A Simplified Model with Soil Water Limitation on Spring Wheat Growth

The authors constructed a simplified model of spring wheat (Triticum aestivum L.) carbon assimilation and dry matter accumulation (DMA) process which consisted of two independent variables, day length (L) and total daily radiation (TDR). Leaf water potential (Ψ) was incorporated into the simplified growth model based on the assumption that both light use efficiency (α) and CO 2 conductance of assimilation (g c) were depressed by water limitation. Finally,Ψ was estimated from a regression equation in which the independent variables were relative soil water content in the upper 80 cm (θ R,80 ), ambient temperature (T a), vapor pressure deficit (VPD), the cumulative leaf water potential below thresholds of -1.5 MPa (Ψ c,1.5 ). Some applications in research program of field experiment of atmosphere_land surface processes in Heihe River region were tested. The simulated data agreed well with the data observed at Linze oasis in 1989 for various levels of water supply and at Zhangye oasis in 1992 in the field. The analysis and simulation using the model demonstrated that the simplified growth model could describe very well the DMA process of spring wheat with and without water limitation in the region of HEIFE (Heihe field experiment).

Experimental, Numerical and Simplified Theoretical Model Study for Internal Solitary Wave Load on FPSO with Emphasis on Scale Effect

Scale effect of ISWs loads on Floating Production Storage and Offloading(FPSO) is studied in this paper. The application conditions of KdV, eKdV and MCC ISWs theories are used in the numerical method. The depthaveraged velocities induced by ISWs are used for the velocity-inlet boundary. Three scale ratio numerical models λ=1, 20 and 300 were selected, which the scale ratio is the size ratio of numerical models to the experimental model.The comparisons between the numerical and former experimental results are performed to verify the feasibility of numerical method. The comparisons between the numerical and simplified theoretical results are performed to discuss the applicability of the simplified theoretical model summarized from the load experiments. Firstly, the numerical results of λ=1 numerical model showed a good agreement with former experimental and simplified theoretical results. It is feasible to simulate the ISWs loads on FPSO by the numerical method. Secondly, the comparisons between the results of three scale ratio numerical models and experimental results indicated that the scale ratios have more significant influence on the experimental horizontal forces than the vertical forces. The scale effect of horizontal forces mainly results from the different viscosity effects associated with the model’s dimension.Finally, through the comparisons between the numerical and simplified theoretical results for three scale ratio models, the simplified theoretical model of the pressure difference and friction forces exerted by ISWs on FPSO is applied for large-scale or full-scale FPSO.

Derivation of Simplified Models of Plan View Pattern Control Function for Plate Mill

The plan view pattern control theoretical models were simplified. Under the condition of constant volume for the plan view pattern compensation, the relation between the thickness and the length can be simplified to the linearity in the segment for the plan view pattern control function. The compensation volume can be dispersed for easy calculation. By comparing the model calculation result with the actual result, it was concluded that the simplified model can be used for the online control process.

The Numerical Scheme Development of a Simplified Frozen Soil Model

In almost all frozen soil models used currently, three variables of temperature, ice content and moisture content are used as prognostic variables and the rate term, accounting for the contribution of the phase change between water and ice, is shown explicitly in both the energy and mass balance equations. The models must be solved by a numerical method with an iterative process, and the rate term of the phase change needs to be pre-estimated at the beginning in each iteration step. Since the rate term of the phase change in the energy equation is closely related to the release or absorption of the great amount of fusion heat, a small error in the rate term estimation will introduce greater error in the energy balance, which will amplify the error in the temperature calculation and in turn, cause problems for the numerical solution convergence. In this work, in order to first reduce the trouble, the methodology of the variable transformation is applied to a simplified frozen soil model used currently, which leads to new frozen soil scheme used in this work. In the new scheme, the enthalpy and the total water equivalent are used as predictive variables in the governing equations to replace temperature, volumetric soil moisture and ice content used in many current models. By doing so, the rate terms of the phase change are not shown explicitly in both the mass and energy equations and its pre-estimation is avoided. Secondly, in order to solve this new scheme more functionally, the development of the numerical scheme to the new scheme is described and a numerical algorithm appropriate to the numerical scheme is developed. In order to evaluate the new scheme of the frozen soil model and its relevant algorithm, a series of model evaluations are conducted by comparing numerical results from the new model scheme with three observational data sets. The comparisons show that the results from the model are in good agreement with these data sets in both the change trend of variables and their magnitude values, and the new scheme, together with the algorithm, is more efficient and saves more computer time.

