Curvature Values Research Articles

Potential damage area detection of bridges based on single-temporal point cloud

Abstract With advantages of 3D representation, non-contact measurements and intensive sampling capability, it has been a research hotspot to detect the potential damage area of bridges with point cloud by TLS. However, TLS is commonly used to detect a potential damage area by comparing multi-temporal point cloud data, which limits the timeliness of bridge inspection. Therefore, aiming to accurately detect the potential damage areas of bridges with single-temporal point cloud, this paper proposes a normalized normal vector constrained coordinate transformation method. First, the distribution of sharp features is revealed in a single-temporal point cloud at potential damage areas, and a neighborhood growth method constrained by the normal distance is proposed to eliminate the sharp features in point cloud, which is prone to cause incorrect or missing curvature values from point cloud. Second, a normalized normal vector constrained coordinate transformation method is proposed to construct Gaussian curvature model, which can improve the accuracy of point cloud curvature and accurately detect the potential damage areas in bridges. At last, an evaluation criterion is proposed to quantify the bridge condition by integrating the characteristics of small-span concrete bridges in urban areas with actual damage data from the experimental bridges. The experimental results show that the proposed method can effectively detect the potential damage areas of the measured bridges.

Shape of the Sagittal Curvatures of the Spine in Young Female Volleyball Players

Background: The issue of the relation betweeen training loads on the shape of the spine of young players is of significant importance, as with the advancement of training seniority, unfavorable changes may be perpetuated resulting in possible consequences in the next stages of ontogenesis. The aim of this study was to assess the formation of the sagittal curvatures of the spine in girls practicing volleyball versus their nonpractising peers. Methods: We examined 60 girls aged 10–13 years, including 30 volleyball players and 30 untrained peers. The Baseline Bubble inclinometer was applied as a research. The data were analyzed based on Mann–Whitney U test and Pearson Chi-square test. Results. There were statistically significant intergroup differences in lumbar lordosis curvature values (Z = −2.67; p = 0.007). The prevalence of correctness values of the thoracic kyphosis curvature, was group-dependent (χ2(1) = 4.34; p = 0.037). Group also determined the prevalence of lumbar lordosis normalities (χ2(1) = 5.41; p = 0.020). Conclusions. Volleyball has a beneficial effect on the formation of the thoracic kyphosis, while the lumbar lordosis is shallowed under the influence of training. This indicates the need for a holistic approach to player training and the need to supplement the technique and tactics training with exercises to strengthen the muscles that stabilize the lumbar spine, improve spinal mobility, learn how to control the anterior tilt of the pelvis and train the fascia.

Interventricular abnormal septum displacement as contributory mechanism for impaired peak oxygen consumption and exercise cardiac output response in heart failure

Abstract Background In Heart failure (HF), the role of septum position and abnormal right ventricular (RV) geometry in determining exercise performance is unknown. Especially an abnormal interventricular septal (IVS) position is a well-known sign of RV pressure overload which affects left ventricular filling and output due to interdependence. Aim We postulated that an abnormal septum displacement during exercise and RV geometry alteration would affect peak exercise oxygen consumption (VO2) and cardiac output (CO) increase. Methods 17 HF patients with reduced ejection fraction (HFrEF) (mean age 71±12) underwent a cardiopulmonary exercise testing imaging (iCPET) with RV 3D-imaging analysis and were compared with a control population (mean age 67±14). 3D imaging of the RV chamber was examined off-line using the 4D RV TomTec software and obtained 3D mesh of the RV model using custom software to obtain the mean curvature value of IVS in 4 regions of: inflow tract (RVIT), outflow tract (RVOT), apical and body.We acquired measurements of curvature during end-diastole (ED) and at end systole (ES) phases and obtained a parametric curvature map. Results HF patients typically exhibited an abnormal of septal curve, with a more leftward configuration either at rest and under exercise (rest =−0.01±0.004 at ED, and −0.01±0.006 at ES; peak exercise= −0.01±0.004 at ED, and −0.01±0.004 at ES, Figure) compared to controls (rest=−0.02±0.003 at ED, and −0.02±0.005 at ES; peak exercise −0.02±0.008 at ED, and −0.03±0.006 at ES, Figure). Notably, the degree of the IVS curvature was found to linearly correlate with an impaired gas exchange performance as lower peak VO2 and a limited CO in HF (respectively r=0.62, p<0.001 and r=0.5, p<0.001 at ED during exercise; r=0.34, p<0.001 at ES during exercise, Figure). Conclusions In HF, the RV geometrical alterations reflected by an abnormal IVS displacement appear as novel contributory factors to a reduced exercise performance, impaired oxygen uptake and decreased CO.

