arXiv subjects

Ekaterina V. Shishkina

Publications and source records attributed to Ekaterina V. Shishkina.

18 recordsLinked to original sources

arXiv2026

Localized oscillation of an Euler--Bernoulli beam with time-varying parameters on a visco-elastic foundation: asymptotics, adiabatic invariant, and equivalent Hamiltonian system

We consider localized oscillation of an Euler--Bernoulli beam on a visco-elastic foundation coupled to a damped discrete oscillator. All parameters of the system independently vary in time in a slow manner. For the conservative case, we use three various analytic approaches. Namely, these are asymptotics, the method based on the adiabatic invariance of the action of a trapped wave, and the consideration of the equivalent Hamiltonian system. All approaches result in the same formula for the amplitude of oscillation. In the dissipative case, we obtain the amplitude of oscillation only utilizing the asymptotic approach.

math-ph↗

arXiv2026

On the adiabatic invariance of the action of a trapped wave

Recently, it has been shown (Gavrilov et al., Nonlinear Dyn, 112, 2024) that in a linear solid discrete-continuous system with several slowly time-varying parameters, the amplitude of a strongly localized mode (a trapped wave) can be calculated as a function of current parameter values and does not depend on the history of the parameter change. This result allows us to introduce the adiabatic invariant for such a system according to the general definition as a quantity that remains approximately constant if the parameters vary slowly. In this paper, we show that, defined in this manner, the adiabatic invariant can be calculated as the ratio of the total energy of the trapped wave to its frequency. This yields a significantly simplified approach to solving a class of problems concerning localized oscillation of continuous systems with discrete inclusions, although the definition of the wave energy can be ambiguous. Thus, we can consider the newly introduced adiabatic invariant as a straightforward generalization of the concept known to Hamiltonian systems. Finally, we introduce an effective Hamiltonian system, which is characterized by the same adiabatic invariant as the trapped wave. This yields another highly straightforward approach to deriving the amplitude evolution law, although further investigation is required.

math-ph↗

arXiv2026

Tracking down the broadband polarimetric properties of PG 1553+113

We report on a nine-month monitoring campaign of the blazar PG 1553+113, relying on three observations carried out in 2025 with the Imaging X-ray Polarimetry Explorer (IXPE) and supported by multi-wavelength facilities. The source displayed pronounced variability across the electromagnetic spectrum, with X-ray flux changes by up to a factor of $\sim5$ and complex evolution of the optical polarization properties, including one of the largest (exceeding $150^{\circ}$) and fastest rotations in the electric vector position angle (EVPA) ever recorded. This swing of the EVPA was also accompanied by a temporary drop of the optical polarization degree to nearly zero. Significant X-ray polarization was observed during the third IXPE pointing, with a polarization degree $Π_{\rm X}\,=(\,18.4\,\pm\,5.8)\%$ and $Ψ_{\rm X}\,=\,74^{\circ} \pm 9^{\circ}$ in the 2--8~keV band, while only upper limits were obtained in the first two epochs. The optical data show that the second IXPE observation occurred shortly after a dramatic optical polarization event characterized by a rapid EVPA swing and strong depolarization. Two possible scenarios may explain the broadband polarimetric behavior: (i) the superposition of two emitting regions with nearly orthogonal magnetic field configurations and variable relative contributions, and (ii) the interaction of a single emitting region with a shock that temporarily reorders the magnetic field. In both cases, the data support a picture in which the X-ray and optical emissions arise from closely related but not strictly co-spatial regions within a dynamically evolving, magnetically structured jet.

astro-ph.HE↗

arXiv2025

Energy transport in the Schrödinger plate

In this paper, we introduce "the Schrödinger plate." This is an infinite two-dimensional linear micro-polar elastic medium, with out-of-plane degrees of freedom, lying on a linear elastic foundation of a special kind. Any free motion of the plate can be corresponded to a solution of the two-dimensional Schrödinger equation for a single particle in the external potential field $V$. The specific dependence of the potential $V$ on the position is taken into account in the properties of the plate elastic foundation. The governing equations of the plate are derived as equations of the two-dimensional constraint Cosserat continuum using the direct approach. The plate dynamics can be described by the classical Germain-Lagrange equation for a plate, but the strain energy is different from the one used in the classical Kirchhoff-Love plate theory. Namely, the Schrödinger plate cannot be imagined as a thin elastic body composed of an isotropic linear material. The main property of the Schrödinger plate is as follows: the mechanical energy propagates in the plate exactly in the same way as the probability density propagates according to the corresponding Schrödinger equation.

