Periodic Variations Research Articles

Multimethod cross-sectional characterization approaching the limits of diamond monophase multilayers

Chemical vapour deposited diamond draws significant scientific interest due to its wide range of mechanical and functional properties, which can be easily tuned by the applied deposition conditions. Here, hot filament chemical vapour deposition was used to synthesize four monophase multilayer diamond thin films with individual layer thickness down to ∼ 300 nm. Extensive structural characterization by scanning electron microscopy and Raman spectroscopy on the cross-section confirmed the different diamond morphologies originating from the different applied process parameters of the individual sublayers, where Raman spectroscopy could give a clear distinction between nano- and microcrystalline diamond down to a layer thickness of ∼ 1 μm. Cross-sectional X-ray nanodiffraction identified exclusively the diamond crystal structure throughout the cross-section of the multilayered diamond thin films. Cross-sectional phase and FWHM analysis allowed to discriminate between the diamond morphologies down to ∼ 500 nm, thus identifying the limitations of monophase diamond multilayers. While the microcrystalline diamond sublayers all exhibit pronounced structural gradients expressed in (i) increasing intensity of the 111 Debye-Scherrer ring, (ii) ⟨110⟩ fibre texture, and periodic variations of (iii) grain size and (iv) residual stress, the nanocrystalline diamond sublayers showed no pronounced cross-sectional variations. In summary, the experimental results provide insights into the cross-sectional evolution of microstructure and residual stress and the limitations of monophase multilayered diamond thin films.

Band gap study of periodic piezoelectric micro-composite laminated plates by finite element method and its application in feedback control

Phononic crystals are materials or structures with periodic variations of elastic constants and density. Elastic waves in phononic crystals cannot propagate within a certain frequency range, called the band gap, due to the interference of their internal structure. This article investigates how fiber orientation affects the band gap properties of periodic micro-composite laminated plates. We examined the impact of five common composite laminate configurations on the system’s band gap and discovered that the antisymmetric configuration had superior high-frequency band gap performance. Based on this finding, we further explored how the antisymmetric angle influenced the system’s band gap. Since the study was conducted at a micro scale, micro structural effects were considered. Therefore, we used the modified coupled stress elastic dynamics and a four-node quadrilateral non-conforming element to discretize the micro composite laminated plate model, which had the nodal compatibility of high-order elasticity theory. Moreover, we employed feedback control to the proposed structure to dynamically adjust the band gap width according to different practical needs. This research supports the design of periodic micro-composite laminated plates and the piezoelectric feedback control system, which can control the vibration and wave propagation behaviors of micro structures using coupled piezoelectric sensors and actuators. The piezoelectric feedback control employed two control methods: direct proportional control and acceleration control. This article compared the single and multiple control methods of these two approaches to determine the optimal control strategy.

Investigation on the turbulent structures in combined wave-current boundary layers

The problem of turbulent vortices and vortex dynamics under the influence of ocean waves is a subject of continuing research in the field of wave-current interaction. Thus, this study investigates the evolution of turbulence structures and vortex interactions in combined wave-current boundary layers, where water waves propagate with currents. Experiments were performed in two glass-walled laboratory channels with water depths of 160 and 400 mm. A two-dimensional two-component (2D2C) Particle Image Velocimetry (PIV) system was used to measure the velocities. Periodic variations in turbulence are observed for combined wave-current flows. Pairs of counter-rotating vortices are identified in the outer region when the combined flow is reversed, leading to destructive vortex interactions. This process leads to a reduction in the turbulent kinetic energy (TKE) and TKE production and dissipation during the passage of the wave trough. A conceptual model of hairpin vortices in combined wave-current flows is proposed in this study. The results of this study provide novel insights into the hydrodynamics of combined wave-current flows.

Doppler Tomography of the Circumstellar Disk of the Be Star κ Draconis

κ Draconis is a binary system with a classical Be star as the primary component. Its emission-line spectrum consists of hydrogen lines, notably the Hα line with peak intensity ratio (V/R) variations phase-locked with the orbital period P = 61.55 days. Among binaries demonstrating the Be phenomenon, κ Dra stands out as one of a few systems with a discernible mass of its secondary component. Based on more than 200 spectra obtained in 2014–2023, we verified the physical parameters and constructed the mass function. We used part of these data obtained in 2014–2021 to investigate regions in the circumstellar disk of the primary component that emit the Hα line using the Doppler tomography method. The results show that the disk has a non-uniform density distribution with a prominent enhancement at Vy ≈ 99 km s−1 and Vx≈−6 km s−1 that corresponds to a cloud-like source of the double-peaked Hα line profile. We argue that this enhancement’s motion is responsible for the periodic variations in the Hα V/R ratio, which is synchronised in orbital phase with the radial velocity (RV) of absorption lines from the atmosphere of the primary component.

