Risk averse shape optimization - risk measures and stochastic orders

Thema der vorliegenden Arbeit ist risikoaverse Formoptimierung. Gewöhnliche Formoptimierung umfasst jene Art von Problemen, bei denen die zu optimierende Variable die Form eines Objekts ist. Hier ist das Objekt ein elastischer Körper auf den eine Kraft einwirkt. Basierend auf den Konzepten der Sensitivitätsanalyse bezüglich Form und Topologie wird eine Algorithmus konstruiert, der den elastischen Körper bezüglich seiner elastischen Eigenschaften und dem dabei insgesamt gebrauchten Volumen sukzessiv verbesssert. Das Resultat ist eine Struktur, die auf die wirkende Kraft so stabil wie möglich reagiert und dabei möglichst geringes Volumen hat. Diese Art von Problemen benötigen effiziente numerische Löser für die zugrundeliegenden partiellen Differentialgleichungen (hier ist dies das Modell der linearen Elastizität). Dazu werden unterschiedliche Finite Elemente Methoden sowie Ansätze zur Gittergenerierung benutzt. Mit den sogenannten Levelset Methoden wird die Entwicklung der Struktur numerisch beschrieben. Unsicherheit kommt dann ins Spiel, wenn die berücksichtigten Kräfte als zufällig angenommen werden. So kann nun das elastische Verhalten des Körpers als Zufallsvariable angesehen werden, die von der Form abhängt. In einem ersten Ansatz wird die Form bezüglich verschiedener Risikomaße optimiert, die vor allem in Modellen der (Finanz-) Okonomie zum Einsatz kommen. Solche Risikomaße definieren unterschiedliche Bewertungen von Risiko, welches einer Zufallsvariable anhängt. Risikoneutrale und risikoaverse Modelle werden zur Formoptimierung benutzt. Eine neue Perspektive eröffnet sich, wenn 'stochastic dominance relations' zur Risikobewertung herangezogen werden. Diese definieren eine Halbordnung auf dem Raum der Zufallsvariablen und ermöglichen es, diese in Relation zu stellen. Ausgehend von einem Benchmark, welches eine gewisse Güte für das Verhalten unter Einwirkung der zufälligen Kräfte beschreibt, kann eine Menge von Formen identifiziert werden, deren Verhalten unter Einwirkung der Kräfte nicht schlechter als das Benchmark ist. Aus dieser Menge werden dann Formen nach einem weiteren Kriterium, z.B. möglichst geringes Volumen, ausgewählt. Auf diese Art und Weise werden Formen mit geringem Volumen gefunden, die aber dennoch die zuvor gestellten Anforderungen erfüllen.In this thesis, risk averse shape optimization of elastic strucures is at issue. Shape optimization, in general, deals with the type of problems where the variable to be optimized is the geometry or the shape of a domain. Here, the domain represents an elastic body which is subjected to a force applied. Relying on the concepts of shape and topology sensitivity analysis an algorithm is implemented which successively improves the elastic body concerning the elastic response and the total volume. Eventually, this procedure results in a body which is, on the one hand, as stiff as possible regarding the force applied and, on the other hand, whose volume is as small as possible. Solving such problems numerically requires an efficient solver for the underlying partial differential equation (here the linearized elasticity model). To this end, different finite element methods and mesh generation approaches are applied. Level set methods are employed to realize the evolution of the elastic body in the discrete setting. Uncertainty is then introduced by considering the force applied to be random. Thus, the elastic body can be interpreted as a parameter defining a random variable. In a first approach risk measures, which are well-known in economics, are proposed to assess random variables. Risk measures give a notion of risk associated with random variables. Risk neutral and risk averse models are discussed and used to optimize over a class of shapes. A new perspective arises when stochastic dominance relations are employed for the assessment of risk. They define an order on the space of random variables and allow to compare these to each other directly. Taking a benchmark random variable associated with a required behavior under uncertainty, a set of acceptable shapes can be identified by comparision to this benchmark. An additional criterion, e.g. minimal volume, is used to select shapes from this set. In that way, shapes with low volume are found which still meet the prescribed requirements

