Individual-tree diameter growth model for Korean pine plantations based on optimized interpolation of meteorological variables

To explore the influence of meteorological variables on the growth of Korean pine(Pinus koraiensis Sieb.et Zucc.) plantations and provide a scientific reference for the production and management of Korean pine,three approaches to interpolate meteorological variables during the growing season(i.e.,May-September) were compared in Heilongjiang Province,China.Optimized meteorological variable interpolation results were then combined with stand and individual tree variables,based on data from 56 sample plots and 2886 sample trees from Korean pine plantations in two regions of the province to develop an individualtree diameter growth model(Model I) and an individualtree diameter growth model with meteorological variables(Model Ⅱ) using a stepwise regression method.Moreover,an individual-tree diameter growth model with regional effects(Model Ⅲ) was developed using dummy variables in the regression,and the significance of introducing these dummy variables was verified with an F-test statistical analysis.The models were validated using an independent data set,and the predictive performance of the three models was assessed via the adjusted coefficient of determination(R_(a)^(2)) and root mean square error(RMSE).The results suggest that the growth increment in tree diameter of Korean pine plantations was significantly correlated with the natural logarithm of initial diameter(ln D),stand basal area(BAS),logarithmic deformation of the stand density index(ln SDI),ratio of basal area of trees larger than the subject tree to their initial diameter at breast height(DBH)(BAL/D),and the maximum growingseason precipitation(Pgmax).The individual-tree diameter growth models of Korean pine plantations developed in this study will provide a good basis for estimating and predicting growth increments of Korean pine forests over larger areas.

PROBABILISTIC MODELS FOR LONG FATIGUE CRACK GROWTH RATES OF LZ50 AXLE STEEL

Experimental study is performed on the probabilistic models for the long fatigue crack growth rates (da/dN) of LZ50 axle steel. An equation for crack growth rate was derived to consider the trend of stress intensity factor range going down to the threshold and the average stress effect. The probabilistic models were presented on the equation. They consist of the probabilistic da/dN-ΔK relations, the confidence-based da/dN-ΔK relations, and the probabilistic- and confidence-based da/dN-ΔK relations. Efforts were made respectively to characterize the effects of probabilistic assessments due to the scattering regularity of test data, the number of sampling, and both of them. These relations can provide wide selections for practice. Analysis on the test data of LZ50 steel indicates that the present models are available and feasible.

Delineation of urban growth boundary based on FLUS model under the perspective of land use evaluation in hilly mountainous areas

With rapid economic development,the size of urban land in China is expanding dramatically.The Urban Growth Boundary(UGB)is an expandable spatial boundary for urban construction in a certain period in order to control the urban sprawl.Reasonable delineation of UGB can inhibit the disorderly spread of urban space and guide the normal development of the city.It is of practical significance for the construction of green urban space.The study utilizes GIS technology to establish a land construction suitability evaluation system for Nankang city,which is experiencing rapid urban expansion,and outlines the preliminary UGB under the future land use simulation(FLUS)model.At the same time,considering the coupled coordination of"Production-Living-Ecological Space",and based on the suitability evaluation,we revised the preliminary UGB by combining the advantages of the patch-generating land use simulation(PLUS)model and the convex hull model to delineate the final UGB.The results show that:1)the comprehensive score of the evaluation of the suitability of the construction of land from high to low shows the distribution of the center of the city to the surrounding circle type spread,the center of the city has the highest suitability score.The results of convex hull model show that the urban expansion type of Nankang is epitaxial.In the future,the urban expansion will mainly occur in the northern part of the city.The PLUS model predicts an increase of 3359.97 hm^(2)of construction land in Nankang by 2035,of which 2022.97 hm^(2)is urban construction land.2)The FLUS model has a prediction accuracy of 86.3%and delineates a preliminary UGB area of 9215.07 hm^(2).3)We used the results of the construction suitability evaluation,PLUS model simulation results,and convex hull model predictions to revise the originally delineated UGB.The final delineated UGB area is 8895.67 hm^(2)and it is capable of meeting the future development of the study area.The results of the delineation can promote sustainable urban development,and the delineation methodology can provide a reference basis for the preparation of territorial spatial planning.

Characterization of grain growth behaviors by BP-ANN and Sellars models for nickle-base superalloy and their comparisons

In order to deeply understand the grain growth behaviors of Ni80A superalloy,a series of grain growth experiments were conducted at holding temperatures ranging from 1223 to 1423 K and holding time ranging from 0 to 3600 s.A back-propagation artificial neural network(BP-ANN)model and a Sellars model were solved based on the experimental data.The prediction and generalization capabilities of these two models were evaluated and compared on the basis of four statistical indicators.The results show that the solved BP-ANN model has better performance as it has higher correlation coefficient(r),lower average absolute relative error(AARE),lower absolute values of mean value(μ)and standard deviation(ω).Eventually,a response surface of average grain size to holding temperature and holding time is constructed based on the data expanded by the solved BP-ANN model,and the grain growth behaviors are described.

