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Ressourceneffiziente Optimierung von Hohlkörpern aus Kunststoff mittels Multiskalensimulation
(2017)

In this study, we investigate the thermo-mechanical relaxation and crystallization behavior of polyethylene using mesoscale molecular dynamics simulations. Our models specifically mimic constraints that occur in real-life polymer processing: After strong uniaxial stretching of the melt, we quench and release the polymer chains at different loading conditions. These conditions allow for free or hindered shrinkage, respectively. We present the shrinkage and swelling behavior as well as the crystallization kinetics over up to 600 ns simulation time. We are able to precisely evaluate how the interplay of chain length, temperature, local entanglements and orientation of chain segments influences crystallization and relaxation behavior. From our models, we determine the temperature dependent crystallization rate of polyethylene, including crystallization onset temperature.

Ressourceneffiziente Optimierung von Hohlkörpern aus Kunststoff mittels Multiskalensimulation
(2017)

Die mechanischen Eigenschaften von extrusionsblasgeformten Kunststoffhohlkörpern hängen wesentlich von den vom Verarbeitungsprozess beeinflussten Materialeigenschaften ab. Ziel der dargestellten Untersuchung ist, prozessabhängige Materialkennwerte in Simulationsprogrammen zu berücksichtigen und damit deren Vorhersagegenauigkeit zu erhöhen. Hierzu ist die Schaffung einer Schnittstelle zwischen Prozess- und Bauteilsimulation notwendig. Darüber hinaus wird vorgestellt, wie Simulationen auf Mikroebene (molekulardynamische Simulationen) genutzt werden können, um Materialkennwerte ohne die Durchführung eines Realexperiments zu ermitteln.

This study investigates the initial stage of the thermo-mechanical crystallization behavior for uni- and biaxially stretched polyethylene. The models are based on a mesoscale molecular dynamics approach. We take constraints that occur in real-life polymer processing into account, especially with respect to the blowing stage of the extrusion blow-molding process. For this purpose, we deform our systems using a wide range of stretching levels before they are quenched. We discuss the effects of the stretching procedures on the micro-mechanical state of the systems, characterized by entanglement behavior and nematic ordering of chain segments. For the cooling stage, we use two different approaches which allow for free or hindered shrinkage, respectively. During cooling, crystallization kinetics are monitored: We precisely evaluate how the interplay of chain length, temperature, local entanglements and orientation of chain segments influence crystallization behavior. Our models reveal that the main stretching direction dominates microscopic states of the different systems. We are able to show that crystallization mainly depends on the (dis-)entanglement behavior. Nematic ordering plays a secondary role.

Herein we report an update to ACPYPE, a Python3 tool that now properly converts AMBER to GROMACS topologies for force fields that utilize nondefault and nonuniform 1–4 electrostatic and nonbonded scaling factors or negative dihedral force constants. Prior to this work, ACPYPE only converted AMBER topologies that used uniform, default 1–4 scaling factors and positive dihedral force constants. We demonstrate that the updated ACPYPE accurately transfers the GLYCAM06 force field from AMBER to GROMACS topology files, which employs non-uniform 1–4 scaling factors as well as negative dihedral force constants. Validation was performed using β-d-GlcNAc through gas-phase analysis of dihedral energy curves and probability density functions. The updated ACPYPE retains all of its original functionality, but now allows the simulation of complex glycomolecular systems in GROMACS using AMBER-originated force fields. ACPYPE is available for download at https://github.com/alanwilter/acpype.

Wo Laborexperimente zu aufwendig, zu teuer, zu langsam oder zu gefährlich oder Stoffeigenschaften gar nicht erst experimentell zugänglich sind, können Computersimulationen von Atomen und Molekülen diese ersetzen oder ergänzen. Sie ermöglichen dadurch Reduktion von Kosten, Entwicklungszeit und Materialeinsatz. Die für diese Simulationen benötigten Molekülmodelle beinhalten zahlreiche Parameter, die der Simulant einstellen oder auswählen muss. Eine passende Parametrierung ist nur bei entsprechenden Kenntnissen über die Auswirkungen der Parameter auf die zu berechnenden Größen und Eigenschaften möglich. Eine Gruppe von Standardparametern in molekularen Simulationen sind die Partialladungen der einzelnen Atome innerhalb eines Moleküls. Die räumliche Ladungsverteilung innerhalb des Moleküls wird durch Punktladungen auf den Atomzentren angenähert. Für diese Annäherung existieren diverse Ansätze für verschiedene Molekülklassen und Anwendungen. In diesem Teilprojekt des Promotionsvorhabens wurde systematisch der Einfluss der Wahl des Partialladungssatzes auf potentielle Energien und ausgewählte makroskopische Eigenschaften aus Molekulardynamik-Simulationen evaluiert. Es konnte gezeigt werden, dass insbesondere bei stark polaren Molekülen die Auswahl des geeigneten Partialladungssatzes entscheidenden Einfluss auf die Simulationsergebnisse hat und daher nicht naiv, sondern nur ganz gezielt getroffen werden darf.

