Waves

In this talk we will discuss shallow water wave models that model waves in the near-shore region of the coast. In this case, various models of Boussinesq type have been proposed, that are based on some simplifying assumptions on the vertical structure of the flow, and plugging these into the Navier-Stokes equations. The results are commonly used 1D and 2D nonlinear water wave models. One such model is the Serre-Green-Naghdi equations. We will present a hybrid DG method for the SGN and its implementation in the deal.II software package. This work is joint with Ali Samii.

Joint work with I Vitebskiy.

Wave propagation in spatially periodic media, such as photonic crystals,
can be qualitatively different
from any uniform substance. The differences are particularly pronounced
when the electromagnetic wavelength
is comparable to the minimal translation of the periodic structure. In
such a case, the periodic medium cannot
be assigned any meaningful refractive index. Still, such important
features as negative refraction and/or

Localization of vibrations is one of the most intriguing
features exhibited by irregular or inhomogeneous media. A striking
(but certainly not unique) example is the so called 'Anderson
localization' of quantum states by a random potential, that was
discovered by Anderson in 1958 and that brought him the Nobel Prize in
1977. Anderson localization is one of the central topics in condensed
matter physics, producing hundreds of papers each year. Yet, there
exists up to now no theoretical framework able to predict exactly what

We study bifurcations of periodic travelling waves in diatomic granular chains
from the anti-continuum limit, when the mass ratio between the light and heavy beads is zero. We show that every limiting periodic wave is uniquely continued with respect to the mass ratio parameter and the periodic waves with the wavelength larger than a certain critical value are spectrally stable.

In this talk, we shall survey some recent results on the wave propagation in
the two species competition systems with Lotka-Volterra type nonlinearity.
This includes systems with continuous and discrete diffusion.
Both monostable and bistable cases shall be discussed.
Questions on minimal wave speed for the monostable case,
propagation failure in the bistable case, monotonicity of wave
profiles, and uniqueness of wave speed in the bistable case shall be addressed.

The usual notions of reaction-diffusion waves or fronts can be viewed as examples of generalized transition waves. These new notions involve uniform limits, with respect to the geodesic distance, to a family of hypersurfaces which are parametrized by time. The existence of transition waves has been proved in various contexts where the standard notions of waves make no sense anymore.

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Classical detection theory for sensing relies on fixed target
illumination and independent identically distributed noise for target and
clutter characterization. Unfortunately in many cases such as sensing and
communications in urban or atmospheric scenarios, we encounter much more
complex clutter and target conditions due to scattering from multiple
sources. As a result we must envision a new sensing scheme to combat noise
not handled by classical sensing methods. We will therefore develop