Radius Ratio Research Articles

Weakly nonlinear analysis of the onset of convection in rotating spherical shells

A weakly nonlinear study is numerically conducted to determine the behaviour near the onset of convection in rotating spherical shells. The mathematical and numerical procedure is described in generality, with the results presented for an Earth-like radius ratio. Through the weakly nonlinear analysis a Stuart–Landau equation is obtained for the amplitude of the convective instability, valid in the vicinity of its onset. Using this amplitude equation we derive a reduced order model for the saturation of the instability via nonlinear effects and can completely describe the resultant limit cycle without the need to solve initial value problems. In particular the weakly nonlinear analysis is able to determine whether convection onsets as a supercritical or subcritical Hopf bifurcation through solving only linear 2D problems, specifically one eigenvalue and two linear boundary value problems. Using this, we efficiently determine that convection can onset subcritically in a spherical shell for a range of Prandtl numbers if the shell is heated internally, confirming previous predictions. Furthermore, by examining the weakly nonlinear coefficients we show that it is the strong zonal flow created through Reynolds and thermal stresses that determines whether convection is supercritical or subcritical.

Longitudinal thermoelastic guided waves in functionally graded hollow cylinders with Green–Naghdi thermoelastic theory

Abstract At present, functional gradient material (FGM) pipelines are widely used in high-temperature environments, and the need for online inspection of such pipelines is becoming more and more urgent. Ultrasonic guided wave is undoubtedly one of the most promising methods for detection, but research on the propagation characteristics of thermoelastic guided wave in high-temperature FGM pipelines is still limited. In this paper, based on Green–Naghdi thermoelastic theory, a theoretical model of longitudinal thermoelastic guided wave in a hollow cylinder of FGM considering temperature effect is established by using the Voigt model, and the governing equations of thermoelastic guided wave are solved by the Legendre series method. The dispersion, displacement, and temperature distribution curves of guided waves in a hollow cylinder of FGM are plotted. The convergence of the method and the influence of the coupling of thermodynamic equations on the dispersion characteristics of guided waves are discussed. The influence of circumferential order, ratio of radius to thickness, gradient index, and temperature change on the dispersion characteristics of guided waves is analyzed. This study provides a theoretical basis for nondestructive testing and evaluation of high-temperature FGM pipelines.

A new method of shrink fit design for large-sized prestress die of hot extrusion: An example of large fan shaft

Due to the remarkable increase in the geometric size, interference fit amount and assembly difficulty of large-sized hot extrusion prestress die, the conventional methods (such as thick wall cylinder theory and empirical value method) of shrink fit design were inapplicable to the pre-stressed die for hot extrusion of fan shaft with a maximum radius of 255 mm. In this study, a new shrink fit design method for large-sized prestress die was proposed by using the finite element method, and two sets of the formulas and nomograms that were easy to use were obtained to determine the interference fit ratio β, the radius ratio of die and stress ring a21, a31. Finally, the shrink fit of the prestressed die for the hot extrusion of the large fan shaft was designed by adopting the introduced new approach, and the hot extrusion experiment was carried out. The results show that the prestressed die for hot extrusion of the large fan shaft designed by the new method not only reduced the material cost by 58.6% compared with the integral die, which had considerable economic advantages but also had outstanding stress-bearing capacity, which could be safely applied for the manufacture of large aero-engine fan shaft, which also verified the feasibility of the new shrink fit design method for large-sized hot extrusion prestress die.

Impact of Lorentz force on forced convective MHD Jeffrey fluid flow through annular sector duct

