Developing theory of probability density function for stochastic modeling of turbulent gas-particle flows

Turbulent gas-particle flows are studied by a kinetic description using a prob- ability density function （PDF）. Unlike other investigators deriving the particle Reynolds stress equations using the PDF equations, the particle PDF transport equations are di- rectly solved either using a finite-difference method for two-dimensional （2D） problems or using a Monte-Carlo （MC） method for three-dimensional （3D） problems. The proposed differential stress model together with the PDF （DSM-PDF） is used to simulate turbulent swirling gas-particle flows. The simulation results are compared with the experimental results and the second-order moment （SOM） two-phase modeling results. All of these simulation results are in agreement with the experimental results, implying that the PDF approach validates the SOM two-phase turbulence modeling. The PDF model with the SOM-MC method is used to simulate evaporating gas-droplet flows, and the simulation results are in good agreement with the experimental results.

Coupling Modeling for Functional Surface of Electronic Equipment

High performance electromechanical equipment is widely used in various fields, such as national defense, industry and so on [ 1]. In addition, the technical level of high performance electromechanical equipment is the embodiment of the national level of science and technology.

Construction of Psychological Adjustment Function Model of Music Education Based on Emotional Tendency Analysis

In the face offierce competition in the social environment,mental health problems gradually get the attention of the public,in order to achieve accurate mental health data analysis,the construction of music education is based on emotional tendency analysis of psychological adjustment function model.Design emotional tendency analysis of music education psychological adjustment function architecture,music teaching goal as psychological adjust-ment function architecture building orientation,music teaching content as a foundation for psychological adjust-ment function architecture and music teaching process as a psychological adjustment function architecture building,music teaching evaluation as the key of building key regulating function architecture,Establish a core literacy oriented evaluation system.Different evaluation methods were used to obtain the evaluation results.Four levels of psychological adjustment function model of music education are designed,and the psychological adjust-ment function of music education is put forward,thus completing the construction of psychological adjustment function model of music education.The experimental results show that the absolute value of the data acquisition error of the designed model is minimum,which is not more than 0.2.It is less affected by a bad coefficient and has good performance.It can quickly converge to the best state in the actual prediction process and has a strong con-vergence ability.

Generalized functional model of maximum and minimum detectable deformation gradient for PALSAR interferometry

Empirical functional models for the maximum and minimum detectable deformation gradient of PALSAR interferometry were established based on coherence and discrete look numbers. Then, a least square regression method was used to fit the model coefficients and thus obtain the generalized functional models for both coherence and look numbers. The experimental results with ALOS PALSAR data of Wenchuan earthquake of China show that the new model works well for judging whether the deformation gradient can be detected by the D-InSAR technology or not. The results can help researchers to choose PALSAR data and to configure processing parameters, and also benefit the interpretation of the measured surface deformation.

Universal triple I fuzzy reasoning algorithm of function model based on quotient space

Aiming at the deficiencies of analysis capacity from different levels and fuzzy treating method in product function modeling of conceptual design, the theory of quotient space and universal triple I fuzzy reasoning method are introduced, and then the function modeling algorithm based on the universal triple I fuzzy reasoning method is proposed. Firstly, the product function granular model based on the quotient space theory is built, with its function granular representation and computing rules defined at the same time. Secondly, in order to quickly achieve function granular model from function requirement, the function modeling method based on universal triple I fuzzy reasoning is put forward. Within the fuzzy reasoning of universal triple I method, the small-distance-activating method is proposed as the kernel of fuzzy reasoning; how to change function requirements to fuzzy ones, fuzzy computing methods, and strategy of fuzzy reasoning are respectively investigated as well; the function modeling algorithm based on the universal triple I fuzzy reasoning method is achieved. Lastly, the validity of the function granular model and function modeling algorithm is validated. Through our method, the reasonable function granular model can be quickly achieved from function requirements, and the fuzzy character of conceptual design can be well handled, which greatly improves conceptual design.

