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- ItemDifferentialgeometrie im Grossen (hybrid meeting)(Zürich : EMS Publ. House, 2021) Hamenstädt, Ursula; Lang, Urs; Weinkove, BenThe field of classical differential geometry has expanded enormously over the last several decades, helped by the development of tools from neighboring fields such as partial differential equations, complex analysis and geometric topology. In the spirit of the previous meetings in the series, this meeting will bring together researchers from apparently separate subfields of differential geometry, but whose work is linked by common themes. In particular, this meeting will emphasize intrinsic geometric questions motivated by the classification and rigidity of global geometric structures and the interaction of curvature with the underlying geometry and topology.
- ItemSharp phase transition for Cox percolation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2022) Hirsch, Christian; Jahnel, Benedikt; Muirhead, StephenWe prove the sharpness of the percolation phase transition for a class of Cox percolation models, i.e., models of continuum percolation in a random environment. The key requirements are that the environment has a finite range of dependence and satisfies a local boundedness condition, however the FKG inequality need not hold. The proof combines the OSSS inequality with a coarse-graining construction.
- ItemArbeitsgemeinschaft mit aktuellem Thema: Polylogarithms(Zürich : EMS Publ. House, 2004) Kings, Guido; Wildeshaus, Jörg[no abstract available]
- ItemThe Mathematical, Computational and Biological Study of Vision(Oberwolfach-Walke : Mathematisches Forschungsinstitut Oberwolfach, 2001) von der Malsburg, Christoph; Mumford, David[no abstract available]
- ItemThe transition of zbMATH towards an open information platform for mathematics (II): A two-year progress report(Berlin : EMS Press, an imprint of the European Mathematical Society (EMS), 2022) Hulek, Klaus; Teschke, Olaf[no abstract available]
- ItemMechanics of Materials: Mechanics of Interfaces and Evolving Microstructure(Zürich : EMS Publ. House, 2016) McDowell, David L.; Müller, Stefan; Werner, Ewald A.Emphasis in modern day efforts in mechanics of materials is increasingly directed towards integration with computational materials science, which itself rests on solid physical and mathematical foundations in thermodynamics and kinetics of processes. Practical applications demand attention to length and time scales which are sufficiently large to preclude direct application of quantum mechanics approaches; accordingly, there are numerous pathways to mathematical modelling of the complexity of material structure during processing and in service. The conventional mathematical machinery of energy minimization provides guidance but has limited direct applicability to material systems evolving away from equilibrium. Material response depends on driving forces, whether arising from mechanical, electromagnetic, or thermal fields. When microstructures evolve, as during plastic deformation, progressive damage and fracture, corrosion, stress-assisted diffusion, migration or chemical/thermal aging, the associated classical mathematical frameworks are often ad hoc and heuristic. Advancing new and improved methods is a major focus of 21st century mechanics of materials of interfaces and evolving microstructure.
- ItemGradient methods for problems with inexact model of the objective(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Stonyakin, Fedor; Dvinskikh, Darina; Dvurechensky, Pavel; Kroshnin, Alexey; Kuznetsova, Olesya; Agafonov, Artem; Gasnikov, Alexander; Tyurin, Alexander; Uribe, Cesar A.; Pasechnyuk, Dmitry; Artamonov, SergeiWe consider optimization methods for convex minimization problems under inexact information on the objective function. We introduce inexact model of the objective, which as a particular cases includes inexact oracle [19] and relative smoothness condition [43]. We analyze gradient method which uses this inexact model and obtain convergence rates for convex and strongly convex problems. To show potential applications of our general framework we consider three particular problems. The first one is clustering by electorial model introduced in [49]. The second one is approximating optimal transport distance, for which we propose a Proximal Sinkhorn algorithm. The third one is devoted to approximating optimal transport barycenter and we propose a Proximal Iterative Bregman Projections algorithm. We also illustrate the practical performance of our algorithms by numerical experiments.
- ItemVerkehrsoptimierung (Traffic and Transport Optimization)(Oberwolfach-Walke : Mathematisches Forschungsinstitut Oberwolfach, 1999) Buckler Powell, Warren; Zimmermann, Uwe[no abstract available]
- ItemOptimality conditions for convex stochastic optimization problems in Banach spaces with almost sure state constraint(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Geiersbach, Caroline; Wollner, WinnifriedWe analyze a convex stochastic optimization problem where the state is assumed to belong to the Bochner space of essentially bounded random variables with images in a reflexive and separable Banach space. For this problem, we obtain optimality conditions that are, with an appropriate model, necessary and sufficient. Additionally, the Lagrange multipliers associated with optimality conditions are integrable vector-valued functions and not only measures. A model problem is given demonstrating the application to PDE-constrained optimization under uncertainty.
- ItemTopology optimization subject to additive manufacturing constraints(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Ebeling-Rump, Moritz; Hömberg, Dietmar; Lasarzik, Robert; Petzold, ThomasIn Topology Optimization the goal is to find the ideal material distribution in a domain subject to external forces. The structure is optimal if it has the highest possible stiffness. A volume constraint ensures filigree structures, which are regulated via a Ginzburg-Landau term. During 3D Printing overhangs lead to instabilities, which have only been tackled unsatisfactorily. The novel idea is to incorporate an Additive Manufacturing Constraint into the phase field method. A rigorous analysis proves the existence of a solution and leads to first order necessary optimality conditions. With an Allen-Cahn interface propagation the optimization problem is solved iteratively. At a low computational cost the Additive Manufacturing Constraint brings about support structures, which can be fine tuned according to engineering demands. Stability during 3D Printing is assured, which solves a common Additive Manufacturing problem.