Present numerical simulation is to investigate the Lorentz force and constant axial pressure gradient effects on flow and heat transfer of electrically conducting magneto-hydrodynamic, [Formula: see text] Jeffrey fluid at fully developed region of annular sector duct. The law of conservation of energy is simulated by taking two thermally boundary conditions, known as [Formula: see text]1 thermally boundary condition (i.e. constant axial heat flux with uniform peripherally temperature in the annular sector duct’s cross section) and [Formula: see text] thermally boundary condition (i.e. constant temperature axially and peripherally). The numerical results are simulated in the following range of parameters: the ratio of radii, [Formula: see text], an apex angle of duct [Formula: see text] by using [Formula: see text] number of fins, Hartman number, [Formula: see text] and the ratio of relaxation time to retardation time, [Formula: see text]. During the simulation, it has been concluded that the other parameter corresponding to Jeffrey fluid (i.e. the retardation time, [Formula: see text]), has ignored due to minor attribution on flow and heat transfer by increasing the value from [Formula: see text] to [Formula: see text]. Hartman number, [Formula: see text], upgrades the [Formula: see text] up to 18.76% and 14.60%, while [Formula: see text] / [Formula: see text] up to 1.82% and 1.47%/1.55% and 1.29% for [Formula: see text] and [Formula: see text] respectively at [Formula: see text] and [Formula: see text] by increasing its value from 0 to 2. At higher [Formula: see text], the difference becomes ignored in the case of [Formula: see text] when we change the annular region along radial direction.

Properties of tsunami-generated electromagnetic variation observed on islands.

Electrically conductive seawater, moving in an ambient magnetic field, generates electromagnetic (EM) variations. Tsunamis are significant contributors to this phenomenon, inducing observable electric and magnetic fluctuations at seafloor and coastal observatories. While understanding of these occurrences in open oceans is robust, knowledge regarding their observation on islands remains limited. This article seeks, through the use of numerical experimentation, to enhance our understanding of tsunami-generated EM (TGEM) variations observed on islands. Utilizing simulations involving conical islands, we identify three key insights regarding EM intensity normalized by the height of incident tsunamis: (i) increased ocean depth surrounding the island amplifies tsunami EM signals, particularly for periods shorter than 20 min; (ii) magnetic field strength at the island is approximately comparable to that observed at the seafloor in the absence of the island when the island radius is smaller than 6 km; and (iii) electric field intensity at the island notably surpasses that observed at the seafloor, especially with smaller island radii ([Formula: see text] 6 km). Additionally, we establish that employing the ratio of island radius to tsunami wavelength near the island coast facilitates the derivation of empirical functions for this phenomenon.This article is part of the theme issue 'Magnetometric remote sensing of Earth and planetary oceans'.

Numerical analysis of heat transfer in annulus composite material at different operation conditions

In this article natural air convection in an inclined annular cage in three dimensions is investigated numerically. This study will examine the impact of the radius ratio of an annulus on heat transfer employing two distinct methods to optimizing effective thermal conductivity: minimizing and maximizing. The annulus is built of graphite/epoxy laminated composite material. There are 12 fins attached to the inner cylinder of the two concentric cylinders that make up the annulus enclosure, which is filled with porous medium. Regarding the annulus's inclination angle “δ”, two scenarios—a horizontal annulus and a vertical annulus—are considered. Constant walls temperature boundary condition and steady state conditions apply to the system with 0.2, 0.3, 0.4 and 0.5 different radius ratio, inclination angle (0o and 90o), and modified Rayleigh number “Ra*” ranged from 10 to 500, The Nusselt number decreased for all parameters as the radius ratio Rr decreased, indicating a wider cold outer cylinder gap. For large values of modified Rayleigh number, the average Nu number ”Nuavg.” decreases with an increase in δ, and increases with a rise in the modified Rayleigh number; for low values of Ra*, δ has no effect. For horizontal, and vertical states “δ=0 o, and 90o respectively, at higher and lower thermal conductivity, the divergence of the average Nusselt is 5.1% and 10%, respectively. In horizontal cylinder adding fins on the inner cylinder is more substantial for due to its impeding effect, and NuL increases with cylinder length. For the outer cold cylinder, a link between Ra* and δ and the average Nusselt number has been established.

Hybrid organic - inorganic filter system for cadmium ions adsorption from aqueous solutions

