Modeling the behavior of elastic materials with stochastic microstructure

Even in the simple linear elastic range, the material behavior is not deterministic, but fluctuates randomly around some expectation values. The knowledge about this characteristic is obviously trivial from an experimentalist’s point of view. However, it is not considered in the vast majority of material models in which “only” deterministic behavior is taken into account. One very promising approach to the inclusion of stochastic effects in modeling of materials is provided by the Karhunen-Lo`eve expansion. It has been used, for example, in the stochastic finite element method, where it yields results of the desired kind, but unfortunately at drastically increased numerical costs. This contribution aims to propose a new ansatz that is based on a stochastic series expansion, but at the Gauß point level. Appropriate energy relaxation allows to derive the distribution of a synthesized stress measure, together with explicit formulas for the expectation and variance. The total procedure only needs negligibly more computation effort than a simple elastic calculation. We also present an outlook on how the original approach in [7] can be applied to inelastic material

The Weak and Strong Lefschetz Properties for Artinian K-Algebras

Let A = bigoplus_{i >= 0} A_i be a standard graded Artinian K-algebra, where char K = 0. Then A has the Weak Lefschetz property if there is an element ell of degree 1 such that the multiplication times ell : A_i --> A_{i+1} has maximal rank, for every i, and A has the Strong Lefschetz property if times ell^d : A_i --> A_{i+d} has maximal rank for every i and d. The main results obtained in this paper are the following. 1) EVERY height three complete intersection has the Weak Lefschetz property. (Our method, surprisingly, uses rank two vector bundles on P^2 and the Grauert-Mulich theorem.) 2) We give a complete characterization (including a concrete construction) of the Hilbert functions that can occur for K-algebras with the Weak or Strong Lefschetz property (and the characterization is the same one). 3) We give a sharp bound on the graded Betti numbers (achieved by our construction) of Artinian K-algebras with the Weak or Strong Lefschetz property and fixed Hilbert function. This bound is again the same for both properties. Some Hilbert functions in fact FORCE the algebra to have the maximal Betti numbers. 4) EVERY Artinian ideal in K[x,y] possesses the Strong Lefschetz property. This is false in higher codimension.Comment: To appear in J. Algebr

An experimental study of adaptive behavior in an oligopolistic market game

We consider an oligopolistic market game, in which the players are competing firm in the same market of a homogeneous consumption good. The consumer side is represented by a fixed demand function. The firms decide how much to produce of a perishable consumption good, and they decide upon a number of information signals to be sent into the population in order to attract customers. Due to the minimal information provided, the players do not have a well--specified model of their environment. Our main objective is to characterize the adaptive behavior of the players in such a situation.Market game, oligopoly, adaptive behavior, learning, Leex

Vibrational entropy and microstructural effects on the thermodynamics of partially disordered and ordered Ni3V

Samples of Ni3V were prepared with two microstructures: (1) with equilibrium D022 order, and (2) with partial disorder (having a large D022 chemical order parameter, but without the tetragonality of the unit cell). For both materials, we measured the difference in their heat capacities from 60 to 325 K, inelastic neutron-scattering spectra at four values of Q at 11 and at 300 K, and Young's moduli and coefficients of thermal expansion. The difference in heat capacity at low temperatures was consistent with a harmonic model using the phonon density of states (DOS) curves determined from the inelastic neutron-scattering spectra. In contrast, at temperatures greater than 160 K the difference in heat capacity did not approach zero, as expected of harmonic behavior. The temperature dependence of the phonon DOS can be used to approximately account for the anharmonic contributions to the differential heat capacity. We also argue that some of the anharmonic behavior should originate with a microstructural contribution to the heat capacity involving anisotropic thermal contractions of the D022 structure. We estimate the difference in vibrational entropy between partially disordered and ordered Ni3V to be Spdis -Sord =(+0.038±0.015)kB /atom at 300 K

Software reliability: Repetitive run experimentation and modeling

A software experiment conducted with repetitive run sampling is reported. Independently generated input data was used to verify that interfailure times are very nearly exponentially distributed and to obtain good estimates of the failure rates of individual errors and demonstrate how widely they vary. This fact invalidates many of the popular software reliability models now in use. The log failure rate of interfailure time was nearly linear as a function of the number of errors corrected. A new model of software reliability is proposed that incorporates these observations