University Of Denmark Research Articles

Yield analysis of a BIPV façade prototype installation

Building integrated photovoltaics (BIPV) typically operate under different conditions compared to standard PV due to non-optimal orientations, poor ventilation, or additional losses in coloured modules. In this work, a test site for BIPV curtain wall façades was constructed at the Technical University of Denmark (DTU) and monitored for a full year. This data is used to analyze various performance aspects, including operating temperatures, power optimizer efficiencies, and DC performance ratios. In addition, parts of the system are modelled in SAM and results of this simulation are used to identify errors. In addition to this analysis, the underlying data set is published for researchers to use in model validation.

Towards Education 4.0: The role of Large Language Models as virtual tutors in chemical engineering

Recent years have seen the rise of Artificial Intelligence (AI) powered generative chatbots, such as OpenAI’s ChatGPT or Microsoft’s Copilot. These tools have simultaneously positively surprised and taken aback people worldwide, raising the question of whether they can or should be used in education, as well as how to properly guide students and teachers on using them safely and ethically. To this end, this work provides (i) a brief overview of the current applications of AI in Higher Education (HE), (ii) a discussion of the ethical and societal concerns associated with the usage of AI models, (iii) the initial steps of the implementation of a chatbot used at the Technical University of Denmark (DTU) able to perform audits for Good Manufacturing Practice (GMP), and (iv) an investigation of the need and opportunities of AI in chemical engineering education. The latter is achieved through quantitative and qualitative analyses of the responses given by both Master’s students and academia/industry practitioners on the introduction and use of AI in education. This paves the way for discussing current perceptions, expectations and concerns of AI models, as well as their limitations and the opportunities they could provide.

Resolution evaluation of the satellite altimetric gravity anomaly models with shipborne gravity data over the Cosmonaut Sea, East Antarctica (44–52° E)

AbstractSeveral satellite gravity anomaly models are freely available to calculate the free‐air gravity anomaly in areas where shipborne gravity measurements are scarce. Two models produced by the Technical University of Denmark (DTU17) and the Scripps Institution of Oceanography (SIOv32.1), respectively, were selected to compute the free‐air anomalies over the Cosmonaut Sea, East Antarctica. A statistical comparison analysis was performed to evaluate the resolution of satellite gravity anomaly models by comparing them with the shipborne surveying date. The radially averaged energy spectra of free‐air anomaly from different sources were calculated and compared over two selected regions to further evaluate the reliability of the data derived from satellite gravity anomaly models. The satellite gravity anomaly models have a better resolution in the ocean basin than in the area near the continental shelf. The comparison analysis revealed that the precision of both DTU17 and SIOv32.1 is close to the shipborne gravity data, but on average, SIOv32.1 is a little bit better than DTU17. The spectral analysis showed that the shipborne measurements may provide higher resolution than the satellite gravity anomaly model at wavelengths shorter than 20 km, and the free‐air data derived from SIOv32.1 have better resolution than the one from DTU17. These shipborne datasets will provide contributions for the updates of the Antarctic gravity anomaly and enable new high‐resolution combined Earth gravity models to be derived in Antarctica.

A newly digitized ice-penetrating radar data set acquired over the Greenland ice sheet in 1971–1979

Abstract. We present an ice-penetrating radar data set acquired over the Greenland ice sheet by aircraft during the years 1971, 1972, 1974, 1978, and 1979. The data set comprises over 177 000 km of flight lines and contains a wealth of information on the state of the Greenland ice sheet, including information on ice thickness and englacial properties. During data collection in the 1970s, the data were recorded on optical film rolls, and in this paper, we document the digitization of these film rolls and their associated geographical information. Our data digitization enables interaction with and analysis of the data and facilitates comparison with modern-day radar observations. The complete data set in full resolution is available in the Stanford Digital Repository (https://doi.org/10.25740/wm135gp2721; Karlsson et al., 2023), with the associated technical reports. Part of the data set is available as low-resolution JPG files at the Technical University of Denmark's data repository (https://doi.org/10.6084/m9.figshare.c.7235299.v1; Karlsson et al., 2024), with associated technical reports and digitized geographical information . The Stanford Digital Repository serves as long-term storage, providing archival historic preservation in perpetuity, and is not intended as a primary data access point. The Technical University of Denmark (DTU) data repository serves as a primary entry point for data access, with files organized according to acquisition year and flight line in a simple folder structure. Here, we release the full data sets to enable the larger community to access and interact with the data (Karlsson et al., 2023).

