ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik

Cover image for Vol. 92 Issue 4

April 2012

Volume 92, Issue 4

Pages 255–338

  1. Cover Picture

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    1. You have free access to this content
      Cover Picture: ZAMM 4/2012

      Article first published online: 12 MAR 2012 | DOI: 10.1002/zamm.201290004

  2. Issue Information

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    1. You have free access to this content
      Issue Information: ZAMM 4 / 2012

      Article first published online: 12 MAR 2012 | DOI: 10.1002/zamm.201209244

  3. Contents

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    1. You have free access to this content
      Contents: ZAMM 4 / 2012 (pages 255–256)

      Article first published online: 12 MAR 2012 | DOI: 10.1002/zamm.201209204

  4. Editor's Choice

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    1. You have free access to this content
      Distributed control of linearized Navier-Stokes equations via discretized input/output maps (pages 257–274)

      J. Heiland and V. Mehrmann

      Article first published online: 12 JAN 2012 | DOI: 10.1002/zamm.201100069

      Thumbnail image of graphical abstract

      The construction of reduced order models for flow control via a direct discretization of the input/output behavior of the system is discussed. The spatially discretized equations are linearized such that an explicit formula for the corresponding input/output map can be used to generate a matrix representation of the input/output map. Estimates for the approximation error are derived and the applicability is illustrated via a numerical example for the control of a driven cavity flow.

  5. Original Papers

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editor's Choice
    6. Original Papers
    1. Multi-pulse orbits and chaotic dynamics in an imperfect circular plate (pages 275–289)

      Y. Huangfu and F. Chen

      Article first published online: 31 OCT 2011 | DOI: 10.1002/zamm.201000166

      Thumbnail image of graphical abstract

      The global bifurcations in mode of an imperfect circular plate are investigated with the case of the 1:1 internal resonance and 1:3 primary resonance. After determining the equations of motion in a suitable form, the energy phase method proposed by Haller and Wiggins is employed to show the existence of the Silnikov-type multi-pulse orbits homoclinic to certain invariant sets for the two cases of Hamiltonian and dissipative perturbation. Furthermore, some complex chaos behaviors are revealed for this class of systems.

    2. Stability and bifurcation in a gene regulatory network model with delay (pages 290–303)

      Z. Wang, Z. Liu and R. Yuan

      Article first published online: 23 DEC 2011 | DOI: 10.1002/zamm.201100079

      Thumbnail image of graphical abstract

      A delayed gene regulatory network model with positive and negative feedbacks is considered. The authors investigate the stability of the positive equilibrium and the existence of Hopf bifurcation of the model by analyzing the associated characteristic transcendental equation. Applying the normal form theory and center manifold theorem, they consider the direction of the Hopf bifurcation and stability of the bifurcating periodic solutions. An example is given and numerical simulations are performed to illustrate the obtained results.

    3. First error bounds for the porous media approximation of the Poisson-Nernst-Planck equations (pages 304–319)

      M. Schmuck

      Article first published online: 12 JAN 2012 | DOI: 10.1002/zamm.201100003

      Thumbnail image of graphical abstract

      The author studies the well-accepted Poisson-Nernst-Planck equations modeling transport of charged particles. By formal multiscale expansions he redrives the porous media formulation obtained by two-scale convergence in two other paper of himself. The main result is the derivation of the error which occurs after replacing a highly heterogeneous solid-electrolyte composite by a homogeneous one. The derived estimates show that the approximation errors for both, the ion densities quantified in L2-norm and the electric potential measured in H1-norm, are of order O(s1/2).

    4. Analysis of a bi-material strip (pages 320–328)

      E. Suhir, W. Gschohsmann and J. Nicolics

      Article first published online: 20 DEC 2011 | DOI: 10.1002/zamm.201100027

      A theory-of-elasticity-based analytical (“mathematical”) model has been developed, in application to an advanced ceramic electrical sensor design, for a bi-material elongated strip experiencing longitudinal displacements distributed over one of its long edges. The actual gage is configured like a thin bi-material plate-like element attached to a thick-and-stiff carrier (substrate). The analysis is a generalization of the authors' study conducted earlier for a single material strip.

    5. Eshelby-Kröner self-consistent elastic model: the geometric mean versus the arithmetic mean – A numerical investigation (pages 329–338)

      S. Fréour and J. Fajoui

      Article first published online: 2 MAR 2012 | DOI: 10.1002/zamm.201100135

      Scale-transition models, such as Eshelby-Kröner self-consistent framework, which are often used for predicting the effective behavior of heterogeneous materials or estimating the distribution of local states from the knowledge of the corresponding macroscopic quantities, require the extensive use of set averages. The present paper is devoted to the comparison of the numerical results provided in pure elasticity by Eshelby-Kröner model depending on the average type chosen for achieving set average operations: either the traditional arithmetic mean or the geometric average. Various numerical applications of the model to the case of predicting either the effective stiffness or the lattice strains of single-phase polycrystals will be provided. The particular case when an extreme grain-shape occurs will also be investigated.

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