Equilibrium points with their associated normal modes describing nonlinear dynam-ics of a spinning shaft with non-constant rotating speed

2018 ◽  
Vol 2 (4) ◽  
pp. 327-373 ◽  
Author(s):  
Fotios Georgiades
Keyword(s):  
Equilibrium Points ◽  
Normal Modes ◽  
Rotating Speed ◽  
Spinning Shaft

scholarly journals Vibrational modes of light nuclei

2018 ◽  
Vol 178 ◽  
pp. 02017
Author(s):  
Lorenzo Fortunato
Keyword(s):  
Spectroscopic Data ◽  
Energy Surface ◽  
Equilibrium Points ◽  
Hessian Matrix ◽  
Normal Modes ◽  
Light Nuclei ◽  
Vibrational Modes ◽  
Large Fluctuations ◽  
Modes Of Vibration ◽  
Scattering Phase

A potential energy surface is constructed for various light nuclei, 3,4He with the Argonne V18 potential and then for alpha- conjugate nuclei like 12C,16O, 20Ne with α – α potentials. Despite the nucleons have large momenta and large fluctuations around the equilibrium points, the minimization suggests the underlying geometric structure. We calculate the Hessian matrix determining the normal modes of vibration. This approach might lead to a new way of fitting the alpha-alpha interactions on the spectroscopic data available for alpha-conjugate nuclei, rather than on scattering phase shift.

Mathematical views of the fractional Chua's electrical circuit described by the Caputo-Liouville derivative

2021 ◽  
Vol 67 (1 Jan-Feb) ◽  
pp. 91
Author(s):  
N. Sene
Keyword(s):  
Caputo Derivative ◽  
Local Stability ◽  
Numerical Scheme ◽  
Equilibrium Points ◽  
Electrical Circuit ◽  
Maximal Lyapunov Exponent ◽  
Electrical Circuits ◽  
Adaptive Controls ◽  
Liouville Derivative

This paper revisits Chua's electrical circuit in the context of the Caputo derivative. We introduce the Caputo derivative into the modeling of the electrical circuit. The solutions of the new model are proposed using numerical discretizations. The discretizations use the numerical scheme of the Riemann-Liouville integral. We have determined the equilibrium points and study their local stability. The existence of the chaotic behaviors with the used fractional-order has been characterized by the determination of the maximal Lyapunov exponent value. The variations of the parameters of the model into the Chua's electrical circuit have been quantified using the bifurcation concept. We also propose adaptive controls under which the master and the slave fractional Chua's electrical circuits go in the same way. The graphical representations have supported all the main results of the paper.

Filtering methods for finite-time normal modes and atmospheric error growth

2000 ◽  
Vol 42 ◽  
pp. 1482
Author(s):  
Mozheng Wei ◽  
Jorgen S. Frederiksen ◽  
Steve Kepert
Keyword(s):  
Finite Time ◽  
Normal Modes ◽  
Error Growth

Dynamics of a delayed competitive system affected by toxic substances with imprecise biological parameters

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5271-5293
Author(s):  
A.K. Pal ◽  
P. Dolai ◽  
G.P. Samanta
Keyword(s):  
Equilibrium Points ◽  
Stable Limit Cycle ◽  
Limit Cycle Oscillation ◽  
Toxic Substances ◽  
Stable Limit ◽  
Biological Parameters ◽  
Delay Model ◽  
Competitive System ◽  
Interval Numbers ◽  
Cycle Oscillation

In this paper we have studied the dynamical behaviours of a delayed two-species competitive system affected by toxicant with imprecise biological parameters. We have proposed a method to handle these imprecise parameters by using parametric form of interval numbers. We have discussed the existence of various equilibrium points and stability of the system at these equilibrium points. In case of toxic stimulatory system, the delay model exhibits a stable limit cycle oscillation. Computer simulations are carried out to illustrate our analytical findings.

Gravitational Waves

2018 ◽  
Author(s):  
Michele Maggiore
Keyword(s):  
Black Hole ◽  
Perturbation Theory ◽  
Gravitational Waves ◽  
Transfer Functions ◽  
Normal Modes ◽  
Cosmological Perturbation ◽  
Tests Of General Relativity ◽  
Pulsar Timing ◽  
Tensor Perturbations ◽  
Stochastic Backgrounds

A comprehensive and detailed account of the physics of gravitational waves and their role in astrophysics and cosmology. The part on astrophysical sources of gravitational waves includes chapters on GWs from supernovae, neutron stars (neutron star normal modes, CFS instability, r-modes), black-hole perturbation theory (Regge-Wheeler and Zerilli equations, Teukoslky equation for rotating BHs, quasi-normal modes) coalescing compact binaries (effective one-body formalism, numerical relativity), discovery of gravitational waves at the advanced LIGO interferometers (discoveries of GW150914, GW151226, tests of general relativity, astrophysical implications), supermassive black holes (supermassive black-hole binaries, EMRI, relevance for LISA and pulsar timing arrays). The part on gravitational waves and cosmology include discussions of FRW cosmology, cosmological perturbation theory (helicity decomposition, scalar and tensor perturbations, Bardeen variables, power spectra, transfer functions for scalar and tensor modes), the effects of GWs on the Cosmic Microwave Background (ISW effect, CMB polarization, E and B modes), inflation (amplification of vacuum fluctuations, quantum fields in curved space, generation of scalar and tensor perturbations, Mukhanov-Sasaki equation,reheating, preheating), stochastic backgrounds of cosmological origin (phase transitions, cosmic strings, alternatives to inflation, bounds on primordial GWs) and search of stochastic backgrounds with Pulsar Timing Arrays (PTA).

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