Long-time properties of MHD turbulence and the role of symmetries

We investigate long-time properties of three-dimensional MHD turbulence in the absence of forcing and examine in particular the role played by the quadratic invariants of the system and by the symmetries of the initial configurations. We observe that, when sufficient accuracy is used, initial conditions with a high degree of symmetries, as in the absence of helicity, do not travel through parameter space over time whereas by perturbing these solutions either explicitly or implicitly using for example single precision for long times, the flows depart from their original behavior and can become either strongly helical, or have a strong alignment between the velocity and the magnetic field. When the symmetries are broken, the flows evolve towards different end states, as predicted by statistical arguments for non-dissipative systems with the addition of an energy minimization principle, as already analyzed in \cite{stribling_90} for random initial conditions using a moderate number of Fourier modes. Furthermore, the alignment properties of these flows, between velocity, vorticity, magnetic potential, induction and current, correspond to the dominance of two main regimes, one helically dominated and one in quasi-equipartition of kinetic and magnetic energy. We also contrast the scaling of the ratio of magnetic energy to kinetic energy as a function of wavenumber to the ratio of eddy turn-over time to Alfv\'en time as a function of wavenumber. We find that the former ratio is constant with an approximate equipartition for scales smaller than the largest scale of the flow whereas the ratio of time scales increases with increasing wavenumber.Comment: 14 pages, 6 figure

The restoration of Loch Leven, Scotland, UK

This paper reviews the progress made towards the restoration of Loch Leven, the largest lake in lowland Scotland, over the last 20 years. In particular, the importance of direct regulation and of setting water quality objectives and targets is examined. Various means of engaging with stakeholders and the general public are also considered. Success criteria and catchment management initiatives are described and briefly reviewed

Should pancreaticoduodenectomy be performed in the elderly?

BACKGROUND/AIMS: Pancreaticoduodenectomy (PD) is indicated in benign or malignant pancreatic head diseases. It is a difficult operation with high morbidity especially in elderly patients. The aim of our study was to determine whether pancreaticoduodenectomy is associated with higher morbidity and mortality in patients ≥ 70 years old. METHODOLOGY: During 17 years, 173 patients were operated by Whipple intervention, whatever the disease. From a prospective database, patients were divided in 2 groups (Group A ≥ 70 years old, Group B <70). RESULTS: Postoperative mortality was not significantly higher in elderly (12% vs. 4.1%; p=0.06). However, re-intervention and morbidity were more important in univariate analysis (p=0.03 and p=0.002 respectively). In multivariate analysis, age ≥ 70 years old was not an independent prognostic factor of mortality (p=0.27) and re-intervention (p=0.07). Whereas age (p=0.04) and preoperative morbidity (p=0.02) were independent prognostic factors of morbidity. CONCLUSIONS: PD requires careful patient selection. However, age should not be a limiting factor

The imprint of large-scale flows on turbulence

We investigate the locality of interactions in hydrodynamic turbulence using data from a direct numerical simulation on a grid of 1024^3 points; the flow is forced with the Taylor-Green vortex. An inertial range for the energy is obtained in which the flux is constant and the spectrum follows an approximate Kolmogorov law. Nonlinear triadic interactions are dominated by their non-local components, involving widely separated scales. The resulting nonlinear transfer itself is local at each scale but the step in the energy cascade is independent of that scale and directly related to the integral scale of the flow. Interactions with large scales represent 20% of the total energy flux. Possible explanations for the deviation from self-similar models, the link between these findings and intermittency, and their consequences for modeling of turbulent flows are briefly discussed

Statistics of Dissipation and Enstrophy Induced by a Set of Burgers Vortices

Dissipation and enstropy statistics are calculated for an ensemble of modified Burgers vortices in equilibrium under uniform straining. Different best-fit, finite-range scaling exponents are found for locally-averaged dissipation and enstrophy, in agreement with existing numerical simulations and experiments. However, the ratios of dissipation and enstropy moments supported by axisymmetric vortices of any profile are finite. Therefore the asymptotic scaling exponents for dissipation and enstrophy induced by such vortices are equal in the limit of infinite Reynolds number.Comment: Revtex (4 pages) with 4 postscript figures included via psfi

Intraperitoneal mesh repair of small ventral abdominal wall hernias with a Ventralex hernia patch

BACKGROUND: Various surgical procedures have been described in the treatment of small ventral abdominal wall hernias. Mesh repair is becoming popular because of a low recurrence rate. AIM: The aim of this prospective study was to evaluate an open intraperitoneal technique using the Bard Ventralex hernia patch in the treatment of small midline ventral hernias. METHODS: 101 patients were operated on (59 male, 42 female) with a mean age of 54.5 years (range 17-85). Mean operative time was 33 min (range 16-65). The median hospital stay was 2 days (range 1-15). RESULTS: Two patients had a hematoma without wound infection. There were 2 recurrences (2%). Mean postoperative follow-up time was 28.5 months (range 6-55). CONCLUSIONS: Our preliminary results suggest that Ventralex hernia patch repair for ventral hernias can be performed with minimal postoperative morbidity and a low recurrence rate

Transformation kinetics of alloys under non-isothermal conditions

The overall solid-to-solid phase transformation kinetics under non-isothermal conditions has been modeled by means of a differential equation method. The method requires provisions for expressions of the fraction of the transformed phase in equilibrium condition and the relaxation time for transition as functions of temperature. The thermal history is an input to the model. We have used the method to calculate the time/temperature variation of the volume fraction of the favored phase in the alpha-to-beta transition in a zirconium alloy under heating and cooling, in agreement with experimental results. We also present a formulation that accounts for both additive and non-additive phase transformation processes. Moreover, a method based on the concept of path integral, which considers all the possible paths in thermal histories to reach the final state, is suggested.Comment: 16 pages, 7 figures. To appear in Modelling Simul. Mater. Sci. En

Entire solutions of hydrodynamical equations with exponential dissipation

We consider a modification of the three-dimensional Navier--Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as \ue ^{|k|/\kd} at high wavenumbers $|k|$. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than \ue ^{-C(k/\kd) \ln (|k|/\kd)} for any $C<1/(2\ln 2)$. The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with $C= C_\star =1/\ln2$. The same behavior with a universal constant $C_\star$ is conjectured for the Navier--Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier--Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.Comment: 29 pages, 3 figures, Comm. Math. Phys., in pres

Transient vortex events in the initial value problem for turbulence

A vorticity surge event that could be a paradigm for a wide class of bursting events in turbulence is studied to examine how the energy cascade is established and how this event could serve as a new test of LES turbulence models. This vorticity surge event is tied to the formation of the energy cascade in a direct numerical simulation by the traditional signatures of a turbulent energy cascade such as spectra approaching -5/3 and strongly Beltramized vortex tubes. A coherent mechanism is suggested by the nearly simultaneous development of a maximum of the peak vorticity $\|\omega\|_\infty$, growth of the dissipation, the appearance of a helically aligned local vortex configuration and strong, transient oscillations in the helicity wavenumber spectrum. This coherence is also examined for two LES models, a traditional purely dissipative eddy viscosity model and a modern method (LANS$-\alpha$) that respects the nonlinear transport properties of fluids. Both LES models properly represent the spectral energy and energy dissipation associated with this vorticity surge event. However, only the model that preserves nonlinear fluid transport properties reproduces the helical properties, including Beltrami-like vortex tubes.Comment: 4 pages, 6 figure