Transverse Oscillations Research Articles

Numerical investigation of synthetic jet effects on vortex-induced vibrations in tandem circular cylinders

ABSTRACT The influence of symmetric synthetic jets, on the upstream cylinder's (Cylinder 1's) leeward side on VIVs of tandem circular cylinders, was numerically investigated at Re = 150, m* = 2.0. The amplitude responses, frequency responses, hydrodynamic forces and wake patterns were analysed in the reduced velocity U* range of 3.0–14.0. The results indicated that synthetic jets with sufficient momentum coefficients (C u = 2.0 and 4.0) could suppress transverse oscillations of both cylinders, resulting in a symmetric +2S wake pattern. While the standard deviations of lift coefficients for Cylinder 1 decreased accordingly, the time-averaged drag coefficients of both cylinders didn't always follow suit. Complex wake patterns, including 2S + 2S, 2P + 2S, 2P + 2P, 2(P + S) + 2P and 2(P + S) + 2(P + S), were observed when synthetic jets can't dominate Cylinder 1's vortex shedding. Galloping responses of both cylinders can also be initiated.

Influence of rope fastening on the spectrum of its natural transverse vibrations

According to the previously developed method, which takes into account the bending stiffness of steel ropes during their transverse oscillation, the ropes of the pedestrian bridge ‘Lovers’ in the city of Tyumen were investigated. The obtained values of tension forces and bending stiffness were within the expected range. The high variation of bending stiffness values forced to pay attention to the accuracy of the initial values of rope lengths, which were obtained from the photograph. To measure the rope lengths, a method of nodal harmonic registration was proposed, but the results obtained by this method were higher than the values obtained from the photograph. The evaluation of measurement errors did not explain this overestimation, which led to the necessity to revise the solution of the differential equation of transverse oscillations. It turned out that previously only its partial solution was considered, assuming a hinged rope attachment, whereas it is cantilevered and has a bending reaction. Taking this feature into account by introducing an additional boundary condition allowed to improve the calculation model and explain the overestimation of the rope length in the method of nodal harmonics.Taking into account the nature of the rope attachment allowed us to introduce a generalised parameter s, which takes zero value for rigid cantilever attachment, and is equal to one for articulated attachment. Then the stiffness weakening inside the anchorage will be manifested by the growth of the parameter s and can be detected by the results of the oscillation spectrum registration.

Phantom Matter: A Challenging Solution to the Cosmological Tensions

The idea of composite dark energy (DE) is quite natural since on general grounds we expect that the vacuum energy density (associated with the cosmological term Λ) may appear in combination with other effective forms of DE, denoted X. Here we deal with model wXCDM, a simplified version of the old ΛXCDM model, and exploit the possibility that X behaves as “phantom matter” (PM), which appears in stringy versions of the running vacuum model (RVM). Unlike phantom DE, the PM fluid satisfies the strong energy condition like usual matter, hence bringing to bear positive pressure at the expense of negative energy. Bubbles of PM may appear in the manner of a transitory “phantom vacuum” tunneled into the late Universe before it heads toward a new de Sitter era, thereby offering a crop field for the growing of structures earlier than expected. Using Type Ia supernovae, cosmic chronometers, transversal baryon acoustic oscillations (BAO 2D), large-scale structure data, and the full cosmic microwave background likelihood from Planck 2018, we find that the H 0 and growth tensions virtually disappear, provided that BAO 2D are the only source of BAO data used in the fit. In contrast, our preliminary analysis using exclusively anisotropic BAO (BAO 3D) indicates that the ability to ease the H 0 tension is significantly reduced as compared to the scenario with BAO 2D, despite the fact that the overall fit to the cosmological data is still better than in the ΛCDM. Finally, our approach with BAO 2D favors quintessence-like behavior of the DE below z ≃ 1.5 at ≳3σ confidence level, which is compatible with the recent DESI measurements.

Real-Time Visualization of Infiltration and Retention of Microplastics with Different Shapes in Porous Media.

