bluuebunny/crossref_metadata_2025 huggingface dataset:
An extended Hamilton functional for the thermodynamic topology optimization of hyperelastic structures
Authors: Junker Philipp , Balzani Daniel
Published: December 2021

We present our work on a new variational approach for thermodynamic topology optimization of hyperelastic structures: building upon our previous works, we follow a thermodynamic approach for deriving a field equation that describes the evolution of the density. The problem of topology optimization is consequently solved without the need of expensive optimization routines. Furthermore, our new formulation can also be applied to hyperelastic structures which show a remarkable difference to structures optimized for small deformations. Important aspects like tension/compression asymmetry and buckling are inherently included in the topology optimization approach due to the large deformation formulation.
Prediction of missing values. Comparison of approaches
Authors: Litvinenko Alexander , Kriemann Ronald , Berikov Vladimir
Published: December 2021

We compare four numerical methods for the prediction of missing values in four different datasets [1]. These methods are 1) the hierarchical maximum likelihood estimation (ℋ‐MLE), and three machine learning (ML) methods, which include 2) k‐nearest neighbors (kNN), 3) random forest, and 4) Deep Neural Network (DNN). From the ML methods, the best results (for considered datasets) were obtained by the kNN method with three (or seven) neighbors. On one dataset, the MLE method showed a smaller error than the kNN method, whereas, on another, the kNN method was better. The MLE method requires a lot of linear algebra computations and works fine on almost all datasets. Its result can be improved by taking a smaller threshold and more accurate hierarchical matrix arithmetics. To our surprise, the well‐known kNN method produces similar results as ℋ‐MLE and worked much faster.
Modeling the Evolution of a cluster of gravitating bodies taking into account their absolutely inelastic collisions
Authors: Kiryan Dmitry , Kiryan George
Published: December 2021

Numerical simulation of evolution of a cluster of a finite number of gravitating bodies interacting only by their intrinsic gravity has been carried out. The goal of the study was to reveal the main characteristic phases of the spatial distribution of material bodies constituting the cluster. In solving the problem, the possibility of interbody collisions was taken into account, the collisions being assumed to be absolutely inelastic. Forces external to the body cluster under consideration were ignored. Among all the internal force factors acting within the cluster, only the gravitational interaction was taken into account. The total mass of all the gravitating bodies of the cluster was assumed to remain constant during the entire evolution. The Cauchy problem with natural initial conditions was considered. To check the process of solution, the so‐called rotation curve was used which represents the current radial distribution of orbital velocities of the cluster bodies. The numerical analysis showed time variations of the model cluster rotation curve and, particularly, the fact that the rotation curve horizontal section is only a short moment in evolution of the gravitating bodies cluster. The results obtained within the scope of classical mechanics show that it is possible to represent all the rotation curve variations for the observed galaxies without appealing to the hypothesis of non‐observable gravitating “dark matter”.
Phase Field Modeling of Dynamic Surface Wetting informed by Molecular Simulations
Authors: Diewald Felix , Wolf Jana , Heier Michaela , Lautenschläger Martin , Stephan Simon , Kuhn Charlotte , Langenbach Kai , Hasse Hans , Müller Ralf
Published: December 2021

Wetting scenarios on the micro scale are becoming more important for a variety of engineering applications. The development of manufacturing techniques that can produce surfaces with a defined microstructure is in the scope of current research efforts. This allows to directly manipulate the wetting properties of a surface. Hence, a need for numerical models that can predict the wetting properties of microstructured surfaces arises. Phase field (PF) models can be applied for this purpose. The present PF model for wetting is informed by molecular dynamics (MD) simulations. It uses the MD based perturbed Lennard‐Jones truncated and shifted (PeTS) equation of state and an MD based viscosity correlation. This approach ensures a sound physical foundation of the model.
Variational based effective models for inelastic materials
Authors: Jezdan Ghina , Govindjee Sanjay , Hackl Klaus
Published: December 2021

Mechanical systems with inelastic materials and given boundary conditions can be generally defined and solved. However, for large systems, this problem becomes non trivial and computationally costly, especially when microstructures occure. Therefore, multi‐scale modeling is used to capture the behavior of the system.

In this study, we present a methodology to provide such models for inelastic materials starting from the variational scheme. Using the variational principle we define the material strain energy and dissipation potential at the coarse scale (macro scale) starting from their counterparts on the fine scale, through the homogenization scheme. Then we solve the material model at the macro level instead of solving the fine scale model or the whole combination of scales. This multi‐scale model offers a reduced number of degrees of freedom and can generally provide the behavior of the system. Moreover, the macro scale model preserves the mathematical structure of the micro scale one. Nevertheless, for this effective model, special care needs to be given to the selection of the inelastic variables solved on the macro scale. This model is illustrated by the application to problems in classical plasticity.
On temporal homogenization in the numerical simulation of atherosclerotic plaque growth
Authors: Frei Stefan , Heinlein Alexander , Richter Thomas
Published: December 2021

