Non linear pseudo-bosons versus hidden Hermiticity. II: The case of unbounded operators

Parallels between the notions of nonlinear pseudobosons and of an apparent non-Hermiticity of observables as shown in paper I (arXiv: 1109.0605) are demonstrated to survive the transition to the quantum models based on the use of unbounded metric in the Hilbert space of states.Comment: 21 p

A stochastic golden rule and quantum Langevin equation for the low density limit

A rigorous derivation of quantum Langevin equation from microscopic dynamics in the low density limit is given. We consider a quantum model of a microscopic system (test particle) coupled with a reservoir (gas of light Bose particles) via interaction of scattering type. We formulate a mathematical procedure (the so-called stochastic golden rule) which allows us to determine the quantum Langevin equation in the limit of large time and small density of particles of the reservoir. The quantum Langevin equation describes not only dynamics of the system but also the reservoir. We show that the generator of the corresponding master equation has the Lindblad form of most general generators of completely positive semigroups

A numerical test of soil layering effects on theoretical and practical Beerkan infiltration runs

With reference to a more compacted and less conductive upper soil layer overlying a less compacted and more conductive subsoil, a simple three-dimensional (3D) infiltration run is expected to yield more representative results of the upper layer than the subsoil. However, there is the need to quantitatively establish what is meant by more representativeness. At this aim, numerically simulated infiltration was investigated for a theoretically unconfined process under a null ponded head of water (d0H0 setup, with d = depth of ring insertion and H = ponded depth of water) and a practical Beerkan run (d1H1 setup, d = H = 1 cm). The considered layered soils differed by both the layering degree (from weak to strong; subsoil more conductive than the upper soil layer by 2.3–32.4 times, depending on the layering degree) and the thickness of the upper soil layer (0.5–3 cm). It was confirmed that water infiltration should be expected to be more representative of the upper soil layer when this layer is the less permeable since, for a 2-h experiment, the instantaneous infiltration rates for the layered soil were 1.0–2.1 times greater than those of the homogeneous low-permeable soil and 1.3–20.7 smaller than those of the homogeneous coarser soil that constituted the subsoil. Similarity with the homogeneous fine soil increased as expected as the upper layer became thicker. For a weak layering condition, the layered soil yielded an intermediate infiltration as compared with that of the two homogeneous soils forming the layered system. For a strong layering degree, the layered soil was more similar to the homogeneous fine soil than to the homogeneous coarse soil. Using the practical setup instead of the theoretical one should have a small to moderate effect on the instantaneous infiltration rates since all the calculated percentage differences between the d1H1 and d0H0 setups fell into the relatively narrow range of −18.8% to +17.4%. A sequential analysis procedure appeared usable to detect layering conditions but with some modifications as compared with the originally proposed procedure. The practical setup enhanced the possibility to recognize the time at which the characteristics of the subsoil start to influence the infiltration process. In conclusion, this investigation contributed to better interpret both the theoretical and the practically established 3D infiltration process in a soil composed of a less conductive upper soil layer overlying a more conductive subsoil and it also demonstrated that modifying the recently proposed sequential analysis procedure only using infiltration data could be advisable to determine the time when layering starts to influence the process

Impact of reforestations with exotic and native species on water repellency of forest soils

Forest duff layer is usually water repellent due to the hydrophobic organic compounds resulting from degradation of tree tissues. Transition from hydrophobic to wettable conditions, or vice versa, is largely controlled by water content. The objective of this investigation was to assess the influence of soil moisture on the degree of soil water repellency (WR) in exotic and native tree forests. Occurrence of WR was investigated by the water drop penetration time (WDPT) and the ethanol percentage (EP) tests. Sampling was conducted in the forest soils of two exotic species (Pinus pinaster, P, and Eucaliptus camaldulensis, E), used in the past for reforestation, and two native species (Quercus ilex, L, and Quercus pubescens, R). The WDPT vs. \u3b8 relationships exhibited a decreasing trend with a transition from hydrophobic to wettable conditions in the range \u3b8 = 0.14 - 0.19 cm3cm-3. The EP vs. \u3b8 relationships showed a maximum in the range \u3b8 = 0.10 - 0.15 cm3cm-3. Hydrophobicity in soils of native species persisted at relatively higher water content compared to exotic ones and it is expected to influence the hydrological processes to a greater extent

Assessing short- and long-term modifications of steady-state water infiltration rate in an extensive Mediterranean green roof

