转移概率流图的概率理论基础与应用方法(Ⅵ)——中止规则对调整型抽样方案复合OC函数影响的进一步讨论

解顺强．转移概率流向图的概率理论基础与应用方法（Ⅵ）—中止规则对调整型抽样方案复合ＯＣ函数影响的进一步讨论．数理统计与管理．１９９８．１７（６）本文运用转移概率流向图及其粘接方法，证明了当检查始于加严抽样方案时，不带中止规则的调整型抽样方案与带中止规则的相应的调整型抽样方案，两者的复合ＯＣ函数相同     

Modelling the role of cell-cell adhesion in the growth and development of carcinomas

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.     

Combinatorial investigations of interfacial failure

Conventional measurements of interfacial strength focus on a single variable, whereas many variables couple nontrivially and simultaneously to define this property. We present a combinatorial methodology that allows the effects of multivariable environments on interfacial strength to be investigated in a high‐throughput, parallel, and quantitative manner. This technique is largely based on the theory of Johnson, Kendall, and Roberts that quantifies adhesion through the contact and separation of a spherical lens and flat substrate. For our experiments, we fabricated a combinatorial library consisting of a two‐dimensional array of spherical caps and a complementary substrate. The array of spherical caps was brought into contact and subsequently separated from the substrate, whereas the relative displacement and contact area of the individual lenses were recorded. With gradient library‐fabrication methods, two adhesion‐controlling parameters can be continuously varied along the orthogonal axes of the array. In this manner, each lens quantifies the interfacial strength at a unique point in parameter space. We demonstrate this multilens contact‐adhesion test by measuring the effect of temperature and coating thickness on the self‐adhesion of polystyrene thin films. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 883–891, 2003     

Deformation and adhesive contact of elastomeric membranes

We have developed a highly sensitive inflation technique for probing adhesive interactions between soft materials. In this method, an elastomeric membrane is placed across a cylindrical glass tube and is pressurized into contact with a substrate. The adhesive interaction between the membrane and the substrate is obtained from the angle of contact, which is determined indirectly from the measured contact radius and applied pressure. An analysis of the membrane profile based on the numerical solution of the axisymmetric Laplace equation is developed. In a nonadhesive situation, where the membrane contact angle is known to be zero, the analysis is used to obtain the relationship between the membrane deformation and the biaxial membrane strain. Linearization of the governing equations is used to develop an analytic solution for the contact angle and energy release rate, making a connection to existing, more restrictive analyses of this problem. Results from three different types of membranes are presented as illustrative applications of the method. The substrate in these experiments is the gold electrode surface of a quartz crystal resonator, and the effect of membrane contact on the crystal resonance is summarized briefly. Adhesive interactions between the membranes are minimized in most cases by adding a grafted polyethylene glycol brush to one or both of the contacting surfaces. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3361–3374, 2007     

First-principles study of the α-Al2O3(0001)/Cu(111) interface

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 W _ad by over a factor of 3. Our computed W _ad 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.     

Polymer brushes near the crystallization density

In this paper, polymer brushes are studied via molecular-dynamics simulations at very high grafting densities, where the crossover between the brush regime and the polymer-crystal regime is taking place. This crossover is directly observed with the structure factor and pair-correlation function. With increasing grafting density, this crystallization is progressing from the core layer of the brush towards the surface layer. The same process is analyzed using the lateral fluctuations of the monomers as a signature of their diminishing mobility. Additionally, bond forces and the chain excess free energy indicate a transition from the brush regime to the overstretched regime, which is in agreement with predictions of a modified self-consistent field theory.