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In this work we explore some aspects of the spectral instability of back hole quasi-normal modes, using a specific model as an example. The model is that of a small bump perturbation to the effective potential of linear axial gravitational waves on a Schwarzschild background, and our focus is on three different aspects of the instability: identifying and distinguishing between the two different types of instabilities studied previously in the literature, quantifying the size of the perturbations applied to the system and testing the validity of the pseudospectral numerical method in providing a convergent result for this measure, and finally, relating the size and other features of the perturbation to the degree of destabilisation of the spectrum. [ABSTRACT FROM AUTHOR]

With the advent of technology, it has become possible to perform direct numerical simulations and the demand for high accuracy computing is increasing. Numerical simulations play an important part in understanding physics of the flow and instability mechanism in flows. For high accuracy, numerical schemes must be chosen that satisfy the physical dispersion relation, should not amplify or attenuate the solution and resolve all possible length and time scales. In the present paper, spectral stability analysis of linear convection equation is performed using first order forward difference (FD1) method and fourth order Runge Kutta (RK4) method, consisting of four stages, for time discretization and a second order central difference (CD2) method for evaluating spatial derivative. The results show that the presence of numerical instability for FD1 method is independent of the CFL number, consistent with the stability analysis which showed FD1 method to be unconditionally unstable. However, for RK4 method, the solution is found to be neutrally stable only for a particular range of CFL number, even stable solution introduced error by attenuating the computed or analytical solution.

In this article, we investigate the spectral stability of periodic traveling waves for a cubic-quintic and double dispersion equation. Using the quadrature method, we find explict periodic waves and we also present a characterization for all positive and periodic solutions for the model using the monotonicity of the period map in terms of the energy levels. The monotonicity of the period map is also useful to obtain the quantity and multiplicity of non-positive eigenvalues for the associated linearized operator and to do so, we use tools of the Floquet theory. Finally, we prove the spectral stability by analyzing the difference between the number of negative eigenvalues of a convenient linear operator restricted to the space constituted by zero-mean periodic functions and the number of negative eigenvalues of the matrix formed by the tangent space associated to the low order conserved quantities of the evolution model. [ABSTRACT FROM AUTHOR]

Metal mixed‐halide perovskite has demonstrated considerable potential in the development of solution‐treated blue light‐emitting diodes (LEDs) with high external quantum efficiency, excellent color purity, and tunable wavelength. However, the severe phase segregation of mixed‐halide perovskite under bias voltage would lead to the spectral instability of LEDs. Therefore, suppressing phase segregation of Br/Cl perovskite towards spectrally stable blue perovskite LEDs (PeLEDs) is a big challenge. In this work, we systematically explore the influence of perovskite component, preparation conditions, and device structures on the spectral stability of PeLEDs. We have observed that the stable spectra increased the proportion of Cs in the A‐site cations, passivator, and the annealing temperature of perovskite films. Finally, we achieve a spectra‐stable and high‐performance blue PeLED under optimized conditions. Our findings provide important guidance for preparing spectrally stable PeLEDs. [ABSTRACT FROM AUTHOR]

We consider linear stability of travelling waves in a thin-film model for two-fluid Couette flow when a thin layer of the more viscous fluid resides next to the stationary wall. We prove that in a neighbourhood of a bifurcation point, characterized by a positive integer kb , the principal branch (kb=1) is spectrally stable while all other branches (kb>1) are spectrally unstable. For larger amplitude travelling waves, we establish a number of conditional theorems where the conditions were checked with help of computer assist for a set of parameter values. Using these theorems, we rigorously confirm earlier numerical evidence (D. Papageorgiou & S. Tanveer, Proc. R. Soc. A, (doi:10.1098/rspa.2019.0367)) on stability and instability of travelling waves over a range of parameters. [ABSTRACT FROM AUTHOR]

This paper is systematically concerned with the solitary waves on the constrained manifold preserved the L 2 -momentum conservation for the generalized singular perturbed KdV equation with L 2 -subcritical, critical and supercritical nonlinearities, which is a long-wave approximation to the capillary-gravity waves in an infinitely long channel with a flat bottom. First, using the profile decomposition in H 2 and the optimal Gagliardo–Nirenberg inequality, we prove the existence of subcritical ground state solitary waves and describe their asymptotic behavior. Second, we obtain some sufficient conditions for the existence and non-existence of critical ground states, and then prove the existence of critical and supercritical ground state solitary waves on the Derrick–Pohozaev manifold by utilizing the new minimax argument and the numerical simulation of the best Gagliardo–Nirenberg embedding constant. Meanwhile, we use the moving plane method to obtain the existence of positive and radially symmetric solutions. Furthermore, we study the concentration behavior of the critical ground state solutions. Finally, the spectral stability of the ground state solitary wave solutions is discussed by using the instability index theorem. [ABSTRACT FROM AUTHOR]

