Fractional Quantum Hall Physics in Jaynes-Cummings-Hubbard Lattices

Jaynes-Cummings-Hubbard arrays provide unique opportunities for quantum emulation as they exhibit convenient state preparation and measurement, and in-situ tuning of parameters. We show how to realise strongly correlated states of light in Jaynes-Cummings-Hubbard arrays under the introduction of an effective magnetic field. The effective field is realised by dynamic tuning of the cavity resonances. We demonstrate the existence of Fractional Quantum Hall states by com- puting topological invariants, phase transitions between topologically distinct states, and Laughlin wavefunction overlap.Comment: 5 pages, 3 figure

The Geometry of the Gibbs-Appell Equations and Gauss' Principle of Least Constraint

We present a generalisation of the Gibbs-Appell equations which is valid for general Lagrangians. The general form of the Gibbs-Appell equations is shown to be valid in the case when constraints and external forces are present. In the case when the Lagrangian is the kinetic energy with respect to a Riemannian metric, the Gibbs function is shown to be related to the kinetic energy on the tangent bundle of the configuration manifold with respect to the Sasaki metric. We also make a connection with the Gibbs-Appell equations and Gauss' principle of least constraint in the general case

Ribbon growing method and apparatus

A method and apparatus are described which facilitate the growing of silicon ribbon. A container for molten silicon has a pair of passages in its bottom through which filaments extend to a level above the molten silicon, so as the filaments are pulled up they drag up molten silicon to form a ribbon. A pair of guides surround the filaments along most of the height of the molten silicon, so that the filament contacts only the upper portion of the melt. This permits a filament to be used which tends to contaminate the melt if it is in long term contact with the melt. This arrangement also enables a higher melt to be used without danger that the molten silicon will run out of any bottom hole

The Looming Battle for Control of Multidistrict Litigation in Historical Perspective

2018 marks fifty years since the passage of the Multidistrict Litigation Act. But instead of thoughts of a golden-anniversary celebration, an old Rodney Dangerfield one-liner comes to mind: “[M]y last birthday cake looked like a prairie fire.” Indeed, after a long period of relative obscurity, multidistrict litigation (MDL) has become a subject of major controversy—and not only among scholars of procedure. For a long time, both within and beyond the rarified world of procedure scholars, MDL was perceived as the more technical, less extreme cousin of the class action, which attracted most of the controversy. My goal in this Article is to shed light on the reasons the Multidistrict Litigation Act was constructed as it was and suggest that those engaged in the current debate ask, after becoming informed by available data, whether those reasons have lost any of their currency. I also offer some tenuous predictions about the path forward, recognizing that the prediction business is a dangerous one in the current political climate. First, I review the history to explain why the MDL framework was built without Rules Committee involvement. Then, I fast-forward to the present day and discuss briefly the nascent proposals to either amend the MDL statute or provide for Federal Rules of Civil Procedure for MDL. Finally, I conclude by assessing the current debate and make some suggestions as this debate winds its way forward. In 1968, the small cadre of judges who developed and fought for the MDL statute won the battle for procedural power. Today, fifty years later, the MDL statute continues to operate as they imagined. However, with success comes scrutiny, and what had been settled is now once again up for debate

Multi-element spherical shell generation

A nozzle assembly in a multi-element spherical shell generation system includes first and second side-by-side spaced apart nozzles and a web portion extending between and connecting the nozzles. The first nozzle has an inner orifice adapted to discharge a first filler material and an outer annular orifice separated from and defined in concentric relation about the inner orifice and adapted to discharge a first shell material. The second nozzle has an inner orifice adapted to discharge a second filler material and an outer annular orifice separated from and defined in concentric relation about the inner orifice and adapted to discharge a second shell material. A multi-element spherical shell can be formed through employment of the nozzle assembly by merger with one another after discharge from the outer orifices of the nozzles of a pair of adjacent annular streams of liquid or molten shell wall material of different compositions and encapsulation by the mixed shell wall materials of a common encapsulated core fluids also simultaneously discharged by the inner orifices nozzles. On the other hand, the pair of encapsulating streams of shell wall material can be of the same materials which merge together and encapsulate core fluids of different compositions which will merge together after discharge from the nozzles

Adjustable steam producing flexible orifice independent of fluid pressure

A self-adjusting choke for a fluids nozzle includes a membrane constructed of a single piece of flexible or elastic material. This flexible material is shaped to fit into the outlet of a nozzle. The body of the membrane has at least two flow channels, from one face to the other, which directs two streams of water to cross at the opening of the nozzle or at some point beyond. The elasticity and thickness of the membrane is selected to match the range of expected pressures and fluid velocities. The choke may have more than two flow channels, as long as they are aligned adjacent to one another and directed towards each other at the exit face. In a three orifice embodiment, one is directed upward, one is directed downward, and the one in the middle is directed forward. In this embodiment all three fluid streams intersect at some point past the nozzle opening. Under increased pressure the membrane will deform causing the orifices to realign in a more forward direction, causing the streams to intersect at a smaller angle. This reduces the force with which the separate streams impact each other, still allowing the separate streams to unify into a single stable spiralling stream in spite of the increased pressure