TSSP ExSci 2025 projects

The main component of the summer program is an active participation in the selected Science research project offered by the staff members of the Nicolaus Copernicus University, please see the topics and their descriptions below. Interested students are welcome to contact possible advisors for more details concerning the foreseen projects and discuss the dates that the project could be undertaken.

Nonlinear evolution equations - topological approach

Nonlinear evolution equations are essential tool in describing phenomena in physics, biology and engineering. They generalize linear equations by incorporating nonlinear effects, which often results in more complex dynamics. Our goal is to understand the mathematical foundations of nonlinear evolution equations, focusing on the semigroup approach for well-posedness theory and topological methods for studying the dynamical properties of solutions. We will explore concepts of homotopy invariants and apply them to specific examples of nonlinear PDEs. In particular our task is to provide effective methods leading to the existence of periodic solutions, stationary points and heteroclitic orbits for reaction-diffusion system and standing wave solutions for nonlinear Schrödinger equation.

Supervisor:	Piotr Kokocki (pkokocki[at]mat.umk.pl)
Time:	July 2025 (+/- one-week shift possible)

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Automatic bug repair using LLMs

This project focuses on assessing limitations of using Large Language Models (LLMs), such as ChatGPT and Copilot, in the task of Automatic Program Repair (APR). The primary objectives involve replicating literature findings and conducting preliminary research to explore limitations associated with APR using LLMs by manipulating input data.

Summer Project Objectives:

• Replicate experiments outlined in literature on using LLMs in APR.
• Contribute to preliminary research by conducting experiments on Python code base.

We will experiment with generating biased or misleading perturbations in data to steer LLM-generated fix to the code in undesirable directions.

Mining Software Repositories (MSR) techniques will complement this exploration. While programming skills are essential, prior experience in APR or LLMs is not mandatory. Tutorials at the project's commencement will equip participants with the necessary knowledge to actively contribute to this topic.

Supervisor:	Piotr Przymus (eror[at]mat.umk.pl , piotr.przymus[at]gmail.com)
Co-supervisor:	Jakub Narębski (jnareb[at]gmail.com)
Time:	July 2025 (+/- one-week shift possible)

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Ultraviolet radiation in high-mass star formation sites of the Milky Way

The interstellar medium consists of atoms and molecules exposed to ultraviolet (UV) photons from stars. At sites of high-mass star formation, the dense parts of molecular clouds are often irradiated by young stars forming in the vicinity. At later evolutionary stages, the high-mass protostars themselves also produce significant amounts of ionising radiation, which influences their birth clouds. In this project, the student will investigate the effect of external UV radiation on high-mass star formation by comparing the spatial distribution of atomic and molecular carbon, as well as dust, towards several regions in the inner Galaxy. The primary database consists of submillimetre strips of atomic and molecular carbon obtained with the Atacama Pathfinder EXperiment (APEX) in Chile. The student will reduce the molecular data, analyse the maps and identify thepresence of UV radiation. The strength of the UV fields and some properties of the clouds will be derived using existing models of photon-dominated regions.

Supervisor:	Agata Karska (agata.karska[at]umk.pl)
Time:	21 July - 15 August 2025

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Where do X-ray low surface brightness clusters sit with respect to filaments?

A recent publication (https://arxiv.org/abs/2412.13258) investigated the positions of gas-rich and gas-poor galaxy clusters in relation to the large-scale structure of the Universe, i.e., their distance to galactic filaments. The authors of the above paper noted that most of the existing filament catalogs contain truncated filaments; this could affect the outcomes and alter the interpretation. The goal of this project is to repeat the analysis using a recently developed continuous filament network [Tugay & Tarnopolski, ApJ 952, 3 (2023)] to verify the published claims. Requirements: programming skills (python, R, or other), general knowledge of extragalactic astronomy, and basic understanding of statistics.