Eu2+-activated metal halides with narrow-band blue emission have attracted special attention in solid-state lighting and full-color display. However, the poor spectral stability and high sensitivity to oxygen and moisture of Eu2+-activated metal halides limit their further development. In this paper, CsBr nanocrystals with tunable size and different Eu2+ ion doping concentrations are precipitated in glass for the first time. Incorporation Eu2+ ions into CsBr nanocrystals enables a narrow-band blue PL at 447 nm with a full width at half-maximum of 24 nm and a high photoluminescence quantum yield of 55.8%. More importantly, these CsBr/Eu2+ nanocrystals in glass possess good spectral stability under different excitation energies and operating temperatures as well as operating currents. Employing CsBr/Eu2+ nanocrystal-doped glass as the blue-emitting convertor, a blue-light-emitting device with an external quantum efficiency of 11.2%, a luminous efficacy of 3.8 lm/W, and a high color purity of 96.6% is realized, and the potential of CsBr/Eu2+ nanocrystal-doped glass toward high-performance white-light-emitting devices is also demonstrated. These results provide an avenue for blue-emitting materials with narrow line width and good spectra stability. [ABSTRACT FROM AUTHOR]

In this manuscript, a general geometric singular perturbation framework to study pattern formations in nonlinear reaction-diffusion (R-D) systems with single or multiple strong localized impurities is developed. In the method, we divide the spatial domain into fast and slow regions respectively near and far away from the positions of impurities. In each region, the limiting fast or slow system is defined separately in terms of different scales. By so doing, the R-D system with strong localized impurities can be transformed into a singularly perturbed problem with suitable slow-fast structure. We then solve the limiting fast and slow flow explicitly and matching them approximately. Accordingly, the existence and stability criterion on the pinned 1-pulse and multiple-pulse solutions can be set up analytically. Numerical simulations are also performed to verify the theoretical predictions. [ABSTRACT FROM AUTHOR]

The existence of breather-type solutions, i.e., solutions that are periodic in time and exponentially localized in space, is a very unusual feature for continuum, nonlinear wave-type equations. Following an earlier work establishing a theorem for the existence of such structures, we bring to bear a combination of analysis-inspired numerical tools that permit the construction of such waveforms to a desired numerical accuracy. In addition, this enables us to explore their numerical stability. Our computations show that for the spatially heterogeneous form of the ϕ 4 model considered herein, the breather solutions are generically unstable. Their instability seems to generically favor the motion of the relevant structures. We expect that these results may inspire further studies towards the identification of stable continuous breathers in spatially heterogeneous, continuum nonlinear wave equation models. [ABSTRACT FROM AUTHOR]

In this work we explore some aspects of the spectral instability of back hole quasi-normal modes, using a specific model as an example. The model is that of a small bump perturbation to the effective potential of linear axial gravitational waves on a Schwarzschild background, and our focus is on three different aspects of the instability: identifying and distinguishing between the two different types of instabilities studied previously in the literature, quantifying the size of the perturbations applied to the system and testing the validity of the pseudospectral numerical method in providing a convergent result for this measure, and finally, relating the size and other features of the perturbation to the degree of destabilisation of the spectrum.

Reaction–diffusion equations (RDEs) model the spatiotemporal evolution of a density field u(x,t)$u({x},t)$ according to diffusion and net local changes. Usually, the diffusivity is positive for all values of u$u$, which causes the density to disperse. However, RDEs with partially negative diffusivity can model aggregation, which is the preferred behavior in some circumstances. In this paper, we consider a nonlinear RDE with quadratic diffusivity D(u)=(u−a)(u−b)$D(u) = (u - a)(u - b)$ that is negative for u∈(a,b)$u\in (a,b)$. We use a nonclassical symmetry to construct analytic receding time‐dependent, colliding wave, and receding traveling wave solutions. These solutions are multivalued, and we convert them to single‐valued solutions by inserting a shock. We examine properties of these analytic solutions including their Stefan‐like boundary condition, and perform a phase plane analysis. We also investigate the spectral stability of the u=0$u = 0$ and u=1$u = 1$ constant solutions, and prove for certain a$a$ and b$b$ that receding traveling waves are spectrally stable. In addition, we introduce a new shock condition where the diffusivity and flux are continuous across the shock. For diffusivity symmetric about the midpoint of its zeros, this condition recovers the well‐known equal‐area rule, but for nonsymmetric diffusivity it results in a different shock position. [ABSTRACT FROM AUTHOR]

With the advent of technology, it has become possible to perform direct numerical simulations and the demand for high accuracy computing is increasing. Numerical simulations play an important part in understanding physics of the flow and instability mechanism in flows. For high accuracy, numerical schemes must be chosen that satisfy the physical dispersion relation, should not amplify or attenuate the solution and resolve all possible length and time scales. In the present paper, spectral stability analysis of linear convection equation is performed using first order forward difference (FD1) method and fourth order Runge Kutta (RK4) method, consisting of four stages, for time discretization and a second order central difference (CD2) method for evaluating spatial derivative. The results show that the presence of numerical instability for FD1 method is independent of the CFL number, consistent with the stability analysis which showed FD1 method to be unconditionally unstable. However, for RK4 method, the solution is found to be neutrally stable only for a particular range of CFL number, even stable solution introduced error by attenuating the computed or analytical solution. [ABSTRACT FROM AUTHOR]

