Conditional Generative Adversarial Network Enabled Localized Stress Recovery of Periodic Composites

Structural damage in heterogeneousmaterials typically originates frommicrostructures where stress concentration occurs.Therefore,evaluating the magnitude and location of localized stress distributions within microstructures under external loading is crucial.Repeating unit cells(RUCs)are commonly used to represent microstructural details and homogenize the effective response of composites.This work develops a machine learning-based micromechanics tool to accurately predict the stress distributions of extracted RUCs.The locally exact homogenization theory efficiently generates the microstructural stresses of RUCs with a wide range of parameters,including volume fraction,fiber/matrix property ratio,fiber shapes,and loading direction.Subsequently,the conditional generative adversarial network(cGAN)is employed and constructed as a surrogate model to establish the statistical correlation between these parameters and the corresponding localized stresses.The stresses predicted by cGAN are validated against the remaining true data not used for training,showing good agreement.This work demonstrates that the cGAN-based micromechanics tool effectively captures the local responses of composite RUCs.It can be used for predicting potential crack initiations starting from microstructures and evaluating the effective behavior of periodic composites.

Theoretical analysis of the surface temperature regulation of an infrared false target subjected to periodical ambient conditions

Infrared false target is an important mean to induce the infrared-guided weapons,and the key issue is how to keep the surface temperature of the infrared false target to be the same as that of the object to be protected.One-dimensional heat transfer models of a metal plate and imitative material were established to explore the influences of the thermophysical properties of imitative material on the surface temperature difference（STD） between the metal plate and imitative material which were subjected to periodical ambient conditions.It is elucidated that the STD is determined by the imitative material’s dimensionless thickness（dim*,） and the thermal inertia(Pim).When dim* is above 1.0,the STD is invariable as long as Pim is a constant.And if the dimensionless thickness of metal plate（d,m*） is also larger than 1.0,the STD approaches to zero as long as Pimis the same as the thermal inertia of metal plate（Pm）.When dim* is between 0.08 and 1,the STD varies irregularly with Pim and dim*.However,if dm* is also in the range of 0.08-1,the STD approaches to zero on condition that Pim=Pm and dim*= dm*.If dim*,is below 0.08,the STD is unchanged when Pimdim* is a constant.And if dm* is also less than 0.08,the STD approaches to zero as long as Pimdim* = Pmdm*.Furthermore,an applicationoriented discussion indicates that the imitative material can be both light and thin via the application of the phase change material with a preset STD because of its high specific heat capacity during the phase transition process.

Applying Periodic Boundary Conditions to Predict Open Water Propeller Performance

Mathematical models of propellers were created that investigate the influence of periodic boundary conditions on predictions of a propeller's performance.Thrust and torque coefficients corresponding to different advance coefficients of DTMB 4119, 4382, and 4384 propellers were calculated.The pressure coefficient distribution of the DTMB 4119 propeller at different sections was also physically tested.Comparisons indicated good agreement between the results of experiments and the simulation.It showed that the periodic boundary condition can be used to rationally predict the open water performance of a propeller.By analyzing the three established modes for the computation, it was shown that using the spline curve method to divide the grids can meet the calculation's demands for precision better than using the rake cutting method.

A study on periodic boundary condition in direct numerical simulation for gas–solid flow

Direct numerical simulation(DNS) of gas–solid flow at high resolution has been carried out by coupling the lattice Boltzmann method(LBM) for gas flow and the discrete element method(DEM) for solid particles. However,the body force periodic boundary condition(FPBC) commonly used to cut down the huge computational cost of such simulation has faced accuracy concerns. In this study, a novel two-region periodic boundary condition(TPBC) is presented to remedy this problem, with the flow driven in the region with body force and freely evolving in the other region. With simulation cases for simple circulating fluidized bed risers, the validity and advantages of TPBC are demonstrated with more reasonable heterogeneity of the particle distribution as compared to the corresponding case with FPBC.

A Molecular Dynamics Simulation for Periodic Boundary Condition in the Bending Process of Ag／Ni Composite Interfaces

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ANALYSIS OF OPEN MICROSTRIP STRUCTURES BY USING DIAKOPTIC METHOD OF LINES COMBINED WITH PERIODIC BOUNDARY CONDITIONS

This paper presents the analysis of open microstrip structures by using diakoptic method of lines (ML) combined with periodic boundary conditions (PBC). The parameters of microstrip patch are obtained from patch current excited by plane wave. Impedance matrix elements are computed by using fast Fourier transform(FFT), and reduced equation is solved by using diakoptic technique. Consequently, the computing time is reduced significantly. The convergence property of simulating open structure by using PBC and the comparison of the computer time between using PBC and usual absorbing boundary condition (ABC) show the validity of the method proposed in this paper. Finally, the resonant frequency of a microstrip patch is computed. The numerical results obtained are in good agreement with those published.

