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We study transverse stability and instability of one-dimensional small-amplitude periodic travelling waves of a generalized Kadomtsev–Petviashvili equation with respect to two-dimensional perturbations, which are either periodic or square-integrable in the direction of the propagation of the underlying one-dimensional wave and periodic in the transverse direction. We obtain transverse instability results in KP-fKdV, KP-ILW and KP-Whitham equations. Moreover, assuming the spectral stability of one-dimensional wave with respect to one-dimensional square-integrable periodic perturbations, we obtain transverse stability results in the aforementioned equations. [ABSTRACT FROM AUTHOR]

The paper is concerned with the stability property under perturbation Q → Q ˜ of different spectral characteristics of a boundary value problem associated in L 2 ([ 0 , 1 ] ; C 2) with the following 2 × 2 Dirac type equation (0.1) L U (Q) y = − i B − 1 y ′ + Q (x) y = λ y , B = ( b 1 0 0 b 2 ) , b 1 < 0 < b 2 , y = col (y 1 , y 2) , with a potential matrix Q ∈ L p ([ 0 , 1 ] ; C 2 × 2) and subject to the regular boundary conditions U y : = { U 1 , U 2 } y = 0. If b 2 = − b 1 = 1 this equation is equivalent to one dimensional Dirac equation. Our approach to the spectral stability relies on the existence of the triangular transformation operators for system (0.1) with Q ∈ L 1 , which was established in our previous works. The starting point of our investigation is the Lipshitz property of the mapping Q → K Q ± , where K Q ± are the kernels of transformation operators for system (0.1). Namely, we prove the following uniform estimate: ‖ K Q ± − K Q ˜ ± ‖ X ∞ , p 2 + ‖ K Q ± − K Q ˜ ± ‖ X 1 , p 2 ⩽ C ⋅ ‖ Q − Q ˜ ‖ p , Q , Q ˜ ∈ U p , r 2 × 2 , p ∈ [ 1 , ∞ ] , on balls U p , r 2 × 2 in L p ([ 0 , 1 ] ; C 2 × 2). It is new even for Q ˜ = 0. Here X ∞ , p 2 , X 1 , p 2 are the special Banach spaces naturally arising in such problems. We also obtained similar estimates for Fourier transforms of K Q ±. Both of these estimates are of independent interest and play a crucial role in the proofs of all spectral stability results discussed in the paper. For instance, as an immediate consequence of these estimates we get the Lipshitz property of the mapping Q → Φ Q (⋅ , λ) , where Φ Q (x , λ) is the fundamental matrix of the system (0.1). Assuming the spectrum Λ Q = { λ Q , n } n ∈ Z of L U (Q) to be asymptotically simple, denote by F Q = { f Q , n } | n | > N a sequence of corresponding normalized eigenvectors, L U (Q) f Q , n = λ Q , n f Q , n. Assuming boundary conditions (BC) to be strictly regular , we show that the mapping Q → Λ Q − Λ 0 sends L p ([ 0 , 1 ] ; C 2 × 2) either into ℓ p ′ or into the weighted ℓ p -space ℓ p ({ (1 + | n |) p − 2 }) ; we also establish its Lipshitz property on compact sets in L p ([ 0 , 1 ] ; C 2 × 2) , p ∈ [ 1 , 2 ]. The proof of the second estimate involves as an important ingredient inequality that generalizes classical Hardy-Littlewood inequality for Fourier coefficients. It is also shown that the mapping Q → F Q − F 0 sends L p ([ 0 , 1 ] ; C 2 × 2) into the space ℓ p ′ (Z ; C ([ 0 , 1 ] ; C 2) of sequences of continuous vector-functions, and has the Lipshitz property on compacts sets in L p ([ 0 , 1 ] ; C 2 × 2) , p ∈ [ 1 , 2 ]. Certain modifications of these spectral stability results are also proved for balls U p , r 2 × 2 in L p ([ 0 , 1 ] ; C 2 × 2) , p ∈ [ 1 , 2 ]. Note also that the proof of the Lipshitz property of the mapping Q → F Q − F 0 involves the deep Carleson-Hunt theorem for maximal Fourier transform, while the proof of this property for the mapping Q → Λ Q − Λ 0 relies on the estimates of the classical Fourier transform and is elementary in character. We apply our previous results to the damped string equation to establish the Riesz basis property and the asymptotic behavior of the eigenvalues of the corresponding dynamic generator under the assumptions d ∈ L 1 [ 0 , ℓ ] , ρ ∈ W 1 , 1 [ 0 , ℓ ] on the damping coefficient and the density of the string, that are weaker than previously treated in the literature. We also establish Lipshitz dependence on d and ρ in ℓ p -spaces of the remainders in the asymptotic formula for the eigenvalues. [ABSTRACT FROM AUTHOR]

