materials, manifesting spatio-chemical heterogeneity. We study the evolution of scalar transport in a chemically heterogeneous material that mimics a green roof soil substrate,…
This paper deals with simulation of flow and transport in porous media such as transport of groundwater contaminants. We first discuss how macro scale equations are derived and which terms have to be closed by models. The transport of…
Stratified spin-up experiments in enclosed cylinders have reported the presence of small pockets of well-mixed fluids but quantitative measurements of the mixedness of the fluid has been lacking. Previous numerical simulations have not…
A variation principle for mass transport in solids is derived that recasts transport coefficients as minima of local thermodynamic average quantities. The result is independent of diffusion mechanism, and applies to amorphous and…
Monin-Obukhov Similarity Theory (MOST), the traditional surface layer theory used to understand the behavior, scaling and exchange of heat, water vapor and carbon dioxide between the land surface and atmosphere relies on a number of…
The effect of coordination on transport is investigated theoretically using random networks of springs as model systems. An effective medium approximation is made to compute the density of states of the vibrational modes, their energy…
Direct numerical simulations are carried out to investigate scalar mixing in an isotropic turbulent flow with a time-periodic forcing. For high amplitudes of the modulation, it is shown that the average mixing rate is negatively affected at…
The purpose of this paper is to develop a new effective approach to higher-order mixing in the semisimple setting. We prove effective exponential mixing of all orders for partially hyperbolic algebraic actions, under a strong spectral-gap…
We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective isto minimise/maximise macroscopic quantities, such as traffic volume or average…
Sampling from unnormalized densities using diffusion models has emerged as a powerful paradigm. However, while recent approaches that use least-squares `matching' objectives have improved scalability, they often necessitate significant…