Periodic Reporting for period 1 - SOMPATY (Spectral Optimization: From Mathematics to Physics and Advanced Technology)
Okres sprawozdawczy: 2020-04-01 do 2023-08-31
The aim of our project is inspired by the innovations that have produced new materials and devices with unusual properties. The theoretical basis of this research is quantum mechanics, naturally in combination with electromagnetism theory. The dynamics of quantum systems is governed by the Schrödinger equation, and the fundamental information is encoded in the spectrum of the corresponding Hamiltonian – or energy – operator. The system in question has a complicated structure, and thus the equations that arise require new mathematical tools to solve them. This can rarely be done explicitly. The same is true in other situations: for instance, in electromagnetic systems with a source and drain, the concept of PT symmetry is crucial, or, in chip design, information about the spectrum of a first-order matrix polynomial is extremely important and corresponds to a complicated system of differential algebraic equations. Most of these problems are connected with the solvability of linear or nonlinear equations and, in particular, of associated boundary value problems. This requires, among other things, rigorous or approximate solutions for such equations. In all these problems, there is a deep interplay between physics, pure and applied mathematics and applications from engineering. A common tie from the mathematical viewpoint is the spectrum which plays also a key role in quantum mechanics. A profound understanding of the relationship between the spectrum, geometry, and topology of the described physical or technological objects, as well as of the influence of their deterministic or random perturbations, is needed if they are to be designed in a better way than just using trial and error.
Key research questions include
WP 1: Numerical schemes for indefinite Sturm-Liouville problems & spectral analysis of signals
WP 2: Linear & nonlinear models of branched structures
WP 3: Spectral theory of singular perturbations and inverse problems
WP 4: Approximation theory & theory of function spaces
The aim of the SOMPATY project is to strengthen research ties between Europe and the Commonwealth of Independent States (CIS), particularly the CIS countries in Asia Minor and Central Asia.
Research and innovation objectives
- To model optical fibre networks, nanoscale waveguides and branched structures, nanomaterials and metamaterials including dissipative materials.
- To contribute to the understanding of novel types of metamaterial structures.
- To deepen spectral optimization methods in inverse problems for integrated circuits.
Networking objectives
- The transfer of knowledge and sharing of experience between the participants, in order to create innovations based on the know-how of the partners in the CIS countries in Asia Minor and Central Asia and the European CIS country of Belarus.
- Revealing the potential of the Hidden Champions in the CIS countries.
- International collaboration and secondments to the CIS countries in order to benefit from the knowledge and good practice of the Hidden Champions.
- The establishment and maintenance of a sustainable innovation network. The hope is that a broader European research community will benefit from a cascading effect.
Key research questions include
WP 1: Numerical schemes for indefinite Sturm-Liouville problems & spectral analysis of signals
WP 2: Linear & nonlinear models of branched structures
WP 3: Spectral theory of singular perturbations and inverse problems
WP 4: Approximation theory & theory of function spaces
The aim of the SOMPATY project is to strengthen research ties between Europe and the Commonwealth of Independent States (CIS), particularly the CIS countries in Asia Minor and Central Asia.
Research and innovation objectives
- To model optical fibre networks, nanoscale waveguides and branched structures, nanomaterials and metamaterials including dissipative materials.
- To contribute to the understanding of novel types of metamaterial structures.
- To deepen spectral optimization methods in inverse problems for integrated circuits.
Networking objectives
- The transfer of knowledge and sharing of experience between the participants, in order to create innovations based on the know-how of the partners in the CIS countries in Asia Minor and Central Asia and the European CIS country of Belarus.
- Revealing the potential of the Hidden Champions in the CIS countries.
- International collaboration and secondments to the CIS countries in order to benefit from the knowledge and good practice of the Hidden Champions.
- The establishment and maintenance of a sustainable innovation network. The hope is that a broader European research community will benefit from a cascading effect.
