http://publications.mfo.de/handle/mfo/62 Mon, 06 Apr 2026 21:14:22 GMT 2026-04-06T21:14:22Z http://publications.mfo.de/handle/mfo/1276 Towards a Mathematical Theory of Turbulence in Fluids Bedrossian, Jacob Fluid mechanics is the theory of how liquids and gases move around. For the most part, the basic physics are well understood and the mathematical models look relatively simple. Despite this, fluids display a dazzling mystery to their motion. The random-looking, chaotic behavior of fluids is known as turbulence, and it lies far beyond our mathematical understanding, despite a century of intense research. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/1276 2016-01-01T00:00:00Z Bedrossian, Jacob Fluid mechanics is the theory of how liquids and gases move around. For the most part, the basic physics are well understood and the mathematical models look relatively simple. Despite this, fluids display a dazzling mystery to their motion. The random-looking, chaotic behavior of fluids is known as turbulence, and it lies far beyond our mathematical understanding, despite a century of intense research. http://publications.mfo.de/handle/mfo/1258 Profinite groups Bartholdi, Laurent Profinite objects are mathematical constructions used to collect, in a uniform manner, facts about infinitely many finite objects. We shall review recent progress in the theory of profinite groups, due to Nikolov and Segal, and its implications for finite groups. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/1258 2016-01-01T00:00:00Z Bartholdi, Laurent Profinite objects are mathematical constructions used to collect, in a uniform manner, facts about infinitely many finite objects. We shall review recent progress in the theory of profinite groups, due to Nikolov and Segal, and its implications for finite groups. http://publications.mfo.de/handle/mfo/1254 The adaptive finite element method 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. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/1254 2016-01-01T00:00:00Z 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. http://publications.mfo.de/handle/mfo/456 Footballs and donuts in four dimensions Klee, Steven In this snapshot, we explore connections between the mathematical areas of counting and geometry by studying objects called simplicial complexes. We begin by exploring many familiar objects in our three dimensional world and then discuss the ways one may generalize these ideas into higher dimensions. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/456 2016-01-01T00:00:00Z Klee, Steven In this snapshot, we explore connections between the mathematical areas of counting and geometry by studying objects called simplicial complexes. We begin by exploring many familiar objects in our three dimensional world and then discuss the ways one may generalize these ideas into higher dimensions. http://publications.mfo.de/handle/mfo/455 The Willmore Conjecture Nowaczyk, Nikolai The Willmore problem studies which torus has the least amount of bending energy. We explain how to think of a torus as a donut-shaped surface and how the intuitive notion of bending has been studied by mathematics over time. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/455 2016-01-01T00:00:00Z Nowaczyk, Nikolai The Willmore problem studies which torus has the least amount of bending energy. We explain how to think of a torus as a donut-shaped surface and how the intuitive notion of bending has been studied by mathematics over time. http://publications.mfo.de/handle/mfo/454 Prime tuples in function fields Bary-Soroker, Lior How many prime numbers are there? How are they distributed among other numbers? These are questions that have intrigued mathematicians since ancient times. However, many questions in this area have remained unsolved, and seemingly unsolvable in the forseeable future. In this snapshot, we will discuss one such problem, the Twin Prime Conjecture, and a quantitative version of it known as the Hardy–Littlewood Conjecture. We will also see that these and other questions about prime numbers can be extended to questions about function fields, and discuss recent progress which has been made to answer them in this context. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/454 2016-01-01T00:00:00Z Bary-Soroker, Lior How many prime numbers are there? How are they distributed among other numbers? These are questions that have intrigued mathematicians since ancient times. However, many questions in this area have remained unsolved, and seemingly unsolvable in the forseeable future. In this snapshot, we will discuss one such problem, the Twin Prime Conjecture, and a quantitative version of it known as the Hardy–Littlewood Conjecture. We will also see that these and other questions about prime numbers can be extended to questions about function fields, and discuss recent progress which has been made to answer them in this context. http://publications.mfo.de/handle/mfo/464 Polyhedra and commensurability Guglielmetti, Rafael; Jacquement, Matthieu This snapshot introduces the notion of commensurability of polyhedra. At its bottom, this concept can be developed from constructions with paper, scissors, and glue. Starting with an elementary example, we formalize it subsequently. Finally, we discuss intriguing connections with other fields of mathematics. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/464 2016-01-01T00:00:00Z Guglielmetti, Rafael Jacquement, Matthieu This snapshot introduces the notion of commensurability of polyhedra. At its bottom, this concept can be developed from constructions with paper, scissors, and glue. Starting with an elementary example, we formalize it subsequently. Finally, we discuss intriguing connections with other fields of mathematics. http://publications.mfo.de/handle/mfo/463 Fokus-Erkennung bei Epilepsiepatienten mithilfe moderner Verfahren der Zeitreihenanalyse Deistler, Manfred; Graef, Andreas Viele epileptische Anfälle entstehen in einer begrenzten Region im Gehirn, dem sogenannten Anfallsursprung. Eine chirurgische Entfernung dieser Region kann in vielen Fällen zu Anfallsfreiheit führen. Aus diesem Grund ist die Frage nach der Lokalisation des Anfallsursprungs aus EEG-Aufzeichnungen wichtig. Wir beschreiben hier ein Verfahren zur Lokalisation des Anfallsursprungs mittels Zeitreihenanalyse, das auf der Schätzung von Spektren im EEG beruht. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/463 2016-01-01T00:00:00Z Deistler, Manfred Graef, Andreas Viele epileptische Anfälle entstehen in einer begrenzten Region im Gehirn, dem sogenannten Anfallsursprung. Eine chirurgische Entfernung dieser Region kann in vielen Fällen zu Anfallsfreiheit führen. Aus diesem Grund ist die Frage nach der Lokalisation des Anfallsursprungs aus EEG-Aufzeichnungen wichtig. Wir beschreiben hier ein Verfahren zur Lokalisation des Anfallsursprungs mittels Zeitreihenanalyse, das auf der Schätzung von Spektren im EEG beruht. http://publications.mfo.de/handle/mfo/462 Wie steuert man einen Kran? 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. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/462 2016-01-01T00:00:00Z 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. http://publications.mfo.de/handle/mfo/461 High performance computing on smartphones 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. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/461 2016-01-01T00:00:00Z 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.