Introducing the nth-Order Features Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (nth-FASAM-N): II. Illustrative Example

This work highlights the unparalleled efficiency of the “nth-Order Function/ Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (nth-FASAM-N) by considering the well-known Nordheim-Fuchs reactor dynamics/safety model. This model describes a short-time self-limiting power excursion in a nuclear reactor system having a negative temperature coefficient in which a large amount of reactivity is suddenly inserted, either intentionally or by accident. This nonlinear paradigm model is sufficiently complex to model realistically self-limiting power excursions for short times yet admits closed-form exact expressions for the time-dependent neutron flux, temperature distribution and energy released during the transient power burst. The nth-FASAM-N methodology is compared to the extant “nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (nth-CASAM-N) showing that: (i) the 1st-FASAM-N and the 1st-CASAM-N methodologies are equally efficient for computing the first-order sensitivities;each methodology requires a single large-scale computation for solving the “First-Level Adjoint Sensitivity System” (1st-LASS);(ii) the 2nd-FASAM-N methodology is considerably more efficient than the 2nd-CASAM-N methodology for computing the second-order sensitivities since the number of feature-functions is much smaller than the number of primary parameters;specifically for the Nordheim-Fuchs model, the 2nd-FASAM-N methodology requires 2 large-scale computations to obtain all of the exact expressions of the 28 distinct second-order response sensitivities with respect to the model parameters while the 2nd-CASAM-N methodology requires 7 large-scale computations for obtaining these 28 second-order sensitivities;(iii) the 3rd-FASAM-N methodology is even more efficient than the 3rd-CASAM-N methodology: only 2 large-scale computations are needed to obtain the exact expressions of the 84 distinct third-order response sensitivities with respect to the Nordheim-Fuchs model’s parameters when applying the 3rd-FASAM-N methodology, while the application of the 3rd-CASAM-N methodology requires at least 22 large-scale computations for computing the same 84 distinct third-order sensitivities. Together, the nth-FASAM-N and the nth-CASAM-N methodologies are the most practical methodologies for computing response sensitivities of any order comprehensively and accurately, overcoming the curse of dimensionality in sensitivity analysis.

Functions of Allusions from Leppihalme’s model

The general function of allusions is often thought to add clarity and significance to ideas and descriptions.However,it would be difficult to establish an exhaustive list of mutually exclusive category

The Usage of Two Dielectric Function Models

This paper presents an overview of the history, modifications, characteristics, and applications of two well known dielectric function models ——the Forouhi-Bloomer model and the Tauc-Lorentz model——which have been widely used for the extraction and parameterization of optical constants in semiconductors and dielectrics. Based on analysis of their inherent characteristics and comparison via demonstrative examples, deeper and wider usage of the two models is predicted.

Molecular properties and potential energy function model of BH under external electric field

Using the density functional B3P86/cc-PV5Z method, the geometric structure of BH molecule under different external electric fields is optimized, and the bond lengths, dipole moments, vibration frequencies, and other physical properties parameters are obtained. On the basis of setting appropriate parameters, scanning single point energies are obtained by the same method and the potential energy curves under different external fields are also obtained. These results show that the physical property parameters and potential energy curves may change with external electric field, especially in the case of reverse direction electric field. The potential energy function without external electric field is fitted by Morse potential, and the fitting parameters are obtained which are in good agreement with experimental values. In order to obtain the critical dissociation electric parameter, the dipole approximation is adopted to construct a potential model fitting the corresponding potential energy curve of the external electric field. It is found that the fitted critical dissociation electric parameter is consistent with numerical calculation, so that the constructed model is reliable and accurate. These results will provide important theoretical and experimental reference for further studying the molecular spectrum, dynamics, and molecular cooling with Stark effect.

