arXiv subjects

Weisheng Zhou

Publications and source records attributed to Weisheng Zhou.

6 recordsLinked to original sources

arXiv2026

Localized gradient enhancement near anisotropic electromagnetic scatterers

This work investigates time-harmonic electromagnetic scattering governed by the Maxwell system, where bounded anisotropic scatterers are embedded in a homogeneous electromagnetic background. We focus on the localized enhancement of the gradients of the total electric and magnetic fields in small boundary-attached neighborhoods of finitely many prescribed points near boundaries of anisotropic electromagnetic scatterers. We show that, through a suitable construction of incident electromagnetic waves, the gradients of both the total electric field and the total magnetic field can be made arbitrarily large in these neighborhoods. The main strategy is based on the introduction of auxiliary boundary-attached electromagnetic neighborhoods and the associated electric and magnetic fields, which exhibit strong gradient variation near the prescribed points. Using the approximation property of Maxwell Herglotz wave functions, these auxiliary fields are then approximated by physically admissible incident waves in the neighborhood of the scatterers. Together with the well-posedness and continuous dependence of the anisotropic scattering problem, this implies that the corresponding scattered field can be controlled to be sufficiently weak in the relevant region. Consequently, the total field is dominated by the incident field near the prescribed points and inherits its large-gradient behavior. The result provides a theoretical mechanism for localized gradient enhancement in anisotropic electromagnetic scattering and may have implications for field concentration, high-resolution probing, and sensitivity analysis of electromagnetic responses in complex media.

math.AP↗

arXiv2026

Robust shape reconstruction of elastic impenetrable scatterers via monotonicity spectral sampling methods

Reconstructing the location and shape of an unknown impenetrable scatterer from far-field measurements is a fundamental inverse problem in elastic scattering. In this paper, we propose monotonicity-based shape characterization theorems and develop corresponding algorithms for rigid and traction-free impenetrable scatterers. By establishing the factorization of the elastic far-field operator and constructing localized wave functions, we derive a sharp monotonicity-based characterization criterion for determining the shape and position of the impenetrable scatterer. This criterion is based on the spectral properties of the \emph{monotonicity operator}, defined as a specific linear combination of the far-field and Herglotz probing operators. Building on this theoretical foundation, we first present a counting-based monotonicity sampling method that evaluates the number of negative eigenvalues of the monotonicity operator. To address the inherent sensitivity of eigenvalue-counting to measurement noise, we further develop two novel monotonicity spectral sampling algorithms that exploit the magnitudes, rather than merely the signs, of the negative eigenvalues. The single-frequency monotonicity spectral sampling method provides robust stability against data perturbations, while the multi-frequency monotonicity spectral sampling method extension aggregates frequency information into a multiscale indicator that balances noise robustness with high-resolution geometric fidelity. Numerical experiments across various scatterer geometries and noise levels demonstrate sharp boundary localization and accurate reconstruction of complex concave features, confirming the effectiveness of the single-frequency and multi-frequency monotonicity spectral sampling methods.

math.AP↗

arXiv2025

Stress concentration via quasi-Minnaert resonance in bubble-elastic structures and applications

Stress concentration in bubble-elastic scattering scenarios has significant applications in engineering blasting and medical treatments. This study provides a comprehensive mathematical analysis of stress concentration in bubbly-elastic structures, induced by the quasi-Minnaert resonance. The quasi-Minnaert resonance manifests as two distinct wave patterns near the bubble's boundary: boundary localization and high-oscillation phenomena. We demonstrate how to leverage the quasi-Minnaert resonance to induce stress concentration in the elastic total wave field near the air bubble's boundary by appropriately selecting the incident elastic wave and high-contrast structure. The interaction between the air bubble and the elastic background couples two physical wave fields-acoustic and elastic waves-across the bubble's boundary. The intricate transmission conditions, combined with the scalar nature of acoustic waves and the vectorial nature of elastic waves, present significant analytical challenges. To address these, we employ layer potential theory and asymptotic analysis to rigorously establish the stress concentration and quasi-Minnaert resonance phenomena in a radially geometry bubble-elastic model. Extensive numerical experiments are conducted to demonstrate the stress concentration phenomenon alongside quasi-Minnaert resonance for various bubble geometries, including a unit disk, a corner domain, an apple-shaped domain in $\mathbb{R}^2$, and a ball in $\mathbb{R}^3$. The findings of this study enhance the understanding of stress concentration mechanisms and their applications in engineering blasting and medical therapies.

