Related papers: Recovering water wave elevation from pressure meas…
In this paper we consider the wave equations with power type nonlinearities including time-derivatives of unknown functions and their weakly coupled systems. We propose a framework of test function method and give a simple proof of the…
We investigate symmetry-protected topological water waves within a strategically engineered square lattice system. Thus far, symmetry-protected topological modes in hexagonal systems have primarily been studied in electromagnetism and…
Coastal erosion describes the displacement of land caused by destructive sea waves, currents or tides. Major efforts have been made to mitigate these effects using groins, breakwaters and various other structures. We try to address this…
By numerical simulation of exact equations of motion (in terms of conformal variables) for planar non-stationary potential flows of an ideal fluid with a free surface over a strongly non-uniform bottom profile, the effect of nonlinear…
We introduce a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$ - $\Omega$ a…
Light Detection and Ranging (LiDAR) are fast emerging sensors in the field of Earth Observation. It is a remote sensing technology that utilizes laser beams to measure distances and create detailed three-dimensional representations of…
The paper introduces a new way to construct dissipative solutions to a second order variational wave equation. By a variable transformation, from the nonlinear PDE one obtains a semilinear hyperbolic system with sources. In contrast with…
A new regularisation of the shallow water (and isentropic Euler) equations is proposed. The regularised equations are non-dissipative, non-dispersive and possess a variational structure. Thus, the mass, the momentum and the energy are…
Because of their capability to preserve steady-states, well-balanced schemes for Shallow Water equations are becoming popular. Among them, the hydrostatic reconstruction proposed in Audusse et al. (2004), coupled with a positive numerical…
Humans have a strong intuitive understanding of physical processes such as fluid falling by just a glimpse of such a scene picture, i.e., quickly derived from our immersive visual experiences in memory. This work achieves such a…
We study iterative signal reconstruction in computed tomography (CT), wherein measurements are produced by a linear transformation of the unknown signal followed by an exponential nonlinear map. Approaches based on pre-processing the data…
We design a nonlinear estimator for channel flows at $Re_{\tau}=180$ and $590$. The nonlinear estimator uses a linear estimator structure based on the linearised Navier-Stokes equations and explicitly calculates the nonlinear forcing from…
In this paper we address the return to equilibrium problem for an axisymmetric floating structure in shallow water. First we show that the equation for the solid motion can be reduced to a delay differential equation involving an…
Nonlinear acoustic evolution is often discussed in the context of wave-steepening that leads to shock formation, and is of special interest in applications where the shock continues to strengthen due to a narrowing of its channel or the…
This paper is concerned with a nonlinear imaging problem, which aims to reconstruct a locally perturbed, perfectly reflecting, infinite plane from intensity-only (or phaseless) far-field or near-field data. A recursive Newton iteration…
Wind-generated waves are often treated as stochastic processes. There is particular interest in their spectral density functions, which are often expressed in some parametric form. Such spectral density functions are used as inputs when…
We consider an inverse problem for the elastic wave of simultaneously reconstructing the impedance and the geometric information of the bounded body that is occupied by a homogeneous and isotropic elastic medium from the measured Cauchy…
Active Flux is a third order accurate numerical method which evolves cell averages and point values at cell interfaces independently. It naturally uses a continuous reconstruction, but is stable when applied to hyperbolic problems. In this…
In this letter a new method based on modified self-organizing maps is presented for the reconstruction of deep ocean current velocities from surface information provided by satellites. This method takes advantage of local correlations in…
This paper is devoted to the stabilization of the water-wave equations with surface tension through of an external pressure acting on a small part of the free surface. It is proved that the energy decays to zero exponentially in time,…