Adaptive optimal control of the signorini's problem

In this article, we present a-posteriori error estimations in context of optimal control of contact problems; in particular of Signorini’s problem. Due to the contact side-condition, the solution operator of the underlying variational inequality is not differentiable, yet we want to apply Newton’s method. Therefore, the non-smooth problem is regularized by penalization and afterwards discretized by finite elements. We derive optimality systems for the regularized formulation in the continuous as well as in the discrete case. This is done explicitly for Signorini’s contact problem, which covers linear elasticity and linearized surface contact conditions. The latter creates the need for treating trace-operations carefully, especially in contrast to obstacle contact conditions, which exert in the domain. Based on the dual weighted residual method and these optimality systems, we deduce error representations for the regularization, discretization and numerical errors. Those representations are further developed into error estimators. The resulting error estimator for regularization error is defined only in the contact area. Therefore its computational cost is especially low for Signorini’s contact problem. Finally, we utilize the estimators in an adaptive refinement strategy balancing regularization and discretization errors. Numerical results substantiate the theoretical findings. We present different examples concerning Signorini’s problem in two and three dimensions

Dual weighted residual error estimation for the finite cell method

The paper presents a goal-oriented error control based on the dual weighted residual method (DWR) for the finite cell method (FCM), which is characterized by an enclosing domain covering the domain of the problem. The error identity derived by the DWR method allows for a combined treatment of the discretization and quadrature error introduced by the FCM. We present an adaptive strategy with the aim to balance these two error contributions. Its performance is demonstrated for some two-dimensional examples

Semi-smooth Newton methods for mixed FEM discretizations of higher-order for frictional, elasto-plastic two-body contact problems

International audienceIn this article a semi-smooth Newton method for frictional two-body contact problems and a solution algorithm for the resulting sequence of linear systems are presented. It is based on a mixed variational formulation of the problem and a discretization by finite elements of higher-order. General friction laws depending on the normal stresses and elasto-plastic material behavior with linear isotropic hardening are considered. Numerical results show the efficiency of the presented algorithm

Parameter Identification by Deep Learning of a Material Model for Granular Media

Classical physical modelling with associated numerical simulation (model-based), and prognostic methods based on the analysis of large amounts of data (data-driven) are the two most common methods used for the mapping of complex physical processes. In recent years, the efficient combination of these approaches has become increasingly important. Continuum mechanics in the core consists of conservation equations that -- in addition to the always necessary specification of the process conditions -- can be supplemented by phenomenological material models. The latter are an idealized image of the specific material behavior that can be determined experimentally, empirically, and based on a wealth of expert knowledge. The more complex the material, the more difficult the calibration is. This situation forms the starting point for this work's hybrid data-driven and model-based approach for mapping a complex physical process in continuum mechanics. Specifically, we use data generated from a classical physical model by the MESHFREE software to train a Principal Component Analysis-based neural network (PCA-NN) for the task of parameter identification of the material model parameters. The obtained results highlight the potential of deep-learning-based hybrid models for determining parameters, which are the key to characterizing materials occurring naturally, and their use in industrial applications (e.g. the interaction of vehicles with sand).Comment: arXiv admin note: text overlap with arXiv:2212.0313

Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems

Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where deep learning algorithms are used to solve problems in mathematics. The latter has popularised the field of scientific machine learning where deep learning is applied to problems in scientific computing. Specifically, more and more neural network architectures have been developed to solve specific classes of partial differential equations (PDEs). Such methods exploit properties that are inherent to PDEs and thus solve the PDEs better than standard feed-forward neural networks, recurrent neural networks, or convolutional neural networks. This has had a great impact in the area of mathematical modeling where parametric PDEs are widely used to model most natural and physical processes arising in science and engineering. In this work, we review such methods as well as their extensions for parametric studies and for solving the related inverse problems. We equally proceed to show their relevance in some industrial applications

