On the formation of small-time curvature singularities in vortex sheets

The Kelvin-Helmholtz model for the evolution of an infinitesimally thin vortex sheet in an inviscid fluid is mathematically ill-posed for general classes of initial conditions. However, if the initial data, say imposed at t=0, is in a certain class of analytic functions then the problem is well-posed for a finite time until a singularity forms, say at t=ts, on the vortex-sheet interface, e.g. as illustrated by Moore (1979). However, if the problem is analytically continued into the complex plane, then the singularity, or singularities, exist for t<ts away from the physical real axis. More specifically, Cowley et al. (1999) found that for a class of analytic initial conditions, singularities can form in the complex plane at t=0+. They posed asymptotic expansions in the neighbourhood of these singularities for 0<t<<1, and found numerical solutions to the governing similarity differential equations. In this paper we obtain new exact solutions to these equations, show that the singularities always correspond to local 3/2-power singularities, and determine both the number and precise locations of all branch points. Further, our analytical approach can be extended to a more general class of initial conditions. These new exact solutions can assist in resolving the small-time behaviour for the numerical solution of the Birkhoff-Rott equations

Peptidyl-prolyl cis-trans isomerases (immunophilins) and their roles in parasite biochemistry, host-parasite interaction and antiparasitic drug action.

Immunophilin is the collective name given to the cyclophilin and FK506-binding protein (FKBP) families. As the name suggests, these include the major binding proteins of certain immunosuppressive drugs: cyclophilins for the cyclic peptide cyclosporin A and FKBPs for the macrolactones FK506 and rapamycin. Both families, although dissimilar in sequence, possess peptidyl-prolyl &lt;i&gt;cis-trans&lt;/i&gt; isomerase activity in vitro and can play roles in protein folding and transport, RNA splicing and the regulation of multiprotein complexes in cells. In addition to enzymic activity, many immunophilins act as molecular chaperones. This property may be conferred by the isomerase domain and/or by additional domains. Recent years have seen a great increase in the number of known immunophilin genes in parasitic protozoa and helminths and in many cases their products have been characterized biochemically and their temporal and spatial expression patterns have been examined. Some of these genes represent novel types: one example is a &lt;i&gt;Toxoplasma gondii&lt;/i&gt; gene encoding a protein with both cyclophilin and FKBP domains. Likely roles in protein folding and oligomerisation, RNA splicing and sexual differentiation have been suggested for parasite immunophilins. In addition, unexpected roles in parasite virulence (Mip FKBP of &lt;i&gt;Trypanosoma cruzi&lt;/i&gt;) and host immuno-modulation (e.g. 18-kDa cyclophilin of &lt;i&gt;Toxoplasma gondii&lt;/i&gt;) have been established. Furthermore, in view of the potent antiparasitic activities of cyclosporins, macrolactones and nonimmunosuppressive derivatives of these compounds, immunophilins may mediate drug action and/or may themselves represent potential drug targets. Investigation of the mechanisms of action of these agents may lead to the design of potent and selective antimalarial and other antiparasitic drugs. This review discusses the properties of immunophilins in parasites and the 'animal model' &lt;i&gt;Caenorhabditis elegans&lt;/i&gt; and relates these to our understanding of the roles of these proteins in cellular biochemistry, host-parasite interaction and the antiparasitic mechanisms of the drugs that bind to them

Quark matter in compact stars?

Ozel, in a recent reanalysis of EXO 0748-676 observational data (astro-ph/0605106), concluded that quark matter probably does not exist in the center of compact stars. We show that the data is actually consistent with the presence of quark matter in compact stars.Comment: 4 pages, LaTeX; New title and overall rewrite to reflect version published in Nature. Conclusions unchange

Wavefields forced by long obstacles on a beta-plane

This paper presents analytical and numerical solutions for steady flow past long obstacles on a beta-plane. In the oceanographically-relevant limit of small Rossby and Ekman numbers nonlinear advection remains important but viscosity appears only through the influence of Ekman pumping. A reduced boundary-layer-type equation is derived giving the long-obstacle limit of an equation described in Page & Johnson (1990). Analytical solutions are presented or described in various asymptotic limits of this equation and compared with previous results for this or related flows. A novel technique for the numerical solution of the boundary-layer equation, based on a downstream-upstream iteration procedure, is described. Some modifications of the asymptotic layer structure described in Page & Johnson (1991) and Johnson & Page (1993) for the weakly nonlinear low-friction regime are outlined for the case of a lenticular obstacle

FLOW PAST CYLINDRICAL OBSTACLES ON A BETA-PLANE

The flow past a cylindrical obstacle in an enclosed channel is examined when the entire configuration is rotating rapidly about an axis which is aligned with that of the obstacle. When viewed from a frame of reference which is rotating with the channel, Coriolis forces dominate and act to constrain the motion to be two-dimensional. The channel is considered to have depth varying linearly across its width, producing effects equivalent to the so-called-beta-plane approximation and permitting waves to travel away from the obstacle, both upstream and downstream. For the eastward flow considered in this paper, this leads to the formation of a lee-wavetrain downstream of the obstacle and, under some conditions, a region of retarded, or 'blocked', flow upstream of the obstacle. The flow regime studied is essentially inviscid, although one form of frictional effect on the flow, introduced through the Ekman layers, is included. The properties of this system are examined numerically and compared with the theoretical predictions from other studies, which are applicable in asymptotic limits of the parameters. In particular, the relevance of 'Long's model' solutions is considered

