Actual Density Research Articles

Effect of a high-resolution global crustal model on gravimetric geoid determination: a case study in a mountainous region

A precise gravimetric geoid model is determined by using Stokes formula assuming that there is no topography above the geoid. Then, the geoid model is simply corrected by considering the constant crustal density of 2670 kg m−3 for topographical mass. In fact, the actual density of topographical mass differs about ±20% from the constant value. Recently a global crustal density model within 30″ resolution has been released by the University of New Brunswick in Canada. The paper is devoted to the study of the effect of using this model on the accuracy of gravimetric geoid in a mountainous region in Turkey. Numerical results prove that the differences in the geoid height due to this model may reach up to several decimetres, which should not be ignored in a precise geoid modelling with 1-cm geoid. Thus, it is concluded that the effect of topographical density variations, contained in this model, is significant and should be taken into account in precise geoid determination, particularly in mountainous regions.

Two-step translation method for time-dependent reliability of structures subject to both continuous deterioration and sudden events

Civil infrastructure can be subjected to different deterioration scenarios (e.g., continuous deterioration and sudden events) during its service life. Time-dependent reliability analysis of a deteriorating system is of vital importance in the structural design, assessment, and management process. In this paper, a general and novel probability density function-informed framework for time-dependent reliability analysis is developed, considering different deterioration processes and system-level performance. Both continuous deterioration and sudden events are considered within the proposed framework. For the scenario with random sudden drops and/or significant differences in deterioration rates, a novel two-step translation method is proposed to assess the probability density of the performance function within the service life of a structure. In this method, translation operation is conducted twice; the first time to build a virtual and differentiable performance function, and the second, to solve the actual probability density function based on the results from the first step. Then, three illustrative examples are assessed: a simple deteriorating case, a component-level case, and a system-level case. The relevant results demonstrate the feasibility and efficiency of the proposed method.

An extended flamelet-based presumed probability density function for predicting mean concentrations of various species in premixed turbulent flames

Direct Numerical Simulation (DNS) data obtained by Dave and Chaudhuri (2020) from a lean, complex-chemistry, hydrogen-air flame associated with the thin-reaction-zone regime of premixed turbulent burning are analyzed to perform a priori assessment of predictive capabilities of the flamelet approach for evaluating mean species concentrations. For this purpose, dependencies of mole fractions and rates of production of various species on a combustion progress variable c, obtained from the laminar flame, are averaged adopting either the actual Probability Density Function (PDF) P(c) extracted from the DNS data or a common presumed β-function PDF. On the one hand, the results quantitatively validate the flamelet approach for the mean mole fractions of all species, including radicals, but only if the actual PDF P(c) is adopted. The use of the β-function PDF yields substantially worse results for the radicals’ concentrations. These findings put modeling the PDF P(c) on the forefront of the research agenda. On the other hand, the mean rate of product creation and turbulent burning velocity are poorly predicted even adopting the actual PDF. These results imply that, in order to evaluate the mean species concentrations, the flamelet approach could be coupled with another model that predicts the mean rate and turbulent burning velocity better. Accordingly, the flamelet approach could be implemented as post-processing of numerical data yielded by that model. Based on the aforementioned findings and implications, a new approach to building a presumed PDF is developed. The key features of the approach consist in (i) adopting a re-normalized flamelet PDF for intermediate values of c and (ii) directly using the mean rate of product creation to calibrate the presumed PDF. Capabilities of the newly developed PDF for predicting mean species concentrations are quantitively validated for all species, including radicals.

Structural characteristics of crab burrows in Hong Kong mangrove forests and their role in ecosystem engineering

