Depletion of Nonlinearity in Magnetohydrodynamic Turbulence: Insights from Analysis and Simulations

We build on recent developments in the study of fluid turbulence [Gibbon \textit{et al.} Nonlinearity 27, 2605 (2014)] to define suitably scaled, order-$m$ moments, $D_m^{\pm}$, of $\omega^\pm= \omega \pm j$, where $\omega$ and $j$ are, respectively, the vorticity and current density in three-dimensional magnetohydrodynamics (MHD). We show by mathematical analysis, for unit magnetic Prandtl number $P_M$, how these moments can be used to identify three possible regimes for solutions of the MHD equations; these regimes are specified by inequalities for $D_m^{\pm}$ and $D_1^{\pm}$. We then compare our mathematical results with those from our direct numerical simulations (DNSs) and thus demonstrate that 3D MHD turbulence is like its fluid-turbulence counterpart insofar as all solutions, which we have investigated, remain in \textit{only one of these regimes}; this regime has depleted nonlinearity. We examine the implications of our results for the exponents $q^{\pm}$ that characterize the power-law dependences of the energy spectra $\mathcal{E}^{\pm}(k)$ on the wave number $k$, in the inertial range of scales. We also comment on (a) the generalization of our results to the case $P_M \neq 1$ and (b) the relation between $D_m^{\pm}$ and the order-$m$ moments of gradients of hydrodynamic fields, which are used in characterizing intermittency in turbulent flows.Comment: 14 pages, 3 figure

Ideal evolution of MHD turbulence when imposing Taylor-Green symmetries

We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the four-fold symmetries of the Taylor-Green vortex generalized to MHD, leading to substantial computer time and memory savings at a given resolution; we also use a re-gridding method that allows for lower-resolution runs at early times, with no loss of spectral accuracy. One magnetic configuration is examined at an equivalent resolution of $6144^3$ points, and three different configurations on grids of $4096^3$ points. At the highest resolution, two different current and vorticity sheet systems are found to collide, producing two successive accelerations in the development of small scales. At the latest time, a convergence of magnetic field lines to the location of maximum current is probably leading locally to a strong bending and directional variability of such lines. A novel analytical method, based on sharp analysis inequalities, is used to assess the validity of the finite-time singularity scenario. This method allows one to rule out spurious singularities by evaluating the rate at which the logarithmic decrement of the analyticity-strip method goes to zero. The result is that the finite-time singularity scenario cannot be ruled out, and the singularity time could be somewhere between $t=2.33$ and $t=2.70.$ More robust conclusions will require higher resolution runs and grid-point interpolation measurements of maximum current and vorticity.Comment: 18 pages, 13 figures, 2 tables; submitted to Physical Review

Effect of increased tensile strength and toughness on reinforcing-bar bond behavior

The research reported here investigated the pull-out behavior of deformed reinforcing bars embedded in fiber-reinforced-concrete (FRC) and high-performance- fiber-reinforced-concrete (HPFRC) matrices exhibiting increased tensile strength and toughness. Increased strength and toughness of the embedding matrix resulted in a significant increase in pull-out strength, strain capacity, and over-all ductility, as well as more stable crack development. Additionally, when sufficient lateral constraint (i.e. cover thickness) was provided, the use of an HPFRC matrix exhibiting strain-hardening behavior resulted in a slip-hardening pull-out response.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31895/1/0000848.pd

Clustering and phase transitions in a 2D superfluid with immiscible active impurities

Phase transitions of a finite-size two-dimensional superfluid of bosons in presence of active impurities are studied by using the projected Gross–Pitaevskii model. Impurities are described with classical degrees of freedom. A spontaneous clustering of impurities during the thermalization is observed. Depending on the interaction among impurities, such clusters can break due to thermal fluctuations at temperatures where the condensed fraction is still significant. The emergence of clusters is found to increase the condensation transition temperature. The condensation and the Berezinskii–Kosterlitz–Thouless transition temperatures, determined numerically, are found to strongly depend on the volume occupied by the impurities: a relative increase up to a 20% of their respective values is observed, whereas their ratio remains approximately constant

On the fatigue response of a bonded repaired aerospace composite using thermography

Lock-in thermography was employed to investigate the repair efficiency of a bonded repaired aerospace composite subjected to step-wise cycling mechanical loading. The studied component (substrate) was artificially damaged with a 5 mm circular notch and subsequently repaired with a tapered bonded patch. Critical and sub-critical damage of the repaired component was monitored via thermography during 5 Hz tension–tension fatigue. The examination of the acquired thermographs enabled the identification of the patch debonding propagation as well as the quantification of the stress magnification at the patch ends and the locus of the circular notch. It was found that fatigue mechanical loading yields both thermoelastic and hysterestic phenomena with the latter being more prominent prior to the failure of the studied repaired component