14,516 research outputs found
Classical and strong convexity of sublevel sets and application to attainable sets of nonlinear systems
Necessary and sufficient conditions for convexity and strong convexity,
respectively, of sublevel sets that are defined by finitely many real-valued
-maps are presented. A novel characterization of strongly convex sets
in terms of the so-called local quadratic support is proved. The results
concerning strong convexity are used to derive sufficient conditions for
attainable sets of continuous-time nonlinear systems to be strongly convex. An
application of these conditions is a novel method to over-approximate
attainable sets when strong convexity is present.Comment: 20 pages, 3 figure
Knowledge Does Not Fall Far from the Tree - A Case Study on the Diffusion of Solar Cells in Germany
The purpose of this paper is to illuminate the geographical diffusion of photovoltaic installations in Germany quantitatively and to test if preexisting photovoltaic systems stimulate further installations nearby; thus we investigate to which extent knowledge flows depend on geographic proximity. We develop an econometric model, which is discrete in time and space, but the level of geographical agglomeration is adjustable in arbitrarily small steps. We find that the probability to install a photovoltaic system dependents on the geographic proximity to agents, who have previously installed a photovoltaic system. In conclusion, our results confirm that knowledge exchange attenuates with distance.
Sample path large deviations for Laplacian models in -dimensions
For Laplacian models in dimension we derive sample path large
deviations for the profile height function, that is, we study scaling limits of
Gaussian integrated random walks and Gaussian integrated random walk bridges
perturbed by an attractive force towards the zero-level, called pinning. We
study in particular the regime when the rate functions of the corresponding
large deviation principles admit more than one minimiser, in our models either
two, three, or five minimiser depending on the pinning strength and the
boundary conditions. This study complements corresponding large deviation
results for gradient systems with pinning for Gaussian random walk bridges in -dimension (\cite{FS04}) and in -dimension (\cite{BFO}), and
recently in higher dimensions in \cite{BCF}. In particular it turns out that
the Laplacian cases, i.e., integrated random walks, show richer and more
complex structures of the minimiser of the rate functions which are linked to
different phases.Comment: 37, 5 figure
Approximately Optimal Controllers for Quantitative Two-Phase Reach-Avoid Problems on Nonlinear Systems
The present work deals with quantitative two-phase reach-avoid problems on
nonlinear control systems. This class of optimal control problem requires the
plant's state to visit two (rather than one) target sets in succession while
minimizing a prescribed cost functional. As we illustrate, the naive approach,
which subdivides the problem into the two evident classical reach-avoid tasks,
usually does not result in an optimal solution. In contrast, we prove that an
optimal controller is obtained by consecutively solving two special
quantitative reach-avoid problems. In addition, we present a fully-automated
method based on Symbolic Optimal Control to practically synthesize for the
considered problem class approximately optimal controllers for sampled-data
nonlinear plants. Experimental results on parcel delivery and on an aircraft
routing mission confirm the practicality of our method.Comment: 14 pages, 7 figure
Creature Care
Caring for a pet is a formidable responsibility that requires intense care and monitoring in order to protect and prolong the life of the animal. Traditionally, caring for a reptile presents a unique challenge for pet owners, who not only need to care for the animal but for the environment as well. Individual species distinctly require precise monitoring and control of environmental parameters such as temperature, humidity, and air quality; and deviation from the nominal values often leads to serious health problems for the reptile. To simplify reptile ownership, a system was designed that measures the critical parameters of a reptile enclosure and automatically regulates the local environment, notifying the user of any issues that require manual intervention. The system provides live and historical data, accessible on the Web via any computer or mobile device, and is capable of alerting the user by email or text message when any problems occur within the system. Additional reminders for feeding and cleaning are also configurable based on the requirements of the species. This design gives peace of mind for the user, ensuring that the animal within the enclosure is being provided the most ideal local environment unique to the species
Large scale Micro-Photometry for high resolution pH-characterization during electro-osmotic pumping and modular micro-swimming
Micro-fluidic pumps as well as artificial micro-swimmers are conveniently
realized exploiting phoretic solvent flows based on local gradients of
temperature, electrolyte concentration or pH. We here present a facile
micro-photometric method for monitoring pH gradients and demonstrate its
performance and scope on different experimental situations including an
electro-osmotic pump and modular micro-swimmers assembled from ion exchange
resin beads and polystyrene colloids. In combination with the present
microscope and DSLR camera our method offers a 2 \mu m spatial resolution at
video frame rate over a field of view of 3920x2602 \mu m^2. Under optimal
conditions we achieve a pH-resolution of 0.05 with about equal contributions
from statistical and systematical uncertainties. Our quantitative
micro-photometric characterization of pH gradients which develop in time and
reach out several mm is anticipated to provide valuable input for reliable
modeling and simulations of a large variety of complex flow situations
involving pH-gradients including artificial micro-swimmers, microfluidic
pumping or even electro-convection.Comment: 5 figures, 15 page
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