dependence of the neutron density in a multiplying medium. keff < 1, subcritical: the neutron density is decreasing as time passes; keff = 1, critical: the neutron density remains unchanged; and keff > 1, supercritical: the neutron density is increasing with time. In the case of a nuclear reactor, neutron flux and power density are proportional, hence during reactor start-up keff > 1, during reactor operation keff = 1 and keff < 1 at reactor shutdown. Computational methods Both fixed-source and criticality calculations can be solved using deterministic methods or stochastic methods. In deterministic methods the transport equation (or an approximation of it, such as diffusion theory) is solved as a differential equation. In stochastic methods such as Monte Carlo discrete particle histories are tracked and averaged in a random walk directed by measured interaction probabilities. Deterministic methods usually involve multi-group approaches while Monte Carlo can work with multi-group and continuous energy cross-section libraries. Multi-group calculations are usually iterative, because the group constants are calculated using flux-energy profiles, which are determined as the result of the neutron transport calculation. Discretization in deterministic methods To numerically solve the transport equation using algebraic equations on a computer, the spatial, angular, energy, and time variables must be discretized. Spatial variables are typically discretized by simply breaking the geometry into many small regions on a mesh. The balance can then be solved at each mesh point using finite difference or by nodal methods. Angular variables can be discretized by discrete ordinates and weighting quadrature sets (giving rise to the SN methods), or by functional expansion methods with the spherical harmonics (leading to the PN methods). Energy variables are typically discretized by the multi-group method, where each energy group represents one constant energy. As few as 2 groups can be sufficient for some thermal reactor problems, but fast reactor calculations may require many more. The time variable is broken into discrete time steps, with time derivatives replaced with difference formulas. Computer codes used in neutron transport Probabilistic codes COG - A LLNL developed Monte Carlo code for criticality safety analysis and general radiation transport (http://cog.llnl.gov) MCBEND - A Monte Carlo code for general radiation transport developed and supported by the ANSWERS Software Service. MCNP - A LANL developed Monte Carlo code for general radiation transport MCS - The Monte Carlo code MCS has been developed since 2013 at Ulsan National Institute of Science and Technology