Linear Fitting Formula Research Articles

Transient temperature analysis and engineering application of steel shell immersed tunnel protected by fireproof board

Based on the Shenzhen-Zhongshan Link, the transient analytical solution of the steel shell immersed tunnel under the protection of fireproof board was deduced and verified through fire test. Then, the variation of the maximum temperature of the bottom steel shell with the thickness and thermal conductivity of the fireproof board was analyzed and suggestions on the selection of fireproof boards were given. Finally, a fitting formula for the maximum temperature of bottom steel shell was proposed. The results show that: (1) When the thermal contact resistance of the steel-concrete interface and the thermal resistance of cavity are 0.01 m2 °C/W and 0.02 m2 °C/W respectively under the case of 25 mm thick fireproof board, the variation of the analytical solution is consistent with test results, and the peak value is similar. (2) Based on the three-dimensional diagram of d -λ-T, with 300 °C as the fire resistance limit of structure, the range of the fireproof board parameters is obtained: when λ reaches 0.14 and 0.4 respectively, d shall not be less than 10 mm and 28.38 mm (3) The scatter points obtained from analysis were fitted using quadratic polynomials and linear functions respectively. Considering the accuracy and simplicity, the linear fitting formula is given as T = 275.66–7.41*d+644.6*λ.

Digital reconstruction of three‐dimensional contours and its application to microstructural evaluation of postblast rock fissure surfaces

AbstractFracture surface contour study is one of the important requirements for characterization and evaluation of the microstructure of rocks. Based on the improved cube covering method and the 3D contour digital reconstruction model, this study proposes a quantitative microstructure characterization method combining the roughness evaluation index and the 3D fractal dimension to study the change rule of the fracture surface morphology after blasting. This method was applied and validated in the study of the fracture microstructure of the rock after blasting. The results show that the fracture morphology characteristics of the 3D contour digital reconstruction model have good correlation with the changes of the blasting action. The undulation rate of the three‐dimensional surface profile of the rock is more prone to dramatic rise and dramatic fall morphology. In terms of tilting trend, the tilting direction also shows gradual disorder, with the tilting angle increasing correspondingly. All the roughness evaluation indexes of the rock fissure surface after blasting show a linear and gradually increasing trend as the distance to the bursting center increases; the difference between the two‐dimensional roughness evaluation indexes and the three‐dimensional ones of the same micro‐area rock samples also becomes increasingly larger, among which the three‐dimensional fissure roughness coefficient JRC and the surface roughness ratio Rs display better correlation. Compared with the linear fitting formula of the power function relationship, the three‐dimensional fractal dimension of the postblast fissure surface is fitted with the values of JRC and Rs, which renders higher correlation coefficients, and the degree of linear fitting of JRC to the three‐dimensional fractal dimension is higher. The fractal characteristics of the blast‐affected region form a unity with the three‐dimensional roughness evaluation of the fissure surface.

Correlation and consistency between two detection methods for serum 25 hydroxyvitamin D levels in human venous blood and capillary blood.

