Stochastic modeling of coherent phenomena in strongly inhomogeneous media

A procedure of numerical simulation for coherent phenomena in multiply scattering media is developed on the basis of the juxtaposition of a Monte Carlo stochastic method with an iterative approach to the solution of the Bethe-Salpeter equation. The time correlation function and the interference component of coherent backscattering are calculated for scalar and electromagnetic fields. The results of simulation are in good agreement with experimental results, as well as with theoretical results obtained by generalizing the Milne solution.     

Kernel principal component analysis for stochastic input model generation

Stochastic analysis of random heterogeneous media provides useful information only if realistic input models of the material property variations are used. These input models are often constructed from a set of experimental samples of the underlying random field. To this end, the Karhunen–Loève (K–L) expansion, also known as principal component analysis (PCA), is the most popular model reduction method due to its uniform mean-square convergence. However, it only projects the samples onto an optimal linear subspace, which results in an unreasonable representation of the original data if they are non-linearly related to each other. In other words, it only preserves the first-order (mean) and second-order statistics (covariance) of a random field, which is insufficient for reproducing complex structures. This paper applies kernel principal component analysis (KPCA) to construct a reduced-order stochastic input model for the material property variation in heterogeneous media. KPCA can be considered as a nonlinear version of PCA. Through use of kernel functions, KPCA further enables the preservation of higher-order statistics of the random field, instead of just two-point statistics as in the standard Karhunen–Loève (K–L) expansion. Thus, this method can model non-Gaussian, non-stationary random fields. In this work, we also propose a new approach to solve the pre-image problem involved in KPCA. In addition, polynomial chaos (PC) expansion is used to represent the random coefficients in KPCA which provides a parametric stochastic input model. Thus, realizations, which are statistically consistent with the experimental data, can be generated in an efficient way. We showcase the methodology by constructing a low-dimensional stochastic input model to represent channelized permeability in porous media.     

Breakdown of a Nonlinear Stochastic Nipah Virus Epidemic Models through Efficient Numerical Methods

Background: Nipah virus (NiV) is a zoonotic virus (transmitted from animals to humans), which can also be transmitted through contaminated food or directly between people. According to a World Health Organization (WHO) report, the transmission of Nipah virus infection varies from animals to humans or humans to humans. The case fatality rate is estimated at 40% to 75%. The most infected regions include Cambodia, Ghana, Indonesia, Madagascar, the Philippines, and Thailand. The Nipah virus model is categorized into four parts: susceptible (S), exposed (E), infected (I), and recovered (R). Methods: The structural properties such as dynamical consistency, positivity, and boundedness are the considerable requirements of models in these fields. However, existing numerical methods like Euler–Maruyama and Stochastic Runge–Kutta fail to explain the main features of the biological problems. Results: The proposed stochastic non-standard finite difference (NSFD) employs standard and non-standard approaches in the numerical solution of the model, with positivity and boundedness as the characteristic determinants for efficiency and low-cost approximations. While the results from the existing standard stochastic methods converge conditionally or diverge in the long run, the solution by the stochastic NSFD method is stable and convergent over all time steps. Conclusions: The stochastic NSFD is an efficient, cost-effective method that accommodates all the desired feasible properties.     

A stochastic mixed finite element heterogeneous multiscale method for flow in porous media

A computational methodology is developed to efficiently perform uncertainty quantification for fluid transport in porous media in the presence of both stochastic permeability and multiple scales. In order to capture the small scale heterogeneity, a new mixed multiscale finite element method is developed within the framework of the heterogeneous multiscale method (HMM) in the spatial domain. This new method ensures both local and global mass conservation. Starting from a specified covariance function, the stochastic log-permeability is discretized in the stochastic space using a truncated Karhunen–Loève expansion with several random variables. Due to the small correlation length of the covariance function, this often results in a high stochastic dimensionality. Therefore, a newly developed adaptive high dimensional stochastic model representation technique (HDMR) is used in the stochastic space. This results in a set of low stochastic dimensional subproblems which are efficiently solved using the adaptive sparse grid collocation method (ASGC). Numerical examples are presented for both deterministic and stochastic permeability to show the accuracy and efficiency of the developed stochastic multiscale method.     

An adaptive emission model for Monte Carlo simulations in highly inhomogeneous media represented by stochastic particle fields

Traditional Monte Carlo ray-tracing (MCRT) methods for continuous participating media are not applicable in media represented by point masses (or stochastic particles) frequently encountered in combustion modeling. In the authors’ previous work several ray models and particle models have been proposed for radiation simulations in such media. In the present paper an efficient emission scheme is developed for MCRT in highly inhomogeneous media represented by particle fields. Ray energies are limited to a narrow range to reduce statistical error, by having particles emit numbers of photons proportional to their emissive power (including combination of weak particles). A method to evaluate the radiative heat source, required by the overall energy equation, is also developed. A particle field representing the highly inhomogeneous medium in a turbulent jet flame is employed to test the proposed methods.     

