Geometric microcanonical theory of two-dimensional truncated Euler flows.

This paper presents a geometric microcanonical ensemble perspective on two-dimensional truncated Euler flows, which contain a finite number of (Fourier) modes and conserve energy and enstrophy. We explicitly perform phase space volume integrals over shells of constant energy and enstrophy. Two applications are considered. In the first part, we determine the average energy spectrum for highly condensed flow configurations and show that the result is consistent with Kraichnan's canonical ensemble description, despite the fact that no thermodynamic limit is invoked. In the second part, we compute the probability density for the largest-scale mode of a free-slip flow in a square, which displays reversals. We test the results against numerical simulations of a minimal model and find excellent agreement with the microcanonical theory, unlike the canonical theory, which fails to describe the bimodal statistics. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.

λ-Navier-Stokes turbulence.

We investigate numerically the model proposed in Sahoo et al. (2017 Phys. Rev. Lett. 118, 164501) where a parameter λ is introduced in the Navier-Stokes equations such that the weight of homochiral to heterochiral interactions is varied while preserving all original scaling symmetries and inviscid invariants. Decreasing the value of λ leads to a change in the direction of the energy cascade at a critical value [Formula: see text]. In this work, we perform numerical simulations at varying λ in the forward energy cascade range and at changing the Reynolds number [Formula: see text]. We show that for a fixed injection rate, as [Formula: see text], the kinetic energy diverges with a scaling law [Formula: see text]. The energy spectrum is shown to display a larger bottleneck as λ is decreased. The forward heterochiral flux and the inverse homochiral flux both increase in amplitude as [Formula: see text] is approached while keeping their difference fixed and equal to the injection rate. As a result, very close to [Formula: see text] a stationary state is reached where the two opposite fluxes are of much higher amplitude than the mean flux and large fluctuations are observed. Furthermore, we show that intermittency as [Formula: see text] is approached is reduced. The possibility of obtaining a statistical description of regular Navier-Stokes turbulence as an expansion around this newly found critical point is discussed. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.

Fluctuations of Electrical Conductivity: A New Source for Astrophysical Magnetic Fields.

We consider the generation of a magnetic field by the flow of a fluid for which the electrical conductivity is nonuniform. A new amplification mechanism is found which leads to dynamo action for flows much simpler than those considered so far. In particular, the fluctuations of the electrical conductivity provide a way to bypass antidynamo theorems. For astrophysical objects, we show through three-dimensional global numerical simulations that the temperature-driven fluctuations of the electrical conductivity can amplify an otherwise decaying large scale equatorial dipolar field. This effect could play a role for the generation of the unusually tilted magnetic field of the iced giants Neptune and Uranus.

Statistical Equilibria of Large Scales in Dissipative Hydrodynamic Turbulence.

We present a numerical study of the statistical properties of three-dimensional dissipative turbulent flows at scales larger than the forcing scale. Our results indicate that the large scale flow can be described to a large degree by the truncated Euler equations with the predictions of the zero flux solutions given by absolute equilibrium theory, both for helical and nonhelical flows. Thus, the functional shape of the large scale spectra can be predicted provided that scales sufficiently larger than the forcing length scale but also sufficiently smaller than the box size are examined. Deviations from the predictions of absolute equilibrium are discussed.

Construction of bicyclo[3.2.1]octanes with four stereogenic centers by organocatalytic domino Michael/Aldol reaction.

An enantio- and diastereoselective organocatalytic domino Michael/Aldol reaction for the direct preparation of synthetically and medicinally relevant bicyclo[3.2.1]octane derivatives with four stereogenic centers, including two quaternary carbons, has been described. The reaction tolerates a large variety of substituents on ß,γ-unsaturated 1,2-ketoesters and cyclic 1,3-ketoesters. It allows for the formation of various bicyclo[3.2.1]octanes in good yields (53-98%), diastereoselectivities (1:1 to 5:1 dr), and enantioselectivities (up to 95:5 ee).

Enantioselective 1,4-additions of ClMeAl(CH=CHR) (R = alkyl, alkenyl, Ph) to cyclohexenones.

Chloromethylvinyl alanes (E)-ClMeAl(CH=CHR) prepared directly from terminal alkynes undergo 1,4-addition to cyclohexenone and 3-methylcyclohexenone in moderate to good yield (30-70%) and good to excellent stereoselectivity (80-98% ee) using readily available copper(I) sources and chiral ligands.