The study assessed the correlation and concordance of 25-hydroxyvitamin D [25(OH)D] levels in capillary and venous plasma collected simultaneously after vitamin D3 supplementation in 42 healthy adults. They were randomly divided into three groups by random number table method. Group A took 1,000 IU vitamin D3 daily, group B took 10,000 IU vitamin D3 every 10 days, and group C took 30,000 IU vitamin D3 every 30 days until the end of the 12th month. Venous blood serum 25(OH)D level was detected by chemiluminescence immunoassay (CLIA) and mass spectrometry (LC-MS) at day 1, day 14, day 28, month 6, and month 12 respectively, the capillary blood serum 25(OH)D level was detected by chemiluminescence immunoassay (CLIA) at the same time. Pearson correlation analysis and linear regression analysis were employed to investigate the relationship and transformation equation between the findings of the two samples and the results obtained from different detection methods within the same sample. The Bland-Altman method, Kappa analysis, and receiver operating characteristic (ROC) curve were utilized for assessing consistency, sensitivity, and specificity. The three groups all reached a stable peak at 6 months, and the average levels of the three groups were 49.21, 42.50 and 43.025 nmol/L, respectively. The average levels of group A were higher than those of group B and group C (P < 0.001). The mean values of serum 25(OH)D measured by LC-MS and CLIA in 42 healthy adults were 45.32 nmol/L and 49.88 nmol/L, respectively, and the mean values of 25(OH)D measured by LC-MS in capillary blood were 52.03 nmol/L, and the difference was statistically significant (P < 0.001). Pearson correlation analysis showed that the linear fitting formula of scatter data was as follows: venous 25(OH)D concentration (nmol/L) = 1.105 * capillary 25(OH)D concentration -7.532 nmol/L, R2 = 0.625. Good agreement was observed between venous and corrected capillary 25(OH)D levels in clinical diagnosis (Kappa value 0.75). The adjusted serum 25(OH)D in capillary blood had a high clinical predictive value. The agreement between the two methods is good when the measured 25(OH)D level is higher. Standardized capillary blood chemiluminescence method can be used for 25(OH)D detection.

Study of mix design and performance of alkali-activated concrete with recycled concrete aggregate

Recycled concrete aggregates (RCA) are produced from demolished buildings and old rigid pavements, which are deemed as solid waste, comprising primarily old aggregate and cement mortar. In this study, the use of RCA was introduced in alkali-activated concrete (AAC) to investigate the feasibility of designing the mix proportion of alkali-activated recycled aggregate concrete (AARAC) using a linear fitting formula. A total of 32 mixes, with the amount of cementitious materials varying from 350 kg/m3 to 500 kg/m3 and the sol ratio from 0.43 to 0.55, were prepared for the regression analysis of the relationships between multiple parameters. The tests for water consumption, compressive strength and durability were included. The experimental results indicate that concrete prepared using high-quality RCA exhibited lower water consumption and higher compressive strength. When the natural aggregate (NA) was replaced by the RCA, the compressive strength reached its highest value of 54.0 MPa. Moreover, as the strength grade increased, the chloride penetration resistance, anti-carbonization performance, and freezing resistance of AARAC gradually increased, while the shrinkage decreased. In conclusion, this study provides a new method for the mix design of AARAC, which contributes to the advancement of solid waste management in the construction industry.

Experimental Investigation on Thermal Conductivity of Straw Boards Based on the Temperature Control Box—Heat Flux Meter Method

Straw boards are the environmentally-friendly and sustainable materials used for building envelopes. To validate a novel alternative test method of thermal conductivity (λ), temperature control box–heat flux meter method (TCB-HFM), and better understand the thermal properties of straw boards, experimental investigation on two types of straw boards using such a method was carried out. Moreover, the control test via the conventional guarded hot plate method (GHP) was conducted to provide a benchmark. Results show that the fluctuation amplitudes of the temperature difference and heat flux density for the TCB-HFM during the steady state are much smaller than a generally acceptable limitation of 5%, and a 5.9% deviation of λ between the two test methods is in a reasonable range. It is indicated that the TCB-HFM can be regarded as an alternative test method to conduct investigations on the thermal properties of materials. Furthermore, the correlation between density and λ is explored and expressed by a linear fitting formula with the determination coefficient (R2) of 0.9193, and the formula is verified to have the feasibility to predict the λ of different types of straw bio-based materials.

Analysis of Crack-Characteristic Stress and Energy Characteristics of Sandstone under Triaxial Unloading Confining Pressure