The study reflects on the problem of heavy metals, namely cadmium, polluting the natural environment. The goal was to select the most efficient adsorber enabling ion exchange between calcium and cadmium in an aqueous environment and subsequently design a material hybrid organic-inorganic, particle-fiber system that adsorbs cadmium from aqueous environments and will be easily included in the technological process. The novelty of this study lies in the use of waste food material – eggshells as a source of biogenic nanoparticles. These are applied to a nanofibrous structure made of polyvinyl butyral in amounts of 8 to 10 %wt by weight by the AC electrospinning. (The experiment was performed with these boundary conditions: temperature was 23°C, and humidity was 42%. The high-electrical voltage amplifier generated a sinusoidal waveform with a frequency of 50 Hz and an amplitude of 32 kV) and were used for ion exchange. In ion exchange, cadmium ions are exchanged with calcium ions based on the principle of chemical similarity of the two elements expressed by the z/r ratio (charge/ radius ratio), the z/r ratio is 2.02 for calcium ions Ca2+ and 2.06 for cadmium Cd2. Separateted nanoparticles of calcium carbonate obtained by burning eggshells (727°C) with dimensions from 100 to 200 nm and a specific surface area of 3.9 m2/g showed the highest adsorption capacity of 99.8%, synthetic calcium carbonate at 71.8%, and ground eggshells the lowest at 25.0%. Designed and laboratory-tested filter system of nanoparticles - nanofibers captures 95.6% and 96.8% of cadmium ions from an aqueous solution within 10 minutes and 90 minutes, respectively, at a concentration of cadmium ions of 10 mg/l, and at several nanoparticles of 0.3 g. The ion exchange is carried out only on the filter surface, and after a specific time, the calcium carbonate nanoparticles are released from the filter probably due to absence of chemical bond between nanoparticles and nanostructures or the low density of the nanofibrous structure. SEM, EDX, FTIR, BET and TGA analysis were used for material evaluation. The adsorption capacity of used nanoparticles and filter adsorbers was evaluated according to residual amounts of cadmium ions in aqueous solutions using ICP-IOS.

Heat Transfer in Annular Channels with the Inner Rotating Cylinder and the Radial Array of Cylinders

Numerical investigations of heat transfer for forced, mixed, and natural convection conditions within an annular channel are carried out. The main objective was to investigate, for the first time, the effect of the radial cylinder array on heat transfer in the annular channel with the rotating cylinder. The governing equations for velocity and temperature with the Boussinesq approximation were solved using the finite-volume method. The heat transfer quantities were obtained for different Rayleigh numbers (104–106), the radius ratios (1.4–2.6), the radial cylinder spacing, and for different rotating velocities in the form of the Richardson number (10−2–104). The Prandtl number was 0.7. It has been shown that radial cylinders do not influence significantly the intensity and the local distribution of heat transfer on the inner rotating cylinder. The Nusselt number was 1.4–2.0 times higher on the radial cylinder array for all convection modes relative to the outer flat surface. For all annuli gaps with radial cylinders, the maximal values of the Nusselt number were observed with an increase of the radial spacing of cylinders.

Hydrodynamic characteristics of cavity fluctuation behind a cone-rod assembly entering water

This study explores the phenomenon of cavity fluctuation occurring behind a cone entering water at a constant velocity. The current simulations reveal that cavity fluctuations arise following deep pinch-off, leading to pronounced pressure oscillations in both the water and air regions. Concurrently, ripples form along the cavity surface, extending from the nose to the tail, resulting in a wavy cylindrical cavity. Notably, when the water entry Froude number is below 10, the load on the cone is predominantly due to pressure oscillations induced by cavity fluctuations, which exceed the slamming load experienced during initial water impact. The study also identifies a significant impact of an attached rod on cavity evolution. Specifically, the frequency of cavity rippling increases with the rod's radius; however, when the rod-to-cone radius ratio is less than 20%, the rod's impact on the cavity dynamics becomes negligible. A theoretical analysis, modeling the cavity as a hollow cylindrical structure, is developed to elucidate the relationship between rippling frequency and rod size. The research results demonstrate that the cavity fluctuation frequency is inversely proportional to the difference in the squared radii of the cone and rod. Furthermore, when the scaling length of the cavity at the pinch-off moment exceeds a ratio of Lp/Rc > 6, the water entry cavity can be accurately modeled as a long cylindrical cavity. The numerical results confirm that the proposed theoretical model provides reliable predictions of the impact of a solid rod on the fluctuation characteristics of the cavity.

