bluuebunny/crossref_metadata_2025 huggingface dataset:
Geometric uncertainties in finite element models of mistuned bladed disks
Authors: Koebelé‐Cousquer Maxime , Proppe Carsten
Published: October 2016

This paper presents a method to develop reduced‐order models of bladed disks with geometric mistuning, which is based on polynomial choas approximation of modes of random eigenvalue subproblems. This method allows to reduce mass and stiffness matrices without evaluating the deviation in these matrices due to mistuning. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Input‐output behaviour of a stochastic Galerkin method for a low pass filter
Authors: Pulch Roland
Published: October 2016

We apply the stochastic Galerkin method to a linear dynamical system, which includes random variables to quantify uncertainties in physical parameters. The input‐output behaviour of the stochastic Galerkin system is described by a transfer function in the frequency domain. The importance of each output component can be estimated by Hardy norms. We investigate a Hardy norm in the case of a linear dynamical system modelling the electric circuit of a low pass filter. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Bat algorithm for optimization of reinforced concrete columns
Authors: Bekdas Gebrail , Nigdeli Sinan Melih
Published: October 2016

In structural mechanics, when the design contains two different materials with opposite mechanical behaviours and costs, the optimum design cannot exactly found. In that case, numerical optimization algorithms are a good source. Reinforced concrete design shows that behaviour since concrete is a cheap material comparing to steel while the tensile strength of concrete is very low to use. The cross sections are effective on the stresses and balance of tensile and compressive forces. This situation shows the importance of the dimension optimization of reinforced concrete members. Also, the number and size of the reinforcements need an optimization. The place of the reinforcements is effective on the place of tensile forces in the calculation of axial force and flexural moment capacity. In this paper, reinforced concrete columns are optimized for the cost minimization by employing a bio‐inspired metaheuristic algorithm called bat algorithm. The idealization of the echolocation behaviour of bats is the inspiration of the bat algorithm. Differently from the algorithms, the bat algorithm uses global and local optimization with a changeable probability. The optimization process considers the security measures and slenderness of the according to the design regulation called ACI 318. The slenderness is taken into consideration by using a magnified design flexural moment, which is factored by a value defined according to the buckling load and axial load of columns. The proposed approach is applied for different numerical cases and the results are compared with the approach using harmony search algorithm. The present approach is effective for the optimization problem. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Step‐size Adaptation in a Multi‐objective Differential Evolution Algorithm
Authors: Boblenz Christian , Bestle Dieter
Published: October 2016

If Differential Evolution (DE) is applied to multi‐objective optimization problems, some of its features like automatic problem‐specific step‐size adaptation gets lost. This can be resolved by modifying the DE equations. Three strategies are proposed and compared with existing algorithms. It is shown, that the proposed strategies deliver a superior convergence and preserve the positive characteristics of DE known from solving mono‐objective optimization problems. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An extended cost estimation model for a multi‐material topology optimization approach
Authors: Falkenberg Paul , Vietor Thomas
Published: October 2016

The manufacturing costs of hybrid parts comprise several different proportions depending on the manufacturing process and the materials used. A simplified cost model based on the material weights is therefore no longer sufficient.

In this paper, an approach for the weight and costs optimization of hybrid parts is presented. An extended costs calculation function regarding additional manufacturing costs and the integration of a new cost objective in the optimization process is investigated. The effects of the consideration of costs on the optimization results will be qualitatively shown on a simple example structure. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A modified metaheuristic optimization approach on the structural identification and damage detection of an experimentally tested wind turbine supporting structure
Authors: Jahjouh Mahmoud , Nackenhorst Udo
Published: October 2016

Wind energy conversion devices (WECDs) are sensitive structures subjected to high force fluctuations, making them prone to damage. Thus, a global identification and damage detection technique is important to keep track of any changes in the structural characteristics of the WECD.

In this contribution, a previously‐developed structural identification and damage detection algorithm, namely: the Modified Adaptive HaRmony SearcH ALgorithm (MARSHAL), is used to perform structural identification and damage detection to a laboratory test model of a WECD supported by a tripile. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An evolution equation based approach to topology optimization
Authors: Jantos Dustin Roman , Junker Philipp , Hackl Klaus
Published: October 2016

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 growth of a optimal structure from a void model space and solve this problem by introducing a variational problem considering the spatial distribution of structure mass (or density field) as variable [3]. By minimizing the Gibbs free energy according to Hamilton's principle in dynamics for dissipative processes, we are able to find an evolution equation for the internal variable describing the density field. Hence, our approach belongs to the growth strategies used for topology optimization. We introduce a Lagrange multiplier to control the total mass within the model space [1]. Thus, the numerical solution can be provided in a single finite element environment as known from material modeling. A regularization with a discontinuous Galerkin approach for the density field enables us to suppress the well‐known checkerboarding phenomena while evaluating the evolution equation within each finite element separately [4]. Therefore, the density field is no additional field unknown but a Gauß‐point quantity and the calculation effort is strongly reduced. Finally, we present solutions of optimized structures for different boundary problems. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Robust Damping in Self‐Excited Mechanical Systems
Authors: Jekel Dominic , Clerkin Eoin , Hagedorn Peter
Published: October 2016

