Holomorphic Chern-Simons-Witten theory: From 2D to 4D conformal field theories

It is well known that rational 2D conformal field theories are connected with Chern-Simons theories defined on 3D real manifolds. We consider holomorphic analogues of Chern-Simons theories defined on 3D complex manifolds (six real dimensions) and describe 4D conformal field theories connected with them. All these models are integrable. We describe analogues of the Virasoro and affine Lie algebras, the local action of which on fields of holomorphic analogues of Chern-Simons theories becomes non-local after pushing down to the action on fields of integrable 4D conformal field theories. Quantization of integrable 4D conformal field theories and relations to string theories are briefly discussed.     

卷积完全匹配层在空爆电磁脉冲2维模拟中的应用

 在分析不同类型完全匹配层特点的基础上,选用了卷积形式完全匹配层（CPML）截断空中核爆电磁脉冲数值模拟的开放边界。从自由空间中电磁波的平面波解和分裂形式的完全匹配层出发,构造了未分裂形式的完全匹配层,应用傅里叶变换的卷积定理,推导出2维旋转椭球-双曲正交坐标系下卷积形式完全匹配层介质中电磁场的迭代形式的离散方程。计算表明,采用CPML吸收边界方法使得截断的外边界处的场的计算误差大大减少。     

Arithmetic of Calabi–Yau varieties and rational conformal field theory

It is proposed that certain techniques from arithmetic algebraic geometry provide a framework which is useful to formulate a direct and intrinsic link between the geometry of Calabi–Yau manifolds and the underlying conformal field theory. Specifically, it is pointed out how the algebraic number field determined by the fusion rules of the conformal field theory can be derived from the number theoretic structure of the cohomological Hasse–Weil L-function determined by Artin’s congruent zeta function of the algebraic variety. In this context, a natural number theoretic characterization arises for the quantum dimensions in this geometrically determined algebraic number field.     

3D modeling of electromagnetic levitation coils

Electromagnetic levitation (EML) enables the handling of samples in a containerless manner, facilitating more precise measurements or manipulation of materials. Currently, EML coil design is based on two-dimensional (2D) mathematical models combined with empirical data and experience. We propose that employing a truly 3D model enables a more accurate and rational coil design. This approach shows significant differences in magnetic field, and the resulting lift and heating properties, when comparing a 2D and a 3D coil. A 3D coil, resembling the geometry of a 2D coil, requires more current to generate the same lift. Reversing the situation, a 3D coil producing the exact same magnetic field as a 2D coil has a vastly different design. Furthermore, we show that the assumption that the magnetic field is homogeneous in the axial plane within the sample volume is invalid, even for small samples, in the upper and lower regions of the coil. Using a 3D model, we design a coil capable of levitating and melting an iridium sphere with a diameter of 6 mm.     

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基于ANSYS对CFETR真空室简化模型进行了2D/3D电磁分析,得到了真空室磁场强度以及电磁力的分布.分析结果显示2D/3D真空室的磁场强度及电磁力分布基本一致,这表明了可以使用2D模型替代3D模型对未来真空室简化模型进行电磁分析.     

2D/3D CFETR真空室电磁计算

基于ANSYS对CFETR真空室简化模型进行了2D/3D电磁分析,得到了真空室磁场强度以及电磁力的分布。分析结果显示2D/3D真空室的磁场强度及电磁力分布基本一致,这表明了可以使用2D模型替代3D模型对未来真空室简化模型进行电磁分析。     

各向异性介质三维电磁响应模拟的Ho-GEBA算法

本文基于积分方程法研究并建立了一种模拟横向同性介质中任意各向异性异常 体三维电磁响应的高阶广义扩展Born近似(Ho-GEBA)算法. 首先利用逐次迭代技术给出积分方程的广义级数展开解, 为保证其收敛性, 引入一种各向异性条件下满足压缩映射的迭代算子. 然后利用异常体区域分解技术, 并结合扩展Born近似原理, 得到各向异性介质三维电磁响应的Ho-GEBA解. 为提高效率, 计算过程中采用并矢Green函数的解析表达式. 最后通过数值计算实例对比验证了本文算法的有效性. 关键词： 高阶广义扩展Born近似 积分方程 电磁模拟 解析Green函数     

Response to comments on boundary problems and electromagnetic constitutive parameters

The positive conclusion on the recognizable existence of the Tellegen parameter, which invalidates the Post constraint, arrived at in the Comment of Sihvola and Tretyakov through the solution of a boundary-value problem relies on a framework of macroscopic electromagnetism that lacks a microscopic basis. But the microscopic viewpoint underlying the framework of modern macroscopic electromagnetism invalidates the boundary conditions used therein, and instead validates the Post constraint.     