Impact of chimney structure and ambient wind on heat pipe heat dissipation

ABSTRACT Spontaneous combustion of coal gangue piles poses a significant environmental threat, and gravity heat pipes are considered a simple and effective solution for managing this issue. This study presents a novel method to achieve efficient heat pipe cooling without relying on ambient wind, by utilizing the chimney effect to enhance the heat dissipation efficiency of the condenser section. Initially, chimney parameters were optimized. Subsequently, the optimal chimney parameters were further examined under conditions with ambient wind. The results indicate that in the absence of ambient wind, a chimney height-to-condenser length ratio of approximately 6:1, a chimney inner radius-to-heat pipe radius ratio of about 1.4:1, and a chimney inlet radius-to-inner radius ratio of around 1.5:1 can increase the airflow velocity over the gravity heat pipe surface by a factor of three. When the chimney is located in an area with ambient wind, setting the ratio of inlet radius to chimney inner radius to 1:1 effectively reduces the adverse impact of wind. The optimized chimney can harness the heat generated by spontaneous combustion of coal gangue piles to enhance heat dissipation at the heat pipe condenser, thereby shortening the remediation time of the gangue pile.

Chest CT assess the impact of omalizumab treatment on airway remodeling in refractory asthma.

BackgroundTo evaluate the benefits of omalizumab treatment in patients through real-world follow-up and assess the impact of omalizumab treatment on airway remodeling using chest CT. MethodsThis is a single-center prospective, observational study included Chinese patients with refractory asthma who received omalizumab treatment from May 2021 to December 2022. We collected real-world clinical data, including their hospitalization information, pulmonary function, FENO, laboratory assessment, ACT scores, chest CT at baseline and every follow-up month. A comparison was made between the pre-treatment and post-treatment laboratory indicators, pulmonary function, airway parameters, and mucous plug scores under chest CT. ResultsThis study included a total of 61 patients with refractory asthma treated with omalizumab. The study found that: ①regardless of whether the treatment lasted for a full four months or not, it significantly improved patient asthma control scores and reduced hospitalization costs and length of stay (p<0.05). ②After four months of treatment, pulmonary ventilation function examination revealed significant improvements (p<0.05) in MEF75, MEF50, MEF75/25, PEF, and FEV1/FVC. ③After four months of omalizumab treatment, the ratio of wall thickness and outer radius (T/D) and wall area percentage (WA%) of the bronchial wall decreased significantly (p<0.05). ④After medication, the expression of airway mucous plugs decreased. ConclusionsOmalizumab treatment can reduce airway wall thickness, decrease the percentage of airway wall area, and the expression of airway mucous plugs, thereby improving airflow limitation. Utilizing chest CT provides a novel and intuitive assessment of the efficacy of omalizumab treatment. Trial registrationThis study was registered in Chinese Clinical Trial Registry, the number is ChiCTR2100046343.

The reverse-encapsulation and core-release process of a compound droplet under thermocapillary effects

This work demonstrates that a core-shell compound droplet can undergo separation into two different phase droplets or be transformed into a reverse-encapsulation droplet under the influence of thermocapillary effects. This study comprehensively investigates the thermocapillary effects on the migration, reverse-encapsulation, and core-release dynamics of compound droplets, with particular emphasis on the interactions among key dimensionless parameters, including the Marangoni number, Reynolds number, and the radius ratio of the inner to the middle fluid of a core-shell compound droplet. Using a reduction-consistent phase field model for incompressible N-phase flows, this research provides an in-depth analysis of the reverse-encapsulation and core-release processes of a compound droplet. The reverse-encapsulation process is characterized by three distinct stages: The initial acceleration stage, the encapsulation stage, and the post-transformation stage. Similarly, the core-release process also has three stages: The initial acceleration stage, the middle fluid contraction stage, and the independent movement stage. The results indicate that the Marangoni number has little influence on the migration velocity, while the tangential surface force (thermocapillary force) is the cause of these processes. The Reynolds number has a significant effect on the encapsulation dynamics, with higher values leading to slower and more turbulent processes. In addition, the radius ratio plays a critical role in determining the reverse-encapsulation and core-release processes, as well as migration behaviors. These findings advance our understanding of multiphase fluid dynamics and have significant implications for applications in microfluidics, targeted drug delivery, and advanced materials synthesis.