Integrating physical simulation data into data ecosystems challenges the compatibility and interoperability of data management tools. Semantic web technologies and relational databases mostly use other data types, such as measurement or manufacturing design data. Standardizing simulation data storage and harmonizing the data structures with other domains is still a challenge, as current standards such as the ISO standard STEP (ISO 10303 ”Standard for the Exchange of Product model data”) fail to bridge the gap between design and simulation data. This challenge requires new methods, such as ontologies, to rethink simulation results integration. This research describes a new software architecture and application methodology based on the industrial standard ”Virtual Material Modelling in Manufacturing” (VMAP). The architecture integrates large quantities of structured simulation data and their analyses into a semantic data structure. It is capable of providing data permeability from the global digital twin level to the detailed numerical values of data entries and even new key indicators in a three-step approach: It represents a file as an instance in a knowledge graph, queries the file’s metadata, and finds a semantically represented process that enables new metadata to be created and instantiated.

Off-lattice Boltzmann methods increase the flexibility and applicability of lattice Boltzmann methods by decoupling the discretizations of time, space, and particle velocities. However, the velocity sets that are mostly used in off-lattice Boltzmann simulations were originally tailored to on-lattice Boltzmann methods. In this contribution, we show how the accuracy and efficiency of weakly and fully compressible semi-Lagrangian off-lattice Boltzmann simulations is increased by velocity sets derived from cubature rules, i.e. multivariate quadratures, which have not been produced by the Gauss-product rule. In particular, simulations of 2D shock-vortex interactions indicate that the cubature-derived degree-nine D2Q19 velocity set is capable to replace the Gauss-product rule-derived D2Q25. Likewise, the degree-five velocity sets D3Q13 and D3Q21, as well as a degree-seven D3V27 velocity set were successfully tested for 3D Taylor-Green vortex flows to challenge and surpass the quality of the customary D3Q27 velocity set. In compressible 3D Taylor-Green vortex flows with Mach numbers Ma={0.5;1.0;1.5;2.0} on-lattice simulations with velocity sets D3Q103 and D3V107 showed only limited stability, while the off-lattice degree-nine D3Q45 velocity set accurately reproduced the kinetic energy provided by literature.

In this contribution, we perform computer simulations to expedite the development of hydrogen storages based on metal hydride. These simulations enable in-depth analysis of the processes within the systems which otherwise could not be achieved. That is, because the determination of crucial process properties require measurement instruments in the setup which are currently not available. Therefore, we investigate the reliability of reaction values that are determined by a design of experiments.
Specifically, we first explain our model setup in detail. We define the mathematical terms to obtain insights into the thermal processes and reaction kinetics. We then compare the simulated results to measurements of a 5-gram sample consisting of iron-titanium-manganese (FeTiMn) to obtain the values with the highest agreement with the experimental data. In addition, we improve the model by replacing the commonly used Van’t-Hoff equation by a mathematical expression of the pressure-composition-isotherms (PCI) to calculate the equilibrium pressure.
Finally, the parameters’ accuracy is checked in yet another with an existing metal hydride system. The simulated results demonstrate high concordance with experimental data, which advocate the usage of approximated kinetic reaction properties by a design of experiments for further design studies. Furthermore, we are able to determine process parameters like the entropy and enthalpy.

