Analysis of unconstrained nonlinear MPC schemes with time varying control horizon

For discrete time nonlinear systems satisfying an exponential or finite time controllability assumption, we present an analytical formula for a suboptimality estimate for model predictive control schemes without stabilizing terminal constraints. Based on our formula, we perform a detailed analysis of the impact of the optimization horizon and the possibly time varying control horizon on stability and performance of the closed loop

Analysis of unconstrained nonlinear MPC schemes with time varying control horizon

For nonlinear discrete time systems satisfying a controllability condition, we present a stability condition for model predictive control without stabilizing terminal constraints or costs. The condition is given in terms of an analytical formula which can be employed in order to determine a prediction horizon length for which asymptotic stability or a performance guarantee is ensured. Based on this formula a sensitivity analysis with respect to the prediction and the possibly time varying control horizon is carried out.Comment: 7 pages, 4 figure

Evolution of helicity in NOAA 10923 over three consecutive solar rotations

We have studied the evolution of magnetic helicity and chirality in an active region over three consecutive solar rotations. The region when it first appeared was named NOAA10923 and in subsequent rotations it was numbered NOAA 10930, 10935 and 10941. We compare the chirality of these regions at photospheric, chromospheric and coronal heights. The observations used for photospheric and chromospheric heights are taken from Solar Vector Magnetograph (SVM) and H_alpha imaging telescope of Udaipur Solar Observatory (USO), respectively. We discuss the chirality of the sunspots and associated H_alpha filaments in these regions. We find that the twistedness of superpenumbral filaments is maintained in the photospheric transverse field vectors also. We also compare the chirality at photospheric and chromospheric heights with the chirality of the associated coronal loops, as observed from the HINODE X-Ray Telescope.Comment: 8 pages, 4 figure

Helicity at Photospheric and Chromospheric Heights

In the solar atmosphere the twist parameter $\alpha$ has the same sign as magnetic helicity. It has been observed using photospheric vector magnetograms that negative/positive helicity is dominant in the northern/southern hemisphere of the Sun. Chromospheric features show dextral/sinistral dominance in the northern/southern hemisphere and sigmoids observed in X-rays also have a dominant sense of reverse-S/forward-S in the northern/southern hemisphere. It is of interest whether individual features have one-to-one correspondence in terms of helicity at different atmospheric heights. We use UBF \Halpha images from the Dunn Solar Telescope (DST) and other \Halpha data from Udaipur Solar Observatory and Big Bear Solar Observatory. Near-simultaneous vector magnetograms from the DST are used to establish one-to-one correspondence of helicity at photospheric and chromospheric heights. We plan to extend this investigation with more data including coronal intensities.Comment: 5 pages, 1 figure, 1 table To appear in "Magnetic Coupling between the Interior and the Atmosphere of the Sun", eds. S.S. Hasan and R.J. Rutten, Astrophysics and Space Science Proceedings, Springer-Verlag, Heidelberg, Berlin, 200

Nonlinear force-free models for the solar corona I. Two active regions with very different structure

With the development of new instrumentation providing measurements of solar photospheric vector magnetic fields, we need to develop our understanding of the effects of current density on coronal magnetic field configurations. The object is to understand the diverse and complex nature of coronal magnetic fields in active regions using a nonlinear force-free model. From the observed photospheric magnetic field we derive the photospheric current density for two active regions: one is a decaying active region with strong currents (AR8151), and the other is a newly emerged active region with weak currents (AR8210). We compare the three-dimensional structure of the magnetic fields for both active region when they are assumed to be either potential or nonlinear force-free. The latter is computed using a Grad-Rubin vector-potential-like numerical scheme. A quantitative comparison is performed in terms of the geometry, the connectivity of field lines, the magnetic energy and the magnetic helicity content. For the old decaying active region the connectivity and geometry of the nonlinear force-free model include strong twist and strong shear and are very different from the potential model. The twisted flux bundles store magnetic energy and magnetic helicity high in the corona (about 50 Mm). The newly emerged active region has a complex topology and the departure from a potential field is small, but the excess magnetic energy is stored in the low corona and is enough to trigger powerful flares.Comment: 11 pages, 11 figure

