In this paper, a mathematical model is presented to describe the evolution of an avascular solid tumour in response to an externally-supplied nutrient. The growth of the tumour depends on the balance between expansive forces caused by cell proliferation and cell-cell adhesion forces which exist to maintain the tumour's compactness. Cell-cell adhesion is incorporated into the model using the Gibbs-Thomson relation which relates the change in nutrient concentration across the tumour boundary to the local curvature, this energy being used to preserve the cell-cell adhesion forces.
Our analysis focuses on the existence and uniqueness of steady, radially-symmetric solutions to the model, and also their stability to time-dependent and asymmetric perturbations. In particular, our analysis suggests that if the energy needed to preserve the bonds of adhesion is large then the radially-symmetric configuration is stable with respect to all asymmetric perturbations, and the tumour maintains a radially-symmetric structure—this corresponds to the growth of a benign tumour. As the energy needed to maintain the tumour's compactness diminishes so the number of modes to which the underlying radially-symmetric solution is unstable increases—this corresponds to the invasive growth of a carcinoma. The strength of the cell-cell bonds of adhesion may at some stage provide clinicians with a useful index of the invasive potential of a tumour. 相似文献
Adhesive energetics and interfacial electronic structures have been computed from first principles for the Cu/Al2O3 interface. Recent transmission electron microscopy results of Cu grown by molecular beam epitaxy on Al2O3(0001) were helpful in modelling the interfacial atomic structure. We found that Al2O3(0001) relaxation effects can lower the work of adhesion Wad by over a factor of 3. Our computed Wad value is in reasonably good agreement with experiment, being somewhat larger, as expected from our assumption of a coherent interface. One might begin to understand this metal/ceramic adhesion as a competition between Cu and Al for oxide formation, which is easily won by Al. However this simple picture is complicated by several indications of a significant metallic/covalent component to the Cu/Al2O3 adhesive bond. 相似文献
Lacquer sap has received much attention as a traditional natural resin because it is a renewable and eco-friendly biopolymer resource unlike artificial coating materials. However, strict drying conditions and long drying times of lacquer sap should be modified to expand its applications. This study presents the first attempt to investigate the effect of different amplitudes of ultrasonic waves on the lacquer sap composed of water-in-oil (W/O) emulsion droplets and the mechanical properties of the resultant film by solvent evaporation. Acoustically induced cavitation via batch ultrasonication facilitates the generation of submicron-sized W/O emulsion. The drying time of sonicated lacquer sap was noticeably shortened as the amplitude of acoustic power increased. Interestingly, the transparency of the film cast from lacquer sap consisting of the smallest emulsion droplets increased significantly, weakening the degree of colour change from caramel-like yellow to dark brown as polymerisation progressed. These are attributed to the effective and frequent contact of laccase enzyme with urushiol at the increased interfacial area of nano-emulsified W/O droplets pulverised by ultrasonic waves. The quinone radical-generation in the interface layer and its transfer to the urushiol oil phase through water-insoluble glycoprotein emulsifier are greatly promoted, resulting in highly cross-linked, dense three-dimensional polymer networks, which also increased the lacquer film hardness after drying. As the emulsion droplet size decreased, the mutual interaction between the catechol moiety of urushiol and the substrates increased, resulting in improved adhesion. The nano-emulsification of the lacquer sap by ultrasonic waves can be used in a simple, effective, and eco-friendly way to shorten the drying time and improve the film characteristics of natural resins. This approach could pave the way for its wide range of applications in industrial fields, taking into account green and sustainable chemistry. 相似文献
In order to clarify the edge and interface effect on the adhesion energy between graphene(Gr)and its substrate,a theoretical model is proposed to study the interaction and strain distribution of Gr/Si system in terms of continuum medium mechanics and nanothermodynamics.We find that the interface separation and adhesion energy are determined by the thickness of Gr and substrate.The disturbed interaction and redistributed strain in the Gr/Si system induced by the effect of surface and interface can make the interface adhesion energy decrease with increasing thickness of Gr and diminishing thickness of Si.Moreover,our results show that the smaller area of Gr is more likely to adhere to the substrate since the edge effect improves the active energy and strain energy.Our predictions can be expected to be a guide for designing high performance of Grbased electronic devices. 相似文献