Crab burrowing activity impacts several important biogeochemical processes within mangrove forests. Burrow morphology has been shown to be variable between brachyuran families, hence the community structure and composition of burrowing crabs may have the potential to impact ecosystems differently. By increasing belowground surface area, volume and bacterial microhabitats, large and complex burrows may differ from smaller and simpler burrows in their impact to nutrient and organic matter distribution. The central aim of this work was to provide a detailed quantification of the scale to which different mangrove crab families impact Hong Kong mangrove ecosystem through their burrowing activities. To achieve this goal, we recorded burrow densities and described specie-specific burrow morphology, through casts and 3D scans, of eight crab species belonging to four families, across three mangrove forests. Where present, the large and complex burrows of Parasesarma bidens (Sesarmidae) increased the total below ground air-sediment surface area per m2 by ~190% and accounted for ~1.9% of excavated volume per m3 of mangrove sediment. On average, the burrows of Metaplax spp. (Varunidae) increased the surface area by ~55%, while the ocypodid and dotillid species accounted for a 10–25% increase across sites. Due to its densities and the complexity of its burrows, P. bidens showed to exert a wide impact on Hong Kong mangrove ecosystems unrivalled by other species. By incorporating species-specific burrow characteristics and actual burrow densities, we were able to accurately estimate the differential bioengineering role of the dominant mangrove crab species. Due to the functional role of crab bioengineering, our estimates are critical to assess Hong Kong mangrove ecosystem functioning and health.

Effects of Land Use Changes on the Soil Physicochemical Properties in South-Western Algeria

Abstract This study shows the impact of the reforestation program by some tree species (Pinus halepensis, Cupressus sempervirens and Eucalyptus camaldulensis) on the soil physicochemical parameters in south-western Algeria steppe. The study was realized on soil samples from the Touadjeur site. One hundred soil samples were taken from the field, followed by physicochemical analyses in the laboratory. A comparison of the soil elements between reforested and unreforested sites considered as a control was carried out. The results show that there are differences in the physicochemical parameters of the soil between the reforestation and the non-reforestation ones constituted by a steppe vegetation. The ANOVA one way test shows a highly significant difference change in soil physical parameters, moisture, holding capacity and saturated hydraulic conductivity, but no change in apparent density, actual density and color. Also, from a chemical point of view, the differences concern the organic matter, organic carbon, pH and certain soil contents. The main differences in soil properties between the reforestation sites and the control site, reflect the consequences of forest management adopted by the forest services, most probably the choice of reforestation species.

Mechanical behavior of polymeric selective laser sintered ligament and sheet based lattices of triply periodic minimal surface architectures

Advances in additive manufacturing triggered a paradigm shift in the design of functional components allowing for complex topology-driven cellular lattices to be incorporated for the aim of reducing weight, enhancing multi-functionality, and facilitating manufacturability. In this paper, the compressive mechanical behavior of different polymeric lattices based on triply periodic minimal surfaces (TPMS) are investigated both experimentally and computationally. The behavior of two classes of TPMS lattices are investigated; sheet- and ligament-based lattices. Samples are fabricated using the laser powder bed fusion technique, selective laser sintering, and characterized using micro-Computed Tomography (micro-CT) and Scanning Electron Microscopy (SEM). A finite-deformation hyperelastic-viscoplastic-damage constitutive model is calibrated and employed to capture the full compressive behavior of lattices. The computational results are compared to and validated against corresponding experimental results. Results show that sheet-based polymeric TPMS lattices exhibit a stretching-dominated mode of deformation and prove to have superior stiffness and strength as compared to TPMS ligament-based lattices. The numerical simulations are in good agreement with experimental results for ligament-based lattices while significant deviation from experimental results is observed for the sheet-based lattices which is attributed to uncertainty in measuring the actual relative density and relatively higher manufacturing defects.

Redshift inference from the combination of galaxy colours and clustering in a hierarchical Bayesian model – Application to realistic N-body simulations

ABSTRACT Photometric galaxy surveys constitute a powerful cosmological probe but rely on the accurate characterization of their redshift distributions using only broad-band imaging, and can be very sensitive to incomplete or biased priors used for redshift calibration. A hierarchical Bayesian model has recently been developed to estimate those from the robust combination of prior information, photometry of single galaxies, and the information contained in the galaxy clustering against a well-characterized tracer population. In this work, we extend the method so that it can be applied to real data, developing some necessary new extensions to it, especially in the treatment of galaxy clustering information, and we test it on realistic simulations. After marginalizing over the mapping between the clustering estimator and the actual density distribution of the sample galaxies, and using prior information from a small patch of the survey, we find the incorporation of clustering information with photo-z’s tightens the redshift posteriors and overcomes biases in the prior that mimic those happening in spectroscopic samples. The method presented here uses all the information at hand to reduce prior biases and incompleteness. Even in cases where we artificially bias the spectroscopic sample to induce a shift in mean redshift of $\Delta \bar{z} \approx 0.05,$ the final biases in the posterior are $\Delta \bar{z} \lesssim 0.003.$ This robustness to flaws in the redshift prior or training samples would constitute a milestone for the control of redshift systematic uncertainties in future weak lensing analyses.

