We consider an abstract parameter dependent saddle-point problem and present a general framework for analyzing robust Schur complement preconditioners. The abstract analysis is applied to a generalized Stokes problem, which yields robustness of the Cahouet-Chabard preconditioner. Motivated by models for two-phase incompressible flows we consider a generalized Stokes interface problem. Applicati...

The negatively charged nitrogen-vacancy defect in diamond is an important atomic-scale structure that can be used as a qubit in quantum computing and as a marker in biomedical applications. Its usefulness relies on the ability to optically excite electrons between well-defined gap states, which requires a clear and detailed understanding of the relevant states and excitation processes. Here we ...

In this paper, we prove new embedding results by means of subspace interpolation theory and apply them to establishing regularity estimates for the biharmonic Dirichlet problem, and for the Stokes and the Navier-Stokes systems on polygonal domains. The main result of the paper gives a stability estimate for the biharmonic problem at the threshold index of smoothness. The classical regularity es...

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An experiment in which the third Stokes parameter thermal emission from a periodic water surface was measured is documented. This parameter is shown to be related to the direction of periodicity of the periodic surface and to approach brightnesses of up to 30 K at X band for the surface used in the experiment. The surface actually analyzed was a _two-layer' periodic surface; the theory of therm...

An elementary field-theoretic mechanism is proposed that allows one Lagrangian to describe a family of particles having different masses but otherwise similar physical properties. The mechanism relies on the observation that the Dyson-Schwinger equations derived from a Lagrangian can have many different but equally valid solutions. Nonunique solutions to the Dyson-Schwinger equations arise when...

The kinetic theory for a fluid of hard spheres which undergo endothermic and/or exothermic reactions with mass transfer is developed. The exact balance equations for concentration, density, velocity, and temperature are derived. The Enskog approximation is discussed and used as the basis for the derivation, via the Chapman-Enskog procedure, of the Navier-Stokes reaction equations under various ...

We consider the Navier–Stokes system in a bounded domain with a smooth boundary. Given a sufficiently regular time-dependent global solution, we construct a finite-dimensional feedback control that is supported by a given open set and stabilizes the linearized equation. The proof of this fact is based on a truncated observability inequality, the regularizing property for the linearized equation...

We study the closure of reduced MHD models. We show how to modify the entropy moment methods to obtain a hierarchy of models of Navier-Stokes type with a correct energy balance. Our procedure is based on the entropy and well adapted to the complicated geometry of the torus. A new correction term due to the geometry is derived, what is important for the stability of the model. We prove the exist...

In this report, a partitioned time stepping algorithm which allows different time steps in the fluid region and the porous region is analyzed for the fully evolutionary Stokes-Darcy problem. This method requires only one, uncoupled Stokes and Darcy sub-physics and sub-domain solve per time step. Under a modest time step restriction of the form 4t ≤ C where C = C(physical parameters) we prove ze...