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We consider the nonlinear Schrödinger equation in n space dimensions iut +Δu + ∣u∣p-1u=0, x ∈ Rn, t>0 and study the existence and stability of standing wave solutions of the form eiwt eiΣkj=1 mjθjϕw(r1, r2, . . . , rk), n=2k and eiwt eiΣkj=1 mjθjϕw(r1, r2, . . . , rk, z), n=2k + 1. For n=2k, (rj, θj) are polar coordinates in R2, j= 1, 2, . . . , k; for n=2k + 1, (rj, θj) are polar coordinates in R2, (rk, θk, z) are cylindrical coordinates in R3, j= 1, 2, . . . , k − 1. We show the existence of functions φw, which are constructed variationally as minimizers of appropriate constrained functionals. These waves are shown to be spectrally stable (with respect to perturbations of the same type), if 1

We study the existence and the stability of periodic steady waves for a nonlinear model, the Lugiato- Lefever equation, arising in optics. Starting from a detailed description of the stability properties of constant solutions, we then focus on the periodic steady waves which bifurcate at the onset of Turing instability. Using a centre manifold reduction, we analyse these Turing bifurcations, and prove the existence of periodic steady waves. This approach also allows us to conclude on the nonlinear orbital stability of these waves for co-periodic perturbations, i.e. for periodic perturbations which have the same period as the wave. This stability result is completed by a spectral stability result for general bounded perturbations. In particular, this spectral analysis shows that instabilities are always due to co-periodic perturbations. [ABSTRACT FROM AUTHOR]

The quantification of impervious surface through remote sensing provides critical information for urban planning and environmental management. The acquisition of quality reference data and the selection of effective predictor variables are two factors that contribute to the low accuracies of impervious surface in urban remote sensing. A hybrid method was developed to improve the extraction of impervious surface from high-resolution aerial imagery. This method integrates ancillary datasets from OpenStreetMap, National Wetland Inventory, and National Cropland Data to generate training and validation samples in a semi-automatic manner, significantly reducing the effort of visual interpretation and manual labeling. Satellite-derived surface reflectance stability is incorporated to improve the separation of impervious surface from other land cover classes. This method was applied to 1-m National Agriculture Imagery Program (NAIP) imagery of three sites with different levels of land development and data availability. Results indicate improved extractions of impervious surface with user’s accuracies ranging from 69% to 90% and producer’s accuracies from 88% to 95%. The results were compared to the 30-m percent impervious surface data of the National Land Cover Database, demonstrating the potential of this method to validate and complement satellite-derived medium-resolution datasets of urban land cover and land use.

We deal with front solutions of the Korteweg-de Vries-Burgers equation which is the simplest one describing long wave propagation in a dissipative media with dispersion in the weakly nonlinear limit. This equation represents a singular perturbation of the hyperbolic Hopf equation, and its nonlinearity is assumed to be presented by a non-convex potential having a concrete expression. Various types of stationary structures of the originating discontinuities are investigated, the domains of their existence are described, and also the analysis of their dynamic stability is undertaken. In the domain of absence of stationary structures, a numeric study of stability of the non-stationary structures has been conducted. We consider self-similar solutions to the problem of arbitrary discontinuity disintegration which consist only of stable discontinuities with a stationary or non-stationary structure and simple waves. The conclusive criterion has been formulated of selection of an admissible discontinuity which is a solution of the Cauchy problem of arbitrary discontinuity disintegration governed by the Hopf equation. [ABSTRACT FROM AUTHOR]

