Current projects

Link: Scaling in stochastic models

Summary: Stochastic models are of great importance in describing numerous phenomena in various fields of science and life. An essential property of time-dependent models is their behavior under time and space scaling. The characteristics of many phenomena can be significantly changed by changing the scale. For example, as we move from the tiny world of particles to the astronomical scales, the laws of nature may behave drastically different. The need for models with specific scaling properties comes from numerous practical applications in medicine, biology, physics, finance, economics and other fields of science. The goal of the project is the construction and investigation of stochastic models with special scaling properties. The emphasis is placed on the study of properties of models in the limits of small or large scales. Among other results, a possible explanation will be provided for the phenomenon related to the scaling of empirical moments, known as Taylor’s law. By replacing the time scale of some standard processes, the new classes of stochastic processes will be constructed and analyzed. These new models will be applied in epidemiology and EEG signal analysis. Furthermore, model for the clasification of neurocognitive outcomes based on scaling parameters will be developed.

Programme: Research projects – Croatian Science Foundation (IP-2022-10)

Team members: Nenad Šuvak, (School of Applied Mathematics and Informatics , J. J. Strossmayer University of Osijek), Ivan Papić (School of Applied Mathematics and Informatics , J. J. Strossmayer University of Osijek), Nikolai Leonenko (Cardiff University), Alla Sikorski (Michigan State University)

Project duration: 15 December 2023 – 14 December 2027

Link: Homogenization and Optimization in Mechanics of Solids

Summary: The main topics of this project are different problems in homogenization, dimension reduction and structural optimization with the special emphasis on the applications in mechanics of solids. The physical idea of homogenization, i.e., averaging a highly heterogeneous media to derive its effective properties has a rather long history. Mathematically, it emerged from difficulties faced with (numerical) analysis of governing partial differential equastions in cases when the material oscilates an a small scale or is significantly thinner in one or two directions. A passage to the limit (with respect to some material parameters,i.e., in appropriate topology) usually leads to models that are expected to be simpler, both from the analytical and numerical point of view. The nature of the oscilations of the material can be assumed to be ergodic, periodic or completely general and thus analysed by (stochastic) two-scale convergence method, compensated compactness approach (H-convergence, H-measures) or calculus of variations techniques (Gamma-convergence). Described procedure is well suited for modelling of composite materials, which are fine mixtures of two or more constituent materials. The special interest arises in high-contrast composites, where one obtains a metamaterial with a band gap structure of the spectrum. Optimizing design of devices made of such responsive material and structural material is of great interest. The research proposed by the project encompasses modelling of such materials, and constitutes of challenging and contemporary problems, including topics of stochastic homogenization of high-contrast media, homogenization and dimension reduction in elasto-plasticity, crystallization, quantitative homogenization for evolution for linear elastic thin structures, homogenization of Kirchhoff-Love and Reissner-Mindlin plate equastion, structural optimization of thin elastic plates and in 3D linearized elasticity, homogenization of Friedrich’s systems.

Programme: Research projects – Croatian Science Foundation (IP-2022-10)

Team members: Matteo Capoferri (Heriot-Watt University), Paolo Piovano (University of Vienna), Sergio Gutierrez (Pontificia Universidad Catolica de Chile), Marin Bužančić (University of Zagreb, Faculty of Chemical Engineering and Technology), Mikhail Cherdantsev (Cardiff University), Ivana Crnjac, (School of Applied Mathematics and Informatics , J. J. Strossmayer University of Osijek), Jelena Jankov (School of Applied Mathematics and Informatics , J. J. Strossmayer University of Osijek), Igor Velčić (University of Zagreb, Faculty of Electrical Engineering and Computing), Josip Žubrinić (University of Zagreb, Faculty of Electrical Engineering and Computing)

Project duration: 23 December 2023 – 22 December 2027

Summary: The project aims to create a three-dimensional virtual environment containing a large number of objects with which the user can interact. Besides user interactions, each object can have its own behavior controlled by artificial intelligence. Moreover, over a local network or the internet, multiple users can access the same virtual environment simultaneously, allowing interaction between users. Ultimately, the project should quickly adapt to create virtual environments applicable across numerous fields.

