##### Gábor Tolnai, Dávid Légrády (2022.08.01 - 2022.12.31)

##### Budapest University of Technology and Economics

**Kivonat:** The GUARDYAN (GPU Assisted Reactor Dynamic Analysis) code developed at the Budapest University of Technology and Economics Institute of Nuclear Techniques directly models the time-dependent phenomena occurring in nuclear reactors. In contrast to conventional reactor dynamics modelling methods, GUARDYAN applies little to no approximations at simulating the physical processes. Price to pay for ultimate accuracy is running time, a real second translates to 6-24h calculation time depending on the complexity of the reactor geometry.

This project aims at increasing the computation eﬃciency by applying variance reduction techniques. This is done by the importance (a.k.a. the adjoint) function used for biasing the interaction laws, for which calculation schemes are being developed in the form of nonanalog Woodcock tracking for free path sampling and scouting samples (sampling importance resampling - SIRS ) for the angular bias.

An accurately pre-calculated adjoint function is needed for the proper biasing, this is computed by GUARDYAN speciﬁcally for the problem at hand. Large computation eﬀort is needed for producing the suﬃciently detailed adjoint for a certain problem, but it can be used for the whole transient scenario. For demonstrating the usefulness of the new variance reduction scheme under development, several test cases of varying complexity should be analysed and the corresponding adjoint function generated demanding large GPU capacity.

##### Márk Margóczi, Dávid Légrády (2022.08.01 - 2022.12.31)

##### Budapest University of Technology and Economics

**Abstract:** Neutron transport calculations of dynamic Monte-Carlo method is emerging new area of research in the nuclear science. The dynamic Monte-Carlo calculation cannot only be
used to foretell neutron kinetics, but to enable more complex dynamic simulations, it can also be coupled with thermal-hydraulic codes. The coupled calculation method raises questions of stability and convergence.

GUARDYAN (GPU Assisted Reactor Dynamic Analysis) is a dynamic Monte Carlobased neutron transport code. The GUARDYAN is able to calculate neutron kinetics, but for more complex reactor physics calculations thermal-hydraulic feedback becomes necessary. To achieve the desired calculations the GUARDIAN has been coupled with a SUBCHANFLOW sub-channel flow simulation code. The simplest tool for testing stability and convergence is the stochastic calculus, within the framework of which neutron kinetics can be approximated with a stochastic differential equation. If the variance contribution term of the equation is defined with Monte-Carlo assumptions, then the stochastic differential equation approximates the dynamic Monte-Carlo method simulation. If the problem is sufficiently simple, the neutron kinetics and thermal-hydraulic of the rector can be derived using analytical formulas. In order to calculate expected value, standard deviation and variance with adequate statistical uncertainty corresponding to the method, these equations must be compared with the solutions of practical problems which require numerous simulation.

Application of GPU cluster supports the publication of scientific journal articles, topic of which is the mapping of the relationship between stochastic differential equations and time-dependent Monte-Carlo-based neutron transport and the investigation of the spread of variance of stochastic neutron kinetics to variance of thermal-hydraulic.

##### Mira Anna Gergácz, Ákos Keresztúri (2022.08.31-12.31)

**Abstract:** Due to the low thermal conductivity of the Martian surface and atmosphere, it is possible that after the recession of the seasonal polar icecap, small icy patches left behind in shady places might be met by direct sunlight during the summer. This work surveyed such frost patches using HiRISE images. Analyzing 110 images out of the available 1400 pieces that fit the selection criteria of location and season, and identified 37 images with smaller ice patches on them. These areas range between 140° and 200° solar longitude in the central latitude band between -40° and -60°. The diameter of the ice patches ranges between 1.5-300 meters, and remains on the surface even after the seasonal polar cap has passed over the area for the duration range of 19-133 martian days.

With the help of The Mars Climate Database (MCD) we simulated the surface temperature and predicted CO2 and H2O ice cover at 22 analyzed areas. Judging by the models, the average noon temperature does not reach the melting point of water, which is 273 K, therefore the occurrence of liquid water on the macroscopic scale is highly unlikely, however there is a possibility that an interfacial premelting of ice (a few nanometers thick waterlayer) might form between the layered and the water ice.