PROBABILISTIC MODELS FOR LONG FATIGUE CRACK GROWTH RATES OF LZ50 AXLE STEEL

Experimental study is performed on the probabilistic models for the long fatigue crack growth rates （da/dN） of LZ50 axle steel. An equation for crack growth rate was derived to consider the trend of stress intensity factor range going down to the threshold and the average stress effect. The probabilistic models were presented on the equation. They consist of the probabilistic da/dN-△K relations, the confidence-based da/dN-△K relations, and the probabilistic- and confidence-based da/dN-△K relations. Efforts were made respectively to characterize the effects of probabilistic assessments due to the scattering regularity of test data, the number of sampling, and both of them. These relations can provide wide selections for practice. Analysis on the test data of LZ50 steel indicates that the present models are available and feasible.

Comparison of six statistical approaches in the selection of appropriate fish growth models

The performance of six statistical approaches,which can be used for selection of the best model to describe the growth of individual fish,was analyzed using simulated and real length-at-age data.The six approaches include coefficient of determination(R2),adjusted coefficient of determination(adj.-R2),root mean squared error(RMSE),Akaike's information criterion(AIC),bias correction of AIC(AICc) and Bayesian information criterion(BIC).The simulation data were generated by five growth models with different numbers of parameters.Four sets of real data were taken from the literature.The parameters in each of the five growth models were estimated using the maximum likelihood method under the assumption of the additive error structure for the data.The best supported model by the data was identified using each of the six approaches.The results show that R2 and RMSE have the same properties and perform worst.The sample size has an effect on the performance of adj.-R2,AIC,AICc and BIC.Adj.-R2 does better in small samples than in large samples.AIC is not suitable to use in small samples and tends to select more complex model when the sample size becomes large.AICc and BIC have best performance in small and large sample cases,respectively.Use of AICc or BIC is recommended for selection of fish growth model according to the size of the length-at-age data.

Predictive ability of genomic selection models for breeding value estimation on growth traits of Pacific white shrimp Litopenaeus vannamei

Genomic selection(GS)can be used to accelerate genetic improvement by shortening the selection interval.The successful application of GS depends largely on the accuracy of the prediction of genomic estimated breeding value(GEBV).This study is a fi rst attempt to understand the practicality of GS in Litopenaeus vannamei and aims to evaluate models for GS on growth traits.The performance of GS models in L.vannamei was evaluated in a population consisting of 205 individuals,which were genotyped for 6 359 single nucleotide polymorphism(SNP)markers by specifi c length amplifi ed fragment sequencing(SLAF-seq)and phenotyped for body length and body weight.Three GS models(RR-BLUP,Bayes A,and Bayesian LASSO)were used to obtain the GEBV,and their predictive ability was assessed by the reliability of the GEBV and the bias of the predicted phenotypes.The mean reliability of the GEBVs for body length and body weight predicted by the dif ferent models was 0.296 and 0.411,respectively.For each trait,the performances of the three models were very similar to each other with respect to predictability.The regression coeffi cients estimated by the three models were close to one,suggesting near to zero bias for the predictions.Therefore,when GS was applied in a L.vannamei population for the studied scenarios,all three models appeared practicable.Further analyses suggested that improved estimation of the genomic prediction could be realized by increasing the size of the training population as well as the density of SNPs.

Growth and inhibition of zinc anode dendrites in Zn-air batteries:Model and experiment

Zinc(Zn)-air batteries are widely used in secondary battery research owing to their high theoretical energy density,good electrochemical reversibility,stable discharge performance,and low cost of the anode active material Zn.However,the Zn anode also leads to many challenges,including dendrite growth,deformation,and hydrogen precipitation self-corrosion.In this context,Zn dendrite growth has a greater impact on the cycle lives.In this dissertation,a dendrite growth model for a Zn-air battery was established based on electrochemical phase field theory,and the effects of the charging time,anisotropy strength,and electrolyte temperature on the morphology and growth height of Zn dendrites were studied.A series of experiments was designed with different gradient influencing factors in subsequent experiments to verify the theoretical simulations,including elevated electrolyte temperatures,flowing electrolytes,and pulsed charging.The simulation results show that the growth of Zn dendrites is controlled mainly by diffusion and mass transfer processes,whereas the electrolyte temperature,flow rate,and interfacial energy anisotropy intensity are the main factors.The experimental results show that an optimal electrolyte temperature of 343.15 K,an optimal electrolyte flow rate of 40 ml·min^(-1),and an effective pulse charging mode.

