Observations on the preparation of polybutadiene containing vinyl cyclopentane units

At low monomer concentrations the use of TMEDA and THF as promoters in the n-BuLi-initiated polymerization of butadiene results in the formation of vinyl cyclopentane chain units in addition to the normal 1,4- and 1,2-microstructure. TMEDA is more effective than THF in promoting formation of the cyclic structure and with TMEDA the cyclic content of the polybutadiene can be as high as 45 wt %. Surprisingly, the use of high levels of THF in conjunction with n-BuLi and TMEDA can actually suppress the formation of cyclic units. The sodium counterion is also shown to yield the cyclic structure with the same promoters.     

An adaptive numerical integration code for a chain of transputers

We consider the calculation of ∫_a^bƒ(x)dx, on a linear chain of transputers of arbitrary length, in which each transputer calculates an approximation to this integral on a subinterval of equal length using an adaptive method based on the ten point Gaussain rule and the twenty-one point Kronrod extension. Extensive numerical testing on a chain of 32 T800s shows that if a large number of function evaluations are needed then linear speed-ups are achievable with any number of transputers.     

Risk management in safety critical areas

This paper examines the lessons to be learned from recent disasters. From these and other evidence it deduces good practice in managing risk in safety critical areas. It explains some methods which may be used to aid decision-making for implementing risk control measures. The paper uses examples drawn from the UK rail transport sector with specific reference to current BR practice.     

A study of B-convergence of Runge-Kutta methods

Computing - This paper deals with the convergence analysis of implicit Runge-Kutta methods as applied to stiff, semilinear systems of the form $$\dot U$$ (t)=QU(t)+g(t, U(t)). A criterion is...     

Bayes-optimal chemotaxis

Chemotaxis plays a crucial role in many biological processes, including nervous system development. However, fundamental physical constraints limit the ability of a small sensing device such as a cell or growth cone to detect an external chemical gradient. One of these is the stochastic nature of receptor binding, leading to a constantly fluctuating binding pattern across the cell's array of receptors. This is analogous to the uncertainty in sensory information often encountered by the brain at the systems level. Here we derive analytically the Bayes-optimal strategy for combining information from a spatial array of receptors in both one and two dimensions to determine gradient direction. We also show how information from more than one receptor species can be optimally integrated, derive the gradient shapes that are optimal for guiding cells or growth cones over the longest possible distances, and illustrate that polarized cell behavior might arise as an adaptation to slowly varying environments. Together our results provide closed-form predictions for variations in chemotactic performance over a wide range of gradient conditions.     

Deriving Sea Surface Salinity and Density Variations From Satellite and Aircraft Microwave Radiometer Measurements: Application to Coastal Plumes Using STARRS

Using brightness temperature Tb measurements from L-band airborne microwave radiometers, with independent sea surface temperature (SST) observations, sea surface salinity (SSS) can be remotely determined with errors of about 1 psu in temperate regions. Nonlinearities in the relationship between Tb, SSS, and SST produce variations in the sensitivity of salinity S to variations in Tb and SST. Despite significant efforts devoted to SSS remote sensing retrieval algorithms, little consideration has been given to deriving density D from remotely sensed SSS and SST. Density is related to S and T through the equation of state. It affects the ocean's static stability and its dynamical response to forcings. By chaining together two empirical relationships (flat-sea emissivity and equation of state) to form an inversion algorithm for sea surface density (SSD) in terms of Tb and SST, we develop a simple L-band SSD retrieval algorithm. We use this to investigate the sensitivity of SSD retrievals to observed Tb and SST and infer errors in D for typical sampling configurations of the airborne Salinity, Temperature, And Roughness Remote Scanner (STARRS) and satellite-borne Soil Moisture and Ocean Salinity (SMOS) and Aquarius radiometers. We then derive D from observations of river plumes obtained using STARRS and demonstrate several oceanographic applications: the observations are used to study variations in T and S effects on D in the Mississippi plume, and the across-shelf density gradient is used to infer surface geostrophic shear and subsurface geostrophic current in the Plata plume. Future basin-scale applications of SSD retrievals from satellite-borne microwave radiometers such as SMOS and Aquarius are anticipated.     

Implementing an ODE code on distributed memory computers

In this paper, it is shown how to adapt an existing package (VODE) for solving systems of ordinary differential equations on serial computers to distributed memory parallel computers. The approach taken is based on waveform relaxation in which the problem is decomposed into a sequence of subproblems which are then solved independently using VODE on each processor. Communication between subtasks is provided by a generic software environment p4. This approach allows the development of general purpose parallel software for ODEs which is both reliable and portable.