### Publications

Aaen PH, Wood J, Bridges D, Zhang L, Johnson E, Pla JA, Barbieri T, Snowden CM, Everett JP, Kearney MJ (2012) Multiphysics modeling of RF and microwave high-power transistors,IEEE Transactions on Microwave Theory and Techniques60(12)pp. 4013-4023 In this paper, we present a multiphysics approach for the simulation of high-power RF and microwave transistors, in which electromagnetic, thermal, and nonlinear transistor models are linked together within a harmonic-balance circuit simulator. This approach is used to analyze a laterally diffused metal-oxide-semiconductor (LDMOS) transistor that has a total gate width of 102 mm and operates at 2.14 GHz. The transistor die is placed in a metal-ceramic package, with bond-wire arrays connecting the die to the package leads. The effects of three different gate bond-pad layouts on the transistor efficiency are studied. Through plots of the spatial distributions of the drain efficiency and the time-domain currents and voltages across the die, we reveal for the first time unique interactions between the electromagnetic effects of the layout and the microwave behavior of the large-die LDMOS power field-effect transistor. © 1963-2012 IEEE.

Martin RJ, Kearney MJ (2015) INTEGRAL REPRESENTATION OF CERTAIN COMBINATORIAL RECURRENCES, COMBINATORICA35(3)pp. 309-315 SPRINGER HEIDELBERG

With the ever-increasing focus on obtaining higher device power conversion efficiencies (PCEs) for organic photovoltaics (OPV), there is a need to ensure samples are measured accurately. Reproducible results are required to compare data across different research institutions and countries and translate these improvements to real-world production. In order to report accurate results, and additionally find the best-practice methodology for obtaining and reporting these, we show that careful analysis of large data sets can identify the best fabrication methodology. We demonstrate which OPV outputs are most affected by different fabrication or measurement methods, and identify that masking effects can result in artificially-boosted PCEs by increasing fill factor and current densities, requiring care when selecting which mask to use. For example, our best performing devices (>6% efficiency) show that the smallest mask areas have not produced a surfeit of the highest performers, with only 11% of the top performing devices measured using a 0.032 cm2 mask area, while 44% used the largest mask (0.64 cm2). This trend holds true for efficiencies going down to 5%, showing that effective fabrication conditions are reproducible with increasing mask areas, and can be translated to even larger device areas. Finally, we emphasise the necessity for reporting the best PCE along with the average value in order to implement changes in real-world production. © 2014 Elsevier B.V.

We consider a self-convolutive recurrence whose solution is the sequence
of coefficients in the asymptotic expansion of the logarithmic derivative
of the confluent hypergeometic function U(a, b, z). By application of the
Hilbert transform we convert this expression into an explicit, non-recursive
solution in which the nth coefficient is expressed as the (n ? 1)th moment of
a measure, and also as the trace of the (n ? 1)th iterate of a linear operator.
Applications of these sequences, and hence of the explicit solution provided,
are found in quantum field theory as the number of Feynman diagrams of a
certain type and order, in Brownian motion theory, and in combinatorics.

Pye AJ, Faux DA, Kearney MJ (2016) Thermoelectric effects in a rectangular Aharonov-Bohm geometry, JOURNAL OF APPLIED PHYSICS119(15)ARTN 154304 AMER INST PHYSICS

Martin RJ, Craster RV, Kearney MJ (2015) Infinite product expansion of the Fokker-Planck equation with steady-state solution, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES471(2179)ARTN 20150084 ROYAL SOC

A detailed study is undertaken of the v{max}=1 limit of the cellular automaton traffic model proposed by Nagel and Paczuski [Phys. Rev. E 51, 2909 (1995)]. The model allows one to analyze the behavior of a traffic jam initiated in an otherwise freely flowing stream of traffic. By mapping onto a discrete-time queueing system, itself related to various problems encountered in lattice combinatorics, exact results are presented in relation to the jam lifetime, the maximum jam length, and the jam mass (the space-time cluster size or integrated vehicle waiting time), both in terms of the critical and the off-critical behavior. This sets existing scaling results in their natural context and also provides several other interesting results in addition.

