Monte Carlo method

Monte Carlo methods are a class of computational algorithms for simulating the behavior of various physical and mathematical systems. They are distinguished from other simulation methods (such as molecular dynamics) by being stochastic, that is nondeterministic in some manner - usually by using random numbers (or more often pseudo-random numbers) - as opposed to deterministic algorithms. A classic use is for the evaluation of definite integrals, particularly multidimensional integrals with complicated boundary conditions.

Related Topics:
Computation - Algorithm - Simulating - Physical - Mathematical - Molecular dynamics - Stochastic - Nondeterministic - Random number - Pseudo-random number - Deterministic algorithm - Definite integral

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Monte Carlo methods are extremely important in computational physics and related applied fields, and have diverse applications from esoteric quantum chromodynamics calculations to designing heat shields and aerodynamic forms. These methods have proven efficient in solving the integro-differential equations defining the radiance field, and thus these methods have been used in global illumination computations which produce photorealistic images of virtual 3D models, with applications in video games, architecture, design, computer generated films, special effects in cinema, business, economics and other fields. They are especially useful in studying systems with a large number of coupled degrees of freedom, such as liquids, disordered materials, and strongly coupled solids.

Related Topics:
Computational physics - Quantum chromodynamics - Heat shield - Aerodynamic - Global illumination - Video games - Architecture - Design - Film

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Interestingly, the Monte Carlo method does not require truly random numbers to be useful. Much of the most useful techniques use deterministic, pseudo-random sequences, making it easy to test and re-run simulations. The only quality usually necessary to make good simulations is for the pseudo-random sequence to appear "random enough" in a certain sense. That is that they must either be uniformly distributed or follow another desired distribution when a large enough number of elements of the sequence are considered.

Related Topics:
Simulation - Uniformly distributed

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Because of the repetition of algorithms and the large number of calculations involved, Monte Carlo is a method suited to calculation using a computer, utilizing many techniques of computer simulation.

Related Topics:
Computer - Computer simulation

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A Monte Carlo algorithm is a numerical Monte Carlo method used to find solutions to mathematical problems (which may have many variables) that cannot easily be solved, for example, by integral calculus, or other numerical methods. Its efficiency relative to other numerical methods increases when the dimension of the problem increases.

Related Topics:
Integral calculus - Dimension

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