However, such simulations still cannot capture the behaviors of interest: Some fail to explode, while others explode but with less energy than a real supernova. So astrophysicists began to simulate stars with a shape parameter as well as a size parameter, and they called these two-dimensional simulations. Of course, real stars are not so symmetric they bulge at the equator, due to rotation. Unfortunately, it doesn’t work: You can’t get a one-dimensional star to explode, and so simulations based on that simplified model cannot represent all of the important aspects of this complex system.
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Astrophysicists call this a one-dimensional theory because all of the quantities depend on one parameter, the distance from the center of the star. It is possible to create a rudimentary theory of supernovas by assuming that the star is perfectly symmetrical. The study of supernovas is a perfect case in point. Now, however, the scientific universe has changed. For example, they might assume the solutions were symmetric, or simplify a problem to two or three variables, or operate at only one size scale or time scale. While scientists and engineers have long been able to write down equations to describe physical systems, before the computer age they could only solve the equations in certain highly simplified cases, literally using a pen and paper or chalk and a blackboard. In scores of applications, from physics to biology to chemistry to engineering, scientists use computer models-whose construction requires the formulation of mathematical and statistical models, the development of algorithms, and the creation of software-to study phenomena that are too big, too small, too fast, too slow, too rare, or too dangerous to study in a laboratory. That is where mathematical sciences enter the story, via computer simulation. How can you study something that cannot be duplicated in a laboratory, would fry you if you got close to it, and rarely even occurs?
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But within our galaxy, the Milky Way, supernovas are exceedingly rare. Such explosions seeded our own solar system with all of its heavier elements they also have taught us, indirectly, a great deal about the size, age, and composition of our universe. Simulations are used to gain insight into the expected quality and operation of those systems and to carry out what-if evaluations of systems that may not yet exist or are not amenable to experimentation.Īs an example, one of the most important and spectacular events in the universe is the explosion of a star into a supernova. Computer simulations, which are built on mathematical modeling, are used daily in scientific research of all types, for informing decision making in business and government, including national defense, and for designing and controlling complex systems such as those for transportation, utilities, and supply chains, and so on.