Innovative CEA-based plant production – from greenhouse-based apllications to vertical farming

Im Gegensatz zur Freilandkultivierung schafft „controlled environment agriculture“ (CEA) durch Einstellung spezifischer abiotischer Faktoren wie Temperatur, Luftfeuchte, CO2-Gehalt, Licht und Nährstoffkonzentration kontinuierliche und reproduzierbare Bedingungen für die Kultivierung von Pflanzen. Die häufigste Anwendung von CEA findet sich in Gewächshäusern, die jedoch aufgrund der Glasstruktur äußeren Veränderungen, wie z.B. tageszeit- und jahreszeitabhängigen Sonnenständen, unterliegen. Wird eine konstante Kultivierungsumgebung unter Ausschluss externer Störfaktoren benötigt, kommen geschlossene Pflanzenwuchskammern (sog. Phytotrone) zum Einsatz, die sich insbesondere in der Art der verfügbaren Beleuchtungsquelle (z.B. Natriumdampflampe vs. LED) und der Nettokultivierungsfläche unterscheiden. Aktuelle Entwicklungen verfolgen die vertikale Kultivierung von Pflanzen über mehrere Ebenen im geschlossenen Produktionssystem, was zu einer signifikanten Erhöhung der Produktionseffizienz bei verringertem Flächenbedarf führt und die Möglichkeit für eine lokale Pflanzenproduktion in urbanen Ballungszentren eröffnet. Auf Basis eigener Forschungsansätze aus dem Fraunhofer-Institut für Molekularbiologie und Angewandte Oekologie IME in Aachen werden exemplarisch verschiedene pflanzenbasierte Anwendungen aus den Bereichen der biopharmazeutischen Produktion (MA et al., 2015) sowie der Nahrungsmittelproduktion im Gewächshaussystem bis zum innovativen orbitropalen Vertical Farming System vorgestellt. Der Kultivierungsmaßstab kann hierbei je nach Bedarf von der Einzelpflanze mit Multiparametertestung bis zur Produktion homogener „Pflanzenbatches“ im Pilotmaßstab variieren. Darüber hinaus wird ein Ausblick auf das neue Fraunhofer IME Innovationsraumkonzept „VertiPROD“ gegeben, das den Fokus auf einen holistischen Ansatz zur Erforschung einer biobasierten vertikalen Produktion unter Berücksichtigung eines zirkulären Stoffmanagements im urbanen Umfeld legt.Im Gegensatz zur Freilandkultivierung schafft „controlled environment agriculture“ (CEA) durch Einstellung spezifischer abiotischer Faktoren wie Temperatur, Luftfeuchte, CO2-Gehalt, Licht und Nährstoffkonzentration kontinuierliche und reproduzierbare Bedingungen für die Kultivierung von Pflanzen. Die häufigste Anwendung von CEA findet sich in Gewächshäusern, die jedoch aufgrund der Glasstruktur äußeren Veränderungen, wie z.B. tageszeit- und jahreszeitabhängigen Sonnenständen, unterliegen. Wird eine konstante Kultivierungsumgebung unter Ausschluss externer Störfaktoren benötigt, kommen geschlossene Pflanzenwuchskammern (sog. Phytotrone) zum Einsatz, die sich insbesondere in der Art der verfügbaren Beleuchtungsquelle (z.B. Natriumdampflampe vs. LED) und der Nettokultivierungsfläche unterscheiden. Aktuelle Entwicklungen verfolgen die vertikale Kultivierung von Pflanzen über mehrere Ebenen im geschlossenen Produktionssystem, was zu einer signifikanten Erhöhung der Produktionseffizienz bei verringertem Flächenbedarf führt und die Möglichkeit für eine lokale Pflanzenproduktion in urbanen Ballungszentren eröffnet. Auf Basis eigener Forschungsansätze aus dem Fraunhofer-Institut für Molekularbiologie und Angewandte Oekologie IME in Aachen werden exemplarisch verschiedene pflanzenbasierte Anwendungen aus den Bereichen der biopharmazeutischen Produktion (MA et al., 2015) sowie der Nahrungsmittelproduktion im Gewächshaussystem bis zum innovativen orbitropalen Vertical Farming System vorgestellt. Der Kultivierungsmaßstab kann hierbei je nach Bedarf von der Einzelpflanze mit Multiparametertestung bis zur Produktion homogener „Pflanzenbatches“ im Pilotmaßstab variieren. Darüber hinaus wird ein Ausblick auf das neue Fraunhofer IME Innovationsraumkonzept „VertiPROD“ gegeben, das den Fokus auf einen holistischen Ansatz zur Erforschung einer biobasierten vertikalen Produktion unter Berücksichtigung eines zirkulären Stoffmanagements im urbanen Umfeld legt

