Hyperbolic conservation laws on the sphere. A geometry-compatible finite volume scheme

We consider entropy solutions to the initial value problem associated with scalar nonlinear hyperbolic conservation laws posed on the two-dimensional sphere. We propose a finite volume scheme which relies on a web-like mesh made of segments of longitude and latitude lines. The structure of the mesh allows for a discrete version of a natural geometric compatibility condition, which arose earlier in the well-posedness theory established by Ben-Artzi and LeFloch. We study here several classes of flux vectors which define the conservation law under consideration. They are based on prescribing a suitable vector field in the Euclidean three-dimensional space and then suitably projecting it on the sphere's tangent plane; even when the flux vector in the ambient space is constant, the corresponding flux vector is a non-trivial vector field on the sphere. In particular, we construct here "equatorial periodic solutions", analogous to one-dimensional periodic solutions to one-dimensional conservation laws, as well as a wide variety of stationary (steady state) solutions. We also construct "confined solutions", which are time-dependent solutions supported in an arbitrarily specified subdomain of the sphere. Finally, representative numerical examples and test-cases are presented.Comment: 22 pages, 10 figures. This is the third part of a series; see also arXiv:math/0612846 and arXiv:math/061284

Recent Advances Concerning Certain Class of Geophysical Flows

This paper is devoted to reviewing several recent developments concerning certain class of geophysical models, including the primitive equations (PEs) of atmospheric and oceanic dynamics and a tropical atmosphere model. The PEs for large-scale oceanic and atmospheric dynamics are derived from the Navier-Stokes equations coupled to the heat convection by adopting the Boussinesq and hydrostatic approximations, while the tropical atmosphere model considered here is a nonlinear interaction system between the barotropic mode and the first baroclinic mode of the tropical atmosphere with moisture. We are mainly concerned with the global well-posedness of strong solutions to these systems, with full or partial viscosity, as well as certain singular perturbation small parameter limits related to these systems, including the small aspect ratio limit from the Navier-Stokes equations to the PEs, and a small relaxation-parameter in the tropical atmosphere model. These limits provide a rigorous justification to the hydrostatic balance in the PEs, and to the relaxation limit of the tropical atmosphere model, respectively. Some conditional uniqueness of weak solutions, and the global well-posedness of weak solutions with certain class of discontinuous initial data, to the PEs are also presented.Comment: arXiv admin note: text overlap with arXiv:1507.0523

Overexpression of ribosomal RNA in prostate cancer is common but not linked to rDNA promoter hypomethylation

Alterations in nucleoli, including increased numbers, increased size, altered architecture and increased function are hallmarks of prostate cancer cells. The mechanisms that result in increased nucleolar size, number and function in prostate cancer have not been fully elucidated. The nucleolus is formed around repeats of a transcriptional unit encoding a 45S ribosomal RNA (rRNA) precursor that is then processed to yield the mature 18S, 5.8S and 28S RNA species. Although it has been generally accepted that tumor cells overexpress rRNA species, this has not been examined in clinical prostate cancer. We find that indeed levels of the 45S rRNA, 28S, 18S and 5.8S are overexpressed in the majority of human primary prostate cancer specimens as compared with matched benign tissues. One mechanism that can alter nucleolar function and structure in cancer cells is hypomethylation of CpG dinucleotides of the upstream rDNA promoter region. However, this mechanism has not been examined in prostate cancer. To determine whether rRNA overexpression could be explained by hypomethylation of these CpG sites, we also evaluated the DNA methylation status of the rDNA promoter in prostate cancer cell lines and the clinical specimens. Bisulfite sequencing of genomic DNA revealed two roughly equal populations of loci in cell lines consisting of those that contained densely methylated deoxycytidine residues within CpGs and those that were largely unmethylated. All clinical specimens also contained two populations with no marked changes in methylation of this region in cancer as compared with normal. We recently reported that MYC can regulate rRNA levels in human prostate cancer; here we show that MYC mRNA levels are correlated with 45S, 18S and 5.8S rRNA levels. Further, as a surrogate for nucleolar size and number, we examined the expression of fibrillarin, which did not correlate with rRNA levels. We conclude that rRNA levels are increased in human prostate cancer, but that hypomethylation of the rDNA promoter does not explain this increase, nor does hypomethylation explain alterations in nucleolar number and structure in prostate cancer cells. Rather, rRNA levels and nucleolar size and number relate more closely to MYC overexpression

On the development of baroclinic waves influenced by friction and heating

The influence of surface skin friction and a specific type of heating on the stability of baroclinic waves in a two-level, quasi-geostrophic model is investigated. It is found that the effect of friction alone changes the neutral stability curve in such a way that a broader band of wavelengths are unstable for a given value of the vertical windshear. The neutral stability curve is independent of the intensity of friction in this case. The effect of heating is to make all waves longer than a certain critical wave length unstable, but the amplification rate is very small for large values of the wavelength. The combined effect of friction and heating will in general tend to stabilize the waves. The amplification rate is investigated in all cases.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43246/1/24_2004_Article_BF00874891.pd

Nucleolus: the fascinating nuclear body

Nucleoli are the prominent contrasted structures of the cell nucleus. In the nucleolus, ribosomal RNAs are synthesized, processed and assembled with ribosomal proteins. RNA polymerase I synthesizes the ribosomal RNAs and this activity is cell cycle regulated. The nucleolus reveals the functional organization of the nucleus in which the compartmentation of the different steps of ribosome biogenesis is observed whereas the nucleolar machineries are in permanent exchange with the nucleoplasm and other nuclear bodies. After mitosis, nucleolar assembly is a time and space regulated process controlled by the cell cycle. In addition, by generating a large volume in the nucleus with apparently no RNA polymerase II activity, the nucleolus creates a domain of retention/sequestration of molecules normally active outside the nucleolus. Viruses interact with the nucleolus and recruit nucleolar proteins to facilitate virus replication. The nucleolus is also a sensor of stress due to the redistribution of the ribosomal proteins in the nucleoplasm by nucleolus disruption. The nucleolus plays several crucial functions in the nucleus: in addition to its function as ribosome factory of the cells it is a multifunctional nuclear domain, and nucleolar activity is linked with several pathologies. Perspectives on the evolution of this research area are proposed