A collocation method for high frequency scattering by convex polygons

We consider the problem of scattering of a time-harmonic acoustic incident plane wave by a sound soft convex polygon. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the computational cost required to achieve a prescribed level of accuracy grows linearly with respect to the frequency of the incident wave. Recently Chandler–Wilde and Langdon proposed a novel Galerkin boundary element method for this problem for which, by incorporating the products of plane wave basis functions with piecewise polynomials supported on a graded mesh into the approximation space, they were able to demonstrate that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency. Here we propose a related collocation method, using the same approximation space, for which we demonstrate via numerical experiments a convergence rate identical to that achieved with the Galerkin scheme, but with a substantially reduced computational cost.

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains.

A benchmark method for global optimization problems in structure determination from powder diffraction data

Quasi-Newton-Raphson minimization and conjugate gradient minimization have been used to solve the crystal structures of famotidine form B and capsaicin from X-ray powder diffraction data and characterize the chi(2) agreement surfaces. One million quasi-Newton-Raphson minimizations found the famotidine global minimum with a frequency of ca 1 in 5000 and the capsaicin global minimum with a frequency of ca 1 in 10 000. These results, which are corroborated by conjugate gradient minimization, demonstrate the existence of numerous pathways from some of the highest points on these chi(2) agreement surfaces to the respective global minima, which are passable using only downhill moves. This important observation has significant ramifications for the development of improved structure determination algorithms.

Optimization of protoplast production in white lupin

The influence, was investigated, of abiotic parameters on the isolation of protoplasts from in vitro seedling cotyledons of white lupin. The protoplasts were found to be competent in withstanding a wide range of osmotic potentials of the enzyme medium, however, −2.25 MPa (0.5 M mannitol), resulted in the highest yield of protoplasts. The pH of the isolation medium also had a profound effect on protoplast production. Vacuum infiltration of the enzyme solution into the cotyledon tissue resulted in a progressive drop in the yield of protoplasts. The speed and duration of orbital agitation of the cotyledon tissue played a significant role in the release of protoplasts and a two step (stationary-gyratory) regime was found to be better than the gyratory-only system.

Optimization of electroless copper plating on polyethylene films modified by surface grafting of vinyl ether of monoethanolamine

Metallized plastics have recently received significant interest for their useful applications in electronic devices such as for integrated circuits, packaging, printed circuits and sensor applications. In this work the metallized films were developed by electroless copper plating of polyethylene films grafted with vinyl ether of monoethanoleamine. There are several techniques for metal deposition on surface of polymers such as evaporation, sputtering, electroless plating and electrolysis. In this work the metallized films were developed by electroless copper plating of polyethylene films grafted with vinyl ether of monoethanoleamine. Polyethylene films were subjected to gamma-radiation induced surface graft copolymerization with vinyl ether of monoethanolamine. Electroless copper plating was carried out effectively on the modified films. The catalytic processes for the electroless copper plating in the presence and the absence of SnCl2 sensitization were studied and the optimum activation conditions that give the highest plating rate were determined. The effect of grafting degree on the plating rate is studied. Electroless plating conditions (bath additives, pH and temperature) were optimized. Plating rate was determined gravimetrically and spectrophotometrically at different grafting degrees. The results reveal that plating rate is a function of degree of grafting and increases with increasing grafted vinyl ether of monoethanolamine onto polyethylene. It was found that pH 13 of electroless bath and plating temperature 40°C are the optimal conditions for the plating process. The increasing of grafting degree results in faster plating rate at the same pH and temperature. The surface morphology of the metallized films was investigated using scanning electron microscopy (SEM). The adhesion strength between the metallized layer and grafted polymer was studied using tensile machine. SEM photos and adhesion measurements clarified that uniform and adhered deposits were obtained under optimum conditions.

Search space pruning and global optimization of multiple gravity assist trajectories with deep space manoeuvres

This paper deals with the design of optimal multiple gravity assist trajectories with deep space manoeuvres. A pruning method which considers the sequential nature of the problem is presented. The method locates feasible vectors using local optimization and applies a clustering algorithm to find reduced bounding boxes which can be used in a subsequent optimization step. Since multiple local minima remain within the pruned search space, the use of a global optimization method, such as Differential Evolution, is suggested for finding solutions which are likely to be close to the global optimum. Two case studies are presented.

RBF equalizer design using directional evolutionary multi-objective optimization

Whilst radial basis function (RBF) equalizers have been employed to combat the linear and nonlinear distortions in modern communication systems, most of them do not take into account the equalizer's generalization capability. In this paper, it is firstly proposed that the. model's generalization capability can be improved by treating the modelling problem as a multi-objective optimization (MOO) problem, with each objective based on one of several training sets. Then, as a modelling application, a new RBF equalizer learning scheme is introduced based on the directional evolutionary MOO (EMOO). Directional EMOO improves the computational efficiency of conventional EMOO, which has been widely applied in solving MOO problems, by explicitly making use of the directional information. Computer simulation demonstrates that the new scheme can be used to derive RBF equalizers with good performance not only on explaining the training samples but on predicting the unseen samples.

Optimization algorithms in FMRF model-based segmentation for LIDAR data and co-registered bands

In this paper, a fuzzy Markov random field (FMRF) model is used to segment land-objects into free, grass, building, and road regions by fusing remotely, sensed LIDAR data and co-registered color bands, i.e. scanned aerial color (RGB) photo and near infra-red (NIR) photo. An FMRF model is defined as a Markov random field (MRF) model in a fuzzy domain. Three optimization algorithms in the FMRF model, i.e. Lagrange multiplier (LM), iterated conditional mode (ICM), and simulated annealing (SA), are compared with respect to the computational cost and segmentation accuracy. The results have shown that the FMRF model-based ICM algorithm balances the computational cost and segmentation accuracy in land-cover segmentation from LIDAR data and co-registered bands.

A new blind equalization algorithm based on convex combination

The convex combination is a mathematic approach to keep the advantages of its component algorithms for better performance. In this paper, we employ convex combination in the blind equalization to achieve better blind equalization. By combining the blind constant modulus algorithm (CMA) and decision directed algorithm, the combinative blind equalization (CBE) algorithm can retain the advantages from both. Furthermore, the convergence speed of the CBE algorithm is faster than both of its component equalizers. Simulation results are also given to verify the proposed algorithm.