18 research outputs found
Planet Formation in the Outer Solar System
This paper reviews coagulation models for planet formation in the Kuiper
Belt, emphasizing links to recent observations of our and other solar systems.
At heliocentric distances of 35-50 AU, single annulus and multiannulus
planetesimal accretion calculations produce several 1000 km or larger planets
and many 50-500 km objects on timescales of 10-30 Myr in a Minimum Mass Solar
Nebula. Planets form more rapidly in more massive nebulae. All models yield two
power law cumulative size distributions, N_C propto r^{-q} with q = 3.0-3.5 for
radii larger than 10 km and N_C propto r^{-2.5} for radii less than 1 km. These
size distributions are consistent with observations of Kuiper Belt objects
acquired during the past decade. Once large objects form at 35-50 AU,
gravitational stirring leads to a collisional cascade where 0.1-10 km objects
are ground to dust. The collisional cascade removes 80% to 90% of the initial
mass in the nebula in roughly 1 Gyr. This dust production rate is comparable to
rates inferred for alpha Lyr, beta Pic, and other extrasolar debris disk
systems.Comment: invited review for PASP, March 2002. 33 pages of text and 12 figure
Stability and nonlinear adjustment of vortices in Keplerian flows
We investigate the stability, nonlinear development and equilibrium structure
of vortices in a background shearing Keplerian flow. We make use of
high-resolution global two-dimensional compressible hydrodynamic simulations.
We introduce the concept of nonlinear adjustment to describe the transition of
unbalanced vortical fields to a long-lived configuration. We discuss the
conditions under which vortical perturbations evolve into long-lived persistent
structures and we describe the properties of these equilibrium vortices. The
properties of equilibrium vortices appear to be independent from the initial
conditions and depend only on the local disk parameters. In particular we find
that the ratio of the vortex size to the local disk scale height increases with
the decrease of the sound speed, reaching values well above the unity. The
process of spiral density wave generation by the vortex, discussed in our
previous work, appear to maintain its efficiency also at nonlinear amplitudes
and we observe the formation of spiral shocks attached to the vortex. The
shocks may have important consequences on the long term vortex evolution and
possibly on the global disk dynamics. Our study strengthens the arguments in
favor of anticyclonic vortices as the candidates for the promotion of planetary
formation. Hydrodynamic shocks that are an intrinsic property of persistent
vortices in compressible Keplerian flows are an important contributor to the
overall balance. These shocks support vortices against viscous dissipation by
generating local potential vorticity and should be responsible for the eventual
fate of the persistent anticyclonic vortices. Numerical codes have be able to
resolve shock waves to describe the vortex dynamics correctly.Comment: 12 pages, 10 figure
Transversality Conditions for Infinite Horizon Variational Problems on Time Scales
We consider problems of the calculus of variations on unbounded time scales.
We prove the validity of the Euler-Lagrange equation on time scales for
infinite horizon problems, and a new transversality condition.Comment: Submitted 6-October-2009; Accepted 19-March-2010 in revised form; for
publication in "Optimization Letters"
A Vicious Tenacity: The Efficiency Strategy Confronted With the Rebound Effect
Studies of the phenomena known as the “rebound effect,” “backfire,” and the “Jevons Paradox” have cast doubt on the effectiveness, in terms of reduction of energy use, of measures based on efficiency gains. Some of them have shown that efficiency improvements are less effective than expected, others have lent strength to the hypothesis that efficiency improvements are counterproductive in the long run. The difference between the two groups is thus all but negligible. Moreover, it is of considerable pragmatic significance as it may undermine the foundations of solid expectations that had led to ongoing systems and repertoires of action. In this paper we provide a model about the hypothesis that the expectations related to the effects that efficiency gains have on energy and resource consumption may exacerbate the rebound effect and that they prevent alternative strategies, that may turn out to be more effective in reducing energy and resource use, to be enacted. In the concluding paragraph, we propose possibilities for further hypothesis and empirical research that could lead to the refinement of the model