scholarly journals Bifurcation of Safe Basins and Chaos in Nonlinear Vibroimpact Oscillator under Harmonic and Bounded Noise Excitations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Rong Haiwu ◽  
Wang Xiangdong ◽  
Luo Qizhi ◽  
Xu Wei ◽  
Fang Tong
Keyword(s):  
Monte Carlo ◽  
Random Noise ◽  
Sudden Change ◽  
Melnikov Method ◽  
Critical Value ◽  
Stochastic Bifurcation ◽  
Bifurcation Parameter ◽  
Bounded Noise ◽  
Chaotic Motions ◽  
Melnikov Integral

The erosion of the safe basins and chaotic motions of a nonlinear vibroimpact oscillator under both harmonic and bounded random noise is studied. Using the Melnikov method, the system’s Melnikov integral is computed and the parametric threshold for chaotic motions is obtained. Using the Monte-Carlo and Runge-Kutta methods, the erosion of the safe basins is also discussed. The sudden change in the character of the stochastic safe basins when the bifurcation parameter of the system passes through a critical value may be defined as an alternative stochastic bifurcation. It is founded that random noise may destroy the integrity of the safe basins, bring forward the occurrence of the stochastic bifurcation, and make the parametric threshold for motions vary in a larger region, hence making the system become more unsafely and chaotic motions may occur more easily.

Chaotic Motions of a Damped and Driven Morse Oscillator

2013 ◽  
Vol 459 ◽  
pp. 505-510
Author(s):  
Liang Qiang Zhou ◽  
Fang Qi Chen
Keyword(s):  
Numerical Methods ◽  
Dissociation Energy ◽  
Melnikov Method ◽  
Critical Value ◽  
Numerical Results ◽  
Morse Oscillator ◽  
Chaotic Motions ◽  
Critical Curves

With the Melnikov method and numerical methods, this paper investigate the chaotic motions of a damped and driven morse oscillator. The critical curves separating the chaotic and non-chaotic regions are obtained, which demonstrate that when the Morse spectroscopic term is fixed, for the case of large values of the period of the excitation, the critical value for chaotic motions decreases as the dissociation energy increases; while for the case of small values of the period of the excitation, the critical value for chaotic motions increases as the dissociation energy increases. It is also shown that when the dissociation energy is fixed, the critical value for chaotic motions always increase as the dissociation energy increases for any value of the period of the excitation. Some new dynamical phenomena are presented for this model. Numerical results verify the analytical ones.

Structural Modal Multifurcation With Internal Resonance: Part 2—Stochastic Approach

1993 ◽  
Vol 115 (2) ◽  
pp. 193-201 ◽  
Author(s):  
R. A. Ibrahim ◽  
B. H. Lee ◽  
A. A. Afaneh
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Axial Load ◽  
Random Excitation ◽  
Stochastic Bifurcation ◽  
Density Level ◽  
Analytical Treatment ◽  
Asymmetric Mode ◽  
Non Gaussian ◽  
Gaussian Closure

Stochastic bifurcation in moments of a clamped-clamped beam response to a wide band random excitation is investigated analytically, numerically, and experimentally. The nonlinear response is represented by the first three normal modes. The response statistics are examined in the neighborhood of a critical static axial load where the normal mode frequencies are commensurable. The analytical treatment includes Gaussian and non-Gaussian closures. The Gaussian closure fails to predict bifurcation of asymmetric modes. Both non-Gaussian closure and numerical simulation yield bifurcation boundaries in terms of the axial load, excitation spectral density level, and damping ratios. The results of both methods are in good agreement only for symmetric response characteristics. In the neighborhood of the critical bifurcation parameter the Monte Carlo simulation yields strong nonstationary mean square response for the asymmetric mode which is not directly excited. Experimental and Monte Carlo simulation exhibit nonlinear features including a shift of the resonance peak in the response spectra as the excitation level increases. The observed shift is associated with a widening effect in the response bandwidth.

Adaptive Sampling Based on GH-Distance for Realistic Image Synthesis

2014 ◽  
Vol 998-999 ◽  
pp. 806-813
Author(s):  
Jian Wang ◽  
Qing Xu
Keyword(s):  
Monte Carlo ◽  
Computer Graphics ◽  
Adaptive Sampling ◽  
Random Noise ◽  
Image Synthesis ◽  
Simulation Methods ◽  
Path Tracing ◽  
Complex Scenes ◽  
Realistic Image ◽  
Better Than

Realistic image synthesis technology is an important part in computer graphics. Monte Carlo based light simulation methods, such as Monte Carlo path tracing, can deal with complex lighting computations for complex scenes, in the field of realistic image synthesis. Unfortunately, if the samples taken for each pixel are not enough, the generated images have a lot of random noise. Adaptive sampling is attractive to reduce image noise. This paper proposes a new GH-distance based adaptive sampling algorithm. Experimental results show that the method can perform better than other similar ones.

scholarly journals Neutrino Transport with the Monte Carlo Method. II. Quantum Kinetic Equations