Laser-induced breakdown spectroscopy (LIBS) has good capability for detecting molecular spectroscopy. Currently, little research has been done on enhancing this capability by depositing nanoparticles on the surface of samples. In this paper, a pulsed Nd:YAG laser with a wavelength of 1064 nm was utilized to excite polymethyl methacrylate (PMMA) targets and generate PMMA plasmas, and five spectral peaks (0−0), (1−1), (2−2), (3−3), and (4−4) of B2Σ+ − X2Σ+ (Δν = 0) transitions of CN molecules were obtained. The CN molecule was produced by the chemical reaction (C + N → CN) between the C atoms in PMMA targets and the N 2 in the air. The effect of nanoparticles on the spectral intensity and spectral stability of CN molecules was studied. And the vibration temperature of CN molecules was calculated by fitting the CN spectra. The results showed that nanoparticles could improve the spectral intensity, stability, and vibrational temperature of the CN molecules, revealing the potential of nanoparticles for enhancing signal intensity and improving analytical sensitivity in molecular LIBS. [ABSTRACT FROM AUTHOR]

Achieving high-performance perovskite light-emitting diodes (PeLEDs) with pure-red electroluminescence for practical applications remains a critical challenge because of the problematic luminescence property and spectral instability of existing emitters. Herein, high-efficiency Rec. 2020 pure-red PeLEDs, simultaneously exhibiting exceptional brightness and spectral stability, based on CsPb(Br/I) 3 perovskite nanocrystals (NCs) capping with aromatic amino acid ligands featuring cation-π interactions, are reported. It is proven that strong cation-π interactions between the PbI 6 -octahedra of perovskite units and the electron-rich indole ring of tryptophan (TRP) molecules not only chemically polish the imperfect surface sites, but also markedly increase the binding affinity of the ligand molecules, leading to high photoluminescence quantum yields and greatly enhanced spectral stability of the CsPb(Br/I) 3 NCs. Moreover, the incorporation of small-size aromatic TRP ligands ensures superior charge-transport properties of the assembled emissive layers. The resultant devices emitting at around 635 nm demonstrate a champion external quantum efficiency of 22.8%, a max luminance of 12 910 cd m -2 , and outstanding spectral stability, representing one of the best-performing Rec. 2020 pure-red PeLEDs achieved so far., (© 2023 Wiley-VCH GmbH.)

Mixed-halide perovskites show tunable emission wavelength across the visible-light range, with optimum control of the light color. However, color stability remains limited due to the notorious halide segregation under illumination or an electric field. Here, a versatile path toward high-quality mixed-halide perovskites with high emission properties and resistance to halide segregation is presented. Through systematic in and ex situ characterizations, key features for this advancement are proposed: a slowed and controllable crystallization process can promote achievement of halide homogeneity, which in turn ensures thermodynamic stability; meanwhile, downsizing perovskite nanoparticle to nanometer-scale dimensions can enhance their resistance to external stimuli, strengthening the phase stability. Leveraging this strategy, devices are developed based on CsPbCl 1.5 Br 1.5 perovskite that achieves a champion external quantum efficiency (EQE) of 9.8% at 464 nm, making it one of the most efficient deep-blue mixed-halide perovskite light-emitting diodes (PeLEDs) to date. Particularly, the device demonstrates excellent spectral stability, maintaining a constant emission profile and position for over 60 min of continuous operation. The versatility of this approach with CsPbBr 1.5 I 1.5 PeLEDs is further showcased, achieving an impressive EQE of 12.7% at 576 nm., (© 2023 Wiley-VCH GmbH.)

Mixed-halide perovskites enable precise spectral tuning across the entire spectral range through composition engineering. However, mixed halide perovskites are susceptible to ion migration under continuous illumination or electric field, which significantly impedes the actual application of perovskite light-emitting diodes (PeLEDs). Here, we demonstrate a novel approach to introduce strong and homogeneous halogen bonds within the quasi-two-dimensional perovskite lattices by means of an interlayer locking structure, which effectively suppresses ion migration by increasing the corresponding activation energy. Various characterizations confirmed that intralattice halogen bonds enhance the stability of quasi-2D mixed-halide perovskite films. Here, we report that the PeLEDs exhibit an impressive 18.3% EQE with pure red emission with CIE color coordinate of (0.67, 0.33) matching Rec. 2100 standards and demonstrate an operational half-life of ∼540 min at an initial luminance of 100 cd m -2 , representing one of the most stable mixed-halide pure red PeLEDs reported to date.

