University of Paderborn

About: University of Paderborn is a education organization based out in Paderborn, Nordrhein-Westfalen, Germany. It is known for research contribution in the topics: Computer science & Context (language use). The organization has 6684 authors who have published 16929 publications receiving 323154 citations.

The Exponentiated Hencky-Logarithmic Strain Energy. Part I: Constitutive Issues and Rank-One Convexity

Abstract: We investigate a family of isotropic volumetric-isochoric decoupled strain energies $$\begin{aligned} F\mapsto W_{\mathrm{eH}}(F):=\widehat{W}_{\mathrm{eH}}(U):=\left \{ \begin{array}{l@{\quad}l} \frac{\mu}{k} e^{k\|\operatorname {dev}_n\log{U}\|^2}+\frac{\kappa}{{2 {\widehat {k}}}} e^{\widehat{k}[\operatorname {tr}(\log U)]^2}&\text{if}\ \det F>0,\\ +\infty&\text{if}\ \det F\leq0, \end{array} \right . \end{aligned}$$ based on the Hencky-logarithmic (true, natural) strain tensor logU, where μ>0 is the infinitesimal shear modulus, $\kappa=\frac{2\mu+3\lambda}{3}>0$ is the infinitesimal bulk modulus with λ the first Lame constant, $k,\widehat{k}$ are additional dimensionless material parameters, F=∇φ is the gradient of deformation, $U=\sqrt{F^{T} F}$ is the right stretch tensor and is the n-dimensional deviatoric part of the strain tensor logU. For small elastic strains, W eH approximates the classical quadratic Hencky strain energy $$\begin{aligned} F\mapsto W_{\mathrm{H}}(F):=\widehat{W}_{\mathrm{H}}(U)&:={\mu}\| \operatorname {dev}_n\log U\|^2+\frac{\kappa}{2}\bigl[\operatorname{tr}( \log U)\bigr]^2, \end{aligned}$$ which is not everywhere rank-one convex. In plane elastostatics, i.e., n=2, we prove the everywhere rank-one convexity of the proposed family W eH, for $k\geq\frac{1}{4}$ and $\widehat{k}\geq\frac{1}{8}$ . Moreover, we show that the corresponding Cauchy (true)-stress-true-strain relation is invertible for n=2,3 and we show the monotonicity of the Cauchy (true) stress tensor as a function of the true strain tensor in a domain of bounded distortions. We also prove that the rank-one convexity of the energies belonging to the family W eH is not preserved in dimension n=3 and that the energies $$\begin{aligned} F\mapsto\frac{\mu}{k}e^{k\|\log U\|^2},\qquad F\mapsto\frac{\mu }{k}e^{\frac{k}{\mu} \bigl(\mu\|\operatorname {dev}_n\log U\|^2+\frac{\kappa}{2}[\operatorname {tr}(\log U)]^2 \bigr)}, \quad F \in\mathrm{GL}^+(n), n\in \mathbb {N}, n\geq2 \end{aligned}$$ are also not rank-one convex.

Twenty Years of Service Guarantee Research: A Synthesis

Abstract: During the past two decades, service guarantees have received increased attention as a means for service firms to attract and retain customers and gain a competitive edge in the marketplace. Although many academic studies, referring to diverse service guarantee aspects, have appeared during this time, a synthesis of research is needed to clarify what researchers have learned about service guarantees and what remains unknown. To evaluate the state of published research on service guarantees, 109 articles published from 1985 to 2008 are collected and analyzed. The resultant review reveals a significant change in the type of research being performed, including a shift toward greater interest in the impact of service guarantees on consumer behavior and service firms. However, a significant shortfall marks empirical work directed toward the internal and operational effects of service guarantees. The effects of service guarantees on service performance, service recovery, and return on service guarantee investments are topics in need of further research.

R-Matrices and Higher Poisson Brackets for Integrable Systems

Abstract: The tri-hamiltonian nature of Lax-equations is revealed: starting with an R-matrix on an associative algebra g equipped with a trace form there are g compatible Poisson brackets with linear, quadratic and cubic dependence on the coordinates. The invariant functions (Casimir functions) on g* are in involution relative to these brackets, they yield a hierarchy of integrable tri-hamiltonian Lax-equations. The results can be applied to solvable PDE’s such as the Korteweg-de Vries equation as well as to finite integrable systems such as the Toda lattice. In these cases the Poisson structures considered here turn out to be abstract versions of the first 3 hamiltonian operators of these equations obtained by their well-known recursion operators.

Nonlinear Metasurface for Simultaneous Control of Spin and Orbital Angular Momentum in Second Harmonic Generation.

Abstract: The spin and orbital angular momentum (SAM and OAM) of light is providing a new gateway toward high capacity and robust optical communications. While the generation of light with angular momentum is well studied in linear optics, its further integration into nonlinear optical devices will open new avenues for increasing the capacity of optical communications through additional information channels at new frequencies. However, it has been challenging to manipulate the both SAM and OAM of nonlinear signals in harmonic generation processes with conventional nonlinear materials. Here, we report the generation of spin-controlled OAM of light in harmonic generations by using ultrathin photonic metasurfaces. The spin manipulation of OAM mode of harmonic waves is experimentally verified by using second harmonic generation (SHG) from gold meta-atom with 3-fold rotational symmetry. By introducing nonlinear phase singularity into the metasurface devices, we successfully generate and measure the topological charges o...