Demographic projection of high-elevation white pines infected with white pine blister rust: a nonlinear disease model.

Matrix population models have long been used to examine and predict the fate of threatened populations. However, the majority of these efforts concentrate on long-term equilibrium dynamics of linear systems and their underlying assumptions and, therefore, omit the analysis of transience. Since management decisions are typically concerned with the short-term (< 100 years), asymptotic analyses could lead to inaccurate conclusions or, worse yet, critical parameters or processes of ecological concern may go undetected altogether. We present a stage-structured, deterministic, nonlinear, disease model which is parameterized for the population dynamics of high-elevation white pines in the face of infection with white pine blister rust (WPBR). We evaluate the model using newly developed software to calculate sensitivity and elasticity for nonlinear population models at any projected time step. We concentrate on two points in time, during transience and at equilibrium, and under two scenarios: a regenerating pine stand following environmental disturbance and a stand perturbed by the introduction of WPBR. The model includes strong density-dependent effects on population dynamics, particularly on seedling recruitment, and results in a structure favoring large trees. However, the introduction of WPBR and its associated disease-induced mortality alters stand structure in favor of smaller stages. Populations with infection probability (beta) > or = 0.1 do not reach a stable coexisting equilibrium and deterministically approach extinction. The model enables field observations of low infection prevalence among pine seedlings to be reinterpreted as resulting from disease-induced mortality and short residence time in the seedling stage. Sensitivities and elasticities, combined with model output, suggest that future efforts should focus on improving estimates of within-stand competition, infection probability, and infection cost to survivorship. Mitigating these effects where intervention is possible is expected to produce the greatest effect on population dynamics over a typical management timeframe.

Nonlinear vortex development in rotating flows.

We present the results of a combined experimental and numerical investigation into steady secondary vortex flows confined between two concentric right circular cylinders. When the flow is driven by the symmetric rotation of both end walls and the inner cylinder, toroidal vortex structures arise through the creation of stagnation points (in the meridional plane) at the inner bounding cylinder or on the mid-plane of symmetry. A detailed description of the flow regimes is presented, suggesting that a cascade of such vortices can be created. Experimental results are reported, which visualize some of the new states and confirm the prediction that they are stable to (mid-plane) symmetry-breaking perturbations. We also present some brief results for the flows driven by the rotation of a single end wall. Vortex structures may also be observed at low Reynolds numbers in this geometry. We show that standard flow visualization methods lead to some interesting non-axisymmetric particle paths in this case.

Numerical bifurcation study of electrohydrodynamic convection in nematic liquid crystals.

We present the results of a numerical investigation of the Ericksen-Leslie equations for the problem of electrohydrodynamic convection in a nematic liquid crystal. The combination of a finite element approach and numerical bifurcation techniques allows us to provide details of the basic flow and include the physically relevant effect of nonslip side walls. We are also able to include material properties as parameters and this permits us to draw comparisons with available experimental data. We then compare and contrast the bifurcation structure with that of Rayleigh-Bénard and Taylor-Couette flows and explore the role of symmetries by including a fringing electric field.

Recovery of ventilation distributions by gas wash-out of a mechanical pump.

A method for deriving virtually continuous distributions of ventilation in the lungs from multiple-breath wash-out of inert, insoluble gases has been tested using a mechanical pump in which two parallel compartments, simulating lung regions, could be differentially ventilated to any desired, and known, extent. With more than moderate non-uniformity, bimodal distributions were always recovered from wash-out data, and with high reproducibility. In a substantial proportion of wash-out experiments ventilation was recovered in regions of very low and very high turnover in addition to the expected modes. These spurious modes may be abolished by various computational devices, none entirely satisfactory. Simultaneous wash-out and wash-in of two or three gases of similar diffusivity give essentially identical solutions. When the pump is operated with the two cylinders out of phase, emptying patterns derived from gas wash-out correspond quite well with those expected from the pump setting. These results help to identify and clarify some of the errors which affect physiological wash-out studies.