The deformation and failure of underground engineering are usually caused by unloading. In this work, triaxial unloading confining pressure tests are carried out to simulate the failure process of rock mass caused by unloading, analyze the crack-characteristic stress, and study the energy evolution of rock under unloading and the pre-peak and post-peak energy characteristics combined with the energy theory. The results show that, when the confining pressure increases from 5 MPa to 20 MPa, crack closure stress σcc, crack initiation stress σci, dilatancy stress σcd, and peak stress σp are 6.34 times, 2.75 times, 1.93 times, and 1.66 times higher than the original, respectively. By comparing the increase in crack-characteristic stress, it can be found that the confining pressure has a large effect on the crack closure stress and crack initiation stress, while the dilatation stress and peak stress have relatively little influence. From the perspective of energy evolution, the pre-peak axial absorption energy U1 increases exponentially, the elastic energy Ue is similar to U1, and the circumferential consumption energy U3 and dissipation energy Ud are small. After reaching the peak stress, the growth rate of U1 decreases slightly, Ue decreases rapidly, and U3 increases rapidly but only as a small fraction of the total energy, while Ud grows almost exponentially and rapidly becomes the main part of the energy. Under each crack-characteristic stress state, the energy characteristic parameters gradually increase with the increase in confining pressure, which is manifested by the increase in slope in the linear fitting formula of energy characteristic parameters. The release process of the releasable elastic energy after the peak stress can be divided into three stages of “slow–fast–slow”, and the energy release process shows an obvious confining pressure effect.

New design method of SET—Based on collapse strength under plastic formation

Excellent collapse strength of solid expandable tubular (SET) after plastic forming is an advantageous guarantee for casing repair, plugging, repeating fracturing and other processes. This performance indicator is not only relevant to factors such as expansion, residual stress, and material, but also closely to the SET selected in the initial design. At present, there are few related studies on the initial design and selection of SET. This paper uses the CAE software to establish SET expansion to collapse process three-dimensional kinetics finite element model, and analyzes the collapse strength of different specifications under different expansion ratios, from the perspective of theoretical and simulation, derives the prediction formula. The results illustrate that the finite element simulation result of this paper and the error of the experiment is below 2%, the form of collapse is consistent with the experiment, the reliability is good; the wall thickness and expansion ratio parameters of the pipe have a more important impact on the types of collapse. When the SET specification is confirmed, the greatest collapse strength is presented a secondary relationship with the expansion ratio. Each specification of SET has the maximum collapse strength, its maximum value is closely connected to the wall thickness and expansion ratio, etc. Combined with a large number of simulation data obtained a linear fitting formula between the original radius ratio D0/t and the optimum expansion ratio. This paper derives D0 theoretical calculation formula based on maximum collapse strength by combination with the optimal expansion ratio, the nominal expansion ratio and geometric theoretical analysis. The results of this paper provide a certain theoretical guidance and research ideas for initial selection and design of SET.

Stress rupture properties and deformation mechanisms of K4750 alloy at the range of 650 °C to 800 °C

The stress rupture properties and deformation mechanisms of K4750 alloy at 650 °C, 700 °C, 750 °C and 800 °C were investigated. As the decrease of temperature and stress, the stress rupture life gradually increased. A Larson-Miller Parameter (LMP) method was used for analyzing the stress rupture life under different conditions. The linear fitting formula between stress (σ) and LMP was derived as σ = 3166.455 − 119.969 × LMP and the fitting coefficient was 0.98. After testing, the dislocation configurations of all stress rupture samples were investigated by transmission electron microscopy (TEM). The temperature and stress had a significant impact on the deformation mechanism, thereby affected the stress rupture life of K4750 alloy. As the increasing stress at a given temperature, the deformation mechanism gradually transformed from Orowan looping to stacking fault shearing. Based on experimental results, the threshold stress at 650 °C, 700 °C, 750 °C and 800 °C for the transition of deformation mechanism was estimated to be about 650 MPa, 530 MPa, 430 MPa and 350 MPa, respectively. Below the threshold stress, γ' phase effectively hindered dislocation motion by Orowan looping mechanism, K4750 alloy had a long stress rupture life. Slightly above the threshold stress, Orowan looping combining stacking fault shearing was the dominant mechanism, the stress rupture life decreased. As the further increase of stress, stacking fault shearing acted as the dominant deformation mechanism, the resistance to dislocation motion decreased rapidly, so the stress rupture life reduced significantly.

