Kevin T. Grosvenor, Niels A. Obers, Subodh P. Patil
SciPost Phys. 19, 071 (2025) ·
published 25 September 2025
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We derive the hydrodynamic equations of perfect fluids without boost invariance [J. de Boer et al., SciPost Phys. 5, 003 (2018)] from kinetic theory. Our approach is to follow the standard derivation of the Vlasov hierarchy based on an a-priori unknown collision functional satisfying certain axiomatic properties consistent with the absence of boost invariance. The kinetic theory treatment allows us to identify various transport coefficients in the hydrodynamic regime. We identify a drift term that effects a relaxation to an equilibrium where detailed balance with the environment with respect to momentum transfer is obtained. We then show how the derivative expansion of the hydrodynamics of flocks can be recovered from boost non-invariant kinetic theory and hydrodynamics. We identify how various coefficients of the former relate to a parameterization of the so-called equation of kinetic state that yields relations between different coefficients, arriving at a symmetry-based understanding as to why certain coefficients in hydrodynamic descriptions of active flocks are naturally of order one, and others, naturally small. When inter-particle forces are expressed in terms of a kinetic theory influence kernel, a coarse-graining scale and resulting derivative expansion emerge in the hydrodynamic limit, allowing us to derive diffusion terms as infrared-relevant operators distilling different parameterizations of microscopic interactions. We conclude by highlighting possible applications.
SciPost Phys. Core 8, 058 (2025) ·
published 28 August 2025
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We consider two-dimensional continuum fluids with odd viscosity under a chiral body force. The chiral body force makes the low-energy excitation spectrum of the fluids gapped, and the odd viscosity allows us to introduce the first Chern number of each energy band in the fluids. Employing a mapping between hydrodynamic variables and U(1) gauge field strengths, we derive a U(1) gauge theory for topologically nontrivial waves. The resulting U(1) gauge theory is given by the Maxwell-Chern-Simons theory with an additional term associated with odd viscosity. We then explicitly solve the equations of motion for the gauge fields in the presence of the boundary and find edge mode solutions. We finally confirm the bulk-boundary correspondence in the context of continuum systems.
SciPost Phys. 14, 080 (2023) ·
published 24 April 2023
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A continuum theory of linearized Helmholtz-Kirchoff point vortex dynamics about a steadily rotating lattice state is developed by two separate methods: firstly by a direct procedure, secondly by taking the long-wavelength limit of Tkachenko's exact solution for a triangular vortex lattice. Solutions to the continuum theory are found, described by arbitrary anti-holomorphic functions, and give power-law localized edge modes. Numerical results for finite lattices show excellent agreement to the theory.
SciPost Phys. Lect. Notes 101 (2025) ·
published 10 October 2025
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Flows are essential to transport resources over large distances. As soon as diffusion becomes time-limiting, flows are needed. Flows are key for the function of multiple human organs, from the blood vasculature to the lungs, the digestive tract, the lymphatic system, and many more. While physics governs the flow dynamics, biology's response to flows governs the flow network architecture. We start with the fluid physics of Stokes flow, the prerequisite to describe the flows in biological flow networks. Then we explore how the network adaptation dynamics of biological flow networks reorganize network architecture to minimize flow dissipation or homogenize transport, storing memories of past flows along the way.
