An asymmetric full velocity difference car-following model

This paper presents a car-following model that considers the asymmetric characteristic of the velocity differences of the vehicles in a traffic stream. The problems of the prevalent general force (GF) model and the full velocity difference (FVD) model were solved. Furthermore, the optimal velocity (OV) model, the GF model, and the FVD model are proved to be the special cases of the proposed asymmetric full velocity difference (AFVD) model. The mathematical model is presented, followed by simulation analysis which demonstrates the properties of the AFVD model.     

A comprehensive overview of a non-parametric probabilistic approach of model uncertainties for predictive models in structural dynamics

In structural dynamics, a predictive model is constructed by developing a mathematical-mechanical model of a designed system in order to predict the response of the real system which is the manufactured system realized from the designed system. The mathematical-mechanical modelling process of the designed system introduces two fundamental types of uncertainties: the data uncertainties and the model uncertainties. Uncertainties have to be taken into account for improving the predictability of the model. Model uncertainties cannot be modelled by using the usual parametric probabilistic approach. Recently, a general non-parametric probabilistic approach of model uncertainties for dynamical systems has been proposed using the random matrix theory. This paper gives a comprehensive overview of this approach in developing its foundations in simple terms and in illustrating all the concepts and the tools introduced in the general theory, by using a simple example. This paper deals with (1) notions of designed systems, real systems, mean models as predictive models, errors and uncertainties; (2) the definition of a simple example in linear elastodynamics; (3) a comprehensive overview of the non-parametric probabilistic approach of model uncertainties for predictive models in structural dynamics; (4) a summary of the random matrix ensembles which are necessary for the non-parametric modelling of random uncertainties; (5) the estimation of the dispersion parameters of the non-parametric probabilistic model using experimental data; (6) the method to solve the stochastic equation of the dynamical system with non-parametric probabilistic model of random uncertainties; (7) a numerical simulation and the validation for the simple example.     

随机森林算法的水果糖分近红外光谱测量

近年来,有关水果糖分等内部品质的近红外光谱测量方法研究很多,并有部分商业化仪器问世。但由于近红外光谱复杂多变,模型的传递性较差,往往所建模型只能针对特定品种甚至特定产地的水果。随机森林(RF)是一种基于决策树的集成算法,通过对分类回归树(CART)模型的集成来提高预测精度。相对于偏最小二乘法(PLS),多元线型回归法(MLR)等方法,随机森林回归方法对非线性数据的解析能力较强。考虑到RF模型的随机性, 通过调试决策树数量(ntree)和分裂变量数目(mtry)等变量来进行模型优选。尝试使用随机森林对不同种类的水果(苹果、梨)糖分进行预测。实验表明,对于同一种类的水果,随机森林和PLS的建模和预测结果均较好。但对于不同种类的水果,随机森林明显增加了模型的预测能力,将建模R2由PLS的0.878提高到了0.999,将建模的RMSEC由0.453降低到了0.015。经过独立的预测集样品对最优RF模型进行检验,预测R2由PLS的0.731提高到为0.888,预测RMSEP由1.148降低到0.334。随机森林在对多种水果糖分预测时,具有明显的优势。这一研究证明了随机森林有望应用于多种水果糖分的近红外光谱测定,进而解决模型的普适性和传递性问题。     

A Specific Case of Generalized Einstein-aether Theories

With the dark energy phenomena explored over a decade,in this present work we discuss a specific case of the generalized Einstein-aether theories,in which the modified Friedmann equation is similar to that in the Dvali-Gabadadze-Porrati(DGP) brane world model.We compute the joint statistic constraints on model parameters in this specific case by using the recent type Ia supernovae(SNe Ia) data,the cosmic microwave background(CMB) shift parameter data,and the baryonic acoustic oscillations(BAOs) data traced by the Sloan Digital Sky Survey(SDSS).Furthermore,we analyze other constrains from the observational Hubble parameter data(OHD).The comparison with the standard cosmological model(cosmological constant Λ cold dark matter(ΛCDM) model) is clearly shown;also we comment on the interesting relation between the coupling constant M in this model and the special accelerate scale in the modified Newtonian dynamics(MOND) model initially given by Milgrom with the hope for interpreting the galaxy rotation curves without introducing mysterious dark matter.     

