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Sergiy Shelyag

Publications and source records attributed to Sergiy Shelyag.

At least 19 recordsLinked to original sources
arXiv2026

Towards understanding stellar variability at the sub m/s level: granulation-induced variability across the optical spectrum

Detecting the radial velocity signal of Earth-mass exoplanets requires the characterisation and removal of granulation-induced radial velocity variability from spectroscopic observations. By coupling three-dimensional (3D) hydrodynamic (HD) simulations to a radiative transfer code, we can isolate and study the effect of granulation on stellar lines. In this study we isolated the impact of granulation on spectral line shapes and shifts for the largest and most diverse synthetic spectral line sample to date. Our aims were twofold. First, we quantified how granulation affects the temporal evolution of shapes and shifts of 72 unblended spectral lines in two wavelength regions: 5500-5600 {\AA} and 6100-6200 {\AA}, from disc centre to the stellar limb. Second, we investigated if spectral lines behave coherently in their line shape variability. We find that weak lines show the largest radial-velocity variability due to granulation, up to 40 m/s at disc centre and 50 m/s at the stellar limb. On the other hand, strong lines exhibit larger variability in equivalent width than weak lines across the stellar disc. In addition, the equivalent width and line depth of a spectral line are strongly linearly correlated with its radial velocity. While granulation affects all three of these quantities, planetary Doppler shifts only affect radial velocities, opening the door to new granulation-mitigation methods. Lastly, we find that the radial velocity and equivalent width of most spectral lines in our sample evolve coherently in time, with the Fe I and Ca I lines behaving the most similarly. Due to the coherency, line blends will not significantly affect the temporal behaviour of RV and line shape, as induced by granulation. Besides, the coherency between spectral lines offer the opportunity to create disc-integrated spectra of many lines simultaneously, which will be explored in future work.

astro-ph.SR↗
arXiv2026

Decoding the Radial Velocity Signatures of Solar Faculae with 3D MHD Simulations

We model the solar radial velocity (RV) signal induced by faculae, the dominant contributor to RV variability in Sun-like stars. We use a representative case of a facular patch transiting the visible solar disk as the Sun rotates to disentangle various physical effects contributing to the RV signal. Our approach is based on 3D radiative magnetohydrodynamic (MHD) simulations of the solar photosphere and upper convection zone with the MURaM code and spectral synthesis with the MPS-ATLAS code. We show that the faculae-induced RV strongly depends on the facular position on the solar disk. Near disk centre, facular magnetic fields inhibit the convective blueshift and thus produce a relative redshift of the solar spectrum. Surprisingly, when located closer to the limb, namely at heliocentric angles greater than about $60^\circ$, faculae produce a relative blueshift. This transition from redshift to blueshift is caused by the effect of magnetic fields on horizontal flows, which dominate the signal near the limb, and on the visibility of these flows. In combination with solar rotation, this centre-to-limb dependence of the facular effect leads to a complex RV profile during the facular transit and, in particular, to a phase lag between the maximum of the RV signal and the facular crossing of the central meridian. We further show that, in contrast to stellar reflex motion, the facular signal strongly depends on the spectral line in which it is measured.

astro-ph.SR↗
arXiv2026

Synthetic disk-integrated absorption lines isolating stellar granulation for high-precision RV studies

