Small amplitude dynamics in phase space

2020 ◽  
pp. 276-340
Keyword(s):  
Phase Space ◽  
Small Amplitude

Weak Double Layers: Existence, Stability, Evidence

1983 ◽  
Vol 38 (11) ◽  
pp. 1170-1183 ◽  
Author(s):  
H. Schamel
Keyword(s):  
Phase Space ◽  
Small Amplitude ◽  
Tuning Fork ◽  
Hot Electrons ◽  
Double Layers ◽  
Slow Electron ◽  
One Dimensional ◽  
Acoustic Branch ◽  
Beam Type ◽  
Electron Acoustic

Two more classes of monotonic double layers complementing the class of beam-type double layers are investigated analytically, and their range of existence is explored in the small amplitude limit. One class preferentially exists for hot ions and electron drifts of the order of electron thermal velocity. The second one, instead, assumes hot electrons and needs almost current-free conditions. The first class, called SEADL, is based on the slow electron acoustic branch and exhibits a tuning-fork configuration in the electron phase space. Its density decreases with increasing potential. The second one (SIADL) rests on the slow ion acoustic branch and. consequently, has a tuning-fork pattern in the ion phase space. Its density increases with the potential. Both classes are found to be linearly stable with respect to one-dimensional, but unstable with respect to two-dimensional electrostatic perturbations. A comparison with experiments suggests an identification of the second type with the double layers obtained by Hollenstein

scholarly journals Multi-Baker Map as a Model of Digital PD Control

2016 ◽  
Vol 26 (02) ◽  
pp. 1650023 ◽  
Author(s):  
Gábor Csernák ◽  
Gergely Gyebrószki ◽  
Gábor Stépán
Keyword(s):  
Phase Space ◽  
Lyapunov Exponent ◽  
Linear Systems ◽  
Small Amplitude ◽  
Chaotic Dynamics ◽  
Largest Lyapunov Exponent ◽  
Two Dimensional ◽  
Smale Horseshoe ◽  
Analytical Proof ◽  
Baker Map

Digital stabilization of unstable equilibria of linear systems may lead to small amplitude stochastic-like oscillations. We show that these vibrations can be related to a deterministic chaotic dynamics induced by sampling and quantization. A detailed analytical proof of chaos is presented for the case of a PD controlled oscillator: it is shown that there exists a finite attracting domain in the phase-space, the largest Lyapunov exponent is positive and the existence of a Smale horseshoe is also pointed out. The corresponding two-dimensional micro-chaos map is a multi-baker map, i.e. it consists of a finite series of baker’s maps.

Global existence of small amplitude solutions to the Vlasov–Poisson system with radiation damping

2015 ◽  
Vol 26 (12) ◽  
pp. 1550098 ◽  
Author(s):  
Jing Chen ◽  
Xianwen Zhang
Keyword(s):  
Fixed Point ◽  
Phase Space ◽  
Small Amplitude ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Local Solution ◽  
Dispersion Property ◽  
Poisson System ◽  
Global Classical Solution ◽  
Three Dimensional Space

In this paper, with some dispersion property and Schauder’s fixed point theorem, we establish the existence of a global classical solution to a damped Vlasov–Poisson system in three-dimensional space under the assumption that the initial datum is sufficiently small and decays at infinity in phase space. Before this work, only a local solution was obtained for the three-dimensional damped Vlasov–Poisson system.

Properties of small-amplitude electron phase-space holes observed by Polar

2005 ◽  
Vol 110 (A9) ◽  
Author(s):  
J. R. Franz ◽  
P. M. Kintner ◽  
J. S. Pickett ◽  
L.-J. Chen
Keyword(s):  
Phase Space ◽  
Small Amplitude

scholarly journals Ion phase-space vortices and their relation to small amplitude double-layers

1987 ◽  
Vol 5 (2) ◽  
pp. 211-217 ◽  
Author(s):  
Hans L. Pécseli
Keyword(s):  
Phase Space ◽  
Laboratory Experiment ◽  
Numerical Simulations ◽  
Dimensional Analysis ◽  
Small Amplitude ◽  
Voltage Drop ◽  
Three Dimensions ◽  
Double Layers ◽  
One Dimensional

The properties of ion phase-space vortices are reviewed with particular attention to their role in the formation of small amplitude double-layers in current-carrying plasmas. In a one-dimensional analysis, many such double-layers simply add up to produce a large voltage drop. A laboratory experiment is carried out in order to investigate the properties of ion phase-space vortices in three dimensions. Their lifetime is significantly reduced as compared with similar results from one-dimensional numerical simulations of the problem.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

RSCVn Stars in the Southern Hemisphere

1979 ◽  
Vol 46 ◽  
pp. 371-384 ◽  
Author(s):  
J.B. Hearnshaw
Keyword(s):  
Light Curve ◽  
Southern Hemisphere ◽  
Orbital Period ◽  
Binary Stars ◽  
Small Amplitude ◽  
Light Variation ◽  
Orbital Phase

RSCVn stars are fully detached binary stars which show intrinsic small amplitude (up to 0.3 amplitude peak-to-peak) light variations, as well as, in most of the known cases, eclipses. The spectra are F to G, IV to V for the hotter component and usually KOIV for the cooler. They are also characterised by abnormally strong H and K emission from the cooler star, or, occasionally, from both components. The orbital and light curve periods are in the range 1 day to 2 weeks. An interesting feature is the migration of the light variations to earlier orbital phase, as the light variation period is shorter than the orbital period by a few parts in 10+4to a few parts in 10+3.

Amplitude Distributions of Cochlear Microphonic Response to an Acoustic Sinusoid in Noise

1968 ◽  
Vol 11 (1) ◽  
pp. 63-76
Author(s):  
Donald C. Teas ◽  
Gretchen B. Henry
Keyword(s):  
Small Amplitude ◽  
Basilar Membrane ◽  
Spectral Composition ◽  
Pass Band ◽  
Cochlear Microphonic ◽  
Filter Output ◽  
Electronic Filter ◽  
Low Pass ◽  
Band Pass ◽  
Instantaneous Voltage

The distributions of instantaneous voltage amplitudes in the cochlear microphonic response recorded from a small segment along the basilar membrane are described by computing amplitude histograms. Comparisons are made between the distributions for noise and for those after the addition to the noise of successively stronger sinusoids. The amplitudes of the cochlear microphonic response to 5000 Hz low-pass noise are normally distributed in both Turn I and Turn III of the guinea pig’s cochlea. The spectral composition of the microphonic from Turn I and from Turn III resembles the output of band-pass filters set at about 4000 Hz, and about 500 Hz, respectively. The normal distribution of cochlear microphonic amplitudes for noise is systematically altered by increasing the strength of the added sinusoid. A decrease of three percent in the number of small amplitude events (±1 standard deviation) in the cochlear microphonic from Turn III is seen when the rms voltage of a 500 Hz sinusoid is at −18 dB re the rms voltage of the noise (at the earphone). When the rms of the sinusoid and noise are equal, the decrease in small voltages is about 25%, but there is also an increase in the number of large voltage amplitudes. Histograms were also computed for the output of an electronic filter with a pass-band similar to Turn III of the cochlea. Strong 500 Hz sinusoids showed a greater proportion of large amplitudes in the filter output than in CM III . The data are interpreted in terms of an anatomical substrate.

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