Seasonal dynamics of cattle grazing behaviors on contrasting landforms of a fenced ranch in northern China

The number of livestock per unit area is commonly used as a proxy of grazing pressure in both experimental studies and grassland management. However, this practice ignores the impact of landform heterogeneity on the spatial distribution of grazing pressure, leading to localized patches of degraded grassland. The spatial distribution of actual grazing density thus needs to be examined. Owing to the corresponding changes in resource availability and energy consumption as livestock move across an elevation gradient, we predict that livestock will preferentially use low-land and that different temporal patterns of grazing pressure will occur in the contrasting landforms. GPS location data and a machine learning technique were used to identify the seasonal pattern and the factors driving grazing pressure on a fenced ranch. Over both low-land and sand-dune landforms, the proportion of time that livestock spent on foraging increased from 63% in July to 67% in August and 69% in September, and non-foraging behavior decreased correspondingly. In low-land, the log-transformed average foraging density significantly increased from 0.61 (i.e., total foraging behaviors in 5 days measured at 50-s intervals per 10 × 10 m grid) in July to 0.66 in August and 0.88 in September, whereas there was no significant change on sand-dunes. From July to September, the relative area of low-land foraged by cattle accounted for 31%, 35%, and 36%, respectively, and in sand-dunes the proportions increased from 45% to 47% to 51%. In low-land, the foraging density was negatively correlated with biomass (P = .07), total digestible nutrients (P < .05), and crude protein (P = .06) and positively correlated with acid detergent fiber (P < .05), whereas no such relationships were observed in sand-dunes. Our results indicate that topographic features should be considered when managing livestock, especially during periods with adverse conditions of herbage quality and quantity.

Regulation of carbon distribution to construct high-sulfur-content cathode in lithium–sulfur batteries

Abstract Lithium–sulfur (Li–S) battery is regarded as one of the most promising next-generation energy storage systems due to the ultra-high theoretical energy density of 2600 Wh kg−1. To address the insulation nature of sulfur, nanocarbon composition is essential to afford acceptable cycling capacity but inevitably sacrifices the actual energy density under working conditions. Therefore, rational structural design of the carbon/sulfur composite cathode is of great significance to realize satisfactory electrochemical performances with limited carbon content. Herein, the cathode carbon distribution is rationally regulated to construct high-sulfur-content and high-performance Li–S batteries. Concretely, a double-layer carbon (DLC) cathode is prepared by fabricating a surface carbon layer on the carbon/sulfur composite. The surface carbon layer not only provides more electrochemically active surfaces, but also blocks the polysulfide shuttle. Consequently, the DLC configuration with an increased sulfur content by nearly 10 wt% renders an initial areal capacity of 3.40 mAh cm−2 and capacity retention of 83.8% during 50 cycles, which is about two times than that of the low-sulfur-content cathode. The strategy of carbon distribution regulation affords an effective pathway to construct advanced high-sulfur-content cathodes for practical high-energy-density Li–S batteries.

A Method for the Estimation of Finely-Grained Temporal Spatial Human Population Density Distributions Based on Cell Phone Call Detail Records

Estimating and mapping population distributions dynamically at a city-wide spatial scale, including those covering suburban areas, has profound, practical, applications such as urban and transportation planning, public safety warning, disaster impact assessment and epidemiological modelling, which benefits governments, merchants and citizens. More recently, call detail record (CDR) of mobile phone data has been used to estimate human population distributions. However, there is a key challenge that the accuracy of such a method is difficult to validate because there is no ground truth data for the dynamic population density distribution in time scales such as hourly. In this study, we present a simple and accurate method to generate more finely grained temporal-spatial population density distributions based upon CDR data. We designed an experiment to test our method based upon the use of a deep convolutional generative adversarial network (DCGAN). In this experiment, the highest spatial resolution of every grid cell is 125125 square metre, while the temporal resolution can vary from minutes to hours with varying accuracy. To demonstrate our method, we present an application of how to map the estimated population density distribution dynamically for CDR big data from Beijing, choosing a half hour as the temporal resolution. Finally, in order to cross-check previous studies that claim the population distribution at nighttime (from 8 p.m. to 8 a.m. on the next day) mapped by Beijing census data are similar to the ground truth data, we estimated the baseline distribution, first, based upon records in CDRs. Second, we estimate a baseline distribution based upon Global Navigation Satellite System (GNSS) data. The results also show the Root Mean Square Error (RMSE) is about 5000 while the two baseline distributions mentioned above have an RMSE of over 13,500. Our estimation method provides a fast and simple process to map people’s actual density distributions at a more finely grained, i.e., hourly, temporal resolution.