Ashwagandha under fire: A critical scientific analysis of regulatory decisions

Ashwagandha (Withania somnifera [L.] Dunal) is one of the most renowned Ayurvedic medicinal plants, extensively used in traditional Indian medicine systems such as Ayurveda, Siddha, Unani, and Sowa Rigpa for millennia. Its medicinal uses of the root are documented in ancient texts such as the Charaka samhita, Sushruta samhita, and various Nighantus. Recognized globally, Ashwagandha is included in numerous pharmacopoeias, including the Ayurvedic Pharmacopoeia of India (API), British Pharmacopoeia, and United States Pharmacopoeia. Despite its extensive use and documented benefits, Ashwagandha faced scrutiny in Denmark. The Danish Veterinary and Food Administration banned Ashwagandha based on a 2020 report by the Technical University of Denmark (DTU). This report has been criticized for its technical, scientific, and ethical flaws, including reliance on unverified sources and omission of significant data from authoritative compendiums such as the API. Notably, the report’s references often included studies that did not adhere to established standards for Ashwagandha extracts. Furthermore, the alleged abortifacient properties cited in the Danish report are not supported by extensive reviews of traditional texts and modern scientific literature, which indicates the safety of Ashwagandha when used appropriately. This article aims to provide a comprehensive evaluation of the Danish report, emphasizing the necessity of adhering to rigorous scientific standards and accurately representing historical and contemporary data on Ashwagandha.

When regulation ignores evidence: The case of Denmark’s Ashwagandha ban and the Technical University of Denmark’s misguided risk assessment

The recent ban on Ashwagandha (Withania somnifera (L.) Dunal) supplements in Denmark, based on a risk assessment by the Technical University of Denmark (DTU), exemplifies the challenges in regulating traditional herbal medicines within modern frameworks. This article critically examines the DTU report, highlighting methodological flaws including overreliance on animal studies and selective literature review. The report’s disregard for Ashwagandha's long history of traditional use and mischaracterization of its effects, particularly alleged abortifacient properties, contradicts a growing body of scientific evidence supporting its safety and efficacy. The current research demonstrating Ashwagandha's benefits in stress reduction, sleep improvement, and cognitive function further underscores the disparity between scientific findings and the DTU’s conclusions. The ban’s implications extend beyond Denmark, raising questions about regulatory consistency and proportionality in evaluating herbal products globally. The Indian Ministry of Ayush’s critique emphasizes the need for a more comprehensive, evidence-based approach for assessing traditional medicines. This controversy may catalyze the development of integrated evaluation methods, such as the Collaborative Medicine and Science framework, bridging diverse knowledge systems in regulatory decision-making. The case underscores the necessity for a global health paradigm that harmonizes traditional and modern medical approaches, ensuring public safety while preserving access to beneficial traditional remedies.

Homogeneous Catalyzed Direct Conversion of Furfural to Gamma-Valerolactone.

Invited for this issue's cover is the group of Martin Nielsen at the Technical University of Denmark. The image shows the chemical components of lignocellulose and the transformation of hemicellulose to GVL via furfural. The Research Article itself is available at 10.1002/cssc.202301608.

Self-reported competence among advanced practice nursing students in Denmark, Finland and Norway: a cross-sectional multicentre study.

The health care systems in the Nordic countries and worldwide are under pressure due to increased longevity and a shortage of nurses. Providing nurses with a high level of education, such as advanced practice nursing, is of great importance to ensure effective, safe and high-quality care. The aim of this study was to investigate self-reported competence using the Nurse Professional Competence Scale Short-Form for the first time among master's students of advanced practice nursing in the Nordic countries and to relate the findings to age, work obligations, child-rearing responsibilities, level of education and clinical nursing experience. A multicentre, cross-sectional design was used in this study conducted at five universities in Denmark, Finland and Norway. The Nurse Professional Competence Scale Short-Form consisting of six competence areas was used with a maximum score of 7 per item for the analysis of single items and a transformed scale from 14.3 to 100 for analysing the competence areas (higher score equals higher self-reported competence). Descriptive and comparative statistics were used to analyse the data. The highest mean score was found for the competence area 'Value-based nursing care'. Students living with home-dwelling children (≤ 18 years) reported significantly higher competence in 'Nursing care', while students ≥33 years reported significantly higher competence in 'Nursing care' and 'Value-based nursing care'. No significant differences were found between students working and those not working alongside their studies, between students with and without further nursing-related education, or between students with long and short experience as nurses. The findings from this study might help to further develop curricula in advanced practice nursing master's programmes to ensure high-quality nursing and sustainable health care in the future. Future high-quality master's programmes might benefit from systematic collaboration between Nordic higher education institutions as also Sweden is planning master's programme. Higher age, having children at home and working while studying should not be considered causes for concern.

