Comparison of monomorphic and polymorphic approaches for uncertainty quantification with experimental investigations

Unavoidable uncertainties due to natural variability, inaccuracies, imperfections or lack of knowledge are always present in real world problems. To take them into account within a numerical simulation, the probability, possibility or fuzzy set theory as well as a combination of these are potentially usable for the description and quantification of uncertainties. In this work, different monomorphic and polymorphic uncertainty models are applied on linear elastic structures with non-periodic perforations in order to analyze the individual usefulness and expressiveness. The first principal stress is used as an indicator for structural failure which is evaluated and classified. In addition to classical sampling methods, a surrogate model based on artificial neural networks is presented. With regard to accuracy, efficiency and resulting numerical predictions, all methods are compared and assessed with respect to the added value. Real experiments of perforated plates under uniaxial tension are validated with the help of the different uncertainty models

Task assignment, sequencing and path-planning in robotic welding cells

A workcell composed of a workpiece and several welding robots is considered. We are interested in minimizing the makespan in the workcell. Hence, one needs i) to assign tasks between the robots, ii) to do the sequencing of the tasks for each robot and iii) to compute the fastest collision-free paths between the tasks. Up to now, task assignment and path-planning were always handled separately, the former being a typical Vehicle Routing Problem whereas the later is modelled using an optimal control problem. In this paper, we present a complete algorithm which combines discrete optimization techniques with collision detection and optimal control problems efficiently

Task assignment, sequencing and path-planning in robotic welding cells

A workcell composed of a workpiece and several welding robots is considered. We are interested in minimizing the makespan in the workcell. Hence, one needs i) to assign tasks between the robots, ii) to do the sequencing of the tasks for each robot and iii) to compute the fastest collisionfree paths between the tasks. Up to now, task assignment and path-planning were always handled separately, the former being a typical Vehicle Routing Problem whereas the later is modelled using an optimal control problem. In this paper, we present a complete algorithm which combines discrete optimization techniques with collision detection and optimal control problems efficientl

Main phase transition in lipid bilayers: phase coexistence and line tension in a soft, solvent-free, coarse-grained model

We devise a soft, solvent-free, coarse-grained model for lipid bilayer membranes. The non-bonded interactions take the form of a weighted-density functional which allows us to describe the thermodynamics of self-assembly and packing effects of the coarse-grained beads in terms of a density expansion of the equation of state and the weighting functions that regularize the microscopic bead densities, respectively. Identifying the length and energy scales via the bilayer thickness and the thermal energy scale, kT, the model qualitatively reproduces key characteristics (e.g., bending rigidity, area per lipid molecules, and compressibility) of lipid membranes. We employ this model to study the main phase transition between the liquid and the gel phase of the bilayer membrane. We accurately locate the phase coexistence using free energy calculations and also obtain estimates for the bare and the thermodynamic line tension.Comment: 21 pages, 12 figures. Submitted to J. Chem. Phy

Generating multi-chain configurations of an inhomogeneous melt from the knowledge of single-chain properties

Mean-field techniques provide a rather accurate description of single-chain conformations in spatially inhomogeneous polymer systems containing interfaces or surfaces. Intermolecular correlations, however, are not described by the mean-field approach and information about the distribution of distance between different molecules is lost. Based on the knowledge of the exact equilibrium single-chain properties in contact with solid substrates, we generate multi-chain configurations that serve as nearly equilibrated starting configurations for molecular dynamics simulations by utilizing the packing algorithm of Auhl and co-workers [J. Chem. Phys. 119, 12718 (2003)] for spatially inhomogeneous systems, i.e., a thin polymer film confined between two solid substrates. The single-chain conformations are packed into the thin film conserving the single-chain properties and simultaneously minimizing local fluctuations of the density. The extent to which enforcing the near-incompressibility of a dense polymer liquid during the packing process is able to re-establish intermolecular correlations is investigated by monitoring intermolecular correlation functions and the structure function of density fluctuations as a function of the distance from the confining solid substrates.Comment: 10 pages, 8 figure

