285 research outputs found

### On the relationship between instability and Lyapunov times for the 3-body problem

In this study we consider the relationship between the survival time and the
Lyapunov time for 3-body systems. It is shown that the Sitnikov problem
exhibits a two-part power law relationship as demonstrated previously for the
general 3-body problem. Using an approximate Poincare map on an appropriate
surface of section, we delineate escape regions in a domain of initial
conditions and use these regions to analytically obtain a new functional
relationship between the Lyapunov time and the survival time for the 3-body
problem. The marginal probability distributions of the Lyapunov and survival
times are discussed and we show that the probability density function of
Lyapunov times for the Sitnikov problem is similar to that for the general
3-body problem.Comment: 9 pages, 19 figures, accepted for publication in MNRA

### A Method of Estimating Residuals in Orbital Theory

The degree of approximation used in determining the orbits of earth satellites is reflected in the residuals (differences between calculated and observed positions). The least-squares procedure generally used to fit theory to observation tends to obscure the significance of theoretical parameters, so that the physical sources of residuals cease to be apparent. A method is outlined herein for estimating the magnitude of the residuals to be expected from an approximate theory presumed to have one missing or incorrect term

### Chaotic zone boundary for low free eccentricity particles near an eccentric planet

We consider particles with low free or proper eccentricity that are orbiting
near planets on eccentric orbits. Via collisionless particle integration we
numerically find the location of the boundary of the chaotic zone in the
planet's corotation region. We find that the distance in semi-major axis
between the planet and boundary depends on the planet mass to the 2/7 power and
is independent of the planet eccentricity, at least for planet eccentricities
below 0.3. Our integrations reveal a similarity between the dynamics of
particles at zero eccentricity near a planet in a circular orbit and with zero
free eccentricity particles near an eccentric planet. The 2/7 law has been
previously explained by estimating the semi-major at which the first order mean
motion resonances are large enough to overlap. Orbital dynamics near an
eccentric planet could differ due to first order corotation resonances that
have strength proportional to the planet's eccentricity. However, we find the
corotation resonance width at low free eccentricity is small. Also the first
order resonance width at zero free eccentricity is the same as that for a zero
eccentricity particle near a planet in a circular orbit. This accounts for
insensitivity of the chaotic zone width to planet eccentricity. Particles at
zero free eccentricity near an eccentric planet have similar dynamics to those
at zero eccentricity near a planet in a circular orbit.Comment: accepted for publication in MNRA

### Noise-assisted spike propagation in myelinated neurons

We consider noise-assisted spike propagation in myelinated axons within a
multi-compartment stochastic Hodgkin-Huxley model. The noise originates from a
finite number of ion channels in each node of Ranvier. For the subthreshold
internodal electric coupling, we show that (i) intrinsic noise removes the
sharply defined threshold for spike propagation from node to node, and (ii)
there exists an optimum number of ion channels which allows for the most
efficient signal propagation and it corresponds to the actual physiological
values.Comment: 8 pages, 12 figures, accepted for publication in Phys. Rev.

### On the Snow Line in Dusty Protoplanetary Disks

The snow line, in Hayashi's (1981) model, is where the temperature of a black
body that absorbed direct sunlight and re-radiated as much as it absorbed,
would be 170~K. It is usually assumed that the cores of the giant planets,
e.g., Jupiter, form beyond the snow line. Since Hayashi, there have been a
series of more detailed models of the absorption by dust of the stellar
radiation, and of accretional heating, which alter the location of the snow
line. We have attempted a "self-consistent" model of a T Tauri disk in the
sense that we used dust properties and calculated surface temperatures that
matched observed disks. We then calculated the midplane temperature for those
disks, with no accretional heating or with small (<10^-8) accretion rates. Our
models bring the snow line in to the neighbourhood of 1 AU; not far enough to
explain the close planetary companions to other stars, but much closer than in
recent starting lines for orbit migration scenarios.Comment: 9 pages, 1 figure, to appear in ApJ,528,200

### Halting Planet Migration in the Evacuated Centers of Protoplanetary Disks

Precise Doppler searches for extrasolar planets find a surfeit of planets
with orbital periods of 3-4 days, and no planets with orbital periods less than
3 days. The circumstellar distance, R_0, where small grains in a protoplanetary
disk reach sublimation temperature (~1500 K) corresponds to a period of ~6
days. Interior to R_0, turbulent accretion due to magneto-rotational
instability may evacuate the disk center. We suggest that planets with orbital
periods of 3-4 days are so common because migrating planets halt once this
evacuated region contains the sites of their exterior 2:1 Lindblad resonances.Comment: 9 pages, 1 figure, to appear in ApJ letter

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