Langevin simulations of protoplasmic streaming in non-Euclidean geometry

Abstract

Abstract The protoplasmic streaming in plant cells enables the transportation of biological materials. This circular flow was experimentally observed with laser Doppler velocimetry, and it was reported that there are two peaks in the velocity distribution. Recently, we reported that these peaks are numerically reproduced by the stochastic or Langevin Navier-Stokes (N-S) simulation technique. However, interactions between fluid and the biological materials have not yet been implemented. In this report, we show that this complex interaction can be simulated in the N-S equation with the Finsler geometry (FG) modeling technique by including an internal directional degree of freedom σ (∈ S 1: circle) corresponding to the small biological materials. We find that the interaction effectively makes the viscosity coefficient small when the variable σ is uniformly aligned.