We present a novel method for constructing high-accuracy, time-varying disk-integrated stellar absorption line profiles that isolate the effects of granulation alone. This framework provides an effectively unlimited supply of physically consistent training data, offering a unique opportunity to study granulation-driven velocity variability with no contamination from other stellar processes or instrumental systematics. Our interpolation scheme enables accurate profile generation at arbitrary limb angles and successfully reproduces observed disk integrated solar bisector shapes from IAG spectra. Using four Fe I lines (525.0, 615.2, 617.3, and 627.1 nm), we produce 1000 model star disk-integrated realisations per line and find an isolated granulation-induced RV scatter of 0.16-0.21 m s^-1. Using our synthetic profiles and assuming infinite signal-to-noise, we find strong correlations between various line-shape metrics and convective blueshift, demonstrating that line-shape diagnostics can, in principle, trace granulation effects. Equivalent width proves the strongest diagnostic, achieving up to 60% scatter reduction. However, the strength of all simple line shape diagnostics rapidly diminishes once photon noise is injected. Even when artificially boosting the signal to represent a spectrum containing ~1000 spectral lines, the achievable improvement with these metrics remains below 10% at typical signal-to-noise ratios. Our results highlight the need for more robust, noise-resilient diagnostics and position our synthetic dataset as a valuable testbed for developing and benchmarking such methods.

astro-ph.SR↗
arXiv2025

Opinion dynamics modelling: distinct attraction and repulsion topologies highlight quantitative effects of trolling

We introduce a model of opinion dynamics based on networked non-linear differential equations. The model combines a linear attraction with a repulsive hyperbolic tangent interaction, labeled controversialness. For low controversialness the model displays universal consensus, which is typical of opinion models. As controversialness increases, opinion behaviours such as polarisation, clustering and dissensus emerge, dependent on the network topology. By placing attractive and repulsive interactions on distinct networks, this model is able to simulate the manipulative effects of trolls by introducing controversy, which may be associated with mis/disinformation, toxic messaging, and encouraging provocative questioning and/or emotional posting. This work offers an analytical and statistical analysis of model results, under a wide variety of topologies and initial conditions, whilst also generalising cluster detection algorithms typically applied to discrete models.

physics.soc-ph↗
arXiv2025

Towards understanding stellar variability at the sub m/s level: Isolating granulation signals in synthetic spectral lines

Granulation in the photospheres of FGK-type stars induces variability in absorption lines, complicating exoplanet detection via radial velocities and characterisation via transmission spectroscopy. We aim to quantify the impact of granulation on the radial velocity and bisector asymmetry of stellar absorption lines of varying strengths and at different limb angles. We use 3D radiation-hydrodynamic simulations from MURaM paired with MPS-ATLAS radiative transfer calculations to synthesise time series' for four Fe I lines at different limb angles for a solar-type star. Our line profiles are synthesised at an extremely high resolution (R = 2,000,000), exceeding what is possible observationally and allowing us to capture intricate line shape variations. We introduce a new method of classifying the stellar surface into three components and use this to parameterise the line profiles. Our parameterisation method allows us to disentangle the contributions from p-modes and granulation, providing the unique opportunity to study the effects of granulation without contamination from p-mode effects. We validate our method by comparing radial velocity power spectra of our granulation time series to observations from the LARS spectrograph. We find that we are able to replicate the granulation component extracted from observations of the Fe I 617 nm line at the solar disk centre. We use our granulation-isolated results to show variations in convective blueshift and bisector asymmetry at different limb angles, finding good agreement with empirical results. We show that weaker lines have higher velocity contrast between granules and lanes, resulting in higher granulation-induced velocity fluctuations. Our parameterisation provides a computationally efficient strategy to construct new line profiles, laying the groundwork for future improvements in mitigating stellar noise in exoplanet studies.

astro-ph.SR↗
arXiv2024

Modeling the effects of a lightbridge on oscillations in a solar pore

Solar pores are ideal magnetic structures for wave propagation and transport of energy radially-outwards across the upper layers of the solar atmosphere. We aim to model the excitation and propagation of magnetohydrodynamic waves in a pore with a lightbridge modelled as two interacting magnetic flux tubes separated by a thin, weaker field, layer. We solve the three-dimensional MHD equations numerically and calculate the circulation as a measure of net torsional motion. We find that the interaction between flux tubes results in the natural excitation of propagating torsional Alfvén waves, but find no torsional waves in the model with a single flux tube. The torsional Alfvén waves propagate with wave speeds matching the local Alfvén speed where wave amplitude peaks.