A technique to optimize the stability of a general mechanical system is outlined. The method relies on decomposing the damping matrix into several component matrices, which may have some special structure or physical relevance. An optimization problem can then be formulated where the ratio of these are varied to either stabilize or make more stable the equilibrium state subject to sensible constraints. For the purpose of this study, we define a system to be more stable if its eigenvalue with largest real part is as negative as possible. The technique is demonstrated by applying it to an introduced non‐dimensionalized variant of a known minimal wobbling disc brake model. In this case, it is shown to be beneficial to shift some damping from the disc to the pins for a system optimized for stability. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Optimisation of Structures with Inelastic Deformations
Authors: Liedmann Jan , Barthold Franz‐Joseph
Published: October 2016

In context of design optimisation, the treatment of inelastic, path‐dependent materials is a topic of interest. As opposed to purely elastic materials, it is necessary to store and analyse the deformation history in order to appropriately describe inelastic material behaviour. For design optimisation of structures sensitivities of all quantities of influence have to be computed so as to use gradient based optimisation algorithms. Considering path‐dependent materials the sensitivities of internal variables that represent the deformation history have to be additionally calculated. A numerical effective way of determining sensitivities is the variational sensitivity analysis. This approach is applied to develop a powerful and effective algorithm to compute sensitivities of the structural response with respect to their geometric design. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Global Optimization of the Shape of a Suborbital Space Vehicle
Authors: Nastase Adriana
Published: October 2016

The determination of the global optimized (GO) shapes of flying configurations leads to extended variational problems with free boundaries. The author has developed special optimization strategies called optimum optimorum and iterative optimum optimorum strategies and have used them for the design of GO shapes of three models, which are of minimum drag at three different supersonic cruising Mach numbers. These optimization strategies can be used for the determination of new GO shapes of more performant supersonic transport aircraft and space vehicles. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Structural design sensitivity analysis in context of non‐linear buckling
Authors: Radau Lukas , Gerzen Nikolai , Barthold Franz‐Joseph
Published: October 2016

Structural stability is an important issue to ensure the safety of thin walled structures. Shell structures are considered in context of linear and non‐linear buckling. The design sensitivity analysis with respect to modifications in shape is motivated. Analytically derived gradient information is employed for shape optimisation purposes using solid shells. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Combined Newton‐Kurchatov method for solving nonlinear operator equations
Authors: Iakymchuk Roman , Shakhno Stepan , Yarmola Halyna
Published: October 2016

We investigate local and semi‐local convergence of the combined Newton‐Kurchatov method under the classical and generalized Lipschitz conditions for solving nonlinear equations. The convergence order of the method is examined and the uniqueness ball for the solution of the nonlinear equation is proved. Numerical experiments are conducted on test problems. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A note on terminology in multigrid methods
Authors: Birken Philipp , Bull Jonathan , Jameson Antony
Published: October 2016

We compare terminology used in the literature on multigrid methods for compressible computational fluid dynamics to that used in linear multigrid theory. Several popular iterative and direct smoothers are presented side‐by‐side using the same terminology. We argue for greater analysis of these methods in order to place them into a more rigorous framework and to identify the most promising candidates for future development. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical solution to low rank perturbed Lyapunov equations by the sign function method
Authors: Benner Peter , Denißen Jonas
Published: October 2016

We investigate the numerical solution to a low rank perturbed Lyapunov equation
ATX + XA = W
via the sign function method (SFM). The sign function method has been proposed to solve Lyapunov equations, see e.g. [1], but here we focus on a framework where the matrix A has a special structure, i. e.
A = B + UCVT,
where B is a blockdiagonal matrix and UCVT is a low rank perturbation. We show that this structure can be kept throughout the sign function iteration but the rank of the perturbation doubles per iteration. Therefore, we apply a low rank approximation to the perturbation in order to keep its numerical rank small. We compare the standard SFM with its structure preserving variant presented in this paper by means of numerical examples from viscously damped mechanical systems. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A Connection between Time Domain Model Order Reduction and Moment Matching
Authors: Hund Manuela , Saak Jens
Published: October 2016