The project is running well:
• 29 journal papers
• till end of 2023 we expect around 60 months of secondments
• 4 conference papers
• 1 paper in conference proceedings
• 6 abstracts/proceedings
• 13 Sompaty online seminars with talks and discussions (https://www.sompaty.eu/events(odnośnik otworzy się w nowym oknie))
Dissemination: Organization of the online format SOMPATY Seminar during the Covid-pandemia, see www.sompaty.eu
Dissemination: Workshops in September 18-22, 2023 in Samarkand, Uzbekistan see: https://mmnw2023.las.uz/index.shtml(odnośnik otworzy się w nowym oknie))
Mathematics for the Micro/Nano-World: From soliton dynamics, nonlinear optics to quantum science and technology
Dissemination: Summer School in September 11-16, 2023 in Samarkand, Uzbekistan https://mmnw2023.las.uz/index.shtml(odnośnik otworzy się w nowym oknie))
Mathematics for the Micro/Nano-World: From soliton dynamics, nonlinear optics to quantum science and technology
Joint preparation of an application for a ERASMUS+ call, Volume 400K Euro:
TU Ilmenau, Prague, TU Graz and U Stockholm and 5 universities from UZ. The main objective of this proposal is to establish a research and training center in Uzbekistan.
Preparation of an university agreement TU Ilmenau—TTPU in Tashkent, UZ.
To underline the cooperation with a university cooperation agreement, will be signed 03/24.
• 29 journal papers
• till end of 2023 we expect around 60 months of secondments
• 4 conference papers
• 1 paper in conference proceedings
• 6 abstracts/proceedings
• 13 Sompaty online seminars with talks and discussions (https://www.sompaty.eu/events(odnośnik otworzy się w nowym oknie))
Dissemination: Organization of the online format SOMPATY Seminar during the Covid-pandemia, see www.sompaty.eu
Dissemination: Workshops in September 18-22, 2023 in Samarkand, Uzbekistan see: https://mmnw2023.las.uz/index.shtml(odnośnik otworzy się w nowym oknie))
Mathematics for the Micro/Nano-World: From soliton dynamics, nonlinear optics to quantum science and technology
Dissemination: Summer School in September 11-16, 2023 in Samarkand, Uzbekistan https://mmnw2023.las.uz/index.shtml(odnośnik otworzy się w nowym oknie))
Mathematics for the Micro/Nano-World: From soliton dynamics, nonlinear optics to quantum science and technology
Joint preparation of an application for a ERASMUS+ call, Volume 400K Euro:
TU Ilmenau, Prague, TU Graz and U Stockholm and 5 universities from UZ. The main objective of this proposal is to establish a research and training center in Uzbekistan.
Preparation of an university agreement TU Ilmenau—TTPU in Tashkent, UZ.
To underline the cooperation with a university cooperation agreement, will be signed 03/24.
Presentation on the German-Kazakh Science Day: Introduction to the SOMPATY project in Almaty, October 12-13, 2023. Below our colleagues Assanoova and Uteshova from Almaty during their presentation.
Joint preparation of an application for a BMBF call of the federal ministry of science and education, Germany (deadline January, 18, 2024), Volume 400K Euro: 5 universities from Germany (Ilmenau, Wuppertal, Luebeck, Chemnitz, Trier, Düsseldorf) and 7 from UZ. The main objective of this proposal is to prepare, with the support of partners at German universities, the TU Ilmenau and others, and to establish a research and training center in Uzbekistan.
GURT-CAMP – a German-Uzbek Research and Training Center for Applied Mathematics and Physics.
It will be a pilot structured Ph.D. program along the experience of "Graduiertenkollegs" in Germany. Such a center will raise the profile of the Uzbek partner institutions and attract better students. The experience gained in this project will help colleagues in other disciplines, other universities and neighboring countries to establish similar infrastructures.
Joint preparation of an application for a BMBF call of the federal ministry of science and education, Germany (deadline January, 18, 2024), Volume 400K Euro: 5 universities from Germany (Ilmenau, Wuppertal, Luebeck, Chemnitz, Trier, Düsseldorf) and 7 from UZ. The main objective of this proposal is to prepare, with the support of partners at German universities, the TU Ilmenau and others, and to establish a research and training center in Uzbekistan.
GURT-CAMP – a German-Uzbek Research and Training Center for Applied Mathematics and Physics.
It will be a pilot structured Ph.D. program along the experience of "Graduiertenkollegs" in Germany. Such a center will raise the profile of the Uzbek partner institutions and attract better students. The experience gained in this project will help colleagues in other disciplines, other universities and neighboring countries to establish similar infrastructures.