A High-Order Conservative Numerical Method for Gross-Pitaevskii Equation with Time-Varying Coefficients in Modeling BEC

We propose a high-order conservative method for the nonlinear Sehodinger/Gross-Pitaevskii equation with time- varying coefficients in modeling Bose Einstein condensation （BEC）. This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method, finely describes the condensate wave function and physical characteristics in some small potential wells. Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method. Moreover, it preserves several conservation laws well and even exactly under some specific conditions.

Entropy weight coefficient model and its application in evaluation of groundwater vulnerability of the Sanjiang Plain

The research of groundwater vulnerability is the basic work to protect the groundwater. For utilizing groundwater resource continuably, groundwater vulnerability evaluation is necessary. Useful reference to protect, exploit and utilize on groundwater resource are provided rationally. According to the real condition of Sanjiang Plain, the indexes system is established based on the traditional DRASTIC model. The new system includes the following seven indexes： Depth of Water, Net Recharge, Aquifer Media, Soil Media, Conductivity of the Aquifer, Land Utilizing Ratio and Populace Density. The related analysis appears that the system is rather reasonable. Because traditional methods, such as analytic hierarchy process and fuzzy mathematics theory, can＇t be avoided human interference in selection of weights, they could lead to an imprecise result. In order to evaluate the groundwater vulnerability reasonably, entropy weight coefficient method is applied for the first time, which provides a new way to groundwater vulnerability evaluation. The method is a model whose weights are insured by the calculation process, so the artificial disturb can be avoided. It has been used to evaluate the groundwater vulnerability in Sanjiang Plain. The satisfied result is acquired. Comparably, the same result is acquired by the other method named projection pursuit evaluation based on real-coded accelerating genetic algorithm. It shows that entropy weight coefficient method is applicable on groundwater vulnerability evaluation. The evaluation result can provide reference on the decision-making departments.

THEORETICAL MODEL OF EFFECTIVE STRESS COEFFICIENT FOR ROCK/SOIL-LIKE POROUS MATERIALS

Physical mechanisms and influencing factors on the effective stress coefficient for rock/soil-like porous materials are investigated, based on which equivalent connectivity index is proposed. The equivalent connectivity index, relying on the meso-scale structure of porous material and the property of liquid, denotes the connectivity of pores in Representative Element Area （REA）. If the conductivity of the porous material is anisotropic, the equivalent connectivity index is a second order tensor. Based on the basic theories of continuous mechanics and tensor analysis, relationship between area porosity and volumetric porosity of porous materials is deduced. Then a generalized expression, describing the relation between effective stress coefficient tensor and equivalent connectivity tensor of pores, is proposed, and the expression can be applied to isotropic media and also to anisotropic materials. Furthermore, evolution of porosity and equivalent connectivity index of the pore are studied in the strain space, and the method to determine the corresponding functions in expressions above is proposed using genetic algorithm and genetic programming. Two applications show that the results obtained by the method in this paper perfectly agree with the test data. This paper provides an important theoretical support to the coupled hydro-mechanical research.

Prediction of Henry's constant in polymer solutions using PCOR equation of state coupled with an activity coefficient model

In this paper,the polymer chain of rotator(PCOR) equation of state(EOS) was used together with an EOS/G^E mixing rule(MHV1) and the Wilson's equation as an excess-Gibbs-energy model in the proposed approach to extend the capability and improve the accuracy of the PCOR EOS for predicting the Henry's constant of solutions containing polymers.The results of the proposed method compared with two equation of state(van der Waals and GC-Flory) and three activity coefficient models(UNIFAC,UNIFAC-FV and Entropic-FV) indicated that the PCOR EOS/Wilson's equation provided more accurate results.The interaction parameters of Wilson's equation were fitted with Henry's constant experimental data and the property parameters of PCOR,a and b,were fitted with experimental volume data(Tait equation).As a result,the present work provided a simple and useful model for prediction of Henry's constant for polymer solutions.

