Application of the conditional source-term estimation model for turbulence–chemistry interactions in a premixed flame

Conditional Source-term Estimation (CSE) is a closure model for turbulence–chemistry interactions. This model uses the first-order CMC hypothesis to close the chemical reaction source terms. The conditional scalar field is estimated by solving an integral equation using inverse methods. It was originally developed and has been used extensively in non-premixed combustion. This work is the first application of this combustion model for a premixed flame. CSE is coupled with a Trajectory Generated Low-Dimensional Manifold (TGLDM) model for chemistry. The CSE-TGLDM combustion model is used in a RANS code to simulate a turbulent premixed Bunsen burner. Along with this combustion model, a similar model which relies on the flamelet assumption is also used for comparison. The results of these two approaches in the prediction of the velocity field, temperature and species mass fractions are compared together. Although the flamelet model is less computationally expensive, the CSE combustion model is more general and does not have the limiting assumption underlying the flamelet model.     

A dual model strategy to transfer multivariate calibration models for near-infrared spectral analysis

A dual-model method is proposed for correcting the calibration model. In the method, a primary calibration model is built using the spectra of a primary instrument and a correction model is established to describe the ratios between the predicted results from the spectra of different instruments. The prediction for the spectra of secondary instrument can be achieved by correcting the prediction of the primary model. A mathematical proof is described for the existence of the correction model, and the model is investigated using a near-infrared spectroscopic dataset of plant leaf samples measured on two instruments. The results show that a precise correction model is obtained and the model can be used to correct the predictions of the primary model. The correlation coefficients between the predicted and the reference ratios are above 0.9, and the prediction error after the correction is at the same level of the primary model.     

Nonlinear optical properties in double-sided nonlinear media with Z-scan technique based on the Huygens——Fresnel principle

We present a theoretical model to analyse the propagation of a Gaussian laser beam through double-sided nonlinear media. This model is based on the Huygens--Fresnel diffraction integral method. This theoretical model is not only consistent with the cascade structure model for a small nonlinear phase-shift but also can be used for a large nonlinear phase-shift. It has been verified that it is suitable to characterize the double-sided nonlinear media compared with the cascade structure model. A good agreement between the experimental data and the results from the theoretical model is obtained. It will be useful for the design of multi-sided nonlinear materials.     

Modelling magnetic defects in antiferromagnetic alloys

A model for the distribution of magnetic moment in antiferromagnetic alloys is developed from a model for ferromagnetic alloys including a magnetic environment effect which has been successful for Ni alloys [5]. This model is compared with the Marshall model for neutron scattering from antiferromagnetic alloys, and the effect of atomic short range order on both models is discussed.     

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.     

Lattice Bhatnagar-Gross-Krook Simulations in 2-D Incompressible Magnetohydrodynamics

Lattice Boltzmann Method is recently developed within numerical schemes for simulating a variety of physical systems. In this paper a new lattice Bhatnagar-Gross-Krook (LBGK) model for two-dimensional incompressible magnetohydrodynamics (IMHD) is presented. The model is an extension of a hydrodynamics lattice BGK model with 9 velocities on a square lattice, resulting in a model with 17 velocities. Most of the existing LBGK models for MHD can be viewed as compressible schemes to simulate incompressible flows. The compressible effect might lead to some undesirable errors in numerical simulations. In our model the compressible effect has been overcome successfully. The model is then applied to the Hartmann flow, giving reasonable results.     

Lattice Bhatnagar-Gross-Krook Simulations in 2-D Incompressible Magnetohydrodynamics

Lattice Boltzmann Method is recently developed within numerical schemes for simulating a variety of physical systems. In this paper a new lattice.Bhatnagar-Gross-Krook （LBGK） model for two-dimensional incompressible magnetohydrodynamics （IMHD） is presented. The model is an extension of a hydrodynamics lattice BGK model with 9 velocities on a square lattice, resulting in a model with 17 velocities. Most of the existing LBGK models for MHD can be viewed as compressible schemes to simulate incompressible flows. The compressible effect might lead to some undesirable errors in numerical simulations. In our model the compressible effect has been overcome successfully. The model is then applied to the Hartmann flow, giving reasonable results.     

Semirealistic models of the cochlea

The aim of this paper is the introduction and comparison of consistent albeit passive mechanical models for the whole cochlea. A widely used transmission line filterbank, which hydrodynamically speaking is a long wave approximation (L model), suffers from a well-known inconsistency: its main modeling assumption is not valid within the resonance region, where most of the overall excitation takes place. In the present paper two approaches to overcome this inconsistency are discussed. One model is the average pressure (AP) model by Duifhuis, the other is obtained by a combination of a long and a short wave approximation (LS model). Considerable differences between the L and the LS model are observed. All models are compared by inserting them into the full integral equation obtained from the hydrodynamic equations and the boundary conditions. Here the LS model fares better than the AP model for small damping, whereas the opposite is true for higher damping. As expected, the L model fails badly in the resonance region.     