Orbital period change of SW Sex star TT Tri

Abstract SW Sex-type stars are the dominate population of cataclysmic variables (CVs) just above the period gap and are vital for understanding of CV evolution. We have monitored TT Tri for nearly 15 yr, and more observations yield a more reliable estimation for its orbital period variation. In this work, we present a detailed analysis about its orbital period variation. TT Tri experiences a rapid period decay with a decay rate of −5.67 × 10−11 s/s plus a period oscillation at about 9.6 years. The oscillation could be caused by the magnetic activities of the low-mass star or/and a circumbinary body, while the rapid period decrease can not be accounted for by the magnetic braking or even including an intensive disk wind. We find that mass overflow though the L3 point can take the angular momentum away effectively and that this mass overflow could account for the rapid period decay observed in TT Tri. We propose that this kind of angular momentum loss may play a crucial role in CV evolution, and further research is in progress.

Aquatic photosynthetic carbon pump driven by periodic temperature variations affects dissolved inorganic carbon and hydrochemical characteristics in a groundwater-fed reservoir

Under the influence of periodic temperature variations, biogeochemical cycling in water bodies is markedly affected by the periodic thermal stratification processes in subtropical reservoirs or lakes. In current studies, there is insufficient research on the influence and mechanism of dissolved inorganic carbon (DIC) distribution in karst carbon-rich groundwater-fed reservoirs under the coupled effects of thermal structure stratification and the biological carbon pump (BCP) effect. To address this issue, the Dalongdong (DLD) reservoir in the subtropical region of southern China was chosen as the site for long-term monitoring and research on relevant physicochemical parameters of water, DIC, and its stable carbon isotope (δ13CDIC), CO2 emission flux, as well as the reservoir's thermal stratification index. The results show that: (1) the DLD reservoir is a typical warm monomictic reservoir, which exhibits regular variations of mixing period-stratification period-mixing period on a yearly scale due to thermal structure changes; (2) DIC was consumed by aquatic photosynthetic organisms in the epilimnion during the stratification period, leading to a decrease in DIC concentration, partial pressure of CO2 (pCO2) and CO2 emission flux, and an increase in stable carbon isotope (δ13CDIC). During the mixing period, the trend was reversed; (3) During the thermal stratification, aquatic photosynthesis and water temperature were the primary factors controlling DIC variations in both the epilimnion and thermocline. Regarding the hypolimnion, calcite dissolution, organic matter decomposition, and water temperature were the dominant controlling factors. These results indicate that although carbon-rich karst groundwater provides a plentiful supply of DIC in the DLD reservoir, its availability is still influenced by variations in the reservoir's thermal structure and the metabolic processes of aquatic photosynthetic organisms. Therefore, to better estimate the regional carbon budget in a reservoir or lake, future studies should especially consider the combined effects of BCP and thermal structure variations on carbon variations.

Research on High-Stability Composite Control Methods for Telescope Pointing Systems under Multiple Disturbances.

During the operation of space gravitational wave detectors, the constellation configuration formed by three satellites gradually deviates from the ideal 60° angle due to the periodic variations in orbits. To ensure the stability of inter-satellite laser links, active compensation of the breathing angle variation within the constellation plane is achieved by rotating the optical subassembly through the telescope pointing mechanism. This paper proposes a high-performance robust composite control method designed to enhance the robust stability, disturbance rejection, and tracking performance of the telescope pointing system. Specifically, based on the dynamic model of the telescope pointing mechanism and the disturbance noise model, an H∞ controller has been designed to ensure system stability and disturbance rejection capabilities. Meanwhile, employing the method of an H∞ norm optimized disturbance observer (HODOB) enhances the nonlinear friction rejection ability of the telescope pointing system. The simulation results indicate that, compared to the traditional disturbance observer (DOB) design, utilizing the HODOB method can enhance the tracking accuracy and pointing stability of the telescope pointing system by an order of magnitude. Furthermore, the proposed composite control method improves the overall system performance, ensuring that the stability of the telescope pointing system meets the 10 nrad/Hz1/2 @0.1 mHz~1 Hz requirement specified for the TianQin mission.

