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In magnetoconvection, the flow is governed by the interplay between gravitational buoyancy and the Lorentz force, with one of these forces dominating in different regimes. In this paper, we develop a model with a single adjustable parameter that accurately captures the smooth transition from a buoyancy-dominated regime to one dominated by the Lorentz force. A perturbative extension of the model accounts for distinct transition features that occur at high Prandtl numbers. We validate the model for magnetoconvection in both the quasistatic regime and at finite magnetic Reynolds numbers using data from direct numerical simulations and existing experimental data sets. The model contains a natural extension to rotating convection and offers a potential generalisation to rotating magnetoconvection., Comment: In press in the International Journal of Heat and Mass Transfer

Due to its peculiar and highly variable nature, the blazar 3C 454.3 has been extensively monitored by the WEBT team. Here, we present for the first time these long-term optical flux and color variability results using data acquired in B, V, R, and I bands over a time span of $\sim$ 2 decades. We include data from WEBT collaborators and public archives such as SMARTS, Steward Observatory, and ZTF. The data are binned and segmented to study the source over this long term when more regular sampling was available. During our study, the long-term spectral variability reveals a redder when brighter (RWB) trend, which, however, stabilizes at a particular brightness cutoff $\sim$ 14.5 mag in the I-band, after which it saturates and evolves into a complex state. This trend indicates increasing jet emission dominance over accretion disk emission until jet emission completely dominates. Plots of the spectral index variation (following $F_{\nu} \propto \nu^{-\alpha}$) reveal a bimodal distribution using a one-day binning. These correlate with two extreme phases of 3C 454.3, an outburst or high flux state and quiescent or low flux state, which are respectively jet and accretion disk dominated. We have also conducted intra-day variability studies of nine light curves and found that six of them are variable. Discrete Correlation Function (DCF) analysis between different optical waveband pairs peak at zero lags, indicating co-spatial emission in different optical bands., Comment: 18 pages, 6 figures, 5 tables

The Schr\"odinger equation is not frequently used in the framework of the classical mechanics, though historically this equation was derived as a simplified equation, which is equivalent to the classical Germain-Lagrange dynamic plate equation. The question concerning the exact meaning of this equivalence is still discussed in modern literature. In this note, we consider the one-dimensional case, where the Germain-Lagrange equation reduces to the Euler-Bernoulli equation, which is used in the classical theory of a beam. We establish a one-to-one correspondence between the set of all solutions (i.e., wave functions $\psi$) of the 1D time-dependent Schr\"odinger equation for a free particle with arbitrary complex valued initial data and the set of ordered pairs of quantities (the beam strain and the particle velocity), which characterize solutions $u$ of the beam equation with arbitrary real valued initial data. Thus, the dynamics of a free infinite Euler-Bernoulli beam can be described by the Schr\"odinger equation for a free particle and vice versa. Finally, we show that for two corresponding solutions $u$ and $\psi$ the mechanical energy density calculated for $u$ propagates in the beam exactly in the same way as the probability density calculated for $\psi$., Comment: 5 pages

Blazars are beamed active galactic nuclei known for their strong multi-wavelength variability on timescales from years down to minutes. We aim to investigate the suitability of the twisting jet model presented in previous works to explain the multi-wavelength behaviour of BL Lacertae, the prototype of one of the blazar classes. According to this model, the jet is inhomogeneous, curved, and twisting, and the long-term variability is due to changes in the Doppler factor due to variations in the orientation of the jet-emitting regions. We analysed optical data of the source obtained during monitoring campaigns organised by the Whole Earth Blazar Telescope (WEBT) in 2019-2022, together with radio data from the WEBT and other teams, and gamma-ray data from the Fermi satellite. In this period, BL Lacertae underwent an extraordinary activity phase, reaching its historical optical and gamma-ray brightness maxima. The application of the twisting jet model to the source light curves allows us to infer the wiggling motion of the optical, radio, and gamma-ray jet-emitting regions. The optical-radio correlation shows that the changes in the radio viewing angle follow those in the optical viewing angle by about 120 days, and it suggests that the jet is composed of plasma filaments, which is in agreement with some radio high-resolution observations of other sources. The gamma-ray emitting region is found to be co-spatial with the optical one, and the analysis of the gamma-optical correlation is consistent with both the geometric interpretation and a synchrotron self-Compton (SSC) origin of the high-energy photons. We propose a geometric scenario where the jet is made up of a pair of emitting plasma filaments in a sort of double-helix curved rotating structure, whose wiggling motion produces changes in the Doppler beaming and can thus explain the observed multi-wavelength long-term variability., Comment: In press for A&A

