This paper presents two dimensional sound-proof acoustic metamaterials having tunable multi-band negative effective mass density. The acoustic metamaterial panel was composed of many periodic funnel-shaped cell units into square lattice. Each unit cell operates as multi-band resonators. By tuning unit cell the local reflected acoustic wave was almost out of phase with the incident wave. It lead...

In this paper, a two-dimensional cellular automaton(CA) associated with a two-dimensional Burgers equation is presented. The 2D Burgers equation is an integrable generalization of the well-known Burgers equation, and is transformed into a 2D diffusion equation by the Cole-Hopf transformation. The CA is derived from the 2D Burgers equation by using the ultradiscrete method, which can transform d...

A plane-wave-expansion method suited to the analysis of surface-acoustic-wave propagation in two-dimensional piezoelectric phononic crystals is described. The surface modes of a square-lattice Y-cut lithium niobate phononic crystal with circular void inclusions with a filling fraction of 63% are identified. It is found that a large full band gap with a fractional bandwidth of 34% exists for sur...

The Schrödinger equation with the central potential is first studied in the arbitrary dimensional spaces and obtained an analogy of the two-dimensional Schrödinger equation for the radial wave function through a simple transformation. As an example, applying an ansatz to the eigenfunctions, we then arrive at an exact closed form solution to the modified two-dimensional Schrödinger equation with...

Using a traveling wave reduction technique, we have shown that Maccari equation, (2?1)-dimensional nonlinear Schrödinger equation, medium equal width equation, (3?1)-dimensional modified KdV–Zakharov– Kuznetsev equation, (2?1)-dimensional long wave-short wave resonance interaction equation, perturbed nonlinear Schrödinger equation can be reduced to the same family of auxiliary elliptic-like equ...

We consider two problems in boundary controllability of coupled wave/Kirchoff systems. Let Ω be a bounded region in R, n ≥ 2, with Lipschitz continuous boundary Γ. In the motivating structural acoustics application, Ω represents an acoustic cavity. Let Γ0 be a flat subset of Γ which represents a flexible wall of the cavity. Let z denote the acoustic velocity potential, which satisfies a wave eq...