Novel formulation of nonlocal electrostatics

The accurate modeling of the dielectric properties of water is crucial for many applications in physics, computational chemistry, and molecular biology. This becomes possible in the framework of nonlocal electrostatics, for which we propose a novel formulation allowing for numerical solutions for the nontrivial molecular geometries arising in the applications mentioned before. Our approach is based on the introduction of a secondary field psi, which acts as the potential for the rotation free part of the dielectric displacement field D. For many relevant models, the dielectric function of the medium can be expressed as the Green's function of a local differential operator. In this case, the resulting coupled Poisson (-Boltzmann) equations for psi and the electrostatic potential phi reduce to a system of coupled partial differential equations. The approach is illustrated by its application to simple geometries.     

Source implementation to eliminate low-frequency artifacts in finite difference time domain room acoustic simulation

The finite difference time domain (FDTD) method is a numerical technique that is straight forward to implement for the simulation of acoustic propagation. For room acoustics applications, the implementation of efficient source excitation and frequency dependent boundary conditions on arbitrary geometry can be seen as two of the most significant problems. This paper deals with the source implementation problem. Among existing source implementation methods, the hard source implementation is the simplest and computationally most efficient. Unfortunately, it generates a large low-frequency modulation in the measured time response. This paper presents a detailed investigation into these side effects. Surprisingly, some of these side effects are found to exist even if a transparent source implementation is used. By combing a time limited approach with a class of more natural source pulse function, this paper develops a source implementation method in FDTD that is as simple and computationally as efficient as a hard source implementation and yet capable of producing results that are virtually the same as a true transparent source. It is believed that the source implementation method developed in this paper will provide an improvement to the practical usability of the FDTD method for room acoustic simulation.     

A comprehensive ESPI based system for combined measurement of shape and deformation of electronic components

This paper describes a very simple and reliable procedure for measuring shape and deformation of electronic components with a single experimental set-up. The procedure is based on two electronic speckle pattern interferometry (ESPI) techniques referred to as conventional ESPI and phase shifting ESPI (PS-ESPI). The present research is motivated by the fact that mismatch in thermal expansion coefficients of the different materials included in electronic packaging (EP) may cause mechanical failures since thermal stresses will change sharply through subsequent loading cycles. ESPI is particularly suitable for measurements on EP since it allows us to perform non–contact testing of non-planar heterogeneous surfaces. It is apparent that gathering detailed topographic information will certainly help us to measure accurately surface deformations of EP along with modeling correctly numerical analysis.As is known, the accuracy of results obtained with ESPI may be significantly improved by phase shifting techniques (PST). Therefore, this paper compares the relative merits of different phase-stepping strategies in order to find which strategy will perform the best for the optical set-up utilized in the experiments. Preliminary investigations on a standard specimen under three-point-bending served to choose properly the optical set-up and phase-stepping procedure which yield the best fringe visibility. Four-phases achieved the best fringe visibility and the minimum number of invalid pixels.These information have been utilized in the experimental campaign on standard and surface mounted technology (SMT) electronic components. ESPI and PS-ESPI have been used for analyzing the transient state and the steady state of devices, respectively. From the experimental results obtained here, it appears possible to measure strains induced by thermal loading cycles. The experimental set-up, based on the Lendeertz's interferometer, proved itself also able to contour specimen surface at a good level of detail. Remarkably, by using the same set-up for deformation and shape measurements we can preserve the pixel by pixel relationship between displacements and surface depth which will hold true if correlation between different exposures is not destroyed.The results obtained in this research justify using PS-ESPI in order to understand better failure mechanisms of electronic components. This fact along with the exact knowledge of object shape may be particularly useful in the different design stages (including FEM modeling and analysis) of electronics for special applications.     

一种适用于任意阶空间差分时域有限差分方法的色散介质通用吸收边界条件算法

基于伸展坐标完全匹配层方程和辅助微分方程 方法, 给出了一种在时域有限差分(FDTD) 计算中适用于常见色散介质的通用边界条件算法. 该算法适用于任意阶的FDTD空间差分, 并且由于所采用的D-H方程独立于计算区域, 所以可以被用于截断任意电介质. 数值试验结果表明, 与卷积完全匹配层 算法相比较, 所提出的吸收边界条件算法不仅通用性强、 计算复杂度低、 计算时间短, 并且吸收效果有明显的提高.     

