尖劈吸波体的研究和微波暗室的模拟

对尖劈形状吸波体的吸波性能进行了研究,并对导弹导引仿真实验用的微波暗室的性能进行分析和仿真.首先对尖劈体的二维反射性能进行了研究,从单条波线反射的原理出发,得到波束平面反射的统计模型.单条波线的反射通过数值模拟得到;波束反射模型则通过对数值模拟的结果进行统计和拟合得到,最终用多项式表示.对于一些简单或特殊的情况,也给出了解析解.通过分析发现,三维反射和二维反射之间有明确的关系.这种关系可以由三维入射角和反射次数决定,而反射次数可以通过二维模型得到.据此将平面反射模型扩展为三维反射模型,从而得到尖劈形状吸波体的三维反射模型.无回波暗室用于模拟没有背景微波辐射的环境,其关键在于选择合适的吸波材料.基于微波反射通量平衡原理,建立了考虑暗室墙面各点之间的相互影响的耦合模型,从而可以求解出在指定的发射源照射之下墙面各点的辐射强度分布.对模型的求解精度和收敛性进行了验证.基于此模型,对一个导弹引导试验进行了数值模拟,推算出了使用两种不同吸波材料时静区接收到的微波信号的信噪比.     

吸波材料与微波暗室问题的数学建模

为了分析微波暗室的性能,采用几何光学的方法,用虚像延拓来刻画辐射波在暗室诸墙面上的反射过程,从而建立微波暗室模型.问题一考虑单个尖劈几何空缺间反射过程的数学模型,利用平面镜成像原理,采用延拓的方法,将尖劈几何空缺空间延拓到一个圆柱上,将入射波在尖劈空缺间的反射过程等价地看成入射波在一个圆柱内的空间直线传播过程,称为"虚像传播直线".问题二中要分析微波暗室的性能,主要采用的指标是静区从诸墙面得到的反射信号的功率之和与从信号源直接得到的微波功率之比y.采用静区延拓的方法,将微波暗室暗箱化,首先建立一个余弦辐射体的点辐射源到一有界平面的辐射模型,然后通过该模型计算点辐射源到各个静区虚像的辐射功率总和作为静区从诸墙面得到的总功率,建立微波暗室的反射模型.实验证明,当采用平板吸波材料时(垂直反射率为0.5),无法满足导引仿真要求,当采用性能较好的尖劈形吸波体时(垂直反射率为0.05),能够满足仿真要求.     

尖劈形吸波体和微波暗室中的数学模型

首先讨论电磁波在尖劈形吸波体形成的空缺中的反射问题.通过建立二维空间内两次相邻反射的数学模型,得到尖劈的几何参数和电磁波出射角、更射次数和辐射强度的关系.然后通过仿真计算出数值结果,并且将其推广到三维情况,得到了"在一定条件下,减小尖劈形吸波体顶角的大小,有利于增加反射次数,增强吸波效果"的结论.针对导弹导引试验中的仿真要求,从电磁波辐射角系数的概念出发,提出了一种计算微波暗室中静区的接收到墙面更射的功率与天线辐射的功率的比值的算法.这种算法物理意义清晰,计算过程简单,可较好的应用在导弹的导引仿真试验的分析中.     

吸波材料与微波暗室吸波性能研究

主要解决入射波在尖劈吸波材料几何空缺间反射过程的问题以及微波暗室性能是否满足导引仿真要求的问题.对于问题一,首先建立了二维情况下入射波线在尖劈几何空缺间反射过程的数学模型,提出了临界状态的概念,根据光学原理,三角几何原理推出了辐射波在各个反射点处的入射角及反射点距尖劈底面高度表达式,求出了最终反射波的方向、辐射强度.最后根据坐标分解法将其拓展到三维空间.对于问题二,综合考虑辐射波在六个面间的相互影响,运用微元法的思想和微积分的相关知识,推导出静区直接接收到微波信号的公式以及微波信号经整个微波暗室内壁一次反射后被静区接收到的微波功率公式,用数值积分的方法求得了静区得到的反射信号的功率与静区直接得到的微波功率之比,并对部分反射光难以计算的问题提出了数学模型修正的建议和方法.     

尖劈吸波体与导引仿真用微波暗室的性能研究

首先,针对尖劈形状吸波体的性能问题,给出了直接计算法和基于镜像模型的方法,并对其进行了对比计算与仿真.其次,对于微波暗室的性能研究,针对不同的复杂度要求,建立了两种数学模型—射线追踪(Ray Tracing)模型和基于Markov链的有限元(FEM,Finite Element Model)模型.建模过程和仿真结果表明,Ray Tracing模型的计算复杂度较低,但电磁波"镜面反射"的假设过于理想,模型较为粗糙,只能用于粗略模拟实际情况.而基于Markov链的FEM模型较Ray Tracing模型更加精确.同时,相比于传统的具有高计算复杂度的FEM模型,基于Markov链的FEM模型计算更加简便,利于计算机仿真实现,而且不降低FEM模型的精确度,可以精确模拟实际情况.     

