511 research outputs found
Electro-thermal rocket Patent
Electrothermal rocket engine using resistance heated heat exchange
Saari's homographic conjecture for planar equal-mass three-body problem under a strong force potential
Donald Saari conjectured that the -body motion with constant
configurational measure is a motion with fixed shape. Here, the configurational
measure is a scale invariant product of the moment of inertia and the potential function , . Namely, . We will show
that this conjecture is true for planar equal-mass three-body problem under the
strong force potential
Exploiting the nonlinear impact dynamics of a single-electron shuttle for highly regular current transport
The nanomechanical single-electron shuttle is a resonant system in which a
suspended metallic island oscillates between and impacts at two electrodes.
This setup holds promise for one-by-one electron transport and the
establishment of an absolute current standard. While the charge transported per
oscillation by the nanoscale island will be quantized in the Coulomb blockade
regime, the frequency of such a shuttle depends sensitively on many parameters,
leading to drift and noise. Instead of considering the nonlinearities
introduced by the impact events as a nuisance, here we propose to exploit the
resulting nonlinear dynamics to realize a highly precise oscillation frequency
via synchronization of the shuttle self-oscillations to an external signal.Comment: 5 pages, 4 figure
On a problem of A. Weil
A topological invariant of the geodesic laminations on a modular surface is
constructed. The invariant has a continuous part (the tail of a continued
fraction) and a combinatorial part (the singularity data). It is shown, that
the invariant is complete, i.e. the geodesic lamination can be recovered from
the invariant. The continuous part of the invariant has geometric meaning of a
slope of lamination on the surface.Comment: to appear Beitr\"age zur Algebra und Geometri
Saari's homographic conjecture for planar equal-mass three-body problem in Newton gravity
Saari's homographic conjecture in N-body problem under the Newton gravity is
the following; configurational measure \mu=\sqrt{I}U, which is the product of
square root of the moment of inertia I=(\sum m_k)^{-1}\sum m_i m_j r_{ij}^2 and
the potential function U=\sum m_i m_j/r_{ij}, is constant if and only if the
motion is homographic. Where m_k represents mass of body k and r_{ij}
represents distance between bodies i and j. We prove this conjecture for planar
equal-mass three-body problem.
In this work, we use three sets of shape variables. In the first step, we use
\zeta=3q_3/(2(q_2-q_1)) where q_k \in \mathbb{C} represents position of body k.
Using r_1=r_{23}/r_{12} and r_2=r_{31}/r_{12} in intermediate step, we finally
use \mu itself and \rho=I^{3/2}/(r_{12}r_{23}r_{31}). The shape variables \mu
and \rho make our proof simple
Potential for Solar System Science with the ngVLA
Radio wavelength observations of solar system bodies are a powerful method of
probing many characteristics of those bodies. From surface and subsurface, to
atmospheres (including deep atmospheres of the giant planets), to rings, to the
magnetosphere of Jupiter, these observations provide unique information on
current state, and sometimes history, of the bodies. The ngVLA will enable the
highest sensitivity and resolution observations of this kind, with the
potential to revolutionize our understanding of some of these bodies. In this
article, we present a review of state-of-the-art radio wavelength observations
of a variety of bodies in our solar system, varying in size from ring particles
and small near-Earth asteroids to the giant planets. Throughout the review we
mention improvements for each body (or class of bodies) to be expected with the
ngVLA. A simulation of a Neptune-sized object is presented in Section 6.
Section 7 provides a brief summary for each type of object, together with the
type of measurements needed for all objects throughout the Solar System
Extrasolar Planet Eccentricities from Scattering in the Presence of Residual Gas Disks
Gravitational scattering between massive planets has been invoked to explain
the eccentricity distribution of extrasolar planets. For scattering to occur,
the planets must either form in -- or migrate into -- an unstable
configuration. In either case, it is likely that a residual gas disk, with a
mass comparable to that of the planets, will be present when scattering occurs.
Using explicit hydrodynamic simulations, we study the impact of gas disks on
the outcome of two-planet scattering. We assume a specific model in which the
planets are driven toward instability by gravitational torques from an outer
low mass disk. We find that the accretion of mass and angular momentum that
occurs when a scattered planet impacts the disk can strongly influence the
subsequent dynamics by reducing the number of close encounters. The
eccentricity of the innermost surviving planet at the epoch when the system
becomes Hill stable is not substantially altered from the gas-free case, but
the outer planet is circularized by its interaction with the disk. The
signature of scattering initiated by gas disk migration is thus a high fraction
of low eccentricity planets at larger radii accompanying known eccentric
planets. Subsequent secular evolution of the two planets in the presence of
damping can further damp both eccentricities, and tends to push systems away
from apsidal alignment and toward anti-alignment. We note that the late burst
of accretion when the outer planet impacts the disk is in principle observable,
probably via detection of a strong near-IR excess in systems with otherwise
weak disk and stellar accretion signatures.Comment: 7 pages, 7 figures. Accepted to Ap
Symmetry, bifurcation and stacking of the central configurations of the planar 1+4 body problem
In this work we are interested in the central configurations of the planar
1+4 body problem where the satellites have different infinitesimal masses and
two of them are diametrically opposite in a circle. We can think this problem
as a stacked central configuration too. We show that the configuration are
necessarily symmetric and the other sattelites has the same mass. Moreover we
proved that the number of central configuration in this case is in general one,
two or three and in the special case where the satellites diametrically
opposite have the same mass we proved that the number of central configuration
is one or two saying the exact value of the ratio of the masses that provides
this bifurcation.Comment: 9 pages, 2 figures. arXiv admin note: text overlap with
arXiv:1103.627
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