Blue perovskite light-emitting diodes (PeLEDs) have attracted enormous attention; however, their unsatisfactory device efficiency and spectral stability still remain great challenges. Unfavorable low-dimensional phase distribution and defects with deeper energy levels usually cause energy disorder, substantially limiting the device's performance. Here, an additive-interface optimization strategy is reported to tackle these issues, thus realizing efficient and spectrally stable blue PeLEDs. A new type of additive-formamidinium tetrafluorosuccinate (FATFSA) is introduced into the quasi-2D mixed halide perovskite accompanied by interface engineering, which effectively impedes the formation of undesired low-dimensional phases with various bandgaps throughout the entire film, thereby boosting energy transfer process for accelerating radiative recombination; this strategy also diminishes the halide vacancies especially chloride-related defects with deep energy level, thus reducing nonradiative energy loss for efficient radiative recombination. Benefitting from homogenized energy landscape throughout the entire perovskite emitting layer, PeLEDs with spectrally-stable blue emission (478 nm) and champion external quantum efficiency (EQE) of 21.9% are realized, which represents a record value among this type of PeLEDs in the pure blue region., (© 2024 Wiley‐VCH GmbH.)

Although brightness and efficiency have been continually improved, the inability to achieve superior efficiency, color stability, and low-efficiency roll-off simultaneously in white organic light-emitting diodes (OLEDs) remains a knotty problem restricting the commercial application. In this paper, emission balance for two different horizontal orientation emitting molecules is maintained by using hole transport materials and bipolar host materials to control carriers' recombination and exciton diffusion. Impressively, the obtained devices exhibit extremely stable white emission with small chromaticity coordinates variation of (0.0023, 0.0078) over a wide brightness range from 1000 to 50000 cd m -2 . Meanwhile, the optimal white OLED realizes the power efficiency, current efficiency, and external quantum efficiency up to 70.68 lm W -1 , 85.53 cd A -1, and 24.33%, respectively at the practical brightness of 1000 cd m -2 . Owing to reduced heterogeneous interfaces and broadening recombination region, this device exhibits a high EQE over 20% under high luminance of 10000 cd m -2 , demonstrating slight efficiency roll-off. The operating mechanism of the device is analyzed by versatile experimental and theoretical evidences, which concludes precise manipulation of charges and excitons is the key points to achieve these excellent performances. This work provides an effective strategy for the design of high-performance white OLEDs., (© 2024 Wiley‐VCH GmbH.)

Compared with red and green perovskite light‐emitting diodes (PeLEDs), blue PeLEDs are still unable to well control spectral stability due to the issues of ion migration and phase separation under external operating conditions. Herein, a strategy using organometallic ligands is reported to achieve spectrally stable PeLEDs. The obtained perovskite film exhibits stable photoluminescence spectra under UV excitation (365nm) and continuous heating of 70 °C. The device delivers an external quantum efficiency (EQE) of 6.7% with 50% lifetime (T50) of 21.6 min. Under high driving voltage (from 2 to 7.5 V), no obvious spectral shift has occurred for the electroluminescence spectrum at 481 nm. This work confirms the positive effect of organometallic ligands in quasi‐2D perovskite and provides a new idea for proposing effective ligands to act on the perovskite luminescence layer in the future. [ABSTRACT FROM AUTHOR]

