Publisher's Synopsis
The Monte Carlo method, also called Monte Carlo analysis, is a means of statistical evaluation of mathematical function s using random samples. This requires a good source of random numbers. There is always some error involved with this scheme, but the larger the number of random samples taken, the more accurate the result. These objects could arise "naturally" as part of the modeling of a real-life system, such as a complex road network, the transport of neutrons, or the evolution of the stock market. In many cases, however, the random objects in Monte Carlo techniques are introduced "artificially" in order to solve purely deterministic problems. In this case the MCM simply involves random sampling from certain probability distributions. In either the natural or artificial setting of Monte Carlo techniques the idea is to repeat the experiment many times (or use a sufficiently long simulation run) to obtain many quantities of interest using the Law of Large Numbers and other methods of statistical inference. Many quantitative problems in science, engineering, and finance are nowadays solved via Monte Carlo techniques. This is one of the main application areas of simulation modeling. Typical applications involve the simulation of inventory processes, job scheduling, vehicle routing, queueing networks, and reliability systems. An important part of Operations Research is Mathematical Programming (mathematical optimization), and here Monte Carlo techniques have proven very useful for providing optimal design, scheduling, and control of industrial systems, as well offering new approaches to solve classical optimization problems such as the traveling salesman problem, the quadratic assignment problem, and the satisfiability problem. The MCM is also used increasingly in the design and control of autonomous machines and robot. Monte Carlo techniques now play an important role in materials science, where they are used in the development and analysis of new materials and structures, such as organic LEDs, organic solar cells and Lithium-Ion batteries. In particular, Monte Carlo techniques play a key role in virtual materials design, where experimental data is used to produce stochastic models of materials. Realizations of these materials can then be simulated and numerical experiments can be performed on them. The physical development and analysis of new materials is often very expensive and time consuming. The virtual materials design approach allows for the generation of more data than can easily be obtained from physical experiments and also allows for the virtual production and study of materials using many different production parameters. Applications of Monte Carlo Method in Science and Engineering expose the broad range of applications of Monte Carlo simulation in the fields of Quantum Physics, Statistical Physics, Reliability, Medical Physics, Polycrystalline Materials, Ising Model, Chemistry, Agriculture, etc. The book chapters included in this volume clearly reflect the current scientific importance of Monte Carlo techniques in various fields of research. Both the static and the dynamic Monte Carlo method are discussed, and the significance of the Monte Carlo method to the modeling of various large scale problems in science and engineering is emphasized.
