Tunable remote pinning of domain walls in magnetic nanowires

Domain wall (DW) pinning in ferromagnetic nanowires is in general a complex process. Distortions of the DW shape make quantitative agreement between modeling and experiment difficult. Here we demonstrate pinning using nanometer scale localized stray fields. This type of interaction gives well-characterized, tailorable potential landscapes that do not appreciably distort the DW. Our experimental results are in excellent quantitative agreement with an Arrhenius-Néel model of depinning--a result only possible when the modeled potential profile agrees fully with that experienced by the DW.     

LP models for pricing diffuse nitrate discharge permits

Nitrate discharges from diffuse agricultural sources significantly contribute to groundwater and surface water pollution. Tradable permit programs have been proposed as a means of controlling nitrate emissions efficiently, but trading is complicated by the dispersed and delayed effects of the diffuse pollution. Hence, markets in nitrate discharge permits should be carefully designed to account for the underlying spatial and temporal interactions. Nitrate permit markets can be designed similar to the modern electricity markets which use LPs to find the equilibrium prices because the two trading problems have close analogy. In this paper, we propose alternative LP models to find efficient permit prices for year-ahead markets. The model structure varies depending on the catchment hydro-geology and long-term goals of the community. We show how the market price structures are driven by the constraint structure under different environmental conditions. We discuss the physical and economic conditions required to assure consistent prices, the modeling of essential and optional constraints in an LP, and the problem of balancing resource allocation over time among delayed-response discharge units. We then extend the LP model to balance resource allocation over time and to improve the market performance.     

Operator algebras with contractive approximate identities: Weak compactness and the spectrum

We continue our study of operator algebras with contractive approximate identities (cais) by presenting a couple of interesting examples of operator algebras with cais, which in particular answer questions raised in previous papers in this series, for example about whether, roughly speaking, ‘weak compactness’ of an operator algebra, or the lack of it, can be seen in the spectra of its elements.     

Scanning moiré at high magnification using optical methods

Methods of employing scanning moiré at high magnification are developed and demonstrated. Modern lithographic techniques for producing custom moiré gratings with a frequency up to 250l/mm are described. On a probing station equipped with a video system, pseudo-color moiré fringes are produced using the scannning lines of the color charge-coupled-device (CCD) camera. Fringe multiplication from 1 to 5 is possible with correct combinations of magnification and grating pitch. An analysis is given to show that strain sensitivity depends only on the number of scanning lines used to record the image. The grating pitch and the magnification are important because they reduce the gage length of the strain measurement. The high-magnification scanning moiré was used to study plastic- strain fields in an aluminum tensile specimen. Local disturbances in the strain field were observed at 2 to 2.5 percent applied strain. These discontinuities became more significant at higher levels of applied strain.     

Series solutions for steady unsaturated flow in irregular porous domains

For the most part, analytical solutions for steady unsaturated infiltration have been restricted to infinite and semi-infinite seepage geometries, using the quasi-linear approximation for the hydraulic conductivity. We provide analytical series methods to solve the steady quasi-linear flow equations, in finite irregular seepage geometries. Unlike the classical approach, the series method has been modified, to cater for arbitrary boundary geometry and surface recharge distributions. The matrix flux potential and the stream function both satisfy the same governing partial differential equation, and the stream function formulation is used to estimate the series coefficients. For a finite vadose zone, the stream function solution does not uniquely determine the matrix flux potential, when flux boundary conditions are used. Consequently, the stream function solution applies to a range of moisture distributions, for given infiltration and evapotranspiration rates through the surface.     

On the quest for positivity in operator algebras

We show that in every nonzero operator algebra with a contractive approximate identity (or c.a.i.), there is a nonzero operator T such that ‖I−T‖?1. In fact, there is a c.a.i. consisting of operators T with ‖I−2T‖?1. So, the numerical range of the elements of our contractive approximate identity is contained in the closed disk center and radius . This is the necessarily weakened form of the result for C^?-algebras, where there is always a contractive approximate identity consisting of operators with 0?T?1 - the numerical range is contained in the real interval [0,1]. So, if an operator algebra has a c.a.i., it must have operators with a “certain amount” of positivity.     

Investigating the arenyl-diene double [3 + 2] photocycloaddition reaction

The double [3 + 2] photocycloaddition reaction involving arenyl-dienes has been used to assemble seven separate [5.5.5.5] fenestrane structures that include ether and aza variants. The primary photolysis step was a meta photocycloaddition reaction, while a secondary photocycloaddition step formed the fenestrane structure. Investigations involving the insertion of an additional methylene group into the basic arenyl-diene skeleton failed to afford the desired [5.5.5.6] fenestrane structure. The presence of an oxime moiety in the aromatic photosubstrate allowed the primary photolysis step to take place; however, an attempted secondary photocycloaddition reaction involving the oxime did not provide the intended polyheterocyclic fenestrane. An alternative strategy to form various "criss-cross" double meta photocycloadducts was investigated and led to the discovery of a Paterno-Büchi cycloaddition reaction between acetone and an angular meta photocycloadduct. Other novel thermally and photochemically mediated skeletal rearrangement reactions were also recorded.     

Electron resonances in VLEED from Cu(111)

The sensitivity of the VLEED I–V curves to the shape and the position of the barrier is shown for the image- type surface barriers. For demonstration and comparison with experimental data the intensities of specularly reflected electron beams from Cu(111) are computed by dynamical theory of electron diffraction. Image plane position changes and modifications of the saturation shape of the surface barrier induce pronounced changes in the I–V curves calculated with the image-type barrier. Presented at the X-th Symposium on Suface Physics, Prague, Czech Republic, July 11–15, 2005.