Abstract Low efficiency and spectral instability caused by the surface defects have been considerable issues for the mixed‐halogen blue emitting perovskite quantum dots light‐emitting diodes (PeQLEDs). Here, an in situ surface passivation to perovskite quantum dots (PeQDs) is realized by introducing the metal cations competitive lattice occupancy assisted with acid‐etching, in which the long‐chain, insulating and weakly bond surface ligands are removed by addition of octanoic acid (OTAC). Meanwhile, the dissolved A‐site cations (Na+) compete with the protonated oleyl amine and are subsequently anchored to the surface vacancies. The preadded lead bromide, acting as inorganic ligands, demonstrates strong bonding to the uncoordinated surface ions. The as‐synthesized PeQDs show the boosted photoluminescence quantum yield (PLQY) and superior stability with longer lifetime. As a result, the PeQLEDs (470 nm) based on the OTAC‐Na PeQDs exhibit an external quantum efficiency of 8.42% in the mixed halogen PeQDs (CsPb(BrxCl1−x)3). Moreover, the device exhibits superior spectra stability with negligible shift. Our competition mechanism in combination with in situ passivation strategy paves a new way for improving the performance of blue PeQLEDs.

The emission peak shift caused by ion motion, especially under high bias voltage, is an obstacle to the development of blue perovskite light‐emitting diodes (PeLEDs). In this work, 3‐Aminopiperidine dihydrochloride (3AP) to construct heterocyclic dication Dion‐Jacobson (DJ) PeLEDs is introduced, and found that 3AP incorporation can retard the halide segregation and chloride loss, leading to the improvement of the emission spectral stability. By increasing the amount of 3AP (DJ phase), emission centers can be tuned from green to blue but the excitonic peak abnormally disappears, indicative of exciton delocalization. Photoluminescence quantum yield (PLQY) and ultrafast spectroscopy indicated that the introduction of 3AP can passivate defects and control the exciton delocalization to facilitate interlayer charge transfer. The external quantum efficiencies (EQE) of the obtained green (513 nm), sky blue (488 nm), and blue (478 nm) PeLEDs reached 3.0%, 7.1%, and 4.8%, respectively, and the maximum luminance is 10956, 1093 and 782 cd m−2, respectively. Most importantly, under high operating voltages from 3 to 10 V, the PeLEDs delivered outstanding spectral stability free of peak shift. [ABSTRACT FROM AUTHOR]

The Novikov equation is a peakon equation with cubic nonlinearity, which, like the Camassa--Holm and the Degasperis--Procesi, is completely integrable. In this paper, we study the spectral and linear stability of peakon solutions of the Novikov equation. We prove spectral instability of the peakons in L²(ℝ). To do so, we start with a linearized operator defined on H²(ℝ) and extend it to a linearized operator defined on weaker functions in L²(ℝ). The spectrum of the linearized operator in L²(ℝ) is proven to cover a closed vertical strip of the complex plane. Furthermore, we prove that the peakons are spectrally unstable on W²,∞(ℝ) and linearly and spectrally stable on H²(ℝ). The result on W²,∞(ℝ) is in agreement with previous work about linear instability and our result on H²(ℝ) is in line with past work on orbital stability. [ABSTRACT FROM AUTHOR]

We consider planar traveling fronts between stable steady states in two-component singularly perturbed reaction-diffusion-advection equations, where a small quantity \delta 2 represents the ratio of diffusion coefficients. The fronts under consideration are large amplitude and contain a sharp interface, induced by traversing a fast heteroclinic orbit in a suitable slow-fast framework. We explore the effect of advection on the spectral stability of the fronts to long wavelength perturbations in two spatial dimensions. We find that for suitably large advection coefficient ν, the fronts are stable to such perturbations, while they can be unstable for smaller values of ν. In this case, a critical asymptotic scaling ν~δ-4/3 is obtained at which the onset of instability occurs. The results are applied to a family of traveling fronts in a dryland ecosystem model. [ABSTRACT FROM AUTHOR]

For a coupled slow-fast FitzHugh-Nagumo (FHN) equation derived from a reaction-diffusion-mechanics (RDM) model, Holzer et al. (2013) studied the existence and stability of the travelling pulse, which consists of two fast orbit arcs and two slow ones, where one fast segment passes the unique fold point with algebraic decreasing and two slow ones follow normally hyperbolic critical curve segments. Shen and Zhang (2021) obtained the existence of the travelling pulse, whose two fast orbit arcs both exponentially decrease, and one of the slow orbit arcs could be normally hyperbolic or not at the origin. Here, we characterize both nonlinear and spectral stability of this travelling pulse. [ABSTRACT FROM AUTHOR]

Tailoring bandgap by mixed‐halide strategy in perovskites has attracted extraordinary attention due to the flexibility of halide ion combinations and has emerged as the most direct and effective approach to precisely tune the emission wavelength throughout the entire visible light spectrum. Mixed‐halide perovskites, yet, still suffered from several problems, particularly phase segregation under external stimuli because of ions migration. Understanding the essential cause and finding sound strategies, thus, remains a challenge for stable and efficient mixed‐halide perovskite light‐emitting diodes (PeLEDs). The review herein presents an overview of the diverse application scenarios and the profound significance associated with mixed‐halide perovskites. We then summarize the challenges and potential research directions toward developing high stable and efficient mixed‐halide PeLEDs. The review thus provides a systematic and timely summary for the community to deepen the understanding of mixed‐halide perovskite materials and resulting PeLEDs. [ABSTRACT FROM AUTHOR]

