General Equilibrium Under Convex Portfolio Constraints and Heterogeneous Risk Preferences

This paper characterizes the equilibrium in a continuous time financial market populated by heterogeneous agents who differ in their rate of relative risk aversion and face convex portfolio constraints. The model is studied in an application to margin constraints and found to match real world observations about financial variables and leverage cycles. It is shown how margin constraints increase the market price of risk and decrease the interest rate by forcing more risk averse agents to hold more risky assets, producing a higher equity risk premium. In addition, heterogeneity and margin constraints are shown to produce both pro- and counter-cyclical leverage cycles. Beyond two types, it is shown how constraints can cascade and how leverage can exhibit highly non-linear dynamics. Finally, empirical results are given, documenting a novel stylized fact which is predicted by the model, namely that the leverage cycle is both pro- and counter-cyclical

A proposal for climate stability on H2-greenhouse planets

A terrestrial planet in an orbit far outside of the standard habitable zone could maintain surface liquid water as a result of H2-H2 collision-induced absorption by a thick H2 atmosphere. Without a stabilizing climate feedback, however, habitability would be accidental and likely brief. In this letter I propose stabilizing climate feedbacks for such a planet that require only that biological functions have an optimal temperature and operate less efficiently at other temperatures. For example, on a planet with a net source of H2 from its interior, H2-consuming life (such as methanogens) could establish a stable climate. If a positive perturbation is added to the equilibrium temperature, H2 consumption by life will increase (cooling the planet) until the equilibrium climate is reestablished. The potential existence of such feedbacks makes H2-warmed planets more attractive astrobiological targets.Comment: 5 pages, 3 figures, accepted at ApJ

Analytical investigation of the decrease in the size of the habitable zone due to limited CO2_2 outgassing rate

The habitable zone concept is important because it focuses the scientific search for extraterrestrial life and aids the planning of future telescopes. Recent work has shown that planets near the outer edge of the habitable zone might not actually be able to stay warm and habitable if CO$_2$ outgassing rates are not large enough to maintain high CO$_2$ partial pressures against removal by silicate weathering. In this paper I use simple equations for the climate and CO$_2$ budget of a planet in the habitable zone that can capture the qualitative behavior of the system. With these equations I derive an analytical formula for an effective outer edge of the habitable zone, including limitations imposed by the CO$_2$ outgassing rate. I then show that climate cycles between a Snowball state and a warm climate are only possible beyond this limit if the weathering rate in the Snowball climate is smaller than the CO$_2$ outgassing rate (otherwise stable Snowball states result). I derive an analytical solution for the climate cycles including a formula for their period in this limit. This work allows us to explore the qualitative effects of weathering processes on the effective outer edge of the habitable zone, which is important because weathering parameterizations are uncertain.Comment: accepted at Ap

A Low-order Model of Water Vapor, Clouds, and Thermal Emission for Tidally Locked Terrestrial Planets

In the spirit of minimal modeling of complex systems, we develop an idealized two-column model to investigate the climate of tidally locked terrestrial planets with Earth-like atmospheres in the habitable zone of M-dwarf stars. The model is able to approximate the fundamental features of the climate obtained from three-dimensional (3D) atmospheric general circulation model (GCM) simulations. One important reason for the two-column model's success is that it reproduces the high cloud albedo of the GCM simulations, which reduces the planet's temperature and delays the onset of a runaway greenhouse state. The two-column model also clearly illustrates a secondary mechanism for determining the climate: the nightside acts as a ``radiator fin'' through which infrared energy can be lost to space easily. This radiator fin is maintained by a temperature inversion and dry air on the nightside, and plays a similar role to the subtropics on modern Earth. Since 1D radiative-convective models cannot capture the effects of the cloud albedo and radiator fin, they are systematically biased towards a narrower habitable zone. We also show that cloud parameters are most important for determining the day--night thermal emission contrast in the two-column model, which decreases and eventually reverses as the stellar flux increases. This reversal is important because it could be detected by future extrasolar planet characterization missions, which would suggest that the planet has Earth-like water clouds and is potentially habitable.Comment: The Astrophysical Journal (in press), 14 pages, 11 figures, 1 tabl

Teacher Contract Non-Renewal in the Rocky Mountains

Success for students in the 21st century increasingly relies on competencies and proficiencies typically available on]y through formal educational processes. Researchers have noted the paramount importance of quality teaching as the important criterion for student success (Haycock, 1998; Marzano, 2003). Recent reforms have increased the expectation that school principals energetically address teacher evaluations and subsequently remove ineffective teachers. These recent reforms tend to have common priorities, including emphasizing high quality teaching, evaluating teachers for merit pay purposes, and linking evaluation to student performance with an emphasis on the removal of ineffective teachers from the classroom

Temperature Structure and Atmospheric Circulation of Dry, Tidally Locked Rocky Exoplanets

Next-generation space telescopes will observe the atmospheres of rocky planets orbiting nearby M-dwarfs. Understanding these observations will require well-developed theory in addition to numerical simulations. Here we present theoretical models for the temperature structure and atmospheric circulation of dry, tidally locked rocky exoplanets with grey radiative transfer and test them using a general circulation model (GCM). First, we develop a radiative-convective model that captures surface temperatures of slowly rotating and cool atmospheres. Second, we show that the atmospheric circulation acts as a global heat engine, which places strong constraints on large-scale wind speeds. Third, we develop a radiative-convective-subsiding model which extends our radiative-convective model to hot and thin atmospheres. We find that rocky planets develop large day-night temperature gradients at a ratio of wave-to-radiative timescales up to two orders of magnitude smaller than the value suggested by work on hot Jupiters. The small ratio is due to the heat engine inefficiency and asymmetry between updrafts and subsidence in convecting atmospheres. Fourth, we show using GCM simulations that rotation only has a strong effect on temperature structure if the atmosphere is hot or thin. Our models let us map out atmospheric scenarios for planets such as GJ 1132b and show how thermal phase curves could constrain them. Measuring phase curves of short-period planets will require similar amounts of time on the James Webb Space Telescope as detecting molecules via transit spectroscopy, so future observations should pursue both techniques.Comment: Accepted in Ap

Asymptotic freedom in a scalar field theory on the lattice

An alternative model to the trivial $\phi^4$-theory of the standard model of weak interactions is suggested, which embodies the Higgs-mechanism, but is free of the conceptual problems of standard $\phi ^4$-theory. We propose a N-component, O(N)-symmetric scalar field theory, which is originally defined on the lattice. The model can be motivated from SU(2) gauge theory. Thereby the scalar field arises as a gauge invariant degree of freedom. The scalar lattice model is analytically solved in the large N limit. The continuum limit is approached via an asymptotically free scaling. The renormalized theory evades triviality, and furthermore gives rise to a dynamically formed mass of the scalar particle.Comment: 10 pages, LaTeX, one figure and a motivation for the particular type of action adde