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Chenkai Liu

Publications and source records attributed to Chenkai Liu.

8 recordsLinked to original sources
arXiv2025

Parity Metamaterials and Dynamic Acoustic Mimicry

While parity transformation represents a fundamental symmetry operation in physics, its implications remain underexplored in metamaterial science. Here, we introduce a framework leveraging parity transformation to construct parity-inverted counterparts of arbitrary three-dimensional meta-atoms, enabling the creation of parity-engineered metamaterial slabs. We demonstrate that the synergy between reciprocity and parity transformation, distinct from mirror operation, guarantees undistorted wave transmission across exceptional bandwidths, independent of structural configuration or meta-atom design specifics. Furthermore, these metamaterials exhibit dynamic acoustic mimicry capability, enabling adaptive blending of reflected signatures into surrounding environments while preserving transmitted wavefront integrity. Validated through numerical simulations and experimental prototypes, this breakthrough offers transformative potential for acoustic camouflage applications, particularly for sonar systems. Our findings reveal fundamental implications of parity transformation in artificial materials, establishing parity engineering as a paradigm for designing ultra-broadband functional materials with unprecedented operational versatility.

cond-mat.mtrl-sci↗
arXiv2025

Metamaterial sound absorbers based on microperforated panels: an approach toward enhanced flexibility and near-limit broadband performance

Traditional microperforated panels (MPPs) and metamaterial-based sound absorbers rely on local resonances or multi-resonator designs, which limit their bandwidth, angular applicability, and ease of fabrication. Leveraging the reciprocity theorem and cavity resonances, we introduce a new class of robust MPP absorbers, termed meta-MPPs, capable of achieving ultrabroadband near-total sound absorption across a range of 0.37 to 10 kHz. These absorbers demonstrate average performance exceeding that of traditional MPPs by over 100%, approaching the theoretical causality limit. Notably, their absorption performance can be tuned between angularly asymmetric and omnidirectional modes and remains highly robust to variations in MPP parameters and geometrical configurations. Validated through simulations and experiments, our findings present a simpler, more robust, and highly adaptable solution for noise control.

physics.app-ph↗
arXiv2023

Ultra-broadband suppression of sound scattering via illusion metamaterials

The scattering of waves is a ubiquitous phenomenon in physics, yet there are numerous scenarios, such as the pursuit of invisibility, where suppressing it is of utmost importance. In comparison to prior methods which are restricted by limited bandwidths, here we present a technique to suppress sound scattering across an ultra-broad spectrum by utilizing illusion metamaterials. This illusion metamaterial, consisting of subwavelength tunnels with precisely crafted internal structures, has the ability to guide acoustic waves around the obstacles and recreate the incoming wavefront on the exit surface. Consequently, two ultra-broadband illusionary effects are produced: disappearing space and time shift. Simultaneously, all signs of sound scattering are removed across an exceptionally wide spectrum, ranging from the quasistatic limit to an upper limit of the spectrum, as confirmed by full-wave simulations and acoustic experiments. Our approach represents a major step forward in the development of broadband functional metamaterials and holds the potential to revolutionize various fields, including acoustic camouflage and reverberation control.

physics.app-ph↗
arXiv2022

A localized criterion for the regularity of solutions to Navier-Stokes equations

The Serrin-Prodi-Ladyzhenskaya type $L^{p,q}$ criteria for the regularity of solutions to the incompressible Navier-Stokes equations are fundamental in the study of the millennium problem posted by the Clay Mathematical Institute about the incompressible N-S equations. In this article, we establish some localized $L^{p,q}$ criteria for the regularity of solutions to the equations. In fact, we obtain some a priori estimates of solutions to the equations depend only on some local $L^{p,q}$ type norms. These local $L^{p,q}$ type norms, are small for reasonable initial value and shall remain to be small for global regular solutions. Thus, deriving the smallness or even the boundedness of the local $L^{p,q}$ type norms is necessary and sufficient to affirmatively answer the millennium problem. Our work provides an interesting and plausible approach to study the millennium problem.

math.AP↗
arXiv2022

Uniqueness and some related estimates for Dirichlet problem with fractional Laplacian

For the fractional Laplace equation, a surprising observation is the non-uniqueness for the basic Dirichlet type problems. In this paper, a somewhat sharp uniqueness condition for the fractional Laplace equation is established. We derive the $L^p$-estimate for fractional Laplacian operators to better understand this phenomena. Several weighted fractional Sobolev spaces appear naturally. We then establish the embedding relations between these spaces. These existence-uniqueness conditions and the spaces we introduce here are intrinsically related to the fractional Laplacian. These are basic properties to the fractional Laplace equations and can be useful in the study of related problems.

math.AP↗
arXiv2022

On the Dirichlet problem for fractional Laplace equation on a general domain

In this paper, we study Dirichlet problems of fractional Laplace (Poisson) equations on a general bounded domain in $\mathbb{R}^n$. Green's functions and Poisson kernels are important tools needed in our study. We first establish the existence of Green's function by an application of Perron's method. After that, the Poisson kernel is constructed based on the Green's function. Several important properties of Green's functions and Poisson kernels are proved. Finally, we show that the solution of a fractional Laplace (Poisson) equation under a given condition must be unique and be given by our Green's function and Poisson kernel.

math.AP↗
arXiv2019

Singular solutions of linear problems with fractional Laplacian

In this paper, we study singular solutions of linear problems with fractional Laplacian. First, we establish Bôcher type theorems on a punctured ball via distributional approach. Then, we develop a few interesting maximum principles on a punctured ball. Our distributional approach only requires the basic local L-1 integrability. We also introduce several simple and useful lemmas, which enable us to unify the treatments for both Laplacian and fractional Laplacian. These theorems, lemmas and the methods introduced here can be adapted and applied in other situations.

math.AP↗