Ergodicity and regularity of invariant measure for branching Markov processes with immigration

In this thesis we consider systems of finitely many particles moving on paths given by a strong Markov process and undergoing branching and reproduction at random times. The branching rate of a particle, its number of offspring and their spatial distribution are allowed to depend on the particle's position and possibly on the configuration of coexisting particles. In addition there is immigration of new particles, with the rate of immigration and the distribution of immigrants possibly depending on the configuration of pre-existing particles as well. In the first two chapters of this work, we concentrate on the case that the joint motion of particles is governed by a diffusion with interacting components. The resulting process of particle configurations was studied by E. Löcherbach (2002, 2004) and is known as a branching diffusion with immigration (BDI). Chapter 1 contains a detailed introduction of the basic model assumptions, in particular an assumption of ergodicity which guarantees that the BDI process is positive Harris recurrent with finite invariant measure on the configuration space. This object and a closely related quantity, namely the invariant occupation measure on the single-particle space, are investigated in Chapter 2 where we study the problem of the existence of Lebesgue-densities with nice regularity properties. For example, it turns out that the existence of a continuous density for the invariant measure depends on the mechanism by which newborn particles are distributed in space, namely whether branching particles reproduce at their death position or their offspring are distributed according to an absolutely continuous transition kernel. In Chapter 3, we assume that the quantities defining the model depend only on the spatial position but not on the configuration of coexisting particles. In this framework (which was considered by Höpfner and Löcherbach (2005) in the special case that branching particles reproduce at their death position), the particle motions are independent, and we can allow for more general Markov processes instead of diffusions. The resulting configuration process is a branching Markov process in the sense introduced by Ikeda, Nagasawa and Watanabe (1968), complemented by an immigration mechanism. Generalizing results obtained by Höpfner and Löcherbach (2005), we give sufficient conditions for ergodicity in the sense of positive recurrence of the configuration process and finiteness of the invariant occupation measure in the case of general particle motions and offspring distributions.

Cost-Effectiveness of Alternative Retrofit Options to Support Decision Making

How to evaluate the cost-effectiveness of repair/retrofit intervention vs. demolition/replacement and what level of shaking intensity can the chosen repairing/retrofit technique sustain are open questions affecting either the pre-earthquake prevention, the post-earthquake emergency and the reconstruction phases. The (mis)conception that the cost of retrofit interventions would increase linearly with the achieved seismic performance (%NBS) often discourages stakeholders to consider repair/retrofit options in a post-earthquake damage situation. Similarly, in a pre-earthquake phase, the minimum (by-law) level of %NBS might be targeted, leading in some cases to no-action. Furthermore, the performance measure enforcing owners to take action, the %NBS, is generally evaluated deterministically. Not directly reflecting epistemic and aleatory uncertainties, the assessment can result in misleading confidence on the expected performance. The present study aims at contributing to the delicate decision-making process of repair/retrofit vs. demolition/replacement, by developing a framework to assist stakeholders with the evaluation of the effects in terms of long-term losses and benefits of an increment in their initial investment (targeted retrofit level) and highlighting the uncertainties hidden behind a deterministic approach. For a pre-1970 case study building, different retrofit solutions are considered, targeting different levels of %NBS, and the actual probability of reaching Collapse when considering a suite of ground-motions is evaluated, providing a correlation between %NBS and Risk. Both a simplified and a probabilistic loss modelling are then undertaken to study the relationship between %NBS and expected direct and indirect losses.

