In what way did a movie use partial differential equations?
Realism in movies has grown tremendously in the past decade, mainly thanks to the work of mathematicians and computer scientists. It also helps that computers have increased in power, memory, speed, and usability. Whenever you see a certain special effect, such as an exploding spacecraft in Star Wars or a swirling maelstrom in Pirates of the Caribbean, most often those seemingly real events are generated through mathematics using special computers and computer software. In many cases the movie’s physical phenomena and interactions were developed with the use of partial differential equations.
Mathematicians develop special numerical methods and algorithms to solve complex equations, while computer scientists use that information to develop the programs to find the solutions. In the past, a movie that needed to depict a whirlpool in the ocean did so with physical props and miniaturization; with faster computers and more efficient computer structures, such as supercomputers, simulations of the whirlpool and their complex interactions are “easy” to depict. Thus, the resulting computer-generated visual effects industries are one of the most sought-after businesses in today’s action-packed movie world.
It’s not only the special effects in movies that have grown by leaps and bounds in the past decade. Computers have also been used to create more realistic animations— from animated characters to vast skyscrapers in an alien city. These seemingly solid, computer-generated animations are actually a mathematical representation of surfaces and volumes. This means the computer animator can add such realistic features to an animation as moving wrinkles in the skin or even the movement of strands of hair—all with the use of mathematics.