Optimal order finite difference approximation of generalized solutions to the biharmonic equation in a cube

We prove an optimal order error bound in the discrete $H^2(\Omega)$ norm for finite difference approximations of the first boundary-value problem for the biharmonic equation in $n$ space dimensions, with $n \in \{2,\dots,7\}$, whose generalized solution belongs to the Sobolev space $H^s(\Omega) \cap H^2_0(\Omega)$, for $\frac{1}{2} \max(5,n) < s \leq 4$, where $\Omega = (0,1)^n$. The result extends the range of the Sobolev index $s$ in the best convergence results currently available in the literature to the maximal range admitted by the Sobolev embedding of $H^s(\Omega)$ into $C(\overline\Omega)$ in $n$ space dimensions

Local Reorientation Dynamics of Semiflexible Polymers in the Melt

The reorientation dynamics of local tangent vectors of chains in isotropic amorphous melts containing semiflexible model polymers was studied by molecular dynamics simulations. The reorientation is strongly influenced both by the local chain stiffness and by the overall chain length. It takes place by two different subsequent processes: A short-time non-exponential decay and a long-time exponential reorientation arising from the relaxation of medium-size chain segments. Both processes depend on stiffness and chain length. The strong influence of the chain length on the chain dynamics is in marked contrast to its negligible effect on the static structure of the melt. The local structure shows only a small dependence on the stiffness, and is independent of chain length. Calculated correlation functions related to double-quantum NMR experiments are in qualitative agreement with experiments on entangled melts. A plateau is observed in the dependence of segment reorientation on the mean-squared displacement of the corresponding chain segments. This plateau confirms, on one hand, the existence of reptation dynamics. On the other hand, it shows how the reptation picture has to be adapted if, instead of fully flexible chains, semirigid chains are considered.Comment: 29 pages, several figures, accepted by Macromolecule

Local chain ordering in amorphous polymer melts: Influence of chain stiffness

Molecular dynamics simulation of a generic polymer model is applied to study melts of polymers with different types of intrinsic stiffness. Important static observables of the single chain such as gyration radius or persistence length are determined. Additionally we investigate the overall static melt structure including pair correlation function, structure function and orientational correlation function.Comment: 13 pages, 15 figures, PCCP accepte

How does the chain extension of poly (acrylic acid) scale in aqueous solution? A combined study with light scattering and computer simulation

This work adresses the question of the scaling behaviour of polyelectrolytes in solution for a realistic prototype: We show results of a combined experimental (light scattering) and theoretical (computer simulations) investigation of structural properties of poly (acrylic acid) (PAA). Experimentally, we determined the molecular weight (M_W) and the hydrodynamic radius (R_H) by static light scattering for six different PAA samples in aqueous NaCl-containing solution (0.1-1 mol/L) of polydispersity D_P between 1.5 and 1.8. On the computational side, three different variants of a newly developed mesoscopic force field for PAA were employed to determine R_H for monodisperse systems of the same M_W as in the experiments. The force field effectively incorporates atomistic information and one coarse-grained bead corresponds to one PAA monomer. We find that R_H matches with the experimental data for all investigated samples. The effective scaling exponent for R_H is found to be around 0.55, which is well below its asymptotic value for good solvents. Additionally, data for the radius of gyration (R_G) are presented.Comment: 17 pages, 3 figures, submitted to Macromolecule

Around-Body Interaction: Leveraging Limb Movements for Interacting in a Digitally Augmented Physical World

Recent technological advances have made head-mounted displays (HMDs) smaller and untethered, fostering the vision of ubiquitous interaction with information in a digitally augmented physical world. For interacting with such devices, three main types of input - besides not very intuitive finger gestures - have emerged so far: 1) Touch input on the frame of the devices or 2) on accessories (controller) as well as 3) voice input. While these techniques have both advantages and disadvantages depending on the current situation of the user, they largely ignore the skills and dexterity that we show when interacting with the real world: Throughout our lives, we have trained extensively to use our limbs to interact with and manipulate the physical world around us. This thesis explores how the skills and dexterity of our upper and lower limbs, acquired and trained in interacting with the real world, can be transferred to the interaction with HMDs. Thus, this thesis develops the vision of around-body interaction, in which we use the space around our body, defined by the reach of our limbs, for fast, accurate, and enjoyable interaction with such devices. This work contributes four interaction techniques, two for the upper limbs and two for the lower limbs: The first contribution shows how the proximity between our head and hand can be used to interact with HMDs. The second contribution extends the interaction with the upper limbs to multiple users and illustrates how the registration of augmented information in the real world can support cooperative use cases. The third contribution shifts the focus to the lower limbs and discusses how foot taps can be leveraged as an input modality for HMDs. The fourth contribution presents how lateral shifts of the walking path can be exploited for mobile and hands-free interaction with HMDs while walking.Comment: thesi

Service Modularization in an Evolving Context: A Comparison between the Old and the New World of Automotive Engineering Services in Germany

Modularity in services has emerged as a promising design approach that offers a sound balance between cost-efficiency in service production and customization. However, the existing literature draws on a narrow scope of service design that considers certain characteristics of service as constraints to the successful adoption of the concept, i.e. service modularization. The growing importance of service as a central logic to explain value creation suggests the need to expand this view and to understand how service modularization and changes in dynamic service contexts may come together. This article makes a first attempt in this direction by exploring service modularization in the light of major restructurings in the field of automotive engineering services (AES) in Germany. Through 22 qualitative interviews with customers and providers of AES, this article presents a conceptual process model that explains how service modularization of AES is propelled by transformational forces in an evolving service context