Representation of three-dimensional mass distribution of the Earth's interior by biorthogonal series and its use for studying internal structure of the planet

This paper utilizes the mathematical concept of approximation within an ellipsoid from a single viewpoint to present the spatial mass distribution function of the Earth's interior and its internal potential.The primary focus lies in constructing the volume distribution of masses in the planet's interior, with the expansion coefficients being linear combinations of the Stokes constants. Several possible approaches are suggested for determining accurately these coefficients employing three-dimensional(biorthogonal)polynomials. By expressing the mass distribution function of the Earth's interior and its internal potential as a series, an algorithm is introduced for the calculation of gravitational energy. It allows us to estimate fluctuations in gravitational energy. The implementation of this algorithm offers the means of establishing the extent to which the Earth deviates from a state of hydrostatic equilibrium as a celestial body.Due to the aforementioned method, calculations have been conducted to validate its effectiveness and reliability. This example is given as an illustration of a given method for studying the internal structure of planets.

A New Distribution Method for Wet Steam Injection Optimization

A new approach and a new related distribution system are proposed to address the issue of uneven steam injection caused by the different suction capacities of the used wells during the application of steam“stimulation”methods for enhanced oil recovery.The new distribution system consists of a swirler,spiral dividing baffles,and critical flow nozzles.Numerical simulations are used to analyze the flow-field and degree of steam homogeneity obtained with such an approach.The results indicate that a higher inlet pressure leads to better results.Additionally,the internal flow field becomes more stable,and the deviation from an even distribution reduces to±4.0%even when the resistance of each branch is inconsistent.Furthermore,field tests have yielded satisfactory results.

Simultaneous estimation of aerosol optical constants and size distribution from angular light-scattering measurement signals

The angular light-scattering measurement（ALSM） method combined with an improved artificial bee colony algorithm is introduced to determine aerosol optical constants and aerosol size distribution（ASD） simultaneously. Meanwhile, an optimized selection principle of the ALSM signals based on the sensitivity analysis and principle component analysis（PCA）is proposed to improve the accuracy of the retrieval results. The sensitivity analysis of the ALSM signals to the optical constants or characteristic parameters in the ASD is studied first to find the optimized selection region of measurement angles. Then, the PCA is adopted to select the optimized measurement angles within the optimized selection region obtained by sensitivity analysis. The investigation reveals that, compared with random selection measurement angles, the optimized selection measurement angles can provide more useful measurement information to ensure the retrieval accuracy. Finally,the aerosol optical constants and the ASDs are reconstructed simultaneously. The results show that the retrieval accuracy of refractive indices is better than that of absorption indices, while the characteristic parameters in ASDs have similar retrieval accuracy. Moreover, the retrieval accuracy in studying L-N distribution is a little better than that in studying Gamma distribution for the difference of corresponding correlation coefficient matrixes of the ALSM signals. All the results confirm that the proposed technique is an effective and reliable technique in estimating the aerosol optical constants and ASD simultaneously.

The Stability Constants of Complexes of BDBPH- Metals and Species Distributions

The stability constants of the mononuclear complexes of BDBPH-Zn(II), Cd(II) and Mn (II) were determined by the potentiometric equilibrium measurements, and species distributions were also discussed. The metal ions do not combine with the ligand until the first two protons of the ligand have almost been completely neutralized. The main species were mononuclear complexes with the diprotonated ligand, MH,L. The three metal ions also form mono- and noprotonated (fully deprotonated) complexes, MHL, ML. The relative order of stabilities of the mononuclear complexes, ML, is Zn(II) > Cd(II) > Mn(II). The ligand has strong tendency to form mononuclear complexes with Zn(II), Cd(II) and Mn(II), and it can also form dinuclear complexes at high pH.

The Study on the Stability Constant and Species Distribution of Eu (III) and Tb (III) Complexes with BDBPH

The stability constants and species distributions of complexes of two lanthanide ions, Eu（Ⅲ） and Tb（Ⅲ）, with a macrocyclic ligand, BDBPH, in 1：1 and 2：lsystem, were determined potentiometrically at 25.0 ℃ and I=0.100 mol L^-l. The two metal ions could form deprotonated mono- or dinuclear complexes with BDBPH after the first two protons of the ligand completely neutralized. At higher pH values, Eu（Ⅲ） could not form hydroxy complexes with BDBPH, while Tb（Ⅲ） could form hydroxy complexes in the type of M2L（OH）, M2L（OH）2, and M2L（OH）3.