In an effort to assist researchers in choosing basis sets for quantum mechanical modeling of molecules (i.e. balancing calculation cost versus desired accuracy), we present a systematic study on the accuracy of computed conformational relative energies and their geometries in comparison to MP2/CBS and MP2/AV5Z data, respectively. In order to do so, we introduce a new nomenclature to unambiguously indicate how a CBS extrapolation was computed. Nineteen minima and transition states of buta-1,3-diene, propan-2-ol and the water dimer were optimized using forty-five different basis sets. Specifically, this includes one Pople (i.e. 6-31G(d)), eight Dunning (i.e. VXZ and AVXZ, X=2-5), twenty-five Jensen (i.e. pc-n, pcseg-n, aug-pcseg-n, pcSseg-n and aug-pcSseg-n, n=0-4) and nine Karlsruhe (e.g. def2-SV(P), def2-QZVPPD) basis sets. The molecules were chosen to represent both common and electronically diverse molecular systems. In comparison to MP2/CBS relative energies computed using the largest Jensen basis sets (i.e. n=2,3,4), the use of smaller sizes (n=0,1,2 and n=1,2,3) provides results that are within 0.11--0.24 and 0.09-0.16 kcal/mol. To practically guide researchers in their basis set choice, an equation is introduced that ranks basis sets based on a user-defined balance between their accuracy and calculation cost. Furthermore, we explain why the aug-pcseg-2, def2-TZVPPD and def2-TZVP basis sets are very suitable choices to balance speed and accuracy.

Molecular modeling is an important subdomain in the field of computational modeling, regarding both scientific and industrial applications. This is because computer simulations on a molecular level are a virtuous instrument to study the impact of microscopic on macroscopic phenomena. Accurate molecular models are indispensable for such simulations in order to predict physical target observables, like density, pressure, diffusion coefficients or energetic properties, quantitatively over a wide range of temperatures. Thereby, molecular interactions are described mathematically by force fields. The mathematical description includes parameters for both intramolecular and intermolecular interactions. While intramolecular force field parameters can be determined by quantum mechanics, the parameterization of the intermolecular part is often tedious. Recently, an empirical procedure, based on the minimization of a loss function between simulated and experimental physical properties, was published by the authors. Thereby, efficient gradient-based numerical optimization algorithms were used. However, empirical force field optimization is inhibited by the two following central issues appearing in molecular simulations: firstly, they are extremely time-consuming, even on modern and high-performance computer clusters, and secondly, simulation data is affected by statistical noise. The latter provokes the fact that an accurate computation of gradients or Hessians is nearly impossible close to a local or global minimum, mainly because the loss function is flat. Therefore, the question arises of whether to apply a derivative-free method approximating the loss function by an appropriate model function. In this paper, a new Sparse Grid-based Optimization Workflow (SpaGrOW) is presented, which accomplishes this task robustly and, at the same time, keeps the number of time-consuming simulations relatively small. This is achieved by an efficient sampling procedure for the approximation based on sparse grids, which is described in full detail: in order to counteract the fact that sparse grids are fully occupied on their boundaries, a mathematical transformation is applied to generate homogeneous Dirichlet boundary conditions. As the main drawback of sparse grids methods is the assumption that the function to be modeled exhibits certain smoothness properties, it has to be approximated by smooth functions first. Radial basis functions turned out to be very suitable to solve this task. The smoothing procedure and the subsequent interpolation on sparse grids are performed within sufficiently large compact trust regions of the parameter space. It is shown and explained how the combination of the three ingredients leads to a new efficient derivative-free algorithm, which has the additional advantage that it is capable of reducing the overall number of simulations by a factor of about two in comparison to gradient-based optimization methods. At the same time, the robustness with respect to statistical noise is maintained. This assertion is proven by both theoretical considerations and practical evaluations for molecular simulations on chemical example substances.

Automated parameterization of intermolecular pair potentials using global optimization techniques
(2014)

In this work, different global optimization techniques are assessed for the automated development of molecular force fields, as used in molecular dynamics and Monte Carlo simulations. The quest of finding suitable force field parameters is treated as a mathematical minimization problem. Intricate problem characteristics such as extremely costly and even abortive simulations, noisy simulation results, and especially multiple local minima naturally lead to the use of sophisticated global optimization algorithms. Five diverse algorithms (pure random search, recursive random search, CMA-ES, differential evolution, and taboo search) are compared to our own tailor-made solution named CoSMoS. CoSMoS is an automated workflow. It models the parameters’ influence on the simulation observables to detect a globally optimal set of parameters. It is shown how and why this approach is superior to other algorithms. Applied to suitable test functions and simulations for phosgene, CoSMoS effectively reduces the number of required simulations and real time for the optimization task.