Simplified Prediction Model for Vortex-Induced Vibrations of Top Tensioned Risers

According to the characteristics of deepwater top tensioned risers, a simplified model is presented to predict the multi-modal response of vortex-induced vibration （VIV） in non-uniform flow based on energy equilibrium theory and the exporimental data from VIV self-excited and forced oscillations of rigid cylinders. The response amplitude of each mode is determined by a balance between the energy fed into the riser over the lock-in regions and the energy dissipated by the fluid damping over the remainders. Compared with the previous prediction models, this method can take fully account of the intrinsic nature of VIV for low mass ratio structures on lock-in regions, added mass and nonlinear fluid damping effect, etc. Moreover, it is the first time to propose the accurate calculating procedure for VIV amplitude correction factor by solving energy equilibrium equation and a closed form solution is presented for the case of a riser of uniform mass and cross-section oscillating in a uniform flow. The predicted values show a reasonable agreement with VIV experiments of riser models in stepped and sheared currents.

Modelling of an hydraulic excavator using simplifiedrefined instrumental variable(SRIV)algorithm

Instead of establishing mathematical hydraulic system models from physical laws usually done with the problems of complex modelling processes, low reliability and practicality caused by large uncertainties, a novel modelling method for a highly nonlinear system of a hydraulic excavator is presented. Based on the data collected in the excavator＇s arms driving experiments, a data-based excavator dynamic model using Simplified Refined Instrumental Variable （SRIV） identification and estimation algorithms is established. The validity of the proposed data-based model is indirectly demonstrated by the performance of computer simulation and the.real machine motion control exoeriments.

Evaporation Erosion During the Relay Contact Breaking Process Based on a Simplified Arc Model

Evaporation erosion of the contacts is one of the fundamental failure mechanisms for relays. In this paper, the evaporation erosion characteristics are investigated for the copper contact pair breaking a resistive direct current （dc） 30 V/10 A circuit in the air. Molten pool simulation of the contacts is coupled with the gas dynamics to calculate the evaporation rate. A simplified arc model is constructed to obtain the contact voltage and current variations with time for the prediction of the current density and the heat flux distributions flowing from the arc into the contacts. The evaporation rate and mass variations with time during the breaking process are presented. Experiments are carried out to verify the simulation results.

Simplified Homogeneous Balance Method and Its Applications to the Whitham-Broer-Kaup Model Equations

A nonlinear transformation of the Whitham-Broer-Kaup (WBK) model equations in the shallow water small-amplitude regime is derived by using a simplified homogeneous balance method. The WBK model equations are linearized under the nonlinear transformation. Various exact solutions of the WBK model equations are obtained via the nonlinear transformation with the aid of solutions for the linear equation.

A Simplified Scheme of the Generalized Layered Radiative Transfer Model

In this paper, firstly, a simplified version （SGRTM） of the generalized layered radiative transfer model （GRTM） within the canopy, developed by us, is presented. It reduces the information requirement of inputted sky diffuse radiation, as well as of canopy morphology, and in turn saves computer resources. Results from the SGRTM agree perfectly with those of the GRTM. Secondly, by applying the linear superposition principle of the optics and by using the basic solutions of the GRTM for radiative transfer within the canopy under the condition of assumed zero soil reflectance, two sets of explicit analytical solutions of radiative transfer within the canopy with any soil reflectance magnitude are derived： one for incident diffuse, and the other for direct beam radiation. The explicit analytical solutions need two sets of basic solutions of canopy reflectance and transmittance under zero soil reflectance, run by the model for both diffuse and direct beam radiation. One set of basic solutions is the canopy reflectance αf （written as α1 for direct beam radiation） and transmittance βf （written as β1 for direction beam radiation） with zero soil reflectance for the downward radiation from above the canopy （i.e. sky）, and the other set is the canopy reflectance （αb） and transmittance βb for the upward radiation from below the canopy （i.e., ground）. Under the condition of the same plant architecture in the vertical layers, and the same leaf adaxial and abaxial optical properties in the canopies for the uniform diffuse radiation, the explicit solutions need only one set of basic solutions, because under this condition the two basic solutions are equal, i.e., αf = αb and βf = βb. Using the explicit analytical solutions, the fractions of any kind of incident solar radiation reflected from （defined as surface albedo, or canopy reflectance）, transmitted through （defined as canopy transmittance）, and absorbed by （defined as canopy absorptance） the canopy and other properties pertinent to the radiative transfer within the canopy can be estimated easily on the ground surface below the canopy （soil or snow surface） with any reflectance magnitudes. The simplified transfer model is proven to have a similar accuracy compared to the detailed model, as well as very efficient computing.