Determination of the Effective Calcium Content of Quicklime by Regression Analysis Using the Digestion Temperatures

Abstract This research involved randomly choosing 155 sets of experimental data that were collected from building companies. These sets of data were the result of lime analyses by sucrose titration done within 12 months by the laboratory attendants. The results of this experimental data were then gathered to be analyzed using the linear fitting formula. The results indicate that the analysis can accurately determine quicklime’s effective calcium content by regression analysis using the digestion temperatures. In addition, the X-ray diffraction method was used to test the quicklime’s calcium content, which verified that the method of linear fitting has good representativeness and practicability. This can greatly optimize the traditional process and has the prospect of being used widely.

A close analogy with archimedes&amp;rsquo; principle: Understanding the relationship between flow resistance and tail vortex zone of square pier through experiments

The flow resistance on the pier has always been treated as a focus issue in fluid mechanics with great significance of application. Square, as an important cross-section form of pillar structure, has been applied widely in practice. To investigate the relationship of the formation mechanism of flow resistance on square pier and the trailing vortex zone of the pillar, in this study, the flow resistance of the square pier and the surrounding flow are firstly measured by pressure sensor and particle image velocimetry (PIV). Then, by analogy with the principle of Archimedes, the relationship between the characteristics of flow, the flow resistance and the trailing vortex zone of the square pier is analyzed in detail under different Reynolds numbers (2500≤ Re ≤20000). According to the experiments, the fitting relation between the time averaged relative volume of the tail vortex zone, the time averaged dimensionless flow resistance and the new time averaged dimensionless coefficient of flow resistance formula with varied Re has been found. It shows a good correlation with all of them and each one related well to Re by a quadratic relation. Both Linear and quadratic fitting of the flow resistance with the volume of trailing vortex zone fits relatively well. The linear fitting formula is recommended in practice of relative large flow.

Combined grand canonical Monte Carlo and finite volume method simulation method for investigation of direct air capture of low concentration CO2 by 5A zeolite adsorbent bed

A method that combines finite volume method (FVM) and grand canonical Monte Carlo (GCMC) method is proposed to investigate the direct air capture of low concentration CO2 by 5A zeolites in an adsorption bed of a space shuttle. In the FVM, the multicomponent Langmuir model and linear fitting formula are used to calculate saturation adsorption capacities and adsorption heat at macro-scale level, respectively. The GCMC method is used to obtain the parameters of the multicomponent Langmuir model and linear fitting formula at micro-scale level. The combined method overcomes the shortcomings of the saturation adsorption capacities and adsorption heat restricted by experiments or empirical formulas. The effects of inlet velocity, particle size, and porosity on heat and mass transfer in the adsorption bed are predicted. The saturation adsorption time for N2 is faster than that for CO2. The competitive adsorption process between CO2 and N2 is divided into three stages, namely, primary, intermediate, and saturation stage. The location of temperature difference peak between solid and gas phase moves toward the outlet of the adsorption bed with increasing velocity, porosity, adsorption time or decreasing particle size. An adsorption bed with high inlet velocity and porosity and small particle size is recommended to achieve improved performance.

Kinetic energy recovery and interface hysteresis of bouncing droplets after inelastic head-on collision

Binary collision of unequal-size droplets was investigated numerically by using the front tracking method, with particular emphasis in studying the kinetic energy recovery and the interface hysteresis of bouncing droplets. The numerical results were sufficiently validated against the high-quality experimental data in the literature to verify the quantitative predictivity of the numerical methodology in simulating droplet bouncing. Distinct stages of droplet deformation and viscous dissipation during droplet collision were revealed and explained for their dependence on the Weber number and the size ratio. A linear fitting formula that well correlates the kinetic energy recovery factor of bouncing droplets with various collision parameters was proposed and would be practically useful in modeling inelastic droplet bouncing in Lagrangian spray simulation. As an interesting post-collision characteristic of bouncing droplets, the interface hysteresis was found to favor smaller droplet deformation by decreasing the size ratio or decreasing the Weber number or increasing the Ohnesorge number.

