Comparison of isotope-based linear and Bayesian mixing models in determining moisture recycling ratio

Stable water isotopes are natural tracers quantifying the contribution of moisture recycling to local precipitation,i.e.,the moisture recycling ratio,but various isotope-based models usually lead to different results,which affects the accuracy of local moisture recycling.In this study,a total of 18 stations from four typical areas in China were selected to compare the performance of isotope-based linear and Bayesian mixing models and to determine local moisture recycling ratio.Among the three vapor sources including advection,transpiration,and surface evaporation,the advection vapor usually played a dominant role,and the contribution of surface evaporation was less than that of transpiration.When the abnormal values were ignored,the arithmetic averages of differences between isotope-based linear and the Bayesian mixing models were 0.9%for transpiration,0.2%for surface evaporation,and–1.1%for advection,respectively,and the medians were 0.5%,0.2%,and–0.8%,respectively.The importance of transpiration was slightly less for most cases when the Bayesian mixing model was applied,and the contribution of advection was relatively larger.The Bayesian mixing model was found to perform better in determining an efficient solution since linear model sometimes resulted in negative contribution ratios.Sensitivity test with two isotope scenarios indicated that the Bayesian model had a relatively low sensitivity to the changes in isotope input,and it was important to accurately estimate the isotopes in precipitation vapor.Generally,the Bayesian mixing model should be recommended instead of a linear model.The findings are useful for understanding the performance of isotope-based linear and Bayesian mixing models under various climate backgrounds.

Evaluation of Nonbreaking Wave-Induced Mixing Parameterization Schemes Based on a One-Dimensional Ocean Model

Surface waves have a considerable effect on vertical mixing in the upper ocean.In the past two decades,the vertical mixing induced through nonbreaking surface waves has been used in ocean and climate models to improve the simulation of the upper ocean.Thus far,several nonbreaking wave-induced mixing parameterization schemes have been proposed;however,no quantitative comparison has been performed among them.In this paper,a one-dimensional ocean model was used to compare the performances of five schemes,including those of Qiao et al.(Q),Hu and Wang(HW),Huang and Qiao(HQ),Pleskachevsky et al.(P),and Ghantous and Babanin(GB).Similar to previous studies,all of these schemes can decrease the simulated sea surface temperature(SST),increase the subsurface temperature,and deepen the mixed layer,thereby alleviating the common thermal deviation problem of the ocean model for upper ocean simulation.Among these schemes,the HQ scheme exhibited the weakest wave-induced mixing effect,and the HW scheme exhibited the strongest effect;the other three schemes exhibited roughly the same effect.In particular,the Q and P schemes exhibited nearly the same effect.In the simulation based on observations from the Ocean Weather Station Papa,the HQ scheme exhibited the best performance,followed by the Q scheme.In the experiment with the HQ scheme,the root-mean-square deviation of the simulated SST from the observations was 0.43℃,and the mixed layer depth(MLD)was 2.0 m.As a contrast,the deviations of the SST and MLD reached 1.25℃ and 8.4 m,respectively,in the experiment without wave-induced mixing.

On the Application of Mixed Models of Probability and Convex Set for Time-Variant Reliability Analysis

In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.

A unified Minorization-Maximization approach for estimation of general mixture models

The mixed distribution model is often used to extract information from heteroge-neous data and perform modeling analysis.When the density function of mixed distribution is complicated or the variable dimension is high,it usually brings challenges to the parameter es-timation of the mixed distribution model.The application of MM algorithm can avoid complex expectation calculations,and can also solve the problem of high-dimensional optimization by decomposing the objective function.In this paper,MM algorithm is applied to the parameter estimation problem of mixed distribution model.The method of assembly and decomposition is used to construct the substitute function with separable parameters,which avoids the problems of complex expectation calculations and the inversion of high-dimensional matrices.

Mixed D-vine copula-based conditional quantile model for stochastic monthly streamflow simulation

Copula functions have been widely used in stochastic simulation and prediction of streamflow.However,existing models are usually limited to single two-dimensional or three-dimensional copulas with the same bivariate block for all months.To address this limitation,this study developed a mixed D-vine copula-based conditional quantile model that can capture temporal correlations.This model can generate streamflow by selecting different historical streamflow variables as the conditions for different months and by exploiting the conditional quantile functions of streamflows in different months with mixed D-vine copulas.The up-to-down sequential method,which couples the maximum weight approach with the Akaike information criteria and the maximum likelihood approach,was used to determine the structures of multivariate Dvine copulas.The developed model was used in a case study to synthesize the monthly streamflow at the Tangnaihai hydrological station,the inflow control station of the Longyangxia Reservoir in the Yellow River Basin.The results showed that the developed model outperformed the commonly used bivariate copula model in terms of the performance in simulating the seasonality and interannual variability of streamflow.This model provides useful information for water-related natural hazard risk assessment and integrated water resources management and utilization.