The effective degree SIR model is a precise model for the SIR disease dynamics on a network. The original ODE model is only applicable for a network with finite degree distributions. The new generating function approach rewrites with model as a PDE and allows infinite degree distributions. In this paper, we first prove the existence of a global solution. Then we analyze the linear and nonlinear stability of the disease-free steady state of the PDE effective degree model, and show that the basic reproduction number still determines both the linear and the nonlinear stability. Our method also provides a new tool to study the effective degree SIS model, whose basic reproduction number has been elusive so far. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability of the ring solution of the N -body problem in the entire sphere $\mathbb {S}^2$ by using the logarithmic potential proposed in Boatto et al. (2016, Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 472, 20160020) and Dritschel (2019, Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 377, 20180349), derived through a definition of central force and Hodge decomposition theorem for 1-forms in manifolds. First, we characterize the ring solution and study its spectral stability, obtaining regions (spherical caps) where the ring solution is spectrally stable for $2\leq N\leq 6$ , while, for $N\geq 7$ , the ring is spectrally unstable. The nonlinear stability is studied by reducing the system to the homographic regular polygonal solutions, obtaining a 2-d.o.f. Hamiltonian system, and therefore some classic results on stability for 2-d.o.f. Hamiltonian systems are applied to prove that the ring solution is unstable at any parallel where it is placed. Additionally, this system can be reduced to 1-d.o.f. by using the angular momentum integral, which enables us to describe the phase portraits and use them to find periodic ring solutions to the full system. Some of those solutions are numerically approximated. [ABSTRACT FROM AUTHOR]

Black solitons are identical in the nonlinear Schrôdinger (NLS) equation with intensity-dependent dispersion and the cubic defocusing NLS equation. We prove that the intensitydependent dispersion introduces new properties in the stability analysis of the black soliton. First, the spectral stability problem possesses only isolated eigenvalues on the imaginary axis. Second, the energetic stability argument holds in Sobolev spaces with exponential weights. Third, the black soliton persists with respect to the addition of a small decaying potential and remains spectrally stable when it is pinned to the minimum points of the effective potential. The same model exhibits a family of traveling dark solitons for every wave speed and we incorporate properties of these dark solitons for small wave speeds in the analysis of orbital stability of the black soliton. [ABSTRACT FROM AUTHOR]

We consider the NLS system of the third-harmonic generation, which was introduced in Sammut et al. (J Opt Soc Am B 15:1488–1496, 1998.). Our interest is in solitary wave solutions and their stability properties. The recent work of Oliveira and Pastor (Anal Math Phys 11, 2021), discussed global well-posedness vs. finite time blow up, as well as other aspects of the dynamics. These authors have also constructed solitary wave solutions, via the method of mountain pass/Nehari manifold, in an appropriate range of parameters. Specifically, the waves exist only in spatial dimensions n = 1 , 2 , 3 . They have also establish some stability/instability results for these waves. In this work, we systematically build and study solitary waves for this important model. We construct the waves in the largest possible parameter space, and we provide a complete classification of their stability. In dimension one, we show stability, whereas in n = 2 , 3 , they are generally spectrally unstable, except for a small region, where they do enjoy an extra pseudo-conformal symmetry. Finally, we discuss instability by blow-up. In the case n = 3 , and for more restrictive set of parameters, we use virial identities methods to derive the strong instability, in the spirit of Ohta’s approach, Ohta (Funkc Ekvacioj 61(1):135–143, 2018). In n = 2 , the virial identities reduce matters, via conservation of mass and energy, to the initial data. Our conclusions mirror closely the well-known results for the scalar cubic focussing NLS, while the proofs are much more involved. [ABSTRACT FROM AUTHOR]

We construct far-from-onset radially symmetric spot and gap solutions in a two-component dryland ecosystem model of vegetation pattern formation on flat terrain, using spatial dynamics and geometric singular perturbation theory. We draw connections between the geometry of the spot and gap solutions with that of traveling and stationary front solutions in the same model. In particular, we demonstrate the instability of spots of large radius by deriving an asymptotic relationship between a critical eigenvalue associated with the spot and a coefficient which encodes the sideband instability of a nearby stationary front. Furthermore, we demonstrate that spots are unstable to a range of perturbations of intermediate wavelength in the angular direction, provided the spot radius is not too small. Our results are accompanied by numerical simulations and spectral computations. [ABSTRACT FROM AUTHOR]

We study bifurcations and spectral stability of solitary waves in coupled nonlinear Schrödinger (CNLS) equations on the line. We assume that the coupled equations possess a solution of which one component is identically zero, and call it a fundamental solitary wave. We establish criteria under which the fundamental solitary wave undergoes a pitchfork bifurcation, and utilize the Hamiltonian-Krein index theory and Evans function technique to determine the spectral and/or orbital stability of the bifurcated solitary waves as well as that of the fundamental one under some nondegenerate conditions which are easy to verify, compared with those of the previous results. We apply our theory to a cubic nonlinearity case and give numerical evidences for the theoretical results. [ABSTRACT FROM AUTHOR]