A new quasi-2-D model for laterally diffused metal-oxide-semiconductor radio-frequency power transistors is described in this paper. We model the intrinsic transistor as a series laterally diffused p-channel and n-type drift region network, where the regional boundary is treated as a reverse-biased p+-n diode. A single set of 1-D energy transport equations is solved across a 2-D cross section in a current-driven form, and specific device features are modeled without having to solve regional boundary node potentials using numerical iteration procedures within the model itself. This fast process-oriented nonlinear physical model is scalable over a wide range of device widths and accurately models direct-current and microwave characteristics. © 2006 IEEE.

© 2015 AIP Publishing LLC.Coherent, i.e., ballistic, thermoelectric transport in electron waveguide structures containing right-angle bends in single, double, and U-bend configurations is investigated. A theory based on Green's functions is used to derive the transmission function (and from that the transport coefficients) and allows for the inclusion of realistic models of spatially distributed imperfections. The results for the single and double-bend structures are presented in more detail than elsewhere in the literature. In the U-bend structure, sharp resonances in the stop-band region of the transmission function lead to large-magnitude peaks in the thermopower and consequently a large thermoelectric figure of merit (of order ten in some instances). These properties are still readily apparent even in the presence of moderate edge roughness or Anderson disorder.

A generalized two-component Pólya urn process, parameterized by a variable a , is studied in terms of the likelihood that due to fluctuations the initially smaller population in a scenario of competing population growth eventually becomes the larger, or is the larger after a certain passage of time. By casting the problem as an inhomogeneous directed random walk we quantify this role-reversal phenomenon through the first passage probability that equality in size is first reached at a given time, and the related exit probability that equality in size is reached no later than a given time. Using an embedding technique, exact results are obtained which complement existing results and provide new insights into behavioural changes (akin to phase transitions) which occur at defined values of a .

A random walk model is presented which exhibits a transition from standard to
anomalous diffusion as a parameter is varied. The model is a variant on the elephant
random walk and differs in respect of the treatment of the initial state, which in the
present work consists of a given number N of fixed steps. This also links the
elephant random walk to other types of history dependent random walk. As well as
being amenable to direct analysis, the model is shown to be asymptotically equivalent
to a non-linear urn process. This provides fresh insights into the limiting form of the
distribution of the walker?s position at large times. Although the distribution is
intrinsically non-Gaussian in the anomalous diffusion regime, it gradually reverts to
normal form when N is large under quite general conditions.

Motivated by recent studies of record statistics in relation to strongly correlated time series, we consider explicitly the drawdown time of a Lévy process, which is defined as the time since it last achieved its running maximum when observed over a fixed time period . We show that the density function of this drawdown time, in the case of a completely asymmetric jump process, may be factored as a function of t multiplied by a function of T ? t. This extends a known result for the case of pure Brownian motion. We state the factors explicitly for the cases of exponential down-jumps with drift, and for the downward inverse Gaussian Lévy process with drift.

The Fokker?Planck equation is a key ingredient of many models in physics, and related subjects, and arises in a diverse array of settings. Analytical solutions are limited to special cases, and resorting to numerical simulation is often the only route available; in high dimensions, or for parametric studies, this can become unwieldy. Using asymptotic techniques, that draw upon the known Ornstein?Uhlenbeck (OU) case, we consider a mean-reverting system and obtain its representation as a product of terms, representing short-term, long-term, and medium-term behaviour. A further reduction yields a simple explicit formula, both intuitive in terms of its physical origin and fast to evaluate. We illustrate a breadth of cases, some of which are 'far' from the OU model, such as double-well potentials, and even then, perhaps surprisingly, the approximation still gives very good results when compared with numerical simulations. Both one- and two-dimensional examples are considered.

The first-passage problem of the Ornstein-Uhlenbeck (OU) process to a boundary is a long-standing problem with no known closed-form solution except in specifc cases. Taking this as a starting-point, and extending to a general mean-reverting process, we investigate the long- and short-time asymptotics using a combination of Hopf-Cole and Laplace transform techniques. As a result we are able to give a single formula that is correct in both limits, as well as being exact in certain special cases. We demonstrate the results using a variety of other models.