Improved cat swarm optimization for parameter estimation of mixed additive and multiplicative random error model

To estimate the parameters of the mixed additive and multiplicative(MAM)random error model using the weighted least squares iterative algorithm that requires derivation of the complex weight array,we introduce a derivative-free cat swarm optimization for parameter estimation.We embed the Powell method,which uses conjugate direction acceleration and does not need to derive the objective function,into the original cat swarm optimization to accelerate its convergence speed and search accuracy.We use the ordinary least squares,weighted least squares,original cat swarm optimization,particle swarm algorithm and improved cat swarm optimization to estimate the parameters of the straight-line fitting MAM model with lower nonlinearity and the DEM MAM model with higher nonlinearity,respectively.The experimental results show that the improved cat swarm optimization has faster convergence speed,higher search accuracy,and better stability than the original cat swarm optimization and the particle swarm algorithm.At the same time,the improved cat swarm optimization can obtain results consistent with the weighted least squares method based on the objective function only while avoiding multiple complex weight array derivations.The method in this paper provides a new idea for theoretical research on parameter estimation of MAM error models.

Three Dimensional Baroclinic Numerical Model for Simulating Fresh and Salt Water Mixing in the Yangtze Estuary

For simulating fresh and salt water mixing in estuaries, a three dimensional nonlinear baroclinic numerical model is developed, in which the gradients of horizontal pressure contain die gradient of barotropic pressure arising from the gradient of tidal level and the gradient of baroclinic pressure due to the gradient of salinity. The Eulerian-Lagrangian method is employed to descretize both the momentum equations of tidal motion and the equation of salt water diffusion so as to improve the computational stability and accuracy. The methods to provide the boundary conditions and the initial conditions are proposed, and the criterion for computational stability of the salinity fields is presented. The present model is used for modeling fresh and salt water mixing in the Yangtze Estuary. Computations show that the salinity distribution has the characteristics of partial mixing pattern, and that the present model is suitable for simulation of fresh and salt water mixing in the Yangtze Estuary.

The effect of the wave-induced mixing on the upper ocean temperature in a climate model

The significant underestimation of sea surface temperature （SST） and the temperature in the upper ocean is one of common problems in present climate models. The influence of the wave-induced mixing on SST and the temperature in the upper ocean was examined based on a global climate model. The results from the model coupled with wave-induced mixing showed a significant improvement in the simulation of SST and the temperature in the upper ocean compared with those of the original model without wave effects. Although there has still a cold bias, the new simulation is much closer to the climatology, especially in the northern ocean and tropical ocean. This study indicates that some important physical processes in the accurate simulation of the ocean may be ignored in present climate models, and the wave-induced mixing is one of those factors. Thus, the wave-induced mixing （ or the effect of surface waves） should be incorporated properly into climate models in order to simulate or forecast the ocean, then climate system, more accurately.

Water model experiments of multiphase mixing in the top-blown smelting process of copper concentrate

We constructed a 1：10 cold water experimental model by geometrically scaling down an Isa smelting furnace. The mixing processes at different liquid heights, lance diameters, lance submersion depths, and gas flow rates were subsequently measured using the conductivity method. A new criterion was proposed to determine the mixing time. On this basis, the quasi-equations of the mixing time as a function of different parameters were established. The parameters of the top-blown smelting process were optimized using high-speed photography. An excessively high gas flow rate or excessively low liquid height would enhance the fluctuation and splashing of liquid in the bath, which is unfavorable for material mixing. Simultaneously increasing the lance diameter and the lance submersion depth would promote the mixing in the bath, thereby improving the smelting efficiency.

