Chaos Chaos Predictability, Turbulence in fluids, Duffing oscillator, Lorenz waterwheel 1 / 10 A chaotic system exhibits a positive Lyapunov exponent of 1.0. How does the separation between two trajectories change after 2 time units? Doubles Quadruples Triples Exponentially increases 2 / 10 A chaotic system has a fractal dimension of 2.5. What does this indicate about the system? The system is one-dimensional. The system has a purely integer dimension. The system exhibits self-similarity with non-integer geometry. The system is non-chaotic. 3 / 10 A particle in a chaotic system exhibits an average separation rate of 0.1 m/s from a neighboring trajectory. If the Lyapunov exponent is 0.2, how much time does it take for the separation to double? 3.5 seconds 10 seconds 15 seconds 20 seconds 4 / 10 A system has a Lyapunov exponent of 0.5. How does the distance between two nearby trajectories change after 10 time units? Increases by a factor of e^{0.5} Increases by a factor of e^{5} Decreases by a factor of e^{5} Remains the same 5 / 10 In a chaotic system, what happens to predictability as time progresses? It remains constant It improves It diminishes It becomes infinite 6 / 10 In fluid dynamics, what term describes the chaotic motion of fluid layers? Laminar flow Turbulence Viscous flow Critical flow 7 / 10 The double pendulum has a total energy E of 20 J. If small perturbations lead to chaotic motion, what remains conserved despite the chaos? Momentum Angular position Energy Lyapunov exponent 8 / 10 The logistic map x_{n+1} = r x_n (1 – x_n) exhibits chaotic behavior for which range of r? r < 2 2 < r < 3 3 < r < 4 r > 4 9 / 10 Which equation models chaos in electrical circuits? Kirchhoff’s law Duffing oscillator Ohm’s law Coulomb’s law 10 / 10 Which famous experiment illustrates chaos theory? Lorenz waterwheel Millikan oil-drop experiment Rutherford scattering experiment Young’s double-slit experiment Your score is By WordPress Quiz plugin