Infiltration and retention of microplastics in porous media are important for understanding their fate in environments and formulating treatment measures. Given porous media opacity, knowledge is usually obtained indirectly by monitoring microplastic concentration in the effluent and measuring microplastic distribution after removing grains in layers. In this study, real-time visualization of infiltration and retention of microplastics in porous media under vertical water flow is performed using an improved reflective index matching method, considering the different shapes and densities of microplastics and size ratios between microplastics and grains. The spherical microplastics have the largest infiltration depths, with trajectories closest to vertical and accompanied by long acceleration durations and low deceleration frequencies. The cylindrical microplastics deviate from vertical and have stronger transverse oscillations and more frequent decelerations, while the flaky microplastics have the most significant transverse displacements. The infiltration depth can be improved by reducing the size ratio between microplastics and grains and increasing the vertical flow rate, while the density of microplastics has a relatively limited effect. Sliding and rotating of microplastics after collision with grains are observed, responsible for deceleration and transverse displacements. Different retention patterns are found, with the number of types being inversely proportional to the number of principal dimensions of the shape.

High-frequency transverse acoustic interactions between two lean-premixed hydrogen combustors connected with cross-fire and cross-talk sections

Large-scale inter-combustor thermoacoustic interactions occur frequently in modern can-annular gas turbine combustion systems due to the presence of an annular cross-talk section upstream of the first stage turbine stator vanes. Although the whole system's modal dynamics depend on the relative dominance of low-frequency planar or high-frequency transverse acoustic waves, the majority of prior studies have chiefly focused on longitudinal mode instabilities. Motivated by the paucity of detailed information, here we examine high-frequency transverse acoustic interactions between two adjacent lean-premixed hydrogen combustors connected via two different pathways, known as cross-fire (XF) and cross-talk (XT) sections. We observe that the dual-combustor system undergoes high-frequency spinning mode in the clockwise direction, manifested as well-defined limit cycles with peak-to-peak amplitude of around 10 kPa. The transverse pressure oscillations, in contrast to the well-established low-frequency mutual synchronization dynamics, are not fully synchronized even in the presence of cross-talk communication. This situation leads to the formation of two closely-spaced 1T modes at 4.76 and 4.86 kHz in the respective hydrogen combustors, accompanied by the beating of the pressure fluctuations solely in the XF tube section. Remarkably, the pressure waves induced near the XF tube section tend to lag behind the pressure waves spinning in the injector face, demonstrating the existence of the angular shift characteristically connected to the high-frequency transverse combustion dynamics.

Numerical study on aerodynamic and aeroacoustic characteristics of sinusoidal wavy square cylinders

This paper numerically investigates the influences of amplitude and wavelength of sinusoidal wavy square cylinders on aerodynamic performance and noise reduction by large eddy simulation along with the Ffowcs Williams–Hawkings equation. The results show that the mean drag, lift fluctuation, and far-field noise of wavy cylinders are all reduced compared to the straight counterpart. The far-field noise of wavy cylinders varies monotonically with amplitude in a specific range but not with wavelength. The case with the largest amplitude demonstrates a significant tonal noise reduction of 47 dB/Hz, while a tonal noise reduction of 23 dB/Hz is observed for the case with the largest wavelength. To explore the mechanisms of noise reduction, the characteristics of a flow field are analyzed. It is found that wavy cylinders attenuate the transverse oscillation of a shear layer and produce more three-dimensional coherent structures in the wake. The wake region is significantly extended due to the delayed vortex shedding, and the mutual interaction between shear layers is remarkably weakened along the entire span. The spanwise coherence is attenuated in a similar way. These lead to the suppression of wall pressure fluctuations and turbulence fluctuations in the wake, which are closely related to far-field noise radiation.

Undersampling effects on observed periods of coronal oscillations

Context. Recent observations of decayless transverse oscillations have revealed two branches in the relationship between period and loop length. One is a linear relationship, interpreted as a standing mode, while the other shows almost no correlation and has not yet been interpreted conclusively. Aims. We investigated the undersampling effect on observed periods of decayless oscillations. Methods. We considered oscillating coronal loops that closely follow the observed loop length distribution. Assuming that all oscillations are standing waves, we modelled a signal that represents decayless oscillations where the period is proportional to the loop length and the amplitude and phase are randomly drawn. We generated a downsampled signal from the original signal by considering different sample rates that mimic temporal cadences of telescopes, and analysed the periods for sampled signals using the fast Fourier transform. Results. When the sampling cadence approaches the actual oscillation period, there is a greater tendency to overestimate the periods in short loops. We find the same two branches in the relationship between loop length and period of the sampled signals as those seen in the observations. Conclusions. We find that long periods of decayless oscillations occurring in short loops could be the result of undersampling.

