scholarly journals Investigation of Chaotic and Strange Nonchaotic Phenomena in Nonautonomous Wien-Bridge Oscillator with Diode Nonlinearity

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
R. Rizwana ◽  
I. Raja Mohamed
Keyword(s):  
Numerical Simulation ◽  
Mean Square Displacement ◽  
Dynamical Variable ◽  
Mean Square ◽  
Maximal Lyapunov Exponent ◽  
Simulation Results ◽  
The One ◽  
Nonlinear Behaviors ◽  
Bifurcation Process ◽  
Electronic Oscillator

We have studied the chaotic and strange nonchaotic phenomena of a simple quasiperiodically forced Wien bridge oscillator circuit with diode as the only nonlinearity in this electronic oscillator system responsible for various nonlinear behaviors. Both the experimental results and the numerical simulation results for their confirmation are provided to show the bifurcation process. Various measures used for the numerical confirmation of SNA are power spectrum, maximal Lyapunov exponent, path of translational variables, mean square displacement, projection of poincaré section, log-log plot, and autocorrelation function. Based upon the numerical results, the birth of SNAs has been identified in the band merging route, intermittency route, and blowout bifurcation route. In addition, the birth of SNAs has been analyzed with peculiar mechanism, namely, “0-1 Test” employing the one state dynamical variable.

scholarly journals Numerical simulation of the fractional Langevin equation

2012 ◽  
Vol 16 (2) ◽  
pp. 357-363 ◽  
Author(s):  
Peng Guo ◽  
Changpin Li ◽  
Fanhai Zeng
Keyword(s):  
Numerical Simulation ◽  
Numerical Algorithm ◽  
Langevin Equation ◽  
Mean Square Displacement ◽  
Mean Square ◽  
Dynamic Behaviors ◽  
Fractional Langevin Equation ◽  
The Mean

In this paper, we study the fractional Langevin equation, whose derivative is in Caputo sense. By using the derived numerical algorithm, we obtain the displacement and the mean square displacement which describe the dynamic behaviors of the fractional Langevin equation.

Pollutant Transport Model and Numerical Simulation in Landfill Site

2012 ◽  
Vol 443-444 ◽  
pp. 424-429
Author(s):  
Ying Zhao ◽  
Qiang Xue ◽  
Lei Liu ◽  
Bing Liang
Keyword(s):  
Numerical Simulation ◽  
Control System ◽  
Simulation Model ◽  
Landfill Leachate ◽  
Transport Model ◽  
Control Measure ◽  
Underground Water ◽  
Seepage Control ◽  
Simulation Results ◽  
The One

The simulation model for describing the transportation and transformation of landfill leachate pollutant in landfill, soil and underground water was established. Taking Wuhan Changshankou landfill for example, the numerical simulation was carried out. The simulation results showed that if there’s no any seepage control measure, the groundwater and soil under landfill will be polluted seriously after MSW was filled; the highest pollutant concetration in landfill was about 25000, and the one in groundwater and soil was about 20000; at the thirtieth year, the pollutant concetration in groundwater and soil still remained up to 10000 although the one in landfill was about 0. The simulation results also showed that the vertical stonewall can’t be used as a nature, and artificial seepage control system must be used.

Numerical Simulation in Rear Axlecap of Automobile Drawing Process and Optimization of Technological Parameters

2010 ◽  
Vol 148-149 ◽  
pp. 1171-1176
Author(s):  
Ju Hua Huang ◽  
Li Xian Li ◽  
Ying Ying Wan ◽  
Jun Tuan Guo
Keyword(s):  
Numerical Simulation ◽  
Rear Axle ◽  
Element Model ◽  
Drawing Process ◽  
Work Efficiency ◽  
Technological Parameters ◽  
Simulation Results ◽  
Quality Of Products ◽  
The One

This paper takes the rear axle cap which is a typical automobile covering part as the research object. 3D and finite element model of it are built, and the drawing process is simulated with Dynaform, then the technological parameters are analyzed and optimized based on the simulation results, finally the part is compared with the one that is processed in practice. The results show that this method is easy and feasible, it not only increase the work efficiency greatly but also improve the quality of products.

