Related papers: Notes on Optimal Flux Fields
Subcritical transition to turbulence in spatially developing boundary layer flows can be triggered efficiently by finite amplitude perturbations. In this work, we employ adjoint-based optimization to identify optimal initial perturbations…
A (unit norm) frame is scalable if its vectors can be rescaled so as to result into a tight frame. Tight frames can be considered optimally conditioned because the condition number of their frame operators is unity. In this paper we…
Interface between two phases of matter are ubiquitous in nature and technology. Determining the correct velocity condition at an interface is essential for understanding and designing of flows over a surface. We demonstrate that both the…
Thermodynamics of superfluids is revisited, clarifying two points. First, the density and pressure distribution for given equilibrium velocities is obtained, with the finding that counter heat currents give rise to a pressure depression and…
The problem of choice of boundary conditions are discussed for the case of numerical integration of the shallow water equations on a substantially irregular relief. In modeling of unsteady surface water flows has a dynamic boundary…
Many physical systems of interest involve the close interaction of a flow in a domain with complex, time-varying boundaries. Treatment of boundaries of this nature is cumbersome due to the difficulty in explicitly tracking boundaries that…
In topology optimization of fluid-dependent problems, there is a need to interpolate within the design domain between fluid and solid in a continuous fashion. In density-based methods, the concept of inverse permeability in the form of a…
We consider a nonlinear system, affine with respect to an unbounded control $u$ which is allowed to range in a closed cone. To this system we associate a Bolza type minimum problem, with a Lagrangian having sublinear growth with respect to…
We analyze the steady-state flow as a function of the initial density for a class of deterministic cellular automata rules (``traffic rules'') with periodic boundary conditions [H. Fuks and N. Boccara, Int. J. Mod. Phys. C 9, 1 (1998)]. We…
The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In…
Upper bounds on the growth of free energy in gyrokinetics are derived. These bounds apply to all local gyrokinetic instabilities in the geometry of a flux tube, i.e. a slender volume of plasma aligned with the magnetic field, regardless of…
A methodology is presented for bounding all higher moments of the local hydrostatic stress field inside random two phase linear thermoelastic media undergoing macroscopic thermomechanical loading. The method also provides a lower bound on…
We seek for lines of minimal distance to finitely many points in the plane. The distance between a line and a set of points is defined by the L^p-norm, 1\leq p\leq \infty, of the vector of vertical or orthogonal distances from the single…
The behavior of the probability density function (PDF) transport equation at the limits of the probability space is studied from the point of view of fluid mechanics. Different boundary conditions are considered depending on the nature of…
Fusion rules in turbulence specify the analytic structure of many-point correlation functions of the turbulent field when a group of coordinates coalesce. We show that the existence of flux equilibrium in fully developed turbulent systems…
We consider the problem of dynamic optimal transport with a density constraint. We derive variational limits in terms of $\Gamma$-convergence for two singular phenomena. First, for densities constrained near a hyperplane we recover the…
The least gradient problem (minimizing the total variation with given boundary data) is equivalent, in the plane, to the Beckmann minimal-flow problem with source and target measures located on the boundary of the domain, which is in turn…
We consider the fluid interface problem given by two incompressible fluids with different densities evolving by Darcy's law. This scenario is known as the Muskat problem for fluids with the same viscosities, being in two dimensions…
The possibility of treating boundary conditions in terms of a bilocal dynamical field is formalized in terms of a boundary action. This allows for a simple path-integral perturbation theory approach to physical effects such as radiation…
In this work we consider a flow network for which the goal is to solve a practical optimal regulation problem in the presence of input saturation. Based on Lyapunov arguments we propose distributed controllers which guarantee global…