Nonlinear stability of periodic traveling wave solutions of systems of viscous conservation laws in the generic case

Extending previous results of Oh-Zumbrun and Johnson-Zumbrun, we show that spectral stability implies linearized and nonlinear stability of spatially periodic traveling wave solutions of viscous systems of conservation laws for systems of generic type, removing a restrictive assumption that wave speed be constant to first order along the manifold of nearby periodic solutions. Key to our analysis is a nonlinear cancellation estimate observed by Johnson and Zumbrun, along with a detailed understanding of the Whitham averaged system. The latter motivates a careful analysis of the Bloch perturbation expansion near zero frequency and suggests factoring out an appropriate translational modulation of the underlying wave, allowing us to derive the sharpened low-frequency estimates needed to close the nonlinear iteration arguments.     

The Transverse Instability of Periodic Waves in Zakharov–Kuznetsov Type Equations

In this paper, we investigate the instability of one‐dimensionally stable periodic traveling wave solutions of the generalized Korteweg‐de Vries equation to long wavelength transverse perturbations in the generalized Zakharov–Kuznetsov equation in two space dimensions. By deriving appropriate asymptotic expansions of the periodic Evans function, we derive an index which yields sufficient conditions for transverse instabilities to occur. This index is geometric in nature, and applies to any periodic traveling wave profile under some minor smoothness assumptions on the nonlinearity. We also describe the analogous theory for periodic traveling waves of the generalized Benjamin–Bona–Mahony equation to long wavelength transverse perturbations in the gBBM–Zakharov–Kuznetsov equation.     

Successive chemical solution deposition of ZnO films on flexible steel substrate: structure, photoluminescence and optical transitions

Zinc oxide is an attractive optoelectronic material with wide applications. Thin ZnO films were prepared on steel foil by successive chemical solution deposition (SCSD). The film structure, room-temperature photoluminescence (PL) and optical absorption characteristics were investigated. This study revealed that films of high structural and optical quality can be prepared by the SCSD method. PL of as-grown films shows a weak green peak at 560 nm and a strong UV peak at 380 nm. Annealing in either air or argon suppresses the green peak and red shifts the UV emission towards 390 nm. The presence of chlorine in the deposition solution destroys the PL of as-grown films. A strong UV emission, however, develops after annealing the films in air. Several optical transitions measured from the film PL and optical absorption coefficients are shown to be related to transitions through the known defect levels in ZnO, such as E₁, L₁, E₃ and V_O ²⁺ levels. PACS 81.16.Be; 81.05.Dz; 78.55.Et; 78.66.Hf; 68.55.Jk     

On the chaotic character of the stochastic heat equation, II

Consider the stochastic heat equation ${\partial_t u = (\varkappa/2)\Delta u+\sigma(u)\dot{F}}$ , where the solution u := u _t (x) is indexed by ${(t, x) \in (0, \infty) \times {\bf R}^d}$ , and ${\dot{F}}$ is a centered Gaussian noise that is white in time and has spatially-correlated coordinates. We analyze the large- ${\|x\|}$ fixed-t behavior of the solution u in different regimes, thereby study the effect of noise on the solution in various cases. Among other things, we show that if the spatial correlation function f of the noise is of Riesz type, that is ${f(x)\propto \|x\|^{-\alpha}}$ , then the “fluctuation exponents” of the solution are ${\psi}$ for the spatial variable and ${2\psi-1}$ for the time variable, where ${\psi:=2/(4-\alpha)}$ . Moreover, these exponent relations hold as long as ${\alpha \in (0, d \wedge 2)}$ ; that is precisely when Dalang’s theory [Dalang, Electron J Probab 4:(Paper no. 6):29, 1999] implies the existence of a solution to our stochastic PDE. These findings bolster earlier physical predictions [Kardar et al., Phys Rev Lett 58(20):889–892, 1985; Kardar and Zhang, Phys Rev Lett 58(20):2087–2090, 1987].     

A Highly Fluorescent Pyrene-Based Sensor for Selective Detection Of Fe3+ Ion in Aqueous Medium: Computational Investigations

In this work, we introduce a highly selective and sensitive fluorescent sensor based on pyrene derivative for Fe(III) ion sensing in DMSO/water media. 2-(pyrene-2-yl)-1-(pyrene-2-ylmethyl)-1H-benzo[d]imidazole (PEBD) receptor was synthesized via simple condensation reaction and confirmed by spectroscopic techniques. The receptor exhibits fluorescence quenching in the presence of Fe(III) ions at 440 nm. ESI–MS and Job’s method were used to confirm the 1:1 molar binding ratio of the receptor PEBD to Fe(III) ions. Using the Benesi-Hildebrand equation the binding constant value was determined as 8.485?×?10³ M^?1. Furthermore, the limit of detection (LOD, 3σ/K) value was found to be 1.81 µM in DMSO/water (95/5, v/v) media. According to the Environmental Protection Agency (EPA) of the United States, it is lower than the acceptable value of Fe³⁺ in drinking water (0.3 mg/L). The presence of 14 other metal ions such Co²⁺, Cr³⁺, Cu²⁺, Fe²⁺, Hg²⁺, Pb²⁺, K⁺, Ni²⁺, Mg²⁺, Cd²⁺, Ca²⁺, Mn²⁺, Al³⁺, and Zn²⁺ did not interfere with the detection of Fe(III) ions. The fluorescence life-time of the receptor PEBD with and without Fe³⁺ ion was found to be 1.097?×?10^?9 s and 0.9202?×?10^?9 s respectively. Similarly, the quantum yield of the receptor PEBD with Fe³⁺ and without Fe³⁺ ion was calculated, and found as 0.05 and 0.25 respectively. Computational studies of the receptor PEBD were carried out with density functional theory (DFT) using B3LYP/ 6-311G (d, p), LANL2DZ level of theory.

Graphical Abstract

     

Size-dependent electronic and optical properties of an exciton in CdSe/CdS/CdSe/CdS multilayer spherical quantum dot

The electronic and optical properties of a single exciton in a CdSe/CdS/CdSe/CdS quantum dot is studied by using effective mass approximation with parabolic confinement. The Coloumbic interaction between electron and hole is included by Hartree potential. A self-consistent technique is used to calculate the energy eigenvalue and wavefunction of exciton. Based on this approximation we investigate the effect of core size, shell thickness, well width on exciton binding energy, absorption spectra, and oscillator strength. The results provide the tuning possibility of electronic and optical properties of multilayer quantum dot with layer thickness.