Analysis of the inflection points of height-diameter models

The inflection point is an important feature of sigmoidal height-diameter(H-D)models.It is often cited as one of the properties favoring sigmoidal model forms.However,there are very few studies analyzing the inflection points of H-D models.The goals of this study were to theoretically and empirically examine the behaviors of inflection points of six common H-D models with a regional dataset.The six models were the Wykoff(WYK),Schumacher(SCH),Curtis(CUR),HossfeldⅣ(HOS),von Bertalanffy-Richards(VBR),and Gompertz(GPZ)models.The models were first fitted in their base forms with tree species as random effects and were then expanded to include functional traits and spatial distribution.The distributions of the estimated inflection points were similar between the two-parameter models WYK,SCH,and CUR,but were different between the threeparameter models HOS,VBR,and GPZ.GPZ produced some of the largest inflection points.HOS and VBR produced concave H-D curves without inflection points for 12.7%and 39.7%of the tree species.Evergreen species or decreasing shade tolerance resulted in larger inflection points.The trends in the estimated inflection points of HOS and VBR were entirely opposite across the landscape.Furthermore,HOS could produce concave H-D curves for portions of the landscape.Based on the studied behaviors,the choice between two-parameter models may not matter.We recommend comparing seve ral three-parameter model forms for consistency in estimated inflection points before deciding on one.Believing sigmoidal models to have inflection points does not necessarily mean that they will produce fitted curves with one.Our study highlights the need to integrate analysis of inflection points into modeling H-D relationships.

Interpreting Larix principis-rupprechtii radial growth in northern China based on the Vaganov-Shashkin model

Changes in annual radial growth is an important indication of climate change. Dendroclimatology studies in northern China have focused on linear statistical analysis,but lacking studies based on the process of ring formation to clarify the radial growth of trees. Tree-ring width standard chronology(STD) was established using samples of Larix principis-rupprechtii collected at 2303 m altitude on Luya Mountain. Using the Vaganov-Shashkin(VS) model to simulate growth and development, the internal physiological mechanism of radial growth is identified. It was concluded that:(1) the growing season of L. principis-rupprechtii was May to September;(2) soil moisture was a significant factor in the early and late growing seasons, and temperature was the dominant factor in its main growth period;and(3) formation of narrow ring widths was closely related to drought stress, the development of wide ring widths will be restricted by increasing future temperatures. The VS model is applicable for radial growth simulation of subalpine coniferous forests and for guiding the cultivation of local tree species in the future.

Application of the Method of Characteristics to Population Balance Models Considering Growth and Nucleation Phenomena

The population balance modeling is regarded as a universally accepted mathematical framework for dynamic simulation of various particulate processes, such as crystallization, granulation and polymerization. This article is concerned with the application of the method of characteristics (MOC) for solving population balance models describing batch crystallization process. The growth and nucleation are considered as dominant phenomena, while the breakage and aggregation are neglected. The numerical solutions of such PBEs require high order accuracy due to the occurrence of steep moving fronts and narrow peaks in the solutions. The MOC has been found to be a very effective technique for resolving sharp discontinuities. Different case studies are carried out to analyze the accuracy of proposed algorithm. For validation, the results of MOC are compared with the available analytical solutions and the results of finite volume schemes. The results of MOC were found to be in good agreement with analytical solutions and superior than those obtained by finite volume schemes.

Microbial Growth and Decay: A Commented Review of the Model

The paper reviews previous publications and reports some comments about a semi empirical model of the growth and decay process of a planktonic microbial culture. After summarizing and reshaping some fundamental mathematical expressions, the paper highlights the reasons for the choice of a suitable time origin that makes the parameters of the model self-consistent. Besides the potential applications to predictive microbiology studies and to effects of bactericidal drugs, the model allows a suitable proxy of the fitness of the microbial culture, which can be of interest for the studies on the evolution across some thousand generations of a Long Term Evolution Experiment.