Origins of the k(-2) spectrum in decaying Taylor-Green magnetohydrodynamic turbulent flows.

We investigate the origins of k(-2) spectrum in a decaying Taylor-Green magnetohydrodynamic flow with zero large scale magnetic flux that was reported by Lee et al. [Phys. Rev. E 81, 016318 (2010)]. So far, a possible candidate for this scaling exponent has been the weak turbulence phenomenology. From our numerical simulations, we observe that current sheets in the magnetic Taylor-Green flow are formed in regions of magnetic discontinuities. Based on this observation and by studying the influence of the current sheets on the energy spectrum, using a filtering technique, we argue that the discontinuities are responsible for the -2 power law scaling of the energy spectra of this flow.

Symmetry breaking of decaying magnetohydrodynamic Taylor-Green flows and consequences for universality.

We investigate the evolution and stability of a decaying magnetohydrodynamic Taylor-Green flow, using pseudospectral simulations with resolutions up to 2048(3). The chosen flow has been shown to result in a steep total energy spectrum with power law behavior k(-2). We study the symmetry breaking of this flow by exciting perturbations of different amplitudes. It is shown that for any finite amplitude perturbation there is a high enough Reynolds number for which the perturbation will grow enough at the peak of dissipation rate resulting in a nonlinear feedback into the flow and subsequently break the Taylor-Green symmetries. In particular, we show that symmetry breaking at large scales occurs if the amplitude of the perturbation is σ(crit)∼Re(-1) and at small scales occurs if σ(crit)∼Re(-3/2). This symmetry breaking modifies the scaling laws of the energy spectra at the peak of dissipation rate away from the k(-2) scaling and towards the classical k(-5/3) and k(-3/2) power laws.

Anomalous exponents at the onset of an instability.

Critical exponents are calculated exactly at the onset of an instability, by using asymptotic expansion techniques. When the unstable mode is subject to multiplicative noise whose spectrum at zero frequency vanishes, we show that the critical behavior can be anomalous; i.e., the mode amplitude X scales with departure from onset µ as ∝µ(ß) with an exponent ß different from its deterministic value. This behavior is observed in a direct numerical simulation of the dynamo instability, and our results provide a possible explanation for recent experimental observations.

Nonlocal interactions in hydrodynamic turbulence at high Reynolds numbers: the slow emergence of scaling laws.

We analyze the data stemming from a forced incompressible hydrodynamic simulation on a grid of 2048(3) regularly spaced points, with a Taylor Reynolds number of R(lambda) ~ 1300. The forcing is given by the Taylor-Green vortex, which shares similarities with the von Kàrmàn flow used in several laboratory experiments; the computation is run for ten turnover times in the turbulent steady state. At this Reynolds number the anisotropic large scale flow pattern, the inertial range, the bottleneck, and the dissipative range are clearly visible, thus providing a good test case for the study of turbulence as it appears in nature. Triadic interactions, the locality of energy fluxes, and longitudinal structure functions of the velocity increments are computed. A comparison with runs at lower Reynolds numbers is performed and shows the emergence of scaling laws for the relative amplitude of local and nonlocal interactions in spectral space. Furthermore, the scaling of the Kolmogorov constant, and of skewness and flatness of velocity increments is consistent with previous experimental results. The accumulation of energy in the small scales associated with the bottleneck seems to occur on a span of wave numbers that is independent of the Reynolds number, possibly ruling out an inertial range explanation for it. Finally, intermittency exponents seem to depart from standard models at high R(lambda), leaving the interpretation of intermittency an open problem.

Anisotropic fluxes and nonlocal interactions in magnetohydrodynamic turbulence.

We investigate the locality or nonlocality of the energy transfer and the spectral interactions involved in the cascade for decaying magnetohydrodynamic (MHD) flows in the presence of a uniform magnetic field B at various intensities. The results are based on a detailed analysis of three-dimensional numerical flows at moderate Reynolds numbers. The energy transfer functions, as well as the global and partial fluxes, are examined by means of different geometrical wave number shells. On the one hand, the transfer functions of the two conserved Elsässer energies E+ and E- are found local in both the directions parallel (k|| direction) and perpendicular (kperpendicular direction) to the magnetic guide field, whatever the B strength. On the other hand, from the flux analysis, the interactions between the two counterpropagating Elsässer waves become nonlocal. Indeed, as the B intensity is increased, local interactions are strongly decreased and the interactions with small k|| modes dominate the cascade. Most of the energy flux in the kperpendicular direction is due to modes in the plane at k||=0, while the weaker cascade in the k|| direction is due to the modes with k||=1. The stronger magnetized flows tend thus to get closer to the weak turbulence limit, where three-wave resonant interactions are dominant. Hence, the transition from the strong to the weak turbulence regime occurs by reducing the number of effective modes in the energy cascade.