Turbulent compressible flows are traditionally simulated using explicit time integrators applied to discretized versions of the Navier-Stokes equations. However, the associated Courant-Friedrichs-Lewy condition severely restricts the maximum time-step size. Exploiting the Lagrangian nature of the Boltzmann equation’s material derivative, we now introduce a feasible three-dimensional semi-Lagrangian lattice Boltzmann method (SLLBM), which circumvents this restriction. While many lattice Boltzmann methods for compressible flows were restricted to two dimensions due to the enormous number of discrete velocities in three dimensions, the SLLBM uses only 45 discrete velocities. Based on compressible Taylor-Green vortex simulations we show that the new method accurately captures shocks or shocklets as well as turbulence in 3D without utilizing additional filtering or stabilizing techniques other than the filtering introduced by the interpolation, even when the time-step sizes are up to two orders of magnitude larger compared to simulations in the literature. Our new method therefore enables researchers to study compressible turbulent flows by a fully explicit scheme, whose range of admissible time-step sizes is dictated by physics rather than spatial discretization.

This work thoroughly investigates a semi-Lagrangian lattice Boltzmann (SLLBM) solver for compressible flows. In contrast to other LBM for compressible flows, the vertices are organized in cells, and interpolation polynomials up to fourth order are used to attain the off-vertex distribution function values. Differing from the recently introduced Particles on Demand (PoD) method , the method operates in a static, non-moving reference frame. Yet the SLLBM in the present formulation grants supersonic flows and exhibits a high degree of Galilean invariance. The SLLBM solver allows for an independent time step size due to the integration along characteristics and for the use of unusual velocity sets, like the D2Q25, which is constructed by the roots of the fifth-order Hermite polynomial. The properties of the present model are shown in diverse example simulations of a two-dimensional Taylor-Green vortex, a Sod shock tube, a two-dimensional Riemann problem and a shock-vortex interaction. It is shown that the cell-based interpolation and the use of Gauss-Lobatto-Chebyshev support points allow for spatially high-order solutions and minimize the mass loss caused by the interpolation. Transformed grids in the shock-vortex interaction show the general applicability to non-uniform grids.

Stably stratified Taylor–Green vortex simulations are performed by lattice Boltzmann methods (LBM) and compared to other recent works using Navier–Stokes solvers. The density variation is modeled with a separate distribution function in addition to the particle distribution function modeling the flow physics. Different stencils, forcing schemes, and collision models are tested and assessed. The overall agreement of the lattice Boltzmann solutions with reference solutions from other works is very good, even when no explicit subgrid model is used, but the quality depends on the LBM setup. Although the LBM forcing scheme is not decisive for the quality of the solution, the choice of the collision model and of the stencil are crucial for adequate solutions in underresolved conditions. The LBM simulations confirm the suppression of vertical flow motion for decreasing initial Froude numbers. To gain further insight into buoyancy effects, energy decay, dissipation rates, and flux coefficients are evaluated using the LBM model for various Froude numbers.

Structural and Dynamical Properties of Polystyrene Determined by Coarse-Graining MD Simulations
(2007)

We present results from a detailed study of a new, optimized coarse-grained (CG) model of polystyrene (PS) and compare it with a recently published one (Harmandaris et al., Macromolecules 2006, 39, 6708). We will explain in detail, what led us to a different mapping scheme and put that into the general framework, with special emphasis on the aspect of time mapping. The new model is tested against the structural and dynamic properties of PS, resulting from atomistic simulations.

The Fraunhofer Institute for Algorithms and Scientific Computing (SCAI) has developed a software tool for the automated parameterization of force fields for molecular simulations using efficient gradient-based algorithms. This tool, combined with well-established simulation techniques, can quantitatively determine many physicochemical properties for given compounds.

Comparison Between Coarse-Graining Models for Polymer Systems: Two Mapping Schemes for Polystyrene
(2007)

This work introduces a semi-Lagrangian lattice Boltzmann (SLLBM) solver for compressible flows (with or without discontinuities). It makes use of a cell-wise representation of the simulation domain and utilizes interpolation polynomials up to fourth order to conduct the streaming step. The SLLBM solver allows for an independent time step size due to the absence of a time integrator and for the use of unusual velocity sets, like a D2Q25, which is constructed by the roots of the fifth-order Hermite polynomial. The properties of the proposed model are shown in diverse example simulations of a Sod shock tube, a two-dimensional Riemann problem and a shock-vortex interaction. It is shown that the cell-based interpolation and the use of Gauss-Lobatto-Chebyshev support points allow for spatially high-order solutions and minimize the mass loss caused by the interpolation. Transformed grids in the shock-vortex interaction show the general applicability to non-uniform grids.