Semiclassical quantization of multidimensional systems

Low order classical perturbation theory is used to obtain semiclassical eigenvalues for a system of three anharmonically coupled oscillators. The results in the low energy region studied here agree well with the "exact" quantum values. The latter had been calculated by matrix diagonalization using a large basis set

Flow-induced currents in nanotubes: a Brownian dynamics approach

Motivated by recent experiments [Science {\bf 299}, 1042 (2003)] reporting that carbon nanotubes immersed in a flowing fluid displayed an electric current and voltage, we numerically study the behaviour of a collection of Brownian particles in a channel, in the presence of a flow field applied on similar but slower particles in a wide chamber in contact with the channel. For a suitable range of shear rates, we find that the flow field induces a unidirectional drift in the confined particles, and is stronger for narrower channels. The average drift velocity initially rises with increasing shear rate, then shows saturation for a while, thereafter starts decreasing, in qualitative agreement with recent theoretical studies [Phys. Rev. B {\bf 70}, 205423 (2004)] based on Brownian drag and ``loss of grip''. Interestingly, if the sign of the interspecies interaction is reversed, the direction of the induced drift remains the same, but the flow-rate at which loss of grip occurs is lower, and the level of fluctuations is higher.Comment: 7 pages, 9 figure

Flow-induced voltage and current generation in carbon nanotubes

New experimental results, and a plausible theoretical understanding thereof, are presented for the flow-induced currents and voltages observed in single-walled carbon nanotube samples. In our experiments, the electrical response was found to be strongly sublinear -- nearly logarithmic -- in the flow speed over a wide range, and its direction could be controlled by an electrochemical biasing of the nanotubes. These experimental findings are inconsistent with the conventional idea of a streaming potential as the efficient cause. Here we present a new, physically appealing, Langevin-equation based treatment of the nanotube charge carriers, assumed to be moving under coulombic forcing by the correlated ionic fluctuations, advected by the liquid in flow. The resulting 'Doppler-shifted' force-force correlation, as seen by the charge carriers drifting in the nanotube, is shown to give a strongly sublinear response, broadly in agreement with experiments.Comment: 11 pages including 3 figures. To appear in Phys. Rev B (2004

Evolution, present status and issues concerning small tank systems in Sri Lanka [Small tanks in Sri Lanka: evolution, present status and issues]

Tank irrigationSmall scale systemsHistoryIrrigation systemsDesignMaintenanceHydrologyPollutionIrrigation managementCultivationFarming systemsWells

Trapping and sorting active particles: motility-induced condensation & smectic defects

We present an experimental realization of the collective trapping phase transition [Kaiser et al., PRL 108, 268307 (2012)], using motile polar granular rods in the presence of a V-shaped obstacle. We offer a theory of this transition based on the interplay of motility-induced condensation and liquid-crystalline ordering and show that trapping occurs when persistent influx overcomes the collective expulsion of smectic defect structures. In agreement with the theory, our experiments find that a trap fills to the brim when the trap angle $\theta$ is below a threshold $\theta_c$, while all particles escape for $\theta > \theta_c$. Our simulations support a further prediction, that $\theta_c$ goes down with increasing rotational noise. We exploit the sensitivity of trapping to the persistence of directed motion to sort particles based on the statistical properties of their activityComment: 6 pages, 5 figures, for supplementary mpg files, see "https://www.dropbox.com/sh/3cmswfoysdn0sb6/AACpEp-G3768B6Y62nDFj_Hea?dl=0". This paper supersedes our earlier version arXiv:1603.08535 and contains substantial new results including revised theoretical treatmen

A Dynamic Renormalization Group Study of Active Nematics

We carry out a systematic construction of the coarse-grained dynamical equation of motion for the orientational order parameter for a two-dimensional active nematic, that is a nonequilibrium steady state with uniaxial, apolar orientational order. Using the dynamical renormalization group, we show that the leading nonlinearities in this equation are marginally \textit{irrelevant}. We discover a special limit of parameters in which the equation of motion for the angle field of bears a close relation to the 2d stochastic Burgers equation. We find nevertheless that, unlike for the Burgers problem, the nonlinearity is marginally irrelevant even in this special limit, as a result of of a hidden fluctuation-dissipation relation. 2d active nematics therefore have quasi-long-range order, just like their equilibrium counterpartsComment: 31 pages 6 figure