Response robustness and safety against jump to contact in AFMs controlled via different techniques

The role of a global dynamics analysis to assess a system robustness and actual safety in operating conditions is investigated by studying the effect of different local and global control techniques on the nonlinear behavior of a noncontact AFM via dynamical integrity concepts and tools

Nonlinear dynamics and control in macro/micro-mechanics: some computational issues

Computational issues in the global dynamics of two systems in micro- and macro-mechanics, with different dimensionality, are addressed. Attention is focused on calculation of integrity measures, determination of saddle manifolds undergoing global bifurcations, implementation of a control procedure for delaying basins erosion, selection of 2D cross-sections of multidimensional basins of attraction for understanding the role of transient dynamics in the global scenario of coupled steady responses

Bifurcation scenarios, dynamical integrity and control of noncontact atomic force microscopes

The research focuses on the description of the global dynamical behavior of a reduced-order model of noncontact Atomic Force Microscope. Different numerical analyses and continuation techniques are carried out to investigate the evolution of the main system periodic solutions and relevant basins of attraction under variations of the most significant system parameters. Local bifurcations, stability boundaries and basin erosion processes around primary and subharmonic resonance regions are studied in presence of both the parametrical horizontal excitation and the external one, and the obtained behavior charts are used not only to compare the results with the literature ones, but also as practical instruments to characterize the operation ranges in terms of the selected parameters. With the same perspective, dynamical integrity concepts, such as detection of basins of attraction, and quantification of their erosion process via integrity measures, are applied to determine acceptable frequency-dependent thresholds associated with a priori safe design targets. Furthermore, an external feedback control is introduced with the aim to take the system response to a selected reference one, thus providing a simple and efficient method to avoid possible unstable motions. Upon checking the effectiveness of the procedure in the weakly nonlinear regime via a perturbation approach, several numerical analyses in the strongly nonlinear regime are accomplished to achieve a description of its dynamical behavior as a function of the newly inserted parameters, and to critically evaluate the effectiveness of the control actuation on the system dynamics, with also a view to the overall response scenario

The Structure and Dynamics of Ions at Aqueous Interfaces Studied via Atomic Force Microscopy

The organisation and kinetics of charges at solid and soft interfaces play a central role in biological signalling processes and are vital for energy storage technologies as well as our understanding of heterogeneous catalysis. At the molecular-scale, such interfacial behaviour remains stubbornly difficult to characterise, due to the short-ranged interactions between ions, their aqueous solvent and surface groups. Thus, continuum-scale models quickly break down, especially close to the interface and with high charge densities. This thesis addresses the question of ionic organisation using atomic force microscopy (AFM), which uniquely combines sub-nanometre spatial resolution and the ability to probe relatively long timescales. The use of small oscillation amplitudes allows the topography of the ionic layer to be mapped while simultaneously extracting physical properties from the sample or the interface itself, with time resolution spanning from tens of milliseconds to minutes. The structure of ions at hydrophilic interfaces is shown to be delicately sensitive to the charges’ molecular structure (in the case of larger buffering agents) and their charge density (for simple alkali cations). Specifically, the cations’ interactions with a model lipid membrane and the waters around it lead to an attractive correlation energy which generates nanoscale networks that evolve over the course of many seconds. These ionic structures directly reduce the effective stiffness of the lipids, providing a mechanism for the spontaneous control of membranes’ mechanical properties. These ionic networks are significant in the case of confined fluids and provide an efficient means of lubrication even under high pressures in sub-nanometre gaps. When sheared, such fluid films are revealed to be non-Newtonian, with dynamics that depend on the velocity and lengthscale of the motion. The results highlight the greatly damped kinetics of ions and water molecules at interfaces, and shed light on the mechanisms behind their transport through and along biomolecules

Exploiting global dynamics of a noncontact atomic force microcantilever to enhance its dynamical robustness via numerical control

A control technique exploiting the global dynamical features is applied to a reduced order model of noncontact AFM, aiming to obtain an enlargement of the system's safe region in parameters space. The method consists of optimally modifying the shape of the system excitation by adding controlling superharmonics, to delay the occurrence of the global events (i.e. homo/heteroclinic bifurcations of some saddle) which trigger the erosion of the basins of attraction leading to loss in safety. The system's main saddles and the bifurcations involving the relevant manifolds are detected through accurate numerical investigations, and their topological characterization allows the determination of the global event responsible for the sharp reduction in the system dynamical integrity. Since an analytical treatment is impossible in applying the control, a fully numerical procedure is implemented. Besides being effective in detecting the value of the optimal superharmonic to be added for shifting the global bifurcation to a higher value of forcing amplitude, the method also proves to succeed in delaying the drop down of the erosion profile, thus increasing the overall robustness of the system during operating conditions

Exploiting global dynamics of a noncontact atomic force microcantilever to enhance its dynamical robustness via numerical control

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