A hybrid VOF and PIC multi-material interface treatment method and its application in the penetration

A hybrid VOF and PIC multi-material interface treatment method for Eulerian method is presented in this study in order to solve the problem that the Eulerian method is not robust enough to treat the dynamic fracture of material. This treatment method is used in the important computational region such as the material interface,large deformation region and fracture region where more particles are added for calculation,while the continuous transport method is used in the other regions. Through this method,a se...     

A Vaidya-type radiating solution in Einstein-Gauss-Bonnet gravity and its application to braneworld

We consider a Vaidya-type radiating spacetime in Einstein gravity with the Gauss-Bonnet combination of quadratic curvature terms. Simply generalizing the known static black hole solutions in Einstein-Gauss-Bonnet gravity, we present an exact solution in arbitrary dimensions with the energy-momentum tensor given by a null fluid form. As an application, we derive an evolution equation for the “dark radiation” in the Gauss-Bonnet braneworld.     

An enthalpy-temperature hybrid method for solving phase-change problems and its application to polymer pyrolysis and ignition

A numerical approach based on the enthalpy method is proposed for solving generalized phase-change problems. The method is applied to predict pyrolysis and ignition of polymeric combustible materials. In contrast to the traditional approach, here both enthalpy and temperature are treated as independent variables, and the conservation equations are solved simultaneously in conjunction with the constitutive equations. Also, the formulation of the constitutive equations for the phase change is not necessarily the same for all of the possible phases, but can be chosen independently according to the characteristics of the physical problem and the requirements of the numerical analysis of each respective phase. Thus with this new approach, which we refer to as the enthalpy-temperature hybrid method, the enthalpy method is applicable to the generalized phase-change problems regardless of the form of the constitutive equations. The proposed method is first applied to a one-dimensional classical freezing problem for verification. It is found that the numerical results for the temperature history and the position of the phase-change interface agree well with the analytic solution existing in the literature. The method is then applied to the numerical simulation of the pyrolysis and ignition of a composite material with a polymer as the matrix and fibreglass as the filling material. Three models of oxygen distribution in the molten layer are considered to explore the melting and oxygen effects on the polymer pyrolysis. Numerical calculation shows that high oxygen concentrations in the molten layer enhance the pyrolysis reaction, resulting in a larger amount of pyrolysate, but in lower surface temperatures of the sample. It also shows that the distribution of oxygen in the molten layer has a strong effect on the pyrolysate rate, and therefore on ignition and combustion of the polymers. Comparison with available experimental data indicates that a model of oxygen distribution in the molten layer that is limited to a thin layer near the surface best describes the ignition process for a homogeneously blended polypropylene/fibreglass composite.     

电阻分联及其应用——电阻串并联的一个逆问题

介绍电路分析的一种新方法,称为电阻分联法.文中附有几个应用实例.这工作可看作是电学中逆问题一例.     

A new perturbation method to the Tent map and its application

Disturbance imposed on the chaotic systems is an effective way to maintain its chaotic good encryption features. This paper proposes a new perturbation method to the Tent map. First it divides the Tent map domain into 2^N parts evenly and selects a particular part from them, then proliferates the Tent map mapping trajectory of this particular part, which can disturb the entire system disturbance. The mathematical analysis and simulated experimental results prove that the disturbed Tent map has uniform invariant distribution and can produce good cryptographic properties of pseudo-random sequence. These facts avoid the phenomenon of short-period caused by the computer's finite precision and reducing the sequence's dependence on the disturbance signal, such that effectively compensate for the digital chaotic system dynamics degradation.     

A new auxiliary equation method and its application to the Sharma-Tasso-Olver model

A new auxiliary equation method, constructed by a first order nonlinear ordinary differential equation with at most an eighth-degree nonlinear term, is first proposed for exploring more exact solutions to nonlinear evolution equations. Being concise and straightforward, the method, with the aid of symbolic computation, is applied to the Sharma-Tasso-Olver model, and some new exact solitary wave solutions are obtained. The approach is also applicable to searches for exact solutions of other nonlinear evolution equations.     

A method of relaying the transverse profile of a laser beam and its application to holography

The holography of engineering plant where only restricted access is available requires a method of piping the pulsed laser beam to a compact, remote head. Because amplifier distortions which occur in pulsed lasers result in far field beam break-up, it is not possible to simply collimate the beam as normally possible with a continuous wave laser. A possible way to transmit the pulsed laser beam is by an optical relay which repeatedly images the output until the launching point is reached.

The use of a relay system to transmit the pulsed laser output 20 m has been demonstrated in the laboratory. Holograms taken at the output of the relay showed a resolution of 18l.p. mm^-1, the same as that achieved when a hologram was taken by expanding the beam immediately at the laser output.     

