Nonlinear dynamics of atomic force microscopy with intermittent contact

When the atomic force microscopy (AFM) in tapping mode is in intermittent contact with a soft substrate, the contact time can be a significant portion of a cycle, resulting in invalidity of the impact oscillator model, where the contact time is assumed to be infinitely small. Furthermore, we demonstrate that the AFM intermittent contact with soft substrate can induce the motion of higher modes in the AFM dynamic response. Traditional ways of modeling AFM (one degree of freedom (DOF) system or single mode analysis) are shown to have serious mistakes when applied to this kind of problem. A more reasonable displacement criterion on contact is proposed, where the contact time is a function of the mechanical properties of AFM and substrate, driving frequencies/amplitude, initial conditions, etc. Multi-modal analysis is presented and mode coupling is also shown. (c) 2006 Published by Elsevier Ltd.

Impact of carrier stiffness and microtopology on two-dimensional kinetics of P-selectin and P-selectin glycoprotein ligand-1 (PSGL-1) interactions

Mechanics and surface microtopology of the molecular carrier influence cell adhesion, but the mechanisms underlying these effects are not well understood. We used a micropipette adhesion frequency assay to quantify how the carrier stiffness and microtopology affected two-dimensional kinetics of interacting adhesion molecules on two apposing surfaces. Interactions of P-selectin with P-selectin glycoprotein ligand-1 (PSGL-1) were used to demonstrate such effects by presenting the molecules on three carrier systems: human red blood cells (RBCs), human promyelocytic leukemia HL-60 cells, and polystyrene beads. Stiffening the carrier alone or in cooperation with roughing the surface lowered the two-dimensional affinity of interacting molecules by reducing the forward rate but not the reverse rate, whereas softening the carrier and roughing the surface had opposing effects in affecting two-dimensional kinetics. In contrast, the soluble antibody bound with similar three-dimensional affinity to surface-anchored P-selectin or PSGL-1 constructs regardless of carrier stiffness and microtopology. These results demonstrate that the carrier stiffness and microtopology of a receptor influences its rate of encountering and binding a surface ligand but does not subsequently affect the stability of binding. This provides new insights into understanding the rolling and tethering mechanism of leukocytes onto endothelium in both physiological and pathological processes.

Monte Carlo approaches to nonlinear optimal control

This paper explores the use of Monte Carlo techniques in deterministic nonlinear optimal control. Inter-dimensional population Markov Chain Monte Carlo (MCMC) techniques are proposed to solve the nonlinear optimal control problem. The linear quadratic and Acrobot problems are studied to demonstrate the successful application of the relevant techniques.

Transition waves and nonlinear interactions in the near wake of a circular cylinder

Transition waves and interactions between two kinds of instability-vortex shedding and transition wave in the near wake of a circular cylinder in the Reynolds number range 3 000-10 000 are studied by a domain decomposition hybrid numerical method. Based on high resolution power spectral analyses for velocity new results on the Reynolds-number dependence of the transition wave frequency, i.e. f(t)/f(s) similar to Re-0.87 are obtained. The new predictions are in good agreement with the experimental results of Wei and Smith but different from Braza's prediction and some early experimental results f(t)/f(s) similar to Re-0.5 given by Bloor et nl. The multi-interactions between two kinds of vortex are clearly visualized numerically. The strong nonlinear interactions between the two independent frequencies (f(t), f(s)) leading to spectra broadening to form the coupling mf(s) +/- nf(t) are predicted and analyzed numerically, and the characteristics of the transition are described. Longitudinal variations of the transition wave and its coupling are reported. Detailed mechanism of the flow transition in the near wake before occurrence of the three-dimensional evolution is provided.

Nonlinear analysis of pile foundation jacket platform

In this paper, the nonlinear collapse of the BOHAI-8 pile foundation jacket platform has been analyzed. The ultimate load and collapse process of two computational models of the structure are given. One model is of fixed support whose length is eight times the pile leg diameter and the other considers the nonlinearity of the soil-pile interaction.

Effect of nonlinear wave-current interaction on flow fields and hydrodynamic forces

A fifth-order theory for solving the problem of interaction between Stokes waves and exponential profile currents is proposed. The calculated flow fields are compared with measurements. Then the errors caused by the linear superposition method and approximate theory are discussed. It is found that the total wave-current field consists of pure wave, pure current and interaction components. The shear current not only directly changes the flow field, but also indirectly does sx, by changing the wave parameters due to wave-current interaction. The present theory can predict the wave kinematics on shear currents satisfactorily. The linear superposition method may give rise to more than 40% loading error in extreme conditions. When the apparent wave period is used and the Wheeler stretching method is adopted to extrapolate the current, application of the approximate theory is the best.

Dynamic analysis of arrest of buckle propagation on a beam on a nonlinear elastic foundation by FEM

Based on the dynamic governing equation of propagating buckle on a beam on a nonlinear elastic foundation, this paper deals with an important problem of buckle arrest by combining the FEM with a time integration technique. A new conclusion completely different from that by the quasi-static analysis about the buckle arrestor design is drawn. This shows that the inertia of the beam cannot be ignored in the analysis under consideration, especially when the buckle propagation is suddenly stopped by the arrestors.