X-ray polarization is a unique new probe of the particle acceleration in astrophysical jets made possible through the Imaging X-ray Polarimetry Explorer. Here we report on the first dense X-ray polarization monitoring campaign on the blazar Mrk 421. Our observations were accompanied by an even denser radio and optical polarization campaign. We find significant short-timescale variability in both X-ray polarization degree and angle, including a $\sim90^\circ$ angle rotation about the jet axis. We attribute this to random variations of the magnetic field, consistent with the presence of turbulence but also unlikely to be explained by turbulence alone. At the same time, the degree of lower-energy polarization is significantly lower and shows no more than mild variability. Our campaign provides further evidence for a scenario in which energy-stratified shock-acceleration of relativistic electrons, combined with a turbulent magnetic field, is responsible for optical to X-ray synchrotron emission in blazar jets., Comment: 23 pages, including 8 pages of appendices. 12 figures, 3 tables. Submitted to ApJ

Observations of quasars show that the polarization position angle of the emission coming from them varies greatly over time, including periods called rotations during which the angle changes in an orderly manner. The study proposes a method for identifying such events and assessing their statistical significance. The operation of the method is demonstrated using the example of long-term polarimetric observations of the blazars CTA 102, 3C 454.3, and OT 081. During the analysis of light curves, 51 rotations of the polarization position angle were found and it was shown that for CTA 102 and 3C 454.3 the rotations are predominantly oriented in one direction., Comment: 21 pages, 12 figures

We offer a new model for the heat transfer and the turbulence intensity in strongly driven Rayleigh-Benard turbulence (the so-called ultimate regime), which in contrast to hitherto models is consistent with the new mathematically exact heat transfer upper bound of Choffrut et al. [J. Differential Equations 260, 3860 (2016)] and thus enables extrapolations of the heat transfer to geo- and astrophysical flows. The model distinguishes between four subregimes of the ultimate regime and well describes the measured heat transfer in various large-Ra experiments. In this new representation, which properly accounts for the Prandtl number dependence, the onset to the ultimate regime is seen in all available large-Ra data sets, though at different Rayleigh numbers, as to be expected for a non-normal-nonlinear instability., Comment: 14 pages, 2 figures

In this paper, we present our novel systems developed for the SemEval-2024 hallucination detection task. Our investigation spans a range of strategies to compare model predictions with reference standards, encompassing diverse baselines, the refinement of pre-trained encoders through supervised learning, and an ensemble approaches utilizing several high-performing models. Through these explorations, we introduce three distinct methods that exhibit strong performance metrics. To amplify our training data, we generate additional training samples from unlabelled training subset. Furthermore, we provide a detailed comparative analysis of our approaches. Notably, our premier method achieved a commendable 9th place in the competition's model-agnostic track and 17th place in model-aware track, highlighting its effectiveness and potential., Comment: 12 pages, 10 tables, 3 figures

We provide scaling relations for the Nusselt number $Nu$ and the friction coefficient $C_{S}$ in sheared Rayleigh-B\'enard convection, i.e., in Rayleigh-B\'enard flow with Couette or Poiseuille type shear forcing, by extending the Grossmann & Lohse (2000,2001,2002,2004) theory to sheared thermal convection. The control parameters for these systems are the Rayleigh number $Ra$, the Prandtl number $Pr$, and the Reynolds number $Re_S$ that characterises the strength of the imposed shear. By direct numerical simulations and theoretical considerations, we show that in turbulent Rayleigh-B\'enard convection, the friction coefficients associated with the applied shear and the shear generated by the large-scale convection rolls are both well described by Prandtl's (1932) logarithmic friction law, suggesting some kind of universality between purely shear driven flows and thermal convection. These scaling relations hold well for $10^6 \leq Ra \leq 10^8$, $0.5 \leq Pr \leq 5.0$, and $0 \leq Re_S \leq 10^4$., Comment: 22 pages, 9 figures, 2 tables. Submitted to J. Fluid Mech