Statische und dynamische Eigenschaften von lösungsmittelfreien Modellen für flüssige Doppelschichtmembranen

Kollektive Phänomene in Lipidmembranen, wie die Porenbildung und die Fusion, die Selbstorganisation zu Doppelschichten oder die laterale Entmischung mehrerer Lipidsorten haben in den letzten Jahren großes Interesse geweckt. All diese Phänomene eint die Tatsache, dass sie auf mesoskopischen Skalen, also Mikrometern und Mikrosekunden, stattfinden. Diese Skalen sind zu klein um in Experimenten direkt beobachtet werden zu können, sie sind aber auf Grund der Vielzahl der beteiligten Freiheitsgrade zu groß für Computersimulationen mit atomarer Auflösung. Vergröberte Modelle verfügen über erheblich weniger Freiheitsgrade und weichere Potentiale und gestatten eine qualitative Untersuchung dieser Phänomene mittels Computersimulationen.Im Rahmen dieser Arbeit wird ein vergröbertes, lösungsmittelfreies Modell für die Simulation von Doppelschichten amphiphiler Moleküle präsentiert und eingehend untersucht. Die Moleküle werden durch lineare Ketten von Punktteilchen beschrieben, die über Federn miteinander verbunden sind. Die ungebundenen Wechselwirkungen entstammen einem klassischen, gewichteten Dichtefunktional für die Freie Energie, das eine Entwicklung bis zur dritten Ordnung in gewichteten molekularen Dichten darstellt. Die auftretenden Entwicklungskoeffizienten und Wichtungsfunktionen ermöglichen es, im Rahmen einer Mean-Field-Näherung die Zustandsgleichung und die lokale Flüssigkeitsstruktur unabhängig voneinander vorzugeben. Wir verwenden Dissipative Particle Dynamics (DPD) Simulationen um die Eigenschaften des Modells numerisch zu untersuchen.Wir untersuchen die Selbstorganisation zu kondensierten Morphologien, das Phasendiagramm von Doppelschichten sowie strukturelle und mechanische Eigenschaften der flüssigen Phase (Lα) und einer Gelphase (Lβ), darunter den statischen Strukturfaktor, die Biegesteifigkeit und die Flächenkompressibilität. Es werden vier Verfahren zur präzisen Lokalisierung des Hauptphasenübergangs (Lβ ↔ Lα) aufgezeigt und die Freie Energie wird als Funktion eines Konformations-Ordnungsparameters berechnet. Die Linienspannung zwischen beiden Phasen wird über das Fluktuationsspektrum der Kontaktlinie und aus der Höhe der freien Energie-Barriere berechnet und verglichen.Weiterhin untersuchen wir die Brown'sche Bewegung einzelner Moleküle, sowie die kollektive Bewegung von Molekülclustern anhand der mittleren quadratischen Verschiebung, der Geschwindigkeits-Autokorrelationsfunktion und des dynamischen Strukturfaktors. Kollektive Diffusion ist nur für sehr kurze Zeiten sichtbar; es existieren keine ausgedehnten Strömungsfelder. Wir untersuchen die Oberflächenviskosität und die Intermonolagenreibung mit jeweils zwei verschiedenen Methoden. Für die Berechnung der Intermonolagenreibung leiten wir eine neue Green-Kubo-Relation ab und präsentieren eine modifizierte Variante der Seifert-Langer-Theorie, die die Dynamik von Undulationsmoden in einem lösungsmittelfreien Modell beschreibt. Schließlich bilden wir unser Modell auf ein noch einfacheres Scheibenmodell ab, in dem alle intramolekularen Freiheitsgrade eliminiert sind, und untersuchen ob es möglich ist, die ausintegrierte Reibung der intramolekularen Freiheitsgrade einzig durch den DPD-Thermostaten zu modellieren