Wet and dry model granulates under mechanical load : a confocal microscopy study

Granular matter, also known as bulk solids, consists of discrete particles with sizes between micrometers and meters. They are present in many industrial applications as well as daily life, like in food processing, pharmaceutics or in the oil and mining industry. When handling granular matter the bulk solids are stored, mixed, conveyed or filtered. These techniques are based on observations in macroscopic experiments, i.e. rheological examinations of the bulk properties. Despite the amply investigations of bulk mechanics, the relation between single particle motion and macroscopic behavior is still not well understood. For exploring the microscopic properties on a single particle level, 3D imaging techniques are required.rnThe objective of this work was the investigation of single particle motions in a bulk system in 3D under an external mechanical load, i.e. compression and shear. During the mechanical load the structural and dynamical properties of these systems were examined with confocal microscopy. Therefor new granular model systems in the wet and dry state were designed and prepared. As the particles are solid bodies, their motion is described by six degrees of freedom. To explore their entire motion with all degrees of freedom, a technique to visualize the rotation of spherical micrometer sized particles in 3D was developed. rnOne of the foci during this dissertation was a model system for dry cohesive granular matter. In such systems the particle motion during a compression of the granular matter was investigated. In general the rotation of single particles was the more sensitive parameter compared to the translation. In regions with large structural changes the rotation had an earlier onset than the translation. In granular systems under shear, shear dilatation and shear zone formation were observed. Globally the granular sediments showed a shear behavior, which was known already from classical shear experiments, for example with Jenike cells. Locally the shear zone formation was enhanced, when near the applied load a pre-diluted region existed. In regions with constant volume fraction a mixing between the different particle layers occurred. In particular an exchange of particles between the current flowing region and the non-flowing region was observed. rnThe second focus was on model systems for wet granular matter, where an additional binding liquid is added to the particle suspension. To examine the 3D structure of the binding liquid on the micrometer scale independently from the particles, a second illumination and detection beam path was implemented. In shear and compression experiments of wet clusters and bulk systems completely different dynamics compared to dry cohesive models systems occured. In a Pickering emulsion-like system large structural changes predominantly occurred in the local environment of binding liquid droplets. These large local structural changes were due to an energy interplay between the energy stored in the binding droplet during its deformation and the binding energy of particles at the droplet interface. rnConfocal microscopy in combination with nanoindentation gave new insights into the single particle motions and dynamics of granular systems under a mechanical load. These novel experimental results can help to improve the understanding of the relationship between bulk properties of granular matter, such as volume fraction or yield stress and the dynamics on a single particle level.rnrn

A study of the turbulence of the neutral medium in two nearby spiral galaxies

The width of the 21 cm line (HI) emitted by spiral galaxies depends on the physical processes that release energy in the Interstellar Medium (ISM). This quantity is called velocity dispersion (σ) and it is proportional first of all to the thermal kinetic energy of the gas. The accepted theoretical picture predicts that the neutral hydrogen component (HI) exists in the ISM in two stable phases: a cold one (CNM, with σ~0.8 km/s) and a warm one (WNM, with σ~8 km/s). However, this is called into question by the observation that the HI gas has usually larger velocity dispersions. This suggests the presence of turbulence in the ISM, although the energy sources remain unknown. In this thesis we want to shed new light on this topic. We have studied the HI line emission of two nearby galaxies: NGC6946 and M101. For the latter we used new deep observations obtained with the Westerbork radio interferometer. Through a gaussian fitting procedure, we produced dispersion maps of the two galaxies. For both of them, we compared the σ values measured in the spiral arms with those in the interarms. In NGC6946 we found that, in both arms and interarms, σ grows with the column density, while we obtained the opposite for M 101. Using a statistical analysis we did not find a significant difference between arm and interarm dispersion distributions. Producing star formation rate density maps (SFRD) of the galaxies, we studied their global and local relations with the HI kinetic energy, as inferred from the measured dispersions. For NGC6946 we obtained a good log-log correlation, in agreement with a simple model of supernova feedback driven turbulence. This shows that in this galaxy turbulent motions are mainly induced by the stellar activity. For M 101 we did not find an analogous correlation, since the gas kinetic energy appears constant with the SFRD. We think that this may indicate that in this galaxy turbulence is driven also by accretion of extragalactic material.

