ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: material absorbs the particle and then shortly after reemits the absorbed energy isotropically. Numerically, the time step is too large for the absorption and emission processes to be resolved separately, such that they appear as one scattering process ( as ). The simulation is initially populated with Monte Carlo particles according to Equation ( 66 ). During each time step, the code creates new Monte Carlo particles to simulate the process of emission. The number of particles created depends on how many particles are already in the simulation: if there are relatively few existing particles, then many are created, but if the number of existing particles is close to the maximum allowed value then few are created. We typically set the maximum to 10 6 particles; we want enough particles to populate every cell and frequency group (Section 3.1 ), but not so many that our simulation runs slowly. For each particle, the details of its creation (location, direction, etc.) are randomly chosen. The cell of creation is randomly chosen with weighting , the amount of energy the cell emits in the time step. Using Equations ( 10 ), ( 33 ), and ( 77 ), we havewhere is the volume of the cell and is the time step for the cell (see below). For simplicity, the radius within the cell and the time within the time step are randomly chosen with uniform weighting; from Equation ( 10 ), the direction is weighted uniformly (isotropically) while the frequency is weighted by . The particle also has an energy weight, equal to the total energy of the photon packet. This is not randomly chosen; instead, all of the particles “emitted” in a time step have the same energy weight, given bywith being the number of Monte Carlo particles emitted in that step. At the end of the time step, the cell temperature is adjusted due to emission using(see below). Particles are also created at the inner boundary of the simulation, the base of the atmosphere. Here the physical process for the creation of the particles is not emission, but the escape of photons from the hot layers beneath the atmosphere. As before, the details of creation are chosen randomly; the time within the time step is chosen with uniform weighting, while from Equation ( 35 ), the direction is weighted by μ and the frequency is weighted by B ν . The energy weight for these particles iswith being the number of particles created at the base in the time step and being the energy entering the simulation from the base of the atmosphere. From Equations ( 35 ) and ( 53 ), we havewhere is the area of the base and is the time step at the base (see Equation ( 67 )). The created particles (photon packets) are transported according to the left-hand side of Equation ( 5 ). If general relativistic effects are ignored, the particles travel in straight lines. For a particle traveling a distance s from the position and moving in the direction initially defined by , where , the new radius of the particle is given by the law of cosines:The