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.

Prediction of impedance responses of protonic ceramic cells using artificial neural network tuned with the distribution of relaxation times

A deep-learning-based framework is proposed to predict the impedance response and underlying electrochemical behavior of the reversible protonic ceramic cell(PCC) across a wide variety of different operating conditions.Electrochemical impedance spectra(EIS) of PCCs were first acquired under a variety of opera ting conditions to provide a dataset containing 36 sets of EIS spectra for the model.An artificial neural network(ANN) was then trained to model the relationship between the cell operating condition and EIS response.Finally,ANN model-predicted EIS spectra were analyzed by the distribution of relaxation times(DRT) and compared to DRT spectra obtained from the experimental EIS data,enabling an assessment of the accumulative errors from the predicted EIS data vs the predicted DRT.We show that in certain cases,although the R^(2)of the predicted EIS curve may be> 0.98,the R^(2)of the predicted DRT may be as low as~0.3.This can lead to an inaccurate ANN prediction of the underlying time-resolved electrochemical response,although the apparent accuracy as evaluated from the EIS prediction may seem acceptable.After adjustment of the parameters of the ANN framework,the average R^(2)of the DRTs derived from the predicted EIS can be improved to 0.9667.Thus,we demonstrate that a properly tuned ANN model can be used as an effective tool to predict not only the EIS,but also the DRT of complex electrochemical systems.

RELAXATION TIME LIMITS PROBLEM FOR HYDRODYNAMIC MODELS IN SEMICONDUCTOR SCIENCE

In this article, two relaxation time limits, namely, the momentum relaxation time limit and the energy relaxation time limit are considered. By the compactness argument, it is obtained that the smooth solutions of the multidimensional nonisentropic Euler-Poisson problem converge to the solutions of an energy transport model or a drift diffusion model, respectively, with respect to different time scales.

A time domain induced polarization relaxation time spectrum inversion method based on a damping factor and residual correction

Relaxation time spectra （RTS） derived from time domain induced polarization data （TDIP） are helpful to assess oil reservoir pore structures. However, due to the sensitivity to the signal-to-noise ratio （SNR）, the inversion accuracy of the traditional singular value decomposition （SVD） inversion method reduces with a decrease of SNR. In order to enhance the inversion accuracy and improve robustness of the inversion method to the SNR, an improved inversion method, based on damping factor and spectrum component residual correction, is proposed in this study. The numerical inversion results show that the oscillation of the RTS derived from the SVD method increased with a decrease of SNR, which makes it impossible to get accurate inversion components. However, the SNR has little influence on inversion components of the improved method, and the RTS has high inversion accuracy and robustness. Moreover, RTS derived from core sample data is basically in accord with the pore-size distribution curve, and the RTS derived from the actual induced polarization logging data is smooth and continuous, which indicates that the improved method is practicable.

Multi-relaxation time lattice Boltzmann simulation of inertial secondary flow in a curved microchannel

The inertial secondary flow is particularly important tbr hydrodynamic lbcusing and particle manipulation m biomed- ical research. In this paper, the development of the inertial secondary flow structure in a curved microchannel was investi- gated by the multi relaxation time lattice Boltzmann equation model with a force term. The numerical results indicate that the viscous and inertial competition dominates the development of secondary flow structure development. The Reynolds number, Dean number, and the cross section aspect ratio influence significantly on the development of the secondary vor- texes. Both the intensity of secondary flow and the distance between the normalized vortex centers are functions of Dean numbers but independent of channel curvature radius. In addition, the competition mechanism between the viscous and inertial effects were discussed by performing the particle focusing experiments. The present investigation provides an improved understanding of the development of inertial secondary flows in curved microchannels.

Concise review of relaxations and approximation algorithms for nonidentical parallel-machine scheduling to minimize total weighted completion times

A class of nonidentical parallel machine scheduling problems are considered in which the goal is to minimize the total weighted completion time. Models and relaxations are collected. Most of these problems are NP-hard, in the strong sense, or open problems, therefore approximation algorithms are studied. The review reveals that there exist some potential areas worthy of further research.