Controlling factors of fluid mobility in the tuff reservoirs of the Huoshiling formation, Dehui fault depression, southeastern Songliao Basin: insights from micro-nano pore structures

This study addresses the unclear understanding of the primary factors controlling fluid mobility in the tuff reservoirs of the Huoshiling Formation from the Dehui Fault Depression, southeastern Songliao Basin. Through physical property analysis, X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM), thin section (TS), pressure-controlled porosimetry (PCP), rate-controlled porosimetry (RCP), and nuclear magnetic resonance experiments (NMR) on ten tuff samples, we conducted a comprehensive and in-depth exploration of the influencing factors that control the mobility of reservoir fluids. The results indicate: 1) The primary mineral types in the tuff reservoirs are quartz, feldspar, and clay minerals, with porosity predominantly characterized by dissolution pores and intergranular pores; 2) Based on the morphology of PCP intrusion curves, the tuff samples from the study area can be categorized into three types, with reservoir quality progressively deteriorating from Type I to Type III; 3) Compared to the movable fluids saturation (MFS), movable fluids porosity (MFP) is more suitable for characterizing fluid mobility. The mobility of fluids is influenced by various factors such as mineral composition, physical property, pore-throat connectivity, pore type and heterogeneity. MFS and MFP show a positive correlation with permeability, the content of quartz and feldspar, median pore-throat radius (R50), average throat radius (ATR), average pore-throat radius ratio (APT), T2 cutoff value (T2-C), average throat radius (RT), sorting coefficient (SC), and intergranular pore dominate space (Inter-DS), while a negative correlation with the content of calcite and clay minerals, average pore-throat radius ratio, and the fractal dimension from NMR (DNMR). This study elucidates the influencing factors of fluid mobility in tuff reservoirs, which has important reference significance for the scientific development of this type of gas reservoir.

Differential correlations of refractive error, axial length, and axial length-to-corneal curvature ratio with anterior segment biometrics in myopic refractive surgery candidates

PurposeTo investigate the correlations of spherical equivalent (SE), axial length (AL), and AL to corneal curvature radius ratio (AL/CR) with anterior segment biometrics in candidates for myopic refractive surgery. MethodsAnterior segment biometrics of 2,478 myopic refractive surgery candidates measured by Pentacam were collected retrospectively. The anterior segment biometrics included anterior corneal curvature (ACC), posterior corneal curvature (PCC), white-to-white corneal diameter (WTW), central corneal thickness (CCT), corneal volume at 3 mm (CV), anterior corneal astigmatism (ACA), posterior corneal astigmatism (PCA), anterior corneal eccentricity (ACE), posterior corneal eccentricity (PCE), anterior corneal asphericity (ACAP), posterior corneal asphericity (PCAP), anterior chamber depth (ACD), and anterior chamber volume (ACV). The eyes were divided into four groups according to the AL: group 1, AL≤24 mm; group 2, 24mm<AL≤26 mm; group 3, 26mm<AL≤28 mm; group 4, AL≥28mm. The correlations between these biometrics with SE, AL, and AL/CR were assessed by Pearson or Spearman correlation tests. A correlation with a coefficient ≥0.3 and a p value <0.05 were considered significant. ResultsIn all AL groups, ACC was positively correlated with SE (r = 0.446 to 0.620) and negatively correlated with AL/CR (r = -0.704 to -0.894), whereas PCC was positively correlated with SE (r = 0.394 to 0.612) and negatively correlated with AL/CR (r = -0.606 to -0.787). WTW was positively correlated with SE (r = 0.304 to 0.474) in every group, and negatively correlated with AL/CR (r = -0.405 and -0.412) in group 1 and 4. ACA was positively correlated with AL (r = 0.310) and AL/CR (r = -0.333) in group 4. ACD was negatively correlated with AL (r = -0.304) in group 4, and positively correlated with AL/CR (r = -0.325) in group 2. ACV was positively correlated with SE (r = 0.344) in group 4, and positively correlated with AL (r = 0.303) in group 2. CCT, CV, PCA, ACE, PCE, ACAP, and PCAP was not significantly correlated with SE, AL, or AL/CR in any of group. ConclusionsDifferential correlations were observed between anterior segment biometrics and SE, AL, and AL/CR, suggesting that various myopia indicators have different effects on ocular structures. These findings may help identify the ocular structures that can be targeted of refractive surgery.

