spectral stability
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2022 ◽  
Vol 32 (2) ◽  
Author(s):  
Siqi Fu ◽  
Weixia Zhu

AbstractWe study spectral stability of the $${\bar{\partial }}$$ ∂ ¯ -Neumann Laplacian on a bounded domain in $${\mathbb {C}}^n$$ C n when the underlying domain is perturbed. In particular, we establish upper semi-continuity properties for the variational eigenvalues of the $${\bar{\partial }}$$ ∂ ¯ -Neumann Laplacian on bounded pseudoconvex domains in $${\mathbb {C}}^n$$ C n , lower semi-continuity properties on pseudoconvex domains that satisfy property (P), and quantitative estimates on smooth bounded pseudoconvex domains of finite D’Angelo type in $${\mathbb {C}}^n$$ C n .


Author(s):  
Yubin Xu ◽  
Zhenlin Hu ◽  
Feng Chen ◽  
Deng Zhang ◽  
Junfei Nie ◽  
...  

Large spectral fluctuations bring large errors in laser-induced breakdown spectroscopy (LIBS) analysis, which impedes the improvement of precision and accuracy, limiting the large-scale application and commercialization. In this work, we...


Author(s):  
Yifei Yue ◽  
Shengnan Liu ◽  
Baohua Zhang ◽  
Zhong-Min Su ◽  
Dongxia Zhu

All-inorganic perovskites (AIP) with three primary colors emission are all-important for AIP application in many field. However, poor spectral stability seriously hinders the development of blue-emission AIP. Here, we achieved...


Nonlinearity ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 170-244
Author(s):  
Ryan Goh ◽  
Björn de Rijk

Abstract We consider pattern-forming fronts in the complex Ginzburg–Landau equation with a traveling spatial heterogeneity which destabilises, or quenches, the trivial ground state while progressing through the domain. We consider the regime where the heterogeneity propagates with speed c just below the linear invasion speed of the pattern-forming front in the associated homogeneous system. In this situation, the front locks to the interface of the heterogeneity leaving a long intermediate state lying near the unstable ground state, possibly allowing for growth of perturbations. This manifests itself in the spectrum of the linearisation about the front through the accumulation of eigenvalues onto the absolute spectrum associated with the unstable ground state. As the quench speed c increases towards the linear invasion speed, the absolute spectrum stabilises with the same rate at which eigenvalues accumulate onto it allowing us to rigorously establish spectral stability of the front in L 2 ( R ) . The presence of unstable absolute spectrum poses a technical challenge as spatial eigenvalues along the intermediate state no longer admit a hyperbolic splitting and standard tools such as exponential dichotomies are unavailable. Instead, we projectivise the linear flow, and use Riemann surface unfolding in combination with a superposition principle to study the evolution of subspaces as solutions to the associated matrix Riccati differential equation on the Grassmannian manifold. Eigenvalues can then be identified as the roots of the meromorphic Riccati–Evans function, and can be located using winding number and parity arguments.


2021 ◽  
Vol 304 ◽  
pp. 229-286
Author(s):  
Yi Li ◽  
Yong Li ◽  
Yaping Wu ◽  
Hao Zhang
Keyword(s):  

2021 ◽  
Vol 298 ◽  
pp. 528-559
Author(s):  
Biagio Cassano ◽  
Lucrezia Cossetti ◽  
Luca Fanelli

2021 ◽  
pp. 1-23
Author(s):  
FÁBIO NATALI ◽  
SABRINA AMARAL

Abstract The purpose of this paper is to present an extension of the results in [8]. We establish a more general proof for the moving kernel formula to prove the spectral stability of periodic traveling wave solutions for the regularized Benjamin–Bona–Mahony type equations. As applications of our analysis, we show the spectral instability for the quintic Benjamin–Bona–Mahony equation and the spectral (orbital) stability for the regularized Benjamin–Ono equation.


2021 ◽  
Vol 104 (8) ◽  
Author(s):  
Srivatsa Chakravarthi ◽  
Christian Pederson ◽  
Zeeshawn Kazi ◽  
Andrew Ivanov ◽  
Kai-Mei C. Fu

2021 ◽  
pp. 3114-3131
Author(s):  
Fanghao Ye ◽  
Qingsong Shan ◽  
Haibo Zeng ◽  
Wallace C. H. Choy

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