On maximum norm contractivity of second order damped single step methods

In this paper we consider A(θ)-stable finite difference methods for numerical solutions of dissipative partial differential equations of parabolic type. Combining two rational approximation methods with different orders of accuracy, where the lower order method is applied n ₀ times (n ₀ fixed) at each time step, we prove the existence of a second order method which is contractive for all time steps. Moreover, we shed light on the conditions on the lower order method which are sufficient (and sometimes necessary) to obtain the optimal order of accuracy. For the one-dimensional heat equation we construct a family of numerical methods which are contractive in the maximum norm for all values of the discretization parameters. We also present numerical examples to illustrate our results. Received: May 2002 / Accepted: January 2003     

A confocal microscopic evaluation of the effects of insulin imprinting on the binding of Concanavalin A by Tetrahymena Pyriformis

With confocal microscopy it is possible to study the Concanavalin A (Con A) binding characteristics of the surface and interior of a single cell by viewing optical sections. It was observed in Tetrahymena pyriformis that Con A bound both to the plasma membrane and to intracellular structures. Incubation of cells with a competing sugar a-methylmannopyranoside, decreased binding. Hormonal imprinting with insulin resulted in an increase in binding of Con A to the cell surface and a decrease in intracellular binding. It is possible that the intracellular binding sites may migrate to the plasma membrane.     

Balance-dendrogram. A new routine of CoDaPack

A statistical analysis of compositional data based on the Aitchison geometry of the simplex requires an appropriate basis for representing the data. A simple and intuitive way of building such a basis employs a sequential binary partition of the compositional vector. The partition, together with some statistical summaries of the coordinates, or balances, can be represented in a dendrogram-type graph. In this paper we introduce an implementation of this methodology inside CoDaPack, which is freeware. An example with real data illustrates the use of the Balance-Dendrogram routine.     

Approximation of powers of some tests in one-way MANOVA type multivariate generalized linear model

The test of an equality of expected values of response vectors in one-way MANOVA type multivariate generalized linear models can be based on deviance or score statistic. This paper aims at approximation of the power of these tests under local alternatives. As indicated by presented simulation study, these approximations perform well over a wide range of models and sample sizes. Approximation of the power of these tests based on a noncentral χ² distribution derived by Fahrmeir [Fahrmeir, L., 1987. Asymptotic testing theory for generalized linear models. Statistics 18 (1), 65-76] is considered for comparison in the simulation study. The approximation derived in this paper performs better for small sample sizes. The simulation study also provides comparison of the considered tests.     

Cross-property connections for copper–graphite composites

Copper–graphite composite materials in the range of 0–10 vol% of carbon phase were prepared from the mixture of copper and graphite powders by hot isostatic pressing. The microstructure, mechanical (tensile strength, elongation to fracture) and physical (electrical and thermal conductivity) properties of composite samples were investigated, and the cross-property connections were calculated. It was shown that electrical and thermal conductivity cross-property (Lorenz number) is almost constant and increases only slightly (no more than 10 % increase was observed). This implies that in the investigated composition range the Lorenz number of a copper–graphite composite system behaves according to Franz–Wiedemann law for pure metals at constant temperature. On the contrary, the conductivity to tensile strength cross-property connections showed significant linear increase (over 200 % in the investigated composition range) for both electrical conductivity and thermal conductivity of composite materials. The cross-property connections of conductivity to the elongation to fracture exhibit a nonlinear dependence on the volume fraction of graphite.     

Models of Ballistic Propagation of Heat at Low Temperatures

Heat conduction at low temperatures shows several effects that cannot be described by the Fourier law. In this paper, the performance of various theories is compared in case of wave-like and ballistic propagation of heat pulses in NaF.     

Connection between stress state and plastic strain increments determined by a computer method

The ratios of the plastic shear strain and tensile strain to the resolved shear strain are determined on the basis of earlier results obtained by computer for 1 0 0 and 1 1 1 textures and nontextured polycrystals in the case of simultaneous shear and extension. It is shown that the plastic deformation increment vector determined by the application of the plastic work equation fulfils the normality condition prescribed by the generalized flow law.     

Mechanical properties of Al-Zn-Mg alloys investigated by microhardness measurements

One of the most simple and economic methods of testing the mechanical properties of alloys is the microhardness measurement. In the present paper we report on the results and the interpretation of experiments carried out on a series of AI-Zn-Mg alloys prepared from high purity base materials. The following results were obtained: (a) the incremental microhardness,HV, was related to the microhardness,HV, of high purity Al and can be given asHV=264(C_mg–0.25C_zn) wherec _mg andC _zn are the concentrations of Mg and Zn respectively, in the as-quenched state after solution heattreatment, (b) the ultimate tensile strength and the microhardness were correlated by the approximation:HV3_u.HV was investigated in the light of the average radius and the volume fraction of zones forming at room temperature. On the basis of the micromechanism of plastic deformation further evidence was found to show that the shearing mechanism is responsible for strengthening by GP zones in AI-Zn-Mg alloys.     

Analysis and optimum design of fibre-reinforced composite structures

The optimal design of a carbon-fibre-reinforced plastic (CFRP) sandwich-like structure with aluminium (Al) webs is addressed. The material parameters are determined using tensile tests, whereafter the results of an analytical model, a numerical model and an experimental setup are compared. The analytical and numerical approximations are then used to optimize the structure in a multi-algorithm approach for minimum cost and maximum stiffness. The selected algorithm and approximation are motivated by their accuracy and computational efficiency. The CFRP plates are optimized with respect to ply arrangement, while the complete sandwich-like structure is optimized with respect to the combination of manufacturing and material cost. Design constraints on maximum deflection of the total structure, buckling of the CFRP composite plates, buckling of the Al webs, stress in the composite plates and stress in the Al stiffeners are included in the formulation. For the different phases in the optimization process, we use the recently proposed particle swarm optimization algorithm, a dynamic search technique and a continuous-discrete optimization technique .