Common use of Numerical solution Clause in Contracts

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. ‌ 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 dϕ m2ϕ + λϕ3 H dNe 3H2 + 2πξ , (2.47) where ξ is Gaussian white noise with zero mean and unit variance.