We investigate the time domain model order reduction (MOR) framework using general orthogonal polynomials by Jiang and Chen [4] and extend their idea by exploiting the structure of the corresponding linear system of equations. Identifying an equivalent Sylvester equation we show a connection to a rational Krylov subspace, and thus moment matching. This theoretical link between the MOR techniques is illustrated by one numerical example. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Convergence Analysis of the Dirichlet‐Neumann Iteration for Finite Element Discretizations
Authors: Monge Azahar , Birken Philipp
Published: October 2016

We analyze the convergence rate of the Dirichlet‐Neumann iteration for the fully discretized unsteady transmission problem. Specifically, we consider the coupling of two linear heat equations on two identical non overlapping domains with jumps in the material coefficients across these. In this context, we derive the iteration matrix of the coupled problem. In the 1D case, the spectral radius of the iteration matrix tends to the ratio of heat conductivities in the semidiscrete spatial limit, but to the ratio of the products of density and specific heat capacity in the semidiscrete temporal one. This explains the fast convergence previously observed for cases with strong jumps in the material coefficients. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On isotropy conditions in second gradient materials
Authors: Münch Ingo , Neff Patrizio
Published: October 2016

In gradient elasticity, isotropy and frame‐indifference requirements are sensitive to the homogeneity of the applied rotation field Q ∈ SO(3). This is in contrast to standard elasticity, where only first gradients of the deformation are under consideration. We use a diffeomorphism to show the effect of inhomogeneous coordinate transformation to the form‐invariance requirement of elastic energy. From a classical geometric rigidity result follows that the appearance of a right‐local SO(3)‐invariance condition is not the general condition for isotropy. The correct statement for isotropy in second gradient elasticity should be a right‐global SO(3)‐invariance condition. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Fast interior point solvers for H1‐regularized PDE‐constrained optimization problems
Authors: Pearson John W. , Gondzio Jacek
Published: October 2016

We consider Newton systems arising from the interior point solution of PDE‐constrained optimization problems. In particular, we examine problems where the control variable is regularized by an H1‐norm within the cost functional. We present preconditioned iterative methods for the resulting matrix systems, and justify the potency of our approach through numerical experiments. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Towards adaptive discontinuous Petrov‐Galerkin methods
Authors: Bringmann P. , Carstensen C. , Gallistl D. , Hellwig F. , Peterseim D. , Puttkammer S. , Rabus H. , Storn J.
Published: October 2016

The discontinuous Petrov‐Galerkin (dPG) method is a minimum residual method with broken test functions for instant stability. The methodology is written in an abstract framework with product spaces. It is applied to the Poisson model problem, the Stokes equation, and linear elasticity with low‐order discretizations. The computable residuum leads to guaranteed error bounds and motivates adaptive refinements. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Multiscale Petrov‐Galerkin FEM for Acoustic Scattering
Authors: Gallistl Dietmar , Peterseim Daniel , Carstensen Carsten
Published: October 2016

We present a pollution‐free Petrov‐Galerkin multiscale finite element method for the Helmholtz problem with large wave number κ. We use standard continuous Q1 finite elements at a coarse discretization scale H as trial functions. The test functions are the solutions of local problems at a finer scale h. The diameter of the support of the test functions behaves like mH for some oversampling parameter m. Provided m is of the order of log(κ) and h is sufficiently small, the resulting method is stable and quasi‐optimal in the regime where H is proportional to κ−1. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Uncertainty Quantification for Two‐Phase Flow in Heterogeneous Porous Media
Authors: Köppel Markus , Rohde Christian
Published: October 2016

The simulation of flow and transport in porous media such as aquifers often involve dealing with complex heterogeneities. They are characterized by varying hydrogeological properties which differ strongly from the adjacent medium and often lead to significant changes of the flow behavior. However detailed information about the location of such heterogeneities is not always known. The deterministic models thus need to be extended stochastically to quantify uncertainties. As mathematical model we use the capillarity‐free fractional flow formulation for two immiscible and incompressible fluid phases in a two‐dimensional and partitioned domain. To cope with the randomly located heterogeneity interfaces we employ a stochastic Galerkin (SG) method [4]. The physical space of this system then is modelled by a central upwind finite volume scheme [5] in combination with mixed finite elements [7]. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Variational integrators of higher order for constrained dynamical systems
Authors: Wenger Theresa , Ober‐Blöbaum Sina , Leyendecker Sigrid
Published: October 2016

The variational integrators presented in [5] are applied to systems with holonomic constraints, yielding constrained higher order variational integrators that are an extension of the constrained Galerkin methods in [4]. The construction of the integrators bases on a discrete version of Hamilton's principle. The inheritance of qualitative properties associated to the solution of the dynamical system to the discrete solution is analysed. Furthermore, the convergence order of the integrators and the computational efficiency is investigated numerically. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the relaxation gap for PDE mixed‐integer optimal control problems
Authors: Hante Falk M.
Published: October 2016

