We show that buoyancy driven flows can be steered in an arbitrary time towards any state by applying as control only an external temperature profile in a subset of small area. More specifically, we prove that the 2D incompressible Boussinesq system on the torus is globally approximately controllable via physically localized heating or cooling. In addition, our controls have an explicitly prescribed structure; even without such structural requirements, large data controllability results for Boussinesq flows driven merely by a physically localized temperature profile were so far unknown. The presented method exploits various connections between the model’s underlying transport-, coupling-, and scaling mechanisms.

We consider the global approximate controllability of the two-dimensional incompressible Navier-Stokes system driven by a physically localized and degenerate force. In other words, the fluid is regulated via four scalar controls that depend only on time and appear as coefficients in an effectively constructed driving force supported in a given subdomain. Our idea consists of squeezing low mode controls into a small region, essentially by tracking their actions along the characteristic curves of a linearized vorticity equation. In this way, through explicit constructions and by connecting Coron's return method with recent concepts from geometric control, the original problem for the nonlinear Navier-Stokes system is reduced to one for a linear transport equation steered by a global force. This article can be viewed as an attempt to tackle a well-known open problem due to Agrachev.

This work examines the controllability of planar incompressible ideal magnetohydrodynamics (MHD). Interior controls are obtained for problems posed in doubly-connected regions; simply-connected configurations are driven by boundary controls. Up to now, only straight channels regulated at opposing walls have been studied. Hence, the present program adds to the literature an exploration of interior controllability, extends the known boundary controllability results, and contributes ideas for treating general domains. To transship obstacles stemming from the MHD coupling and the magnetic field topology, a divide-and-control strategy is proposed. This leads to a family of nonlinear velocity-controlled sub-problems which are solved using J.-M. Coron's return method. The latter is here developed based on a reference trajectory in the domain's first cohomology space.

We study the small-time global approximate controllability for incompressible magnetohydrodynamic (MHD) flows in smoothly bounded two- or three-dimensional domains. The controls act on arbitrary nonempty open portions of each connected boundary component, while linearly coupled Navier slip-with-friction conditions are imposed along the uncontrolled parts of the boundary. Some choices for the friction coefficients give rise to interacting velocity and magnetic field boundary layers. We obtain sufficient dissipation properties of these layers by a detailed analysis of the corresponding asymptotic expansions. For certain friction coefficients, or if the obtained controls are not compatible with the induction equation, an additional pressure-like term appears. We show that such a term does not exist for problems defined in planar simply-connected domains and various choices of Navier slip-with-friction boundary conditions.

We provide deterministic controllability conditions that imply exponential mixing properties for randomly forced constrained dynamical systems with possibly unbounded state space. As an application, new ergodicity results are obtained for non-smooth models in elasto-plasticity driven by various types of noise, including white noise. It is thereby illustrated how tools from control theory can be utilized to tackle regularity issues that commonly arise in the qualitative study of constrained systems.

Air-liquid interface (ALI) lung cell models cultured on permeable transwell inserts are increasingly used for respiratory hazard assessment requiring controlled aerosolization and deposition of any material on ALI cells. The approach presented herein aimed to assess the transwell insert-delivered dose of aerosolized materials using the VITROCELL (R) Cloud12 system, a commercially available aerosol-cell exposure system. An inter-laboratory comparison study was conducted with seven European partners having different levels of experience with the VITROCELL (R) Cloud12. A standard operating procedure (SOP) was developed and applied by all partners for aerosolized delivery of materials, i.e., a water-soluble molecular substance (fluorescence-spiked salt) and two poorly soluble particles, crystalline silica quartz (DQ12) and titanium dioxide nanoparticles (TiO2 NM-105). The material dose delivered to transwell inserts was quantified with spectrofluorometry (fluorescein) and with the quartz crystal microbalance (QCM) integrated in the VITROCELL (R) Cloud12 system. The shape and agglomeration state of the deposited particles were confirmed with transmission electron microscopy (TEM). Inter-laboratory comparison of the device-specific performance was conducted in two steps, first for molecular substances (fluorescein-spiked salt), and then for particles. Device- and/or handling-specific differences in aerosol deposition of VITROCELL (R) Cloud12 systems were characterized in terms of the so-called deposition factor (DF), which allows for prediction of the transwell insert-deposited particle dose from the particle concentration in the aerosolized suspension. Albeit DF varied between the different labs from 0.39 to 0.87 (mean (coefficient of variation (CV)): 0.64 (28%)), the QCM of each VITROCELL (R) Cloud 12 system accurately measured the respective transwell insert-deposited dose. Aerosolized delivery of DQ12 and TiO2 NM-105 particles showed good linearity (R2 > 0.95) between particle concentration of the aerosolized suspension and QCM-determined insert-delivered particle dose. The VITROCELL (R) Cloud 12 performance for DQ12 particles was identical to that for fluorescein-spiked salt, i.e., the ratio of measured and salt-predicted dose was 1.0 (29%). On the other hand, a ca. 2-fold reduced dose was observed for TiO2 NM-105 (0.54 (41%)), which was likely due to partial retention of TiO2 NM-105 agglomerates in the vibrating mesh nebulizer of the VITROCELL (R) Cloud12. This inter-laboratory comparison demonstrates that the QCM integrated in the VITROCELL (R) Cloud 12 is a reliable tool for dosimetry, which accounts for potential variations of the transwell insert-delivered dose due to device-, handling- and/or material-specific effects. With the detailed protocol presented herein, all seven partner laboratories were able to demonstrate dose-controlled aerosolization of material suspensions using the VITROCELL (R) Cloud12 exposure system at dose levels relevant for observing in vitro hazard responses. This is an important step towards regulatory approved implementation of ALI lung cell cultures for in vitro hazard assessment of aerosolized materials.

This article is concerned with the global exact controllability for ideal incompressible magnetohydrodynamics in a rectangular domain where the controls are situated in both vertical walls. First, global exact controllability via boundary controls is established for a related Elsässer type system by applying the return method, introduced in Coron [Math. Control Signals Syst. 5 (1992) 295–312]. Similar results are then inferred for the original magnetohydrodynamics system with the help of a special pressure-like corrector in the induction equation. Overall, the main difficulties stem from the nonlinear coupling between the fluid velocity and the magnetic field in combination with the aim of exactly controlling the system. In order to overcome some of the obstacles, we introduce ad-hoc constructions, such as suitable initial data extensions outside of the physical part of the domain and a certain weighted space.

We study the large time behavior of solutions to a linear transmission problem in one space dimension. The problem at hand models a thermoelastic material with second sound confined by a purely elastic one. We shall characterize all equilibrium states of the considered system and prove that every solution approaches one designated equilibrium state with an exponential rate as time goes to infinity. Hereto, we apply methods from the theory of strongly continuous semigroups. In particular, we obtain uniform resolvent bounds for the underlying generator. This removes the largeness assumption of elastic wave speeds imposed in Meng and Wang (Anal Appl (Singap) 13, 2015) for having an exponential energy decay rate when the problem only has the trivial equilibrium. In an appendix, we provide a similar exponential stability result for the case where heat conduction is modeled using Fourier's law.