Year: 2025
Type: preprint
Abstract: We develop a unified kinetic theory for ordered fluids, which systematically extends the phase space with the appropriate generalized angular momenta. Our theory yields a uniquely determined mesoscopic model for any continuum with microstructure that is characterized by Capriz's order parameter manifold. We illustrate our theory with three running examples: liquids saturated with non-diffusive gas bubbles, liquids composed of calamitic (rodlike) molecules, and liquids composed of calamitic molecules with additional head-to-tail symmetry. We discuss the symmetries of the microscopic interactions via Noether's theorem, and use them to characterize the conserved quantities mesoscopic dynamics. We derive the mesoscopic model for ordered fluids from a kinetic point of view assuming that the microscopic interactions are of weak nature when it comes to the ordering of the fluid. Lastly, we discuss under which conditions an H-theorem result holds at the mesoscopic scale and for which Vlasov potential we can expect the emergence of collective behavior.
Source: arXiv (Cornell University)
Authors: Carrillo, José A., Farrell, Patrick E., Medaglia, Andrea, Zerbinati, Umberto
Institutions: University of Oxford, University of Ferrara, Charles University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: DMS-EPSRC: Stability Analysis for Nonlinear Partial Differential Equations across Multiscale Applications, Spectral element methods for fractional differential equations, with applications in applied analysis and medical imaging, G1175115578, G210041235, G2262748287, G2281333282, G2601397997, G2691952350, G300979063, G34346518, G3452655474, G3480869486, G3681454997, G4042783231, G4162891482, G425668148, G5080475149, G5180915604, G5195188938, G567365627, SysGenX: Composable software generation for system-level simulation at Exascale, G6700243956, G7084143925, PRISM: Platform for Research In Simulation Methods, G7853015121
OpenAlex ID: W6948161567
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