We solve the open problem of spectral stability of smooth periodic waves in the Camassa–Holm equation. The key to obtaining this result is that the periodic waves of the Camassa–Holm equation can be characterized by an alternative Hamiltonian structure, different from the standard formulation common to the Korteweg‐de Vries equation. The standard formulation has the disadvantage that the period function is not monotone and the quadratic energy form may have two rather than one negative eigenvalues. We prove that the nonstandard formulation has the advantage that the period function is monotone and the quadratic energy form has only one simple negative eigenvalue. We deduce a precise condition for the spectral and orbital stability of the smooth periodic travelling waves and show numerically that this condition is satisfied in the open region where the smooth periodic waves exist. [ABSTRACT FROM AUTHOR]

The existence, uniqueness, and stability of periodic traveling waves for the fractional Benjamin–Bona–Mahony equation is considered. In our approach, we give sufficient conditions to prove a uniqueness result for the single‐lobe solution obtained by a constrained minimization problem. The spectral stability is then shown by determining that the associated linearized operator around the wave restricted to the orthogonal of the tangent space related to the momentum and mass at the periodic wave has no negative eigenvalues. We propose the Petviashvili's method to investigate the spectral stability of the periodic waves for the fractional Benjamin–Bona–Mahony equation, numerically. Some remarks concerning the orbital stability of periodic traveling waves are also presented. [ABSTRACT FROM AUTHOR]

We numerically study solitary waves in the coupled nonlinear Schrödinger equations. We detect pitchfork bifurcations of the fundamental solitary wave and compute eigenvalues and eigenfunctions of the corresponding eigenvalue problems to determine the spectral stability of solitary waves born at the pitchfork bifurcations. Our numerical results demonstrate the theoretical ones which the authors obtained recently. We also compute generalized eigenfunctions associated with the zero eigenvalue for the bifurcated solitary wave exhibiting a saddle-node bifurcation, and show that it does not change its stability type at the saddle-node bifurcation point. [ABSTRACT FROM AUTHOR]

In this paper, we investigate spectral stability of traveling wave solutions to 1D quantum hydrodynamics system with nonlinear viscosity in the (ρ , u) , that is, density and velocity, variables. We derive a sufficient condition for the stability of the essential spectrum and we estimate the maximum modulus of eigenvalues with non-negative real part. In addition, we present numerical computations of the Evans function in sufficiently large domain of the unstable half-plane and show numerically that its winding number is (approximately) zero, thus giving a numerical evidence of point spectrum stability. [ABSTRACT FROM AUTHOR]

We analyze the spectral stability of small-amplitude, periodic, traveling-wave solutions of the Kawahara equation. These solutions exhibit high-frequency instabilities when subject to bounded perturbations on the whole real line. We introduce a formal perturbation method to determine the asymptotic growth rates of these instabilities, among other properties. Explicit numerical computations are used to verify our asymptotic results. [ABSTRACT FROM AUTHOR]

Motivated by pulse-replication phenomena observed in the FitzHugh--Nagumo equation, we investigate traveling pulses whose slow/fast profiles exhibit canard-like transitions. We show that the spectra of the PDE linearization about such pulses may contain many point eigenvalues that accumulate onto a union of curves as the slow scale parameter approaches zero. The limit sets are related to the absolute spectrum of the homogeneous rest states involved in the canard-like transitions. Our results are formulated for general systems that admit an appropriate slow/fast structure. [ABSTRACT FROM AUTHOR]

We consider the periodic standing waves in the derivative nonlinear Schrödinger (DNLS) equation arising in plasma physics. By using a newly developed algebraic method with two eigenvalues, we classify all periodic standing waves in terms of eight eigenvalues of the Kaup–Newell spectral problem located at the end points of the spectral bands outside the real line. The analytical work is complemented with the numerical approximation of the spectral bands, this enables us to fully characterize the modulational instability of the periodic standing waves in the DNLS equation. [ABSTRACT FROM AUTHOR]

We obtain explicit characterization of orbital and spectral stability of solitary wave solutions to the U(1)-invariant 1D Klein–Gordon equation coupled to an anharmonic oscillator. We also give the complete analysis of the spectrum of the linearization at a solitary wave. [ABSTRACT FROM AUTHOR]

