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Phase mixing of chaotic orbits exponentially distributes these orbits through their accessible phase space. This phenomenon, commonly called ‘‘chaotic mixing,’’ stands in marked contrast to phase mixing of regular orbits which proceeds as a power law in time. It is operationally irreversible; hence, its associated e-folding time scale sets a condition on… (More)

- Courtlandt L. Bohn, Ioannis Sideris
- Physical review letters
- 2003

The formation of beam halos has customarily been described in terms of a particle-core model in which the space-charge field of the oscillating core drives particles to large amplitudes. This model involves parametric resonance and predicts a hard upper bound to the orbital amplitude of the halo particles. We show that the presence of colored noise due to… (More)

104202-1 We investigate how collective modes and colored noise conspire to produce a beam halo with much larger amplitude than could be generated by either phenomenon separately. The collective modes are lowest-order radial eigenmodes calculated self-consistently for a configuration corresponding to a direct-current, cylindrically symmetric, warm-fluid… (More)

This paper summarises an investigation of the effects of low amplitude noise and periodic driving on phase space transport in three-dimensional Hamiltonian systems, a problem directly applicable to systems like galaxies, where such perturbations reflect internal irregularities and/or a surrounding environment. A new diagnostic tool is exploited to quantify… (More)

014202-1 We investigate the validity of theVlasov-Poisson equations for calculating properties of systems of N charged particles governed by time-independent Hamiltonians. Through numerical experiments we verify that there is a smooth convergence toward a continuum limit as N ! 1 and the particle charge q ! 0 such that the system charge Q qN remains fixed.… (More)

Integrations in fixed N-body realisations of smooth density distributions corresponding to a chaotic galactic potential can be used to derive reliable estimates of the largest (finite time) Lyapunov exponent χS associated with an orbit in the smooth potential generated from the same initial condition, even though the N -body orbit is typically characterised… (More)

- Henry E. Kandrup, Ioannis Sideris
- Physical review. E, Statistical, nonlinear, and…
- 2001

This paper summarizes a numerical investigation of the statistical properties of orbits evolved in "frozen," time-independent N-body realizations of smooth, time-independent density distributions corresponding to integrable potentials, allowing for 10(2.5) < or = N < or = 10(5.5). Two principal conclusions were reached: (1) In agreement with recent work by… (More)

This paper explores how orbits in a galactic potential can be impacted by large amplitude time-dependences of the form that one might associate with galaxy or halo formation or strong encounters between pairs of galaxies. A period of time-dependence with a strong, possibly damped, oscillatory component can give rise to large amounts of transient chaos, and… (More)

- Henry E. Kandrup, Ioannis Sideris, Courtlandt L. Bohn
- Physical review. E, Statistical, nonlinear, and…
- 2002

This paper uses the assumptions of ergodicity and a microcanonical distribution to compute estimates of the largest Lyapunov exponents in lower-dimensional Hamiltonian systems. That the resulting estimates are in reasonable agreement with the actual values computed numerically corroborates the intuition that chaos in such systems can be understood as… (More)

This paper summarises an investigation of chaos in a toy potential which mimics much of the behaviour observed for the more realistic triaxial generalisations of the Dehnen potentials, which have been used to model cuspy triaxial galaxies both with and without a supermassive black hole. The potential is the sum of an anisotropic harmonic oscillator… (More)