Gilbert Field House research collection, 1823, 1966, 1968, n.d.

In 1968 the National Historic Sites, Dept. of Indian Affairs and Northern Development undertook to learn more about its recent acquisition, the Gilbert Field House. The house is located in Niagara-on-the-Lake, Ont. along the Niagara Parkway, on what was part of the original land grant to Gilbert Field, a United Empire Loyalist. The house and contents were severely damaged during the War of 1812. After the war Gilbert’s widow, Eleanor, submitted claims for war losses.

The application of Raman and anti-stokes Raman spectroscopy for in situ monitoring of structural changes in laser irradiated titanium dioxide materials

The use of Raman and anti-stokes Raman spectroscopy to investigate the effect of exposure to high power laser radiation on the crystalline phases of TiO₂ has been investigated. Measurement of the changes, over several time integrals, in the Raman and anti-stokes Raman of TiO₂ spectra with exposure to laser radiation is reported. Raman and anti-stokes Raman provide detail on both the structure and the kinetic process of changes in crystalline phases in the titania material. The effect of laser exposure resulted in the generation of increasing amounts of the rutile crystalline phase from the anatase crystalline phase during exposure. The Raman spectra displayed bands at 144 cm^-1 (A1g), 197 cm^-1 (Eg), 398 cm^-1 (B1g), 515 cm^-1 (A1g), and 640 cm^-1 (Eg) assigned to anatase which were replaced by bands at 143 cm^-1 (B1g), 235 cm^-1 (2 phonon process), 448 cm^-1 (Eg) and 612 cm^-1 (A1g) which were assigned to rutile. This indicated that laser irradiation of TiO₂ changes the crystalline phase from anatase to rutile. Raman and anti-stokes Raman are highly sensitive to the crystalline forms of TiO₂ and allow characterisation of the effect of laser irradiation upon TiO₂. This technique would also be applicable as an in situ method for monitoring changes during the laser irradiation process

Accurate series solutions for gravity-driven Stokes waves

In the past, high order series expansion techniques have been used to study the nonlinear equations that govern the form of periodic Stokes waves moving steadily on the surface of an inviscid fluid. In the present study, two such series solutions are recomputed using exact arithmetic, eliminating any loss of accuracy due to accumulation of round-off error, allowing a much greater number of terms to be found with confidence. It is shown that higher order behaviour of series generated by the solution casts doubt over arguments that rely on estimating the series’ radius of convergence. Further, the exact nature of the series is used to shed light on the unusual nature of convergence of higher order Pade approximants near the highest wave. Finally, it is concluded that, provided exact values are used in the series, these Pade approximants prove very effective in successfully predicting three turning points in both the dispersion relation and the total energy.

Exponential asymptotics with multiple stokes lines

When asymptotic series methods are applied in order to solve problems that arise in applied mathematics in the limit that some parameter becomes small, they are unable to demonstrate behaviour that occurs on a scale that is exponentially small compared to the algebraic terms of the asymptotic series. There are many examples of physical systems where behaviour on this scale has important effects and, as such, a range of techniques known as exponential asymptotic techniques were developed that may be used to examinine behaviour on this exponentially small scale. Many problems in applied mathematics may be represented by behaviour within the complex plane, which may subsequently be examined using asymptotic methods. These problems frequently demonstrate behaviour known as Stokes phenomenon, which involves the rapid switches of behaviour on an exponentially small scale in the neighbourhood of some curve known as a Stokes line. Exponential asymptotic techniques have been applied in order to obtain an expression for this exponentially small switching behaviour in the solutions to orginary and partial differential equations. The problem of potential flow over a submerged obstacle has been previously considered in this manner by Chapman & Vanden-Broeck (2006). By representing the problem in the complex plane and applying an exponential asymptotic technique, they were able to detect the switching, and subsequent behaviour, of exponentially small waves on the free surface of the flow in the limit of small Froude number, specifically considering the case of flow over a step with one Stokes line present in the complex plane. We consider an extension of this work to flow configurations with multiple Stokes lines, such as flow over an inclined step, or flow over a bump or trench. The resultant expressions are analysed, and demonstrate interesting implications, such as the presence of exponentially sub-subdominant intermediate waves and the possibility of trapped surface waves for flow over a bump or trench. We then consider the effect of multiple Stokes lines in higher order equations, particu- larly investigating the behaviour of higher-order Stokes lines in the solutions to partial differential equations. These higher-order Stokes lines switch off the ordinary Stokes lines themselves, adding a layer of complexity to the overall Stokes structure of the solution. Specifically, we consider the different approaches taken by Howls et al. (2004) and Chap- man & Mortimer (2005) in applying exponential asymptotic techniques to determine the higher-order Stokes phenomenon behaviour in the solution to a particular partial differ- ential equation.

Peter Alwast talks to Grant Stevens

This interview was published in the catalogue for Peter Alwast's solo exhibition, "Future Perfect", at the Institute of Modern Art, Brisbane, in August 2011.

Numerical methods of the variable-order Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative

Rayleigh–Stokes problems have in recent years received much attention due to their importance in physics. In this article, we focus on the variable-order Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative. Implicit and explicit numerical methods are developed to solve the problem. The convergence, stability of the numerical methods and solvability of the implicit numerical method are discussed via Fourier analysis. Moreover, a numerical example is given and the results support the effectiveness of the theoretical analysis.