Optimal Control for Switched Systems with Pre-defined Order and Switch-Dependent Dynamics

The optimal control problem for switched systems, with a predefined order of switches, is considered. The differential equations may depend explicitly on previous switching instants, and the latter may be state dependent. The solution is based on the Calculus-of-Variations, which leads to a single two-point boundary-value problem. A new condition for the Hamiltonian jump at the switching instants is obtained. Simple numerical examples demonstrate the results.     

Comparison of the performance of three ion mobility spectrometers for measurement of biogenic amines

The performance of three different types of ion mobility spectrometer (IMS) devices: GDA2 with a radioactive ion source (Airsense, Germany), UV-IMS with a photo-ionization source (G.A.S. Germany) and VG-Test with a corona discharge source (3QBD, Israel) was studied. The gas-phase ion chemistry in the IMS devices affected the species formed and their measured reduced mobility values. The sensitivity and limit of detection for trimethylamine (TMA), putrescine and cadaverine were compared by continuous monitoring of a stream of air with a given concentration of the analyte and by measurement of headspace vapors of TMA in a sealed vial. Preprocessing of the mobility spectra and the effectiveness of multivariate curve resolution techniques (MCR-LASSO) improved the accuracy of the measurements by correcting baseline effects and adjusting for variations in drift time as well as enhancing the signal to noise ratio and deconvolution of the complex data matrix to their pure components. The limit of detection for measurement of the biogenic amines by the three IMS devices was between 0.1 and 1.2 ppm (for TMA with the VG-Test and GDA, respectively) and between 0.2 and 0.7 ppm for putrescine and cadaverine with all three devices. Considering the uncertainty in the LOD determination there is almost no statistically significant difference between the three devices although they differ in their operating temperature, ionization method, drift tube design and dopant chemistry. This finding may have general implications on the achievable performance of classic IMS devices.     

The bimolecular hydrogen-deuterium exchange behavior of protonated alkyl dipeptides in the gas phase

As part of an ongoing characterization of the intrinsic chemical properties of peptides, thermal hydrogen-deuterium exchange has been studied for a series of fast-atom-bombardment-generated protonated alkyldipeptides and related model compounds in the reaction with D₂O, CH₃OD, and ND₃ in a Fourier transform ion cyclotron resonance mass spectrometer. Despite the very large basicity difference between the dipeptides and the D₂O and CH₃OD exchange reagents, efficient exchange of all active hydrogen atoms occurs. From the kinetic data it appears that exchange of the amino, amide, and hydroxyl hydrogens proceeds with different efficiencies, which implies that the proton in thermal protonated dipeptides is immobile. The selectivity of the exchange at the different basic sites is governed by the nature of both the dipeptide and the exchange reagent. The results indicate that reversible proton transfer in the reaction complexes, which effectuates the deuterium incorporation, is assisted by formation of multiple hydrogen bonds between the reagents. Exchange is considered to proceed via the intermediacy of different competing intermediate complexes, each of which specifically leads to deuterium incorporation at different basic sites. The relative stabilization of the competing intermediate complexes can be related to the relative efficiencies of deuterium incorporation at different basic sites in the dipeptide. For all protonated dipeptides studied, the exchange in the reaction with ND₃ proceeds with unit efficiency, whereas all active hydrogen atoms are exchanged equally efficiently. Evidently specific multiple hydrogen bond formations are far less important in the reversible proton transfers with the relatively basic ammonia, which allows effective randomization of all active hydrogen atoms in the reaction complexes.     

Real-time analysis of partially polarized light with a space-variant subwavelength dielectric grating

A novel method for real-time polarization measurement is presented. The method is based on a space-variant wave plate that we realized as a computer-generated space-variant subwavelength dielectric grating. The Stokes parameters of the incident beam are determined by Fourier analysis of the space-variant intensity transmitted through the grating and an analyzer. We discuss the design and realization of such wave plates and demonstrate our technique with polarization measurements of both polarized and partially polarized CO(2)-laser radiation at a wavelength of 10.6 mum.     

Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings

Space-variant Pancharatnam-Berry phase optical elements based on computer-generated subwavelength gratings are presented. By continuously controlling the local orientation and period of the grating we can achieve any desired phase element. We present a theoretical analysis and experimentally demonstrate a Pancharatnam-Berry phase-based diffraction grating for laser radiation at a wavelength of 10.6microm.     

Formation of helical beams by use of Pancharatnam-Berry phase optical elements

Spiral phase elements with topological charges based on space-variant Pancharatnam-Berry phase optical elements are presented. Such elements can be achieved by use of continuous computer-generated space-variant subwavelength dielectric gratings. We present a theoretical analysis and experimentally demonstrate spiral geometrical phases for infrared radiation at a wavelength of 10.6microm .     

Study of the membrane effect on turbulent mixing measurements in shock tubes

The effect of the thin membrane on the time evolution of the shock wave induced turbulent mixing between the two gases initially separated by it is investigated using two different sets of experiments. In the first set, in which a single-mode large-amplitude initial perturbation was studied, two gas combinations (air/SF and air/air) and two membrane thicknesses were used. The main conclusion of these experiments was that the tested membrane has a negligible effect on the evolution of the mixing zone, which evolves as predicted theoretically. In the second set, in which similar gas combinations and membrane thicknesses were used, small amplitude random-mode initial perturbation, caused by the membrane rupture, rather than the large amplitude single-mode initial perturbation used in the first set, was studied. The conclusions of these experiments were: (1) The membrane has a significant effect on the mixing zone during the initial stages of its growth. This has also been observed in the air/air experiment where theoretically no growth should exist. (2) The membrane effect on the late time evolution, where the mixing zone width has reached a relatively large-amplitude, was relatively small and in good agreement with full numerical simulations. The main conclusion from the present experiments is that the effect of the membrane is important only during the initial stages of the evolution (before the re-shock), when the perturbations have very small amplitudes, and is negligible when the perturbations reach relatively large amplitudes. Received 29 August 1998 / Accepted 25 December 1998     

Excited-state intermolecular proton transfer of firefly luciferin III. Proton transfer to a mild base

Steady-state and time-resolved techniques were employed to study the excited-state proton transfer (ESPT) from d-luciferin, the natural substrate of the firefly luciferase, to the mild acetate base in aqueous solutions. We found that in 1 M aqueous solutions of acetate or higher, a proton transfer (PT) process to the acetate takes place within 30 ps in both H(2)O and D(2)O solutions. The time-resolved emission signal is composed of three components. We found that the short-time component decay time is 300 and 600 fs in H(2)O and D(2)O, respectively. This component is attributed either to a PT process via the shortest water bridged complex available, ROH··H(2)O··Ac(-), or to PT taking place within a contact ion pair. The second time component of 2000 and 3000 fs for H(2)O and D(2)O, respectively, is attributed to ROH* acetate complex, whose proton wire is longer by one water molecule. The decay rate of the third, long-time component is proportional to the acetate concentration. We attribute it to the diffusion-assisted reaction as well as to PT process to the solvent.