An adaptive non-raster scanning method in atomic force microscopy for simple sample shapes

It is a significant challenge to reduce the scanning time in atomic force microscopy while retaining imaging quality. In this paper, a novel non-raster scanning method for high-speed imaging is presented. The method proposed here is developed for a specimen with the simple shape of a cell. The image is obtained by scanning the boundary of the specimen at successively increasing heights, creating a set of contours. The scanning speed is increased by employing a combined prediction algorithm, using a weighted prediction from the contours scanned earlier, and from the currently scanned contour. In addition, an adaptive change in the height step after each contour scan is suggested. A rigorous simulation test bed recreates the x-y specimen stage dynamics and the cantilever height control dynamics, so that a detailed parametric comparison of the scanning algorithms is possible. The data from different scanning algorithms are compared after the application of an image interpolation algorithm (the Delaunay interpolation algorithm), which can also run on-line.We would like to acknowledge the support of the Engineering and Physical Sciences Research Council (EPSRC) (grant nos. EP/I034882/1 & EP/I034831/1)

Square Patterns and Quasi-patterns in Weakly Damped Faraday Waves

Pattern formation in parametric surface waves is studied in the limit of weak viscous dissipation. A set of quasi-potential equations (QPEs) is introduced that admits a closed representation in terms of surface variables alone. A multiscale expansion of the QPEs reveals the importance of triad resonant interactions, and the saturating effect of the driving force leading to a gradient amplitude equation. Minimization of the associated Lyapunov function yields standing wave patterns of square symmetry for capillary waves, and hexagonal patterns and a sequence of quasi-patterns for mixed capillary-gravity waves. Numerical integration of the QPEs reveals a quasi-pattern of eight-fold symmetry in the range of parameters predicted by the multiscale expansion.Comment: RevTeX, 11 pages, 8 figure

A Multi-mode Transverse Dynamic Force Microscope - Design, Identification and Control

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.The transverse dynamic force microscope (TDFM) and its shear force sensing principle permit true non-contact force detection in contrast to typical atomic force microscopes. The two TDFM measurement signals for the cantilever allow, in principle, two different scanning modes of which, in particular, the second presented here permits a full-scale non-contact scan. Previous research mainly focused on developing the sensing mechanism, whereas this work investigates the vertical axis dynamics for advanced robust closed-loop control. This paper presents a new TDFM digital control solution, built on field-programmable gate array (FPGA) equipment running at high implementation frequencies. The integrated control system allows the implementation of online customizable controllers, and raster-scans in two modes at very high detection bandwidth and nano-precision. Robust control algorithms are designed, implemented, and practically assessed. The two realized scanning modes are experimentally evaluated by imaging nano-spheres with known dimensions in wet conditions.Engineering and Physical Sciences Research Council (EPSRC

Nonlinear Competition Between Small and Large Hexagonal Patterns

Recent experiments by Kudrolli, Pier and Gollub on surface waves, parametrically excited by two-frequency forcing, show a transition from a small hexagonal standing wave pattern to a triangular ``superlattice'' pattern. We show that generically the hexagons and the superlattice wave patterns bifurcate simultaneously from the flat surface state as the forcing amplitude is increased, and that the experimentally-observed transition can be described by considering a low-dimensional bifurcation problem. A number of predictions come out of this general analysis.Comment: 4 pages, RevTex, revised, to appear in Phys. Rev. Let

Real-time sliding mode observer scheme for shear force estimation in a transverse dynamic force microscope

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this record.This paper describes a sliding mode observer scheme for estimation of the shear force affecting the cantilever in a Transverse Dynamic Force Microscope (TDFM). The vertically oriented cantilever is oscillated in proximity to the specimen under investigation. The amplitude of oscillation of the cantilever tip is affected by these shear forces. They are created by the ordered-water layer above the specimen. The oscillation amplitude is therefore a measure of distance between the tip and the surface of the specimen. Consequently, the estimation of the shear forces provides useful information about the specimen characteristics. For estimating the shear forces, an approximate finite dimensional model of the cantilever is created using the method of lines. This model is subsequently reduced for its model order. An unknown input sliding mode observer has been used to reconstruct the unknown shear forces using only tip position measurements and the cantilever excitation. This paper describes the development of the sliding mode scheme and presents experimental results from the TDFM set up at the Centre for Nanoscience and Quantum Information (NSQI) at Bristol University

Amplitude equations and pattern selection in Faraday waves

We present a systematic nonlinear theory of pattern selection for parametric surface waves (Faraday waves), not restricted to fluids of low viscosity. A standing wave amplitude equation is derived from the Navier-Stokes equations that is of gradient form. The associated Lyapunov function is calculated for different regular patterns to determine the selected pattern near threshold. For fluids of large viscosity, the selected wave pattern consists of parallel stripes. At lower viscosity, patterns of square symmetry are obtained in the capillary regime (large frequencies). At lower frequencies (the mixed gravity-capillary regime), a sequence of six-fold (hexagonal), eight-fold, ... patterns are predicted. The regions of stability of the various patterns are in quantitative agreement with recent experiments conducted in large aspect ratio systems.Comment: 12 pages, 1 figure, Revte

Parametrically Excited Surface Waves: Two-Frequency Forcing, Normal Form Symmetries, and Pattern Selection