用时变雷诺方程模型模拟孤立波与半圆型防波堤的相互作用

以时变雷诺方程为控制方程,用k-ε模型封闭该方程,采用体积函数(VOF)方法来跟踪波动自由表面,建立了二维垂向波浪数学模型,并用已有的实验资料进行了验证．随后用该模型模拟了半圆型防波堤与孤立波在淹没、平顶水位、完全露顶且不越浪3种典型工况下的相互作用过程．得到了半圆堤附近的流场、压强场和波面的变形过程．结果表明,在淹没状态下,半圆堤背浪面的底部会产生涡旋;平顶水位时,由于越浪的冲击作用,在半圆堤的背浪面将逐渐形成一对较大的涡旋,而半圆堤背浪面的底部,速度始终相对较小;而在露顶不越浪时,半圆堤的迎浪面会出现波浪的二次爬升的现象．为进一步研究结构物附近的污染物的输移扩散和泥沙运动提供基础．     

算子值半圆分布及其渐进自由矩阵模型

给出了算子值半圆分布的各阶公式.引入算子值随机变量之间一种新的关系-半独立,并在此意义下给出算子值半圆分布的随机矩阵模型.最后证明了若干个半独立的半圆元的矩阵模型是渐进自由的.     

夹芯型雷达吸波结构的多目标优化

通过引入一个无量纲参数,将重量和雷达吸波性能两个优化目标结合于同一个目标函数中,提出了针对含有多孔材料芯层的夹芯型雷达吸波结构（RASS）的一种多目标优化设计方法．优化模型为承受均布载荷的悬臂夹芯板,考虑4种不同形式的芯层．由传输矩阵法和周期矩量法计算出镜面反射率的平均值,作为表征吸波性能的指标;而面板屈服、芯层剪切破坏和面板起皱则作为优化设计中的力学性能约束．优化结果表明,以填充超轻质海绵体的复合材料二维点阵为芯层的夹芯结构,比含有多孔泡沫或六角蜂窝芯层的夹芯结构更适合作为轻质夹芯型雷达吸波结构．Kagome二维点阵则表现出优于正方二维点阵的吸波性能．     

Poisson比对弯曲波在变截面梁中传播特性的影响

基于Timoshenko理论和梁几何不连续处位移连续和力平衡条件,得到弯曲波在变截面梁中反射和透射系数矩阵,进而研究材料Poisson比对弯曲波在梁变截面处传播特性的影响.结果显示,在负Poisson比阶段,透射传播波的振幅和能量有显著下降趋势,反射传播波振幅和能量上升明显.这说明负Poisson比有利于反射传播波在变截面处的生成,对透射传播波有抑制作用.此外通过对衰减波能量的分析,得到Euler-Bernoulli理论即使在低频范围内,有时会产生较大误差,因此在使用Euler-Bernoulli理论时应慎重.     

理想传导弹性体中能量耗散的磁-热-弹性波

广义能量耗散弹性理论(TEWED,G-NⅢ理论)广泛应用于均匀磁场作用下的时谐平面波在无限大的理想导电弹性体中传播的研究.提出了更普遍的有复杂参数的色散方程,通过运用Ieguerre 方法解决复杂条件下耦合磁-热-弹性波的问题,表明耦合磁-热-弹性波问题相当于改进的膨胀波及通过有限热波速度、热弹性耦合、热扩散率及外加磁场修正的、有限速度热波的传播问题.在G-NⅢ模型(TEWED)中,耦合磁-热-弹性波传播时发生衰减和色散,扩散的热量由热传播方程中的阻尼项考虑,而在G-N Ⅱ模型没有发生衰减和耗散.最后给出了类铜材料的数值结果.     

基于几何光学法和惠更斯原理的微波暗室性能分析

微波暗室在导弹导引仿真中已广泛使用,针对导弹导引仿真试验中用到的微波暗室的静区性能评估问题,分别建立了基于几何光学法和惠更斯原理的评价分析模型.此模型考虑了暗室空间内各个壁面电磁辐射的相互影响,将壁面看作次级余弦辐射体,建立了描述壁面任一点垂直辐射强度的积分微分方程.通过离散方法将问题转化为求解线性方程组的数值问题.计算得到暗室壁面辐射强度分布以及性能指标γ.结果表明,垂直反射率为0.5时不满足要求,而0.05时满足要求.最后考察了模型的收敛性,随着离散度的增高,计算结果趋于稳定.     

