Intensity Distribution Function Research Articles

Bias Correction of IMERG Data in the Mountainous Areas of Sumatra Based on A Single Gauge Observation

The performance of surface precipitation data from satellite precipitation products (SPPs) in mountainous areas has greater error and bias than in plain areas. In this study, linear scaling (LS), local intensity (LOCI), power transformation (PT), and cumulative distribution function (CDF) methods are used to correct the bias of Integrated Multi-Satellite Retrievals for Global Precipitation Measurement (IMERG) data in the mountainous region of Sumatra based on long-term and high-resolution optical rain gauge (ORG) observations. The ORG is installed at Equatorial Atmospheric Observatory (EAO) in Kototabang, West Sumatra, Indonesia (100.32 °E, 0.20 °S, 865 m above sea level (ASL) with an observation period from 2002 to 2016. The impact of the bias correction method is tested based on accuracy and capability detection tests. The bias correction method is more effective at the daily resolution than the hourly resolution of the IMERG data in the mountainous region of Sumatra. The LS method exhibited the best improvement in accuracy with reduced root-mean-square error (RMSE) and relative bias (RB), although there was no significant increase in coefficient correlation (CC) values. However, the accuracy improvement was not observed in the bias correction for hourly data. The lack of improvement in the accuracy of the hourly IMERG data is due to the high local variability of rainfall in the mountainous area of Sumatra. The high data variability causes large differences in the mean and variance of the IMERG calibration and evaluation data periods. On the other hand, the LOCI, PT, and CDF methods were successfully improved the rain detection capability of IMERG, as indicated by the better critical succession index (CSI) values compared to the original hourly and daily IMERG data. It increased the CSI value by reducing false alarms for rain with intensity below 2 mm/h. Furthermore, the CDF method can improve the analysis of extreme rainfall in the mountainous region of Sumatra by improving the estimation of the extreme rainfall index. Therefore, these methods can be applied to improve the accuracy and detectability of IMERG data in the mountainous region of Sumatra. However, the scale factor and transfer function constructed in this study need to be further evaluated on other rain gauge observation data in Sumatra’s mountainous region to improve performance. HIGHLIGHTS The LS method shows the best improvement in the accuracy of IMERG data in the mountainous area of Sumatera compared to the LOCI, PT, and CDF methods, as indicated by the largest decrease in RMSE and RB values CSI values prove that LOCI, PT, and CDF methods successfully improve the detection capability of IMERG hourly and daily data in the mountainous region of Sumatra The CDF method shows the best quality in improving extreme rainfall observations in the mountainous region of Sumatra GRAPHICAL ABSTRACT

Lensless imaging in one shot using the complex degree of coherence obtained by multiaperture interferences.

The van Cittert-Zernike theorem states that the Fourier transform of the intensity distribution function of a distant, incoherent source is equal to the complex degree of coherence. In this Letter, we present a method for measuring the complex degree of coherence in one shot by recording the interference patterns produced by multiple aperture pairs. The intensity of the sample is obtained by Fourier transforming the complex degree of coherence. The experimental verification by using a simple object is presented together with a discussion on how the method could be improved for imaging more complex samples.

Analytical calculation method of a liquid-cooling eddy current brake considering magnetic saturation and skin effect

In this article, a clear and concise analytical method for predicting the performance of a Liquid-cooling eddy current brake (LC-ECB) is proposed. The LC-ECB has a coolant channel in the rotor to allow direct cooling of the inner surface of the stator. The static air-gap magnetic field distribution is obtained by the dynamic magnetic equivalent circuit (MEC) method, and the magnetic flux leakage and global magnetic saturation effects are fully considered. The magnetic field intensity distribution function of the eddy current reaction magnetic field is derived for the first time based on Ampere circuital theorem. Considering the local magnetic saturation and skin effect, a novel double-iteration algorithm based on the conservation principle of magnetic pressure drop is applied to obtain the transient air-gap flux density distribution, and then the brake torque expression is obtained. The finite element method (FEM) and experimental results show that the proposed method is feasible and effective. The new model is easy to program and can be easily used in the initial design and optimization of LC-ECB.