On the algebraic formulation of collective models. I. The mass quadrupole collective model

This paper is the first in a series of three which together present a microscopic formulation of the Bohr-Mottelson (BM) collective model of the nucleus. In this article the mass quadrupole collective (MQC) model is defined and shown to be a generalization of the BM model. The MQC model eliminates the small oscillation assumption of BM and also yields the rotational and CM(3) submodels by holonomic constraints on the MQC configuration space. In addition, the MQC model is demonstrated to be an algebraic model, so that the state space of the MQC model carries an irrep of a Lie algebra of microscopic observables, the MQC algebra. An infinite class of new collective models is then given by the various inequivalent irreps of this algebra. A microscopic embedding of the BM model is achieved by decomposing the representation of the MQC algebra on many-particle state space into its irreducible components. In the second paper this decomposition is studied in detail. The third paper presents the symplectic model, which provides the realization of the collective model in the harmonic oscillator shell model.     

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.     

The phase structure of mixed lattice gauge theories

The mixed compact-non-compact U(1) model is shown to be equivalent to a compact U(1) Higgs model. It is argued that the mixed SO(3)-SU(2) model is dual to an SO(3) gauge theory coupled to a scalar field in the fundamental representation. The degrees of freedom are Z(2) monopoles and charges or, in a dual picture, monopoles and loops. This picture is supported by a Monte Carlo calculation. The implications for the SU(2) transition region are discussed.     

多腔体心脏磁场模型的研究与应用

利用核磁共振图像(MRI)中提取的人体和心脏边界,根据边界元方法(BEM)建立了一个考虑左、右心房和心室的多腔体心脏磁场模型.分析了用该模型得到的36通道心脏磁场数据和特定时刻的磁场图.并在此基础上,研究了完全性右束支传导阻滞(CRBBB)和完全性左束支传导阻滞(CLBBB)病人ST-T段的心脏电活动.结果显示,用移动单电流偶极子模拟的单束支电兴奋传导所产生的磁场图与用超导量子干涉器(SQUID)测量的CRBBB/CLBBB病人数据绘制的心脏复极时的心磁图(MCG)十分相似.结果表明,该多腔体心脏BEM模型可用于CLBBB/CRBBB病人心脏磁场逆问题的研究.此外,文中给出了两个评价指标:测量平面上多腔体与单腔体的心脏磁场强度极大值之比,以及两种模型的36个测量点上磁场强度均方根之比.分析表明,多腔体心脏模型更贴近人体心脏的实际情况.该模型中心脏组织电导率参数的取值,以及等效电流偶极子的位置和个数决定了磁场的强度和分布.     

基于无导数优化方法的数值模式误差估计

初始场误差和模式误差是制约数值预报准确率的两个关键因素,本文主要考虑利用历史观测资料实现时空演变的模式误差的估计问题.通过把模式误差综合考虑成为准确模式中的未知项,把历史资料看作是带有未知项的准确模式的特解,构造了求解时空演变的模式误差项的反问题及其最优控制问题.给出了一个解决最优控制问题的无导数优化方法,该方法的优点是不需要建立原数值模式的切线性模式与伴随模式,它只需在增加一个外强迫项的基础上运行原数值模式即可实现模式误差项的最优估计.关于Burgers方程的算例表明,无论模式的初始状态是否准确已知,无导数优化方法都能有效解决时空演变的模式误差的最优估计问题,它为实际业务模式利用历史数据提取模式误差信息并显著地改进预报效果提供了一种方便可行的数值方法与理论依据.     

Directed self-organized critical patterns emerging from fractional Brownian paths

We discuss a family of clusters corresponding to the region whose boundary is formed by a fractional Brownian path y(i) and by the moving average function . Our model generates fractal directed patterns showing spatio-temporal complexity, and we demonstrate that the cluster area, length and duration exhibit the characteristic scaling behavior of SOC clusters. The function C_n(i) acts as a magnifying lens, zooming in (or out) the ‘avalanches’ formed by the cluster construction rule, where the magnifying power of the zoom is set by the value of the amplitude window n. On the basis of the construction rule of the clusters and of the relationship among the exponents, we hypothesize that our model might be considered to be a generalized stochastic directed model, including the Dhar–Ramaswamy (DR) model and the stochastic models as particular cases. As in the DR model, the growth and annihilation of our clusters are obtained from the set of intersections of two random walk paths, and we argue that our model is a variant of the directed self-organized criticality scheme of the DR model.     

