Related papers: Mixing for generic passive scalars by incompressib…
Although continuous density estimation has received abundant attention in the Bayesian nonparametrics literature, there is limited theory on multivariate mixed scale density estimation. In this note, we consider a general framework to…
We examine the dispersion of a passive scalar released in an incompressible fluid flow in an unbounded domain. The flow is assumed to be spatially periodic, with zero spatial average, and random in time, in the manner of the random-phase…
Diffusivity, a measure for how rapidly a fluid self-mixes, shows an intimate, but seemingly fragmented, connection to thermodynamics. On one hand, the "configurational" contribution to entropy (related to the number of mechanically-stable…
At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…
The ability to quantify distinctness of a cluster structure is fundamental for certain simulation studies, in particular for those comparing performance of different classification algorithms. The intrinsic integral measure based on the…
Continuous diffusion and flow matching models could represent a powerful alternative to autoregressive approaches for language modelling (LM), as they unlock a host of advantages currently reserved for continuous modalities, including…
In our recent works we proposed a theory of turbulence in inertial gas flow via the mean field effect of an intermolecular potential. We found that, in inertial flow, turbulence indeed spontaneously develops from a laminar initial…
Physical understanding of how the interplay between symmetries and nonlinear effects can control the scaling and multiscaling properties in a coupled driven system, such as magnetohydrodynamic turbulence or turbulent binary fluid mixtures,…
Periodic forcing of flow in compressible porous media is an important driver for solute dispersion and mixing in geological and engineered porous media subject for example to tides, pumping and recharge cycles, or fluid injection and…
We study relative dispersion of passive scalar in non-ideal cases, i.e. in situations in which asymptotic techniques cannot be applied; typically when the characteristic length scale of the Eulerian velocity field is not much smaller than…
Fluids can behave in a highly irregular, turbulent way. It has long been realised that, therefore, some weak notion of solution is required when studying the fundamental partial differential equations of fluid dynamics, such as the…
Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some…
Transport and mixing processes in fluid flows can be studied directly from Lagrangian trajectory data, such as obtained from particle tracking experiments. Recent work in this context highlights the application of graph-based approaches,…
Flow matching has emerged as a simulation-free alternative to diffusion-based generative modeling, producing samples by solving an ODE whose time-dependent velocity field is learned along an interpolation between a simple source…
Scaling has been proposed as a powerful tool to analyze the properties of complex systems, and in particular for cities where it describes how various properties change with population. The empirical study of scaling on a wide range of…
We show sufficient conditions under which the \textsc{BallWalk} algorithm mixes fast in a bounded connected subset of $\Real^n$. In particular, we show fast mixing if the space is the transformation of a convex space under a smooth…
Mixture models are often used to identify meaningful subpopulations (i.e., clusters) in observed data such that the subpopulations have a real-world interpretation (e.g., as cell types). However, when used for subpopulation discovery,…
A multicomponent extension of our recent theory of simple fluids [ U.M.B. Marconi and S. Melchionna, Journal of Chemical Physics, 131, 014105 (2009) ] is proposed to describe miscible and immiscible liquid mixtures under inhomogeneous, non…
For exchangeable data, mixture models are an extremely useful tool for density estimation due to their attractive balance between smoothness and flexibility. When additional covariate information is present, mixture models can be extended…
The use of the annual maximum series for flood frequency analyses limits the considered information to one event per year and one sample that is assumed to be homogeneous. However, flood may have different generating processes, such as…