Comprehensive Review of Tunnel Blasting Evaluation Techniques and Innovative Half Porosity Assessment Using 3D Image Reconstruction

To meet the increasing demand for rapid and efficient evaluation of tunnel blasting quality, this study presents To meet the increasing demand for rapid and efficient evaluation of tunnel blasting quality, this study presents a comprehensive review of the current state of the art in tunnel blasting evaluation, organized into five key areas: Blasting Techniques and Optimization, 3D Reconstruction and Visualization, Monitoring and Assessment Technologies, Automation and Advanced Techniques, and Half Porosity in Tunnel Blasting. Each section provides an indepth analysis of the latest research and developments, offering insights into enhancing blasting efficiency, improving safety, and optimizing tunnel design. Building on this foundation, we introduce a digital identification method for assessing half porosity through 3D image reconstruction. Utilizing the Structure from Motion (SFM) technique, we re-construct the 3D contours of tunnel surfaces and bench faces after blasting. Curvature values are employed as key indicators for extracting 3D point cloud data from boreholes. The acquired postblasting point cloud data is processed using advanced software that incorporates the RANSAC algorithm to accurately project and fit the borehole data, leading to the determination of the target circle and borehole axis. The characteristics of the boreholes are analyzed based on the fitting results, culminating in the calculation of half porosity. Field experiments conducted on the Huangtai Tunnel (AK20 + 970.5 to AK25 + 434), part of the new National Highway 109 project, provided data from shell holes generated during blasting. These data were analyzed and compared with traditional onsite measurements to validate the proposed method’s effectiveness. The computed half porosity value using this technique was 58.7%, showing minimal deviation from the traditional measurement of 60%. This methodology offers significant advantages over conventional measurement techniques, including easier equipment acquisition, non-interference with construction activities, a comprehensive detection range, rapid processing speed, reduced costs, and improved accuracy. The findings demonstrate the method’s potential for broader application in tunnel blasting assessments.

Heart rate variability series during physical activity analyzed with multifractal techniques

Abstract Our study uses multifractal techniques to analyze time series of heart rate variability series (RR time series) during rest and physical activity. Subsets of the RR time series data were extracted for each stage. The multifractal spectra of the RR time series data were constructed using the method developed by Chhabra and Jensen. Then, parameters such as width, symmetry, and curvature of the multifractal spectra were calculated. The multifractal spectra obtained at resting stage were broad, skewed to the right, and they had small curvatures around in the maximum. On the contrary, the subsets of the RR time series obtained during physical activity were narrow, skewed to the left, and showed an increased curvature value around the maximum. In addition, these multifractal spectrum parameters shown significant differences in series of subjects who perform physical activity regularly and sedentary. Furthermore, the results obtained from this study were compared with data from previous works involving patients with congestive heart failure and healthy subjects.

KeraRing Implantation with Femtosecond Laser in Keratoconus Treatment at Different Stages

Objective: To investigate the reliability and effectiveness of femtosecond laser-assisted KeraRing (Mediphacos, Belo Horizonte, Brazil) implantation in treating keratoconus. Methods: Intrastromal corneal ring segments (KeraRing, Mediphacos, Brazil) were implanted in 15 eyes of 14 patients unable to tolerate contact lenses. Femtosecond laser (Intralase, 60 Hz) was used for corneal tunnel creation. Based on the distribution of ectatic area on the cornea, dual segments were implanted in 9 eyes, while single segments were implanted in 6 eyes. Preoperative and postoperative uncorrected visual acuity (UCVA), best-corrected visual acuity (BCVA), objective and subjective refraction, and topographic corneal curvature (K) values of the cases were compared using the Wilcoxon test. Results: The mean age of patients was 25±7.46 (range: 15-39) years, with a mean postoperative follow-up period of 10.8±7.37 (range: 1-24 months). BCVA improved in all eyes during the follow-up period, increasing from a mean of 0.12±0.1 to 0.38±0.24 (p

Accuracy of implant custom abutments according to different radius of curvature value

Accuracy of implant custom abutments according to different radius of curvature value

SAP 2000 Validates Deflection in Multilayer Test

Multilayer testing is one of the non-standard testing methods that has the potential to be developed in the future, so it requires special validation of its results. In this study, validation was carried out using SAP 2000 software, focusing on the calculation of downward curvature that occurs under the concrete layer. The study was conducted on test objects in closed conditions with certain dimensions. The test results showed that there was a difference between the downward curvature values ​​produced from multilayer testing and calculations with SAP 2000. The difference in downward curvature between the two methods was recorded at 15.29%. This difference indicates that more validation is needed to ensure the accuracy of the multilayer testing method in future structural applications.