Galactic fountain flows in high-resolution hydrodynamical simulations of galaxy disks

Feedback from the most massive components of a young stellar cluster deeply affects the surrounding ISM driving an expanding over-pressured hot gas cavity in it. In spiral galaxies these structures may have sufficient energy to break the disk and eject large amount of material into the halo. The cycling of this gas, which eventually will fall back onto the disk, is known as galactic fountains. We aim at better understanding the dynamics of such fountain flow in a Galactic context, frame the problem in a more dynamic environment possibly learning about its connection and regulation to the local driving mechanism and understand its role as a metal diffusion channel. The interaction of the fountain with a hot corona is hereby analyzed, trying to understand the properties and evolution of the extraplanar material. We perform high resolution hydrodynamical simulations with the moving-mesh code AREPO to model the multi-phase ISM of a Milky Way type galaxy. A non-equilibrium chemical network is included to self consistently follow the evolution of the main coolants of the ISM. Spiral arm perturbations in the potential are considered so that large molecular gas structures are able to dynamically form here, self shielded from the interstellar radiation field. We model the effect of SN feedback from a new-born stellar cluster inside such a giant molecular cloud, as the driving force of the fountain. Passive Lagrangian tracer particles are used in conjunction to the SN energy deposition to model and study diffusion of freshly synthesized metals. We find that both interactions with hot coronal gas and local ISM properties and motions are equally important in shaping the fountain. We notice a bimodal morphology where most of the ejected gas is in a cold $10^4$ K clumpy state while the majority of the affected volume is occupied by a hot diffuse medium. While only about 20\% of the produced metals stay local, most of them quickly diffuse through this hot regime to great scales.

Sea level trends in the Mediterranean from tide gauges and satellite altimetry

Sea level variation is one of the parameters directly related to climate change. Monitoring sea level rise is an important scientific issue since many populated areas of the world and megacities are located in low-lying regions. At present, sea level is measured by means of two techniques: the tide gauges and the satellite radar altimetry. Tide gauges measure sea-level relatively to a ground benchmark, hence, their measurements are directly affected by vertical ground motions. Satellite radar altimetry measures sea-level relative to a geocentric reference and are not affected by vertical land motions. In this study, the linear relative sea level trends of 35 tide gauge stations distributed across the Mediterranean Sea have been computed over the period 1993-2014. In order to extract the real sea-level variation, the vertical land motion has been estimated using the observations of available GPS stations and removed from the tide gauges records. These GPS-corrected trends have then been compared with satellite altimetry measurements over the same time interval (AVISO data set). A further comparison has been performed, over the period 1993-2013, using the CCI satellite altimetry data set which has been generated using an updated modeling. The absolute sea level trends obtained from satellite altimetry and GPS-corrected tide gauge data are mostly consistent, meaning that GPS data have provided reliable corrections for most of the sites. The trend values range between +2.5 and +4 mm/yr almost everywhere in the Mediterranean area, the largest trends were found in the Northern Adriatic Sea and in the Aegean. These results are in agreement with estimates of the global mean sea level rise over the last two decades. Where GPS data were not available, information on the vertical land motion deduced from the differences between absolute and relative trends are in agreement with the results of other studies.

Molecular Dynamics Simulation of a PNA·DNA·PNA Triple Helix in Aqueous Solution

Molecular dynamics simulations have been used to explore the conformational flexibility of a PNA·DNA·PNA triple helix in aqueous solution. Three 1.05 ns trajectories starting from different but reasonable conformations have been generated and analyzed in detail. All three trajectories converge within about 300 ps to produce stable and very similar conformational ensembles, which resemble the crystal structure conformation in many details. However, in contrast to the crystal structure, there is a tendency for the direct hydrogen-bonds observed between the amide hydrogens of the Hoogsteen-binding PNA strand and the phosphate oxygens of the DNA strand to be replaced by water-mediated hydrogen bonds, which also involve pyrimidine O2 atoms. This structural transition does not appear to weaken the triplex structure but alters groove widths and so may relate to the potential for recognition of such structures by other ligands (small molecules or proteins). Energetic analysis leads us to conclude that the reason that the hybrid PNA/DNA triplex has quite different helical characteristics from the all-DNA triplex is not because the additional flexibility imparted by the replacement of sugar−phosphate by PNA backbones allows motions to improve base-stacking but rather that base-stacking interactions are very similar in both types of triplex and the driving force comes from weak but definate conformational preferences of the PNA strands.

