Methods And Applications Of Wavelet Theory In Specific Adhesion Of Elastic Media

The cell is the basic unit of higher organisms, and the human body is composed of tens of trillions of cells. Cells need through the surface specific force of the molecular bond to adhere other cells or extracellular matrix to realize some physiological functions like differentiation, growth and movement. We define the specific force as the specific adhesion. Specific adhesion plays a key role in cell recognition, signal transduction, tumor metastasis, wound healing and other physiological and pathological processes. Therefore, it is very important to study the cell specific adhesion.Researchers have made a lot of work on specific adhesion. Since the specific adhesion model is an Integral differential equations with initial conditions, strong nonlinearity and singularity, which makes the job of looking for the solution of the model becomes very difficult, a nd impede the development of studying specific cell adhesion. The wavelet function has very good characteristics, such as orthogonality, compact support, interpolation and so on, which has very important application value in the numerical calculation. Therefore, this paper firstly introduced the generalized coiflets wavelet. Then set up the specific adhesion model regarding elastic medium and the specific adhesion model of molecular cluster key elastic medium. At last the wavelet Galerkin method for solving the strongly nonlinear singular Integral differential equations gets good accuracy.The research shows that:(1) the adhesion region is expressed as the stress concentration at both ends, and the greater the stress concentration factor, the more obvious the stress concentration. When the external load is larger, the destruction of adhesion begins from the two ends to the middle;(2) the shape of the contact interface can obviously affect the stress distribution of the interface and we can change the stress distribution by changing the shape of the interface;(3) The smaller the stress concentration factor, the greater the adhesion strength while the larger the re closure rate of the single disconnected molecular bond;(4) The greater the new closure rate is, the shorter the time required for the structure to reach a stable state, and it is the main factors that affect the stability of a single disconnected molecular bond;(5) The number of adhesive patches in the cluster group is not significant to the adhesi on strength of single cycle. That is, the adhesion strength of the whole structure is almost a linear relationship with the number of adhesive patches;(6) the external force and the contact angle can significantly affect the specific adhesion. The larger the loading angle, the smaller the adhesion strength and the longer the stability time;(7) the adhesion strength is related to the loading rate. The adhesion strength increases with the increase of loading rate,but the increase is smaller and smaller. These findings will be beneficial to the development of our understanding of the specific adhesion and the future research work.