NONLINEAR BEHAVIORS OF GEAR SHIFTING DIGITAL PHASE LOCKED LOOPS

2012 ◽  
Vol 22 (08) ◽  
pp. 1250204 ◽  
Author(s):  
XI CHEN ◽  
BINGO WING-KUEN LING ◽  
LI-MIN SUN
Keyword(s):  
Numerical Simulation ◽  
Adaptive Control ◽  
Steady State ◽  
Initial Conditions ◽  
Phase Locked Loops ◽  
Control Parameters ◽  
Dynamical Behaviors ◽  
Digital Phase Locked Loops ◽  
Simulation Results ◽  
Nonlinear Behaviors

Applying gear shifting algorithms to the implementation of Phase Locked Loops (PLLs) can significantly improve their performances. However, the behaviors of gear shifting digital PLLs (GSDPLLs) have not been fully studied due to the existence of newly adaptive control parameters. These parameters play a very important role in the design of GSDPLLs. In this paper, various nonlinear behaviors of GSDPLLs including the steady state periodic behaviors, divergent behaviors and chaotic behaviors, are studied. In particular, the effects of the initial conditions of GSDPLLs on their dynamical behaviors are investigated. The obtained results are useful for the design of GSDPLLs. Numerical simulation results are presented for illustrations.

Hyperchaos in the Fractional-Order Lü System and its Synchronization

2014 ◽  
Vol 905 ◽  
pp. 464-468 ◽  
Author(s):  
Tian Zeng Li ◽  
Yu Wang
Keyword(s):  
Numerical Simulation ◽  
Fractional Order ◽  
Control Parameter ◽  
Coupling Method ◽  
Lü System ◽  
Simulation Results ◽  
The One ◽  
Lu System

The hyperchaotic behaviors in the fractional hyperchaotic Lü system are studied. And we give the lowest orders for generating hyperchaos with different control parameter. Hyperchaos synchronization of Lü system is theoretically and numerically studied using the one-way coupling method. The numerical simulation results demonstrate the effectiveness and validity of the method.

scholarly journals A New Explicit Magnus Expansion for Nonlinear Stochastic Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 183
Author(s):  
Xiaoling Wang ◽  
Xiaofei Guan ◽  
Pei Yin
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Stochastic Equation ◽  
Iterative Technique ◽  
Magnus Expansion ◽  
Nonlinear Stochastic Differential Equations ◽  
Drift Term ◽  
Theoretical Predictions ◽  
Simulation Results ◽  
The One

In this paper, based on the iterative technique, a new explicit Magnus expansion is proposed for the nonlinear stochastic equation d y = A ( t , y ) y d t + B ( t , y ) y ∘ d W . One of the most important features of the explicit Magnus method is that it can preserve the positivity of the solution for the above stochastic differential equation. We study the explicit Magnus method in which the drift term only satisfies the one-sided Lipschitz condition, and discuss the numerical truncated algorithms. Numerical simulation results are also given to support the theoretical predictions.

The Simulation and Experiment Study on the Gas Flow in the No-Loaded and Cold Vacuum High-Pressure Gas Quenching Furnace

2011 ◽  
Vol 48-49 ◽  
pp. 1310-1314
Author(s):  
Zhi Jian Wang ◽  
Xiao Feng Shang
Keyword(s):  
Numerical Simulation ◽  
High Pressure ◽  
Gas Flow ◽  
Flow Distribution ◽  
Simulation Method ◽  
Flow State ◽  
Gas Quenching ◽  
Simulation And Experiment ◽  
Simulation Results ◽  
The One

In order to learn gas flow state in the vacuum high pressure gas quenching furnace, this paper simulates and tests the gas flow under the no-loaded and cold state. Hot wire anemometer is used to measure the speeds of some feature points, on the one hand to provide boundary conditions for the numerical simulation, and on the other hand to compare with the numerical simulation results. FLUENT software is used to simulate the gas flow of nozzle-type vacuum high-pressure gas quenching furnace. The results show that at the center of the furnace appears high-pressure low-speed zone in which is resulted by the gas collision there, and the vortex also appears in the area around the furnace. The results mean that the cooling rate of works will be slow there. Different exit velocities of five nozzles cause the uneven flow distribution, which will affect the cooling uniformity of works. The comparison between the simulation results and the measured results shows that the error is within 10%. It means that numerical simulation method to predict gas flow is feasible and the results are reliable in high pressure gas quenching furnace.