Climate Impacts of Convective Cloud Microphysics in NCAR CAM5

Abstract We improved the treatments of convective cloud microphysics in the NCAR Community Atmosphere Model version 5.3 (CAM5.3) by 1) implementing new terminal velocity parameterizations for convective ice and snow particles, 2) adding graupel microphysics, 3) considering convective snow detrainment, and 4) enhancing rain initiation and generation rate in warm clouds. We evaluated the impacts of improved microphysics on simulated global climate, focusing on simulated cloud radiative forcing, graupel microphysics, convective cloud ice amount, and tropical precipitation. Compared to CAM5.3 with the default convective microphysics, the too-strong cloud shortwave radiative forcing due primarily to excessive convective cloud liquid is largely alleviated over the tropics and midlatitudes after rain initiation and generation rate is enhanced, in better agreement with the CERES-EBAF estimates. Geographic distributions of graupel occurrence are reasonably simulated over continents; whereas the graupel occurrence remains highly uncertain over the oceanic storm-track regions. When evaluated against the CloudSat–CALIPSO estimates, the overestimation of convective ice mass is alleviated with the improved convective ice microphysics, among which adding graupel microphysics and the accompanying increase in hydrometeor fall speed play the most important role. The probability distribution function (PDF) of rainfall intensity is sensitive to warm rain processes in convective clouds, and enhancement in warm rain production shifts the PDF toward heavier precipitation, which agrees better with the TRMM observations. Common biases of overestimating the light rain frequency and underestimating the heavy rain frequency in GCMs are mitigated.

Study on the Optical Parameters of Different Particle Sizes Considering Particle Group Reflectivity

With the rapid advancements in laser and detection technology, it is now possible to obtain the physical properties of particles. Analyzing the physical properties of particles can establish the foundation for further research on the optical field transmission of particles in the micron range. The transport model of unpolarized particles is constructed by applying the unpolarized transport technology, and the Stokes vector is used to calculate the transport characteristics of the particle to obtain the four-dimensional mathematical vector that represents average light intensity. A random matrix is established with the help of the Markov chain to transmit unpolarized characteristic parameters of particles and to investigate the energy levels of a vast number of particles. According to the Mie scattering theory, the spatial intensity distribution function of light scattering is calculated, and the experiment on the characteristic parameter of the particle is carried out based on the results of a photoelectric detector, and compared with the numerical simulation. By analyzing the mathematical model, the accuracy and effectiveness of the model are verified, which provides theoretical support for further research on particle physics.

Asymptotic behavior of seismic hazard curves

Hazard curves from probabilistic seismic hazard analysis (PSHA) are plots of the rate of earthquakes exceeding ground motion intensity values vs such threshold values, for a site of interest. In classical PSHA, these curves can be transformed to provide the probability of exceedance of ground motion intensity values in any time interval, utilizing the properties of the homogeneous Poisson process (HPP). In turn, these probability curves can be seen as the plot of the complementary cumulative distribution function of the maximum intensity observed, at the site, in the time interval of interest. One consequence of the HPP framework, within which PSHA is developed, is that, for large time intervals, it can be argued that these curves could asymptotically lead to a probabilistic model for extreme value (EV) random variables. This is discussed, with a simple engineering approach, in this short note, where it is found – via case studies – that exceedance hazard curves seem to converge towards an EV distribution (i.e., the EV type II or Fréchet), with a pace that is impacted by the discontinuity inherent to the curves. It is also seen that other common models, typically used to provide an analytical format to probabilistic curves, do not show the same level of convergence. Besides providing further insights on the results of PSHA, this study can possibly be useful for those cases where a closed-form equation for the hazard curve could be needed, such as reliability-based calibration of building codes, or seismic risk studies involving seismic hazard approximation/extrapolation.

