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Microstructured materials, such as architected metamaterials and phononic crystals, exhibit complex wave propagation phenomena due to their internal structure. While full-scale numerical simulations can capture these effects, they are…
When tiny soft ferromagnetic particles are placed along a liquid interface and exposed to a vertical magnetic field, the balance between capillary attraction and magnetic repulsion leads to self-organization into well-defined patterns.…
We investigate the internal observability of the wave equation with Dirichlet boundary conditions in tilings. The paper includes a general result relating internal observability problems in general domains to their tiles, and a discussion…
We propose a mathematical model for describing propagating confined modes in domain walls of intermediate angle between domains. The proposed model is derived from the linearised Bloch equations of motion and after reasonable assumptions,…
Three-dimensional simulations with fully resolved hydrodynamics are performed to study the collective motion of model swimmers in confinement. We show that certain swimming mechanisms can lead to traveling wave-like collective motion even…
Ferro- and ferrimagnets play host to small-signal, microwave-frequency magnetic excitations called spin waves, the quanta of which are known as magnons. Over the last decade, the field of spin-wave dynamics has contributed much to our…
We present experimental results on hydrothermal waves in long and narrow 1D channels. In a bounded channel, we describe the primary and secondary instabilities leading to waves and modulated waves in terms of convective/absolute…
The propagation of acoustic waves in a poro-elastic medium of infinite extension containing spherical cavities randomly distributed is investigated. The scattering coefficients are computed in the low frequency limit using the sealed pore…
We demonstrate with experiments and simulations how microscopic self-propelled particles navigate through environments presenting complex spatial features, which mimic the conditions inside cells, living organisms and future lab-on-a-chip…
Some recent papers proposed the use of the satellite images of Google Earth in teaching physics, in particular to see some behaviours of waves. Reflection, refraction, diffraction and interference are easy to be found in these satellite…
Wave-like spatial statistics in walking-droplet quantum analogs are typically attributed to spatial or temporal nonlocal wave effects. We show instead that such behavior arises generically from the low-dimensional nonlinear dynamics of an…
We consider solitary water waves on a rotational, unidirectional flow in a two-dimensional channel of finite depth. Ovsyannikov has conjectured in 1983 that the solitary wave is uniquely determined by the Bernoulli constant, mass flux and…
We have preformed experiments on a liquid curtain falling from a horizontal, wetted, tube and lateraly constrained by two vertical wires. The fluid motion nearly reduces to a free-fall, with a very low detachment velocity below the tube.…
For some class of mappings, there are investigated problems connected with a possibility of continuous extension to a boundary on Riemannian manifolds. In particular, for so-called ring mappings, there is proved a result related to…
Some of the most impressive singular wave fronts seen in Nature are the transbasin oceanic internal waves, which may be observed from the Space Shuttle as they propagate and interact with each other, for example, in the South China Sea. The…
This thesis deals with some theoretical aspects of deterministic freak wave generation in the wave basin of a hydrodynamic laboratory. We adopt the spatial nonlinear Schr\"odinger equation as a mathematical model to describe the deformation…
This paper is concerning the inverse conductive scattering of acoustic waves by a bounded inhomogeneous object with possibly embedded obstacles inside. A new uniqueness theorem is proved that the conductive object is uniquely determined by…
We highlight an intrinsic connection between classical quadrature domains and the well-studied theme of removable singularities of analytic sets in several complex variables. Exploiting this connection provides a new framework to recover…
The effect of the modulation instability on the propagation of solitary waves along one-dimensional discrete nonlinear Schr\"odinger equation with cubic nonlinearity is revisited. A self-contained quasicontinuum approximation is developed…
The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. Under the assumption that the vorticity is a negative constant whose absolute value is sufficiently large, we…