Problem On The Acoustic Cloak By $0$ to $R_1$ Transformation

TL;DR

This paper demonstrates that the 0 to R1 radial spherical coordinate transformation cannot be used to create an effective acoustic cloak because the pressure wave penetrates the inner sphere, preventing true cloaking.

Contribution

It proves that the 0 to R1 transformation fails to produce an acoustic invisibility cloak due to pressure wave penetration and boundary invariance issues.

Findings

Pressure wave field is invariant under transformation.

Pressure at the inner boundary R1 is non-zero, allowing wave penetration.

The transformation cannot induce acoustic cloaking.

Abstract

The $0$ to $R_1$ radial spherical coordinate transformation method can be making electromagnetic (EM) invisible cloak. However the cloak by transformation optic has infinite speed and exceeding light speed etc fundamental difficulties. In this paper, we discover problem on acoustic cloak by transformation and prove that in the $0$ to $R_1$ radial spherical coordinate transformation, the pressure wave field $P(r_p)=P(r)$ is invariant, in the physical inner spherical surface boundary $r=R_1$, $P(R_1)$ is not zero. the acoustic field propagation penetrate into the inner sphere $r < R_1$.Therefore, the inner sphere $r < R_1$ can not be cloaked. The GL simulation figures of the pressure acoustic wave propagation penetrate into the inner sphere $r \le R_1$ are presented in figure 1 to figure 12.The pressure wave is setting to zero that cause the scattering wave to disturb incident pressure acoustic wave outside of the outer sphere $r \ge R_2$ that make the whole sphere $r \ge R_2$ will be deltected. GL method simulation is presented in figure 13. we discovered and proved that $0$ to $R_1$ sphere radial transformation can not be used to induce acoustic no scattering cloak.