Laboratory test and design methods of horizontal-ellipse corrugated-steel-plate–utility-tunnel with varying top–side plate ratios

Corrugated steel-plate culverts, particularly in horizontal ellipse form, are commonly used in large-span projects. Despite the guidelines on plate radius ratios, the impact of these ratios on mechanical properties remains unexplored. This gap highlights the need for research to guide utility tunnel design because existing studies mainly focus on round culverts compressed into elliptical shapes. Therefore, this study conducted backfill, simulated vehicle live load, and ultimate-load tests on two horizontal-ellipse corrugated steel utility tunnel structures with different top-side plate ratios to examine their response characteristics under various load conditions. Moreover, they were compared with those of existing design methods to offer new insights for the design analysis of soil–steel structures. The results demonstrated that the ratio significantly influenced bending moment distribution, and the critical section was concentrated beneath the loading pad for live loads. The ultimate capacity varied with the ratio, with the higher ratio specimen reaching approximately 92.5 % of the capacity of its counterpart. Both specimens failed via tri-plastic hinge mechanisms, with reduced capacity as corrugations flattened. The Canadian Highway Bridge Design Code, which considers thrust force and bending moment, accurately predicted bearing capacity than the other methods in this study. These findings are vital for optimising design and ensuring safety in horizontal-ellipse corrugated steel utility tunnels.

On the boundary-layer asymmetry in two-dimensional annular Rayleigh–Bénard convection subject to radial gravity

Radial unstable stratification is a potential source of turbulence in the cold regions of accretion disks. To investigate this thermal effect, here we focus on two-dimensional Rayleigh–Bénard convection in an annulus subject to radially dependent gravitational acceleration $g \propto 1/r$ . Next to the Rayleigh number $Ra$ and Prandtl number $Pr$ , the radius ratio $\eta$ , defined as the ratio of inner and outer cylinder radii, is a crucial parameter governing the flow dynamics. Using direct numerical simulations for $Pr=1$ and $Ra$ in the range from $10^7$ to $10^{10}$ , we explore how variations in $\eta$ influence the asymmetry in the flow field, particularly in the boundary layers. Our results show that in the studied parameter range, the flow is dominated by convective rolls and that the thermal boundary-layer (TBL) thickness ratio between the inner and outer boundaries varies as $\eta ^{1/2}$ . This scaling is attributed to the equality of velocity scales in the inner ( $u_i$ ) and outer ( $u_o$ ) regions. We further derive that the temperature drops in the inner and outer TBLs scale as $1/(1+\eta ^{1/2})$ and $\eta ^{1/2}/(1+\eta ^{1/2})$ , respectively. The scalings and the temperature drops are in perfect agreement with the numerical data.

Linear instability in thermally stratified quasi-Keplerian flows

Quasi-Keplerian flow, a special regime of Taylor–Couette co-rotating flow, is of great astrophysical interest for studying angular momentum transport in accretion disks. The well-known magnetorotational instability (MRI) successfully explains the flow instability and generation of turbulence in certain accretion disks, but fails to account for these phenomena in protoplanetary disks where magnetic effects are negligible. Given the intrinsic decrease of the temperature in these disks, we examine the effect of radial thermal stratification on three-dimensional global disturbances in linearised quasi-Keplerian flows under radial gravitational acceleration mimicking stellar gravity. Our results show a thermo-hydrodynamic linear instability for both axisymmetric and non-axisymmetric modes across a broad parameter space of the thermally stratified quasi-Keplerian flow. Generally, a decreasing Richardson or Prandtl number stabilises the flow, while a reduced radius ratio destabilises it. This work also provides a quantitative characterisation of the instability. At low Prandtl numbers $Pr$ , we observe a scaling relation of the linear critical Taylor number $Ta_c\propto Pr^{-6/5}$ . Extrapolating the observed scaling to high $Ta$ and low $Pr$ may suggest the relevance of the instability to accretion disks. Moreover, even slight thermal stratification, characterised by a low Richardson number, can trigger the flow instability with a small axial wavelength. These findings are qualitatively consistent with the results from a traditional local stability analysis based on short wave approximations. Our study refines the thermally induced linearly unstable transition route in protoplanetary disks to explain angular momentum transport in dead zones where MRI is ineffective.