Effect of optical pumping on the momentum relaxation time of graphene in the terahertz range

The momentum relaxation time of a photoexcited graphene in the THz frequency range has been studied by using terabertz time domain spectroscopy under optical pumping at room temperature. It is found that the momentum relaxation time of the graphene as a function of the optical pumping intensity exhibits a threshold behavior. The features of the momentum relaxation time as a function of the optical pumping intensity are also investigated. The results are useful for understanding the basic underlying physics of graphene scattering as well as finding the possible applications in carbon- based electronics.

Effective relaxation time and viscosity of the earth inferred from the postseismic vertical deformations of the 1990 MS=7.0 Gonghe earthquake

The postseismic vertical deformation rates of the 1990 Gonghe M S=7.0 earthquake appears to have decreased exponentially. Based on Okada′s coseismic surface displacement solution caused by a uniform fault slip in an elastic homogeneous half space, we derived its postseismic surface displacement by using a single layer standard linear solid model, and further derived a simplified formula for determining the effective relaxation time and viscosity of the earth, which is independent of the dislocation parameters of the causative fault. From the postseismic vertical deformation of the 1990 Gonghe earthquake, we inferred that the effective relaxation time defined by τ = η/μ is 2.6 years, and the effective viscosity η is about 10 18 Pa·s.

MICROSTRUCTURE AND THERMAL STRESS RELAXATION OF ZrO_2－Ni FUNCTIONALLY GRADED MATERIAL

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Combined immersed boundary method and multiple-relaxation-time lattice Boltzmann flux solver for numerical simulations of incompressible flows

A method combining the immersed boundary technique and a multi- relaxation-time （MRT） lattice Boltzmann flux solver （LBFS） is presented for numerical simulation of incompressible flows over circular and elliptic cylinders and NACA 0012 Airfoil. The method uses a simple Cartesian mesh to simulate flows past immersed complicated bodies. With the Chapman-Enskog expansion analysis, a transform is performed between the Navier-Stokes and lattice Boltzmann equations （LBEs）. The LBFS is used to discretize the macroscopic differential equations with a finite volume method and evaluate the interface fluxes through local reconstruction of the lattice Boltzmann solution. The immersed boundary technique is used to correct the intermediate velocity around the solid boundary to satisfy the no-slip boundary condition. Agreement of simulation results with the data found in the literature shows reliability of the proposed method in simulating laminar flows on a Cartesian mesh.

A Numerical Algorithm Based on Quadratic Finite Element for Two-Dimensional Nonlinear Time Fractional Thermal Diffusion Model

In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+
t2)is obtained,which is verified by the numerical results.

Effect of relaxation time on the squeezed correlations of bosons for evolving sources in relativistic heavy-ion collisions

The squeezed back-to-back correlation(SBBC)of a boson-antiboson pair is sensitive to the time distribution of the particle-emitting source,and the SBBC function for an evolving source is expected to be affected by the relaxation time of the system.In this study,we investigated the effect of relaxation time on the SBBC function.We propose a method for calculating the SBBC function with relaxation-time approximation for evolving sources.SBBC functions of D^(0)D^(-0)in relativistic heavy-ion collisions were investigated using a hydrodynamic model.We found that the relaxation time reduces the amplitudes of the SBBC functions.This becomes apparent for long relaxation times and large initial relative deviations of the chaotic and squeezed amplitudes from their equilibrium values in the temporal steps.

