Power computation for the triboelectric nanogenerator

We consider, from a mathematical perspective, the power generated by a contact-mode triboelectric nanogenerator, an energy harvesting device that has been well studied recently. We encapsulate the behaviour of the device in a differential equation, which although linear and of first order, has periodic coefficients, leading to some interesting mathematical problems. In studying these, we derive approximate forms for the mean power generated and the current waveforms, and describe a procedure for computing the Fourier coefficients for the current, enabling us to show how the power is distributed over the harmonics. Comparisons with accurate numerics validate our analysis

Illustrating field emission theory by using Lauritsen plots of transmission probability and barrier strength

This technical note relates to the theory of cold field electron emission (CFE). It starts by suggesting that, to emphasize common properties in relation to CFE theory, the term 'Lauritsen plot' could be used to describe all graphical plots made with the reciprocal of barrier field (or the reciprocal of a quantity proportional to barrier field) on the horizontal axis. It then argues that Lauritsen plots related to barrier strength (G) and transmission probability (D) could play a useful role in discussion of CFE theory. Such plots would supplement conventional Fowler-Nordheim (FN) plots. All these plots would be regarded as particular types of Lauritsen plot. The Lauritsen plots of -G and lnD can be used to illustrate how basic aspects of FN tunnelling theory are influenced by the mathematical form of the tunnelling barrier. These, in turn, influence local emission current density and emission current. Illustrative applications used in this note relate to the well-known exact triangular and Schottky-Nordheim barriers, and to the Coulomb barrier (i.e., the electrostatic component of the electron potential energy barrier outside a model spherical emitter). For the Coulomb barrier, a good analytical series approximation has been found for the barrier-form correction factor; this can be used to predict the existence (and to some extent the properties) of related curvature in FN plots.Comment: Based on a poster presented at the 25th International Vacuum Nanoelectronics Conference, Jeju, S. Korea, July 2012. Version 3 incorporates small changes made at proof stag

Considerations on bubble fragmentation models

n this paper we describe the restrictions that the probability density function (p.d.f.) of the size of particles resulting from the rupture of a drop or bubble must satisfy. Using conservation of volume, we show that when a particle of diameter, D0, breaks into exactly two fragments of sizes D and D2 = (D30−D3)1/3 respectively, the resulting p.d.f., f(D; D0), must satisfy a symmetry relation given by D22 f(D; D0) = D2 f(D2; D0), which does not depend on the nature of the underlying fragmentation process. In general, for an arbitrary number of resulting particles, m(D0), we determine that the daughter p.d.f. should satisfy the conservation of volume condition given by m(D0) ∫0D0 (D/D0)3 f(D; D0) dD = 1. A detailed analysis of some contemporary fragmentation models shows that they may not exhibit the required conservation of volume condition if they are not adequately formulated. Furthermore, we also analyse several models proposed in the literature for the breakup frequency of drops or bubbles based on different principles, g(ϵ, D0). Although, most of the models are formulated in terms of the particle size D0 and the dissipation rate of turbulent kinetic energy, ϵ, and apparently provide different results, we show here that they are nearly identical when expressed in dimensionless form in terms of the Weber number, g*(Wet) = g(ϵ, D0) D2/30 ϵ−1/3, with Wet ~ ρ ϵ2/3 D05/3/σ, where ρ is the density of the continuous phase and σ the surface tension

Bifurcation curves of subharmonic solutions

We revisit a problem considered by Chow and Hale on the existence of subharmonic solutions for perturbed systems. In the analytic setting, under more general (weaker) conditions, we prove their results on the existence of bifurcation curves from the nonexistence to the existence of subharmonic solutions. In particular our results apply also when one has degeneracy to first order -- i.e. when the subharmonic Melnikov function vanishes identically. Moreover we can deal as well with the case in which degeneracy persists to arbitrarily high orders, in the sense that suitable generalisations to higher orders of the subharmonic Melnikov function are also identically zero. In general the bifurcation curves are not analytic, and even when they are smooth they can form cusps at the origin: we say in this case that the curves are degenerate as the corresponding tangent lines coincide. The technique we use is completely different from that of Chow and Hale, and it is essentially based on rigorous perturbation theory.Comment: 29 pages, 2 figure

Impact of retrospective data verification to prepare the ICON6 trial for use in a marketing authorization application