Nodes and energy flow in the transverse oscillations of resonantly end-driven stretched strings with viscous damping

Abstract Most of the works that analyze the forced oscillations of strings assume that, although they can support a tension T, they are perfectly elastic/flexible entities that do not have losses. In this work we will show that the incorporation of losses, even maintaining the analysis in a linear regime, allows us to clarify some details of the behavior that is observed in the forced oscillations of a real string. By introducing a dissipative force into the analysis, it is possible to predict not only the resonance frequencies but also how the oscillation amplitudes depend on the strength of the driving force. We can also analyze the variation of the amplitude of the antinodes when the excitation frequency approaches the resonance frequency. This amplitude variation has a behavior very similar to that of the resonance amplitude of a spring-mass oscillator. It is generally recognized that the nodes of a string, in forced oscillation, are not points of absolute rest because the energy of vibration must be transmitted through these points. However, it is difficult to find works that analyze the peculiar properties of this small movement. In this work we calculate the amplitudes of the nodes and deduce the peculiar properties of their movement. We also calculate the time averaged energy that flows along the string, from its excitation point to its fixed end.

Investigation of the dynamics of transverse oscillations of a vertical rod under gravity, friction, and thermal expansion

The paper considers the mathematical formulation of the problem of transverse oscillations of a vertical rod under gravity, friction and external pulse effect, leading to thermal expansion of the rod. The dynamics of the system under consideration corresponds to the behavior of a fuel element (FE) in a pulsed reactor and is related to the dynamic stability of the processes occurring in it.The FE dynamics is described by inhomogeneous linear differential equation of the fourth order with non-constant coefficients. Initial boundary conditions are not smooth since they correspond to the instant heating of the part of the FE surface exposed to neutron pulse radiation. The general solution of the homogeneous linear equation can be found using the concept of generalized functions expressed as a series expansion in terms of coordinate eigenfunctions dependent on p parameter. The p parameter is related with the FE mass and at some certain values results in bifurcation points of the boundary value problem for eigenfunctions. The partial solution can be found in several ways: using the Fourier transform, the method of Green's function, and in terms of series expansion by eigenfunctions.Eigenfunction expansion coefficients in an explicit form have been obtained and the numerical solution accuracy has been estimated for some important particular cases. The results of the obtained exact solutions appear to be very close to the results of the ANSYS numerical estimations. In the future the obtained exact solutions will be used as input data to simulate self-consistent system dynamics of more than 400 FE. Therefore, the advantage of the exact solution in practical use is that its calculation is much faster as compared with the finite element method done with ANSYS.

Transverse Oscillations and Kelvin–Helmholtz Instability in Curved Arcade Loops with Siphon Flows

The effect of plasma flow in curved arcade loops on transverse waves and oscillations is examined analytically. The model under study is a semicircular magnetic slab with finite transverse extensions and a mass flow inside, in the zero-β plasma approximation. It is found that in the quasi-perpendicular propagation limit, the model supports two fast surface modes: one with higher (FSW+) and another with lower (FSW−) frequency. For a weak flow, the frequency of the FSW+ (FSW−) increases (decreases) as the flow speed grows in both propagating and quasi-standing wave regimes. We show that the FSW+ and FSW− are subjected to the Kelvin–Helmholtz (KH) instability, and the threshold flow is greater (less than) the internal Alfvén speed for the FSW+ (FSW−). The presence of plasma flow results in modifying the period ratio P 1/2P 2 of the fundamental harmonic to the first overtone with P 1/2P 2 less (more) than 1 for the FSW+ (FSW−), and this effect degenerates in the straight waveguide limit. The sub-Alfvénic flow can prohibit resonant absorption of kink modes when the frequencies of the FSW+ and FSW− become out of the Alfvén continuum. It is also shown that in the static case and for a weak flow case, the FSW+ (FSW−) is interpreted as a vertically (horizontally) polarized kink mode, while for moderate flow, both modes have oblique polarization. We apply the developed theory to interpret the observational cases of kink oscillations in coronal loops with signatures of a siphon flow and the onset of KH instability induced by the blowout jet along a loop-shaped magnetic structure.