多路音频信号的数字化光纤传输系统

在信息传输的各个领域中，光纤作为传输信号媒介的应用得以迅速发展。光纤的音频多路数字化传输也是光纤领域目前开发的热点课题之一，它充分利用光纤本身所具有的各种特点，使音频信号的传输更有效、更可靠。本文利用串行信号的时分复用技术，完成了多路音频数字化信号的光纤传输。提出信号传输中,数据信号和控制信号的复用及解复用解决方法。     

复相介质平稳随机场热传导方程的多尺度模型与计算

本文讨论复相介质(含孔洞)的热传导问题,其中几何形状,大小和材料分布形态构成一平稳随机场,针对这一问题,提出多尺度模型和算法,并给出数值实验结果。     

Analysis and design of electromagnetic band gap structures with stratified and inhomogeneous media

In this study, a generalized and easy to use method based on Hill's equation and chain matrix concept is used to analyze the electromagnetic wave propagation in stratified dielectric and inhomogeneous media with arbitrary profiles.Numerical simulations are performed to compute the reflection and transmission of several Electromagnetic Bandgap (EBG) structures for various permittivity profiles and given polarization as well as incidence angles of driving fields.Multilayer structures are analyzed and optimized to enhance their selectivity performances. Obtained results agree excellently well with other published data.     

Acceleration of test particles in one-dimensional random force fields

The aim of this research is to study acceleration of test particles in random space-time dependent force fields, by using or generalizing some tools developed in particular for the study of stochastic differential equations with time-dependent random parameters. Preliminary results given here are: a generalization of the Markov property to space-time, connected with a condition of non-repeated interaction, two-valued fields having this property allowing exact application of the widely used Bourret (or first order smoothing) approximation; the energy spectrum at exit of a bounded slab containing a space-dependent random field, the transmission coefficient of the slab and the mean energy gain of transmitted particles.     

A STOCHASTIC NEWMARK METHOD FOR ENGINEERING DYNAMICAL SYSTEMS

The purpose of this study is to develop a stochastic Newmark integration principle based on an implicit stochastic Taylor (Ito-Taylor or Stratonovich-Taylor) expansion of the vector field. As in the deterministic case, implicitness in stochastic Taylor expansions for the displacement and velocity vectors is achieved by introducing a couple of non-unique integration parameters, α and β. A rigorous error analysis is performed to put bounds on the local and global errors in computing displacements and velocities. The stochastic Newmark method is elegantly adaptable for obtaining strong sample-path solutions of linear and non-linear multi-degree-of freedom (m.d.o.f.) stochastic engineering systems with continuous and Lipschitz-bounded vector fields under (filtered) white-noise inputs. The method has presently been numerically illustrated, to a limited extent, for sample-path integration of a hardening Duffing oscillator under additive and multiplicative white-noise excitations. The results are indicative of consistency, convergence and stochastic numerical stability of the stochastic Newmark method (SNM).     

Reflection and transmission of Laguerre Gaussian beam from uniaxial anisotropic multilayered media

Based on angular spectrum expansion and 4 × 4 matrix theory, the reflection and transmission characteristics of a Laguerre Gaussian(LG) beam from uniaxial anisotropic multilayered media are studied. The reflected and transmitted beam fields of an LG beam are derived. In the case where the principal coordinates of the uniaxial anisotropic media coincide with the global coordinates, the reflected and transmitted beam intensities from a uniaxial anisotropic slab and three-layered media are numerically simulated. It is shown that the reflected intensity components of the incident beam, especially the TM polarized incident beam, are smaller than the transmitted intensity components. The distortion of the reflected intensity component is more evident than that of the transmitted intensity component. The distortion of intensity distribution is greatly affected by the dielectric tensor and the thickness of anisotropic media. We finally extend the application of the method to general anisotropic multilayered media.     

Green functions of scalar particles in stochastic fields

A variational method of evaluating functional integrals is proposed. This method is used to investigate the asymptotic behavior of the scalar-particle Green functions in stochastic fields. The equations for the Green functions in Euclidean space in stochastic fields are written. The solutions of these equations are represented in the form of a functional integral and then they are averaged over Gaussian stochastic fields. The variational method formulated above is used to evaluate the asymptotic behavior of these Green functions. The following equations are considered in this paper: a stochastic contribution to the mass of a scalar particle, a gauge stochastic field, and a weak stochastic contribution to the flat metric of Euclidean space.     

Modulated spatial transmission signals in the photonic bandgap

This paper describes the spatial transmission of electromagnetically induced transparency and four-wave mixing signals in the photonic bandgap structure, which are modulated using the adjustable parameters of light fields. The spatial transmission patterns of the relevant signals are experimentally investigated with respect to the optical nonlinear Kerr effect that occurs in the modulation process. The experimental results reveal the spatial transmission patterns of the probe transmission and the four-wave mixing signals, such as focusing, defocusing, shifting, and spatial splitting. This study explains how the tunable parameters of light fields and their interactions with each other can regulate the spatial transmission of the light fields by changing the refractive indices of media, which provides a new research perspective and a degree of experimental technology support for more efficient all-optical communications.     