It is shown that certain undercompressive shock profile solutions of the modified Korteweg-de Vries-Burgers equation $$ partial_t u + partial_x(u^3) = partial_x^3 u + alpha partial_x^2 u, quad alpha geq 0 $$ are spectrally stable when $alpha$ is sufficiently small, in the sense that their linearized perturbation equations admit no eigenvalues having positive real part except a simple eigenvalue of zero (due to the translation invariance of the linearized perturbation equations). This spectral stability makes it possible to apply a theory of Howard and Zumbrun to immediately deduce the asymptotic orbital stability of these undercompressive shock profiles when $alpha$ is sufficiently small and positive.

We construct various periodic traveling wave solutions of the Ostrovsky/Hunter--Saxton/short pulse equation and its KdV regularized version. For the regularized short pulse model with small Coriolis parameter, we describe a family of periodic traveling waves which are a perturbation of appropriate KdV solitary waves. We show that these waves are spectrally stable. For the short pulse model, we construct a family of traveling peakons with corner crests. We show that the peakons are spectrally stable as well. [ABSTRACT FROM AUTHOR]

In this work, the traveling wave solutions of a one-dimensional reaction-diffusion equation with advection are studied. The traveling wave solutions are obtained using the G ′/ G -expansion method. The shock thickness and spectral stability have been discussed for the obtained solution in the parameter interval. The essential spectra of the perturbed and linearized differential operator about the traveling antikink and kink solutions at the equilibrium states are obtained. The point spectrum is calculated using Evans function with Lie midpoint method and Magnus method. It is shown that, for a symmetric potential well, the traveling kink and antikink solutions which connect the stable equilibrium states of the system are stable. It is observed that the perturbation on the advection exhibits contrasting effect on the solution properties (shock thickness and the eigenvalue) of kink and antikink solutions. Variation of the reaction coefficient leads to instability of the solutions, unlike the diffusion coefficient which enhances the stability. On the other hand, the variation of reaction and diffusion coefficients show the monotonic effect on the shock thickness of the traveling kink and antikink solutions. This study is expected to be useful in analyzing the slow or fast invasion and stability of the population movement in different steady states. [ABSTRACT FROM AUTHOR]

The FitzHugh-Nagumo equations are known to admit fast traveling pulses that have monotone tails and arise as the concatenation of Nagumo fronts and backs in an appropriate singular limit, where a parameter $$\varepsilon $$ goes to zero. These pulses are known to be nonlinearly stable with respect to the underlying PDE. Recently, the existence of fast pulses with oscillatory tails was proved for the FitzHugh-Nagumo equations. In this paper, we prove that the fast pulses with oscillatory tails are also nonlinearly stable. Similar to the case of monotone tails, stability is decided by the location of a nontrivial eigenvalue near the origin of the PDE linearization about the traveling pulse. We prove that this real eigenvalue is always negative. However, the expression that governs the sign of this eigenvalue for oscillatory pulses differs from that for monotone pulses, and we show indeed that the nontrivial eigenvalue in the monotone case scales with $$\varepsilon $$ , while the relevant scaling in the oscillatory case is $$\varepsilon ^{2/3}$$ . [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamic behavior of traveling waves for the Sharma-Tasso-Olver equation. The spectral stability of traveling wave solutions are shown by the spectral energy estimate method. Interactions between two solitary waves are described by the extended homoclinic test function method. Three types of interaction are presented. The type of interactions depend on the phase shift parameter $$\epsilon $$ . The local fission and fusion phenomena of solitary wave interactions are investigated and exhibited mathematically and graphically, and they have no relationship with the parameter $$\alpha $$ which are different from the previous works. The local fission and fusion phenomena of solitary waves occur when the phase shift parameter $$0<\epsilon \ll 1$$ or $$\epsilon \gg 1$$ . These results might provide us with useful information on the dynamics of the relevant physical fields. [ABSTRACT FROM AUTHOR]

