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SUMMARY:Accelerating time averaging by adding a Lie derivative of an auxil
 iary function - Professor Sergei Chernyshenko (Imperial College London)
DTSTART:20221104T124500Z
DTEND:20221104T134500Z
UID:TALK183482@talks.cam.ac.uk
CONTACT:Paras Vadher
DESCRIPTION:Obtaining time-averaged quantities with sufficient accuracy ca
 n be challenging computationally for systems with a chaotic behaviour.  We
  replace the quantity being averaged with another quantity having the same
  average but such that it is easier to average. If W(t) is a bounded diffe
 rentiable function\, then the infinite time average of its derivative is z
 ero. Hence\, rather than numerically averaging the quantity of interest\, 
 which we will denote F\, one can average F+dW/dt. We explore first the sim
 plest way of choosing W(t)\, which is to ensure that the fluctuation ampli
 tude of F+dW/dt is smaller than the fluctuation amplitude of F. For this\,
  F and dW/dt should be correlated. This can often be achieved by taking W(
 t)=V(x(t))\, where x is the state of the dynamical system. The talk will d
 iscuss our tests of this idea. (A spoiler: the acceleration is only modera
 te but is worth doing because it is easy. Further improvement requires pro
 gress on interesting and challenging problems.) \n
LOCATION:LR12
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