arXiv subjects

Alexey Kuznetsov

Publications and source records attributed to Alexey Kuznetsov.

At least 19 recordsLinked to original sources

arXiv2026

Dual-Perspective Microwave and Hard X-ray Constraints of Asymmetric Nonthermal Loops in an X-class Flare

We report dual-perspective microwave and HXR observations of an X-class flare on 2024 May 15, taking advantage of the unique geometry of a front-side view from the Earth and a back-side perspective from the Solar Orbiter (SolO). Using spatially resolved imaging spectroscopy from Siberian Radioheliograph (SRH) together with Chashan Broadband Solar millimeter spectrometer (CBSmm) and STIX data, we identify a set of nonthermal flaring loops in an asymmetric magnetic field, with microwave sources located near the loop top and HXR sources associated with the southern footpoint. Compared with HXR, the microwave emission shows an opposite ascending trend, an increasing time lag in time profile, and a distinctive ``SHH'' spectral pattern, which we attribute to energy-dependent trapping and precipitation of energetic electrons in an asymmetric magnetic configuration. Flux pulsations and their spectral and polarization signatures are consistent with intermittent particle acceleration rather than MHD wave modulation. Microwave magnetic diagnostics, corroborated by non-linear force free field (NLFFF) extrapolation, provide key constraints on the three-dimensional magnetic configuration. The dual-perspective flux profile comparison and consistent QPP signatures across wavelengths together support a self-consistent picture of energy-dependent electron trapping, precipitation, and transport in these asymmetric loops.

astro-ph.SR↗

arXiv2026

Solar Radio Burst Fine Structures

Solar radio bursts exhibit intricate variability in time, space, and frequency, often displaying a rich variety of fine frequency-time structures such as spikes, drift pairs, striae in Type III bursts, and herringbone patterns in Type II bursts, etc. Historically, limited spatial, spectral, and temporal resolution has hindered detailed investigation of these narrow-band, rapidly evolving features, restricting progress in identifying their physical origins and underlying processes at these scales. Advances in high-time-frequency-resolution solar imaging now offer transformative opportunities. Recent sub-second imaging spectroscopy has revealed that many fine structures challenge existing theoretical models, pointing to the need for new frameworks and a reassessment of current interpretations. The Square Kilometre Array (SKA), with its full-Stokes imaging spectroscopy at sub-second cadences, will provide unprecedented data essential for resolving these long-standing questions. These capabilities promise to significantly deepen our understanding of electron acceleration and transport, magnetic reconnection, and coronal plasma turbulence, thereby advancing our knowledge of solar energetic processes and improving assessments of their space-weather impacts.

astro-ph.SR↗

arXiv2026

Mehler formula for Wronskians of Hermite polynomials

We prove that the bilinear generating function for Wronskians of Hermite polynomials can be expressed as the classical Mehler kernel multiplied by a polynomial, thereby extending the result of Pupasov-Maksimov for exceptional Hermite polynomials. We establish several properties of the polynomials appearing in this extended version of the Mehler formula and present four conjectures about them.

math.CA↗

arXiv2026

Modeling the Thermal Low-Frequency Radio Sun with Ray Tracing

Incoherent radio emission at meter--decimeter wavelengths provides a key diagnostic of the coronal thermal plasma, but at frequencies below $\sim$\,1\,GHz coronal refraction can substantially bend ray paths and modify the apparent source size and brightness distribution. We develop a forward-modeling framework that combines refractive ray tracing through a global 3D coronal model with radiative transfer along each ray. The method tracks the ray-tube cross-sectional area $S(s)$ using a step-wise perturbation retracing approach and incorporates a geometric magnification term proportional to $d\ln S/ds$ to enforce flux conservation under focusing/defocusing. Thermal free--free emission and absorption are then computed with the \texttt{GRFF} radiative transfer code to produce synthetic radio maps over 40--800\,MHz. Applying the framework to Carrington rotation 2298, we find that including propagation effects allows the quiet-Sun background spectrum to be well reproduced. However, active region brightness is less accurately modeled, suggesting that additional physical factors should be considered in future work. These results establish a physics-based method for generating low-frequency quiet-Sun synthetic images suitable for quantitative comparison with interferometric observations and for assessing how propagation effects shape the observed morphology.