腔体内传输线耦合的电磁仿真软件与传输线方程的混合算法

研究了一种有限积分法软件与传输线方程相结合的混合算法,用于解决复杂电磁环境下屏蔽腔体内传输线的电磁耦合问题。利用有限积分法软件实现屏蔽腔体的建模,仿真得到腔体内部空间电磁场分布,并设置电场探针提取出传输线的激励场。利用传输线方程建立腔体内传输线的耦合模型,将得到的传输线激励场引入到传输线方程作为等效分布电压和电流源。利用时域有限差分(FDTD)格式对传输线方程进行离散,从而迭代求解出传输线终端负载上的电压和电流响应。通过与文献以及传统数值算法的计算结果进行对比,验证混合算法的正确性。研究表明,该混合算法在模拟电大尺寸腔体内传输线的电磁耦合方面,具有较高的精度和计算效率。     

Effective-dielectric-constant method for the problem of wave diffraction by a close-spaced dielectric grating

A simple method for determination of effective dielectric constants is proposed that allows a close-spaced two-dimensionally periodic dielectric layer with rectangular elements to be replaced by a homogeneous and anisotropic layer of the same thickness. The method makes it unnecessary to solve the complicated problem of determination of the fields within the elements for calculation of the plane-wave reflection and transmission coefficients in a long-wave approximation, which considerably simplifies the calculations. Comparison with known solutions obtained by rigorous methods for one-dimensionally periodic gratings shows exact agreement of the results. The method is easily extended to magnetodielectric media as well as to multicomponent media, including those whose dielectric constants are functions of the coordinate perpendicular to the layer.Academician A. L. Mints Radio-Engineering Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 3-4, pp. 286–294, March–April, 1993.     

随机结构多孔介质等效热导率数值计算

本文对二维颗粒弥散多孔介质的辐射导热耦合等效热导率进行了数值计算研究。首先采用随机生成结构方法(Random generate-growth method,RGGM)生成实际多孔材料的复杂结构。在此基础上,采用离散坐标法及有限容积法求解了复杂结构内部辐射导热耦合换热,进而计算得到材料的等效热导率。根据建立的材料随机结构模型及等效热导率数值计算模型,分别研究了衰减系数、弥散相体积分数、温度等因素对材料等效热导率的影响,并将数值计算结果与理论计算结果进行对比,吻合较好,反映出模型用于预测实际多孔材料等效热导率的有效性。     

The Exergy Losses Analysis in Adiabatic Combustion Systems including the Exhaust Gas Exergy

The entropy generation analysis of adiabatic combustion systems was performed to quantify the exergy losses which are mainly the exergy destroyed during combustion inside the chamber and in the exhaust gases. The purpose of the present work was therefore: (a) to extend the exergy destruction analysis by including the exhaust gas exergy while applying the hybrid filtered Eulerian stochastic field (ESF) method coupled with the FGM chemistry tabulation strategy; (b) to introduce a novel method for evaluating the exergy content of exhaust gases; and (c) to highlight a link between exhaust gas exergy and combustion emissions. In this work, the adiabatic Sandia flames E and F were chosen as application combustion systems. First, the numerical results of the flow and scalar fields were validated by comparison with the experimental data. The under-utilization of eight stochastic fields (SFs), the flow field results and the associated scalar fields for the flame E show excellent agreement contrary to flame F. Then, the different exergy losses were calculated and analyzed. The heat transfer and chemical reaction are the main factors responsible for the exergy destruction during combustion. The chemical exergy of the exhaust gases shows a strong relation between the exergy losses and combustion emission as well as the gas exhaust temperature.     

Angular spectrum approach for the computation of group and phase velocity surfaces of acoustic waves in anisotropic materials

The decomposition of an acoustic wave into its angular spectrum representation creates an effective base for the calculation of wave propagation effects in anisotropic media. In this method, the distribution of acoustic fields is calculated in arbitrary planes from the superposition of the planar components with proper phase shifts. These phase shifts depend on the ratio of the distance between the planes to the normal component of the phase slowness vector. In anisotropic media, the phase shifts depend additionally on the changes of the slowness with respect to the direction of the propagation vector and the polarization. Those relations are obtained from the Christoffel equation. The method employing the fast Fourier transformation algorithm is especially suited for volume imaging in anisotropic media, based on holographic detection in transmission of acoustic waves generated by a point source. This technique is compared with measurements on crystals performed by phase-sensitive scanning acoustic microscopy.     

New spectroscopic method for the determination of optical rotatory dispersion

A new spectroscopic methodology is proposed to measure optical rotatory dispersion(ORD)of optically active media.ORD is obtained from a three-step phase shifting algorithm using transmission spectra taken at three independent probing angles.Optical rotation angles of four sugar solutions are investigated.The results obtained by using the new method show excellent agreement with the reference data,indicating the new method can be used as a reliable way for studying ORD of optically active media.