Preface

This Special Issue presents selected contributions from the WindEurope Annual Event 2024 Conference that took place 20-22 March in Bilbao. A total of 23 papers are included, addressing one (or more) of the conference themes:• Resource assessment• Turbine technology• Wind farm: installation and operations• Floating offshore wind• Digitalisation• Environmental sustainability and social acceptance• Grid and system integration• Renewable hydrogen and Power-to-X. Conference Committee for the Scientific Program • Amir R. Nejad, Professor, NTNU• Nicolaos Cutululis, Professor, Technical University of Denmark (DTU)• Simon Watson, Professor, Delft University of Technology• Julia Gottschall, Chief Scientist, Fraunhofer IWES• A. Mehrad Kazemi Amiri, Research Associate, Strathclyde University• Jan Helsen, Professor, Vrije Universiteit BrusselWe thank all, more than 30, reviewers for their engagement and effort, without which these proceedings would not have been possible. As with previous WindEurope events, the European Academy of Wind Energy (EAWE) has been responsible for organizing the review process for scientific contributions and has contributed to the development of the conference sessions. WindEurope has been responsible for the organization and logistics of the conference, and we thank their highly professional staff and their associates for the excellent collaboration. Proceedings editor Amir R. Nejad, Professor, Norwegian University of Science and Technology (NTNU)

Academic citizenship and a world in crisis

In this paper I consider how the university might contribute to a regenerated commons. I discuss the problems of global citizenship as a heuristic, putting in its place, Appiah’s notion of cosmopolitanism to describe the Global Humanities bachelor program at my own higher education institution—Roskilde University in Denmark. I then consider the academic citizen as one participating in a space of dialogue and exchange where differences are recognized and the world is read through the lens of pluralism rather than over-confident and singular commitments to social justice, human rights or some idealized commons that threatens yet another dominant/dominating worldview. I end the paper with a reflection on the theme of hopelessness—viewing universities as central to creating academic citizens geared to the logic of deficit-thinking, endless development and abstract progress. Rather than trying to overcome hopelessness, we might be better advised to embrace it as one aspect of a broad and inclusive humanistic imagination; one where there are many knowledges but where most will not be encountered, and where there are no simple solutions

Dose Rate Calibration of β Radiation Source in Risø TL/OSL-DA-20 Reader Device

This research is focused on determining the dose rate calibration of beta irradiation source in the Risø brand TL/OSL-DA-20 model thermoluminescence (TL) and optically stimulated luminescence (OSL) reader device manufactured by DTU Physics which is an integral component of the Technical University of Denmark (DTU). The beta radiation source of this device comprises a pellet-shaped Strontium ceramic made from the 90Sr/90Y radionuclide, with a half-life of approximately 29.1 years. This investigation provides a thorough examination of reproducing equivalent dose levels by comparing reproduced OSL signals with the OSL signals of calibration quartz crystals which were previously exposed to a 5 Gy beta radiation emission. Throughout this process, dose durations and equivalent dose levels were analysed on optically stimulated luminescence signals. The collected OSL data aims to ensure the precise calibration of the radioactive source, contributing to reliable results in dosimetric measurements. This calibrated device is utilized in the Luminescence Laboratory co-run by the Physics Department and Nuclear Materials Research and Application Center of Selçuk University. The determined dose rate of the beta radiation source is found as 0.065 Gy/second.