##### Mihály András Pocsai, Imre Ferenc Barna, Gábor Bíró, Gergely Gábor Barnaföldi (2021.10.01 - 2022.08.31)

##### Wigner Research Centre for Physics

**Abstract:** In the concept of plasma based particle acceleration, the particles are accelerated in the wakefield generated by a driver pulse, which may be either a beam of charged particles or a short, intense laser pulse, instead of guiding,collimating and them in vacuum with strong electromagnetic fields [1]. The witness bunch is usually injected in the plasma from an external source, but in case of electron acceleration using a laser pulse as a driver pulse, at sufficiently high laser intensities, some of the plasma electrons are being trapped in the wakefield generated by the laser pulse. This phenomenon is referred as self-injection. In the schemes mentioned above, the driver bunches transfer their energy to the witness bunches through the plasma waves they generate. In the CERN–AWAKE experiment the wakefield is generated by a train of proton microbunches, produced from the SPS proton beam via the self-modulation instability [2]. In this experiment it is essential for the plasma to be ultrahomogeneous, furthemore, at prescribed points of the plasma, the plasma density has to follow the prescribed density ramps accurately. The plasma itself is produced by photoionising the rubidium vapour with a 120 fs long, intense, infra-red laser pulse. Therefore studying the corresponding photoionisation phenomena is a relevant sub-topic of the CERN–AWAKE experiment.

The processes in question have been already studied earlier via quantum mechanical simulations [3]. In our approach, we expanded the solution of the time-dependent Schrödinger-equaion (TDSE) on the basis of the eigenfunctions of the free Hamiltonian-operator of the Rubidium atom. The expansion coeffitiens are timedependent. Substituting this Ansatz into the TDSE, one obtains a first order, linear ODE system, referred as Coupled Channel Equations. Every channel, i. e. every time-dependent expansion coeffitient gives the occupation amplitude of the corresponding bound or continuum state of the rubidium atom. From the final state wave function, the total photoinisation probabilities, the photoelectron energy spectra, angular distributions and energy-and-angle resolved spectra can be obtained.

**References:**

[1] T. Tajima, J.M. Dawson: „Laser electron accelerator". Phys. Rev. Lett 43, 267–270 (1979).

[2] C. Petit-Jean-Genaz, G. Arduini, P. Michel, V. R. W. Schaa, (eds.), Proceedings, 5th International Particle Accelerator Conference (IPAC2014): Dresden, Germany, June 15–20, 2014, JACoW Conferences (CERN, Geneva, Switzerland, 2014).

[3] M.A. Pocsai, I.F. Barna and K. Tőkési: „Photoionisation of Rubidium in strong laser fields". Eur. Phys. J. D 73, 74 (2019).

##### Andor Menczer (ELTE), Áron Vízkeleti (Wigner RCP), Mihály Máté (Wigner RCP) and Örs Legeza (Wigner RCP) - (2022.09.01 - 2022.11.30)

**Abstract:** Numerical simulation of quantum systems where strong interaction between atomic spins and itinerant electrons is present, and at the same time cannot be described with perturbative methods are in the focus of modern physics. These simulations are challenging because computational resources, in general, scale exponentially with system size. Developing algorithms to simulate these systems with polynomial complexity is one of the most heavily researched subjects today.

The density-matrix renormalization group (DMRG) algorithm is one such method, with the additional advantage that the underlying tensor algebra, in light of the conserved quantum numbers, can be broken up into millions of independent tasks. This makes this algorithm ideal for MPI and GPU based massive parallelization. Our research group have been researching the subject for two decades. A GPU based kernel application have been implemented recently thanks to Andor Menczer (ELTE graduate student). In this project we would like to test, and based on the results, optimize this application. At the same time, we would also like to apply it to two-dimensional electron systems, strongly correlated molecular clusters, and atomic nuclei.

The project involves Andor Menczer (ELTE), Áron Vízkeleti (WignerFK), Mihály Máté (WignerFK) and Örs Legeza (WignerFK). The source code was written in Matlab, and a standalone version was compiled using Matlab Compiler. We wish to carry out the testing, fine-tuning and application to large systems in steps. The GPU kernel was built using the Matlab Paralelization Toolbox, and CODA Coder. For the first step, we would like to ask for a three months long interval of access to one of the nodes (cluster 1, 2, 3, 4) that access NVIDIA graphics cards.

