Elliptic Reconstruction and a Posteriori Error Estimates for Fully Discrete Semilinear Parabolic Optimal Control Problems

This article studies a posteriori error analysis of fully discrete finite element approximations for semilinear parabolic optimal control problems. Based on elliptic reconstruction approach introduced earlier by Makridakis and Nochetto [25], a residual based a posteriori error estimators for the state, co-state and control variables are derived. The space discretization of the state and co-state variables is done by using the piecewise linear and continuous finite elements, whereas the piecewise constant functions are employed for the control variable. The temporal discretization is based on the backward Euler method. We derive a posteriori error estimates for the state, co-state and control variables in the $L^\infty(0,T;L^2(\Omega))$-norm. Finally, a numerical experiment is performed to illustrate the performance of the derived estimators.     

Ab initio excited-state dynamics of the photoactive yellow protein chromophore

The photoisomerization mechanism of the neutral form of the photoactive yellow protein (PYP) chromophore is investigated using ab initio quantum chemistry and first-principles nonadiabatic molecular dynamics (ab initio multiple spawning or AIMS). We identify the nature of the two lowest-lying excited states, characterize the short-time behavior of molecules excited directly to S2, and explain the origin of the experimentally observed wavelength-dependent photoisomerization quantum yield.     

Eroded myelin figures

Myelin figures with unusual surface morphology were observed on contacting Tween85 with water. Myelins, which are normally smooth rodlike forms in other surfactants, are in this system found to be with an irregular, rough surface with vesiclelike structures adhered to the myelin tubes. Besides these, smooth myelin figures were also observed. We term the myelin figures with a rough surface eroded myelin figures. The same myelin could show a coexistence of smooth and rough areas with a sharp boundary between the smooth surface at one end whereas the other end shows a rough texture. The transformation of smooth myelins into eroded forms were observed often whereas the reverse is quite rare. In the later stage, the tip of the eroded myelin figures transforms into tentacles and acts as a source for new myelins and the growth of vesiclelike structures which were expelled into the surrounding medium. The eroded myelin figures are stable for a longer period in comparison to simple, smooth rodlike forms. By studying the myelin growth at different temperatures, it was found that eroded myelin figures were stable in the temperature range of 22-42 degrees C and at > 42 degrees C only smooth myelin figures were observed.     

Positron annihilation studies of poly(N‐isopropyl acrylamide) gel in mixed solvents

Positron annihilation lifetime spectroscopy was used to characterize the reentrant volume‐phase‐transition behavior of poly(N‐isopropyl acrylamide) hydrogel in an ethanol/water mixed solvent. The polymer gel was synthesized with γ irradiation. The ortho‐positronium lifetime (τ₃) in the gel slowly increased with an increase in the ethanol content in the mixed solvent. τ₃ was not influenced by the volume phase transition. The ortho‐positronium intensity decreased with the collapse of the gel in an approximately 10% ethanol/water mixture. When swelled in pure ethanol, τ₃ initially increased with the solvent amount in the gel, showing the destruction of intramolecular hydrogen bonding and the relaxation of polymer chains. The lower critical solution temperature of the gel in the 10% ethanol/water mixture was lower than that in pure water, and τ₃ for various solvent contents showed behavior similar to that seen in pure solvent. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 1028–1036, 2002     

Effect of Artabotrys odoratissimus extract as an environmentally sustainable inhibitor for mild steel corrosion in 0.5 M H2SO4 media

Artabotrys odoratissimus inhibitory effect on mild steel (MS) corrosion in 0.5 M H₂SO₄ solution has been assessed utilizing mass loss, electrochemical potentiodynamic polarization, and impedance spectroscopy techniques. The Artabotrys odoratissimus plant has a wide range of bioactive compounds. Phytochemicals were tested for ethanolic Artabotrys odoratissimus leaves extract (AOLE) using the FeCl₃ test, Salkowaski's test, and others. Corrosion tests were conducted at varying inhibitor concentrations and temperatures. The inhibitory impact of AOLE on corrosion of MS was reported to improve with increasing concentration. Polarization experiments revealed that AOLE is a mixed kind of inhibitor and the inhibition efficacy (η_w) for MS is 93.27% for 1.25 g/L AOLE. For Electrochemical impedance spectroscopy (EIS), maximal inhibitory efficacy (η_w) was 91.62% due to AOLE adsorption on the MS surface. The obtained results using each methodology are highly consistent and closely resemble each other. The adsorption of AOLE molecules on an MS surface from the bulk of the solution causes the inhibitor's inhibition action, and the adsorption mechanism follows Langmuir adsorption isotherm. The computed $\Delta G_{ads}^o$ values ranged between ?32.919 and ?33.520 kJ mol^?1, implying a spontaneous and exothermic inhibitory action. The thermodynamic and activation parameters are often used to understand corrosion inhibition mechanisms. The comparison of corrosion product and pure extract FT-IR spectrum indicates the nature of AOLE adsorption on the MS surface. The surface morphology of MS samples was assessed using atomic force microscopy (AFM), scanning electron microscope (SEM), and contact angle techniques.