Design and verification of controller for a small coaxial dual-rotor aircraft

In recent years, coaxial dual-rotor aircraft has attracted much attention due to its unique aerodynamic layout. However, it is difficult to miniaturize the coaxial dual-rotor aircraft that relies on the principle of periodic pitch variation due to complex structure and control difficulties. This study proposes a small cylindrical coaxial dual-rotor aircraft based on a vector motor seat. For the control problems of such coaxial dual-rotor aircraft, a position and attitude controller based on neural networks and adaptive cascaded PID control is designed. A control system model was established and tested using MATLAB/Simulink. The proposed control scheme’s soundness and efficiency were confirmed by creating a prototype and performing flight trials. The results show that compared with the classic PID controller, the control effect of the controller has improved by 36.3% to 54.6%. In the centripetal rotation flight simulation experiment, the displacement error does not exceed 0.2 m, the speed error does not exceed 0.05 m/s, and the attitude angle error does not exceed 0.01 rad. This validates the effectiveness of the designed controller, indicating that the controller can enhance the stability of the system and achieve stable hovering and flight.

Numerical study on improved mass and heat transfer performance in a solid oxide electrolysis cell with sine wave flow field

In this paper, the periodic variation of sine wave is used to promote the transport and diffusion process of reactive gases; and the relationship between the performance of a solid oxide electrolysis cell (SOEC) and the mass and heat transfer capabilities of its flow field is thoroughly examined. The impact of variations in the amplitude and frequency of the sine wave on the SOEC's electrolysis efficiency, its mass and heat transfer properties, and fluid flow dynamics are explored. The results indicate that longitudinal flow velocity of the gas in the sine wave flow channel is increased by 26.96–80.76% at a current density of 10000 A/m2, and this kind of flow channel exhibits superior gas transport performance. Moreover, the temperature-uniformity index and the maximum thermal stress of the positive-electrolyte-negative (PEN) structure are decreases by 18.93–22.67% and 20%, respectively. It indicates that this configuration is capable of reducing thermal stress and enhancing the uniformity of temperature distribution at high current-densities. Increasing the amplitude and frequency improves the comprehensive performance of the flow field. More specifically, frequency has a greater impact on flow field performance than amplitude.

Open-access digital elevation model (DEM) selection for flood inundation modelling using HEC-RAS in Capital City of Nusantara

Flood is a classic but complex issue in most regions of Indonesia. Nusantara, the future capital of Indonesia, is now undergoing construction but the site continues to experience flooding due to high intensity rainfall. To overcome this challenge, identification of flood points in those areas needs to be done. Digital Elevation Models (DEM) are the most important component in modeling flood inundation in data-sparse areas. High-accuracy DEMs have been found to give better flood estimation but the availability of such data is very limited. Therefore, open-access DEMs, such as SRTM, DEMNAS, and MERIT-Hydro, are the most common choices used in modeling flood inundation in Indonesia. Each data set may provide varying model outcomes, due to different data processing methods. These results often lead to confusion as to which result should be used in subsequent studies. In this study, flood inundation in Nusantara will be generated using different DEMs and HEC-RAS hydraulic modeling with 25-, 50-, and 100-year return period rainfall events. The return period rainfall was obtained by calibrating Global Precipitation Measurement (GPM) satellite rain data. The results provide various flood inundation conditions, MERIT-Hydro tends to present higher flood depths. Followed by DEMNAS and SRTM which have lower flood depths. On the other hand, the use of return period variation gives a linear increase in flood depth for the DEMNAS model. While a decline in increment occurred in the SRTM and MERIT-Hydro models when the two big year return periods were applied. This research can be considered for the Nusantara development planning.

Pinwheel Outflow Induced by Stellar Mass Loss in a Coplanar Triple System

We develop a physical framework for interpreting complex circumstellar patterns whorled around asymptotic giant branch (AGB) stars by investigating stable, coplanar triple systems using hydrodynamic and particle simulations. The introduction of a close tertiary body causes an additional periodic variation in the orbital velocity and trajectory of the AGB star. As a result, the circumstellar outflow builds a fine non-Archimedean spiral pattern superimposed upon the Archimedean spiral produced by the outer binary alone. This fine spiral can be approximated by off-centered circular rings that become tangent to each other at the location of the Archimedean spiral. The superimposed fine pattern fades out relatively quickly as a function of distance from the center of the system, in contrast to the dominant Archimedean spiral pattern, which presents a much slower fractional density decrease with radius. The different rates of radial decrease of the density contrast in the two superimposed patterns, coupled with their different time and spatial scales, lead to an apparent, but illusory radial change in the observed pattern interval, as has been reported, for example, in CW Leo. The function describing the detailed radial dependence of the expansion velocity is different in the two patterns, which may be used to distinguish them. The shape of the circumstellar whorled pattern is further explored as a function of the orbital eccentricity and the inner companion’s mass. Although this study is confined to stable, coplanar triple systems, the results are likely applicable to moderately noncoplanar systems and open interesting avenues for studying noncoplanar systems.

