Abstract basins of attraction

Abstract basins appear naturally in different areas of several complex variables. In this survey we want to describe three different topics in which they play an important role, leading to interesting open problems

Lab and Field Tests of a Low-Cost 3-Component Seismometer for Shallow Passive Seismic Applications

We performed laboratory tests and field surveys to evaluate the performance of a low-cost 3-component seismometer, consisting of three passive electromagnetic spring-mass sensors, whose 4.5 Hz natural frequency is extended down to 0.5 Hz thanks to hyper damping. Both lab and field datasets show that the −3 dB band of the seismometer ranges approximately from 0.7 to 39 Hz, in agreement with the nominal specifications. Median magnitude frequency response curves obtained from processing field data indicate that lower corner of the −3 dB band could be extended down to 0.55 Hz and the nominal sensitivity may be overestimated. Lab results confirm the non-linear behavior of the passive spring-mass sensor expected for high-level input signals (a few to tens of mm/s) and field data confirm relative timing accuracy is ±10 ms (1 sample). We found that absolute timing of data collected with USB GPS antennas can be affected by lag as large as +0.5 s. By testing two identical units, we noticed that there could be differences around 0.5 dB (i.e., about 6%) between the components of the same unit as well as between the same component of the two units. Considering shallow passive seismic applications and mainly focusing on unstable slope monitoring, our findings show that the tested seismometer is able to identify resonance frequencies of unstable rock pillars and to generate interferograms that can be processed to estimate subsurface velocity variations

NMR and μ+\mu^{+}SR detection of unconventional spin dynamics in Er(trensal) and Dy(trensal) molecular magnets

Measurements of proton Nuclear Magnetic Resonance (1H NMR) spectra and relaxation and of Muon Spin Relaxation ($\mu^{+}$SR) have been performed as a function of temperature and external magnetic field on two isostructural lanthanide complexes, Er(trensal) and Dy(trensal) featuring crystallographically imposed trigonal symmetry. Both the nuclear 1/T1 and muon $\lambda$ longitudinal relaxation rates, LRR, exhibit a peak for temperatures T lower than 30K, associated to the slowing down of the spin dynamics, and the width of the NMR absorption spectra starts to increase significantly at T ca. 50K, a temperature sizably higher than the one of the LRR peaks. The LRR peaks have a field and temperature dependence different from those previously reported for all Molecular Nanomagnets. They do not follow the Bloembergen-Purcell-Pound scaling of the amplitude and position in temperature and field and thus cannot be explained in terms of a single dominating correlation time $\tau$c determined by the spin slowing down at low temperature. Further, for T lower than 50K the spectral width does not follow the temperature behavior of the magnetic susceptibility chi. We suggest, using simple qualitative considerations, that the observed behavior is due to a combination of two different relaxation processes characterized by the correlation times $\tau$LT and $\tau$HT, dominating for T lower than 30K and T higher than 50K, respectively. Finally, the observed flattening of LRR for T lower than 5K is suggested to have a quantum origin

Dynamics of transcendental Hénon maps-II

Transcendental Hénon maps are the natural extensions of the well investigated complex polynomial Hénon maps to the much larger class of holomorphic automorphisms. We prove here that transcendental Hénon maps always have non-trivial dynamical behavior, namely that they always admit both periodic and escaping orbits, and that their Julia sets are non-empty and perfect

Dynamics of transcendental hÉnon maps III: Infinite entropy

Very little is currently known about the dynamics of non-polynomial entire maps in several complex variables. The family of transcendental Hénon maps offers the potential of combining ideas from transcendental dynamics in one variable and the dynamics of polynomial Hénon maps in two. Here we show that these maps all have infinite topological and measure theoretic entropy. The proof also implies the existence of infinitely many periodic orbits of any order greater than two

Long-term hydrogeophysical monitoring of the internal conditions of river levees

To evaluate the vulnerability of the earthen levee of an irrigation canal in San Giacomo delle Segnate, Italy, a customized electrical resistivity tomography (ERT) monitoring system was installed in September 2015 and has been continuously operating since then. Thanks to a meteorological station deployed at the study site, we could investigate the relationship between the inverted resistivity values and different parameters, namely air temperature, rainfall and water level in the canal. Air temperature seems to have a minor but not negligible influence on resistivity variations, especially at shallow depth. A model of soil temperature versus depth was used to correct resistivity sections for air temperature variations through the different seasons. Changes of the water level in the canal and rainfall significantly affect measured resistivity values. At the study site, the most important variations of resistivity are related to saturation and dewatering processes in the irrigation periods. Although we explored the effect of drawdown procedures on resistivity data, this process, causing rapid variations of resistivity values, is still not completely understood because the canal is rapidly emptied during rainfall events. Therefore, the effect of variations of the water level in the canal on levee resistivity cannot be distinguished from the effect of rainfalls. To study the effect of water level variations alone, we considered the beginning of the irrigation period when the dry canal is gradually filled and we observed a smooth trend of resistivity changes. The effect of rainfall on the data was studied during different periods of the year and at different depths of the levee so that the resistivity variations could be evaluated under different conditions. To convert the inverted resistivity sections into water content maps, an empirical and site-dependent relationship between resistivity and water content was obtained using core samples. Water content data can then be used for the implementation of stability analysis using custom modeling. This study introduces an efficient technique to monitor earthen levees and to control the evolution of seepage and water saturation in pseudo-real time. Such a technique can be exploited by Public Administrations to reduce hydrogeological risks significantly

Indirect Impact Assessment of Pluvial Flooding in Urban Areas Using a Graph-Based Approach: The Mexico City Case Study

This paper presents the application of a graph-based methodology for the assessment of flood impacts in an urban context. In this methodology, exposed elements are organized as nodes on a graph, which is used to propagate impacts from directly affected nodes to other nodes across graph links. Compared to traditional approaches, the main advantage of the adopted methodology lies in the possibility of identifying and understanding indirect impacts and cascading effects. The application case concerns floods numerically reconstructed in Mexico City in response to rainfall events of increasing return periods. The hazard reconstruction was carried out by using a simplified hydrological/hydraulic model of the urban drainage system, implemented in EPASWMM, the Storm Water Management Model developed by the United States Environmental Protection Agency. The paper shows how the impacts are propagated along different orders of the impact chain for each return period and compares the risk curves between direct and indirect impact. It also highlights the extent to which the reduction in demand of services from consumers and the loss of services from suppliers are respectively contributing to the final indirect impacts. Finally, it illustrates how different impact mitigation measures can be formulated based on systemic information provided by the analysis of graph properties and taking into account indirect impacts

Stereodivergent Synthesis of 5-Aminopipecolic Acids and Application in the Preparation of a Cyclic RGD Peptidomimetic as a nanomolar αVβ3 Integrin Ligand

A stereodivergent strategy was devised to obtain enantiopure cis and trans 5-aminopipecolic acids (5-APAs) in suitably protected forms to be employed in peptide synthesis as conformationally constrained \u3b1- and \u3b4-amino acids. The cis isomer was used as a \u3b4-amino acid to construct a cyclic RGD-containing peptidomimetic, the ability of which to compete with biotinylated vitronectin for the binding to the isolated \u3b1V\u3b23 integrin was measured (IC50 = 4.2 \ub1 0.9 nM). A complete 1H NMR and computational conformational analysis was performed to elucidate the reasons for the high affinity of this cyclic peptidomimetic in comparison with Cilengitide