Beetle-Swarm Evolution Competitive Algorithm for Bridge Sensor Optimal Placement in SHM

In structural heath monitoring (SHM), for the sake of optimizing the bridge sensor placement, a beetle-swarm evolution competitive algorithm is proposed with the group evolutionary competition mechanism introducing into beetle antennae search optimization (BAS). This paper uses high-dimensional dynamic coverage coding to initialize the beetle's location as binary codes, which avoids that the original BAS can only solve the continuous optimization problem, and ensures the dispersion of effective information in individuals, so that the coding rules are consistent with the actual coverage density for bridge sensors. In the process of evolutionary, horizontal mutation, crossover, phagocytosis and elimination among individuals are added to improve the diversity of individual evolution, which may avoid the algorithm falling into local optimum, and make the excellent individuals tend to be better. Lastly, the example analysis of Ha-Qi bridge shows that beetle-swarm evolution competitive algorithm has fast convergence speed and global optimization ability, and it is suitable for solving the sensor placement optimization for large bridge.

Insights into the regulation of FeNa catalysts modified by Mn promoter and their tuning effect on the hydrogenation of CO2 to light olefins

This study unravels the effect of Mn promoter on the surface enrichment and competition of promoters and the evolutions of the chemical and structural of Fe species during the reaction, and illustrates the regulation of FeMn and FexCy for CO2 conversion and hydrogenation of intermediates. With the contents of Mn promoter increasing from 0.5% to 10.0%, the selectivity of light olefins decreasing from 38.73% to 30.58% and the ratio of olefin to paraffin decreases from 4.97 to 3.56. The surface ratio of Mn/Fe and Na/Fe is much higher than the impregnation ratio, which confirms the surface enrichment of Mn and Na promoters. It turns out that the iron oxides are transformed into iron carbides in the bulks and oligomeric FexOy on the surface after reaction. The enrichment of Mn promoters leads to more surface Fe species near the Mn promoters for the strong adsorption of CO2 and decreases the surface actual density of FexCy sites for the hydrogenation of CO to hydrocarbons, which consequently decreases the conversion of CO2 and the FTY value. The increasing content of Mn promoters from 0.5% to 3.0% also increases the adsorption ability of H2 on the surface of iron carbides, which is possibly associated with the hydrogenation of intermediates and leading to decreasing of the ratio of olefins to paraffins ranging from C2-C4.

Ultrasound-assisted hydration of wheat grains at different temperatures and power applied: Effect on acoustic field, water absorption and germination

Wheat has been increasingly employed as malt in the food industry. As the malting process demands long processing time, ultrasound can be a clean intensifying alternative. This work studied the ultrasound-assisted hydration of wheat grains at different nominal input power (0−1500 W) and temperatures (15−25 °C). The actual acoustic field within the reactor was characterized. The effects of the studied variables on hydration kinetics were assessed separately by the Weibull and Peleg Models. Thermodynamic parameters were evaluated. Grains germination was also addressed under the studied conditions. Increasing temperature as well as higher acoustic density caused an improvement in the hydration kinetics, reaching 72 % when both variables were combined. Hydration was an endothermic and non-spontaneous process. In the range of actual acoustic density (0.061–0.102 W mL−1) and hydration temperature, the maximum germination was kept at ∼5 days with 86 % germinated grains.

From the index case to global spread: the global mobility based modelling of the COVID-19 pandemic implies higher infection rate and lower detection ratio than current estimates.