We plan to publish the simulation results in prestigious international journals, like the ones our previous work appeared in [1,2]

[1] The density matrix renormalization group algorithm on kilo-processor architectures: implementation and trade-offs, Csaba Nemes, Gergely Barcza, Zoltán Nagy, Örs Legeza, Péter Szolgay, Computer Physics Communications Volume 185, Issue 6, June 2014, Pages 1570-1581

[2] Massively parallel quantum chemical density matrix renormalization group method, Jiří Brabec, Jan Brandejs, Karol Kowalski, Sotiris Xantheas, Örs Legeza, Libor Veis, Computational Chemistry, https://doi.org/10.1002/jcc.26476

##### István Papp, Larissa Bravina, Mária Csete, Igor N. Mishustin, Dénes Molnár, Anton Motornenko, Leonid M. Satarov, Horst Stöcker, Daniel D. Strottman, András Szenes, Dávid Vass, Tamás S. Biró, László P. Csernai, Norbert Kroó (2022.07.01 - 2022.12.31)

**Abstract:** Our dependence on fossil fuels grew more and more in the last century and today we are urged to find alternative energy sources. Laser driven fusion is a promising option for clean and safe energy production. The most successful configuration up to now uses indirect drive, the thermal radiation coming from a cylindrical Hohlraum. After the target is compressed by the incoming light, it develops Rayleigh-Taylor instabilities. An ongoing activity at Wigner Research Centre’s Nanoplasmonic Laser Fusion National Laboratory (NAPLIFE) collaboration is aiming for improving the chances of fusion by high-power short laser pulses and target fabrication, combining recent discoveries in heavy-ion collisions and optics [1]. Our aim is studying in simulations the surface plasmonic effect of resonant gold nano-antennas in different monomer mediums. The monomer serves only experimental purposes, proving the effectiveness of the nanorods. The plasmonic effect is vital for the project, since it will be used to manipulate the target’s absorption properties. The different layers of monomers with different gold nanoparticle densities will be studied, taking into account the lifetime of plasmons using a kinetic plasma model for conducting electrons [2]. The results will be essencial for future experiments in ELI-ALPS Szeged laser facility.

[1] L.P Csernai, N. Kroo and I. Papp, Radiation dominated implosion with nanoplasmonics, Laser and Particle Beams, Volume 36, Issue 2, June 2018 , pp. 171-178

[2] I. Papp, L. Bravina, M. Csete, et al., Kinetic model evaluation of the resilience of plasmonic nanoantennas for laser-induced fusion, PRX Energy, Vol. 1, Iss. 2 (2022)

##### Sudár Ákos, Varga-Kőfaragó Mónika, Barnaföldi Gergely Gábor és Légrády Dávid (2021.07.01 - 2022.08.31)

##### Wigner Research Centre for Physics és BME Institute of Nuclear Techniques

**Abstract:** The goal of development of proton computed tomography is the accurate measurement of the relative stopping power (RSP) distribution of the patient, which is necessary to reduce safety zones around the tumor in proton therapy. During the pCT imaging the patient is imaged by protons, which has determined direction and energy before they go into the patient, and their direction and energy is measured after they come out of the patient. From this information the most likely path (MLP) and the energy deposition in the patient can be determined. The 3D image is reconstructed from the measured data with the use of order suppressed expectation maximalization (OSEM) algorithm, which is an accelerated version of maximum likelihood expectation maximalization (ML-EM) algorithm. The goal of the current project is to develop an image reconstruction code, which runs in parallel threads of CPU and use GPU as well to minimize the image reconstruction time. This software will be used in the future to reconstruct the measured data of a pCT detector developed by the Bergen pCT Collaboration. This work would be contribution to the work of the group and their later publications.

##### Ernő Dávid, Dávid El-Saig, Zoltán Lehóczky and Gergely Gábor Barnaföldi (2021.12.01 - 2022.08.31)

##### Wigner RCP and Lombiq Technologies Ltd. cooperation

**Abstract:** Hastlayer by Lombiq Technologies allows software developers of the .NET platform to utilize FPGAs as compute accelerators. It converts standard .NET constructs into equivalent hardware implementations, automatically enhancing the performance while lowering the power consumption of suitable algorithms. Developers keep writing .NET programs as usual, no hardware design knowledge is required.

Hastlayer needs dedicated firmware and software components for each supported hardware platforms. In collaboration with Wigner RC there are already several supported platforms (like Microsoft Catapult cards and the Xilinx Alveo FPGA card family). The aim of the next development phase is to enable Hastlayer support for embedded platforms like FPGA cards based on the Xilinx Zynq family members.

Wigner's task is to develop the necessary firmware framework to run the Hastlayer-generated hardware cores and if there is a need then customize the Linux operating system running on the embedded ARM CPU cores.