CORRELATION BETWEEN HYSTERESIS OF GAS-LIQUID MASS TRANSFER AND LIQUID DISTRIBUTION IN A TRICKLE BED

The hysteresis of gas-liquid mass transfer rate and the corresponding radial liquiddistribution in a trickle bed reactor are measured to provide evidence for the correlation between thesetwo behaviors.Experimental results indicate that the hysteresis of gas-liquid mass transfer originatesfrom the nonuniformity of the hydrodynamic state of gas-liquid flow and the radial maldistributionof local kgia corresponds very well to the radial maldistribution of liquid flow in the bed.The localliquid flow rate is also found to be nonuniform in the azimuthal direction.In view of maldistributedliquid flow even in the pulsing flow regime,the conventional plug flow model seems oversimplifiedfor describing the behavior of a trickle bed.

Inference on Constant-Partially Accelerated Life Tests for Mixture of Pareto Distributions under Progressive Type-II Censoring

The main purpose of this paper is to obtain the inference of parameters of heterogeneous population represented by finite mixture of two Pareto (MTP) distributions of the second kind. The constant-partially accelerated life tests are applied based on progressively type-II censored samples. The maximum likelihood estimates (MLEs) for the considered parameters are obtained by solving the likelihood equations of the model parameters numerically. The Bayes estimators are obtained by using Markov chain Monte Carlo algorithm under the balanced squared error loss function. Based on Monte Carlo simulation, Bayes estimators are compared with their corresponding maximum likelihood estimators. The two-sample prediction technique is considered to derive Bayesian prediction bounds for future order statistics based on progressively type-II censored informative samples obtained from constant-partially accelerated life testing models. The informative and future samples are assumed to be obtained from the same population. The coverage probabilities and the average interval lengths of the confidence intervals are computed via a Monte Carlo simulation to investigate the procedure of the prediction intervals. Analysis of a simulated data set has also been presented for illustrative purposes. Finally, comparisons are made between Bayesian and maximum likelihood estimators via a Monte Carlo simulation study.

Inference for constant-stress accelerated life test with Type-I progressively hybrid censored data from Burr-XII distribution

This paper proposes a simple constant-stress accel- erated life test （ALT） model from Burr type XII distribution when the data are Type-I progressively hybrid censored. The maximum likelihood estimation （MLE） of the parameters is obtained through the numerical method for solving the likelihood equations. Approxi- mate confidence interval （CI）, based on normal approximation to the asymptotic distribution of MLE and percentile bootstrap Cl is derived. Finally, a numerical example is introduced and then a Monte Carlo simulation study is carried out to illustrate the pro- posed method.

Optimization of the Water Distribution Networks with Differential Evolution (DE) and Mixed Integer Linear Programming (MILP)

Nowadays, due to increasing population and water shortage and competition for its consumption, especially in the agriculture, which is the largest consumer of water, proper and suitable utilization and optimal use of water resources is essential. One of the important parameters in agriculture field is water distribution network. In this research, differential evolution algorithm (DE) was used to optimize Ismail Abad water supply network. This network is pressurized network and includes 19 pipes and 18 nodes. Optimization of the network has been evaluated by developing an optimization model based on DE algorithm in MATLAB and the dynamic connection with EPANET software for network hydraulic calculation. The developing model was run for the scale factor (F), the crossover constant (Cr), initial population (N) and the number of generations (G) and was identified best adeptness for DE algorithm is 0.6, 0.5, 100 and 200 for F and Cr, N and G, respectively. The optimal solution was compared with the classical empirical method and results showed that implementation cost of the network by DE algorithm was 10.66% lower than the classical empirical method.

Distribution of Ag(I), Li(I)-Cs(I) Picrates, and Na(I) Tetraphenylborate with Differences in Phase Volume between Water and Diluents

Ionic strength conditions in distribution experiments with single ions are very important for evaluating their distribution properties. Distribution experiments of picrates (MPic) with M = Ag(I) and Li(I)-Cs(I) into o-dichlorobenzene (oDCBz) were performed at 298 K by changing volume ratios (Vorg/V) between water and oDCBz phases, where “org” shows an organic phase. Simultaneously, an analytic equation with the Vorg/V variation was derived in order to analyze such distribution systems. Additionally, the AgPic distribution into nitrobenzene (NB), dichloromethane, and 1,2-dichloroethene (DCE) and the NaB(C6H5) 4 (=NaBPh4) one into NB and DCE were studied at 298 K under the conditions of various Vorg/V values. So, extraction constants (Kex) for MPic into the org phases, their ion-pair formation constants (KMA,org) for MA = MPic in the org ones, and standard distribution constants () for the M(I) transfers between the water and org bulk phases with M = Ag and Li-Cs were determined at the distribution equilibrium potential (dep) of zero V between the bulk phases and also the Kex (NaA), KNaA,org, and values were done at A-=BPh-4. Here, the symbols Kex, KMA,org, and or were defined as [MA] org/[M+][A-], [MA] org/[M+]org [A-]org, and [M+]org/[M+] or [A-]org/[A-] at dep = 0, respectively. Especially, the ionic strength dependences of Kex and KMPic,org were examined at M = Li(I)-K(I) and org = oDCBz. From above, the conditional distribution constants, KD,BPh4 and KD,Cs, were classified by checking the experimental conditions of the I, Iorg, and dep values.