astro-ph.SR↗
arXiv2024

Periodic Solutions of a Delay Differential Equation with a Periodic Multiplier

A simple non-autonomous scalar differential equation with delay, exponential decay, nonlinear negative feedback and a periodic multiplicative coefficient is considered. It is shown that stable slowly oscillating periodic solutions with the period of the feedback coefficient, and also with the double period of the feedback coefficient exist. The periodic solutions are built explicitly in the case of piecewise constant feedback function and the periodic coefficient. The periodic dynamics are shown to persist under small perturbations of the equation which make it smooth. The results are confirmed and illustrated by numerical simulations.

math.DS↗
arXiv2024

Extremization to Fine Tune Physics Informed Neural Networks for Solving Boundary Value Problems

We propose a novel method for fast and accurate training of physics-informed neural networks (PINNs) to find solutions to boundary value problems (BVPs) and initial boundary value problems (IBVPs). By combining the methods of training deep neural networks (DNNs) and Extreme Learning Machines (ELMs), we develop a model which has the expressivity of DNNs with the fine-tuning ability of ELMs. We showcase the superiority of our proposed method by solving several BVPs and IBVPs which include linear and non-linear ordinary differential equations (ODEs), partial differential equations (PDEs) and coupled PDEs. The examples we consider include a stiff coupled ODE system where traditional numerical methods fail, a 3+1D non-linear PDE, Kovasznay flow and Taylor-Green vortex solutions to incompressible Navier-Stokes equations and pure advection solution of 1+1 D compressible Euler equation. The Theory of Functional Connections (TFC) is used to exactly impose initial and boundary conditions (IBCs) of (I)BVPs on PINNs. We propose a modification to the TFC framework named Reduced TFC and show a significant improvement in the training and inference time of PINNs compared to IBCs imposed using TFC. Furthermore, Reduced TFC is shown to be able to generalize to more complex boundary geometries which is not possible with TFC. We also introduce a method of applying boundary conditions at infinity for BVPs and numerically solve the pure advection in 1+1 D Euler equations using these boundary conditions.

cs.LG↗
arXiv2024

Information Geometry of Evolution of Neural Network Parameters While Training

Artificial neural networks (ANNs) are powerful tools capable of approximating any arbitrary mathematical function, but their interpretability remains limited, rendering them as black box models. To address this issue, numerous methods have been proposed to enhance the explainability and interpretability of ANNs. In this study, we introduce the application of information geometric framework to investigate phase transition-like behavior during the training of ANNs and relate these transitions to overfitting in certain models. The evolution of ANNs during training is studied by looking at the probability distribution of its parameters. Information geometry utilizing the principles of differential geometry, offers a unique perspective on probability and statistics by considering probability density functions as points on a Riemannian manifold. We create this manifold using a metric based on Fisher information to define a distance and a velocity. By parameterizing this distance and velocity with training steps, we study how the ANN evolves as training progresses. Utilizing standard datasets like MNIST, FMNIST and CIFAR-10, we observe a transition in the motion on the manifold while training the ANN and this transition is identified with over-fitting in the ANN models considered. The information geometric transitions observed is shown to be mathematically similar to the phase transitions in physics. Preliminary results showing finite-size scaling behavior is also provided. This work contributes to the development of robust tools for improving the explainability and interpretability of ANNs, aiding in our understanding of the variability of the parameters these complex models exhibit during training.

cs.LG↗
arXiv2024

Periodic Solutions in a Simple Delay Differential Equation

Simple form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback coefficient. The periodic solutions are built explicitly in the case of piecewise constant nonlinearities involved. The periodic dynamics are shown to persist under small perturbations of the equation which make it smooth. The theoretical results are verified by extensive numerical simulations.

