Related papers: Continuous and Discrete Adjoints to the Euler Equa…
In 1966, Arnold [1] showed that the Lagrangian flow of ideal incompressible fluids (described by Euler equations) coincide with the geodesic flow on the manifold of volume preserving diffeomorphisms of the fluid domain. Arnold's proof and…
In this study, we find the optimal control boundary (i.e., actuator velocity) that cancels the acoustic reverberations inside drop-on-demand inkjet printheads at a specific time. We formulate an optimization problem to minimize the total…
The dynamics along the particle trajectories for the 3D axisymmetric Euler equations are considered. It is shown that if the inflow is rapidly increasing (pushy) in time, the corresponding laminar profile of the incompressible Euler flow is…
We construct new stationary weak solutions of the 3D Euler equation with compact support. The solutions, which are piecewise smooth and discontinuous across a surface, are axisymmetric with swirl. The range of solutions we find is different…
We present a new software system PETSc TSAdjoint for first-order and second-order adjoint sensitivity analysis of time-dependent nonlinear differential equations. The derivative calculation in PETSc TSAdjoint is essentially a high-level…
Recently, there has been an increasing interest in using tools from dynamical systems to analyze the behavior of simple optimization algorithms such as gradient descent and accelerated variants. This paper strengthens such connections by…
In this work, we propose an adjoint-based optimization procedure to control the onset of the Rayleigh-B\'enard instability with a melting front. A novel cut cell method is used to solve the Navier-Stokes equations in the Boussinesq…
We study the strong approximation of stochastic differential equations with discontinuous drift coefficients and (possibly) degenerate diffusion coefficients. To account for the discontinuity of the drift coefficient we construct an…
We discuss exterior and classical interior alternatives for evaluating fluid flow induced forces on bodies. The discussion aims at a reduction of the total shape derivative, achieved through a decoupling of control and objective in the…
Adjoint-based sensitivity analysis is routinely used today to assess efficiently the effect of open-loop control on the linear stability properties of unstable flows. Sensitivity maps identify regions where small-amplitude control is the…
The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the previous notions of self-adjoint and quasi self-adjoint…
We study the mathematical properties of time-dependent flows of incompressible fluids that respond as an Euler fluid until the modulus of the symmetric part of the velocity gradient exceeds a certain, a-priori given but arbitrarily large,…
As a simplified model for subsurface flows elliptic equations may be utilized. Insufficient measurements or uncertainty in those are commonly modeled by a random coefficient, which then accounts for the uncertain permeability of a given…
We study the convergence of the derivative expansion for flow equations. The convergence strongly depends on the choice for the infrared regularisation. Based on the structure of the flow, we explain why optimised regulators lead to better…
Our objective is to study the observability and unique continuation property of the adjoint of a linearized compressible fluid structure interaction model in a 2D channel. Concerning the structure we will consider a damped Euler-Bernoulli…
We discuss general bosonic configurations of four-dimensional N=2 supergravity coupled to vector multiplets in (t,s) space-time. The supergravity theories with Euclidean and neutral signature are described by the so-called para-special…
We devise an iterative scheme for numerically calculating dynamical two-point correlation functions in integrable many-body systems, in the Eulerian scaling limit. Expressions for these were originally derived in Ref. [1] by combining the…
We consider the classical compressible Euler's Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the…
Hamilton's principle plays a central role in fluid mechanics as a fundamental tool for deriving governing equations, analyzing conservation laws, and designing structure-preserving numerical schemes. However, its classical formulation is…
This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. The proposed procedure has several features which distinguishes it from the other procedures for the problem. First of all a sliding…