Corrosion Study of Current Collectors for Magnesium Batteries

The transition to renewable energy requires a significant amount of low-cost energy storage systems. Regarding batteries, magnesium provides a highly abundant raw material which is less sensitive to air in comparison to lithium, crucial to the mass production and safety. Promising candidates for intercalation materials on the cathode side are Prussian green FeFe(CN)6 with a electrochemical potential of around 0,9 V vs. Mg or the Chevrel phase Mo6S8 which shows a high specific capacity of around 120 mAh/g. Magnesium perchlorate-based electrolytes provide a practicable solution for fundamental work in the early stage of cathode research, yet are not compatible with Mg metal due to corrosion. Therefore, the organo-metallic all phenyl complex (APC) based electrolyte is a potential candidate for magnesium full cells. However, both systems contain highly reactive chloride species which cause severe corrosion of the current collector. In this work, potential materials for current collectors (carbon coated Al and Ni) are investigated applying linear sweep voltammetry, chronoamperometry and electrochemical impedance spectroscopy. A graphite based current collector is identified as the most promising candidate due to its high corrosion resistivity of 2 V vs. Mg/Mg2+ and low areal density, which helps to increase the energy density of practical Mg batteries

Detailed analysis of metagenome datasets obtained from biogas-producing microbial communities residing in biogas reactors does not indicate the presence of putative pathogenic microorganisms

Background: In recent years biogas plants in Germany have been supposed to be involved in amplification and dissemination of pathogenic bacteria causing severe infections in humans and animals. In particular, biogas plants are discussed to contribute to the spreading of Escherichia coli infections in humans or chronic botulism in cattle caused by Clostridium botulinum. Metagenome datasets of microbial communities from an agricultural biogas plant as well as from anaerobic lab-scale digesters operating at different temperatures and conditions were analyzed for the presence of putative pathogenic bacteria and virulence determinants by various bioinformatic approaches. Results: All datasets featured a low abundance of reads that were taxonomically assigned to the genus Escherichia or further selected genera comprising pathogenic species. Higher numbers of reads were taxonomically assigned to the genus Clostridium. However, only very few sequences were predicted to originate from pathogenic clostridial species. Moreover, mapping of metagenome reads to complete genome sequences of selected pathogenic bacteria revealed that not the pathogenic species itself, but only species that are more or less related to pathogenic ones are present in the fermentation samples analyzed. Likewise, known virulence determinants could hardly be detected. Only a marginal number of reads showed similarity to sequences described in the Microbial Virulence Database MvirDB such as those encoding protein toxins, virulence proteins or antibiotic resistance determinants. Conclusions: Findings of this first study of metagenomic sequence reads of biogas producing microbial communities suggest that the risk of dissemination of pathogenic bacteria by application of digestates from biogas fermentations as fertilizers is low, because obtained results do not indicate the presence of putative pathogenic microorganisms in the samples analyzed

Platelet-Released Growth Factors Induce Genes Involved in Extracellular Matrix Formation in Human Fibroblasts