Spiral structure can occupy a significant part of the galaxy, but properly accounting for it in photometric decomposition is rarely done. This may lead to significant errors in the parameters determined. To estimate how exactly neglecting the presence of spiral arms affects the estimation of galaxy decomposition parameters, we perform fitting of 29 galaxies considering spiral arms as a separate component. In this study, we utilize 3.6$\mu$m-band images from the S$^4$G survey and use a new 2D photometric model where each spiral arm is modeled independently. In our model, the light distribution both along and across the arm can be varied significantly, as well as its overall shape. We analyze the differences between models with and without spiral arms, and show that neglecting spiral arms in decomposition causes errors in estimating the parameters of the disk, the bulge, and the bar. We retrieve different parameters of the spiral arms themselves, including their pitch angles, widths, and spiral-to-total luminosity ratio, and examine various relations between them and other galaxy parameters. In particular, we find that the spiral-to-total ratio is higher for galaxies with more luminous discs and with higher bulge-to-total ratios. We report that the pitch angle of spiral arms decreases with increasing bulge or bar fraction. We measure the width of the spiral arms to be 53\% of the disc scale length, on average. We examine the contribution of the spiral arms to the azimuthally-averaged brightness profile and find that spiral arms produce a ``bump'' on this profile with a typical height of 0.3--0.7 mag., Comment: submitted to MNRAS

We investigate states of rapidly rotating Rayleigh-B\'enard convection in a cylindrical cell over a range of Rayleigh number $3\times10^5\leq Ra \leq 5\times10^{9}$ and Ekman number $10^{-6} \leq Ek \leq 10^{-4}$ for Prandtl number $Pr = 0.8$ and aspect ratios $1/5 \leq \Gamma \leq 5$ using direct numerical simulations. We characterize, for perfectly insulating sidewall boundary conditions, the first transition to convection via wall mode instability and the nonlinear growth and instability of the resulting wall mode states including a secondary transition to time dependence. We show how the radial structure of the vertical velocity $u_z$ and the temperature $T$ is captured well by the linear eigenfunctions of the wall mode instability where the radial width of $u_z$ is $\delta_{u_z} \sim Ek^{1/3} r/H$ whereas $\delta_T \sim e^{-k r}$ ($k$ is the wavenumber of an laterally infinite wall mode state). The disparity in spatial scales for $Ek = 10^{-6}$ means that the heat transport is dominated by the radial structure of $u_z$ since $T$ varies slowly over the radial scale $\delta_{u_z}$. We further describe how the transition to a state of bulk convection is influenced by the presence of the wall mode states. We use temporal and spatial scales as measures of the local state of convection and the Nusselt number $Nu$ as representative of global transport. Our results elucidate the evolution of the wall state of rotating convection and confirm that wall modes are strongly linked with the boundary zonal flow (BZF) being the robust remnant of nonlinear wall mode states. We also show how the heat transport ($Nu$) contributions of wall modes and bulk modes are related and discuss approaches to disentangling their relative contributions.

In 2022 the BL Lac object S4 0954+65 underwent a major variability phase, reaching its historical maximum brightness in the optical and $\gamma$-ray bands. We present optical photometric and polarimetric data acquired by the Whole Earth Blazar Telescope (WEBT) Collaboration from 2022 April 6 to July 6. Many episodes of unprecedented fast variability were detected, implying an upper limit to the size of the emitting region as low as $10^{-4}$ parsec. The WEBT data show rapid variability in both the degree and angle of polarization. We analyse different models to explain the polarization behaviour in the framework of a twisting jet model, which assumes that the long-term trend of the flux is produced by variations in the emitting region viewing angle. All the models can reproduce the average trend of the polarization degree, and can account for its general anticorrelation with the flux, but the dispersion of the data requires the presence of intrinsic mechanisms, such as turbulence, shocks, or magnetic reconnection. The WEBT optical data are compared to $\gamma$-ray data from the Fermi satellite. These are analysed with both fixed and adaptive binning procedures. We show that the strong correlation between optical and $\gamma$-ray data without measurable delay assumes different slopes in faint and high brightness states, and this is compatible with a scenario where in faint states we mainly see the imprint of the geometrical effects, while in bright states the synchrotron self-Compton process dominates., Comment: 12 pages, 13 figures, in press for MNRAS

