Interfaces and Mixing - Non-equilibrium Dynamics and Conservation Laws at Continuous and Kinetic Scales

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Background

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 purification of water requires a better understanding of non-equilibrium transport of interfaces and mixing.

Interfacial transport and mixing and non-equilibrium processes are exceedingly challenging to study.
Their dynamics 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. Interfacial transport and mixing 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 transport may lead to self-organization and order, thus offering new opportunities for diagnostics and control. Capturing properties of interfaces and mixing, enabling their accurate description and conservative properties, solving the boundary value problems - can aid better understanding of the fundamental of Eulerian and Lagrangian dynamics, and developing methods of control of non-equilibrium transport in nature and technology.
Significant success was recently achieved in understanding of interfacial transport and 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, and for applying the fundamentals of non-equilibrium transport to address the contemporary challenges of modern science, technology and society.

Our Research Topic builds upon recent achievements in the understanding 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. The Research Topic brings together mathematicians and scientists from applied mathematics, applied analysis, dynamical and complex systems, stochastic processes and data analysis, dynamics of fluid and plasmas, industrial mathematics and material science. Our Research Topic motivates the discussions of rigorous mathematical problems, theoretical approaches and state-of-the-art numerical simulations along with advanced data analysis techniques. It serves to explore the state-of-the-art in the areas of interfaces and non-equilibrium transport, to elaborate the methods of studies of boundary value problems at kinetic and at continuous scales, and to chart new research directions in this field.

Note: This Research Topic builds on this 2019 Matrix seminar, and the contributing authors include leading experts and researchers at experienced and early stages of their carriers.

Keywords: interfaces and mixing, non-equilibrium dynamics, conservation laws, boundary value problem, Eulerian and Lagrangian transports

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