Supervisor:	Mariusz Tarnopolski (mariusz.tarnopolski[at]umk.pl)
Time:	July 2025 (+/- one-week shift possible)

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Transportable optical clocks and quantum computers

Transportable optical clocks and quantum computers represent cutting-edge advancements in quantum technology. Optical clocks utilizing ultracold atoms achieve extraordinary precision, reaching 10⁻¹⁸, while quantum computers based on similar principles promise unprecedented computational power. However, making these devices transportable presents a significant challenge due to their complex setups, usually requiring extensive laboratory infrastructure and collaborative expertise. This project focuses on the development of compact, transportable systems for optical clocks and quantum computers. Key activities include designing and implementing methods for continuous ultracold atom production, spatial transfer via hollow-core optical fibers, and cooling with frequency-modulated dipole trap light. Additionally, constructing ultra-stable lasers and miniaturized cooling systems will be explored to enable portability. These systems will not only support optical clocks and quantum computers but also enhance other atomic sensors. A crucial objective is achieving robust, continuous operation of these transportable devices without compromising their performance. The work integrates theoretical modeling, simulations, and experimental studies, with applications in fundamental physics, dark matter detection, and atom-light interactions. The project benefits from collaborations with world-leading quantum metrology institutions, including NIST (USA), LNE-SYRTE (France), the University of Amsterdam (Netherlands), and the University of Bonn (Germany), as well as industry partners like Menlo (Germany) and AQT (Austria). Specific tasks will be tailored to the participant's skills and interests, offering opportunities to contribute to revolutionary advancements in portable quantum technologies.

Supervisor:	Sławomir Bilicki (slawko[at]fizyka.umk.pl)
Time:	July 2025 (+/- one-week shift possible)

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Construction of active optical atomic clock

The performance of all state-of-the-art optical atomic clocks is fundamentally limited by the optical frequency oscillator, specifically the clock laser used to probe the ultra-narrow optical atomic transition. The clock laser is essential because optical clocks are passive devices (Rev. Mod. Phys. 87, 637 (2015)), requiring an external laser field to interrogate the extremely narrow atomic transition—known as the clock transition.
The proposed research program focuses on constructing a novel superradiant continuous optical clock setup. The two main goals of the proposed internship are to gain experience in collaborative research within a team environment and to learn about the operation and construction of optical atomic clocks.
The internship will emphasize experimental and technical aspects, including assembling experimental setups and operating passive optical lattice clocks. Specific tasks may include: assembly and maintenance of ultra-high vacuum technology, laser stabilization and line narrowing, electronics development, optical path length stabilization, operation of optical frequency combs, high-Q optical cavity design and characterization, heat transfer simulations, calculation of vibration-insensitive support points, investigation of fundamental noise limits in optical cavities.
To a lesser extent, the internship may involve theoretical work, such as: developing improved methods for controlling superradiance in high-Q cavities (cavity quantum electrodynamics), performing simulations and calculations to determine optimal operating conditions or improve efficiency, exploring potential applications in fundamental physics, such as gravitational wave detection (Physics Letters B, 2023, vol. 846, 138260) or dark matter searches (Science Advances, vol. 40, no. 12, aau4869).

Supervisor:	Marcin Bober (bober[at]fizyka.umk.pl)
Time:	July 2025 (+/- one-week shift possible)

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Analytical excited-state energy gradients for molecules in solution

The calculation of emission spectra of organic molecules used in organic light emitting diodes (OLEDs) requires performing geometry optimizations of the molecules in their excited state [1]. However, simple gas-phase geometry optimizations are typically not enough because photoluminescence measurements are usually performed in solution and the molecular geometry can be significantly affected by the presence of the solvent. A simple approach to include solvation effects is to use a polarizable continuum model (PCM), where the influence of the solvent on the solute is modeled using a set of point charges distributed on the surface of a cavity enclosing the solute molecule. The goal of the project is to implement excited state gradients at the time-dependent density functional theory (TDDFT) level, including solvent effects described using the conductor-like polarizable continuum model (CPCM, or conductor-like screening model, COSMO) [2, 3]. The implementation will be carried out in the VeloxChem program [4] and will be used to determine the excited state geometries in solution of a series of organic molecules with OLED applications.

References:
[1] A. A. Safanov et al., J. Mol. Model. 23, 164 (2017)
[2] F. Liu et al., J. Chem. Theory Comput. 11, 3131 (2015)
[3] J. Liu and W. Liang, J. Chem. Phys. 138, 024101 (2013)
[4] Z. Rikevicius et al., WIREs Comput. Mol. Sci. 10, e1457 (2020).

