Vergangene Projekte - Past Projects

Laufende Projekte - Current Projects

Projekte mit der Industrie - Industrial Projects

Sparse Control and Modeling of Multi-Agents systems

Kurzbeschreibung - Abstract

This project is aimed at studying the modeling, optimal control, and controllability problems for multi-agent systems. In recent years there has been a fast growing interest in defining and analyzing mathematical agents. The reason is that examples of networks of models of multiple interacting agents are ubiquitous: biological networks (genetic regulation, ecosystems); technological networks (Internet); economical networks (production and distribution networks, financial networks), and social networks (scientific collaboration networks, Facebook). Usually individual based models, described by suitable dynamical systems, constitute the basis for developing continuum descriptions of the agent distribution, governed by suitable partial differential equations.

Projektleiter - Project Manager: Prof. Dr. Alfio Borzì

Beteiligte Wissenschaftlerinnen und Wissenschaftler - Participating scientists: Dr. Marco Caponigro

Laufzeit: - Projekt period: 01.2016 - 12.2016

Förderinstitution: - Funding institution: Bayerisch-Französisches Hochschulzentrum (BFHZ)

Genehmigungssumme - Funding amount: 3.545,00 €

Genehmigungsdatum - Granting date: 15.01.2016

Förderkennzeichen - Funding number: FK42-15

Entwicklung einer funktionellen 3D MR-basierten Diagnostik der intestinalen Obstruktion - Parallel Multigrid Imaging and Compressed Sensing for Dynamic 3D Magnetic Resonance Imaging

Kurzbeschreibung - Abstract

Aim of this project is to develop a dynamic 3D MR with high temporal and spatial resolution, to evaluate the impact of intus susception in an ex vivo model for the clinical outlet obstruction, and to validate these data by patient data. In this project techniques for the acquisition and reconstruction of 3D MR images will be developed. To this end, accelerated MR sequences will be developed by using parallel imaging and methods including prior knowledge (compressed sensing) as well as reconstruction techniques for these dynamic 3D MR images using multigrid schemes for clinical acceptable reconstruction times. This research work will be carried out promoting a joint interdisciplinary collaboration between the Institut für Mathematik, the Institut für Röntgendiagnostik, and the Klinik für Allgemein-, Viszeral-, Gefäß- und Kinderchirurgie, Universitaetsklinikum Würzburg.

Projektpartner - Project Partners:

Priv.-Doz. Dr. med. Christoph Isbert, Stellvertretender Klinikdirektor der Klinik & Poliklinik für Allgemein- und Viszeralchirurgie, Gefäß- und Kinderchirurgie, Universitätsklinikum Würzburg
Prof. Dr. Herbert Köstler, Institut für Röntgendiagnostik, Universität Würzburg
Prof. Dr. Alfio Borzì, Lehrstuhl für Wissenschaftliches Rechnen, Universität Würzburg

Laufzeit: - Projekt period: 01.2013 - 12.2015

Förderinstitution: - Funding institution: IZKF (Interdisziplinäres Zentrum für Klinische Forschung) der Universität Würzburg

Genehmigungssumme - Funding amount: 358.000 € gesamt (Anteil Borzì: 132.000 €)

Genehmigungsdatum - Granting date: 10.2012

Förderkennzeichen - Funding number: F-254

Weizmann Workshop 2013 on "Multilevel Computational Methods and Optimization"

Kurzbeschreibung - Abstract

This workshop brings together world-class experts from many different countries to exhibit and discuss recent research on multilevel computational methods for optimization in a wide variety of topics and applications. Talks will cover diverse disciplines, including physics, biology, chemistry, economics, environment, earth sciences, computer science, and engineering. This workshop is an occasion to celebrate the publication of the 40th anniversary of Achi Brandt’s seminal paper on multi-level techniques.

