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.

Flow mixing model of liquid phase in an internal airlift loop reactor

Residence time distribution (RTD) analysis of liquid phase was conducted in an internal airlift loop reactor (AL) and a bubble column (BC) with the tracer response technique. These data were simulated and compared through several flow mixing models. The modeling results of two-parameter model indicated that there were higher ratio of full mixing zones and lower ratio of bypass flow in AL than in BC. Then a completely mixed-plug flow parallel combined (four-parameter) model was established. Modeling results show that it is more precise and more obvious than two-parameter model.

Development of a refined helical fuel mixing model and application to a helical fuel rod bundle

Fuel assemblies have a decisive impact on the performance and safety of nuclear reactors.Helical fuel has huge potential for application in small module reactors(SMRs)due to its advantages in volume power density and safety.Typical helical fuel elements are usually trilobal or cruciform in cross-section.The fuel rods are helically twisted in the axial direction,eliminating the need for spacer grids as the fuel rods are self-supporting.In this paper,a refined subchannel division approach is proposed based on the crossflow mechanism of helical fuel assemblies.Then,a refined helical fuel mixing model framework,including the helical fuel distributed resistance method and directed crossflow method,is developed and implemented in a helical fuel rod bundle to investigate the mixing characteristics.Validation is provided by a 5×5 helical fuel bundle mixing experiment.The refined model predicts about 92.7%of the data with the±10%error range.Compared with existing helical fuel mixing models,the refined mixing model has higher axial accuracy and radial spatial resolution,and can accurately predict the twist angledependent crossflow rate and entry effect.Meanwhile,the refined helical fuel mixing model framework is universal and can be effectively used for the mixing prediction of arbitrary geometric helical fuel after the calibration of coefficients.

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.

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.

Adaptive Random Effects/Coefficients Modeling

Adaptive fractional polynomial modeling of general correlated outcomes is formulated to address nonlinearity in means, variances/dispersions, and correlations. Means and variances/dispersions are modeled using generalized linear models in fixed effects/coefficients. Correlations are modeled using random effects/coefficients. Nonlinearity is addressed using power transforms of primary (untransformed) predictors. Parameter estimation is based on extended linear mixed modeling generalizing both generalized estimating equations and linear mixed modeling. Models are evaluated using likelihood cross-validation (LCV) scores and are generated adaptively using a heuristic search controlled by LCV scores. Cases covered include linear, Poisson, logistic, exponential, and discrete regression of correlated continuous, count/rate, dichotomous, positive continuous, and discrete numeric outcomes treated as normally, Poisson, Bernoulli, exponentially, and discrete numerically distributed, respectively. Example analyses are also generated for these five cases to compare adaptive random effects/coefficients modeling of correlated outcomes to previously developed adaptive modeling based on directly specified covariance structures. Adaptive random effects/coefficients modeling substantially outperforms direct covariance modeling in the linear, exponential, and discrete regression example analyses. It generates equivalent results in the logistic regression example analyses and it is substantially outperformed in the Poisson regression case. Random effects/coefficients modeling of correlated outcomes can provide substantial improvements in model selection compared to directly specified covariance modeling. However, directly specified covariance modeling can generate competitive or substantially better results in some cases while usually requiring less computation time.

Generalized Height-Diameter Models for Pinus montezumae Lamb. and Pinus pseudostrobus Lindl. Plantations in Michoacan, Mexico

Tree height (H) in a natural stand or forest plantation is a fundamental variable in management, and the use of mathematical expressions that estimate H as a function of diameter at breast height (d) or variables at the stand level is a valuable support tool in forest inventories. The objective was to fit and propose a generalized H-d model for Pinus montezumae and Pinus pseudostrobus established in forest plantations of Nuevo San Juan Parangaricutiro, Michoacan, Mexico. Using nonlinear least squares (NLS), 10 generalized H-d models were fitted to 883 and 1226 pairs of H-d data from Pinus montezumae and Pinus pseudostrobus, respectively. The best model was refitted with the maximum likelihood mixed effects model (MEM) approach by including the site as a classification variable and a known variance structure. The Wang and Tang equation was selected as the best model with NLS;the MEM with an additive effect on two of its parameters and an exponential variance function improved the fit statistics for Pinus montezumae and Pinus pseudostrobus, respectively. The model validation showed equality of means among the estimates for both species and an independent subsample. The calibration of the MEM at the plot level was efficient and might increase the applicability of these results. The inclusion of dominant height in the MEM approach helped to reduce bias in the estimates and also to better explain the variability among plots.