Study of hydrodynamic characteristics in oscillating wave surge converter

In the realm of renewable energy, researchers worldwide have been paying close attention to developing the Oscillating Wave Surge Converter (OWSC) device. This device has the potential to harness the power of ocean waves and convert it into a reliable source of clean energy. Hydrodynamic characteristics are essential parameters in developing OWSC devices. Therefore, this research conducted a hydrodynamic study on the OWSC device with variations in ocean wave periods, including T= 1.5, 1.7, 1.9, 2.1, and 2.3. The Boundary Element Method (BEM) describes the interaction between sea waves and floating body structures. This method assumes incompressible, inviscid, and irrotational flow. A numerical approach is used as a calculation method followed by verification and validation to support the level of actualization. The research results showed that the incident wave caused the OWSC device to experience a deviation from its equilibrium position in the form of an oscillating flap inclination angle as a form of hydrodynamic characteristics. The sea wave period correlatedwith the rate of change in flap position over time, including the maximum deviation in the flap angle. As a power plant, the performance of the OWSC device can work at reasonably short-wave period intervals based on the device's ability to produce mechanical power. The highest average mechanical power was achieved in the T= 1.5 period of 34.49 Watts with an efficiency of up to 52.43%. The OWSC device requires a high intensity of wave energy in a short duration to generate optimal mechanical power. It is important to note that optimal mechanical power generation is crucial for the OWSC device to function effectively. Therefore, the device should be placed in a location where the wave energy intensity is consistently high.

Formation conditions of Jixian System cherts in the Qishan area, Ordos Basin: Implications for marine redox conditions and paleoecology

Abundant chert bands and nodules are discovered throughout the Mesoproterozoic Jixian System in the Ordos Basin. These cherts faithfully record the Jixian period oceanic conditions and paleoecology. However, the diagenetic mechanism of the cherts remains unclear and controversial. To understand the origin of these cherts, we performed a multitracer study by combining field reconnaissance, petrological analyses, Si isotope analysis, and major and trace element analysis of chert samples from the Qishan section. The results show that Jixian cherts had a high Al/(Al + Fe + Mn) value (~0.48), showed a flat distribution of rare earth elements in seawater, and most of the Fe/Ti values are <20. A weak negative Ce anomaly (~0.97) indicates the contribution of REY to weakly oxygenated seawater. The high isotopic composition of silicon (δ30Si = 0.74 ‰-1.35 ‰) and the average Siex value of 37.52 indicate that there is a source of biological silica, and the relationship between Eu/Eu* and Y/Ho and δ30Si shows that the hydrothermal and volcanic influences were less and correlated with seawater. The chert bands were closely related to biological activities. The chert nodules were influenced by hydrothermal activity. Secondary cherts were related to diagenesis, but the nature of siliceous fluids remains unchanged, still characterized by biogenic activity origins. The sea oxygen concentration in the Jixian period had increased, with periodic variations in the intensity of biological activities affecting the pH of the water body, or biological photosynthesis binding SiO2 colloid in water, affecting chert sediments, leading to frequent interlayering between dolomite and chert bands. Episodic hydrothermal fluids and late-stage diagenetic processes jointly influenced the formation of cherts. This study bears significant significance in enhancing our understanding of the sedimentary environment and the origin of cherts during the Jixian period in the Ordos Basin.