We study the spectral instability of supersonic solitary waves taking place in a nonlinear model of an elastic electrically conductive micropolar medium. As a result of linearization about the soliton solution, an inhomogeneous scalar equation is obtained. This equation leads to a generalized spectral problem. To establish instability, it is necessary to make sure of the existence of an unstable eigenvalue (an eigenvalue with a positive real part). The corresponding proof of instability is carried out using the local construction at the origin and the asymptotics at infinity of the Evans function, which depends only on the spectral parameter. This function is analytic in the right complex half-plane and has at least one zero on the positive real half-axis for a certain range of physical parameters of the problem in question. This zero coincides with the unstable eigenvalue of the generalized spectral problem. [ABSTRACT FROM AUTHOR]

Metal halide perovskite light‐emitting diodes (PeLEDs) are promising high‐definition display candidates due to their narrow emission bandwidth and wide color gamut. However, efficient and stable pure‐red PeLEDs have rarely been achieved. Herein, a robust and strongly‐coordinated sulfate anion passivation strategy is reported to achieve a spectrally stable and efficient pure‐red PeLED with an electroluminescent peak at 630 nm and full width at half maximum of 27 nm. Octylammonium sulfate is employed to construct a PbSO4 layer on the surface of CsPbI3−xBrx nanocrystals, which can effectively inhibit phase separation under UV light, humidity, or heat treatment. Using sulfate passivated CsPbI3−xBrx NC film, pure red PeLEDs with high external quantum efficiency of 12.6%, excellent spectral stability, and an operational half‐life time of over 300 min (T50@100 cd cm−2) are fabricated. This work provides a new avenue to improve performance of pure red PeLEDs via strong‐coordinated sulfate passivation. [ABSTRACT FROM AUTHOR]

We present a spacetime DG method for 1D spatial domains and three linear hyperbolic, damped hyperbolic, and parabolic PDEs. The latter two correspond to Maxwell-Cattaneo-Vernotte (MCV) and Fourier heat conduction problems. The method is called the tent-pitcher spacetime DG method (tpSDG) due to its resemblance to the causal spacetime DG method (cSDG) wherein the solution advances in time by pitching spacetime patches. The tpSDG method extends the applicability of such methods from hyperbolic to parabolic and hyperbolic PDEs. For problems with a spatially uniform mesh, a transfer matrix approach is derived wherein the inflow, boundary, and source term values are mapped to the solution coefficient and output values. This resembles a finite difference scheme, but with grid points at the Gauss points of the spatial elements and arbitrarily tunable order of accuracy in spacetime. The spectral stability analysis of the method provides stability correction factors for the parabolic case. Numerical examples demonstrate the applicability of the method to problems with heterogeneous material properties. • Extended spacetime tent-pitcher methods from hyperbolic to hyperbolic-parabolic PDEs. • Transfer matrices relate inflow and outflow solutions of a patch at the Gauss points. • Polynomial order-independent stability limit of tent-pitcher method is shown for wave equation. • The stability limit for parabolic heat conduction is obtained using the transfer matrices. • The transfer matrix method advances the solution of 1D uniform grids with tunable order. [ABSTRACT FROM AUTHOR]

Producing efficient blue and deep blue perovskite LEDs (PeLEDs) still represents a significant challenge in optoelectronics. Blue PeLEDs still have problems relating to color, luminance, and structural and electrical stability so new materials are needed to achieve better performance. Recent reports suggest using low n states (n = 1, 2, 3) to achieve blue electroluminescence in Ruddlesden–Popper (RP) perovskite films. However, there are fewer reports on the other quasi‐2D structure, Dion–Jacobson (DJ) perovksites, despite their highly desirable optical properties, due to the difficulty in achieving charge injection. To resolve this issue, herein, w e have mixed DJ phase precursors, propane‐1,3‐diammonium (PDA) bromide into RP phase perovskites and fabricated low‐dimensional PeLEDs. It is found that these specific precursors aid in suppressing both the low n (n = 1) and high n (n ≥ 4) quasi‐2D RP phases and is an effective strategy in blue‐shifting sky‐blue RP perovskites into the sub‐470 nm region. With optimization of the PDA concentration and device layers, it is achieved an external quantum efficiency of 1.5% at 469 nm and stable electroluminescence for the first deep blue PeLED to be reported using DJ perovskites. [ABSTRACT FROM AUTHOR]

We study the transverse spectral stability of the one‐dimensional small‐amplitude periodic traveling wave solutions of the (2+1)‐dimensional Konopelchenko–Dubrovsky (KD) equation. We show that these waves are transversely unstable with respect to two‐dimensional perturbations that are periodic in both directions with long wavelength in the transverse direction. We also show that these waves are transversely stable with respect to perturbations which are either mean‐zero periodic or square‐integrable in the direction of the propagation of the wave and periodic in the transverse direction with finite or short wavelength. We discuss the implications of these results for special cases of the KD equation—namely, KP‐II and mKP‐II equations. [ABSTRACT FROM AUTHOR]