Effect of impeller type and scale-up on spatial distribution of shear rate in a stirred tank

The main spatial distribution features of shear rate in a stirred tank operated with five different radial and axial flow impellers were presented with particle image velocimetry(PIV)experiments.Not only the average shear rate in the whole tank but also the local value in the vicinity of impeller increases linearly with impeller speed.Furthermore,the shear coefficient(Ks,imp)at the impeller outlet is linearly related to the impeller flow number(Nq)and decreases with the increase of Nq in general at the constant power consumption per unit volume(Pv).During scale-up based on the constant Pv and geometric similarity,CFD results show that the volume-averaged shear rate(cavg)for RDT decreases faster than that of other impellers with the impeller tip velocity(Utip).The novel multi-blade combined(MBC)impeller with the increased height-to-diameter ratio of the stirred tank is able to more effectively improve the distribution uniformity of shear rate at the same Pv after scale-up.These studies provide a data basis for selecting the impeller types and improving the shear rate environment in the large-scale stirred tank.

Cation Distribution in Co_0.7Me_0.3Fe₂O₄(Me = Zn, Ni and Mn)

Co0.7Me0.3Fe2O4 (Me = Zn, Ni and Mn) were synthesized through co-precipitation method. Cationic distribution for these ferrites was proposed on the basis of magnetization measurements and available occupancy of the substituent ions into the spinel lattice. Theoretical lattice constant calculations confirm the proposed cationic distributions were the correct ones.

Prediction of Symmetrical and Asymmetrical of Diurnal Global Solar Irradiance Distribution—New Approach

A simple formula to predict the received global solar irradiance q(t), W/m2 for clear days is suggested on pure theoretical basis. It is expressed in terms of the length of the local day time td which is well defined in literatures on meteorological basis. The introduced distribution is also a function of the maximum value of the daily received irradiance qmax. which in turn is expressed in term of the solar constant. This renders the trial to be a closed system. Thus the obtained distribution is not a semi empirical one. Both cases of symmetrical and asymmetrical distributions for q(t) are considered. For its simplicity it can be easily integrated along the length of the day to get the daily totals of solar energy received by unit horizontal area. This is important for practical applications. Comparison between computed according to the present model and published experimental meteorological data in Barcelona (Spain), Hong Kong (China), Jeddah and Makkah (Saudi Arabia) is given as illustrative examples. Better fitting relative to the published trials for the same locations are obtained. The introduced model itself gives good fitting for the intermediate intervals points of the local day time which is the more effective region. The estimated relative error is 12% for Hong Kong, and it is 7% for Barcelona, Jeddah and Makah.

Distribution Equilibrium of o-Phthalic Acid and trans-Butenedioic in Water and Di-n-butyl Phthalate

The organic dissolvent （di-n-butyl phthalate） needs to be washed by water to recycle itself in the process of recovering maleic anhydride by organic dissolvent. The design and optimization of the extraction process require the distribution coefficients of the organic solutes, o-phthalic acid and trans-butenedioic in water and di-n-butyl phthalate, on which the extraction efficiency depends. In this study, the distribution coefficients of o-phthalic acid and trans-butenedioic in water and di-n-butyl phthalate（DBP） at 298.15 K, 318.15 K and 333.15 K were determined respectively by acid-alkali titration. The dissociation constants of o-phthalic acid and trans-butenedioic at those temperatures were obtained by fitting the measured hydrogen-ion concentrations and the known solute concentrations in the aqueous solution containing the two organic solutes. Then the distribution constants were calculated. Both the distribution coefficients and the distribution constants increase along with the temperature increasing. And the distribution coefficients at 333.15 K are large enough to ensure the efficiency of extraction process. In addition, the mutual solubility of water and di-n-butyl phthalate at 298.15 K, 318.15 K and 333.15 K was also measured respectively by High Performance Liquid Chromatography and Karl Fischer Watertitration, which was not more than 0.50/0（mass fraction）.

