Impulsive systems

Impulsive systems arise when dynamics produce discontinuous trajectories. Discontinuties occur when movements of states happen over a small interval that resembles a point-mass measure. We adopt the formalism in which the controlled dynamic inclusion is the sum of a slow and a fast time velocities belonging to two distinct vector fields. Fast time velocities are controlled by a vector valued Borel measure. The trajectory of impulsive systems is a function of bounded variation. To give a definition of solutions, a notion of graph completion of the control measure is needed. In the nonimpulsive case, a solution can be defined as a limit of a sequence of approximate arcs which converge to an absolutely continuous arc. Even in simple cases it shows that this is not a good way to define solutions of the impulsive systems. The key point is that the approximate controls converge to two different graph completions. Introduction contains examples in which we discuss the need for the impulsive systems, their relation to the hybrid systems. A paradox related to the convergence of approximate arcs is illustrated. Chapter 1 contains preliminary results in nonimpulsive systems and mathematical analysis in general. Chapter 2 precisely defines impulsive systems, discusses two different solution concepts and proves properties of graph completions. Chapter 3 is entirely dedicated to adaptation of the Euler approximating schemes to the impulsive system. Two different schemes are offered. For one of them a measure which drives the system needs to be specified. We used it to show that the approximate trajectories graph-converge to a solution. The other sampling technique constructs a measure along with the solution. We use it in Chapter 4. Chapter 4 deals with issues when a trajectory remains within a closed set. This property is called invariance. Notions of weak and strong invariance for the impulsive systems are introduced and proximal characterizations are proved. In the case of weak invariance, two proofs are offered: one based on a sampling technique from Chapter 3 and other based on selections theory. The final chapter of this thesis discusses directions in future research

GPS & Roadpricing

I denne artikel præsenteres analysemetoderne og resultaterne fra et eksamensprojekt omhandlende en analyse af GPS kvaliteten i forhold til roadpricing i København. Denne undersøgelse af GPS kvaliteten, er foretaget i tilknytning til det danske AKTA forsøg, hvor GPS data er indsamlet for 500 biler over en 2-årig periode (2001-2003). Artiklen præsenterer således en analyse af GPS nøjagtigheden med henblik på at undersøge om kvalitet og pålidelighed er tilstrækkelig, til implementering af et GPS-baseret roadpricingssystem i København. Både antallet af synlige satellitter og HDOP (horizontal dilution of precision) blev analyseret i forhold til bebyggelsestætheden ved brug af forskellige digitale kort i GIS. Analyseresultaterne viser at satellit tilgængeligheden i København på nuværende tidspunkt ikke er tilstrækkelig til at sikre et pålideligt roadpricingssystem. De lukkede gaderum og den tætte bebyggelse i indre København forhindrer adskillige satellitsignaler i at nå ned i gadeniveau, hvilket bevirker for mange afbrydelser i positioneringen. Behovet for integrerede hjælpesystemer er indlysende og der findes flere forskellige muligheder, for eksempel integration med andre positioneringssystemer eller andre globale navigations satellit systemer (GNSS)

Optical coherence tomography for laser transmission joining processes in polymers and semiconductors

Laser transmission welding applications become wide spread technology in joining transparent and turbid materials. The requirement of higher throughputs and lesser rejects support the need of alternative methods to commonly used machine vision or temperature measurements. Optical coherence tomography delivers the opportunity to qualitatively assess transmission welding seems and welding spots even in three dimensions. Fourier Domain Mode Lock Lasers (FDMLs) used in OCT enable high throughput by high sweep rates. Preliminary results of OCT used for qualitatively assessment of laser transmission welded polymers and fiber reinforced plastics are shown as well as first approaches of using OCT in a silicon chip bonding process

Laser-based molecular delivery and its applications in plant science

Lasers enable modification of living and non-living matter with submicron precision in a contact-free manner which has raised the interest of researchers for decades. Accordingly, laser technologies have drawn interest across disciplines. They have been established as a valuable tool to permeabilize cellular membranes for molecular delivery in a process termed photoinjection. Laser-based molecular delivery was first reported in 1984, when normal kidney cells were successfully transfected with a frequency-multiplied Nd:YAG laser. Due to the rapid development of optical technologies, far more sophisticated laser platforms have become available. In particular, near infrared femtosecond (NIR fs) laser sources enable an increasing progress of laser-based molecular delivery procedures and opened up multiple variations and applications of this technique. This review is intended to provide a plant science audience with the physical principles as well as the application potentials of laser-based molecular delivery. The historical origins and technical development of laser-based molecular delivery are summarized and the principle physical processes involved in these approaches and their implications for practical use are introduced. Successful cases of laser-based molecular delivery in plant science will be reviewed in detail, and the specific hurdles that plant materials pose will be discussed. Finally, we will give an outlook on current limitations and possible future applications of laser-based molecular delivery in the field of plant science

Wavefront sensorless adaptive optics for optical coherence tomography guided femtosecond laser surgery in the posterior eye

Surgery with fs-laser in the posterior part of the eye could be useful for separation of tractional epiretinal membrane and vitreous floaters treatment. However, focus degradation occurs near the retina due to induced aberrations by cornea and lens. To overcome this issue, adaptive optics with wavefront sensor and wavefront modulator can be utilized. We demonstrate an alternative concept for image guided femto second laser (fs-laser) surgery in the posterior eye with wavefront sensorless adaptive optics (WFSLAO). Our laboratory setup consists of an 800 nm fs-laser and a superluminescent diode (SLD) with 897.2 nm central wavelength. The SLD is used for optical coherence tomography (OCT) whereby the light for the OCT sample arm and the fs-laser share the same optical path which contains a deformable mirror, scanner and focusing optics. Energy calibrated photodiodes are used to measure the threshold energy for a laser induced optical breakdown inside a water filled chamber that acts as simple eye model. OCT image based metrics were used to determine a set of Zernike polynomials that describe a near optimal deformable mirror state. Such a mirror state improved OCT resolution and at the same time lowered the required fs-laser energy for a laser induced optical breakdown inside the eye model substantially. © COPYRIGHT SPIE