Characterisation of extreme winter precipitation in Mediterranean coastal sites and associated anomalous atmospheric circulation patterns

We present an analysis of daily extreme precipitation events for the extended winter season (October–March) at 20 Mediterranean coastal sites covering the period 1950–2006. The heavy tailed behaviour of precipitation extremes and estimated return levels, including associated uncertainties, are derived applying a procedure based on the Generalized Pareto Distribution, in combination with recently developed methods. Precipitation extremes have an important contribution to make seasonal totals (approximately 60% for all series). Three stations (one in the western Mediterranean and the others in the eastern basin) have a 5-year return level above 100 mm, while the lowest value (estimated for two Italian series) is equal to 58 mm. As for the 50-year return level, an Italian station (Genoa) has the highest value of 264 mm, while the other values range from 82 to 200 mm. Furthermore, six series (from stations located in France, Italy, Greece, and Cyprus) show a significant negative tendency in the probability of observing an extreme event. The relationship between extreme precipitation events and the large scale atmospheric circulation at the upper, mid and low troposphere is investigated by using NCEP/NCAR reanalysis data. A 2-step classification procedure identifies three significant anomaly patterns both for the western-central and eastern part of the Mediterranean basin. In the western Mediterranean, the anomalous southwesterly surface to mid-tropospheric flow is connected with enhanced moisture transport from the Atlantic. During ≥5-year return level events, the subtropical jet stream axis is aligned with the African coastline and interacts with the eddy-driven jet stream. This is connected with enhanced large scale ascending motions, instability and leads to the development of severe precipitation events. For the eastern Mediterranean extreme precipitation events, the identified anomaly patterns suggest warm air advection connected with anomalous ascent motions and an increase of the low- to mid-tropospheric moisture. Furthermore, the jet stream position (during ≥5-year return level events) supports the eastern basin being in a divergence area, where ascent motions are favoured. Our results contribute to an improved understanding of daily precipitation extremes in the cold season and associated large scale atmospheric features.

Miocene basin development and volcanism along a strike-slip to flat-slab subduction transition: Stratigraphy, geochemistry, and geochronology of the central Wrangell volcanic belt, Yakutat-North America collision zone

New geochronologic, geochemical, sedimentologic, and compositional data from the central Wrangell volcanic belt (WVB) document basin development and volcanism linked to subduction of overthickened oceanic crust to the northern Pacific plate margin. The Frederika Formation and overlying Wrangell Lavas comprise >3 km of sedimentary and volcanic strata exposed in the Wrangell Mountains of south-central Alaska (United States). Measured stratigraphic sections and lithofacies analyses document lithofacies associations that reflect deposition in alluvial-fluvial-lacustrine environments routinely influenced by volcanic eruptions. Expansion of intrabasinal volcanic centers prompted progradation of vent-proximal volcanic aprons across basinal environments. Coal deposits, lacustrine strata, and vertical juxtaposition of basinal to proximal lithofacies indicate active basin subsidence that is attributable to heat flow associated with intrabasinal volcanic centers and extension along intrabasinal normal faults. The orientation of intrabasinal normal faults is consistent with transtensional deformation along the Totschunda-Fairweather fault system. Paleocurrents, compositional provenance, and detrital geochronologic ages link sediment accumulation to erosion of active intrabasinal volcanoes and to a lesser extent Mesozoic igneous sources. Geochemical compositions of interbedded lavas are dominantly calc-alkaline, range from basaltic andesite to rhyolite in composition, and share geochemical characteristics with Pliocene-Quaternary phases of the western WVB linked to subduction-related magmatism. The U/Pb ages of tuffs and Ar-40/Ar-39 ages of lavas indicate that basin development and volcanism commenced by 12.5-11.0 Ma and persisted until at least ca. 5.3 Ma. Eastern sections yield older ages (12.5-9.3 Ma) than western sections (9.6-8.3 Ma). Samples from two western sections yield even younger ages of 5.3 Ma. Integration of new and published stratigraphic, geochronologic, and geochemical data from the entire WVB permits a comprehensive interpretation of basin development and volcanism within a regional tectonic context. We propose a model in which diachronous volcanism and transtensional basin development reflect progressive insertion of a thickened oceanic crustal slab of the Yakutat microplate into the arcuate continental margin of southern Alaska coeval with reported changes in plate motions. Oblique northwestward subduction of a thickened oceanic crustal slab during Oligocene to Middle Miocene time produced transtensional basins and volcanism along the eastern edge of the slab along the Duke River fault in Canada and subduction-related volcanism along the northern edge of the slab near the Yukon-Alaska border. Volcanism and basin development migrated progressively northwestward into eastern Alaska during Middle Miocene through Holocene time, concomitant with a northwestward shift in plate convergence direction and subduction collision of progressively thicker crust against the syntaxial plate margin.