Energy concentration pipe based on passive jet control for enhancing flow induced vibration energy harvesting

Passive control is a classic method for enhancing the energy harvesting from flow-induced vibrations. This study introduces the Energy Concentration Pipe (ECP), a hollow pipe featuring a passive windward suction inlet and jet outlets, mounted on a circular cylinder to improve the performance of flow-induced vibration energy harvester. The effects of ECP configurations—single outlet, symmetrical dual outlet, and asymmetrical dual outlet—are investigated both experimentally and numerically. Experimental results demonstrate that the ECP significantly broadens the lock-in region and generates higher output voltage compared to conventional cylinders. Specifically, the lock-in region of the symmetrical dual outlet configuration increases by 108.33%, meanwhile the maximum output voltage improves by 12.69% over the baseline case. Numerical simulations further elucidate the mechanisms of the ECP, identifying the energy concentration phenomenon. An additional portion of incoming airflow, along with its energy, is channeled through the ECP and jetted into the wake vortex behind the cylinder, altering the wake vortex shedding process. The wake structure is characterized by large primary vortex pairs and smaller secondary vortices. The energy concentration also results in larger and stronger wake vortices, enhancing unsteadiness and broadening the lock-in region. Moreover, a transverse oscillation of vortices induces additional excitation on the cylinder due to pressure oscillation, leading to larger vibration amplitude and higher output voltage.

Fabrication and testing of the transition section between modules of a wakefield accelerator

The fabrication process is presented for a typical transition section located between each cylindrical corrugated waveguide structure comprising the wakefield accelerator module. The transition section includes couplers for extracting the 180 GHz TM01 accelerating mode and separate couplers for extracting the 190 GHz HE11 dipole mode, both modes induced by the electron bunch traversing the cylindrical corrugated waveguide structure. Extraction of the high-power accelerating mode reduces the heat load due to the subterahertz wave power dissipation within the corrugated accelerating structure. Extraction of the low-power dipole mode serves the purpose of detecting the electron bunch transverse oscillations within the wakefield accelerator and identifying the onset of beam breakup instability. Comprehensive testing of the fully functional transition section with an electron beam was done at the Accelerator Test Facility in Brookhaven National Laboratory which verified the functionality of the transition section. Published by the American Physical Society 2024

Two successive EUV waves and a transverse oscillation of a quiescent prominence

ABSTRACT In this paper, we carry out multiwavelength observations of two successive extreme-ultraviolet (EUV) waves originating from active region (AR) NOAA 13575 and a transverse oscillation of a columnar quiescent prominence on 2024 February 9. A hot channel eruption generates an X3.4 class flare and the associated full-halo coronal mass ejection (CME), which drives the first EUV wave front (WF1) at a speed of $\sim$835 km s$^{-1}$. WF1 propagates in the south-east direction and interacts with the prominence, causing an eastward displacement of the prominence immediately. Then, a second EUV wave front (WF2) is driven by a coronal jet at a speed of $\sim$831 km s$^{-1}$. WF2 follows WF1 and decelerates from $\sim$788 to $\sim$603 km s$^{-1}$ before arriving at and touching the prominence. After reaching the maximum displacement, the prominence turns back and swings for 1–3 cycles. The transverse oscillation of horizontal polarization is most evident in 304 Å. The initial displacement amplitude, velocity in the plane of the sky, period, and damping time fall in the ranges of 12–34 Mm, 65–143 km s$^{-1}$, 18–27 min, and 33–108 min, respectively. There are strong correlations among the initial amplitude, velocity, period, and height of the prominence. Surprisingly, the oscillation is also detected in 1600 Å, which is totally in phase with that in 304 Å.

A Pseudo-Spectral Method for Wall Shear Stress Estimation from Doppler Ultrasound Imaging in Coronary Arteries.

