Exactly Conservative Integrators

Traditional numerical discretizations of conservative systems generically yield an artificial secular drift of any nonlinear invariants. In this work we present an explicit nontraditional algorithm that exactly conserves these invariants. We illustrate the general method by applying it to the three-wave truncation of the Euler equations, the Lotka--Volterra predator--prey model, and the Kepler problem. This method is discussed in the context of symplectic (phase space conserving) integration methods as well as nonsymplectic conservative methods. We comment on the application of our method to general conservative systems.Comment: 30 pages, postscript (1.3MB). Submitted to SIAM J. Sci. Comput

Electrochemical Evaluation of LaNi_(5–x)Ge_x Metal Hydride Alloys

We report a detailed evaluation of Ge-substituted LaNi_5 for electrochemical application as a negative electrode in alkaline rechargeable cells. Alloys with small substitutions of Ge for Ni show operating pressures, chargeability, cyclic lifetime, and kinetics for hydrogen absorption and desorption all superior to those found in many other substituted LaNi_5 alloys. These improved properties were achieved with a minimal reduction in hydrogen storage capacity

Assessing the outcome of orthognathic surgery by three-dimensional soft tissue analysis

Studies of orthognathic surgery often focus on pre-surgical versus post-surgical changes in facial shape. In contrast, this study provides an innovative comparison between post-surgical and control shape. Forty orthognathic surgery patients were included, who underwent three different types of surgical correction: Le Fort I maxillary advancement, bilateral sagittal split mandibular advancement, and bimaxillary advancement surgery. Control facial images were captured from volunteers from local communities in Glasgow, with patterns of age, sex, and ethnic background that matched those of the surgical patients. Facial models were fitted and Procrustes registration and principal components analysis used to allow quantitative analysis, including the comparison of group mean shape and mean asymmetry. The primary characteristic of the difference in shape was found to be residual mandibular prognathism in the group of female patients who underwent Le Fort I maxillary advancement. Individual cases were assessed against this type of shape difference, using a quantitative scale to aid clinical audit. Analysis of the combined surgical groups provided strong evidence that surgery reduces asymmetry in some parts of the face such as the upper lip region. No evidence was found that mean asymmetry in post-surgical patients is greater than that in controls

Electrochemical Studies on LaNi5–xSnx Metal Hydride Alloys

Electrochemical studies were performed on LaNi5–xSnx with 0 <= x <= 0.5. We measured the effect of the Sn substituent on the kinetics of charge-transfer and diffusion during hydrogen absorption and desorption, and the cyclic lifetimes of LaNi5–-xSnx electrodes in 250 mAh laboratory test cells. We report beneficial effects of making small substitutions of Sn for Ni in LaNi5 on the performance of the metal hydride alloy anode in terms of cyclic lifetime, capacity, and kinetics. The optimal concentration of Sn in LaNi5–xSnx alloys for negative electrodes in alkaline rechargeable secondary cells was found to lie in the range 0.25 <= x <= 0.3

Electrochemical Properties of LaNi5–xGex Alloys in Ni-MH Batteries

Electrochemical studies were performed on LaNi5–xGex metal hydride alloys with 0 <= x <= 0.5. We carried out single-electrode studies to understand the effects of the Ge substituent on the hydrogen absorption characteristics, the electrochemical capacity, and the electrochemical kinetics of hydrogen absorption and desorption. The electrochemical characteristics of the Ge-substituted alloys are compared to those of the Sn-substituted alloys reported earlier. LaNi5–xGex alloys show compositional trends similar to LaNi5–xSnx alloys, but unlike the Sn-substituted alloys, Ge-substituted alloys continue to exhibit facile kinetics for hydrogen absorption/desorption at high solute concentrations. Cycle lives of LaNi5–xGex electrodes were measured in 300 mAh laboratory test cells and were found to be superior to the Sn-substituted LaNi5 and comparable to a Mm(Ni,Co,Mn,Al)5 alloy. The optimum Ge content for LaNi5–xGex metal hydride alloys in alkaline rechargeable cells is in the range 0.4 <= x <= 0.5

Kinetic distance and kinetic maps from molecular dynamics simulation

Characterizing macromolecular kinetics from molecular dynamics (MD) simulations requires a distance metric that can distinguish slowly-interconverting states. Here we build upon diffusion map theory and define a kinetic distance for irreducible Markov processes that quantifies how slowly molecular conformations interconvert. The kinetic distance can be computed given a model that approximates the eigenvalues and eigenvectors (reaction coordinates) of the MD Markov operator. Here we employ the time-lagged independent component analysis (TICA). The TICA components can be scaled to provide a kinetic map in which the Euclidean distance corresponds to the kinetic distance. As a result, the question of how many TICA dimensions should be kept in a dimensionality reduction approach becomes obsolete, and one parameter less needs to be specified in the kinetic model construction. We demonstrate the approach using TICA and Markov state model (MSM) analyses for illustrative models, protein conformation dynamics in bovine pancreatic trypsin inhibitor and protein-inhibitor association in trypsin and benzamidine

Modelling the quark propagator

The quark propagator is at the core of lattice hadron spectrum calculations as well as studies in other nonperturbative schemes. We investigate the quark propagator with an improved staggered action (Asqtad) and an improved gluon action, which provides good quality data down to small quark masses. This is used to construct ans\"{a}tze suitable for model hadron calculations as well as adding to our intuitive understanding of QCD.Comment: Lattice2002(spectrum