Supervisor:	Iulia Emilia Brumboiu (iubr[at]umk.pl)
Co-supervisor:	Erik Vitols (evitols[at]doktorant.umk.pl)
Time:	July 2025 (+/- one-week shift possible)

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Optimized extraction of the inter-atomic exchange coupling from electronic structure calculations

Understanding the nature of magnetism has always been a great challenge in the field of condensed matter physics. A crucial development of the last two decades has been the rise of multi-scale magnetic simulations. At the lowest level, the fundamental exchange coupling is extracted from first-principles calculations and then used to build an effective Heisenberg model, which is in turn solved via various methods [1]. In the last few years, the importance of relativistic corrections to the exchange coupling has been recognized in several studies on the formation of complex magnetic structures and topological states [2]. However, the calculation of the magnetic exchange coupling may be very costly in the presence of spin-orbit coupling, regarding both memory and computation. The scope of the present project is precisely to improve on the existing routines implemented in the Relativistic Spin-Polarized toolkit (RSPt) [3,4]. The fundamental task will be to conceptualize the computational procedure, find possibilities for optimization and finally distribute memory and computational load across different cores, using the Message Passing Interface (MPI) framework. Basic knowledge of Fortran 90 (or later versions) is required.

References:
[1] Reviews of Modern Physics 95, 035004 (2023)
[1] Physical Review Letters 131, 196702 (2023)
[3] Physical Review B 102, 115162 (2020)
[4] Science 351, aad3000 (2016)

Supervisor:	Igor Di Marco (igor.dimarco[at]umk.pl)
Time:	July 2025 (+/- one-week shift possible)

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New nanostructured photosensitive materials for optoelectronics

The main goal of this project is to investigate new silver nanostructured azobenzene thin films as photosensitive materials for optoelectronics and photonics. This nanohybrid materials will combine the light-responsive azo function (cis-trans isomerization) with AgNPs. Silver nanoparticles will be synthesised using green chemistry methods. Surface plasmon resonance of AgNPs could be modulated by the photoisomerization of azobenzene molecules adsorbed onto their surface, leading to reversible changes in their optical properties. Student will be synthesised AgNPs, prepared nanostructurized hybrid samples and conduct a comprehensive study of materials to better understand their optical properties and mechanisms of photoactivation. The initial results will be used to design novel photosensitive materials with desired properties.

Supervisor:	Dorota Kowalska (dorota[at]fizyka.umk.pl)
Time:	July 2025 (+/- one-week shift possible)

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Thermoelectric properties of PEDOT:PSS acid trated

The main goal of this project is to investigate thermoelectric properties of PEDOT:PSS acid trated by measuring figure of merit in room temperature. In order to do this Seebeck coefficient, thermal and electrical conductivity have to been known. All parameters can be measured at Thermoelectric Laboratory in Torun.

Supervisor:	Michał Pawlak (mpawlak[at]umk.pl)
Time:	July 2025 (+/- one-week shift possible)

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Developing methods for regularization of quantum-mechanical operators

Some of the relativistic and QED operators include singular terms. The expectation values of singular operators usually converge much slower with the number of the Gaussian-type basis functions used to expand the wave function than the expectation values of non-singular operators. There are theoretical methods for regularizing operators. To reduce the accuracy loss in the calculations of the expectation values of local/singular operators, it was proposed to replace these operators by equivalent operators but less singular and less local [1,2,3]. Drachman proposed the so-called regularization approach, to construct such replacement operators based on the work of Trivedi [3]. However, it also happens that the resulting matrix elements of the regularized quantum operators, calculated in the basis functions, are very sensitive to changes in some parameters of the basis. This leads to the emergence of numerical instabilities. The task of the project is to try to numerically stabilize the derived algorithms.

References:
1. Hiller J., Sucher J. and Feinberg, G., Phys. Rev. A, 18 (1978)
2. Drachman R. J. and Sucher J., Phys. Rev. A, 20 (1979)
3. Trivedi H. P., J. Phys. B, 13 (1980)

Supervisor:	Monika Stanke (ms[at]umk.pl)
Time:	July 2025 (+/- one-week shift possible)

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Study of Flatland realm with density functional theory

