Related papers: An Euler Poincar\'e framework for the multilayer G…
We develop a framework for the multiple scattering of a polarized wave. We consider particles with spin propagating in a medium filled with scatterers. We write the amplitudes of each spin eigenstate in a local, mobile frame. One of the…
A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is…
In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic up in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a…
In this work, we study the nonlinear traveling waves in density stratified fluids with depth varying shear currents. Beginning the formulation of the water-wave problem due to [1], we extend the work of [4] and [18] to examine the interface…
We develop a numerical a framework to study phoretic particle dynamics in two dimensions. The particles are modeled as chemically active rigid circles, which can emit or absorb a solute into surrounding fluid. The interaction between…
We consider 2D free surface gravity waves in prismatic channels with bathymetric variations uniquely in the transverse direction. Starting from the Saint-Venant equations (shallow water equations) we derive a 1D transverse averaged model…
A method is developed to construct the solutions of one and many variable, linear differential equations of arbitrary order. Using this, the $N$-particle Sutherland model, with pair-wise inverse sine-square interactions among the particles,…
The Lagrangian fluid description is employed to solve the initial value problem for one-dimensional, compressible fluid flows represented by the Euler-Poisson system. Exact nonlinear and time-dependent solutions are obtained, which exhibit…
In this thesis we consider the free surface flow due to a submerged source in a channel of finite depth. This problem has been considered previously in the literature, with some disagreement about whether or not a train of waves exist on…
The boundary conditions at the deformable interface between two contacting fluids are derived for the general case of the large-amplitude perturbations. The interface is modeled as perturbed free boundary that evolves in time, and the…
We study traveling wave solutions to the free boundary problem associated to a generalized Navier-Stokes Fourier system, which models a viscous, incompressible, heat-conducting fluid. The fluid is assumed to occupy a horizontally infinite…
Two-dimensional problem of evanescent wave scattering by dielectric or metallic cylinders near the interface between two dielectric media is solved numerically by boundary integral equations method. A special Green function was proposed to…
In this paper, we present an original derivation process of a non-hydrostatic shallow water-type model which aims at approximating the incompressible Euler and Navier-Stokes systems with free surface. The closure relations are obtained by…
In this paper we study two multidimensional nonlinear dispersive systems: the Serre-Green-Naghdi (SGN) equations describing dispersive shallow water flows, and Iordanskii-Kogarko-Wijngaarden (IKW) equations describing fluids containing…
We provide an in-depth exploration of the mass-transport properties of Pollard's exact solution for a zonally-propagating surface water-wave in infinite depth. Without resorting to approximations we discuss the Eulerian mass transport of…
Euler-Poincare equations are derived for the dynamical folding of charged molecular strands (such as DNA) modeled as flexible continuous filamentary distributions of interacting rigid charge conformations. The new feature is that the…
We present a hydrodynamic model of spreading epithelial monolayers as polar viscous fluids, with active contractility and traction on the substrate. The combination of both active forces generate an instability that leads to nonlinear…
We consider the two-dimensional water-wave problem with a general non-zero vorticity field in a fluid volume with a flat bed and a free surface. The nonlinear equations of motion for the chosen surface and volume variables are expressed…
Currently, Eulerian flow solvers are very efficient in accurately resolving flow structures near solid boundaries. On the other hand, they tend to be diffusive and to dampen high-intensity vortical structures after a short distance away…
We describe a map-based model which reproduces many of the behaviors seen in partial differential equations (PDE's). Like PDE's, we show that this model can support an infinite number of stationary solutions, traveling solutions, breathing…