Integrating a novel irrigation approximation method with a process-based remote sensing model to estimate multi-years'winter wheat yield over the North China Plain

Accurate estimation of regional winter wheat yields is essential for understanding the food production status and ensuring national food security.However,using the existing remote sensing-based crop yield models to accurately reproduce the inter-annual and spatial variations in winter wheat yields remains challenging due to the limited ability to acquire irrigation information in water-limited regions.Thus,we proposed a new approach to approximating irrigations of winter wheat over the North China Plain(NCP),where irrigation occurs extensively during the winter wheat growing season.This approach used irrigation pattern parameters(IPPs)to define the irrigation frequency and timing.Then,they were incorporated into a newly-developed process-based and remote sensing-driven crop yield model for winter wheat(PRYM–Wheat),to improve the regional estimates of winter wheat over the NCP.The IPPs were determined using statistical yield data of reference years(2010–2015)over the NCP.Our findings showed that PRYM–Wheat with the optimal IPPs could improve the regional estimate of winter wheat yield,with an increase and decrease in the correlation coefficient(R)and root mean square error(RMSE)of 0.15(about 37%)and 0.90 t ha–1(about 41%),respectively.The data in validation years(2001–2009 and 2016–2019)were used to validate PRYM–Wheat.In addition,our findings also showed R(RMSE)of 0.80(0.62 t ha–1)on a site level,0.61(0.91 t ha–1)for Hebei Province on a county level,0.73(0.97 t ha–1)for Henan Province on a county level,and 0.55(0.75 t ha–1)for Shandong Province on a city level.Overall,PRYM–Wheat can offer a stable and robust approach to estimating regional winter wheat yield across multiple years,providing a scientific basis for ensuring regional food security.

IMPROVED AERODYNAMIC APPROXIMATION MODEL WITH CASE-BASED REASONING TECHNIQUE FOR MDO OF AIRCRAFT

To increase the efficiency of the multidisciplinary optimization of aircraft, an aerodynamic approximation model is improved. Based on the study of aerodynamic approximation model constructed by the scaling correction model, case-based reasoning technique is introduced to improve the approximation model for optimization. The aircraft case model is constructed by utilizing the plane parameters related to aerodynamic characteristics as attributes of cases, and the formula of case retrieving is improved. Finally, the aerodynamic approximation model for optimization is improved by reusing the correction factors of the most similar aircraft to the current one. The multidisciplinary optimization of a civil aircraft concept is carried out with the improved aerodynamic approximation model. The results demonstrate that the precision and the efficiency of the optimization can be improved by utilizing the improved aerodynamic approximation model with ease-based reasoning technique.

RBMDO Using Gaussian Mixture Model-Based Second-Order Mean-Value Saddlepoint Approximation

Actual engineering systems will be inevitably affected by uncertain factors.Thus,the Reliability-Based Multidisciplinary Design Optimization(RBMDO)has become a hotspot for recent research and application in complex engineering system design.The Second-Order/First-Order Mean-Value Saddlepoint Approximate(SOMVSA/-FOMVSA)are two popular reliability analysis strategies that are widely used in RBMDO.However,the SOMVSA method can only be used efficiently when the distribution of input variables is Gaussian distribution,which significantly limits its application.In this study,the Gaussian Mixture Model-based Second-Order Mean-Value Saddlepoint Approximation(GMM-SOMVSA)is introduced to tackle above problem.It is integrated with the Collaborative Optimization(CO)method to solve RBMDO problems.Furthermore,the formula and procedure of RBMDO using GMM-SOMVSA-Based CO(GMM-SOMVSA-CO)are proposed.Finally,an engineering example is given to show the application of the GMM-SOMVSA-CO method.

