Numerical Methods for Stiff Two-Point Boundary Value Problems

We consider the two-point boundary value problem for stiff systems of ordinary differential equations. For systems that can be transformed to essentially diagonally dominant form with appropriate smoothness conditions, a priori estimates are obtained. Problems with turning points can be treated with this theory, and we discuss this in detail. We give robust difference approximations and present error estimates for these schemes. In particular we give a detailed description of how to transform a general system to essentially diagonally dominant form and then stretch the independent variable so that the system will satisfy the correct smoothness conditions. Numerical examples are presented for both linear and nonlinear problems.

Mode-specific chemisorption of CH4 on Pt{110}-(1 x 2) explored by first-principles molecular dynamics

The chemisorption of CH4 on Pt{110}-(1 x 2) has been studied by vibrational analysis of the reaction pathway defined by the potential energy surface and, in time reversal, by first-principles molecular dynamics simulations of CH4 associative desorption, with the electronic structure treated explicitly using density functional theory. We find that the symmetric stretch vibration ν1 is strongly coupled to the reaction coordinate; our results therefore provide a firm theoretical basis for recently reported state-resolved reactivity measurements, which show that excitation of the ν1 normal mode is the most efficient way to enhance the reaction probability

An assessment of the impact of trees upon archaeology within a relict wetland

An evaluation of a surviving stretch of the Abbot's Way, in the Somerset Levels and Moors, was undertaken to assess the consequences of the previous management regime and inform future management of the site. The scheduled site appeared to have been dewatered and desiccated as a consequence of tree planting and the effects of a deep, adjacent drainage ditch during the previous decade. The evaluation considered the condition of the Neolithic timbers and associated palaeoenvironmental record from three trenches and, where possible, compared the results with those obtained form the 1974 excavation (Girling, 1976). The results of this analysis suggest that the hydrological consequences of tree planting and colonization had a detrimental effect on both the condition of the timbers and insect remains. However, pollen and plant macro-fossils survived well although there was modern contamination. A trench opened outside the scheduled area. where the ground was waterlogged and supported a wet acid grassland flora, revealed similar problems of survival and condition. This almost certainly reflects a period of peat extraction and an associated seasonally fluctuating water table in the 1950s and 1960s; in fact pollen survived better in the scheduled dewatered area. These results are compared with those recovered from the Sweet Track which was evaluated in 1996. Both sites have been subject to recent tree growth but the Sweet Track has been positively managed in terms of hydrology. The most notable difference between the two sites is that insects and wood survived better at the Sweet Track sites than at the Abbot's Way. Insects seem to be a more sensitive indicator of site desiccation than plant remains. It is recommended that any programme of management of wetland for archaeology should avoid deliberate tree planting and natural scrub and woodland generation. It should also take into account past as well as present land use.

Nuclear accumulation of myocyte muscle LIM protein is regulated by heme oxygenase 1 and correlates with cardiac function in the transition to failure

Impaired mechanosensing leads to heart failure and we have previously shown that a decreased ratio of cytoplasmic to nuclear CSRP3/Muscle LIM protein (MLP ratio) is associated with a loss of mechanosensitivity. Here we tested whether passive or active stress/strain was important in modulating the MLP ratio and determined whether this correlated with heart function during the transition to failure. We exposed cultured neonatal rat myocytes to 10% cyclic mechanical stretch at 1 Hz, or electrically paced myocytes at 6.8 V (1 Hz) for 48 h. The MLP ratio decreased 50% (P < 0.05, n = 4) only in response to electrical pacing, suggesting impaired mechanosensitivity. Inhibition of contractility with 10 μM blebbistatin resulted in a ∼3 fold increase in the MLP ratio (n = 8, P < 0.05), indicating that myocyte contractility regulates nuclear MLP. Inhibition of histone deacetylase (HDAC) signaling with trichostatin A increased nuclear MLP following passive stretch, suggesting that HDACs block MLP nuclear accumulation. Inhibition of heme-oxygenase1 (HO-1) activity with PPZII blocked MLP nuclear accumulation. To examine how mechanosensitivity changes during the transition to heart failure, we studied a guinea pig model of angiotensin II infusion (400 ng/kg/min) over 12 weeks. Using subcellular fractionation we showed that the MLP ratio increased 88% (n = 4, P < 0.01) during compensated hypertrophy, but decreased significantly during heart failure (P < 0.001, n = 4). The MLP ratio correlated significantly with the E/A ratio (r = 0.71, P < 0.01 n = 12), a clinical measure of diastolic function. These data indicate for the first time that myocyte mechanosensitivity as indicated by the MLP ratio is regulated primarily by myocyte contractility via HO-1 and HDAC signaling.

Equilibrium behavior of symmetric ABA triblock copolymer melts

Melts of ABA triblock copolymer molecules with identical end blocks are examined using self-consistent field theory (SCFT). Phase diagrams are calculated and compared with those of homologous AB diblock copolymers formed by snipping the triblocks in half. This creates additional end segments which decreases the degree of segregation. Consequently, triblock melts remain ordered to higher temperatures than their diblock counterparts. We also find that middle-block domains are easier to stretch than end-block domains. As a result, domain spacings are slightly larger, the complex phase regions are shifted towards smaller A-segment compositions, and the perforated-lamellar phase becomes more metastable in triblock melts as compared to diblock melts. Although triblock and diblock melts exhibit very similar phase behavior, their mechanical properties can differ substantially due to triblock copolymers that bridge between otherwise disconnected A domains. We evaluate the bridging fraction for lamellar, cylindrical, and spherical morphologies to be about 40%–45%, 60%–65%, and 75%–80%, respectively. These fractions only depend weakly on the degree of segregation and the copolymer composition.