Flat galaxies with dark matter halos - existence and stability

We consider a model for a flat, disk-like galaxy surrounded by a halo of dark matter, namely a Vlasov-Poisson type system with two particle species, the stars which are restricted to the galactic plane and the dark matter particles. These constituents interact only through the gravitational potential which stars and dark matter create collectively. Using a variational approach we prove the existence of steady state solutions and their nonlinear stability under suitably restricted perturbations.Comment: 39 page

Turbulence and passive scalar transport in a free-slip surface

We consider the two-dimensional (2D) flow in a flat free-slip surface that bounds a three-dimensional (3D) volume in which the flow is turbulent. The equations of motion for the two-dimensional flow in the surface are neither compressible nor incompressible but strongly influenced by the 3D flow underneath the surface. The velocity correlation functions in the 2D surface and in the 3D volume scale with the same exponents. In the viscous subrange the amplitudes are the same, but in the inertial subrange the 2D one is reduced to 2/3 of the 3D amplitude. The surface flow is more strongly intermittent than the 3D volume flow. Geometric scaling theory is used to derive a relation between the scaling of the velocity field and the density fluctuations of a passive scalar advected on the surface.Comment: 11 pages, 10 Postscript figure

Neurodegeneration and Epilepsy in a Zebrafish Model of CLN3 Disease (Batten Disease)

The neuronal ceroid lipofuscinoses are a group of lysosomal storage disorders that comprise the most common, genetically heterogeneous, fatal neurodegenerative disorders of children. They are characterised by childhood onset, visual failure, epileptic seizures, psychomotor retardation and dementia. CLN3 disease, also known as Batten disease, is caused by autosomal recessive mutations in the CLN3 gene, 80–85% of which are a ~1 kb deletion. Currently no treatments exist, and after much suffering, the disease inevitably results in premature death. The aim of this study was to generate a zebrafish model of CLN3 disease using antisense morpholino injection, and characterise the pathological and functional consequences of Cln3 deficiency, thereby providing a tool for future drug discovery. The model was shown to faithfully recapitulate the pathological signs of CLN3 disease, including reduced survival, neuronal loss, retinopathy, axonopathy, loss of motor function, lysosomal storage of subunit c of mitochondrial ATP synthase, and epileptic seizures, albeit with an earlier onset and faster progression than the human disease. Our study provides proof of principle that the advantages of the zebrafish over other model systems can be utilised to further our understanding of the pathogenesis of CLN3 disease and accelerate drug discovery

Atlantic salmon cardiac primary cultures:An in vitro model to study viral host pathogen interactions and pathogenesis

Development of Salmon Cardiac Primary Cultures (SCPCs) from Atlantic salmon pre-hatch embryos and their application as in vitro model for cardiotropic viral infection research are described. Producing SCPCs requires plating of trypsin dissociated embryos with subsequent targeted harvest from 24h up to 3 weeks, of relevant tissues after visual identification. SCPCs are then transferred individually to chambered wells for culture in isolation, with incubation at 15-22°. SCPCs production efficiency was not influenced by embryo's origin (0.75/ farmed or wild embryo), but mildly influenced by embryonic developmental stage (0.3 decline between 380 and 445 accumulated thermal units), and strongly influenced by time of harvest post-plating (0.6 decline if harvested after 72 hours). Beating rate was not significantly influenced by temperature (15-22°) or age (2-4 weeks), but was significantly lower on SCPCs originated from farmed embryos with a disease resistant genotype (F = 5.3, p<0.05). Two distinct morphologies suggestive of an ex vivo embryonic heart and a de novo formation were observed sub-grossly, histologically, ultra-structurally and with confocal microscopy. Both types contained cells consistent with cardiomyocytes, endothelium, and fibroblasts. Ageing of SCPCs in culture was observed with increased auto fluorescence in live imaging, and as myelin figures and cellular degeneration ultra-structurally. The SCPCs model was challenged with cardiotropic viruses and both the viral load and the mx gene expression were measurable along time by qPCR. In summary, SCPCs represent a step forward in salmon cardiac disease research as an in vitro model that partially incorporates the functional complexity of the fish heart