Global and local optimization using radial basis function response surface models

The focus of this paper is the optimization of complex multi-parameter systems. We consider systems in which the objective function is not known explicitly, and can only be evaluated through computationally intensive numerical simulation or through costly physical experiments. The objective function may also contain many local extrema which may be of interest. Given objective function values at a scattered set of parameter values, we develop a response surface model that can dramatically reduce the required computation time for parameter optimization runs. The response surface model is developed using radial basis functions, producing a model whose objective function values match those of the original system at all sampled data points. Interpolation to any other point is easily accomplished and generates a model which represents the system over the entire parameter space. This paper presents the details of the use of radial basis functions to transform scattered data points, obtained from a complex continuum mechanics simulation of explosive materials, into a response surface model of a function over the given parameter space. Response surface methodology and radial basis functions are discussed in general and are applied to a global optimization problem for an explosive oil well penetrator.     

Photocarrier injection and the I-V characteristics of La0.8Sr0.2MnO3/SrTiO3:Nb heterojunctions

Oxide heterojunctions made of p-type La_0.8Sr_0.2MnO₃ (LSMO) and niobium-doped n-type SrTiO₃ (STO:Nb) have been fabricated by the pulsed laser deposition (PLD) technique and characterized under UV light irradiation by measuring the current-voltage, photovoltaic properties and the junction capacitance. It is shown that the heterojunctions work as an efficient UV photodiode, in which photogenerated holes in the STO:Nb substrate are injected to the LSMO film. The maximum surface hole density Q/e and external quantum efficiency γ are estimated to be 8.3×10¹² cm⁻² and 11% at room temperature, respectively. They are improved significantly in a p-i-n junction of LSMO/STO/STO:Nb, where Q/e and γ are 3.0×10¹³ cm⁻² and 27%, respectively.     

Magnetisation reversal in media with perpendicular anisotropy

In this paper, we discuss two key aspects of magnetisation reversal in magnetic thin films with perpendicular anisotropy. Firstly, a study has been made of the additional field required to erase data written perpendicular to a thin film recording disk as the linear data density is increased. It has been found that an increase in data density from 40 to 360 kfci results in an increase of 1.25 kOe in the field required to erase the data. Secondly, the effect of varying the level of exchange coupling by co-sputtering CoCrPt samples with SiO₂ has been studied using a characterisation technique that is independent of the self-demagnetising field. It has been found that the samples are fully exchange de-coupled when the film contains >9.8% SiO₂ and the activation volume of reversal remains constant for higher levels of SiO₂.     

Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory

In this paper the nonlinear wave equation $$u_u - u_{xx} + v(x)u(x,t) + \varepsilon u^3 (x,t) = 0$$ is studied. It is shown that for a large class of potentials,v(x), one can use KAM methods to construct periodic and quasi-periodic solutions (in time) for this equation.     

A Tensor product generalized ADI method for the method of planes

We consider solving separable, second order, linear elliptic prtial differential equations in three independent variables. If the partial differential opertor separates into two terms, one depending on x and y, and one depending on z, then we use the method of planes to obtain a discrete problem, which we write in tensor product from as We apply a new interative method, the tensor product generalized alternating direction implicit method, to solve the discrete problem. We study a specific implementation that uses Hermite bicubic collocation in the xy direction and symmetric finite differences in the z direction. We demostrate that this method is a fast and accurate way to solve the large linear systems arising from three-dimensional elliptic problems.     

Diels-Alder chemistry on alkene functionalized films

A substrate-independent method has been devised for ring formation at solid surfaces. This entails the aminolysis reaction of allylamine with maleic anhydride pulsed plasma polymer films to yield terminal alkene groups at the surface. Subsequent exposure to 1,3-cyclohexadiene leads to a Diels-Alder type (4 + 2) cycloaddition reaction to give a mixture of endo- and exo-bicyclo[2.2.2]oct-2-ene rings.     

Fluorescence detection and quantitation of recombinant proteins containing oligohistidine tag sequences directly in sodium dodecyl sulfate-polyacrylamide gels

Two fluorophore-nitrilotriacetic acid conjugates, Pro-Q Sapphire 365 and Pro-Q Sapphire 488 oligohistidine gel stains, have been developed for the fluorescence detection of fusion proteins containing oligohistidine tags directly in sodium dodecyl sulfate polyacrylamide gels, without the requirement for electroblotting, reporter enzymes or secondary detection reagents. Pro-Q Sapphire 365 oligohistidine gel stain exhibits bright-blue fluorescence (emission maximum = 450 nm) when illuminated with UV-A or UV-B light from a standard ultraviolet transilluminator. Pro-Q Sapphire 488 oligohistidine gel stain exhibits bright-green fluorescence (emission maximum = 515 nm) when illuminated with visible light from a laser-based gel scanner equipped with a 470 nm second-harmonic generation (SHG) or 488 nm argon-ion laser source. Typically, 25-65 ng of oligohistidine-tagged fusion protein in whole cell lysates is detectable using either stain. After documenting the fluorescence signal from the Pro-Q Sapphire dyes, gels may be post-stained with the red-fluorescent SYPRO Ruby protein gel stain in order to reveal the total protein pattern.     

Selenomethionine contents of NIST wheat reference materials

Values of the total selenium and selenomethionine (Semet) content of four wheat-based reference materials have been obtained by gas chromatography-stable isotope dilution mass spectrometry methods. The total Se method is an established one, and the results obtained with it are consistent with previously-assigned values. The Semet method (previously reported by our laboratory) is based on reaction with CNBr. Our data indicate that the four wheat samples (wheat gluten, durum wheat, hard red spring wheat, and soft winter wheat), though having a 30-fold range in total Se content, all have about 45% of their total Se values in the form of selenomethionine. Investigation of the CNBr-based method suggests that additional experiments are needed to verify that all selenomethionine in the wheat samples is accounted for, but also indicates that the values obtained are within 15% of the true values. As the form in which Se occurs in foods and dietary supplements is important from a nutritional perspective, adding information about Se speciation to total Se values in appropriate reference materials makes these materials more valuable in relevant analytical work.