Prediction of the structure of polymer-coated cardboards produced by thermocompression using I-optimal design of experiment.

The production of contrasted polymer-coated cardboards is necessary to establish the structure/properties relationships and produce the « just necessary » packaging materials. For that purpose, the impact of the processing parameters on the resulting structure of polymer-coated cardboards was modeled using a statistical Design of Experiment (DOE) approach. Five independent factors were considered: three numeric continuous factors, the pressure, the temperature, and the duration of thermocompression, one numeric discrete factor, the initial polymer film thickness, and one categorical factor, the cardboard basis weight. Four responses were considered: the thicknesses of each of the three layers constituting polymer-coated cardboards (i.e., the free polymer, the impregnated, and the free cardboard) and the material’s curvature. The choice of the adequate DOE was first assessed using a Scoping Design and coupled with the characterization of the used polymer, i.e., poly(3-hydroxybutyrate-co-3-hydroxyvalerate (PHBV). The I-optimal DOE was found to be the most suitable and was therefore implemented. To validate the model, the DOE was then used to produce two targeted structures, one with no impregnation of the polymer and another one with a complete impregnation of the cardboard. The values of thicknesses and curvature were not significantly different from the model predictions, therefore verifying the model.

Geospatial modeling of wildfire susceptibility on a national scale in Montenegro: A comparative evaluation of F-AHP and FR methodologies

Abstract Wildfires pose a significant ecological, environmental, and socioeconomic challenge in southeastern Europe. The preservation of wildlands is not only essential but also a foremost priority for Montenegro, a country recognized as the world’s first ecological state. Consequently, the development of optimal methodologies and models is of paramount importance to enhance fire protection measures. With this objective in mind, this study strives to create a wildfire susceptibility model on a national scale for Montenegro. The study employed seven natural and anthropogenic causative criteria: vegetation type; aspect; slope; elevation; climate classification; distance from road; and population. The modeling process integrates both natural and anthropogenic causal criteria, employing the Fuzzy Analytic Hierarchy Process (F-AHP) and Frequency Ratio (FR) within geoinformatics environment. The outcomes of the F-AHP model reveal that 72.84% of the total area is categorized as having high to very high susceptibility. Conversely, based on the FR model, only 29.07% of the area falls within these susceptibility levels. In terms of validation, the area under curvature values indicates good performance of the F-AHP model. In contrast, the FR model demonstrates poor performance. These novel findings, pertaining to Montenegro at a national scale, offer valuable insights for preemptive wildfire safeguarding efforts. Moreover, the methodologies employed, with necessary modifications, hold potential for application in geographically diverse regions.

Constructing superparaelectric state for NaNbO3-based ceramics electrostatic supercapacitors

A crucial prerequisite for developing high-performance energy storage devices for high pulsed power systems is the urgent necessity to acquire dielectric ceramics with high recoverable energy density (Wrec) and ultrahigh energy efficiency (η), particularly through an environmentally friendly lead-free approach. Here, superparaelectric state with ultra-small nanodomains in NaNbO3-based ceramics is successfully induced by implementing a superparaelectric modulation strategy. This innovation not only reduces the curvature value of the polarization–electric field (P-E) curve, but also produces negligible remanent polarization (Pr) and a linear-like P-E curve, obtaining outstanding efficiency (η) of 92.2 % and high energy storage density (Wrec) of 7.05 J/cm3. This achievement not only opens new avenues for enhancing the energy storage performance of dielectric ceramics but also heralds extensive applications of this material in high-pulse power electronic devices.

