Directed harmonic currents for laminations on certain compact complex surfaces

Let ℒ be a Lipschitz lamination by Riemann surfaces embedded in M. If M is a complex torus, ℂℙ1 × ℂℙ1 or 𝕋1 × ℂℙ1 and there is no directed closed current then there exists a unique directed harmonic current of mass one. Moreover, if ℒ is embedded in M = ℂℙ1 × ℂℙ1 and has no compact leaves, then there is no directed closed current. If ℒ is not Lipschitz, then slightly weaker results are obtained.

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Directed harmonic currents near hyperbolic singularities

Ergodic Theory and Dynamical Systems ◽

10.1017/etds.2017.2 ◽

2017 ◽

Vol 38 (8) ◽

pp. 3170-3187 ◽

Cited By ~ 4

Author(s):

VIÊT-ANH NGUYÊN

Keyword(s):

Mass Distribution ◽

Holomorphic Foliation ◽

Holomorphic Foliations ◽

Harmonic Current ◽

Lelong Number ◽

Harmonic Currents ◽

Hyperbolic Singularity ◽

Compact Complex Surfaces ◽

Global Result ◽

Local Result

Let $\mathscr{F}$ be a holomorphic foliation by curves defined in a neighborhood of $0$ in $\mathbb{C}^{2}$ having $0$ as a hyperbolic singularity. Let $T$ be a harmonic current directed by $\mathscr{F}$ which does not give mass to any of the two separatrices. We show that the Lelong number of $T$ at $0$ vanishes. Then we apply this local result to investigate the global mass distribution for directed harmonic currents on singular holomorphic foliations living on compact complex surfaces. Finally, we apply this global result to study the recurrence phenomenon of a generic leaf.

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A Novel Method for Harmonic Current Injection with Sensor Supported Adaptation on Permanent Magnet Synchronous Machines

Machines ◽

10.3390/machines9080139 ◽

2021 ◽

Vol 9 (8) ◽

pp. 139

Author(s):

Matthias Vollat ◽

Dominik Krahe ◽

Frank Gauterin

Keyword(s):

Permanent Magnet ◽

Current Injection ◽

Synchronous Machines ◽

Permanent Magnet Synchronous Machine ◽

Permanent Magnet Synchronous Machines ◽

Harmonic Current ◽

Harmonic Currents ◽

Sensor Signals ◽

Novel Method ◽

Higher Harmonic

To reduce torque oscillations in electric motors, harmonic current injection (HCI) has been used in industry for some time. For this purpose, higher harmonic currents calculated in advance are injected into the machine. Since the general conditions for the machine can change during its life cycle, this article presents a method that makes it possible to change the parameters of HCI during operation. For this purpose, sensor signals are used to detect the reaction of the electric motor to small variations of the HCI parameters. The knowledge gained in this way is used to make further suitable variations. FEM simulations were used to verify the effectiveness of the approach. The results show that the algorithm can independently optimize the HCI parameters during runtime and reduces the amplitude of the 6th harmonic in the torque by 87% for a permanent magnet synchronous machine.

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