A parameterization scheme of vertical mixing due to inertial internal wave breaking in the ocean general circulation model

Based on the theoretical spectral model of inertial internal wave breaking （fine structure） proposed previ- ously, in which the effects of the horizontal Coriolis frequency component f-tilde on a potential isopycnal are taken into account, a parameterization scheme of vertical mixing in the stably stratified interior be- low the surface mixed layer in the ocean general circulation model （OGCM） is put forward preliminarily in this paper. Besides turbulence, the impact of sub-mesoscale oceanic processes （including inertial internal wave breaking product） on oceanic interior mixing is emphasized. We suggest that adding the inertial inter- hal wave breaking mixing scheme （F-scheme for short） put forward in this paper to the turbulence mixing scheme of Canuto et al. （T-scheme for short） in the OGCM, except the region from 15°S to 15°N. The numeri- cal results ofF-scheme by usingWOA09 data and an OGCM （LICOM, LASG/IAP climate system ocean model） over the global ocean are given. A notable improvement in the simulation of salinity and temperature over the global ocean is attained by using T-scheme adding F-scheme, especially in the mid- and high-latitude regions in the simulation of the intermediate water and deep water. We conjecture that the inertial internal wave breaking mixing and inertial forcing of wind might be one of important mechanisms maintaining the ventilation process. The modeling strength of the Atlantic meridional overturning circulation （AMOC） by using T-scheme adding F-scheme may be more reasonable than that by using T-scheme alone, though the physical processes need to be further studied, and the overflow parameterization needs to be incorporated. A shortcoming in F-scheme is that in this paper the error of simulated salinity and temperature by using T-scheme adding F-scheme is larger than that by using T-scheme alone in the subsurface layer.

PREDICTION OF THE MIXING ENTHALPIES OF BINARY LIQUID ALLOYS BY MOLECULAR INTERACTION VOLUME MODEL

The mixing enthalpies of 23 binary liquid alloys are calculated by molecular interaction volume model （MIVM）, which is a two-parameter model with the partial molar infinite dilute mixing enthalpies. The predicted values are in agreement with the experimental data and then indicate that the model is reliable and convenient.

A harmonic analyzed parameterization of tide-induced mixing for ocean models

The tide-induced mixing plays an important role in the regulation of ocean circulation.Numerical simulation of continental shelf circulation is found to exhibit an unreasonable vertical thermohaline structure without consideration of tide effects.In this study,we establish a harmonic analyzed parameterization of tide-induced（HAT） mixing,by which means to derive time-depended function of mixing coefficient based on harmonic analysis of the vertical mixing coefficient.By employing HAT mixing parameterization scheme,a series of numerical experiments are conducted for the Yellow Sea.Numerical results show that an ocean circulation model with the HAT mixing involved is capable of reproducing the reasonable thermohaline structure of the Yellow Sea Cold Water Mass,similar to structures produced by explicit tidal forcing on the open boundary.The advantage of the HAT method is its faster computation time,compared with models that directly resolve explicit tidal motion.The HAT parameterization for the tide-induced mixing has potential to improve both the accuracy and efficiency of ocean circulation and climate models.

Identification of Mixtures of Two Types of Body Fluids Using the Multiplex Methylation System and Random Forest Models

Objective Body fluid mixtures are complex biological samples that frequently occur in crime scenes,and can provide important clues for criminal case analysis.DNA methylation assay has been applied in the identification of human body fluids,and has exhibited excellent performance in predicting single-source body fluids.The present study aims to develop a methylation SNaPshot multiplex system for body fluid identification,and accurately predict the mixture samples.In addition,the value of DNA methylation in the prediction of body fluid mixtures was further explored.Methods In the present study,420 samples of body fluid mixtures and 250 samples of single body fluids were tested using an optimized multiplex methylation system.Each kind of body fluid sample presented the specific methylation profiles of the 10 markers.Results Significant differences in methylation levels were observed between the mixtures and single body fluids.For all kinds of mixtures,the Spearman’s correlation analysis revealed a significantly strong correlation between the methylation levels and component proportions(1:20,1:10,1:5,1:1,5:1,10:1 and 20:1).Two random forest classification models were trained for the prediction of mixture types and the prediction of the mixture proportion of 2 components,based on the methylation levels of 10 markers.For the mixture prediction,Model-1 presented outstanding prediction accuracy,which reached up to 99.3%in 427 training samples,and had a remarkable accuracy of 100%in 243 independent test samples.For the mixture proportion prediction,Model-2 demonstrated an excellent accuracy of 98.8%in 252 training samples,and 98.2%in 168 independent test samples.The total prediction accuracy reached 99.3%for body fluid mixtures and 98.6%for the mixture proportions.Conclusion These results indicate the excellent capability and powerful value of the multiplex methylation system in the identification of forensic body fluid mixtures.