A Simplified Nonlinear Model of Vertical Vortex-Induced Force on Box Decks for Predicting Stable Amplitudes of Vortex-Induced Vibrations

Wind-tunnel tests of a large-scale sectional model with synchronous measurements of force and vibration responses were carried out to investigate the nonlinear behaviors of vertical vortex-induced forces （VIFs） on three typical box decks （i.e., fully closed box, centrally slotted box, and semi-closed box）. The mechanisms of the onset, development, and self-limiting phenomenon of the vertical vortex-induced vibration （VlV） were also explored by analyzing the energy evolution of different vertical VIF components and their contributions to the vertical VIV responses. The results show that the nonlinear components of the vertical VIF often differ from deck to deck; the most important components of the vertical VIF, governing the stable amplitudes of the vertical VIV responses, are the linear and cubic components of velocity contained in the self-excited aerodynamic damping forces. The former provides a constant negative damping ratio to the vibration system and is thus the essential power driving the development of the VIV amplitude, while the latter provides a positive damping ratio proportional to the square of the vibration velocity and is actually the inherent factor making the VIV amplitude self-limiting. On these bases, a universal simplified nonlinear mathematical model of the vertical VIF on box decks of bridges is presented and verified in this paper; it can be used to predict the stable amplitudes of the vertical VIV of long-span bridges with satisfactory accuracy.

Simplified Thermodynamic Model for Pro-Eutectoid Ferrite Formation in Multicomponent Structural Steel

By introducing aparameter of difference in ferrite formation temperature between binary Fe-C and multicomponent system,and referring to the thermodynamic model for Fe-C binary system,a simplified thermodynamic model for pro-eutectoid ferrite formation in Fe-ΣXiC multicomponent structural steels(Xi=Mn,Si,Mo,Cr,Ni or Ti,etc)was suggested.The comparison of the calculated Ae3 temperatures with the measured data of steels 42 shows that the relative standard deviation and root-mean-square(RMS)error between them are only 0.71% and 8.92 K,respectively.However,the deviations between the same measured data and the values calculated from the superelement model are as high as 1.86% and 23.83 K,respectively.It can be concluded that the simplified thermodynamic model for pro-eutectoid ferrite formation in multicomponent structural steels is acceptable and the calculated Ae3 temperatures are in good agreement with the experimental data.

A Simplified Model for SO_(2) Generation during Spontaneous Combustion of Coal Gangue

A simplified model for SO_(2) generation during spontaneous combustion of coal gangue was put forward and validated using the measured data.Using the proposed model,the effects of initial temperature inside the gangue and fresh air supply on SO_(2) generation were discussed.The results showed that,higher initial temperature inside the gangue could accelerate the oxidation rate of FeS_(2) and increase the maximum concentration of SO_(2).If initial temperature inside the gangue increased by about 37%,the total SO_(2) generation increased by 166%.Fresh air supply had less significant effect on the oxidation rate of FeS_(2).However,the higher the fresh air supply was,the more FeS_(2) could be oxidized,which ultimately produced more SO_(2).Although the computed results and the measured data concerning the inner locations inside the gangue had a certain degree of error,the proposed model can provide a relatively precise total release of SO_(2) within acceptable accuracy.Besides,this method provides a useful prototype to predict the generation of hazardous materials,such as CO,NO_(x),and chlorine during the spontaneous combustion of coal gangue.

Towards a semi-empirical model of the sea ice thickness based on hyperspectral remote sensing in the Bohai Sea

Sea ice thickness is one of the most important input parameters for the prevention and mitigation of sea ice disasters and the prediction of local sea environments and climates. Estimating the sea ice thickness is currently the most important issue in the study of sea ice remote sensing. With the Bohai Sea as the study area, a semiempirical model of the sea ice thickness（SEMSIT） that can be used to estimate the thickness of first-year ice based on existing water depth estimation models and hyperspectral remote sensing data according to an optical radiative transfer process in sea ice is proposed. In the model, the absorption and scattering properties of sea ice in different bands（spectral dimension information） are utilized. An integrated attenuation coefficient at the pixel level is estimated using the height of the reflectance peak at 1 088 nm. In addition, the surface reflectance of sea ice at the pixel level is estimated using the 1 550–1 750 nm band reflectance. The model is used to estimate the sea ice thickness with Hyperion images. The first validation results suggest that the proposed model and parameterization scheme can effectively reduce the estimation error associated with the sea ice thickness that is caused by temporal and spatial heterogeneities in the integrated attenuation coefficient and sea ice surface. A practical semi-empirical model and parameterization scheme that may be feasible for the sea ice thickness estimation using hyperspectral remote sensing data are potentially provided.