2021 ◽  
Vol 257 (2) ◽  
pp. 55
Author(s):  
Chinami Kato ◽  
Hiroki Nagakura ◽  
Taiki Morinaga
Keyword(s):  
Monte Carlo ◽  
Technical Problem ◽  
Sudden Change ◽  
Kinetic Equations ◽  
Mean Free Path ◽  
High Energy ◽  
The Monte Carlo Method ◽  
Numerical Treatments ◽  
Quantum Feature ◽  
Statistical Noise

Abstract Neutrinos have a unique quantum feature as flavor conversions. Recent studies suggested that collective neutrino oscillations play important roles in high-energy astrophysical phenomena. The quantum kinetic equation (QKE) is capable of describing the neutrino flavor conversion, transport, and matter collision self-consistently. However, we have experienced many technical difficulties in their numerical implementation. In this paper, we present a new QKE solver based on a Monte Carlo (MC) approach. This is an upgraded version of our classical MC neutrino transport solver; in essence, a flavor degree of freedom including mixing state is added into each MC particle. This extension requires updating numerical treatments of collision terms, in particular for scattering processes. We deal with the technical problem by generating a new MC particle at each scattering event. To reduce statistical noise inherent in MC methods, we develop the effective mean free path method. This suppresses a sudden change of flavor state due to collisions without increasing the number of MC particles. We present a suite of code tests to validate these new modules with comparison to the results reported in previous studies. Our QKE-MC solver is developed with fundamentally different philosophy and design from other deterministic and mesh methods, suggesting that it will be complementary to others and potentially provide new insights into physical processes of neutrino dynamics.

scholarly journals Evidence for Recent Polygenic Selection on Educational Attainment and Intelligence Inferred from Gwas Hits: A Replication of Previous Findings Using Recent Data

Psych ◽  
2019 ◽  
Vol 1 (1) ◽  
pp. 55-75 ◽  
Author(s):  
Davide Piffer
Keyword(s):  
Monte Carlo ◽  
Educational Attainment ◽  
Spatial Autocorrelation ◽  
Association Studies ◽  
Random Noise ◽  
Genome Wide Association Studies ◽  
Socioeconomic Variables ◽  
1000 Genomes ◽  
Polygenic Scores ◽  
Polygenic Selection

Genetic variants identified by three large genome-wide association studies (GWAS) of educational attainment (EA) were used to test a polygenic selection model. Weighted and unweighted polygenic scores (PGS) were calculated and compared across populations using data from the 1000 Genomes (n = 26), HGDP-CEPH (n = 52) and gnomAD (n = 8) datasets. The PGS from the largest EA GWAS was highly correlated to two previously published PGSs (r = 0.96–0.97, N = 26). These factors are both highly predictive of average population IQ (r = 0.9, N = 23) and Learning index (r = 0.8, N = 22) and are robust to tests of spatial autocorrelation. Monte Carlo simulations yielded highly significant p values. In the gnomAD samples, the correlation between PGS and IQ was almost perfect (r = 0.98, N = 8), and ANOVA showed significant population differences in allele frequencies with positive effect. Socioeconomic variables slightly improved the prediction accuracy of the model (from 78–80% to 85–89%), but the PGS explained twice as much of the variance in IQ compared to socioeconomic variables. In both 1000 Genomes and gnomAD, there was a weak trend for lower GWAS significance SNPs to be less predictive of population IQ. Additionally, a subset of SNPs were found in the HGDP-CEPH sample (N = 127). The analysis of this sample yielded a positive correlation with latitude and a low negative correlation with distance from East Africa. This study provides robust results after accounting for spatial autocorrelation with Fst distances and random noise via an empirical Monte Carlo simulation using null SNPs.

scholarly journals AN ADAPTIVE TEST OF STOCHASTIC MONOTONICITY

2020 ◽  
pp. 1-42
Author(s):  
Denis Chetverikov ◽  
Daniel Wilhelm ◽  
Dongwoo Kim
Keyword(s):  
Monte Carlo ◽  
Conditional Distribution ◽  
Asymptotic Properties ◽  
Nonparametric Test ◽  
Critical Value ◽  
Data Driven ◽  
Local Alternatives ◽  
Stochastic Monotonicity ◽  
Adaptive Test ◽  
Finite Samples

We propose a new nonparametric test of stochastic monotonicity which adapts to the unknown smoothness of the conditional distribution of interest, possesses desirable asymptotic properties, is conceptually easy to implement, and computationally attractive. In particular, we show that the test asymptotically controls size at a polynomial rate, is nonconservative, and detects certain smooth local alternatives that converge to the null with the fastest possible rate. Our test is based on a data-driven bandwidth value and the critical value for the test takes this randomness into account. Monte Carlo simulations indicate that the test performs well in finite samples. In particular, the simulations show that the test controls size and, under some alternatives, is significantly more powerful than existing procedures.