Möglichkeiten des Carving-Schwunges im Skifahren und Snowboarden

Nowadays, skiers and snowboarders leave drifted turns behind. Carving is a password to enter all winter resorts. Ski and snowboard equipment is produced in such a way as to comply as much as possible with the developing trends in both skiing and snowboarding techniques. This paper is a comparison of classical skis and Alpine snowboard, in other words, a comparison between the old and the new. It also initiates a discussion on lateral balance which influences both skiers and snowboarders. In the measurements, classical slalom skis and a slalom snowboard were used. The goal was to point out the different possibilities of the carving turn performance. The intention was to emphasize the contribution of snowboarding technique to skiing. The results presented indicate the better racing performance on a snowboard compared to classical non-carving slalom skis. Though skis are faster in a straight run, the snowboard proved to be faster in the turns. This may be a guideline for coaches to analyze the technique of their team members and take into account the results when creating a workout.Uvod Karving zavoj najviši je doseg tehnike skijanja i daskanja na snijegu. Koristeci karving zavoj, vozač često mijenja smjer vožnje i smanjuje gubitak brzine. Postojeća konstrukcija strukiranih skija, vezova i dasaka za snijeg (monoskija) omogućuje optimalan pritisak na unutarnji rub tako da vozač može zasjeći, “rezbariti” snježnu površinu na najprimjereniji način uz minimalan otpor i gubitak na brzini. Razmotrimo li raspon samih gibanja, uočit ćemo da daske za snowboard pružaju bolje pretpostavke za bolji i brži karving zavoj. Veći opseg pokreta, osobito postraničnih gibanja težišta tijela, pomaže prebacivanju monoskije na unutarnji rub. Također, promjena rubljenja može biti brža ako daskaš izbjegava otklizavanja. Mi smo ocjenjivali sposobnost izvođenja lateralno uravnoteženih zavoja na obje strane. Metoda Proveli smo i inter- i intra-individualnu dvodimenzionalnu kinematičku analizu, kao i nezavisno mjerenje vremena vožnje dva vozača vrhunske i skijaške i snowboarding vještine te profesionalne tehnike vožnje. Prvi vozač imao je uobičajeni stav, jaču lijevu nogu te nešto koordiniraniju desnu nogu. Drugi je imao obrnuti stav, snažniju desnu nogu i koordiniraniju lijevu nogu. Za ispitivanje koordinacijske preferencije i snage koristili smo dvije metode: udaranje lopte nogom i penjanje na stolicu kao dio kružnog testa od deset zadataka. Kamera je bila postavljena na radnom mjestu u sredini kruga. Iz takvog položaja zadani pokret vidi se kao po ravnoj liniji. Tako smo mogli koristiti dvodimenzionalnu kinematicku analizu. Rotacija kamere bila je kompenzirana kalibracijom tla uz pomoć čvrstih točaka. Frekvencija snimanja bila je 50 snimaka u sekundi. Ispitivali smo po jedan cjeloviti osnovni zavoj i paralelni zavoj od brijega. U obje situacije označili smo vrata. Nezavisno vrijeme mjerenja korišteno je radi kompenzacije nekih kinematičkih pogrešaka u analizi vožnje zavoja. Usporedili smo vremena vožnje zavoja s vremenima ravne vožnje duge 14 metara. Svaki je sportaš nakon probnog pokušaja odvezao po tri vožnje. U mjerenjima, koja su provedena 1999. godine, koristili smo klasične slalomske skije i slalomsku dasku za snijeg. U vrijeme pojavljivanja strukiranih skija željeli smo naglasiti različite mogućnosti izvedbe karving zavoja te istaknuti doprinos tehnike daskanja na snijegu tehnici skijanja. Analizirali smo najbržu vožnju. Način starta bio je jednak i za skijanje i za daskanje na snijegu u svakoj situaciji. Startalo se okretanjem skije ili daske preko ruba startne platforme. Vozači nisu imali mogućnost izvesti ni jedan jedini dodatni pokret ni rukama ni nogama kako bi si dali početno ubrzanje. Rezultati U svim situacijama paralelnog zavoja od brijega utvrdili smo manji gubitak relativne brzine u vožnji na monoskiji u usporedbi s klasičnom skijaškom vožnjom. U većini situacija u izvedbi osnovnog zavoja vozači su postizali veće relativno ubrzanje na kraju zavoja. S obzirom na mali uzorak, dobiveni su rezultati ograničene valjanosti. Analiza vožnji dvaju vozača može poslužiti samo za približnu usporedbu. Oba su vozača postigla bolju postraničnu ravnotežu u paralelnom zavoju od brijega na skijama. Prvi je pokazao bolju daskašku tehniku te je postigao dobru postraničnu ravnotežu u izvedbi zavoja od brijega, a također i na monoskiji. Drugi je vozač pokazao potpuno jednaku izvedbu desnog i lijevog zavoja na skijama, što je bilo 44% vremena zaostatka u odnosu na ravnu vožnju. Drugi je vozač bio brži na monoskiji u desnu stranu, što je, u ovom slučaju, bio prednji zavoj. Vremensko kašnjenje iznosilo je 42,8%. U zavoju leđima (lijevi zavoj) vremensko kašnjenje bilo je 47%. Viša lateralna kvaliteta može biti rezultat simetričnog stava na skijama u poziciji vožnje. Pokreti skijaša u