Mixed‐integer optimal control problems require taking discrete and continuous control decisions for the optimization of a dynamical system. We consider dynamics governed by partial differential equations of evolution type and assess the problem by relaxation and rounding strategies. For this solution approach, we present a priori estimates for semilinear evolutions on Banach spaces concerning the optimality gap. The theoretical results show that the gap can be made arbitrary small. We demonstrate the numerical performance of the approach on benchmark problems of parabolic type motivated from thermal manufacturing and of hyperbolic type motivated from traffic flow control. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Adaptive fuzzy sliding mode control of the cart‐pole underactuated system
Authors: Bessa Wallace M. , Kreuzer Edwin
Published: October 2016

In this work, an intelligent control scheme is proposed for the stabilization of the cart‐pole underactuated system. The adopted approach is primarily based on a smooth sliding mode controller, but an adaptive fuzzy inference system is embedded within the boundary layer in order to improve the control performance. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Controllability of the powerslide motion of an automobile with different actuation inputs
Authors: Edelmann Johannes , Plöchl Manfred
Published: October 2016

Both human drivers and driver assist systems may apply steering and throttle commands to master several driving situations. In order to study the effectiveness of redundant inputs, modal controllability and observability measures are analysed for both regular steady‐state cornering and, alternatively, inherent unstable powerslide motion. In contrast to regular cornering, both inputs are effective at powerslide motion. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Further Improvements in High Gain Observer Design for Systems with Structured Nonlinearities
Authors: Franke Mirko , Röbenack Klaus
Published: October 2016

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. Necessary and in some sense sufficient conditions for this maximum Lipschitz constant are given in [1]. These results has been improved in [2,3] by taking the structure of the linear part into account.

Having a system with one single nonlinearity, the results given in [2,3] are strict. If multiple nonlinearities occur, even this approach tends to be to conservative. In this case, one could additionally take the internal structure of the nonlinearities into account which leads to a larger set of systems for which convergence of the observer error can be guaranteed.

Our new approach is based on an approximation of the structured singular value [4] which yields existence conditions in terms of linear matrix inequalities (LMIs). These LMIs may as well be used for the numerical computation of the observer gain. We demonstrate the advantage of our method on an example. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Stability preserving model reduction for linearly coupled linear time‐invariant systems
Authors: Benner Peter , Grundel Sara , Mlinarić Petar
Published: October 2016

We develop a stability preserving model reduction method for linearly coupled linear time‐invariant (LTI) systems. The method extends the work of Monshizadeh et al. for multi‐agent systems with identical LTI agents. They propose using Bounded Real Balanced Truncation to preserve a sufficient condition for stability of the coupled system. Here, we extend this idea to arbitrary linearly coupled LTI systems using the sufficient condition for stability introduced by Reis and Stykel. The model reduction error bounds for this method also follow from results of Reis and Stykel, which allows the adaptive choice of reduced orders. We demonstrate the method on Reis's and Stykel's coupled string‐beam example. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Reliability of disturbance rejection control based on the geometrical disturbance decoupling
Authors: Oveisi Atta , Nestorović Tamara
Published: October 2016

In this note, a reliable disturbance decoupled control system based on the geometrical technique is proposed. For this purpose, first, the conditions for nominal disturbance detection and rejection is introduced by using invariant subspaces. Then, the fragility issue of the controller/observer is addressed with appropriate H∞ constraints in the form of some linear matrix inequalities (LMIs). In contrast to conventional pole placement method suitable for systems by neglecting sources of uncertainty, in the presented method, the disturbance rejection problem reduces to a quadratic stability problem. It is observed that the proposed method has a better attenuation performance than classical observer‐based non‐fragile controller. © 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Local Decompositions of Second Order Infinite‐Dimensional Systems
Authors: Rams Hubert , Schöberl Markus , Schlacher Kurt
Published: October 2016

This article deals with the local system decomposition of infinite‐dimensional systems, which are described by second‐order nonlinear partial differential equations. It will be shown that the existence of a certain codistribution allows a local triangular decomposition of the generalized system vector field and the boundary conditions. Based on this triangular decomposition, non‐accessibility follows by a simple structural analysis. Throughout the article differential geometric methods are applied, highlighting the geometric picture behind the system description. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Local steering problem for a class of control‐affine systems with application to continuous crystallization processes
Authors: Zuyev Alexander , Benner Peter
Published: October 2016

In this paper, a nonlinear control‐affine system that describes the dynamics of a continuous crystallizer with fines trap is considered. We study the approximate steering problem for this system, i. e. the problem of constructing an admissible open‐loop control that steers the system from a given initial state to a neighborhood of the target state. This problem is reduced to solving a system of algebraic equations with respect to the control parameters. We show that the resulting algebraic system is locally solvable in a neighborhood of the equilibrium point. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the error behaviour of the filtered back projection
Authors: Beckmann Matthias , Iske Armin
Published: October 2016