A multiscale gradient-dependent plasticity model for size effects

The mechanical behaviour of polycrystalline material is closely correlated to grain size. In this study, we investigate the size-dependent phenomenon in multi-phase steels using a continuum dislocation dynamic model coupled with viscoplastic self-consistent model. We developed a dislocation-based strain gradient plasticity model and a stress gradient plasticity model, as well as a combined model, resulting in a theory that can predict size effect over a wide range of length scales. Results show that strain gradient plasticity and stress gradient plasticity are complementary rather than competing theories. The stress gradient model is dominant at the initial strain stage, and is much more effective for predicting yield strength than the strain gradient model. For larger deformations, the strain gradient model is dominant and more effective for predicting size-dependent hardening. The numerical results are compared with experimental data and it is found that they have the same trend for the yield stress. Furthermore, the effect of dislocation density at different strain stages is investigated, and the findings show that the Hall–Petch relation holds for the initial strain stage and breaks down for higher strain levels. Finally, a power law to describe the size effect and the transition zone between the strain gradient and stress gradient dominated regions is developed.     

Offline estimation of decay time for an optical cavity with a low pass filter cavity model

This Letter presents offline estimation results for the decay-time constant for an experimental Fabry-Perot optical cavity for cavity ring-down spectroscopy (CRDS). The cavity dynamics are modeled in terms of a low pass filter (LPF) with unity DC gain. This model is used by an extended Kalman filter (EKF) along with the recorded light intensity at the output of the cavity in order to estimate the decay-time constant. The estimation results using the LPF cavity model are compared to those obtained using the quadrature model for the cavity presented in previous work by Kallapur et?al. The estimation process derived using the LPF model comprises two states as opposed to three states in the quadrature model. When considering the EKF, this means propagating two states and a (2×2) covariance matrix using the LPF model, as opposed to propagating three states and a (3×3) covariance matrix using the quadrature model. This gives the former model a computational advantage over the latter and leads to faster execution times for the corresponding EKF. It is shown in this Letter that the LPF model for the cavity with two filter states is computationally more efficient, converges faster, and is hence a more suitable method than the three-state quadrature model presented in previous work for real-time estimation of the decay-time constant for the cavity.     

An exactly solvable model for the large polaron

We present an exactly diagonalizable model Hamiltonian for the large polaron derived by analyzing the variational ansatz by Haga-Larsen (HL) for the Fröhlich Hamiltonian. The lowest energy eigenvalue of the model Hamiltonian for fixed wave numbers reproduces the energy of the variational ansatz by Haga-Larsen and is, therefore, an upper bound with respect to the corresponding energy eigenvalue of the Fröhlich Hamiltonian. This is valid for any momentum which is proven by extending the Haga-Larsen approach. Furthermore, since all integrations can be performed analytically, the model Hamiltonian is easily tractable. The energy eigenvalue spectrum of the model Hamiltonian is studied below and above the phonon-emission threshold. The quality of the model Hamiltonian is determined by the variational ansatz of Haga and Larsen. Incorporating an improved energy-momentum relation, a generalized model Hamiltonian is derived possessing a larger validity range with respect to the coupling strength. Furthermore, a second exactly diagonalizable model Hamiltonian based on improved Wigner-Brillouin perturbation theory due to Warmenbol, Peeters, and Devreese (WPD) is presented. It is briefly demonstrated that one is able to construct all mentioned model Hamiltonians also in the 2D polaron problem. In contrast to the 3D case, where the HL-type model Hamiltonian possesses the higher quality for any momentum, in the 2D case, it works well only for small momenta. For large momenta, only the WPD-type model Hamiltonian describes the energy-momentum relation correctly. We demonstrate the usefulness of the model Hamiltonian concept by exactly calculating the one-electron Green’s function for all mentioned model Hamiltonians and comment why significant advantages of the model Hamilton concept for the treating of low-dimensional systems (planar semiconducting quantum-well structures) can be expected.     

相变过程的格子Boltzmann方法模拟

应用Shan提出的伪势多相模型替代R-K着色模型,建立一种新的描述气液相变过程的格子Boltzmann理论模型,模拟蒸发(高密度转化为低密度)过程.改进了计算效率,且得到较好的计算结果.同时应用该模型从孔隙尺度模拟了多孔介质中的相变现象,验证了该模型模拟复杂相变问题的可行性.     

A new ignition time model applied to super knock

An ignition time model is developed to model super knock in a compression engine. The model assumes that thermoacoustic interaction is the primary mechanism for the onset of super knock. By ignoring diffusive effects, a simple transport equation for the time to ignition of a fluid particle is derived. The significantly reduced cost of the chemistry model allows for complex hydrocarbon fuels to be simulated. Additionally, a zonal model for the secondary ignition of a charge due to the action of an expanding flame is developed. The flame compresses the unburned gas, causing the temperature and pressure to rise, which yields a pre-ignition in the unburned gas before the charge is engulfed by the flame. It is shown that the ignition time model compares well to the detailed chemical model with less than 1% difference in the prediction of ignition delay. Using this ignition time model, a multi-dimensional simulation of super knock in a rapid compression machine corresponding to the configuration of Wang et al. [1] is performed. It is found that interaction of the shock with the flame and the side wall of the cylinder significantly enhances the strength of the shock, and the in-cylinder pressure exceeds 300 bar. From the pressure rise predicted by the simulation, it is concluded that simulated ignition is a super knock event. Since the ignition time model excludes diffusive effects on the chemistry, it is proposed that acoustic resonance of the cylinder is the primary driver in the development of super knock for the configuration under examination and that inhomogeneous ignition due to transient flame compression could be a key mechanism for super knock.     

