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).

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.

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.

A Simplified Model for Buckling and Post-Buckling Analysis of Cu Nanobeam Under Compression

Both of Buckling and post-buckling are fundamental problems of geometric nonlinearity in solid mechanics.With the rapid development of nanotechnology in recent years,buckling behaviors in nanobeams receive more attention due to its applications in sensors,actuators,transistors,probes,and resonators in nanoelectromechanical systems(NEMS)and biotechnology.In this work,buckling and post-buckling of copper nanobeam under uniaxial compression are investigated with theoretical analysis and atomistic simulations.Different cross sections are explored for the consideration of surface effects.To avoid complicated high order buckling modes,a stressbased simplified model is proposed to analyze the critical strain for buckling,maximum deflection,and nominal failure strain for post-buckling.Surface effects should be considered regarding critical buckling strain and the maximum post-buckling deflection.The critical strain increases with increasing nanobeam cross section,while themaximumdeflection increases with increasing loading strain but stays nearly the same for different cross sections,and the underlying mechanisms are revealed by our model.The maximum deflection is also influenced by surface effects.The nominal failure strains are captured by our simulations,and they are in good agreement with the simplified model.Our results can be used for helping design strain gauge sensors and nanodevices with self-detecting ability.

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.

Simplified Model for Evaluation of VIV-induced Fatigue Damage of Deepwater Marine Risers

A simplified empirical model for fatigue analysis of deepwater marine risers due to vortex-induced vibration (VIV) in non-uniform current is presented. A simplified modal vibration equation is employed according to the characteristics of deepwater top tensioned risers. The response amplitude of each mode is determined by a balance between the energy feeding into the riser over the lock-in regions and the energy dissipated by the fluid damping over the remainder based on the data from self-excited oscillation and forced oscillation experiments of rigid cylinders. Multi-modal VIV fatigue loading is obtained by the square root of the sum of squares approach. Compared with previous works, this model can take fully account of the main intrinsic natures of VIV for low mass ratio structures on lock-in regions, added mass and nonlinear fluid damping. In addition, a closed form solution of fatigue damage is presented for the case of a riser with uniform mass and cross-section oscillating in a uniform flow. Fatigue analysis of a typical deepwater riser operating in Gulf of Mexico and West Africa shows that the current velocity profiles affect the riser’s fatigue life significantly and the most dangerous locations of the riser are also pointed out.

A Simplified Model for Generating 3D Realistic Sound in the Multimedia and Virtual Reality Systems

It is a key feature to embed 3D realistic sound effect in the future multimedia and virtual reality systems. Recent research on acoustics and psychoacoustics reveals the important cues for sound localization and sound perception. One promising approach to generate 3D realistic sound effect uses two earphones by simulating the sound waveforms from sound source to eardrum. This paper summarizes two methods for generating 3D realistic sound and points out their inherent drawbacks. To overcome these drawbacks we propose a simplified model to generate 3D realistic sound at any positions in the horizontal plane based on the results of sound perception and localization. Experimental results show that the model is correct and efficient.

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.

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.

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.

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 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.

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.

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.

Operation optimization of prefabricated light modular radiant heating system:Thermal resistance analysis and numerical study

The utilization of prefabricated light modular radiant heating system has demonstrated significant increases in heat transfer efficiency and energy conservation capabilities.Within prefabricated building construction,this new heating method presents an opportunity for the development of comprehensive facilities.The parameters for evaluating the effectiveness of such a system are the upper surface layer’s heat flux and temperature.In this paper,thermal resistance analysis calculation based on a simplified model for this unique radiant heating system analysis is presented with the heat transfer mechanism’s evaluation.The results obtained from thermal resistance analysis calculation and numerical simulation indicate that the thermal resistance analysis method is highly accurate with temperature discrepancies ranging from 0.44℃ to−0.44℃ and a heat flux discrepancy of less than 7.54%,which can meet the requirements of practical engineering applications,suggesting a foundation for the prefabricated radiant heating system.

An efficient physics-guided Bayesian framework for predicting ground settlement profile during excavations in clay

Recently,the application of Bayesian updating to predict excavation-induced deformation has proven successful and improved prediction accuracy significantly.However,updating the ground settlement profile,which is crucial for determining potential damage to nearby infrastructures,has received limited attention.To address this,this paper proposes a physics-guided simplified model combined with a Bayesian updating framework to accurately predict the ground settlement profile.The advantage of this model is that it eliminates the need for complex finite element modeling and makes the updating framework user-friendly.Furthermore,the model is physically interpretable,which can provide valuable references for construction adjustments.The effectiveness of the proposed method is demonstrated through two field case studies,showing that it can yield satisfactory predictions for the settlement profile.

A simplified simulation method of friction pendulum bearings

In order to improve the computation efficiency and simulation accuracy,a novel simplified simulation method for friction pendulum bearing( FPB) is proposed. The behavior of FPB was analyzed based on the stress characteristics of the slider of FPB. Then,a novel simplified FPB model with a single pendulum and a nonlinear spring was established. The mechanical behavior of the simplified model was analyzed and it conformed well to the basic requirements of FPB. Furthermore,shaking table tests of a concrete slab block structure isolated by four FPBs were carried out, followed by finite element simulations of the test using the proposed simplified model.Three waves and eleven loading scenarios were selected in the test. The results show that the overall trend of the relative displacement time-history curves,the horizontal acceleration time-history curves and the vertical acceleration time-history curves from the numerical simulation match in a good manner with those obtained from the tests. Specifically,it is found that the difference of the peak value within these curves between the simulation and test results is less than 15%,which means that the proposed simplified model can be used to simulate the FPB behaviors under dynamic loadings with acceptable accuracy for engineering purposes.

A NEW MODEL FOR ESTIMATION OF DIFFUSION COEFFICIENT OF PHENOL DESORPTION WITHIN POLYMERIC RESIN UNDER ULTRASOUND

A new model, phase equilibrium-kinetics model (PEKM), for estimation of diffusion coefficient was proposed in this paper. Kinetic experiments of phenol desorption on NKAII resin in the presence and the absence of ultrasound were separately conducted, and diffusion coefficients of phenol within an adsorbent particle were estimated by means of proposed PEKM and classic simplified model. Results show that the use of ultrasound not only changes the phase equilibrium state of NKA II resin/phenol/water system which had been equilibrium at normal condition, but also enhances diffusion of phenol within the resin. The diffusion coefficient of phenol in the resin in the field of ultrasound increases in an order of magnitude in comparison with the diffusion coefficient determined under no ultrasound. Experimental results also indicated that the diffusion coefficients estimated by PEKM were more accurate than that estimated by the classic simplified model.