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- ItemModelling the spread of brain tumours(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2015) Swan, Amanda; Murtha, AlbertThe study of mathematical biology attempts to use mathematical models to draw useful conclusions about biological systems. Here, we consider the modelling of brain tumour spread with the ultimate goal of improving treatment outcomes.
- ItemThe adaptive finite element method(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2016) Gallistl, DietmarComputer 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.
- ItemSeeing through rock with help from optimal transport(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2022) Frederick, Christina; Yang, YunanGeophysicists and mathematicians work together to detect geological structures located deep within the earth by measuring and interpreting echoes from manmade earthquakes. This inverse problem naturally involves the mathematics of wave propagation, but we will see that a different mathematical theory – optimal transport – also turns out to be very useful.
- ItemDrugs, herbicides, and numerical simulation(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) Benner, Peter; Mena, Hermann; Schneider, RenéThe Colombian government sprays coca fields with herbicides in an effort to reduce drug production. Spray drifts at the Ecuador-Colombia border became an international issue. We developed a mathematical model for the herbicide aerial spray drift, enabling simulations of the phenomenon.
- ItemThe mystery of sleeping sickness – why does it keep waking up?(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2015) Funk, SebastianSleeping 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.
- ItemShape space – a paradigm for character animation in computer graphics(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2020) Heeren, Behrend; Rumpf, MartinNowadays 3D computer animation is increasingly realistic as the models used for the characters become more and more complex. These models are typically represented by meshes of hundreds of thousands or even millions of triangles. The mathematical notion of a shape space allows us to effectively model, manipulate, and animate such meshes. Once an appropriate notion of dissimilarity measure between different triangular meshes is defined, various useful tools in character modeling and animation turn out to coincide with basic geometric operations derived from this definition.
- ItemHigh performance computing on smartphones(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2016) Patera, Anthony T.; Urban, KarstenNowadays 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.
- ItemMathematics plays a key role in scientific computing(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2017) Shu, Chi-WangI attended a very interesting workshop at the research center MFO in Oberwolfach on “Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws”. The title sounds a bit technical, but in plain language we could say: The theme is to survey recent research concerning how mathematics is used to study numerical algorithms involving a special class of equations. These equations arise from computer simulations to solve application problems including those in aerospace engineering, automobile design, and electromagnetic waves in communications as examples. This topic belongs to the general research area called “scientific computing”.
- ItemMolecular Quantum Dynamics(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2017) Hagedorn, George A.; Lasser, CarolineWe 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.
- ItemModeling communication and movement: from cells to animals and humans(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2015) Eftimie, RalucaCommunication 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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