Monte Carlo

Introduction

A Monte Carlo is a program that attempts to simulate some process by randomly sampling from a set of known distributions that characterise it. The random sampling is done using a random number generator that typically returns a value r in the range:-

 0. <= r < 1.

Some examples of random number generators are:-

Fortran CERNlib's RANLUX
C++ ROOT's TRandom

From this starting point it is possible to generate both discrete and continuous processes. As an example of the former, consider the tossing of a coin. Values of the random number r less than 0.5 could be assigned heads and the remainder tails. As an example of the later consider an exponential decay with a decay constant t. This can be produced by the function

-t*log(r)

A wide variety distributions can be generated analytically in this way. In cases where the distribution to be simulated is only available as a histogram, it can be sampled with r by:-

Normalising the histogram to unity.
Returning the value x where the integrated area from the start of the histogram to the point x has the value r.

HEP Monte Carlos

All HEP experiments use Monte Carlos. The software can be roughly divided into two areas:-

Physics This includes the simulation of such things as
- The interaction of a particle on a nucleus
- The decay of a nucleus
- The propagation of a particle through a medium
Individual experimental groups tend not to don't write their own software, but instead collaborate to produce codes that can be shared. Some examples are:-
- GEANT4 Written in C++
- Fluka
- GEANT3 Fortran based, no longer being developed and soon to be obsolete by GEANT4.
Detector Response Software to simulation
- The way the passage of particles is detected, typically by ionisation or Cerenkov light
- The information is recorded, typically by digitizing signals
- Read out by the DAQ
is normally the area left to individual experimental groups to work on. Nowadays the software is usually written in C++ although some older codes that use Fortran can still be found. People working on Monte Carlo software need to know about Software Development

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Last modified: Tue Oct 19 18:38:50 BST 2004