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SUMMARY:Interplay of dynamical instability\, stochasticity\, and nonlinear
  energy transfer in fluid and mechanical systems
DTSTART:20120316T093000
DTSTAMP:20260414T072349Z
UID:9e24436bf137c6f3036b8440f119edcbf50a6fbe231ad11a59802505
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dr. Themistoklis Sapsis\, New York University\nWe present a ne
 w perspective for complex systems based on the interplay between energy ex
 changes (energy transfer rates\, energy cascades\, and spectra)\, dynamica
 l features (such as instabilities\, bifurcations\, and Lyapunov exponents)
 \, and statistical characteristics (such as probability density functions\
 , correlation functions\, and rare events). All of these notions have been
  used in the past\, usually independently from each other\, to describe co
 mplexity in various scientific fields. Turbulence is perhaps the most famo
 us example of such complexity although mechanical systems may also present
  similar features. We establish a rigorous link showing inherent interplay
  and connections of the above viewpoints\, and highlighting the necessity 
 to consider them from a unified perspective. To demonstrate this we focus 
 on the problem of unstable fluid flows. First\, we present an efficient un
 certainty quantification scheme that allows for the nonlinear evolution of
  statistics based on a stochastic\, order-reduction framework.  Using thi
 s stochastic approach\, which fully respects and accounts for the nonlinea
 r dynamical features of the system\, we illustrate how linearly stable and
  unstable modes operate synergistically with essentially nonlinear\, conse
 rvative\, energy transfer mechanisms to produce an energy cascade which re
 sults in collapse of the probability measure in low-dimensional sets. The 
 aforementioned findings are based on rigorous theorems that are demonstrat
 ed by specific numerical applications. In the last part of the talk we sho
 w how these ideas can be used for the design of mechanical analogues of tu
 rbulent energy cascades\, in order to perform irreversible nonlinear targe
 ted energy transfer between structural components of mechanical systems. I
 n particular\, by attaching light-weighted\, essentially nonlinear\, attac
 hments to a main structure we are able to passively ‘guide’ energy to 
 specific modes of motion.
LOCATION:MEB10
STATUS:CONFIRMED
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