内爆靶丸X射线轫致辐射谱的重建方法及应用北大核心CSCD

提出了一种对内爆靶丸X射线轫致谱重建的方法。该方法的目的是通过重建内爆靶丸的轫致辐射谱,得到内爆靶丸有价值的信息。这种方法将轫致谱能段分为五个部分,假设每个部分的平均能量强度相等,用一种包含了五个不同滤片组的多能段针孔相机对同一个内爆靶丸进行成像,并且用IP板进行接收。五组不同的像可以给出五个不同的线形方程组,这样就可以还原出轫致辐射谱。使用该方法还原了在神光Ⅲ原型装置上内爆靶丸的轫致辐射谱,并据此给出了内爆热斑的温度,所得的结果与用示踪元素特征谱线给出的温度符合得较好,证实该方法和结果是可靠的。     

A mixed integral equation of mechanics and a generalized projection method of its solution

A mixed multidimensional integral equation containing integral operators of various types is studied. The case in which the equation has one compact, self-adjoint, and strongly positive operator (with constant limits of integration) and two non-self-adjoint integral Volterra operators (with a variable upper limit of integration) is considered. To solve the equation, an effective projection method allowing one to obtain the result in a form with explicitly distinguished principal singularities is proposed.     

A method of moments solution to a three-dimensional whisker structure

A method of moments solution to a three-dimensional whisker structure in a rectangular waveguide is presented. Theoretical results are compared with and verified by corresponding experimental measurements. As a result, it is shown that the orientation of the whisker with typical dimensions is not significant for the impedance tuning.     

基于相位差混合处理方法的高分辨力成像技术

为了提高成像系统的分辨能力, 并尽量减小系统的复杂度, 本文将相位差波前探测技术和相位差图像恢复技术结合起来构成相位差混合处理方法, 给出了点目标和扩展目标情况下混合处理方法的数值仿真结果, 并针对点目标情况进行了实验验证. 实验表明, 在像差较大的情况下, 直接用事后处理方法无法得到满意的结果. 在三种湍流强度下, 经混合方法处理后得到光斑的半高宽分别由自适应光学系统校正后的5.1, 5.1和5.0个像素减小到3.3, 3.2和3.0个像素. 可以看出, 利用相位差混合处理方法得到的图像明显优于单独的事后图像处理方法和自适应光学校正, 相位差混合处理方法在高分辨力成像领域有着巨大的应用潜力.     

Kinetic theory of hydrodynamic flows. I. The generalized normal solution method and its application to the drag on a sphere

We consider the flow of a dilute gas around a macroscopic heavy object. The state of the gas is described by an extended Boltzmann equation where the interactions between the gas molecules and the object are taken into account in computing the rate of change of the distribution function of the gas. We then show that the extended Boltzmann is equivalent to the usual Boltzmann equation, supplemented by boundary conditions imposed on the distribution function at the surface of the object. The remainder of the paper is devoted to a study of the solution of the extended Boltzmann equation in the case that the mean free path of a gas molecule is small compared to some characteristic dimension of the macroscopic object. We show that the Chapman-Enskog normal solution of the ordinary Boltzmann equation is not in general a solution of the extended equation near the surface of the object and must be supplemented by a boundary layer term. We then introduce a projection operator method which allows us to decompose the solution of the extended equation into a normal solution part and a boundary layer part when the gas flow is sufficiently slow. As a specific example of the method we consider the flow around a sphere, and derive the Stokes-Boussinesq form for the frequency-dependent force on the sphere for arbitrary slip coefficient. This derivation is the first one that starts from the Boltzmann equation for a general dilute gas and incorporates the effect of the boundary layer on the drag force.Work supported by the National Science Foundation.     

基于FDTD的时域混合方法及其在天线前门耦合数值模拟中的应用

强电磁脉冲环境下的平台-机载天线一体化耦合计算属于典型多尺度时域电磁计算问题,采用传统的FDTD方法数值模拟时,由于精细结构的存在导致网格量巨大,计算效率低下。介绍了一种将非均匀FDTD方法与细导线FDTD方法以及多网格集总元件FDTD方法相结合的时域混合方法,能够有效降低计算开销,结合并行计算技术,快速计算得到天线端口上耦合产生的瞬态电压和电流响应,并将该方法成功应用于无人机平台-天线一体化前门耦合数值模拟中。     

Phase transition of a diblock copolymer and homopolymer hybrid system induced by different properties of nanorods

We investigated phase transitions in a diblock copolymer–homopolymer hybrid system blended with nanorods(NRs)by using the time-dependent Ginzburg–Landau theory. We systematically studied the effects of the number, length and infiltration properties of the NRs on the self-assembly of the composites and the phase transitions occurring in the material.An analysis of the phase diagram was carried out to obtain the formation conditions of sea island structure nanorodbased aggregate, sea island structure nanorod-based dispersion, lamellar structure nanorod-based multilayer arrangement and nanowire structure. Further analysis of the evolution of the domain sizes and the distribution of the nanorod angle microphase structure was performed. Our simulation provides theoretical guidance for the preparation of ordered nanowire structures and a reference to improve the function of a polymer nanocomposite material.     