physics.class-ph↗

arXiv2025

Detection of Compton scattering in the jet of 3C 84

3C 84 is the brightest cluster galaxy in the Perseus Cluster. It is among the closest radio-loud active galaxies and among the very few that can be detected from low frequency radio up to TeV $γ$-rays. Here we report on the first X-ray polarization observation of 3C~84 with the Imaging X-ray Polarimetry Explorer, for a total of 2.2 Msec that coincides with a flare in $γ$-rays. This is the longest observation for a radio-loud active galaxy that allowed us to reach unprecedented sensitivity, leading to the detection of an X-ray polarization degree of $\rmΠ_X=4.2\pm1.3\%$ ($\sim3.2σ$ confidence) at an X-ray electric vector polarization angle of $\rm ψ_X=163^{\circ}\pm9^{\circ}$, that is aligned with the radio jet direction on the sky. Optical polarization observations show fast variability about the jet axis as well. Our results strongly favor models in which X-rays are produced by Compton scattering from relativistic electrons -- specifically Synchrotron Self-Compton -- that takes places downstream, away from the supermassive black hole.

astro-ph.HE↗

arXiv2025

Unveiling blazar synchrotron emission: a multiwavelength polarimetric study of HSP and LSP populations

Polarimetric properties of blazars allow us to put constraints on the acceleration mechanisms that fuel their powerful jets. By studying the multiwavelength polarimetric behaviour of high synchrotron peaked (HSP) and low synchrotron peaked (LSP) blazars, we aim to explore differences in their emission mechanisms and magnetic field structure in the acceleration region. In this study, we take advantage of several X-ray polarisation observations of HSP by the IXPE, including four new observations of Mrk 501, and optical polarisation observations of LSP from RoboPol and many others. We find that the polarisation degree (PD) distribution of HSP in X-rays is systematically higher than in optical and mm-radio wavelengths, as reported in previous IXPE publications. The distribution of the X-ray electric vector position angles (PA) is centered around the jet axis with most of the observations consistent with zero difference within uncertainties. In fact, the distribution of the offset of the PA from the jet axis is consistent between the LSP and HSP populations (with PA measured in optical for the first, X-ray for the latter), suggesting a common magnetic field structure close to the acceleration region, in strong support of the emerging energy stratified picture of particle acceleration followed by energy loss in blazar jets.

astro-ph.HE↗

arXiv2025

Anti-localization of non-stationary quasi-waves in a strongly nonlinear $β$-FPUT chain

Recently, a new general wave phenomenon, namely "the anti-localization of non-stationary linear waves", has been introduced and discussed (Shishkina et al., J. Sound. Vib. 553, 2023, 117673). This is zeroing of the propagating component for a non-stationary wave-field near a defect in infinitely long wave-guides. The phenomenon is known to be observed in both continuum and discrete mechanical systems with a defect, provided that the frequency spectrum for the corresponding homogeneous system possesses a stop-band. In this paper, we show that the anti-localization is also quite common for nonlinear systems. To demonstrate this, we numerically solve several non-stationary problems for an infinite strongly nonlinear $β$-FPUT chain with a defect. In our opinion, the anti-localization essentially influences the processes of heat transfer in linear and nonlinear lattices.

nlin.PS↗

arXiv2025

Determining the origin of the X-ray emission in blazars through multiwavelength polarization

The origin of the high-energy emission in astrophysical jets from black holes is a highly debated issue. This is particularly true for jets from supermassive black holes that are among the most powerful particle accelerators in the Universe. So far, the addition of new observations and new messengers have only managed to create more questions than answers. However, the newly available X-ray polarization observations promise to finally distinguish between emission models. We use extensive multiwavelength and polarization campaigns as well as state-of-the-art polarized spectral energy distribution models to attack this problem by focusing on two X-ray polarization observations of blazar BL Lacertae in flaring and quiescent $γ$-ray states. We find that regardless of the jet composition and underlying emission model, inverse-Compton scattering from relativistic electrons dominates at X-ray energies.

