$Phoenix — f(t) = A(1 - e^{-t/τ₁})e^{t/τ₂}, τ₂ > τ₁$ Tap to zoom

Phoenix

f(t) = A(1 - e^{-t/τ₁})e^{t/τ₂}, τ₂ > τ₁

An exponential recovery that exceeds the initial value — the function rises past where it began.

Rising past where you began

Part of: RESILIENCE

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Forged — σ_y(ε) = σ₀ + Kε^n

Forged

σ_y(ε) = σ₀ + Kε^n

Growth — dN/dt = r(K' - N), K' > K

Growth

dN/dt = r(K' - N), K' > K

$Recovery — x(t) = x_eq + (x₀-x_eq)e^{-t/τ} + overshoot$

Recovery

x(t) = x_eq + (x₀-x_eq)e^{-t/τ} + overshoot

$Repair — G(t) = G₀(1 - e^{-t/τ_r}) · H(t-t_d)$

Repair

G(t) = G₀(1 - e^{-t/τ_r}) · H(t-t_d)