Nonlinear dynamos at infinite magnetic Prandtl number

The dynamo instability is investigated in the limit of infinite magnetic Prandtl number. In this limit the fluid is assumed to be very viscous so that the inertial terms can be neglected and the flow is slaved to the forcing. The forcing consist of an external forcing function that drives the dynamo flow and the resulting Lorentz force caused by the back reaction of the magnetic field. The flows under investigation are the Archontis flow, and the ABC flow forced at two different scales. The investigation covers roughly three orders of magnitude of the magnetic Reynolds number above onset. All flows show a weak increase of the averaged magnetic energy as the magnetic Reynolds number is increased. Most of the magnetic energy is concentrated in flat elongated structures that produce a Lorentz force with small solenoidal projection so that the resulting magnetic field configuration was almost force-free. Although the examined system has zero kinetic Reynolds number at sufficiently large magnetic Reynolds number the structures are unstable to small scale fluctuations that result in a chaotic temporal behavior

Selective decay by Casimir dissipation in fluids

The problem of parameterizing the interactions of larger scales and smaller scales in fluid flows is addressed by considering a property of two-dimensional incompressible turbulence. The property we consider is selective decay, in which a Casimir of the ideal formulation (enstrophy in 2D flows, helicity in 3D flows) decays in time, while the energy stays essentially constant. This paper introduces a mechanism that produces selective decay by enforcing Casimir dissipation in fluid dynamics. This mechanism turns out to be related in certain cases to the numerical method of anticipated vorticity discussed in \cite{SaBa1981,SaBa1985}. Several examples are given and a general theory of selective decay is developed that uses the Lie-Poisson structure of the ideal theory. A scale-selection operator allows the resulting modifications of the fluid motion equations to be interpreted in several examples as parameterizing the nonlinear, dynamical interactions between disparate scales. The type of modified fluid equation systems derived here may be useful in modelling turbulent geophysical flows where it is computationally prohibitive to rely on the slower, indirect effects of a realistic viscosity, such as in large-scale, coherent, oceanic flows interacting with much smaller eddies

Exact solvability of superintegrable Benenti systems

We establish quantum and classical exact solvability for two large classes of maximally superintegrable Benenti systems in $n$ dimensions with arbitrarily large $n$. Namely, we solve the Hamilton--Jacobi and Schr\"odinger equations for the systems in question. The results obtained are illustrated for a model with the cubic potential.Comment: 15 pages, LaTeX 2e, no figures; in the updated version a number of typos were fixed and other minor changes were mad

On the accuracy of conservation of adiabatic invariants in slow-fast systems

Let the adiabatic invariant of action variable in slow-fast Hamiltonian system with two degrees of freedom have two limiting values along the trajectories as time tends to infinity. The difference of two limits is exponentially small in analytic systems. An iso-energetic reduction and canonical transformations are applied to transform the slow-fast systems to form of systems depending on slowly varying parameters in a complexified phase space. On the basis of this method an estimate for the accuracy of conservation of adiabatic invariant is given for such systems.Comment: 27 pages, 14 figure

Role of Rip2 in development of tumor-infiltrating MDSCs and bladder cancer metastasis.

Tumor invasion and metastases represent a complex series of molecular events that portends a poor prognosis. The contribution of inflammatory pathways mediating this process is not well understood. Nod-like receptors (NLRs) of innate immunity function as intracellular sensors of pathogen motifs and danger molecules. We propose a role of NLRs in tumor surveillance and in programming tumor-infiltrating lymphocytes (TILs). In this study, we examined the downstream serine/threonine and tyrosine kinase Rip2 in a murine model of bladder cancer. In Rip2-deficient C57Bl6 mice, larger orthotopic MB49 tumors developed with more numerous and higher incidence of metastases compared to wild-type controls. As such, increased tumor infiltration of CD11b+ Gr1hi myeloid-derived suppressor cells (MDSCs) with concomitant decrease in T cells and NK cells were observed in Rip2-deficient tumor bearing animals using orthotopic and subcutaneous tumor models. Rip2-deficient tumors showed enhanced epithelial-to-mesenchymal transition, with elevated expression of zeb1, zeb2, twist, and snail in the tumor microenvironment. We found that the absence of Rip2 plays an intrinsic role in fostering the development of granulocytic MDSCs by an autocrine and paracrine effect of granulocytic colony stimulating factor (G-CSF) expression. Our findings suggest that NLR pathways may be a novel modality to program TILs and influence tumor metastases

Helicity Conservation via the Noether Theorem

The conservation of helicity in ideal barotropic fluids is discussed from a group theoretical point of view. A new symmetry group is introduced i.e. the alpha group of translations. It is proven via the Noether theorem that this group generates helicity conservation.Comment: 7 pages of te

Integrability of one degree of freedom symplectic maps with polar singularities

In this paper, we treat symplectic difference equations with one degree of freedom. For such cases, we resolve the relation between that the dynamics on the two dimensional phase space is reduced to on one dimensional level sets by a conserved quantity and that the dynamics is integrable, under some assumptions. The process which we introduce is related to interval exchange transformations.Comment: 10 pages, 2 figure

An Exact Universal Gravitational Lensing Equation

We first define what we mean by gravitational lensing equations in a general space-time. A set of exact relations are then derived that can be used as the gravitational lens equations in all physical situations. The caveat is that into these equations there must be inserted a function, a two-parameter family of solutions to the eikonal equation, not easily obtained, that codes all the relevant (conformal) space-time information for this lens equation construction. Knowledge of this two-parameter family of solutions replaces knowledge of the solutions to the geodesic equations. The formalism is then applied to the Schwarzschild lensing problemComment: 12 pages, submitted to Phys. Rev.

Nucleosynthesis of Elements in Low to Intermediate Mass Stars through the AGB Phase

We present a review of the main phases of stellar evolution with particular emphasis on the nucleosynthesis and mixing mechanisms in low- and intermediate-mass stars. In addition to explicit studies of the effects of the first, second and third dredge-up, we also discuss cool bottom processing and hot bottom burning.Comment: 30 pages, latex, 18 figures, uses style files aipproc.cls aipproc.sty epsf.sty ; to be published in (refereed) conference proceedings "Astrophysical Implications of the Laboratory Study of Presolar Materials", ed. T. Bernatowitz and E. Zinner (AIP: Sunnyside, NY), in press; also available at http://www.maths.monash.edu.au/~boothroy