A Deep Learning Approach to Shape Optimization Problems for Flexoelectric Materials Using the Isogeometric Finite Element Method

A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization problems.To improve the fitting ability of the neural network,we use the idea of pre-training to determine the structure of the neural network and combine different optimizers for training.The isogeometric analysis-finite element method(IGA-FEM)is used to discretize the flexural theoretical formulas and obtain samples,which helps ANN to build a proxy model from the model shape to the target value.The effectiveness of the proposed method is verified through two numerical examples of parameter optimization and one numerical example of shape optimization.

Generalized nth-Order Perturbation Method Based on Loop Subdivision Surface Boundary Element Method for Three-Dimensional Broadband Structural Acoustic Uncertainty Analysis

In this paper,a generalized nth-order perturbation method based on the isogeometric boundary element method is proposed for the uncertainty analysis of broadband structural acoustic scattering problems.The Burton-Miller method is employed to solve the problem of non-unique solutions that may be encountered in the external acoustic field,and the nth-order discretization formulation of the boundary integral equation is derived.In addition,the computation of loop subdivision surfaces and the subdivision rules are introduced.In order to confirm the effectiveness of the algorithm,the computed results are contrasted and analyzed with the results under Monte Carlo simulations(MCs)through several numerical examples.

Analysis on characteristics of extreme precipitation indices and atmospheric circulation in Northern Shanxi

This article utilizes daily precipitation data from 28 national meteorological stations in northern Shanxi Province spanning from 1972 to 2020,and the US NCEP/NCAR monthly average reanalysis and ERA5 monthly average reanalysis data.The study employs techniques such as empirical orthogonal function(EOF)decomposition,MannKendall mutation and other methods to investigate the spatiotemporal distribution of extreme precipitation index in northern Shanxi and their correlation with atmospheric circulation.The research results show that:the absolute index,relative index,intensity index and sustained dry period index(CDD)in the continuous index appear from southwest to northeast.The spatial distribution characteristics of the central region decrease,while the continuous wet period(CWD)decreases from the central to the east and west.The three indices Rx1day,Rx5day,and CWD mutated in 1978,1975,and 1983 respectively,and other extreme precipitation indices all appeared in a sudden change from a low-value period to a high-value period occurred around 2010.In the high-value years of the summer extreme precipitation index,there is a significant negative anomaly in the height field in the mid-high latitude regions of Eurasia.Northern Shanxi is controlled by a broad low-pressure trough in the Lake Baikal area.Water vapor transported via the east,west,and south routes converges in the northern Shanxi region and encounters cold air from the north.There is a strong upward motion anomaly at 500 hPa in the troposphere,and the dynamic conditions of upper-level divergence and lower-level convergence lead to more summer extreme precipitation in the northern Shanxi region.Conversely,in the low-value years of the summer extreme precipitation index,northern Shanxi is affected by a strong high-pressure ridge north of Lake Baikal.There is a downward motion anomaly at 500 hPa,and the northern Shanxi region lacks water vapor.The cold and warm air cannot converge,and both the water vapor conditions and dynamic conditions are poor,which is not conducive to the production of extreme precipitation in northern Shanxi.

Subdivision Surface-Based Isogeometric Boundary Element Method for Steady Heat Conduction Problems with Variable Coefficient

The present work couples isogeometric analysis(IGA)and boundary element methods(BEM)for three dimensional steady heat conduction problems with variable coefficients.The Computer-Aided Design(CAD)geometries are built by subdivision surfaces,and meantime the basis functions of subdivision surfaces are employed to discretize the boundary integral equations for heat conduction analysis.Moreover,the radial integration method is adopted to transform the additional domain integrals caused by variable coefficients to the boundary integrals.Several numerical examples are provided to demonstrate the correctness and advantages of the proposed algorithm in the integration of CAD and numerical analysis.

Estimating the Age of Oil-tea Camellia Trees

To determine the age of oil-tea camellia trees, regression equations including Logistic, Mitscherlich, Gompertz, Korf, and Richards were used to calculate accumulative growth rate using basal trunk disc and investigate the relations between the age of oil-tea camellia trees and their growth rate of secondary trunk. The Gompertz equation Y=71.296 1exp （-3.874 4exp （-0.006 4t）） was the most optimal equation to simulate the accumulative growth rate of basal trunk disc. This equation could be used to estimate the age of oil-tea camellia trees that grow under similar environmental conditions. The Korf equation Y=576.900 1exp （-4.153 0x -0.314 2 ） was the best equation to describe the relation between the age and growth rate of different secondary trunks. With the adjustment coefficient and average growth of different secondary trunk discs, it is possible to predict the age of ancient oil-tea camellia trees that grow under similar environmental conditions. In addition, taking three or more discs from the same diameter group and calculating their average growth rate could lead to more accurate results. For trees that grow in different areas, environmental conditions should be carefully considered when using the above two equations to predict the age of ancient oil-tea camellia trees.

Construction of Rooting System during Camellia oleifera Tissue Culture

An rooting experiment of tissue culture plantlets was carried out with sterile plantlets obtained from the stem segments of a good clone of Camellia oleifera as materials. The results showed that basic medium and illumination condition are factors crucial to rooting of C. oleifera. With 1/4MS as basic medium, the treat- ment with the addition of 0.5 mg/L NAA and soaking in 2 000 mg/L KIBA, containing 30 mg/L sucrose and subjected to dark culture of 20 d was the optimal treat- ment, achieving a rooting rate of 86. 7%.

Effects of Different Picking Time and Different Geographical Provenances on Oil Content of Camellia oleifera

This paper studied effects of different picking time and different geographical provenances on oil content of Camellia oleifera. The results showed that different picking time had significant effects on the oil content of cold dew seeds and frost's descent seeds. With the delay of picking time,the oil content of cold dew seeds,frost's descent seeds,dry seeds and oil content of seed kernels were significantly increased.There was a significantly positive correlation between the oil content of fresh fruit of cold dew seeds and frost's descent seeds and the dry seed yield of fresh seeds and the oil content of fresh fruit( P < 0. 05),and the correlation coefficient was greater than 0. 85. Besides,the oil content of seed kernels of cold dew seeds was closely correlated with the seed yield of fresh seeds,oil content of fresh fruit,and oil content of fresh seeds. In the process of C. oleifera breeding,the thin coat,high seed yield and high oil content can be taken as the key research directions for future breeding. The oil content of ordinary C. oleifera seeds in 18 counties( cities) was 36. 42%-63. 33%,indicating that there were significant differences in the oil content of C. oleifera in different geographical provenances. In conclusion,according to the study of different picking time,the recommended picking time of cold dew seeds in Hunan area is around October 10,while the best picking time of frost's descent seeds is about October 30. The oil content of C. oleifera fruit in different geographical provenances is quite different. During the development of C. oleifera fruit,the cultivation and management of C. oleifera should be strengthened to increase the oil content of C. oleifera.

Isogeometric Boundary Element Method for Two-Dimensional Steady-State Non-Homogeneous Heat Conduction Problem

The isogeometric boundary element technique(IGABEM)is presented in this study for steady-state inhomogeneous heat conduction analysis.The physical unknowns in the boundary integral formulations of the governing equations are discretized using non-uniform rational B-spline(NURBS)basis functions,which are utilized to build the geometry of the structures.To speed up the assessment of NURBS basis functions,the Bezier extraction´approach is used.To solve the extra domain integrals,we use a radial integration approach.The numerical examples show the potential of IGABEM for dimension reduction and smooth integration of CAD and numerical analysis.