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02/26/02 Colloquium
DR. GREGOR KOVACIC
DEPARTMENT OF MATHEMATICS
RENSSELAER POLYTECHNIC INSTITUTE
DEPARTMENT OF MATHEMATICS
RENSSELAER POLYTECHNIC INSTITUTE
HAMILTONIAN AND STATISTICAL MECHANICS OF THE TRUNCATED BURGERS-HOPF EQUATION
Abstract: Recently, A. Majda and I. Timofeyev have introduced the Truncated Burgers-Hopf Equation as a prototypical test case for statistical mechanics. The talk will review the remarkable properties of this system, such as energy equipartition for a majority of randomly-chosen initial conditions, and correlation scaling that conforms with a simple dimensional argument. In addition, the newly-discovered Hamiltonian structure of the problem will be discussed. The relevance of the cubic Hamiltonian for the energy spectrum will be described within a statistical framework that includes both direct numerical simulations of the equation and a purely geometric Monte-Carol computation.