Related papers: Recovering water wave elevation from pressure meas…
Nonlinear systems and interaction forces are pervasive in many scientific fields, such as nanoscale metrology and materials science, but their accurate identification is challenging due to their complex behaviour and inaccessibility of…
We introduce a new method for the reconstruction of a function from linear measurements by means of oblique projections. The space spanned by the measurement vectors may be different from the subspace in which the function is reconstructed.…
Recovering 3D geometry of underwater scenes is challenging because of non-linear refraction of light at the water-air interface caused by the camera housing. We present a light field-based approach that leverages properties of angular…
In this article, we investigate an inverse problem for a semi-linear wave equation posed on bounded domain in $\mathbb{R}^{n+1}$, with $n \geq 2$. Our primary objective is to reconstruct the damping coefficient, the linear and nonlinear…
We consider the propagation of surface water waves in a straight planar channel perturbed at the bottom by several thin curved tunnels and wells. We propose a method to construct non reflecting underwater topographies of this type at an…
Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give…
We develop a rigorous asymptotic derivation for two mathematical models of water waves that capture the full nonlinearity of the Euler equations up to quadratic and cubic interactions, respectively. Specifically, letting epsilon denote an…
We present a method for reconstructing two-dimensional velocity fields at specified length scales using observational data from tracer particles in a flow, without the need for interpolation or smoothing. The algorithm, adapted from…
Predictions of the wave-induced response of floating structures that are moored in a harbour or coastal waters require an accurate description of the (nonlinear) evolution of waves over variable bottom topography, the interactions of the…
The paper develops a method for recovering a one-dimensional rough surface profile from scattered wave field, using a single receiver and repeated measurements when the surface is moving with respect to source and receiver. This extends a…
In this short note, we derive a system of two nonlocal equations for the water-wave problem following the work of [AFM06]. Specifically, we consider a fluid with a one-dimensional free surface for an irrotational fluid both with, and…
A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…
A generalized version of the $abcd$-Boussinesq class of systems is derived to accommodate variable bottom topography in two-dimensional space. This extension allows for the conservation of suitable energy functionals in some cases and…
Fourier-based wavefront sensors, such as the Pyramid Wavefront Sensor (PWFS), are the current preference for high contrast imaging due to their high sensitivity. However, these wavefront sensors have intrinsic nonlinearities that constrain…
We are concerned with the reconstruction of a one dimensional wave equation, where the potential is known in a neighborhood of one of the end points of the boundary. We show then the sought potential can be determined by one single…
We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…
In the last fifteen years, a great progress has been made in the understanding of the nonlinear resonance dynamics of water waves. Notions of scale- and angle-resonances have been introduced, new type of energy cascade due to nonlinear…
This is a study of the Euler equations for free surface water waves in the case of varying bathymetry, considering the problem in the shallow water scaling regime. In the case of rapidly varying periodic bottom boundaries this is a problem…
A great deal of theoretical and experimental efforts have been devoted in the last decades to the study of long-wavelength photodetection mechanisms in field-effect transistors hosting two-dimensional (2D) electron systems. A particularly…