The Universal Aspect Ratio of Vortices in Rotating Stratified Flows: Theory and Simulation

We derive a relationship for the vortex aspect ratio $\alpha$ (vertical half-thickness over horizontal length scale) for steady and slowly evolving vortices in rotating stratified fluids, as a function of the Brunt-Vaisala frequencies within the vortex $N_c$ and in the background fluid outside the vortex $\bar{N}$, the Coriolis parameter $f$, and the Rossby number $Ro$ of the vortex: $\alpha^2 = Ro(1+Ro) f^2/(N_c^2-\bar{N}^2)$. This relation is valid for cyclones and anticyclones in either the cyclostrophic or geostrophic regimes; it works with vortices in Boussinesq fluids or ideal gases, and the background density gradient need not be uniform. Our relation for $\alpha$ has many consequences for equilibrium vortices in rotating stratified flows. For example, cyclones must have $N_c^2 > \bar{N}^2$; weak anticyclones (with $|Ro| \bar{N}^2$. We verify our relation for $\alpha$ with numerical simulations of the three-dimensional Boussinesq equations for a wide variety of vortices, including: vortices that are initially in (dissipationless) equilibrium and then evolve due to an imposed weak viscous dissipation or density radiation; anticyclones created by the geostrophic adjustment of a patch of locally mixed density; cyclones created by fluid suction from a small localised region; vortices created from the remnants of the violent breakups of columnar vortices; and weakly non-axisymmetric vortices. The values of the aspect ratios of our numerically-computed vortices validate our relationship for $\alpha$, and generally they differ significantly from the values obtained from the much-cited conjecture that $\alpha = f/\bar{N}$ in quasi-geostrophic vortices.Comment: Submitted to the Journal of Fluid Mechanics. Also see the companion paper by Aubert et al. "The Universal Aspect Ratio of Vortices in Rotating Stratified Flows: Experiments and Observations" 201

Linkage of modules over Cohen-Macaulay rings

Inspired by the works in linkage theory of ideals, the concept of sliding depth of extension modules is defined to prove the Cohen-Macaulyness of linked module if the base ring is merely Cohen-Macaulay. Some relations between this new condition and other module-theory conditions such as G-dimension and sequentially Cohen-Macaulay are established. By the way several already known theorems in linkage theory are improved or recovered by new approaches.Comment: 12 Page

Teratogenic effects of gabapentin on the skeletal system of Balb/C mice fetuses

Objectives: To evaluate the effects of gabapentin )GBP( administration on mice fetuses. Methods: This study was carried out in Birjand University of Medical Sciences during 2008. Thirty Balb/c pregnant mice were divided randomly into 3 groups: 2 experimental groups that received 25 mg/kg )I( and 50 mg/kg )II( of GBP intraperitoneally for the first 15 days of pregnancy, and a control group that received normal saline. External observations of day 18 fetuses and skeleton double staining were performed. Results: Both experimental groups showed similar disorders that can be categorized as the following: 1( decrease of fetal body weight and increase of fetal resorption, 2( macroscopic malformations, and 3( skeletal malformations. Fetal body weights were significantly lower, and fetus resorptions were significantly higher in both treated groups compared to the control group. Macroscopic malformations included exencephaly, limbs defects, brachygnathia, vertebral column deformity, and fetuses with severe retarded growth. Skeletal malformations included delayed ossification, scoliosis, calvaria deformity, and mandibular hypoplasia. Conclusion: This study revealed that GBP can induce previously unreported severe malformations if it is used continuously during the implantation, neurulation, and organogenesis stages of pregnancy. Therefore, it is suggested that great caution should be exercised in using GBP during the early stages of pregnancy until further studies are performed to better understand these effects

Plane Cremona maps: saturation and regularity of the base ideal

One studies plane Cremona maps by focusing on the ideal theoretic and homological properties of its homogeneous base ideal ("indeterminacy locus"). The {\em leitmotiv} driving a good deal of the work is the relation between the base ideal and its saturation. As a preliminary one deals with the homological features of arbitrary codimension 2 homogeneous ideals in a polynomial ring in three variables over a field which are generated by three forms of the same degree. The results become sharp when the saturation is not generated in low degrees, a condition to be given a precise meaning. An implicit goal, illustrated in low degrees, is a homological classification of plane Cremona maps according to the respective homaloidal types. An additional piece of this work relates the base ideal of a rational map to a few additional homogeneous "companion" ideals, such as the integral closure, the $\boldsymbol\mu$-fat ideal and a seemingly novel ideal defined in terms of valuations.Comment: New version only 36 pages, one typo correcte