takvom stavu su djelomično slicni najprirodnijem obliku ljudskog kretanja-hodanju. Brža vožnja na skijama nego na dasci za snijeg u ravnoj vožnji bila je vjerojatno uzrokovana većom kontaktnom površinom skija. Posljedica toga je manje specifično trenje na skijama. Na dionici ravne vožnje, na polovici od ukupno mjerenog vremena, dostignuta brzina na skijama i na monoskiji približno je slična, dok su na ciljnoj crti monoskije bile definitivno brže. U usporedbi sa zavojima na skijama, u daskaškim zavojima bilo je manje otklizavanja, što znači da su bili brži. Kod zahtjevniih paralelih zavoja od brijega prvi je vozač postigao dobro uravnoteženu postraničnu izvedbu i na skijama i na monoskiji. To je predstavljeno vremenom zaostatka u odnosu na ravnu vožnju koje iznosi 24.8% u obje strane na skijama i 12.2%, odnosno 12.8 % na daski. Drugi je vozač također pokazao dobre postranično uravnotežene zavoje na skijama. U desnu stranu vrijeme zaostatka bilo je 28%, dok je ulijevo bilo 31.3%. Na monoskiji je bio znatno bolji u desnu stanu (njegov prednji zavoj), gdje mu je vrijeme zaostatka iznosilo 19,3%. Vrijeme zaostatka u lijevu stranu (zavoj leđima) bilo je 31%. Ispitivani daskaški osnovni zavoji bili su brži od svih zavoja na skijama u svim vožnjama. Slično tome, ubrzanje mjereno između startne i ciljne linije bilo je brže na monoskiji kod tri od ukupno četiri vožnje. Bolja izvedba obojice vozača na njihovoj prednjoj strani može se objasniti različitim naginjanjem u zavoju. Kod zavoja leđima (stražnji zavoj), vozač se naginje preko ravnine svojih peta, koje su, u usporedbi s prstima, manje osjetljive. Dok se naginje unatrag, vozaču je ograničena vizualna kontrola, što automatski znači da ne može dovoljno kontrolirati rubljenje daske. To je također i odgovor na veće postranične razlike u daskaškim zavojima u odnosu na skijaške zavoje. Općenito, veca postignuta brzina na monoskiji rezultat je karving tehnike kojom se izbjegava otklizavanje kraja daske. Konstrukcija daske za snijeg i stav vozaca omogućuju jače rubljenje i pritisak na unutarnji rub. Zaključak Rezultati analiza potvrđuju navedene pretpostavke o bržim zavojima na monoskiji. Veća postranična smirenost trupa u izvedbi na skijama, a kod prvog sportaša i na monoskiji, potvrdila je nalaze da su sportaši više sportske i tehničke razine izvedbe lateralno više uravnoteženi. U odnosu na taj nalaz mi smatramo da daskaški pokreti u zavoju kod skijaša znače napredovanje, kao i da je moguć prenijeti pozitivan transfer daskaške tehnike na elemente skijaške tehnike. - U slučaju dvojice testiranih vozača klasično skijanje pokazalo se bržim u ravnoj vožnji. S druge strane, monoskija je bila brža u zavojima zbog svoje strukirane izvedbe. - U daskaškim zavojima oba su vozača bila brža u svom prednjem zavoju. - Uspoređujući desni i lijevi zavoj kod svakog vozača utvrdili smo da postoji veća razlika u izvedbi daskaških zavoja, što može imati isti, gore spomenuti uzrok (prednji zavoj). U usporedbi sa skijama, slalomska monoskija je kraća i većih rubova. Stoga daska za snijeg ima bolje mehaničke preduvjete za izvedbu karving zavoja. Oni mogu biti izvedeni jakim pritiskom unutarnjeg ruba daske i rubljenjem pod širokim kutom. U izvedbi tehnike daskaš se u zavoju može nagnuti znatno više od skijaša. Implementacija progresivnih mehaničkih i funkcionalnih kvaliteta u proizvodnji strukiranih skija urodila je novim idejama za daljnje unaprebenje tehnike skijaških zavoja. U posljednje vrijeme ovaj trend javlja se čak i u slalomu.In der Technik der Ski- und Snowboard-Schwünge ist eine deutliche Reduzierung der Rutschbewegung von Skiern, bzw. vom Snowboard bemerkbar. Carving ist ein Hennwort, mit dem man alle Wintersportörte betritt. Die Ski- und Snowboard-Ausrüstung ist dem progressiven Trend der Schwungtechnik maximal angepasst. Unsere Studie stellt einen Vergleich zwischen den Schwüngen auf klassischen Skiern und den Schwüngen auf dem alpinen Snowboard dar, nämlich, einen Vergleich zwischen der alten und der neuen Fahrtechnik. Sie befasst sich auch mit der Problematik der Lateralität, die sowohl die Skifahrer als auch die Snowboarder beinflusst. In den Messungen wurden die klassischen Skier und das Slalom-Snowboard angewandt. Das Ziel der Studie war, sowohl auf die unterschiedlichen Möglichkeiten des Carving-Schwunges als auch auf den geleisteten Beitrag der Snowboardtechnik zu Skifahren aufmerksam zu machen. Die dargestellten Ergebnisse deuten auf bessere Snowboard-Fahrleistungen im Vergleich zu den klassischen nicht-carving Slalom-Skiern. Obwohl die Skifahrer auf klassischen Skiern schneller fuhren auf der schnurgeraden Strecke, war das Snowboard schneller in den Bögen. Diese Ergebnisse könnten den Trainern helfen, sowohl die Schwungtechnik ihrer Mannschaftsglieder zu analysieren als auch die in dieser Studie erhaltenen Ergebnisse in Betracht zu ziehen, wenn sie das Trainingsplan gestalten