Remaining useful life prediction based on nonlinear random coefficient regression model with fusing failure time data

Remaining useful life(RUL) prediction is one of the most crucial elements in prognostics and health management(PHM). Aiming at the imperfect prior information, this paper proposes an RUL prediction method based on a nonlinear random coefficient regression(RCR) model with fusing failure time data.Firstly, some interesting natures of parameters estimation based on the nonlinear RCR model are given. Based on these natures,the failure time data can be fused as the prior information reasonably. Specifically, the fixed parameters are calculated by the field degradation data of the evaluated equipment and the prior information of random coefficient is estimated with fusing the failure time data of congeneric equipment. Then, the prior information of the random coefficient is updated online under the Bayesian framework, the probability density function(PDF) of the RUL with considering the limitation of the failure threshold is performed. Finally, two case studies are used for experimental verification. Compared with the traditional Bayesian method, the proposed method can effectively reduce the influence of imperfect prior information and improve the accuracy of RUL prediction.

Activity Coefficient Models to Describe Vapor-Liquid Equilibrium in Ternary Hydro-Alcoholic Solutions

In this study,three semipredictive activity coefficient models:Wilson,non-random-two liquid model(NRTL),and universal quasi-chemical model(UNIQUAC),have been used for modeling vapor-liquid equilibrium properties of ternary mixtures that include substances found in alcoholic distillation processes of wine and musts.In particular,vapor-liquid equilibrium in ternary mixtures containing water + ethanol + congener has been modeled using parameters obtained from binary and ternary mixture data.The congeners are substances that although present in very low concentrations,of the order of part per million,are important enological parameters.The results given by these different models have been compared with literature data and conclusions about the accuracy of the models studied are drawn,recommending the best models for correlating and predicting phase equilibrium properties of this type of mixtures.

Efficient Shrinkage Estimation about the Partially Linear Varying Coefficient Model with Random Effect for Longitudinal Data

In this paper, an efficient shrinkage estimation procedure for the partially linear varying coefficient model (PLVC) with random effect is considered. By selecting the significant variable and estimating the nonzero coefficient, the model structure specification is accomplished by introducing a novel penalized estimating equation. Under some mild conditions, the asymptotic properties for the proposed model selection and estimation results, such as the sparsity and oracle property, are established. Some numerical simulation studies and a real data analysis are presented to examine the finite sample performance of the procedure.

Quasi Maximum Likelihood for MESS Varying Coefficient Panel Data Models with Fixed Effects

The study of spatial econometrics has developed rapidly and has found wide applications in many different scientific fields,such as demog­raphy,epidemiology,regional economics,and psychology.With the deepening of research,some scholars find that there are some model specifications in spatial econometrics,such as spatial autoregressive(SAR)model and matrix exponential spatial specification(MESS),which cannot be nested within each other.Compared with the common SAR models,the MESS models have computational advantages because it eliminates the need for logarithmic determinant calculation in maxi­mum likelihood estimation and Bayesian estimation.Meanwhile,MESS models have theoretical advantages.However,the theoretical research and application of MESS models have not been promoted vigorously.Therefore,the study of MESS model theory has practical significance.This paper studies the quasi maximum likelihood estimation for ma­trix exponential spatial specification(MESS)varying coefficient panel data models with fixed effects.It is shown that the estimators of model parameters and function coefficients satisfy the consistency and asymp­totic normality to make a further supplement for the theoretical study of MESS model.

Congregated electron phase and Wagner model applied in titanium distribution behavior in low-titanium slag

For studying the carbon thermal reduction rules of titanium in hot metal and providing a theoretical basis for the blast furnace（BF） hearth protection, the distribution behavior of titanium between low-titanium slag system of CaO-SiO2-MgO-Al2O3-TiO2 and hot metal was studied using analytical reagents in a temperature range from 1350 °C to 1600 °C. Through high temperature melting, rapid quenching, chemical analysis and thermodynamic model calculating, the results showed that the increase of reaction temperature, which improved the titanium distribution L（Ti） and lowered the system activity coefficient γsys, leads to the rise of equilibrium constant. Combined with Wagner and congregated electron phase models, the data obtained in distribution experiments were used to fit out the Gibbs free energy formula of titanium carbothermic reduction. Finally, the relations between the contents of Si and Ti in hot metal and the titanium load to reach the minimum w（Ti） for the formation of Ti C were given.