A combined GCMC and LBM simulation method for CH4 capture in Cu-BTC particle adsorption bed

Two-dimensional Lattice Boltzmann Method (LBM) combined with grand canonical Monte Carlo (GCMC) approach is proposed to investigate the heat and mass transfer of methane (CH4) adsorption in Cu-BTC particle adsorption bed. In interfacial boundary, saturation adsorption capacities are obtained by GCMC method to replace empirical values. The diffusion and adsorption heat in particle interior are fully considered. Langmuir-Freundlich model and linear fitting formula are used to calculate the saturation adsorption capacities in Langmuir adsorption kinetics model and the adsorption heat in heat transfer in LBM model at mesoscopic level, respectively. At micro-scale level, GCMC method is used to obtain parameters of Langmuir-Freundlich and linear fitting formula. The effects of porosity and particle size on CH4 adsorption are discussed. Results show that the time for the saturation adsorption decreases with an increase in porosity and increases with increased particle size. In fluid region and particle interior, temperature peak decreases with increasing porosity and particle size. Nonuniformity of temperature exists both in fluid region and solid particles. The adsorption properties in Cu-BTC adsorption bed, such as the relation between external and internal heat and mass transfer, is predicted intuitively by GCMC and LBM combined simulation method.

An analysis of radiographic parameters comparison between lumbar spine latericumbent and full-length lateral standing radiographs

Background ContextThe lumbar spine latericumbent and full-length lateral standing radiographs are most commonly used to assess lumbar disorder. However, there are few literatures on the difference and correlation of the sagittal parameters between the two shooting positions. PurposeThe study aimed to investigate the difference of sagittal parameters in spine lateral radiographs between latericumbent and upright positions, identify the correlation, and establish a preliminary linear fitting formula. Study DesignThe study is a prospective study on radiographic evaluation of sagittal alignment using latericumbent and upright positions. Patient SampleOne hundred fifty-seven patients were recruited from the orthopedics clinic of a single medical center. Outcome MeasureAngle measurement, the intra- and interobserver measurement reliability of measurement, and analysis of the angle measurement were carried out. MethodThe sagittal alignment of 157 patients were assessed using Surgimap software from two kinds of lateral radiographs to acquire the following parameters: lumbar lordosis (LL), pelvic incidence (PI), pelvic tilt (PT), sacral slope (SS), L4–L5 intervertebral angle (IVA4–5), L4–L5 intervertebral height index (IHI4–5), and PI–LL. The Kolmogorov-Smirnov test, paired t test, Pearson correlation analysis, and multivariate linear regression analysis were used to analyze the data. ResultsThe results showed significantly statistical difference in LL, SS, PT, IVA4–5, and PI–LL, except for PI and IHI4–5, between the two positions. There was a significant relativity between standing LL and latericumbent LL (r=0.733, p<.01), PI (r=0.611, p<.01), and SS (r=0.626, p<.01). The predictive formula of standing LL was 12.791+0.777 latericumbent LL+0.395 latericumbent PI−0.506 latericumbent SS (adjusted R2=0.619, p<.05). ConclusionNot all of sagittal parameters obtained from two positions are identical. Thus, the full-spine lateral standing films are difficult to be replaced. The surgeon should give sufficient consideration to the difference between the two views. We may primarily predict standing LL with the formula when we could not get whole-spine lateral standing radiographs.

The Impact of Interpixel Capacitance in CMOS Detectors on PSF Shapes and Implications for WFIRST

Unlike optical CCDs, near-infrared detectors, which are based on CMOS hybrid readout technology, typically suffer from electrical crosstalk between the pixels. The interpixel capacitance (IPC) responsible for the crosstalk affects the point-spread function (PSF) of the telescope, increasing the size and modifying the shape of all objects in the images while correlating the Poisson noise. Upcoming weak lensing surveys that use these detectors, such as WFIRST, place stringent requirements on the PSF size and shape (and the level at which these are known), which in turn must be translated into requirements on IPC. To facilitate this process, we present a first study of the effect of IPC on WFIRST PSF sizes and shapes. Realistic PSFs are forward-simulated from physical principles for each WFIRST bandpass. We explore how the PSF size and shape depends on the range of IPC coupling with pixels that are connected along an edge or corner; for the expected level of IPC in WFIRST, IPC increases the PSF sizes by ∼5%. We present a linear fitting formula that describes the uncertainty in the PSF size or shape due to uncertainty in the IPC, which could arise for example due to unknown time evolution of IPC as the detectors age or due to spatial variation of IPC across the detector. We also study of the effect of a small anisotropy in the IPC, which further modifies the PSF shapes. Our results are a first, critical step in determining the hardware and characterization requirements for the detectors used in the WFIRST survey.