In this paper, we analyze conditions under which the spectrum of the Sturm–Liouville operator on a certain smooth curve is localized near a countable number of rays. In the case where the potential is piecewise analytical, an asymptotic of eigenvalues is found for each series localized near the corresponding ray. The result obtained allows one to generalize the well-known formula for the asymptotic of the distribution function of the spectrum stated by Davies in the case of a finite number of localization rays. [ABSTRACT FROM AUTHOR]

We present a numerical approach for determination of the spectral stability of solitary waves by computing eigenvalues and eigenfunctions of the corresponding eigenvalue problems, along with their continuation, for nonlinear wave equations in one space dimension. We illustrate the approach for the nonlinear Schrödinger (NLS) equation with a small potential, and numerically determine the spectral stability of solitary waves near bifurcation points along with computations of eigenfunctions and eigenvalues. The numerical results demonstrate some theoretical ones the authors recently obtained for the example. [ABSTRACT FROM AUTHOR]

Halide perovskites are promising emitters for light‐emitting diodes (LEDs) due to their outstanding optoelectronic properties, i.e., tunable bandgap, high photoluminescence quantum efficiency, and excellent color purity. However, in contrast to their green and red cousins, the present blue perovskite LEDs are still suffering from poor operational lifetime and electroluminescence shift during bias operation, hindering their practical applications in full‐color information displays. Developing rational strategies to achieve efficient and stable blue perovskite LEDs is one of the urgent tasks in this community. Herein, through substituting the Pb site with strontium ions, blue perovskite films with stable emission under relatively harsh working conditions, i.e., high electrical bias, constant thermal heating, and UV illumination, are obtained, which accordingly guarantees spectrally stable blue perovskite LEDs with external quantum efficiency of 4.1%. Moreover, different alkaline‐earth metal ions are also investigated to further explore the effects of B‐site ion substitution on the performance of perovskite LEDs. This work demonstrates an alternative path for the development of spectral‐stable blue perovskite LEDs. [ABSTRACT FROM AUTHOR]

We characterize the type stability of the five-vortex problem in the plane, where it is assumed that configuration is a rhombus vortex problem with a central vortex. More precisely, we suppose that the opposite vortices have the same vorticity Γ 1 = Γ 2 = 1 and Γ 3 = Γ 4 = Γ ≠ 0 and the vortex at the center has vorticity Γ 0 ≠ 0 . The stability is given in terms of the size of the rhombus and the vorticities. [ABSTRACT FROM AUTHOR]

In this paper, we study the essential spectrum of the operator obtained by linearizing at traveling waves that occur in the one-dimensional version of the M5-model for mesenchymal cell movement inside a directed tissue made up of highly aligned fibers. We show that traveling waves are spectrally unstable in L2(ℝ; ℂ3) as the essential spectrum includes the imaginary axis. Tools in the proof include exponential dichotomies and Fredholm properties. We prove that a weighted space Lw2(ℝ; ℂ3) with the same function for the tree variables of the linearized operator is no suitable to shift the essential spectrum to the left of the imaginary axis. We find a pair of appropriate weight functions whereby on the weighted space Lwα2(ℝ; ℂ2) × Lwε2(ℝ; ℂ) the essential spectrum lies on {Reλ<0}, outside the imaginary axis. [ABSTRACT FROM AUTHOR]

We use a geometric approach to prove the existence of smooth travelling wave solutions of a nonlinear diffusion–reaction equation with logistic kinetics and a convex nonlinear diffusivity function which changes sign twice in our domain of interest. We determine the minimum wave speed, c ∗ , and investigate its relation to the spectral stability of a desingularised linear operator associated with the travelling wave solutions. [ABSTRACT FROM AUTHOR]

