Bounds on solutions of the rotating, stratified, incompressible, non-hydrostatic, three-dimensional Boussinesq equations

We study the three-dimensional, incompressible, non-hydrostatic Boussinesq fluid equations, which are applicable to the dynamics of the oceans and atmosphere. These equations describe the interplay between velocity and buoyancy in a rotating frame. A hierarchy of dynamical variables is introduced whose members $\Omega_{m}(t)$ ($1 \leq m < \infty$) are made up from the respective sum of the $L^{2m}$-norms of vorticity and the density gradient. Each $\Omega_{m}(t)$ has a lower bound in terms of the inverse Rossby number, $Ro^{-1}$, that turns out to be crucial to the argument. For convenience, the $\Omega_{m}$ are also scaled into a new set of variables $D_{m}(t)$. By assuming the existence and uniqueness of solutions, conditional upper bounds are found on the $D_{m}(t)$ in terms of $Ro^{-1}$ and the Reynolds number $Re$. These upper bounds vary across bands in the $\{D_{1},\,D_{m}\}$ phase plane. The boundaries of these bands depend subtly upon $Ro^{-1}$, $Re$, and the inverse Froude number $Fr^{-1}$. For example, solutions in the lower band conditionally live in an absorbing ball in which the maximum value of $\Omega_{1}$ deviates from $Re^{3/4}$ as a function of $Ro^{-1},\,Re$ and $Fr^{-1}$.Comment: 24 pages, 3 figures and 1 tabl

Vlasov moments, integrable systems and singular solutions

The Vlasov equation for the collisionless evolution of the single-particle probability distribution function (PDF) is a well-known Lie-Poisson Hamiltonian system. Remarkably, the operation of taking the moments of the Vlasov PDF preserves the Lie-Poisson structure. The individual particle motions correspond to singular solutions of the Vlasov equation. The paper focuses on singular solutions of the problem of geodesic motion of the Vlasov moments. These singular solutions recover geodesic motion of the individual particles.Comment: 16 pages, no figures. Submitted to Phys. Lett.

Ionic Capillary Evaporation in Weakly Charged Nanopores

Using a variational field theory, we show that an electrolyte confined to a neutral cylindrical nanopore traversing a low dielectric membrane exhibits a first-order ionic liquid-vapor pseudo-phase-transition from an ionic-penetration "liquid" phase to an ionic-exclusion "vapor" phase, controlled by nanopore-modified ionic correlations and dielectric repulsion. For weakly charged nanopores, this pseudotransition survives and may shed light on the mechanism behind the rapid switching of nanopore conductivity observed in experiments.Comment: This version is accepted for publication in PR

A single H/ACA small nucleolar RNA mediates tumor suppression downstream of oncogenic RAS.

Small nucleolar RNAs (snoRNAs) are a diverse group of non-coding RNAs that direct chemical modifications at specific residues on other RNA molecules, primarily on ribosomal RNA (rRNA). SnoRNAs are altered in several cancers; however, their role in cell homeostasis as well as in cellular transformation remains poorly explored. Here, we show that specific subsets of snoRNAs are differentially regulated during the earliest cellular response to oncogenic RASG12V expression. We describe a novel function for one H/ACA snoRNA, SNORA24, which guides two pseudouridine modifications within the small ribosomal subunit, in RAS-induced senescence in vivo. We find that in mouse models, loss of Snora24 cooperates with RASG12V to promote the development of liver cancer that closely resembles human steatohepatitic hepatocellular carcinoma (HCC). From a clinical perspective, we further show that human HCCs with low SNORA24 expression display increased lipid content and are associated with poor patient survival. We next asked whether ribosomes lacking SNORA24-guided pseudouridine modifications on 18S rRNA have alterations in their biophysical properties. Single-molecule Fluorescence Resonance Energy Transfer (FRET) analyses revealed that these ribosomes exhibit perturbations in aminoacyl-transfer RNA (aa-tRNA) selection and altered pre-translocation ribosome complex dynamics. Furthermore, we find that HCC cells lacking SNORA24-guided pseudouridine modifications have increased translational miscoding and stop codon readthrough frequencies. These findings highlight a role for specific snoRNAs in safeguarding against oncogenic insult and demonstrate a functional link between H/ACA snoRNAs regulated by RAS and the biophysical properties of ribosomes in cancer

The structure of a resuscitation-promoting factor domain from Mycobacterium tuberculosis shows homology to lysozymes

Resuscitation-promoting factor (RPF) proteins reactivate stationary-phase cultures of (G+C)-rich Gram-positive bacteria including the causative agent of tuberculosis, Mycobacterium tuberculosis. We report the solution structure of the RPF domain from M. tuberculosis Rv1009 (RpfB) solved by heteronuclear multidimensional NMR. Structural homology with various glycoside hydrolases suggested that RpfB cleaved oligosaccharides. Biochemical studies indicate that a conserved active site glutamate is important for resuscitation activity. These data, as well as the presence of a clear binding pocket for a large molecule, indicate that oligosaccharide cleavage is probably the signal for revival from dormancy

Radio Astronomy

Contains reports on five research projects.National Science Foundation (Grant AST82-14296)National Aeronautics and Space Administration (Grant NAG W-373)National Aeronautics and Space Administration (Grant NAG5-537)U.S. Navy - Office of Naval Research (Contract N00014-84-C-2082)SM Systems and Research, Inc.Defense Advanced Research Project Agency (Contract MDA903-82-K-0521