可见光/近红外光谱技术快速测定橙汁柠檬酸含量

为了快速无损测定橙汁的柠檬酸含量,提出了一种用可见光/近红外光谱技术进行检测的新方法。选用高效液相色谱法作为光谱柠檬酸测定的标定方法。采用平滑点数为5的移动平滑法对原始光谱进行预处理消除噪声。由于采集的光谱数据量非常大,为了减少建模时间,建模之前采用小波变换对经过预处理的大量光谱数据进行降维压缩,并在Matlab7.01中通过自编程序实现此变换。利用光谱专用分析软件Unscrambler 9.5,对压缩后的新变量进行分析,建立偏最小二乘(PLS)校正模型。考虑到不同小波基及分解尺度对数据压缩的影响,采用预测平方和PRESS值最小的评价标准,选择最佳的小波基Db4及分解尺度5。用于本实验的样本总数为40,其中30个样本进行建模,10个用于预测。用校正集相关系数(r)和标准偏差(SEC)作为校正模型的评价指标,预测结果采用预测相关系数(r)和预测标准偏差(SEP)来评定。文章将基于小波变换的PLS模型与直接建立的PLS模型进行了比较,偏最小二乘法结合小波变换的模型预测相关系数为r=0.901, 预测标准偏差SEP=0.937;而由PLS建立的模型其预测相关系数r=0.849,预测标准偏差SEP=1.662。由此可见,由偏最小二乘法结合小波变换所得模型效果优于单独使用偏最小二乘法的结果。     

Mass Generation in a Fermionic Model with Finite Range Time Dependent Interactions

Bardeen, Cooper and Schrieffer in their paper on the theory of superconductivity introduced a model of interacting fermions (BCS model) in which the (instantaneous) interaction is only between electrons of opposite momentum and spin (Cooper pairs). Subsequently it was claimed that in the thermodynamic limit the BCS model is equivalent to the (exactly solvable) quadratic mean field BCS model in which the phenomenon of mass generation is present; a rigorous proof of this equivalence is however still an open problem. In this paper we consider an interacting fermionic model in which the Cooper pairs interact through a finite range time dependent interaction. For this model (quartic in the fermions and not solvable) we are able to prove the generation of mass in the thermodynamic limit and its equivalence with the mean field BCS model. The proof is achieved by a convergent perturbation expansion about mean field theory.     

Modeling of pedestrian evacuation based on the particle swarm optimization algorithm

By applying the evolutionary algorithm of Particle Swarm Optimization (PSO), we have developed a new pedestrian evacuation model. In the new model, we first introduce the local pedestrian’s density concept which is defined as the number of pedestrians distributed in a certain area divided by the area. Both the maximum velocity and the size of a particle (pedestrian) are supposed to be functions of the local density. An attempt to account for the impact consequence between pedestrians is also made by introducing a threshold of injury into the model. The updating rule of the model possesses heterogeneous spatial and temporal characteristics. Numerical examples demonstrate that the model is capable of simulating the typical features of evacuation captured by CA (Cellular Automata) based models. As contrast to CA-based simulations, in which the velocity (via step size) of a pedestrian in each time step is a constant value and limited in several directions, the new model is more flexible in describing pedestrians’ velocities since they are not limited in discrete values and directions according to the new updating rule.     

便携式近红外光谱仪对涤/棉混纺织物的快速无损鉴别

利用便携式近红外光谱仪对376个涤/棉混纺织物进行研究,利用定量分析模型中的偏最小二乘法(partical least squares,PLS)作为校正方法,结合涤/棉混纺织物中涤、棉含量设定的定性鉴别系数,建立了涤/棉混纺织物的半定量-定性分析校正模型。该模型对涤/棉混纺织物进行定性鉴别的同时得出其相对含量,分析结果具有半定量性质。在建模过程中,采用Savitzky-Golay导数法,消除噪声和基线漂移对光谱的影响,并研究了波段选择和不同预处理方法对定性校正模型的影响。纯棉的主要吸收峰位于1 400~1 600 nm,纯涤的主要吸收峰位于1 600~1 800 nm,随着涤或棉含量的增加,其相应的吸收峰强度增强,因此,建模波段以涤、棉主要吸收峰区间为基本波段,进行双向扩展,得到最佳波长区间1 100~2 500 nm(相关系数0.6,波点数934)。利用所建校正模型对验证集样本进行预测,结果表明,在1 100~2 500 nm处,预处理方法为Savitzky-Golay导数、多元散射校正与均值中心化相结合时,该模型评价参数较佳,其中RC(校正集相关系数)0.978,RP(验证集相关系数)0.940,SEC(校正标准差)1.264,SEP(预测标准差)1.590,样品预测正确率达93.4%。表明该定性分析校正模型能够较好地对涤/棉混纺织物进行半定量-定性预测。     

Development and validation of a new LBM-MRT hybrid model with enthalpy formulation for melting with natural convection

This article presents a new model to simulate melting with natural convection of a phase change material. For the phase change problem, the enthalpy formulation is used. Energy equation is solved by a finite difference method, whereas the fluid flow is solved by the multiple relaxation time (MRT) lattice Boltzmann method. The model is first verified and validated using the data from the literature. Then, the model is applied to a tall brick filled with a fatty acid eutectic mixture and the results are presented. The main results are (1) the spatial convergence rate is of second order, (2) the new model is validated against data from the literature and (3) the natural convection plays an important role in the melting process of the fatty acid mixture considered in our work.     

