A general method for finding extremal states of Hamiltonian dynamical systems, with applications to perfect fluids

In addition to the Hamiltonian functional itself, non-canonical Hamiltonian dynamical systems generally possess integral invariants known as ‘Casimir functionals’. In the case of the Euler equations for a perfect fluid, the Casimir functionals correspond to the vortex topology, whose invariance derives from the particle-relabelling symmetry of the underlying Lagrangian equations of motion. In a recent paper, Vallis, Carnevale & Young (1989) have presented algorithms for finding steady states of the Euler equations that represent extrema of energy subject to given vortex topology, and are therefore stable. The purpose of this note is to point out a very general method for modifying any Hamiltonian dynamical system into an algorithm that is analogous to those of Vallis etal. in that it will systematically increase or decrease the energy of the system while preserving all of the Casimir invariants. By incorporating momentum into the extremization procedure, the algorithm is able to find steadily-translating as well as steady stable states. The method is applied to a variety of perfect-fluid systems, including Euler flow as well as compressible and incompressible stratified flow.

An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted

Characterization and antimicrobial efficacy against E. coli of a helium/air plasma at atmospheric pressure created in a plastic package

A plasma source, sustained by the application of a floating high voltage (±15 kV) to parallel-plate electrodes at 50 Hz, has been achieved in a helium/air mixture at atmospheric pressure (P = 105 Pa) contained in a zip-locked plastic package placed in the electrode gap. Some of the physical and antimicrobial properties of this apparatus were established with a view to ascertain its performance as a prototype for the disinfection of fresh produce. The current–voltage (I–V) and charge–voltage (Q–V) characteristics of the system were measured as a function of gap distance d, in the range (3 × 103 ≤ Pd ≤ 1.0 × 104 Pa m). The electrical measurements showed this plasma source to exhibit the characteristic behaviour of a dielectric barrier discharge in the filamentary mode and its properties could be accurately interpreted by the two-capacitance in series model. The power consumed by the discharge and the reduced field strength were found to decrease quadratically from 12.0 W to 4.5 W and linearly from 140 Td to 50 Td, respectively, in the range studied. Emission spectra of the discharge were recorded on a relative intensity scale and the dominant spectral features could be assigned to strong vibrational bands in the 2+ and 1− systems of N2 and ${\rm N}_2^+$ , respectively, with other weak signatures from the NO and OH radicals and the N+, He and O atomic species. Absolute spectral intensities were also recorded and interpreted by comparison with the non-equilibrium synthetic spectra generated by the computer code SPECAIR. At an inter-electrode gap of 0.04 m, this comparison yielded typical values for the electron, vibrational and translational (gas) temperatures of (4980 ± 100) K, (2700 ± 200) K and (300 ± 100) K, respectively and an electron density of 1.0 × 1017 m−3. A Boltzmann plot also provided a value of (3200 ± 200 K) for the vibrational temperature. The antimicrobial efficacy was assessed by studying the resistance of both Escherichia coli K12 its isogenic mutants in soxR, soxS, oxyR, rpoS and dnaK selected to identify possible cellular responses and targets related with 5 min exposure to the active gas in proximity of, but not directly in, the path of the discharge filaments. Both the parent strain and mutants populations were significantly reduced by more than 1.5 log cycles in these conditions, showing the potential of the system. Post-treatment storage studies showed that some transcription regulators and specific genes related to oxidative stress play an important role in the E. coli repair mechanism and that plasma exposure affects specific cell regulator systems.

Helium ion microscopy visualizes lipid nanodomains in mammalian cells

Cell membranes are composed of two-dimensional bilayers of amphipathic lipids, which allow a lateral movement of the respective membrane components. These components are arranged in an inhomogeneous manner as transient micro- and nanodomains, which are believed to be crucially involved in the regulation of signal transduction pathways in mammalian cells. Because of their small size (diameter 10-200 nm), membrane nanodomains cannot be directly imaged using conventional light microscopy. Here, we present direct visualization of cell membrane nanodomains by helium ion microscopy (HIM). We show that HIM is capable to image biological specimens without any conductive coating, and that HIM images clearly allow the identification of nanodomains in the ultrastructure of membranes with 1.5 nm resolution. The shape of these nanodomains is preserved by fixation of the surrounding unsaturated fatty acids while saturated fatty acids inside the nanodomains are selectively removed. Atomic force microscopy, fluorescence microscopy, 3D structured illumination microscopy and direct stochastic optical reconstruction microscopy provide additional evidence that the structures in the HIM images of cell membranes originate from membrane nanodomains. The nanodomains observed by HIM have an average diameter of 20 nm and are densely arranged with a minimal nearest neighbor distance of ~15 nm.