An FDTD analysis of photonic crystal waveguides comprising third-order nonlinear materials

A finite difference time domain (FDTD) study of two-dimensional photonic crystals containing nonlinear materials is presented in this paper. An appropriate Z-transform oriented formulation of the FDTD method for the simulation of third-order nonlinear Kerr- and Raman-type media is analyzed and applied to model nonlinear photonic crystal waveguide structures. For their reflectionless termination a novel perfectly matched layer (PML) is proposed and evaluated comparatively to other periodic and inhomogeneous absorbers. Furthermore, the absorbing efficiency of the proposed PML is investigated varying its parameters.     

An evaluation of solution algorithms and numerical approximation methods for modeling an ion exchange process

The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte-Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward difference formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte-Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC–FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.     

Radiative properties of optical board embedded with optical black holes

Unique radiative properties, such as wavelength-selective transmission or absorption, have been intensively studied. Historically, geometries for wavelength-selective of light absorption were developed based on metallic periodical structures, which were only applied in the case of TM wave incidence due to the excitation of surface plasmons. In this paper, we develop an alternative approach to selective wavelength of light absorption (both TE and TM waves), based on an optical board periodical embedded with optical black holes. Numerical work was carried out to study such structure’s radiative properties within the wavelength range of 1-100 μm. The electromagnetic wave transmission through such a structure is predicted by solving Maxwell’s equations using the finite-difference time-domain (FDTD) method. Spectral absorptance varies with the period of optical black holes. When the incidence wavelength is much larger than the inner core radius, most of the light energy will be transmitted through the inner core. Otherwise, the energy will be mainly absorbed. Numerical results of the radiative properties of the optical board with different incidence wavelengths are also obtained. The effect of the oblique incidence wave is investigated. This study helps us gain a better understanding of the radiative properties of an optical board embedded with optical black holes and develop an alternative approach to selective light absorption.     

MC-Smooth: A mass-conserving,smooth vorticity–velocity formulation for multi-dimensional flows

A novel vorticity–velocity formulation of the Navier–Stokes equations – the Mass-Conserving, Smooth (MC-Smooth) vorticity–velocity formulation – is developed in this work. The governing equations of the MC-Smooth formulation include a new second-order Poisson-like elliptic velocity equation, along with the vorticity transport equation, the energy conservation equation, and N_spec species mass balance equations. In this study, the MC-Smooth formulation is compared to two pre-existing vorticity–velocity formulations by applying each formulation to confined and unconfined axisymmetric laminar diffusion flame problems. For both applications, very good to excellent agreement for the simulation results of the three formulations has been obtained. The MC-Smooth formulation requires the least CPU time and can overcome the limitations of the other two pre-existing vorticity–velocity formulations by ensuring mass conservation and solution smoothness over a broader range of flow conditions. In addition to these benefits, other important features of the MC-Smooth formulation include: (1) it does not require the use of a staggered grid, and (2) it does not require excessive grid refinement to ensure mass conservation. The MC-Smooth formulation is a computationally attractive approach that can effectively extend the applicability of the vorticity–velocity formulation.     

Finite difference computation of head-related transfer function for human hearing

Modeling the head-related transfer function (HRTF) is a key to many applications in spatial audio. To understand and predict the effects of head geometry and the surrounding environment on the HRTF, a three-dimensional finite-difference time domain model (3D FDTD) has been developed to simulate acoustic wave interaction with a human head. A perfectly matched layer (PML) is used to absorb outgoing waves at the truncated boundary of an unbounded medium. An external source is utilized to reduce the computational domain size through the scattered-field/total-field formulation. This numerical model has been validated by analytical solutions for a spherical head model. The 3D FDTD code is then used as a computational tool to predict the HRTF for various scenarios. In particular, a simplified spherical head model is compared to a realistic head model up to about 7 kHz. The HRTF is also computed for a realistic head model in the presence of a wall. It is demonstrated that this 3D FDTD model can be a useful tool for spatial audio applications.     