Effects of Periodic Boundary Condition on Traffic Waves

In this paper, we use the speed-gradient model proposed by Jiang et al. [Transp. Res. B 36 （2002） 405] to study the effect of boundary condition on shock and rarefaction wave. Our numerical results show that this model can reproduce the evolution of the two traffic waves, which further proves that this model can be used to perfectly explore the consequences caused by various boundary conditions.

Periodic Boundary Conditions for Finite-Differentiation-Method Fast-Fourier-Transform Micromagnetics

We describe an accurate periodic boundary condition （PBC） called the symmetric PBC in the calculation of the magnetostatie interaction field in the finite-differentiation-method fast-Fourier-transform （FDM-FFT） micromagneties. The micromagnetic cells in the regular mesh used by the FDM-FFT method are finite-sized elements, but not geometrical points. Therefore, the key PBC operations for FDM-FFT methods are splitting and relocating the micromagnetic cell surfaces to stay symmetrically inside the box of half-total sizes with respect to the origin. The properties of the demagnetizing matrix of the split micromagnetic cells are discussed, and the sum rules of demagnetizing matrix are fulfilled by the symmetric PBC.

Coseismic site response and slope instability using periodic boundary conditions in the material point method

This paper proposed the explicit generalized-a time scheme and periodic boundary conditions in the material point method(MPM)for the simulation of coseismic site response.The proposed boundary condition uses an intuitive particle-relocation algorithm ensuring material points always remain within the computational mesh.The explicit generalized-a time scheme was implemented in MPM to enable the damping of spurious high frequency oscillations.Firstly,the MPM was verified against finite element method(FEM).Secondly,ability of the MPM in capturing the analytical transfer function was investigated.Thirdly,a symmetric embankment was adopted to investigate the effects of ground motion arias intensity(I_(a)),geometry dimensions,and constitutive models.The results show that the larger the model size,the higher the crest runout and settlement for the same ground motion.When using a Mohr-Coulomb model,the crest runout increases with increasing I_(a).However,if the strain-softening law is activated,the results are less influenced by the ground motion.Finally,the MPM results were compared with the Newmark sliding block solution.The simplified analysis herein highlights the capabilities of MPM to capture the full deformation process for earthquake engineering applications,the importance of geometry characterization,and the selection of appropriate constitutive models when simulating coseismic site response and subsequent large deformations.

Spectral Asymptotics for Laplacian with Mixed Boundary-value Condition

Let Ω be a non-empty bounded open set in Rn(n ≥1) with boundary (?)Ω=Γ1∪Γ2. WedefineIn this paper, we consider the following variational eigenvalue problem:where △ denotes the Laplacian in Ω. We say that the scalar λ is an eigenvalue of (P) if

Integral Operator Solving Process of the Boundary Value Problem of Abstract Kinetic Equation with the First Kind of Critical Parameter and Generalized Periodic Boundary Conditions

In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space which consists of functions with vector valued in a general Banach space, and then describe the solution of these abstract boundary value problem by the abstract linear integral operator of Volterra type. We call this process the integral operator solving process.

PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS

We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.

Analysis of Meteorological Conditions during the Blossom Period of Apple and Peach in Haiyang City

Through observing the phenology of two kinds of fruit trees,apple and peach trees,during their flowering periods in the past seven years,the meteorological conditions in the flowering stages were analyzed and summarized in this paper.The late frost weather situation occurred in late April in Haiyang City also was elaborated in the paper.According to the data analysis,the terrain effect had induced a large temperature differences between north and south in April in Haiyang.Early flowering of fruit trees is as early as 5 to 8 days in the northern region than that in the southern region;accumulated temperature which was greater than or equal to 0 ℃ and the date of the temperature stably through a boundary,were the important meteorological indicators of the fruit trees' early flowering.The late frost in mid-late April is meteorological disasters of the fruit trees flowering period.The weather background of the occurred late frost,the disaster reasons and the measures for the prevention of late frost were proposed.

