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SUMMARY:Generalizing the Reynolds number from turbulence to Self Organized
  Criticality and ecosystems - Sandra C. Chapman (University of Warwick)
DTSTART:20080424T093000Z
DTEND:20080424T110000Z
UID:TALK11773@talks.cam.ac.uk
CONTACT:Christian Franzke
DESCRIPTION:In fluid turbulence a single control parameter\, the Reynolds 
 number R_E\, which is a function of macroscopic system variables is suffic
 ient to quantify the transition from ordered (laminar) to disordered (turb
 ulent) flow. We suggest that a wider class of systems has this property\, 
 including Self Organized Criticality (SOC) and ecosystem models for specie
 s abundance. These systems can all be driven into a state with defining ch
 aracteristics: they have many degrees of freedom (d.o.f.)\; are driven\, d
 issipating and out of equilibrium\; are on average in a steady state\; and
  show scaling over a large dynamic range. The Reynolds number expresses th
 e number of d.o.f.\, or energy carrying modes in the system. For avalanche
  models exhibiting SOC\, d.o.f. refer to avalanche sizes and the Reynolds 
 number R_A that we identify is simply the well known ratio of the driving 
 rate to system dissipation rate. The SOC slowly driven interaction dominat
 ed limit is reached by taking R_A to zero\; we show this maximizes the num
 ber of d.o.f. in the opposite sense to fluid turbulence. This result clari
 fies the much debated relationship between turbulence and SOC. In ecosyste
 ms\, the Reynolds number R_B that we propose depends on the rate at which 
 biomass\, or energy\, is supplied to\, and is removed from\, an ecosystem.
  As R_B increases so does the abundance of species\, or d.o.f.\, as in flu
 id turbulence. This points to the possibility of a critical value of the R
 eynolds number at which the onset of diversification of species occurs.
LOCATION:British Antarctic Survey\, Room 307
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