期刊
PHYSICA D-NONLINEAR PHENOMENA
卷 436, 期 -, 页码 -出版社
ELSEVIER
DOI: 10.1016/j.physd.2022.133322
关键词
Hagen-Poiseuille flows in networks; Biological networks; Flows in microchannels; Networks
A class of equations describing low Reynolds number steady flows of incompressible and viscous fluids in networks made of straight channels has been derived. The adaptive conductivities describe the transverse channel elasticities, and a steady state tree geometry for the graph connecting sources and sinks is reached asymptotically in time. A phase transition tuned by an order parameter for the adapted steady state graph has been found.
We derive a class of equations describing low Reynolds number steady flows of incompressible and viscous fluids in networks made of straight channels, with several sources and sinks and adaptive conductivities. A graph represents the network, and the fluxes at sources and sinks control the flow. The adaptive conductivities describe the transverse channel elasticities, mirroring several network structures found in physics and biology. Minimising the dissipated energy per unit of time, we have found an explicit form for the adaptation equations and, asymptotically in time, a steady state tree geometry for the graph connecting sources and sinks is reached. A phase transition tuned by an order parameter for the adapted steady state graph has been found. (C) 2022 Elsevier B.V. All rights reserved.
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