Analytical solution of a convection-dispersion model with time-dependent transport coefficients
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In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...
We present a numerical model for the simulation of 3D mono-dispersed sediment dynamics in a Newtonian flow with free surfaces. The physical model is a macroscopic model for the transport of sediment based on a sediment concentration with a single momentum ...
The seminal work of DiPerna and Lions (Invent Math 98(3):511-547, 1989) guarantees the existence and uniqueness of regular Lagrangian flows for Sobolev vector fields. The latter is a suitable selection of trajectories of the related ODE satisfying addition ...
Multiscale problems, such as modelling flows through porous media or predicting the mechanical properties of composite materials, are of great interest in many scientific areas. Analytical models describing these phenomena are rarely available, and one mus ...
An accurate solution of the wave equation at a fluid-solid interface requires a correct implementation of the boundary condition. Boundary conditions at acousto-elastic interface require continuity of the normal component of particle velocity and traction, ...
The basis of the discrete element method is to model masses interacting with each other through different forces and constraints. On each mass, the second law of Newton is applied to obtain a differential equation. From this equation and boundary condition ...
The explicit split-operator algorithm has been extensively used for solving not only linear but also nonlinear time-dependent Schrödinger equations. When applied to the nonlinear Gross–Pitaevskii equation, the method remains time-reversible, norm-conservin ...
Geometric integrators of the Schrödinger equation conserve exactly many invariants of the exact solution. Among these integrators, the split-operator algorithm is explicit and easy to implement but, unfortunately, is restricted to systems whose Hamiltonian ...
In this work, we focus on the Dynamical Low Rank (DLR) approximation of PDEs equations with random parameters. This can be interpreted as a reduced basis method, where the approximate solution is expanded in separable form over a set of few deterministic b ...
In this paper we consider the equation for equivariant wave maps from R3+1 to S-3 and we prove global in forward time existence of certain C-infinity-smooth solutions which have infinite critical Sobolev norm (H) overdot(3/4) (R-3) x (H) overdot(1/2) (R-3) ...