MD&MC There are two dominant methods of simulation for complex many particle systems 1)Molecular Dynamics Solve the classical equations of motion from mechanics. Particles interact via a given interaction potential. ● Deterministic behaviour(within numerical precision). Find temporal evolution. 2)Monte Carlo Simulation ● Find mean values (expectation values)of some system components. Random behaviour from given probability distribution laws. The Monte Carlo technique is a very far spread technique, because it is not limited to systems of particles
There are two dominant methods of simulation for complex many particle systems 1) Molecular Dynamics • Solve the classical equations of motion from mechanics. • Particles interact via a given interaction potential. • Deterministic behaviour (within numerical precision). • Find temporal evolution. 2) Monte Carlo Simulation • Find mean values (expectation values) of some system components. • Random behaviour from given probability distribution laws. The Monte Carlo technique is a very far spread technique, because it is not limited to systems of particles. MD & MC
The origin of the name The name refers to the grand casino in the Principality of Monaco at Monte Carlo,which is well-known around the world as an icon of gambling AN E VENI N G IN M ON TE C ARL O
The origin of the name The name refers to the grand casino in the Principality of Monaco at Monte Carlo, which is well-known around the world as an icon of gambling
Application of Monte Carlo method CAD MeCad MCNP CAD-Modell von ITER Konversion in Monte Carlo-Geometrie Monte-Carlo-Modell (Vertikalschnitt) Nuclear reactor design Diffusion Monte Carlo 8P5 Sico24▣-130 Econometrics Radiation cancer therapy and more Oil well exploration Traffic flow
Application of Monte Carlo method Monte Carlo and more Nuclear reactor design Radiation cancer therapy Traffic flow Econometrics Oil well exploration Diffusion
Monte Carlo method This is a kind of "experimental statistics".In other branches of science,for example physics,the relationship between theory and experiment can be depicted in this way: Equipment, Experimental Theoretical Observation Physics Physics In statistics,theory developed from simple observations in card and dice games in the 17th century and later.The fully-fledged"experimental"approach,now known as Monte Carlo and thus acknowledging the origins of statistics in gambling,had to await the development of fast personal computers and random-number generators: Gambling: Cards,Dice Then Experimental Theoretical Very recent Statistics Statistics Random- Monte- Fast PCs number Carlo generators methods
Theoretical Physics Experimental Physics Equipment, Observation Gambling: Cards, Dice Fast PCs Randomnumber generators MonteCarlo methods Experimental Statistics Theoretical Statistics Then Very recent Monte Carlo method This is a kind of “experimental statistics”. In other branches of science, for example physics, the relationship between theory and experiment can be depicted in this way: In statistics, theory developed from simple observations in card and dice games in the 17th century and later. The fully-fledged “experimental” approach, now known as Monte Carlo and thus acknowledging the origins of statistics in gambling, had to await the development of fast personal computers and random-number generators:
Monte Carlo method Monte Carlo methods are stochastic techniques. > The basic concept is that games of chance can be played to approximate solutions to real world problems. >Monte Carlo methods solve non-probabilistic problems using probabilistic methods. > The Monte Carlo method provides approximate solutions to a variety of mathematical problems by performing statistical sampling experiments on a computer. > The method applies to problems with no probabilistic content as well as to those with inherent probabilistic structure
Monte Carlo methods are stochastic techniques. The basic concept is that games of chance can be played to approximate solutions to real world problems. Monte Carlo methods solve non-probabilistic problems using probabilistic methods. The Monte Carlo method provides approximate solutions to a variety of mathematical problems by performing statistical sampling experiments on a computer. The method applies to problems with no probabilistic content as well as to those with inherent probabilistic structure. Monte Carlo method