Ecosystem service multifunctionality of mixed conifer-broad-leaved forests under climate change and forest management based on matrix growth modelling

Climate change and forest management are recognized as pivotal factors influencing forest ecosystem services and thus multifunctionality.However,the magnitude and the relative importance of climate change and forest management effects on the multifunctionality remain unclear,especially for natural mixed forests.In this study,our objective is to address this gap by utilizing simulations of climate-sensitive transition matrix growth models based on national forest inventory plot data.We evaluated the effects of seven management scenarios(combinations of various cutting methods and intensities)on the future provision of ecosystem services and multifunctionality in mixed conifer-broad-leaved forests in northeastern China,under four climate scenarios(SSP1-2.6,SSP2-4.5,SSP5-8.5,and constant climate).Provisioning,regulating,cultural,and supporting services were described by timber production,carbon storage,carbon sequestration,tree species diversity,deadwood volume,and the number of large living trees.Our findings indicated that timber production was significantly influenced by management scenarios,while tree species diversity,deadwood volume,and large living trees were impacted by both climate and management separately.Carbon storage and sequestration were notably influenced by both management and the interaction of climate and management.These findings emphasized the profound impact of forest management on ecosystem services,outweighing that of climate scenarios alone.We found no single management scenario maximized all six ecosystem service indicators.The upper story thinning by 5%intensity with 5-year interval(UST5)management strategy emerged with the highest multifunctionality,surpassing the lowest values by more than 20%across all climate scenarios.In conclusion,our results underlined the potential of climate-sensitive transition matrix growth models as a decision support tool and provided recommendations for long-term strategies for multifunctional forest management under future climate change context.Ecosystem services and multifunctionality of forests could be enhanced by implementing appropriate management measures amidst a changing climate.

A Rice Growth Models (RGM) System by Object-Oriented Programming with Visual C++

Object-oriented programming divides the crop production into subsystems and simulates their behaviors. Many classes were designed to simulate the behaviors of different parts or different physiological processes in crop production system. At the same time, many classes have to be employed for bettering user's interface. But how to manage these classes on a higher level to cooperate them into a perfect system is another problem to study. The Rice Growth Models (RGM) system represents an effort to define and implement a framework to manage these classes. In RGM system, the classes were organized into the model-document-view architecture to separate the domain models, data management and user interface. A single document with multiple views interface frame window was adopted in RGM. In the architectures, the simulation models only exchange data with documents while documents act as intermediacies between simulation models and interfaces. Views get data from documents and show the results to users. The classes for the different functions can be grouped into different architectures. Different architectures communicate with each other through documents. The classes for the different functions can be grouped into different architectures. By using the architecture, communication between classes is more efficient. Modeler can add classes in architectures or other architectures to extend the system without having to change system structure, which is useful for construction and maintenance of agricultural system models.

Problems with models assessing influences of tree size and inter-tree competitive processes on individual tree growth:a cautionary tale

In forest growing at any one site, the growth rate of an individual tree is determined principally by its size, which reflects its metabolic capacity, and by competition from neighboring trees. Competitive effects of a tree may be proportional to its size;such competition is termed ‘sym-metric’ and generally involves competition below ground for nutrients and water from the soil. Competition may also be ‘asymmetric’, where its effects are disproportionate to the size of the tree;this generally involves competition above ground for sunlight, when larger trees shade smaller, but the reverse cannot occur. This work examines three model systems often seen as exemplars relating individual tree growth rates to tree size and both competitive processes. Data of tree stem basal area growth rates in plots of even- aged, monoculture forest of blackbutt (Eucalyptus pilularis Smith) growing in sub-tropical eastern Australia were used to test these systems. It was found that none could distin-guish between size and competitive effects at any time in any one stand and, thus, allow quantification of the contribution of each to explaining tree growth rates. They were prevented from doing so both by collinearity between the terms used to describe each of the effects and technical problems involved in the use of nonlinear least-squares regression to fit the models to any one data set. It is concluded that quite new approaches need to be devised if the effects on tree growth of tree size and competitive processes are to be quantified and modelled successfully.

The Impact of the Digital Economy on Financial Regulatory Costs: An Empirical Analysis Based on the Solow Growth Model

As a novel economic form,the digital economy is reshaping the financial regulatory landscape and significantly impacting regulatory costs.This paper incorporates the digital economy and financial regulatory costs into the classic Solow growth model,uncovering an inverted U-shaped relationship between them.A subsequent mechanism analysis explains the rationale behind this relationship.To empirically examine this relationship in China,the paper utilizes inter-provincial panel data from 2013 to 2021 and employs methodologies such as the two-way fixed effects and moderating effects models.These analyses have important implications for the sound and sustainable development of China’s financial industry.The findings indicate:(a)As China’s digital economy develops,its impact on financial regulatory costs follows an inverted U-shaped pattern,initially increasing and then declining.This conclusion remains valid after robustness tests.(b)The influence of the digital economy on regulatory costs depends on favorable external conditions.Specifically,the impact is more pronounced in regions and periods with better digital infrastructure and more abundant human capital.(c)Additionally,redundant resources moderate this impact,which can weaken the inverted U-shaped relationship.Our findings not only provide a theoretical foundation for understanding the impact of the digital economy on financial regulatory costs but also offer valuable policy insights for optimizing financial regulation in China.