Platelet concentrate products are increasingly used in many medical disciplines due to their regenerative properties. As they contain a variety of chemokines, cytokines, and growth factors, they are used to support the healing of chronic or complicated wounds. To date, underlying cellular mechanisms have been insufficiently investigated. Therefore, we analyzed the influence of Platelet-Released Growth Factors (PRGF) on human dermal fibroblasts. Whole transcriptome sequencing and gene ontology (GO) enrichment analysis of PRGF-treated fibroblasts revealed an induction of several genes involved in the formation of the extracellular matrix (ECM). Real-time PCR analyses of PRGF-treated fibroblasts and skin explants confirmed the induction of ECM-related genes, in particular transforming growth factor beta-induced protein (TGFBI), fibronectin 1 (FN1), matrix metalloproteinase-9 (MMP-9), transglutaminase 2 (TGM2), fermitin family member 1 (FERMT1), collagen type I alpha 1 (COL1A1), a disintegrin and metalloproteinase 19 (ADAM19), serpin family E member 1 (SERPINE1) and lysyl oxidase-like 3 (LOXL3). The induction of these genes was time-dependent and in part influenced by the epidermal growth factor receptor (EGFR). Moreover, PRGF induced migration and proliferation of the fibroblasts. Taken together, the observed effects of PRGF on human fibroblasts may contribute to the underlying mechanisms that support the beneficial wound-healing effects of thrombocyte concentrate products

Impact of process temperature and organic loading rate on cellulolytic/hydrolytic biofilm microbiomes during biomethanation of ryegrass silage revealed by genome-centered metagenomics and metatranscriptomics

Background: Anaerobic digestion (AD) of protein-rich grass silage was performed in experimental two-stage two-phase biogas reactor systems at low vs. increased organic loading rates (OLRs) under mesophilic (37 °C) and thermophilic (55 °C) temperatures. To follow the adaptive response of the biomass-attached cellulolytic/hydrolytic biofilms at increasing ammonium/ammonia contents, genome-centered metagenomics and transcriptional profiling based on metagenome assembled genomes (MAGs) were conducted. Results: In total, 78 bacterial and archaeal MAGs representing the most abundant members of the communities, and featuring defined quality criteria were selected and characterized in detail. Determination of MAG abundances under the tested conditions by mapping of the obtained metagenome sequence reads to the MAGs revealed that MAG abundance profiles were mainly shaped by the temperature but also by the OLR. However, the OLR effect was more pronounced for the mesophilic systems as compared to the thermophilic ones. In contrast, metatranscriptome mapping to MAGs subsequently normalized to MAG abundances showed that under thermophilic conditions, MAGs respond to increased OLRs by shifting their transcriptional activities mainly without adjusting their proliferation rates. This is a clear difference compared to the behavior of the microbiome under mesophilic conditions. Here, the response to increased OLRs involved adjusting of proliferation rates and corresponding transcriptional activities. The analysis led to the identification of MAGs positively responding to increased OLRs. The most outstanding MAGs in this regard, obviously well adapted to higher OLRs and/or associated conditions, were assigned to the order Clostridiales (Acetivibrio sp.) for the mesophilic biofilm and the orders Bacteroidales (Prevotella sp. and an unknown species), Lachnospirales (Herbinix sp. and Kineothrix sp.) and Clostridiales (Clostridium sp.) for the thermophilic biofilm. Genome-based metabolic reconstruction and transcriptional profiling revealed that positively responding MAGs mainly are involved in hydrolysis of grass silage, acidogenesis and/or acetogenesis. Conclusions: An integrated-omics approach enabled the identification of new AD biofilm keystone species featuring outstanding performance under stress conditions such as increased OLRs. Genome-based knowledge on the metabolic potential and transcriptional activity of responsive microbiome members will contribute to the development of improved microbiological AD management strategies for biomethanation of renewable biomass. © 2020 The Author(s)