Numerical analysis of propagation characteristics of electromagnetic wave in lossy left-handed material media

The propagation characteristics of electromagnetic wave in lossy left-handed materials (LHM) are studied using finite-difference time-domain (FDTD) method base on auxiliary differential equation (ADE) technology. The LHM medium is realized with lossy Drude models for both the negative electric permittivity and the negative magnetic permeability. The discretized ADE-FDTD equations are derived in detail. The incident wave used in the simulation is a multiple cycle m-n-m pulses source. The term of Poynting's vector E_xH_y was calculated. These numerical results demonstrate conclusively that the phase velocity direction of electromagnetic wave propagation and the direction of the Poynting vectors are anti-parallel in LHM. The amplitude of electric field is reduced with the enhancive distance of LHM slab. It is also demonstrated that the energy of electromagnetic wave in the LHM slab is obviously attenuated, and the attenuation of energy becomes stronger with the angular plasma frequency ω_p increasing. These results indicate that LHM stealth is effective in theory, and reasonable selection of the large negative index of refraction can greatly enhance its effectiveness.     

卷积完全匹配层截断3维金属矩形波导的应用研究

 讨论了高功率微波源模拟中波导开放边界截断的需求,分析了不同类型完全匹配层(PML)的特点,选用卷积形式PML截断色散波导器件的开放边界。从自由空间电磁波的平面波解和分裂形式的PML出发,构造了未分裂形式的PML,用傅里叶变换的卷积定理,导出了直角坐标系下卷积完全匹配层(CPML)介质中电磁场的迭代形式的离散方程。在不同频率和模式激励源作用下,模拟计算了CPML截断矩形波导开放边界的性能,数值结果表明最大相对误差都小于-70 dB,远好于Mur吸收边界的截断效果。     

改进的三维电磁PIC系统模拟并行算法

为了更好地实现对大尺度器件的模拟,以及更系统地验证和解决高功率微波系统在设计和实验中负载变化等影响,在进一步深入研究电磁PIC并行算法的基础上,运用MPI消息传递函数做出了改进。提出了一种整体建模、分段解析的并行算法,并从并行时序算法入手,通过减少一次同步提高了计算的效率。最后经过一个磁绝缘线振荡器进行验证,改进的算法正确,并且当计算进程数4个增加到16个时,计算速度能提高2.5倍左右。     

静电放电火花产生的电磁场树枝模型

 静电放电火花产生的电磁脉冲会对电子系统的正常工作造成严重的干扰，甚至造成系统的损伤。利用时域有限差分法建立了静电放电火花产生的电磁场的数值模型，模型中充分考虑了放电电极上的静电荷对电场的影响。把由此模型放电计算的电磁场值与由此解析方法得到的场值进行了比较，结果吻合良好。由此可以用此模型来研究静电放电火花产生的电磁场与电子系统的能量耦合问题。     

熔石英表面划痕附近电磁场分布模拟分析

 亚表面缺陷是造成固体激光器光学器件损伤阈值过低的重要原因，而表面划痕是缺陷中重要的一种。使用时域有限差分方法（FDTD）模拟了熔石英表面圆柱形、三角形划痕对激光电磁场的调制作用，绘出了2维电磁场强度分布图，计算出划痕尺寸不同时电磁场的最大强度。数值计算结果表明，尺寸为二倍波长的划痕可以获得最大的电磁场强度，此时容易导致自聚焦；亚波长级和足够大尺寸的划痕作用基本可以忽略。一定尺寸的划痕，深度越大，最大场强也越大，但当划痕过深时最大场强反而会降低。     