math-ph↗

arXiv2025

Quasi-Minnaert Resonances in High-contrast acoustic Structures and Applications to Invisibility Cloaking

This paper investigates a novel quasi-Minnaert resonance phenomenon in acoustic wave propagation through high-contrast medium in both two and three dimensions, occurring in the sub-wavelength regime. These media are characterized by physical properties significantly distinct from those of a homogeneous background. The quasi-Minnaert resonance is defined by two primary features: boundary localization, where the $L^2$-norms of the internal total field and the external scattered field exhibit pronounced concentration near the boundary, and surface resonance, marked by highly oscillatory behavior of the fields near the boundary. In contrast to classical Minnaert resonances, which are associated with a discrete spectral spectrum tied to physical parameters, quasi-Minnaert resonances exhibit analogous physical phenomena but with a continuous spectral spectrum. Using layer potential theory and rigorous asymptotic analysis, we demonstrate that the coupling between a high-contrast material structure, particularly with radial geometries, and a carefully designed incident wave is critical for inducing quasi-Minnaert resonances. Extensive numerical experiments, involving radial geometries (e.g., unit disks and spheres) and general-shaped geometries (e.g., hearts, Cassini ovals, and clovers in $\mathbb{R}^2$, and spheres in $\mathbb{R}^3$), validate the occurrence of these resonances. Furthermore, we numerically demonstrate that quasi-Minnaert resonances induce an invisibility cloaking effect in the high-contrast medium. These findings have significant implications for mathematical material science and the development of acoustic cloaking technologies.

physics.optics↗

arXiv2025

Inverse elastic obstacle scattering problems by monotonicity method

We consider the elastic wave scattering problem involving rigid obstacles. This work addresses the inverse problem of reconstructing the position and shape of such obstacles using far-field measurements. A novel monotonicity-based approach is developed for this purpose. By factorizing the far-field operator and utilizing the existence of localized wave functions, we derive a shape characterization criterion for the obstacle boundary. The proposed method employs monotonicity tests to determine the geometric relationship between any given test domain and the actual scatterer. As a result, the shape and location of rigid elastic obstacles can be uniquely identified without requiring any initial guesses or prior knowledge of the physical parameters of the homogeneous background medium.

math.AP↗

arXiv2025

Quasi-Minnaert Resonances in 2D Elastic Wave Scattering with Applications

In our earlier work [13], we introduced a novel quasi-Minnaert resonance for three-dimensional elastic wave scattering in the sub-wavelength regime. Therein, we provided a rigorous analysis of the boundary localization and surface resonance phenomena for both the total and scattered waves, achieved through carefully selected incident waves and tailored physical parameters of the elastic medium. In the present study, we focus on quasi-Minnaert resonances in the context of two-dimensional elastic wave scattering. Unlike the 3D case [13], the 2D setting introduces fundamental theoretical challenges stemming from (i) the intrinsic coupling between shear and compressional waves, and (ii) the complex spectral properties of the associated layer potential operators. By combining layer potential techniques with refined asymptotic analysis and strategically designed incident waves, we rigorously establish quasi-Minnaert resonances in both the internal and scattered fields. In addition, the associated stress concentration effects are quantitatively characterized. Notably, the boundary-localized nature of the scattered field reveals potential applications in near-cloaking (via wave manipulation around boundaries). Our results contribute to a more comprehensive framework for studying resonance behaviors in high-contrast elastic systems.

math.AP↗