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The area swept out under a one-dimensional Brownian motion till its first-passage time is analysed using a Fokker-Planck technique. We obtain an exact expression for the area distribution for the zero drift case, and provide various asymptotic results for the non-zero drift case, emphasising the critical nature of the behaviour in the limit of vanishing… (More)

- Michael J. Kearney
- Physical review. E, Statistical, nonlinear, and…
- 2006

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… (More)

- Michael J. Kearney, Peter Shiu
- Electr. J. Comb.
- 2002

Let s(N) denote the edge length of the smallest square in which one can pack N unit squares. A duality method is introduced to prove that s(6) = s(7) = 3. Let nr be the smallest integer n such that s(n + 1) ≤ n + 1/r. We use an explicit construction to show that nr ≤ 27r/2+O(r), and also that n2 ≤ 43.

An exact expression for the distribution of the area swept out by a drifted Brownian motion till its first-passage time is derived. A study of the asymptotic behaviour confirms earlier conjectures and clarifies their range of validity. The analysis leads to a simple closed-form solution for the moments of the Airy distribution. PACS numbers: 02.50.-r,… (More)

We derive , the joint probability density of the maximum ) , ( m t M P M and the time at which this maximum is achieved, for a class of constrained Brownian motions. In particular, we provide explicit results for excursions, meanders and reflected bridges associated with Brownian motion. By subsequently integrating over m t M , the marginal density is… (More)

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−… (More)

- Lynn J. Rozanski, Chris T. G. Smith, +7 authors Ravi de Silva
- 2014

A Critical look at Organic Photovoltaic Fabrication Methodology: Defining performance enhancement parameters relative to active area L.J. Rozanski, Chris T.G. Smith, Keyur K. Gandhi, Michail J. Beliatis, G. Dinesha M.R. Dabera, K.D.G. Imalka Jayawardena, A.A. Damitha T. Adikaari 1 , Michael J. Kearney and S. Ravi P. Silva* Advanced Technology Institute,… (More)

We consider the asymptotic expansion of the logarithmic derivative of the Airy function , and also its reciprocal ) ( Ai / ) ( i A z z ) ( i A / ) ( Ai z z , as z . In particular, we derive simple, closed-form solutions for the coefficients which appear in these expansions, of interest since they are encountered in a wide variety of problems. The… (More)

- Somenath Chakrabarty, Óscar J. C. Dias, +7 authors M Desaix
- 2016

Direct variational methods are used to find simple approximate solutions of the Thomas–Fermi equations describing the properties of self-gravitating radially symmetric stellar objects both in the non-relativistic and ultra-relativistic cases. The approximate solutions are compared and shown to be in good agreement with exact and numerically obtained… (More)

- A. A. Damitha, T. Adikaari, S. R. P. Silva, Michael J. Kearney, John M. Shannon
- 2005

Excimer laser crystallisation is used to fabricate nanocrystalline thin film silicon Schottky barrier solar cells, in a superstrate configuration with indium tin oxide as the front contact and chromium as the back contact. 150 nm thick intrinsic absorber layers are used for the solar cells, and was crystallised using an excimer laser with different laser… (More)