astro-ph.SR↗

arXiv2025

Fourier transform pairs and Eisenstein-type series related to Jacobi elliptic functions

We compute Fourier transforms of functions expressed as a ratio of one of the Jacobi elliptic functions divided by $\sinh(\pi x)$ or $\cosh(\pi x)$. In many cases, the resulting Fourier transform remains within the same class of functions. Applying the Mellin transform, we obtain sixteen Eisenstein-type series $\zeta_{j,l}(s,\tau)$, for which we establish several results: analytic continuation with respect to the variable $s$, a functional equation connecting $\zeta_{j,l}(s,\tau)$ and $\zeta_{l,j}(1-s,-1/\tau)$, and explicit expressions for $\zeta_{j,l}(s,\tau)$ when $s$ runs through a sequence of positive even or odd integers.

math.CA↗

arXiv2025

Approximating functions on ${\mathbb R}^+$ by exponential sums

We present a new method for approximating real-valued functions on ${\mathbb R}^+$ by linear combinations of exponential functions with complex coefficients. The approach is based on a multi-point Pad\'e approximation of the Laplace transform and employs a highly efficient continued fraction technique to construct the corresponding rational approximant. We demonstrate the accuracy of this method through a variety of examples, including the Gaussian function, probability density functions of the lognormal and Gompertz-Makeham distributions, the hockey stick and unit step functions, as well as a function arising in the approximation of the gamma and Barnes $G$-functions.

math.NA↗

arXiv2025

Nanoscale lattice heterostructure in high Tc superconductors

Low temperature superconductivity was known since 1957 to be described by BCS theory for an effective single band metals controlled by the density of states at the Fermi level, very far from band edges, the electron phonon coupling, and the energy of the boson in the pairing interaction w0, but BCS has failed to predict high temperature superconductivity in different materials above about 23 K. High temperature superconductivity above 35 K since 1986 has been a matter of materials science where manipulating the lattice complexity of high temperature superconducting ceramic oxides (HTSC) has driven material scientists to grow new HTSC quantum materials up to 138K in HgBa2Ca2Cu3O8 (Hg1223) at ambient pressure and near room temperature in pressurized hydrides. This perspective covers the major results of materials scientist in these last 39 years investigating the role of lattice inhomogeneity detected in these new quantum complex materials. We highlight the nanoscale heterogeneity in these complex materials and elucidate their special role played in the physics for HTSC. Especially, it is pointed out that the geometry of lattice and charge complex heterogeneity at nanoscale is essential and intrinsic in the mechanism of rising quantum coherence at high temperature

cond-mat.supr-con↗

arXiv2025

A Flare-related Decimetric Type-IV Radio Burst Induced by the X2 Radiation of Electron Cyclotron Maser Emission

The radiation mechanism of decimetric wideband and pulsating radio bursts from the Sun (in terms of decimetric type-IV (t-IVdm) burst) and other flaring stars is a long-standing problem. Early investigations were based on the leading-spot hypothesis for the sun and yielded contradictory results. Here, we analyzed the flare-associated t-IVdm burst on 20110924 with medium-strong levels of polarization and from sources near a sunspot. We found that the emission is intermittent and the maximum $T_B$ exceeds 10$^{11}$ K, with well-defined upper and lower frequency cutoffs. The radio sources are left-handed polarized, located above the sunspot with a negative polarity. The sources align well with the sites of the second harmonic of the local electron gyrofrequency. These findings provide essential evidence that the burst is induced by the electron cyclotron maser emission (ECME) in the harmonic X mode. We further modeled the transport of downward-streaming energetic electrons along a coronal loop and found most electrons get mirrored within the specific altitude range of 20-100 Mm. This explains why such bursts tend to have well-defined spectral ranges. We also found the ECME-radiating energetic electrons exhibit a shell-like VDF instead of the generally-presumed loss-cone distribution. The study greatly expands the application of ECME in solar radio astronomy and provides solar samples for similar bursts from other flaring stars.

astro-ph.SR↗

arXiv2025

The Efficiency of Harmonic Emissions Excited by Energetic Electrons in Coronal Loops

