On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime

We consider a two-dimensional atomic mass spring system and show that in the small displacement regime the corresponding discrete energies can be related to a continuum Griffith energy functional in the sense of Gamma-convergence. We also analyze the continuum problem for a rectangular bar under tensile boundary conditions and find that depending on the boundary loading the minimizers are either homogeneous elastic deformations or configurations that are completely cracked generically along a crystallographic line. As applications we discuss cleavage properties of strained crystals and an effective continuum fracture energy for magnets

An analysis of crystal cleavage in the passage from atomistic models to continuum theory

We study the behavior of atomistic models in general dimensions under uniaxial tension and investigate the system for critical fracture loads. We rigorously prove that in the discrete-to-continuum limit the minimal energy satisfies a particular cleavage law with quadratic response to small boundary displacements followed by a sharp constant cut-off beyond some critical value. Moreover, we show that the minimal energy is attained by homogeneous elastic configurations in the subcritical case and that beyond critical loading cleavage along specific crystallographic hyperplanes is energetically favorable. In particular, our results apply to mass spring models with full nearest and next-to-nearest pair interactions and provide the limiting minimal energy and minimal configurations.Comment: The final publication is available at springerlink.co

A comparison of the eigenvalues of the Dirac and Laplace operator on the two-dimensional torus

We compare the eigenvalues of the Dirac and Laplace operator on a two-dimensional torus with respect to the trivial spin structure. In particular, we compute their variation up to order 4 upon deformation of the flat metric, study the corresponding Hamiltonian and discuss several families of examples.Comment: Latex2.09, 28 pages, with figure

Variety Steering Concept for Mass Customization

In this paper we make the distinction between subjective and objective customer needs. The subjective needs are the individually realized and articulated requirements, whereas the objective needs are the real ones perceived by a fictive neutral perspective. We show that variety in mass customization has to be orientated on the objective needs. In order to help mass customizers better evaluate the degree to which they can fulfill the objective needs as well as their internal complexity level we have developed a key metrics system model. We also present a conceptual application showing how to use this model to support decision making related to the introduction or reduction of product variants.Variety Management; Complexity; Production/Operations Management

Key Metrics System for Variety Steering in Mass Customization

The main goal of this paper is to provide a key metrics system for variety steering in mass customization. We distinguish between objective and subjective customer needs. The subjective needs are the individually realized and articulated requirements, whereas the objective needs are the real ones perceived by a fictive neutral perspective. We show that variety in mass customization has to be orientated on the objective needs. In order to help mass customizers better evaluate the degree to which they can fulfill the objective needs as well as their internal complexity level, we have developed a key metrics system model. We also present a conceptual application showing how to use this model to support decision making related to the introduction or reduction of product variants.Variety Management; Complexity; Production/Operations Management

Electron Energy-Loss Spectroscopy: A versatile tool for the investigations of plasmonic excitations

The inelastic scattering of electrons is one route to study the vibrational and electronic properties of materials. Such experiments, also called electron energy-loss spectroscopy, are particularly useful for the investigation of the collective excitations in metals, the charge carrier plasmons. These plasmons are characterized by a specific dispersion (energy-momentum relationship), which contains information on the sometimes complex nature of the conduction electrons in topical materials. In this review we highlight the improvements of the electron energy-loss spectrometer in the last years, summarize current possibilities with this technique, and give examples where the investigation of the plasmon dispersion allows insight into the interplay of the conduction electrons with other degrees of freedom

Исследование рапределения совокупности валютных пар методами факторного анализа

Рассматривается возможность оценки совместного распределения совокупностиприращений котировок валютных пар, используя представление всей совокупности в виде каноническойфакторной модели. Показана принципиальная возможность построения такой модели для выбраннойсовокупности признаков, сделана оценка распределений обобщенных и характерных факторов и на ее основе смоделировано многомерное распределение всей совокупности исходных признаков

Dirac eigenvalues and total scalar curvature

It has recently been conjectured that the eigenvalues $\lambda$ of the Dirac operator on a closed Riemannian spin manifold $M$ of dimension $n\ge 3$ can be estimated from below by the total scalar curvature: $$\lambda^2 \ge \frac{n}{4(n-1)} \cdot \frac{\int_M S}{vol(M)}.$$ We show by example that such an estimate is impossible.Comment: 9 pages, LaTeX, uses pstricks macro package. to appear in Journal of Geometry and Physic