1 / 4

Monte Carlo Simulation Methods

Monte Carlo Simulation Methods. - ideal gas. Calculating properties by integration. Theoretical background to Metropolis. Markov chain of events: - the outcome of each trial depends only on the preceding trial - each trial belongs to a finite set of possible outcomes

antoinette
Download Presentation

Monte Carlo Simulation Methods

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Monte Carlo Simulation Methods - ideal gas

  2. Calculating properties by integration

  3. Theoretical background to Metropolis Markov chain of events: - the outcome of each trial depends only on the preceding trial - each trial belongs to a finite set of possible outcomes mn - probability of moving from state m to n =(1, 2,…. m, n,…N) - probability that the system is in a particular state (2)= (1).  (3)= (2). = (1). .  limit=limN (1) N - limiting (equilibrium) distribution mn - probability to choose the two states m,n between which the move is to be made (stochastic matrix). mn = mn. pmn - where p is the probability to accept the move mn = mn if n > m mn = mn. (n/m) if n < m and if n=m In practice if the energy of the n state is lower the move is accepted, if not a random number between 0 and 1 is compared to the Boltzmann factor exp(-∆V(rN)/kT). If the Boltzmann factor is greater then the Random number the move is accepted.

  4. Implementation rand(0,1)≤ exp(-∆V(rN)/kT) Random number generators Linear congruential method

More Related