Polymer Stretching by Turbulence

The stretching of a polymer chain by a large scale chaotic flow is considered. The steady state which emerges as a balance of the turbulent stretching and anharmonic resistance of the chain is quantitatively described, i.e. the dependency on the flow parameters (Lyapunov exponent statistics) and the chain characteristics (the number of beads and the inter-bead elastic potential) is made explicit.Comment: 4 pages, no figures, Submitted to PRL November 8, 1999; resubmitted February 22, 200

On how a joint interaction of two innocent partners (smooth advection & linear damping) produces a strong intermittency

Forced advection of passive scalar by a smooth $d$-dimensional incompressible velocity in the presence of a linear damping is studied. Acting separately advection and dumping do not lead to an essential intermittency of the steady scalar statistics, while being mixed together produce a very strong non-Gaussianity in the convective range: $q$-th (positive) moment of the absolute value of scalar difference, $$ is proportional to $r^{\xi_{q}}$, $\xi _{q}=\sqrt{d^{2}/4+\alpha dq/[ (d-1)D]}-d/2$, where $\alpha /D$ measures the rate of the damping in the units of the stretching rate. Probability density function (PDF) of the scalar difference is also found.Comment: 4 pages, RevTex, Submitted to Phys. Fluid

Mean Field Control for Efficient Mixing of Energy Loads

We pose an engineering challenge of controlling an Ensemble of Energy Devices via coordinated, implementation-light and randomized on/off switching as a problem in Non-Equilibrium Statistical Mechanics. We show that Mean Field Control} with nonlinear feedback on the cumulative consumption, assumed available to the aggregator via direct physical measurements of the energy flow, allows the ensemble to recover from its use in the Demand Response regime, i.e. transition to a statistical steady state, significantly faster than in the case of the fixed feedback. Moreover when the nonlinearity is sufficiently strong, one observes the phenomenon of "super-relaxation" -- where the total instantaneous energy consumption of the ensemble transitions to the steady state much faster than the underlying probability distribution of the devices over their state space, while also leaving almost no devices outside of the comfort zone.Comment: 7 pages, 5 figure