Phantom ducks and models of excitability

We study a system which may serve as a prototype model for excitability. Its long-term behavior is governed by a globally attracting fixed point, but it has the interesting property that an appropriate small perturbation of the equilibrium situation elicits a large (transient) response. Using singular perturbation techniques, the threshold for excitation is determined. Asymptotic expansions for the threshold are given and their validity is proved. An associated system is studied, which yields further quantitative information on the position of the threshold.     

Dual-cure processes: towards deformable crosslinked coatings

Two dual-cure processes consisting of a UV-initiated radical polymerization followed by either a UV-induced cationic polymerisation, or a thermal addition reaction, were investigated. The feasibility of the processes was studied using an acrylate-oxetane monomer for the UV/UV combination, and an acrylated oligoester for the UV/Heat combination. It was shown by FTIR and Tg measurements, that both steps of each process could be performed efficiently and separately. This allowed the production of a deformable partially cured coating, whose cure can then be completed, leading to the required final properties. Furthermore, it was demonstrated that the increase of the functionality of the reactive diluent led to a decrease of the thermal crosslinking extent. This is probably due to the reduced mobility of the reactive species that is caused by an enhanced UV crosslinking taking place during the first step.     

Existence of Quasipattern Solutions of the Swift–Hohenberg Equation

We consider the steady Swift–Hohenberg partial differential equation, a one-parameter family of PDEs on the plane that models, for example, Rayleigh–Bénard convection. For values of the parameter near its critical value, we look for small solutions, quasiperiodic in all directions of the plane, and which are invariant under rotations of angle ${\pi/q, q \geqq 4}$ . We solve an unusual small divisor problem and prove the existence of solutions for small parameter values, then address their stability with respect to quasi-periodic perturbations.     

Ultraviolet–ultraviolet dual‐cure process based on acrylate oxetane monomers

A dual‐cure process consisting of two subsequent ultraviolet‐initiated radical and cationic polymerizations was investigated. The process was studied with two acrylate oxetane monomers, one of them having a spacer between the two polymerizable moieties. It was shown by Fourier transform infrared (FTIR) that the first (radical) step was performed successfully for both systems. As for the second (cationic) step, only the monomer with the spacer was able to polymerize, allowing the crosslinking of the polyacrylic chains generated by the first step. The efficiency of the process was confirmed by differential scanning calorimetry because the glass‐transition temperatures of the cured films were ?16 and + 34 °C after the first and second steps, respectively. The dual cure of this system was further analyzed by real‐time FTIR, which showed that 86% of the acrylate and 80% of the oxetane moieties were converted after 20 and 50 s of light exposure, respectively. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 469–475, 2003     

Integral resource capacity planning for inpatient care services based on bed census predictions by hour

The design and operations of inpatient care facilities are typically largely historically shaped. A better match with the changing environment is often possible, and even inevitable due to the pressure on hospital budgets. Effectively organizing inpatient care requires simultaneous consideration of several interrelated planning issues. Also, coordination with upstream departments like the operating theatre and the emergency department is much-needed. We present a generic analytical approach to predict bed census on nursing wards by hour, as a function of the Master Surgical Schedule and arrival patterns of emergency patients. Along these predictions, insight is gained on the impact of strategic (ie, case mix, care unit size, care unit partitioning), tactical (ie, allocation of operating room time, misplacement rules), and operational decisions (ie, time of admission/discharge). The method is used in the Academic Medical Center Amsterdam as a decision-support tool in a complete redesign of the inpatient care operations.     

Singular Hopf Bifurcation in Systems with Fast and Slow Variables

Summary. We study a general nonlinear ODE system with fast and slow variables, i.e., some of the derivatives are multiplied by a small parameter. The system depends on an additional bifurcation parameter. We derive a normal form for this system, valid close to equilibria where certain conditions on the derivatives hold. The most important condition concerns the presence of eigenvalues with singular imaginary parts, by which we mean that their imaginary part grows without bound as the small parameter tends to zero. We give a simple criterion to test for the possible presence of equilibria satisfying this condition. Using a center manifold reduction, we show the existence of Hopf bifurcation points, originating from the interaction of fast and slow variables, and we determine their nature. We apply the theory, developed here, to two examples: an extended Bonhoeffer—van der Pol system and a predator-prey model. Our theory is in good agreement with the numerical continuation experiments we carried out for the examples. Received October 24, 1996; revised October 31, 1997; accepted November 3, 1997     

The contributions of W.A. harris Jr. to difference equations

William Ashton Harris Jr. was born December 18, 1930 in New Orleans, Louisiana, USA. He studied mathematics with minors in physics and appl ied mechanics (elasticity) at the University of Minnesota receiving his Ph.D. in mathematics in 1955 with the thesis "A boundary value problem for a system of ordinary linear differential equations involving powers of a parameter". His thesis advisor was Professor H.L. Turrittin.He remained at the University of Minnesota and became professor in 1968. In 1970 he moved to the University of Southern California where he stayed until his untimely death on January 8, 1998. He has held visiting appointments at several other universities.     

UV-curing under oxygen-deficient conditions

Four different coating formulations have been formulated with different amounts of photoinitiator and cured under different atmospheres (21, 5, 1 and 0% of oxygen). Surface cure and through cure were assessed for each combination. It was observed that the cure process for all formulations was strongly affected by the atmospheric conditions, and that the formulations required substantially less photoinitiator if cured under 5% of oxygen if compared to curing under air. Calculations show that the lower price of the formulation due to the decreased photoinitiator level may outweigh the additional equipment and running costs in specific cases. Therefore, UV-inertisation is not only attractive from a product quality point-of-view, but can also offer economic advantages.