Numerical solution Sample Clauses
Numerical solution. In this section, we look at the numerical solution corresponding to the parameter choices we have made above. Before symmetry breaking the field lies at the origin ϕ = 0 until ϕ0 drops sufficiently for the potential at the origin to become tachyonic. Classically, of course, the field would then not move anywhere because dV/dϕ = 0 at the origin, and if we were to introduce a small perturbation away from ϕ = 0 as an initial condition, then classically our final solution would depend strongly on this perturbation. To get around this problem, we evolve the field using the ▇▇▇▇▇▇▇▇ equation which takes into account the stochastic quantum fluctuations the field receives 3H2 + 2πξ , (2.47) where ξ is Gaussian white noise with zero mean and unit variance.
Numerical solution. Intuitively, no matter which action the agent decides to choose, the key to solve this problem is to find the converging state. In other words, we need to define when the cost of action vanishes at a specific action. Observing the cost function, we find that at state x = 0 and x = 6, the cost of taking any action u ∈ U will be 0. Also, if the agent takes action c = 0 at state x = 0 and x = 6, the next state x′ remains the same based on the model f (x, u). Thus we find the equilibrium state-action pair (xe, ue) = (0, 0) and (xe, ue) = (6, 0) such that