BackgroundSince the outbreak of the COVID-19 pandemic, multiple efforts of modelling of the geo-temporal transmissibility of the virus have been undertaken, but none describes the pandemic spread at the global level. The aim of this research is to provide a high-resolution global model of the pandemic that overcomes the problem of biased country-level data on the number of infected cases. To achieve this we propose a novel SIR-type metapopulation transmission model and a set of analytically derived model parameters. We used them to perform a simulation of the disease spread with help of the Global Epidemic and Mobility (GLEAM) framework embedding actual population densities, commute patterns and long-range travel networks. The simulation starts on 17 November 2019 with the index case (presymptomatic, yet infectious) in Wuhan, China, and results in an accurate prediction of the number of diagnosed cases after 154 days in multiple countries across five continents. In addition, the model outcome shows high compliance with the results of a random screening test conducted on pregnant women in the New York area.MethodsWe have built a modified SIR metapopulation transmission model and parameterized it analytically either by setting the values of the parameters based on the literature, or by assuming their plausible values. We compared our results with the number of diagnosed cases in twenty selected countries, ones which provide reliable statistics but differ substantially in terms of strength and speed of undertaken Non-Drug Interventions. The obtained 95% confidence intervals for the predictions are in agreement with the empirical data.ResultsThe parameters that successfully model the pandemic are: the basic reproduction number R0, 4.4; a latent non-infectious period of 1.1. days followed by 4.6 days of the presymptomatic infectious period; the probability of developing severe symptoms, 0.01; the probability of being diagnosed when presenting severe symptoms of 0.6; the probability of diagnosis for cases with mild symptoms or asymptomatic, 0.001.DiscussionParameters that successfully reproduce the observed number of cases indicate that both R0 and the prevalence of the virus might be underestimated. This is in concordance with the newest research on undocumented COVID-19 cases. Consequently, the actual mortality rate is putatively lower than estimated. Confirmation of the pandemic characteristic by further refinement of the model and screening tests is crucial for developing an effective strategy for the global epidemiological crisis.

Effect of Cell Density on the Removal of Microcystis by Coagulation

Objectives:This study evaluated the removal of &lt;i&gt;Microcystis&lt;/i&gt; by coagulation in raw waters with three different cell densities.Methods:Raw waters were prepared at three different cell densities (target cell densities of 10,000, 100,000, and 1,000,000 cell/mL; actual cell densities of 9,950, 102,000, and 991,000 cell/mL) by adding &lt;i&gt;Microcystis&lt;/i&gt; into surface water from Nakdong river. Jar-tests were conducted with PACL, alum, illite, and loess at dosages of 0-150 mg/L.Results and Discussion:Regardless of coagulant types, the removal rates of &lt;i&gt;Microcystis&lt;/i&gt; increased as the coagulant dosages increased. PACl and alum exhibited higher removal rates than illite and loess; PACl was the best coagulant to remove &lt;i&gt;Microcystis&lt;/i&gt;. Removal of chlorophyll-a was highest when PACl added at 20.4 mg/L, and no significant increase in removal rate was observed with higher dosages of PACl. However, removal rates of chlorophyll-a by illite and loess gradually increased as the dosages increased.Conclusions:With the coagulants tested in this study, removal rates of &lt;i&gt;Microcystis&lt;/i&gt; increased as the coagulant dosages increased. Removal rates of &lt;i&gt;Microcystis&lt;/i&gt; increased as the cell densities increased probably because &lt;i&gt;Microcystis&lt;/i&gt; acted as particles which could enhance the coagulation efficiency.

БЕНТОНИТ ЛОЙҚАСИ, МАЪДАНЛИ ЎҒИТЛАР МЕЪЁРЛАРИ ҲАМДА СУҒОРИШ ТАРТИБЛАРИНИ БИРГАЛИКДА ҚЎЛЛАШНИНГ КУЗГИ БУҒДОЙДАГИ МАҲСУЛДОРЛИГИ

The use of bentonite clay in addition to the rate of mineral fertilizers N150P105K75kg/ha before sowing winter wheat every year in a 1:1 system (cotton-grain) under conditions of typical gray soils of the Tashkent region with irrigation in the order of 60-70-60 and 70-80-70 % of pre-irrigated soil moisture, relative to LFMC, had a positive effect on the agrophysical properties of the soil, on the growth and development of the plant. Relative to the control variant, by the end of the growing season, the actual density of winter wheat increased to 54-59 m2/piece, growth to 4,3-6,8 cm, the number of common stems to 1,0-1,050 million/ha and the number of productive stems to 758,0-774,0 thousand/ha, achieved up to 12,5-13,4 center of additional grain yield.