Background: The ICON6 trial (ISRCTN68510403) is a phase III academic-led, international, randomized, three-arm, double-blind, placebo-controlled trial of the addition of cediranib to chemotherapy in recurrent ovarian cancer. It investigated the use of placebo during chemotherapy and maintenance (arm A), cediranib alongside chemotherapy followed by placebo maintenance (arm B) and cediranib throughout both periods (arm C). Results of the primary comparison showed a meaningful gain in progression-free survival (time to progression or death from any cause) when comparing arm A (placebo) with arm C (cediranib). As a consequence of the positive results, AstraZeneca was engaged with the Medical Research Council trials unit to discuss regulatory submission using ICON6 as the single pivotal trial. / Methods: A relatively limited level of on-site monitoring, single data entry and investigator’s local evaluation of progression were used on trial. In order to submit a license application, it was decided that (a) extensive retrospective source data verification of medical records against case report forms should be performed, (b) further quality control checks for accuracy of data entry should be performed and (c) blinded independent central review of images used to define progression should be undertaken. To assess the value of these extra activities, we summarize the impact on both efficacy and safety outcomes. / Results: Data point changes were minimal; those key to the primary results had a 0.47% error rate (36/7686), and supporting data points had a 0.18% error rate (109/59,261). The impact of the source data verification and quality control processes were analyzed jointly. The conclusion drawn for the primary outcome measure of progression-free survival between arm A and arm C was unchanged. The log-rank test p-value changed only at the sixth decimal place, the hazard ratio does not change from 0.57 with the exception of a marginal change in its upper bound (0.74–0.73) and the median progression-free survival benefit from arm C remained at 2.4 months. Separately, the blinded independent central review of progression scans was performed as a sensitivity analysis. Estimates and p values varied slightly but overall demonstrated a difference in arms, which is consistent with the initial result. Some increases in toxicity were observed, though these were generally minor, with the exception of hypertension. However, none of these increases were systematically biased toward one arm. / Conclusion: The conduct of this pragmatic, academic-sponsored trial was sufficient given the robustness of the results, shown by the results remaining largely unchanged following retrospective verification despite not being designed for use in a marketing authorization. The burden of such comprehensive retrospective effort required to ensure the results of ICON6 were acceptable to regulators is difficult to justify

Navier-Stokes Simulation of a Heavy Lift Slowed-Rotor Compound Helicopter Configuration

Time accurate numerical simulations were performed using the Reynolds-averaged Navier-Stokes (RANS) flow solver OVERFLOW for a heavy lift, slowed-rotor, compound helicopter configuration, tested at the NASA Langley 14- by 22-Foot Subsonic Tunnel. The primary purpose of these simulations is to provide support for the development of a large field of view Particle Imaging Velocimetry (PIV) flow measurement technique supported by the Subsonic Rotary Wing (SRW) project under the NASA Fundamental Aeronautics program. These simulations provide a better understanding of the rotor and body wake flows and helped to define PIV measurement locations as well as requirements for validation of flow solver codes. The large field PIV system can measure the three-dimensional velocity flow field in a 0.914m by 1.83m plane. PIV measurements were performed upstream and downstream of the vertical tail section and are compared to simulation results. The simulations are also used to better understand the tunnel wall and body/rotor support effects by comparing simulations with and without tunnel floor/ceiling walls and supports. Comparisons are also made to the experimental force and moment data for the body and rotor

Direct aerosol chemical composition measurements to evaluate the physicochemical differences between controlled sea spray aerosol generation schemes

Controlled laboratory studies of the physical and chemical properties of sea spray aerosol (SSA) must be under-pinned by a physically and chemically accurate representation of the bubble-mediated production of nascent SSA particles. Bubble bursting is sensitive to the physico-chemical properties of seawater. For a sample of seawater, any important differences in the SSA production mechanism are projected into the composition of the aerosol particles produced. Using direct chemical measurements of SSA at the single-particle level, this study presents an intercomparison of three laboratory-based, bubble-mediated SSA production schemes: gas forced through submerged sintered glass filters ("frits"), a pulsed plunging-waterfall apparatus, and breaking waves in a wave channel filled with natural seawater. The size-resolved chemical composition of SSA particles produced by breaking waves is more similar to particles produced by the plunging waterfall than those produced by sintered glass filters. Aerosol generated by disintegrating foam produced by sintered glass filters contained a larger fraction of organic-enriched particles and a different size-resolved elemental composition, especially in the 0.8–2 μm dry diameter range. Interestingly, chemical differences between the methods only emerged when the particles were chemically analyzed at the single-particle level as a function of size; averaging the elemental composition of all particles across all sizes masked the differences between the SSA samples. When dried, SSA generated by the sintered glass filters had the highest fraction of particles with spherical morphology compared to the more cubic structure expected for pure NaCl particles produced when the particle contains relatively little organic carbon. In addition to an intercomparison of three SSA production methods, the role of the episodic or "pulsed" nature of the waterfall method on SSA composition was under-taken. In organic-enriched seawater, the continuous operation of the plunging waterfall resulted in the accumulation of surface foam and an over-expression of organic matter in SSA particles compared to those produced by a pulsed plunging waterfall. Throughout this set of experiments, comparative differences in the SSA number size distribution were coincident with differences in aerosol particle composition, indicating that the production mechanism of SSA exerts important controls on both the physical and chemical properties of the resulting aerosol with respect to both the internal and external mixing state of particles. This study provides insight into the inextricable physicochemical differences between each of the bubble-mediated SSA generation mechanisms tested and the aerosol particles that they produce, and also serves as a guideline for future laboratory studies of SSA particles