Shape Asymmetry Research Articles

Investigation on coupling vibration characteristics of asymmetric rails with variable cross-sections based on modal separation

In railway turnouts, asymmetric switch rails with variable cross-sections are designed for wheel load transitions. However, the dynamic characteristics of these specially shaped switch rails are not yet fully understood. This paper investigates the vibration characteristics of switch rails through theoretical simulations, on-site admittance tests, and operational deflection shape (ODS) measurements. The study reveals that the modes of the switch rail involve multi-directional coupling vibrations, making the mode types indiscernible through direct observation. To address this, a modal separation method is proposed, based on the calculation of modal mass. The vertical vibration of the switch rail can be categorized into three types: torsional mode, vertical bending mode, and reverse torsion mode of the rail head and base above 600 Hz. As the position approaches the switch rail point, the degree of cross-sectional asymmetry increases, which consequently intensifies torsional vibration. Cross-sectional asymmetry is identified as the primary factor causing the coupling of bending-torsional vibrations, while variable cross-sections contribute to mode shape asymmetry and the gradual alteration of natural frequency along the rail.

Surface Phonons and Possible Structural Phase Transition in a Topological Semimetal PbTaSe2

AbstractTopological insulators are characterized by protected gapless surface or edge states but insulating bulk states which is due to the presence of spin‐orbit interactions and time‐reversal symmetry. Here, an in‐depth investigation of a topological nodal line semimetal PbTaSe2 via temperature, polarization dependent Raman spectroscopy, and temperature dependent single crystal X‐ray diffraction (SC‐XRD) measurements is reported. The analysis shows signature of electron‐phonon coupling as reflected in the Fano asymmetry in line shape of M1‐M4 modes and anomalous temperature variation of line‐width of P3‐P4 modes. Further polarization dependent phonon symmetry changes at different temperature (6K and 300K), discontinuities in bulk phonon dynamics for P2‐P5 modes, and disappearance of phonon modes, i.e., M1‐M5, on decreasing temperature indicates toward a thermally induced structural phase transition which is also supported by the SC‐XRD results. Hence based on the findings, it is proposed that M1‐M4 modes are surface phonon modes, the material undergoes a thermally induced structural phase transition from α to β phase at Tα→β ≈ 150 K or is in close proximity to the β phase and another transition below TCDW+β ≈ 100K which is possibly due to the interplay of remanent completely commensurate charge density wave (CCDW) of 1H‐TaSe2 and β phase.

DOES SHAPE SYMMETRY EXIST IN THE LUNATE BONE? TOWARDS DEVELOPMENT OF A PATIENT-SPECIFIC LUNATE IMPLANT

IntroductionKienböck's disease is generally defined as the collapse of the lunate bone, and this may lead to early wrist osteoarthritis. Replacing the collapsed lunate with an implant has regained renewed interest with the advancing technology of additive manufacturing, enabling the design of patient-specific implants. The aims of this project are (1) to determine how accurate it is to use the contralateral lunate shape as a template for patient-specific lunate implants, and (2) to study the effects of shape variations wrist kinematics using 4D-computed tomography (CT) scanning.MethodsA 3D statistical shape model (SSM) of the lunate was built based on bilateral CT scans of 54 individuals. Using SMM, shape variations of the lunate were identified and the intra- and inter-subject shape variations were compared by performing an intraclass correlation analysis. A radiolucent motor-controlled wrist-holder was designed to guide flexion/extension and radial/ulnar deviation of ex vivo wrist specimens under 4D-CT scanning. In this pilot, three shape mode variations were tested per specimen in two specimens were. After post-processing each CT, the scapholunate angle (SLA) and capitolunate angle (CLA) were measured.ResultsThe shape of the lunate was not symmetrical, defined as exceeding the intra-subject variation in five different shape modes. The FE tests show a generalized increase in scapholunate and capitolunate angle when using lunate implants, and comparing variation of shape modes showed that shape mode 3 has a significant effect on the measured angles (p<0.05).DiscussionThe design of patient-specific lunate implants may prove to be challenging using a ‘mirror’-design as it will lead to a degree of shape asymmetry. The pilot study, to determine the effects of those shape variations on wrist kinematics suggest that the degree of shape variation observed indeed may alter the wrist kinematics, although this needs to be further investigated in study using more specimens.