Thermal relaxation and mechanical relaxation of rice gel

Rice gel was prepared by simulating the production processes of Chinese local rice noodles,and the properties of thermal relaxation and mechanical relaxation during gelatinization were studied by differential scanning calorimetry(DSC) measurement and dynamic rheometer.The results show that during gelatinization,the molecular chains of rice starch undergo the thermal relaxation and mechanical relaxation.During the first heating and high temperature holding processes,the starch crystallites in the rice slurry melt,and the polymer chains stretch and interact,then viscoelastic gel forms.The cooling and low temperatures holding processes result in reinforced networks and decrease the viscoelasticity of the gel.During the second heating,the remaining starch crystallites further melt,the network is reinforced,and the viscoelasticity increases.The viscoelasticity,the molecular conformation and texture of the gel are adjusted by changing the temperature,and finally construct the gel with the textural characteristics of Chinese local rice noodle.

The Influence of Organo-Clay Ratio in the HIPS-OMMT Nanocomposites Analyzed by Proton Spin-Lattice and Spin-Spin Relaxation Times

Spin-lattice and spin-spin relaxation times are one of the most attractive tools in the solid-state nuclear magnetic resonance spectroscopy to evaluate the level of clay dispersion in the nanocomposite matrices. The efficiency of the relaxation processes can be used to evaluate the nanoparticles intermolecular interactions and, consequently, the dispersion of them in the polymer matrix, the molecular dynamic of the hybrid compounds, as well as the molecular domains formation in an organic material. The determination of relaxation parameters was carried out to evaluate the organoclay exfoliation and intercalation process in the polymeric matrix, in addition to their dispersion and distribution in the matrix. The proton NMR relaxation data showed that the polymeric nanomaterials investigated presented good intermolecular interaction that promoted good nanoparticles dispersion and distribution in the hybrid materials. The proportion of 2% clay promoted a greater heterogeneity in the matrix compared to other ratios;1% clay influenced only to the higher molecular rigidity phase;and 3% clay had a decrease in heterogeneity compared to 2% though still influenced the matrix as a whole. These results prove the efficiency of NMR technique in the evaluation of nanofillers interaction with polymer matrices, as well as their dispersion and distribution.

Simulating high Reynolds number flow in two-dimensional lid-driven cavity by multi-relaxation-time lattice Boltzmann method

By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improved greatly, especially on simulating high Reynolds number （Re） flow. As a discovery, the super-stability analysed by Lallemand and Luo is verified and the complex structure of the cavity flow is also exhibited in our numerical simulation when Re is high enough. To the best knowledge of the authors, the maximum of Re which has been investigated by direct numerical simulation is only around 50 000 in the literature; however, this paper can readily extend the maximum to 1000 000 with the above combination.

Microstructure and thermal expansion of copper-based amorphous alloys during structural relaxation

(Cu43Zr48Al9)98Y2 amorphous alloy bar was prepared by the arc melting copper mold absorption casting method,and then,the amorphous alloy was annealed at different temperatures for different times.The influence of heating rate on thermal expansion and thermal stability was studied by thermomechanical analysis(TMA),and the microstructure evolution of the amorphous alloy during structural relaxation and crystallization was studied by XRD and TEM.Results show that the structural evolution behavior of the(Cu43Zr48Al9)98Y2 amorphous alloy can be divided into five different stages(structural relaxation preparation stage,structural relaxation stage,first crystallization stage,second crystallization stage,and grain growth stage).When the heating rate is 20 K/min,the amorphous alloy has the smallest thermal expansion coefficient and the best thermal stability.The width of the supercooled liquid region is 66.42 K.Samples with different relaxation states were prepared by annealing at the heating rate of 20 K/min.The structural evolution of amorphous alloys with different relaxation states is as follows:amorphous→CuZr2+AlCu2Zr7→CuZr2+AlCu2Zr7+CuZr(B2)+CuZr(M)+Cu10Zr7→CuZr2+AlCu2Zr7+CuZr(B2)+CuZr(M).After annealing at 706 K and 726 K(in the supercooled liquid region)for 1.5 h,the amorphous-nanocrystalline composites were obtained.When the annealing temperature is 706 K,the crystallization process of the sample is as follows:amorphous→Cu10Zr7→Cu10Zr7+CuZr,and for the sample at 726 K,it is as follows:amorphous→CuZr2+AlCu2Zr7+Cu10Zr7→Cu10Zr7+CuZr2→CuZr2+CuZr(B2)+Cu10Zr7.

