Index Analysis
DAEs are no ODEs. Actually, Differential agebraic equations (DAEs) are a mixture of ordinary differential equations (ODEs) and algebraic relations. This may create difficulties, which are not seen at the first sight. The analysis shows that due this mixture hidden differentiation might occur. Recalling from analysis that differentiation is not an unbounded operator, such a process is much more difficult to handle than the integrals used for solving ODEs. E.g. imagine a sinosoidal signal of small amplitude but with high frequency, such as a numerical error, the derivative is of much larger magnitude.
Clearly, the more derivatives involved in the exact solution of a DAE, the more one needs to be careful in numerical computations. The index is a measure for this difficutly. That is why it is important to know the index before simulation.
Group members working on that field
- Andreas Bartel
- Michael Günther
Cooperations
- Giuseppe Ali (Academia)
- Sascha Baumanns (Academia)
- Caren Tischendorf (Academia)
Publications
- 2024
4930.
Bohrmann-Linde, Claudia; Kiesling, Elisabeth; Brunnert, Rainer; Strippel, C.; Landau, R.; Geller, Heidrun
Bilingual Chemistry
In Claudia Bohrmann-Linde, Rainer Brunnert, Elisabeth Kiesling, Editor, Band 1
Herausgeber: Bergische Universität Wuppertal
November 20244929.
Aydonat, Simay; Campagna, Davide; Kumar, Sourabh; Storch, Sonja; Neudecker, Tim; Göstl, Robert
Accelerated Mechanochemical Bond Scission and Stabilization against Heat and Light in Carbamoyloxime Mechanophores
Journal of the American Chemical Society, 146 (46) :32117-32123
November 2024
ISSN: 0002-78634928.
Göstl, Robert; Storch, Sonja
Trendbericht Makromolekulare Chemie 2024
Nachrichten aus der Chemie, 72 (10) :52-59
Oktober 20244927.
Synthesis of N2-Substituted 1,2,3-Triazoles
Organic Letters, 2024
Oktober 2024
Herausgeber: ACS4926.
Broschinski, Christian; Majer, Felix; He, Siyang; Kuehne, Alexander J. C.; Göstl, Robert
Mechanochemical Activation of Red-Light-Excited Triplet–Triplet Annihilation Photon Upconversion
ACS Applied Optical Materials, 2 (9) :1764–1769
September 20244925.
[german] Gökkus, Yasemin; Gutenberg, Janna; Kiesling, Elisabeth; Kremer, Richard; Wernicke, Anne; Bohrmann-Linde, Claudia
Sprachsensibler Chemieunterricht digital umgesetzt – Ein Seminarexkurs im Rahmen des Praxissemesters
DiMawe – Zeitschrift für Konzepte und Arbeitsmaterialien für Lehrer*innenbildung und Unterricht, 6 (1)
September 20244924.
anti-Dihydroxylation of olefins enabled by in situ generated peroxyacetic acid
Green Chemistry, 2024
09 2024
Herausgeber: RCS
ISSN: 1463-92704923.
[german] Hüsken, Daniel; Meuter, Nico
Galvanische Zellen erkunden – Eine ergänzende Lernumgebung zur Einführung in die elektrochemische Spannungsreihe
Unterricht Chemie, 202/203 :68-73
September 20244922.
[german] Zeller, Diana; Grandrath, Rebecca
Eigene interaktive Lernbücher gestalten – Ein Überblick für die Produktion mit Book Creator und Pages
Unterricht Chemie, 202/203 :8-13
September 20244921.
[german] Cornelius, Soraya; Bohrmann-Linde, Claudia
Der Fleck muss weg! – Mit Selbstlernbüchern digitale Lernumgebungen zum Kompetenzerwerb für die Produktion eines Erklärvideos schaffen
Unterricht Chemie, 202/203 :56-61
September 20244920.