Terrain Correction in the Gradient Calculation of Spontaneous Potential Data

AbstractTerrain correction is to eliminate the effect of terrain relief around measurement points on observation results in gravitational and geoelectrical prospecting. Because the microscopic mechanism of spontaneous potential anomalies formed by terrains is rather complex, it is difficult to obtain an analytic formula, whereas a more intuitive method can be adopted instead to find out the fitting formula between these two variables. According to the study, in spontaneous potential gradient calculation, spontaneous potential anomalies caused by topography can be divided into two types: one is that anomalies have a mirror‐image relation with terrain relief, which accounts for the majority of cases; the other one is that anomalies have an inverted mirror‐image relation with terrain relief. The relation between a majority of anomalies and terrain relief could be linear, quadratic or exponential, among which linear relation is the primary. As for which fitting relation should be adopted specifically, it can be decided by selecting a typical terrain and spontaneous potential curve first and judging through the law of variations; and trial calculation method can be adopted as well to choose the appropriate fitting formula by comparing the correction effects.The Ordos Basin was selected to be the research site in this paper and the terrain correction method which is applicable to spontaneous potential gradient calculation was put forward. Through the comparison of the correction results of three kinds of fitting formulas, it was concluded that the linear fitting formula can better describe the relationship between relative height and spontaneous potential correction amount in the surveyed area. Terrain correction can effectively eliminate the correlation between relative height and spontaneous potential. The corrected spontaneous potential curves can reflect subsurface geological structure better, and the anomalies showed by the spontaneous potential contour map can be more prominent. Terrain relief can influence the appearance of anomalies in spontaneous potential gradient calculation, especially when the area of rugged terrain is comparable to the area of target geological bodies, which may make it difficult to distinguish these two anomalies. Thus the study on terrain correction has great importance in practice.

Statistical removal of Faraday rotation in vector magnetograms taken by filter-type magnetographs

Based on the spectral scan data of NOAA AR 10325, 10484 and 10377 obtained with the Solar Magnetic Field Telescope at Huairou Solar Observing Station, we analyse the azimuthal differences (ΔδΦ) between the line centre and the line wing -0.12 A of Fe 1 λ 5324.19 caused by Faraday rotation. Grids of the longitudinal field B z and inclination ψ for intervals of 100 G and 3° are made. It is found that the azimuthal rotations are of the same magnitude when B z is in a 100-G interval. The amplitudes of azimuthal differences obviously increase with increasing B z and decrease with increasing ψ. Averaging ΔδΦ in each 100-G interval of B z and making a linear fit between and B z , then we obtain the correlation between the observed azimuthal difference and B z depicted by the linear fitting formula (1), namely ΔδΦ° = 0.0114 |Β z |. In addition, through the simulation we also obtain the azimuthal rotation at the line centre of Fe I λ5324.19 described by the fitting formula (2), namely δΦ 0.00 = 0.0254 |B z | - 3.975 x 10 -6 B 2 . We also present a third fitting formula (3), namely ΔδΦ t = 0.0149 |B z | - 1.455 x 10 -6 B z 2 , which describes the azimuthal differences between the line centre and the line wing -0.12 A. Formula (3) is consistent with the observational results of the three active regions. We correct the vector magnetograms of the three active regions with formulae (1) and (3) and find that the electric current J z , the current helicity He, and the average force-free field factor α av calculated from the correct magnetograms are nearly equivalent to those measured at the line wing -0.12 A. Furthermore, we calculate J z with 393 corrected vector magnetograms and find that formulae (1) and (3) can remove part of the false current whereas formula (2) can remove most of it.