Determination of the Henry’s Law Constant of Hexane in High-Viscosity Polymer Systems

The Henry’s law constant of volatiles in polymer systems is a crucial parameter reflecting the gas-liquid equilibrium,which is very important for devolatilization.In this research,polyolefin elastomer(POE)-cyclohexane and polydimethylsiloxane(PDMS)-hexane systems were studied,and the Henry’s law constant was obtained by measuring the gas phase equilibrium partial pressure when polymer solutions containing different mass fractions of volatiles reached a saturated state.The effects of temperature,type of volatiles,and polymer viscosity on the gas phase equilibrium partial pressure and Henry’s law constant of the volatiles were investigated.The results indicate that,with the increase of temperature and polymer viscosity,the gas phase equilibrium partial pressure and Henry’s law constant of volatiles increase.As temperature increases,the solubility of gas in liquid decreases.The relationship between the Henry’s law constant and temperature is consistent with the Arrhenius law.In the PDMS-hexane system,the gas phase equilibrium partial pressure and Henry’s law constant of n-hexane are higher than those of cyclohexane.The obtained Henry’s law constants can be used as a reference for perfecting the devolatilization process and improving the devolatilization effect.

Revisiting the Curie-Von Schweidler Law for Dielectric Relaxation and Derivation of Distribution Function for Relaxation Rates as Zipf’s Power Law and Manifestation of Fractional Differential Equation for Capacitor

The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations;and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.

具备故障重构能力的双极直流接口变换器最优运行区域

中低压直流配电系统中,现有的双极直流接口变换器通常无法在进入单极运行模式下实现故障阻断与重构功能。基于一种互联分布式电源与双极直流系统的故障重构型直流接口变换器拓扑,分析单双极性运行模式的工作性能。在正常的双极运行模式下,变换器通过最小峰值电流控制策略,实现开关器件电流应力有效降低。在短路故障导致的单极运行模式下,变换器通过故障重构策略与恒功率传输控制策略,消除短路故障对正常端口的不利影响,维持关键负荷的连续供电。同时给出变换器在单双极模式的优化控制策略下的软开关运行区域,从而精确刻画出变换器的最优运行区域。实验结果证明理论分析的正确性,研究工作有助于指导中低压直流配电系统的工程实践。

基于韦布尔分布下改进型恒虚警检测器的检测性能分析

为了提高恒虚警检测器(constant false alarm rate detector,CFAR)在有干扰目标存在的杂波环境下的检测性能,提出了5种基于自适应删除(automatic censored mean level detector,ACMLD)恒虚警算法与均值类算法的改进型,并在韦布尔分布模型下对影响背景杂波功率估计的参考单元长度和干扰目标个数进行检测概率分析。结果表明:基于该改进型检测器可有效提高有干扰目标的检测性能,其中改进型单侧自适应删除(single automatic censored mean level detector,SACMLD)算法适合在一侧参考窗均匀的情况下使用,而自适应删除最小(adaptive censored smallest of detector,ACSO)算法适合两侧参考窗都不均匀的情况下使用。文中提出的基于韦布尔分布下改进型恒虚警检测器可为铁路、航空等多目标环境检测提供参考。

基于PI控制的内燃动车组柴油机恒功率控制技术

柴油机在非恒功率输出时,不仅燃料效率低,而且可能会产生较大的机械应力,导致机械部件的磨损和破坏。为确保内燃动车组柴油机高效运行,基于内燃动车组柴油发电机组恒功率输出的运行模式,文章提出了一种比例-积分控制方法,实现了负载侧牵引系统功率稳定跟随柴油发电机组的输出功率目标值,通过负载侧恒功率运行保障发电机组的恒功率稳定输出,从而提高柴油机燃油经济性。经过仿真及试验测试验证,采用此控制方法,负载功率稳态波动在±2%以内,实现了内燃动车组柴油机恒功率运行及负载功率对目标值的实时跟随。

高温层压机热场分布对微波基板性能的影响

采用多物理仿真软件COMSOL对高温层压机热场分布进行模拟,分析不同热场对微波基板性能的影响。根据理论预测与实验结果对层压机加热管位置进行了合理调整,调整后基板表面质量、相对介电常数均匀性和剥离强度均得到了改善,消除了基板表面褶皱,相对介电常数均匀性Cv值达到0.000 3,剥离强度超过2.4 N/mm。同时,基板厚度也实现稳定可控,基板厚度的过程能力指数Cpk达到1.0。借助统计控制过程(SPC)技法和COMSOL软件解决了高温层压机热场存在的问题,大幅度降低了实验成本,为解决实际生产中遇到的问题提供了有效工具。