光子结构猜想的仿真验证

从龚祖同院士的类氢光子结构模型和北大学者的电磁场粒子模型出发,提出了等效作用和动态光子层的概念,并在此基础上,利用蒙特卡罗法和伽尔顿板法,对光的干涉、衍射现象进行了定量分析和仿真实验,验证了光子结构猜想的正确性.     

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.     

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.     

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.     

基于光的波粒二象性猜想的数学建模与仿真

光具有波粒二象性,诸多学者都对此提出了不同猜想,用以合理解释光的直线传播、衍射和干涉等问题.对三种基于光的波粒二象性的猜想进行了数学建模与仿真验证.以Matlab为工具对光的衍射等现象的进行了数学仿真,并与《光学原理》中的相关结果作了对比,最终验证了猜想的正确性.     

二维矩形条带装箱问题的改进左下角定位模型

针对不可旋转二维矩形条带装箱问题(2DR-SPP),基于两矩形的左下角单元坐标及其覆盖区域的关系,提出并证明了两矩形在条带箱中发生重叠的充分必要条件,然后根据此充分必要条件得到了禁止矩形重叠的约束条件,建立了问题的线性整数规划模型.增添旋转90~0后所得的矩形数据至原有的矩形数据中,基于更新后的矩形数据,修改不可旋转2DR-SPP的数学模型,得到了可旋转情形下问题的线性整数规划模型.算例结果验证了所建模型的有效性和准确性.     

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.     

中国城乡居民养老制度可持续性的精算研究

围绕我国城乡居民养老保险体系可持续化问题,从中国实际出发,分层次、多角度的分析了当前我国的养老保险制度.首先,针对中国养老保险基金问题,基于当前养老保险体制,分别从三个层次入手,建立中国城乡居民养老保险基金收支模型;其次,基于养老制度的可持续性,建立了养老金缺口模型,并对养老金缺口的未来趋势进行了合理预测;最后,对所建立的模型进行了评价及推广.     

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.     

企业技术创新的多目标模糊决策模型及MATLAB实现

针对企业技术创新过程中的多目标决策优化问题的模糊性,运用多目标决策模糊集理论进行研究,建立数学模型并基于M ATLAB程序,较好地克服了过去各方案评价结果分辨率不高和优劣性评价的不足之处,并通过实证分析和计算机模拟计算,证实了模型的科学性,也说明模型具有较强的可靠性和实用性.     

设备空间磁场预测的传感器布阵优化

本文研究了铁磁性设备周围空间传感器布阵的问题。我们建立了关于传感器位置和数量优化的数学模型,并通过遗传算法对模型进行求解。首先,本文选用对传感器数量和距离要求较少的旋转椭球体作为磁场远场换算的模型。在旋转椭球体模型中,传感器分布位置不当会导致磁场计算系数矩阵的条件数过大,模型将出现病态,因而计算得到的远场磁场结果不可靠。所以,本文以旋转椭球体模型中的系数矩阵条件数为优化目标,建立数学模型优化单个设备上方传感器的数量与位置分布,并利用遗传算法对模型求解。其次,通过实验验证了本模型对于单个设备的传感器位置和数量优化是有效的,且所用传感器数量少,计算结果可靠。最后,将单个设备传感器位置和数量的优化模型推广到多个设备,以两个设备为代表用同时优化和分别优化两种方法计算传感器位置,根据实验计算这两种方法都具有较高的远场磁场计算精度,但分开优化的方法在实际计算更加简便、容易操作。     

The Cauchy problem for a spin-liquid model in three space dimensions

In this paper, we study the Cauchy problem for magnetic fluid of spin-liquid type with Mermin-Ho relation in the three-dimensional space and prove global existence and uniqueness of solutions. The proof is based on the equivalence relation between smooth solutions of the spin-liquid model and the systems of Schrödinger equations with Abelian gauge field. The Sobolev spaces with fractional derivatives are also used in our estimates.     

Convergence rate of solutions toward stationary solutions to a two-phase model with magnetic field in a half line

In this paper, we study an asymptotic behavior of a solution to the outflow problem for a two-phase model with magnetic field. Our idea mainly comes from [1] and [2] which investigate the asymptotic stability and convergence rates of stationary solutions to the outflow problem for an isentropic Navier–Stokes equation. For the two-phase model with magnetic field, we also obtain the asymptotic stability and convergence rates of global solutions towards corresponding stationary solutions if the initial perturbation belongs to the weighted Sobolev space. The proof is based on the weighted energy method.     

