Two-fluid tokamak equilibria with reversed magnetic shear and sheared flow

The aim of the present work is to investigate tokamak equilibria with reversed magnetic shear and sheared flow, which may play a role in the formation of internal transport barriers (ITBs), within the framework of two-fluid model. The study is based on exact self-consistent solutions in cylindrical geometry by means of which the impact of the magnetic shear, s, and the "toroidal" (axial) and "poloidal" (azimuthal) ion velocity components on the radial electric field, its shear and the shear of the ExB velocity is examined. For a wide parametric regime of experimental concern it turns out that the contributions of the toroidal and poloidal velocity and pressure gradient terms to the electric field, its shear and ExB velocity shear are of the same order of magnitude. The impact of s on ExB velocity shear through the pressure gradient term is stronger than that through the velocity terms. The results indicate that, alike MHD, the magnetic shear and the sheared toroidal and poloidal velocities act synergetically in producing electric fields and therefore ExB velocity shear profiles compatible with ones observed in discharges with ITBs; owing to the pressure gadient term, however, the impact of s on the electic field, its shear and the shear of ExB velocity is stronger than that in MHD.Comment: 25 pages, 21 figure

Dualizability of automatic algebras

We make a start on one of George McNulty's Dozen Easy Problems: "Which finite automatic algebras are dualizable?" We give some necessary and some sufficient conditions for dualizability. For example, we prove that a finite automatic algebra is dualizable if its letters act as an abelian group of permutations on its states. To illustrate the potential difficulty of the general problem, we exhibit an infinite ascending chain $\mathbf A_1 \le \mathbf A_2 \le \mathbf A_3 \le ...b$ of finite automatic algebras that are alternately dualizable and non-dualizable

Influence of dietary linoleic acid intake with different fat intakes on arachidonic acid concentrations in plasma and platelet lipids and eicosanoid biosynthesis in female volunteers

Background/Aim: N-6 fatty acids are considered to promote diseases prevalent in industrialized countries and characterized by an increased eicosanoid biosynthesis from arachidonic acid (AA). We investigated the impact of the linoleic acid (LA) intake on AA levels in humans. Methods: Six healthy female volunteers (age range 2334 years) were given liquid formula diets (LFD) devoid of AA for 6 weeks, providing a constant intake of zero energy% (LFD 0: protein 15%, carbohydrates 85%) or 20 energy% (LFD 20: protein 15%, carbohydrates 55%, fat 30%) LA, for 3 weeks each. Fatty acids of plasma cholesteryl esters and platelet lipids were determined each week, and the prostaglandin biosynthesis was measured in 24-hour urine samples. Results: LFD 0 increased (+31% of initial value) and LFD 20 lowered (-30% of initial value) the percentage of AA in plasma cholesteryl esters and platelet lipids. Moreover, absence of dietary AA lowered the percentages of AA in plasma (-31% week 0 vs. week 6) and platelet (-11%) lipids, indicating a low transformation of LA. LFD 0 reduced urinary metabolite levels of prostaglandins D, E, and F in 24-hour urine samples (-48%, p < 0.001) within 24 h, but did not significantly affect platelet aggregation (-10%) and thromboxane formation (-25%). LFD 20 significantly lowered platelet aggregation (-25%) and thromboxane formation (-43%). The prostaglandin metabolite levels increased during the first 10 days, declined thereafter, and were lower than the preexperimental values at the end of the 3-week period. Conclusions: The results show that dietary LA does not increase the AA levels in plasma or platelet lipids and does not persistently contribute to prostaglandin biosynthesis which is increased by AA intake with Western diets

The small-scale dynamo: Breaking universality at high Mach numbers

(Abridged) The small-scale dynamo may play a substantial role in magnetizing the Universe under a large range of conditions, including subsonic turbulence at low Mach numbers, highly supersonic turbulence at high Mach numbers and a large range of magnetic Prandtl numbers Pm, i.e. the ratio of kinetic viscosity to magnetic resistivity. Low Mach numbers may in particular lead to the well-known, incompressible Kolmogorov turbulence, while for high Mach numbers, we are in the highly compressible regime, thus close to Burgers turbulence. In this study, we explore whether in this large range of conditions, a universal behavior can be expected. Our starting point are previous investigations in the kinematic regime. Here, analytic studies based on the Kazantsev model have shown that the behavior of the dynamo depends significantly on Pm and the type of turbulence, and numerical simulations indicate a strong dependence of the growth rate on the Mach number of the flow. Once the magnetic field saturates on the current amplification scale, backreactions occur and the growth is shifted to the next-larger scale. We employ a Fokker-Planck model to calculate the magnetic field amplification during the non-linear regime, and find a resulting power-law growth that depends on the type of turbulence invoked. For Kolmogorov turbulence, we confirm previous results suggesting a linear growth of magnetic energy. For more general turbulent spectra, where the turbulent velocity v_t scales with the characteristic length scale as u_\ell\propto \ell^{\vartheta}, we find that the magnetic energy grows as (t/T_{ed})^{2\vartheta/(1-\vartheta)}, with t the time-coordinate and T_{ed} the eddy-turnover time on the forcing scale of turbulence. For Burgers turbulence, \vartheta=1/2, a quadratic rather than linear growth may thus be expected, and a larger timescale until saturation is reached.Comment: 10 pages, 3 figures, 2 tables. Accepted at New Journal of Physics (NJP