Time function of surface subsidence based on Harris model in mined-out area

The surface subsidence is a common environmental hazard in mined-out area. Based on careful analysis of the regularity of surface subsidence in mined-out area, we proposed a new time function based on Harris curve model in consideration of the shortage of current surface subsidence time functions. By analyzing the characteristics of the new time function, we found that it could meet the dynamic process, the velocity change process and the acceleration change process during surface subsidence. Then its rationality had been verified through project cases. The results show that the proposed time function model can give a good reflection of the regularity of surface subsidence in mined-out area and can accurately predict surface subsidence. And the prediction data of the model are a little greater than measured data on condition of proper measured data quantity, which is safety in the engineering. This model provides a new method for the analysis of surface subsidence in mined-out area and reference for future prediction, and it is valuable to engineering application.

Rough function model and rough membership function

Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyzed. The rough function model is generalized based on rough set theory, and the scheme of rough function theory is made more distinct and complete. Therefore, the transformation of the real function analysis from real line to scale is achieved. A series of basic concepts in rough function model including rough numbers, rough intervals, and rough membership functions are defined in the new scheme of the rough function model. Operating properties of rough intervals similar to rough sets are obtained. The relationship of rough inclusion and rough equality of rough intervals is defined by two kinds of tools, known as the lower （upper） approximation operator in real numbers domain and rough membership functions. Their relative properties are analyzed and proved strictly, which provides necessary theoretical foundation and technical support for the further discussion of properties and practical application of the rough function model.

Time lag characteristics of sap flow in seed-maize and their implications for modeling transpiration in an arid region of Northwest China

Plant capacity for water storage leads to time lags between basal stem sap flow and transpiration in various woody plants. Internal water storage depends on the sizes of woody plants. However, the changes and its influencing factors in time lags of basal stem flow during the development of herbaceous plants including crops remain unclear. A field experiment was conducted in an arid region of Northwest China to examine the time lag characteristics of sap flow in seed-maize and to calibrate the transpiration modeling. Cross-correlation analysis was used to estimate the time lags between stem sap flow and meteorological driving factors including solar radiation（R_s） and vapor pressure deficit of the air（VPD_（air））. Results indicate that the changes in seed-maize stem sap flow consistently lagged behind the changes in R_s and preceded the changes in VPD_（air） both on hourly and daily scales, suggesting that light-mediated stomatal closures drove sap flow responses. The time lag in the maize＇s sap flow differed significantly during different growth stages and the difference was potentially due to developmental changes in capacitance tissue and/or xylem during ontogenesis. The time lags between stem sap flow and R_s in both female plants and male plants corresponded to plant use of stored water and were independent of total plant water use. Time lags of sap flow were always longer in male plants than in female plants. Theoretically, dry soil may decrease the speed by which sap flow adjusts ahead of shifts in VPD_（air） in comparison with wet soil and also increase the speed by which sap flow adjusts to R_s. However, sap flow lags that were associated with R_s before irrigation and after irrigation in female plants did not shift. Time series analysis method provided better results for simulating seed-maize sap flow with advantages of allowing for fewer variables to be included. This approach would be helpful in improving the accuracy of estimation for canopy transpiration and conductance using meteorological measurements.

A power function model for simulating creep mechanical properties of salt rock

In this paper,a new micro-creep model of salt rock is proposed based on a linear parallel bonded model(LPBM)using the two-dimensional particle flow code(PFC2D).The power function weakening form is assumed to describe the variation of the parallel bonded diameter(PBD)over time.By comparing with the parallel-bonded stress corrosion(PSC)model,a smaller stress fluctuation and smoother creep strain−time curves can be obtained by this power function model at the same stress level.The validity and adaptability of the model to simulate creep deformation of salt rock are verified through comparing the laboratory creep test curves and the Burgers model fitting result.The numerical results reveal that this model can be capable of capturing the creep deformation and damage behavior from the laboratory observations.

Development of Mathematical Model on Preparation of Functionally Graded Material by Co-sedimentation

From the process of sedimentation the mathematical relationships among deposition Volume and powder properties as well as sedimentation parameters were deduced. Based on the formula a mathematical model was set up and simulated through the computer. At last the validity of mathematical model was supported by the representative experiment on Ti-Mo system FGM prepared by co-sedimentation.