A temporal homogenization approach for the numerical simulation of atherosclerotic plaque growth is extended to fully coupled fluid‐structure interaction (FSI) simulations. The numerical results indicate that the two‐scale approach yields significantly different results compared to a simple heuristic averaging, where only stationary long‐scale FSI problems are solved, confirming the importance of incorporating stress variations on small time‐scales. In the homogenization approach, a periodic fine‐scale problem, which is periodic with respect to the heart beat, has to be solved for each long‐scale time step. Even if no exact initial conditions are available, periodicity can be achieved within only 2–3 heart beats by simple time‐stepping.
Modelling the dynamic contact forces during orthogonal turn‐milling
Authors: Knape Katharina , Nitzschke Steffen , Woschke Elmar
Published: December 2021

The aim of this work is to numerically calculate the effective cutting forces during orthogonal turn‐milling using the well‐known analytical approach introduced by Victor/Kienzle in connection with a multi‐body system. Starting with a routine that numerically computes the mill's infeed with the implemented dexel model, it is possible to reconstruct and follow the tool's outline and track caused by its rotation. Hence, the acting cutting forces can be determined.
A general sandwich‐type model for delamination failure in angle‐ply laminates under thermo‐mechanical loading
Authors: Frey Christopher , Dölling Sebastian , Becker Wilfried
Published: December 2021

We propose a highly efficient analytical closed‐form approach to assess the interlaminar stresses at the free edge in symmetric angle‐ply laminates under uniform axial extension and homogeneous thermal loading. The model is based on a two‐dimensional generalized plane strain representation of the structural situation – a so‐called general sandwich‐type model. Using the results of this approach we predict the delamination onset by means of a coupled stress and energy criterion within the framework of finite fracture mechanics. For comparative purposes we use numerical results from a cohesive zone model as well as experimental findings from the literature.
Lattice Boltzmann Method for Antiplane Shear with Non‐Mesh Conforming Boundary Conditions
Authors: Müller Henning , Schlüter Alexander , Müller Ralf
Published: December 2021

Lattice Boltzmann methods [1] have been extended beyond their initial usage in transport problems, and can be used to solve a broader range of partial differential equations, e.g. the wave equation [2]. Thereby they can be utilized for fracture mechanics [3]. In the context of antiplane shear deformation we previously examined a stationary crack [4, 5] with a finite width. In this work we present two implementation strategies for non‐mesh conforming boundary conditions, for which the bounding geometry does not need to adhere to the underlying lattice. This rectifies problems in modeling the crack. A numerical example shows the improvement compared to the previous results.
A novel approach for the consideration of plastic material behavior in thermodynamic topology optimization
Authors: Kick Miriam , Junker Philipp
Published: December 2021

In order to find optimal structures for realistic applications, it is essential to include the real material behavior in the optimization process. For this purpose, this research focuses on thermodynamic topology optimization accounting for plasticity for which a surrogate material model is developed. Characteristically, the stress/strain diagram resulting from physical loading and unloading shows a hysteresis for classical plasticity models. Our material model takes only the physical loading during the optimization process into account. To this end, during a virtual unloading in the optimization process, the dissipation of energy is suppressed which yields the same elasto/plastic deformation state as for physical loading. By using this novel material model, optimized structures can be computed without resourceful classical path‐dependent plasticity computation.
Semi‐analytical assessment of free‐edge stress fields in circular cylindrical cross‐ply laminated shells subjected to transverse loads
Authors: Kappel Andreas , Mittelstedt Christian
Published: December 2021

The present work deals with the semi‐analytical assessment of the three‐dimensional stress fields in circular cylindrical symmetrically and unsymmetrically laminated cross‐ply shells undergoing different transverse loads. Starting from a closed‐form plane‐strain analysis in the innermost regions of the laminated shell, the elasticity solution is upgraded by a higher‐order displacement‐based approach which enables the developed method to capture the three‐dimensional stress state due to the free‐edge effect in thick, finite‐length composite laminated shells. In order to realize this, the shell panel is discretized into a number of numerical layers with respect to the thickness direction. By introducing a priori unknown displacement functions in the interfaces of those numerical plies and by making use of the principle of minimum elastic potential, a system of coupled ordinary differential equations is obtained, which, however, can be solved by utilizing the state‐space approach. The results of the developed analysis method are verified through comparison with existing analytical approaches in the literature and finite element simulations and it can be noted that the semi‐analytical approach works with comparable accuracy, however, only at a fraction of the computational effort coming with full‐scale three‐dimensional finite element computations.
Modeling the Mullins effect of rubbers used in constrained‐layer damping applications
Authors: Jackstadt Alexander , Frölich Felix , Weidenmann Kay , Kärger Luise
Published: December 2021

