On the relation of standard and helical magnetorotational instability

The magnetorotational instability (MRI) plays a crucial role for cosmic structure formation by enabling turbulence in Keplerian disks which would be otherwise hydrodynamically stable. With particular focus on MRI experiments with liquid metals, which have small magnetic Prandtl numbers, it has been shown that the helical version of this instability (HMRI) has a scaling behaviour that is quite different from that of the standard MRI (SMRI). We discuss the relation of HMRI to SMRI by exploring various parameter dependencies. We identify the mechanism of transfer of instability between modes through a spectral exceptional point that explains both the transition from a stationary instability (SMRI) to an unstable travelling wave (HMRI) and the excitation of HMRI in the inductionless limit. For certain parameter regions we find new islands of the HMRI.Comment: 48 pages, 13 figure

A dynamical system approach to a class of radial weighted fully nonlinear equations

Abstract. In this paper we study existence, nonexistence and classification of radial positive solutions of some weighted fully nonlinear equations involving Pucci extremal operators. Our results are entirely based on the analysis of the dynamics induced by an autonomous quadratic system which is obtained after a suitable transformation. This method allows to treat both regular and singular solutions in a unified way, without using energy arguments. In particular we recover known results on regular solutions for the fully nonlinear non weighted problem by alternative proofs. We also slightly improve the classification of the solutions for the extremal operator M−

Existence, nonexistence and uniqueness for Lane-Emden type fully nonlinear systems

We study existence, nonexistence, and uniqueness of positive radial solutions for a class of nonlinear systems driven by Pucci extremal operators under a Lane-Emden coupling configuration. Our results are based on the analysis of the associated quadratic dynamical system and energy methods. For both regular and exterior domain radial solutions we obtain new regions of existence and nonexistence. Besides, we show an exclusion principle for regular solutions, either in RN or in a ball, by exploiting the uniqueness of trajectories produced by the flow. In particular, for the standard Lane-Emden system involving the Laplacian operator, we prove that the critical hyperbola of regular radial positive solutions is also the threshold for existence and nonexistence of radial exterior domain solutions with Neumann boundary condition. As a byproduct, singular solutions with fast decay at infinity are also found

On unique continuation principles for some elliptic systems

In this paper we prove unique continuation principles for some systems of elliptic partial differential equations satisfying a suitable superlinearity condition. As an application, we obtain nonexistence of nontrivial (not necessarily positive) radial solutions for the Lane-Emden system posed in a ball, in the critical and supercritical regimes. Some of our results also apply to general fully nonlinear operators, such as Pucci's extremal operators, being new even for scalar equations.Comment: 18 page

Dynamics of nitrogen concentration on intercropped ryegrass.

The dynamics of nitrogen (N) in ryegrass intercropped with different forage species with regard to dry matter (DM) accumulation within an agroecological transition system was evaluated. Annual ryegrass was intercropped with black oats (RY + BO), white clover (RY + WC) and forage peanut (RY + FP). The experimental design was completely randomized, with three replications. The study applied the N dilution model for plant tissue which comparatively uses modifiable factors of the environment at optimal levels. The model shows decline in N concentration due to the DM accumulation of temperate grass pastures. Data were compared to model by the root mean square deviation analysis. Dilution coefficient (β), used in all pasture samples, was lower than -0.60. Highest N concentration decline in plant tissues, due to DM accumulation, occurred in RY + WC pastures (β = -0.94), followed by RY + FP (β = - 0.86) and RY + BO (β = - 0.67), respectively. Ryegrass intercropped with white clover showed the highest N content in plant tissue, with a nitrogen nutrition index close to the proposed model