The Statistical Similarity of Repeating and Non-Repeating Fast Radio Bursts

In this paper, we present a sample of 21 repeating fast radio bursts (FRBs) detected by different radio instruments before September 2021. Using the Anderson–Darling test, we compared the distributions of extra-Galactic dispersion measure (DME) of non-repeating FRBs, repeating FRBs and all FRBs. It was found that the DME values of three sub-samples are log-normally distributed. The DME of repeaters and non-repeaters were drawn from a different distribution on basis of the Mann–Whitney–Wilcoxon test. In addition, assuming that the non-repeating FRBs identified currently may be potentially repeators, i.e., the repeating FRBs to be universal and representative, one can utilize the averaged fluence of repeating FRBs as an indication from which to derive an apparent intensity distribution function (IDF) with a power-law index of a1=1.10±0.14 (a2=1.01±0.16, the observed fluence as a statistical variant), which is in good agreement with the previous IDF of 16 non-repeating FRBs found by Li et al. Based on the above statistics of repeating and non-repeating FRBs, we propose that both types of FRBs may have different cosmological origins, spatial distributions and circum-burst environments. Interestingly, the differential luminosity distributions of repeating and non-repeating FRBs can also be well described by a broken power-law function with the same power-law index of −1.4.

Malaria parasites release vesicle subpopulations with signatures of different destinations.

Malaria is the most serious mosquito‐borne parasitic disease, caused mainly by the intracellular parasite Plasmodium falciparum. The parasite invades human red blood cells and releases extracellular vesicles (EVs) to alter its host responses. It becomes clear that EVs are generally composed of sub‐populations. Seeking to identify EV subpopulations, we subject malaria‐derived EVs to size‐separation analysis, using asymmetric flow field‐flow fractionation. Multi‐technique analysis reveals surprising characteristics: we identify two distinct EV subpopulations differing in size and protein content. Small EVs are enriched in complement‐system proteins and large EVs in proteasome subunits. We then measure the membrane fusion abilities of each subpopulation with three types of host cellular membranes: plasma, late and early endosome. Remarkably, small EVs fuse to early endosome liposomes at significantly greater levels than large EVs. Atomic force microscope imaging combined with machine‐learning methods further emphasizes the difference in biophysical properties between the two subpopulations. These results shed light on the sophisticated mechanism by which malaria parasites utilize EV subpopulations as a communication tool to target different cellular destinations or host systems.

Multi-scale study water and ions transport in the cement-based materials:from molecular dynamics to random walk

The transport properties of water and ions play a key role in the durability of cement-based materials. However, little work has been done to study the diffusion behaviors of water and ions in a multi-scale view. Therefore, the current paper presented a multi-scale molecular dynamics fed random walk (MD-RW) simulation scheme for the purpose of obtaining the diffusion coefficients of water and ions in the calcium-silicate-hydrate (C–S–H) gel. At nanoscale, MD simulations were used to obtain the diffusion coefficients of water and ions in the C–S–H with nanopore size ranging from 0.5 nm to 5 nm since pore size has a crucial effect on the diffusion behavior of water and ions. Then these results were utilized as the input parameters for random walk simulation to scale the confining effect up and derive the effective diffusion coefficients of water and ions in the C–S–H gel at mesoscale. The results acquired from mean square displacement, atomic intensity distribution function and radial distribution function show that water molecules and Cl ions would form Ca–Cl, Ca–O ion-clustering and hydrogen bonds with C–S–H substrate which will restrict the transport of water molecules and Cl ions. In addition, with the size of gel pore increases from 0.5 nm to 5 nm, the diffusion coefficient of water increases from 0.016 to 1.85 × 10−9 m2 s−1 and the diffusion coefficient of Cl ions increases from 0.002 to 0.75 × 10−9 m2 s−1. In the random walk simulation, the diffusion coefficients of water and Cl ion were derived as 1.01 × 10−12 m2 s−1 and 1.2 × 10−13 m2 s−1 in the FCC packing model and 1.55 × 10−11 m2 s−1 and 1.77 × 10−12 m2 s−1 in the BCC packing model respectively, which reaches reasonable agreement with the previous studies results. Unlike traditional reverse methods which back-calculate these coefficients from macroscopic experimental results and hypothesized microstructure, this study presents the first bottom-up method deriving the transport properties of C–S–H gel directly from the physicochemical characteristics and microstructure, which has relevant significance for the study of concrete resistance to ion erosion and provides a basis for designing durable concrete.