Automated wash and reuse of disposable pipette tips in a SARS-CoV-2 RT-qPCR diagnostic pipeline

The Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) pandemic led to global shortages in laboratory consumables, in particular for automated PCR. The Technical University of Denmark supported Danish hospitals from 2020 to 2022, conducting SARS-CoV-2 RT-qPCR on around 10,000 patient samples daily. We encountered shortages of disposable pipette tips used with automated liquid handlers that transferred oropharyngeal swab samples to 96-well microplates before RNA extraction. To enable tip reuse, we developed an automated protocol for washing tips with a 0.5 % sodium hypochlorite solution. This effectively eliminated carry-over of genomic material and the wash solution remained effective when stored in an open reservoir at ambient temperatures for 24 h. A three-day validation setup demonstrated the robustness of the tip wash protocol. Reducing the number of tips used for transferring samples to 96-well microplates from 96 to 8 enabled us to mitigate pipette tip shortages, lower costs, and minimize plastic waste generation.

Evaluating the Impact of the Recent Combined and Satellite-Only Global Geopotential Model on the Gravimetric Geoid Model

Geoid represents Earth’s surface, ocean, and gravitational field, which influence the elevations, shape, and mass distribution of the geopotential surface, a hypothetical surface that is perpendicular to the direction of gravity at every point. This geopotential surface serves as a reference for measuring elevations and is used as a fundamental reference surface for geodetic and surveying purposes. In this study, the Least Squares Modification of Stokes Formula (LSMS) with Additive Corrections (AC), also known as the KTH method, is used to generate a new gravimetric geoid model for Peninsular Malaysia. The KTH method was developed at the Royal Institute of Technology (KTH) in Stockholm-Sweden. The dataset used is the most recent global digital elevation model, Shuttle Radar Topography Mission (SRTM) 1 Arc-Second Global, generated by the National Aeronautics and Space Administration (NASA) and the National Imagery and Mapping Agency (NIMA). In addition to this elevation data, the dataset includes the Global Geopotential Model (GGM), which is composed of the XGM2016, XGM2019e, Tongji_GGMG2021S, and Tongji-Grace02k models. Furthermore, it incorporates sets of regional gravity data, including terrestrial gravity, airborne gravity, and marine gravity anomalies, all of which are derived from the Technical University of Denmark (DTU 21). The actual 45 Global Navigation Satellite System (GNSS)-levelling points data have been compared to the gravimetric geoid model developed in this study and the geoid acquired from Department of Survey and Mapping Malaysia (DSMM). According to the statistical results, NXGM2019e provides better accuracy, with the Root Mean Square Error (RMSE) geoid model errors of ±0.033 m, compared to the deviations in free-air anomalies, XGM2019e, which has the minimum RMSE of 10.291 mGal. Meanwhile, Tongji-GMMG2021S has the maximum RMSE of 14.792 mGal. The geoid is derived from the XGM2019e model and has maximum and minimum values of 0.032 m and 0.147 m, respectively, with mean residuals of 0.089 m. In conclusion, the XGM2019e has the potential to determine a precise local geoid model for Peninsular Malaysia

Multi-View Jujube Tree Trunks Stereo Reconstruction Based on UAV Remote Sensing Imaging Acquisition System

High-quality agricultural multi-view stereo reconstruction technology is the key to precision and informatization in agriculture. Multi-view stereo reconstruction methods are an important part of 3D vision technology. In the multi-view stereo 3D reconstruction method based on deep learning, the effect of feature extraction directly affects the accuracy of reconstruction. Aiming at the actual problems in orchard fruit tree reconstruction, this paper designs an improved multi-view stereo structure based on the combination of remote sensing and artificial intelligence to realize the accurate reconstruction of jujube tree trunks. Firstly, an automatic key frame extraction method is proposed for the DSST target tracking algorithm to quickly recognize and extract high-quality data. Secondly, a composite U-Net feature extraction network is designed to enhance the reconstruction accuracy, while the DRE-Net feature extraction enhancement network improved by the parallel self-attention mechanism enhances the reconstruction completeness. Comparison tests show different levels of improvement on the Technical University of Denmark (DTU) dataset compared to other deep learning-based methods. Ablation test on the self-constructed dataset, the MVSNet + Co U-Net + DRE-Net_SA method proposed in this paper improves 20.4% in Accuracy, 12.8% in Completion, and 16.8% in Overall compared to the base model, which verifies the real effectiveness of the scheme.