The fundamental solution describing non-stationary elastic wave scattering on an isotopic defect in a one-dimensional harmonic chain is obtained in an asymptotic form. The chain is subjected to unit impulse point loading applied to a particle far enough from the defect. The solution is a large time asymptotics at a moving point of observation, and it is in excellent agreement with the corresponding numerical calculations. At the next step, we assume that the applied point impulse excitation has random amplitude. This allows one to model the heat transport in the chain and across the defect as the transport of the mathematical expectation for the kinetic energy and to use the conception of the kinetic temperature. To provide a simplified continuum description for this process, we separate the slow in time component of the kinetic temperature. This quantity can be calculated using the asymptotics of the fundamental solution for the deterministic problem. We demonstrate that there is a thermal shadow behind the defect: the order of vanishing for the slow temperature is larger for the particles behind the defect than for the particles between the loading and the defect. The presence of the thermal shadow is related to a non-stationary wave phenomenon, which we call the anti-localization of non-stationary waves. Due to the presence of the shadow, the continuum slow kinetic temperature has a jump discontinuity at the defect. Thus, the system under consideration can be a simple model for the non-stationary phenomenon, analogous to one characterized by the Kapitza thermal resistance. Finally, we analytically calculate the non-stationary transmission function, which describes the distortion (caused by the defect) of the slow kinetic temperature profile at a far zone behind the defect., Comment: 26 pages, 7 figures

The area of fractional calculus has made its way into various pure and applied scientific fields, as evidenced by its integration into numerous disciplines. An increasing number of researchers are exploring various approaches to incorporating fractional calculus into stochastic analysis. In this paper, we generalise the Wiener chaos expansion by constructing a fractional Wiener chaos expansion based on the parabolic cylinder function with an exponential factor. In the process, we demonstrate that this parabolic cylinder function with an exponential factor, which we call "a power normalised parabolic cylinder function" acts as an extension of a Hermite polynomial and retains the same martingale properties inherent in the Hermite polynomial, as well as other basic properties of Hermite polynomials. Hence, it is accurate to state that power normalised cylindrical functions can be viewed as fractional versions of Hermite polynomials.

Quasistatic magnetoconvection of a low Prandtl number fluid ($\textrm{Pr}=0.025)$ with a vertical magnetic field is considered in a unit aspect ratio box with no-slip boundaries. At high relative magnetic field strengths, given by the Hartmann number $\textrm{Ha}$, the onset of convection is known to result from a sidewall instability giving rise to the wall mode regime. Here, we carry out 3D direct numerical simulations of unprecedented length to map out the parameter space at $\textrm{Ha} = 200, 500, 1000$, varying the Rayleigh number ($\textrm{Ra}$) between $6\times10^5 \lesssim \textrm{Ra} \lesssim 5\times 10^8$. We track the development of stable equilibria produced by this primary instability, identify bifurcations leading to limit cycles, and eventually to chaotic dynamics. At {$\textrm{Ha}=200$}, the steady wall mode solution undergoes a symmetry-breaking bifurcation producing a state featuring a coexistence between wall modes and a large-scale roll in the centre of the domain which persists to higher $\textrm{Ra}$. However, under a stronger magnetic field at $\textrm{Ha}=1000$, the steady wall mode solution undergoes a Hopf bifurcation producing a limit cycle which further develops to solutions that shadow an orbit homoclinic to a saddle point. Upon a further increase in $\textrm{Ra}$, the system undergoes a subsequent symmetry break producing a coexistence between wall modes and a large-scale roll, although the large-scale roll exists only for a small range of $\textrm{Ra}$, and chaotic dynamics primarily arise due to a mixture of chaotic wall mode dynamics and arrays of cellular structures.

In magnetoconvection, the flow of electromagnetically conductive fluid is driven by a combination of buoyancy forces, which create the fluid motion due to thermal expansion and contraction, and Lorentz forces, which distort the convective flow structure in the presence of a magnetic field. The differences in the global flow structures in the buoyancy-dominated and Lorentz-force-dominated regimes lead to different heat transport properties in these regimes, reflected in distinct dimensionless scaling relations of the global heat flux (Nusselt number $\textrm{Nu}$) versus the strength of buoyancy (Rayleigh number $\textrm{Ra}$) and electromagnetic forces (Hartmann number $\textrm{Ha}$). Here, we propose a theoretical model for the transition between these two regimes for the case of a quasistatic vertical magnetic field applied to a convective fluid layer confined between two isothermal, a lower warmer and an upper colder, horizontal surfaces. The model suggests that the scaling exponents $\gamma$ in the buoyancy-dominated regime, $\textrm{Nu}\sim\textrm{Ra}^\gamma$, and $\xi$ in the Lorentz-force-dominated regime, $\textrm{Nu}\sim(\textrm{Ha}^{-2}\textrm{Ra})^\xi$, are related as $\xi=\gamma/(1-2\gamma)$, and the onset of the transition scales with $\textrm{Ha}^{-1/\gamma}\textrm{Ra}$. These theoretical results are supported by our Direct Numerical Simulations for $10\leq \textrm{Ha}\leq2000$, Prandtl number $\textrm{Pr}=0.025$ and $\textrm{Ra}$ up to $10^9$ and data from the literature.

