Normality of the maximum principle for nonconvex constrained Bolza problems

We consider a Bolza optimal control problem with state constraints. It is well known that under some technical assumptions every strong local minimizer of this problem satisfies first order necessary optimality conditions in the form of a constrained maximum principle. In general, the maximum principle may be abnormal or even degenerate and so does not provide a sufficient information about optimal controls. In the recent literature some sufficient conditions were proposed to guarantee that at least one maximum principle is nondegenerate, cf. [A.V. Arutyanov, S.M. Aseev, Investigation of the degeneracy phenomenon of the maximum principle for optimal control problems with state constraints, SIAM J. Control Optim. 35 (1997) 930–952; F. Rampazzo, R.B. Vinter, A theorem on existence of neighbouring trajectories satisfying a state constraint, with applications to optimal control, IMA 16 (4) (1999) 335–351; F. Rampazzo, R.B. Vinter, Degenerate optimal control problems with state constraints, SIAM J. Control Optim. 39 (4) (2000) 989–1007]. Our aim is to show that actually conditions of a similar nature guarantee normality of every nondegenerate maximum principle. In particular we allow the initial condition to be fixed and the state constraints to be nonsmooth. To prove normality we use J. Yorke type linearization of control systems and show the existence of a solution to a linearized control system satisfying new state constraints defined, in turn, by linearization of the original set of constraints along an extremal trajectory.     

Aspect-ratio dependent oscillatory thermocapillary convection in the floating half zone

The dependency of the critical Marangoni number on the geometrical aspect ratio of the floating half zone is essential to predict the onset of oscillatory thermocapillary convection.The experimental studies in the microgravity conditions on floating half zones of several centimeters in diameter have predicted that the critical Marangoni number increases with the increasing aspect ratio,and the terrestrial experimental studies have predicted the contradictory conclusion for floating half zones of several mil...     

Non-Gravitational Effects with Density-Matching in Evaluating the Influence of Sedimentation on Colloidal Coagulation

The method of density matching between the solid and liquid phases is often adopted to effectively eliminate the effect of sedimentation of suspensions in studies on dynamic behaviour of a colloidal system. However, the associated changes in the solvent composition may bring side effects to the properties investigated and therefore might lead to a faulty conclusion if the relevant correction is not made. To illustrate the importance of this side effect, we present an example of the sedimentation influence on the coagulation rate of suspensions of 2μm （diameter） polystyrene. The liquid mixtures, in the proper proportions of water （H2O）, deuterium oxide （D2O） and methanol （MeOH） as the liquid phase, density-matched and unmatched experiments are performed. Besides the influence of viscosity, the presence of methanol in solvent media, used to enhance the sedimentation effect, causes significant changes （reduction） in rapid coagulation rates compared to that in pure water. Without the relevant corrections for those non-gravitational factors it seems that gravitational sedimentation would retard the coagulation. The magnitude of the contribution from the non-gravitational factor is quantitatively determined, making the relevant correction possible. After necessary the influence of the sedimentation on coagulation rates at corrections for all factors, our experiments show that the initial stage of the coagulation is not observable.     

Proton beam writing of Nd:GGG crystals as new waveguide laser sources

Focused proton beam writing has been utilized to fabricate optical channel waveguides in Nd:GGG crystals. The 1?MeV proton beam irradiation creates a local modified region with positive refractive index changes at the end of the proton trajectory, in which the channel waveguide could confine the light field in a symmetric way. Room-temperature laser emission has been achieved at 1063.7?nm, with absorbed pump power of 61?mW (at 808?nm). The obtained slope efficiency of the Nd:GGG waveguide laser system is as high as 66%, which is, to our best knowledge, the highest value for integrated lasers from ion beam processed channel waveguide systems.     

Optical travelator: transport and dynamic sorting of colloidal microspheres with an asymmetrical line optical tweezers

We report the transport, funnelling and dynamic sorting of colloidal microspheres in an aqueous suspension using line optical tweezers with asymmetrical intensity profiles. The line tweezers readily trapped and propelled the microspheres along the length of the line tweezers. Using this simple technique, transporting and funnelling of microspheres within a microscopic region were demonstrated. To illustrate the dynamic particle-sorting capability of the line tweezers, a binary colloidal system comprising of microspheres with diameters of 1.1 μm and 3.2 μm were driven past the line tweezers by electrophoresis. As the optical trapping force is dependent on the size of the microspheres, the line tweezers was able to change the path of the larger spheres while exerting little influence on the smaller spheres thus sorting the two types of microspheres. At optimized laser power and flow rate of microspheres, sorting efficiency greater than 90% has been achieved. PACS 42.15.Eq; 87.80.Cc; 87.80.Fe; 82.70.Dd