The filtered back projection (FBP) formula allows us to reconstruct bivariate functions from given Radon samples. However, the FBP formula is numerically unstable and low‐pass filters with finite bandwidth and a compactly supported window function are employed to make the reconstruction by FBP less sensitive to noise. In this paper we analyse the inherent reconstruction error which is incurred by the application of a low‐pass filter with finite bandwidth. We present L2‐error estimates on Sobolev spaces of fractional order along with asymptotic convergence rates, where the filter's bandwidth goes to infinity. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Iterative Phase Retrieval with Sparsity Constraints
Authors: Loock Stefan , Plonka Gerlind
Published: October 2016

We consider the problem of iterative phase retrieval in near‐field X‐ray propagation imaging. Single‐distance measurements ask for strong a priori information about the specimen that are not always accessible, e.g. the specimen's support. We propose to exploit sparsity of real‐valued cartoon‐like images using soft‐thresholding of shearlet coefficients. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Adaptive Modelling, Simulation and Optimization of Gas and Water Supply Networks
Authors: Domschke Pia , Kolb Oliver , Lang Jens
Published: October 2016

We consider the simulation and optimisation of transport processes through gas and water supply networks. Using a consistent modeling of the network, adjoint equations for the whole system including initial, coupling and boundary conditions can be derived. These are suitable to compute gradients for optimization tasks but can also be used to estimate the accuracy of models and the discretization with respect to a given cost functional. We show the applicability of an adaptive algorithm that automatically steers the discretization and models while maintaining a given accuracy in an optimisation framework. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An efficient linear solver for the hybridized discontinuous Galerkin method
Authors: Jaust Alexander , Schütz Jochen , Aizinger Vadym
Published: October 2016

Discretizing partial differential equations by an implicit solving technique ultimately leads to a linear system of equations that has to be solved. The number of globally coupled unknowns is especially large for discontinuous Galerkin (DG) methods. It can be reduced by using hybridized discontinuous Galerkin (HDG) methods, but still efficient linear solvers are needed. It has been shown that, if hierarchical basis functions are used, a hierarchical scale separation (HSS) ansatz can be an efficient solver. In this work, we couple the HDG method with an HSS solver to solve a scalar nonlinear problem. It is validated by comparing the results with results obtained by GMRES with ILU(3) preconditioning as linear solver. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An adjoint‐based pressure correction scheme
Authors: Reiss Julius
Published: October 2016

Incompressible flows are solenoidal, i. e. the divergence of the flow field is zero. This is an algebraic constraint on the solution in time. The pressure has to be determined, so that the constraint is fulfilled. To calculate the pressure often a Poisson equation is derived, which is then solved by an iterative method. Instead of this the constraint is here formulated as an optimization problem. The objective functional is taken as the square of the norm of the divergence. A gradient based optimization is performed to calculate the pressure in every time step of the simulation. By this an alternative iterative scheme is derived. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Efficient Time Integration of IMEX Type using Exponential Integrators for Compressible, Viscous Flow Simulation
Authors: Straub Veronika , Ortleb Sigrun , Birken Philipp , Meister Andreas
Published: October 2016

We investigate the adaption of the recently developed exponential integrators called EPIRK in the so‐called domain‐based implicit‐explicit (IMEX) setting of spatially discretized PDE's. The EPIRK schemes were shown to be efficient for sufficiently stiff problems and offer high precision and good stability properties like A‐ and L‐stability in theory. In practice, however, we can show that these stability properties are dependent on the parameters of the interior approximation techniques.

Here, we introduce the IMEX‐EPIRK method, which consists of coupling an explicit Runge‐Kutta scheme with an EPIRK scheme. We briefly analyze its linear stability, show its conservation property and set up a CFL condition. Though the method is convergent of only first order, it demonstrates the advantages of this novel type of schemes for stiff problems very well. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Limit‐point / limit‐circle classification of second‐order differential operators arising in PT quantum mechanics
Authors: Büttner Florian , Trunk Carsten
Published: October 2016

We consider a second‐order differential equation
−y″ + q(x)y(x) = λy(x)
with complex‐valued potential q and eigenvalue parameter λ ∈ ℂ. In PT quantum mechanics the potential q is given by
q(x) = −(ix)N+2
on a contour Γ ⊂ ℂ. Via a parametrization we obtain two differential equations on [0, ∞) and (−∞, 0]. We give a limit‐point/limit‐circle classification of this problem via WKB‐analysis. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the parametric eigenvalue behavior of matrix pencils under rank one perturbations
Authors: Gernandt Hannes , Trunk Carsten
Published: October 2016