Using Oil Analysis to Study the Wear Condition of Bearing in Trunnion of Convertor During/After Run-in Period

The bearings in the trunnion of convertor are characterized by low-speed, heavy-load and huge-dimension. In case they experience failure in operation, the output of the convertor and even that of the whole product line would be affected and the huge loss would be resulted in. Thus it is very important to master the working conditions of the bearings. Vibration and oil analysis are two main techniques to monitor the conditions of the rotary machine at present. But normal vibration analysis cannot be used here because of the limitation of their sensors in signal collecting for the rotary frequencies of the bearings are too low. In this paper, the wear condition of the bearing on the driving side of the No.5 convertor during/after the run-in period was monitored through oil analysis including atomic emissive spectrum and ferrography. It has been observed that its run-in period was as long as 19 months. This is mainly attributed to the relative short accumulated working time of the bearing.

SECOND-ORDER OPTIMALITY CONDITIONS FOR OPTIMAL CONTROL PROBLEMS GOVERNED BY 3-DIMENSIONAL NEVIER-STOKES EQUATIONS

This article is concerned with second-order necessary and sufficient optimality conditions for optimal control problems governed by 3-dimensional Navier-Stokes equations. The periodic state constraint is considered.

EIGENFUNCTION EXPANSION FOR STURM-LIOUVILLE PROBLEMS WITH TRANSMISSION CONDITIONS AT ONE INTERIOR POINT

The purpose of this article is to extend some spectral properties of regular Sturm- Liouville problems to the special type discontinuous boundary-value problem, which consists of a Sturm-Liouville equation together with eigenparameter-dependent boundary conditions and two supplementary transmission conditions. We construct the resolvent operator and Green＇s function and prove theorems about expansions in terms of eigenfunctions in modified Hilbert space L2[a, b].

STURM-LIOUVILLE PROBLEMS WITH EIGENDEPENDENT BOUNDARY AND TRANSMISSIONS CONDITIONS

The purpose of this paper is to extend some fundamental spectral properties of regular Sturm-Liouville problems to special kind discontinuous boundary value problem, which consist of a Sturm-Liouville equation with piecewise continuous potential together with eigenvalue parameter on the boundary and transmission conditions. The authors suggest their own approach for finding asymptotic approximations formulas for eigenvalues and eigenfunctions of such discontinuous problems.

Existence and Stability Property of Almost Periodic Solutions in Discrete Almost Periodic Systems

In this paper, we consider an almost periodic system which includes a system of the type , where k is a positive integer, aij are almost periodic in n and satisfy aij(n)≥0 for i≠j,? for 1≤j≤m. In the special case where aij(n) are constant functions, above system is a mathematical model of gas dynamics and was treated by T. Carleman and R. D. Jenks for differential systems. In the main theorem, we show that if the m X m matrix (aij(n)) is irreducible, then there exists a positive almost periodic solution which is unique and has some stability. Moreover, we can see that this result gives R. D. Jenks’ result for differential model in the case where aij(n) are constant functions. In Section 3, we consider the linear system with variable cofficients . Even in nonlinear problems, this linear system plays an important role, as their variational equations, and it is requested to determine the uniform asymptotically stability of the zero solution from the information about A(n). In order to obtain the existence of almost periodic solutions of both linear and nonlinear almost periodic discrete systems: above linear system and? for 1≤i≤m, respectively, we shall consider between certain stability properties, which are referred to as uniformly asymptotically stable, and the diagonal dominance matrix condition.

Existence and Uniqueness of Almost Periodic Solution for a Mathematical Model of Tumor Growth

This article is concerned with a mathematical model of tumor growth governed by 2nd order diffusion equation . The source of mitotic inhibitor is almost periodic and time-dependent within the tissue. The system is set up with the initial condition C(r, 0) = C0(r) and Robin type inhomogeneous boundary condition . Under certain conditions we show that there exists a unique solution for this model which is almost periodic.

Factors influencing electromagnetic scattering from the dielectric periodic surface

The scattering characteristics of the periodic surface of infinite and finite media are investigated in detail.The Fourier expression of the scattering field of the periodic surface is obtained in terms of Huygens’ s principle and Floquet’s theorem.Using the extended boundary condition method(EBCM) and T-matrix method, the scattering amplitude factor is solved,and the correctness of the algorithm is verified by use of the law of conservation of energy.The scattering cross section of the periodic surface in the infinitely long region is derived by improving the scattering cross section of the finite period surface.Furthermore, the effects of the incident wave parameters and the geometric structure parameters on the scattering of the periodic surface are analyzed and discussed.By reasonable approximation, the scattering calculation methods of infinite and finite long surfaces are unified.Besides, numerical results show that the dielectric constant of the periodic dielectric surface has a significant effect on the scattering rate and transmittance.The period and amplitude of the surface determine the number of scattering intensity peaks, and, together with the incident angle, influence the scattering intensity distribution.