The Wall Shear Stress (WSS) is the component tangential to the boundary of the normal stress tensor in an incompressible fluid, and it has been recognized as a quantity of primary importance in predicting possible adverse events in cardiovascular diseases, in general, and in coronary diseases, in particular. The quantification of the WSS in patient-specific settings can be achieved by performing a Computational Fluid Dynamics (CFD) analysis based on patient geometry, or it can be retrieved by a numerical approximation based on blood flow velocity data, e.g., ultrasound (US) Doppler measurements. This paper presents a novel method for WSS quantification from 2D vector Doppler measurements. Images were obtained through unfocused plane waves and transverse oscillation to acquire both in-plane velocity components. These velocity components were processed using pseudo-spectral differentiation techniques based on Fourier approximations of the derivatives to compute the WSS. Our Pseudo-Spectral Method (PSM) is tested in two vessel phantoms, straight and stenotic, where a steady flow of 15mL/min is applied. The method is successfully validated against CFD simulations and compared against current techniques based on the assumption of a parabolic velocity profile. The PSM accurately detected Wall Shear Stress (WSS) variations in geometries differing from straight cylinders, and is less sensitive to measurement noise. In particular, when using synthetic data (noise free, e.g., generated by CFD) on cylindrical geometries, the Poiseuille-based methods and PSM have comparable accuracy; on the contrary, when using the data retrieved from US measures, the average error of the WSS obtained with the PSM turned out to be 3 to 9 times smaller than that obtained by state-of-the-art methods. The pseudo-spectral approach allows controlling the approximation errors in the presence of noisy data. This gives a more accurate alternative to the present standard and a less computationally expensive choice compared to CFD, which also requires high-quality data to reconstruct the vessel geometry.

Kelvin-Helmholtz instability and heating in oscillating loops perturbed by power-law transverse wave drivers

Context. Instabilities in oscillating loops are believed to be essential for dissipating the wave energy and heating the solar coronal plasma. Aims. Our aim is to study the development of the Kelvin-Helmholtz (KH) instability in an oscillating loop that is driven by random footpoint motions. Methods. Using the PLUTO code, we performed 3D simulations of a straight gravitationally stratified flux tube. The loop footpoints are embedded in chromospheric plasma, in the presence of thermal conduction and an artificially broadened transition region. Using drivers with a power-law spectrum, one with a red noise spectrum and one with the low-frequency part subtracted, we excited standing oscillations and the KH instability in our loops, after one-and-a-half periods of the oscillation. Results. We see that our broadband drivers lead to fully deformed, turbulent loop cross-sections over the entire coronal part of the loop due to the spatially extended KH instability. The low RMS velocity of our driver without the low-frequency components supports the working hypothesis that the KH instability can easily manifest in oscillating coronal loops. We report for the first time in driven transverse oscillations of loops the apparent propagation of density perturbations due to the onset of the KH instability, from the apex towards the footpoints. Both drivers input sufficient energy to drive enthalpy and mass flux fluctuations along the loop, while also causing heating near the driven footpoint of the oscillating loop, which becomes more prominent when a low-frequency component is included in the velocity driver. Finally, our power-law driver with the low-frequency component provides a RMS input Poynting flux of the same order as the radiative losses of the quiet-Sun corona, giving us promising prospects for the contribution of decayless oscillations in coronal heating.

Testing the cosmic distance duality relation with Type Ia supernova and transverse BAO measurements

In this work, we test the cosmic distance duality relation (CDDR) by comparing the angular diameter distance (ADD) derived from the transverse Baryon Acoustic Oscillations (BAO) data with the luminosity distance (LD) from the Pantheon type Ia supernova (SNIa) sample. The binning method and Gaussian process are employed to match ADD data with LD data at the same redshift. First, we use nonparametric and parametric methods to investigate the impact of the specific prior values of the absolute magnitude MB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_\ extrm{B}$$\\end{document} from SNIa observations and the sound horizon scale rs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_\ extrm{s}$$\\end{document} from transverse BAO measurements on the CDDR tests. The results obtained from the parametric and non-parametric methods indicate that specific prior values of MB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_\ extrm{B}$$\\end{document} and rs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_\ extrm{s}$$\\end{document} lead to significant biases on the CDDR test. Then, to avoid these biases, we propose a method independent of MB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_\ extrm{B}$$\\end{document} and rs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_\ extrm{s}$$\\end{document} to test CDDR by considering the fiducial value of κ≡10MB5rs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa \\equiv 10^{M_\ extrm{B} \\over 5}r_\ extrm{s}$$\\end{document} as a nuisance parameter and then marginalizing its influence with a flat prior in the analysis. No violation of the CDDR is found, and the transverse BAO measurement can be used as a powerful tool to verify the validity of CDDR in the cosmological-model-independent method.