We study the eigenvalues of rank one perturbations of regular matrix pencils depending linearly on a complex parameter. We prove properties of the corresponding eigenvalue sets including a convergence result as the parameter tends to infinity and an eigenvalue interlacing property for real valued pencils having real eigenvalues only. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On Boundary Damped Inhomogeneous Timoshenko Beams.
Authors: Picard Rainer , Watson Bruce A.
Published: October 2016

We consider the model equations for the Timoshenko beam as a first order system in the framework of evolutionary equations as developed in [1]. The focus is on boundary damping, which is implemented as a dynamic boundary condition. A change of material laws allows to include a large class of cases of boundary damping. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Some new results on the well‐posedness of hyperbolic evolution equations
Authors: Schmid Jochen
Published: October 2016

We summarize some recently obtained results on the well‐posedness of hyperbolic linear evolution equations. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
G‐convergence and the weak operator topology
Authors: Waurick Marcus
Published: October 2016

We show that a bounded sequence (an)n of symmetric d × d‐matrix valued functions is G‐convergent if and only if ((ι∗︁anι)−1 )n converges in the weak operator topology. Here ι: R(grad0) ↪ L2(Ω)d denotes the (canonical) embedding from the range of the weak gradient grad0 defined on H10(Ω) into L2(Ω)d, where Ω ⊆ ℝd is open and bounded. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The mathematics behind Jost Bürgi's method for calculating sine tables
Authors: Ullrich Peter
Published: October 2016

Jost Bürgi (1552–1632) is not only one of the first persons who set up tables of logarithms for practical use but also invented a method to calculate highly precise tables of the sine function with small increment of the argument, and this with only a modest amount of calculations. Bürgi's manuscript on his method, however, was never published by him and got lost for almost four centuries until Menso Folkerts discovered it, cf. [2]. The article [1] on this manuscript gives a proof for the correctness of this method which, however, relies on the Theorem of Perron‐Frobenius that is over three centuries younger than Bürgi's method. The present contribution discusses how Bürgi may have come to his method and what considerations may have convinced him that it should work. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Where can we really prove instances of the Paris‐Harrington principle?
Authors: Freund Anton
Published: October 2016

A fundamental question in mathematical logic asks: What are the minimal assumptions and deduction principles required to prove a particular theorem? Now consider the special case of a theorem that can be established by checking a finite number of decidable cases — think of a single instance of the finite Ramsey theorem. In this particular situation the answer to our question is trivial: The theorem can be demonstrated by an explicit verification, thus without the use of any “strong” proof principles. This answer, however, is not very satisfying: An explicit verification may be unfeasible if there is an enormous number of cases to check. At the same time there might be a short and meaningful proof using stronger proof methods. Such a situation suggests a modified question: What are the minimal assumptions and deduction principles required for a reasonably short proof of the given theorem? Our contribution explores this question for instances of the Paris‐Harrington principle. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Herbrand's theorem revisited
Authors: Afshari Bahareh , Hetzl Stefan , Leigh Graham E.
Published: October 2016

We present recent results on the deepening connection between proof theory and formal language theory. To each first‐order proof with prenex cuts of complexity at most Πn/Σn, we associate a typed (non‐deterministic) tree grammar of order n (equivalently, an order n recursion scheme) that abstracts the computation of Herbrand sets obtained through Gentzen‐style cut elimination. Apart from offering a means to compute Herbrand expansions directly from proofs with cuts, these grammars provide a structural counterpart to Herbrand's theorem that opens the door to tackling a number of questions in proof theory such as proof equivalence, proof compression and proof complexity. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Categorical tools for state sum constructions
Authors: Schweigert Christoph , Fuchs Jürgen
Published: October 2016

Surface defects in (extended) three‐dimensional topological field theories have important applications, ranging from solid state physics to computations of Brauer‐Picard groups of representation categories. We present some categorical tools that are needed in such a construction, including in particular a category‐valued trace. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical reduction of self‐consistent field models of macromolecular systems
Authors: Disterhoft Alexej , Raasch Thorsten , Schmid Friederike
Published: October 2016

We report on the first application of model reduction techniques to the numerical simulation of self‐consistent field (SCF) models for polymer melts at equilibrium. As a complement to the classical SCF iteration, the parametric reaction‐diffusion equations for the chain propagators are treated by a reduced basis (RB) approximation from spaces of bandlimited functions. Numerical examples in a spatially one‐dimensional, periodic setting show that the approach is feasible, although not all requirements of an orthodox RB scheme are satisfied. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Learning parametrised regularisation functions via quotient minimisation
Authors: Benning Martin , Gilboa Guy , Schönlieb Carola‐Bibiane
Published: October 2016

