A modified NaSch model with density-dependent randomization for traffic flow

Based on the Nagel-Schreckenberg (NaSch) model of traffic flow, a modified cellular automaton (CA) traffic model with the density-dependent randomization (abbreviated as the DDR model) is proposed to simulate traffic flow. The fundamental diagram obtained by simulation shows the ability of this modified NaSch model to capture the essential features of traffic flow, e.g., synchronized flow, metastable state, hysteresis and phase separation at higher densities. Comparisons are made between this DDR model and the NaSch model, also between this DDR model and the VDR model. And the underlying mechanism is analyzed. All these results indicate that the presented model is reasonable and more realistic.     

一类大气浅水波方程的近似解

研究了一类非线性浅水波方程，利用同论映射理论和方法，得到了相应系统的近似解. 关键词： 浅水波 非线性 同伦映射 近似解     

The N-soliton solution of a two-component modified nonlinear Schrödinger equation

The N-soliton solution is presented for a two-component modified nonlinear Schrödinger equation which describes the propagation of short pulses in birefringent optical fibers. The solution is found to be expressed in terms of determinants. The proof of the solution is carried out by means of an elementary theory of determinants. The generalization of the 2-component system to the multi-component system is discussed as well as a (2+1)-dimensional nonlocal equation arising from its continuum limit.     

Combined Wronskian solutions to the 2D Toda molecule equation

By combining two pieces of bi-directional Wronskian solutions, molecule solutions in Wronskian form are presented for the finite, semi-infinite and infinite bilinear 2D Toda molecule equations. In the cases of finite and semi-infinite lattices, separated-variable boundary conditions are imposed. The Jacobi identities for determinants are the key tool employed in the solution formulations.     

Understanding the adsorption of 4H-1,2,4-triazole derivatives on mild steel surface in molar hydrochloric acid

This study examines the use of some 4H-triazole derivatives, namely 3,5-diphenyl-4H-1,2,4-triazole (DHT), 3,5-bis(4-pyridyl)-4H-1,2,4-triazole (4-PHT) and 3,5-bis(4-methyltiophenyl)-4H-1,2,4-triazole (4-MTHT) for corrosion and dissolution protection of mild steel in normal hydrochloric acid solution. The inhibiting efficiency of the different additives is evaluated by means of weight loss and electrochemical techniques such as ac impedance measurements and polarisation curves. The experimental results obtained reveal that 4-MTHT is the best effective inhibitor and the inhibition efficiency is found to be in the following order: 4-MTHT > 4-PHT > DHT. The variation in inhibitive efficiency mainly depends on the type and nature of the substituents present in the inhibitor molecule. Polarisation curves show that theses triazoles are mixed-type inhibitors in 1 M HCl. The inhibition efficiency increases with 4H-triazole derivatives concentration and attains the maximum value of 99.6% in the case of 4-MTHT at 5 × 10⁻⁴ M. The results obtained from weight loss electrochemical studies were in reasonable agreement. The adsorption of 4H-triazole derivatives on the steel surface obeys to the Langmuir isotherm model. The thermodynamic data of adsorption and activation are determined and discussed. The fundamental thermodynamic functions were used to glean important information about the 4H-triazoles inhibitory behaviour. Molecular modeling was used to get better insight, about structural and electronic effects in relation to the inhibition efficiencies.     

Three Types of Expression in Dark-Soliton Perturbation Theory Based on Squared Jost Solutions

Three types of expression in the dark-soliton perturbation theory based on squared Jost solutions are invesgigaged in ghis paper. It is shown that there are three formally different results about the effects of perturbagion on a dark soliton, and it is proved by means of a transformation between two integral variables that they are essentially equivalent.     

2种天然絮凝剂对薄荷水提液的絮凝研究和比较

为了克服传统中药提取工艺中有效成分损失率高、生产成本高、工艺复杂等缺点,采用天然无毒的高分子絮凝剂壳聚糖和矿物絮凝剂膨润土对薄荷水提液进行净化除杂.利用间歇试验方法,以絮凝率和总黄酮损失率作为指标,考察了絮凝剂用量、温度、搅拌速度等因素对絮凝效果的影响,并利用正交试验确定了薄荷水提液的最佳絮凝条件.结果表明,壳聚糖絮凝效果优于膨润土,当壳聚糖投加量为0.741g·L-1,絮凝温度30℃,搅拌速度40r·min-1时,絮凝率可达到92.75%,总黄酮损失率为10.75%.在此基础上,通过絮凝前后粒径比较及絮体形态分析,对中药絮凝机理进行了深入探讨.     

Nizhnik-Novikov-Veselov方程的非李点对称及其精确解(英文)

对于非线性物理系统的有限对称群,一个新的方法被提出.将该方法作用于Nizhnik-Novikov-Veselov(NNV)方程,李点和非李点对称能同时得到,而使用经典李群法只能得到李点对称.最后,通过对称变化群能得到许多新的孤子解.     

Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order

In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin-Bona-Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method.     

Dimer Coverings on the Sierpinski Gasket

We present the number of dimer coverings N _d (n) on the Sierpinski gasket SG _d (n) at stage n with dimension d equal to two, three, four or five. When the number of vertices, denoted as v(n), of the Sierpinski gasket is an even number, N _d (n) is the number of close-packed dimers. When the number of vertices is an odd number, no close-packed configurations are possible and we allow one of the outmost vertices uncovered. The entropy of absorption of diatomic molecules per site, defined as , is calculated to be ln (2)/3 exactly for SG ₂. The numbers of dimers on the generalized Sierpinski gasket SG _d,b (n) with d=2 and b=3,4,5 are also obtained exactly with entropies equal to ln (6)/7, ln (28)/12, ln (200)/18, respectively. The number of dimer coverings for SG ₃ is given by an exact product expression, such that its entropy is given by an exact summation expression. The upper and lower bounds for the entropy are derived in terms of the results at a certain stage for SG _d (n) with d=3,4,5. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of with d=3,4,5 can be evaluated with more than a hundred significant figures accurate. This paper is written during the Lung-Chi Chen visit to PIMS, University of British Columbia. The author thanks the institute for the hospitality.