is the Stefan–Boltzmann constant, and the Boltzmann constant is set to one. The case of convective energy transport does not have a known rigorous mathematical formulation, and involves turbulence in the gas. Convective energy transport is usually modeled using mixing length theory. This treats the gas in the star as containing discrete elements which roughly retain the temperature, density, and pressure of their surroundings but move through the star as far as a characteristic length, called the mixing length. For a monatomic ideal gas, when the convection is adiabatic, meaning that the convective gas bubbles don't exchange heat with their surroundings, mixing length theory yields where is the adiabatic index, the ratio of specific heats in the gas. (For a fully ionized ideal gas, .) When the convection is not adiabatic, the true temperature gradient is not given by this equation. For example, in the Sun the convection at the base of the convection zone, near the core, is adiabatic but that near the surface is not. The mixing length theory contains two free parameters which must be set to make the model fit observations, so it is a phenomenological theory rather than a rigorous mathematical formulation. Also required are the equations of state, relating the pressure, opacity and energy generation rate to other local variables appropriate for the material, such as temperature, density, chemical composition, etc. Relevant equations of state for pressure may have to include the perfect gas law, radiation pressure, pressure due to degenerate electrons, etc. Opacity cannot be expressed exactly by a single formula. It is calculated for various compositions at specific densities and temperatures and presented in tabular form. Stellar structure codes (meaning computer programs calculating the model's variables) either interpolate in a density-temperature grid to obtain the opacity needed, or use a fitting function based on the tabulated values. A similar situation occurs for accurate calculations of the pressure equation of state. Finally, the nuclear energy generation rate is computed from nuclear physics experiments, using reaction networks to compute reaction rates for each individual reaction step and equilibrium abundances for each isotope in the gas. Combined with a set of boundary conditions, a solution of these equations completely describes the behavior of the star. Typical boundary conditions set the values of the observable parameters appropriately at the surface () and center () of the star: , meaning the pressure at the surface of the