A lattice Boltzmann model for Maxwell’s equations

In this paper, a lattice Boltzmann model for the Maxwell’s equations is proposed by taking separate sets of distribution functions for the electric and magnetic fields, and a lattice Boltzmann model for the Maxwell vorticity equations with third order truncation error is proposed by using the higher-order moment method. At the same time, the expressions of the equilibrium distribution function and the stability conditions for this model are given. As numerical examples, some classical electromagnetic phenomena, such as the electric and magnetic fields around a line current source, the electric field and equipotential lines around an electrostatic dipole, the electric and magnetic fields around oscillating dipoles are given. These numerical results agree well with classical ones.     

Global existence of solutions to a magnetohydrodynamic‐omega model

In this paper, some sufficient conditions in terms of the magnetic field are established to guarantee global existence of solutions to a magnetohydrodynamic‐omega model.     

Biomagnetic viscoelastic fluid flow over a stretching sheet

Of concern in this paper is an investigation of biomagnetic flow of a non-Newtonian viscoelastic fluid over a stretching sheet under the influence of an applied magnetic field generated owing to the presence of a magnetic dipole. The viscoelasticity of the fluid is characterised by Walter’s B fluid model. The applied magnetic field has been considered to be sufficiently strong to saturate the ferrofluid. The magnetization of the fluid is considered to vary linearly with temperature as well as the magnetic field intensity. The theoretical treatment of the physical problem consists of reducing it to solving a system of non-linear coupled differential equations that involve six parameters, which are solved by developing a finite difference technique. The velocity profile, the skin-friction, the wall pressure and the rate of heat transfer at the sheet are computed for a specific situation. The study shows that the fluid velocity increases as the rate of heat transfer decreases, while the local skin-friction and the wall pressure increase as the magnetic field strength is increased. It is also revealed that fluid viscoelasticity has an enhancing effect on the local skin-friction. The study will have an important bearing on magnetic drug targeting and separation of red cells as well as on the control of blood flow during surgery.     

Derivation of lower critical magnetic field for anisotropic Ginzburg-Landau model in superconductivity

In this paper, the authors discuss the vortex structure of an anisotropic Ginzburg-Landau model for superconducting thin film proposed by Du. We obtain the estimate for the lower critical magnetic field $ H_{C_1 } $ H_{C_1 } which is the first critical value of h _ex corresponding to the first phase transition in which vortices appear in the superconductor. We also find local minimizers of the anisotropic superconducting thin film with a large parameter κ, and for the applied magnetic field near the critical field we discuss the asymptotic behavior of the local minimizers.     

A numerical model for magnetic chromatography

In this paper, we present details of a mathematical model for magnetic chromatography (MC) systems where strong distorted magnetic fields are used to separate particles from a colloidal mixture. The model simulates the effect of magnetic field gradients on particle motion, and includes calculation of the fluid flow, magnetic field, and particle concentration field. It is based on the finite-volume method (FVM) and uses an expanding-grid technique to handle domains with large aspect ratios. The model has been validated against the results from an analytical model. The numerical model has been used to simulate the performance of a real MC system under various operating conditions.     

Performance modeling and analysis of blood flow in elastic arteries

The effect of magnetic field has been examined on rheological models of blood. One. of them is the Power Law model and the other is the generalized Maxwell model. It is noticed that the magnetic field has a significant effect on the flow phenomena. The investigation shows that the model considered here is capable of taking into account the rheological properties affecting the blood flow and hemodynamic features, which may be important for medical doctors to predict diseases for individuals on the basis of the pattern of flow for an elastic artery in the presence of a transverses magnetic field. The effects of a magnetic field have been used to control the flow, which may be useful in certain hypertension cases, etc.     

Exterior problem of magnetic field in Darwin model and its numerical solution

In this paper, we consider the solutions of magnetic field in the Darwin model to the Maxwell's equations in 2D unbounded domain. We first deduce the variational formulation and prove the well‐posedness of the weak solution, and then prove the existence and uniqueness of the infinite element solution. Error estimate and the numerical examples are provided. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008