3,745 research outputs found
Degenerate self-similar measures, spectral asymptotics and small deviations of Gaussian processes
We find the logarithmic small ball asymptotics for the -norm with
respect to a degenerate self-similar measures of a certain class of Gaussian
processes including Brownian motion, Ornstein - Uhlenbeck process and their
integrated counterparts.Comment: 15 pages, 1 figur
Trapped modes in zigzag graphene nanoribbons
We study a scattering on an ultra-low potential in zigzag graphene
nanoribbon. Using mathematical framework based on the continuous Dirac model
and augumented scattering matrix, we derive a condition for the existence of a
trapped mode. We consider the threshold energies where the continuous spectrum
changes its multiplicity and show that the trapped modes may appear for
energies slightly less than a threshold and its multiplicity does not exceeds
one. We prove that trapped modes do not appear outside the threshold, provided
the potential is sufficiently small
Team organization may help swarms of flies to become invisible in closed waveguides
We are interested in a time harmonic acoustic problem in a waveguide
containing flies. The flies are modelled by small sound soft obstacles. We
explain how they should arrange to become invisible to an observer sending
waves from and measuring the resulting scattered field at the same
position. We assume that the flies can control their position and/or their
size. Both monomodal and multimodal regimes are considered. On the other hand,
we show that any sound soft obstacle (non necessarily small) embedded in the
waveguide always produces some non exponentially decaying scattered field at
for wavenumbers smaller than a constant that we explicit. As a
consequence, for such wavenumbers, the flies cannot be made completely
invisible to an observer equipped with a measurement device located at
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