FDTD analysis on the effect of plasma parameters on the reflection coefficient of the electromagnetic wave

In this paper, the dielectric constant of dispersive medium is written as rational polynomial function, and the relationship between D and E is derived in time-domain. It is named shift operator FDTD (SO-FDTD) method. Compared to the analytical solution, the high accuracy and efficiency of this method is verified by calculating the reflection coefficient of the electromagnetic wave through a cold plasma slab. The effect on reflection coefficient is calculated by using the SO-FDTD method. The result shows that some factors effect on reflection coefficient. They are as follows: plasma thickness, electron density, electron distribution and incident frequency. And on most conditions, parabola distribution helps reduce reflection coefficient more effectively than homogeneous distribution.     

建筑墙体对电磁脉冲响应的FDTD分析

 采用时域有限差分法和傅里叶变换对电磁脉冲作用于建筑墙体后发生的反射和透射进行了比较全面的研究分析。采用周期边界实现了不同建筑墙体对电磁脉冲响应的数值计算，对计算的结果进行了讨论分析，研究结果表明：钢筋阵对低频段的屏蔽效果很好，当频率增加时，屏蔽效果变差。混凝土墙的频域波形具有明显的周期性，存在许多谐振频率，谐振时透过很大，谐振频率由墙的厚度、磁导率和介电常数决定，要提高墙的屏蔽效果必须增加墙的电导率，以达到一个比较好的屏蔽效果。钢筋混凝土墙的屏蔽效果和反射特性由钢筋和混凝土墙共同调制决定。     

高功率电磁脉冲对砷化镓金属半导体场效应管的影响

 采用时域有限差分方法,通过求解麦克斯韦方程、热传导方程和载流子方程,模拟了在电磁脉冲辐射下,场效应管器件温度和端口散射参数的变化过程。研究了不同幅度脉冲序列和上升沿不同的脉冲对砷化镓金属半导体场效应管的影响,对比了各种不同脉冲作用下场效应管性能的变化规律。该方法克服了传统电路模型无法模拟电磁波与器件内部活动粒子作用过程的缺点,可以直接模拟器件温度和散射参数在高功率电磁脉冲辐射下的时域变化过程。     

On the sensitivity of the 2D electromagnetic invisibility cloak

A computational study of the sensitivity of the two dimensional (2D) electromagnetic invisibility cloaks is performed with the finite element method. A circular metallic object is covered with the cloak and the effects of absorption, gain and disorder are examined. Also the effect of covering the cloak with a thin dielectric layer is studied.     

JEMS-FDTD软件在运输机电磁特性仿真中的应用

复杂电磁环境的研究包括多方面内容,其中飞行器的电磁环境效应研究受到了较多的关注。随着计算机技术的飞速发展,利用数值模拟技术获得飞行器电磁特性已经成为飞行器电磁环境效应研究的一个重要手段。我们将自主研发的大规模并行三维时域全波电磁模拟软件JEMS-FDTD应用于运输机整机电磁特性仿真,计算并分析了飞机的电磁耦合散射特性,获得了飞行器在电磁脉冲照射下的时域/频域、近场/远场等电磁信息。计算中为保证精度采用了非均匀以及高阶FDTD计算技术。     

电磁脉冲与窄缝腔体耦合共振特性分析

 应用时域有限差分法模拟计算了电磁脉冲对窄缝和窄缝腔体的线性耦合过程。通过定义能量耦合传输系数，分析耦合能量随窄缝宽度和厚度及时间的变化关系，得出在正弦波调制的高斯脉冲源激励下，窄缝和窄缝腔体的耦合共振特性。     

A high accuracy algorithm for 3D periodic electromagnetic scattering

We develop a highly accurate numerical method for scattering of 3D electromagnetic waves by doubly periodic structures. We approximate scattered fields using the Müller boundary integral formulation of Maxwell’s equations. The accuracy is achieved as singularities are isolated through the use of partitions of unity, leaving smooth, periodic integrands that can be evaluated with high accuracy using trapezoid sums. The removed singularities are resolved through a transformation to polar coordinates. The method relies on the ideas used in the free space scattering algorithm of Bruno and Kunyansky.