Complex-envelope alternating-direction-implicit FDTD method for simulating active photonic devices with semiconductor/solid-state media

A complex-envelope (CE) alternating-direction-implicit (ADI) finite-difference time-domain (FDTD) approach to treat light-matter interaction self-consistently with electromagnetic field evolution for efficient simulations of active photonic devices is presented for the first time (to our best knowledge). The active medium (AM) is modeled using an efficient multilevel system of carrier rate equations to yield the correct carrier distributions, suitable for modeling semiconductor/solid-state media accurately. To include the AM in the CE-ADI-FDTD method, a first-order differential system involving CE fields in the AM is first set up. The system matrix that includes AM parameters is then split into two time-dependent submatrices that are then used in an efficient ADI splitting formula. The proposed CE-ADI-FDTD approach with AM takes 22% of the time as the approach of the corresponding explicit FDTD, as validated by semiconductor microdisk laser simulations.     

Discrete vs. continuum-scale simulation of radiative transfer in semitransparent two-phase media

The mathematical formulation of the continuum approach to radiative transfer modeling in two-phase semi-transparent media is numerically validated by comparing radiative fluxes computed by (i) direct, discrete-scale and (ii) continuum-scale approaches. The analysis is based on geometrical optics. The discrete-scale approach uses the Monte Carlo ray-tracing applied directly to real 3D geometry measured by computed tomography. The continuum-scale approach is based on a set of continuum-scale radiative transfer equations and associated radiative properties, and employs the Monte Carlo ray-tracing for computations of radiative fluxes and for computations of the radiative properties. The model two-phase media are reticulate porous ceramics and a particle packed bed, each composed of semitransparent solid and fluid phases. The results obtained by the two approaches are in good agreement within the limits of statistical uncertainty. The continuum-scale approach leads to a reduction in computational time by approximately one order of magnitude, and is therefore suited to treat radiative transfer problems in two-phase media in a wide range of engineering applications.     

Entropy Generation Analysis in Turbulent Reacting Flows and Near Wall: A Review

This paper provides a review of different contributions dedicated thus far to entropy generation analysis (EGA) in turbulent combustion systems. We account for various parametric studies that include wall boundedness, flow operating conditions, combustion regimes, fuels/alternative fuels and application geometries. Special attention is paid to experimental and numerical modeling works along with selected applications. First, the difficulties of performing comprehensive experiments that may support the understanding of entropy generation phenomena are outlined. Together with practical applications, the lumped approach to calculate the total entropy generation rate is presented. Apart from direct numerical simulation, numerical modeling approaches are described within the continuum formulation in the framework of non-equilibrium thermodynamics. Considering the entropy transport equations in both Reynolds-averaged Navier–Stokes and large eddy simulation modeling, different modeling degrees of the entropy production terms are presented and discussed. Finally, exemplary investigations and validation cases going from generic or/and canonical configurations to practical configurations, such as internal combustion engines, gas turbines and power plants, are reported. Thereby, the areas for future research in the development of EGA for enabling efficient combustion systems are highlighted. Since EGA is known as a promising tool for optimization of combustion systems, this aspect is highlighted in this work.     

Modeling a sensitive pressure and temperature sensor using rectangular PCF by 2-D FDTD technique

We propose a sensitive pressure and temperature sensor depends on hollow core rectangular photonic crystal fiber. The proposed modeling is carried out by implementing 2-D finite difference time domain (FDTD) method. The two parameters like pressure and temperature plays a vital role in reservoir engineering to increase the production rates of oil well and our sensor technique is depend on the transmission peak wavelength shift which is caused by temperature/pressure change, and geometrical parameter of the structure of rectangular PCF. Here we have done simulation for various work using 2-D FDTD method application to sensing. We have shown the proposed design which provides the sensitivity with linear dependence of the resonance wavelength over refractive index of PCF holes at a operating wavelength of 1.55 μm.     

