A critical survey of approximate scattering wave theories from random rough surfaces

This review is intended to provide a critical and up-to-date survey of the analytical approximate methods that are encountered in scattering from random rough surfaces. The underlying principles of the different methods are evidenced and the functional form of the corresponding scattering amplitude or cross-section is given. The reader is referred to the original papers in order to obtain the explicit expressions of the coefficients and kernels. We have tried to identify the main strengths and weaknesses of the various theories. We provide synthetic tables of their respective performances, according to a dozen important requirements a valuable method should meet. Both scalar acoustic and vector electromagnetic theories are equally addressed.     

Analytical comparison between the surface current integral equation and the second-order small-slope approximation

This paper is the third in a series discussing a new approximate bistatic model for electromagnetic scattering from perfectly conducting rough surfaces. Our previous approach supplemented the Kirchhoff model through the addition of new terms involving linear orders in slope and surface elevation differences that arise naturally from a second iteration of the surface current integral equation. This completion of the Kirchhoff was shown to provide the correct first-order small perturbation method (SPM-1) in the general bistatic context. The agreement with SPM-1 was achieved because differences of surface heights are no longer expanded in powers of surface slope. While consistent with SPM, our previous formulation fails to reconverge toward the Kirchhoff model, at some incidence and scattered angles, when the illuminated surface satisfies the high frequency roughness condition. This weakness is also shared with the first-order small slope approximation (SSA-1) which is structurally equivalent to our previous formulation where the polarization is independent of surface roughness. The second-order small slope approximation (SSA-2), which satisfies the SPM-1 and second-order small perturbation method (SPM-2) limits by construction, was shown by Voronovich to converge toward the tangent plane approximation of the Kirchhoff model under high frequency conditions. In the present paper, we show that, in addition to the linear orders in our previous model, one must now include cross-terms between slope and surface elevation to ensure convergence toward both high frequency and small perturbation limits. With the inclusion of these terms, our new formulation becomes comparable to the SSA-2 (second-order kernel) without the need to evaluate all the quadratic order slope and elevations terms. SSA-2 is more complete, however, in the sense that it guarantees convergence toward the second-order Bragg limit (SPM-2) in the fully dielectric case in addition to both SPM-1 and Kirchhoff. Our new generalization is shown to explain correctly extra depolarization in specular conditions to be caused by surface curvature and surface autocorrelation for incoherent and coherent scattering, respectively. This result will have large repercussions on the interpretation of bistatically reflected signals such as those from GPS.     

Existence of standing waves for dirac fields with singular nonlinearities

We prove the existence of stationary states for nonlinear Dirac equations of the form (E) $$i\sum\limits_{\mu = 0}^3 {\gamma ^\mu \partial _\mu \psi - M\psi + F\left( {\bar \psi \psi } \right)\psi = 0,} $$ whereM>0 andF is a singular self-interaction. In particular, in the model case whereF(s)=?s ^?α, for some 0<α<1, and for every ω>M, there exists a solution of (E) of the form ψ(t, x)=e ^iωt?(x), wherex ₀=t andx=(x ₁,x ₂,x ₃), such that ? has compact support. IF 0<α<1/3, then ? is of classC ¹. If 1/3<α<1, then ? is continuously differentiable, except on some sphere {|x|=R}, where |??| is infinite.     

Carbon‐based Nanosensors for Salicylate Determination in Pharmaceutical Preparations

Thiourea derivative‐based carbon paste electrode (TUD1‐CPE) was constructed as a potentiometric sensor for the determination of salicylate anion in pharmaceutical formulations, Aspocid® and Aspirin®. The optimized CPE contained 45.5 % graphite, 0.5 % reduced graphene oxide (rGO), 46.0 % nitrophenyl octyl ether (NPOE) plasticizer, 5.0 % TUD1 ionophore, and 3.0 % tridodecylmethyl ammonium chloride as additive. The incorporation of NPOE of high dielectric constant, and rGO in electrode caused better performance of the sensor; Nernstian response of 59.0 mV decade^?1 in the concentration range of 10^?1–10^?5 mole L^?1, a detection limit of 1×10^?5 mole L^?1 in a very short response time of 6 seconds. The prepared sensor showed high selectivity against similar anions (i. e. , benzoate, I^?, SCN^?). Selectivity was confirmed by calculating the formation constant (K_β) using sandwich membrane method, where K_β for TUD1‐salicylate is 10^0.43. Theoretical calculations at DFT‐B3LY/6‐31G** level of theory were performed to find interaction mechanism, Energies of HOMO and LUMO orbitals, non‐linear optical (NLO) properties (the electronic dipole moment (μ), first‐order hyperpolarizability (β), the hyper‐Rayleigh scattering (β_HRS) and the depolarization ratio (DR)), and other global properties; these calculations showed lower values of β and DR, higher value of β_HRS, and the shortest lengths of the four N?H bonds between TUD1 and salicylate which confirm their strong complexation and salicylate‐selectivity. Also, all the studied anion‐TUD1 exhibited relatively high NLO properties, and these results were considered as a preliminary study for investigating new types of NLO bearing materials. The sensors were applied successfully for the determination of salicylate anion in Aspocid® and Aspirin®.     

Reactions of P(III)-Halides with Calix[4]Resorcinarenes

Abstract

Reactions of calix[4]resorcinarenes, bearing aliphatic radicals of different length, with P(III)-halides results in the formation of cyclic chlorophosphites and chlorophosphates.     

Semi-wet growth and characterization of multi-functional nano-engineered mixed metal oxides for industrial application

This review paper covers the low temperature wet growth of nano-engineered particles of ZnO-based mixed metal oxides, their growth mechanism, and characterization using X-ray diffraction, SEM, TEM and IR, UV–visible, and XPS spectral techniques. Main focus of this article is centered on low temperature semi-wet methods of synthesis that are suitable for large scale production of zinc oxide-based systems mixed with iron oxide, copper oxide, nickel oxide and cobalt oxide. These mixed metal oxides have broad industrial applications as catalyst, semiconductors, adsorbents, superconductors, electro-ceramics, and antifungal agents in addition to extensive applications in medicines. This paper discusses the low-cost and environment friendly synthesis of these mixed metal oxides, measurement of properties and applicability of these materials systems.     

Dioxygen Binding in the Active Site of Histone Demethylase JMJD2A and the Role of the Protein Environment

JMJD2A catalyses the demethylation of di‐ and trimethylated lysine residues in histone tails and is a target for the development of new anticancer medicines. Mechanistic details of demethylation are yet to be elucidated and are important for the understanding of epigenetic processes. We have evaluated the initial step of histone demethylation by JMJD2A and demonstrate the dramatic effect of the protein environment upon oxygen binding using quantum mechanics/molecular mechanics (QM/MM) calculations. The changes in electronic structure have been studied for possible spin states and different conformations of O₂, using a combination of quantum and classical simulations. O₂ binding to this histone demethylase is computed to occur preferentially as an end‐on superoxo radical bound to a high‐spin ferric centre, yielding an overall quintet ground state. The favourability of binding is strongly influenced by the surrounding protein: we have quantified this effect using an energy decomposition scheme into electrostatic and dispersion contributions. His182 and the methylated lysine assist while Glu184 and the oxoglutarate cofactor are deleterious for O₂ binding. Charge separation in the superoxo‐intermediate benefits from the electrostatic stabilization provided by the surrounding residues, stabilizing the binding process significantly. This work demonstrates the importance of the extended protein environment in oxygen binding, and the role of energy decomposition in understanding the physical origin of binding/recognition.