Magnetic reconnection is a key process that drives the energy release in solar flares. This process can occur at multiple locations along the coronal loop. The reconnection generates energetic electrons capable of exciting wave modes and emissions as they propagate through the loop. In this follow-up study, we investigate the influence of the injection site location of these energetic electrons - either at the looptop (LT) or at the leg of the loop around a footpoint (FP) - on the excitation of wave modes especially the second harmonic emissions (X2) in coronal loops. Our simulations reveal that the injection location significantly impacts the spatial distribution and intensity of excited wave modes. When electrons are injected at the LT, electromagnetic X2, and Z modes dominate along the loop, with minimal excitation of Langmuir waves (Yousefzadeh et al. 2021; 2022). Conversely, the present study reveals that injection close to FP leads to a strong Langmuir wave excitation throughout the loop, particularly as electrons ascend toward the LT. We find that X2 and Z modes are consistently excited at the injection site with different intensities, regardless of the injection location. However, electron injection near the FP scenario creates favorable conditions for significant Langmuir wave generation, potentially leading to plasma emission under specific circumstances. These findings emphasize the importance of electron injection location in determining the properties of the excited and emitted waves in solar coronal loops.

astro-ph.SR↗

arXiv2025

Simple and accurate approximations to the Riemann zeta function

We develop approximations for the Riemann zeta function that enable high-precision computation within the critical strip and other vertical strips. These approximations combine the main sum of the Riemann-Siegel formula with a simple approximation of the remainder term, which involves only elementary functions and certain precomputed coefficients obtained via Gaussian quadrature. Additionally, we provide approximations for the derivative of the Riemann zeta function and present extensive numerical evidence demonstrating the accuracy of these approximations.

math.NT↗

arXiv2024

On series expansions of zeros of the deformed exponential function

For $q \in (0, 1)$, the deformed exponential function $f(x) = \sum_{n \geq 1} x^n q^{n(n-1)/2}/n!$ is known to have infinitely many simple and negative zeros $\{x_k(q)\}_{k \geq 1}$. In this paper, we analyze the series expansions of $-x_k(q)/k$ and $k/x_k(q)$ in powers of $q$. We prove that the coefficients of these expansions are rational functions of the form $P_n(k)/Q_n(k)$ and $\widehat{P}_n(k)/Q_n(k)$, where $Q_n(k) \in {\mathbb Z}[k]$ is explicitly defined and the polynomials $P_n(k), \widehat{P}_n(k)\in {\mathbb Z}[k]$ can be computed recursively. We provide explicit formulas for the leading coefficients of $P_n(k)$ and $\widehat{P}_n(k)$ and compute the coefficients of these polynomials for $n \leq 300$. Numerical verification shows that $P_n(k)$ and $\widehat{P}_n(k)$ take non-negative values for all $k \in \mathbb{N}$ and $n\le 300$, offering further evidence in support of conjectures by Alan Sokal.

math.CA↗

arXiv2024

Electron acceleration and transport in the 2023-03-06 solar flare

We investigated in detail the M5.8 class solar flare that occurred on 2023-03-06. This flare was one of the first strong flares observed by the Siberian Radioheliograph in the microwave range and the Advanced Space-based Solar Observatory in the X-ray range. The flare consisted of two separate flaring events (a "thermal" and a "cooler" ones), and was associated with (and probably triggered by) a filament eruption. During the first part of the flare, the microwave emission was produced in an arcade of relatively short and low flaring loops. During the second part of the flare, the microwave emission was produced by energetic electrons trapped near the top of a large-scale flaring loop; the evolution of the trapped electrons was mostly affected by the Coulomb collisions. Using the available observations and the GX Simulator tool, we created a 3D model of the flare, and estimated the parameters of the energetic electrons in it.

astro-ph.SR↗

arXiv2024

Darboux Transformation of Diffusion Processes

Darboux transformation of a second-order linear differential operator is a well-known technique with many applications in mathematics and physics. We study Darboux transformation from the point of view of Markov semigroups of diffusion processes. We construct the Darboux transform of a diffusion process through a combination of Doob's $h$-transform and a version of Siegmund duality. Our main result is a simple formula that connects transition probability densities of the two processes. We provide several examples of Darboux transformed diffusion processes related to Brownian motion and Ornstein-Uhlenbeck process. For these examples, we compute explicitly the transition probability density and derive its spectral representation.

