Ockham’s Calculus of Strict Implication

In his main work Summa Logicae written around 1323, William of Ockham developed a system of propositional modal logic which contains almost all theorems of a modern calculus of strict implication. This calculus is formally reconstructed here with the help of modern symbols for the operators of conjunction, disjunction, implication, negation, possibility, and necessity.     

Experimental and numerical investigation of tendons and tendon cells

Tendon injuries are a common problem in medicine. While healthy tendons do not rupture, tendon injuries are mostly accompanied by pathological changes and microruptures. Unfortunately, still less is known about the underlying processes. Thus, in the present study, we introduce artificial damages into native tendon tissue and investigate its mechanical behaviour experimentally. In the second part of this study, we propose a theoretical model for predicting the mechanical behaviour of the damaged tendon and present its validity. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Phosphoramidites as Synthons for Polynucleotide Synthesis

Abstract

Methods for the rapid synthesis of DNA and RNA are described. The procedures involve using nucleoside phosphoramidites as synthons and silica as a polymeric support. Additionally, a novel reaction involving nucleoside O-alkyl methylphosphonothioates is described.     

Optofluidic droplet router

This contribution presents an optofluidic droplet router which is able to route and steer microdroplets using optically induced forces created solely by the bulk photovoltaic effect on a nonlinear substrate. The combination of microfluidic tools with the properties of a photorefractive crystal allows for the generation of dielectrophoretic forces that can be either repulsive, leading to virtual barriers, or attractive, creating virtual rails. The sign of these forces is solely determined by the electrical properties of the liquid medium under investigation. Moreover, the induced structures on the bottom of the microfluidic channel are optically reconfigurable, so that the same device can easily be adopted for different purposes. Appropriate droplet‐generating devices are fabricated by UV illumination of SU‐8 and polydimethylsiloxane replica molding of the master structures. The bottom of the channels is formed by an iron‐doped lithium niobate crystal, whose internal electric fields are induced by structured illumination patterns and exert dielectrophoretic forces on droplets in the microfluidic section.

     

A surface oriented solid formulation based on a hybrid Galerkin-collocation method

The contribution is concerned with a numerical method to analyze the mechanical behavior of 3D solids. The method employs directly the geometry defined by the boundary representation modeling technique, which is frequently used in CAD to define solids. It combines the benefits of the isogeometric analysis methodology with the scaled boundary finite element method. In the present approach, only the boundary surfaces of the solid are discretized. No tensor-product structure of three-dimensional objects is exploited to parametrize the physical domain. The weak form is applied only on the boundary surfaces. The governing partial differential equations of elasticity are transformed to an ordinary differential equation (ODE) of Euler type. The isogeometric Galerkin approach is employed to approximate the displacement response at the boundary surfaces. It exploits the two-dimensional NURBS objects to parametrize the boundary surfaces. To solve the Euler type ODE, the NURBS based collocation approach is applied. The accuracy of the method is validated against the analytical solutions. The presented method is able to analyze solids, which are bounded by an arbitrary number of surfaces. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application and modification of the POD method and the POD-DEIM for model reduction in porous-media simulations

Researchers with a continuum-mechanical background typically use a multi-phasic and multi-component modelling approach for materials with a saturated porous microstructure. Therefore, the mechanical behaviour is considered in a continuum-mechanical manner and solved using the finite-element method (FEM). The developed models need to be complex enough to capture the relevant properties of the considered materials, what often results in expensive simulations with a very large number of degrees of freedom (DOF). The aim of the present contribution is to reduce the computing time of these simulations through model-reduction methods, while the accuracy of the solution needs to be maintained. Therefore, the method of proper-orthogonal decomposition (POD) for linear problems and the discrete-empirical-interpolation method (DEIM) in combination with the POD method (POD-DEIM) for nonlinear problems are investigated. Using the POD method, a given data set is approximated with a low-dimensional subspace. To generate this data set, the vector of unknowns of the FE simulation is stored in a pre-computation in the full (unreduced) system in each time-step (so-called “snapshots” of the system). Dealing with porous-media problems, the primary variables are the solid displacement, the pore pressure and, depending on the particular problem, other primary variables. Following this, the primary variables have entries with very huge differences in their absolute values. As a result, non-negligible rounding errors may occur when applying the POD method. To overcome this problems, modifications of the classical POD method need to be performed for such problems. The present contribution discusses this issue and presents results for the reduced simulations of porous media. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)