Introduction 1.2

Introduction 1.2 - Experiments - mathematical description -...

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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble .” – Dirac, 1929. The equations that describe quantum mechanics, classical mechanics, gas/fluid flow, electrical/magnetic fields induced by static or moving charges, are well known. But analytical solutions are often intractable. The invention of computers has provided a new exciting direction – to solve the complex equations numerically, in a computer simulation. Experiments - mathematical description - computer simulation Once a certain number of experiments have been performed, it is necessary to describe the results mathematically. If we succeed in describing the phenomenon with mathematical equations, then we can predict the behavior of the system of interest for a wide range of conditions, including the ones for which experiments are difficult, too expensive, or not possible at all.
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Introduction 1.2 - Experiments - mathematical description -...

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