Exploration of the ultimate patterning potential achievable with high resolution focused ion beams

Controlled and reproducible fabrication of nano-structured materials will be one of the main industrial challenges in the next few years. We have recently proposed exploitation of the nano-structuring potential of a high resolution Focused Ion Beam Tool, to overcome basic limitations of current nano-fabrication techniques. The aim of this article is to present some new routes for material patterning, which benefit from ion-induced local property modifications or damage. In the experiments we describe hereafter an ultra-sharp pencil of 30 keV gallium ions is used to tailor the characteristics of several materials at a scale of a few nanometres. The experimental results are then compared to simulations. First, we simulate the control of collisional defects generated in a thin magnetic layer under FIB irradiation. The results explain the stable magnetic structures we have obtained experimentally. This was achieved with a low surface ion dose (10¹² to 10¹⁴ ions/cm²). In addition we have explored the promising direction of Bottom-up or self-organization processes using a FIB instrument. We have defined artificial surface defects. These defects created by the impact of an 8-nm FWHM probe were used to pin the diffusion and to organize nanometre-sized gold clusters on a graphite surface. PACS 79.20.Rf; 81.07.-b     

Structural and magnetic properties of FIB-irradiated microstructures on a Pt/Co multilayer

We present a study of the structural and magnetic effects induced by focused 30 keV Ga⁺ ion beam irradiation on a Pt(2.8 nm)/[Pt(0.6 nm)/Co(0.3 nm)]₆/Pt(6.5 nm) ferromagnetic multilayer, using transmission electron microscopy, optical and magneto-optical microscopy. The work is of relevance to high-density data-storage applications, where media planarity is crucial for device reliability.     

Dynamic algorithm selection for pareto optimal set approximation

This paper presents a meta-algorithm for approximating the Pareto optimal set of costly black-box multiobjective optimization problems given a limited number of objective function evaluations. The key idea is to switch among different algorithms during the optimization search based on the predicted performance of each algorithm at the time. Algorithm performance is modeled using a machine learning technique based on the available information. The predicted best algorithm is then selected to run for a limited number of evaluations. The proposed approach is tested on several benchmark problems and the results are compared against those obtained using any one of the candidate algorithms alone.     

Explicit Solutions of Quadratic FBSDEs Arising From Quadratic Term Structure Models

We provide explicit solutions of certain forward-backward stochastic differential equations (FBSDEs) with quadratic growth. These particular FBSDEs are associated with quadratic term structure models of interest rates and characterize the zero-coupon bond price. The results of this paper are naturally related to similar results on affine term structure models of Hyndman (Math. Financ. Econ. 2(2):107–128, 2009) due to the relationship between quadratic functionals of Gaussian processes and linear functionals of affine processes. Similar to the affine case a sufficient condition for the explicit solutions to hold is the solvability in a fixed interval of Riccati-type ordinary differential equations. However, in contrast to the affine case, these Riccati equations are easily associated with those occurring in linear-quadratic control problems. We also consider quadratic models for a risky asset price and characterize the futures price and forward price of the asset in terms of similar FBSDEs. An example is considered, using an approach based on stochastic flows that is related to the FBSDE approach, to further emphasize the parallels between the affine and quadratic models. An appendix discusses solvability and explicit solutions of the Riccati equations.     

Covers of some varietal products

Received November 3, 1995; accepted in final form September 9, 1996.     

Estimating and Visualizing Conditional Densities

Abstract

We consider the kernel estimator of conditional density and derive its asymptotic bias, variance, and mean-square error. Optimal bandwidths (with respect to integrated mean-square error) are found and it is shown that the convergence rate of the density estimator is order n ^–2/3. We also note that the conditional mean function obtained from the estimator is equivalent to a kernel smoother. Given the undesirable bias properties of kernel smoothers, we seek a modified conditional density estimator that has mean equivalent to some other nonparametric regression smoother with better bias properties. It is also shown that our modified estimator has smaller mean square error than the standard estimator in some commonly occurring situations. Finally, three graphical methods for visualizing conditional density estimators are discussed and applied to a data set consisting of maximum daily temperatures in Melbourne, Australia.     

k-ary monoids of term operations

Communicated by Norman R. Reilly     

Interval Dismantlable Lattices

A finite lattice is interval dismantlable if it can be partitioned into an ideal and a filter, each of which can be partitioned into an ideal and a filter, etc., until you reach 1-element lattices. In this note, we find a quasi-equational basis for the pseudoquasivariety of interval dismantlable lattices, and show that there are infinitely many minimal interval non-dismantlable lattices.     

Surface acoustic wave studies of subsurface damage

We have measured the attenuation of surface acoustic waves on polished substrates and correlated the frequency-dependent attenuation with sub-surface damage. The damage was produced in single crystal lithium niobate samples by lapping and polishing with commercially available diamond compound. Surface acoustic wave attenuation on these samples was measured from 100 MHz to 1.5 GHz using interdigital transducers, thus covering depths ranging from 35 μm to 2 μm below the lithium niobate surface