Effect of Probe Lifting Height in Jumping Mode AFM for Living Cell Imaging

Atomic force microscopy(AFM)is one of the effective methods for imaging the morphological and physical properties of living cells in a near-physiological environment.However,several problems caused by the adhesion of living cells and extension of the cell membranes seriously affect the image quality during living cell imaging,hindering the study of living cells.In this work,jumping mode AFM imaging was used to image living cells at varied probe lifting heights to meet image quality requirements,and image quality related to the probe lifting height is discussed in detail.The jumping mode was divided into three parts based on the varying heights of the lifted probe,namely near-contact mode,half-jumping mode,and full-jumping mode,and the causes of their imaging drawbacks were analyzed.At an appropriate lifting height,the probe can be completely free from the influence of cell adhesion and self-excited oscillation,thus avoiding the occurrence of“trail”phenomena and invalid points in the imaging of living cells and improving the image quality.Additionally,this work provides a new approach to calculating the lateral force through the adhesion of trace and retrace scanning at a low height,which is important for studying the extension characteristics of the cell membrane.

SOME DYNAMICAL PROPERTIES OF THE UNIVERSAL UNFOLDING OF PITCHFORK

From the point of view of dynamics, the phenomenon of mode jumping in the imperfect pitchfork problem is discussed. The dynamical mechanism of model jumping of structures, such as plate and shell, that is brought about by the extremum instability, is explained. Finally, we give numerical simulation to show the validity of our results.

Receding horizon H_∞ control for discrete-time Markovian jump linear systems

Receding horizon H∞ control scheme which can deal with both the H∞ disturbance attenuation and mean square stability is proposed for a class of discrete-time Markovian jump linear systems when minimizing a given quadratic performance criteria. First, a control law is established for jump systems based on pontryagin’s minimum principle and it can be constructed through numerical solution of iterative equations. The aim of this control strategy is to obtain an optimal control which can minimize the cost function under the worst disturbance at every sampling time. Due to the difficulty of the assurance of stability, then the above mentioned approach is improved by determining terminal weighting matrix which satisfies cost monotonicity condition. The control move which is calculated by using this type of terminal weighting matrix as boundary condition naturally guarantees the mean square stability of the closed-loop system. A sufficient condition for the existence of the terminal weighting matrix is presented in linear matrix inequality （LMI） form which can be solved efficiently by available software toolbox. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.

JUMPING INSTABILITIES IN THE POST-BUCKLING OF A BEAM ON A PARTIAL NONLINEAR FOUNDATION

Mode jumping is an instability phenomenon in the post-buckling region, which causes a sudden change in the equilibrium configuration and is thus harmful to structure. The con- figuration of a partial elastic foundation can directly induce mode coupling from the buckling stage and through the whole post-buckling region. The mode coupling effect due to the configuration of partial foundation on mode jumping is investigated and demonstrated to be an important factor of determining mode jumping. By properly choosing the partial elastic foundation configuration, mode jumping can be avoided.