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A new mathematical model representing dynamic cerebral autoregulation as a flow dependent feedback mechanism is presented. Two modelling parameters are introduced, lambda, the rate of restoration, and tau, a time delay. Velocity profiles are found for a general arterial blood pressure, allowing the model to be applied to any experiment that uses changes in arterial blood pressure to assess dynamic cerebral autoregulation. Two such techniques, thigh cuffs and a lower body negative pressure box, which produce step changes and oscillatory variations in arterial blood pressure respectively, are investigated. Results derived using the mathematical model are compared with data from the two experiments. The comparisons yield similar estimates for lambda and tau, suggesting these parameters are independent of the pressure change stimulus and depend only on the main features of the dynamic cerebral autoregulation process. The modelling also indicates that for imposed oscillatory variations in arterial blood pressure a small phase difference between pressure and velocity waveforms does not necessarily imply impaired autoregulation. It is shown that the ratio between the variation in maximum velocity and pressure variation can be used, along with the phase difference, to indicate the nature of the autoregulatory response.

One of the main problems in welding is to produce consistent weld profiles. Simple heat-flow models of the weldpool, which are currently used to predict the shape of the solid-liquid boundary, do not take account of fluid motion which is observed in practice and the effect of such motion could be significant. Electromagnetic j × B forces due to the welding arc have been proposed as a major cause of the motion and we attempt here to develop existing flow models towards more practical welding situations. We consider the steady-state flow of an incompressible viscous conducting fluid in a hemispherical container due to various axisymmetric representations of the distributed current sources which can arise in arc welding. A solution is found for sufficiently small currents that inertial effects may be ignored and no singularities appear in the velocity field. We discover that varying the current distribution can lead to qualitatively different flow patterns, i.e. poloidal flows in opposite directions and breakup into two distinct counter-rotating loops.

Abstract.Constitutive equations are discussed for a mixture of any number of materials with elastic and viscous properties in which the constituents may have different temperatures.