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The algebraic structures called quandles constitute a complete invariant for tame knots. However, determining when two quandles are isomorphic is an empirically hard problem, so there is some dissatisfaction with quandles as knot invariants. We have confirmed this apparent difficulty, showing within the framework of Borel reducibility that the general isomorphism problem for quandles is as complex...
In this short note, we address the discretization of optimal control problems with higher order polynomials. We develop a necessary and sufficient condition to ensure that weak limits of discrete feasible controls are feasible for the original problem. We show by means of a simple counterexample that a naive discretization by higher order polynomials can lead to non‐feasible limits of sequences of...
Despite its significance in nonlinear controller design, the verification of the property of differential flatness and the identification of so‐called flat outputs is a continuing research topic. However, the difficulty of both verification and identification heavily depends on the representation of the system. This contribution shows that flatness may be a far less complicated matter, depending on...
Due to their simple implementation based on a constant gain matrix, high gain observers are very common in practical applications. We consider systems whose dynamics can be decomposed into a linear and a nonlinear part, where the nonlinear part meets some Lipschitz condition. In many cases there exists a finite bound on the maximum feasible Lipschitz constant for which the error dynamics can be stabilized...
The aim of this work is to give a procedure to compute an ISS Lyapunov function (ISS ‐ input‐to‐state stability) for a large‐scale networked control system (NCS) in which sensors, controllers and actuators are connected via multiple communication networks that operate asynchronously, [1]. The main idea is that the NCS is modeled as an interconnection of controlled subsystems and (hybrid) error systems,...
We study disturbance decoupling for linear descriptor systems. Compared to previous approaches, where state feedback is used, we use the concept of behavioral feedback which allows to study a larger class of systems. We derive geometric characterizations for solvability of the disturbance decoupling problem following the classical approach. Exploiting the freedom in the choice of the behavioral feedback...
The objective of topology optimization is to find a mechanical structure with maximum stiffness and minimal amount of used material for given boundary conditions [2]. There are different approaches. Either the structure mass is held constant and the structure stiffness is increased or the amount of used material is constantly reduced while specific conditions are fulfilled. In contrast, we focus on...
The rheological behaviour of protein solutions containing bubbles at rest, but particularly during fluid mechanical transport is not sufficiently investigated yet. Protein foams have a great importance in food production because of their special sensory properties. A suspension that contains bubbles in a Newtonian liquid exhibits inherently a complex rheological behaviour, such as elastic effects,...
The Jungebad apparatus is used to generate oil‐dispersion baths in medical applications. The oil‐water dispersion is produced by dispersing medically‐effective oil while filling the bathtub. The aim is to produce smaller droplets in comparison to conventionally produced oil‐dispersion baths to generate a high surface‐to‐volume ratio of the oil. Additionally, the oil should be dispersed homogenously...
An ODE model to predict the temperature field of periodic open cell metal foams applied in catalysis as carrier structures is presented. The catalytic and highly endothermic reaction takes place in a porous layer which surround the struts of the foam and releases gas from a fluid. The one‐dimensional model includes dependencies of the foam structure (strut radius, shape of strut), process conditions...
An explicit algebraic turbulent‐stress model is built in the framework of so‐called Rodi's weak‐equilibrium approximation, which, taking into account the known model representations for the pressure‐strain‐rate correlation and turbulence‐dissipation rate, reduces the differential equations for the Reynolds‐tensor components to a system of quasi‐linear algebraic equations for the five independent components...
Für den wasserbaulichen Entwurf von Wasserkraftanlagen und ihre strömungsmechanische Optimierung werden neben dem rein auf Erfahrungswerten basierenden Entwurf vor allem experimentelle Untersuchungen am physikalischen Teilmodell oder Vollmodell im Wasserbaulabor eingesetzt. Strömungsmechanische Untersuchungen mit Hilfe numerischer Strömungsprogramme auf der Basis von 2D‐ und 3D‐Verfahren kommen teilweise...
In the proposed phase field model a continuous order parameter indicates the phase distribution (liquid/gas). An energy density functional which is dependent on the surface tensions and defined by three contributions yields the total energy of the system. An equilibrium state is then computed by minimizing this energy of the system using an evolution equation. Details of the algorithmic implementation...
To describe material behaviour more precisely than nowadays, tomorrows simulation software will include multi‐scale homogenisation techniques. State of the art are various scale bridging strategies, like FE‐ODE, FE‐Phasefield or FE2‐Method. We are dealing with the FE2‐Method, see [3], [4], which gives us the possibility to take the geometric, discrete micro‐structure of a material into account. Furthermore,...
In the context of clinical treatment, reliable models of biological materials can provide further information of the occurring processes. For this purpose, the prediction of various simulation scenarios or real‐time simulations is desirable. A broad variety of biological materials, such as intervertebral discs or skeletal muscles, exhibit a porous microstructure and are conveniently simulated using...
This contribution focuses on the effective heat conductivity of short fibre reinforced materials. For this purpose, a representative volume element (RVE), which is able to represent all possible fibre orientation distributions, is introduced and modelled in ABAQUS. Subsequently, the effective heat conductivity of the RVE is derived, employing a numerical homogenisation scheme, and a phenomenological...
A material model is presented, which describes the material behavior of rubbery materials in the case of uniaxial tension/compression. It includes the characteristic nonlinearity of rubber at large strains as well as strain induced softening called Mullins effect. The generalization to arbitrary deformations is done with the concept of representative directions, published by Freund & Ihlemann...
In transformation induced plasticity (TRIP) steel a diffusionless austenitic‐martensitic phase transformation induced by plastic deformation can be observed, resulting in excellent macroscopic properties. In particular low‐alloyed TRIP steels, which can be obtained at lower production costs than high‐alloyed TRIP steel, combine this mechanism with a heterogeneous arrangement of different phases at...
The overall deformation behavior of rubber‐toughened polymers (e.g. PC/ABS blends) exhibits a pronounced plastic dilatancy. As this volume increase results from diverse micromechanisms the appropriate structure of a macroscopic model is not obvious. In this contribution, different material models featuring plastic dilatancy are compared with regard to their ability to capture the deformation behavior...
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