Programme: Internal project of the Department of Mathematics – Strengthening cooperation with the economy

Project collaborators: Luka Borozan (coordinator), Bartol Borozan (collaborator), Antonio Janjić (collaborator), Leon Vilagoš (collaborator) Neven Kopecki (collaborator), Bruno Bugarić (collaborator) i Sven Viland (collaborator)

Project duration: 1 May 2021 – 1 May 2025

Link: STUDENT ENTREPRENEURSHIP – 404: theory

Summary: The education program ‘STUDENT ENTREPRENEURSHIP – 404’ aims to introduce high school students from the Osijek-Baranja County area to entrepreneurship concepts as a career-building idea through initiating entrepreneurial ventures. The education program seeks to familiarize students with the world of entrepreneurship and, through age-appropriate methodology, ensure their understanding of basic entrepreneurial concepts.

Programme: Entrepreneurship encouragement program

Project partners: Faculty of Electrical Engineering, Computer Science, and Information Technology (FERIT) and the Faculty of Economics in Osijek (EFOS)

Project collaborators: Domagoj Ševerdija, Domagoj Matijević i Mateja Đumić

Project duration: 15 December 2022 – 30 May 2023

Link: Algorithm supporting real-time pollen tracking IoT system based on artificial intelligence

Summary: Optimus Consulting Ltd. (OC) will be the leading organization and sending partner in this experiment. The OC team has gained project experience in applying IoT technologies in various industrial sectors. The hosting partner is the University of Osijek (UO), possessing expertise in developing artificial intelligence (AI) algorithms. One of UO’s priorities is establishing cooperation with small and medium-sized enterprises and transferring knowledge from the academic community to the industry: OC will acquire knowledge about real-time AI software solutions that detect and classify pollen allergens in the air and methods of integrating the software solution into IoT-supported systems, making the technology available to a wide range of citizens at very favorable economic criteria. Based on the existing experiment, the teams will consider the possibility of predicting the degree of pollen allergen contamination and ways to commercialize the proposed solution in the future.

Programme: SMART4ALL – Horizon2020 Programme H2020-DT-2018-2020

Project collaborators: Nataša Kovač (Optimus Consulting), Slobodan Jelić (Department of Mathematics)

Project duration: 1 October 2022 – 31 December 2022

Summary: Within the project, mathematical models will be developed to predict the natural gas consumption of end-users based on given input parameters. The models will focus on temperature-dependent consumption measured at specific relevant measurement and control stations that aggregate a larger number of end consumers. Input data for the models include historical consumption trends and historical as well as forecasted meteorological values. In addition to model development, support will be provided to PPD company collaborators in implementing the models in the form of software solutions.

Programme: Internal project of the Department of Mathematics – Strengthening cooperation with the economy

Project collaborators: Department of Mathematics, J. J. Strossmayer University of Osijek: Danijel Grahovac (collaborator), Nenad Šuvak, Dominik Mihalčić

Trajanje projekta: 1 November 2022 – 1 November 2023

Summary:The project aims to strengthen the capacities of primary school education institutions in Osijek-Baranja County, Virovitica-Podravina County and other areas gravitating to these counties with the aim of improving the STEM skills of educational staff. The project provides for the establishment of the Regional Science Centre (hereinafter: the RSC) based in Osijek-Baranja County (Josip Kozarac Elementary School, Josipovac Punitovački) with a branch office in Virovitica-Podravina County (Josip Kozarac Elementary School, Slatina, and Suhopolje Elementary School). Project activities aimed at establishing a system of strengthening STEM skills will take place in the RSC and the branch office, which will be applicable after the project in the entire area of Pannonian Croatia, but also in the wider region. The Regional Science Centre of Pannonian Croatia aims to attract schools from the area in order to provide teaching staff and students with high-quality access to all necessary content for working in the STEM field and capacity development.

