Observation and evaluation of the synchronous ligand atom pyramidal inversions in binuclear rhenium carbonyl halide complexes of disulphides and diselenides: an X-ray crystal structure of [Re2Br2(CO)6(C6H5CH2SeSeCH2C6H5)]

The dinuclear complexes [Re₂X₂(CO)₆(RCH₂EECH₂R)] (X = Cl or Br, R = Ph or Me₃Si, E = S or Se) have been prepared and characterized. A variable temperature ¹H NMR study on these complexes demonstrated the pyramidal atomic inversion process at the coordinated sulphur and selenium atoms. Total band-shape fittings were used to yield activation parameters for the rate process, in which the two sulphur or selenium atoms undergo synchronous or correlated inversion.     

Stability of a fluid in a horizontal saturated porous layer: effect of non-linear concentration profile, initial, and boundary conditions

Carbon dioxide injected into saline aquifers dissolves in the resident brines increasing their density, which might lead to convective mixing. Understanding the factors that drive convection in aquifers is important for assessing geological CO₂ storage sites. A hydrodynamic stability analysis is performed for non-linear, transient concentration fields in a saturated, homogenous, porous medium under various boundary conditions. The onset of convection is predicted using linear stability analysis based on the amplification of the initial perturbations. The difficulty with such stability analysis is the choice of the initial conditions used to define the imposed perturbations. We use different noises to find the fastest growing noise as initial conditions for the stability analysis. The stability equations are solved using a Galerkin technique. The resulting coupled ordinary differential equations are integrated numerically using a fourth-order Runge–Kutta method. The upper and lower bounds of convection instabilities are obtained. We find that at high Rayleigh numbers, based on the fastest growing noise for all boundary conditions, both the instability time and the initial wavelength of the convective instabilities are independent of the porous layer thickness. The current analysis provides approximations that help in screening suitable candidates for homogenous geological CO₂ sequestration sites.     

Modeling Human Motor Systems in Nonlinear Dynamics: Intentionality and Discrete Movement Behaviors

Attempts to understand human movement systems from the perspective of nonlinear dynamics have increased in recent years, although research has almost exclusively focused on modeling rhythmical movements as limit cycle oscillators. Only a limited amount of work has been undertaken on discrete movements, generally only in the form of numerical simulations and mathematical models. In this paper we briefly overview the key findings from previous research on movement systems as nonlinear dynamical systems, and report data from a behavioral experiment on the coordination observed in a prehension movement under both discrete and rhythmical conditions. In a rhythmical condition subjects grasped dowels in time to a metronomic beat, whereas in a discrete condition a target dowel was grasped within a predetermined movement time. A scanning procedure was implemented to monitor changes in the time of relative final hand closure during hand transport to the dowel. For each condition, a pre-test and post-test of 10 trials were also conducted either side of the scanning trial block. No effects between condition or trial block were noted and there was a large amount of within-subject variability in the coordination data. The findings support previous theoretical modeling suggesting that subject intentionality acts as a more powerful constraint on the intrinsic dynamics of the movement system in discrete compared to rhythmical conditions. The high levels of individual variability were interpreted as being due to the competition between specific and non-specific control parameters (e.g., the subject's intentionality and the metronomic beat). It is concluded that discrete prehension movements appear amenable to a nonlinear dynamical analysis. The data also point to the innovative use of within-subject analyses in future work modeling motor systems as nonlinear dynamical systems.     

Features of the turbulent wall pressure field on a long towed cylinder

Turbulent wall pressure fluctuation correlation functions were measured in water on a towed cylindrical model of length 129.8 m and diameter 3.8 cm for steady speeds ranging from 6.2 to 15.5 m/s. The drag on the model was measured with a strut-mounted load cell to provide estimates of the momentum thickness and friction velocity that are used for scaling the correlation functions. Very high momentum thickness Reynolds numbers Re_θ were achieved, and varied from 4.8 × 10⁵ to 1.1 × 10⁶. The ratio of boundary layer thickness to cylinder radius was approximately 24, which is an order of magnitude greater than previous laboratory investigations. The ratio of momentum thickness to viscous length scale is significantly greater than for flat plate cases at comparable Re_θ. A similarity scaling is shown to be more effective than outer or inner boundary layer scalings for collapsing the correlation functions. Comparisons with the early streamwise and transverse correlation measurements of Willmarth and Yang are favorable, and show consistent trends of a more rapid loss of correlated energy for cylindrical turbulent boundary layers than for flat plate cases. Convection velocities are also presented and shown to collapse well with separation scaled on outer variables. A simple model that relates the peak of the correlation function to the average coherence levels is shown to be valid for spatial separations less than the approximate momentum thickness.     

Computing parent nodes in threaded binary trees

We give three algorithms for computing the parent of a node in a threaded binary tree, and calculate the average case complexity of each. By comparing these to the unit cost of obtaining the parent of a node with an explicit parent-pointer field, it is possible to balance runtime and storage cost with respect to the task of finding parent nodes in binary trees. The results obtained show that, although the worst case complexity for ann-node tree is obviouslyO(n) for all three algorithms, the average case complexity for two input distributions is asymptotic (from below) to either 3 or 2.     

Task‐performing dynamics in irregular,biomimetic networks

Understanding self‐organized collective dynamics—especially in sparsely connected, noisy, and imperfect networks—has important implications for designing and optimizing task‐performing technological systems as well as for deciphering biological structures and functions. We note that stomatal arrays on plant leaves might provide an ideal example of task‐performance in this context. Guided by observations of stomatal networks, we examined a simple model of task‐performing, collective dynamics that included state noise, spatial rule heterogeneity, dynamic modules, and network rewiring. Our results indicate that task‐performance in such networks can actually be enhanced by various kinds of spatial and temporal irregularity. © 2007 Wiley Periodicals, Inc. Complexity 12: 14–21, 2007     

Estimating Moments of the Effective Lead Time for a Stock Control Model with Independent Normal Lead Times

In multiple sourcing, replenishment orders for one stock item may be placed at the same time with several suppliers. In order to determine the re-order level and the size of the buffer stock, we then need to estimate the mean and variance of the effective lead time, i.e. the smallest of the lead times. Previous work on this topic has assumed that the mean and variance are either known or may be estimated from large samples, but the number of observations typically available is small. This paper presents a Bayesian approach to the problem when the lead times are independent and normally distributed, although it is shown that the method may be used in more general circumstances. The computational procedures are described and illustrated with an example.     

Elementary School Chemistry: Has its Potential been Realized?

Examples of lesson sequences are described to illustrate how chemical content can be used with well established teaching-learning models. These approaches place an emphasis on children constructing their own chemical ideas and using a wide range of science investigation skills. Mention is made of some literature which indicates the types of chemical ideas possessed by children. These results provide guidance for teachers, but hopefully readers will be challenged to see that while there is definitely a role for elementary school chemistry its full potential simply has not been realized.