The benefits of incorporating rubber interlayers in lightweight laminates, such as fiber‐metal laminates, in order to compensate for their usually undesirable dynamic behavior have been studied in previous works [1,2]. In such constrained‐layer damping laminates, the rubber layers undergo large deformations due to their comparably low stiffness. This motivates the consideration of large strain phenomena commonly found in rubbers even when global laminate deformations are small such as in linear dynamic analysis. This work specifically addresses the cyclic softening of filled rubbers commonly known as the Mullins effect. As this effect significantly influences the elastic properties of the material, a change in the dynamic behavior of the laminate is to be expected. A constitutive model based on the work of Dorfmann and Ogden [3] for the prediction of the cyclic softening as well as residual strains upon unloading is presented in this study. Special consideration is given to the implementation of the model for use in a commercial implicit finite element solver by building on the work of Connolly et al. [4]. The model is validated against experimental data and compared to a current state‐of‐the‐art model with regard to its predictive quality and computational efficiency. Furthermore, the experimental identification of material parameters for said model is addressed.
Computing the effective crack energy of microstructures via quadratic cone solvers
Authors: Ernesti Felix , Schneider Matti , Böhlke Thomas
Published: December 2021

Recently, mathematically well‐defined homogenization results for the Francfort‐Marigo fracture model were established. To solve the resulting cell formula, efficient computational methods were developed and improvements on solver and discretization techniques were investigated.

We discuss an approach for solving the governing cell formula based on a rewriting as a second order cone problem, a specific normal form for optimization problems. For such a formulation, potent high‐accuracy optimization solvers are available. We demonstrate our approach on heterogeneous two‐dimensional microstructures.
MSM building and projection for the analysis of time‐resolved spectra
Authors: Sechi Renata , Weber Marcus , Heyne Karsten
Published: December 2021

Understanding the kinetics between the components of time‐resolved spectra is a crucial step in the study of photo‐activated processes. However, modeling the kinetics requires usually some a priori knowledge about the system. In our approach, we build a Markov State Model (MSM) from the spectral data, and obtain a Koopman transition matrixK(τ). With genPCCA, an invariant subspace projection, we project the process into its metastable components. The result of the application of gen‐PCCA is a transition matrixKc(τ), from which we can read the transition probability between the metastable components of the reaction. We discuss the application of this analysis method to the transient absorption spectrum of brominated Al‐corrole.
Phase‐field modelling and simulation of fracture in viscoelastic materials
Authors: Dammaß Franz , Ambati Marreddy , Kästner Markus
Published: December 2021

Herein, a unified phase‐field formulation of fracture in viscoelastic materials is presented. The model is characterised by a pseudo‐energy functional from which the governing equations for the phase‐field and the viscous internal variables are derived. Depending on the specific choice of the parameters, the formulation has flexibility in capturing the coupling between viscous mechanisms and fracture. By means of a numerical study, different assumptions on the coupling are compared.
Pressure‐robustness for the Stokes equations on anisotropic meshes
Authors: Kempf Volker
Published: December 2021

Pressure‐robustness has been widely studied since the conception of the notion and the introduction of the reconstruction approach for classical mixed methods in [1]. Using discretizations capable of yielding velocity solutions that are independent of the pressure approximation has been recognized as essential, and a large number of recent articles attest to this fact, e.g., [2, 3]. Apart from the pressure‐robustness aspect, incompressible flows exhibit anisotropic phenomena in the solutions which can be dealt with by using anisotropic mesh grading. The recent publications [4,5] deal with the combination of both challenges. We briefly revisit the results from [4] and provide an insightful new numerical example.
Semi‐analytical method for the stress analysis of transverse cracks in composite structures
Authors: Peiler Clemens , Kappel Andreas , Mittelstedt Christian
Published: December 2021

In this paper a semi‐analytical approach is developed which enables the computation of the stress field in the vicinity of a transverse crack in symmetric cross‐ply laminated plates subjected to an in‐plane tensile load. Due to the assumption of a plane state of strain, the analytical model can be reduced to a two‐dimensional plate strip. After a discretization of the considered laminate into mathematical layers with respect to the thickness direction, the displacements for the undamaged part are derived by making use of the classical laminate plate theory. To incorporate transverse cracks into the formulation, the closed‐form analytical solution is upgraded by a so‐called ‘local solution’ that incorporates unknown displacement functions, specified in the interfaces of the numerical layers, as well Lagrangian interpolation functions of different order. The governing equations are determined by means of the principle of minimum elastic potential and eventually yield a quadratic eigenvalue problem which requires numerical evaluation. The obtained formulation of the previously defined interface displacements includes unknown ‘weight factors' which have to be characterized by adequate boundary and continuity conditions. Consequently, by solving the resulting linear system of equations, a full‐scale representation of the displacement‐, strain‐ and stress field within the damaged laminate is obtained. The semi‐analytical method is verified by comparison with numerical results of detailed finite element simulations. Using only a fraction of the computational effort, the results of the semi‐analytical approach show comparable accuracy to the finite element method.
Simulating sea ice drift in the Southern Ocean incorporating real wind data using the LSFEM
Authors: Schwarz Carina , Schröder Jörg
Published: December 2021

The viscous‐plastic sea ice model of [2] describes the motion of sea ice on large scales. The numerical model of the sea ice drift considers velocities and stresses and is coupled with the field quantities ice thickness and ice concentration, which are modeled by transient advection equations. Here, the viscosity in sense of a non‐Newtonian fluid depends on velocity gradients, as well as on ice concentration and ice thickness. This leads to a strong nonlinearity of the constitutive model.

