AHermitian C^(2) Differential Reproducing Kernel Interpolation Meshless Method for the 3D Microstructure-Dependent Static Flexural Analysis of Simply Supported and Functionally Graded Microplates

This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant.

Robust H_∞ guaranteed cost satisfactory fault-tolerant control for discrete-time systems with quadratic D stabilizability

The problem of robust H∞ guaranteed cost satisfactory fault-tolerant control with quadratic D stabilizability against actuator failures is investigated for a class of discrete-time systems with value-bounded uncertainties existing in both the state and control input matrices.Based on a more practical and general model of actuator continuous gain failures,taking the transient property,robust behaviour on H∞ performance and quadratic cost performance requirements into consideration,sufficient conditions for the existence of satisfactory fault-tolerant controller are given and the effective design steps with constraints of multiple performance indices are provided.Meanwhile,the consistency of the regional pole index,H∞ norm-bound constraint and cost performance indices is set up for fault-tolerant control.A simulation example shows the effectiveness of the proposed method.

What will I be like at eighty? How human values contribute to expected real and ideal self-images in old age in a Germanic/Austrian cultural context

According to Grawe’s Consistency Theory, congruence between an individual’s aims and reality is fundamental for psychological health. We examined the real and ideal self-images of N = 440 participants in a Germanic/Austrian cultural context as perceived in presence and as anticipated for an age of 80 years and examined their relationship to value orientations as a coping resource. From adjective ratings on the Semantic Differential for the real self-image at presence, two dimensions were extracted, one representing Warmth (W) and one representing Competence (C) in the sense of the Stereotype Content Model. Cluster analysis yielded one type of respondents with a cautiously optimistic, and one with a moderately pessimistic view of the present and the future. A third cluster devalued W and C in favor of Religiosity and Conservatism and had the highest degree of congruence between real and ideal self-images. Thus, hypotheses with regard to Religiosity and Conservatism as coping resources were confirmed.

Self-assembly of Asymmetric Dimer Particles in Supported Copolymer Bilayer

Using self-consistent field and density functional theories, we investigate the self-assembly behavior of asymmetric dimer particles in a supported AB block copolymer bilayer. Asymmetric dimer particles are amphiphilic molecules composed by two different spheres. One prefers to A block of copolymers and the other likes B block when they are introduced into the copolymer bilayer. The two layer structure of the dimer particles is formed within the bilayer. Due to the presence of the substrate surface, the symmetry of the two leaflets of the bilayer is broken, which may lead to two different layer structures of dimer particles within each leaflet of the bilayer. With the increasing concentration of the asymmetric dimer particles, in-plane structure of the dimer particles undergoes sparse square, hexagonal, dense square, and cylindrical structures. In a further condensed packing, a bending cylindrical structure comes into being. Here we verify that the entropic effect of copolymers, the enthalpy of the system and the steric repulsion of the dimer particles are three important factors determing the self-assembly of dimer particles within the supported copolymer bilayer.

DEFORMATION OF COPOLYMER MICELLES INDUCED BY AMPHIPHILIC DIMER PARTICLES

Combining self-consistent-field theory and density-functional theory, we systematically study the deformation of copolymer micelles induced by the presence of amphiphilic dimer particles. Due to the amphiphilic nature, dimer particles tend to accumulate onto the interface of the copolymer micelle. With increasing concentration of the symmetric dimer particles, which are made of two identical spherical particles, the micelle deforms from the initial sphere to ellipse, dumbbell, and finally separates into two micelles. Furthermore, asymmetric dimer particles, composed by two particles with different sizes, are considered to investigate the influence of geometry of dimer particles on the deformation of the micelle. It is found that the micelle inclines to deform into dumbbell due to the additional curvature originating in the gathering of asymmetric dimer particles onto the interface of the micelle. The present study on the deformation of micelles is useful to understand the possible shape variation in the course of cell division/fusion.

Putting Consistent Theories Together in Institutions

The problem of putting consistent theories together in institutions is dis-cussed. A general necessary condition for consistency of the resulting theory iscarried out, and some sufficient conditions are given for diagrams of theories inwhich shapes are tree bundles or directed graphs. Moreover, some transforma-tions from complicated cases to simple ones are established.