[german] Kiesling, Elisabeth; Bohrmann-Linde, Claudia
What to do with CO2? – Eine bilinguale Schülerlaboreinheit als Beitrag zu BNE
Unterricht Chemie, 202/203 :86-91
September 20244919.
[german] Zeller, Diana
Schritt für Schritt zum digitalen Versuchsprotokoll – Digitale Lernumgebungen mit Miro umsetzen
Unterricht Chemie, 202/203 :27-31
September 20244918.
[german] Zeller, Diana; Bohrmann-Linde, Claudia; Wlotzka, Petra
Selbstgesteuert und selbstorganisiert lernen – Digitale Lernumgebungen für den Chemieunterricht gestalten und einsetzen
Unterricht Chemie, 202/203 :2-7
September 20244917.
[English] Schrader, Claudia; Diekmann, Charlotte; Schulz, Paulina; Mack, Nils; Bohrmann, Claudia; Zeller, Diana
Hands-on training: Effects on virtual presence, learning-centered emotions, cognitive load and learning outcome when learning with virtual reality
Computers in Human Behavior Reports (100487)
09 20244916.
[german] Zeller, Diana; Bohrmann-Linde, Claudia; Diekmann, Charlotte; Mack, Nils; Schrader, Claudia
Die Teilchenebene in 3D erkunden – Potenziale und Herausforderungen von Virtual Reality im Unterricht
Unterricht Chemie, 202/203 :80-85
September 20244915.
Ishaqat, Aman; Hahmann, Johannes; Lin, Cheng; Zhang, Xiaofeng; He, Chuanjiang; Rath, Wolfgang H.; Habib, Pardes; Sahnoun, Sabri E. M.; Rahimi, Khosrow; Vinokur, Rostislav; Mottaghy, Felix M.; Göstl, Robert; Bartneck, Matthias; Herrmann, Andreas
In Vivo Polymer Mechanochemistry with Polynucleotides
Advanced Materials, 36 (32) :2403752
August 2024
ISSN: 1521-40954914.
Fan, Jilin; Xuan, Mingjun; Zhang, Kuan; Vinokur, Rostislav; Zheng, Lifei; Göstl, Robert; Herrmann, Andreas
Accelerated Mechanophore Activation and Drug Release in Network Core-Structured Star Polymers Using High-Intensity Focused Ultrasound
Small Science, 4 (8) :2400082
August 20244913.
Fan, Jilin; Zhang, Kuan; Xuan, Mingjun; Gao, Xiang; Vinokur, Rostislav; Göstl, Robert; Zheng, Lifei; Herrmann, Andreas
High-Intensity Focused Ultrasound-Induced Disulfide Mechanophore Activation in Polymeric Nanostructures for Molecule Release
CCS Chemistry, 6 (8) :1895-1907
August 20244912.
A Formal Synthesis of (+)-Hannokinol Using a Chiral Horner–Wittig Reagent
Molecules, 29 :3710
07 2024
Herausgeber: MDPI
ISSN: 1420-30494911.
4910.
Synthesis of the monomeric counterpart of Marinomycin A and B
Organic & Biomolecular Chemistry, 2024
06 2024
Herausgeber: RSC4909.
Xu, Zhuo; Tucsnak, Marius
LQR control for a system describing the interaction between a floating solid and the surrounding fluid
06 20244908.
Aydonat, Simay; Hergesell, Adrian H.; Seitzinger, Claire L.; Lennarz, Regina; Chang, George; Sievers, Carsten; Meisner, Jan; Vollmer, Ina; Göstl, Robert
Leveraging mechanochemistry for sustainable polymer degradation
Polymer Journal, 56 (4) :249-268
April 2024
ISSN: 1349-05404907.
Glück, Jochen; Mui, Jonathan
Non-positivity of the heat equation with non-local Robin boundary conditions
04 20244906.
Rath, Wolfgang H.; Göstl, Robert; Herrmann, Andreas
Mechanochemical Activation of DNAzyme by Ultrasound
Advanced Science, 11 (8) :2306236
Februar 2024
ISSN: 2198-3844