Unveiling the True Nature of Plasma Dynamics from the Reference Frame of a Superpenumbral Fibril

The magnetic geometry of the solar atmosphere, combined with projection effects, makes it difficult to accurately map the propagation of ubiquitous waves in fibrillar structures. These waves are of interest due to their ability to carry energy into the chromosphere and deposit it through damping and dissipation mechanisms. To this end, the Interferometric Bidimensional Spectrometer at the Dunn Solar Telescope was employed to capture high-resolution Hα spectral scans of a sunspot, with the transverse oscillations of a prominent superpenumbral fibril examined in depth. The oscillations are reprojected from the helioprojective Cartesian frame to a new frame of reference oriented along the average fibril axis through nonlinear force-free field extrapolations. The fibril was found to be carrying an elliptically polarized, propagating kink oscillation with a period of 430 s and a phase velocity of 69 ± 4 km s−1. The oscillation is damped as it propagates away from the sunspot with a damping length of approximately 9.2 Mm, resulting in the energy flux decreasing at a rate on the order of 460 W m−2/Mm. The Hα line width is examined and found to increase with distance from the sunspot, a potential sign of a temperature increase. Different linear and nonlinear mechanisms are investigated for the damping of the wave energy flux, but a first-order approximation of their combined effects is insufficient to recreate the observed damping length by a factor of at least 3. It is anticipated that the reprojection methodology demonstrated in this study will aid with future studies of transverse waves within fibrillar structures.

Impurity modes in two-dimensional strongly coupled complex plasma crystals

Complex plasma fluctuation processes have been extensively studied in many aspects, especially lattice waves in strongly coupled plasma crystals, which are of great significance for understanding fundamental physical phenomena. A challenge of experimental investigations in two-dimensional strongly coupled complex plasma crystals is to keep the main body and foreign particles of different masses on the same horizontal plane. To solve the problem, we have proposed a potential well formed by two negatively biased grids to bind the negatively charged particles in a two-dimensional (2D) plane, thus achieving a 2D plasma crystal in the microgravity environment. The study of such phenomena in complex plasma crystals under microgravity environment then becomes possible. In this paper, we focus on the continuum spectrum, including both phonon and optic branches of the impurity mode in a 2D system in microgravity environments. The results show the dispersion relation of the longitudinal and transverse impurity oscillation modes and their properties. Considering the macroscopic visibility of complex mesoscopic particle lattices, theoretical and experimental studies on this kind of complex plasma systems will help us further understand the physical nature of a wide range of condensed matters.

On the solvability of an inverse boundary problem for the equation of transverse oscillation of the rod

In this article, the solvability of an inverse boundary problem for the 2D equation of transverse oscillation of the rod from knowledge of additional condition is studied. To investigate the solvability of the inverse problem, we first consider an auxiliary inverse boundary value problem and prove its equivalence to the original problem in a certain sense. Using the contraction mappings principle existence and uniqueness of the solution of an equivalent problem is proved. Further, using the equivalency, the existence and uniqueness theorems of the classical solution of the original problem are proved.

Characteristics and energy flux distributions of decayless transverse oscillations depending on coronal regions

It has been proposed that the slope (delta ) of the power-law distribution between the energy flux and oscillation frequency could determine whether high-frequency transverse oscillations make a dominant contribution to the heating ($ A meta-analysis of decayless transverse oscillations revealed that high-frequency oscillations potentially play a key role in heating the solar corona. We aim to investigate whether or not (and, if so, how) the distributions of the energy flux contained in transverse oscillations, and their slopes, depend on the coronal region in which the oscillation occurs. We analysed transverse oscillations from 41 quiet Sun (QS) loops and 22 active region (AR) loops observed by Solar Orbiter/Extreme Ultraviolet Imager (EUI) hrieuv . We estimated the energy flux and energy using analysed oscillation parameters and loop properties, such as periods, displacement amplitudes, loop lengths, and minor radii of the loops. We find that about 71<!PCT!> of QS loops and 86 <!PCT!> of AR loops show decayless oscillations, and that the amplitude does not change depending on different regions, but the difference in the period is more pronounced. Although the power law slope ($ in AR is steeper than that ($ in QS, both of them are significantly less than the critical slope of 1. Our statistical study demonstrates that high-frequency transverse oscillations can heat the QS. For ARs, the total energy flux is insufficient unless yet-unobserved oscillations with frequencies of up to 0.17 Hz are present. Future EUI campaigns will be planned to confirm whether a corresponding high-frequency oscillation exists.