On the relation between viscoelastic and magnetohydrodynamic flows and their instabilities

We demonstrate a close analogy between a viscoelastic medium and an electrically conducting fluid containing a magnetic field. Specifically, the dynamics of the Oldroyd-B fluid in the limit of large Deborah number corresponds to that of a magnetohydrodynamic (MHD) fluid in the limit of large magnetic Reynolds number. As a definite example of this analogy, we compare the stability properties of differentially rotating viscoelastic and MHD flows. We show that there is an instability of the Oldroyd-B fluid that is physically distinct from both the inertial and elastic instabilities described previously in the literature, but is directly equivalent to the magnetorotational instability in MHD. It occurs even when the specific angular momentum increases outwards, provided that the angular velocity decreases outwards; it derives from the kinetic energy of the shear flow and does not depend on the curvature of the streamlines. However, we argue that the elastic instability of viscoelastic Couette flow has no direct equivalent in MHD.Comment: 21 pages, 3 figures, to be published in J. Fluid Mec

Destabilization by noise of tranverse perturbations to heteroclinic cycles: a simple model and an example from dynamo theory

We show that transverse perturbations from structurally stable heteroclinic cycles can be destabilized by surprisingly small amounts of noise, even when each individual fixed point of the cycle is stable to transverse modes. A condition that favours this process is that the linearization of the dynamics in the transverse direction be characterized by a non-normal matrix. The phenomenon is illustrated by a simple two-dimensional switching model and by a simulation of a convectively driven dynamo

A self-sustaining nonlinear dynamo process in Keplerian shear flows

A three-dimensional nonlinear dynamo process is identified in rotating plane Couette flow in the Keplerian regime. It is analogous to the hydrodynamic self-sustaining process in non-rotating shear flows and relies on the magneto-rotational instability of a toroidal magnetic field. Steady nonlinear solutions are computed numerically for a wide range of magnetic Reynolds numbers but are restricted to low Reynolds numbers. This process may be important to explain the sustenance of coherent fields and turbulent motions in Keplerian accretion disks, where all its basic ingredients are present.Comment: 4 pages, 7 figures, accepted for publication in Physical Review Letter

Constraining the Star Formation Histories of Spiral Bulges

Long-slit spectroscopic observations of line-strengths and kinematics made along the minor axes of four spiral bulges are reported. Comparisons are made between central line-strengths in spiral bulges and those in other morphological types. The bulges are found to have central line-strengths comparable with those of single stellar populations (SSPs) of approximately solar abundance or above. Negative radial gradients are observed in line-strengths, similar to those in elliptical galaxies. The bulge data are consistent with correlations between Mg2, and central velocity dispersion observed in elliptical galaxiess. In contrast to elliptical galaxies, central line-strengths lie within the loci defining the range of and Mg2 achieved by Worthey's (1994) solar abundance ratio, SSPs. The implication of solar abundance ratios indicates differences in the star formation histories of spiral bulges and elliptical galaxies. A ``single zone with in- fall'' model of galactic chemical evolution, using Worthey's (1994) SSPs, is used to constrain possible star formation histories in our sample. We show that , Mg2 and Hbeta line-strengths observed in these bulges cannot be reproduced using primordial collapse models of formation but can be reproduced by models with extended in-fall of gas and star formation (2-17 Gyr) in the region modelled. One galaxy (NGC 5689) shows a central population with luminosity weighted average age of ~5 Gyr, supporting the idea of extended star formation. Kinematic substructure, possibly associated with a central spike in metallicity, is observed at the centre of the Sa galaxy NGC 3623.Comment: 14 pages. MNRAS latex file. Accepted for publication in MNRA

Pressure coefficients of Raman modes of carbon nanotubes resolved by chirality: Environmental effect on graphene sheet

Studies of the mechanical properties of single-walled carbon nanotubes are hindered by the availability only of ensembles of tubes with a range of diameters. Tunable Raman excitation spectroscopy picks out identifiable tubes. Under high pressure, the radial breathing mode shows a strong environmental effect shown here to be largely independent of the nature of the environment . For the G-mode, the pressure coefficient varies with diameter consistent with the thick-wall tube model. However, results show an unexpectedly strong environmental effect on the pressure coefficients. Reappraisal of data for graphene and graphite gives the G-mode Grueuneisen parameter gamma = 1.34 and the shear deformation parameter beta = 1.34.Comment: Submitted to Physical Review