Nonlinear closures for scale separation in supersonic magnetohydrodynamic turbulence

Turbulence in compressible plasma plays a key role in many areas of astrophysics and engineering. The extreme plasma parameters in these environments, e.g. high Reynolds numbers, supersonic and super-Alfvenic flows, however, make direct numerical simulations computationally intractable even for the simplest treatment -- magnetohydrodynamics (MHD). To overcome this problem one can use subgrid-scale (SGS) closures -- models for the influence of unresolved, subgrid-scales on the resolved ones. In this work we propose and validate a set of constant coefficient closures for the resolved, compressible, ideal MHD equations. The subgrid-scale energies are modeled by Smagorinsky-like equilibrium closures. The turbulent stresses and the electromotive force (EMF) are described by expressions that are nonlinear in terms of large scale velocity and magnetic field gradients. To verify the closures we conduct a priori tests over 137 simulation snapshots from two different codes with varying ratios of thermal to magnetic pressure ($\beta_\mathrm{p} = 0.25, 1, 2.5, 5, 25$) and sonic Mach numbers ($M_s = 2, 2.5, 4$). Furthermore, we make a comparison to traditional, phenomenological eddy-viscosity and $\alpha-\beta-\gamma$ closures. We find only mediocre performance of the kinetic eddy-viscosity and $\alpha-\beta-\gamma$ closures, and that the magnetic eddy-viscosity closure is poorly correlated with the simulation data. Moreover, three of five coefficients of the traditional closures exhibit a significant spread in values. In contrast, our new closures demonstrate consistently high correlation and constant coefficient values over time and and over the wide range of parameters tested. Important aspects in compressible MHD turbulence such as the bi-directional energy cascade, turbulent magnetic pressure and proper alignment of the EMF are well described by our new closures.Comment: 15 pages, 6 figures; to be published in New Journal of Physic

New Renormalization Group Equations and the Naturalness Problem

Looking for an observable manifestation of the so-called unnaturalness of scalar fields we introduce a seemingly new set of differential equations for connected Green functions. These equations describe the momentum dependence of the Green functions and are close relatives to the previously known renormalization group equations. Applying the new equations to the theory of scalar field with $\phi^4$ interaction we identify a relation between the four-point Green function and the propagator which expresses the unnaturalness of the scalar field. Possible manifestations of the unnaturalness at low momenta are briefly discussed.Comment: 12 revtex pages; a coefficient has been corrected in eq. (34), four new references added; final version to appear in Phys. Rev.

The Hubbard model on a complete graph: Exact Analytical results

We derive the analytical expression of the ground state of the Hubbard model with unconstrained hopping at half filling and for arbitrary lattice sites.Comment: Email:[email protected]

Coherent spin-current oscillations in transverse magnetic fields

We address the coherence of the dynamics of spin-currents with components transverse to an external magnetic field for the spin-1/2 Heisenberg chain. We study current autocorrelations at finite temperatures and the real-time dynamics of currents at zero temperature. Besides a coherent Larmor oscillation, we find an additional collective oscillation at higher frequencies, emerging as a coherent many-magnon effect at low temperatures. Using numerical and analytical methods, we analyze the oscillation frequency and decay time of this coherent current-mode versus temperature and magnetic field.Comment: 4 pages, 5 figures (and supplemental material: 4 pages, 6 figures

Extended Heat-Fluctuation Theorems for a System with Deterministic and Stochastic Forces

Heat fluctuations over a time \tau in a non-equilibrium stationary state and in a transient state are studied for a simple system with deterministic and stochastic components: a Brownian particle dragged through a fluid by a harmonic potential which is moved with constant velocity. Using a Langevin equation, we find the exact Fourier transform of the distribution of these fluctuations for all \tau. By a saddle-point method we obtain analytical results for the inverse Fourier transform, which, for not too small \tau, agree very well with numerical results from a sampling method as well as from the fast Fourier transform algorithm. Due to the interaction of the deterministic part of the motion of the particle in the mechanical potential with the stochastic part of the motion caused by the fluid, the conventional heat fluctuation theorem is, for infinite and for finite \tau, replaced by an extended fluctuation theorem that differs noticeably and measurably from it. In particular, for large fluctuations, the ratio of the probability for absorption of heat (by the particle from the fluid) to the probability to supply heat (by the particle to the fluid) is much larger here than in the conventional fluctuation theorem.Comment: 23 pages, 6 figures. Figures are now in color, Eq. (67) was corrected and a footnote was added on the d-dimensional cas