A nonlinear small-deformation theory for transient droplet electrohydrodynamics

The deformation of a viscous liquid droplet suspended in another liquid and subject to an applied electric field is a classic multiphase flow problem best described by the Melcher-Taylor leaky dielectric model. The main assumption of the model is that any net charge in the system is concentrated on the interface between the two liquids as a result of the jump in Ohmic currents from the bulk. Upon application of the field, the drop can either attain a steady prolate or oblate shape with toroidal circulating flows both inside and outside arising from tangential stresses on the interface due to action of the field on the surface charge distribution. Since the pioneering work of \cite{taylor1966}, there have been numerous computational and theoretical studies to predict the deformations measured in experiments. Most existing theoretical models, however, have either neglected transient charge relaxation or nonlinear charge convection by the interfacial flow. In this work, we develop a novel small-deformation theory accurate to second order in electric capillary number ${O}(Ca_E^2)$ for the complete Melcher-Taylor model that includes transient charge relaxation, charge convection by the flow, as well as transient shape deformation. The main result of the paper is the derivation of coupled evolution equations for the induced electric multipoles and for the shape functions describing the deformations on the basis of spherical harmonics. Our results, which are consistent with previous models in the appropriate limits, show excellent agreement with fully nonlinear numerical simulations based on an axisymmetric boundary-element formulation and with existing experimental data in the small-deformation regime.Comment: An online code in MATLAB that reproduces the results in this paper is available on request by emailing dstn(at)ucsd(dot)ed

Heavy quark state production in Pb-Pb collisions at sNN\sqrt{s_{NN}}=5.02 TeV

We estimate differential rapidity cross sections for $J/\Psi$, $\Psi(2S)$, $\Upsilon(1S)$, $\Upsilon(2S)$, and $\Upsilon(3S)$ production via Pb-Pb collisions at proton-proton energy $\equiv \sqrt{s_{pp}}$ =5.02 TeV. For the $\Psi(2S)$, $\Upsilon(3S)$ states we use the mixed heavy quark hyrid theory, with these states being approximately 50\% standard and 50\% hybrid charmonium, bottomonium meson states. This is an extension of previous work on heavy quark state production via Cu-Cu and Au-Au collisions at $\sqrt{s_{pp}}$=200 GeV.Comment: 7 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1309.5374, arXiv:1411.368

Common Origin of Non-zero θ13\theta_{13} and Baryon Asymmetry of the Universe in a TeV scale Seesaw Model with A4A_4 Flavour Symmetry

We study the possibility of generating non-zero reactor mixing angle $\theta_{13}$ and baryon asymmetry of the Universe within the framework of an $A_4$ flavour symmetric model. Using the conventional type I seesaw mechanism we construct the Dirac and Majorana mass matrices which give rise to the correct light neutrino mass matrix. Keeping the right handed neutrino mass matrix structure trivial so that it gives rise to a (quasi) degenerate spectrum of heavy neutrinos suitable for resonant leptogenesis at TeV scale, we generate the non-trivial structure of Dirac neutrino mass matrix that can lead to the light neutrino mixing through type I seesaw formula. Interestingly, such a setup naturally leads to non-zero $\theta_{13}$ due to the existence of anti-symmetric contraction of the product of two triplet representations of $A_4$. Such antisymmetric part of triplet products usually vanish for right handed neutrino Majorana mass terms, leading to $\mu-\tau$ symmetric scenarios in the most economical setups. We constrain the model parameters from the requirement of producing the correct neutrino data as well as baryon asymmetry of the Universe for right handed neutrino mass scale around TeV. The $A_4$ symmetry is augmented by additional $Z_3 \times Z_2$ symmetry to make sure that the splitting between right handed neutrinos required for resonant leptogenesis is generated only by next to leading order terms, making it naturally small. We find that the inverted hierarchical light neutrino masses give more allowed parameter space consistent with neutrino and baryon asymmetry data.Comment: 26 pages, 12 figures, 2 figures added, version accepted for publication in Phys. Rev.

J/ΨJ/\Psi, Ψ(2S)\Psi(2S) Production in pp Collisions at E=510 GeV

This brief report is an extension of studies of $J/\Psi,\Psi(2S)$ production in pp collisions at the BNL with E=$\sqrt{s}$=200 GeV to E=510 GeV at PHENIX.Comment: 3 pages, 1 figur