Ponderomotive potential effects on strong field two-photon double ionization in neon

Abstract In the context of the recently reported experiment on photoionization in neon atom, we theoretically study the photoionization of neon atom at a comparatively intense laser field. The calculated photoelectron spectrum for a Gaussian laser pulse show an asymmetric double peak line shape at a pulse duration of 14.2 fs and peak intensity of 1 × 1015 W cm−2. A systematic study clearly indicates that the ponderomotive potential of the photoelectron released during photoionization of neon is instrumental in causing the visible asymmetry. Interestingly, for similar laser parameters asymmetry in the photoelectron spectrum gets significantly reduced for a Sech2 shaped laser pulse. Time resolved photoelectron spectrum reveals that even for a Sech2 shaped laser pulse the two peak photoelectron spectrum is initially asymmetric and evolves into a symmetric line shape with increase in time. The results clearly indicate that irrespective of laser pulse shape asymmetry shows a non-linear decrease as a function of time. Our study also shows the possibility of controlling the asymmetry by varying the pulse duration. The calculations establishes a correlation between the effects of direct double ionization and ponderomotive potential on the asymmetry of the photoelectron spectrum at different pulse durations.

Asymmetric sample shapes complicate planar biaxial testing assumptions by intensifying shear strains and stresses

Planar biaxial testing offers a physiologically relevant approach for mechanically characterizing thin deformable soft tissues, but often relies on erroneous assumptions of uniform strain fields and negligible shear strains and forces. In addition to the complex mechanical behavior exhibited by soft tissues, constraints on sample size, geometry, and aspect ratio often restrict sample shape and symmetry. Using simple PDMS gels, we explored the unknown and unquantified effects of sample shape asymmetry on planar biaxial testing results, including shear strain magnitudes, shear forces measured at the sample’s boundary, and the homogeneity of strains experienced at the center of each sample. We used a combination of finite element modeling and experimental validation to examine PDMS gels of varying levels of asymmetry, allowing us to identify effects of sample shape without confounding factors introduced by the nonlinear, spatially variable, and anisotropic properties of soft tissues. Both biaxial simulations and experiments, which showed strong agreement, revealed that sample shape asymmetry led to significantly larger shear strains, shear forces, and overestimation of principal stresses. Excluding these shear forces resulted in an underestimation of shear moduli during inverse mechanical characterizations. Even in the simplest of deformable biomaterials, sample shape asymmetry should be avoided as it can induce drastic increases in shear strains and shear forces, invalidating traditional planar biaxial testing analyses. Alternatively, sample shape asymmetry may be exploited to generate more robust estimates of constitutive parameters in more complex materials, which could lead to a refined understanding and inference of mechanical behavior.

Dawn‐Dusk Asymmetry of the Magnetopause Distance Under the Parker Spiral Configuration of the IMF

AbstractThe dawn‐dusk asymmetry of the magnetopause radial distance under the Parker (and ortho‐Parker) configuration of the interplanetary magnetic field (IMF) is investigated. An extensive data set of about 50,000 magnetopause crossings identified in the data from the THEMIS A‐E, Magion 4, Geotail, and Interball‐1 satellites is used for this purpose. It is shown that the magnetopause radial distances are larger at the side where the IMF is quasi‐parallel to the bow shock normal than at the side where IMF is quasi‐perpendicular to the bow shock normal. The effect is more significant at the flanks than close to the subsolar point. This introduces a significant asymmetry of the magnetopause shape, with the difference in the magnetopause radial distances being as large as about one Earth radius beyond the terminator. The experimental results are confirmed by a global magnetohydrodynamic (MHD) model, demonstrating that the asymmetry can be explained by MHD effects, without considering foreshock transients. This MHD model is further used to investigate the evolution of individual pressure components across the magnetopause and contrast them in quasi‐parallel and quasi‐perpendicular cases.

Intra and interspecies discrimination of three teleost species collected from the Komo Estuary in Gabon in relation to living depth levels using otolith shape analysis

ABSTRACT This study aimed to examine otolith shape and fluctuating asymmetry (FA) in pelagic Ethmalosa fimbriata, demersal Galeoides decadactylus, and benthic Cynoglossus monodi and assess their population status to inform on management procedures and verify whether or not otolith shape differs with living depth levels of these species in Lebe fishing site located along Komo Estuary, central-western Gabon. At intraspecies level, otolith shape analysis showed a bilateral asymmetry only in left and right otoliths between males and females of E. fimbriata and C. monodi. DFA separated between left and right and left-left and right-right otoliths shape of males and females within each species. At interspecies level, a significant bilateral asymmetry in left and right otolith shape was found among males and females of each species. DFA completely separated the left and right otoliths of both males and females of three species and confirmed the presence of three separate populations representing the three species, which should be managed separately. A significant FA on right and left otolith shapes was found among males and females at intra and interspecies levels. Accordingly, results indicated a close relationship between asymmetry of otolith shape and pelagic and benthic life characteristics of E. fimbriata and C. monodi.