Large-scale flow effects, energy transfer, and self-similarity on turbulence.

The effect of large scales on the statistics and dynamics of turbulent fluctuations is studied using data from high resolution direct numerical simulations. Three different kinds of forcing, and spatial resolutions ranging from 256(3) to 1024(3), are being used. The study is carried out by investigating the nonlinear triadic interactions in Fourier space, transfer functions, structure functions, and probability density functions. Our results show that the large scale flow plays an important role in the development and the statistical properties of the small scale turbulence. The role of helicity is also investigated. We discuss the link between these findings and intermittency, deviations from universality, and possible origins of the bottleneck effect. Finally, we briefly describe the consequences of our results for the subgrid modeling of turbulent flows.

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 nonlocal 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.

Dramatic improvement of the enantiomeric excess in the asymmetric conjugate addition reaction using new experimental conditions.

The asymmetric conjugate addition of dialkylzincs is usually performed with Cu(OTf)(2) in toluene. We show that by using a copper carboxylate in Et(2)O, THF, or EtOAc, we strongly improve the enantioselectivity with a given ligand. Ee values up to 99.1% could be reached with new ligands based on the induced atropisomerism of a simple biphenol unit. In addition, we show that the Lewis acid effect of Cu(OTf)(2) is not a significant.

Shear instability of fluid interfaces: stability analysis.

We examine the linear stability of fluid interfaces subjected to a shear flow. Our main object is to generalize previous work to an arbitrary Atwood number, and to allow for surface tension and weak compressibility. The motivation derives from instances in astrophysical systems where mixing across material interfaces driven by shear flows may significantly affect the dynamical evolution of these systems.

Enantioselective copper-catalyzed conjugate addition of dialkyl zinc to nitro-olefins

[reaction: see text]The copper-catalyzed asymmetric conjugate addition of dialkylzinc onto various nitro-olefins has been carried out with excellent results. An enantiomeric excess of up to 94% was obtained using 0.5% Cu(OTf)2 and 1% of chiral trivalent phosphorus ligand.

A regulated telemedicine system for day to day application in remote areas.

The NIVEMES project creates an international network of Health Service providers which offer Telemedicine-Teleconsultation services to Remote, Isolated places and to ship vessels for both routine and emergency situations. The base of the system is the powerful Multimedia Health Record, with the ability to manage conventional data, images, videos and biosignals, acquired directly from the medical device. National and international medical codification schemata are employed such as ICD-X and WHO standards. Telemedicine and Computing in Health Care are rapidly covering a pending gap, not fulfilled by current bureaucratic and telematic procedures. However even from the first test fields conducted during the past year, it is obvious that a variety of new training needs has arisen. The users of such systems need to be instructed new ways of conducting their business, of taking advantage of the services, even a new way of perceiving health care provision. The user interface of the software is kept simple, thus getting acquainted with it requires minimum effort; however there are other issues on which training is required to best exploit the advantages the system offers. The telemedical networks spawned in each country must be co-ordinated, and the user needs to know where and how he/she will acquire the necessary support. Home-cared patients will have to operate medical devices and telemedical software, a task which although made easy from today's technology, it still requires some basic training, specially as far as elderly users are concerned. The NIVEMES system uncovers a set of new training needs, but it offers at the same time a vehicle for educating the professional health-carers. The Health Record comprises a multimedia, explicit account of the patient history, which can be used for detailed and integrated study from trainee health carers of all levels (as well as from officers on board, people taking care of home-confined patients and others), on real data or in a simulated environment. At the same time the telemedicine facilities may increase the effectiveness of junior doctors working in remote areas and enhance the confidence residents have about their local health centres. Systems like NIVEMES prove that new user needs arise nowadays and employment of modern tools requires training in modern methods and in a new way of thinking.