In [8], we discussed the hurdles of large scale sea ice models and possible solutions of an implementation within a least‐squares finite element method (LSFEM). Previous studies on sea ice model implementations have shown that the LSFEM is a promising solution to the numerically difficult problem, cf. [9] and [7]. In this work, another essential aspect of sea ice research comes into play: embedding real data into the numerical solution is an important field of research in sea ice and ocean modeling. Here, we show a 2D boundary value problem for simulating sea ice drift in the Southern Ocean incorporating real wind data from the ERA‐5 project [1].
PDE Constrained Inverse Problems arising from Turbulence Modeling
Authors: Pochampalli Rohit , Gauger Nicolas R.
Published: December 2021

Turbulence models, which are a means to fix the closure problem arising from Reynolds averaging of Navier‐Stokes equations, are economical stop‐gaps but suffer from accuracy issues. Modifying turbulence models by incorporating corrections in their functional form is one approach to improve their accuracy. We estimate correction functionals for the Spalart ‐ Allmaras turbulence model, based on an inverse problem with PDE constraints emphasizing the issue of regularization.
An enhanced algorithmic scheme for relaxed incremental variational damage formulations at finite strains
Authors: Köhler Maximilian , Neumeier Timo , Peterseim Daniel , Peter Malte A. , Balzani Daniel
Published: December 2021

Relaxed damage formulations enable to overcome the mesh dependency induced by a loss of ellipticity. However, such approaches require the construction of a convex hull of the associated energy potential. Within this contribution, an improved one‐dimensional, relaxed damage formulation of [1] with a successive, computationally optimal convexification scheme, see [2], is presented. Instead of solving a non‐convex optimization problem at the material point level, we iterate over a discrete grid and build consecutively linear Taylor expansions to construct the convex hull. Due to the reduced computational effort, integration of the one‐dimensional mechanical model over orientation distributions to obtain the three‐dimensional response as proposed in [3] becomes more feasible.
IMEX‐DG Schemes for Advection‐Diffusion Problems using Term‐based or Domain‐based IMEX Splitting
Authors: Ortleb Sigrun
Published: December 2021

IMEX partitioning may be based on a decomposition of the computational domain into two subgrids by implicitly discretizing the unknowns on the smallest cells while explicit time stepping is applied to moderately sized elements. Alternatively, advection‐diffusion IMEX splitting applies implicit time discretization only to the viscous terms while inviscid terms are discretized explicitly. Analytical investigations have shown that a careful choice of both the specific IMEX scheme and the particular DG approach yield an additional stability property of such schemes resulting in time step restrictions independent of grid refinement. In this contribution, we will compare the domain‐based IMEX partitioning to advection‐diffusion splitting with respect to time step restrictions and efficiency.
Simulating mechanical systems with frictional contact using a nonsmooth generalized‐alpha method
Authors: Capobianco Giuseppe , Harsch Jonas , Eugster Simon R. , Leine Remco I.
Published: December 2021

In this paper, we introduce a nonsmooth generalized‐alpha method for the simulation of mechanical systems with frictional contact. In many engineering applications, such systems are composed of rigid and flexible bodies, which are interconnected by joints and can come into contact with each other or their surroundings. Prominent examples are automotive, wind turbine, and robotic systems. It is known from structural mechanics applications, that generalized‐alpha schemes perform well for flexible multibody systems without contacts. This motivated the development of nonsmooth generalized‐alpha methods for the simulation of mechanical systems with frictional contacts [2, 3, 5]. Typically, the Gear‐Gupta‐Leimkuhler approach is used to stabilize the unilateral constraint, such that numerical penetration of the contact bodies can be avoided ‐ a big issue of the most popular time‐stepping schemes such as Moreau's scheme. The nonsmooth generalized‐alpha method presented in this paper is derived in [2] and in contrast to [3,5] accounts for set‐valued Coulomb‐type friction on both velocity and acceleration level. Finally, we validate the method using a guided flexible hopper as a benchmark mechanical system.
Investigating Schmidt number effects in turbulent electroconvection using one‐dimensional turbulence
Authors: Klein Marten , Schmidt Heiko
Published: December 2021

