Related papers: A variational framework for flow optimization usin…
An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow, powers of mean and inverse mean curvature flow, etc. Error estimates are proven for semi- and full…
We investigate the modes of deformation of an initially spherical bubble immersed in a homogeneous and isotropic turbulent background flow. We perform direct numerical simulations of the two-phase incompressible Navier-Stokes equations,…
We establish long-time and large-data existence of a suitable weak solution to three-dimensional internal unsteady flows described by Kolmogorov's two-equation model of turbulence. The governing system of equations is completed by initial…
We consider a hyperbolic system of three conservation laws in one space variable. The system is a model for fluid flow allowing phase transitions; in this case the state variables are the specific volume, the velocity and the mass density…
The dynamics of a single fluid bilayer membrane in an external hydrodynamic flow field is considered. The deterministic equation of motion for the configuration is derived taking into account both viscous dissipation in the surrounding…
We introduce a class of stochastic advection problems amenable to analysis of turbulent transport. The statistics of the flow field are represented as a continuous time Markov process, a choice that captures the intuitive notion of…
We present a parametric finite element approximation of two-phase flow. This free boundary problem is given by the Navier--Stokes equations in the two phases, which are coupled via jump conditions across the interface. Using a novel…
We employ a canonical variational framework for the predictive characterization of structural instabilities that develop during the diffusion-driven transient swelling of hydrogels under geometrical constraints. The variational formulation…
We consider a system of nonlinear partial differential equations describing the motion of an incompressible chemically reacting generalized Newtonian fluid in three space dimensions. The governing system consists of a steady…
We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…
A major limitation of online algorithms that track the optimizers of time-varying nonconvex optimization problems is that they focus on a specific local minimum trajectory, which may lead to poor spurious local solutions. In this paper, we…
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to…
This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…
We study the modeling of a compressible two-phase flow in a porous medium. The governing free boundary problem is known as the Verigin problem with phase transition. We introduce a novel variational framework to construct weak solutions.…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
Linear stability analysis currently fails to predict turbulence transition in canonical viscous flows. We show that two alternative models of the boundary condition for incipient perturbations at solid walls produce linear instabilities…
A variational principle for determining unstable periodic orbits of flows as well as unstable spatio-temporally periodic solutions of extended systems is proposed and implemented. An initial loop approximating a periodic solution is evolved…
Turbulent flows are chaotic and unsteady, but their statistical distribution converges to a statistical steady state. Engineering quantities of interest typically take the form of time-average statistics such as $ \frac{1}{t} \int_0^t f (…
Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…
Obtaining sharp estimates for quantities involved in a given model is an integral part of the modeling process. For dynamical systems whose orbits display a complicated, perhaps chaotic, behaviour, the aim is usually to estimate time or…