The Ice Cap Zone: A Unique Habitable Zone for Ocean Worlds

Traditional definitions of the habitable zone assume that habitable planets contain a carbonate-silicate cycle that regulates CO2 between the atmosphere, surface, and the interior. Such theories have been used to cast doubt on the habitability of ocean worlds. However, Levi et al (2017) have recently proposed a mechanism by which CO2 is mobilized between the atmosphere and the interior of an ocean world. At high enough CO2 pressures, sea ice can become enriched in CO2 clathrates and sink after a threshold density is achieved. The presence of subpolar sea ice is of great importance for habitability in ocean worlds. It may moderate the climate and is fundamental in current theories of life formation in diluted environments. Here, we model the Levi et al. mechanism and use latitudinally-dependent non-grey energy balance and single-column radiative-convective climate models and find that this mechanism may be sustained on ocean worlds that rotate at least 3 times faster than the Earth. We calculate the circumstellar region in which this cycle may operate for G-M-stars (Teff = 2,600 to 5,800 K), extending from about 1.23 to 1.65, 0.69 to 0.954, 0.38 to 0.528 AU, 0.219 to 0.308 AU, 0.146 to 0.206 AU, and 0.0428 to 0.0617 AU for G2, K2, M0, M3, M5, and M8 stars, respectively. However, unless planets are very young and not tidally locked, our mechanism would be unlikely to apply to stars cooler than a ~M3. We predict C/O ratios for our atmospheres (about 0.5) that can be verified by the JWST mission.Comment: Published in the Monthly Notices of the Royal Astronomical Society (31 pages, 7 Figures, 1 Table) https://doi.org/10.1093/mnras/sty76

λ\lambda-symmetries for discrete equations

Following the usual definition of $\lambda$-symmetries of differential equations, we introduce the analogous concept for difference equations and apply it to some examples.Comment: 10 page

Lie discrete symmetries of lattice equations

We extend two of the methods previously introduced to find discrete symmetries of differential equations to the case of difference and differential-difference equations. As an example of the application of the methods, we construct the discrete symmetries of the discrete Painlev\'e I equation and of the Toda lattice equation

On the integrability of a new lattice equation found by multiple scale analysis

In this paper we discuss the integrability properties of a nonlinear partial difference equation on the square obtained by the multiple scale integrability test from a class of multilinear dispersive equations defined on a four points lattice

Pandemic Flu and the Potential for U.S. Economic Recession: A State-by-State Analysis

Considers how a severe health pandemic outbreak could impact the United States economy and delineates the potential financial loss each state could face

Shortchanging America's Health 2008: A State-by-State Look at How Federal Public Health Dollars Are Spent

Examines public health indicators in each state, in combination with federal and state funding for programs to promote health. Includes state rankings by funding per capita, percentage of population who are uninsured, disease rates, and other indicators

Multiscale expansion and integrability properties of the lattice potential KdV equation

We apply the discrete multiscale expansion to the Lax pair and to the first few symmetries of the lattice potential Korteweg-de Vries equation. From these calculations we show that, like the lowest order secularity conditions give a nonlinear Schroedinger equation, the Lax pair gives at the same order the Zakharov and Shabat spectral problem and the symmetries the hierarchy of point and generalized symmetries of the nonlinear Schroedinger equation.Comment: 10 pages, contribution to the proceedings of the NEEDS 2007 Conferenc

Saccadic latency in amblyopia.

We measured saccadic latencies in a large sample (total n = 459) of individuals with amblyopia or risk factors for amblyopia, e.g., strabismus or anisometropia, and normal control subjects. We presented an easily visible target randomly to the left or right, 3.5° from fixation. The interocular difference in saccadic latency is highly correlated with the interocular difference in LogMAR (Snellen) acuity-as the acuity difference increases, so does the latency difference. Strabismic and strabismic-anisometropic amblyopes have, on average, a larger difference between their eyes in LogMAR acuity than anisometropic amblyopes and thus their interocular latency difference is, on average, significantly larger than anisometropic amblyopes. Despite its relation to LogMAR acuity, the longer latency in strabismic amblyopes cannot be attributed either to poor resolution or to reduced contrast sensitivity, because their interocular differences in grating acuity and in contrast sensitivity are roughly the same as for anisometropic amblyopes. The correlation between LogMAR acuity and saccadic latency arises because of the confluence of two separable effects in the strabismic amblyopic eye-poor letter recognition impairs LogMAR acuity while an intrinsic sluggishness delays reaction time. We speculate that the frequent microsaccades and the accompanying attentional shifts, made while strabismic amblyopes struggle to maintain fixation with their amblyopic eyes, result in all types of reactions being irreducibly delayed