Turbulent electroconvection denotes a fluctuating multiphysical flow in which hydrodynamics and electrokinetics interact on multiple scales. The dynamical processes at work are entangled down to the molecular‐diffusive scales that are determined by the Schmidt (Sc) and Reynolds (Re) number. Turbulence properties are generally nonuniversal which leads to high numerical resolution requirements. We address the numerical challenges associated with accuracy and feasibility by utilizing a stochastic one‐dimensional turbulence (ODT) model. Here, ODT is applied to turbulent Couette flow of dilute electrolytes as canonical problem for turbulent electroconvection. For Sc ⩾ O(10), ODT predicts an increase of the skin friction drag due to electrohydrodynamically (EHD) enhanced small‐scale eddy production once the flow is sufficiently turbulent.
Cryosuction‐induced fracturing in multiphase porous materials: Numerical modeling and experimental validation
Authors: Heider Yousef , Sweidan Abdel Hassan , Markert Bernd
Published: December 2021

Whether naturally‐ or artificially‐induced due to human activities, decreasing or increasing the suction in multiphase‐fluid‐saturated porous materials can lead to enormous changes in their thermo‐hydromechanical properties. In this, both the mathematical description and the numerical modeling of the coupled problem present a challenging task. The following contribution considers the instance related to micro‐cryosuction‐induced fractures, which can be observed in saturated and unsaturated porous materials under freezing conditions. This research focuses on continuum porous media mechanics extended by a diffusive phase‐field fracture method. For the cryosuction‐induced fractures in saturated porous media, the water freezing is treated as a phase‐change process. This is modeled using a phase‐field approach, in which the thermal energy derives the phase change and, thus, leads to the occurrence of micro‐cryosuction due to the formation of the ice phase.
An efficient solver for a Cosserat rod of non‐constant width applied to a problem of fluid‐structure interaction
Authors: Schoppmann Karl , Löhrer Bastian , Tschisgale Silvio , Fröhlich Jochen , de Langre Emmanuel
Published: December 2021

The paper addresses a fluid‐structure problem involving a trapezoidal ribbon which undergoes large static reconfiguration, yielding a drag force independent of the velocity over a sizable velocity range. With experimental reference data on shape and drag available in the literature, the paper reports on Large Eddy Simulations of the configuration providing ample information on the surrounding transitional flow field and the distribution of forces along the structure. To obtain these results, a new implementation of a Cosserat solver was developed permitting non‐constant properties along the structure.
Efficient numerical treatment of a gradient damage model for materials undergoing large deformations
Authors: Riesselmann Johannes , Junker Philipp , Balzani Daniel
Published: December 2021

In this contribution we present a gradient damage formulation (cf. [1]) for hyperelastic materials undergoing large deformations, which is based on the small strain formulation of [2]. Through discretizing the gradient extended damage field with the neighbored element method the damage update can be performed at the element level. Although local update iterations remain present, the global system of equations goes without any additional degrees of freedom compared to purely elastic computations. Furthermore, in the case of severely damaged material, an element erosion based stabilization technique is considered. Computing efficiency and numerical robustness is demonstrated in several numerical examples.
Predictive modeling and simulation of silica aerogels by using aggregation algorithms
Authors: Abdusalamov Rasul , Pandit Prakul , Itskov Mikhail , Milow Barbara , Rege Ameya
Published: December 2021

Silica aerogels are highly porous solids with very low densities and thermal conductivities. Their high porosity results in a fractal morphology which has a strong influence on their mechanical properties. The geometric structure of silica aerogels can be described by diffusion‐limited cluster‐cluster aggregation (DLCA) models.

In this work, the DLCA method is implemented to model silica aerogel networks and investigate the influence of different input parameters, as for example, varying particle sizes on their fractal properties. The resulting model networks are characterized for their fractal properties and compared with the small angle X‐ray scattering (SAXS) results of silica aerogels. Furthermore, their mechanical properties are simulated using the finite element method. There, the effect of varying densities on their mechanical properties is examined. In addition, an artificial neural network (ANN) is trained based on the input parameters of the DLCA algorithm to predict the fractal properties of the silica aerogel model. By inverting the ANN it is possible to identify the necessary inputs to generate desired fractal morphologies with specific mechanical properties.
On the computation of physically realizable generalized flat inputs for nonlinear single‐output systems from a geometric point of view
Authors: Fritzsche Klemens , Guo Yuhang , Röbenack Klaus
Published: December 2021

Physical realizability is a structural property of (classical) flat inputs for state space systems which originate from higher order differential equations. These state space systems contain a derivative array, i.e., an integrator chain. Flat input injections into this array, however, structurally prevents from the reversal of the order reduction. Using a generalized flat input definition, we demonstrate how physical realizability can be achieved.
Applications of the asymptotic homogenization to materials with periodic and non‐periodic micro structures
Authors: Sheshenin Sergey , Artamonova Nina , Klementyev Petr
Published: December 2021

