scholarly journals Phase-space transport in cuspy triaxial potentials: can they be used to construct self-consistent equilibria?

2002 ◽  
Vol 319 (1) ◽  
pp. 43-62 ◽  
Author(s):  
Christos Siopis ◽  
Henry E. Kandrup
Keyword(s):  
Phase Space ◽  
Phase Space Transport ◽  
Self Consistent

Mel'nikov analysis of phase space transport in a N-degree-of-freedom Hamiltonian system

1997 ◽  
Vol 30 (3) ◽  
pp. 1365-1374 ◽  
Author(s):  
Vassilios M. Rothos ◽  
Tassos C. Bountis
Keyword(s):  
Phase Space ◽  
Hamiltonian System ◽  
Degree Of Freedom ◽  
Phase Space Transport

Properties of cross-well chaos in an impacting system

1994 ◽  
Vol 347 (1683) ◽  
pp. 391-410 ◽  
Keyword(s):  
Phase Space ◽  
Poincaré Map ◽  
Poincare Map ◽  
Chaotic Motions ◽  
Higher Harmonics ◽  
Potential Wells ◽  
Duffing's Equation ◽  
Duffing’S Equation ◽  
Phase Space Transport ◽  
Basin Boundaries

In this paper we present results on chaotic motions in a periodically forced impacting system which is analogous to the version of Duffing’s equation with negative linear stiffness. Our focus is on the prediction and manipulation of the cross-well chaos in this system. First, we develop a general method for determining parameter conditions under which homoclinic tangles exist, which is a necessary condition for cross-well chaos to occur. We then show how one may manipulate higher harmonics of the excitation in order to affect the range of excitation amplitudes over which fractal basin boundaries between the two potential wells exist. We also experimentally investigate the threshold for cross-well chaos and compare the results with the theoretical results. Second, we consider the rate at which the system crosses from one potential well to the other during a chaotic motion and relate this to the rate of phase space flux in a Poincare map defined in terms of impact parameters. Results from simulations and experiments are compared with a simple theory based on phase space transport ideas, and a predictive scheme for estimating the rate of crossings under different parameter conditions is presented. The main conclusions of the paper are the following: (1) higher harmonics can be used with some effectiveness to extend the region of deterministic basin boundaries (in terms of the amplitude of excitation) but their effect on steady-state chaos is unreliable; (2) the rate at which the system executes cross-well excursions is related in a direct manner to the rate of phase space flux of the system as measured by the area of a turnstile lobe in the Poincare map. These results indicate some of the ways in which the chaotic properties of this system, and possibly others such as Duffing’s equation, are influenced by various system and input parameters. The main tools of analysis are a special version of Melnikov’s method, adapted for this piecewise-linear system, and ideas of phase space transport.

scholarly journals Phase space transport in the interaction between shocks and plasma turbulence

2021 ◽  
Vol 118 (21) ◽  
pp. e2026764118
Author(s):  
Domenico Trotta ◽  
Francesco Valentini ◽  
David Burgess ◽  
Sergio Servidio
Keyword(s):  
Phase Space ◽  
Vlasov Equation ◽  
Coarse Graining ◽  
Plasma Turbulence ◽  
Turbulent Jet ◽  
Plasma Transport ◽  
Space Plasmas ◽  
Collisionless Shocks ◽  
Phase Space Transport

The interaction of collisionless shocks with fully developed plasma turbulence is numerically investigated. Hybrid kinetic simulations, where a turbulent jet is slammed against an oblique shock, are employed to address the role of upstream turbulence on plasma transport. A technique, using coarse graining of the Vlasov equation, is proposed, showing that the particle transport strongly depends on upstream turbulence properties, such as strength and coherency. These results might be relevant for the understanding of acceleration and heating processes in space plasmas.