Beam Approximation for Dynamic Analysis of Launch Vehicles Modelled as Stiffened Cylindrical Shells

A beam approximation method for dynamic analysis of launch vehicles modelled as stiffened cylindrical shells is proposed.Firstly,an initial beam model of the stiffened cylindrical shell is established based on the cross-sectional area equivalence principle that represents the shell skin and its longitudinal ribs as a beam with annular cross-section,and the circumferential ribs as lumped masses at the nodes of the beam elements.Then,a fine finite element model(FE model)of the stiffened cylindrical shell is constructed and a modal analysis is carried out.Finally,the initial beam model is improved through model updating against the natural frequencies and mode shapes of the fine FE model of the shell.To facilitate the comparison between the mode shapes of the fine FE model of the stiffened shell and the equivalent beam model,a weighted nodal displacement coupling relationship is introduced.To prevent the design parameters used in model updating from converging to incorrect values,a pre-model updating procedure is added before the proper model updating.The results of two examples demonstrate that the beam approximation method presented in this paper can build equivalent beam models of stiffened cylindrical shells which can reflect the global longitudinal,lateral and torsional vibration characteristics very well in terms of the natural frequencies.

Dynamics of Jaynes-Cummings Model in the Absence of Rotating-Wave Approximation

The Jaynes-Cummings model （JCM） is studied in the absence of the rotating-wave approximation （RWA） by a coherent-state expansion technique. In comparison with the previous paper in which the coherent-state expansion was performed only to the third order, we carry out in this paper a complete expansion to demonstrate exactly the dynamics of the JCM without the RWA. Our study gives a systematic method to solve the non-RWA problem, which would be useful in various physical systems, e.g., in a system with an ultracold trapped ion experiencing the running waves of lasers.

Wind Structure in an Intermediate Boundary Layer Model Based on Ekman Momentum Approximation

A quasi three–dimensional, intermediate planetary boundary layer (PBL) model is developed by including inertial acceleration with the Ekman momentum approximation, but a nonlinear eddy viscosity based on Blackadar’s scheme was included to improve the theoretical model proposed by Tan and Wu (1993). The model could keep the same complexity as the classical Ekman model in numerical, but extends the conventional Ekman model to include the horizontal accelerated flow with the Ekman momentum approximation. A comparison between this modified Ekman model and other simplified accelerating PBL models is made. Results show that the Ekman model overestimates (underestimates) the wind speed and pumping velocity in the cyclonic (anticyclonic) shear flow due to the neglect of the acceleration flow, however, the semi–geostrophic Ekman model overestimates the acceleration effects resulting from the underestimating (overestimating) of the wind speed and pumping velocity in the cyclonic (anticyclonic) shear flow. The Ekman momentum approximation boundary layer model could be applied to the baroclinic atmosphere. The baroclinic Ekman momentum approximation boundary layer solution has both features of classical baroclinic Ekman layer and the Ekman momentum approximate boundary lager.

A population-level model from the microscopic dynamics in Escherichia coli chemotaxis via Langevin approximation

Recent extensive studies of Escherichia coli （E. coli） chemotaxis have achieved a deep understanding of its mi- croscopic control dynamics. As a result, various quantitatively predictive models have been developed to describe the chemotactic behavior of E. coli motion. However, a population-level partial differential equation （PDE） that rationally incorporates such microscopic dynamics is still insufficient. Apart from the traditional Keller-Segel （K-S） equation, many existing population-level models developed from the microscopic dynamics are integro-PDEs. The difficulty comes mainly from cell tumbles which yield a velocity jumping process. Here, we propose a Langevin approximation method that avoids such a difficulty without appreciable loss of precision. The resulting model not only quantitatively repro- duces the results of pathway-based single-cell simulators, but also provides new inside information on the mechanism of E. coli chemotaxis. Our study demonstrates a possible alternative in establishing a simple population-level model that allows for the complex microscopic mechanisms in bacterial chemotaxis.

