Complex deformations of Bjorken flow

Through a complex shift of the time coordinate, a modification of Bjorken flow is introduced which interpolates between a glasma-like stress tensor at forward rapidities and Bjorken-like hydrodynamics around mid-rapidity. A Landau-like full-stopping regime is found at early times and rapidities not too large. Approximate agreement with BRAHMS data on the rapidity distribution of produced particles at top RHIC energies can be achieved if the complex shift of the time coordinate is comparable to the inverse of the saturation scale. The form of the stress tensor follows essentially from symmetry considerations, and it can be expressed in closed form.Comment: 14 pages, 4 figures. v2: Minor error corrected, conclusions unchange

Microfluidic-SANS: flow processing of complex fluids

Understanding and engineering the flow-response of complex and non-Newtonian fluids at a molecular level is a key challenge for their practical utilisation. Here we demonstrate the coupling of microfluidics with small angle neutron scattering (SANS). Microdevices with high neutron transmission (up to 98%), low scattering background ([Image: see text]), broad solvent compatibility and high pressure tolerance (≈3–15 bar) are rapidly prototyped via frontal photo polymerisation. Scattering from single microchannels of widths down to 60 μm, with beam footprint of 500 μm diameter, was successfully obtained in the scattering vector range 0.01–0.3 Å(−1), corresponding to real space dimensions of [Image: see text]. We demonstrate our approach by investigating the molecular re-orientation and alignment underpinning the flow response of two model complex fluids, namely cetyl trimethylammonium chloride/pentanol/D(2)O and sodium lauryl sulfate/octanol/brine lamellar systems. Finally, we assess the applicability and outlook of microfluidic-SANS for high-throughput and flow processing studies, with emphasis of soft matter

The Chern-Ricci flow on complex surfaces

The Chern-Ricci flow is an evolution equation of Hermitian metrics by their Chern-Ricci form, first introduced by Gill. Building on our previous work, we investigate this flow on complex surfaces. We establish new estimates in the case of finite time non-collapsing, anologous to some known results for the Kahler-Ricci flow. This provides evidence that the Chern-Ricci flow carries out blow-downs of exceptional curves on non-minimal surfaces. We also describe explicit solutions to the Chern-Ricci flow for various non-Kahler surfaces. On Hopf surfaces and Inoue surfaces these solutions, appropriately normalized, collapse to a circle in the sense of Gromov-Hausdorff. For non-Kahler properly elliptic surfaces, our explicit solutions collapse to a Riemann surface. Finally, we define a Mabuchi energy functional for complex surfaces with vanishing first Bott-Chern class and show that it decreases along the Chern-Ricci flow.Comment: 45 page

Generalized Kahler Geometry and the Pluriclosed Flow

In prior work the authors introduced a parabolic flow for pluriclosed metrics, referred to as pluriclosed flow. We also demonstrated that this flow, after certain gauge transformations, gives a class of solutions to the renormalization group flow of the nonlinear sigma model with B-field. Using these transformations, we show that our pluriclosed flow preserves generalized Kahler structures in a natural way. Equivalently, when coupled with a nontrivial evolution equation for the two complex structures, the B-field renormalization group flow also preserves generalized Kahler structure. We emphasize that it is crucial to evolve the complex structures in the right way to establish this fact.Comment: Final version, to appear in Nuc. Phys.

On the evolution of a Hermitian metric by its Chern-Ricci form

We consider the evolution of a Hermitian metric on a compact complex manifold by its Chern-Ricci form. This is an evolution equation first studied by M. Gill, and coincides with the Kahler-Ricci flow if the initial metric is Kahler. We find the maximal existence time for the flow in terms of the initial data. We investigate the behavior of the flow on complex surfaces when the initial metric is Gauduchon, on complex manifolds with negative first Chern class, and on some Hopf manifolds. Finally, we discuss a new estimate for the complex Monge-Ampere equation on Hermitian manifolds.Comment: 37 pages, v3 corrected typos, final version to appear in J. Differential Geo