Mathematical modeling of mixed convective MHD Falkner-Skan squeezed Sutterby multiphase flow with non-Fourier heat flux theory and porosity

In a wide variety of mechanical and industrial applications,e.g.,space cooling,nuclear reactor cooling,medicinal utilizations(magnetic drug targeting),energy generation,and heat conduction in tissues,the heat transfer phenomenon is involved.Fourier’s law of heat conduction has been used as the foundation for predicting the heat transfer behavior in a variety of real-world contexts.This model’s production of a parabolic energy expression,which means that an initial disturbance would immediately affect the system under investigation,is one of its main drawbacks.Therefore,numerous researchers worked on such problem to resolve this issue.At last,this problem was resolved by Cattaneo by adding relaxation time for heat flux in Fourier’s law,which was defined as the time required to establish steady heat conduction once a temperature gradient is imposed.Christov offered a material invariant version of Cattaneo’s model by taking into account the upper-connected derivative of the Oldroyd model.Nowadays,both models are combinedly known as the Cattaneo-Christov(CC)model.In this attempt,the mixed convective MHD Falkner-Skan Sutterby nanofluid flow is addressed towards a wedge surface in the presence of the variable external magnetic field.The CC model is incorporated instead of Fourier’s law for the examination of heat transfer features in the energy expression.A two-phase nanofluid model is utilized for the implementation of nano-concept.The nonlinear system of equations is tackled through the bvp4c technique in the MATLAB software 2016.The influence of pertinent flow parameters is discussed and displayed through different sketches.Major and important results are summarized in the conclusion section.Furthermore,in both cases of wall-through flow(i.e.,suction and injection effects),the porosity parameters increase the flow speed,and decrease the heat transport and the influence of drag forces.

A novel model to evaluate spatial structure in thinned conifer-broadleaved mixed natural forests

In order to ensure the effective analysis and reconstruction of forests,it is key to ensure the quantitative description of their spatial structure.In this paper,a distance model for the optimal stand spatial structure based on weighted Voronoi diagrams is proposed.In particular,we provide a novel methodological model for the comprehensive evaluation of the spatial structure of forest stands in natural mixed conifer-broadleaved forests and the formulation of management decision plans.The applicability of the rank evaluation and the optimal solution distance model are compared and assessed for different standard sample plots of natural mixed conifer-broadleaved forests.The effect of crown width on the spatial structure unit of the trees is observed to be higher than that of the diameter at breast height.Moreover,the influence of crown length is greater than that of tree height.There are nine possible spatial structure units determined by the weighted Voronoi diagram for the number of neighboring trees in the central tree,with an average intersection of neighboring crowns reaching 80%.The rank rating of natural forest sample plots is correlated with the optimal solution distance model,and their results are generally consistent for natural forests.However,the rank rating is not able to provide a quantitative assessment.The optimal solution distance model is observed to be more comprehensive than traditional methods for the evaluation of the spatial structure of forest stands.It can effectively reflect the trends in realistic stand spatial structure factors close to or far from the ideal structure point,and accurately assesses the forest spatial structure.The proposed optimal solution distance model improves the integrated evaluation of the spatial structure of forest stands and provides solid theoretical and technical support for sustainable forest management.

Mixing of miscible shear-thinning fluids in a lid-driven cavity

The concentration and velocity fields of two refractive index matched miscible shear-thinning fluids in a lid-driven cavity were investigated by using planar laser-induced fluorescence and particle image velocimetry,as well by computational fluid dynamics.Quantitative analyses show that the results obtained by flow simulations with the species transport model are in good agreement with the experimental results.The effects of different parameters were studied by using the intensity of segregation.For two fluids with the same rheological parameters,the relative amounts of liquids H_(1)/H and the power-law index n dominate the mixing process while the Reynolds number Re plays a marginal role.As for two fluids with density difference,buoyancy has significant influence on the mixing process.The dimensionless group Ar/Re(redefined such as to include shear thinning behavior)is proposed for assessing the effect of buoyancy and rheological properties on the mixing of miscible shear-thinning fluids.