Dynamic Modeling and Stability Analysis for Spinning Circular Solar Sail Considering Periodically Time-Varying Characteristics

The spinning circular solar sail is a promising spacecraft for long-duration missions. This work reveals its structural dynamic and stability behavior under the periodically time-varying solar radiation pressure and gravitational force. The geometric stiffness generated by the centrifugal force due to spinning and the coupling effect between the deformation and solar radiation pressure are taken into account. The von Kármán plate theory is adopted by neglecting the high-frequency in-plane vibrations and considering the effect of the in-plane internal force on the transverse vibration. The partial differential equation of the spinning solar sail is derived and further spatially discretized into periodically time-varying equations of motion. Effects of Poisson ratio and radius ratio on natural frequencies and mode shapes are analyzed, and curve veering phenomena are then observed. Steady-state periodic responses of the solar sail under the solar radiation pressure with different orbit distances, incident angles, and spinning angular velocities are analyzed. The stability analysis is rigorously performed by the Floquet theory rather than the commonly used approach of conducting the eigenvalue analysis at a series of specific discrete time nodes. Moreover, the stability boundary associated with transverse vibrations is determined, which contributes to the parameter design of the spinning solar sail.

Correlation between repeated low-level red light-induced afterimage and axial changes in myopia control

PurposeTo explore the correlation between afterimages induced by repeated low-level red light (RLRL) and changes in refraction. MethodPatients who used RLRL for myopia control from 2023.02 to 2024.06 were included in this study. The afterimage appeared on a gray background (RGB 217,217,217; Lab 87,0,0). Afterimage color was recorded with CIELAB nomenclature (R, G, B; L, a, b), and afterimage duration (T) was recorded in seconds. Axial length (AL) and axial length-to-corneal radius ratio (AL/CR) were followed up at 1-, and 3-month. Participants were divided into groups based on a = 0 for GroupR (a>0,red bias in afterimage) and GroupG (a<0,green bias in afterimage); b = 0 for GroupY (b>0,yellow bias in afterimage) and GroupB (b<0,blue bias in afterimage), and T = 50.50 for GroupS (T<50.50,shorter afterimage duration) and GroupL (T>50.50,longer afterimage duration). ResultsA total of 52 participants were included in this study, with an age of 9.25 (1.75) years, 27 (51.92 %) males. The T median (P25, P75) was 50.50 (31.25,85.50) s. After RLRL treatment, divided by a = 0, GroupG showed significantly more shortening in the AL changes than GroupR at 1month and 3months (both P<0.05) and the AL/CR changes difference was not significant. Divided by T = 50.50, GroupS showed significantly greater shortening in the AL changes than GroupL at only 1month (P<0.05) and the AL/CR changes difference was not significant. Divided by b = 0, the difference between GroupY and GroupB was not statistically significant (P>0.05). ConclusionThe change of AL after RLRL treatment showed a correlation to the afterimage. Patients with green afterimage and shorter afterimage duration have a better AL shortening after RLRL treatment. Afterimage may serve as a biomarker for more effective myopia control.

The effect of hygroscopic liquids on the spatial controlling of condensation on low-temperature surfaces

Condensation is a ubiquitous natural phenomenon with both detrimental and beneficial implications. The key point to minimize its harmful effects while harnessing its potential for various applications is the spatial controlling of condensation. In recent years, using hygroscopic liquids for spatially controlling condensation has gradually emerged as a promising strategy. However, the underlying mechanisms and influencing parameters of controlling condensation with hygroscopic liquids remain insufficiently understood. In this paper, the effect of hygroscopic droplets in suppressing condensation on low-temperature surfaces, specifically -15 ℃ to 15 ℃, under different conditions, including substrate temperature, cooling time, droplet volume are studied. A typical hygroscopic liquid, dipropylene glycol, was employed to illustrate this issue. The results indicated that distinct ring-shaped dry zone forms around dipropylene glycol droplets on low-temperature surfaces, evidencing their efficacy in inhibiting condensation. Experiments and theoretical analysis reveal that the ratio of the dry-zone radius to the droplet radius is a function of substrate surface temperature, scaling as 1/(Tdew-Tc). The results also show that cooling time has a negligible effect on this ratio over short periods. Furthermore, the ratio slightly decreases with increasing droplet volume at higher substrate temperatures, while remaining nearly constant at lower temperatures. These findings may enhance our understanding of the condensation inhibition effect of hygroscopic droplets and also provide valuable insights for potential applications in condensation control.