scholarly journals A New Dynamical Parameter for the Study of Sticky Orbits in a 3D Galactic Model

2011 ◽  
Vol 20 (3) ◽  
Author(s):  
Euaggelos E. Zotos
Keyword(s):  
Dynamical System ◽  
Classical Method ◽  
Elliptical Galaxy ◽  
Dynamical Model ◽  
Dynamical Parameter ◽  
2D System ◽  
Galactic Model ◽  
Dense Nucleus

AbstractA 3D dynamical model is used to study the motion in the central parts of an elliptical galaxy, hosting a massive and dense nucleus. Our aim is to investigate the regular or chaotic character of the motion, with emphasis in the different chaotic components, as well as the sticky regions of the dynamical system. In order to define the character of the motion in the 2D system, we use the classical method of the Poincaré x − p

scholarly journals Disks Controlling Chaos in a 3D Dynamical Model for Elliptical Galaxies

2011 ◽  
Vol 20 (1) ◽  
Author(s):  
Euaggelos E. Zotos
Keyword(s):  
Phase Plane ◽  
Elliptical Galaxy ◽  
Elliptical Galaxies ◽  
Dynamical Model ◽  
Dynamical Parameter ◽  
Secondary Resonances ◽  
Homogeneous Core ◽  
2D System ◽  
New Phase ◽  
Disk Component

AbstractA 3D dynamical model with a quasi-homogeneous core and a disk component is used for the chaos control in the central parts of elliptical galaxy. Numerical experiments in the 2D system show a very complicated phase plane with a large chaotic sea, considerable sticky layers and a large number of islands, produced by secondary resonances. When the mass of the disk increases, the chaotic regions decrease gradually, and, finally, a new phase plane with only regular orbits appears. This evolution indicates that disks in elliptical galaxies can act as the chaos controllers. Starting from the results obtained in the 2D system, we locate the regions in the phase space of the 3D system, producing regular and chaotic orbits. For this we introduce and use a new dynamical parameter, the S(w) spectrum, which proves to be useful as a fast indicator and allows us to distinguish the regular motion from chaos in the 3D potentials. Other methods for detecting chaos are also discussed.

scholarly journals On the Solution of an Imprecisely Defined Nonlinear Time-Fractional Dynamical Model of Marriage

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 689 ◽  
Author(s):  
Rajarama Mohan Jena ◽  
Snehashish Chakraverty ◽  
Dumitru Baleanu
Keyword(s):  
Dynamical System ◽  
Fuzzy Numbers ◽  
Initial Conditions ◽  
Coupled System ◽  
Dynamical Model ◽  
Transform Method ◽  
System Parameters ◽  
Nonlinear Coupled System ◽  
Differential Transform ◽  
Fractional Dynamical System

The present paper investigates the numerical solution of an imprecisely defined nonlinear coupled time-fractional dynamical model of marriage (FDMM). Uncertainties are assumed to exist in the dynamical system parameters, as well as in the initial conditions that are formulated by triangular normalized fuzzy sets. The corresponding fractional dynamical system has first been converted to an interval-based fuzzy nonlinear coupled system with the help of a single-parametric gamma-cut form. Further, the double-parametric form (DPF) of fuzzy numbers has been used to handle the uncertainty. The fractional reduced differential transform method (FRDTM) has been applied to this transformed DPF system for obtaining the approximate solution of the FDMM. Validation of this method was ensured by comparing it with other methods taking the gamma-cut as being equal to one.

Study on the Hamilton Dynamical System of Wheel-and-Rail Dynamical Model of High-Speed Train

2015 ◽  
Vol 713-715 ◽  
pp. 99-102
Author(s):  
Hong Yun Shen ◽  
Jian Hua Du ◽  
Yu Lin Wang
Keyword(s):  
Dynamical System ◽  
Dry Friction ◽  
High Speed ◽  
Dynamical Model ◽  
High Speed Train ◽  
Damping Force ◽  
Nonlinear Dynamical ◽  
Dynamical Behaviors ◽  
Practical Engineering

The study on dynamical model of wheel and rail of high-speed train has attracted many researchers nowadays. According to the damping force and the dry friction between wheel and rail, the dynamical model of wheel and rail of high-speed train is constructed and the Hamilton dynamical system of this model is analyzed to discuss its nonlinear dynamical behaviors, which will benefit the practical engineering of high-speed train.

Models for the Formation and Evolution of Spherical Galaxies

1974 ◽  
Vol 58 ◽  
pp. 191-194
Author(s):  
Richard B. Larson
Keyword(s):  
Star Formation ◽  
Galaxy Formation ◽  
Stellar Evolution ◽  
Elliptical Galaxy ◽  
Elliptical Galaxies ◽  
Dynamical Model ◽  
Model Calculations ◽  
Formation And Evolution

Detailed dynamical model calculations based on a conventional collapse picture of galaxy formation, and conventional assumptions concerning star formation and stellar evolution, are found to be able to reproduce satisfactorily the basic structural and photometric properties of elliptical galaxies. The quasar phenomenon may be identifiable with the formation of the nucleus of a giant elliptical galaxy.

