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Edited and reviewed by: José S. Andrade Jr., Federal University of Ceara, Brazil

This article was submitted to Statistical and Computational Physics, a section of the journal Frontiers in Applied Mathematics and Statistics

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Interfacial transport and mixing are non-equilibrium processes coupling kinetic to macroscopic scales. They occur in fluids, plasmas and materials over celestial events to molecules. Examples include supernovae and fusion, planetary convection and reactive fluids, wetting and adhesion, turbulence and turbulent mixing, nano-fabrication and bio-technology. Addressing the societal challenges posed by alternative energy sources, efficient use of non-renewable resources and climate change requires a better understanding of non-equilibrium transport of interfaces and mixing [

Non-equilibrium dynamics of interfaces and interfacial mixing are exceedingly challenging to study. These processes often involve sharp changes of vector and scalar fields, and may also include strong accelerations and shocks, radiation transport and chemical reactions, diffusion of species and electric charges, among other effects. They are inhomogeneous, anisotropic, non-local, and statistically unsteady. At macroscopic scales, their spectral and invariant properties differ substantially from those of canonical turbulence. At atomistic and meso-scales, the non-equilibrium dynamics depart dramatically from the standard scenario given by Gibbs ensemble averages and the quasi-static Boltzmann equation. At the same time, non-equilibrium dynamics of interfaces and interfacial mixing may lead to self-organization and order, thus providing with new opportunities for diagnostics and control. Capturing properties of interfaces and mixing, enabling their accurate description and conservative properties, solving the boundary value problems within Eulerian and Lagrangian frameworks—can aid better understanding of non-equilibrium dynamics in nature and technology [

Significant success was recently achieved in understanding of interfaces and interfacial mixing on the sides of theoretical analysis, large-scale numerical simulations, and data analysis. This success opens new opportunities for studies of fundamentals of non-equilibrium dynamics across the scales, for developing a unified description of particles and fields on the basis of synergy of theory, numeric and data analysis, and for applying these fundamentals to address the contemporary challenges of modern science, technology and society [

This Research Topic builds upon recent achievements in the understanding of interfacial transport and mixing using theoretical analysis, large-scale numerical simulations, and data analysis, and is focused on conservation laws and boundary value problems, from continuous to kinetic scales. It brings together mathematicians and scientists from applied mathematics and applied analysis, dynamical systems and data analysis, fluid dynamics and industrial mathematics [

We expect this Research Topic of papers to explore and to assess the state-of-the-art in the fundamentals of interfaces and mixing and their non-equilibrium dynamics; to elaborate the novel methods of studies of boundary value problems at kinetic and at continuous scales; and to chart new research directions in this fundamental and actively developing research area of mathematical physics.

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