An efficient evolutionary multi-objective framework for MEMS design optimisation: validation, comparison and analysis

The application of multi objective evolutionary algorithms (MOEA) in the design optimisation of microelectromechanical systems (MEMS) is of particular interest in this research. MOEA is a class of soft computing techniques of biologically inspired stochastic algorithms, which have proved to outperform their conventional counterparts in many design optimisation tasks. MEMS designers can utilise a variety of multi-disciplinary design tools that explore a complex design search space, however, still follow the traditional trial and error approaches. The paper proposes a novel framework, which couples both modelling and analysis tools to the most referenced MOEAs (NSGA-II and MOGA-II). The framework is validated and evaluated through a number of case studies of increasing complexity. The research presented in this paper unprecedentedly attempts to compare the performances of the mentioned algorithms in the application domain. The comparative study shows significant insights into the behaviour of both of the algorithms in the design optimisation of MEMS. The paper provides extended discussions and analysis of the results showing, overall, that MOGA-II outperforms NSGA-II, for the selected case studies.     

Classification of three-dimensional quadratic diffeomorphisms with constant Jacobian

The 3-D quadratic diffeomorphism is defined as a map with a constant Jacobian. A few such examples are well known. In this paper, all possible forms of the 3-D quadratic diffeomorphisms are determined. Some numerical results are also given and discussed.      

Hyperbolification of dynamical systems: The case of continuous-time systems

We present a new method to generate chaotic hyperbolic systems. The method is based on the knowledge of a chaotic hyperbolic system and the use of a synchronization technique. This procedure is called hyperbolification of dynamical systems. The aim of this process is to create or enhance the hyperbolicity of a dynamical system. In other words, hyperbolification of dynamical systems produces chaotic hyperbolic (structurally stable) behaviors in a system that would not otherwise be hyperbolic. The method of hyperbolification can be outlined as follows. We consider a known n-dimensional hyperbolic chaotic system as a drive system and another n-dimensional system as the response system plus a feedback control function to be determined in accordance with a specific synchronization criterion. We then consider the error system and apply a synchronization method, and find sufficient conditions for the errors to converge to zero and hence the synchronization between the two systems to be established. This means that we construct a 2n-dimensional continuous-time system that displays a robust hyperbolic chaotic attractor. An illustrative example is given to show the effectiveness of the proposed hyperbolification method.     

Effect of varying pore size of AAO films on refractive index and birefringence measured by prism coupling technique

Anodic aluminum oxide (AAO) films with different pore sizes were prepared to modulate the effective refractive index and birefringence. To investigate the relationship between the refractive index and the pore size of the AAO film, optical constants were obtained using a prism coupler with various lasers. With experimental results, the dispersion curve of alumina itself without pores was extracted using a theoretical anisotropic model. We demonstrated that AAO films could offer a wide range of refractive index and birefringence values for optical device applications. Furthermore, index profiles as a function of the thickness of the AAO films were obtained by inverse Wentzel-Kramer-Brillouin approximation to examine the optical homogeneity.     

Gallium-nitride-based plasmonic multilayer operating at 1.55 μm

In this Letter, we have designed and fabricated a III-V semiconductor multilayer based on surface plasmon resonance (SPR) operating at the telecom wavelength. Optimization of the optogeometrical parameters and the metal/semiconductor layers required for this novel structure was conducted accurately by theoretical tools using the Maxwell equations. Technological fabrication of the device and its experimental characterizations using an evanescent coupling configuration was performed: the results have confirmed the existence of SPR associated to a sharp width response. This study could be a first step in the design of new plasmonic-semiconductor-based optical devices such as modulators and switches.     

Laser smoothing of sub-micron grooves in hydroxyl-rich fused silica

Nano- to micrometer-sized surface defects on UV-grade fused silica surfaces are known to be effectively smoothed through the use of high-temperature localized CO₂ laser heating, thereby enhancing optical properties. However, the details of the mass transport and the effect of hydroxyl content on the laser smoothing of defective silica at sub-micron length scales are still not completely understood. In this study, we examine the morphological evolution of sub-micron, dry-etched periodic surface structures on type II and type III SiO₂ substrates under 10.6 μm CO₂ laser irradiation using atomic force microscopy (AFM). In situ thermal imaging was used to map the transient temperature field across the heated region, allowing assessment of the T-dependent mass transport mechanisms under different laser-heating conditions. Computational fluid dynamics simulations correlated well with experimental results, and showed that for large effective capillary numbers (N_c > 2), surface diffusion is negligible and smoothing is dictated by capillary action, despite the relatively small spatial scales studied here. Extracted viscosity values over 1700-2000 K were higher than the predicted bulk values, but were consistent with the surface depletion of OH groups, which was confirmed using confocal Raman microscopy.     

Laser-based dynamic evaporation and surface shaping of fused silica with assist gases: a path to rimless laser machining

Evaporation and ablation are fundamental processes which drive laser-material processing performance. In applications where surface shape is important, control of the temperature field and the resulting spatially varying material response must be considered. For that purpose, assist gases are useful in, first, lowering treatment temperatures and, second, in changing interfacial and bulk chemistry to limit capillary-driven flow. Additionally, laser-matter coupling is influenced by pulse length as it determines the heat affected zone. Using infrared imaging of CO₂ laser-heated fused silica and surface profile measurements, we derive temperature and time dependent pitting rates along with shapes for a range of gases that include hydrogen, nitrogen, air, and helium. In the range of 1,500–4,500 K, evaporation, flow, and densification are shown to contribute to the pit shape. Analysis reveals a strong and complex dependence of rim formation on heating time and gas chemistry, mostly by lowering treatment temperature. Under dynamic heating, chemicapillarity appears to help in lowering rim height, in spite of the reactants mass transport limitations. Results on this gas-assisted approach suggest the possibility for sub-nanometer “rimless” laser-based machining.     

The effect of modulating a parameter in the logistic map

The effect of using the output of one logistic map to modulate the accessible parameter of a second logistic map is examined. Rigorous analytical results provide some predictions on the effect of this type of modulation, and those effects are tested numerically.     

About the boundedness of 3-D continuous-time quadratic systems

In this paper, we generalize all the existing results in the current literature for the upper bound of a general 3-D quadratic continuous-time system. In particular, we find large regions in the bifurcation parameter space of this system where it is bounded.