In the kingdom of Flatland, the search for the brave knight spread across the land. The challenge posed by King Wave Function Theory I was not for the faint of heart. Many had tried to simplify the arcane complexities of electron interactions in this two-dimensional world, but none had succeeded.
One day, a young alchemist named TPPS student stepped forward. Known for his curiosity and knack for finding patterns in chaos, Sir TPPS was intrigued by the king's idea of Density Functional Theory (DFT). He believed that by studying the distribution of electron density rather than tracking each individual electron, the mysteries of the atomic world could be unraveled more efficiently.
But this journey was not without peril. The TPPS student had to navigate the treacherous realms of approximations, slay the dragons of exchange-correlation energies, and decipher the cryptic runes of computational algorithms. His first task was to implement the DFT method in the quantum theory program developed in the King Wave Function Theory I and explore the kingdom of flatland.
Will Sir TPPS succeed in his quest to simplify the electronic realm? Only time—and the kingdom's most daring computations—will tell.
Potential candidates should be well-motivated to pursue scientific work. Good mathematical and programing (preferebly python) skills and basic knowledge of quantum chemistry and the Linux operating system will be more than welcome.

• derivation and implementation
• analysis of the results

Supervisor:	Szymon Śmiga (szsmiga[at]fizyka.umk.pl)
Time:	July 2025 (+/- one-week shift possible)

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Exploring inhibitory mechanisms and ligand diversity in KATP channels

ATP-sensitive potassium (KATP) channels are critical protein complexes present in the pancreas, heart, and blood vessels. Although these isoforms share structural similarities, they exhibit varying sensitivities to different inhibitors and ligands, influencing their biological functions. Understanding these differences is essential for designing effective therapeutic strategies, especially for conditions like diabetes and cardiovascular diseases. This project focuses on comparing the three primary KATP channel isoforms – pancreatic, cardiac, and vascular – in their interactions with inhibitors and ligands. Participants will construct molecular models using existing structures and homology models. By analyzing protein sequences with bioinformatics tools, they will identify key motifs and ligand-binding sites. Classical and enhanced molecular dynamics (MD) simulations will be performed to study ligand binding and understand structural differences between the isoforms. Familiarity with MD simulations is preferred but not required. However, programming skills in Python are essential for this project, as they will be used for processing, analyzing, and visualizing simulation data. Participants will gain practical experience in computational biology and protein-ligand interaction studies.

Supervisor:	Katarzyna Walczewska-Szewc (kszewc[at]fizyka.umk.pl)
Time:	mid-June - mid-July 2025 (+/- one-week shift possible)

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Automation of the frequency-shifting system for the laser beam

The aim of the project is to design and implement a system optimizing the frequency shift of a laser beam. An acousto-optic modulator will be used to change the beam's frequency. Optical elements that optimize the laser beam's direction after passing through the modulator will be placed on piezoelectric translation stages, whose positions can be controlled using a driver. The goal of the work is to develop a program for positioning the optical elements and to set up and calibrate the entire system based on feedback obtained from a photodiode. Throughout the project, the student will conduct all tasks under the supervision and guidance of the project supervisor.

Supervisor:	Marcin Witkowski (marcin_w[at]fizyka.umk.pl)
Time:	July 2025 (+/- one-week shift possible)

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Toward New Radiative Transfer Modeling

Modeling the spectra of molecules detected in astrophysical environments requires consideration of both radiative and collisional processes. Radiative transfer models describe the interaction of radiation with molecules, while collisional processes, influenced by the medium's density and temperature, impact energy level populations. By solving radiative transfer and statistical equilibrium equations, these models provide insights into the physical conditions, composition, and dynamics of environments like cometary atmospheres and interstellar clouds. However, conventional models typically focus exclusively on the observed molecule, neglecting potential state changes in the perturber. This simplification is particularly inadequate in scenarios where the observed molecule and the perturber are identical, or where the perturber exhibits a dense and complex energy level structure, as is the case of systems such as CO-CO, H₂O-H₂O, or HCN-H₂O.
The proposed project aims to investigate the impact of the initial population distributions of the perturber on the radiative transfer modeling of the observed molecules. By accounting for this effect, the project seeks to improve the accuracy of radiative transfer models in environments where the systems listed above play a significant role, such as cometary atmospheres.
This project will require strong programming skills, preferably in Python, to develop and refine computational models. While prior knowledge of radiative transfer modeling is not mandatory, a basic understanding would be a valuable addition to the candidate's skillset.

Supervisor:	Michał Żółtowski (mzoltowski[at]umk.pl)
Co-supervisor:	Hubert Jóźwiak (hubert.jozwiak[at]umk.pl)
Time:	July 2025 (+/- one-week shift possible)

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