We construct a new Evans function for quasi-periodic solutions to the linearisation of the sine-Gordon equation about a periodic travelling wave. This Evans function is written in terms of fundamental solutions to a Hill's equation. Applying the Evans-Krein function theory of Kollár and Miller (SIAM Rev 56(1):73–123, 2014) to our Evans function, we provide a new method for computing the Krein signatures of simple characteristic values of the linearised sine-Gordon equation. By varying the Floquet exponent parametrising the quasi-periodic solutions, we compute the linearised spectra of periodic travelling wave solutions of the sine-Gordon equation and track dynamical Hamiltonian–Hopf bifurcations via the Krein signature. Finally, we show that our new Evans function can be readily applied to the general case of the nonlinear Klein–Gordon equation with a non-periodic potential. [ABSTRACT FROM AUTHOR]

We examine micromagnetic pattern formation in chiral magnets, driven by the competition of Heisenberg exchange, Dzyaloshinskii–Moriya interaction, easy-plane anisotropy and thermodynamic Landau potentials. Based on equivariant bifurcation theory, we prove existence of lattice solutions branching off the zero magnetization state and investigate their stability. We observe in particular the stabilization of quadratic vortex–antivortex lattice configurations and instability of hexagonal skyrmion lattice configurations, and we illustrate our findings by numerical studies. [ABSTRACT FROM AUTHOR]

This paper establishes the spectral stability in exponentially weighted spaces of smooth traveling monotone fronts for reaction diffusion equations of Fisher-KPP type with nonlinear degenerate diffusion coefficient. It is assumed that the former is degenerate, that is, it vanishes at zero, which is one of the equilibrium points of the reaction. A parabolic regularization technique is introduced in order to locate a subset of the compression spectrum of the linearized operator around the wave, whereas the point spectrum is proved to be stable with the use of energy estimates. Detailed asymptotic decay estimates of solutions to spectral equations are required in order to close the energy estimates. It is shown that all fronts traveling with speed above a threshold value are spectrally stable in an appropriately chosen exponentially weighted L 2 -space. [ABSTRACT FROM AUTHOR]

This paper concerns the investigation of the stability properties of relative equilibria which are rigidly rotating vortex configurations sometimes called vortex crystals, in the N-vortex problem. Such a configurations can be characterized as critical point of the Hamiltonian function restricted on the constant angular impulse hyper-surface in the phase space (topologically a pseudo-sphere whose coefficients are the circulation strengths of the vortices). Relative equilibria are generated by the circle action on the so-called shape pseudo-sphere (which generalize the standard shape sphere appearing in the study of the N-body problem). Inspired by the planar N-body problem, and after a geometrical and dynamical discussion of the problem, we investigate the relation intertwining the stability of relative equilibria and the inertia indices of the central configurations generating such equilibria. In the last section we applied our main results to some symmetric three and four vortices relative equilibria. [ABSTRACT FROM AUTHOR]

[Display omitted] • Homogeneity of a mono-layer QDs decides spectral stability of QLEDs in time scale. • Defects, driving bias, current density and operation time also affect EL stability. • Spectrally stable 4 and 64 mm2 QLEDs are achieved with low efficiency roll-off. • Efficient QLEDs with pure-blue to deep-blue emissions are achieved. • The QLEDs show high stability after being stored for a year. Mixed-halide perovskite quantum dots (QDs) light-emitting diodes (QLEDs) with blue emission still suffer from low efficiency due to surface defects and halide migration. The issue of halide migration in the mixed-halide perovskite QLEDs under increasing biases have been basically solved. However, under continuous driving, the QLEDs still face the problem of halide migration or electroluminescence (EL) peak shift. In this work, we found that when ligand passivation effects on mixed-halide perovskite QDs are similar, the homogeneity of a mono-layer QDs film plays a decisive role in suppressing halide migration and improving the EL spectral stability of the QLEDs under continuous driving. Moreover, 4 and 64 mm2 QLEDs with emission peaks from pure-blue to deep-blue and low efficiency roll-off were fabricated and the analysis results show that factors, such as chlorine content or defects in the QDs, driving bias, operation time at the driving bias and current density, also matter in the EL spectral stability of the QLEDs. In addition, we found that the devices exhibit similar performance after being stored for a year, demonstrating high stability of the devices with homogeneous mono-layer QDs structure. Our work provides a timely and systematic guide on achieving spectrally stable and efficient blue QLEDs with high color purity based on mixed-halide perovskite QDs. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear water wave model describing the evolution of the internal tides in the coastal zone. First, we prove the existence of minimizers for the corresponding energy functional on the L 2 -norm constrained manifold by the concentrated compactness principle, and thus we obtain a ground state traveling wave solution of the model. Moreover, we show that the solution has exponential decay in the far field. Finally, we show that the traveling wave solution is non-degenerate, and thus the spectral stability of the solution can be obtained by using the instability index theory. • The existence of constrained solitary waves is proved using the concentrated compactness principle. • The exponential decay estimate of the solution in the far field is obtained using the spectral analysis. • The spectral stability of solitary wave solutions is investigated using the instability index theory. [ABSTRACT FROM AUTHOR]

