Explicit approximate controllability of the Schr\"odinger equation with a polarizability term

We consider a controlled Schr\"odinger equation with a dipolar and a polarizability term, used when the dipolar approximation is not valid. The control is the amplitude of the external electric field, it acts non linearly on the state. We extend in this infinite dimensional framework previous techniques used by Coron, Grigoriu, Lefter and Turinici for stabilization in finite dimension. We consider a highly oscillating control and prove the semi-global weak $H^2$ stabilization of the averaged system using a Lyapunov function introduced by Nersesyan. Then it is proved that the solutions of the Schr\"odinger equation and of the averaged equation stay close on every finite time horizon provided that the control is oscillating enough. Combining these two results, we get approximate controllability to the ground state for the polarizability system

The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation

We consider the motion of a planar rigid body in a potential flow with circulation and subject to a certain nonholonomic constraint. This model is related to the design of underwater vehicles. The equations of motion admit a reduction to a 2-dimensional nonlinear system, which is integrated explicitly. We show that the reduced system comprises both asymptotic and periodic dynamics separated by a critical value of the energy, and give a complete classification of types of the motion. Then we describe the whole variety of the trajectories of the body on the plane.Comment: 25 pages, 7 figures. This article uses some introductory material from arXiv:1109.321

Axial Concentration Profiles and NO Flue Gas in a Pilot-Scale Bubbling Fluidized Bed Coal Combustor

Atmospheric bubbling fluidized bed coal combustion of a bituminous coal and anthracite with particle diameters in the range 500-4000 ím was investigated in a pilot-plant facility. The experiments were conducted at steady-state conditions using three excess air levels (10, 25, and 50%) and bed temperatures in the 750-900 °C range. Combustion air was staged, with primary air accounting for 100, 80, and 60% of total combustion air. For both types of coal, high NO concentrations were found inside the bed. In general, the NO concentration decreased monotonically along the freeboard and toward the exit flue; however, during combustion with high air staging and low to moderate excess air, a significant additional NO formation occurred near the secondary air injection point. The results show that the bed temperature increase does not affect the NO flue gas concentration significantly. There is a positive correlation between excess air and the NO flue gas concentration. The air staging operation is very effective in lowering the NO flue gas, but there is a limit for the first stage stoichiometry below which the NO flue gas starts rising again. This effect could be related with the coal rank

The Tetraspanins CD9 and CD81 Regulate CD9P1-Induced Effects on Cell Migration

CD9P-1 is a cell surface protein with immunoglobulin domains and an unknown function that specifically associates with tetraspanins CD9 and CD81. Overexpression of CD9P-1 in HEK-293 cells induces dramatic changes in cell spreading and migration on various matrices. Experiments using time-lapse videomicroscopy revealed that CD9P-1 expression has led to higher cell motility on collagen I but lower motility on fibronectin through a β1-integrins dependent mechanism. On collagen I, the increase in cell motility induced by CD9P-1 expression was found to involve integrin α2β1 and CD9P-1 was observed to associate with this collagen receptor. The generation of CD9P-1 mutants demonstrated that the transmembrane and the cytoplasmic domains are necessary for inducing effects on cell motility. On the other hand, expression of tetraspanins CD9 or CD81 was shown to reverse the effects of CD9P-1 on cell motility on collagen I or fibronectin with a concomitant association with CD9P-1. Thus, the ratio of expression levels between CD9P-1 and its tetraspanin partners can regulate cell motility

An estimation of the controllability time for single-input systems on compact groups

Geometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters of the flag manifolds; the latter are also explicitly computed in the paper

Controllability of quantum systems with relatively bounded control potentials

We study the regularity of solutions of bilinear quantum systems of the type x= (A+u(t)B)x where the state x belongs to some complex infinite dimensional Hilbert space, the (possibly unbounded) linear operators A and B are skew-adjoint and the control u is a real valued function of bounded variations. Under suitable regularity assumptions on the operators A and B, it is possible to extend the definition of solution for BV controls and infer continuity of the propagators. While the regularity of the propagators represents an obstacle to exact controllability, on the other hand it is used to present fine estimates on the convergence of finite dimensional approximation schemes. We will then prove exact controllability in projections for bilinear quantum systems with piecewise constant controls taking only two values. As a consequence we extend approximate controllability results to linear quantum systems of the type x=−iH(u(t))x with nonlinear dependence on the control