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High‐dimensional metastable molecular dynamics (MD) can often be characterised by a few features of the system, that is, collective variables (CVs). Thanks to the rapid advance in the area of machine learning and deep learning, various deep learning‐based CV identification techniques have been developed in recent years, allowing accurate modelling and efficient simulation of complex molecular systems. In this paper, we look at two different categories of deep learning‐based approaches for finding CVs, either by computing leading eigenfunctions of transfer operator associated to the underlying dynamics, or by learning an autoencoder via minimisation of reconstruction error. We present a concise overview of the mathematics behind these two approaches and conduct a comparative numerical study of these two approaches on illustrative examples. [ABSTRACT FROM AUTHOR]

The paper presents a polynomial chaos approach for direct appoximation of cyclic modes of a tuned bladed rotor with all blades having the same randomly modified geometry. In order to validate this approach, accuracy of the approximation is evaluated for a simple rotor and is compared with other approximation methods, where eigenfrequencies and eigenvectors are obtained using polynomial approximation of structural matrices. The results show the good accuracy of the polynomial chaos approach. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In this paper, an approach for controlling the macro-step size in connection with co-simulation methods [1, 2, 4] is suggested. The investigated step-size controller is tailored for semi-implicit co-simulation techniques. Concretely, we consider predictor/corrector co-simulation approaches [3]. By comparing variables from the predictor and the corrector step, an error estimator for the local error can be constructed. Making use of the estimated local error, a step-size controller for the macro step-size can be implemented. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The flow through corrugated pipes is known to lead to strong whistling tones which may be harmful in many industrial appliances. The mechanism is known to originate from a coupling between vortex shedding at the edges of the cavities forming the wall of the tube and the acoustical modes of the pipe. The latter depend upon the effective velocity of sound c eff within the corrugated pipe. The purpose of this paper is to compute accurately this effective velocity of sound through an asymptotic calculation valid in the long-wave limit. Results are given for a number of geometries used in previous works, and compared with a simple model in which the effective speed of sound is function of the geometry of the pipe. The latter is found to work best for short cavities but significant disagreement is found for longer cavities. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In this paper, the Ni/Al hybrid open-cell foams are characterized on different hierarchical levels by means of experiments and numerical modeling from the atomic to the microscale. In this case, it is possible to compare the elastic-plastic behavior at different scales in order to attain a deeper understanding of the multiscale properties of the Ni/Al hybrid foams. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In the present paper a multifield approach towards ideal elastoplasticity is presented and its numerical implementation is touched. Furthermore, the strategy of static condensation is applied to this ansatz. With the help of an axisymmetric model problem its realization is demonstrated and compared to the pure multifield approach. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The paper presents a comparative study of the finite element method (FEM) and the scaled boundary finite element method (SBFEM) for the numerical evaluation of the volume‐averaged stress of composites. Two‐dimensional meso‐scale models of concrete represented by digital images and discretized using an automatic mesh generation algorithm are considered. The different computational approaches are discussed and compared with respect to accuracy and efficiency for both scenarios. [ABSTRACT FROM AUTHOR]

Numerical simulations of the human heart can guide medical doctors and researchers only if properly validated. This work presents a computational framework to validate mathematical models of cardiac electrophysiology at the tissue level. Specifically, we focus on the transmural wedge experiment as proposed by Antzelevitch in 1996. This experimental setup is easily reproduced and allows to probe key modeling assumptions and components before organ level simulations are performed. Our results highlight the need to further investigate the conductivity tensor, which, by modifying wave propagation, will affect the ECG morphology at the organ level. [ABSTRACT FROM AUTHOR]

The present study deals with the shock wave profiles in the macroscopic multi-temperature (MT) model of binary gaseous mixtures. For that purpose we have adopted the hyperbolic model developed within the framework of extended thermodynamics [1] in which we include viscosity and thermal conductivity to eliminate restriction on parameters. This allows us to compare our results with more sophisticated kinetic solutions, which were computed for hypothetic mixtures of gases [2]. Numerical implementation of the MT model is considerably simpler than the one for Boltzmann equations for mixtures or the direct simulation Monte Carlo method (DSMC). (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]