math.DS↗
arXiv2024

Explicit Periodic Solutions in a Delay Differential Equation

We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known idea of reduction to interval maps is used in the case under consideration, when both the defining nonlinearity and the periodic coefficient are piece-wise constant functions. The stable periodic dynamics persist under a smoothing procedure in a small neighborhood of the discontinuity set. This work continues the research in recent paper [7] on stable periodic solutions of differential delay equations with periodic coefficients.

math.DS↗
arXiv2022

Modelling host population support for combat adversaries

We consider a model of adversarial dynamics consisting of three populations, labelled Blue, Green and Red, which evolve under a system of first order nonlinear differential equations. Red and Blue populations are adversaries and interact via a set of Lanchester combat laws. Green is divided into three sub-populations: Red supporters, Blue supporters and Neutral. Green support for Red and Blue leads to more combat effectiveness for either side. From Green's perspective, if either Red or Blue exceed a size according to the capacity of the local population to facilitate or tolerate, then support for that side diminishes; the corresponding Green population reverts to the neutral sub-population, who do not contribute to combat effectiveness of either side. The mechanism for supporters deciding if either Blue or Red are too big is given by a logistic-type interaction term. The intent of the model is to examine the role of influence in complex adversarial situations typical in counter-insurgency, where victory requires a genuine balance between maintaining combat effectiveness and support from a third party whose backing is not always assured.

math.DS↗
arXiv2022

Small-scale solar jet formation and their associated waves and instabilities

Studies on small-scale jets' formation, propagation, evolution, and role, such as type I and II spicules, mottles, and fibrils in the lower solar atmosphere's energetic balance, have progressed tremendously thanks to the combination of detailed observations and sophisticated mathematical modelling. This review provides a survey of the current understanding of jets, their formation in the solar lower atmosphere, and their evolution from observational, numerical, and theoretical perspectives. First, we review some results to describe the jet properties, acquired numerically, analytically and through high-spatial and temporal resolution observations. Further on, we discuss the role of hydrodynamic and magnetohydrodynamic instabilities, namely Rayleigh-Taylor and Kelvin-Helmholtz instabilities, in jet evolution and their role in the energy transport through the solar atmosphere in fully and partially ionised plasmas. Finally, we discuss several mechanisms of magnetohydrodynamic wave generation, propagation, and energy transport in the context of small-scale solar jets in detail. This review identifies several gaps in the understanding of small-scale solar jets and some misalignments between the observational studies and knowledge acquired through theoretical studies and numerical modelling. It is to be expected that these gaps will be closed with the advent of high-resolution observational instruments, such as Daniel K. Inouye Solar Telescope, Solar Orbiter, Parker Solar Probe, and Solar CubeSats for Linked Imaging Spectropolarimetry, combined with further theoretical and computational developments.

astro-ph.SR↗
arXiv2022

New approach for analysing dynamical processes on the surface of photospheric vortex tubes

The majority of studies on multi-scale vortex motions employ a two-dimensional geometry by using a variety of observational and numerical data. This approach limits the understanding the nature of physical processes responsible for vortex dynamics. Here we develop a new methodology to extract essential information from the boundary surface of vortex tubes. 3D high-resolution magnetoconvection MURaM numerical data has been used to analyse photospheric intergranular velocity vortices. The Lagrangian Averaged Vorticity Deviation (LAVD) technique was applied to define the centers of vortex structures and their boundary surfaces based on the advection of fluid elements. These surfaces were mapped onto a constructed envelope grid that allows the study of the key plasma parameters as functions of space and time. Quantities that help in understanding the dynamics of the plasma, e.g. Lorentz force, pressure force, plasma-$β$ were also determined. Our results suggest that, while density and pressure have a rather global behaviour, the other physical quantities undergo local changes, with their magnitude and orientation changing in space and time. At the surface, the mixing in the horizontal direction is not efficient, leading to appearance of localized regions with higher/colder temperatures. In addition, the analysis of the MHD Poynting flux confirms that the majority of the energy is directed in the horizontal direction. Our findings also indicate that the pressure and magnetic forces that drive the dynamics of the plasma on vortex surfaces are unbalanced and therefore the vortices do not rotate as a rigid body.