Terrestrial feeding in aquatic turtles: environment-dependent feeding behavior modulation and the evolution of terrestrial feeding in Emydidae

Evolutionary transitions between aquatic and terrestrial environments are common in vertebrate evolution. These transitions require major changes in most physiological functions, including feeding. Emydid turtles are ancestrally aquatic, with most species naturally feeding only in water, but some terrestrial species can modulate their feeding behavior appropriately for both media. In addition, many aquatic species can be induced to feed terrestrially. A comparison of feeding in both aquatic and terrestrial environments presents an excellent opportunity to investigate the evolution of terrestrial feeding from aquatic feeding, as well as a system within which to develop methods for studying major evolutionary transitions between environments. Individuals from eight species of emydid turtles (six aquatic, two terrestrial) were filmed while feeding underwater and on land. Bite kinematics were analyzed to determine whether aquatic turtles modulated their feeding behavior in a consistent and appropriate manner between environments. Aquatic turtles showed consistent changes between environments, taking longer bites and using more extensive motions of the jaw and hyoid when feeding on land. However, these motions differ from those shown by species that naturally feed in both environments and mostly do not seem to be appropriate for terrestrial feeding. For example, more extensive motions of the hyoid are only effective during underwater suction feeding. Emydids evolving to feed on land probably would have needed to evolve or learn to overcome many, but not all, aspects of the intrinsic emydid response to terrestrial feeding. Studies that investigate major evolutionary transitions must determine what responses to the new environment are shown by naïve individuals in order to fully understand the evolutionary patterns and processes associated with these transitions.

The Extremely Red, Young L Dwarf PSO J318.5338-22.8603: a Free-Floating Planetary-Mass Analog to Directly Imaged Young Gas-Giant Planets

We have discovered using Pan-STARRS1 an extremely red late-L dwarf, which has (J - K)(MKO) = 2.78 and (J - K) (2MASS) = 2.84, making it the reddest known field dwarf and second only to 2MASS J1207-39b among substellar companions. Near-IR spectroscopy shows a spectral type of L7 +/- 1 and reveals a triangular H-band continuum and weak alkali (K I and Na I) lines, hallmarks of low surface gravity. Near-IR astrometry from the Hawaii Infrared Parallax Program gives a distance of 24.6 +/- 1.4 pc and indicates a much fainter J-band absolute magnitude than field L dwarfs. The position and kinematics of PSO J318.5-22 point to membership in the beta Pic moving group. Evolutionary models give a temperature of 1160(-40)(+30) K and a mass of 6.5(-1.0)(+1.3) M-Jup, making PSO J318.5-22 one of the lowest mass free-floating objects in the solar neighborhood. This object adds to the growing list of low-gravity field L dwarfs and is the first to be strongly deficient in methane relative to its estimated temperature. Comparing their spectra suggests that young L dwarfs with similar ages and temperatures can have different spectral signatures of youth. For the two objects with well constrained ages (PSO J318.5-22 and 2MASS J0355+11), we find their temperatures are approximate to 400 K cooler than field objects of similar spectral type but their luminosities are similar, i.e., these young L dwarfs are very red and unusually cool but not "underluminous." Altogether, PSO J318.5-22 is the first free-floating object with the colors, magnitudes, spectrum, luminosity, and mass that overlap the young dusty planets around HR 8799 and 2MASS J1207-39

