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.

The genesis of the Brazilian vernacular: insights from the indigenization of Portuguese in Angola

This study uses the model of partial restructuring developed in Holm (2004), which compared the sociolinguistic history and synchronic structure of Brazilian Vernacular Portuguese (BVP) with that of four other non-creole vernaculars. Holm (2004) argued that the transmission of the European source languages from native to non-native speakers had led to partial restructuring, in which part of the source languages’ morphosyntax was retained, but a significant number of substrate and interlanguage features were introduced. It identified the linguistic processes that lead to partial restructuring, bringing into focus a key span on the continuum of contact-induced language change which has not previously been analyzed. The present study focuses more tightly on the genesis of BVP and attempts to reconstruct with greater precision the contribution of Bantu languages to its development in the seventeenth and eighteenth centuries by comparing specific areas of its synchronic syntax to corresponding structures in Angolan Vernacular Portuguese, which is currently undergoing indigenization (Holm and Inverno 2005; Inverno forthcoming a, b). The main focus is on the verb phrase (verbal morphology, auxiliaries, negation, and non-verbal predicates) and the noun phrase (number and gender agreement, possessive constructions and pronouns)

Extending human lifespan and the precautionary paradox

This paper argues that a precautionary approach to scientific progress of the sort advocated by Walter Glannon with respect to life-extending therapies involves both incoherence and irresolvable paradox. This paper demonstrates the incoherence of the precautionary approach in many circumstances and argues that with respect to life-extending therapies we have at present no persuasive reasons for a moratorium on such research

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