Green roof detention capacity is related to the steady-state infiltration rate, is, of the growing medium. With the aim to investigate short- and long-term modifications of the detention capacity of an extensive Mediterranean green roof, three mini-disk infiltrometer (MDI) measurement campaigns were conducted at construction, after one season and after five years of operation. A laboratory experiment was designed to separately measure is in the upper and the lower part of the substrate profile. During the first operating season, field is increased by a factor of 2.4 and 1.9 for near-saturated (applied pressure head, h0 = -30 mm) and quasi-saturated conditions (h0 = -5 mm), respectively. Similar rainfall height did not induce significant modifications in the upper layer of the laboratory columns, even if contribution of small pores to water infiltration tended to increase. Differently, is significantly decreased by a factor of 3.4-5.3 in the lower layer. After the simulated rainfall, the upper layer was less packed (mean bulk density, & rho;b = 1.083 kg m-3) and the lower layer was more packed (& rho;b = 1.218 kg m-3) as compared with the initial density (& rho;b = 1.131 kg m-3) and the lower part enriched in small particles. Short-term modifications in the experimental plot were thus attributed to fine particles washing-off and bulk density decrease in the upper layer, yielding an overall more conductive porous medium. After five years of green roof operation, field is did not further increase thus showing that the washing/clogging mechanism was complete after one season or it was masked by counteracting processes, like root development and hydrophobicity

Application of minidisk infiltrometer to estimate water repellency in Mediterranean pine forest soils

Assessment of soil water repellency (SWR) was conducted in the decomposed organic floor layer (duff) and in the mineral soil layer of two Mediterranean pine forests, one in Italy and the other in Spain, by the widely-used water drop penetration time (WDPT) test and alternative indices derived from infiltration experiments carried out by the minidisk infiltrometer (MDI). In particular, the repellency index (RI) was calculated as the adjusted ratio between ethanol and water soil sorptivities whereas the water repellency cessation time (WRCT) and the specifically proposed modified repellency index (RIm) were derived from the hydrophobic and wettable stages of a single water infiltration experiment. Time evolution of SWR and vegetation cover influence was also investigated at the Italian site. All indices unanimously detected severe SWR conditions in the duff of the pine forests. The mineral subsoils in the two forests showed different wettability and the clay-loam subsoil at Ciavolo forest was hydrophobic even if characterized by organic matter (OM) content similar to the wettable soil of an adjacent glade. It was therefore assumed that the composition rather than the total amount of OM influenced SWR. The hydraulic conductivity of the duff differed by a factor of 3.8-5.8 between the two forested sites thus influencing the vertical extent of SWR. Indeed, the mineral subsoil of Javea showed wettable or weak hydrophobic conditions probably because leaching of hydrophobic compounds was slowed or prevented at all. Estimations of SWR according to the different indices were in general agreement even if some discrepancies were observed. In particular, at low hydrophobicity levels the SWR indices gathered from the MDI tests were able to signal sub-critical SWR conditions that were not detected by the traditional WDPT index. The WRCT and modified repellency index RIm yielded SWR estimates in reasonable agreement with those obtained with the more cumbersome RI test and, therefore, can be proposed as alternative procedures for SWR assessment

Correspondence between theory and practice of a Beerkan infiltration experiment

The Beerkan infiltration experiment is carried out by inserting the ring a short depth into the soil and establishing a positive head of water on the infiltration surface for at least a part of the run. Nevertheless, the data are analyzed by assuming a fully unconfined infiltration process (ring insertion depth, d = 0 cm) and a null ponded depth of water (H = 0 cm). The influence of ring insertion and ponded water on an infiltration process of 2 h sampled every minute was tested in this numerical investigation. Five soils varying from sand to silt loam, three ring radii (5–15 cm), and the Beerkan-specific range of values for both d and H (between 0 and 1 cm) were considered. The differences between the theoretical (d = H = 0 cm) and the practical (d = H = 1 cm) setups varied from −10.4 to +8.6% for the mean infiltration rate and from −10.2 to +8.3% for the final cumulative infiltration. These differences were small, and they decreased in absolute value by considering a soil-dependent ring radius. In particular, nearly negligible differences were detected using a small ring in coarse-textured soils and a large ring in fine-textured soils. In the coarser soils, inserting the ring and establishing a ponded depth of water did not alter the estimated coefficients of the two-parameter infiltration model appreciably with the cumulative linearization method, because these coefficients differed between the theoretical and practical setups by no more than 9.2%. In fine soils, linearization could not be possible regardless of the considered setup, or it was the use of d = H = 1 cm instead of d = H = 0 cm that impeded a convincing linearization of the data. In conclusion, the good correspondence, in many circumstances, between the theoretical and the practical Beerkan infiltration experiment reinforced the interest in this simple experiment as a practical means to collect infiltration data in the field