Design Methodology of Wind Turbine Rotor Models Based on Aerodynamic Thrust and Torque Equivalence

Limited by scaling effects, the physical model tests of FOWTs (floating offshore wind turbines) cannot simulate the aerodynamic loads on rotors correctly. To solve this problem, the real-time hybrid model tests in wind tunnels were developed and provided a feasible solution for the aerodynamic simulation. To perform the wind tunnel tests, the design of aerodynamic equivalent rotor models is most critical. In this study, an innovative methodology of aerodynamic equivalent design for the wind turbine rotors is developed based on GA (genetic algorithm). The NREL (National Renewable Energy Laboratory) 5 MW and DTU (Technical University of Denmark) 10 MW rotors are employed for the case studies to validate the proposed methodology. According to the results, the model-scale aerodynamic thrust performance can be accurately matched with the prototype in the entire region between cut-in and cut-out wind speeds, which allows the rotor model to provide correct thrust at different wind speeds. The variance of the aerodynamic torque with the wind speeds for the developed model is also in good agreement with the prototype, which could be beneficial for the design of the model-scale active pitch control strategy. Moreover, the applicability of the fitness functions of GA is discussed.

Suppression of precipitation bias in wind velocities from continuous-wave Doppler lidars

Abstract. In moderate to heavy precipitation, raindrops may deteriorate the accuracy of Doppler lidar measurements of the line-of-sight wind velocity because their projected velocity in the beam direction differs greatly from that of air. Therefore, we propose a method for effectively suppressing the adverse effects of rain on velocity estimation by sampling the Doppler spectra faster than the time taken for a raindrop to transit through the beam. By using a special averaging procedure, we can suppress the strong rain signal by sampling the spectrum at 3 kHz. A proof-of-concept field measurement campaign was performed on a moderately rainy day with a maximum rain intensity of 4 mm h−1 using three ground-based continuous-wave Doppler lidars at the Risø campus of the Technical University of Denmark. We demonstrate that the rain bias can effectively be removed by normalizing the noise-flattened 3 kHz sampled Doppler spectra with their peak values before they are averaged down to 50 Hz prior to the determination of the speed. In comparison to the sonic anemometer measurements acquired at the same location, the wind velocity bias at 50 Hz (20 ms) temporal resolution is reduced from up to −1.58 m s−1 for the original raw lidar data to −0.18 m s−1 for the normalized lidar data after suppressing strong rain signals. This reduction in the bias occurs during the minute with the highest amount of rain when the focus distance of the lidar is 103.9 m and the corresponding probe length is 9.8 m. With the smallest probe length, 1.2 m, the rain-induced bias is only present at the period with the highest rain intensity and is also effectively eliminated with the procedure. Thus, the proposed method for reducing the impact of rain on continuous-wave Doppler lidar measurements of air velocity is promising and does not require much computational effort.

The entangled becoming in humanities doctoral education

PurposeInstitutional framings of doctoral education mostly do not recognize the existential dimension of doctoral experience. This paper aims to offer an expanded understanding of experiences of doctoral researchers in the humanities with the concept of entangled becoming. This concept is developed through an existential lens by using Søren Kierkegaard’s philosophy – particularly his emphasis on emotions such as passion, anxiety and despair – and Denise Batchelor’s derived concept of vulnerable voices.Design/methodology/approachThe conceptual framing is used for an empirical study based on ethnographic interviews with 10 doctoral researchers and supplementary observational notes from fieldwork at a university in Denmark. Two of the interview cases were selected to showcase variation across lived experiences and how doctoral researchers voice their entangled becoming.FindingsCommon experiences such as loneliness, insecurity(ies), vulnerability(ies) or passion for one’s research were identified across the interviews. On the other hand, this study shows that each doctoral journey in the humanities envelops a distinct web of entanglements, entailing distinct navigation, that makes each case a unique story and each doctoral voice a specific one.Originality/valueCombining an existential philosophical perspective with a qualitative study, the paper offers an alternative perspective for doctoral education. It connects the humanities doctoral experience to the broader condition of human existence and the sophisticated uniqueness of each researcher’s becoming.

Toxicometabolomics as a tool for next generation environmental risk assessment.