Effect of steam-treatment time on the length and structure of single-walled and double-walled carbon nanotubes

A major challenge to turn the potential of carbon nanotubes (CNTs) into customer applications is to reduce or eliminate their toxicity. Taking into account health and safety concerns, intensified research efforts have been conducted to improve the biocompatibility of CNTs, including the development of new shortening and purification strategies. Ideally, the methods used for improving the biocompatibility of CNTs should not alter the electronic properties of CNTs. Herein, we report on the shortening of a sample containing single-walled and double-walled CNTs using steam and obtain new insights in the properties of the steam-treated CNTs. The present study shows that short CNTs (median length ca. 200 nm) can be obtained under the reported conditions. Raman analysis reveals that wider and outer nanotubes undergo more significant changes than the narrower and inner ones, especially after a prolonged steam treatment

Identificación de plagas de chapulín en el norte–centro de México

Short carbon nanotubes (CNTs) are desired for a variety of applications. As a consequence, several strategies have been reported to cut and shorten the length of as-produced CNTs via chemical and physical routes. The efficiency of a given strategy largely depends on the physico-chemical characteristics of the CNTs employed. In order to be able to directly compare the advantages and disadvantages of commonly used protocols, a single batch of chemical vapor deposition single-walled CNTs (SWCNTs) and a batch of multi-walled CNTs (MWCNTs) were subjected to four cutting/shortening strategies, namely acid cutting, piranha treatment, steam shortening and ball milling. The length distribution was assessed by means of scanning electron microscopy. Sample purity and CNT wall structure were determined by Raman spectroscopy, thermogravimetric analysis and magnetic measurements. Within the employed experimental conditions, piranha treatment turned out to be the most efficient to achieve short SWCNTs with a narrow length distribution in a good yield, whereas a mixture of sulfuric/nitric acid was preferred in the case of MWCNTs. A subsequent short steam treatment allowed to remove functional groups present in the samples, leading to median length distributions of 266 nm and 225 nm for SWCNTs and MWCNTs respectively after the combined protocols