Crystal Growth Models of Dexamethasone Sodium Phosphate in a MSMPR Reactive Crystallizer

The reactive crystallization process of dexamethasone sodium phosphate was investigated in a continuous mixed-suspension, mixed-product-removal(MSMPR) crystallizer. Analyzing experimental data, it was found that the growth of product crystal was size-dependent. The Bransom, CR, ASL, M J2 and M J3 size-dependent growth models were discussed in details. Using experimental steady state population density data of dexamethasone sodium phosphate, parameters of five size-dependent growth models were determined by the method of non-linear least-squares. By comparison of experimental population density and linear growth rate data with those obtained from the five size-dependent growth models, it was found that the MJ3 model predicts the growth more accurately than do the other four models. Based on the theory of population balance, the crystal nucleation and growth rate equations of dexamethasone sodium phosphate were determined by non-linear regression method. The effects of different operation parameters such as supersaturation, magma density and temperature on the quality of product crystal were also discussed, and the optimal operation conditions were derived.

Novel models for simulating maize growth based on thermal time and photothermal units: Applications under various mulching practices

Maize (Zea mays L.) is one of the three major food crops and an important source of carbohydrates for maintaining food security around the world.Plant height (H),stem diameter (SD),leaf area index (LAI) and dry matter (DM) are important growth parameters that influence maize production.However,the combined effect of temperature and light on maize growth is rarely considered in crop growth models.Ten maize growth models based on the modified logistic growth equation (Mlog) and the Mitscherlich growth equation (Mit) were proposed to simulate the H,SD,LAI and DM of maize under different mulching practices based on experimental data from 2015–2018.Either the accumulative growing degree-days (AGDD),helio thermal units (HTU),photothermal units (PTU) or photoperiod thermal units (PPTU,first proposed here) was used as a single driving factor in the models;or AGDD was combined with either accumulative actual solar hours (ASS),accumulative photoperiod response (APR,first proposed here) or accumulative maximum possible sunshine hours (ADL) as the dual driving factors in the models.The model performances were evaluated using seven statistical indicators and a global performance index.The results showed that the three mulching practices significantly increased the maize growth rates and the maximum values of the growth curves compared with non-mulching.Among the four single factor-driven models,the overall performance of the Mlog_(PTU)Model was the best,followed by the Mlog_(AGDD)Model.The Mlog_(PPTU)Model was better than the Mlog_(AGDD)Model in simulating SD and LAI.Among the 10 models,the overall performance of the Mlog_(AGDD–APR)Model was the best,followed by the Mlog_(AGDD–ASS)Model.Specifically,the Mlog_(AGDD–APR)Model performed the best in simulating H and LAI,while the Mlog_(AGDD–ADL)and Mlog_(AGDD–ASS)models performed the best in simulating SD and DM,respectively.In conclusion,the modified logistic growth equations with AGDD and either APR,ASS or ADL as the dual driving factors outperformed the commonly used modified logistic growth model with AGDD as a single driving factor in simulating maize growth.

Growth models and site index table of natural Korean pine forests

According to the growth characteristics of natural Korean pine (Pinus Koraiensis) forests, 6 equations such as Chapman-Richards equation, Logistic equation, Power equation, and so on were selected to ftt for the growth modeIs for Korean pine forest. The growth models were developed based on 208 random trees and 24o dominant trees. Results show that the Chapman-Richards equation is the best model for estimating tree height by age and DBH, while the Parabola equation is fittest for predicting DBH by age or estimating age from DBH. The site index table of Korean pine forest was compiled by using the proportional method with the Chapman-Richards equation as the guide curve and vaIidated by accuracy test.

Growth and yield models for Dahurian larch plantations

Several equations were selected using nonlinear regression analysis for setting up growth and yield modehe of Dahurian larch (Laris gmelinii Rupr.) plantations. Data of 405 stem analysis trees were collected from 336 temporary plots throughout the Daxing’an Mountains. Results showed that the Richards equation was the best model for estimating tree height, stand mean height and stand dominant height by age, the Power equation was the fdiest model for predicting tree volume by DBH and tree height, and the Logarithmic stand vofume equation was good for predicting stand volume from age, mean height. basal area and other stand variables. These models can be used to construct volume tabIes, site index table and other forestry tables for Dahurian ghantations.