基于光的波粒二象性猜想的数学仿真

从现有的经典物理光学理论和专业实验结果出发,运用数学思维,综合光子理论,建立了基于光的波粒二象性猜想的四种数学模型.针对光微子碰撞猜想,建立了基于光子碰撞后概率分布的模型.针对光子作为电磁场自我旋转的猜想,分别从专业证明和数学模型分析方面建立了电磁场偏转模型和光子旋转模型.最后建立了我们自己的猜想模型——光子蜂窝网络模型.该模型引入了"光子域"、"光子电力"、"光子磁力"、"光子键"等概念,从五个子模型出发,定性解释了四个光学现象,合理回答了题目提出的三大问题,并定量证明了衍射光强分布.     

基于光子结构猜想的波动性现象建模仿真研究

综合龚祖同院士的光子类氢原子结构论和北大俎栋林教授的光子电磁场结构论,提出了两种结构相统一的理论猜想.基于猜想对单缝衍射、双缝干涉以及多缝干涉中光强与光子尺度、细缝宽度等参数的关系进行建模,并以双缝干涉为例进行了仿真实验.通过实验结果与经典波动光学中光强分布的对比,验证了模型的合理性.     

光子结构的猜想及其数学仿真

通过研究光的波粒二象性,对光子结构进行了研究并提出了自建光子模型.自建光子模型具有以下特性:①光子与原子核存在引力作用;②光子的电场与磁场交替变换使其具备了相位效应,且光强由光子数与光子相位和两个因素决定.在此基础上,通过借鉴天体物理中关于二体运动的三种轨迹,利用其中结论对大量原子核的引力作用进行概率分析,使用中心极限定理提出出射角度基本符合高斯分布的假设.接着对光子的相位叠加效应进行了分析.最后,对大量光子进行模拟仿真,并将仿真结果与单缝衍射、双缝干涉、多缝干涉现象等实验现象进行了对比.     

光的波粒二象性探索

光具有波粒二象性,但很难从光的某一特定现象中同时看到这两种性质.如果能用粒子性解释波动性,光的两种性质就能得到完美的统一.分别对龚祖同光子模型、前进电磁场光子模型进行数学建模和MATLAB仿真,并与已有的实验结果比较.发现两个模型都存在不足,进而提出改进的光子模型,从粒子的角度,对展现光的波动性质的干涉、衍射以及偏振现象进行解释.     

正负电子三光子湮没的实验研究

本文报告对正负电子三光子湮没进行的一系列实验的结果,包括三光子湮没光子的能量与角度关联、三光子湮没光子的角分布、三光子湮没光子的能谱、三光子湮没光子的线极化、测量三光子湮没强度的方法和三重态电子偶素衰变中轴子的上限。     

光子迁移中的一个逆问题

在[1]里已经讨论了如何根据光子密度n(x,u)(实验测得),得到总截面σ(x)的近似值,本文利用最小二乘法讨论如何通过n次观测求得σ(x)的近似值.     

甲苯分子3p Rydberg态的偏振多光子电离谱的研究

利用量子理论的微扰论,通过适当选择张量基矢,推导出分子C_2v点群的简并三光子跃迁张量图,由近似法首次获得了三光子跃迁偏振比值.实验上用共振多光子电离(RMPI)技术,探测了气相甲苯分子的能量在52630～54050cm^-1范围的RMPI(3+1)谱,归属了共振跃迁电子态为3p Rydberg态,对所观测到的4个振动带测量了偏振比,根据理论计算结果对电子态和振动态的跃迁作了对称性归属.     

单光子探测用于光子统计测量的研究

实验研究了通过记录每一个光子事件直接测量微弱脉冲激光(平均光子数 ≈0.1, 脉冲持续时间10 ns)的Mandel 参数. 在基于Hanbury-Brown-Twiss探测结构, 取样时间内每个单光子计数器最多探测到一个光子的情况下, 测量发现低于阈值电流工作的二极管激光呈Super-Poisson统计分布. 另外验证了工作于远高于阈值电流的二极管激光(强度噪声主要为散粒噪声)的Poisson分布相干态的Mandel 参数 Q_C约为- /2. 在测量误差内, 实验结果与理论分析一致.     

具有相位阻尼的Milburn主方程控制的双光子JC模型

该文利用超算子技术求出了相位阻尼下非共振双光子JC模型主方程的解析解，研究了其相位阻尼对光子数分布振荡，原子数反转与恢复和亚泊松光子分布等非经典效应的影响。研究表明：相位阻尼能抑制原子反转与恢复和腔场的非经典效应。     

基于线性偏振光子对学说的数学建模与仿真

北京大学学者猜想单个光子只有左旋光子、右旋光子两种.一个左旋光子与一个右旋光子可以组成一个线性偏振光子对.在合理假设基础上,从光的波粒二象性的认识出发,基于这种猜想分别对双缝干涉、单缝衍射、多缝衍射等实验建立光子的运动方程,利用复数积分法得到相应的光强分布模型.并用Matlab软件进行数学仿真,得到猜想的实验结果与波恩的实验结果相符合.     

An operator splitting strategy for fluid–structure interaction problems with thin elastic structures in an incompressible Newtonian flow

We present a computational framework based on the use of the Newton and level set methods to model fluid–structure interaction problems involving elastic membranes freely suspended in an incompressible Newtonian flow. The Mooney–Rivlin constitutive model is used to model the structure. We consider an extension to a more general case of the method described in Laadhari (2017) to model the elasticity of the membrane. We develop a predictor–corrector finite element method where an operator splitting scheme separates different physical phenomena. The method features an affordable computational burden with respect to the fully implicit methods. An exact Newton method is described to solve the problem, and the quadratic convergence is numerically achieved. Sample numerical examples are reported and illustrate the accuracy and robustness of the method.     

