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SUMMARY:Concentration fluctuations in a bacterial suspension - Subramanian
 \, G (Engineering Mechanics Unit\, JNCASR\, Bangalore)
DTSTART:20130625T100000Z
DTEND:20130625T104500Z
UID:TALK45903@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Recent analyses and simulations have identified an instability
  of a quiescent bacterial suspension above a threshold concentration\, (nL
 3)crit = (5/C)(L/U	au)\, where n is the bacterium number density\, L and U
  the bacterium length and swimming speed\, t the mean interval between tum
 bles\, and C a measure of the intrinsic force-dipole. This instability is 
 thought to underlie the large-scale coherent motions observed in experimen
 ts. There\, however\, remains a discrepancy between theory and simulations
 . While the former predicts a spatially homogeneous instability with coupl
 ed orientation and velocity fluctuations\, simulations have observed large
 -scale concentration fluctuations. Even in the stable regime\, solutions o
 f the linearized equations reveal significant concentration fluctuations. 
 \n\nWe will formulate an analytical solution that illustrates the lineariz
 ed evolution of the velocity\, orientation and concentration fields in a b
 acterial suspension starting from an arbitrary initial condition. The anal
 ysis relies on a remarkable correspondence between orientation fluctuation
 s in a bacterial suspension and vorticity fluctuations in an inviscid flui
 d. The governing operators in both cases possess singular continuous spect
 ra in addition to discrete modes. The dynamics of the singular orientation
  modes leads to transient growth of concentration fluctuations in the mann
 er that the singular vorticity modes lead to kinetic energy growth in high
 -Reynolds-number shearing flows. We will discuss the velocity\, orientatio
 n and stress correlations\, emerging from an uncorrelated Poisson field\, 
 both below and above the critical concentration.\n\nWe also analyze the ro
 le of tumbling as a source of fluctuations. Regarding a tumble as a linear
  collision governed by Poisson statistics allows one to write down the ori
 entation-space noise\, and this in turn leads to the analog of the fluctua
 ting hydrodynamic equations for a bacterial suspension.\n\nCo-author: Dona
 ld Koch (Chemical and bio-molecular engineering\, Cornell University\, NY\
 , USA.)\n
LOCATION:Seminar Room 1\, Newton Institute
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