Flow computations of multi-stages by URANS and flux balanced mixing models

The quasi-steady methods based on mixing models have been widely applied to flow computations of turbomachinery multi- stages in aerospace engineering. Meanwhile, the unsteady numerical simulation has also been used due to its ability in obtaining time-dependent flow solutions. In the paper, two different mixing treatments and the corresponding flux balanced ones are presented to exchange the flow solutions on the interfaces between adjacent blade rows. The four mixing treatments are then used for flow computations of a subsonic 1.5-stage axial turbine and a quasi-l.5-stage transonic compressor rotor. The results are compared with those by unsteady numerical method, which is implemented by using the sliding mesh technique. The effects of the quasi-steady and unsteady computation methods on the conservation of flow solutions across the interfaces are presented and addressed. Furthermore, the influence of mixing treatments on shock wave and flow separation of the transonic compressor rotor is presented in detail. All the results demonstrate that the flux balanced mixing treatments can be used for multi-stage flow computations with improved performance on interface conservation, even in the complex flows.

The Additive Hazard Mixing Models

This paper is concerned with the aging and dependence properties in the additive hazard mixing models including some stochastic comparisons. Further, some useful bounds of reliability functions in additive hazard mixing models are obtained.

Effects of Atomic Mixing in Inertial Confinement Fusion by Multifluid Interpenetration Mix Model

The effects of atomic-level rnixing are systemically investigated in a multifluid interpenetration mix model ,and results are compared with the single-fluid model＇s simulations and experimental data. It is shown that increasing the model free parameter α, shock Mach number, and the initial density discontinuity makes the mix length and fraction of mixing particle increase, resulting in the lower shock temperatures compared with the results of single-fluid model without mixing. Recent high-compressibility direct-drive spherical implosions on OMEGA are simulated by the interpenetration mix modal. The calculations with atomic mixing between fuel and shell match quite well with the observations. Without considering any mixing, the calculated neutron yields and ion temperatures are overpredicted; while inclusion of the interpenetration mix model with the adjustable parameter α could fit the simulated neutron yields and ion temperatures well with experimental data.

Solution of Self-similar Equations of the k-ε Model in the Shear Turbulent Mixing Problem and Its Numerical Simulation

The paper presents the k-ε model equations of turbulence with a single set of constants chosen by the authors, which is appropriate to simulate a wide range of turbulent flows. The model validation has been performed for a number of flows and its main results are given in the paper. The turbulent mixing of flow with shear in the tangential velocity component is discussed in details. An analytical solution to the system of ordinary differential equations of the k-ε model of turbulent mixing has been found for the self-similar regime of flow. The model coefficients were chosen using simulation results for some simplest turbulent flows. The solution can be used for the verification of codes. The numerical simulation of the problem has been performed by the 2D code EGAK using this model. A good agreement of the numerical simulation results with the self-similar solution, 3D DNS results and known experimental data has been achieved. This allows stating that the k-ε model constants chosen by the authors are acceptable for the considered flow.

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.

DOWNCOMER MIXING AND ITS EFFECT ON DISTILLATION TRAY EFFICIENCY

In this paper, the measurement of liquid mixing in a downcomer of segmental type of distillation column is presented. The extent of liquid mixing is calculated by means of a mixing pool model. The results indicate that liquid mixing in a downcomer is actually incomplete. It is a significant correction to the assumption of complete downcomer mixing or no downcomer mixing which is generally adopted in many distillation calculations. Besides, the present results are used in a two dimensional eddy diffusion model to calculate the distillation tray efficiency. It is shown that the assumption of complete downcomer mixing is closer to the actual situation than that of no downcomer mixing.

Reliability Analysis of a Mixed Redundant Model in C 3I System

Aim To define a mixed redundant model(MRM), improving the reliability of C 3I system. Methods The model combined the technology characters of two? unit system with one warm stand by unit and function substitute system. The reliability and availability equations of MRM were deduced. Results and Conclusion Compared with several other reliability models, it has obvious effect upon improving the system reliability. The effect? cost rate is very high among these models. The model can be used in reliability design, evaluation and check of C 3I system. Only a little attached cost is needed to improve C 3I system reliability effectively.

Simulation of quasi-dimensional model for diesel engine working process

In order to satisfy the demand of validity and real time operating performance of diesel engine model used in hardware-in-the-loop simulation system,a simplified quasi-dimensional model for diesel engine working process was proposed,which was based on the phase-divided spray mixing model.The software MATLAB/Simulink was utilized to simulate diesel engine performance parameters.The comparisons between calculated results and experimental data show that the relative error of power and brake specific fuel consumption is less than 2.8%,and the relative error of nitric oxide and soot emissions is less than 9.1%.At the same time,the average computational time for simulation of one working process with the new model is 36 s,which presents good real time operating performance of the model.The simulation results also indicate that the nozzle flow coefficient has great influence on the prediction precision of performance parameters in diesel engine simulation model.

