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 $N$-body motion with constant configurational measure is a motion with fixed shape. Here, the configurational measure $\mu$ is a scale invariant product of the moment of inertia $I=\sum_k m_k |q_k|^2$ and the potential function $U=\sum_{i<j} m_i m_j/|q_i-q_j|^\alpha$, $\alpha >0$. Namely, $\mu = I^{\alpha/2}U$. We will show that this conjecture is true for planar equal-mass three-body problem under the strong force potential $\sum_{i<j} 1/|q_i-q_j|^2$

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