David Corcoran

Automated mirror design using an evolution strategy

We describe how an evolution strategy is used to automate the design of luminaire reflectors. In particular, we outline a computer simulation, consisting of a 2-D optical reflector with point light source, which is implemented for this purpose. The reflector shape is modeled using a Bezier curve representation, and photometric distributions are calculated in the near, middle and far fields using a ray-tracing approach. The automation of the design process is achieved through the use of a novel evolution strategy, termed differential evolution. For the effective operation of differential evolution, a merit function specific to luminaire reflector design is presented. Finally, we describe our investigation into the validity of the evolution strategy approach to reflector design. Based on our results, we propose that the technique is not only valid but also feasible.

Pattern formation induced by an electric field in a polymer-air-polymer thin film system†

Strong electric fields produce forces that can overcome the surface tension in thin liquid polymer films and in this way induce an instability of the free surface of the film, that triggers the formation of structures on a micrometer length scale. Here, we study experimentally a polymer–air–polymer system for several combinations of polymer films. These results are accompanied by theoretical considerations based on coupled long-wave time evolution equations for the two free surface profiles. The linear stability and nonlinear time evolution are investigated and compared to the experimental findings. The prediction that the instability always evolves through a mirror mode that couples the two surfaces in an anti-phase manner agrees well with the experimental results. The model describes well the linear (early stage) evolution of the instability. In the non-linear (later stage) evolution, topographical differences in the instability pattern occur if the mobilities of the two layers significantly differ and an unpredicted acceleration of growth is seen in thinner less mobile films. Possible reasons for the mismatch are discussed.

Stability of Ultrathin Nanocomposite Polymer Films Controlled by the Embedding of Gold Nanoparticles

Thin and ultrathin polymer films combined with nanoparticles (NPs) are of significant interest as they are used in a host of industrial applications. In this paper we describe the stability of such films (hpoly ≤ 30 nm) to dewetting, specifically, how the development of a spinodal instability in a composite NP-polymer layer is controlled by the embedding of Au NPs. At working temperatures (T = 170 °C) above the polymer glass transition temperature (Tg ≈ 100 °C) the absence of Au NPs leads to film rupture by nucleation dewetting, while their presence over a large surface area enhances the development of a spinodal instability without destroying the film continuity. When the NPs embed, the surface undulations are suppressed. The dynamics change from an unstable to a stable state, and the thin composite NP-polymer layer returns to a flat configuration, while the wavelength of the pattern remains constant. Moreover, we demonstrate from a thermodynamic perspective that NPs will remain on the surface or embed in the polymer film depending on their free energy, which is determined by the NP interactions with the underlying polymer, the native SiOx layer, and the Si substrate.

Effect of Au nanoparticle spatial distribution on the stability of thin polymer films.

The stability of thin poly(methyl-methacrylate) (PMMA) films of low molecular weight on a solid substrate is controlled by the areal coverage of gold nanoparticles (NPs) present at the air-polymer interface. As the polymer becomes liquid the Au NPs are free to diffuse, coalesce, and aggregate while the polymer film can change its morphology through viscous flow. These processes lead at the same time to the formation of a fractal network of Au NPs and to the development of spinodal instabilities of the free surface of the polymer films. For thinner films a single wavelength is observed, while for thicker films two wavelengths compete. With continued heating the aggregation process results in a decrease in coverage, the networks evolve into disordered particle assemblies, while the polymer films flatten again. The disordering occurs first on the smallest scales and coincides (in thicker films) with the disappearance of the smaller wavelength. The subsequent disordering on larger scales causes the films to flatten.

The stability of thin polymer films as controlled by changes in uniformly sputtered gold

The stability of polystyrene thin films of low molecular weight on a solid substrate is shown to be controlled by the presence of uniformly distributed gold sputtered at the air–polymer interface. Continuous gold coverage causes the formation of wrinkles. High coverage and Au nanoparticle (NP) density leads to the development of a spinodal instability while low coverage and NP density retards the nucleation dewetting mechanism that beads up the thin polymer film into drops when no coverage is present. Heating at temperature larger than the polymer glass transition temperature for extended periods allows the gold NPs to coalesce and rearrange. The area of polymer surface covered by NPs decreases as a result and this drives the films from unstable to metastable states. When the gold NPs are interconnected by polymer chains a theoretically predicted spinodal instability that patterns the film surface is experimentally observed. Suppression of the instability and a return to a flat film occurs when the polymer interconnections between particles are broken. While the polymer films maintain their physical continuity changes in their chemical surface composition and thickness are observed. The observed film metastability is nevertheless in agreement with theoretical prediction that includes these surface changes.

Automated mirror design for an extended light source

A computer package, Automated Mirror Design, has been developed by us to automate the design of luminaire reflectors. In this paper, new improvements to the algorithm for Automated Mirror Design are presented. We have previously reported a study on a series of point-light source luminaire problems. We now report on the operation of Automated Mirror Design for non-trivial light sources. In particular, reflector designs are presented for an extended light source, which produce limited Lambertian output and return no radiation to the source. Finally, the operation of differential evolution relies on the use of an appropriate merit function to determine the quality of proposed mirror designs. Merit function specific to the Lambertian output design problem are discussed.

The Onset to Criticality in a Sheared Granular Medium

Abstract. We have studied the temporal behaviour of an externally sheared granular medium in the transition from “mixed sliding and stick-slip” to “stick-slip” motion. These dynamic phases are morphologically distinct and are defined by the angular scale velocities of the system. The regime of stick-slip motion appears to be associated with a 2 nd order rigidity phase transition, and the probability density distributions of slip event size are partial power laws with exponents that are robust to the changing scale velocities.

Molecular Dynamic Simulation of a Metal Crystal under Stress

We present a Molecular Dynamics study of stresses generated in a metal film (aluminum and copper) on a substrate. It is shown that the surface has limited influence on intrinsic stresses beyond a few atoms distance. Surface relaxation at an open surface was found to be consistent with accepted values for copper but the anomalous outward relaxation of the surface layers reported in some studies of aluminum was not recovered. Instead the surface layer relaxed inwards. The atomic structure surrounding a single vacancy in a crystal at temperatures from 100 to 300 K was also studied. A vacancy was found to occupy a volume less than an atomic volume; the contraction was just 0.95, which is considerably less than the previously‐predicted values.

Non-Imaging Optical Design Using Differential Evolution

The application of differential evolution to non-imaging optical design is explored here. The objective is to create a mirror shape which reflects light from a source to produce a desired light distribution in some target region. Differential evolution uses a cost measure to numerically determine the quality of a proposed solution against a desired solution and various cost measures specific to non-imaging optical design are examined. A reverse engineering strategy is used to test the design methodology for a point light source, which lends insight into the differential evolution approach, and validates it for two geometric classes of problems. In these the target distribution comes from either a parabolic mirror shape or an elliptical mirror shape. The methodology is also validated for an extended light source.