We propose a novel strategy for the computation of adaptive regularisation functions. The general strategy consists of minimising the ratio of a parametrised regularisation function; the numerator contains the regulariser with a desirable training signal as its argument, whereas the denominator contains the same regulariser but with its argument being a training signal one wants to avoid. The rationale behind this is to adapt parametric regularisations to given training data that contain both wanted and unwanted outcomes. We discuss the numerical implementation of this minimisation problem for a specific parametrisation, and present preliminary numerical results which demonstrate that this approach is able to recover total variation as well as second‐order total variation regularisation from suitable training data. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Adaptive first integral preserving methods for PDEs
Authors: Ringholm Torbjørn
Published: October 2016

We present a method for constructing first integral preserving numerical schemes for time‐dependent partial differential equations on non‐uniform grids, using a finite difference approach for spatial discretization and discrete gradients for time stepping. The method is extended to accommodate spatial adaptivity. A numerical experiment is carried out where the method is applied to the Sine‐Gordon equation with moving mesh adaptivity. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Mathematical research data
Authors: Koprucki Thomas , Tabelow Karsten , Kleinod Ilka
Published: October 2016

The generation and processing of research data for modeling and simulation is an important part of the scientific work at WIAS. Together with scientific software it plays an essential role for the transfer of mathematical research results to industry or to other scientific disciplines. In the face of the emerging digital science agenda research data is now more and more recognized as an essential foundation for scientific work. The importance of research data is also emphasized by the recent adoption of the “DFG Guidelines on the Handling of Research Data” by the Deutsche Forschungsgemeinschaft and the Open Data Pilot within the EU Horizon 2020 programme. In this contribution we present our definition of research data in mathematical modeling and simulation and requirements for its management. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Synthesis and properties of bromide‐ functionalized poly(isobutylene‐co‐p‐ methylstyrene) random copolymer
Authors: Xie Yi , Chang Jin‐jie , Wu Yi‐bo , Yang Dan , Wang Hao , Zhang Tao , Li Shu‐xin , Guo Wen‐li
Published: October 2016

Poly(isobutylene‐co‐p‐methylstyrene) (IB/p‐MS) random copolymer is a new generation of polyisobutylene‐based elastomers. The cationic copolymerization of IB with p‐MS was thoroughly examined by using 2‐chloro‐2,4,4‐trimethylpentane/ethylaluminiumsesquichloride/electron donor as initiating system. IB/p‐MS random copolymers with high molecular weight were obtained at elevated temperature through the addition of ethyl acetate; the reaction proceeded in a mildly exothermic manner. Although the reactivity ratios of comonomer pairs differ by close to an order of magnitude, p‐MS was uniformly distributed in the chains. IB/p‐MS random copolymer can be brominated by adding molecular bromine into the copolymer solution, thereby yielding a completely saturated polymer backbone with a chemically reactive site. The types and selection of appropriate vulcanization systems for bromide‐functionalized IB/p‐MS random copolymers are also discussed. © 2016 Society of Chemical Industry
ACADEMIC SELF‐EFFICACY AMONG JUNIOR HIGH SCHOOL STUDENTS IN GHANA: EVALUATING FACTOR STRUCTURE AND MEASUREMENT INVARIANCE ACROSS GENDER
Authors: Ansong David , Eisensmith Sarah R. , Masa Rainier D. , Chowa Gina A.
Published: October 2016

Self‐efficacy is a universal construct, but few validated measures exist for researchers in developing countries to use in assessing youths’ perceptions of their ability to achieve academic success. This study examined the cross‐cultural suitability and psychometric properties of an academic self‐efficacy scale (ASES) adapted for the Ghanaian context. ASES construct validity was assessed with a sample of 4,289 Ghanaian junior high‐school students and exploratory and confirmatory factor analysis. Invariance testing assessed the scale's measurement equivalence by gender and temporal stability of gender equivalence. The ASES is a valid, reliable one‐dimensional scale for assessing young Ghanaians’ perceptions of their academic capabilities, and it works equally well across genders. As adapted, ASES is a valid scale with utility for researchers examining predictors and effects of academic self‐efficacy. The ASES has important implications for decisions regarding investment in programs aimed at improving academic self‐efficacy of youth, both in sub‐Saharan Africa and the increasingly diverse American public schools.
Nanoscale fissure formation in AlxGa1–xN/GaN heterostructures and their influence on Ohmic contact formation
Authors: Smith M. D. , Thomson D. , Zubialevich V. Z. , Li H. , Naresh‐Kumar G. , Trager‐Cowan C. , Parbrook P. J.
Published: October 2016

