Modeling of Ion Transport in High Strain Ionomers by Monte Carlo Simulation Compared to Continuum Model

The transport of charge due to electric stimulus is the primary mechanism of actuation for a class of polymeric active materials known as ionomeric polymer transducers (IPTs). A two-dimensional ion hopping model has been built to describe ion transport in the IPT. In a Monte Carlo simulation, a square lattice of 50nm × 50nm is investigated containing 200 cations and 200 anions. Step voltages are applied between the electrodes of the IPT, causing the thermally-activated hopping between multiwell energy structures. The energy barrier height includes three parts: intrinsic energy, energy height due to the electric field and energy height due to ion-ion interactions. Periodic boundary conditions have been applied in the direction perpendicular to the electric field. The influence of the electrodes on both faces of IPT is formulated by the method of image charges. The charge density profile over the material has been calculated by the ion distribution in steady state. The Monte Carlo simulation is repeated multiple times to obtain an average result of the charge density. The averaged profile shows regions of cation depletion close to the anode, charge neutrality in the central part and ion accumulation close to the cathode, which qualitatively agrees with the results from conventional continuum models. To quantatively examine the Monte Carlo simulation of the ion hopping model, comparisons with a computational model of transport and electromechanical transduction are performed. This computational model is based upon a coupled chemo-electrical multi-field formulation and computes the spatio-temporal charge density profile to an applied potential at the boundaries. It can be seen that both methods, the statistical theory and the continuum theory, match quite well and are both able to represent the actual behavior inside the IPT. Moreover, experiments are performed to validate the current density calculated by the Monte Carlo simulation. The active material is Nafion 117 (Dupont) in the form of a cantilevered transducer with conductive electrodes on both surfaces and with mobile Na+ counter-ions. Voltage inputs are provided by a dSPACE DS 1102 DSP and amplified using an HP power amplifier. The current is measured by placing a small resistor in series with the sample, between the sample and ground. The voltage across the resistor is amplified and measured by dSPACE. The electrical current is calculated by dividing the voltage drop across the resistor by its resistance. Current density in both simulation results and experimental results exhibits an exponential decay over time.

Field observations of long-period, surf-zone standing waves in relation to contrasting beach morphologies

Field observations of water-surface oscillation and horizontal flow velocity spectra were carried out in the surf zones of contrasting beach-inshore morphodynamic states. The observations were made under conditions of long-period (7.5-11 s), moderate-energy (height 1 .2-2.3 m) swell on different beaches encompassing the full range of states from the steep. reflective extreme to the flat, dissipative extreme and including intermediate states involving different scales of rhythmic surf-zone topography and rip circulations. Experiments on all types of topography reveal standing surf-zone oscillations at periods longer than incident wave period. At least some of these appear to be edge waves. The actual frequencies are dependent on the morphodynamic state of the surf zone and beach. The standing waves with shortest period are zero-mode subharmonic edge waves which consistently occur on highly reflective beaches where they cause cusps spaced at one-half the edge-wave length. The standing waves with lowest frequency were observed on the flattest and most dissipative beach and comprised a wide band of infragravity frequencies. These oscillations could cause the multiple parallel bars. Intermediate frequencies occur in the presence of the pronounced bar-trough and rhythmic topographies of intermediate morphodynamic states.

Approximate Trajectories for Maximum Range

On reading the paper by D. J. Bell in the February edition of the Journal, I noticed that there was no mention of an adaptation of the energy height approach to solutions of maximum range trajectories. I was surprised to find no documentation concerned with this approach and would like to indicate this technique which I have used several times.

An Energy Approach to Climb Performance Estimation of a Turbo-Jet Transport Aircraft

SummaryThe climb performance of a turbo-jet transport aircraft is considered, using the concept of the energy height. The analytical formulae used in evaluating the time needed, distance covered and fuel consumed during climb under various conditions are developed. It is concluded that the application of this energy approach method to the climb performance estimation of a turbojet transport aircraft will prove satisfactory from the points of view both of the accuracy of the results and of saving some of the considerable time needed for the climb calculation by the conventional method. A numerical example is given to illustrate the usefulness, applicability and flexibility of this method.