Optimal Control of Large Deformation Elasticity by Fiber Tension

Object of our interest is an elastic body Ω ⊂ ℝ³ which we can deform by applying a tension along certain given short fibers inside the body. The deformation of the body is desribed by a hyperelastic model with polyconvex energy density and a special energy functional for the tension along the fibers. We seek to apply (possibly large) deformations to the body so that a desired shape is obtained. To this end, we formulate an optimal control problem for the fiber tension field. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparison of numerical homogenization techniques in BT-CFO multiferroic particle composites

This work is restricted to linear material behavior, i.e. the structure is considered to be in a perfectly poled state. Different numerical homogenization methods are investigated and used to calculate effective properties of a 0-2 composite modelled in reprensentative volume elements. Bariumtitanate (BT) and cobaltferrite (CFO) are employed in the Finite Element model, where the roles of matrix and inclusion are mutable in principle. Mixed magnetoelectromechanical boundary conditions based on different homogenization theories are applied to the model. The calculated macroscopic behaviors described by the different approaches are compared and presented in the paper. The special focus is on the prediction of coefficients of magnetoelectric coupling with respect to an optimization of the structural arrangement of the composite. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of Surfactant Concentration in a Coupled Bulk Surface Problem

Surface active agents (surfactants) are on high interest for physical and chemical industries. Their presence lowers the surface tension of fluids. This is used to achieve special flow properties. These mechanisms are not only influenced by the overall amount of surfactant. They highly depend on the local surfactant distribution. The surfactant concentration is modeled by two convection diffusion equations, one in the bulk and the other on its surface. Adsorption- and desorption processes are included and lead to a (non linear) coupling of both equations. We present a numerical scheme for solving the coupled problem. Additionally, first analytical results will be given. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

K-Theory of Surfaces at the Prime 2

We prove that for smooth surfaces over real closed fields, and a class of smooth projective surfaces over a real number field, the map between mod 2 algebraic and étale K-theory is an isomorphism in sufficiently large degrees. For a class of smooth projective surfaces over a real closed field, including rational surfaces, complete intersections and K3-surfaces over the real numbers, we explicate the abutment of the mod 2 motivic cohomology to algebraic K-theory spectral sequence.     

The idle period of the finite G/M/1 queue with an interpretation in risk theory

We consider a G/M/1 queue with restricted accessibility in the sense that the maximal workload is bounded by 1. If the current workload V _t of the queue plus the service time of an arriving customer exceeds 1, only 1−V _t of the service requirement is accepted. We are interested in the distribution of the idle period, which can be interpreted as the deficit at ruin for a risk reserve process R _t in the compound Poisson risk model. For this risk process a special dividend strategy applies, where the insurance company pays out all the income whenever R _t reaches level 1. In the queueing context we further introduce a set-up time a∈[0,1]. At the end of every idle period, an arriving customer has to wait for a time units until the server is ready to serve it.     

On Mincʼs sheltered middle path

This paper shows that a construction, which was introduced by Piotr Minc in connection with a problem that came from Helly type theorems and that allows to replace three PL-arcs with a “sheltered middle path”, can in the case of general (non-PL) paths result in the topologist?s sine curve.     

Inverse closed ultradifferential subalgebras

In previous work we have shown that classical approximation theory provides methods for the systematic construction of inverse-closed smooth subalgebras. Now we extend this work to treat inverse-closed subalgebras of ultradifferentiable elements. In particular, Carleman classes and Dales–Davie algebras are treated. As an application the result of Demko, Smith and Moss, and Jaffard on the inverse of a matrix with exponential decay is obtained within the framework of a general theory of smoothness.     

Energy harvesting through arterial wall deformation: A FEM approach to fluid–structure interactions and magneto-hydrodynamics

Engineers are confronted with the energy demand of active medical implants in patients with increasing life expectancy. Scavenging energy from the patient’s body is envisioned as an alternative to conventional power sources. Joining in this effort towards human-powered implants, we propose an innovative concept that combines the deformation of an artery resulting from the arterial pressure pulse with a transduction mechanism based on magneto-hydrodynamics. To overcome certain limitations of a preliminary analytical study on this topic, we demonstrate here a more accurate model of our generator by implementing a three-dimensional multiphysics finite element method (FEM) simulation combining solid mechanics, fluid mechanics, electric and magnetic fields as well as the corresponding couplings. This simulation is used to optimize the generator with respect to several design parameters. A first validation is obtained by comparing the results of the FEM simulation with those of the analytical approach adopted in our previous study. With an expected overall conversion efficiency of 20% and an average output power of 30 μW, our generator outperforms previous devices based on arterial wall deformation by more than two orders of magnitude. Most importantly, our generator provides sufficient power to supply a cardiac pacemaker.     

Bernstein theorems for length and area decreasing minimal maps

In this article we prove Liouville and Bernstein theorems in higher codimension for length and area decreasing maps between two Riemannian manifolds. The proofs are based on a strong elliptic maximum principle for sections in vector bundles, which we also present in this article.