Mean square displacement of a Brownian particle with traps. The one-dimensional case

1990 ◽  
Vol 150 (5-7) ◽  
pp. 296-298 ◽  
Author(s):  
A.M. Berezhkovskii ◽  
Yu.A. Makhnovskii ◽  
R.A. Suris
Keyword(s):  
Brownian Particle ◽  
Mean Square Displacement ◽  
Dimensional Case ◽  
Mean Square ◽  
One Dimensional ◽  
The One

scholarly journals Analysis of Mobile 3-D Radar Error Registration when Radar Sways with Platform

2013 ◽  
Vol 67 (3) ◽  
pp. 451-472
Author(s):  
L. Chen ◽  
G.H. Wang ◽  
Y. He ◽  
I. Progri
Keyword(s):  
Numerical Simulation ◽  
Kalman Filter ◽  
Lower Bound ◽  
State Vector ◽  
Time Varying ◽  
Mean Square ◽  
Dependent Variables ◽  
Simulation Results ◽  
New Variables ◽  
Mean Square Errors

For mobile radars installed on a gyro-stabilised platform (GSP) that can steadily follow an East-North-Up (ENU) frame, attitude biases (ABs) of the platform and offset biases (OBs) of the radar are linear dependent variables. Therefore ABs and OBs are unobservable in the linearized registration equations; however, when combining them as new variables, the system becomes observable, and this model has been called the unified registration model (URM). Unlike GSP mobile radars, un-stabilised GSP (or UGSP) mobile radars are installed on the platform directly and rotate with the platform simultaneously. For UGSP, it is testified that both types of biases are independent and observable because the time-varying attitude angles (AAs)1 of the platform are included in the registration equations, which destroy the dependencies of both kinds of biases and lead us to propose a completely different linearized registration model– the All Augmented Model (AAM). AAM employs all OBs and ABs in the state vector and a Kalman filter (KF) to produce their estimates. Numerical simulation results show that the estimated performance of AAM is close to the Cramér-Rao lower bound (CRLB) and that the Root Mean Square Errors (RMSEs) of the rectified measurements by using AAM are more than 500 m smaller than by URM in all directions.

scholarly journals Output Pulse Characteristics of a Mamyshev Fiber Oscillator

Photonics ◽  
2021 ◽  
Vol 8 (12) ◽  
pp. 590
Author(s):  
Haili Han ◽  
Nan-Kuang Chen ◽  
Liqiang Zhang ◽  
Yanru Xie ◽  
Zhen Tian ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Pulse Duration ◽  
Group Velocity Dispersion ◽  
Wide Spectrum ◽  
Output Pulse ◽  
Central Wavelength ◽  
Passive Fiber ◽  
Simulation Results ◽  
The One ◽  
Pulse Characteristics

The dependence of the output pulse characteristics of a Mamyshev fiber oscillator on cavity parameters is investigated in detail. We analyze the change in pulse spectrum bandwidth, pulse duration, dechirped pulse duration and chirp with the change in fiber group velocity dispersion, fiber nonlinearity, gain, and filters by putting forward a numerical model. In particular, as one of the most important components, the effect of filters bandwidth and the central wavelength interval between them is discussed. The passive fibers are classified into two kinds according to their locations in the cavity, which are the one before the gain fiber and the one after the gain fiber. Numerical simulation results show that a wide spectrum can be obtained by increasing the nonlinearity of the second passive fiber, while the change in nonlinearity of the first passive fiber has a weak effect on spectrum broadening. A wide spectrum could also be obtained by increasing the nonlinearity or the small-signal gain coefficient of the gain fiber. A Yb-doped Mamyshev fiber oscillator is demonstrated. The results show the increase in pump power, which agrees reasonably well with the numerical simulation results.

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