Crystallization, microstructure and energy storage behavior of borate glass–ceramics

The borate glass–ceramics with a great energy storage density were fabricated using the melt-quenching method and then heat-treated technology. The microstructure, dielectric properties, energy storage properties and charge–discharge behavior were discussed. The dielectric constant increases monotonically with the increase of crystallization temperature, but the breakdown strength and energy storage density show a trend of increasing first and then decreasing, which is opposite to the activation energy reflecting the interfacial polarization. When the crystallization temperature is 750 °C, the activation energy reaches the lowest value. The glass–ceramics heated at 750 °C have the high breakdown strength of 1487 kV/cm, the maximum energy density of 9.61 J/cm3 and high energy efficiency of 89%, while the actual discharge density reaches the maximum value of 0.4811 J/cm3 under a voltage applied of 500 kV/cm, which makes the materials suitable for applications in energy storage, especially in high power and pulsed power systems.

High power density Al-air batteries with commercial three-dimensional aluminum foam anode

Aluminum (Al) is the desired material for metal-air batteries, owing to its attractive electrochemical performance. Unfortunately, the actual power densities of the batteries are relatively low. This research describes a high power density Al-air battery equipped with commercial three-dimensional (3D) Al foam as the anode coupled with dual cathodes in NaOH electrolyte. The corrosion responses and electrochemical performances of the 3D Al foam are investigated in 1, 2, and 4 mol L−1 NaOH solutions. Compared with the dense Al plate, the Al foam owns better electrochemical performances in 4 mol L−1 NaOH solution. The peak power density of the Al foam (80.6 mW cm−2) increases by ~ 56.84%, relative to the Al plate (51.2 mW cm−2). At 100 mA cm−2, the capacity density of Al foam reaches 1983 mAh g−1, and the energy density comes to 1567 Wh Kg−1. Considering the cost and performance, the commercial 3D Al foam anode with a large specific surface and small electrode polarization is expected to be a promising anode material for the Al-air batteries.

Oxide Edge Trap Density Extraction in Silicon Nanowire MOSFET From Tunnel Current Noise Measurement in Gated Diode Like Arrangement

Edge traps in the gate oxide of silicon nanowire MOSFETs have been extracted from tunnel current noise measurement in a gated diode like arrangement. We have found that, low frequency noise in tunnel current results from collective response of the edge traps available within the gate oxide surrounding band-to-band generation (BTBG) region of silicon nanowire, and when the BTBG region is accessed by favorable terminal biases. From detail modeling of the phenomenon, we derived a closed form expression of the tunneling current noise power spectral density (PSD) employing which oxide edge trap density in nanowire MOSFET had been extracted through its fit with the experimental noise PSD data. We furthermore validated our model for different BTBG biases, and contrasted our result with the bulk oxide trap density in identical MOSFET, while the latter was separately estimated from the gate current noise PSD measurement. Mismatch between the oxide bulk trap and edge trap concentrations has been found, whereby actual edge trap density remains otherwise hidden from the widely employed gate current noise measurement technique. It is because, the present scheme improves the resolution of the extracted oxide edge trap concentration in surrounded gate MOSFET owing to constricted tunnel current flow near the corner of the gate which imposes selectivity on the oxide edge traps

Measuring protein surface density on glass substrate using fluorescence fluctuation spectroscopy

Surface functionalization implies to know the surface density of proteins, which, for cellular biology, impacts on cells behavior (motility, spreading, and fate). Contradictory, the quantification of this parameter is lacking. We studied the surface density of deposited proteins on glass using the Image Correlation Spectroscopy (ICS) technique as part of the Fluorescence Fluctuation Microscopy (FFM) methods. As the confocal microscope scans the surface, the proteins deposited on it contribute to the image through the confocal point spread function (PSF). The width of the image autocorrelation is equal to the width of the PSF; its amplitude provides the average number of proteins within the PSF, proportional to the surface density. Nevertheless, the assessment of the surface density can be underestimated if the surface coverage is not uniform or overestimated if a background contributes to the fluorescence signal. Hence, we combine the ICS and photobleaching (pICS) to detect these artifacts and estimate the actual surface density. The pICS method makes it possible to have a better control of the estimation of the surface density. We noticed that the surface density of proteins increased with their initial concentration in solutions. Overall, FFM is a quantitative technique to infer the surface density of protein.