Multi-Pulse Chaotic Motion for a Non-Autonomous Buckled Plate by Using the Extended Melnikov Method

2007 ◽  
Author(s):  
Wei Zhang ◽  
Jun-Hua Zhang ◽  
Ming-Hui Yao
Keyword(s):  
Thin Plate ◽  
Chaotic Dynamics ◽  
Melnikov Method ◽  
Type Equation ◽  
Rectangular Thin Plate ◽  
Governing Equations ◽  
Chaotic Motions ◽  
Simply Supported ◽  
Extended Melnikov Method ◽  
Two Degree Of Freedom

The multi-pulse Shilnikov orbits and chaotic dynamics for a parametrically excited, simply supported rectangular buckled thin plate are studied by using the extended Melnikov method. Based on von Karman type equation and the Galerkin’s approach, two-degree-of-freedom nonlinear system is obtained for the rectangular thin plate. The extended Melnikov method is directly applied to the non-autonomous governing equations of the thin plate. The results obtained here show that the multipulse chaotic motions can occur in the thin plate.

Bifurcations and Chaos in Forced, Coupled Pendula

2001 ◽  
Author(s):  
Kazuyuki Yagasaki
Keyword(s):  
Averaging Method ◽  
Nonlinear Behavior ◽  
Melnikov Method ◽  
Original System ◽  
Chaotic Motions ◽  
Small Perturbations ◽  
Small Oscillations ◽  
Codimension One ◽  
Averaged Systems ◽  
Direct Numerical Integration

Abstract We consider forced, coupled pendula and show that they exhibit very complicated dynamics using the averaging method and Melnikov-type techniques. First, the averaged system for small oscillations of the pendula near the hanging state is analyzed. Codimension-one and -two local bifurcations at which several non-synchronized periodic orbits and quasiperiodic orbits are born in the original system are detected. The validity of the theoretical results is demonstrated by comparison with direct numerical integration results. Moreover, chaotic motions, which result from the Shilnikov type phenomena in the averaged systems, are observed in numerical simulations. Second, the second-order averaging method is applied to small perturbations of rotary orbits with no damping and external forcing. Analyzing the averaged system, we can describe nonlinear behavior in the original system. Finally, using a generalization of Melnikov method, we prove the occurrence of many other homo-clinic phenomena, which also yield chaotic dynamics.

Multi-Pulse Chaotic Dynamics of Eccentric Rotating Composite Laminated Circular Cylindrical Shell by Using the Extended Melnikov Method

2019 ◽  
Author(s):  
Yan Zheng ◽  
Wei Zhang ◽  
Tao Liu
Keyword(s):  
Cylindrical Shell ◽  
Normal Form ◽  
Chaotic Dynamics ◽  
Multiple Scales ◽  
Circular Cylindrical Shell ◽  
Melnikov Method ◽  
Global Dynamics ◽  
Chaotic Motions ◽  
Extended Melnikov Method ◽  
Averaged Equations

Abstract The researches of global bifurcations and chaotic dynamics for high-dimensional nonlinear systems are extremely challenging. In this paper, we study the multi-pulse orbits and chaotic dynamics of an eccentric rotating composite laminated circular cylindrical shell. The four-dimensional averaged equations are obtained by directly using the multiple scales method under the case of the 1:2 internal resonance and principal parametric resonance-1/2 subharmonic resonance. The system is transformed to the averaged equations. From the averaged equation, the theory of normal form is used to find the explicit formulas of normal form. Based on the normal form obtained, the extended Melnikov method is utilized to analyze the multi-pulse global homoclinic bifurcations and chaotic dynamics for the eccentric rotating composite laminated circular cylindrical shell. The analysis of global dynamics indicates that there exist the multi-pulse jumping orbits in the perturbed phase space of the averaged equation. From the averaged equations obtained, the chaotic motions and the Shilnikov type multi-pulse orbits of the eccentric rotating composite laminated circular cylindrical shell are found by using numerical simulation. The results obtained above mean the existence of the chaos for the Smale horseshoe sense for the eccentric rotating composite laminated circular cylindrical shell.

scholarly journals Evaluating Noise Sensitivity on the Time Series Determination of Lyapunov Exponents Applied to the Nonlinear Pendulum

2003 ◽  
Vol 10 (1) ◽  
pp. 37-50 ◽  
Author(s):  
L.F.P. Franca ◽  
M.A. Savi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Time Series ◽  
Lyapunov Exponents ◽  
Random Noise ◽  
Noise Sensitivity ◽  
Correct Identification ◽  
Chaotic Motions ◽  
Nonlinear Pendulum

This contribution presents an investigation on noise sensitivity of some of the most disseminated techniques employed to estimate Lyapunov exponents from time series. Since noise contamination is unavoidable in cases of data acquisition, it is important to recognize techniques that could be employed for a correct identification of chaos. State space reconstruction and the determination of Lyapunov exponents are carried out to investigate the response of a nonlinear pendulum. Signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the signal. Basically, the analyses of periodic and chaotic motions are carried out. Results obtained from mathematical model are compared with the one obtained from time series analysis, evaluating noise sensitivity. This procedure allows the identification of the best techniques to be employed in the analysis of experimental data.

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