012407 - Lecture 2 Evolutionary Process What is(or what...

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01/24/2007: Lecture 2 Evolutionary Process: What is (or, what will we mean by) an "evolutionary process?" The word "evolution" comes up a lot in science and engineering (e.g. RLC circuit with sources.) From a vector x whose entries are capacitor voltages and inductor currents we can generically write an ODE: = + Dxt Axt Et = Dxt dxdt E(t) is a vector of functions dependent on sources This equation governs the time-"evolution" of state variables (ie, entries in x(t)) If you have nonlinear stuff, get: ( )= ( ( ), ( ) ) Dx t f x t E t -> which is a non-linear ODE. Dynamical Systems Theory studies things like this. In Newtonian physics, similarly, for a system of N particles – let: x i = position of particle i p i = momentum of particle i then (m i = mass of pt. i) = × ( ) Dxit 1mi pi t = ( ) Dpit fi t <-- net force on particle I (can depend on {xj, pj} and our "exogenous" forces.)
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  • Spring '07
  • Algorithms, Force, z=xp= 2N-dimensional vector, Dynam ical Systems, key functional molecules

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