A New Window for Studying Intermediate Polars and Tilted Accretion Disk Precession

TV Col is a long-period eclipsing intermediate polar (IP) prototype star for the negative superhump (NSH) system. We investigate the eclipse minima, eclipse depth, and NSH amplitude based on TESS photometry. Using the same analytical method as for SDSS J081256.85+191157.8, we find periodic variations of O − C for eclipse minima and NSH amplitudes with periods of 3.939(25) days and 3.907(30) days, respectively. The periodic variation of the NSH amplitude of TV Col confirms that periodic changes in NSH amplitude in response to the tilted disk precession may be universal, which is further evidence that the origin of the NSHs is related to the tilted disk precession. We suggest that the variation in NSH amplitude may be similar to the superorbital signal, coming from the periodic change in visual brightness of the energy released by streams touching the tilted disk with tilted disk precession. Finally, we find for the first time that the eclipse depth exhibits biperiodic variations with periods of P 1 = 3.905(11) days and P 2 = 1.953(4) days, respectively. P 2 is about half of P 1 and the disk precession period (P 1 ≈ P prec ≈ 2 × P 2). We suggest that P 1 may come from the periodic change in the brightness of the eclipse center due to tilted disk precession, while P 2 may come from two accretion curtains precessing together with the tilted disk, but more verification and discussion are necessary. The discovery of biperiodic variations in eclipse depth provides a new window for studying IPs and tilted disk precession.

Exploring ionospheric dynamics: a comprehensive analysis of GNSS TEC estimations during the solar phases using linear function model

Abstract The modeling and forecasting of Total Electron Content (TEC) play a major role in influencing signals from satellite-based navigation systems and impact the performance of diverse satellite-dependent technologies. The intensity of solar ionizing radiation and the state of geomagnetic field activity influence the Global Navigation Satellite System (GNSS)-TEC. This paper uses a Linear TEC Function (LTF) climatology model to understand ionospheric behavior under solar and geomagnetic activities that cause variations in the electron distribution of the ionosphere medium. The LTF model integrates representations of solar EUV photon (MgII) and geomagnetic (SYMH) activities, incorporating solar-modulated oscillations (periodic variations) at four seasonal cycles and a linear trend. The LTF model examined the time series of GPS-TEC at a location (geographic 34.95° N, 134.05° E) with a time resolution of 1 h, from 1997 to 2016, covering solar cycles 23 and 24. The Root Mean Square Deviation (RMSD) and correlation coefficient between the GNSS-TEC and model TEC (LTF) was 5.30 TECU and 95 %. The results indicate that solar components, as well as annual and semi-annual variations, have a significant impact on the daily average TEC. Solar activity appears to be the predominant determining factor of TEC during the solar phases of cycles 23 and 24. In contrast, periodic influences primarily outline TEC during periods characterized by minimal solar activity. The geomagnetic component presents an increased influence, particularly during storm periods. The model demonstrates superior performance in Total TEC modeling compared to other state-of-the-art approaches.

Early Identification and Dynamic Stability Evaluation of High-Locality Landslides in Yezhi Site Area, China by the InSAR Method

In mountainous regions, high-locality landslides have the characteristics of a latent disaster process with a wide disaster range, which can easily cause large casualties. Therefore, early landslide identification and dynamic stability evaluation are significant. We first used multi-temporal synthetic aperture radar data to detect potential landslides at Yezhi Site Area during the 2015–2020 period, identifying and mapping a total of 18 active landslides. The study area was found to have an average deformation rate between −15 and 10 mm/y during the period. Then, time series and spatiotemporal deformation characteristics of landslides were examined using interferogram stacking and small baseline interferometry techniques. The results show that the majority of the landslide deformations detected exhibit a periodic variation trend, and the study area was in a slow deformation state before 2017. Finally, combined with detection results, Google Earth optical images, and field investigations, it is concluded that the main factors affecting the time series deformation and spatial distribution of landslides in the study area are rainfall, geological factors, and engineering activities. The results of this study provide valuable technical references and support for early identification and dynamic stability evaluation of regional active landslides in complex terrain, especially for high-locality landslides.

The puzzling orbital residuals of XTE J1710–281: Is a Jovian planet orbiting the binary system?

is a transient eclipsing binary system with a period close to 3.28 hours that hosts a neutron star. The average eclipse duration is 420 seconds, and eclipse arrival times reported in the literature span from 1999 to 2017. A previous analysis of the eclipse arrival times using the eclipse timing technique revealed a complex pattern of delays, indicating the presence of three orbital glitches. These glitches correspond to sudden variations in the orbital period and allow for the identification of four distinct epochs, during which the orbital period derivative was estimated to be $-1.8 $ s s$^ $ s s$^ $ s s$^ $, and $0.09 $ s s$^ $, respectively. We reanalyzed the 78 eclipse arrival times spanning 18 years utilizing the eclipse timing technique to derive the corresponding delays as a function of time. We find that the observed delays align well with a fitting model that employs an eccentric sine function characterized by an amplitude of $6.1 0.5$ s, an eccentricity of $0.38 0.17$, and a period of $17.1 1.5$ years. Additionally, we identified the orbital period to be 3.28106345(13) hours, with a reference epoch of $T_0=54112.83200(2)$ MJD. We obtained an upper limit to the orbital period derivative of $3.6 $ s s$^ From the average value of the eclipse duration, we estimate that the companion star has a mass of 0.22 for a neutron star mass of 1.4 and that the inclination of the source is $ degrees. The companion star is in thermal equilibrium. The orbital period derivative is consistent with a conservative mass transfer scenario, where the angular momentum loss due to magnetic braking dominates over gravitational radiation angular momentum loss if the former is present. The eccentric modulation can be explained by a third body with a mass of 2.7 Jovian masses, orbiting with a revolution period close to 17 years and an eccentricity of 0.38.