Hybrid graded element model for transient heat conduction in functionally graded materials

This paper presents a hybrid graded element model for the transient heat conduction problem in functionally graded materials （FGMs）. First, a Laplace transform approach is used to handle the time variable. Then, a fundamental solution in Laplace space for FGMs is constructed. Next, a hybrid graded element is formulated based on the obtained fundamental solution and a frame field. As a result, the graded properties of FGMs are naturally reflected by using the fundamental solution to interpolate the intra-element field. Further, Stefest＇s algorithm is employed to convert the results in Laplace space back into the time-space domain. Finally, the performance of the proposed method is assessed by several benchmark examples. The results demonstrate well the efficiency and accuracy of the proposed method.

Dissipation source function and an improvement to LAGFD-WAM model

In this paper, a new theoretical expression of dissipation term is presented on the basis of statistical model of breaking wave, which is an improvement to LAGFD-WAM wave model. The computational results in three typical wind fields show a good improvement to LAGFD-WAM model and a better accuracy in comparison with the observed data in the South China Sea.

Evaluation of the Effects of Cypermethrin on Female Reproductive Function by Using Rabbit Model and of the Protective Role of Chinese Propolis

The prophylactic effects of Chinese propolis against cypermethrin toxicity were evaluated by performing ovary and uterus histopathology, as well as by characterizing ovarian function, embryos, and litters. Cypermethrin induced atypia in the ovary and uterus, and decreased the ovulation sites and the number of embryos. Cypermethrin-induced oxidative stress during pregnancy, decreased the parturition rate as well as the number and weight of offspring and increased the incidence of morphological malformations in the offspring. Administration of propolis to cypermethrin-treated animals mitigated cypermethrin-induced reproductive toxicity.

Three-Component Model for Bidirectional Reflection Distribution Function of Thermal Coating Surfaces

We present a bidirectional reflection distribution function （BRDF） model for thermal coating surfaces based on a three-component reflection assumption, in which the specular reflection is given according to the microfacet theory and Snell＇s law, the multiple reflection is considered Nth cosine distributed, and the volume scattering is uniformly distributed in reflection angles according to the experimental results. This model describes the reflection characteristics of thermal coating surfaces more completely and reasonably. Simulation and measurement results of two thermal coating samples SR107 and S781 are given to validate that this three-component model significantly improves the modeling accuracy for thermal coating surfaces compared with the existing BRDF models.

The Roughness of Model Function to the Basis Functions

The roughness of the model function f（x） to the basis functions has been identified. When the model function is continuous segment, its roughness does not depend on the behavior of the first segment, but depends on ＂h＂, the shift in the slope of two consecutive segments. If the distribution of design is uniform, f（x） is continuous segment function, and h is constant, then the maximum roughness is h2/192 obtained at the midpoint of the observations. Suppose that we have a sequence of designs {Pn（x）} then its corresponding distribution {Fn （x）} converges weakly to some distribution F（x）. Let D（f） be a set of discontinuous points off（x）, it is possible to take the limit of the roughness if D（f） has zero （dF）-measure. The behavior of maximum roughness of the discontinuous segment function has been studied by using grid points.

Establishment of European Regional Ionosphere Model Based on Spherical Harmonic Functions

In order to study the temporal and spatial variation characteristics of the regional ionosphere and the modeling accuracy,the experiment is based on the spherical harmonic function model,using the GPS,Glonass,and Galileo dual-frequency observation data from the 305th-334th day of the European CORS network in 2019 to establish a global ionospheric model.By analyzing and evaluating the accuracy of the global ionospheric puncture points,VTEC,and comparing code products,the test results showed that the GPS system has the most dense puncture electricity distribution,the Glonass system is the second,and the Galileo system is the weakest.The values of ionospheric VTEC calculated by GPS,Glonass and Galileo are slightly different,but in terms of trends,they are the same as those of ESA,JPL and UPC.GPS data has the highest accuracy in global ionospheric modeling.GPS,Glonass and Galileo have the same trend,but Glonass data is unstable and fluctuates greatly.