32 research outputs found
Stability of Travelling Waves for Reaction-Diffusion Equations with Multiplicative Noise
We consider reaction-diffusion equations that are stochastically forced by a
small multiplicative noise term. We show that spectrally stable travelling wave
solutions to the deterministic system retain their orbital stability if the
amplitude of the noise is sufficiently small.
By applying a stochastic phase-shift together with a time-transform, we
obtain a semilinear sPDE that describes the fluctuations from the primary wave.
We subsequently develop a semigroup approach to handle the nonlinear stability
question in a fashion that is closely related to modern deterministic methods
Determination of the Carrier-Envelope Phase of Few-Cycle Laser Pulses with Terahertz-Emission Spectroscopy
The availability of few-cycle optical pulses opens a window to physical
phenomena occurring on the attosecond time scale. In order to take full
advantage of such pulses, it is crucial to measure and stabilise their
carrier-envelope (CE) phase, i.e., the phase difference between the carrier
wave and the envelope function. We introduce a novel approach to determine the
CE phase by down-conversion of the laser light to the terahertz (THz) frequency
range via plasma generation in ambient air, an isotropic medium where optical
rectification (down-conversion) in the forward direction is only possible if
the inversion symmetry is broken by electrical or optical means. We show that
few-cycle pulses directly produce a spatial charge asymmetry in the plasma. The
asymmetry, associated with THz emission, depends on the CE phase, which allows
for a determination of the phase by measurement of the amplitude and polarity
of the THz pulse