##### Gábor Bíró, Gábor Papp, Gergely Gábor Barnaföldi, Balázs Majoros (2021. 06.01 – 2022.08.31)

##### Wigner Research Centre for Physics and Eötvös University

**Abstract:** At the world largest particle accelerators such as the Large Hadron Collider at CERN or the Relativistic Heavy Ion Collider at BNL, hundreds of thousands of interesting interactions may occur in every second. A special subset of these events are the high-energy heavy-ion collisions, aiming to investigate the birth of the Universe itself. These experimental measurements are always accompanied by numerical calculations, such as Monte Carlo event generators. However, these calculations are computationally very intensive: even with a state-of-the-art desktop machine many CPU hours (days, weeks sometimes) are needed to simulate only a few seconds of real experimental data. Additionally, with the future improvements of the LHC it will be an even bigger challenge to catch up computationally. The HIJING++ framework is the next generation of high-energy heavy-ion Monte Carlo event generators. Equipped with the latest theoretical models, it is designed to perform precise calculations in a flexible, fast, CPU parallel way. Using multicore architectures, a decent speedup can be achieved, reducing the necessary computational time and the additional costs as well.

##### Anna Horváth, Balázs Bámer, Gergely Gábor Barnaföldi and Dávid Légrády (2022.01.01 - 2022.07.30)

##### Wigner Research Centre for Physics

**Abstract:** We investigate the optical trajectories in non-linear optical medium applying standard description. We apply modern machine learning techniques for the image reconstruction.

##### Forgács-Dajka Emese, Kővári Emese, Kovács Tamás (2022.01.01 - 2022.03.30)

##### Eötvös Loránd University, Center for Astrophysics and Space Science

**Abstract:** Mean motion resonances (MMRs) play an important role in shaping the dynamics of the Solar system bodies. MMRs in the Solar system usually occur between a planet and small bodies, e.g. the members of the Hilda group of asteroids are in a 3:2, while the Trojan asteroids are in a 1:1 MMR with Jupiter. Based on the geometrical meaning of the resonance variable, an efficient method has been introduced and described in Forgács-Dajka, Sándor & Érdi (2018), by which mean motion resonances can be easily found without any a priori knowledge of them. The efficiency of this method - named FAIR - is clearly demonstrated by using some known members of different families of asteroids being in mean motion resonances with a planet.
The region beyond Neptune contains a significant number of asteroids (TNOs) where diverse orbits can be encountered, so providing this space region an inexhaustible repository of various dynamic problems. Here we can find very elongated orbits, or even very oblique ones, the explanation of which can be very important from the point of view of planetary evolution. In the first part of our research, we will systematically apply the method FAIR to identify the dynamically relevant MMRs between TNOs and Neptune. Our plans also include the construction of an online database listing both the dynamic and physical properties of individual TNOs.

##### Kővári Emese, Kovács Tamás, Forgács-Dajka Emese (2022.01.01 - 2022.03.30)

##### Eötvös Loránd University, Center for Astrophysics and Space Science

**Abstract:** The trans-Neptunian space is of great interest of dynamical studies with an inexhaustible number of intriguing problems to be solved. Our aim is to carry out a large-scale survey of trans-Neptunian objects (TNOs) by means of dynamical maps. In the first part of the research, we concentrate on the dynamical role of mean-motion resonances (MMRs) among the TNOs, and the tools of understanding are dynamical maps of classical chaos indicators. In the second part, our focus becomes the quantification of the chaotic diffusion and that of the stability times of the small bodies. The chaotic diffusion is of fundamental importance for its rate will determine the long-term dynamics of a given celestial system. To estimate the rate of the diffusion (that is, to compute the diffusion coefficients) in the case of the 4125 TNOs selected in the first part of our study, we initiate the use of the Shannon entropy. This latter quantity allows, on the one hand, to measure the extent of unstable regions in the phase space (and thus serves as an indicator of chaos), and also enables the direct measurement of the diffusion coefficients. The characteristic times of stability - in the case of normal diffusion - are then achieved by taking the inverse of the diffusion coefficients. In the knowledge of the chaotic diffusion and stability times for as large a TNO sample as the one indicated above, the overall structure of the trans-Neptunian space might be mapped as well, along with the specification of dynamical classes or the update of the existing ones.

##### Kovács Tamás, Kővári Emese, Forgács-Dajka Emese (2022.01.01 - 2022.03.30)

##### Eötvös Loránd University, Center for Astrophysics and Space Science

**Abstract:** The long-term dynamical evolution is a crucial point in recent planetary research. Although, the amount of observational data is continuously growing and the precision allows us to obtain accurate planet orbits, the canonical stability analysis still requires N-body simulations and phase space trajectory investigations. We propose a method for stability analysis of planetary motion based on the generalized Rényi entropy obtained from a scalar measurement. The radial velocity data of the central body in gravitational three-body problem is used as the basis of a phase space reconstruction procedure. Then, Poincaré's recurrence theorem contributes to find a natural partitioning in the reconstructed phase space to obtain the Rényi entropy. High performance computing of phase space reconstruction and matrix manipulations allows us to investigate large data sets and long time series. It turns out that the entropy-based stability analysis is in good agreement with other chaos detection methods.

