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Type: report × Subject: Numerics and Scientific Computing ×

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Now showing 1 - 10 of 27
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    Wie steuert man einen Kran?
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2016) Altmann, Robert; Heiland, Jan
    Die Steuerung einer Last an einem Kran ist ein technisch und mathematisch schwieriges Problem, da die Bewegung der Last nur indirekt beeinflusst werden kann. Anhand eines Masse-Feder-Systems illustrieren wir diese Schwierigkeiten und zeigen wie man mit einem zum konventionellen Lösungsweg alternativen Optimierungsansatz die auftretenden Komplikationen teilweise umgehen kann.
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    Data assimilation: mathematics for merging models and data
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2018) Morzfeld, Matthias; Reich, Sebastian
    When you describe a physical process, for example, the weather on Earth, or an engineered system, such as a self-driving car, you typically have two sources of information. The first is a mathematical model, and the second is information obtained by collecting data. To make the best predictions for the weather, or most effectively operate the self-driving car, you want to use both sources of information. Data assimilation describes the mathematical, numerical and computational framework for doing just that.
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    The adaptive finite element method
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2016) Gallistl, Dietmar
    Computer simulations of many physical phenomena rely on approximations by models with a finite number of unknowns. The number of these parameters determines the computational effort needed for the simulation. On the other hand, a larger number of unknowns can improve the precision of the simulation. The adaptive finite element method (AFEM) is an algorithm for optimizing the choice of parameters so accurate simulation results can be obtained with as little computational effort as possible.
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    Modeling communication and movement: from cells to animals and humans
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2015) Eftimie, Raluca
    Communication forms the basis of biological interactions. While the use of a single communication mechanism (for example visual communication) by a species is quite well understood, in nature the majority of species communicate via multiple mechanisms. Here, I review some mathematical results on the unexpected behaviors that can be observed in biological aggregations where individuals interact with each other via multiple communication mechanisms.
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    Molecular Quantum Dynamics
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2017) Hagedorn, George A.; Lasser, Caroline
    We provide a brief introduction to some basic ideas of Molecular Quantum Dynamics. We discuss the scope, strengths and main applications of this field of science. Finally, we also mention open problems of current interest in this exciting subject.
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    Darcy's law and groundwater flow modelling
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2015) Schweizer, Ben
    Formulations of natural phenomena are derived, sometimes, from experimentation and observation. Mathematical methods can be applied to expand on these formulations, and develop them into better models. In the year 1856, the French hydraulic engineer Henry Darcy performed experiments, measuring water flow through a column of sand. He discovered and described a fundamental law: the linear relation between pressure difference and flow rate – known today as Darcy’s law. We describe the law and the evolution of its modern formulation. We furthermore sketch some current mathematical research related to Darcy’s law.
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    High performance computing on smartphones
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2016) Patera, Anthony T.; Urban, Karsten
    Nowadays there is a strong demand to simulate even real-world engineering problems on small computing devices with very limited capacity, such as a smartphone. We explain, using a concrete example, how we can obtain a reduction in complexity – to enable such computations – using mathematical methods.
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    A short story on optimal transport and its many applications
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2018) Santambrogio, Filippo
    We present some examples of optimal transport problems and of applications to different sciences (logistics, economics, image processing, and a little bit of evolution equations) through the crazy story of an industrial dynasty regularly asking advice from an exotic mathematician.
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    Prony’s method: an old trick for new problems
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2018) Sauer, Tomas
    In 1795, French mathematician Gaspard de Prony invented an ingenious trick to solve a recovery problem, aiming at reconstructing functions from their values at given points, which arose from a specific application in physical chemistry. His technique became later useful in many different areas, such as signal processing, and it relates to the concept of sparsity that gained a lot of well-deserved attention recently. Prony’s contribution, therefore, has developed into a very modern mathematical concept.
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    The mystery of sleeping sickness – why does it keep waking up?
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2015) Funk, Sebastian
    Sleeping sickness is a neglected tropical disease that affects rural populations in Africa. Deadly when untreated, it is being targeted for elimination through case finding and treatment. Yet, fundamental questions about its transmission cycle remain unanswered. One of them is whether transmission is limited to humans, or whether other species play a role in maintaining circulation of the disease. In this snapshot, we introduce a mathematical model for the spread of Trypanosoma brucei, the parasite responsible for causing sleeping sickness, and present some results based on data collected in Cameroon. Understanding how important animals are in harbouring Trypanosoma brucei that can infect humans is important for assessing whether the disease could be reintroduced in human populations even after all infected people have been successfully treated.