Decay laws for three-dimensional magnetohydrodynamic turbulence

Decay laws for three-dimensional magnetohydrodynamic turbulence are obtained from high-resolution numerical simulations using up to 512^3 modes...

Normal Cones and Thompson Metric

The aim of this paper is to study the basic properties of the Thompson metric $d_T$ in the general case of a real linear space $X$ ordered by a cone $K$. We show that $d_T$ has monotonicity properties which make it compatible with the linear structure. We also prove several convexity properties of $d_T$ and some results concerning the topology of $d_T$, including a brief study of the $d_T$-convergence of monotone sequences. It is shown most of the results are true without any assumption of an Archimedean-type property for $K$. One considers various completeness properties and one studies the relations between them. Since $d_T$ is defined in the context of a generic ordered linear space, with no need of an underlying topological structure, one expects to express its completeness in terms of properties of the ordering, with respect to the linear structure. This is done in this paper and, to the best of our knowledge, this has not been done yet. The Thompson metric $d_T$ and order-unit (semi)norms $|\cdot|_u$ are strongly related and share important properties, as both are defined in terms of the ordered linear structure. Although $d_T$ and $|\cdot|_u$ are only topological (and not metrical) equivalent on $K_u$, we prove that the completeness is a common feature. One proves the completeness of the Thompson metric on a sequentially complete normal cone in a locally convex space. At the end of the paper, it is shown that, in the case of a Banach space, the normality of the cone is also necessary for the completeness of the Thompson metric.Comment: 36 page

Frame-insensitive expression cloning of fluorescent protein from <i>Scolionema suvaense</i>

Expression cloning from cDNA is an important technique for acquiring genes encoding novel fluorescent proteins. However, the probability of in-frame cDNA insertion following the first start codon of the vector is normally only 1/3, which is a cause of low cloning efficiency. To overcome this issue, we developed a new expression plasmid vector, pRSET-TriEX, in which transcriptional slippage was induced by introducing a DNA sequence of (dT)14 next to the first start codon of pRSET. The effectiveness of frame-insensitive cloning was validated by inserting the gene encoding eGFP with all three possible frames to the vector. After transformation with one of these plasmids, E. coli cells expressed eGFP with no significant difference in the expression level. The pRSET-TriEX vector was then used for expression cloning of a novel fluorescent protein from Scolionema suvaense. We screened 3658 E. coli colonies transformed with pRSET-TriEX containing Scolionema suvaense cDNA, and found one colony expressing a novel green fluorescent protein, ScSuFP. The highest score in protein sequence similarity was 42% with the chain c of multi-domain green fluorescent protein like protein “ember” from Anthoathecata sp. Variations in the N- and/or C-terminal sequence of ScSuFP compared to other fluorescent proteins indicate that the expression cloning, rather than the sequence similarity-based methods, was crucial for acquiring the gene encoding ScSuFP. The absorption maximum was at 498 nm, with an extinction efficiency of 1.17 × 105 M−1·cm−1. The emission maximum was at 511 nm and the fluorescence quantum yield was determined to be 0.6. Pseudo-native gel electrophoresis showed that the protein forms obligatory homodimers

Kinetic Energy Decay Rates of Supersonic and Super-Alfvenic Turbulence in Star-Forming Clouds

We present numerical studies of compressible, decaying turbulence, with and without magnetic fields, with initial rms Alfven and Mach numbers ranging up to five, and apply the results to the question of the support of star-forming interstellar clouds of molecular gas. We find that, in 1D, magnetized turbulence actually decays faster than unmagnetized turbulence. In all the regimes that we have studied 3D turbulence-super-Alfvenic, supersonic, sub-Alfvenic, and subsonic-the kinetic energy decays as (t-t0)^(-x), with 0.85 < x < 1.2. We compared results from two entirely different algorithms in the unmagnetized case, and have performed extensive resolution studies in all cases, reaching resolutions of 256^3 zones or 350,000 particles. We conclude that the observed long lifetimes and supersonic motions in molecular clouds must be due to external driving, as undriven turbulence decays far too fast to explain the observations.Comment: Submitted to Phys. Rev. Letters, 29 Nov. 1997. 10 pages, 2 figures, also available from http://www.mpia-hd.mpg.de/theory/preprints.html#maclo