The first part of the paper presents the application of the asymptotic homogenization for determining the effective elastic and elasto‐plastic properties and stress concentrations in the B4C/2024Al composite using 3D x‐ray images of the internal structure. For comparison, calculations were performed for a dispersed composite with an aluminum matrix, in which boron carbide inclusions were simulated by ellipsoids. The elasto‐plastic behavior of the real structure of the B4C/2024Al composite was investigated in computational experiments on uniform compression, uniaxial tension, and a combination of pure shear and uniform compression. The calculation results were compared with experimental data. The second study concerns the application of asymptotic homogenization to metamaterials. Metamaterials may have unusual behaviour such as tension–bending coupling or tension–torsion coupling. Most metamaterials have a periodic structure in Cartesian coordinates. We studied tension‐compression‐shear coupling provided by the metamaterial using second order asymptotic representation.
Geometrically and physically nonlinear coupled consolidation problem
Authors: Artamonova Nina , Sheshenin Sergey
Published: December 2021

Consolidation is the process of soil compaction under load as water is squeezed out of a porous medium [1]. A physically and geometrically nonlinear formulation of the consolidation problem is developed. The developed nonlinear consolidation model is applied to simulate hyperelastic deformation of a biological material saturated with blood or plasma and elastoplastic deformation of porous water‐saturated soil.
Estimating divergence‐free flows via neural networks
Authors: Kabanov Dmitry I. , Espath Luis , Kiessling Jonas , Tempone Raul F.
Published: December 2021

We apply neural networks to the problem of estimating divergence‐free velocity flows from given sparse observations. Following the modern trend of combining data and models in physics‐informed neural networks, we reconstruct the velocity flow by training a neural network in such a manner that the network not only matches the observations but also approximately satisfies the divergence‐free condition. The assumption is that the balance between the two terms allows to obtain the model that has better prediction performance than a usual data‐driven neural network. We apply this approach to the reconstruction of truly divergence‐free flow from the noiseless synthetic data and to the reconstruction of wind velocity fields over Sweden.
Kolmogorov's similarity hypotheses application in research of the turbulent swirl flows in pipe generated by the various axial fan geometries
Authors: Čantrak Ðorđe S. , Janković Novica Z. , Nedeljković Miloš S.
Published: December 2021

Kolmogorov has formulated his two hypotheses of similarity in 1941 considering local‐isotropic turbulence, and later has refined his theory [1, 2]. In this paper are discussed three turbulent swirl flows generated by the three various axial fan types in‐built in the pipe. The spectral characteristics of the generated turbulent swirl flows are determined on the basis on the LDA (laser Doppler anemometry) experimental data for the circumferential velocity. In the inertial subranges these curves have the same tangent and obey the “‐ 5/3” Kolmogorov law. It is shown that in the generated turbulent swirl flows occur eddies of various scales, encompassing very wide spectra of wave numbers, i.e. frequencies.
Virtual testing of as‐designed additively manufactured lattice structures
Authors: Gebhardt Ulrike , Kästner Markus , Gustmann Tobias , Hufenbach Julia Kristin , Kühn Uta , Hirsch Franz , Berner Matthias
Published: December 2021

Lattice structures and their characterization are much discussed in current research. The complex manufacturing process of laser powder bed fusion with its repeated melting and remelting of metallic powder influences the resulting material properties.

Within this contribution the influence of process parameters on the overall behaviour of lattice structure compression test specimens is inherently described within the material model which is derived from tensile tests of additively manufactured material test specimens. The simulation of the lattice structures is performed with an isotropic elastic‐plastic material model on the as‐designed geometry, neglecting all geometric deviations caused by the manufacturing process. The comparison to compression experiments on the same, additively manufactured geometry, shows surprisingly good agreement. The potential of this approach is evaluated on compression tests with as‐built test specimens as well as test specimens which were heat treated after manufacturing.
A Modified Minibatch Sampling Method for Parameter Estimation in Hidden Markov Models using Stochastic Variational Bayes
Authors: Majumder Reetam , Gobbert Matthias K. , Neerchal Nagaraj K.
Published: December 2021

Parameter estimation using stochastic variatonal Bayes (SVB) under a mean field assumption can be carried out by sampling a single data point at each iteration of the optimization algorithm. However, when latent variables are dependent like in hidden Markov models (HMM), a larger sample is required at each iteration to capture that dependence. We describe a minibatch sampling procedure for HMMs where the emission process can be segmented into independent and identically distributed blocks. Instead of sampling a block and using all elements within it, we divide the block into subgroups and sample subgroups from different blocks using simple random sampling with replacement. Simulation results are provided for an HMM for precipitation data, where each block of 90 days represents 3 months of wet season data. SVB based on the proposed sampling method is shown to provide parameter estimates comparable with existing methods.
Efficient monolithic solution of FE2 problems
Authors: Lange Nils , Hütter Geralf , Abendroth Martin , Kiefer Bjoern
Published: December 2021

The concurrent FE2‐method is a very powerful and flexible computational tool for multi‐scale problems. However the computational effort is very high. The conventional, staggered (“nested Newton”) solution scheme solves the microscopic problem iteratively within each macroscopic Newton‐Raphson (NR) iteration, although the macroscopic deformation gradients as boundary conditions at the micro scale are only estimates. In this contribution a monolithic FE2scheme is proposed, solving the displacements of both scales in a common NR loop, which proved being faster by saving expansive micro‐scale iterations.
Computational modelling of compressible cementitious composite materials
Authors: Iskhakov Tagir , Timothy Jithender J. , Meschke Günther
Published: December 2021