In this article we would like to consider some approaches to non-integer integro-differentiations and its implementation in computer algebra system Wolfram Mathematics.

The geostrophic turbulence in rapidly rotating thermal convection exhibits characteristics shared by many highly turbulent geophysical and astrophysical flows. In this regime, the convective length and velocity scales, heat flux, and kinetic and thermal dissipation rates are all diffusion-free, meaning that they are independent of the viscosity and thermal diffusivity. Our direct numerical simulations (DNS) of rotating Rayleigh--B\'enard convection in domains with no-slip top and bottom and periodic lateral boundary conditions for a fluid with the Prandtl number $Pr=1$ and extreme buoyancy and rotation parameters (the Rayleigh number up to $Ra=3\times10^{13}$ and the Ekman number down to $Ek=5\times10^{-9}$) indeed demonstrate these diffusion-free scaling relations, in particular, that the dimensionless convective heat transport scales with the supercriticality parameter $\widetilde{Ra}\equiv Ra\,Ek^{4/3}$ as $Nu-1\propto \widetilde{Ra}^{3/2}$, where $Nu$ is the Nusselt number. We further derive and verify in the DNS that with the decreasing $\widetilde{Ra}$ the geostrophic turbulence regime undergoes a transition into another geostrophic regime where the convective heat transport scales as $Nu-1\propto \widetilde{Ra}^{3}$., Comment: 13 pages, 3 figures

Fermi-LAT observations provide continuous and regularly-sampled measurements of gamma-ray photon flux for hundreds of blazars. Many of these light curves, spanning almost 15 years, have been thoroughly examined for periodicity in multiple studies. However, the possibility that blazars may exhibit irregularly repeating flaring patterns in their gamma-ray light curves has not been systematically explored. In this study, we aim to find repeating episodes of flaring activity in the 100 brightest blazars using Fermi-LAT light curves with various integration times. We use a Bayesian Blocks representation to convert the time series into strings of symbols and search for repeating sub-strings using a fuzzy search algorithm. As a result, we identify 27 repeated episodes in the gamma-ray light curves of 10 blazars. We find that the patterns are most likely produced in structured jets composed of a fast spine and a slower sheath. When individual emission features propagate in the spine, they scatter seed photons produced in the non-uniform sheath through the inverse Compton mechanism, resulting in a set of gamma-ray flares with a similar profile every such passage. Additionally, we explore the theoretically-predicted possibility that the spine-sheath structure facilitates the production of high-energy neutrinos in blazar jets. Using the catalogue of track-like events detected by the IceCube neutrino telescope, we find evidence supporting this hypothesis at a $2.8\sigma$ significance level., Comment: Published, PR https://vo.astro.spbu.ru/964/

In Rayleigh-B\'enard convection (RBC), the size of a flow domain and its aspect ratio $\varGamma$ (a ratio between the spatial length and height of the domain) affect the shape of the large-scale circulation (LSC). For some aspect ratios, the flow dynamics include a three-dimensional oscillatory mode known as a jump-rope vortex (JRV), however, the effects of varying aspect ratios on this mode are not well investigated. In this paper, we study these aspect-ratio effects in liquid metals, for a low Prandtl number $Pr=0.03$. Direct numerical simulations and experiments are carried out for a Rayleigh number range $2.9 \times 10^4 \leq Ra \leq 1.6 \times 10^6$ and square cuboid domains with $\varGamma=2$, $2.5$, $3$ and $5$. Our study demonstrates that a repeating pattern of a JRV encountered at an aspect ratio $\varGamma \approx 2.5$ is the basic structural unit that builds up to a lattice of interlaced JRVs at the largest aspect ratio. The size of the domain determines how many structural units are self-organized within the domain; the number of the realized units is expected to scale as $\varGamma^2$ with sufficiently large and growing $\varGamma$. We find the oscillatory modes for all investigated $\varGamma$, however, they are more pronounced for $\varGamma=2.5$ and $\varGamma=5$. Future studies for large-aspect ratio domains of different shapes would enhance our understanding of how the JRVs adjust and reorganize at such scaled-up geometries, and answer the question of whether they are indeed the smallest superstructure units., Comment: 26 pages, 16 figures

In this small paper, we study a boundary value problem for an equation of parabolic-hyperbolic type. The goal is to show how we can prove existence and uniqueness theorem for a regular solution.