A Synchronous Moon as a Possible Cause of Mars' Initial Triaxiality

AbstractThe paper addresses the possibility of a young Mars having had a massive moon, which synchronized the rotation of Mars, and gave Mars an initial asymmetric triaxiality to be later boosted by geological processes. It turns out that a moon of less than a third of the lunar mass was capable of producing a sufficient initial triaxiality. The asymmetry of the initial tidal shape of the equator depends on timing: the initial asymmetry is much stronger if the synchronous moon shows up already at the magma‐ocean stage. From the moment of synchronization of Mars' rotation with the moon's orbital motion, and until the moon was eliminated (as one possibility, by an impact in the beginning of the Late Heavy Bombardment), the moon was sustaining an early value of Mars' rotation rate.

Unraveling the complex interplay between abnormal hemorheology and shape asymmetry in flow through stenotic arteries

Background and Objective:Stenosis or narrowing of arteries due to the buildup of plaque is a common occurrence in atherosclerosis and coronary artery disease (CAD), limiting blood flow to the heart and posing substantial cardiovascular risk. While the role of geometric irregularities in arterial stenosis is well-documented, the complex interplay between the abnormal hemorheology and asymmetric shape in flow characteristics remains unexplored. Methods:This study investigates the influence of varying hematocrit (Hct) levels, often caused by conditions such as diabetes and anemia, on flow patterns in an idealized eccentric stenotic artery using computational fluid dynamics simulations. We consider three physiological levels of Hct, 25%, 45%, and 65%, representing anemia, healthy, and diabetic conditions, respectively. The numerical simulations are performed for different combinations of shape eccentricity and blood rheological parameters, and hemodynamic indicators such as wall shear stress (WSS), oscillatory shear index (OSI), are relative residence time (RRT) are calculated to assess the arterial health. Results:Our results reveal the significant influence of Hct level on stenosis progression. CAD patients with anemia are exposed to lower WSS and higher OSI, which may increase the propensity for plaque progression and rupture. However, for CAD patients with high Hct level—as is often the case in diabetes—the WSS at the minimal lumen area increases rapidly, which may also lead to plaque rupture and cause adverse events such as heart attacks. These disturbances promote endothelial dysfunction, inflammation, and thrombus formation, thereby intensifying cardiovascular risk. Conclusions:Our findings underscore the significance of incorporating hemorheological parameters, such as Hct, into computational models for accurate assessment of flow dynamics. We envision that insights gained from this study will inform the development of tailored treatment strategies and interventions in CAD patients with common comorbidities such as diabetes and anemia, thus mitigating the adverse effects of abnormal hemorheology and reducing the ever-growing burden of cardiovascular diseases.

Distinctive morphological variation of saccular otoliths in relation to hermaphroditism type in Sarpa salpa and Serranus scriba (Teleostei: Perciformes) from the Mediterranean Sea in Bizerte, Tunisia

This study aimed to describe and compare the morphological characteristics of saccular otoliths (sagittae) in the protandrous hermaphrodite Sarpa salpa and the synchronous hermaphrodite Serranus scriba collected from the Bizerte site located in northwestern Tunisia, and to examine the effect of hermaphroditism type on the otolith shape and size at the inter- and intraspecific levels, using elliptical Fourier analysis. At the interspecific level, a significant bilateral asymmetry in shape was observed between the left and right otoliths. At the intraspecific level, a significant bilateral asymmetry in shape was detected between the left and right otoliths only in S. scriba. Discriminant function analysis (DFA) produced two separate main groups corresponding to the two species, and intrasexually differentiated between left and right otoliths in S. salpa. In addition, a significant bilateral asymmetry was found in Lo, Wo, Ao, and Po in S. salpa and in Po only in synchronous S. scriba. Thus, protandrous hermaphroditism did not affect otolith shape in S. salpa, but showed an apparent bilateral asymmetry in otolith size. However, synchronous hermaphroditism exhibited a significant bilateral asymmetry in otolith shape and Po only in S. scriba. The causes of this significant inter- and intraspecific bilateral asymmetry observed in otolith shape and size were discussed.