Study on the Safety Degree of Ship Capsizing in Stochastic Waves

2017 ◽  
Vol 33 (01) ◽  
pp. 24-30
Author(s):  
Jianwei Zhang ◽  
Wanqing Wu ◽  
Junquan Hu
Keyword(s):  
Phase Space ◽  
Transport Theory ◽  
Melnikov Function ◽  
Statistical Characteristics ◽  
Fast Fourier Transformation ◽  
Random Wave ◽  
Random Waves ◽  
Phase Space Transport ◽  
Heading Angle ◽  
Ship Capsizing

To quantify ship capsizing, from the energy perspective, the safety degree of a ship in waves is estimated based on stochastic Melnikov function and phase space transport theory. Considering the influence of nonlinear damping moment, nonlinear restoring moment, as well as the random waves, a nonlinear single degree of freedom differential equation for ship rolling is established. Transform the random wave moment from time domain to frequency domain by fast Fourier transformation, the random Melnikov function and rate of phase flux are extended to include the effects of navigation speed and heading angle and the safety degree of ship capsizing is quantified according to its statistical characteristics. Through an example, the accuracy of Melnikov function and phase space transport theory are verified and the effects of ship speed and heading angle on phase space transport rate are also quantified. This method is demonstrated properly to quantify the safety degree of ship capsizing and some valuable reference can be provided for the further research on ship stability criteria.

scholarly journals Phase Space Structure and Transport in a Caldera Potential Energy Surface

2018 ◽  
Vol 28 (13) ◽  
pp. 1830042 ◽  
Author(s):  
Matthaios Katsanikas ◽  
Stephen Wiggins
Keyword(s):  
Phase Space ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Periodic Orbits ◽  
Central Region ◽  
Invariant Manifolds ◽  
Energy Surface ◽  
Unstable Periodic Orbits ◽  
Phase Space Transport ◽  
The Family

We study phase space transport in a 2D caldera potential energy surface (PES) using techniques from nonlinear dynamics. The caldera PES is characterized by a flat region or shallow minimum at its center surrounded by potential walls and multiple symmetry related index one saddle points that allow entrance and exit from this intermediate region. We have discovered four qualitatively distinct cases of the structure of the phase space that govern phase space transport. These cases are categorized according to the total energy and the stability of the periodic orbits associated with the family of the central minimum, the bifurcations of the same family, and the energetic accessibility of the index one saddles. In each case, we have computed the invariant manifolds of the unstable periodic orbits of the central region of the potential, and the invariant manifolds of the unstable periodic orbits of the families of periodic orbits associated with the index one saddles. The periodic orbits of the central region are, for the first case, the unstable periodic orbits with period 10 that are outside the stable region of the stable periodic orbits of the family of the central minimum. In addition, the periodic orbits of the central region are, for the second and third cases, the unstable periodic orbits of the family of the central minimum and for the fourth case the unstable periodic orbits with period 2 of a period-doubling bifurcation of the family of the central minimum. We have found that there are three distinct mechanisms determined by the invariant manifold structure of the unstable periodic orbits that govern the phase space transport. The first mechanism explains the nature of the entrance of the trajectories from the region of the low energy saddles into the caldera and how they may become trapped in the central region of the potential. The second mechanism describes the trapping of the trajectories that begin from the central region of the caldera, their transport to the regions of the saddles, and the nature of their exit from the caldera. The third mechanism describes the phase space geometry responsible for the dynamical matching of trajectories originally proposed by Carpenter and described in [Collins et al., 2014] for the two-dimensional caldera PES that we consider.

Noise-induced phase space transport in two-dimensional Hamiltonian systems

1999 ◽  
Vol 60 (2) ◽  
pp. 1567-1578 ◽  
Author(s):  
Ilya V. Pogorelov ◽  
Henry E. Kandrup
Keyword(s):  
Phase Space ◽  
Hamiltonian Systems ◽  
Two Dimensional ◽  
Phase Space Transport

Orbital Complexity, Short-Time Lyapunov Exponents, and Phase Space Transport in Time-Independent Hamiltonian Systemsa

1998 ◽  
Vol 867 (1 NONLINEAR DYN) ◽  
pp. 41-60 ◽  
Author(s):  
CHRISTOS SIOPIS ◽  
BARBARA L. ECKSTEIN ◽  
HENRY E. KANDRUP
Keyword(s):  
Phase Space ◽  
Lyapunov Exponents ◽  
Phase Space Transport ◽  
Short Time
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