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End date: 2015 × Start date: 2015 × Type: Report ×

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Now showing 1 - 10 of 194
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    Direct transfer of magnetic sensor devices to elastomeric supports for stretchable electronics
    (Hoboken, NJ : Wiley, 2015) Melzer, Michael; Karnaushenko, Daniil; Lin, Gungun; Baunack, Stefan; Makarov, Denys; Schmidt, Oliver G.
    A novel fabrication method for stretchable magnetoresistive sensors is introduced, which allows the transfer of a complex microsensor systems prepared on common rigid donor substrates to prestretched elastomeric membranes in a single step. This direct transfer printing method boosts the fabrication potential of stretchable magnetoelectronics in terms of miniaturization and level of complexity, and provides strain‐invariant sensors up to 30% tensile deformation.
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    Biomimetic microelectronics for regenerative neuronal cuff implants
    (Hoboken, NJ : Wiley, 2015) Karnaushenko, Daniil; Münzenrieder, Niko; Karnaushenko, Dmitriy D.; Koch, Britta; Meyer, Anne K.; Baunack, Stefan; Petti, Luisa; Tröster, Gerhard; Makarov, Denys; Schmidt, Oliver G.
    Smart biomimetics, a unique class of devices combining the mechanical adaptivity of soft actuators with the imperceptibility of microelectronics, is introduced. Due to their inherent ability to self‐assemble, biomimetic microelectronics can firmly yet gently attach to an inorganic or biological tissue enabling enclosure of, for example, nervous fibers, or guide the growth of neuronal cells during regeneration.
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    Self‐assembled on‐chip‐integrated giant magneto‐impedance sensorics
    (Hoboken, NJ : Wiley, 2015) Karnaushenko, Daniil; Karnaushenko, Dmitriy D.; Makarov, Denys; Baunack, Stefan; Schäfer, Rudolf; Schmidt, Oliver G.
    A novel method relying on strain engineering to realize arrays of on‐chip‐integrated giant magneto‐impedance (GMI) sensors equipped with pick‐up coils is put forth. The geometrical transformation of an initially planar layout into a tubular 3D architecture stabilizes favorable azimuthal magnetic domain patterns. This work creates a solid foundation for further development of CMOS compatible GMI sensorics for magnetoencephalography.
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    Anisotropic finite element mesh adaptation via higher dimensional embedding
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Dassi, Franco; Si, Hang; Perotto, Simona; Streckenbach, Timo
    In this paper we provide a novel anisotropic mesh adaptation technique for adaptive finite element analysis. It is based on the concept of higher dimensional embedding, which was exploited in [1-4] to obtain an anisotropic curvature adapted mesh that fits a complex surface in ℝ3. In the context of adaptive finite element simulation, the solution (which is an unknown function ƒ: Ω ⊂; ℝd → ℝ) is sought by iteratively modifying a finite element mesh according to a mesh sizing field described via a (discrete) metric tensor field that is typically obtained through an error estimator. We proposed to use a higher dimensional embedding, Φf(x) := (x1, …, xd, s f (x1, …, xd), s ∇ f (x1, …, xd))t, instead of the mesh sizing field for the mesh adaption. This embedding contains both informations of the function ƒ itself and its gradient. An isotropic mesh in this embedded space will correspond to an anisotropic mesh in the actual space, where the mesh elements are stretched and aligned according to the features of the function ƒ. To better capture the anisotropy and gradation of the mesh, it is necessary to balance the contribution of the components in this embedding. We have properly adjusted Φf(x) for adaptive finite element analysis. To better understand and validate the proposed mesh adaptation strategy, we first provide a series of experimental tests for piecewise linear interpolation of known functions. We then applied this approach in an adaptive finite element solution of partial differential equations. Both tests are performed on two-dimensional domains in which adaptive triangular meshes are generated. We compared these results with the ones obtained by the software BAMG - a metric-based adaptive mesh generator. The errors measured in the L2 norm are comparable. Moreover, our meshes captured the anisotropy more accurately than the meshes of BAMG.
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    Quantum diffusion
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2015) Knowles, Antti
    If you place a drop of ink into a glass of water, the ink will slowly dissipate into the surrounding water until it is perfectly mixed. If you record your experiment with a camera and play the film backwards, you will see something that is never observed in the real world. Such diffusive and irreversible behaviour is ubiquitous in nature. Nevertheless, the fundamental equations that describe the motion of individual particles – Newton’s and Schrödinger’s equations – are reversible in time: a film depicting the motion of just a few particles looks as realistic when played forwards as when played backwards. In this snapshot, we discuss how one may try to understand the origin of diffusion starting from the fundamental laws of quantum mechanics.
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    On the evolution of the empirical measure for the hard-sphere dynamics
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Pulvirenti, Mario; Simonella, Sergio
    We prove that the evolution of marginals associated to the empirical measure of a finite system of hard spheres is driven by the BBGKY hierarchical expansion. The usual hierarchy of equations for L1 measures is obtained as a corollary. We discuss the ambiguities arising in the corresponding notion of microscopic series solution to the Boltzmann-Enskog equation.
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    Existence, numerical convergence, and evolutionary relaxation for a rate-independent phase-transformation model
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Heinz, Sebastian; Mielke, Alexander
    We revisit the two-well model for phase transformation in a linearly elastic body introduced and studied in [MTL02]. This energetic rate-independent model is posed in terms of the elastic displacement and an internal variable that gives the phase portion of the second phase. We use a new approach based on mutual recovery sequences, which are adjusted to a suitable energy increment plus the associated dissipated energy and, thus, enable us to pass to the limit in the construction of energetic solutions. We give three distinct constructions of mutual recovery sequences which allow us (i) to generalize the existence result in [MTL02], (ii) to establish the convergence of suitable the evolutionary relaxation from the pure-state model to the relaxed mixture model. All these results rely on weak converge and involve the H-measure as an essential tool.
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    Error estimates of B-spline based finite-element method for the wind-driven ocean circulation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Rotundo, Nella; Kim, Tae-Yeon; Jiang, Wen; Heltai, Luca; Fried, Eliot
    We present the error analysis of a B-spline based finite-element approximation of the stream-function formulation of the large scale winddriven ocean circulation. In particular, we derive optimal error estimates for h-refinement using a Nitsche-type variational formulations of the two simplied linear models of the stationary quasigeostrophic equations, namely the Stommel and StommelMunk models. Numerical results on rectangular and embedded geometries confirm the error analysis.
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    Homogenization of Cahn-Hilliard-type equations via evolutionary Gamma-convergence
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Liero, Matthias; Reichelt, Sina
    In this paper we discuss two approaches to evolutionary Gamma-convergence of gradient systems in Hilbert spaces. The formulation of the gradient system is based on two functionals, namely the energy functional and the dissipation potential, which allows us to employ Gamma-convergence methods. In the first approach we consider families of uniformly convex energy functionals such that the limit passage of the time-dependent problems can be based on the theory of evolutionary variational inequalities as developed by Daneri and Savare 2010. The second approach uses the equivalent formulation of the gradient system via the energy-dissipation principle and follows the ideas of Sandier and Serfaty 2004. We apply both approaches to rigorously derive homogenization limits for Cahn-Hilliard-type equations. Using the method of weak and strong two-scale convergence via periodic unfolding, we show that the energy and dissipation functionals Gamma-converge. In conclusion, we will give specific examples for the applicability of each of the two approaches.