Project partner: Osijek-Baranja County (project beneficiary), Virovitica-Podravina County, Josip Kozarac Elementary School – Josipovac Punitovački, Josip Kozarac Elementary School – Slatina, Suhopolje Elementary School, Josip Juraj Strossmayer University of Osijek (Department of Mathematics, Department of Physics, Department of Biology and Department of Chemistry), Business Incubator BIOS d.o.o. Osijek, Centre of Excellence of Split-Dalmatia County, Vitensenteser Innlandet Giovik, Norway and Cluster for Eco-Social Innovation and Development CEDRA Split

Programme:Local Development and Poverty Reduction, which forms part of the Financial Mechanisms of the EEA and the Kingdom of Norway

Team members: Department of Mathematics, Josip Juraj Strossmayer University of Osijek: Snježana Majstorović (Josip Juraj Strossmayer University of Osijek Project Coordinator), Kristian Sabo, Mirta Benšić, Zdenka Kolar-Begović, Rebeka Čorić, Jelena Jankov, Darija Brajković Zorić

Project duration: 15 July 2022 – 14 April 2024

Link: Creative STEM Revolution in Slavonia

Summary: Creative STEM Revolution in Slavonia is a project of the Children′s Creative Center DOKKICA and the Association for Community Development Kreaktiva which aims to develop sustainable programs for the active participation of children and youth as well as the general population in the popularization of STEM in Eastern Croatia in all five Slavonian counties. In cooperation with Josip Juraj Strossmayer University and its affiliations, Department of Mathematics, Department of Physics, Faculty of Civil Engineering and Arhitecture, Faculty of Food Technology and Nikola Tesla Technical School in Vukovar, an innovative and interactive STEM Park will be designed and installed in Osijek as a permanent exhibition for popularization of science. The STEM park will be built on the grounds of the university campus and will be used by civil society organizations in the development and implementation of programs to promote science among children, youth and the general population. The project will provide education, equipment, programs and activities needed by the civil society organizations to continue to play an active role in promoting and popularizing science among their users and the public, as a prerequisite for changing awareness of the importance of science in Croatia.

Project partner: Children′s Creative Center DOKKICA (Lead Beneficiary), Association for Community Development Kreaktiva, Department of Mathematics and Department of Physics J. J. Strossmayer University of Osijek, Faculty of Civil Engineering and Architecture Osijek, Faculty of Food Technology Osijek i Nikola Tesla Technical School in Vukovar

Team members: Department of Mathematics, J. J. Strossmayer University of Osijek: Ljerka Jukić Matić, Ljiljana Primorac Gajčić, Darija Brajković Zorić i Ivana Tucak – Roguljić (student)

Project duration: May 2021 – May 2023

Summary: In this project we plan to consider 6 research topics. In particular, we will consider: 1. Solve parametric Lyapunov equations using reduced basis techniques, 2. Exploitation of the structure and the use of Krylov subspaces, 3. Identification of dominant reachable and observable subspaces, 4. The use of tensor techniques for data-driven approaches, 5. The use of low-rank updates to Lyapunov solutions for optimization of damper locations, 6. The use of frequency-weighted damping via non-smooth optimization. Within this project the two research groups will share knowledge through joint work and discussions during visits to the guest institution, seminar talks and student lectures. Both groups are performing research within the area of systems and control theory, numerical linear algebra and scientific computing. Therefore, they have similar scientific interests, but their main scientific focus has been in different specializations. This project will create strong synergies for their research, since their general closeness ensures they speak a common scientific language, while their specialization ideally complement each other for the investigated tasks. The cooperation of the groups from Magdeburg and Osijek will result in new efficient approaches for damping optimization as well as the fruitful future collaboration between these two research groups and individual researchers.

