104 research outputs found
Thomas Decomposition of Algebraic and Differential Systems
In this paper we consider disjoint decomposition of algebraic and non-linear
partial differential systems of equations and inequations into so-called simple
subsystems. We exploit Thomas decomposition ideas and develop them into a new
algorithm. For algebraic systems simplicity means triangularity, squarefreeness
and non-vanishing initials. For differential systems the algorithm provides not
only algebraic simplicity but also involutivity. The algorithm has been
implemented in Maple
Injection of Orbital Angular Momentum and Storage of Quantized Vortices in Polariton Superfluids
We report the experimental investigation and theoretical modeling of a rotating polariton superfluid relying on an innovative method for the injection of angular momentum. This novel, multipump injection method uses four coherent lasers arranged in a square, resonantly creating four polariton populations propagating inwards. The control available over the direction of propagation of the superflows allows injecting a controllable nonquantized amount of optical angular momentum. When the density at the center is low enough to neglect polariton-polariton interactions, optical singularities, associated with an interference pattern, are visible in the phase. In the superfluid regime resulting from the strong nonlinear polariton-polariton interaction, the interference pattern disappears and only vortices with the same sign are persisting in the system. Remarkably, the number of vortices inside the superfluid region can be controlled by controlling the angular momentum injected by the pumps
On the generalised Ritt problem as a computational problem
The Ritt problem asks if there is an algorithm that tells whether one prime
differential ideal is contained in another one if both are given by their
characteristic sets. We give several equivalent formulations of this problem.
In particular, we show that it is equivalent to testing if a differential
polynomial is a zero divisor modulo a radical differential ideal. The technique
used in the proof of equivalence yields algorithms for computing a canonical
decomposition of a radical differential ideal into prime components and a
canonical generating set of a radical differential ideal. Both proposed
representations of a radical differential ideal are independent of the given
set of generators and can be made independent of the ranking.Comment: 9 page
Merging of vortices and antivortices in polariton superfluids
Quantised vortices are remarkable manifestations on a macroscopic scale of the coherent nature of
quantum fluids, and the study of their properties is of fundamental importance for the understanding
of this peculiar state of matter. Cavity-polaritons, due to their double light-matter nature, offer
a unique controllable environment to investigate these properties. In this work we theoretically
investigate the possibility to deterministically achieve the annihilation of a vortex with an antivortex
through the increase of the polariton density in the region surrounding the vortices. Moreover we
demonstrate that by means of this mechanism an array of vortex-antivortex pairs can be completely
washed out
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