Stable Routh-Padé-type approximation in model reduction of interval systems

An interval Pade-type approximation is introduced and then Routh-Pade-type method （IRPTM） is presented to model reduction in interval systems. The denominator in reduced model is obtained from the stable Routh table, and its numerator is constructed by the interval Pade-type definition. Compared to the existing Routh-Pade method, IRPTM does not need to solve linear interval equations theoretical analysis shows that IRPTM has example is given to illustrate our method. Hence, we do not have to compute smaller computational cost than that interval division in the process. Moreover, of Routh-Pade method. A typical numerical

Dynamics of Rabi model under second-order Born Oppenheimer approximation

We apply the second-order Born-Oppenheimer （BO） approximation to investigate the dynamics of the Rabi model, which describes the interaction between a two-level system and a single bosonic mode beyond the rotating wave approxi- mation. By comparing with the numerical results, we find that our approach works well when the frequency of the two-level system is much smaller than that of the bosonic mode.

Extended Quark Potential Model from Random Phase Approximation

The quark potential model is extended to include the sea quark excitation using the random phase approx-imation. The effective quark interaction preserves the important QCD properties - chiral symmetry and confinementsimultaneously. A primary qualitative analysis shows that the π meson as a well-known typical Goldstone boson andthe other mesons made up of valence qq quark pair such as the ρ meson can also be described in this extended quarkpotential model.

Extended Quark Potential Model From Random Phase Approximation

The quark potential model is extended to include the sea quark excitation using the random phase approximation. The effective quark interaction preserves the important QCD properties — chiral symmetry and confinement simultaneously. A primary qualitative analysis shows that the π meson as a well-known typical Goldstone boson and the other mesons made up of valence quark pair such as the ρ meson can also be described in this extended quark potential model.

Effective Hamiltonian of the Jaynes–Cummings model beyond rotating-wave approximation

The Jaynes–Cummings model with or without rotating-wave approximation plays a major role to study the interaction between atom and light. We investigate the Jaynes–Cummings model beyond the rotating-wave approximation. Treating the counter-rotating terms as periodic drivings, we solve the model in the extended Floquet space. It is found that the full energy spectrum folded in the quasi-energy bands can be described by an effective Hamiltonian derived in the highfrequency regime. In contrast to the Z_(2) symmetry of the original model, the effective Hamiltonian bears an enlarged U(1)symmetry with a unique photon-dependent atom-light detuning and coupling strength. We further analyze the energy spectrum, eigenstate fidelity and mean photon number of the resultant polaritons, which are shown to be in accordance with the numerical simulations in the extended Floquet space up to an ultra-strong coupling regime and are not altered significantly for a finite atom-light detuning. Our results suggest that the effective model provides a good starting point to investigate the rich physics brought by counter-rotating terms in the frame of Floquet theory.

Magnetic Properties of One-Dimensional Ferromagnetic Mixed-Spin Model within Tyablikov Decoupling Approximation

In this paper, we apply the two-time Green's function method, and provide a simple way to study themagnetic properties of one-dimensional spin-(S, s) Heisenberg ferromagnets.The magnetic susceptibility and correlationfunctions are obtained by using the Tyablikov decoupling approximation.Our results show that the magnetic susceptibilityand correlation length are a monotonically decreasing function of temperature regardless of the mixed spins.It isfound that in the case of S = s, our results of one-dimensional mixed-spin model is reduced to be those of the isotropicferromagnetic Heisenberg chain in the whole temperature region.Our results for the susceptibility are in agreement withthose obtained by other theoretical approaches.

High—Temperature Cutoff Approximation of the 3D kinetic Ising Model

A single-spin transition critical dynamics is used to investigate the three-dimensional kinetic Ising model on an anisotropic cubic lattice. We first derive the fundamental dynamical equations, and then linearize them by a cutoff approximation. We obtain the approximate solutions of the local magnetization and equal-time pair correlation function in zero field. In which the axial-decoupling terms , and as higher infinitesimal quantity are ignored, where . We think that it is reasonable as the temperature of the system is very high. The result of what we obtain in this paper can go back to the one-dimensional Glauber's theory as long as .

