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.     

Langevin dynamic simulation of hysteresis in a field-swept Landau potential

Numerical simulations are done of Langevin dynamics for a uniform-orderparameter, field-swept Landau model,= –|a/2|m ²+|b/4|m ⁴–mh(t) , to study hysteresis effects. The field is swept at a constant rateh(t)=h(0)+ht. The stochastic jump values of the field {h_J from an initially prepared metastable minimumm(0) are recorded, on passage to a global minimum m(). The results are: (a) The mean jump¯h _J(h) increases (hysteresis loop widens) with h, confirming a previous theoretical criterion based on rate competition between field-sweep and inverse mean first-passage time (FPT); (b) The broad jump distribution(h _J,h) is related to intrinsically large FPT fluctuations ( ²–²)/ ² O(1), and can be quantitatively understood. Possible experimental tests of the ideas are indicated.     

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