Mathematical analysis of plasmonic resonance for 2-D photonic crystal

In this article, we study the plasmonic resonance of infinite photonic crystal mounted by the double negative nanoparticles in two dimensions. The corresponding physical model is described by the Helmholz equation with so called Bloch wave condition in a periodic domain. By using the quasi-periodic layer potential techniques and the spectral theorem of quasi-periodic Neumann–Poincaré operator, the quasi-static expansion of the near field in the presence of nanoparticles is derived. Furthermore, when the magnetic permeability of nanoparticles satisfies the Drude model, we give the conditions under which the plasmonic resonance occurs, and the rate of blow up of near field energy with respect to nanoparticle's bulk electron relaxation rate and filling factor are also obtained. It indicates that one can appropriately control the bulk electron relaxation rate or filling factor of nanoparticle in photonic crystal structure such that the near field energy attains its maximum, and enhancing the efficiency of energy utilization.     

Conservative finite-difference scheme for the problem of propagation of a femtosecond pulse in a photonic crystal with combined nonlinearity

A conservative finite-difference scheme is constructed for the problem of propagation of a light pulse in a one-dimensional nonlinear photonic crystal with combined nonlinearity. The invariants of the corresponding differential problem and their difference analogues are given. The scheme is compared with those based on the widespread splitting method. For combined cubic and quadratic nonlinearity in photonic crystal layers, it is shown that the classical splitting method is ineffective, since it requires time steps that are smaller by one or more orders of magnitude. The finite-difference scheme proposed conserves the propagation invariants, which cannot be achieved for splitting schemes even on considerably finer grids. Nonreflecting conditions substantially improve the efficiency of conservative finite-difference schemes as applied to the simulation of complex nonlinear effects in photonic crystals, which require much smaller steps in space and time than those used in the case of linear propagation. The simulation is based on the approach proposed by the authors for the given class of problems.     

介质与结构三维动力相互作用分析的半解析边界元—半解析有限元结合法

本文将半解析边界元一半解析有限无结合法用于介质与结构的动力相互作用研究:用半解析边界元法分析具有复杂地表面的半无限介质,用半解析有限元法分析具有任意截面形状的柱体结构,利用介质与结构交界面上的位移相容条件和力平衡条件,将介质与结构联系起来。联立京解上述半解析边界元方程和半解析有限元方程,对应每一时间步进,可同时求出介质与结构交界面上的位移、速度、加速度和相互作用力以及地表面的运动情况.与目前广泛研究的边界元—有限元结合法相比,本方法在介质与结构二个个区域各降低了一维空间,因而离散单元数和计算工作量大幅度减少,人工输入数据非常简单.文中还考虑了地下结构的长跨比效应、厚度效应和介质效应.     

结构—饱和土壤相互作用的固结有限元分析

讨论了结构与饱和土壤相互作用的固结分析问题.对于结构利用多重子结构分析技术实现向饱和土交界面上的凝聚.从而建立了结构与饱和土壤相互作用的固结控制方程.文中给出了问题求解的一次性算法方案,采取压力主从关系的手段处理边界上的不排水条件.文末给出数值算例.本文工作为大型结构与土体相互作用固结分析研究工作的深入创造了条件.     

A DLM/FD/IB Method for Simulating Cell/Cell and Cell/Particle Interaction in Microchannels

A spring model is used to simulate the skeleton structure of the red blood cell （RBC） membrane and to study the red blood cell （RBC） rheology in Poiseuille flow with an immersed boundary method. The lateral migration properties of many cells in Poiseuille flow have been investigated. The authors also combine the above methodology with a distributed Lagrange multiplier/fictitious domain method to simulate the interaction of cells and neutrally buoyant particles in a microchannel for studying the margination of particles.     

Diffusion-limited aggregation with a local particle drift

A simple model with a local particle drift is proposed to extend the diffusion-limited aggregation model. Here the attractive or the repulsive interaction between a flight particle and the aggregation cluster is taken into account. In our model the drift force depends on the local aggregation structure. The effects of the strength and the range of the particle-particle interaction on the fractal structure of the aggregations are elucidated from the scaling property of an integrated pair correlation function. From the present computer simulation results, it is found that while the attractive interaction tends to decrease the fractal dimension, the repulsive one increases it.     

Where Forward-Looking and Backward-Looking Models Meet

The present paper begins by deriving an instantaneous formulation for the backward-looking (reinforcement based learning) satisfaction balance model of Gray and Tallman (1984). This model is then used to generate interactional data from four simulated agents in a network interaction experiment. Because this initial model does not generate stable interaction structures in the network experiment, it is altered step by step in the direction of a forward-looking (agent with goals) model that has been shown to generate such stable interaction structures. The purpose of the modifications are to learn what aspects of the forward-looking model are needed to evolve a stable interaction structure, and to learn how these aspects may be incorporated into a model that remains essentially reinforcement based.     

Nonlinear optical media in photonic crystal waveguides: Intrinsic localized modes and device applications

A review is given of some of the properties of photonic crystal waveguides containing or interacting with nonlinear optical media including discussions of potential device applications. An introduction is given to photonic crystals, photonic crystal waveguide technologies, the properties of Kerr nonlinear dielectric media, the properties of new types of excitations in these systems known as intrinsic localized modes, and optical bistability. Device designs for switches, waveguide couplers, interferometers, transistors, photonic crystal receivers and transmitters, and photonic crystal sensors are reviewed. © 2007 Wiley Periodicals, Inc. Complexity 12: 18–32, 2007