High-order FDTD methods for transverse electromagnetic systems in dispersive inhomogeneous media

This Letter introduces a novel finite-difference time-domain (FDTD) formulation for solving transverse electromagnetic systems in dispersive media. Based on the auxiliary differential equation approach, the Debye dispersion model is coupled with Maxwell's equations to derive a supplementary ordinary differential equation for describing the regularity changes in electromagnetic fields at the dispersive interface. The resulting time-dependent jump conditions are rigorously enforced in the FDTD discretization by means of the matched interface and boundary scheme. High-order convergences are numerically achieved for the first time in the literature in the FDTD simulations of dispersive inhomogeneous media.     

The element level time domain (ELTD) method for the analysis of nano-optical systems: II. Dispersive media

We study a 3-dimensional, dual-field, fully explicit method for the solution of dispersive Maxwell's equations in the time domain on unstructured, tetrahedral grids. In a previous paper, we investigated the element level time domain (ELTD) algorithm for solving electromagnetic problems with parameters independent of the excitation frequency content, i.e. nondispersive materials. The suitability of the ELTD method for the numerical analysis of nanometer structured systems in the optical frequencies was thoroughly studied. This paper introduces the generalization of the method and its implementation as a computer code for problems with dispersive material properties. We profit from the ELTD formulation in conjunction with the auxiliary differential equation (ADE) approach for modeling dispersion. Examples with analytical solutions are solved and verified in order to benchmark the method. Eventually, to demonstrate the potential of the method, we consider the structure of a single field emitter and solve for the electromagnetic fields when illuminated by a plane wave. We have obtained a flexible and versatile method of 2nd order accuracy that is applicable to both dispersive and nondispersive problems with a wide range of nano-optical configurations.     

Simple and Efficient PML Algorithm for Truncating Nonlinear FDTD Domains Based on the Z -Transform Method

Based on the Z-transform method, a simple, efficient and unsplit-field implementation of the Stretched Coordinate Perfectly Matched Layer (SC-PML) is proposed for truncating the nonlinear dispersive Finite Difference Time Domain (FDTD) lattices. In addition, the nonlinear FDTD formulations using the Z-transform method are reformulated with the advantage of a simple derivative process. The proposed algorithm is validated through two numerical examples carried out in one dimensional and two dimensional domains which include Lorentz dispersion as well as Kerr and Raman nonlinearities.     

Number-resolved master equation approach to quantum measurement and quantum transport

In addition to the well-known Landauer–Büttiker scattering theory and the nonequilibrium Green’s function technique for mesoscopic transports, an alternative (and very useful) scheme is quantum master equation approach. In this article, we review the particle-number (n)-resolved master equation (n-ME) approach and its systematic applications in quantum measurement and quantum transport problems. The n-ME contains rich dynamical information, allowing efficient study of topics such as shot noise and full counting statistics analysis. Moreover, we also review a newly developed master equation approach (and its n-resolved version) under self-consistent Born approximation. The application potential of this new approach is critically examined via its ability to recover the exact results for noninteracting systems under arbitrary voltage and in presence of strong quantum interference, and the challenging non-equilibrium Kondo effect.     

Regge Calculus: A Unique Tool for Numerical Relativity

The application of Regge calculus, a lattice formulation of general relativity, is reviewed in the context of numerical relativity. Particular emphasis is placed on problems of current computational interest, and the strengths and weaknesses of the lattice approach are highlighted. Several new and illustrative applications are presented, including initial data for the head on collision of two black holes, and the time evolution of vacuum axisymmetric Brill waves.     

Solving Schrödinger Bridges via Maximum Likelihood

The Schrödinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution. As well as applications in the natural sciences, problems of this kind have important applications in machine learning such as dataset alignment and hypothesis testing. Whilst the theory behind this problem is relatively mature, scalable numerical recipes to estimate the Schrödinger bridge remain an active area of research. Our main contribution is the proof of equivalence between solving the SBP and an autoregressive maximum likelihood estimation objective. This formulation circumvents many of the challenges of density estimation and enables direct application of successful machine learning techniques. We propose a numerical procedure to estimate SBPs using Gaussian process and demonstrate the practical usage of our approach in numerical simulations and experiments.