Novel treatments for the radiative-magnetive Ellis hybrid nanofluids flow inside stenotic shrinking artery with imposed convective slip boundary conditions and entropy generation: An application in cardiovascular disease

This research delves into the theoretical and computational analysis of blood flow dynamics within a constricted, porous artery using a novel hybrid nanofluid model known as the Ellis model, which incorporates gold and silver nanoparticles. The investigation encompasses a spectrum of physical phenomena, including magnetic effects, Darcy-Forchheimer porous medium flow, viscous dissipation, and non-linear thermal radiation. Additionally, a convective slip boundary condition is applied at the arterial surface. By transforming the governing nonlinear partial differential equations into nonlinear ordinary differential equations, the study facilitates a comprehensive analysis. Subsequently, employing the bvp4c algorithm in MATLAB enables the numerical solution of these equations, yielding dual solutions for the system. Graphical representations are then utilized to elucidate various profiles, including velocity, temperature, skin friction coefficient, Nusselt number, and entropy. The findings highlight intriguing trends, such as the contrasting behaviors of skin friction and Nusselt number between the Au/Blood nanofluid and the Au − Ag/Blood hybrid nanofluid. Dual solutions can not be found beyond the critical values of suction (Sc) and curvature (γc) parameters. The critical values Sc are 2.3554 and 2.3170; γc are 0.2248 and 0.2654 for Au/Blood and Au − Ag/Blood, respectively. Moreover, insights are gained into the influence of magnetic field, Darcy-Forchheimer parameters on velocity reduction and the effect of the Ellis fluid, velocity slip parameters on temperature reduction profile. The heat transference rate increases in the situation of augmentation in shrinking parameyer and thermal radiation effect, which helps remove the toxic plaque from the blood flowing at the surface of the artery. Notably, the study underscores the significance of nanoparticle presence, porous and magnetic field parameters in enhancing entropy near the artery, with implications for cancer treatment and stroke prevention strategies.

Transitioning Low-Temperature GDC Socs: Lab to Commercialization Scale

Solid oxide fuel cells (SOFCs) electrochemically convert hydrogen and oxygen into electricity, heat, and water with high efficiency (~55%) [1], while in reverse operation, water and electricity are converted to hydrogen and oxygen in solid oxide electrolysis cells (SOECs). Appropriately designed solid oxide cells (SOCs) can operate in both SOFC and SOEC mode.Conventional SOCs typically demand elevated operating temperatures (800-1000°C), resulting in higher cost and accelerated degradation issues. Lowering operating temperatures below 600°C reduces thermal stresses, shortens start-up times, and broadens applications [2].Ce1-xGdxO2-δ (GDC), due to its superior oxygen ion conductivity at reduced temperatures, has lower ohmic losses than competing electrolyte materials. Thus, our 1.2 cm diameter circular anode supported GDC cell with 0.31 cm2 active area exhibits exceptional power densities, reaching approximately 3 watt per square centimeter at 650°C. Through optimal design, these cells exhibit exceptional performances in fuel cell mode, significantly enhancing efficiency and effectiveness when operating as an electrolyzer for fuel generation. This advance in performance is a result of mitigating the leakage current issues typical of ceria-based electrolytes through precise engineering of the cathodic microstructure and surface chemistry modification [3].The transition from lab-scale to large-scale commercialization (with active areas of 16 cm² &; 81 cm²) presents significant challenges such as tailoring material properties for large-cell versus button-cell synthesis while maintaining high performance levels.In this work we explore the challenges encountered during the scaling-up process. We report on fabrication strategies employed to achieve cell flatness, maintain high efficiency, ensure cost-effectiveness, and achieve long-term stability. Specifically, we have fabricated graded anode-supported cells [4] by developing an innovative lamination strategy involving tapes oriented perpendicular to each other. This approach notably contributed to achieving superior electrolyte densification and resulted in significantly flatter (low curvature values) with respect to both horizontal and vertical axes in cartesian coordinate space. When compared to the flatness values of 10x10 cm2 commercially available cells, our cells demonstrated remarkably flatter curvatures as shown in figure 1. This characteristic has proven highly beneficial for stack assembly, minimizing issues such as cell cracking and reducing sealing-related problems. By optimizing the cathode scaffold and infiltration process on larger area cells through a spray-coating machine, scaling up challenges are effectively mitigated compared to the button cell approach, where scaffold preparation and infiltration were performed using blade coating and a hand pipette, respectively. This approach effectively tackles electronic conduction issues in ceria-based electrolytes, leading to higher Open Circuit Voltages (OCVs) in fuel cell mode and increased efficiencies in reversible mode.