Organisation - Organizers:
Ronen Basri, (Weizmann Institute, Dept. of Computer Science)
Alfio Borzì (University of Würzburg, Chair of Mathematics IX 'Scientific Computing')
James Brannick (Pennsylvania State University, Mathematics Department)
Meirav Galun (Weizmann Institute, Dept. of Computer Science)
Cornelis W. Oosterlee (TU Delft, Institute of Applied Mathematics and CWI, Amsterdam)
Irad Yavneh (Technion - Israel Institute of Technology, Computer Science Department)

Datum: - date: 30.04. - 02.05.2013

Förderinstitution: - Funding institution: The Weizmann Institute of Science - WIS-CSP Foundation

Genehmigungsdatum - Granting date: 2012

ESF OPTPDE Workshop on "Modeling and Control of Large Interacting Dynamical Systems"

Kurzbeschreibung - Abstract

This Workshop aims at fostering investigation and application of networks of dynamical systems and their mean-field continuous limits. In particular, mean-field problems, crowd motion, transportation, and the dynamics of stochastic systems and related Fokker-Planck equations, are among the main topics of this workshop. These are emerging research topics in applied mathematics that pose new challenges in the theory of finite- and infinite-dimensional dynamical systems and in the formulation of fast (possibly real-time) simulation and control algorithms.

Organisation - Organizers: Prof. Dr. Alfio Borzì, Dr. Julien Salomon

Datum: - date: 10.-12.09.2013

Förderinstitution: - Funding institution: ESF ( European Science Foundation)

Genehmigungssumme - Funding amount: 24.000,00 €

Genehmigungsdatum - Granting date: 12.2012

Förderkennzeichen - Funding number: 4540

Shape and Material Optimization of mechanical and optical systems

Kurzbeschreibung - Abstract

The Projekt "Shape and Material Optimization of mechanical and optical systems" will investigate new methods of shape and material optimization and applied to mechanical and optical systems. Optimization problems will be observed in detail where eigenfunctions and eigenvalues of these systems should be designed by the shape and material distribution that certain mechanical and/or optical characteristics will be optimized. In mechanical systems Eigenfunctions indeed describe deformations of solid objects (e.g. plates) by vibrations. The frequency of these vibrations will be calculated by the Eigenvalues. The possibility to influence the shape of the Eigenfunctions will offer the possibility to design these systems in a way to make them more resistant under vibrations. Eigenvalues and Eigenvalues define in optical systems under which frequency spectrum and with whih optical characteristics these systems work. The modelling of optical Eigenfunctions for example means to optimize the depth of field.

Projektleiter - Project Manager: Prof. Dr. Alfio Borzì

Beteiligte Wissenschaftlerinnen und Wissenschaftler - Participating scientists: Dr. Marco Verani

Laufzeit: - Projekt period: 12.2012 - 12.2013

Förderinstitution: - Funding institution: Bayerische Forschungsallianz (BayFOR)

Genehmigungssumme - Funding amount: 4.500,00 €

Genehmigungsdatum - Granting date: 18.01.2013

Förderkennzeichen - Funding number: BayIntAn_Uni_Würzburg_2014_38

Optimal Control of Stochastic and Crowd Models

Kurzbeschreibung - Abstract

The control of stochastic processes and crowd models is a very active research field because of many real-world applications in technology, social sciences, and finance. The purpose is to control the probability density function (PDF) of these models that completely characterizes the shape of the statistical distribution of the dynamics. For this purpose, a new control framework based on the Fokker-Planck equation is proposed that governs the evolution of the PDF. Within this framework, it will be possible to design robust controllers in a deterministic way that outperforms many state-of-the art methodologies. In this project, we focus on numerical simulation and optimization schemes to implement our Fokker-Planck strategy and investigate different models and objectives, including mass transport problems and quantum control problems.