In this contribution, we summarize recent results [8, 9] on the stability analysis of periodicwavetrains for the sine-Gordon and general nonlinearKlein-Gordon equations. Stability is considered both from the point of view of spectral analysis of the linearized problem and from the point of view of the formal modulation theory of Whitham [12]. The connection between these two approaches is made through a modulational instability index [9], which arises from a detailed analysis of the Floquet spectrum of the linearized perturbation equation around the wave near the origin. We analyze waves of both subluminal and superluminal propagation velocities, as well as waves of both librational and rotational types. Our general results imply in particular that for the sine-Gordon case only subluminal rotationalwaves are spectrally stable. Our proof of this fact corrects a frequently cited one given by Scott [11]. [ABSTRACT FROM AUTHOR]

Perovskite quantum dots light-emitting diodes (PQLEDs), due to the advantages of high luminous efficiency, high color purity, adjustable spectral range, etc., has an excellent prospect in the next generation of high-definition displays. As an indispensable part of displays, blue PQLEDs are usually achieved by mixing halogen, which, however, will lead to halogen ion migration and phase separation of perovskite material at high temperature and bias pressure, thus make the electroluminescent spectrum redshift. In this manuscript, we propose a strategy to inhibit phase separation of blue perovskite quantum dots (PQDs) by introducing alkali metal, and obtain stable perovskite quantum dot light-emitting diodes. The PQLEDs based on this strategy show an external quantum efficiency (EQE) of 1.87% and a brightness of 3757 cd m−2, and can still guarantee stable electroluminescence (EL) spectra at a bias of up to 14 V. The work is beneficial for probing into the mechanism of suppressing the phase separation of mixed halogen blue PQDs and offer a promising strategy to enhance the color stability of blue PQLEDs. [Display omitted] • Alkali metal is introduced into blue perovskite quantum dots (PQDs). • Phase separation of blue PQDs is effectively inhibited. • Perovskite quantum dot light-emitting devices (PQLEDs) are fabricated. • The device guarantee stable electroluminescence spectra at a bias of up to 14 V. [ABSTRACT FROM AUTHOR]

In the present contribution we investigate some features of dynamical lattice systems near periodic traveling waves. First, following the formal averaging method of Whitham, we derive modulation systems expected to drive at main order the time evolution of slowly modulated wavetrains. Then, for waves whose period is commensurable to the lattice, we prove that the formally-derived first-order averaged system must be at least weakly hyperbolic if the background waves are to be spectrally stable, and, when weak hyperbolicity is met, the characteristic velocities of the modulation system provide group velocities of the original system. Historically, for dynamical evolutions obeying partial differential equations, this has been proved, according to increasing level of algebraic complexity, first for systems of reaction–diffusion type, then for generic systems of balance laws, at last for Hamiltonian systems. Here, for their semi-discrete counterparts, we give at once simultaneous proofs for all these cases. Our main analytical tool is the discrete Bloch transform, a discrete analogue to the continuous Bloch transform. Nevertheless, we needed to overcome the absence of genuine space-translation invariance, a key ingredient of continuous analyses. [ABSTRACT FROM AUTHOR]

In the spectral stability analysis of localized patterns to singular perturbed evolution problems, one often encounters that the Evans function respects the scale separation. In such cases the Evans function of the full linear stability problem can be approximated by a product of a slow and a fast reduced Evans function, which correspond to properly scaled slow and fast singular limit problems. This feature has been used in several spectral stability analyses in order to reduce the complexity of the linear stability problem. In these studies the factorization of the Evans function was established via geometric arguments that need to be customized for the specific equations and solutions under consideration. In this paper we develop an alternative factorization method. In this analytic method we use the Riccati transformation and exponential dichotomies to separate slow from fast dynamics. We employ our factorization procedure to study the spectra associated with spatially periodic pulse solutions to a general class of multicomponent, singularly perturbed reaction-diffusion equations. Eventually, we obtain expressions of the slow and fast reduced Evans functions, which describe the spectrum in the singular limit. The spectral stability of localized periodic patterns has so far only been investigated in specific models such as the Gierer-Meinhardt equations. Our spectral analysis significantly extends and formalizes these existing results. Moreover, it leads to explicit instability criteria. [ABSTRACT FROM AUTHOR]