Reaction-nonlinear diffusion partial differential equations can exhibit shock-fronted travelling wave solutions. Prior work by Li et al. (Physica D 423:132916, 2021) has demonstrated the existence of such waves for two classes of regularizations, including viscous relaxation (see Li et al. in Physica D 423:132916, 2021). Their analysis uses geometric singular perturbation theory: for sufficiently small values of a parameter ε > 0 characterizing the ‘strength’ of the regularization, the waves are constructed as perturbations of a singular heteroclinic orbit. Here we show rigorously that these waves are spectrally stable for the case of viscous relaxation. Our approach is to show that for sufficiently small ε > 0 , the ‘full’ eigenvalue problem of the regularized system is controlled by a reduced slow eigenvalue problem defined for ε = 0 . In the course of our proof, we examine the ways in which this geometric construction complements and differs from constructions of other reduced eigenvalue problems that are known in the wave stability literature. [ABSTRACT FROM AUTHOR]

We consider the nonlinear Dirac equation with Soler-type nonlinearity concentrated at one point and present a detailed study of the spectrum of linearization at solitary waves. We then consider two different perturbations of the nonlinearity which break the $ \mathbf{SU}(1,1) $ symmetry: the first preserving and the second breaking the parity symmetry. We show that a particular perturbation which breaks the $ \mathbf{SU}(1,1) $ symmetry but not the parity symmetry also preserves the spectral stability of solitary waves. Then we consider a particular perturbation which breaks both the $ \mathbf{SU}(1,1) $ symmetry and the parity symmetry and show that this perturbation destroys the stability of weakly relativistic solitary waves. This instability is due to the bifurcations of positive-real-part eigenvalues from the embedded eigenvalues $ \pm 2\omega \mathrm{i} $. [ABSTRACT FROM AUTHOR]

We prove spectral stability results for the $ curl curl $ operator subject to electric boundary conditions on a cavity upon boundary perturbations. The cavities are assumed to be sufficiently smooth but we impose weak restrictions on the strength of the perturbations. The methods are of variational type and are based on two main ingredients: the construction of suitable Piola-type transformations between domains and the proof of uniform Gaffney inequalities obtained by means of uniform a priori $ H^2 $-estimates for the Poisson problem of the Dirichlet Laplacian. The uniform a priori estimates are proved by using the results of V. Maz'ya and T. Shaposhnikova based on Sobolev multipliers. Connections to boundary homogenization problems are also indicated.

This paper studies the stability of weak dispersive shock profiles for a quantum hydrodynamics system in one space dimension with nonlinear viscosity and dispersive (quantum) effects due to a Bohm potential. It is shown that, if the shock amplitude is sufficiently small, then the profiles are spectrally stable. This analytical result is consistent with numerical estimations of the location of the spectrum [43]. The proof is based on energy estimates at the spectral level, on the choice of an appropriate weighted energy function for the perturbations involving both the dispersive potential and the nonlinear viscosity, and on the montonicity of the dispersive profiles in the small-amplitude regime. [ABSTRACT FROM AUTHOR]

We revisit the existence and stability of the critical front in the extended Fisher-KPP equation, refining earlier results of Rottschäfer and Wayne (J Differ Equ 176(2):532–560, 2001) which establish stability of fronts without identifying a precise decay rate. Our main result states that the critical front is marginally spectrally stable, with essential spectrum touching the imaginary axis but with no unstable point spectrum. Together with the recent work of Avery and Scheel (SIAM J Math Anal 53(2):2206–2242, 2021; Commun Am Math Soc, 2:172–231, 2022), this establishes both sharp stability criteria for localized perturbations to the critical front, as well as propagation at the linear spreading speed from steep initial data, thereby extending front selection results beyond systems with a comparison principle. Our proofs are based on far-field/core decompositions which have broader use in establishing robustness properties and bifurcations of invasion fronts. [ABSTRACT FROM AUTHOR]

Reduced‐dimensional perovskite light‐emitting diodes (PeLEDs) have shown great potential in solution‐processed high‐definition displays. However, the inferior electroluminescent (EL) performance of blue PeLEDs has become a huge challenge for their commercialization. The inefficient domain control [number of PbX6− layers (n)] and deleterious phase segregation make the blue PeLEDs suffer from low EL efficiency and poor spectral stability. Here, a rational strategy for perovskite crystallization control by adjusting the precursor concentration is proposed for improving phase distribution and suppressing ion migration in reduced‐dimensional mixed‐halide blue perovskite films. Based on this method, efficient sky‐blue PeLEDs exhibit a maximum external quantum efficiency (EQE) of 8.5% with stable EL spectra at 482 nm. Additionally, spectrally stable pure‐blue PeLEDs at 474 and 468 nm are further obtained with maximum EQEs of 4.0% and 2.4%, respectively. These findings may provide an alternative scheme for manipulating perovskite crystallization dynamics toward efficient and stable PeLEDs. [ABSTRACT FROM AUTHOR]

We quantify the subcriticality of the bilaplacian in dimensions greater than four by providing explicit repulsivity/smallness conditions on complex additive perturbations under which the spectrum remains stable. Our assumptions cover critical Rellich-type potentials too. As a byproduct we obtain uniform resolvent estimates in weighted spaces. Some of the results are new also in the self-adjoint setting. [ABSTRACT FROM AUTHOR]