Nanoplatelets (NPLs) share excellent luminescent properties with their symmetric quantum dots counterparts and entail special characters benefiting from the shape, like the thickness-dependent bandgap and anisotropic luminescence. However, perovskite NPLs, especially those based on iodide, suffer from poor spectral and phase stability. Here, stable CsPbI 3 NPLs obtained by accelerating the crystallization process in ambient-condition synthesis are reported. By this kinetic control, the rectangular NPLs into quasi-square NPLs are tuned, where enlarged width endows the NPLs with a lower surface-area-to-volume ratio (S/V ratio), leading to lower surficial energy and thus improved endurance against NPL fusion (cause for spectral shift or phase transformation). The accelerated crystallization, denoting the fast nucleation and short period of growth in this report, is enabled by preparing a precursor with complete transformation of PbI 2 into intermediates (PbI 3 - ), through an additional iodide supplier (e.g., zinc iodide). The excellent color stability of the materials remains in the light-emitting diodes under various bias stresses., (© 2023 The Authors. Small published by Wiley‐VCH GmbH.)

The stationary structure stability of discontinuous solutions to nonlinear hyperbolic equations describing the propagation of quasi-transverse waves with velocities close to characteristic ones are studied. A procedure to analyze spectral (linear) stability of these solutions is described. The main focus is the stability analysis of special discontinuities, the stationary structure of which is represented by the integral curve connecting two saddle points corresponding to the states in front of and behind the discontinuity. This analysis is done using the properties of the Evans function, an analytic function on the right complex half-plane, which has zeros in this domain if and only if there exist unstable modes of linearization around a solution representing a special discontinuity with the structure. [ABSTRACT FROM AUTHOR]

We consider the Sturm–Liouville operator T0 on the semi-axis (0,+∞) with the potential eiθq, where 0 < θ < π and q is a real-valued function that may have arbitrarily slow growth at infinity. This operator does not meet any condition of the Keldysh theorem: T0 is non-self-adjoint and its resolvent does not belong to the Neumann–Schatten class for any p < ∞. We find conditions for q and perturbations of V under which the localization or the asymptotics of its spectrum is preserved. [ABSTRACT FROM AUTHOR]

Reported here are results concerning the global well-posedness in the energy space and existence and stability of standing-wave solutions for 1-dimensional three-component systems of nonlinear Schrödinger equations with quadratic nonlinearities. For two particular systems we are interested in, the global well-posedness is established in view of the a priori bounds for the local solutions. The standing waves are explicitly obtained and their spectral stability is studied in the context of Hamiltonian systems. For more general Hamiltonian systems, the existence of standing waves is accomplished with a variational approach based on the Mountain Pass Theorem. Uniqueness results are also provided in some very particular cases. [ABSTRACT FROM AUTHOR]