Species mixing reduces drought susceptibility of Scots pine (Pinus sylvestris L.) and oak (Quercus robur L., Quercus petraea (Matt.) Liebl.) – Site water supply and fertility modify the mixing effect

Tree species mixing has been widely promoted as a promising silvicultural tool for reducing drought stress. However, so far only a limited number of species combinations have been studied in detail, revealing inconsistent results. In this study, we analysed the effect of mixing Scots pine and oak (pedunculate oak and sessile oak) trees on their drought response along a comprehensive ecological gradient across Europe. The objective was to improve our knowledge of general drought response patterns of two fundamental European tree species in mixed versus monospecific stands. We focused on three null hypotheses: () tree drought response does not differ between Scots pine and oak, () tree drought response of Scots pine and oak is not affected by stand composition (mixture versus monoculture) and () tree drought response of Scots pine and oak in mixtures and monocultures is not modified by tree size or site conditions. To test the hypotheses, we analysed increment cores of Scots pine and oak, sampled in mixed and monospecific stands, covering a wide range of site conditions. We investigated resistance (the ability to maintain growth levels during drought), recovery (the ability to restore a level of growth after drought) and resilience (the capacity to recover to pre-drought growth levels), involving site-specific drought events that occurred between 1976 and 2015. In monocultures, oak showed a higher resistance and resilience than Scots pine, while recovery was lower. Scots pine in mixed stands exhibited a higher resistance, but also a lower recovery compared with Scots pine in monocultures. Mixing increased the resistance and resilience of oak. Ecological factors such as tree size, site water supply and site fertility were found to have significant effects on the drought response. In the case of Scots pine, resistance was increased by tree size, while recovery was lowered. Resistance of oak increased with site water supply. The observed mixing effect on the tree drought response of Scots pine and oak was in some cases modified by the site conditions studied. Positive mixing effects in terms of resistance and resilience of oak increased with site water supply, while the opposite was found regarding recovery. In contrast, site fertility lessened the positive mixing effect on the resistance of Scots pine. We hypothesise that the observed positive mixing effects under drought mainly result from water- and/or light-related species interactions that improve resource availability and uptake according to temporal and spatial variations in environmental conditions.This work was supported by the European Union as part of the ERA-Net SUMFOREST project REFORM – Mixed species forest management. Lowering risk, increasing resilience (2816ERA02S, PCIN2017-026) and the Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 778322. All contributors thank their national funding institutions for supporting the establishment, mensuration and analysis of the studied triplets. The first author wants to thank the German Federal Ministry of Food and Agriculture (BMEL) for financial support through the Federal Office for Agriculture and Food (BLE) (grant number 2816ERA02S), as well as the Bayerische Staatsforsten (BaySF) and Landesbetrieb Forst Brandenburg for providing suitable research sites. Research on the Lithuanian triplets (LT 1, LT 2) was made possible by the national funding institution Research Council of Lithuania (LMTLT) (agreement number S-SUMFOREST-17-1). The French site FR 1 belongs to the OPTMix experimental site (https://optmix.irstea.fr), which is supported annually by Ecofor, Allenvi, and the French national research infrastructure ANAEE-F. A special thank is due to Peter Biber for supporting the statistical analysis

Stand growth and structure of mixed-species and monospecific stands of Scots pine (Pinus sylvestris L.) and oak (Q. robur L., Quercus petraea (Matt.) Liebl.) analysed along a productivity gradient through Europe