Evaluation of Moving Grid Adjustment (MGA) Method in Field Variation Control

Spatial variation is often encountered when large scale field trials are conducted which can result in biased estimation or prediction of treatment (i.e. genotype) values. An effective removal of spatial variation is needed to ensure unbiased estimation or prediction and thus increase the accuracy of field data evaluation. A moving grid adjustment (MGA) method, which was proposed by Technow, was evaluated through Monte Carlo simulation for its statistical properties regarding field spatial variation control. Our simulation results showed that the MGA method can effectively account for field spatial variation if it does exist;however, this method will not change phenotype results if field spatial variation does not exist. The MGA method was applied to a large-scale cotton field trial data set with two representative agronomic traits: lint yield (strong field spatial pattern) and lint percentage (no field spatial pattern). The results suggested that the MGA method was able to effectively separate the spatial variation including blocking effects from random error variation for lint yield while the adjusted data remained almost identical to the original phenotypic data. With application of the MGA method, the estimated variance for residuals was significantly reduced (62.2% decrease) for lint yield while more genetic variation (29.7% increase) was detected compared to the original data analysis subject to the conventional randomized complete block design analysis. On the other hand, the results were almost identical for lint percentage with and without the application of the MGA method. Therefore, the MGA method can be a useful addition to enhance data analysis when field spatial pattern exists.

WOMBAT—A tool for mixed model analyses in quantitative genetics by restricted maximum likelihood (REML)

WOMBAT is a software package for quantitative genetic analyses of continuous traits, fitting a linear, mixed model; estimates of covariance components and the resulting genetic parameters are obtained by restricted maximum likelihood. A wide range of models, comprising numerous traits, multiple fixed and random effects, selected genetic covariance structures, random regression models and reduced rank estimation are accommodated. WOMBAT employs up-to-date numerical and computational methods. Together with the use of efficient compilers, this generates fast executable programs, suitable for large scale analyses. Use of WOMBAT is illustrated for a bivariate analysis. The package consists of the executable program, available for LINUX and WINDOWS environments, manual and a set of worked example, and can be downloaded free of charge from http：//agbu. une.edu.au/-kmeyer/wombat.html

Evaluation of Subgrid-scale Models in Large-eddy Simulations of Turbulent Flow in a Centrifugal Pump Impeller

The current research of large eddy simulation （LES） of turbulent flow in pumps mainly concentrates in applying conventional subgrid-scale （SGS） model to simulate turbulent flow, which aims at obtaining the flow field in pump. The selection of SGS model is usually not considered seriously, so the accuracy and efficiency of the simulation cannot be ensured. Three SGS models including Smagorinsky-Lilly model, dynamic Smagorinsky model and dynamic mixed model are comparably studied by using the commercial CFD code Fluent combined with its user define function. The simulations are performed for the turbulent flow in a centrifugal pump impeller. The simulation results indicate that the mean flows predicted by the three SGS models agree well with the experimental data obtained from the test that detailed measurements of the flow inside the rotating passages of a six-bladed shrouded centrifugal pump impeller performed using particle image velocimetry （PIV） and laser Doppler velocimetry （LDV）. The comparable results show that dynamic mixed model gives the most accurate results for mean flow in the centrifugal pump impeller. The SGS stress of dynamic mixed model is decompose into the scale similar part and the eddy viscous part. The scale similar part of SGS stress plays a significant role in high curvature regions, such as the leading edge and training edge of pump blade. It is also found that the dynamic mixed model is more adaptive to compute turbulence in the pump impeller. The research results presented is useful to improve the computational accuracy and efficiency of LES for centrifugal pumps, and provide important reference for carrying out simulation in similar fluid machineries.

Analysis of Mixed Model in Gear Transmission Based on ADAMS

The traditional method of mechanical gear driving simulation includes gear pair method and solid to solid contact method. The former has higher solving efficiency but lower results accuracy; the latter usually obtains higher precision of results while the calculation process is complex, also it is not easy to converge. Currently, most of the researches are focused on the description of geometric models and the definition of boundary conditions. However, none of them can solve the problems fundamentally. To improve the simulation efficiency while ensure the results with high accuracy, a mixed model method which uses gear tooth profiles to take the place of the solid gear to simulate gear movement is presented under these circumstances. In the process of modeling, build the solid models of the mechanism in the SolidWorks firstly; Then collect the point coordinates of outline curves of the gear using SolidWorks API and create fit curves in Adams based on the point coordinates; Next, adjust the position of those fitting curves according to the position of the contact area; Finally, define the loading conditions, boundary conditions and simulation parameters. The method provides gear shape information by tooth profile curves; simulates the mesh process through tooth profile curve to curve contact and offer mass as well as inertia data via solid gear models. This simulation process combines the two models to complete the gear driving analysis. In order to verify the validity of the method presented, both theoretical derivation and numerical simulation on a runaway escapement are conducted. The results show that the computational efficiency of the mixed model method is 1.4 times over the traditional method which contains solid to solid contact. Meanwhile, the simulation results are more closely to theoretical calculations. Consequently, mixed model method has a high application value regarding to the study of the dynamics of gear mechanism.