Study on the early warning and forecasting of flash floods in small watersheds based on the rainfall pattern of risk probability combination

Flash floods cause great harm to people’s lives and property safety. Rainfall is one of the main causes of flash floods in small watersheds. The uncertainty of rainfall events results in inconsistency between the traditional single rainfall pattern and the actual rainfall process, which poses a great challenge for the early warning and forecasting of flash floods. To carry out the effective flash flood early warning and forecasting, this paper proposes a novel rainfall pattern by coupling total rainfall and peak rainfall intensity based on copula functions, i.e., the rainfall pattern of risk probability combination (RPRPC). On this basis, the Hydrologic Engineering Center-Hydrologic Modeling System (HEC-HMS) hydrological model is used to simulate the rainfall-runoff process, the trial algorithm is used to calculate the critical rainfall (CR), and the optimistic-general-pessimistic (O–G-P) early warning mode considering the decision maker's risk preference is proposed. The small watershed of Xinxian in Henan province, China, is taken as a case study for calculation. The results show that the RPRPC is feasible and closer to the actual rainfall process than the traditional rainfall pattern, Frank copula function is the best for determining the joint distribution function of total rainfall and peak rainfall intensity, and the HEC-HMS model can be applied to small watersheds in hilly areas. Additionally, both RPRPC and antecedent soil moisture condition (ASMC) have influence on CR, and the variation of RPRPC will change the influence of ASMC on CR. Finally, the effectiveness of O–G-P early warning mode is verified.

Focusing properties of azimuthally polarized helico-conical Lorentz-Gauss beams

We investigate the focusing properties of azimuthally polarized Lorentz-Gauss beams with helico-conical phase wavefront (APLG-HCBs). Without phase modulation, polarization state of azimuthally polarized Lorentz-Gauss beams is axisymmetric, and vibration direction at any point is along azimuthal. Combined with helico-conical phase wavefront, the field distribution can be altered, which can broader applications for magnetic measurement, optical tweezers technology and parallel optical imaging. In this paper, we calculate the intensity distribution function and describe the effects of topological charge m, eccentricity parameter K and numerical aperture NA on evolution of focal field intensity and gradient force mode.

Effects of coupling a stochastic convective parameterization with the Zhang–McFarlane scheme on precipitation simulation in the DOE E3SMv1.0 atmosphere model

Abstract. A stochastic deep convection parameterization is implemented into the US Department of Energy (DOE) Energy Exascale Earth System Model (E3SM) Atmosphere Model version 1.0 (EAMv1). This study evaluates its performance in simulating precipitation. Compared to the default model, the probability distribution function (PDF) of rainfall intensity in the new simulation is greatly improved. The well-known problem of “too much light rain and too little heavy rain” is alleviated, especially over the tropics. As a result, the contribution from different rain rates to the total precipitation amount is shifted toward heavier rain. The less frequent occurrence of convection contributes to suppressed light rain, while more intense large-scale and convective precipitation contributes to enhanced heavy total rain. The synoptic and intraseasonal variabilities of precipitation are enhanced as well to be closer to observations. The sensitivity of the rainfall intensity PDF to the model vertical resolution is examined. The relationship between precipitation and dilute convective available potential energy in the stochastic simulation agrees better with that in the Atmospheric Radiation Measurement (ARM) observations compared with the standard model simulation. The annual mean precipitation is largely unchanged with the use of the stochastic scheme except over the tropical western Pacific, where a moderate increase in precipitation represents a slight improvement. The responses of precipitation and its extremes to climate warming are similar with or without the stochastic deep convection scheme.