Frequency conversion in novel materials and its application to high resolution gas sensing

We have constructed a compact room-temperature mid-infrared spectrometer and gas sensor, based on quasi-phase matched difference-frequency generation in periodically poled ferroelectric crystals of the KTiOPO₄ family, namely: KTiOPO₄, KTiOAsO₄ and RbTiOAsO₄. The wide tunabilty of the spectrometer (3.1–3.75 μm) enables us to cover an entire vibrational band of gases such as methane and nitrous oxide. The high spectral resolution (1 MHz) is used to investigate the spectral profile of the hyperfine components of a single rotational transition. The sensitivity of the described spectrometer is 75 parts per million. Applications of this technology include the detection of polluting or toxic gases, biomedical sensing, atmospheric research, volcanic monitoring and industrial process control.     

Mapping deformation method and its application to nonlinear equations

An extended mapping deformation method is proposed for finding new exact travelling wave solutions of nonlinear partial differential equations (PDEs). The key idea of this method is to take full advantage of the simple algebraic mapping relation between the solutions of the PDEs and those of the cubic nonlinear Klein－Gordon equation. This is applied to solve a system of variant Boussinesq equations. As a result, many explicit and exact solutions are obtained, including solitary wave solutions, periodic wave solutions, Jacobian elliptic function solutions and other exact solutions.     

An improved acoustical wave propagator method and its application to a duct structure

The pseudospectral time-domain method has long been used to describe the acoustical wave propagation. However, due to the limitation and difficulties of the fast Fourier transform (FFT) in dealing with nonperiodic problems, the dispersion error is inevitable and the numerical accuracy greatly decreases after the waves arrive at the boundary. To resolve this problem, the Lagrange-Chebyshev interpolation polynomials were used to replace the previous FFT, which, however, brings in an additional restriction on the time step. In this paper, a mapped Chebyshev method is introduced, providing the dual benefit of preserving the spectral accuracy and overcoming the time step restriction at the same time. Three main issues are addressed to assess the proposed technique: (a) Spatial derivatives in the system operator and the boundary treatment; (b) parameter selections; and (c) the maximum time step in the temporal operator. Furthermore, a numerical example involving the time-domain evolution of wave propagation in a duct structure is carried out, with comparisons to those obtained by Euler method, the fourth-order Runge-Kutta method, and the exact analytical solution, to demonstrate the numerical performance of the proposed technique.     

Closed form solution to a second order boundary value problem and its application in fluid mechanics

The Adomian decomposition method is used by many researchers to investigate several scientific models. In this Letter, the modified Adomian decomposition method is applied to construct a closed form solution for a second order boundary value problem with singularity.     

Exact solution of a model for πd induced reactions and its application to pion-nucleus reactions

Reduction techniques are applied to πd elastic scattering and π-absorption in a theory without anti-nucleons. In a one-pion approximation we derive two sets of exact coupled-channel equations for respectively the amplitudes T_πd,NN, T_{Nδ, NN} and T_{πd, πd}, T_{d, NΔ}- Alternatively we express in terms of the absorption amplitude T_{πd, NN} available solutions for a three-body problem restricted to the πd and NΔ channels. We explicitly demonstrate that our model (which comes close to the one of Thomas, Mizutani and Koltun) strictly respects the Pauli principle and avoids double-counting. Using the same technique we determine amplitudes for the (π, 2N) reaction and for π (in)elastic scattering on general nuclei in terms of amplitudes amongst the NN, NNπ channels. Both the elastic amplitude and the πA optical potential are shown to decompose into a multiple scattering part based on an input πN amplitude without the P₁₁ partial wave and calculable absorption corrections.     

A perturbation method to the tent map based on Lyapunov exponent and its application

Perturbation imposed on a chaos system is an effective way to maintain its chaotic features. A novel parameter perturbation method for the tent map based on the Lyapunov exponent is proposed in this paper. The pseudo-random sequence generated by the tent map is sent to another chaos function — the Chebyshev map for the post processing. If the output value of the Chebyshev map falls into a certain range, it will be sent back to replace the parameter of the tent map. As a result, the parameter of the tent map keeps changing dynamically. The statistical analysis and experimental results prove that the disturbed tent map has a highly random distribution and achieves good cryptographic properties of a pseudo-random sequence. As a result, it weakens the phenomenon of strong correlation caused by the finite precision and effectively compensates for the digital chaos system dynamics degradation.