##### István Csabai, Ákos Gellért, Balázs Pál (2022.01.01 - 2022.03.30)

##### ELTE Department of Physics of Complex Systems

**Abstract:** The COVID-19 epidemic created an extraordinary situation for the whole humanity, claiming millions of lives and causing a significant economic setback. At the same time, the international research community has rapidly generated an order of magnitude larger data set than ever before, which can contribute to understanding the evolution and dynamics of the epidemic, to its containment and to the prevention of similar pandemics. The GISAID and COVID-19 Data Portal databases contain millions of complete SARS-CoV-2 genomes. The genetic sequences can be obtained relatively easily and quickly thanks to modern genome sequencers, but it is very difficult to tell how rapidly a given variant will spread or how serious disease will it cause, solely based on the genetic sequences and the mutations. The genetic information is transcribed into proteins, and the spatial structure, charge distribution and interaction of the proteins with the host proteins determine the function of the virus, the so called phenotype. In summary, the genotype-phenotype problem is the estimation of the behaviour of a virus based on genetic information.

In the last year, the rapidly developing artificial intelligence approach has achieved a milestone that can significantly help genotype-phenotype research. Using the Alphafold2 method, the spatial structure of large proteins can be determined with sufficient accuracy in a reasonable time. The machine learning-based Alphafold2 method requires significant computational, mainly GPU, capacity.

We are collaborating with EMBL-EBI on the development of a SARS-CoV-2 genetic archive in the framework of a H2020 project. We aim to complement this with 3D structures of proteins of as many variants as possible and to use these structures to advance the genotype-phenotype question.

##### Dr. Papp Gábor (ELTE), Bíró Gábor (Wigner FK), Feiyi Liu (ELTE), Xiangna Chen (CCNU, Wuhan), Dudás Bence (ELTE), Misur Patricia (ELTE) (2021.06.01-08.31)

**Abstract:** One effective way to kill localized cancerous tumors that are not accessible by surgery is radiation treatment with a proton (or heavier ions as He or C, respectively). In the process, one treatment is usually sufficient compared to conventional radiation therapy, since the proton is very well focused, (with an accuracy of 1 mm, heavier ions with even greater accuracy). However, because the in matter penetration profiles of proton and gamma rays are different, CT tomography does not calibrate the proton beam and does not allow accurate device alignment, resulting in practice in treatment that is far less accurate than the theoretical limit. Greater accuracy can be achieved by proton tomography using a proton beam used for treatment at a higher energy. To detect particles passing through the patient, we developed a detector system based on ALPIDE chips and CERN technology in the framework of the international pCT collaboration (https://wiki.uib.no/pct/index.php/Main_Page). Because processing of the detector signals is a time-consuming process, we want to speed it up by using a neural network: the goal is to develop and train a neural network that can tell the direction and energy of protons leaving the body based on detector signals. By measuring these at several angles, a tomographic image of the examined area can be obtained and the data required for the treatment can be calculated.

##### Emese Forgács-Dajka*, István Balla** (2021.05.01-2021.11.31)

* Eötvös University, Dept. of Astronomy

** Solar Physics and Space Plasma Research Centre (SP2RC), Department of Applied Mathematics, The University of Sheffield

**Abstract:** We investigate the nature and properties of shock waves propagating in an oblique direction to the ambient magnetic field in a partially ionised plasma modelling the plasma of solar prominences. In particular, we aim to analyse the observational signature of these shocks and investigate how our results can explain the recent observations of propagating bright blobs in solar prominences by Lin et al. (2012).

The equations of compressional single-fluid magnetohydrodynamic (MHD) equations are reduced with the help of a multiple scaling method to a well-known Burgers equation whose coefficients depend on the propagation angle of shock waves, plasma-β and the ionisation degree of the plasma. Our model is well-adapted for the separate discussion of shock waves arising from the nonlinear steepening of slow or fast magnetoacoustic waves. Using the standard jump conditions across the shock front (assuming a weak dissipation) we determine the jump in thermodynamic quantities that will be useful for comparison with observations.

Using the Cole-Hopf transform we solve the governing equation as an initial value problem of a diffusion-like equation and investigate the time necessary for a Gaussian initial wave profile to evolve into a shock, whose thickness is of the order of a few ion mean free path.