Related papers: Mixing for generic passive scalars by incompressib…
We investigate topological mixing of compatible random substitutions. For primitive random substitutions on two letters whose second eigenvalue is greater than one in modulus, we identify a simple, computable criterion which is equivalent…
Mixed damping is a physical effect that occurs when a heavy species is coupled to a relativistic fluid which is itself free streaming. As a cross-case between collisional damping and free-streaming, it is crucial in the context of…
We investigate the existence of weak solutions to a multi-component system, consisting of compressible chemically reacting components, coupled with the compressible Stokes equation for the velocity. Specifically, we consider the case of…
A partial differential equation governing the global evolution of the joint probability distribution of an arbitrary number of local flow observations, drawn randomly from a control volume, is derived and applied to examples involving…
A new concept of semi-compressible fluids is introduced for slightly compressible visco-elastic fluids (typically rather liquids than gasses) where mass density variations are negligible in some sense, while being directly controlled by…
Amorphous glassy materials of diverse nature -- concentrated emulsions, granular materials, pastes, molecular glasses -- display complex flow properties, intermediate between solid and liquid, which are at the root of their use in many…
Self-similar stable mixed moving average processes can be related to nonsingular flows through their minimal representations. Self-similar stable mixed moving averages related to dissipative flows have been studied, as well as processes…
Self-sustained oscillations in cavity-flows can be strongly influenced by shear layer instability acting together with feedback and modulation mechanisms. When coherently organized, these oscillations lock-on at a fundamental frequency and…
The majority of available numerical algorithms for interfacial two-phase flows either treat both fluid phases as incompressible (constant density) or treat both phases as compressible (variable density). This presents a limitation for the…
In this paper we analyze the transport of passive tracers by deterministic stationary incompressible flows which can be decomposed over an infinite number of spatial scales without separation between them. It appears that a low order…
Transport of scalar fields in compressible flow is investigated. The effective equations governing the transport at scales large compared to those of the advecting flow are derived by using multi-scale techniques. Ballistic transport…
Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…
The microscopic approach to the description of the phase behaviour and critical phenomena in binary fluid mixtures is proposed. It is based on the method of collective variables with a reference system. The physical nature of the order…
Collapsibility deals with the conditions under which a conditional (on a covariate W) measure of association between two random variables X and Y equals the marginal measure of association, under the assumption of homogeneity over the…
Finite mixture models are statistical models which appear in many problems in statistics and machine learning. In such models it is assumed that data are drawn from random probability measures, called mixture components, which are…
When a mixture of two viscous liquids flows past a solid wall there is an ambiguity in the use of the no-slip boundary condition. It is not obvious whether the mass-averaged velocity, the volume-averaged velocity, the individual species…
Estimating density ratios between pairs of intractable data distributions is a core problem in probabilistic modeling, enabling principled comparisons of sample likelihoods under different data-generating processes across conditions and…
Hydrodynamic equations for ideal incompressible fluid are written in terms of generalized stream function. Two-dimensional version of these equations is transformed to the form of one dynamic equation for the stream function. This equation…
Versatile mixed finite element methods were originally developed by Chen and Williams for isothermal incompressible flows in "Versatile mixed methods for the incompressible Navier-Stokes equations," Computers & Mathematics with…
In its continuous version, the entropy functional measuring the information content of a given probability density may be plagued by a "measure" problem that results from improper weighting of phase space. This issue is addressed…