Physical mechanism-corrected degradation trend prediction network under data missing

Accurate degradation trend prediction (DTP) is crucial for optimizing equipment operation and maintenance, thereby boosting production efficiency. This study introduces a novel Data Repair and Dual-data-stream LSTM (DR-DLSTM) network to tackle the challenge of missing data in equipment DTP. The proposed DR-DLSTM framework employs convex optimization to consider both the trend and periodic variations in the data, incorporating polynomial and trigonometric functions into the implicit feature matrix to construct latent vectors for missing data rectification. The network features a Dual-LSTM block with dual data streams to enhance feature extraction, with two gating update units correlating time series components and redistributing feature weights. The Dual-LSTM enables separate and accurate prediction of trend and periodic components, thereby enhancing the feature extraction capability of the prediction model. Additionally, the integration of physical rule information through Fourier and wavelet transform frequency correction modules allows for dynamic adjustments in prediction outcomes, from global trends to localized details. The DR-DLSTM's effectiveness is demonstrated through comprehensive comparisons with state-of-the-art models across multiple datasets, highlighting its superior performance. The results demonstrate the superiority of the proposed model. These algorithms were implemented in Python using Torch on a 2.9 GHz Intel I7 CPU and TITAN Xp GPU.

Study on the impact of wave characteristics on the performance of full-scale tidal turbine

The operation of tidal turbines is inevitably influenced by waves, and extensive research has undoubtedly been conducted on this topic. However, most investigations of such studies have utilized small-scale turbines, with a primary focus on the load characteristics of the turbines themselves. There is a slight deficiency in attention to the wave characteristics that contribute to these loads. To bridge this gap, this study develops a computational fluid dynamics (CFD) model of a full-scale tidal turbine. The model's accuracy is assessed through flume experiments using a scaled-down version, validating the numerical approach against wave conditions. Employing actual tidal flow velocity and wave data as input, this study specifically examines how variations in wave period and height affect turbine performance. The analysis reveals a nuanced decrease in time-averaged performance with increases in wave period and height. Load fluctuations arise from wave impacts, turbine rotor rotation, and their interaction. With the increase in wave period or height, the fluctuations caused by the wave impacts and the interaction increase, while those induced by rotor rotation exhibit a slow growth trend but essentially remain stable.

Flickering pulsations in bright X-ray pulsars: the evidence of gravitationally lensed and eclipsed accretion column

ABSTRACT It is expected that the extreme mass accretion rate onto strongly magnetized neutron stars results in the appearance of accretion columns above the stellar surface. For a distant observer, rotation of a star results in periodic variations of X-ray flux. Because the mass accretion rate fluctuates around the average value, the pulse profiles are not stable and demonstrate fluctuations as well. In the case of bright X-ray pulsars, however, pulse fluctuations are not solely attributed to variations in the mass accretion rate. They are also influenced by the variable height of the columns, which is dependent on the mass accretion rate. This study delves into the process of pulse profile formation in bright X-ray pulsars, taking into account stochastic fluctuations in the mass accretion rate, the corresponding variations in accretion column geometry, and gravitational bending. Our analysis reveals that potential eclipses of accretion columns by a neutron star during their spin period should manifest specific features in pulse profile variability. Applying a novel pulse profile analysis technique, we successfully detect these features in the bright X-ray transient V 0332+53 at luminosities $\gtrsim 2\times 10^{38}\, {\rm erg\ \rm s^{-1}}$. This detection serves as compelling evidence for the eclipse of an accretion column by a neutron star. Detection of the eclipse places constraints on the relation between neutron star mass, radius, and accretion column height. Specifically, we can establish an upper limit on the accretion column height, which is crucial for refining theoretical models of extreme accretion.