Search

The Observe of nonlinear equations is limited to diffusion of alternatively particular cases and one must supportto different strategies of approximation. In this article, we've got mentioned the stableness of 2nd order, 3rdorder linear and non-linear systems by way of function roots. In the case of non-linear system we linearize the nonlinear machine below certain distinct conditions and have a look at the stableness of essential factors of the linearized systems. We have also discussed stability of second and third order linear and non-linear differential equations are studied by characteristic roots by Liapunov’s method. Necessary theories had been offered, carried out and illustrated with examples. A self -contained idea for homogeneous linear and non-linear system of 2ndorder and 3rd order be built with the aid of the usage of fundamental concept of differential equation. The results show good agreement with the results obtained by both methods mentioned above and graphically by utilizing MATHEMATICA and MATLAB.

A study of static and dynamic properties for liquid Fe using orbital free ab-initio molecular dynamics (OF-AIMD) simulation technique at thermodynamic states near the melting point is presented for the first time. The OF-AIMD simulation method is related to the density functional theory. Different static magnitudes such as static structure factors, isothermal compressibility, pair distribution functions and coordination numbers obtained from simulation are described. And the dynamic properties for both single and collective dynamics such as dynamic structure factors, diffusion coefficients, adiabatic sound velocity, and shear viscosity are also reported. The evaluated results for static and dynamic properties are found to be good in agreement with the available experimental data. Most importantly, a comparison with some KS-AIMD results shows that the degree of accuracy of the present OF-AIMD study is as good as that of the KS-AIMD.

The traffic simulation model includes Lane Changing (LC) trajectory that should be able to provide traffic safety by informing the unknown driving trajectory. Difficult types of hindrances such as deceleration, confusion for collision, expected velocity, effects of LC action, etc. will impact LC driver behavior. This study extracts the risk factors from real data and determines the influenced factors of risk perception-based LC decision using a logistic model. Then the effects on these influenced factors are investigated by comparing the before and after LC maneuvers for LC execution. The logistic model provides the influenced factors by 81.51% accuracy of LC decision using the testing dataset (30% of full dataset). The research has found that 20.07% subject vehicle velocities increases for LC execution, and other risk factors such as gaps likely decrease that suggested they are more risk to the collision after LC execution. Therefore, this study is important for decreasing the traffic crash in LC situation.

The vicinity of the on-ramp and off-ramp in the freeway road may experience high collisions in time-varying situations. The binary decision (lane changing and lane keeping) is required in the Discretionary Lane Changing (DLC) by analysing the time-impact factors. In this research, the time-effect factors are used for the binary decision in the DLC, and the cumulative probability distribution functions of these factors are used to demonstrate the influence on the lane changing. The odd ratios of the binary logit model also show that the probability increases or decreases by increasing time of some factors. The accuracy of the decision-making model is 84% by using the Next Generation SIMulation (NGSIM) data. This model shall apply to the decision of the DLC for the next generation of autonomous vehicles on the freeway road.

Lane-changing (LC) problem may cause serious accidents or create a painful traffic jam at multi-lane roads. Existing LC simulation model was created with some limitations (less fitted, without velocity and acceleration profiles, high curvature) by using well known trajectory curve such as Hyperbolic Tangent Curve (HTC), Sine-Based Curve (SC), Polynomial Curve (PC). In this study, a new parametric curve had been proposed by using curvilinear coordinate system and fitted against Next Generation Simulation (NGSIM) real dataset. Further, new profiles of velocity and acceleration were designed using the proposed LC trajectory curve. The curvature of proposed model was zero-based curvature both at LC starting and ending points. This proposed curvature was compared with two models such as HTC and SC. The average root-mean-square-error of proposed model decreased with 1.84% for left LC and 15.48% for right LC compared to HTC model and 1.74% for left LC and 15.60% for right LC compared to SC model. Similarly, the proposed model for velocity and acceleration profiles improved significantly from PC model. The proposed parametric curve solves the gap and collision points of LC vehicle with a front vehicle and rear vehicle at target lane and can be used in real LC path planning.

Car-following analysis is a very reliable research for any kind of traffic system which gives to the drivers more important information about roads during the last sixty years. In this study, diplomatic information will be produced by using Gipps car-following-model (GCFM). Many researchers have explored the traffic system for the car drivers by avoiding any struggle into the road. For this reason, GCFM is proven to be a very effective car-following model. For analysis of the GCFM, the authors have collected the car-following data from Shanghai-Nanjing Expressway road, China. By using high resolution car-following video, MATLAB software has been used to extract the data in excel. The extracted data are compared with simulation data that has been generated from GCFM car following factor, such as position, speed, gap and headway by using MATLAB software. Here, the simulation data results show that Gipps model can validate with real trajectory data by using Goodness of Fit (Gof) model as Root Mean Square Error (RMSE).

Previous studies show that parameter value for car following model, such as, maximum and minimum headway, acceleration, and gap are necessary but there is a big error found while comparing between original and simulated data. Therefore, it is not appropriately applicable to determine the real driver behavior for the different traffic systems. In this study, the calibration method has been proposed to estimate the model parameter and to find the best fit to the car following model. Here, Intelligent Driver Model (IDM) has been used for simulating car behavior and data have been collected from NGSIM eastbound I-80 in the San Francisco Bay area in Emeryville, CA, USA. Simultaneous perturbation stochastic approximation algorithm (SPSAA) has been used as the calibration model in the system to calculate parameters. The calculation has been made by using MATLAB software. SPSAA is proven to have a very much lower error between original simulation data and real trajectory observation I-80 data. Furthermore, this paper investigates that such kinds of estimated parameter are more appropriate to be used in different traffic system.

Safe and comfortable journeys in the traffic systems greatly depend on the drivers' behaviour. Car following mode (CFM) describes the drivers' behaviour by following the paths of preceding drivers in a traffic flow. Intelligent driver model (IDM) is the most popular CFM for safe and comfortable journeys. This research compares the calibrated methods with each other for Beijing data by using genetic-algorithm (GA), sequential-quadratic-programming (SQP) and simultaneous-perturbation-stochastic-approximation (SPSA). Findings reveal that the IDM simulation parameters, such as maximum-acceleration, maximum-deceleration, desired-speed, minimum-headway and minimum-jam-distance, differ from the IDM calibration parameters by -66.21%, -36.57%, -44.98%, -98.77%, -9.76% respectively for SPSA. Findings also show that the negative percentage values represent the decrease from the IDM simulation parameters, and the positive percentage values represent the increase from the same parameters. The comparison results show that the IDM calibration parameters are more precise with SPSA than GA and SQP for safe and comfortable journeys.