High-frequency spectral distribution of the equilibrium radiation energy in a plasma

We establish that the difference of the spectral distribution of the equilibrium radiation energy in matter from the Planck formula in the high-frequency range is determined by the imaginary part of the transverse dielectric permittivity of the matter. Based on this, we show that in a rarified high-temperature fully ionized nonrelativistic plasma, the high-frequency spectral distribution of the equilibrium radiation energy differs essentially from the Planck formula because of the power-law character of the decrease in the frequency, which is due to the presence of matter.     

一个具有电荷和磁偶极矩黑洞的量子非热辐射及其辐射粒子射程的特征

一个稳态轴对称非Kerr-Newman黑洞时空中的粒子能级分布与电磁四维势有关，黑洞电荷和磁偶极矩的存在以及裸奇点的出现都对粒子能级分布有影响，粒子能级分布与方向有关.此黑洞的量子非热辐射及其粒子的平均射程与辐射粒子的能量范围有关。     

Dynamics of a coupled atmosphere–ocean model

We consider a coupled atmosphere–ocean model, which involves hydrodynamics, thermodynamics and nonautonomous interaction at the air–sea interface. First, we show that the coupled atmosphere–ocean system is stable under the external fluctuation in the atmospheric energy balance relation. Then, we estimate the atmospheric temperature feedback in terms of the freshwater flux, heat flux and the external fluctuation at the air–sea interface, as well as the earth's longwave radiation coefficient and the shortwave solar radiation profile. Finally, we prove that the coupled atmosphere–ocean system has time-periodic, quasiperiodic and almost periodic motions, whenever the external fluctuation in the atmospheric energy balance relation is time-periodic, quasiperiodic and almost periodic, respectively.     

Planning accelerated life tests with random effects of test chambers

In accelerated life tests (ALTs), test units are often tested in multiple test chambers along with different stress conditions. The nonhomogeneity of test chambers precludes the complete randomized experiment and may affect the life‐stress relationship of the test product. The chamber‐to‐chamber variation should be taken into account for ALT planning so as to obtain more accurate test results. In this paper, planning ALTs under a nested experimental design structure with random test chamber effects is studied. First, by a 2‐phase approach, we illustrate to what extent different test chamber assignments to stress conditions may impact the estimation of unknown parameters. Then, D‐optimal test plans with 2 test chambers are considered. To construct the optimal design, we establish the generalized linear mixed model for failure‐time data and apply a quasi‐likelihood method, where test chamber assignments, as well as other decision variables that are required for planning ALTs, are simultaneously determined.     

Mathematical modeling of temperature pulsation in a thick anode in optoelectronic systems

A numerical method is applied to analyze the one-dimensional model of temperature pulsation inside a two-layer anode with temperature-dependent thermophysical coefficients. The analysis allows for surface thermal radiation, secondary electron emission, and distribution of electron energy losses by penetration depth into the target. Penetration of pulsations deep into the target is observed.Translated from Matematicheskoe Modelirovanie i Reshenie Obratnykh Zadach Matematicheskoi Fiziki, pp. 215–217, 1993.     

Pointwise structure of a radiation hydrodynamic model in one-dimension

In this paper, we study the nonlinear stability and the pointwise structure around a constant equilibrium for a radiation hydrodynamic model in 1-dimension, in which the behavior of the fluid is described by a full Euler equation with certain radiation effect. It is well-known that the classical solutions of the Euler equation in 1-D may blow up in finite time for general initial data. The global existence of the solution in this paper means that the radiation effect stabilizes the system and prevents the formation of singularity when the initial data is small. To study the precise effect of the radiation in this model, we also treat the pointwise estimates of the solution for the original nonlinear problem by combining the Green's function for the linearized radiation hydrodynamic equations with the Duhamel's principle. The result in this paper shows that the pointwise structure of this model is similar to that of full Navier-Stokes equations in 1-D.     

Global existence of strong solutions to the Cauchy problem for a 1D radiative gas

We consider a one-dimensional radiation hydrodynamics model in the case of the equilibrium diffusion approximation which is described by the compressible Navier-Stokes system with the additional terms in the pressure and internal energy respectively, which embody the effect of radiation. Under the physical growth conditions on the heat conductivity, we establish the existence and uniqueness of strong solutions to the Cauchy problem with large initial data, where the initial density and velocity may have differing constant states at infinity. Moreover, we show that if there is no vacuum in the initial density, then, the vacuum and concentration of the density will never occur in any finite time.