The electrolytic efficiency in magnesium (Mg) production by molten salt electrolysis is mainly affected by the chloride content, which is determined by the metal content in the cooled molten salt. Laser-induced breakdown spectroscopy (LIBS) is a potential element detection method in cooled molten salt element detection. However, the cooled molten chloride salt is easily deliquescent, which greatly affects the LIBS detection results. To solve the problem, a liquid-phase precipitation method based on the addition of a dispersant named as controlled uniform precipitation (CUP) method was proposed to pretreat the samples. Compared with the conventional powder compacting method and precipitation method, the CUP obtained the highest spectral stability and detection accuracy. The average relative standard deviation (ARSD) of Mg, Ca, and Na decreased from the 51.80%, 77.04%, and 44.01% to 6.77%, 6.27%, and 29.97%, the determination coefficient of the calibration curve (R2) increased from 0.044, 0.084, and -0.109 to 0.974, 0.954, and 0.802, and the average relative error (ARE) decreased from 58.49%, 52.46%, and 99.78% to 8.58%, 11.28%, and 29.38%, respectively, compared with the powder compacting method. Further investigation showed that the CUP method suppressed the sample deliquescence and the coffee ring effect, leading to the performance improvement of LIBS quantitative detection. The CUP provided an effective method of detecting metal elements for deliquescent samples and showed applied potential for other precipitable elements detection. [Display omitted] • A new sample pretreatment method named controlled uniform precipitation (CUP) is first proposed in LIBS. • A comprehensive sample analysis combining SEM images and LIBS mapping. • Outstanding quantitative detection thanks to the addition of dispersant in CUP method. • The CUP method significantly suppressed the coffee ring effect. [ABSTRACT FROM AUTHOR]

Keller–Segel system models prototype of the population-based chemotaxis, which describes the oriented or partially oriented movement of cells in response to a chemical signal produced by the cells themselves. This paper focuses on dynamics of a class of Keller–Segel systems with a large diffusion. We obtain several different kinds of traveling waves and characterize their spectral stability. The main tools are geometric singular perturbation theory, qualitative theory and spectral analysis via the method of nonlocal eigenvalue problem. [ABSTRACT FROM AUTHOR]

We prove spectral stability results for the curlcurl operator subject to electric boundary conditions on a cavity upon boundary perturbations. The cavities are assumed to be sufficiently smooth but we impose weak restrictions on the strength of the perturbations. The methods are of variational type and are based on two main ingredients: the construction of suitable Piola-type transformations between domains and the proof of uniform Gaffney inequalities obtained by means of uniform a priori H²-estimates for the Poisson problem of the Dirichlet Laplacian. The uniform a priori estimates are proved by using the results of V. Maz'ya and T. Shaposhnikova based on Sobolev multipliers. Connections to boundary homogenization problems are also indicated. [ABSTRACT FROM AUTHOR]

A compressible viscous-dispersive Euler system in one space dimension in the context of quantum hydrodynamics is considered. The dispersive term is due to quantum effects described through the Bohm potential and the viscosity term is of linear type. It is shown that small-amplitude viscousdispersive shock profiles for the system under consideration are spectrally stable, proving in this fashion a previous numerical observation by Lattanzio et al. [28, 29]. The proof is based on spectral energy estimates which profit from the monotonicty of the profiles in the small-amplitude regime. [ABSTRACT FROM AUTHOR]

The Blue electroluminescence (EL) with high brightness and spectral stability is imperative for full-color perovskite display technologies meeting the Rec. 2020 standard. However, deep-blue perovskite light-emitting diodes (PeLEDs) lag behind their green- or red-emitting counterparts in brightness, quantum efficiency, and operational stability. Additionally, the Cl - /Br - mixed-halide perovskites with wide bandgap typically designed for deep-blue emitters are prone to degradation quickly under high operating bias due to low energy for halide migrations and vacancies formation, posing a significant challenge to spectral/operative stabilities. To address these issues, high-performance deep-blue PeLEDs are demonstrated by tuning the interface properties with Br-2ETP, a self-assembled monolayer (SAM) molecule engineered for a high dipole moment. The Br-2EPT-based hole-injecting interface facilitates favorable energy level alignment between indium tin oxide and the deep-lying valence band of the perovskite layer, suppressing the hole-injecting barrier and non-radiative charge recombination. Excellent perovskite film morphologies are observed at the top and buried surfaces by Br-2EPT, improving the balance of carrier injection for light emission efficiency. Consequently, the devices exhibit deep-blue electroluminescence at 457 nm, with an external quantum efficiency of 6.56% and spectral/operative stabilities., (© 2024 Wiley‐VCH GmbH.)

