commit a0db5aad6f4edd425de4a9626dcf4af1f5021ebe
parent eb3ae5aded2c3dc3c126fd4c0bb3d5ddce90c9de
Author: Minerva_juppiter <94231606+minerva-jupiter@users.noreply.github.com>
Date: Mon, 6 Jul 2026 12:13:06 +0900
Update README.md
Diffstat:
1 file changed, 2 insertions(+), 2 deletions(-)
diff --git a/README.md b/README.md
@@ -160,7 +160,7 @@ Rather than simulating wave reflection through complex fluid dynamics (changes i
Energy in an acoustic system is proportional to the square of the time derivative of displacement ($(\partial x / \partial t)^2$). We apply a damping constant $a$ to this derivative. To preserve the sign of the wave (preventing signal rectification and DC offset), the damping is implemented as a sign-preserving cubic non-linearity. Given an input displacement $x_{\text{in}}[n]$, a delayed resonant displacement $x_{\text{resonance}}[n]$, and the total previous displacement $x[n-1]$, the system state $x[n]$ is updated as:
-$$x[n] = (x_{\text{in}}[n] + x_{\text{resonance}}[n]) \cdot a \cdot (x[n-1] - (x_{\text{in}}[n] + x_{\text{resonance}}[n]))^2$$
+$$x[n] = (x_{\text{in}}[n] + x_{\text{resonance}}[n]) - a \cdot ((x_{\text{in}}[n] + x_{\text{resonance}}[n]) - x[n-1])$$
#### 2. Physical Validity (D’Alembert’s Solution)
@@ -199,7 +199,7 @@ The core simulation is based on a displacement-driven delay-line model, where th
The total displacement $x[n]$ is calculated as a damped non-linear function of the input and the delayed resonant state. To preserve the sign of the displacement wave and avoid DC rectification, a sign-preserving cubic function is used. Given a damping constant $a$ ($0 < a \le 1$):
-$$x[n] = (x_{\text{in}}[n] + x_{\text{resonance}}[n]) \cdot a \cdot \left( x[n-1] - (x_{\text{in}}[n] + x_{\text{resonance}}[n]) \right)^2$$
+$$x[n] = (x_{\text{in}}[n] + x_{\text{resonance}}[n]) - a \cdot \left((x_{\text{in}}[n] + x_{\text{resonance}}[n]) - x[n-1] \right)$$
Where $x[n-1]$ represents the previous total displacement, capturing the system's memory.