Motivated by experimental observations of exotic standing wave patterns in the two-frequency Faraday experiment, we investigate the role of normal form symmetries in the pattern selection problem. With forcing frequency components in ratio m/n, where m and n are co-prime integers, there is the possibility that both harmonic and subharmonic waves may lose stability simultaneously, each with a different wavenumber. We focus on this situation and compare the case where the harmonic waves have a longer wavelength than the subharmonic waves with the case where the harmonic waves have a shorter wavelength. We show that in the former case a normal form transformation can be used to remove all quadratic terms from the amplitude equations governing the relevant resonant triad interactions. Thus the role of resonant triads in the pattern selection problem is greatly diminished in this situation. We verify our general results within the example of one-dimensional surface wave solutions of the Zhang-Vinals model of the two-frequency Faraday problem. In one-dimension, a 1:2 spatial resonance takes the place of a resonant triad in our investigation. We find that when the bifurcating modes are in this spatial resonance, it dramatically effects the bifurcation to subharmonic waves in the case of forcing frequencies are in ratio 1/2; this is consistent with the results of Zhang and Vinals. In sharp contrast, we find that when the forcing frequencies are in ratio 2/3, the bifurcation to (sub)harmonic waves is insensitive to the presence of another spatially-resonant bifurcating mode.Comment: 22 pages, 6 figures, late

Transition to Turbulence and Effect of Initial Conditions on 3D Compressible Mixing in Planar Blast-wave-driven Systems

Perturbations on an interface driven by a strong blast wave grow in time due to a combination of Rayleigh-Taylor, Richtmyer-Meshkov, and decompression effects. In this paper, results from three-dimensional numerical simulations of such a system under drive conditions to be attainable on the National Ignition Facility [E. M. Campbell, Laser Part. Beams, 9(2), 209 (1991)] are presented. Using the multi-physics, adaptive mesh refinement, higher order Godunov Eulerian hydrocode, Raptor [L. H. Howell and J.A. Greenough, J. Comp. Phys. 184, 53 (2003)], the late nonlinear instability evolution, including transition to turbulence, is considered for various multimode perturbation spectra. The 3D post-transition state differs from the 2D result, but the process of transition proceeds similarly in both 2D and 3D. The turbulent mixing transition results in a reduction in the growth rate of the mixing layer relative to its pre-transition value and, in the case of the bubble front, relative to the 2D result. The post-transition spike front velocity is approximately the same in 2D and 3D. Implications for hydrodynamic mixing in core-collapse supernova are discussed

Optimisation of a nano-positioning stage for a Transverse Dynamic Force Microscope

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.This paper describes the optimisation of a nano-positioning stage for a Transverse Dynamic Force Microscope (TDFM). The nano-precision stage is required to move a specimen dish within a horizontal region of 1 μm × 1 μm and with a resolution of 0.3 nm. The design objective was to maximise positional accuracy during high speed actuation. This was achieved by minimising out-of-plane distortions and vibrations during actuation. Optimal performance was achieved through maximising out-of-plane stiffness through shape and material selection as well optimisation of the anchoring system. Several shape parameters were optimised including the shape of flexural beams and the shape of the dish holder. Physical prototype testing was an essential part of the design process to confirm the accuracy of modelling and also to reveal issues with manufacturing tolerances. An overall resonant frequency of 6 kHz was achieved allowing for a closed loop-control frequency of 1.73 kHz for precise horizontal motion control. This resonance represented a 12-fold increase from the original 500 Hz of a commercially available positioning stage. Experimental maximum out-of-plane distortions below the first resonance frequency were reduced from 0.3 μm for the first prototype to less than 0.05 μm for the final practical prototype

Numerical simulation of supernova-relevant laser-driven hydro experiments on OMEGA

In ongoing experiments performed on the OMEGA laser [J. M. Soures et al., Phys. Plasmas 5, 2108 (1996)] at the University of Rochester Laboratory for Laser Energetics, nanosecond laser pulses are used to drive strong blast waves into two-layer targets. Perturbations on the interface between the two materials are unstable to the Richtmyer–Meshkov instability as a result of shock transit and the Rayleigh–Taylor instability during the deceleration-phase behind the shock front. These experiments are designed to produce a strongly shocked interface whose evolution is a scaled version of the unstable hydrogen–helium interface in core-collapse supernovae such as SN 1987A. The ultimate goal of this research is to develop an understanding of the effect of hydrodynamic instabilities and the resulting transition to turbulence on supernovae observables that remain as yet unexplained. The authors are, at present, particularly interested in the development of the Rayleigh–Taylor instability through the late nonlinear stage, the transition to turbulence, and the subsequent transport of material within the turbulent region. In this paper, the results of numerical simulations of two-dimensional (2D) single and multimode experiments are presented. These simulations are run using the 2D Arbitrary Lagrangian Eulerian radiation hydrodynamics code CALE [R. T. Barton, Numerical Astrophysics (Jones and Bartlett, Boston, 1985)]. The simulation results are shown to compare well with experimental radiography. A buoyancy-drag model captures the behavior of the single-mode interface, but gives only partial agreement in the multimode cases. The Richtmyer–Meshkov and target decompression contributions to the perturbation growth are both estimated and shown to be significant. Significant dependence of the simulation results on the material equation of state is demonstrated, and the prospect of continuing the experiments to conclusively demonstrate the transition to turbulence is discussed. © 2004 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71253/2/PHPAEN-11-7-3631-1.pd