Cross Validation Based Model Averaging for Varying-Coefficient Models with Response Missing at Random

In this paper, a model averaging method is proposed for varying-coefficient models with response missing at random by establishing a weight selection criterion based on cross-validation. Under certain regularity conditions, it is proved that the proposed method is asymptotically optimal in the sense of achieving the minimum squared error.

The Mixed Spin-1/2 and Spin-1 Ising–Heisenberg Model in the Mean-Field Approximation: a New Approach

Thermodynamic properties of the mixed spin-1 and spin-1/2 Ising-Heisenberg model are studied on a honeycomb lattice using a new approach in the mean-field approximation to analyze the effects of longitudinal Dz and transverse Dx crystal fields. The phase diagrams are calculated in detail by studying the thermal variations of the order parameters, i.e., magnetizations and quadrupole moments, and compared with the literature to assess the reliability of the new approach. It is found that the model yields both second- and first-order phase transitions, and tricritical points. The compensation behavior of the model is also investigated for the sublattice magnetizations, and longitudinal and transverse quadrupolar moments. The latter type of compensation is observed in the literature but its possible importance is overlooked.

Quasi-Monte Carlo Approximations for Exponentiated Quadratic Kernel in Latent Force Models

In this project, we consider obtaining Fourier features via more efficient sampling schemes to approximate the kernel in LFMs. A latent force model (LFM) is a Gaussian process whose covariance functions follow an Exponentiated Quadratic (EQ) form, and the solutions for the cross-covariance are expensive due to the computational complexity. To reduce the complexity of mathematical expressions, random Fourier features (RFF) are applied to approximate the EQ kernel. Usually, the random Fourier features are implemented with Monte Carlo sampling, but this project proposes replacing the Monte-Carlo method with the Quasi-Monte Carlo (QMC) method. The first-order and second-order models’ experiment results demonstrate the decrease in NLPD and NMSE, which revealed that the models with QMC approximation have better performance.

APPROXIMATION TECHNIQUES FOR APPLICATION OF GENETIC ALGORITHMS TO STRUCTURAL OPTIMIZATION

Although the genetic algorithm (GA) has very powerful robustness and fitness, it needs a large size of population and a large number of iterations to reach the optimum result. Especially when GA is used in complex structural optimization problems, if the structural reanalysis technique is not adopted, the more the number of finite element analysis (FEA) is, the more the consuming time is. In the conventional structural optimization the number of FEA can be reduced by the structural reanalysis technique based on the approximation techniques and sensitivity analysis. With these techniques, this paper provides a new approximation model-segment approximation model, adopted for the GA application. This segment approximation model can decrease the number of FEA and increase the convergence rate of GA. So it can apparently decrease the computation time of GA. Two examples demonstrate the availability of the new segment approximation model.

Refinement of an Analytical Approximation of the Surface Potential in MOSFETs

A refinement of an analytical approximation of the surface potential in MOSFETs is proposed by introducing a high-order term. As compared to the conventional treatment with accuracy between 1nV and 0. 03mV in the cases with an oxide thickness tox = 1 ～ 10nm and substrate doping concentration Na = 1015 ～ 1018 cm-3 , this method yields an accuracy within about 1pV in all cases. This is comparable to numerical simulations, but does not require trading off much computation efficiency. More importantly, the spikes in the error curve associated with the traditional treatment are eliminated.

Structural Stability of the Financial Market Model: Continuity of Superhedging Price and Model Approximation

The present paper continues the topic of our recent paper in the same journal,aiming to show the role of structural stability in financial modeling.In the context of financial market modeling,structural stability means that a specific“no-arbitrage”property is unaffected by small(with respect to the Pompeiu–Hausdorff metric)perturbations of the model’s dynamics.We formulate,based on our economic interpretation,a new requirement concerning“no arbitrage”properties,which we call the“uncertainty principle”.This principle in the case of no-trading constraints is equivalent to structural stability.We demonstrate that structural stability is essential for a correct model approximation(which is used in our numerical method for superhedging price computation).We also show that structural stability is important for the continuity of superhedging prices and discuss the sufficient conditions for this continuity.