Osservazione e modellazione del deflusso sottosuperficiale laterale saturo in un ripido versante naturale

I versanti sono unità morfologiche fondamentali che governano la risposta idrologica dei bacini idrografici durante le precipitazioni più intense. Nonostante la loro riconosciuta importanza idrologica, è ancora necessario condurre approfonditi studi, sia a carattere sperimentale che teoretico, per meglio comprendere i meccanismi di generazione e trasporto del deflusso sottosuperficiale laterale saturo nei versanti. In questo contributo sono presentati i risultati di un monitoraggio di lungo periodo del flusso laterale di falda intercettato per mezzo di una trincea drenante installata su d’un ripido versante naturale nel bacino del Lago di Baratz, Sardegna. I dati raccolti vengono utilizzati per sviluppare una relazione di tipo esponenziale tra la conducibilità idraulica laterale satura (KS) e lo spessore della falda (T), valida alla scala di versante. I flussi osservati e i livelli di falda sono simulati con un modello numerico orizzontale 1D, basato sulla soluzione simultanea della legge del moto e dell’equazione di bilancio idrico, e implementato tramite uno schema risolutivo alle differenza finite. Le principali assunzioni del modello sono che nel suolo il flusso sottosuperficiale saturo sia regolato dalla legge di Darcy, e che si verifichi sempre l’istantaneo raggiungimento di un profilo di equilibrio idrostatico del carico di suzione nella zona vadosa. Il modello richiede la specifica della curva di ritenzione idrica del suolo e della relazione KS(T) ottenute sperimentalmente. I risultati della simulazione indicano che il modello è in grado di riprodurre in modo adeguato i dati osservati. Il flusso di falda è ben riprodotto, sia in termini di tempi di risposta che di portate drenate. Pertanto, il modello sviluppato può essere un utile strumento di previsione della risposta idrologica in versanti naturali a forte pendenza

SCHEMA SPERIMENTALE PER LA STIMA DELLA CONDUCIBILITÀ IDRAULICA LATERALE ALLA SCALA DI VERSANTE

La conducibilità idraulica alla saturazione, KS, è un parametro fondamentale per la simulazione del flusso idrico nel suolo. La memoria illustra un approccio sperimentale per la stima della KS laterale alla scala di versante. La metodologia proposta è stata applicata in due aree contigue ricoperte, rispettivamente, da macchia mediterranea e prato. Sono stati registrati i livelli di falda e i deflussi idrici sottosuperficiali, e queste misure sono state usate per il calcolo della KS del suolo tramite l’equazione di Darcy. Il monitoraggio è stato effettuato durante il periodo piovoso compreso tra gennaio e giugno 2014. In aprile, inoltre, sono state eseguite prove di pioggia artificiale con intensità di 30 e 70 mm h-1. Durante le precipitazioni naturali, il valore massimo di KS stimato nel prato è stato di 2870 mm h-1, mentre è stato pari a 2400 mm h-1 nel corso delle prove di saturazione artificiale. Il valore massimo di KS pari 4000 mm h-1 è stato ottenuto, nella macchia, durante le prove di pioggia artificiale. Per contro, valori minori di KS sono stati ottenuti durante le piogge naturali a causa delle basse portate sottosuperficiali registrate. La metodologia proposta è risultata idonea per la stima di valori della conducibilità idraulica rappresentativi per le aree di interesse. Tali informazioni potranno garantire una maggiore attendibilità della modellizzazione dei processi idrologici a scala di versante e di bacino

Quasi-Continuous Symmetries of Non-Lie Type

We introduce a smooth mapping of some discrete space-time symmetries into quasi-continuous ones. Such transformations are related with q-deformations of the dilations of the Euclidean space and with the non-commutative space. We work out two examples of Hamiltonian invariance under such symmetries. The Schrodinger equation for a free particle is investigated in such a non-commutative plane and a connection with anyonic statistics is found.Comment: 18 pages, LateX, 3 figures, Submitted Found. Phys., PACS: 03.65.Fd, 11.30.E