We show that in a model obtained by forcing with a countable support iteration of Mathias forcing of length ω2, the distributivity number of P(ω)/fin is ω2, whereas the distributivity number of r.o.(P(ω)/fin) 2 is ω1. This answers an old problem of Balcar, Pelant and Simon, and others.

Gentner and Rautenbach conjectured that the size of a minimum zero forcing set in a connected graph on n vertices with maximum degree 3 is at most 1 3 n + 2. We disprove this conjecture by constructing a collection of connected graphs {Gn} with maximum degree 3 on arbitrarily large number of vertices, having zero forcing number at least 4 9 |Gn|.

The dependence of mixing efficiency on time-varying forcing is studied by direct numerical simulation (DNS) of Kelvin–Helmholtz (KH) instability. Time-dependent forcing fields are designed to reproduce a wavelike oscillation by solving the equations of motion in a tilted coordinate frame and allowing the tilt angle to vary in time. Mixing efficiency Gc is defined as the ratio of potential energ...

Recent MHD dynamo simulations for magnetic Prandtl number > 1 demonstrate that when MHD turbulence is forced with sufficient kinetic helicity, the saturated magnetic energy spectrum evolves from having a single peak below the forcing scale to become doubly peaked with one peak at the system (=largest) scale and one at the forcing scale. The system scale field growth is well modeled by a recent ...

In this paper, we propose computational approaches for the zero forcing problem, the connected zero forcing problem, and the problem of forcing a graph within a specified number of timesteps. Our approaches are based on a combination of integer programming models and combinatorial algorithms, and include formulations for zero forcing as a dynamic process, and as a set-covering problem. We explo...

The quasigeostrophic equation is a prototypical geophysical fluid model. In this paper, we consider time-periodic motions of this model under dissipation and time-dependent wind forcing. We show that when the wind forcing is time-periodic and the spatial square-integral of the wind forcing is bounded in time, the full nonlinear quasigeostrophic model has time-periodic motions, under some condit...

The Teacher Forcing algorithm trains recurrent networks by supplying observed sequence values as inputs during training and using the network’s own one-stepahead predictions to do multi-step sampling. We introduce the Professor Forcing algorithm, which uses adversarial domain adaptation to encourage the dynamics of the recurrent network to be the same when training the network and when sampling...