Comparison of monomorphic and polymorphic approaches for uncertainty quantification with experimental investigations

Unavoidable uncertainties due to natural variability, inaccuracies, imperfections or lack of knowledge are always present in real world problems. To take them into account within a numerical simulation, the probability, possibility or fuzzy set theory as well as a combination of these are potentially usable for the description and quantification of uncertainties. In this work, different monomorphic and polymorphic uncertainty models are applied on linear elastic structures with non-periodic perforations in order to analyze the individual usefulness and expressiveness. The first principal stress is used as an indicator for structural failure which is evaluated and classified. In addition to classical sampling methods, a surrogate model based on artificial neural networks is presented. With regard to accuracy, efficiency and resulting numerical predictions, all methods are compared and assessed with respect to the added value. Real experiments of perforated plates under uniaxial tension are validated with the help of the different uncertainty models

Comparison of various uncertainty models with experimental investigations regarding the failure of plates with holes

Unavoidable uncertainties due to natural variability, inaccuracies, imperfections or lack of knowledge are always present in real world problems. To take them into account within a numerical simulation, the probability, possibility or fuzzy set theory as well as a combination of these are potentially usable for the description and quantification of uncertainties. In this work, different monomorphic and polymorphic uncertainty models are applied on linear elastic structures with non-periodic perforations in order to analyze the individual usefulness and expressiveness. The first principal stress is used as an indicator for structural failure which is evaluated and classified. In addition to classical sampling methods, a surrogate model based on artificial neural networks is presented. With regard to accuracy, efficiency and resulting numerical predictions, all methods are compared and assessed with respect to the added value. Real experiments of perforated plates under uniaxial tension are validated with the help of the different uncertainty models

Local surrogate responses in the Schwarz alternating method for elastic problems on random voided domains

Imperfections and inaccuracies in real technical products often influence the mechanical behavior and the overall structural reliability. The prediction of real stress states and possibly resulting failure mechanisms is essential and a real challenge, e.g. in the design process. In this contribution, imperfections in elastic materials such as air voids in adhesive bonds between fiber-reinforced composites are investigated. They are modeled as arbitrarily shaped and positioned. The focus is on local displacement values as well as on associated stress concentrations caused by the imperfections. For this purpose, the resulting complex random one-scale finite element model is numerically solved by a new developed surrogate model using an overlapping domain decomposition scheme based on Schwarz alternating method. Here, the actual response of local subproblems associated with isolated material imperfections is determined by a single appropriate surrogate model, that allows for an accelerated propagation of randomness. The efficiency of the method is demonstrated for imperfections with elliptical and ellipsoidal shape in 2D and 3D and extended to arbitrarily shaped voids. For the latter one, a local surrogate model based on artificial neural networks (ANN) is constructed. Finally, a comparison to experimental results validates the numerical predictions for a real engineering problem

Regulatory T Cells in an Endogenous Mouse Lymphoma Recognize Specific Antigen Peptides and Contribute to Immune Escape.

Foxp3+ regulatory T cells (Tregs) sustain immune homeostasis and may contribute to immune escape in malignant disease. As a prerequisite for developing immunologic approaches in cancer therapy, it is necessary to understand the ontogeny and the antigenic specificities of tumor-infiltrating Tregs. We addressed this question by using a λ-MYC transgenic mouse model of endogenously arising B-cell lymphoma, which mirrors key features of human Burkitt lymphoma. We show that Foxp3+ Tregs suppress antitumor responses in endogenous lymphoma. Ablation of Foxp3+ Tregs significantly delayed tumor development. The ratio of Treg to effector T cells was elevated in growing tumors, which could be ascribed to differential proliferation. The Tregs detected were mainly natural Tregs that apparently recognized self-antigens. We identified MHC class II-restricted nonmutated self-epitopes, which were more prevalent in lymphoma than in normal B cells and could be recognized by Tregs. These epitopes were derived from proteins that are associated with cellular processes related to malignancy and may be overexpressed in the tumor