Various approaches to studying the stability of solutions of nonlinear PDEs lead to explicit formulae determining the stability or instability of the wave for a wide range of classes of equations. However, these are typically specialized to a particular equation and checking the stability conditions may not be straightforward. We present results for a large class of problems that reduce the determination of spectral stability of a wave to a simple task of locating zeros of explicitly constructed polynomials. We study spectral stability of small-amplitude periodic waves in scalar Hamiltonian problems as a perturbation of the zero-amplitude case. A necessary condition for stability of the wave is that the unperturbed spectrum is restricted to the imaginary axis. Instabil- ity can come about through a Hamiltonian-Hopf bifurcation, i.e., of a collision of purely imaginary eigenvalues of the Floquet spectrum of opposite Krein signature. In recent work on the stability of small-amplitude waves the dispersion relation of the unperturbed problem was shown to play a central role. We demonstrate that the dispersion relation provides even more explicit information about wave stability: we construct a polynomial of half the degree of the dispersion relation, and its roots directly characterize not only collisions of eigenvalues at zero amplitude but also an agreement or a disagreement of their Krein signatures. Based on this explicit information it is possible to detect instabilities of non-zero-amplitude waves. In our analysis we stay away from the possible instabil- ities at the origin of the spectral plane corresponding to modulation or Benjamin{Fair instability. Generalized KdV and its higher-order analogues are used as illustrating examples. [ABSTRACT FROM AUTHOR]

We investigate the point spectrum associated with travelling wave solutions in a Keller–Segel model for bacterial chemotaxis with small diffusivity of the chemoattractant, a logarithmic chemosensitivity function and a constant, sublinear or linear consumption rate. We show that, for constant or sublinear consumption, there is an eigenvalue at the origin of order two. This is associated with the translation invariance of the model and the existence of a continuous family of solutions with varying wave speed. These point spectrum results, in conjunction with previous results in the literature, imply that in these cases the travelling wave solutions are absolute unstable if the chemotactic coefficient is above a certain critical value, while they are transiently unstable otherwise. • Travelling wave solutions are transiently unstable for a range of parameter values. • The point eigenvalue of order two at the origin persists for small diffusion. • The constant consumption model is spectrally stable in the weighted function space. • The spectral gap vanishes for linear consumption. • Eigenfunctions for the origin are contained in the weighted function space. [ABSTRACT FROM AUTHOR]

We analyze the spectral stability of small-amplitude, periodic, traveling-wave solutions of a Boussinesq–Whitham system. These solutions are shown numerically to exhibit high-frequency instabilities when subject to bounded perturbations on the real line. We use a formal perturbation method to estimate the asymptotic behavior of these instabilities in the small-amplitude regime. We compare these asymptotic results with direct numerical computations.

• The proposal was made to introduce gelatin into the test solution to utilize the coffee ring effect of liquid droplets for the enrichment of heavy metals in the solution. • The influence of different gelatin mass fractions on the deposition morphology of droplet surfaces and the LIBS spectral intensity was analyzed. • The spectral enhancement mechanism of four different substrate materials, namely Zn plate, Al plate, Ni plate, and Polymethyl methacrylate plate, was investigated. In order to enhance the stability and lower the detection limit of Laser-Induced Breakdown Spectroscopy (LIBS) technology, gelatin was introduced into the test solution in this study to enrich heavy metals using the coffee ring effect. The effects of different gelatin mass fractions on the surface deposition morphology of droplets and the intensity of spectroscopy were analyzed. Explored the spectral enhancement mechanisms of four substrate materials. The results demonstrated that the best coffee ring enrichment was achieved with a gelatin mass fraction of 2.5 %. The signal-to-noise ratios of Cu and Cr were enhanced by 5.5 and 3.6, and the relative standard deviations decreased by 59.5 % and 53.8 %. When Zn plate was used as the substrate material, the detection limits for Cu and Cr were 0.715 mg/L and 3.881 mg/L. The research indicates that surface-enhanced LIBS based on coffee ring enrichment can improve spectral stability and lower the detection limit. [ABSTRACT FROM AUTHOR]

We study the spectral and orbital stability of elliptic function solutions for the focusing modified Korteweg-de Vries (mKdV) equation and construct the corresponding breather solutions to exhibit stable or unstable dynamic behaviors. The elliptic function solutions of the mKdV equation and related fundamental solutions of the Lax pair are exactly represented by theta functions. Based on the 'modified squared wavefunction' (MSW) method, we construct all linear independent solutions of the linearized mKdV equation and then provide a necessary and sufficient condition of the spectral stability for elliptic function solutions with respect to subharmonic perturbations. In the case of spectrum stability, the orbital stability of elliptic function solutions is established in a suitable Hilbert space. Using Darboux-Bäcklund transformation, we construct breather solutions to exhibit unstable or stable dynamic behavior. Through analyzing the asymptotic behavior, we find that the breather solution under the cn-type solution background is equivalent to the elliptic function solution adding a small perturbation as t → ± ∞. [ABSTRACT FROM AUTHOR]