astro-ph.HE↗

arXiv2025

High optical to X-ray polarization ratio reveals Compton scattering in BL Lacertae's jet

Blazars, supermassive black hole systems (SMBHs) with highly relativistic jets aligned with the line of sight, are the most powerful long-lived emitters of electromagnetic emission in the Universe. We report here on a radio to gamma-ray multiwavelength campaign on the blazar BL Lacertae with unprecedented polarimetric coverage from radio to X-ray wavelengths. The observations caught an extraordinary event on 2023 November 10-18, when the degree of linear polarization of optical synchrotron radiation reached a record value of 47.5%. In stark contrast, the Imaging X-ray Polarimetry Explorer (IXPE) found that the X-ray (Compton scattering or hadron-induced) emission was polarized at less than 7.4% (3sigma confidence level). We argue here that this observational result rules out a hadronic origin of the high energy emission, and strongly favors a leptonic (Compton scattering) origin, thereby breaking the degeneracy between hadronic and leptonic emission models for BL Lacertae and demonstrating the power of multiwavelength polarimetry to address this question. Furthermore, the multiwavelength flux and polarization variability, featuring an extremely prominent rise and decay of the optical polarization degree, is interpreted for the first time by the relaxation of a magnetic "spring" embedded in the newly injected plasma. This suggests that the plasma jet can maintain a predominant toroidal magnetic field component parsecs away from the central engine.

astro-ph.HE↗

arXiv2024

Energy transport in a free Euler-Bernoulli beam in terms of Schrödinger's wave function

The Schrödinger 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 $ψ$) of the 1D time-dependent Schrödinger 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 Schrödinger equation for a free particle and vice versa. Finally, we show that for two corresponding solutions $u$ and $ψ$ the mechanical energy density calculated for $u$ propagates in the beam exactly in the same way as the probability density calculated for $ψ$.

math-ph↗

arXiv2024

A Two-Week $IXPE$ Monitoring Campaign on Mrk 421

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.

astro-ph.HE↗

arXiv2024

Universal formal asymptotics for localized oscillation of a discrete mass-spring-damper system of time-varying properties, embedded into a one-dimensional medium described by the telegraph equation with variable coefficients

We consider a quite general problem concerning a linear free oscillation of a discrete mass-spring-damper system. This discrete sub-system is embedded into a one-dimensional continuum medium described by the linear telegraph equation. In a particular case, the discrete sub-system can move along the continuum one at a sub-critical speed. Provided that the dissipation in both discrete and continuum sub-systems is absent, if parameters of the sub-systems are constants, under certain conditions (the localization conditions), a non-vanishing oscillation localized near the discrete sub-system can be possible. In the paper we assume that the dissipation in the damper and the medium is small, and all discrete-continuum system parameters are slowly varying functions in time and in space (when applicable), such that the localization condition is fulfilled for the instantaneous values of the parameters in a certain neighbourhood of the discrete sub-system position. This general statement can describe a number of mechanical systems of various nature. We derive the expression for the leading-order term of a universal asymptotics, which describes a localized oscillation of the discrete sub-system. In the non-dissipative case, the leading-order term of the expansion for the amplitude is found in the form of an algebraic expression, which involves the instantaneous values of the system parameters. In the dissipative case, the leading-order term for the amplitude, generally, is found in quadratures in the form of a functional, which depends on the history of the system parameters, though in some exceptional cases the result can be obtained as a function of time and the instantaneous limiting values of the system parameters. Finally, we have justified the universal asymptotics by numerical calculations for some particular cases.

physics.class-ph↗

arXiv2023

Non-stationary elastic wave scattering and energy transport in a one-dimensional harmonic chain with an isotopic defect

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.

cond-mat.stat-mech↗

arXiv2023

Galaxies decomposition with spiral arms -- II: 29 galaxies from S$^4$G

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$μ$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.

astro-ph.GA↗

arXiv2023

The anti-localization of non-stationary linear waves and its relation to the localization. The simplest illustrative problem