Flow past a circular cylinder on a β-plane

This paper gives analytical and numerical solutions for both westward and eastward flows past obstacles on a beta-plane. The flows are considered in the quasi-geostrophic limit where nonlinearity and viscosity allow deviations from purely geostrophic flow. Asymptotic solutions for the layer structure in almost-inviscid flow are given for westward flow past both circular and more elongated cylindrical obstacles. Structures are given for all strengths of nonlinearity from purely linear flow through to strongly nonlinear flows where viscosity is negligible and potential vorticity conserved. These structures are supported by accurate numerical computations. Results on detraining nonlinear western boundary layers and corner regions in Page & Johnson (1991) are used to present the full structure for eastward flow past an obstacle with a bluff rear face, completing previous analysis in Page & Johnson (1990) of eastward flow past obstacles without rear stagnation points. Viscous separation is discussed and analytical structures proposed for separated flows. These lead to predictions for the size of separated regions that reproduce the behaviour observed in experiments and numerical computations on beta-plane flows

Inhibition of synaptic transmission and G protein modulation by synthetic CaV2.2 Ca2+ channel peptides

Abstract: Modulation of presynaptic voltage-dependent Ca+ channels is a major means of controlling neurotransmitter release. The CaV 2.2 Ca2+ channel subunit contains several inhibitory interaction sites for Gβγ subunits, including the amino terminal (NT) and I–II loop. The NT and I–II loop have also been proposed to undergo a G protein-gated inhibitory interaction, whilst the NT itself has also been proposed to suppress CaV 2 channel activity. Here, we investigate the effects of an amino terminal (CaV 2.2[45–55]) ‘NT peptide’ and a I–II loop alpha interaction domain (CaV 2.2[377–393]) ‘AID peptide’ on synaptic transmission, Ca2+ channel activity and G protein modulation in superior cervical ganglion neurones (SCGNs). Presynaptic injection of NT or AID peptide into SCGN synapses inhibited synaptic transmission and also attenuated noradrenaline-induced G protein modulation. In isolated SCGNs, NT and AID peptides reduced whole-cell Ca2+ current amplitude, modified voltage dependence of Ca2+ channel activation and attenuated noradrenaline-induced G protein modulation. Co-application of NT and AID peptide negated inhibitory actions. Together, these data favour direct peptide interaction with presynaptic Ca2+ channels, with effects on current amplitude and gating representing likely mechanisms responsible for inhibition of synaptic transmission. Mutations to residues reported as determinants of Ca2+ channel function within the NT peptide negated inhibitory effects on synaptic transmission, Ca2+ current amplitude and gating and G protein modulation. A mutation within the proposed QXXER motif for G protein modulation did not abolish inhibitory effects of the AID peptide. This study suggests that the CaV 2.2 amino terminal and I–II loop contribute molecular determinants for Ca2+ channel function; the data favour a direct interaction of peptides with Ca2+ channels to inhibit synaptic transmission and attenuate G protein modulation. Non-technical summary: Nerve cells (neurones) in the body communicate with each other by releasing chemicals (neurotransmitters) which act on proteins called receptors. An important group of receptors (called G protein coupled receptors, GPCRs) regulate the release of neurotransmitters by an action on the ion channels that let calcium into the cell. Here, we show for the first time that small peptides based on specific regions of calcium ion channels involved in GPCR signalling can themselves inhibit nerve cell communication. We show that these peptides act directly on calcium channels to make them more difficult to open and thus reduce calcium influx into native neurones. These peptides also reduce GPCR-mediated signalling. This work is important in increasing our knowledge about modulation of the calcium ion channel protein; such knowledge may help in the development of drugs to prevent signalling in pathways such as those involved in pain perception

Higgs bosons near 125 GeV in the NMSSM with constraints at the GUT scale

We study the NMSSM with universal Susy breaking terms (besides the Higgs sector) at the GUT scale. Within this constrained parameter space, it is not difficult to find a Higgs boson with a mass of about 125 GeV and an enhanced cross section in the diphoton channel. An additional lighter Higgs boson with reduced couplings and a mass <123 GeV is potentially observable at the LHC. The NMSSM-specific Yukawa couplings lambda and kappa are relatively large and tan(beta) is small, such that lambda, kappa and the top Yukawa coupling are of order 1 at the GUT scale. The lightest stop can be as light as 105 GeV, and the fine-tuning is modest. WMAP constraints can be satisfied by a dominantly higgsino-like LSP with substantial bino, wino and singlino admixtures and a mass of ~60-90 GeV, which would potentially be detectable by XENON100.Comment: 20 pages, 14 figure