13,085 research outputs found
Control of nonlinear systems in regions of state space
Control of nonlinear systems in regions of state spac
A discrete-time differential dynamic programming algorithm with application to optimal orbit transfer
Discrete time differential dynamic programming algorithm with application to optimal orbit transfe
The great dichotomy of the Solar System: small terrestrial embryos and massive giant planet cores
The basic structure of the solar system is set by the presence of low-mass
terrestrial planets in its inner part and giant planets in its outer part. This
is the result of the formation of a system of multiple embryos with
approximately the mass of Mars in the inner disk and of a few multi-Earth-mass
cores in the outer disk, within the lifetime of the gaseous component of the
protoplanetary disk. What was the origin of this dichotomy in the mass
distribution of embryos/cores? We show in this paper that the classic processes
of runaway and oligarchic growth from a disk of planetesimals cannot explain
this dichotomy, even if the original surface density of solids increased at the
snowline. Instead, the accretion of drifting pebbles by embryos and cores can
explain the dichotomy, provided that some assumptions hold true. We propose
that the mass-flow of pebbles is two-times lower and the characteristic size of
the pebbles is approximately ten times smaller within the snowline than beyond
the snowline (respectively at heliocentric distance and
, where is the snowline heliocentric distance), due to ice
sublimation and the splitting of icy pebbles into a collection of
chondrule-size silicate grains. In this case, objects of original sub-lunar
mass would grow at drastically different rates in the two regions of the disk.
Within the snowline these bodies would reach approximately the mass of Mars
while beyond the snowline they would grow to Earth masses. The
results may change quantitatively with changes to the assumed parameters, but
the establishment of a clear dichotomy in the mass distribution of protoplanets
appears robust, provided that there is enough turbulence in the disk to prevent
the sedimentation of the silicate grains into a very thin layer.Comment: In press in Icaru
Measurement of the Density of Base Fluids at Pressures 0.422 to 2.20 Gpa
The influence of pressure on the density of six base fluids is experimentally studied for a range of pressures from 0.422 to 2.20 GPa. An important parameter used to describe the results is the change in relative volume with change in pressure dv sub r/dp. For pressures less than the solidification pressure (p ps) a small change in pressure results in a large change in dv sub r/ps. For pressures greater than the solidification pressure (p ps) there is no change in dv sub r/dp with changing pressure. The solidification pressures of the base fluids varies considerably, as do the slopes that the experimental data assumes for p ps. A new formula is developed that describes the effect of pressure on density in terms of four constants. These constants vary for the different base fluids tested
Origin of the Thermal Radiation in a Solid-State Analog of a Black-Hole
An effective black-hole-like horizon occurs, for electromagnetic waves in
matter, at a surface of singular electric and magnetic permeabilities. In a
physical dispersive medium this horizon disappears for wave numbers with
. Nevertheless, it is shown that Hawking radiation is still emitted if
free field modes with are in their ground state.Comment: 13 Pages, 3 figures, Revtex with epsf macro
A rapidly expanding Bose-Einstein condensate: an expanding universe in the lab
We study the dynamics of a supersonically expanding ring-shaped Bose-Einstein
condensate both experimentally and theoretically. The expansion redshifts
long-wavelength excitations, as in an expanding universe. After expansion,
energy in the radial mode leads to the production of bulk topological
excitations -- solitons and vortices -- driving the production of a large
number of azimuthal phonons and, at late times, causing stochastic persistent
currents. These complex nonlinear dynamics, fueled by the energy stored
coherently in one mode, are reminiscent of a type of "preheating" that may have
taken place at the end of inflation.Comment: 12 pages, 7 figure
Trans-Planckian Tail in a Theory with a Cutoff
Trans-planckian frequencies can be mimicked outside a black-hole horizon as a
tail of an exponentially large amplitude wave that is mostly hidden behind the
horizon. The present proposal requires implementing a final state condition.
This condition involves only frequencies below the cutoff scale. It may be
interpreted as a condition on the singularity. Despite the introduction of the
cutoff, the Hawking radiation is restored for static observers. Freely falling
observers see empty space outside the horizon, but are "heated" as they cross
the horizon.Comment: 17 pages, RevTe
Hawking radiation without black hole entropy
In this Letter I point out that Hawking radiation is a purely kinematic
effect that is generic to Lorentzian geometries. Hawking radiation arises for
any test field on any Lorentzian geometry containing an event horizon
regardless of whether or not the Lorentzian geometry satisfies the dynamical
Einstein equations of general relativity. On the other hand, the classical laws
of black hole mechanics are intrinsically linked to the Einstein equations of
general relativity (or their perturbative extension into either semiclassical
quantum gravity or string-inspired scenarios). In particular, the laws of black
hole thermodynamics, and the identification of the entropy of a black hole with
its area, are inextricably linked with the dynamical equations satisfied by the
Lorentzian geometry: entropy is proportional to area (plus corrections) if and
only if the dynamical equations are the Einstein equations (plus corrections).
It is quite possible to have Hawking radiation occur in physical situations in
which the laws of black hole mechanics do not apply, and in situations in which
the notion of black hole entropy does not even make any sense. This observation
has important implications for any derivation of black hole entropy that seeks
to deduce black hole entropy from the Hawking radiation.Comment: Uses ReV_TeX 3.0; Five pages in two-column forma
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