SOLUTIONS Micro-scale modelling: method and initial results

E-print/Working paper (2005)

Solvability of invariant systems of differential equations on the hyperbolic plane

Speeches/Talks (2022)

In the Euclidean case, it is well-known, by Malgrange and Ehrenpreis, that linear differential operators with constant coefficients are solvable. However, what happens, if we genuinely extend this ... [more ▼]

In the Euclidean case, it is well-known, by Malgrange and Ehrenpreis, that linear differential operators with constant coefficients are solvable. However, what happens, if we genuinely extend this situation and consider systems of linear invariant differential operators, is still solvable? In case of Rn (for some positive integer n), the question has been proved mainly by Hörmander. We will show that this remains still true for Riemannian symmetric spaces of non-compact type X = G/K. More precisely, we will present a possible strategy to solve this problem by using the Fourier trans- form and its Paley-Wiener(-Schwartz) theorem for (distributional) sections of vector bundles over X. We will get complete solvability for the hyperbolic plane H2 = SL(2, R)/SO(2) and beyond. This work was part of my doctoral dissertation supervised by Martin Olbrich. [less ▲]

Solvability of systems of invariant differential equations on symmetric spaces G/K

Doctoral thesis (2021)

We study the Fourier transform for distributional sections of vector bundles over symmetric spaces of non-compact type. We show how this can be used for questions of solvability of systems of invariant ... [more ▼]

We study the Fourier transform for distributional sections of vector bundles over symmetric spaces of non-compact type. We show how this can be used for questions of solvability of systems of invariant differential equations in analogy to Hörmander’s proof of the Ehrenpreis-Malgrange theorem. We get complete solvability for the hyperbolic plane H2 and partial results for finite products H2 × · · · × H2 and the hyperbolic 3-space H3. [less ▲]

Solvent effects on crystal nucleation in colloidal suspensions

Scientific Conference (2013)

Solvent hydrodynamics speed up crystal nucleation in suspensions of hard spheres

in Europhysics Letters (2014), 105

We present a computer simulation study on the crystal nucleation process in suspensions of hard spheres, fully taking into account the solvent hydrodynamics. If the dynamics of crystallization in this ... [more ▼]

We present a computer simulation study on the crystal nucleation process in suspensions of hard spheres, fully taking into account the solvent hydrodynamics. If the dynamics of crystallization in this system were purely diffusive, the crystal nucleation rate would be inversely proportional to the solvent viscosity. However, we observe that the nucleation rate is enhanced at high viscosities with respect to the diffusive behaviour. This effect might explain the large discrepancy between the nuclation rates obtained by simulation and experiment that have been reported in the literature so far. [less ▲]

Solving Chisini's functional equation

in Aequationes Mathematicae (2010), 79(3), 237-260

We investigate the n-variable real functions G that are solutions of the Chisini functional equation F(x) = F(G(x),...,G(x)), where F is a given function of n real variables. We provide necessary and ... [more ▼]

We investigate the n-variable real functions G that are solutions of the Chisini functional equation F(x) = F(G(x),...,G(x)), where F is a given function of n real variables. We provide necessary and sufficient conditions on F for the existence and uniqueness of solutions. When F is nondecreasing in each variable, we show in a constructive way that if a solution exists then a nondecreasing and idempotent solution always exists. We also provide necessary and sufficient conditions on F for the existence of continuous solutions and we show how to construct such a solution. We finally discuss a few applications of these results. [less ▲]

Solving equations with negatives or crossing the formalizing gap

in Vlassis, Joëlle (Ed.) Proceedings of the 25th International conference for the Psychology of M athematics Education (PME 25) (2001)

Solving the FIXML2Code-case Study with HenshinTGG

in Rose, Louis M.; Krause, Christian; Horn, Tassilo (Eds.) Proceedings of the 7th Transformation Tool Contest - part of the Software Technologies: Applications and Foundations (STAF 2014) federation of conferences (2014)

Triple graph grammars (TGGs) provide a formal framework for bidirectional model transformations. As in practice, TGGs are primarily used in pure model-to-model transformation scenarios, tools for text-to ... [more ▼]

Triple graph grammars (TGGs) provide a formal framework for bidirectional model transformations. As in practice, TGGs are primarily used in pure model-to-model transformation scenarios, tools for text-to-model and model-to-text transformations make them also applicable in text-to-text transformation contexts. This paper presents a solution for the text-to-text transformation case study of the Transformation Tool Contest 2014 on translating FIXML (an XML notation for financial transactions) to source code written in Java, C# or C++. The solution uses the HenshinTGG tool for specifying and executing model-to-model transformations based on the formal concept of TGGs as well as the Xtext tool for parsing XML content to yield its abstract syntax tree (text-to-model transformation) and serialising abstract syntax trees to source code (model-to-text transformation). The approach is evaluated concerning a given set of criteria. [less ▲]

Solving the three dimensional quadratic assignment problem on a computational grid

in Cluster Computing (2014), 17(2), 205-217

The exact resolution of large instances of combinatorial optimization problems, such as three dimensional quadratic assignment problem (Q3AP), is a real challenge for grid computing. Indeed, it is ... [more ▼]

The exact resolution of large instances of combinatorial optimization problems, such as three dimensional quadratic assignment problem (Q3AP), is a real challenge for grid computing. Indeed, it is necessary to reconsider the resolution algorithms and take into account the characteristics of such environments, especially large scale and dynamic availability of resources, and their multi-domain administration. In this paper, we revisit the design and implementation of the branch and bound algorithm for solving large combinatorial optimization problems such as Q3AP on the computational grids. Such gridification is based on new ways to effi- ciently deal with some crucial issues, mainly dynamic adaptive load balancing and fault tolerance. Our new approach allowed the exact resolution on a nation-wide grid of a dif- ficult Q3AP instance. To solve this instance, an average of 1,123 computing cores were used for less than 12 days with a peak of around 3,427 computing cores. [less ▲]

„Solvitur ambulando“. Pilgerräume bei Werner Herzog: Vom Gehen im Eis und Wolfgang Büscher: Berlin – Moskau

in Börnchen, Stefan; Mein, Georg (Eds.) Weltliche Wallfahrten. Auf der Spur des Realen. (2010)