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Name: _________________________ | Period: ___________________ |

This test consists of 15 multiple choice questions and 5 short answer questions.

## Multiple Choice Questions

**1. What is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space?**
**(a)** Oscillation. **(b)** Dynamical system. **(c)** Boundary layer. **(d)** Pattern formation.

**2. In control theory, a system is _____ if any of the roots of its characteristic equation has real part greater than zero.**
**(a)** Changing. **(b)** Stable. **(c)** Unchanging. **(d)** Unstable.

**3. According to Gleick, Albert Libchaber had a similar background to who, living as a refugee during World War II?**
**(a)** Benoit Mandelbrot. **(b)** Leo Kadanoff. **(c)** Michael Barnsley. **(d)** Albert Libchaber.

**4. In what year was Mitchell Feigenbaum awarded the Wolf Prize in Physics?**
**(a)** 1977. **(b)** 1980. **(c)** 1983. **(d)** 1986.

**5. What mathematical term refers to a bifurcation in which the system switches to a new behavior with twice the period of the original system in a discrete dynamical system?**
**(a)** Software visualization. **(b)** Dynamic equilibrium. **(c)** Period doubling bifurcation. **(d)** The Navier-Stokes equation.

**6. What refers to the spread of momentum between particles of matter, usually in the liquid state?**
**(a)** Theoretical physics. **(b)** Chaos theory. **(c)** Momentum diffusion. **(d)** Turbulent flow.

**7. In fluid dynamics, what condition for viscous fluids states that at a solid boundary, the fluid will have zero velocity relative to the boundary?**
**(a)** No-slip condition. **(b)** Chaos theory. **(c)** Period doubling bifurcation. **(d)** Momentum diffusion.

**8. When was Heinz-Otto Peitgen born?**
**(a)** 1939. **(b)** 1948. **(c)** 1942. **(d)** 1945.

**9. Who is attributed with the following quote in Chapter 5, "Strange Attractors": "Big whorls have little whorls which feed on their velocity, and little whorls have lesser whorls and so on to viscosity"?**
**(a)** Lewis F. Richardson. **(b)** Mitchell Feigenbaum. **(c)** Johann Wolfgang von Goethe. **(d)** Harry L. Swinney.

**10. In vector calculus, what refers to a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change?**
**(a)** Cantor dust. **(b)** Gradient. **(c)** Boundary layer. **(d)** Euclidean space.

**11. Who along with Heinz-Otto Peitgen studied phase transitions, nonmagnetization and magnetization in materials and their picture of those boundaries showed the complex beauty that began to seem to natural?**
**(a)** Feigenbaum. **(b)** Kadanoff. **(c)** Richter. **(d)** Mandelbrot.

**12. Who began to call the global construction of fractals "the chaos game" according to the author in Chapter 8, "Images of Chaos"?**
**(a)** Conrad Aiken. **(b)** Leo Kadanoff. **(c)** Albert Libchaber. **(d)** Michael Barnsley.

**13. Who was a German writer, pictorial artist, biologist, theoretical physicist, and polymath?**
**(a)** Harry Swinney. **(b)** Johann Wolfgang von Goethe. **(c)** Jean Racine. **(d)** Gustav Mahler.

**14. Where was Heinz-Otto Peitgen born?**
**(a)** Johannesburg, South Africa. **(b)** Nimbin, Australia. **(c)** Nümbrecht, Germany. **(d)** Warsaw, Poland.

**15. When did Albert Libchaber win the Wolf Prize in Physics?**
**(a)** 1955. **(b)** 1986. **(c)** 1971. **(d)** 1952.

## Short Answer Questions

**1.** Where did Mitchell Feigenbaum attend for graduate study in electrical engineering but changed his area to physics?

**2.** Albert Libchaber graduated with a bachelor degree in mathematics from what institution?

**3.** Albert Libchaber made the first experimental observation of the _____ that leads to chaos and turbulence in convective Rayleigh-Benard systems.

**4.** What is a sub-discipline of fluid mechanics that deals with the natural science of fluids (liquids and gases) in motion?

**5.** What exists when a reversible reaction ceases to change its ratio of reactants/products, but substances move between the chemicals at an equal rate, meaning there is no net change?

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