Analysis of Spinal-Pelvic Sagittal Plane Parameters in Patients with Lumbar Vertebral Posterior Ring Apophysis Separation

To investigate the characteristics of the spinal-pelvic sagittal sequence in patients with lumbar vertebral posterior ring apophysis separation (PRAS). A retrospective analysis was conducted on 119 hospitalized patients with PRAS, and 119 adults without symptoms of low back and leg pain were selected as the control. General data and spinal-pelvic sagittal parameters were collected and analyzed. Compared to the control group, the pelvic incidence (PI), sacral slope (SS), lumbar lordosis (LL), and thoracic kyphosis of the PRAS group were significantly lower, while the pelvic tilt (PT), sagittal vertical axis, and PI minus LL were significantly higher. There was no significant difference in thoracolumbar kyphosis between the 2 groups. In patients with PRAS, the LL value of lumbar curvature was moderately correlated with thoracic kyphosis and SS, while PI, PT, and SS were pairwise correlated, indicating that the change in one parameter is often accompanied by simultaneous changes in other parameters if PRAS happens. The correlation between different parameters could provide guidance for the diagnosis of PRAS. In terms of LL type, the PRAS group was mainly of Roussouly type I, while the control group was mainly of type II, and the difference in the composition ratio was statistically significant. As reflected by the spinal-pelvic sagittal parameters, the patients with PRAS exhibited reduced thoracic and lumbar curvature, posterior PT, and fewer vertebral bodies involved in LL. These morphological characteristics indicate the changes of the mechanical structure of the spine.

Effect of Temperature on Damage Identification of Laminated Composite by Means Numerical Methods

This study aims to examine the effect of temperature on damage detection in laminated composite materials. In this context, a carbon-reinforced composite plate with [0/90]s stacking sequence is modeled as intact and delaminated by the finite element method. The dimensions, thicknesses, materials used, and stacking sequences of the plates modeled as intact and delaminated are the same. The delamination in the delaminated plate is modeled as the gap in the middle of the plate. These modeled plates were analyzed at different temperature values between -50oC / +50oC. The natural frequencies, mode shapes, and modal curvatures of the plate were obtained by modal analysis. The variation of these data obtained with temperature was examined and the effect of temperature on these data was compared. According to the analysis results, it was observed that the effect of temperature on natural frequency values and modal curvature values was similar to the effect of delamination. The decrease in natural frequencies and the changes in modal curvatures due to delamination occurred with the increase in temperature even in the absence of delamination.

On the dual diffusion flow of Powell–Eyring hybrid nanofluid with motile microorganism and non-uniform heat source using Darcy–Forchheimer model

This communication elaborates the rheological behavior of bioconvection flow of Powell–Eyring hybrid nanofluid over a stretchable heated cylinder embedded in Darcy–Forchheimer porous medium. The single and two-phase nanofluid models are used as mixture model by taking volumetric friction and dual diffusion of injected nanomaterial’s, while the Buongiorno model takes the dual diffusion of nanomaterials, allowing us to evaluate the thermophoresis and Brownian diffusion properties. The governing equations are solved with an efficient Runge–Kutta–Fehlberg numerical technique. The effects of appropriate parameters on flow, temperature, concentration, and motile microorganism. Our findings reveal that the fluid velocity increases with curvature parameter, while detract with Darcy and porosity parameter. Temperature is increasing function of Brownian, thermophoresis and heat source parameters. The concentration and motile profile increases with curvature parameter. An escalating trend for energy and mass transport was seen against curvature and thermophoresis parameter. Higher values of Curvature and Schmidt number depict positive impact on nanoparticle concentration, while the results for chemical reaction are conflicting. An increasing value of Brownian and thermophoresis parameters promote higher temperature. The temperature and thermal boundary layer thickness are also affected by the heat source and sink parameters in opposite manner.

