Related papers: Wave manipulation via delay-engineered periodic po…
In this brief note, we consider a wave equation that has both trapping and a complex potential. For this problem, we prove a uniform bound on the energy and a Morawetz (or integrated local energy decay) estimate. The equation is a model…
In this work, we optically trapping microparticles with higher order Frozen Wave using holographic optical tweezers. Frozen Waves are diffraction resistant optical beams, obtained by superposing copropagating Bessel beams with the same…
We suggest a spatially local feedback mechanism for stabilizing periodic orbits in spatially extended systems. Our method, which is based on a comparison between present and past states of the system, does not require the external…
Time reflection and refraction are temporal analogies of the spatial boundary effects derived from Fermat's principle. They occur when classical waves strike a time boundary where an abrupt change in the properties of the medium is…
A high energy density plasma embedded in a neutral gas is able to launch an outward-propagating nonlinear electrostatic ionization wave that traps energetic electrons. The trapping maintains a strong sheath electric field, enabling rapid…
Recently, new artificial material has been proposed to control an electromagnetic wave-metasurface, a two-dimensional metamaterial. Compared with a three-dimensional bulky metamaterial, this artificial plane material with sub-wavelength…
It is considered the electromagnetic wave in the frame moving transverse to the wave. Due to the velocity of the frame with respect to a preferred reference frame the oscillations of phase arise. The oscillations of phase yield the third…
We discuss in detail properties of trapped atomic condensates with anisotropic dipole interactions. A practical procedure for constructing anisotropic low energy pseudo potentials is proposed and justified by the agreement with results of…
We consider solutions of the KPP-type equations with a periodically varying reaction rate, and compactly supported initial data. It has been shown by M. Bramson in the case of the constant reaction rate that the lag between the position of…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
Faraday waves are a classic example of a system in which an extended pattern emerges under spatially uniform forcing. Motivated by systems in which uniform excitation is not plausible, we study both experimentally and theoretically the…
We generalize the invariant imbedding theory of the wave propagation and derive new invariant imbedding equations for the propagation of arbitrary number of coupled waves of any kind in arbitrarily-inhomogeneous stratified media, where the…
We construct a Dirac equation in $\kappa$-Minkowski spacetime and analyse its implications. This $\kappa$-deformed Dirac equation is expanded as a power series involving derivatives with respect to commutative coordinates and the…
In the early days of quantum mechanics Kapitza and Dirac predicted that matter waves would scatter off the optical intensity grating formed by two counter-propagating light waves [1]. This interaction, driven by the ponderomotive potential…
We consider the waveguiding by thin patterned slabs embedded in a homogeneous medium. In the longwave limit, the wave spectra of slabs are found to be well described by a single frequency-independent parameter, which we call the "guiding…
Perturbative partial-wave amplitudes diverge in cases with a massless exchanged particle in the $t$-channel. We argue that the divergence is an artifact of perturbation theory and give a prescription for the all-orders correction factor…
A potential flow model is derived for a large flap-type oscillating wave energy converter in the open ocean. Application of the Green's integral theorem in the fluid domain yields a hypersingular integral equation for the jump in potential…
This work presents the first optical trapping experimental demonstration of micro-particles with Frozen Waves. Frozen Waves are an efficient method to model longitudinally the intensity of non-diffracting beams obtained by superposing…
This paper deals with the boundary stabilization problem of a one-dimensional wave equation with a switching time-delay in the boundary. We show that the problem is well-posed in the sense of semigroups theory of linear operators. Then, we…
Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is…