Projektleiter - Project Manager: Prof. Dr. Alfio Borzì

Beteiligte Wissenschaftlerinnen und Wissenschaftler - Participating scientists: Dr. Julien Salomon

Laufzeit: - Projekt period: 10.2012 - 12.2013

Förderinstitution: - Funding institution: Bayerisch-Französisches Hochschulzentrum (BFHZ)

Genehmigungssumme - Funding amount: 4.500,00 €

Genehmigungsdatum - Granting date: 29.09.2012

Förderkennzeichen - Funding number: FK10-12

Kontrollierbarkeit und optimale Steuerung interagierender quanten-dynamischer Systeme (COCIQS) - Controllability and Optimal Control of Interacting Quantum Dynamical Systems (COCIQ)

Kurzbeschreibung - Abstract

The goal to achieve full control on complex, high-dimensional quantum systems in an optimal manner poses new challenges for system and control theory. The issue is of paramount importance for the development of future key technologies, such as quantum computing, quantum communication and the manipulation of nanosystems. New challenges arise if the interaction structure is fully taken into account to enable new control strategies. This research project aims at achieving a fundamental understanding of controllability properties and optimal control strategies for finite-dimensional interacting quantum dynamical systems, where structural properties arising from the global tensor product structure of the state spaces will play a crucial role. Our methods will combine techniques from nonlinear control, Lie group theory, and optimal control on function spaces.

Projektleiter - Project Manager: Prof. Dr. Alfio Borzì

Beteiligte Wissenschaftlerinnen und Wissenschaftler - Participating scientists: Prof. Dr. Uwe Helmke

Laufzeit: - Projekt period: 10.2011 - 10.2014

Förderinstitution: - Funding institution: DFG

Genehmigungssumme - Funding amount: 185.000,00 €

Genehmigungsdatum - Granting date: 25.10.2011

Förderkennzeichen - Funding number: Bo3580/2-1

Mathematische Theorie direkter und inverser transienter Wirbelstromprobleme - Mathematical theory of direct and inverse transient eddy current problems

Kurzbeschreibung - Abstract

Transient excitation currents generate electromagnetic fields which in turn induce electric currents in proximal conductors. Mathematically, this can be described by partial differential equations, the eddy-current equations, which are obtained by neglecting the dielectric displacement currents in Maxwells equations. The eddy-current equations are of parabolic-elliptic type: In insulating regions, the field instantaneously adapts to the excitation (elliptic behaviour), while in conducting regions, this adaptation takes some time due to the induced eddy currents (parabolic behaviour). Eddy current effects are used for remotely detecting conducting objects and to non-invasively identify flaws inside a conductor. In mathematical terms this leads to the inverse problem of reconstructing the conductivity coefficient in the eddy current equations from knowledge of the solution(s). Goal of the project is to utilize a unified variational theory for the parabolic-elliptic equations to theoretically study identifiability questions in the inverse problem and derive rigorously justified reconstruction strategies.

Projektleiter - Project Manager: Prof. Dr. Bastian von Harrach

Beteiligte Wissenschaftlerinnen und Wissenschaftler - Participating scientists: Dipl.-Math. Lilian Arnold

Laufzeit: - Projekt period: 08.2010 - 07.2013

Förderinstitution: - Funding institution: DFG

Genehmigungsdatum - Granting date: 17.08.2010

ESF OPTPDE Workshop:
Schnelle Verfahren für die Simulation, Inversion und Steuerung von Wellengleichungsmodellen -
Fast Solvers for Simulation, Inversion, and Control of Wave Propagation Problems

Kurzbeschreibung - Abstract

This Workshop aims at fostering development and application of fast computational techniques to direct and inverse wave problems that are of primal importance in strategic scientific and engineering areas. The ESFWaves workshop will also provide a forum for reseachers to discuss recent advances on the modeling and approximation of wave phenomena and on the formulation of control and inverse problems governed by time-dependent and standing wave equations as Maxwell and Helmholtz equations.

Organisation - Organizers: Prof. Dr. Alfio Borzì, Prof. Dr. Cornelis W. Oosterlee

Datum - date: 26.-28.09.2011

Förderinstitution - Funding institution: ESF ( European Science Foundation)

Genehmigungssumme - Funding amount: 23.000,00 €

Genehmigungsdatum - Granting date: 07.03.2011

Förderkennzeichen - Funding number: 3351