Mask image grayscale regulation for projection stereolithography in tissue engineering

The mask-image-projection-based stereolithography (MIP-SL) is one of the most promising methods for preparing biological scaffolds. In this paper, a mask image planning method based on grayscale regulation is proposed based on the characteristics of the bio-scaffold structure. It is based on support vector machine method and iterative method to intelligently regulate mask pixel gray value, which can achieve low exposure error and accordingly better curing quality. Furthermore, in order to discuss the properties of grayscale regulation, single pixel light intensity function acquisition experiment and stereolithography simulation based on light intensity function and mask grayscale regulation experiment were carried out. Results show that the light intensity distribution function of single pixel follows Gaussian distribution, and the light intensity energy between adjacent pixels will affect each other. The grayscale regulation scheme can improve the degree of reduction of the cured shape of the resin and is beneficial to the curing accuracy.

Effects of the slit width on the subsidiary maxima in multiple-slit diffraction: Analytical solutions

We present analytical solutions for the subsidiary maxima in multiple-slit diffraction, considering a nonzero slit width. To find the angular position of the subsidiary and principal maxima, the intensity distribution function is differentiated with respect to the phase associated with the angular position. To solve the resulted transcendental equation analytically, the derivative and phase are expanded in the order of a∕d (a: slit width; d: slit separation), and a set of equations is established by setting each term of the derivative as zero. Solving the equations for the coefficients in the phase, we analytically obtain the phase for the subsidiary maxima as a function of the slit number and a∕d up to the twelfth order in a∕d.

Mechanism and Experimental Study of Femtosecond-Laser Super-Resolution Processing Based on Beam Shaping Technology

The three-dimensional microsolid can be fabricated by scanning point-by-point inside the polymer material according to the predetermined trajectory in femtosecond-laser two-photon direct writing mode. In the process of machining, the shape and intensity distribution of focus spot are changed by some processing parameters, which affect the processing accuracy and surface quality. Based on Fresnel diffraction theory and the intensity distribution function of focal spot, the focal spot shape is simulated and the main factors affecting the light intensity distribution are analyzed theoretically and simulated numerically. We propose a shaping method to improve the asymmetric shape of the facula by adding a prefocusing lens. According to the mechanism of femtosecond-laser super-resolution processing, we propose a beam shaping method using four-ring complex transmittance phase plate to achieve super-resolution processing. The phase plate was optimized on the global optimization algorithm and genetic algorithm. The validation experiment was carried out by scanning the photochromic material film with pulsed laser and reading the fluorescence signal of the photochromic point with single photon confocal. The experimental results show that the facula distribution is approximately symmetrical, and the size of facula is decreased obviously. The compression ratio is basically consistent with the theoretical calculation results. Therefore, super-resolution processing can be achieved by adding pre-focusing lens and phase plate to shaping the laser beam. The results of theoretical and experimental studies provide sufficient basis for improving the machining accuracy and surface quality of microdevices.

Analysis on Intensity Matching Coefficient of Power Distribution Circuit Based on System Reliability Theory

The design intensities of four parts, i.e. ground conductor, hardware fittings, pole tower and foundation are greatly different, so it is difficult to evaluate the reliability of the whole power distribution circuit exactly. In this thesis, the intensity distribution functions of ground conductor, hardware fittings, pole tower and foundation have been calculated respectively, and then based on the system reliability theory, the reasonable failure sequence of power distribution circuit conforming to economic optimization principle is recommended. Under the assumed failure sequence, the calculation about intensity matching coefficient at the target confidence level is implemented, and finally, the intensity matching coefficients of ground conductor, hardwire fittings, pole tower and foundation of power distribution circuit are given.

