Related papers: Using multiscale norms to quantify mixing and tran…

Transport maps can ease the sampling of distributions with non-trivial geometries by transforming them into distributions that are easier to handle. The potential of this approach has risen with the development of Normalizing Flows (NF)…

Concentration of measure is a phenomenon in which a random variable that depends in a smooth way on a large number of independent random variables is essentially constant. The random variable will "concentrate" around its median or…

For the problem of efficiently supplying material to a spatial region from a single source, we present a simple scaling argument based on branching network volume minimization that identifies limits to the scaling of sink density. We…

As granular materials flow and settle, interactions among particles of different sizes or properties drive mixing and segregation, producing rich dynamics that reshape systems ranging from industrial hoppers to planetary surfaces. A…

Emerging applications of machine learning in numerous areas involve continuous gathering of and learning from streams of data. Real-time incorporation of streaming data into the learned models is essential for improved inference in these…

The reverse perturbation method [Phys. Rev. E 59, 4894 (1999)] for shearing simple liquids and measuring their viscosity is extended to the Vicsek-model (VM) of active particles [Phys. Rev. Lett. 75, 1226 (1995)] and its metric-free…

Depth-averaged systems of equations describing the motion of fluid-sediment mixtures have been widely adopted by scientists in pursuit of models that can predict the paths of dangerous overland flows of debris. As models have become…

Unstable shear layers in environmental and industrial flows roll up into a series of vortices, which often form complex nonlinear merging patterns like pairs and triplets. These patterns crucially determine the subsequent turbulence, mixing…

How finite-sized material lines stretch in chaotic (mono-scale) and turbulent (multi-scale) flows remains a central but unresolved problem that governs mixing, transport and reaction. We show elongation is controlled by a finite-sampling…

Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…

A central feature of quantum metrology is the possibility of Heisenberg scaling, a quadratic improvement over the limits of classical statistics. This scaling, however, is notoriously fragile to noise. While for some noise types it can be…

Poincar{\'e} inequalities are ubiquitous in probability and analysis and have various applications in statistics (concentration of measure, rate of convergence of Markov chains). The Poincar{\'e} constant, for which the inequality is tight,…

Heterogeneity is a key aspect of complex networks, often emerging by looking at the distribution of node properties, from the milestone observations on the degree to the recent developments in mixing pattern estimation. Mixing patterns, in…

Transport equations for even-order structure functions are written for a passive scalar mixing fed by a mean scalar gradient, with a Schmidt number $\mathit{Sc}=1$. Direct numerical simulations (DNS), in a range of Reynolds numbers…

Monin-Obukhov similarity theory (MOST) stands at the center of understanding of atmospheric surface-layer turbulence. Based on the hypothesis that a single length scale determined by surface fluxes governs the turbulent exchange of…

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…

This paper is devoted to the homogenization of weakly coupled cooperative parabolic systems in strong convection regime with purely periodic coefficients. Our approach is to factor out oscillations from the solution via principal…

There are many cases in collider physics and elsewhere where a calibration dataset is used to predict the known physics and / or noise of a target region of phase space. This calibration dataset usually cannot be used out-of-the-box but…

Stochastic dynamics of a nonconserved scalar order parameter near its critical point, subject to random stirring and mixing, is studied using the field theoretic renormalization group. The stirring and mixing are modelled by a random…

The following work compares two popular mixed finite elements used to model subsurface flow and transport in heterogeneous porous media; the lowest order Raviart-Thomas element and the variational multiscale stabilized element. Comparison…