Empirical Mode Decomposition for Dynamic AFM Microcantilevers in Air and Liquid Environment

2018 ◽  
Author(s):  
Il Kwang Kim ◽  
Jea Woong Jang ◽  
Soo Il Lee
Keyword(s):  
Orthogonal Decomposition ◽  
Operating Conditions ◽  
Liquid Environment ◽  
Tapping Mode ◽  
Force Microscopy ◽  
Hydrodynamic Damping ◽  
Atomic Force ◽  
Mode Decomposition ◽  
Proper Orthogonal ◽  
Smooth Orthogonal Decomposition

The modal decomposition of tapping mode atomic force microscopy microcantilevers in air and liquid environment was experimentally investigated to identify their complex responses. In experiment, the flexible microcantilevers and a flat HOPG sample were used. The responses of the microcantilevers were obtained to extract the linearized modes and orthogonal values using the methods for the proper orthogonal decomposition and the smooth orthogonal decomposition. The influence of the tapping setpoints and the hydrodynamic damping forces were investigated with the multi-mode response of microcantilevers. The results show that the first mode is dominant under normal operating conditions in tapping mode. However, at lower setpoint, the flexible microcantilever behaved uncertain modal distortion near the tip on the sample. The dynamics tapping effect and the damping between microcantilever and liquid influenced their responses.

Proper Orthogonal Decomposition of Tapping Microcantilevers in Liquid Atomic Force Microscopy

2015 ◽  
Author(s):  
Il Kwang Kim ◽  
Soo Il Lee
Keyword(s):  
Atomic Force Microscopy ◽  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Modal Decomposition ◽  
Tapping Mode ◽  
Force Microscopy ◽  
Atomic Force ◽  
Proper Orthogonal Modes ◽  
Proper Orthogonal ◽  
Mode Atomic Force Microscopy

The modal decomposition of tapping mode atomic force microscopy microcantilevers in liquid environments was studied experimentally. Microcantilevers with different lengths and stiffnesses and two sample surfaces with different elastic moduli were used in the experiment. The response modes of the microcantilevers were extracted as proper orthogonal modes through proper orthogonal decomposition. Smooth orthogonal decomposition was used to estimate the resonance frequency directly. The effects of the tapping setpoint and the elastic modulus of the sample under test were examined in terms of their multi-mode responses with proper orthogonal modes, proper orthogonal values, smooth orthogonal modes and smooth orthogonal values. Regardless of the stiffness of the microcantilever under test, the first mode was dominant in tapping mode atomic force microscopy under normal operating conditions. However, at lower tapping setpoints, the flexible microcantilever showed modal distortion and noise near the tip when tapping on a hard sample. The stiff microcantilever had a higher mode effect on a soft sample at lower tapping setpoints. Modal decomposition for tapping mode atomic force microscopy can thus be used to estimate the characteristics of samples in liquid environments.

scholarly journals From snapshots to modal expansions – bridging low residuals and pure frequencies

2016 ◽  
Vol 802 ◽  
pp. 1-4 ◽  
Author(s):  
Bernd R. Noack
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Operating Conditions ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Simple Method ◽  
Reduced Order ◽  
Mode Decomposition ◽  
Optimality Property ◽  
Proper Orthogonal

Data-driven low-order modelling has been enjoying rapid advances in fluid mechanics. Arguably, Sirovich (Q. Appl. Maths, vol. XLV, 1987, pp. 561–571) started these developments with snapshot proper orthogonal decomposition, a particularly simple method. The resulting reduced-order models provide valuable insights into flow physics, allow inexpensive explorations of dynamics and operating conditions, and enable model-based control design. A winning argument for proper orthogonal decomposition (POD) is the optimality property, i.e. the guarantee of the least residual for a given number of modes. The price is unpleasant frequency mixing in the modes which complicates their physical interpretation. In contrast, temporal Fourier modes and dynamic mode decomposition (DMD) provide pure frequency dynamics but lose the orthonormality and optimality property of POD. Sieber et al. (J. Fluid Mech., vol. 792, 2016, pp. 798–828) bridge the least residual and pure frequency behaviour with an ingenious interpolation, called spectral proper orthogonal decomposition (SPOD). This article puts the achievement of the TU Berlin authors in perspective, illustrating the potential of SPOD and the challenges ahead.

scholarly journals Scaling law to determine peak forces in tapping-mode AFM experiments on finite elastic soft matter systems

2017 ◽  
Vol 8 ◽  
pp. 968-974 ◽  
Author(s):  
Horacio V Guzman
Keyword(s):  
Soft Matter ◽  
Scaling Law ◽  
Soft Materials ◽  
Operating Conditions ◽  
Peak Force ◽  
Liquid Environment ◽  
Tapping Mode ◽  
Force Microscopy ◽  
Mechanics Model ◽  
Tapping Mode Afm

Analytical equations to estimate the peak force will facilitate the interpretation and the planning of amplitude-modulation force microscopy (tapping mode) experiments. A closed-form analytical equation to estimate the tip–sample peak forces while imaging soft materials in liquid environment and within an elastic deformation regime has been deduced. We have combined a multivariate regression method with input from the virial–dissipation equations and Tatara’s bidimensional deformation contact mechanics model. The equation enables to estimate the peak force based on the tapping mode observables, probe characteristics and the material properties of the sample. The accuracy of the equation has been verified by comparing it to numerical simulations for the archetypical operating conditions to image soft matter with high spatial resolution in tapping-mode AFM.

Modeling the Turbulent Wake Behind a Wall-Mounted Square Cylinder

2020 ◽  
Author(s):  
Christian Amor ◽  
José M Pérez ◽  
Philipp Schlatter ◽  
Ricardo Vinuesa ◽  
Soledad Le Clainche
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Turbulent Wake ◽  
Orthogonal Decomposition ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Square Cylinder ◽  
Complex Flow ◽  
Reduced Order ◽  
Mode Decomposition ◽  
Proper Orthogonal

Abstract This article introduces some soft computing methods generally used for data analysis and flow pattern detection in fluid dynamics. These techniques decompose the original flow field as an expansion of modes, which can be either orthogonal in time (variants of dynamic mode decomposition), or in space (variants of proper orthogonal decomposition) or in time and space (spectral proper orthogonal decomposition), or they can simply be selected using some sophisticated statistical techniques (empirical mode decomposition). The performance of these methods is tested in the turbulent wake of a wall-mounted square cylinder. This highly complex flow is suitable to show the ability of the aforementioned methods to reduce the degrees of freedom of the original data by only retaining the large scales in the flow. The main result is a reduced-order model of the original flow case, based on a low number of modes. A deep discussion is carried out about how to choose the most computationally efficient method to obtain suitable reduced-order models of the flow. The techniques introduced in this article are data-driven methods that could be applied to model any type of non-linear dynamical system, including numerical and experimental databases.

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