physics.flu-dyn↗
arXiv2021

Effect of stress on cardiorespiratory synchronization of Ironmen athletes

The aim of this paper is to investigate the cardiorespiratory synchronization in athletes subjected to extreme physical stress combined with a cognitive stress tasks. ECG and respiration were measured in 14 athletes before and after the Ironmen competition. Stroop test was applied between the measurements before and after the Ironmen competition to induce cognitive stress. Synchrogram and empirical mode decomposition analysis were used for the first time to investigate the effects of physical stress, induced by the Ironmen competition, on the phase synchronization of the cardiac and respiratory systems of Ironmen athletes before and after the competition. A cognitive stress task (Stroop test) was performed both pre- and post-Ironman event in order to prevent the athletes from cognitively controlling their breathing rates. Our analysis showed that cardiorespiratory synchronization increased post-Ironman race compared to pre-Ironman. The results suggest that the amount of stress the athletes are recovering from post-competition is greater than the effects of the Stroop test. This indicates that the recovery phase after the competition is more important for restoring and maintaining homeostasis, which could be another reason for stronger synchronization.

q-bio.QM↗
arXiv2020

Solar Vortex Tubes: Vortex Dynamics in the Solar Atmosphere

In this work, a state-of-the-art vortex detection method, Instantaneous Vorticity Deviation, is applied to locate three-dimensional vortex tube boundaries in numerical simulations of solar photospheric magnetoconvection performed by the MURaM code. We detected three-dimensional vortices distributed along intergranular regions and displaying coned shapes that extend from the photosphere to the low chromosphere. Based on a well-defined vortex center and boundary, we were able to determine averaged radial profiles and thereby investigate the dynamics across the vortical flows at different height levels. The solar vortex tubes present nonuniform angular rotational velocity, and, at all height levels, there are eddy viscosity effects within the vortices, which slow down the plasma as it moves toward the center. The vortices impact the magnetic field as they help to intensify the magnetic field at the sinking points, and in turn, the magnetic field ends up playing an essential role in the vortex dynamics. The magnetic field was found to be especially important to the vorticity evolution. On the other hand, it is shown that, in general, kinematic vortices do not give rise to magnetic vortices unless their tangential velocities at different height levels are high enough to overcome the magnetic tension.

astro-ph.SR↗
arXiv2019

High-resolution spectropolarimetric observations of the temporal evolution of magnetic fields in photospheric bright points

Context. Magnetic bright points (MBPs) are dynamic, small-scale magnetic elements often found with field strengths of the order of a kilogauss within intergranular lanes in the photosphere. Aims. Here we study the evolution of various physical properties inferred from inverting high-resolution full Stokes spectropolarimetry data obtained from ground-based observations of the quiet Sun at disc centre. Methods. Using automated feature-tracking algorithms, we studied 300 MBPs and analysed their temporal evolution as they evolved to kilogauss field strengths. These properties were inferred using both the NICOLE and SIR Stokes inversion codes. We employ similar techniques to study radiative magnetohydrodynamical simulations for comparison with our observations. Results. Evidence was found for fast (~30 - 100s) amplification of magnetic field strength (by a factor of 2 on average) in MBPs during their evolution in our observations. Similar evidence for the amplification of fields is seen in our simulated data. Conclusions. Several reasons for the amplifications were established, namely, strong downflows preceding the amplification (convective collapse), compression due to granular expansion and mergers with neighbouring MBPs. Similar amplification of the fields and interpretations were found in our simulations, as well as amplification due to vorticity. Such a fast amplification will have implications for a wide array of topics related to small-scale fields in the lower atmosphere, particularly with regard to propagating wave phenomena in MBPs.

astro-ph.SR↗