Temperature field model in surface grinding: a comparative assessment

Grinding is a crucial process in machining workpieces because it plays a vital role in achieving the desired precision and surface quality.However,a significant technical challenge in grinding is the potential increase in temperature due to high specific energy,which can lead to surface thermal damage.Therefore,ensuring control over the surface integrity of workpieces during grinding becomes a critical concern.This necessitates the development of temperature field models that consider various parameters,such as workpiece materials,grinding wheels,grinding parameters,cooling methods,and media,to guide industrial production.This study thoroughly analyzes and summarizes grinding temperature field models.First,the theory of the grinding temperature field is investigated,classifying it into traditional models based on a continuous belt heat source and those based on a discrete heat source,depending on whether the heat source is uniform and continuous.Through this examination,a more accurate grinding temperature model that closely aligns with practical grinding conditions is derived.Subsequently,various grinding thermal models are summarized,including models for the heat source distribution,energy distribution proportional coefficient,and convective heat transfer coefficient.Through comprehensive research,the most widely recognized,utilized,and accurate model for each category is identified.The application of these grinding thermal models is reviewed,shedding light on the governing laws that dictate the influence of the heat source distribution,heat distribution,and convective heat transfer in the grinding arc zone on the grinding temperature field.Finally,considering the current issues in the field of grinding temperature,potential future research directions are proposed.The aim of this study is to provide theoretical guidance and technical support for predicting workpiece temperature and improving surface integrity.

Abnormal Behavior Detection and Recognition Method Based on Improved ResNet Model

The core technology in an intelligent video surveillance system is that detecting and recognizing abnormal behaviors timely and accurately.The key breakthrough point in recognizing abnormal behaviors is how to obtain the effective features of the picture,so as to solve the problem of recognizing them.In response to this difficulty,this paper introduces an adjustable jump link coefficients model based on the residual network.The effective coefficients for each layer of the network can be set after using this model to further improving the recognition accuracy of abnormal behavior.A convolution kernel of 1×1 size is added to reduce the number of parameters for the purpose of improving the speed of the model in this paper.In order to reduce the noise of the data edge,and at the same time,improve the accuracy of the data and speed up the training,a BN(Batch Normalization)layer is added before the activation function in this network.This paper trains this network model on the public ImageNet dataset,and then uses the transfer learning method to recognize these abnormal behaviors of human in the UTI behavior dataset processed by the YOLO_v3 target detection network.Under the same experimental conditions,compared with the original ResNet-50 model,the improved model in this paper has a 2.8%higher accuracy in recognition of abnormal behaviors on the public UTI dataset.

Incorporating shape constraints in generalized additive modelling of the height-diameter relationship for Norway spruce

Background： Measurements of tree heights and diameters are essential in forest assessment and modelling. Tree heights are used for estimating timber volume, site index and other important variables related to forest growth and yield, succession and carbon budget models. However, the diameter at breast height （dbh） can be more accurately obtained and at lower cost, than total tree height. Hence, generalized height-diameter （h-d） models that predict tree height from dbh, age and other covariates are needed. For a more flexible but biologically plausible estimation of covariate effects we use shape constrained generalized additive models as an extension of existing h-d model approaches. We use causal site parameters such as index of aridity to enhance the generality and causality of the models and to enable predictions under projected changeable climatic conditions. Methods： We develop unconstrained generalized additive models （GAM） and shape constrained generalized additive models （SCAM） for investigating the possible effects of tree-specific parameters such as tree age, relative diameter at breast height, and site-specific parameters such as index of aridity and sum of daily mean temperature during vegetation period, on the h-d relationship of forests in Lower Saxony, Germany. Results： Some of the derived effects, e.g. effects of age, index of aridity and sum of daily mean temperature have significantly non-linear pattern. The need for using SCAM results from the fact that some of the model effects show partially implausible patterns especially at the boundaries of data ranges. The derived model predicts monotonically increasing levels of tree height with increasing age and temperature sum and decreasing aridity and social rank of a tree within a stand, The definition of constraints leads only to marginal or minor decline in the model statistics like AIC An observed structured spatial trend in tree height is modelled via 2-dimensional surface fitting. Conclusions： We demonstrate that the SCAM approach allows optimal regression modelling flexibility similar to the standard GAM but with the additional possibility of defining specific constraints for the model effects. The longitudinal character of the model allows for tree height imputation for the current status of forests but also for future tree height prediction.