Nanoscale surface fissures on AlxGa1–xN/GaN (15 nm/1 µm) heterostructures grown by metalorganic vapour phase epitaxy (MOVPE) were imaged using tapping‐mode atomic force microscopy (AFM) and electron channelling contrast imaging (ECCI). Fissure formation was linked to threading dislocations, and was only observed in samples cooled under H2 and NH3, developing with increasing barrier layer Al content. No strain relaxation was detected regardless of fissure formation up to barrier layer Al composition fractions of x = 0.37. A reduction of measured channel carrier density was found in fissured samples at low temperature. This instability is attributed to shallow trap formation associated with fissure boundaries. For Ti/Al/Ni/Au Ohmic contact formation to high Al content barrier layers, fissures were found to offer conduction routes to the 2DEG that allow for low resistance contacts, with fissure‐free samples requiring additional optimisation of the metal stack and anneal conditions to achieve contact resistivity of order those measured in fissured samples. In addition, the effects of fissures were found to be detrimental to thermal stability of sheet and contact resistance, suggesting that fissure formation compromises the integrity of the 2DEG.
Protonated Hydrogen Cyanide
Authors: Goetz Nadine R. , Axhausen Joachim A. H. , Soltner Theresa , Rotter Christiane , Kornath Andreas J.
Published: October 2016

Trimethylsilylcyanide reacts with superacidic solutions AF/MF5 (A=H, D; M=As, Sb) to form their corresponding salts [ACNA]+[MF6]−, which are protonated forms of hydrogen cyanide and Me3SiF as by‐product. The salts have been characterized by vibrational spectroscopy and a single‐crystal X‐ray structure analysis. [DCND]+[AsF6]− crystallizes in the triclinic space group P‐1 with one formula unit in the unit cell. The disordered cations are linked with two strong hydrogen bonds to [SbF6]− anions to form chains. The crystal structure and the vibrational spectra are compared to the quantum‐chemically calculated (PBE1PBE/6‐311++G(3df,3dp)) [HCNH(HF)2]+ and [DCND(HF)2]+ units which simulate the H⋅⋅⋅F hydrogen bridges found in the solid state. The vibrational modes of the [DCND]+ cation are strongly mixed. For their discussion 13C and 15N isotopomers have been prepared by the reaction of KCN isotopomers with the superacidic solution AF/AsF5.
Surface–Enhanced Raman Spectroscopy Label–free Detection of DNA Complementary PolyA and PolyT Polybases on Ag/TiO2 Platform
Authors: He Lijie , Langlet Michel , Stambouli Valerie
Published: October 2016

An original, robust, and low cost Ag°/TiO2 platform has been used for the Surface‐Enhanced Raman Spectroscopy (SERS) detection of polyA‐NH2 and polyT complementary bases. Three procedures have been assessed to immobilize the polybases in various concentrations on the SERS platform, namely immobilization of polybases alone, immobilization of the polyA‐NH2+polyT mixture, and two‐step immobilization of the polyA‐NH2•polyT system. Derived SERS spectra have been analyzed and are discussed in terms of spectrum reproducibility, influence of polybase concentration in solution, orientation of polybases at the SERS platform surface, as well as feasibility of complementary polybase hybridization. This study allows us envisaging a simple hybridization procedure using the polyA‐NH2•polyT system and an efficient SERS detection of in situ hybridization features through intensity measurements of the adenine vibration mode at 1330 cm−1.
Three‐Component Synthesis of 3‐Aminoalkylindoles using Iron(III) Phosphate
Authors: Aghaalikhani Soheyla , Behbahani Farahnaz K.
Published: October 2016

Catalytic synthesis of 3‐substituted indole derivatives by a one‐pot three‐component coupling reaction between aldehyde, N‐methyl aniline and indole in the presence of FePO4 is described. Aldehydes having both electron‐donating and electron‐withdrawing groups were used and resulted the desired products in high yields Simple procedure, easy work up and employing of reusable and green catalyst are advantages of this protocol.
A Molecular Lock with Hydrogen Sulfate as “Key” and Fluoride as “Hand”: Computing Based Insights on the Functioning Mechanism
Authors: Paul Suvendu , Karar Monaj , Mitra Swastika , Sher Shah Selim A. , Majumdar Tapas , Mallick Arabinda
Published: October 2016

The present work demonstrates a new fully regenerative, molecular machine‐like “ON‐OFF‐ON” chemosensor based on a β‐carboline molecule “OFF‐ON‐OFF” cycle. It behaves as a molecular lock that requires a hydrogen sulfate (HSO4−) ion as “key” to open the lock and a fluoride (F−) ion as “hand” that removes the key from the lock to close the lock. The reversibility and reusability of sensor for the detection of hydrogen sulfate and fluoride ions were tested for six cycles. Experimental and computational studies reveal that the proton transfer process from hydrogen sulfate (HSO4−) ion to the pyridinic nitrogen atom of norharmane leading to the formation of a hydrogen bonded ion pair (HBIP) provides the optical changes in the visible region that are advantageous for real time and on‐site application.