Double-diffusive erosion of the core of Jupiter

We present Direct Numerical Simulations of the transport of heat and heavy elements across a double-diffusive interface or a double-diffusive staircase, in conditions that are close to those one may expect to find near the boundary between the heavy-element rich core and the hydrogen-helium envelope of giant planets such as Jupiter. We find that the non-dimensional ratio of the buoyancy flux associated with heavy element transport to the buoyancy flux associated with heat transport lies roughly between 0.5 and 1, which is much larger than previous estimates derived by analogy with geophysical double-diffusive convection. Using these results in combination with a core-erosion model proposed by Guillot et al. (2004), we find that the entire core of Jupiter would be eroded within less than 1Myr assuming that the core-envelope boundary is composed of a single interface. We also propose an alternative model that is more appropriate in the presence of a well-established double-diffusive staircase, and find that in this limit a large fraction of the core could be preserved. These findings are interesting in the context of Juno's recent results, but call for further modeling efforts to better understand the process of core erosion from first principles.Comment: Accepted for publication in Ap

Methods for network generation and spectral feature selection: especially on gene expression data

2019 Fall.Includes bibliographical references.Feature selection is an essential step in many data analysis pipelines due to its ability to remove unimportant data. We will describe how to realize a data set as a network using correlation, partial correlation, heat kernel and random edge generation methods. Then we lay out how to select features from these networks mainly leveraging the spectrum of the graph Laplacian, adjacency, and supra-adjacency matrices. We frame this work in the context of gene co-expression network analysis and proceed with a brief analysis of a small set of gene expression data for human subjects infected with the flu virus. We are able to distinguish two sets of 14-15 genes which produce two fold SSVM classification accuracies at certain times that are at least as high as classification accuracies done with more than 12,000 genes

Cassini Ring Seismology as a Probe of Saturn's Interior I: Rigid Rotation

Seismology of the gas giants holds the potential to resolve long-standing questions about their internal structure and rotation state. We construct a family of Saturn interior models constrained by the gravity field and compute their adiabatic mode eigenfrequencies and corresponding Lindblad and vertical resonances in Saturn's C ring, where more than twenty waves with pattern speeds faster than the ring mean motion have been detected and characterized using high-resolution Cassini Visual and Infrared Mapping Spectrometer (VIMS) stellar occultation data. We present identifications of the fundamental modes of Saturn that appear to be the origin of these observed ring waves, and use their observed pattern speeds and azimuthal wavenumbers to estimate the bulk rotation period of Saturn's interior to be $10{\rm h}\, 33{\rm m}\, 38{\rm s}^{+1{\rm m}\, 52{\rm s}}_{-1{\rm m}\, 19{\rm s}}$ (median and 5%/95% quantiles), significantly faster than Voyager and Cassini measurements of periods in Saturn's kilometric radiation, the traditional proxy for Saturn's bulk rotation period. The global fit does not exhibit any clear systematics indicating strong differential rotation in Saturn's outer envelope.Comment: 19 pages, 6 figures, 3 tables, accepted to ApJ; a bug fix improves the fit, predicts faster bulk spin periods (Figure 4) and virtually eliminates evidence for strong radial differential rotation (Figure 5

Saturn's Rings as a Seismograph to Probe Saturn's Internal Structure

As it has already done for Earth, the Sun, and the stars, seismology has the potential to radically change the way the interiors of giant planets are studied. In a sequence of events foreseen by only a few, observations of Saturn's rings by the Cassini spacecraft have rapidly broken ground on giant planet seismology. Gravity directly couples the planet's normal mode oscillations to the orbits of ring particles, generating spiral waves whose frequencies encode Saturn's internal structure and rotation. These modes have revealed a stably stratified region near Saturn's center and provided a new constraint on Saturn's rotation

Parental Kidnapping: Can the Uniform Child Custody Jurisdiction Act and Federal Parental Kidnapping Prevention Act of 1980 Effectively Deter It?

Despite the adoption in forty-four states of the Uniform Child Custody Jurisdiction Act, kidnapping remains a widespread alternative for parents who seek custody of their children. The author discusses how the willingness of courts to entertain the custody petition of a parent who has kidnapped his child has provided incentive for child-snatching, and probes section 8 of the Act, which sets forth guidelines for courts to use in determining whether to hear such petitions. Selected cases are presented to illustrate a proper interpretation and application of section 8 in light of the Act\u27s overall purpose. Finally, the author explains the role of the Parental Kidnapping Prevention Act of 1980, which represents limited federal intervention in the child custody arena

Torts - Negligent Supervision - College Liability - Student Intoxication Injury

The United States Court of Appeals for the Third Circuit has held that a college has no liability for prima facie negligence when students consume alcohol at an off-campus, college sponsored, extracurricular activity which results in student injury. Bradshaw v. Rawlings, 612 F.2d 135 (3d Cir. 1979), cert. denied, 100 S. Ct. 1836 (1980)