Wavelet method applied to specific adhesion of elastic solids via molecular bonds

Abstract

We propose a wavelet method to analyze the stochastic-elastic problem of specific adhesion between two elastic solids via ligand-receptor bond clusters, which is governed by a nonlinear integro-differential equation with a singular Cauchy kernel to describe the mean-field coupling between deformation of elastic materials and stochastic behavior of the molecular bonds. To solve this problem, Galerkin method based on a wavelet approximation scheme is adopted, and special treatment which transforms the singular Cauchy kernel into a smooth one has been proposed to avoid the cumbersome calculation of singular integrals. Numerical results demonstrate that the method is fully capable of solving the specific adhesion problems with complex nonlinear and singular equations. Based on the proposed method, investigations are performed to reveal the relation between steady-state pulling force and mean surface separation under different stress concentration indexes, which is crucial for assembling the overall constitutive relations for multicellular tumor spheroids and polymer-matrix microcomposites.

Application of Wavelet Methods in Computational Physics

“…[69] By using the Coiflet WGM, researchers have extensively studied various static and dynamic problems including the buckling and vibration control problems of beams, plates, and intelligent structures. [17,[70][71][72][73][74][75][76][77] These Coiflet-based WGMs have been widely acknowledged by peers, and have been directly cited and applied in the analysis of problems such as the vibration control of large-scale space structures, [78,79] the time-varying inhomogeneous electromagnetic problems, [80] non-homogeneous electric large-raywaveguide problems, [81] stochastic thermodynamics problems, [82] as well as material mechanics, [83] and fluid mechanics. [84][85][86][87][88] Although the Generalized WGM has achieved certain success in various fields, particularly in linear problems where it has demonstrated higher accuracy than the conventional Galerkin method, it encounters a bottleneck in solving nonlinear problems.…”