Traditionally applied methodology in environmental risk assessment (ERA) has fallen out of step with technological advancements and regulatory requirements, challenging effectiveness and accuracy of the assessments. Extensive efforts have been focused towards a transition to a more data-driven and mechanistically-based next generation risk assessment. Metabolomics can produce detailed and comprehensive molecular insight into affected biochemical processes. Combining metabolomics with environmental toxicology can help to understand the mechanisms and/or modes of action underlying toxicity of environmental pollutants and inform adverse outcome pathways, as well as facilitate identification of biomarkers to quantify effects and/or exposure. This Technical Report describes the activities and work performed within the frame of the European Food Risk Assessment Fellowship Programme (EU-FORA), implemented at the section 'Environmental Chemistry and Toxicology' at the Department of Environmental Science at Aarhus University in Denmark with synergies to an ongoing H2020 RIA project 'EndocRine Guideline Optimisation' (ERGO). In accordance with the 'training by doing' principles of the EU-FORA, the fellowship project combined the exploration of the status of scientific discussion on methodology in ERA through literature study with hands-on training, using the metabolomics analysis pipeline established at Aarhus University. For the hands-on training, an amphibian metamorphosis assay (OECD test no.231) was used as a proof-of-concept toxicometabolomics study case. Both a targeted biomarker - and an untargeted metabolomics approach was applied.

The Most Cited Modern Articles in Refractive Surgery (2010-2020).

To provide a comprehensive analysis of the most highly cited modern articles in refractive surgery, those published between 2010 and 2020, and compare these results to a list of the most highly cited articles in refractive surgery from all timepoints. The Scopus database was searched for articles pertaining to refractive surgery using multiple search terms to identify the top 100 most cited articles in refractive surgery published between 2010 and 2020. Articles were reviewed for relevance and ranked based on total citations accrued. The 100 most cited modern articles in refractive surgery were identified. The article with the most citations by Sekundo et al has garnered nearly 600 citations to date. Almost all articles (88%) included in the top 100 had 200 or more citations. Intraocular lens (34 articles), keratorefractive lenticule extraction (ie, small incision lenticule extraction) (27 articles), and laser in situ keratomileusis (17 articles) were the predominant topics. Aarhus University in Denmark generated the most articles (5), whereas numerous articles originated from multiple countries, including the United States (16), United Kingdom (10), France (8), Spain (8), China (7), and Germany (7). This list provides a comprehensive assessment of the most cited modern articles in refractive surgery and demonstrates key focuses and trends in the field over the past decade. Intraocular lens and keratorefractive lenticule extraction were the primary topics. There was a broader representation of procedures, topics, authors, and country of origin as compared to prior work. [J Refract Surg. 2023;39(11):784-790.].

Preface

Proceeding of the 43rd Risø International Symposium on Materials Science: Composites for wind energy: Manufacturing, Operation and End-of-life L.P. Mikkelsen, J. BeausonThe focus of the 43rd Risø Symposium is on composites for wind energy. This symposium takes a life cycle perspective and addresses manufacturing, performance during operation, and end-of-life of composites for wind energy. Over the last 40 years, wind turbine blades have grown an order of magnitude. Today, the longest blades exceed 100 meters and weigh 50 tons. Because of this growth in blade size, the cost of wind energy can now compete with fossil-based energy sources in market terms.As society is thriving towards a zero-emission future, the wind energy sector is foreseen to expand further. Longer wind turbine blades with improved overall lifetime, reliability, recyclability, sustainability, operability, and maintainability are some of the objectives set for this component. To address these upcoming and ambitious requirements, the contributions are dedicated to the manufacturing, operation, and performance, as well as end-of-life strategies for wind turbine blades.The Proceedings contain 6 invited papers and 36 contributed papers.The 43rd International Risø Symposium on Materials Science is organized by the Division of Wind Energy Materials and Components at the Department of Wind and Energy Systems, Technical University of Denmark (DTU). We want to thank all those at DTU who have assisted in the preparations for the symposium. We appreciate additionally the support from the international advisory committee consisting of Douglas Cairns, US; Kristofer Gamstedt, SE; John W. Hutchinson, US; Yasuo Kitane, JP; Kristiina Oksman, SE; Kim Pickering, NZ; Marino Quaresimin, IT; Jon Spangenberg, DK; Michael Sutcliffe, UK; Yentl Swolfs, BE; Ramesh Talreja, US; Michael Wisnom, UK; Philip Withers, UK.We gratefully acknowledge financial support from the following sources: Danish Center for Applied Mathematics and Mechanics, Otto Mønsteds Fond and Knud Højgaards Fond.