Size-Controllable and Monodispersed Lipid Nanoparticle Production with High mRNA Delivery Efficiency Using 3D-Printed Ring Micromixers.

Lipid nanoparticles (LNPs) are gaining recognition as potentially effective carriers for delivery of therapeutic agents, including nucleic acids (DNA and RNA), for the prevention and treatment of various diseases. Much effort has been devoted to the implementation of microfluidic techniques for the production of monodisperse and stable LNPs and the improvement of encapsulation efficiency. Here, we developed three-dimensional (3D)-printed ring micromixers for the production of size-controllable and monodispersed LNPs with a high mRNA delivery efficiency. The effects of flow rate and ring shape asymmetry on the mixing performance were initially examined. Furthermore, the physicochemical properties (such as hydrodynamic diameter, polydispersity, and encapsulation efficiency) of the generated LNPs were quantified as a function of these physical parameters via biochemical analysis and cryo-electron microscopy imaging. With a high production rate of 68 mL/min, our 3D-printed ring micromixers can be used to manufacture LNPs with diameters less than 90 nm, low polydispersity (<0.2), and high mRNA encapsulation efficiency (>91%). Despite the simplicity of the ring-shaped mixer structure, we can produce mRNA-loaded LNPs with exceptional quality and high throughput, outperforming costly commercial micromixers.

Diffusion dynamics of an overdamped active ellipsoidal Brownian particle in two dimensions

Shape asymmetry is the most abundant in nature and has attracted considerable interest in recent research. The phenomenon is widely recognized: a free ellipsoidal Brownian particle displays anisotropic diffusion during short time intervals, which subsequently transitions to an isotropic diffusion pattern over longer timescales. We have further expanded this concept to incorporate active ellipsoidal particles characterized by an initial self-propelled velocity. This paper provides analytical and simulation results of diffusion dynamics of an active ellipsoidal particle. The active ellipsoidal particle manifests three distinct regimes in its diffusion dynamics over time. In the transient regime, it displays diffusive behavior followed by a super-diffusive phase, and in the longer time duration, it transitions to purely diffusive dynamics. We investigated the diffusion dynamics of a free particle as well as a particle in a harmonic trap, and a particle subject to a constant field force. Moreover, we have studied the rotational diffusion dynamics and torque production resulting from an external constant force field. Furthermore, our investigation extends to the examination of the scaled average velocity of an ellipsoidal active particle, considering both a constant force field and a one-dimensional ratchet.

Intensive agriculture increases fluctuating asymmetry of dorsal head shape in Iberian asp viper populations

AbstractHabitats resulting from agricultural intensification harbour a wide array of stressors for resident organisms. Environmental stress during development can leave imprints on the phenotype that are useful as indicators of its impairment. Among them, fluctuating asymmetry (FA), considered the morphological manifestation of developmental instability (DI), may reflect the increment of developmental noise and the inefficiency of buffering mechanisms. Here, we evaluated for the first time the impact of intensive agriculture on the development of a viviparous reptile, the asp viper, Vipera aspis (Linnaeus 1758), by means of FA. To this end, we first quantified unsigned asymmetry indexes (uAI) of dorsal head shape captured by geometric morphometrics (GM) and of seven pholidotic traits in 127 and 482 individuals, respectively. Using linear models, we then tested for variation in uAI according to habitat type. Furthermore, we tested the effect of climatic variables with a potential influence on development, and thus, on FA. We performed analyses at the V. aspis zinnikeri subspecies range and at the population level, including three well‐sampled natural localities (NAT) and three sites of intensive agriculture (AGR). We found significantly higher FA levels in dorsal head shape in individuals from agricultural habitats than in those from natural habitats, which suggests that asp viper development is impaired by stressors resulting from agricultural intensification. Our results also point to a lower sensitivity of traditional morphological tools to capture the signal that intensive agriculture leaves on development and a lack of capacity of climatic factors in isolation to predict variation in the degree of asymmetry. In addition to encouraging the use of high‐precision methods, we hypothesize on the overall effect of different stressors linked to intensive agriculture as the real constraint.

Shape variations of pelvis in different classes of dogs using geometric morphometry.

