A stochastic framework for recursive computation of spline functions: Part II,smoothing splines

Many of the optimal curve-fitting problems arising in approximation theory have the same structure as certain estimation problems involving random processes. We develop this structural correspondence for the problem of smoothing inaccurate data with splines and show that the smoothing spline is a sample function of a certain linear least-squares estimate. Estimation techniques are then used to derive a recursive algorithm for spline smoothing.     

Photochemical reduction of uranyl ion with triethylamine

Uranyl ion is photochemically reduced to uranium(IV) in the presence of triethylamine and triethylamine is oxidized to secondary amine and acetaldehyde. On the basis of product analysis, temperature independent quantum yields for uranium(IV) formation and abnormal Stern-Volmer plots rule out the simple collisional photochemical annihilation of excited uranyl ion with triethylamine. Static annihilation has a significant contribution in addition to dynamic annihilation.     

Combustion waves in a model with chain branching reaction and their stability

In this paper the travelling wave solutions in the adiabatic model with the two-step chain branching reaction mechanism are investigated both numerically and analytically in the limit of equal diffusivity of reactant, radicals and heat. The properties of these solutions and their stability are investigated in detail. The behaviour of combustion waves are demonstrated to have similarities with the properties of non-adiabatic one-step combustion waves in that there is a residual amount of fuel left behind the travelling waves and the solutions can exhibit extinction. The difference between the non-adiabatic one-step and adiabatic two-step models is found in the behaviour of the combustion waves near the extinction condition. It is shown that the flame velocity drops down to zero as the extinction condition is reached. Prospects of further work are also discussed.     

A weight-function approach for determining watershed initial conditions for combustion waves

In many generic combustion models, one finds that a combustionwave will develop with a specific wave speed. However, thereare possible initial temperature profiles which do not evolveinto such waves, but rather die out to the ambient temperature.There can exist, in some models, a clear distinction betweenthose initial conditions that do evolve into combustion wavesand those that do not; this is sometimes referred to as thewatershed initial condition. When fuel consumption is consideredto be negligible, analytical methods can be used to obtain theexact watershed. In this paper, we consider the problem of determiningpseudo-watersheds and ascertaining the relationship betweenthese pseudo-watersheds and the exact watersheds. In the processa novel weight-function approach for infinite spatial domainsis developed.     

Effect of collimator size and absorber thickness on gamma ray attenuation measurements for bakelite and perspex

The mass attenuation coefficient (μ _m) of 662 keV gamma rays have been measured in the extended media of bakelite and perspex under different collimation conditions. The increase in attenuation coefficient is seen with increase in sample thickness as well as with collimator size due to the contribution of multiple scattered photons in the uncollided beam of 662 keV gamma rays.     

Analysis of a chemostat model with variable yield coefficient: Tessier kinetics

We investigate a chemostat model in which the growth rate is given by a Tessier expression with a variable yield coefficient. We combine analytical results with path-following methods. The washout conditions are found. When washout does not occur we establish the conditions under which the reactor performance and reactor productivity are maximised. We also determine the parameter region in which oscillations may be generated in the reactor. We briefly discuss the implications of our results for comparing the performance of a single bioreactor against a cascade of two bioreactors.     

Performance analysis of a constrained resource sharing system

We consider a queueing system where the servers are arranged in a circle, and each arriving customer requires a pair of resources that is shared by its server with the respective neighbors on either side. If either resource is being used, the customer is denied service. Customers arrive at each server according to independent Poisson processes, and lengths of service times at each server have an exponential distribution. We derive a closed-form formula for the expected fraction of busy servers at any time in terms of the number of servers and the utilization factor (defined as the arrival rate times the mean service-time duration). This allows us to evaluate system performance when these parameters are varied, and to determine whether denying service to arrivals at alternate servers improves performance. We relate the system to Dijkstra's dining philosophers problem, which is an abstraction for resource sharing in an operating system. This revised version was published online in June 2006 with corrections to the Cover Date.     

Radionuclides in produced water from Norwegian oil and gas installations — concentrations and bioavailability

Substantial amounts of produced water, containing elevated levels of radionuclides (mainly ²²⁶Ra and ²²⁸Ra) are discharged to the sea as a result of oil and gas production on the Norwegian Continental Shelf. So far no study has assessed the potential radiological effects on marine biota in connection with radionuclide discharges to the North Sea. The main objective of the project is to establish radiological safe discharge limits for radium, lead and polonium associated with other components in produced water from oil and gas installations on the Norwegian continental shelf.This study reports results indicating that the presence of added chemicals such as scale inhibitors in produced water has a marked influence on the formation of radium and barium sulphates when produced water is mixed with sea water. Thus, the mobility and bioavailability of radium (and barium) will be larger than anticipated. Also, the bioavailability of food-borne radium is shown to increase due to presence of such chemicals.