Validity of the limp model for porous materials: a criterion based on the Biot theory

The validity of using the limp model for porous materials is addressed in this paper. The limp model is derived from the poroelastic Biot model assuming that the frame has no bulk stiffness. Being an equivalent fluid model accounting for the motion of the frame, it has fewer limitations than the usual equivalent fluid model assuming a rigid frame. A criterion is proposed to identify the porous materials for which the limp model can be used. It relies on a new parameter, the frame stiffness influence (FSI), based on porous material properties. The critical values of FSI under which the limp model can be used are determined using a one-dimensional analytical modeling for two boundary sets: absorption of a porous layer backed by a rigid wall and radiation of a vibrating plate covered by a porous layer. Compared with other criteria, the criterion associated with FSI provides information in a wider frequency range and can be used for configurations that include vibrating plates.     

A generalized Westervelt equation for nonlinear medical ultrasound

A model equation is derived for nonlinear medical ultrasound. Unlike the existing models, which use spatial coordinates, material coordinates are used and hence a model for a heterogeneous medium is able to be derived. The equation is a generalization of the Westervelt equation, and includes the nonlinearity, relaxation, and heterogeneity of soft tissue. The validity of the generalized Westervelt equation as a model equation for a Piola-Kirchoff acoustic pressure and as an equation for the acoustic pressure is discussed. In the second case it turns out that the model follows from two geometric approximations which are valid when the radius of curvature of the phase fronts is much larger than the particle displacements. The model is exact for plane waves and includes arbitrary nonlinearity in the stress-strain relation.     

Integrability of the Rabi model

The Rabi model is a paradigm for interacting quantum systems. It couples a bosonic mode to the smallest possible quantum model, a two-level system. I present the analytical solution which allows us to consider the question of integrability for quantum systems that do not possess a classical limit. A criterion for quantum integrability is proposed which shows that the Rabi model is integrable due to the presence of a discrete symmetry. Moreover, I introduce a generalization with no symmetries; the generalized Rabi model is the first example of a nonintegrable but exactly solvable system.     

基于守恒高阶模型的动态交通分配建模与仿真

针对路网中的动态交通分配问题,采用高阶守恒模型（CHO）进行建模与数值研究,并推广高阶守恒模型二进二出路口的Riemann问题;同时将高阶守恒模型与动态网络加载（DNL）模型相结合,通过变分不等式对动态网络加载模型进行分析.数值模拟采用一阶有限体积法求解高阶守恒模型,同时采用梯度下降方法迭代求解动态网络加载模型的变分不等式问题,最终以动态用户最优条件为目标实现分配均衡.数值结果表明CHO模型与DNL模型结合解决动态交通分配问题是可行的,对传统模型的研究有一定的指导意义.     

A ray model for hard parallel noise barriers in high-rise cities

A ray model is developed and validated for prediction of the insertion loss of hard parallel noise barriers placed in an urban environment either in front of a row of tall buildings or in a street canyon. The model is based on the theory of geometrical acoustics for sound diffraction at the edge of a barrier and multiple reflections by the ground, barrier and fa?ade surfaces. It is crucial to include the diffraction and multiple reflection effects in the ray model as they play important roles in determining the overall sound pressure levels for receivers located between the fa?ade and the near-side barrier. Comparisons of the ray model with a wave-based boundary element formulation show reasonably good agreement over a broad frequency range. Results of scale model experimental studies are also presented. It is demonstrated that the ray model agrees tolerably well with the scale model experimental data.     

Changing spectrum estimation

An autoregressive (AR) model with time varying coefficients is used for the modeling of non-stationary covariance time series. A stochastically perturbed linear constraint model is presented as a model of time varying AR coefficients. The overall model for the time series is fitted by using the Kalman filter and Akaike's AIC criterion. An estimate of a changing spectrum is obtained by the fitted model and the fixed interval smoother Examples are given to illustrate the procedure.     

Numerical Analysis of the Rebellious Voter Model

The rebellious voter model, introduced by Sturm and Swart (2008), is a variation of the standard, one-dimensional voter model, in which types that are locally in the minority have an advantage. It is related, both through duality and through the evolution of its interfaces, to a system of branching annihilating random walks that is believed to belong to the ‘parity-conservation’ universality class. This paper presents numerical data for the rebellious voter model and for a closely related one-sided version of the model. Both models appear to exhibit a phase transition between noncoexistence and coexistence as the advantage for minority types is increased. For the one-sided model (but not for the original, two-sided rebellious voter model), it appears that the critical point is exactly a half and two important functions of the process are given by simple, explicit formulas, a fact for which we have no explanation.