In this present work we consider the periodic standing wave solutions for the coupled nonlinear Schrödinger equations. We restrict our problem to two cases and construct the solutions explicitly. Then we make the stability analysis for each case. We show that the relevant stationary solutions are spectrally stable for certain parameters. For those parameters, we also present our numerical results in the spectral analysis. [ABSTRACT FROM AUTHOR]

Frequently encountered in nature, internal solitary waves in stratified fluids have been investigated experimentally, theoretically, and numerically. Mathematically, these waves are exact solutions of the incompressible 2D Euler equations. Contrasting with a rich existence theory and the development of methods for their computation, their stability analysis has hardly received attention at a rigorous mathematical level. This paper proposes a new approach to the investigation of stability of internal solitary waves in a continuously stratified fluid and carries out the following four steps of this approach: (I) to formulate the eigenvalue problem as an infinite-dimensional spatial-dynamical system, (II) to introduce finite-dimensional truncations of the spatial-dynamics description, (III) to demonstrate that each truncation, of any order, permits a well-defined Evans function, (IV) to prove absence of small zeros of the Evans function in the small-amplitude limit. The latter notably implies the low-frequency spectral stability of small-amplitude waves to arbitrarily high truncation order. [ABSTRACT FROM AUTHOR]

Extracting the confined light is of critical significance in achieving highly energy efficient organic light emitting diodes. To address the task of extracting the confined light, we here synthesize a new type of liquid prepolymer, which spontaneously forms wrinkles upon ultra-violet light exposure. The spontaneously formed organic wrinkle is successfully applied not only in extracting the confined light but also in inducing angular spectral stability. Simulations demonstrate that the wrinkles can lower incident angle of light impinging on the substrate/air interface and thus help extract a large portion of light delivered to the substrate. In particular, it is shown that geometrical optimization of the size and aspect ratio of wrinkles is important in obtaining the highest light extraction. With the simplicity of the process and size controllability, the proposed wrinkle-based approach can be readily realized over a large area, opening up a new avenue in various photonics applications. [ABSTRACT FROM AUTHOR]

As part of the EnMAP preparation activities this study aims at estimating the uncertainty in the EnMAP L2A ground reflectance product using the simulated scene of Barrax, Spain. This dataset is generated using the EnMAP End-to-End Simulation tool, providing a realistic scene for a well-known test area. Focus is set on the influence of the expected radiometric calibration stability and the spectral calibration stability. Using a Monte-Carlo approach for uncertainty analysis, a larger number of realisations for the radiometric and spectral calibration are generated. Next, the ATCOR atmospheric correction is conducted for the test scene for each realisation. The subsequent analysis of the generated ground reflectance products is carried out independently for the radiometric and the spectral case. Findings are that the uncertainty in the L2A product is wavelength-dependent, and, due to the coupling with the estimation of atmospheric parameters, also spatially variable over the scene. To further illustrate the impact on subsequent data analysis, the influence on two vegetation indices is briefly analysed. Results show that the radiometric and spectral stability both have a high impact on the uncertainty of the narrow-band Photochemical Reflectance Index (PRI), and also the broad-band Normalized Difference Vegetation Index (NDVI) is affected. [ABSTRACT FROM AUTHOR]

We study front solutions of a system that models combustion in highly hydraulically resistant porous media. The spectral stability of the fronts is tackled by a combination of energy estimates and numerical Evans function computations. Our results suggest that there is a parameter regime for which there are no unstable eigenvalues. We use recent works about partially parabolic systems to prove that in the absence of unstable eigenvalues the fronts are convectively unstable. [ABSTRACT FROM AUTHOR]