Investigation of Seasonal and Latitudinal Effects on the Expression of Clock Genes in Drosophila

2017 ◽  
Vol 27 (10) ◽  
pp. 1750153 ◽  
Author(s):  
Seyede Sanaz Hosseini ◽  
Fahimeh Nazarimehr ◽  
Sajad Jafari
Keyword(s):  
Dynamical System ◽  
Experimental Data ◽  
Drosophila Melanogaster ◽  
Clock Genes ◽  
Strange Attractors ◽  
Dynamical Model ◽  
Different Seasons ◽  
Latitudinal Variations

The primary goal in this work is to develop a dynamical model capturing the influence of seasonal and latitudinal variations on the expression of Drosophila clock genes. To this end, we study a specific dynamical system with strange attractors that exhibit changes of Drosophila activity in a range of latitudes and across different seasons. Bifurcations of this system are analyzed to peruse the effect of season and latitude on the behavior of clock genes. Existing experimental data collected from the activity of Drosophila melanogaster corroborate the dynamical model.

scholarly journals Construction of a Second-order Six-dimensional Hamiltonian-conserving Scheme

2021 ◽  
Vol 257 (2) ◽  
pp. 40
Author(s):  
Shiyang Hu ◽  
Xin Wu ◽  
Enwei Liang
Keyword(s):  
Black Hole ◽  
Numerical Solutions ◽  
Elliptical Galaxy ◽  
Second Order ◽  
Physical Models ◽  
New Method ◽  
Hamiltonian Problems ◽  
Black Hole Background ◽  
Galactic Model ◽  
Energy Conserving

Abstract Research has analytically shown that the energy-conserving implicit nonsymplectic scheme of Bacchini, Ripperda, Chen, and Sironi provides a first-order accuracy to numerical solutions of a six-dimensional conservative Hamiltonian system. Because of this, a new second-order energy-conserving implicit scheme is proposed. Numerical simulations of a galactic model hosting a BL Lacertae object and magnetized rotating black hole background support these analytical results. The new method with appropriate time steps is used to explore the effects of varying the parameters on the presence of chaos in the two physical models. Chaos easily occurs in the galactic model as the mass of the nucleus, the internal perturbation parameter, and the anisotropy of the potential of the elliptical galaxy increase. The dynamics of charged particles around the magnetized Kerr spacetime is easily chaotic for larger energies of the particles, smaller initial angular momenta of the particles, and stronger magnetic fields. The chaotic properties are not necessarily weakened when the black-hole spin increases. The new method can be used for any six-dimensional Hamiltonian problems, including globally hyperbolic spacetimes with readily available (3 + 1) split coordinates.

scholarly journals Unveiling the Influence of Dark Matter in Axially Symmetric Galaxies

2013 ◽  
Vol 30 ◽  
Author(s):  
Nicolaos D. Caranicolas ◽  
Euaggelos E. Zotos
Keyword(s):  
Dark Matter ◽  
Elliptical Galaxy ◽  
Equations Of Motion ◽  
Dark Matter Halo ◽  
Meridional Plane ◽  
Axially Symmetric ◽  
Indicator Method ◽  
Galactic Model ◽  
Fast Lyapunov Indicator ◽  
Regular And Chaotic Motion

AbstractWe investigate the regular or chaotic nature of orbits of stars moving in the meridional plane (R,z) of an axially symmetric galactic model with a dense, massive spherical nucleus and a dark matter halo component. In particular, we study the influence of the fractional portion of the dark matter, by computing in each case the percentage of chaotic orbits, as well as the percentages of orbits of the main regular resonant families. In an attempt to distinguish between regular and chaotic motion, we use the fast Lyapunov indicator method to extensive samples of orbits obtained by integrating numerically the equations of motion as well as the variational equations. Furthermore, a technique which is based mainly on the field of spectral dynamics that utilises the Fourier transform of the time series of each coordinate is used for identifying the various families of regular orbits and also to recognise the secondary resonances that bifurcate from them. Two cases are studied in our work: (i) the case where we have a disk galaxy model and (ii) the case where our model represents an elliptical galaxy. A comparison with early related work is also made.

The Preliminary Study on Wheel-and-Rail Dynamical Model of High-Speed Train

2014 ◽  
Vol 1082 ◽  
pp. 501-504
Author(s):  
Jian Hua Du ◽  
Hong Yun Shen ◽  
Yu Lin Wang
Keyword(s):  
Dynamical System ◽  
Dry Friction ◽  
Theoretical Basis ◽  
High Speed ◽  
Dynamical Model ◽  
High Speed Train ◽  
Damping Force ◽  
Preliminary Study

the study on dynamical model of wheel and rail of high-speed train is a focus nowadays. In this paper, the dynamical model of wheel and rail of high-speed train is constructed according to the damping force and the dry friction between wheel and rail. The dynamics of the model was studied and the dynamical system of wheel and rail without collision was analyzed, which povides the theoretical basis for engineering.

scholarly journals A Method for Parameters Estimation in a Dynamical Model of Ebola Virus Transmission in Sierra Leone

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Li Li ◽  
Li-Xia Du ◽  
Ziheng Yan ◽  
Jie Zhang ◽  
Yong-Ping Wu
Keyword(s):  
Sierra Leone ◽  
Ebola Virus ◽  
Classical Method ◽  
Fitness Function ◽  
Virus Transmission ◽  
Optimal Solution ◽  
Real Data ◽  
Hemorrhagic Fever ◽  
Parameters Estimation ◽  
Dynamical Model

Ebola is an infectious virus that causes Ebola hemorrhagic fever in primates and humans, which was first found in 1976. The Ebola virus outbreak in West Africa in 2014 was the largest ever. A lot of researchers use mathematical models to analyze the characteristics of infectious diseases. However, many parameters in the model cannot be estimated completely. To ease the difficulty, we proposed an approach to estimate the parameter based on genetic algorithm (GA). GA uses the natural selection method of the fittest to find the optimal solution of the model. The least residual squares sum is used as fitness function to measure the performance of GA in parameter estimation. Moreover, we used a dynamical model and the real data of Ebola in Sierra Leone to verify the validity of GA. The experimental results indicate that the GA has strong competitiveness compared with the classical method, and it is a feasible method for estimating the parameters of infectious disease models.

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