Optimization for friction damped post-tensioned steel frame based on simplified FE model and GA

The post-tensioned(PT)energy-dissipating connection for steel frames has drawn the attention of many researchers for its good seismic performance.Friction mechanisms,such as friction damped PT steel connections,are the approaches typically used to improve energy-dissipating capacity.The mechanical behavior of PT connections has been extensively investigated.The seismic performance of PT frames should be optimized by employing a suitable design of a friction device.In this study,the influence of f_(max)on the seismic behavior of a PT frame is investigated.The_(max)static frictional force f_(max)is optimized based on a genetic algorithm(GA).Results indicate that the reasonable distribution of f_(max)can evidently improve seismic performance.Consequently,the GA method can be effectively utilized for seeking the optimal combination of f_(max)if the simplified finite element model is adopted.Results derived will provide a foundation for analysis and design of PT frame structures.

Simplified Wave Models Applicability to Shallow Mud Flows Modeled as Power-Law Fluids

Simplified wave models- such as kinematic,diffusion and quasi-steady- are widely employed as a convenient replacement of the full dynamic one in the analysis of unsteady open-channel flows,and especially for flood routing.While their use may guarantee a significant reduction of the computational effort,it is mandatory to define the conditions in which they may be confidently applied.The present paper investigates the applicability conditions of the kinematic,diffusion and quasisteady dynamic shallow wave models for mud flows of power-law fluids.The power-law model describes in an adequate and convenient way fluids that at low shear rates fluids do not posses yield stress,such as clay or kaolin suspensions,which are frequently encountered in Chinese rivers.In the framework of a linear analysis,the propagation characteristics of a periodic perturbation of an initial steady uniform flow predicted by the simplified models are compared with those of the full dynamic one.Based on this comparison,applicability criteria for the different wave approximations for mud flood of power-law fluids are derived.The presented results provide guidelines for selecting the appropriate approximation for a given flow problem,and therefore they may represent a useful tool for engineering predictions.

Comparative Study among Different Semi-Empirical Models for Soil Salinity Prediction in an Arid Environment Using OLI Landsat-8 Data

Salt-affected soils, caused by natural or human activities, are a common environmental hazard in semi-arid and arid landscapes. Excess salts in soils affect plant growth and production, soil and water quality and, therefore, increase soil erosion and land degradation. This research investigates the performance of five different semi-empirical predictive models for soil salinity spatial distribution mapping in arid environment using OLI sensor image data. This is the first attempt to test remote sensing based semi-empirical salinity predictive models in this area: the Kingdom of Bahrain. To achieve our objectives, OLI data were standardized from the atmosphere interferences, the sensor radiometric drift, and the topographic and geometric distortions. Then, the five semi-empirical predictive models based on the Normalized Difference Salinity Index (NDSI), the Salinity Index-ASTER (SI-ASTER), the Salinity Index-1 (SI-1), the Soil Salinity and Sodicity Index-1 and Index-2 (SSSI-1 and SSSI-2), developed for slight and moderate salinity in agricultural land, were implemented and applied to OLI image data. For validation purposes, a fieldwork was organized and different important spots-locations representing different salinity levels were visited, photographed, and localized using an accurate GPS (σ ≤ ±30 cm). Based on this a priori knowledge of the soil salinity, six validation sites were selected to reflect non-saline, low, moderate, high and extreme salinity classes, descriptive statistics extracted from polygons and/or transects over these sites were used. The obtained results showed that the models based on NDSI, SI-1 and SI-ASTER all failed to detect salinity bounds for both extreme salinity (Sabkhah) and non-saline conditions. In Fact, NDSI and SI-ASTER gave respectively only 35% dS/m and 25% dS/m in extreme salinity validation site, while SI-1 and SI-ASTER indicated 38% dS/m and 39% dS/m in non-saline validation site. Therefore, these three models were deemed inadequate for the study site. However, both SSSI-1 and SSSI-2 allowed a detection of the previous salinity bounds and furthermore described similarly and correctly the urban-vegetation areas and the open-land areas. Their predicted EC is around 10% dS/m for non-saline urban soil, about 25% dS/m for low salinity urban-vegetation soil, approximately 30% to 75% dS/m, respectively, for moderate to high salinity soils. SSSI-2 based semi-empirical salinity models was able to differentiate the high salinity versus extreme salinity in areas where both exist and was very accurate to highlight the pure salt where SSSI-1 has reach saturation for both salinity classes. In conclusion, reliable salinity map was produced using the model based on SSSI-2 and OLI sensor data that allows a better characterization of the soil salinity problem in an Arid Environment.