Simulation analysis of wear characteristics of connecting rod bearing bush based on improved mixed lubrication model

The failure rate of crankpin bearing bush of diesel engine under complex working conditions such as high temperature,dynamic load and variable speed is high.After serious wear,it is easy to deteriorate the stress state of connecting rod body and connecting rod bolt,resulting in serious accidents such as connecting rod fracture and body damage.Based on the mixed lubrication characteristics of connecting rod big endbearing shell of diesel engine under high explosion pressure impact load,an improved mixed lubrication mechanism model is established,which considers the influence of viscoelastic micro deformation of bearing bush material,integrates the full film lubrication model and dry friction model,couples dynamic equation of connecting rod.Then the actual lubrication state of big end bearing shell is simulated numerically.Further,the correctness of the theoretical research results is verified by fault simulation experiments.The results show that the high-frequency impact signal with fixed angle domain characteristics will be generated after the serious wear of bearing bush and the deterioration of lubrication state.The fault feature capture and alarm can be realized through the condition monitoring system,which can be applied to the fault monitoring of connecting rod bearing bush of diesel engine in the future.

Research on Mixed Logic Dynamic Modeling and Finite Control Set Model Predictive Control of Multi-Inverter Parallel System

Parallel connection of multiple inverters is an important means to solve the expansion,reserve and protection of distributed power generation,such as photovoltaics.In view of the shortcomings of traditional droop control methods such as weak anti-interference ability,low tracking accuracy of inverter output voltage and serious circulation phenomenon,a finite control set model predictive control(FCS-MPC)strategy of microgrid multiinverter parallel system based on Mixed Logical Dynamical(MLD)modeling is proposed.Firstly,the MLD modeling method is introduced logical variables,combining discrete events and continuous events to form an overall differential equation,which makes the modeling more accurate.Then a predictive controller is designed based on the model,and constraints are added to the objective function,which can not only solve the real-time changes of the control system by online optimization,but also effectively obtain a higher tracking accuracy of the inverter output voltage and lower total harmonic distortion rate(Total Harmonics Distortion,THD);and suppress the circulating current between the inverters,to obtain a good dynamic response.Finally,the simulation is carried out onMATLAB/Simulink to verify the correctness of the model and the rationality of the proposed strategy.This paper aims to provide guidance for the design and optimal control of multi-inverter parallel systems.

The Hydrodynamic Behaviour of Euboean Gulf Coastal Areas and the Mixing of the Physico-Chemical Characteristics of Urban Sewage Discharged into Them under the Influence of Climate Change

The hydrodynamic circulation within the marine environment is a complex phenomenon, characterized by the interplay of strong tidal forces, atmospheric influences, and bathymetric features. The physical and hydrodynamic attributes of this flow play a pivotal role in promoting vertical mixing of seawater masses, thereby facilitating the integration of their physical and chemical parameters, including nutrients and oxygen. Additionally, they are instrumental in governing the dispersion and diffusion of pollutants originating from urban sewage, contributing to the overall water renewal process and environmental quality. This study investigates the potential impact of anticipated increases in average air temperatures on water column stratification in coastal regions susceptible to these dynamic influences. These areas receive treated urban sewage, and the study aims to assess how these temperature changes might influence the dispersion and mixing of pollutant loads present in these coastal waters.

The relationship between compartment models and their stochastic counterparts:A comparative study with examples of the COVID-19 epidemic modeling

Deterministic compartment models(CMs)and stochastic models,including stochastic CMs and agent-based models,are widely utilized in epidemic modeling.However,the relationship between CMs and their corresponding stochastic models is not well understood.The present study aimed to address this gap by conducting a comparative study using the susceptible,exposed,infectious,and recovered(SEIR)model and its extended CMs from the coronavirus disease 2019 modeling literature.We demonstrated the equivalence of the numerical solution of CMs using the Euler scheme and their stochastic counterparts through theoretical analysis and simulations.Based on this equivalence,we proposed an efficient model calibration method that could replicate the exact solution of CMs in the corresponding stochastic models through parameter adjustment.The advancement in calibration techniques enhanced the accuracy of stochastic modeling in capturing the dynamics of epidemics.However,it should be noted that discrete-time stochastic models cannot perfectly reproduce the exact solution of continuous-time CMs.Additionally,we proposed a new stochastic compartment and agent mixed model as an alternative to agent-based models for large-scale population simulations with a limited number of agents.This model offered a balance between computational efficiency and accuracy.The results of this research contributed to the comparison and unification of deterministic CMs and stochastic models in epidemic modeling.Furthermore,the results had implications for the development of hybrid models that integrated the strengths of both frameworks.Overall,the present study has provided valuable epidemic modeling techniques and their practical applications for understanding and controlling the spread of infectious diseases.