Oscillations and secondary bifurcations in nonlinear magnetoconvection

Complicated bifurcation structures that appear in nonlinear systems governed by partial differential equations (PDEs) can be explained by studying appropriate low-order amplitude equations. We demonstrate the power of this approach by considering compressible magnetoconvection. Numerical experiments reveal a transition from a regime with a subcritical Hopf bifurcation from the static solution, to one where finite-amplitude oscillations persist although there is no Hopf bifurcation from the static solution. This transition is associated with a codimension-two bifurcation with a pair of zero eigenvalues. We show that the bifurcation pattern found for the PDEs is indeed predicted by the second-order normal form equation (with cubic nonlinearities) for a Takens-Bogdanov bifurcation with Z2 symmetry. We then extend this equation by adding quintic nonlinearities and analyse the resulting system. Its predictions provide a qualitatively accurate description of solutions of the full PDEs over a wider range of parameter values. Replacing the reflecting (Z2) lateral boundary conditions with periodic [O(2)] boundaries allows stable travelling wave and modulated wave solutions to appear; they could be described by a third-order system

Observation of liquid–liquid phase transitions in ethane at 300 K

We have conducted Raman spectroscopy experiments on liquid ethane (C2H6) at 300 K, obtaining a large amount of data at very high resolution. This has enabled the observation of Raman peaks expected but not previously observed in liquid ethane and a detailed experimental study of the liquid that was not previously possible. We have observed a transition between rigid and nonrigid liquid states in liquid ethane at ca. 250 MPa corresponding to the recently proposed Frenkel line, a dynamic transition between rigid liquid (liquidlike) and nonrigid liquid (gaslike) states beginning in the subcritical region and extending to arbitrarily high pressure and temperature. The observation of this transition in liquid (subcritical) ethane allows a clear differentiation to be made between the Frenkel line (beginning in the subcritical region at higher density than the boiling line) and the Widom lines (emanating from the critical point and not existing in the subcritical region). Furthermore, we observe a narrow transition at ca. 1000 MPa to a second rigid liquid state. We propose that this corresponds to a state in which orientational order must exist to achieve the expected density and can view the transition in analogy to the transition in the solid state away from the orientationally disordered phase I to the orientationally ordered phases II and III

Vicious walkers, friendly walkers and Young tableaux II: With a wall

We derive new results for the number of star and watermelon configurations of vicious walkers in the presence of an impenetrable wall by showing that these follow from standard results in the theory of Young tableaux, and combinatorial descriptions of symmetric functions. For the problem of $n$-friendly walkers, we derive exact asymptotics for the number of stars and watermelons both in the absence of a wall and in the presence of a wall.Comment: 35 pages, AmS-LaTeX; Definitions of n-friendly walkers clarified; the statement of Theorem 4 and its proof were correcte

The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence

A numerical model of isotropic homogeneous turbulence with helical forcing is investigated. The resulting flow, which is essentially the prototype of the alpha^2 dynamo of mean-field dynamo theory, produces strong dynamo action with an additional large scale field on the scale of the box (at wavenumber k=1; forcing is at k=5). This large scale field is nearly force-free and exceeds the equipartition value. As the magnetic Reynolds number R_m increases, the saturation field strength and the growth rate of the dynamo increase. However, the time it takes to built up the large scale field from equipartition to its final super-equipartition value increases with magnetic Reynolds number. The large scale field generation can be identified as being due to nonlocal interactions originating from the forcing scale, which is characteristic of the alpha-effect. Both alpha and turbulent magnetic diffusivity eta_t are determined simultaneously using numerical experiments where the mean-field is modified artificially. Both quantities are quenched in a R_m-dependent fashion. The evolution of the energy of the mean field matches that predicted by an alpha^2 dynamo model with similar alpha and eta_t quenchings. For this model an analytic solution is given which matches the results of the simulations. The simulations are numerically robust in that the shape of the spectrum at large scales is unchanged when changing the resolution from 30^3 to 120^3 meshpoints, or when increasing the magnetic Prandtl number (viscosity/magnetic diffusivity) from 1 to 100. Increasing the forcing wavenumber to 30 (i.e. increasing the scale separation) makes the inverse cascade effect more pronounced, although it remains otherwise qualitatively unchanged.Comment: 21 pages, 26 figures, ApJ (accepted