Comparison of numerical simulations and experiments in conical gas–solid spouted bed

Flow behavior of gas and particles in conical spouted beds is experimentally studied and simulated using the twofluid gas-solid model with the kinetic theory of granular flow.The bed pressure drop and fountain height are measured in a conical spouted bed of 100 mm I.D.at different gas velocities.The simulation results are compared with measurements of bed pressure drop and fountain height.The comparison shows that the drag coefficient model used in cylindrical beds under-predicted bed pressure drop and fountain height in conical spouted beds due to the partial weight of particles supported by the inclined side walls.It is found that the numerical results using the drag coefficient model proposed based on the conical spouted bed in this study are in good agreement with experimental data.The present study provides a useful basis for further works on the CFD simulation of conical spouted bed.

Hydrodynamic Characteristics of Three Rows of Vertical Slotted Wall Breakwaters

In this study, we examine the hydrodynamic characteristics of three rows of vertical slotted wall breakwaters in which the front and middle walls are permeable and partially immersed in a water channel of constant depth, whereas the third wall is impermeable. The wave–structure interaction and flow behavior of this type of breakwater arrangement are complicated and must be analyzed before breakwaters can be appropriately designed. To study the hydrodynamic breakwater performance, we developed a mathematical model based on the eigenfunction expansion method and a least squares technique for predicting wave interaction with three rows of vertical slotted wall breakwaters. We theoretically examined the wave transmission, reflection, energy loss, wave runup, and wave force under normal regular waves. Comparisons with experimental measurements show that the mathematical model results adequately reproduce most of the important features. The results of this investigation provide a better understanding of the hydrodynamic performance of triple-row vertical slotted wall breakwaters.

Durability of sea-sand containing concrete:Effects of chloride ion penetration

This paper describes an orthogonal experiment on the effect of water/cement ratio,water consumption per cubic meter,curing time,and type of sand on the response＂resistance to chloride ion penetration＂.A sea-sand containing concrete was used for the trials.An analysis of chloride ion diffusion coefficients at different factor levels was performed.A predictive model of chloride ion diffusion in concrete is developed through regression analysis.The experimental results show that when the water/cement ratio varies from 0.45 to 0.60,and the water consumption per cubic meter varies from 185 to 215 kg,and the curing time varies from 30 to 180 d then the size of the effects fall in the order（most significant first）： curing time,type of sand,water consumption per cubic meter,and water/cement ratio.Chloride ion penetration is reduced,and better durability of the concrete is observed,with longer curing times,less water consumption per cubic meter,and a smaller water/cement ratio.