The ossa coxae are the bones that connect the hindlimbs to the axial skeleton. The right and left os coxae join at the median plane to form the pelvis. In this study, variations in pelvis shape and the asymmetric structure of the pelvis were investigated across different classes of dogs. To achieve this, computed tomography images of the pelvis were obtained from 35 dogs, and 3D modelling of the pelvis was created. Subsequently, 45 landmarks were identified on these models. As a result of the Principal Component Analysis, the shape variation was observed in the pelvic canal and crista iliaca. Directional asymmetry between Principal Component 1 and Principal Component 2 accounted for 33.84% of the total variation, while fluctuating asymmetry contributed 23.66%. Canonical variate analysis revealed that canonical variate (CV) 1 explained 56.56% of the total variation between groups, with CV 2 explained 28.98%. Male dogs exhibited greater pelvic variation than females. Procrustes ANOVA indicated that the greatest proportion of shape variation corresponds to the effect of differences among individuals. While directional asymmetry was statistically significant, fluctuating asymmetry was not. Male dogs displayed more pronounced pelvic shape asymmetry, typically towards the right. Gundogs had a narrower pelvic canal and a wide crista iliaca, whereas terriers had a wider pelvic canal and smaller crista iliaca in shape. Geometric morphometry enables statistical analysis and the derivation of average shapes from samples, making it a vital tool in veterinary anatomy. This study provides insights into pelvic geometric morphometry across different classes of dogs.

Combined axial load-biaxial bending interaction method for L-shaped CFSP shear walls

This paper reports the development of axial load and biaxial bending interaction method for L-shaped concrete-filled steel plate (CFSP) composite shear walls based on fiber section analysis model using the uniaxial constitutive relationship of materials. Owing to the complex interaction between the two perpendicular wall limbs (web and flange) of an L-shaped shear wall, the contour shape of the My-Mz curve is asymmetric. Linear transformation was employed to reduce the asymmetry of the contour shape, eliminate the influence of dimension, and perform parametric analysis. The analysis results indicate that when 0° ≤ θ(neutral axis angle) ≤ 90°, the influence of width-to-thickness ratio (hw1/bw) and shape coefficient (γ) on the coefficient that controls the contour shape (α) was negligible. The effect of shape coefficient (γ), steel content ratio (ρ), compressive strength of unconfined concrete (fc0), and yield strength of steel plate (fyp) on α is not significant for −180° ≤ θ ≤ −90°. Further, simplified equations were suggested to determine α. The axial load-moment interaction curve expressions for distinctive loading directions were determined by establishing the calculation method for the curve's characteristic points (axial load capacity, bending capacity, boundary points). Subsequently, the characteristic points were combined with the contour shape of the axial load-moment interaction curve derived by fitting the finite element simulation data to generate the axial load-moment interaction curve equations. A design approach was finally formulated based on the equations for the biaxial moment capacity curve and the axial load-moment interaction curves of the characteristic loading directions.

Asymmetrical Lateral Crus Steal in Geometric Tip Reshaping.

A key component of a well-performed rhinoplasty is to obtain the proper, aesthetic shape of the nasal tip. Various surgical techniques have been developed to achieve this effect. In this work, the author wanted to focus not only on the satisfactory shape of the nose, but above all on its main role-functionality. In this article, the asymmetrical lateral crus steal (ALCS) technique is proposed, which in its assumption will enable narrowing, better defining and rotating of the nasal tip, and at the same time enhancing nasal patency. We present a retrospective analysis within the group of 267 patients who underwent primary open-approach rhinoplasty that included the ALCS technique. The mean follow-up time was 12 months. A total of 232 patients achieved very good postoperative results without observation of any serious complications related to breathing difficulties or asymmetry of the nasal tip shape. ALCS is a relatively simple surgical technique to perform. The use of the ALCS suture creates the possibility of proper profiling of the nasal tip while improving the respiratory functions of the nose.

AI-generated faces show lower morphological diversity than real faces do

Some recent studies suggest that artificial intelligence can create realistic human faces subjectively unrecognizable from faces of real people. We have compared static facial photographs of 197 real men with a sample of 200 male faces generated by artificial intelligence to test whether they converge in basic morphological characteristic such as shape variation and bilateral asymmetry. Both datasets depicted standardized faces of European men with a neutral expression. Then we used geometric morphometrics to investigate their facial morphology and calculate the measures of shape variation and asymmetry. We found that the natural faces of real individuals were more variable in their facial shape than the artificially generated faces were. Moreover, the artificially synthesized faces showed lower levels of facial asymmetry than the control group. Despite the rapid development of generative adversarial networks, natural faces are thus still statistically distinguishable from the artificial ones by objective measurements. We recommend the researchers in face perception, that aim to use artificially generated faces as ecologically valid stimuli, to check whether their stimuli morphological variance is comparable with that of natural faces in a target population.