19 Pág.Past failures of monocultures, caused by wind-throw or insect damages, and ongoing climate change currently strongly stimulate research into mixed-species stands. So far, the focus has mainly been on combinations of species with obvious complementary functional traits. However, for any generalization, a broad overview of the mixing reactions of functionally different tree species in different mixing proportions, patterns and under different site conditions is needed, including assemblages of species with rather similar demands on resources such as light. Here, we studied the growth of Scots pine and oak in mixed versus monospecific stands on 36 triplets located along a productivity gradient across Europe, reaching from Sweden to Spain and from France to Georgia. The set-up represents a wide variation in precipitation (456–1250 mm year−1), mean annual temperature (6.7–11.5 °C) and drought index by de Martonne (21–63 mm °C−1). Stand inventories and increment cores of trees stemming from 40- to 132-year-old, fully stocked stands on 0.04–0.94-ha-sized plots provided insight into how species mixing modifies stand growth and structure compared with neighbouring monospecific stands. On average, the standing stem volume was 436 and 360 m3 ha−1 in the monocultures of Scots pine and oak, respectively, and 418 m3 ha−1 in the mixed stands. The corresponding periodical annual volume increment amounted to 10.5 and 9.1 m3 ha−1 year−1 in the monocultures and 10.5 m3 ha−1 year−1 in the mixed stands. Scots pine showed a 10% larger quadratic mean diameter (p < 0.05), a 7% larger dominant diameter (p < 0.01) and a 9% higher growth of basal area and volume in mixed stands compared with neighbouring monocultures. For Scots pine, the productivity advantages of growing in mixture increased with site index (p < 0.01) and water supply (p < 0.01), while for oak they decreased with site index (p < 0.01). In total, the superior productivity of mixed stands compared to monocultures increased with water supply (p < 0.10). Based on 7843 measured crowns, we found that in mixture both species, but especially oak, had significantly wider crowns (p < 0.001) than in monocultures. On average, we found relatively small effects of species mixing on stand growth and structure. Scots pine benefiting on rich, and oak on poor sites, allows for a mixture that is productive and most likely climate resistant all along a wide ecological gradient. We discuss the potential of this mixture in view of climate change.The authors wish to thank the European Union for funding the project ?Mixed species forest management. Lowering risk, increasing resilience (REFORM)? (#2816ERA02S, PCIN2017-026) under the framework of Sumforest ERA-NET. All contributors thank their national funding institutions to establish, measure and analyse data from the triplets. The first author also thanks the Bayerische Staatsforsten (BaySF) for supporting the establishment of the plots and the Bavarian State Ministry for Nutrition, Agriculture, and Forestry for permanent support of the project W 07 ?Long-term experimental plots for forest growth and yield research? (#7831-22209-2013). The French site (FR-1) belongs to the OPTMix experimental site (https://optmix.irstea.fr), which is supported annually by Ecofor, Allenvi, and the French national research infrastructure ANAEE-F. Research on the Lithuanian triplets was made possible by the national funding institution Research Council of Lithuania (LMTLT), agreement No. S-SUMFOREST-17-1. Thanks are also due to Ulrich Kern for the graphical artwork. Finally, we thank two anonymous reviewers for their constructive criticism.Peer reviewe

Global disparities in surgeons’ workloads, academic engagement and rest periods: the on-calL shIft fOr geNEral SurgeonS (LIONESS) study

: The workload of general surgeons is multifaceted, encompassing not only surgical procedures but also a myriad of other responsibilities. From April to May 2023, we conducted a CHERRIES-compliant internet-based survey analyzing clinical practice, academic engagement, and post-on-call rest. The questionnaire featured six sections with 35 questions. Statistical analysis used Chi-square tests, ANOVA, and logistic regression (SPSS® v. 28). The survey received a total of 1.046 responses (65.4%). Over 78.0% of responders came from Europe, 65.1% came from a general surgery unit; 92.8% of European and 87.5% of North American respondents were involved in research, compared to 71.7% in Africa. Europe led in publishing research studies (6.6 ± 8.6 yearly). Teaching involvement was high in North America (100%) and Africa (91.7%). Surgeons reported an average of 6.7 ± 4.9 on-call shifts per month, with European and North American surgeons experiencing 6.5 ± 4.9 and 7.8 ± 4.1 on-calls monthly, respectively. African surgeons had the highest on-call frequency (8.7 ± 6.1). Post-on-call, only 35.1% of respondents received a day off. Europeans were most likely (40%) to have a day off, while African surgeons were least likely (6.7%). On the adjusted multivariable analysis HDI (Human Development Index) (aOR 1.993) hospital capacity &gt; 400 beds (aOR 2.423), working in a specialty surgery unit (aOR 2.087), and making the on-call in-house (aOR 5.446), significantly predicted the likelihood of having a day off after an on-call shift. Our study revealed critical insights into the disparities in workload, access to research, and professional opportunities for surgeons across different continents, underscored by the HDI