Using a process-oriented methodology to precisely evaluate temperature suitability for potato growth in China using GIS

A process-oriented methodology to conduct precise evaluation temporally and spatially on temperature suitability for potato growth was applied in China. Arable lands in China were gridded with 1 km×1 km geographic units, and potential potato phenology in each unit was automatically identified in terms of the potato planting initial temperature and effective accu- mulated temperature. A temperature thermal response coefficient model was used to compute a temperature suitability value for each day of potato phenology in each geographic unit. In addition, five temperature suitability ranking methods were applied to define suitable areas： （1） upper fourth quantile, （2） median, （3） expected value＋1/4 standard deviation, （4） expected value＋1/2 standard deviation, （5） expected value＋1 standard deviation. A validation indicator was innovated to test the effectiveness of the five ranking methods. The results showed that from a strict degree point of view, the five methods sequence was as follows： 1=3〉4〉2〉5, with a and c determined as the two best ranking methods. For methods 1 and 3, the suitable potato growing area was 1 of 57.76× 10^4 km2. In addition, the suitable, areas were spatially coincident with the main potato producing counties. The study output technically supports the proposal from China＇s government that there is a large potential area to grow winter-ploughed potato in South China because the potential suitable area for growing potato is approximately 2×10^7 ha. In southeast Heilongjiang and east Jilin, where it is hilly and mountainous, there are still some potentially suitable areas for potato growing accounting for nearly 2.32×10^6 ha. The authors suggest to optimize the agricultural regionalization and layout in China and to adjust the cropping pattern structure.

Static analysis of ultra-thin beams based on a semi-continuum model

A linear semi-continuum model with discrete atomic layers in the thickness direction was developed to investigate the bending behaviors of ultra-thin beams with nanoscale thickness.The theoretical results show that the deflection of an ultra-thin beam may be enhanced or reduced due to different relaxation coefficients.If the relaxation coefficient is greater/less than one,the deflection of micro/nano-scale structures is enhanced/reduced in comparison with macro-scale structures.So,two opposite types of size-dependent behaviors are observed and they are mainly caused by the relaxation coefficients.Comparisons with the classical continuum model,exact nonlocal stress model and finite element model （FEM） verify the validity of the present semi-continuum model.In particular,an explanation is proposed in the debate whether the bending stiffness of a micro/nano-scale beam should be greater or weaker as compared with the macro-scale structures.The characteristics of bending stiffness are proved to be associated with the relaxation coefficients.

Damage model of fresh concrete in sulphate environment

A model of damage to fresh concrete in a corrosive sulphate environment was formulated to investigate how and why the strength of corroded concrete changes over time. First, a corroded concrete block was divided into three regions: an expanded and dense region; a crack-development region; and a noncorroded region. Second, based on the thickness of the surface corrosion layer and the rate of loss of compressive strength of the corroding region, a computational model of the concrete blocks' corrosion-resistance coefficient of compressive strength in a sulphate environment was generated. Third, experimental tests of the corrosion of concrete were conducted by immersing specimens in a corrosive medium for 270 d. A comparison of the experimental results with the computational formulae shows that the calculation results and test results are in good agreement. A parameter analysis reveals that the corrosion reaction plays a major role in the corrosion of fresh concrete containing ordinary Portland cement,but the diffusion of the corrosion medium plays a major role in the corrosion of concrete mixtures containing fly ash and sulphate-resistant cement. Fresh concrete with a high water-to-cement ratio shows high performance during the whole experiment process whereas fresh concrete with a low water-to-cement ratio shows poor performance during the late experiment period.

Modified DIX model for ion-exchange equilibrium of L-phenylalanine on a strong cation-exchange resin

L-phenylalanine, one of the nine essential amino acids for the human body, is extensively used as an ingredient in food, pharmaceutical and nutrition industries. A suitable equilibrium model is required for purification of L-phenylalanine based on ion-exchange chromatography. In this work, the equilibrium uptake of L-phenylalanine on a strong acid-cation exchanger SH11 was investigated experimentally and theoretically. A modified Donnan ion-exchange （DIX） model, which takes the activiW into account, was established to predict the uptake of L-phenylalanine at various solution pH values. The model parameters including selectivity and mean activity coefficient in the resin phase are presented. The modified DIX model is in good agreement with the experimental data. The optimum operating pH value of 2.0, with the highest t-phenylalanine uptake on the resin, is predicted by the model. This basic information combined with the general mass transfer model will lay the foundation for the prediction of dynamic behavior of fixed bed separation process.