A parametric study of cochlear input impedance

In this paper various aspects of the cat cochlear input impedance Zc (omega) are implemented using a transmission line model having perilymph viscosity and a varying cross-sectional scalae area. These model results are then compared to the experimental results of Lynch et al. [J. Acoust. Soc. Am. 72, 108-130 (1982)]. From the model, the following observations are made about the cochlear input impedance: (a) Scalae area variations significantly alter the model Zc (omega); (b) the use of anatomically measured area improves the fits to the experimental data; (c) improved agreement between model and experimental phase is obtained when perilymph viscosity and tapering are included in the cochlear model for frequencies below approximately 150 Hz; (d) when model scalae tapering and perilymph viscosity are chosen to match physiological conditions, the effect of the helicotrema impedance on Zc (omega) is insignificant; and (e) the cochlear map, which is defined as the position of the basilar membrane peak displacement as a function of stimulus frequency, can have an important effect on Zc (omega) for frequencies below 500 Hz. A nonphysiological cochlear map can give rise to cochlear standing waves, which result in oscillations in Zc (omega). Scalae tapering and perilymph viscosity contribute significantly to the damping of these standing waves. These observations should dispel the previous notion that Zc (omega) is determined solely by parameters of the cochlea close to the stapes, and the notion that Zc (omega) is dominated by the helicotrema at low frequencies.     

Isomorphic shell model for closed-shell nuclei

The classical part of the isomorphic model for closed-shell nuclei is presented based on two physical assumptions, namely (a) the nucleons of a closed shell nucleus, considered at their most probable positions, are in an instantaneous dynamic equilibrium on spherical shells, and (b) the dimensions of the shells are determined by their close packing given that a neutron and a proton are represented by hard spheres of definite sizes. The first assumption leads to the instantaneous angular structure, and the second to the instantaneous radial structure of closed-shell nuclei. Applications of the model coming from this classical part alone and presented here are structural justification of all magic numbers, neutron (proton) and charge rms radii, nuclear densities of closed-shell nuclei, and Coulomb, kinetic, and binding energies. All the predictions are in good agreement with experimental data. A characteristic novelty of the isomphic model is that assumption (a) is related to the independent particle model, and assumption (b) to the liquid-drop model. The isomorphic model may provide a link between these two basic nuclear physics models since it incorporates features of both.     

Coloring random triangulations

We introduce and solve a two-matrix model for the tri-coloring problem of the vertices of a random triangulation. We present three different solutions: (i) by orthogonal polynomial techniques, (ii) by use of a discrete Hirota bilinear equation, (iii) by direct expansion. The model is found to lie in the universality class of pure two-dimensional quantum gravity, despite the non-polynomiality of its potential.     

Enhancing Gauge Symmetries of Non-Abelian Supersymmetric Chern-Simons Model

In this article, we study gauge symmetries of the Non-Abelian Supersymmetric Chern-Simons model (SCS) of SU(2) group at (2+1)-dimensions in the framework of the formalism of constrained systems. Since, broken gauge symmetries in this physical system lead to the presence of nonphysical degrees of freedom, the Non-Abelian SCS model is strictly constrained to second-class constraints. Hence, by introducing some auxiliary fields and using finite order BFT method, we obtain a gauge symmetric model by converting second-class constraint to first-class ones. Ultimately, the partition function of the model is obtained in the extended phase space.     

Traffic flow characteristics in a mixed traffic system consisting of ACC vehicles and manual vehicles: A hybrid modelling approach

In this paper, we have investigated traffic flow characteristics in a traffic system consisting of a mixture of adaptive cruise control (ACC) vehicles and manual-controlled (manual) vehicles, by using a hybrid modelling approach. In the hybrid approach, (i) the manual vehicles are described by a cellular automaton (CA) model, which can reproduce different traffic states (i.e., free flow, synchronised flow, and jam) as well as probabilistic traffic breakdown phenomena; (ii) the ACC vehicles are simulated by using a car-following model, which removes artificial velocity fluctuations due to intrinsic randomisation in the CA model. We have studied the traffic breakdown probability from free flow to congested flow, the phase transition probability from synchronised flow to jam in the mixed traffic system. The results are compared with that, where both ACC vehicles and manual vehicles are simulated by CA models. The qualitative and quantitative differences are indicated.