A DTSD model based on PS-InSAR surface multi-type deformation monitoring of villages in the mining area

Evaluating building damage in mining areas using Interferometric Synthetic Aperture Radar (InSAR) has inherent challenges. This work presents a Delaunay Triangulation of Surface Deformation (DTSD) model that utilizes Permanent Scatter InSAR to analyze various types of deformations in villages. This model created a network of irregular triangles using Delaunay triangulation and PS points as the input. The calculation involved determining the inclination of triangular edges and the torsion of spatial Bezier curves fitted by these edges. The PS points' maximum inclination and curvature values were identified by solving over-determined equations. Results from a slurry injection mine in Huaibei, China, indicate that the various types of deformations in the neighboring communities were below 8 %, and the buildings experienced minimal damage. The DTSD model offers a theoretical framework for monitoring and assessing various types of surface deformation and designing essential zones for building protection.

Bakry–Émery–Ricci curvature: an alternative network geometry measure in the expanding toolbox of graph Ricci curvatures

Abstract The characterization of complex networks with tools originating in geometry, for instance through the statistics of so-called Ricci curvatures, is a well established tool of network science. Various types of such Ricci curvatures capture different aspects of network geometry. In the present work, we investigate Bakry–Émery–Ricci curvature, a notion of discrete Ricci curvature that has been studied much in geometry, but so far has not been applied to networks. We explore on standard classes of artificial networks as well as on selected empirical ones to what the statistics of that curvature are similar to or different from that of other curvatures, how it is correlated to other important network measures, and what it tells us about the underlying network. We observe that most vertices typically have negative curvature. Furthermore, the curvature distributions are different for different types of model networks. We observe a high positive correlation between Bakry–Émery–Ricci and both Forman–Ricci and Ollivier–Ricci curvature, and in particular with the augmented version of Forman–Ricci curvature while comparing them for both model and real-world networks. We investigate the correlation of Bakry–Émery–Ricci curvature with degree, clustering coefficient and vertex centrality measures. Also, we investigate the importance of vertices with highly negative curvature values to maintain communication in the network. Additionally, for Forman–Ricci, Augmented Forman–Ricci and Ollivier–Ricci curvature, we compare the robustness of the networks by comparing the sum of the incident edges and the minimum of the incident edges as vertex measures and find that the sum identifies vertices that are important for maintaining the connectivity of the network. The computational time for Bakry–Émery–Ricci curvature is shorter than that required for Ollivier–Ricci curvature but higher than for Augmented Forman–Ricci curvature. We therefore conclude that for empirical network analysis, the latter is the tool of choice.

Infraspecific Variation in Silene Seed Tubercles.

The seeds of many species in the order Caryophyllales exhibit surface protuberances called tubercles. While tubercle shape and distribution have often been proposed as taxonomic criteria, paradoxically, their description has primarily relied on adjectives, with quantitative data on tubercle width, height, and other measurements lacking in the literature. Recently, a quantitative analysis of seed surface tubercles based on tubercle width, height, and curvature values (maximum and average curvature, and maximum to average curvature ratio) was proposed and applied to individual populations of a total of 31 species, with 12 belonging to Silene subg. Behenantha and 19 to S. subg. Silene. Tubercles were classified into two categories: echinate and rugose. Echinate tubercles exhibited higher values of height and curvature, and lower width, and were more prevalent in species of S. subg. Behenantha, while the rugose type was more abundant in S. subg. Silene. This work explored infraspecific differences in tubercle size and shape. For this, measurements of tubercle width, height and curvature were applied to 31 populations of eight species of Silene. Significant differences between populations were observed for most of the species examined. A particular tubercle type, previously described as umbonate or mammillate, was identified in S. nocturna seeds, characterized by high curvature values.

The Role of Lipid Intrinsic Curvature in the Droplet Interface Bilayer.

Model bilayers are constructed from lipids having different intrinsic curvatures using the droplet interface bilayer (DIB) method, and their static physicochemical properties are determined. Geometrical and tensiometric measurements are used to derive the free energy of formation (ΔF) of a two-droplet DIB relative to a pair of isolated aqueous droplets, each decorated with a phospholipid monolayer. The lipid molecules employed have different headgroup sizes but identical hydrophobic tail structure, and each is characterized by an intrinsic curvature value (c0) that increases in absolute value with decreasing size of headgroup. Mixtures of lipids at different ratios were also investigated. The role of curvature stress on the values of ΔF of the respective lipid bilayers in these model membranes is discussed and is illuminated by the observation of a decrement in ΔF that scales as a near linear function of c02. Overall, the results reveal an association that should prove useful in studies of ion channels and other membrane proteins embedded in model droplet bilayer systems that will impact the understanding of protein function in cellular membranes composed of lipids of high and low curvature.