The integrity of tunnel structures deployed in difficult geological conditions such as expansive soils can be improved by incorporating compressible layers in the tunnel lining. Such compressible lining materials can be obtained by embedding weak inclusions (Expanded polystyrene, Expanded glass beads, Air voids) into a cement paste material. The material properties of these individual constituents as well as their geometry affect the overall material behaviour of such cementitious composites. Design of the compressible tunnel lining for specific geological conditions can be improved by choosing optimal characteristics of the composite constituents. This procedure can be enhanced by using a simulation based data driven framework. For compaction simulation of the cementitious composite, a multiscale voxel based model is proposed. To account for the influence of the composite microstructure, the model is enhanced by continuum micromechanics.
Another Hilbert inequality and critically separated interpolation nodes
Authors: Kunis Stefan , Rolfes Julian
Published: December 2021

Abstract: Estimates on the condition number of Vandermonde matrices have implications on several algorithms ranging from polynomial interpolation to sparse super resolution in fluorescence microscopy. Classically, the situation is studied for monomials on real intervals, the complex unit disk, and the complex unit circle. Except for roots of unity and well separated nodes on the unit circle, the condition number grows strongly with increasing polynomial degree. Here, we show that the condition number of the Vandermonde matrix for a particular instance of critically separated nodes on the complex unit circle grows logarithmically with the polynomial degree. The proof is based on a variant of Hilbert's inequality with remainder term.
Consideration of the crystallization heat in the crystallization simulation of semi‐crystalline thermoplastics
Authors: Horn Tobias Daniel , Wulf Hans , Ihlemann Jörn
Published: December 2021

Moderate cooling rates form a spherulite structure when semi‐crystalline thermoplastics are cooled from quiescent melt. In a simulation of the spherulite structure evolution, both the crystallization kinetics and the temperature development must be taken into account. In this paper, the consideration of the crystallization heat in the simulation of the temperature development is demonstrated using polybutylene terephthalate. It is shown, that the consideration of the crystallization heat is necessary in order to calculate the correct evolution of spherulite structure.
Stochastic segmentation on images with uncertain data
Authors: Theilen Elin , Preusser Tobias
Published: December 2021

The present work considers a stochastic segmentation method on images in the presence of noise within a PDE‐based image processing framework. Classical methods are not able to capture the error propagation of uncertain estimated input data and their impact on the final segmentation result, which can be of great importance for clinical decisions. Therefore, an intrusive generalized polynomial chaos (gPC) expansion for a stochastic level‐set based geodesic active contours method is proposed. Employing an operator splitting and a stochastic Galerkin projection a deterministic and symmetric non‐linear hyperbolic system can be obtained, which can be treated using common numerical methods.
Stochastic Modeling of a Lifted Methane/Air Jet Flame with Detailed Chemistry
Authors: Starick Tommy , Lignell David O. , Schmidt Heiko
Published: December 2021

This preliminary numerical study investigates a lifted methane/air jet flame in a vitiated coflow by means of the One‐Dimensional Turbulence (ODT) model. In the considered Cabra Burner configuration [Combust. Flame 143 491‐506 (2005)], a jet flame issues from a central nozzle into a vitiated coflow of hot combustion products from lean premixed hydrogen/air flames. ODT is a map‐based model for turbulent flow simulations which uses a stochastic formulation for the turbulent advection. The diffusion and reaction effects along the one‐dimensional domain are considered by temporally advancing deterministic evolution equations. ODT simulations are performed with a representation of the methane/air chemistry by a reduced 19‐species mechanism with 15 reactions and a detailed 53‐species mechanism with 325 reactions. In this work, we present centerline profile of temperature and species concentrations obtained from ODT simulations using a cylindrical ODT‐formulation. Additionally, two‐dimensional renderings of the temperature distribution are shown. Although the simulation of reactive jet configurations by means of ODT is not novel, the complex stabilization region depending on the flow conditions represents a challenge for the model. Considering the reduced order of the model, ODT is able to predict the flow characteristics and reasonably matches the existing experimental data.
Finite element analysis of a 2D cantilever on a noisy intermediate‐scale quantum computer
Authors: Mielke André , Ricken Tim
Published: December 2021

Quantum computing is a promising new computing paradigm that may yield both significant speedup over classical algorithms as well as new ways to think about problems and finding novel solution algorithms. While large‐scale error‐corrected quantum computers are still under development, a selection of noisy intermediate‐scale quantum processing units is readily made available by some companies via cloud access. Despite the lack of error correction, these units can be used to test established quantum algorithms on custom problem setups. Here, we solve the finite element problem of a two‐dimensional cantilever, completely fixed on one side and loaded on the opposite side, on a 15‐qubit QPU from IBM.
Infinite‐horizon optimal control – Asymptotics and dissipativity
Authors: Faulwasser Timm , Kellett Christopher M.
Published: December 2021

