Michael R. Cullen

Bio: Michael R. Cullen is an academic researcher. The author has contributed to research in topics: Boundary value problem & Engineering mathematics. The author has an hindex of 3, co-authored 3 publications receiving 1352 citations.

Advanced engineering mathematics

Abstract: Systems of Differential Equations Fourier Series and Boundary-Value Problems Numerical Analysis Complex Analysis. Zill's writing style has been highly praised by reviewers as easy-to-read, understandable and helpful to readers.

Differential Equations with Boundary-Value Problems

Abstract: This edition of the expanded version of Zill's "A First Course in Differential Equations with Modeling Applications", places greater emphasis on modelling and the use of technology in problem solving and features more everyday applications. Both Zill texts are identical through the first nine chapters, but this version includes six, additional chapters that provide in-depth coverage of boundary-value problem-solving and partial differential equations, subjects introduced in the first nine chapters. Understandable, step-by-step solutions are provided for every example.

Nonlinear energy harvesting.

Abstract: Ambient energy harvesting has been in recent years the recurring object of a number of research efforts aimed at providing an autonomous solution to the powering of small-scale electronic mobile devices. Among the different solutions, vibration energy harvesting has played a major role due to the almost universal presence of mechanical vibrations. Here we propose a new method based on the exploitation of the dynamical features of stochastic nonlinear oscillators. Such a method is shown to outperform standard linear oscillators and to overcome some of the most severe limitations of present approaches. We demonstrate the superior performances of this method by applying it to piezoelectric energy harvesting from ambient vibration.

A continuum theory for the flow of pedestrians

Abstract: The equations of motion governing the two-dimensional flow of pedestrians are derived for flows of both single and multiple pedestrian types. Two regimes of flow, a high-density (subcritical) and a low-density (supercritical) flow regimes, are possible, rather than two flow regimes for each type of pedestrian. A subcritical flow always fills the space available. However, a supercritical flow may either fill the space available or be self-confining for each type of pedestrian, depending on the boundary location. Although, the equations governing these flows are simultaneous, time-dependent, non-linear, partial differential equations, remarkably they may be made conformally mappable. The solution of these equations becomes trivial in many situations. Free streamline calculations, utilizing this property, reveal both upstream and downstream separation of the flow of pedestrians around an obstacle. Such analysis tells much about the nature of the assumptions used in various models for the flow of pedestrians. The present theory is designed for the development of general techniques to understand the motion of large crowds. However, it is also useful as a predictive tool. The behavior predicted by these equations of motion is compared with aerial observations for the Jamarat Bridge near Mecca, Saudi Arabia. It is shown that, for this important case, pedestrians, that is pilgrims, aim at achieving each immediate goal in minimum time rather than achieving all goals in overall minimum time. Typical of many examples, this case illustrated the strong dependence of path on the psychological state of the pedestrians involved. It is proposed that the flow of pedestrians over the Jamarat Bridge be improved by appropriate barrier placement, that force an effective global view of the goals.

A Biologist's Guide to Mathematical Modeling in Ecology and Evolution

Abstract: Scientists perform experiments and gather data to gain evidence for or against various hypotheses about how the world works. This sounds straightforward, but exactly how we use this data to make quantitative statements about various hypotheses requires a bit more care. In fact, there are two related, but philosophically distinct, approaches to scientific inference. To some extent these two approaches parallel the frequency interpretation and the subjective interpretation of probability. “Classical” statistical analysis is most closely allied with the frequency interpretation, whereas “Bayesian” analysis is allied with the subjective interpretation.

Hygroscopic growth and critical supersaturations for mixed aerosol particles of inorganic and organic compounds of atmospheric relevance

Abstract: The organic fraction of atmospheric aerosols contains a multitude of compounds and usually only a small fraction can be identified and quantified. However, a limited number of representative organic compounds can be used to describe the water-soluble organic fraction. In this work, initiated within the EU 5FP project SMOCC, four mixtures containing various amounts of inorganic salts (ammonium sulfate, ammonium nitrate, and sodium chloride) and three model organic compounds (levoglucosan, succinic acid and fulvic acid) were studied. The interaction between water vapor and aerosol particles was studied at different relative humidities: at subsaturation using a hygroscopic tandem differential mobility analyzer (H-TDMA) and at supersaturation using a cloud condensation nuclei spectrometer (CCN spectrometer). Surface tensions as a function of carbon concentrations were measured using a bubble tensiometer. Parameterizations of water activity as a function of molality, based on hygroscopic growth, are given for the pure organic compounds and for the mixtures, indicating van't Hoff factors around 1 for the organics. The Zdanovskii-Stokes-Robinson (ZSR) mixing rule was tested on the hygroscopic growth of the mixtures and it was found to adequately explain the hygroscopic growth for 3 out of 4 mixtures, when the limited solubility of succinic acid is taken into account. One mixture containing sodium chloride was studied and showed a pronounced deviation from the ZSR mixing rule. Critical supersaturations calculated using the parameterizations of water activity and the measured surface tensions were compared with those determined experimentally.