Continuous Frechet differentiability with respect to a Lipschitz domain and a stability estimate for direct acoustic scattering problems

We consider direct acoustic scattering problems with eithera sound-soft or sound-hard obstacle, or lossy boundary conditions,and establish continuous Fréchet differentiability withrespect to the shape of the scatterer of the scattered fieldand its corresponding far-field pattern. Our proof is basedon the implicit function theorem, and assumes that the boundaryof the scatterer as well as the deformation are only Lipschitzcontinuous. From continuous Fréchet differentiability,we deduce a stability estimate governing the variation of thefar-field pattern with respect to the shape of the scatterer.We illustrate this estimate with numerical results obtainedfor a two-dimensional high-frequency acoustic scattering problem.     

Abridged Continuous Data Assimilation for the 2D Navier–Stokes Equations Utilizing Measurements of Only One Component of the Velocity Field

We introduce a continuous data assimilation (downscaling) algorithm for the two-dimensional Navier–Stokes equations employing coarse mesh measurements of only one component of the velocity field. This algorithm can be implemented with a variety of finitely many observables: low Fourier modes, nodal values, finite volume averages, or finite elements. We provide conditions on the spatial resolution of the observed data, under the assumption that the observed data is free of noise, which are sufficient to show that the solution of the algorithm approaches, at an exponential rate asymptotically in time, to the unique exact unknown reference solution, of the 2D Navier–Stokes equations, associated with the observed (finite dimensional projection of) velocity.     

Spectrophotometric analysis of stability of gold nanoparticles during catalytic reduction of 4-nitrophenol

Spectrophotometric monitoring of 4-nitrophenol (4-NP) reduction by sodium borohydride (NaBH₄) using gold nanoparticles (GNPs) as a catalyst has been extensively studied, but the stability of GNPs in terms of change in the surface plasmon resonance (SPR) at different temperatures has not been explored. In the present investigation, our aim was to evaluate the SPR stability of GNPs as a catalyst during the reduction of 4-NP at different elevated temperatures (i.e. 30–60 °C) and sodium borohydride concentrations. Sensitivity of this degradation process toward concentration of GNPs at a range of temperatures is also evaluated. The spectrophotometric results reveal that up to 45 °C, 12 ± 1.5 nm catalyst has a consistent optical density (OD) during the entire 4-NP reduction process, which is related to the surface integrity of catalyst atoms. As the temperature approached 50 °C, the OD gradually decreased and showed a blue shift as the reaction proceeded, which could be related to a decrease in particle size or surface dissolution of gold atoms. The present study may find application in the design of catalysts for the reduction of organic pollutants in industrial wastewater at a range of temperatures.     

Entropy production minimization and non-Darcy resistance within wavy motion of Sutterby liquid subject to variable physical characteristics

Journal of Thermal Analysis and Calorimetry - Non-Darcy resistance in peristaltic transport of Sutterby liquid in curved configuration is modeled. Variable characteristics of material (i.e.,...     

Global asymptotic stability of the higher order equation $$x_{n+1} = \frac{ ax_{n}+bx_{n-k}}{A+Bx_{n-k}}$$

In this paper, we investigate the local and global stability and the period two solutions of all nonnegative solutions of the difference equation,

$$\begin{aligned} x_{n+1} = \frac{ ax_{n}+bx_{n-k}}{A+Bx_{n-k}} \end{aligned}$$

where a, b, A, B are all positive real numbers, \(k \ge 1\) is a positive integer, and the initial conditions \(x_{-k},x_{-k+1},...,x_{0}\) are nonnegative real numbers. It is shown that the zero equilibrium point is globally asymptotically stable under the condition \(a+b \le A\), and the unique positive solution is also globally asymptotically stable under the condition \(a-b \le A \le a+b\). By the end, we study the global stability of such an equation through numerically solved examples.

     

Transition metal-free direct nucleophilic α-substitution of Morita–Baylis–Hillman alcohols with amines and thiols

An efficient transition metal-free allylic nucleophilic α-substitution of Morita–Baylis–Hillman alcohols with both aliphatic and aromatic amines in refluxing toluene, using activated molecular sieves as additives, is described herein. The reaction proceeded with exclusive α-regioselectivity in moderate to excellent yields with the formation of water as the sole by-product. Under the same conditions, upon treatment of some thiols with the title substrates, allylic sulfides were obtained in excellent yields and high regioselectivity.     

A Metal‐Free Synthesis of 2‐Alkyl(or Aryl) Thiomethyl‐2‐cyclohexenones from Cyclic Morita–Baylis–Hillman Bromides

Under mild conditions, an efficient and rapid S‐allylation of thiols with cyclic Morita–Baylis–Hillman (MBH) bromides without the need of a transition‐metal catalyst or an expensive additive is described herein. Treatment of the MBH bromides with various thiols or ethane‐1,2‐dithiol in the presence of Et₃N regioselectively affords the corresponding 2‐alkyl(or aryl) thiomethyl‐2‐cyclohexenones or the perhydro benzo[1,4]dithiepinone, respectively, in moderate to good yields (40 – 73%). The reaction is rapid and carried out in THF at room temperature.     

Charge transfer complexes of picolines with sigma- and pi-acceptors

In the present study CT complexes of 2-, 3- and 4-Picolines with (DDQ) 2, 3-dichloro-5, 6-dicyano parabenzoquinone (pi-acceptor) and (I(2)) Iodine (sigma-acceptor) have been investigated spectrophotometrically in three different solvents (CCl(4), CHCl(3) and CH(2)Cl(2)) at six different temperatures. The formation constants of the CT complexes were determined by the Benesi-Hildebrand equation. The thermodynamic parameters were calculated by Van(')t Hoff equation. The DeltaH degrees , DeltaG degrees and DeltaS degrees values are all negative implying that the formation of studied complexes is exothermic in nature.     

All-angle-negative-refraction and ultra-refraction for liquid surface waves in 2D phononic crystals

We analyse transport properties of linear liquid waves propagating within arrays of immersed rigid circular cylindrical obstacles fixed to a rough bottom. A comparison between Multipole and Finite Element methods is drawn in the case of Robin boundary conditions coupled with Floquet-Bloch boundary conditions. We find that the first band is concave yet nearly flat (associated waves of small negative group velocity) and it displays a cut-off (zero-frequency stop band associated with a singular perturbation). Thanks to this anomalous dispersion in such fluid filled structures, we achieve both ultra-refraction and negative refraction for waves propagating at their surface. Potential applications lie in a omnidirective ‘water antenna’ and a convergent flat ‘water lens’. The latter one is demonstrated experimentally.