We analyze the Benney model for interaction of short and long waves in resonant water wave interactions. Our particular interest is in the periodic traveling waves, which we construct and study in detail. The main results are that, for all natural values of the parameters, the periodic dnoidal waves are spectrally stable with respect to perturbations of the same period. For another natural set of parameters, we construct the snoidal waves, which exhibit instabilities, in the same setup. Our results are the first instability results in this context. On the other hand, the spectral stability established herein improves significantly on the work of Angulo, Corcho, and Hakkaev [Adv. Difference Equ., 16 (2011), pp. 523--550], which established stability of the dnoidal waves, on a subset of parameter space, by relying on the Grillakis--Shatah theory. Our approach, which turns out to give definite answer for the entire domain of parameters, relies on the instability index theory, as developed by Kapitula, Kevrekidis, and Sandstede [Phys. D, 3--4 (2004), pp. 263--282]; Kapitula, Kevrekidis, and Sandstede [Phys. D, 195 (2004), no. 3--4, 263--282], Phys. D, 201 (2005), pp. 199--201]; Lin and Zeng [Instability, Index Theorem, and Exponential Trichotomy for Linear Hamiltonian PDEs, 2021]; and Pelinovsky [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 461 (2005), pp. 783--812]. Interestingly, end even though the linearized operators are explicit, our spectral analysis requires subtle and detailed analysis of matrix Schr\"odinger operators in the periodic context, which support some interesting features. [ABSTRACT FROM AUTHOR]

We prove spectral instability of peakons in the b-family of Camassa-Holm equations that includes the integrable cases of b = 2 and b = 3. We start with a linearized operator defined on functions in H1(R) ∩W1,∞(R) and extend it to a linearized operator defined on weaker functions in L2(R). For b ̸= 5 2, the spectrum of the linearized operator in L2(R) is proved to cover a closed vertical strip of the complex plane. For b = 5 2, the strip shrinks to the imaginary axis, but an additional pair of real eigenvalues exists due to projections to the peakon and its spatial translation. The spectral instability results agree with the linear instability results in the case of the Camassa-Holm equation for b = 2. [ABSTRACT FROM AUTHOR]

Localized patterns in singularly perturbed reactionâ€"diffusion equations typically consist of slow parts, in which the associated solution follows an orbit on a slow manifold in a reduced spatial dynamical system, alternated by fast excursions, in which the solution jumps from one slow manifold to another, or back to the original slow manifold. In this paper we consider the existence and stability of stationary and travelling localized patterns that do not exhibit such jumps, i.e. that are completely embedded in a slow manifold of the singularly perturbed spatial dynamical system. These ‘slow patterns’ have rarely been considered in the literature, for two reasons: (i) in the classical Grayâ€"Scott/Giererâ€"Meinhardt type models that dominate the literature, the flow on the slow manifold is typically linear and thus cannot exhibit homoclinic pulse or heteroclinic front solutions; (ii) the slow manifolds occurring in the literature are typically ‘vertical’, i.e. given by u ≡ u 0, where u is the fast variable, so that the stability problem is determined by a simple (decoupled) scalar equation. The present research concerns a general system of singularly perturbed reactionâ€"diffusion equations and is motivated by several explicit ecosystem models that do give rise to non-vertical normally hyperbolic slow manifolds on which the flow may exhibit both homoclinic and heteroclinic orbits that correspond to either stationary or travelling localized slow patterns. The associated spectral stability problems are at leading order given by a nonlinear, but scalar, eigenvalue problem with Sturmâ€"Liouville characteristics and we establish that homoclinic pulse patterns are typically unstable, while heteroclinic fronts can either be stable or unstable. However, we also show that homoclinic pulse patterns that are asymptotically close to a heteroclinic cycle may be stable. This result is obtained by explicitly determining the leading order approximations of four critical asymptotically small eigenvalues. By this analysis, that involves several orders of magnitude in the small parameter, we also obtain full control over the nature of the bifurcationsâ€"saddle-node, Hopf, global, etcâ€"that determine the existence and stability of the (stationary and/or travelling) heteroclinic fronts and/or homoclinic pulses. Finally, we show that heteroclinic orbits may correspond to stable (slow) interfaces in two-dimensional space, while the homoclinic pulses must be unstable as localized stripes, even when they are stable in one space dimension. [ABSTRACT FROM AUTHOR]

Despite heavy research, the efficiencies of blue perovskite light-emitting diodes (LEDs) lag behind those of their green and red cousins. One of the most critical problems is the lack of technology to obtain both high blue emission and spectral stability of perovskite in thin films. Herein, we employ low-temperature synthesis of CsPbBr 3 nanoplates (NPLs) by anti-solvent assisted crystallization method using green ethylacetate anti-solvent, which show high absolute photoluminescence quantum yield (PLQY = 90.2%), blue emission at 464 nm with a narrow emission line width (15 nm), small Stokes shift (5 nm) and the average PL decay lifetime (6.91 ns). Significantly, there is no obvious QY loss at different storage conditions. Furthermore, the PL can be tuned from blue to green (457–513 nm) by controlling the amount of precursor injected into anti-solvent. For the first time, we utilize all-bromide-based inorganic perovskites to fabricate ultraviolet-pumped white LEDs (UV-WLEDs) and optimize the chromaticity coordinate of WLEDs, whose CIE color temperature (CCT) is 6083 K. Finally, highly efficient blue LED device using CsPbBr 3 nanoplates (464 nm) with high external quantum efficiency (EQE) of 2.03% was fabricated and spectral stability of CsPbBr 3 nanoplates under constant current density was demonstrated. This work will be expected to facilitate the development of the blue light source for WLEDs and displays. [ABSTRACT FROM AUTHOR]

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.)