Derivation and Experimental Verification of the Near-field 2D and 3D Optical Intensities From a Finite-size Light Emitting Diode (LED)

We derive the near-field light intensity distributions of an inorganic LED on its surface and in volumetric space. Our closed-form solution for 3D intensity distribution for a finite-size LED is consistent with Lambert's Cosine Law, which provides the 3D intensity distribution for an infinitesimal, flat light source. We also derive the formula for the 2D intensity distribution on a diode surface showing its similarity to a Gaussian function, which is typically used to approximate the surface light intensity profile for an LED and a laser diode. Our 2D intensity distribution function produces light propagation similar to the Gaussian beam propagation in space. However, unlike the Gaussian approximation, our formula invariably produces this behavior without assuming the refractive index inside the diode follows a quadratic function of the transverse spatial domains. Our 2D and 3D spatial intensity formulas in near-field for LEDs offer a unique way to calculate the peak intensity that occurs at the center of the flat LED source. We demonstrate, as expected, that the peak intensity increases with the size of the LED source as well as the brightness of each radiative electron-hole pair, which is a function of the drive current and quantum efficiency of the LED.

Theoretical analysis of the magnetic field and eddy current within a rectangular giant magnetostrictive material plate

In this paper, we present the distribution functions of magnetic field intensity and eddy current intensity within a rectangular magnetostrictive material plate. Firstly, on the basis of Maxwell's theory, the mathematical model for the magnetic field within the plate is established. Then, the governing equation for determining the magnetic field is solved by Fourier transform; an error in Stoll's book (1983) is corrected. Furthermore, the function of eddy current intensity is deduced. Next, the expressions of the magnetic field and eddy current are given in the case of the external magnetic field and the plate makes an angle of θ. Lastly, taking rectangular giant magnetostrictive plate is parallel to external magnetic field as example, the influencing factors of the inner magnetic field and eddy current are unveiled: the skin effect is enhanced with the increase of the exciting frequency, the relative permeability or conductivity; the higher the relative permeability or conductivity, the more significant the eddy current density increases.

Application of Textural Features in the Analysis of Breakstone Grading

Accuracy of breakstone grain-size analysis using digital images in the initial method and its modification based on algorithm proposed by D. Rubin is compared. A modification with averaging offeatures in all directions and the method with a classification feature represented by difference of intensity distribution functions of fragment projections are described. The results obtained using these methods in a series of tests on grading of five breakstone fractions measured in a certified laboratory. It is shown that the modified method by D. Rubin with averaging in all directions provides the highest accuracy.

Queue-Aware Power Consumption Minimization in Two-Tier Heterogeneous Networks

In this paper, we study the network average power consumption minimization problem in a two-tier heterogeneous network by optimally tuning the activation ratio of micro base stations (BSs) under the quality of service (QoS) constraints of the network mean queueing delay and the network signal-to-interference ratio (SIR) coverage. With the consideration of dynamic packets arrivals, each BS can either be busy or be idle depending on its queueing status. The network performance is thus critically determined by the traffic intensity of each BS. With the assumption of universal frequency reuse, the average traffic intensity of each tier is characterized by a set of fixed-point equations, which can be solved by a proposed iterative method. By using the approximation that BSs of the same tier have the same SIR coverage, the cumulative distribution function of the traffic intensity of each tier is further obtained. On that basis, the network average power consumption per area, the network mean queueing delay, and the network SIR coverage are characterized. Numerical results demonstrate that if the idle power coefficient is below a certain threshold, then the optimal activation ratio equals the one to minimize the network average power consumption per area; otherwise, the optimal activation ratio can be obtained according to the QoS constraints. It is further shown that universal frequency reuse outperforms spectrum partitioning in terms of both the network average power consumption and the network SIR coverage in the considered scenario.