Description of martensitic transformation kinetics in Fe-C-X(X = Ni,Cr,Mn,Si) system by a modified model

Controlling the content of athermal martensite and retained austenite is important to improving the mechanical properties of high-strength steels,but a mechanism for the accurate description of martensitic transformation during the cooling process must be addressed.At present,frequently used semi-empirical kinetics models suffer from huge errors at the beginning of transformation,and most of them fail to exhibit the sigmoidal shape characteristic of transformation curves.To describe the martensitic transformation process accurately,based on the Magee model,we introduced the changes in the nucleation activation energy of martensite with temperature,which led to the varying nucleation rates of this model during martensitic transformation.According to the calculation results,the relative error of the modified model for the martensitic transformation kinetics curves of Fe-C-X(X = Ni,Cr,Mn,Si) alloys reached 9.5% compared with those measured via the thermal expansion method.The relative error was approximately reduced by two-thirds compared with that of the Magee model.The incorporation of nucleation activation energy into the kinetics model contributes to the improvement of its precision.

Study on the Principle Model and Simplification of Subway Station Itemized Energy Consumption

Owing to the constant modernization and urbanization of China,most cities have subways,and the total power consumption of subway stations has been rising,which contradicts with China’s green goals.In this regard,energy consumption indicators for major energy use projects in subway stations should be established,comprehensive evaluation and detailed research on the current situation of subway operation should be conducted,and specific energy-saving measures should be taken from a diversified perspective.It is crucial to systematically sort out the principle of sub-item energy consumption in subway stations,and practice and explore the specific simplification measures of the principle model of sub-item energy consumption,so as to lay a solid foundation for achieving the goal of reducing energy consumption of subway stations.

A preliminary study on simplified simulation model of spring wheat growth

In the model developed in this paper, taking the characters and requirements of meteorological services into account, some conventional meteorological observations which are easy to be obtained have been ch.osen, and mathematical equations describing micro-growth processes of crops have been established on the basis of the field experiments, laboratorial analysis and computer's modelling tests with time interval of ten-days for several years (1987-1989), in accordance with the known biological and physical rules and corresponding reference literatures. It is a preliminary simplified simulation model of spring wheat growth in optimal water and nutrient conditions. The field experiments show that simulation results of this simplified model are satisfactory. The potential operational application and theoretical sense are significant in the meteorological forecast of yield and in the assessment of influences of climatic change on agriculture.

Numerical Simulation Investigation of the Impact of Simplified Architectural Canopy Models on the Distribution of Flow Filed

A series of simulations of air flow through three kinds of2 D vegetation canopies along with different canopy morphology have been conducted by computational fluid dynamics( CFD). Two different turbulent closure models have been used, including standard k-ε turbulent model and RNG k-ε turbulent model with or without source / sink terms,respectively,for the purpose of wind energy applications. In this study,the complicated morphology of3 D vegetation canopy is simplified to three types of 2D simplified canopy model analyzed by the main parameter leaf area index( LAI). Effects of branches and leaves on airflow are also modelled by introducing circles into the 2D simplified canopy model with or without source / sink terms by adding drag force terms in the momentum and turbulent energy equations in porous sub-domains.The main model parameters of source / sink terms are identified thanks to experimental data obtained by direct wind tunnel measurements of the air flow speeds through a branch of Osmanthus fragrans. Moreover,three different canopy shapes of the vegetation canopy are introduced into the simulation. The predictive skills of single-and two-equation( k-ε) models with or without source / sink to compute profiles of mean velocity( u),turbulent kinetic energy( TKE),TKE dissipation rate( ε) and turbulent intensity( I) are compared against datasets collected from other works and field measurements. In conclusion, it is demonstrated that vegetation canopy model 1 using RNG or standard k-ε turbulent model with source / sink terms proves to be a physically accurate and numerically robust method. The method which is better than other two vegetation canopy models is recommended for future use in simulating turbulent flows within and above the canopy in 3D in more details.