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Breakup of a liquid jet into a chain of droplets is common in nature and industry. Previous researchers developed profound mathematic and fluid dynamic models to address this breakup phenomenon starting from tiny perturbations. However, the…
In this pedagogically motivated work, the process of migration in reflection seismics has been considered from a rigorously mathematical viewpoint. An inclined subsurface reflector with a constant dipping angle has been shown to cause a…
This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for inverse elastic scattering problems with phaseless far field data. Systematically, we study two basic models, i.e., inverse scattering of plane…
A simple model of irreversible aggregation under differential sedimentation of particles in a fluid is presented. The structure of the aggregates produced by this process is found to feed back on the dynamics in such a way as to stabilise…
Seismic imaging is the numerical process of creating a volumetric representation of the subsurface geological structures from elastic waves recorded at the surface of the Earth. As such, it is widely utilized in the energy and construction…
The dissolution of solids has created spectacular geomorphologies ranging from centimeter-scale cave scallops to the kilometer-scale "stone forests" of China and Madagascar. Mathematically, dissolution processes are modeled by a Stefan…
We present an investigation into the response of a viscous fluid flowing over a sloped bed across a spatially finite patch of basal lubrication. We present a simple analytical model that captures the fundamental structure of such…
We introduce a novel approach to study the longitudinal hydrodynamic expansion of the quark-gluon fluid created in heavy-ion collisions. It consists of two steps: First, we apply the maximum entropy method to reconstruct the freeze-out…
We investigate the inverse scale space flow as a decomposition method for decomposing data into generalised singular vectors. We show that the inverse scale space flow, based on convex and absolutely one-homogeneous regularisation…
4D seismic inversion is the leading method to quantitatively monitor fluid flow dynamics in the subsurface, with applications ranging from enhanced oil recovery to subsurface CO2 storage. The process of inverting seismic data for reservoir…
A numerical method based upon the immersed boundary technique for the fluid-solid coupling and on a soft-sphere approach for solid-solid contact is used to perform direct numerical simulation of the flow-induced motion of a thick bed of…
We introduce in this study an algorithm for the imaging of faults and of slip fields on those faults. The physics of this problem are modeled using the equations of linear elasticity. We define a regularized functional to be minimized for…
Near-surface turbulent flows beneath a free surface are reconstructed from sparse measurements of the surface height variation, by a novel neural network algorithm known as the {\em SHallow REcurrent Decoder} (SHRED). The reconstruction of…
We present a novel method for reconstructing the shape of an object from measured gradient data. A certain class of optical sensors does not measure the shape of an object, but its local slope. These sensors display several advantages,…
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…
We computed a Lennard Jones frozen liquid with a free surface using classical molecular dynamics. The structure factor curves on the free surface of this sample was calculated for different depths knowing that we have periodic boundary…
Gravity-driven turbulent bedload transport has been extensively studied over the past century in regard to its importance for Earth surface processes such as natural riverbed morphological evolution. In the present contribution, the…
We investigate experimentally the early stage of the generation of waves by a turbulent wind at the surface of a viscous liquid. The spatio-temporal structure of the surface deformation is analyzed by the optical method Free Surface…
We propose a multi-layer approach to simulate hyperpycnal and hypopycnal plumes in flows with free surface. The model allows to compute the vertical profile of the horizontal and the vertical components of the velocity of the fluid flow.…
We introduce a data-adaptive inversion method that integrates classical or deep learning-based approaches with iterative graph Laplacian regularization, specifically targeting acoustic impedance inversion - a critical task in seismic…