Pointwise split of the short-time cutoff error

The error is bounded by a fixed normal-phase polynomial on the negative phase region and by radius-decaying shell terms elsewhere.

noncomputable def ESS.buShortShellCoeff (scale R c₁ : ℝ) : ℝ

The radius-dependent coefficient of the spatial shell error.

Equations

• ESS.buShortShellCoeff scale R c₁ = (9 * (c₁ * scale) + 54) * (CKN.cutoffGradientConstant / (2 * R)) + 3 * (CKN.cutoffSecondDerivativeConstant / (2 * R) ^ 2)

theorem ESS.buShortShellCoeff_nonneg {scale R c₁ : ℝ} (hscale : 0 < scale) (hR : 0 < R) (hc₁ : 0 ≤ c₁) : 0 ≤ buShortShellCoeff scale R c₁

The spatial shell coefficient is nonnegative.