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

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

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

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

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

Mathematical and computer modeling of electro-optic systems using a generic modeling approach

The conventional approach to modelling electro-optic sensor systems is to develop separate models for individual systems or classes of system, depending on the detector technology employed in the sensor and the application. However, this ignores commonality in design and in components of these systems. A generic approach is presented for modelling a variety of sensor systems operating in the infrared waveband that also allows systems to be modelled with different levels of detail and at different stages of the product lifecycle. The provision of different model types (parametric and image-flow descriptions) within the generic framework can allow valuable insights to be gained

Cdc7 is a potent anti-cancer target in pancreatic cancer due to abrogation of the DNA origin activation checkpoint.

PURPOSE: Cdc7 is a serine/threonine kinase which is responsible for the 'firing' of replication origins leading to initiation of DNA replication. Inhibition or depletion of Cdc7 in normal cells triggers a DNA origin activation checkpoint causing a reversible G1 arrest. Here we investigate Cdc7 as a novel therapeutic target in pancreatic cancer. EXPERIMENTAL DESIGN: Cdc7 target validation was performed by immunoexpression profiling in a cohort of 73 patients with pancreatic adenocarcinoma including 24 controls. Secondly Cdc7 kinase was targeted in Capan-1 and PANC-1 pancreatic cancer cell line models using either an siRNA against Cdc7 or alternatively a small molecule inhibitor (SMI) of Cdc7 (PHA-767491). RESULTS: Cdc7 was significantly overexpressed in pancreatic adenocarcinoma compared to benign pancreatic tissue (median LI 34.3% vs. 1.3%; P<0.0001). Cdc7 knockdown using siRNA in Capan-1 and PANC-1 cells resulted in marked apoptotic cell death when compared with control cells. A prominent sub-G1 peak was seen on flow cytometry (sub-G1 51% vs. 3% and 45% vs. 0.7% in Capan-1 and PANC-1 cells, respectively). Annexin V labelling confirmed apoptosis in 64% vs. 11% and 75% vs. 8%, respectively. Western blotting showed cleavage of PARP-1 and caspase-3 and presence of γH2A.X. TUNEL assay showed strong staining in treated cells. These results were mirrored following Cdc7 kinase inhibition with PHA-767491. CONCLUSIONS: Our findings show that Cdc7 is a potent anti-cancer target in pancreatic adenocarcinoma and that Cdc7 immunoexpression levels might be used as a companion diagnostic to predict response to therapeutic siRNAs or SMIs directed against this kinase