Related papers: On Gradient Flows with Obstacles and Euler's Elast…
In this paper we discuss the motion of a beam in interaction with fluids. We allow the beam to move freely in all coordinate directions. We consider the case of a beam situated in between two different fluids as well as the case where the…
In this paper, we are interested in the dynamics of charged particles interacting with the incompressible viscous flow. More precisely, we consider the Vlasov-Poisson or Vlasov-Poisson-Fokker-Planck equation coupled with the incompressible…
We investigate a variational approach to nonpotential perturbations of gradient flows of nonconvex energies in Hilbert spaces. We prove existence of solutions to elliptic-in-time regularizations of gradient flows by combining the…
We derive the system of differential equations for the gradient flow characterizing the training process of linear in-context learning in full generality. Next, we explore the geometric structure of the gradient flows in two instances,…
This work shows how the early stages of perturbation growth in a viscosity-stratified flow are different from those in a constant-viscosity flow, and how nonlinearity is a crucial ingredient. We derive the viscosity-varying adjoint…
Few rigorous results are derived for fully developed turbulence. By applying the scaling properties of the Navier-Stokes equation we have derived a relation for the energy spectrum valid for unforced or decaying isotropic turbulence. We…
We report on recent work on adaptive timestep control for weakly instationary gas flows [16, 18, 17] carried out within SFB 401, TPA3. The method which we implement and extend is a space-time splitting of adjoint error representations for…
Systematic deflection of microparticles off of initial streamlines is a fundamental task in microfluidics, aiming at applications including sorting, accumulation, or capture of the transported particles. In a large class of setups,…
The description of electron-electron interactions in transport problems is both analytically and numerically difficult. Here we show that a much simpler description of electron transport in the presence of interactions can be achieved in…
We study step-wise time approximations of non-linear hyperbolic initial value problems. The technique used here is a generalization of the minimizing movements method, using two time-scales: one for velocity, the other (potentially much…
Variational formulations for viscous flows which lead to the Navier-Stokes equation are examined. Since viscosity leads to dissipation and, therefore, to the irreversible transfer of mechanical energy to heat, thermal degrees of freedom…
Training learning parameterizations to solve optimal power flow (OPF) with pointwise constraints is proposed. In this novel training approach, a learning parameterization is substituted directly into an OPF problem with constraints required…
This work analyzes accelerating and decelerating wall-driven flows by quantifying the upper bound of transient energy growth using a Lyapunov-type approach. By formulating the linearized Navier-Stokes equations as a linear time-varying…
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…
The free boundary free elastic flow is the steepest descent gradient flow for the elastic energy of curves meeting parallel lines perpendicularly. In this article we prove that the straight line has, measured in Euler's scale-invariant…
Transmission-constrained problems in power systems can be cast as polynomial optimization problems whose coefficients vary over time. We consider the complications therein and suggest several approaches. On the example of the…
We study the construction of subgrid-scale models for large-eddy simulation of incompressible turbulent flows. In particular, we aim to consolidate a systematic approach of constructing subgrid-scale models, based on the idea that it is…
Using limited observations of the velocity field of the two-dimensional Navier-Stokes equations, we successfully reconstruct the steady body force that drives the flow. The number of observed data points is less than 10\% of the number of…
In Cardaliaguet-Ley (2006) we have defined a viscosity solution for the gradient flow of the exterior Bernoulli free boundary problem. We prove here that the associated energy is non decreasing along the flow. This justifies the "gradient…
Linearized flow past a submerged obstacle with an elastic sheet resting on the flow surface are studied in the limit that the bending length is small compared to the obstacle depth, in two and three dimensions. Gravitational effects are…