Programme: The programme aimed at encouraging the exchange of project participants between the Ministry of Science and Education of the Republic of Croatia and the DAAD

Project partner: Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg

Team members: Department of Mathematics, University of Osijek: Zoran Tomljanović, Ninoslav Truhar, Ivica Nakić, Suzana Miodragović, Matea Ugrica, Marinela Pilj Vidaković, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg: Jens Saak, Ion Victor Gosea, Pawan Goyal, Davide Palitta, Igor Pontes Duff, Jennifer Przybilla

Project duration: January 2021 – December 2022

Link: CA18232 Mathematical models for interacting dynamics on networks

Summary: Many physical, biological, chemical, financial or even social phenomena can be described by dynamical systems. It is quite common that the dynamics arises as a compound effect of the interaction between sub-systems in which case we speak about coupled systems. This Action shall study such interactions in particular cases from three points of view: 1. the abstract approach to the theory behind these systems, 2. applications of the abstract theory to coupled structures like network, neighbouring domains divided by permeable membranes, possibly non-homogeneous simplical complexes, etc., 3. modelling real-life situations within this framework. The purpose of this Action is to bring together leading groups in Europe working on a range of issues connected with modelling and analysing mathematical models for dynamical systems on networks. It aims to develop a semigroup approach to various (non-)linear dynamical systems on network as well as numerical methods based on modern variational methods and applying them to road traffic, biological systems, and further real-life models. The Action also explores the possibility of estimating solutions and long time behaviour of these systems by collecting basic combinatorial information about underlying networks.

Programme: Cost Action 18232

Project partners:

Team members: Zoran Tomljanović (Department of Mathematics, University of Osijek)

Project duration: 4 October 2019 – 3 October 2023

Link: GAMe-based learning in MAthematics – GAMMA

Sažetak: Ideja projekta je, u vremenima u kojima su STEM vještine potreba, iskoristiti učeničku poveznanost s digitalnim tehnologijama u cilju prezentacije nastavnih sadržaja matematike na zanimljiv i učenicima aktualan način. Glavni cilj projekta je razvoj priručnika za nastavnike i scenarija poučavanja baziranih na učenju kroz igru za određene nastavne teme koje se javljaju u kurikulumima matematike za učenike u dobi 14-18 godina, u svim projektnim zemljama. Nadamo se da ćemo razvojem kvalitetnih metodičkih materijala potaknuti nastavnike na primjenu digitalnih igara u počavanju matematičkih tema, što će učenicima omogućiti lakše savladavanje gradiva i ukazati im na važnost STEM-a. Dugoročno, nadamo se da ćemo na ovaj način navesti učenike da biraju studije u području STEM-a.

Program: Erasmus+, Key action: KA2 – Cooperation for innovation and the exchange of good practices, Action Type: KA201: Strategic Partnership for school education

Partner na projektu: Elektrotehnička i prometna škola Osijek, Hrvatska, Amsterdam University of Applied Sciences, Faculty of Education, Nizozemska, Satakunta University of Applied Sciences, Finska, National and Kapodistrian University of Athens, School of Philosophy, Department of Educational Studies, Grčka, First Senior High School of Peristeri Athens, Grčka, Porin Lyseon lukio General Upper Secondary School, Finska, Srednja škola Markantuna de Dominisa Rab, Hrvatska i Agencija za odgoj i obrazovanje, Hrvatska

Suradnici na projektu: Mirela Jukić Bokun, Dragana Jankov Maširević, Mihaela Ribičić Penava, Darija Marković, Ljerka Jukić Matić, i Mateja Đumić

Trajanje projekta: 1. listopada 2020. – 30. rujna 2023.

Summary: The main focus of scientific research is divided into four research themes distinguished by the external influence in linear time invariant systems. The first three research themes contain topics that are fundamental for vibration reduction: the homogeneous case, the case with a given external force, and the Multiple-Input Multiple-Output case (MIMO case). Since that the first three research themes have mutual connections and wide applications, we will include specific research theme IV that will aim to integrate the research themes I-III and various prominent applications. PhD student will be dedicated to the non-homogeneous case, which means that student will work on research themes that studies vibration reduction in case with a given external force and MIMO case. Also, since application of obtained results in practical examples is very important, PhD student will also study this kind of applications.

Programme: Young Researchers’ Career Development Project – Training of Doctoral Students

Mentor’s name and surname: Zoran Tomljanović

PhD name and surname: Marinela Pilj Vidaković

Project duration: 1 September 2020 – 1 September 2024