A novel approach to producing high-color-purity blue-light-emitting diodes based on single-crystalline Ruddlesden-Popper perovskites (RPPs) is reported. The utilization of a pure bromide composition eliminates any possibility of halide segregation, which can otherwise lead to undesired shifts in the emission wavelength or irreversible degradation of the spectral line width. Phase-pure PEA 2 MAPb 2 Br 7 single crystals with a lateral size exceeding 1 cm 2 can be synthesized using the inverse temperature crystallization method. To prepare RPP layers with a thickness of less than 50 nm, we employ a thinning process of the initially thick bulk crystals, followed by a dry-transfer process to place them onto a hole transport layer and an indium-tin-oxide-coated glass substrate. By utilizing polydimethylsiloxane as a handling layer, deformations of the bulk RPP crystal and exfoliated RPP layer, as well as the formation of defects such as pinholes, can be effectively suppressed. Subsequent depositions of an electron transport layer and a metal contact complete the fabrication of electroluminescence (EL) devices. The EL devices utilizing the single-crystalline RPP demonstrate excellent spectral stability across a broad range of the applied bias voltage spanning from 4.5 to 10 V, exhibiting a significantly narrow line width of 14 nm at an emission wavelength of 440 nm that can potentially cover 99.3% of the Rec. 2020 color gamut. The sharp EL emission spectrum can be effectively preserved, avoiding any broadening of the line width, by suppressing Joule heating throughout the device operation, in addition to the intrinsic stability of single-crystalline RPPs.

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.

In this paper, we study numerically the existence and stability of some special solutions of the nonlinear beam equation: utt + uxxxx + u- ∣u∣p-1 u = 0 when p = 3 and p = 5. For the standing wave solutions u(x, t) = eiωtφω(x) we numerically illustrate their existence using variational approach. Our numerics illustrate the existence of both ground states and excited states. We also compute numerically the threshold value ω* which separates stable and unstable ground states. Next, we study the existence and linear stability of periodic traveling wave solutions u(x, t) = ϕc(x+ct). We present numerical illustration of the theoretically predicted threshold value of the speed c which separates the stable and unstable waves. [ABSTRACT FROM AUTHOR]

We model an artery with perivascular soft tissue as a uniform cylindrical membrane tube surrounded by a flexible substrate with distributed stiffness. We derive the equations of motion of the arterial model, and obtain evolution equation derived in the long wavelength limit from the general equations of motion. We analyze the stability of axisymmetric perturbations at the bifurcation state taking into the consideration of surrounding soft tissue stiffness and constant axial stretch. We observe that the surrounding soft tissues progressively reduce the domain of real valued solutions with increasing constant axial stretch. The results suggest that the stationary solitary wave solution is unstable. [ABSTRACT FROM AUTHOR]

We consider standing wave solutions of various dispersive models with non-standard form of the dispersion terms. Using index count calculations, together with the information from a variational construction, we develop sharp conditions for spectral stability of these waves. [ABSTRACT FROM AUTHOR]

We construct bi-frequency solitary waves of the nonlinear Dirac equation with the scalar self-interaction, known as the Soler model (with an arbitrary nonlinearity and in arbitrary dimension) and the Dirac--Klein--Gordon with Yukawa self-interaction. These solitary waves provide a natural implementation of qubit and qudit states in the theory of quantum computing. We show the relation of ±2wi eigenvalues of the linearization at a solitary wave, Bogoliubov SU(1; 1) symmetry, and the existence of bi-frequency solitary waves. We show that the spectral stability of these waves reduces to spectral stability of usual (one-frequency) solitary waves. [ABSTRACT FROM AUTHOR]