Influence of Ga^+ ion irradiation on thermal relaxation of exchange bias field in exchange-coupled CoFe/IrMn bilayers

This paper reports that the CoFe/IrMn bilayers are deposited by magnetron sputtering on the surfaces of thermallyoxidized Si substrates. It investigates the thermal relaxations of both non-irradiated and Ca^＋ ion irradiated CoFe/IrMn bilayers by means of holding the bilayers in a negative saturation field. The results show that exchange bias field decreases with the increase of holding time period for both non-irradiated and Ca^＋ ion irradiated CoFe/IrMn bilayers. Exchange bias field is also found to be smaller upon irradiation at higher ion dose. This reduction of exchange bias field is attributed to the change of energy barrier induced by ion-radiation.

A multiple-relaxation-time lattice Boltzmann method for high-speed compressible flows

This paper presents a coupling compressible model of the lattice Boltzmann method. In this model, the multiplerelaxation-time lattice Boltzmann scheme is used for the evolution of density distribution functions, whereas the modified single-relaxation-time （SRT） lattice Boltzmann scheme is applied for the evolution of potential energy distribution functions. The governing equations are discretized with the third-order Monotone Upwind Schemes for scalar conservation laws finite volume scheme. The choice of relaxation coefficients is discussed simply. Through the numerical simulations, it is found that compressible flows with strong shocks can be well simulated by present model. The numerical results agree well with the reference results and are better than that of the SRT version.

Thermal relaxation of exchange bias field in an exchange coupled CoFe/IrMn bilayer

This paper reports that a CoFe/IrMn bilayer was deposited by high vacuum magnetron sputtering on silicon wafer substrate; the thermal relaxation of the CoFe/IrMn bilayer is investigated by means of holding the film in a negative saturation field at various temperatures. The exchange bias decreases with increasing period of time while holding the film in a negative saturation field at a given temperature. Increasing the temperature accelerates the decrease of exchange field. The results can be explained by the quantitative model of the nucleation and growth of antiferromagnetic domains suggested by Xi H Wet al. [2007 Phys. Rev. B 75 014434], and it is believed that two energy barriers exist in the investigated temperature range.

Estimation of the kinetic parameters for thermal decomposition of HNIW and its adiabatic time-to-explosion by Kooij formula

A differential/integral method to estimate the kinetic parameters(apparent activation energy Eaand pre-exponential factor A) for thermal decomposition reaction of energetic materials based on Kooij formula are applied to study the nonisothermal decomposition reaction kinetics of hexanitrohexaazaisowurtzitane(HNIW) by analyzing nonisothermal DSC curve data. The apparent activation energy(Ea) obtained by the integral isoconversional non-isothermal method based on Kooij formula is used to check the constancy and validity of apparent activation energy by the differential/integral method based on Kooij formula. The most probable mechanism function of thermal decomposition reaction of HNIW is determined by a logical choice method. The equations for calculating the critical temperatures of thermal explosion(Tb) and adiabatic time-toexplosion(tTIad) based on Kooij formula are used to calculate the values of Tband tTIadto evaluate the thermal safety and heat-resistant ability of HNIW. All the original data needed for analyzing the kinetic parameters are from nonisothermal DSC curves. The results show that the kinetic model function in differential form and the values of Eaand A of decomposition reaction of HNIW are 3(1 a)[ ln(1 a)]2/3, 152.73 kJ mol 1and 1011.97s 1, respectively, and the values of self-accelerating decomposition temperature(TSADT), Tband tTIadare 486.55 K, 493.11 K and52.01 s, respectively.