Hot subdwarfs in close binaries observed from space

Detailed studies of hot subdwarf B (sdB) stars with red dwarf (dM) or brown dwarf (BD) companions can shed light on the effects of binarity on late stellar evolution. Such systems exhibit a strong, quasi-sinusoidal reflection effect due to irradiation of the cool companion, and some even show primary and secondary eclipses. For this work, we computed Fourier transforms of TESS light curves of sdB+dM/BD binaries and investigate correlations between the relative amplitudes and phases of their harmonics and system parameters. We show that the reflection effect shape strongly depends on the orbital inclination, with nearly face-on systems having much more sinusoidal shapes than nearly edge-on systems. This information is encoded by the relative strength of the first harmonic in the Fourier transform. By comparing observations of solved systems to synthetic light curves generated by lcurve, we find that the inclination of non-eclipsing systems with high signal-to-noise light curves can be determined to within ≈10° simply by measuring their orbital periods and first harmonic strengths. We also discovered a slight asymmetry in the reflection effect shape of sdB+dM/BD binaries using the relative phase of the first harmonic. From our analysis of synthetic light curves, we conclude the asymmetry results from relativistic beaming of both stellar components. This marks the first time Doppler beaming has been detected in sdB+dM/BD systems. Although advanced modeling is necessary to quantify the effects of secondary parameters, such as limb darkening, the temperature ratio, and the radius ratio on the reflection effect shape, our pilot study demonstrates that it might be possible to extract both the inclination angle and cool companion velocity from the light curves of non-eclipsing systems.

Dimorphos’s Orbit Period Change and Attitude Perturbation due to Its Reshaping after the DART Impact

On 2022 September 26 (UTC), NASA's Double Asteroid Redirection Test (DART) mission achieved a successful impact on Dimorphos, the secondary component of the near-Earth binary asteroid system (65803) Didymos. Subsequent ground-based observations suggest a significant reshaping of Dimorphos, with its equatorial axis ratio changing from 1.06 to ∼1.3. Here we report the effects of this reshaping event on Dimorphos's orbit and attitude. Given the reported reshaping magnitude, our mutual dynamics simulations show that approximately 125 s of the observed 33 minute orbit period change after the DART impact may have resulted from reshaping. This value, however, is sensitive to the precise values of Dimorphos's post-impact axis ratios and may vary by up to 2 times that amount, reaching approximately 250 s within the current uncertainty range. While the rotational state of the body is stable at the currently estimated axis ratios, even minor changes in these ratios or the introduction of shape asymmetry can render its attitude unstable. The perturbation to Dimorphos’s orbital and rotational state delivered by the impact directly, combined with any reshaping, leads to a strong possibility for a tumbling rotation state. To accurately determine the momentum enhancement factor (β) through measurements by the European Space Agency’s Hera spacecraft and to evaluate the effectiveness of the kinetic deflection technique for future planetary defense initiatives, the effects of reshaping should not be overlooked.

How higher charmonia shape the puzzling data of the e+e−→ηJ/ψ cross section

Recently, the BESIII collaboration performed a precise measurement of the e+e−→ηJ/ψ cross section. It is puzzling that the resonance parameters of the reported Y(4230) show a substantial divergence from the previously measured results in both the open-charmed and hidden-charmed decay channels, and the line shape asymmetry of the data approaching 4.2 GeV also suggests that it might be difficult to characterize the details of the structure around 4.2 GeV by a single resonance. This has motivated our great curiosity about how the charmonium states are distributed in the measured energy range and how they shape the puzzling data of the e+e−→ηJ/ψ cross section. In this work, we use five theoretically constructed charmonia in the range of 4.0–4.5 GeV, i.e., ψ(4040), ψ(4160), ψ(4220), ψ(4380), and ψ(4415), to apply a combined fit to the data, in which their calculated decay ratios into ηJ/ψ via hadronic loop mechanism are taken as input. The fit results can reproduce the measured cross section data well, especially for the subtle line shape around 4.2 GeV, showing that the structure around 4.2 GeV is possible from the contribution of both ψ(4160) and ψ(4220). Published by the American Physical Society 2024