This note discusses the interplay between dissipativity and the asymptotics of continuous‐time infinite‐horizon optimal control problems. We focus on the results on convergence of optimal primal solutions derived in [6]. Moreover, we present a result on the attractivity of the infinite‐horizon optimal adjoint trajectories, which is closely related to transversality conditions for infinite‐horizon optimal control problems. Proofs and further results can be found in [6].
Preparation and properties of polyaniline‐silver composite by glucose reduction
Authors: Han Zhuowei , Liu Qi , Zhao Hui , Shi Yujing , Liu Yinuo , Chen Jianbo
Published: December 2021

In this article, an environmentally friendly and simple one‐pot synthesis method to prepare polyaniline‐silver composite materials is presented by using glucose as the reducing agent. The structure and morphology of the composites are confirmed and characterized by UV–visible spectroscopy, Fourier transform‐infrared spectroscopy, X‐ray diffraction, thermogravimetric analysis, and scanning electron microscopy (SEM). Based on the SEM micrographs, the polyaniline‐silver composites with typical morphology of intercalated nanoflowers are synthesized for the first time. In addition, the electrical conductivity, oxidation resistance, and antibacterial property of the composites are enhanced compared with those of polyaniline. This study is expected to provide insights and opportunities for improving the preparation methods and conditions of polyaniline‐silver composites.
The genome of the endangered Macadamia jansenii displays little diversity but represents an important genetic resource for plant breeding
Authors: Sharma Priyanka , Murigneux Valentine , Haimovitz Jasmine , Nock Catherine J. , Tian Wei , Kharabian Masouleh Ardashir , Topp Bruce , Alam Mobashwer , Furtado Agnelo , Henry Robert J.
Published: December 2021

Macadamia, a recently domesticated expanding nut crop in the tropical and subtropical regions of the world, is one of the most economically important genera in the diverse and widely adapted Proteaceae family. All four species of Macadamia are rare in the wild with the most recently discovered, M. jansenii, being endangered. The M. jansenii genome has been used as a model for testing sequencing methods using a wide range of long read sequencing techniques. Here, we report a chromosome level genome assembly, generated using a combination of Pacific Biosciences sequencing and Hi‐C, comprising 14 pseudo‐molecules, with a N50 of 52 Mb and a total genome assembly size of 758 Mb of which 56% is repetitive. Completeness assessment revealed that the assembly covered −97.1% of the conserved single copy genes. Annotation predicted 31,591 protein coding genes and allowed the characterization of genes encoding biosynthesis of cyanogenic glycosides, fatty acid metabolism, and anti‐microbial proteins. Re‐sequencing of seven other genotypes confirmed low diversity and low heterozygosity within this endangered species. Important morphological characteristics of this species such as small tree size and high kernel recovery suggest that M. jansenii is an important source of these commercial traits for breeding. As a member of a small group of families that are sister to the core eudicots, this high‐quality genome also provides a key resource for evolutionary and comparative genomics studies.
Caring to know a name: An examination of New York City student attitudes towards knowing a tree's name
Authors: Wyner Yael , Doherty Jennifer H.
Published: December 2021

Societal Impact Statement

As the world becomes more urbanized, people place less value on knowing the biodiversity that surrounds them. Engagement with trees is hindered by an additional barrier, plant blindness, the tendency of people to ignore plants entirely. To help educators make tree diversity learning meaningful to students, this research aims to understand whether observing trees improves student dispositions towards knowing and observing trees, whether positive dispositions improve student learning about trees, and the reasons why urban middle school students care or do not care to know tree names.

To improve student engagement with local plant diversity, we developed a curriculum for New York City (NYC) students (Grades 6–8, ages 11–14) to help them scientifically observe the trees they pass daily.

This study reports results from preassessments/postassessments that explore students' dispositions towards knowing and observing trees and how these dispositions relate to learning. Participants included 150 intervention and 100 comparison students. In addition, 19 students were interviewed at three different time points.

Findings indicate that a tree observation and identification curriculum positively influenced students' dispositions towards knowing and observing trees, but 6 months after implementation, student interest had returned near to where it had begun. In addition, socioeconomic status had little impact on students' dispositions, and no relationship was found between dispositions and learning. Findings also show that as a baseline, about 25% of students care about knowing a tree's name. We grouped the reasons students provided into 17 categories, 10 for caring and 7 for not caring. The most frequently stated categories for caring were liking to know, knowing a name helps me know more, and knowing a tree's name helps me know my surroundings. The most stated categories for not caring were that knowing a tree's name is unimportant for my day‐to‐day life and all trees look the same.

Student reasons for caring and not caring are a compelling guide to the difficult task of making trees meaningful for students, an important step for empowering students to learn more about the trees that surround them.