math.PR↗

arXiv2024

A Multi-Peak Solar Flare with a High Turnover Frequency of The Gyrosynchrotron Spectra from the Loop-Top Source

The origin of multiple peaks in lightcurves of various wavelengths remains illusive during flares. Here we discuss the flare of SOL2023-05-09T03:54M6.5 with six flux peaks as recorded by a tandem of new microwave and Hard X-ray instruments. According to its microwave spectra, the flare represents a high-turnover frequency (>15 GHz) event. The rather-complete microwave and HXR spectral coverage provides a rare opportunity to uncover the origin of such event together with simultaneous EUV images. We concluded that (1) the microwave sources originates around the top section of the flaring loops with a trend of source spatial dispersion with frequency;(2) the visible movement of the microwave source from peak to peak originates from the process of new flaring loops appearing sequentially along the magnetic neutral line; 3) the optically-thin microwave spectra are hard with the indices varying from -1.2 to -0.4, and the turnover frequency always exceeds 15 GHz; 4) higher turnover/peak frequency corresponds to stronger peak intensity and harder optically-thin spectra. Using the Fokker-Planck and GX simulator codes we obtained a good fit to the observed microwave spectra and spatial distribution of the sources at all peaks, if assuming the radiating energetic electrons have the same spatial distribution and single-power-law spectra but with the number density varying in a range of 30%. We conclude that the particle acceleration in this flare happens in a compact region nearing the looptop. These results provide new constraints on the acceleration of energetic electrons and the underlying flare intermittent reconnection process.

astro-ph.SR↗

arXiv2024

Extending the Meijer $G$-function

By replacing the Euler gamma function by the Barnes double gamma function in the definition of the Meijer $G$-function, we introduce a new family of special functions, which we call $K$-functions. This is a very general class of functions, which includes as special cases Meijer $G$-functions (thus also all hypergeometric functions ${}_p F_q$) as well as several new functions that appeared recently in the literature. Our goal is to define the $K$-function, study its analytic and transformation properties and relate it to several functions that appeared recently in the study of random processes and the fractional Laplacian. We further introduce a generalization of the Kilbas-Saigo function and show that it is a special case of $K$-function.

math.CA↗

arXiv2024

Limits of Random Motzkin paths with KPZ related asymptotics

We study Motzkin paths of length $L$ with general weights on the edges and end points. We investigate the limit behavior of the initial and final segments of the random Motzkin path viewed as a pair of processes starting from each of the two end points as $L$ becomes large. We then study macroscopic limits of the resulting processes, where in two different regimes we obtain Markov processes that appeared in the description of the stationary measure for the KPZ equation on the half line and of conjectural stationary measure of the hypothetical KPZ fixed point on the half line. Our results rely on the behavior of the Al-Salam--Chihara polynomials in the neighbourhood of the upper end of their orthogonality interval and on the limiting properties of the $q$-Pochhammer and $q$-Gamma functions as $q\nearrow 1$.

math.PR↗

arXiv2023

Series expansions for the Riemann zeta function

We prove a general result on representing the Riemann zeta function as a convergent infinite series in a complex vertical strip containing the critical line. We use this result to re-derive known expansions as well as to discover new series representations of the Riemann zeta function in terms of the incomplete gamma functions, generalized hypergeometric functions and Meijer $G$-functions.

math.NT↗

arXiv2023

On the dual representations of Laplace transforms of Markov processes

We provide a general framework for dual representations of Laplace transforms of Markov processes. Such representations state that the Laplace transform of a finite-dimensional distribution of a Markov process can be expressed in terms of a Laplace transform involving another Markov process, but with coefficients in the Laplace transform and time indices of the process interchanged. Dual representations of Laplace transforms have been used recently to study open ASEP and to describe stationary measures of the open KPZ equation. Our framework covers both recently discovered examples in the literature and several new ones, involving general L\'evy processes and certain birth-and-death processes.

math.PR↗