We introduce a new wave phenomenon, which can be observed in continuum and discrete systems, where a trapped mode exists under certain conditions, namely, the anti-localization of non-stationary linear waves. This is zeroing of the non-localized propagating component of the wave-field in a neighbourhood of an inclusion. In other words, it is a tendency for non-stationary waves to propagate avoiding a neighbourhood of an inclusion. The anti-localization is caused by a destructive interference of the harmonics involved into the representation of the solution in the form of a Fourier integral. The anti-localization is associated with the waves from the pass-band, whereas the localization related with a trapped mode is due to poles inside the stop-band. In the framework of a simple illustrative problem considered in the paper, we have demonstrated that the anti-localization exists for all cases excepting the boundary of the domain in the parameter space where the wave localization occurs. Thus, the anti-localization can be observed in the absence of the localization as well as together with the localization. We also investigate the influence of the anti-localization on the wave-field in whole.

physics.class-ph↗

arXiv2023

Unsteady ballistic heat transport in a 1D harmonic crystal due to a source on an isotopic defect

In the paper we apply asymptotic technique based on the method of stationary phase and obtain the approximate analytical description of thermal motions caused by a source on an isotopic defect of an arbitrary mass in a 1D harmonic crystal. It is well known that localized oscillation is possible in this system in the case of a light defect. We consider the unsteady heat propagation and obtain formulae, which provide continualization (everywhere excepting a neighbourhood of a defect) and asymptotic uncoupling of the thermal motion into the sum of the slow and fast components. The slow motion is related with ballistic heat transport, whereas the fast motion is energy oscillation related with transformation of the kinetic energy into the potential one and in the opposite direction. To obtain the propagating component of the fast and slow motions we estimate the exact solution in the integral form at a moving point of observation. We demonstrate that the propagating parts of the slow and the fast motions are "anti-localized" near the defect. The physical meaning of the anti-localization is a tendency for the unsteady propagating wave-field to avoid a neighbourhood of a defect. The effect of anti-localization increases with the absolute value of the difference between the alternated mass and the mass of a regular particle, and, therefore, more energy concentrates just behind the leading wave-front of the propagating component. The obtained solution is valid in a wide range of a spatial co-ordinate (i.e., a particle number), everywhere excepting a neighbourhood of the leading wavefront.

cond-mat.stat-mech↗

arXiv2022

Non-stationary oscillation of a string on the Winkler foundation subjected to a discrete mass-spring system non-uniformly moving at a sub-critical speed

We consider non-stationary free and forced transverse oscillation of an infinite taut string on the Winkler foundation subjected to a discrete mass-spring system non-uniformly moving at a given sub-critical speed. The speed of the mass-spring system is assumed to be a slowly time-varying function. To describe a non-vanishing free oscillation we use an analytic approach based on the method of stationary phase and the method of multiple scales. The moving oscillator is characterized by a partial frequency, which can be greater or less than the cut-off frequency. Accordingly, a sub-critical uniformly accelerated motion generally has two stages. At the first stage there exists a trapped mode, and, therefore, a part of the wave energy is localized near the moving oscillator and does not propagate away. For this stage we obtain the analytic solution in a simple form describing non-vanishing free oscillation and verify it numerically. For the second stage there is no trapped mode, and all the wave energy propagate away. This stage is investigated numerically, and some unexpected results are obtained. Additionally, we consider the case of the oscillator with a destabilizing spring. The dynamics of the system in the latter case is quite different from the case of commonly used stabilizing spring, since the system loses the stability during an accelerated motion. We also take into consideration the forced oscillation caused by an external load being a superposition of harmonics with time-varying parameters (the amplitude and the frequency).

physics.class-ph↗

arXiv2020

Passage through a resonance for a mechanical system, having time-varying parameters and possessing a single trapped mode. The principal term of the resonant solution

We consider a forced oscillation and passage through resonance for an infinite-length system, having time-varying parameters and possessing a single trapped mode. The system is a string, lying on the Winkler foundation and equipped with a discrete linear mass-spring oscillator of time-varying stiffness. We obtain the principal term of the asymptotic expansion for the resonant solution describing the motion of the inclusion (i.e., the mass-spring oscillator). The obtained result was verified by independent numerical calculations based on solution of the corresponding partial differential equation by means of the method of finite differences. The comparison demonstrates a good agreement in a neighbourhood of the instant of resonance.

physics.class-ph↗