J Waggle wrote: "Do you have reference supporting that outer beespush to the center of the cluster?"

No, I confess it is only a commonsense assumption, which is not inconsistent with the mathematical model in your reference. The model is interesting but appears simplistic. 

The model shows  that cluster temperatures can result from individual bees taking action to regulate their individual temperatures.  i.e.there is no need to assume all the bee brains connect wirelessly into a giant computer. It says: individual bees in the mantel can pack closer by better aligning with neighbours, so increasing heat transfer with neighbours  (and inadvertently but beneficially reducing convection losses from the cluster overall); if still cold bees heat themselves by shivering.
  
By common observation, colonies consume 30  to  60lbs of stores during the winter clustering. The bees cannot fill that much into their stomachs before clustering, so individual bees must be able to refill from time to time.  Those in the mantel will need to shiver most so will run out of food fastest. 
There seem only two ways bees in the mantel can refuel: 1) by food sharing bee to bee from the inside to the outside of the cluster - unlikely as the bees are too tightly packed to align head to head; or the outer bees work their way to the hollow centre and are then fed by the active house bees or fill themselves from the open food cells in the hollow core.

We all know the winter cluster forms on the bottom of the combs and flows upwards as stores are consumed. It is not fixed in position. so the individual bees certainly do move.
    
Overall, the model seems overly mathematical and insufficiently attentive to bee biology. 

It notes that bees cluster as a swarm (which is just a ball of bees)  but then considers the winter cluster on combs without (so far as I saw on a quick read) taking into account the conductivity of the combs and the fact that the combs require some bees to lie horizontally spaced apart by the cell walls and so unable to pack more closely when they wish. The winter cluster must be a combination of vertically hanging bees able to adjust the packing density and these horizontal bees at fixed spacing and must be very complex indeed to model. 

Or maybe I read through the article too fast? 

In haste 
Robin 
  



________________________________
 From: J. Waggle <[log in to unmask]>
To: [log in to unmask] 
Sent: Saturday, 22 March 2014, 22:32
Subject: Re: [BEE-L] Extreme Cold Wipes out Honey Bees Across Iowa
 

>Why a single bee?  All the outer bees on the lower part of the cluster would be the coldest , so first to use up food in tummies due to greatest shuddering to keep warm.  So a whole wave would need to press their way inside to re-fuel.  The following wave would push them always in the same direction, upwards, setting up a persistent 'convection' current. 
Robin

Do you have reference supporting that outer bees
push to the center of the cluster?  I would love to 
see any related info. Thanks 

All I can find is references that state bees on the mantel
of a cluster are unaware of conditions at the core of the
cluster, therfore, how would they know that they need
to press their way inside?

"....Bees on the mantle are
not aware of the conditions of the bees in the core\ and
those in the core do not produce excess heat in order
to warm the bees on the mantle[ The regulation of the
core temperature near a set point results from each bee
attempting to remain at a comfortable temperature
within the..."

http://each.uspnet.usp.br/sistcomplexos/SC1/Thermoregulation_in_bee_hives/SelfOrganizationHoneyBees.pdf

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