Solution structure and interaction of cupiennin 1a, a spider venom peptide, with phospholipid bilayers

The solution structure of cupiennin 1a, a 35 residue, basic antibacterial peptide isolated from the venom of the spider Cupiennius salei, has been determined by nuclear magnetic resonance (NMR) spectroscopy. The peptide was found to adopt a helix−hinge−helix structure in a membrane mimicking solvent. The hinge may play a role in allowing the amphipathic N-terminal helix and polar C-terminal helix to orient independently upon membrane binding, in order to achieve maximal antibacterial efficacy. Solid-state 31P and 2H NMR was used to further study the effects of cupiennin 1a on the dynamic properties of lipid membranes, using zwitterionic chain deuterated dimyristoylphosphatidylcholine (d54-DMPC) and anionic dimyristoylphosphatidylglycerol (DMPG) multilamellar vesicles. In d54-DMPC alone, cupiennin 1a caused a decrease in the 31P chemical shift anisotropy, indicating some interaction with the lipid head groups, and a decrease in order over the entire acyl chain. In contrast, for the mixed (d54-DMPC/DMPG) lipid system cupiennin 1a appeared to induce lateral separation of the two lipids as evidenced by the 31P spectra, in which the peptide preferentially interacted with DMPG. Little effect was observed on the deuterated acyl chain order parameters in the d54-DMPC/DMPG model membranes. Furthermore, 31P NMR relaxation measurements confirmed a differential effect on the lipid motions depending upon the membrane composition. Therefore, subtle differences are likely in the mechanism by which cupiennin 1a causes membrane lysis in either prokaryotic or eukaryotic cells, and may explain the specific spectrum of activity.

Differential GPS as a monitoring tool on Volcano Santa Ana (Illamatepec) and the Coatepeque Caldera, El Salvador

We used differential GPS measurements from a 13 station GPS network spanning the Santa Ana Volcano and Coatepeque Caldera to characterize the inter-eruptive activity and tectonic movements near these two active and potentially hazardous features. Caldera-forming events occurred from 70-40 ka and at Santa Ana/Izalco volcanoes eruptive activity occurred as recently as 2005. Twelve differential stations were surveyed for 1 to 2 hours on a monthly basis from February through September 2009 and tied to a centrally located continuous GPS station, which serves as the reference site for this volcanic network. Repeatabilities of the averages from 20-minute sessions taken over 20 hours or longer range from 2-11 mm in the horizontal (north and east) components of the inter-station baselines, suggesting a lower detection limit for the horizontal components of any short-term tectonic or volcanic deformation. Repeatabilities of the vertical baseline component range from 12-34 mm. Analysis of the precipitable water vapor in the troposphere suggests that tropospheric decorrelation as a function of baseline lengths and variable site elevations are the most likely sources of vertical error. Differential motions of the 12 sites relative to the continuous reference site reveal inflation from February through July at several sites surrounding the caldera with vertical displacements that range from 61 mm to 139 mm followed by a lower magnitude deflation event on 1.8-7.4 km-long baselines. Uplift rates for the inflationary period reach 300 mm/yr with 1σ uncertainties of +/- 26 – 119 mm. Only one other station outside the caldera exhibits a similar deformation trend, suggesting a localized source. The results suggest that the use of differential GPS measurements from short duration occupations over short baselines can be a useful monitoring tool at sub-tropical volcanoes and calderas.