The Casimir–Polder effect for an approximate Pauli–Fierz model: the atom plus wall case

We study a system composed of a hydrogen atom interacting with an infinite conductor wall. The interaction energy decays like $L^{- 3}$ , where is the distance between the atom and the wall, due to the emergence of the van der Waals forces. In this paper we show how, considering the contributions from the quantum fluctuations of the electromagnetic field, the interaction is weakened to a decay of order L ́4 giving rise to the retardation effects which fall under the name of Casimir-Polder effect. The analysis is done by studying a suitable Pauli-Fierz model associated to the system, in dipole approximation and reduced to the interaction with 0 and 1 photo

The Casimir-Polder effect for an approximate Pauli-Fierz model: the atom plus wall case

We study a system composed of a hydrogen atom interacting with an infinite conductor wall. The interaction energy decays like $L^{-3}$, where $L$ is the distance between the atom and the wall, due to the emergence of the van der Waals forces. In this paper we show how, considering the contributions from the quantum fluctuations of the electromagnetic field, the interaction is weakened to a decay of order $L^{-4}$ giving rise to the retardation effects which fall under the name of Casimir-Polder effect. The analysis is done by studying a suitable Pauli-Fierz model associated to the system, in dipole approximation and reduced to the interaction with 0 and 1 photon

Ground State Properties in the Quasi-Classical Regime

We study the ground state energy and ground states of systems coupling non-relativistic quantum particles and force-carrying Bose fields, such as radiation, in the quasi-classical approximation. The latter is very useful whenever the force-carrying field has a very large number of excitations,and thus behaves in a semiclassical way, while the non-relativistic particles, on the other hand, retain their microscopic features. We prove that the ground state energy of the fully microscopic model converges to the one of a nonlinear quasi-classical functional depending on both the particles' wave function and the classical configuration of the field. Equivalently, this energy can be interpreted as the lowest energy of a Pekar-like functional with an effective nonlinear interaction for the particles only. If the particles are confined, the ground state of the microscopic system converges as well, to a probability measure concentrated on the set of minimizers of the quasi-classical energy.Comment: 52 pages, pdfLaTe

A study on the aptitude of color hue, value, and transparency for geographic relevance encoding in mobile maps

Depicting the right amount of information on mobile maps is still challenging. With this research we investigate which of the three visual variables hue, value, and transparency optimally directs visual attention to the correct encoding of the geographic relevance of on small displays? We hypothesize that transparency is best suited to let users see symbols in the correct order of high to low relevance and that they intuitively understand this encoding of symbols for value and transparency, but not for hue. In a user study with 27 participants, we tested the suitability of the three visual variables for mobile maps with eye tracking. Results for a perceptual viewing task where no further knowledge or a task was provided, showed no significant differences between the three visual variables for time to first fixation and scanning the symbols in the correct order of relevance. A second search task for the most relevant restaurant, results showed that only transparency seems to reliably encode geographic relevance. “Darker is more” is only partially understood and the traffic light metaphor is unsuitable for encoding ordered geographic relevance on mobile maps. These results are in line with other work and offer guidelines for mobile map design

Misura indiretta della deformazione delle rotaie del bacino n.1 dell\u27INSEAN: correzione in tempo reale della misura delle immersioni per le prove in assetto libero

In the present report we analyzed the deformation of the rails of the towing tank n.1 at INSEAN and its influence on the measurement of sinkage and trim for classical resistance tests. The rails of the towing Tank n.1, through the years, have undergone a deformation mainly in the terminal segment (last 100 meters). This deformation (of order of few millimeters) makes very problematic the measurement with the model in fixed conditions, but also affects the measurement of trim and, mainly, sinkage in free conditions. In particular, it influences the measurement of the submersion at bow and stern due to the changing distance between carriage and water surface during the run. The introduced error is a function of the carriage position along the basin. It is important to remark that the maximum deformation is about 3 mm and mostly regards the end of the rails, while for the initial segment of the rails (up to 200 meters) the deformation is lower than 1 mm. The compromise is to limit the tests with the model in fixed condition at 200 meters, while for the free conditions test a correction for the submersion measurements has to be applied in order to improve the quality of data and extend the run to the rails end. A function fr(x), where x is the carriage position along the rails has been obtained by fitting the acquired data by a ultrasonic probe during a carriage run.Il presente rapporto riguarda la misura delle deformazioni delle rotaie del bacino n.1 dell\u27INSEAN e la loro influenza sulla misura degli assetti nelle prove di rimorchio in assetto libero. Le rotaie del bacino n.1 dell\u27INSEAN, nel corso degli anni, hanno subito una deformazione principalmente nel tratto finale della corsa. Tale deformazione - dell\u27ordine di pochi millimetri - rende problematiche le misure di campo in assetto bloccato, ma incide anche sulla correttezza delle misure delle immersioni per le prove in assetto libero. In particolare introduce nella misura un errore dipendente dalla posizione del carro lungo la corsa dovuto alla differente distanza delle rotaie e quindi del carro dalla superficie libera. ? da rimarcare il fatto che la massima deformazione (circa 3 mm) si ha nella parte finale della corsa, mentre nella parte centrale la deformazione ? dell\u27ordine del millimetro. Come detto, nelle prove ad assetto bloccato sarebbe problematico operare una correzione e si preferisce allo stato attuale limitare la corsa alla parte centrale del bacino, dove le deformazioni sono meno influenti sulla misura finale. D\u27altra parte la limitazione della corsa per le prove in assetto libero che sono le pi? frequenti comporterebbe un aumento delle corse importante. Per questo tipo di prove, considerando che la resistenza non ? affetta da questo errore, si ? deciso di operare una correzione della misura degli assetti in tempo reale. A partire dalla misura della distanza della superficie libera dal carro durante la corsa, ? stata sviluppata una funzione continua fr(x) in grado di descrivere, per ogni posizione x del carro, l\u27entit? della deformazione, al fine di apportare le opportune correzioni alle misure delle immersioni in tempo reale in fase di acquisizione

On boundedness of isomerization paths for non- and semirelativistic molecules

This article focuses on isomerizations of molecules, i.e. chemical reactions during which a molecule is transformed into another one with the same atoms in a different spatial configuration. We consider the special case in which the system breaks into two submolecules whose internal geometry is solid during the whole procedure. We prove, under some conditions, that the distance between the two submolecules stays bounded during the entire reaction. To this end, we provide an asymptotic expansion of the interaction energy between two molecules, including multipolar interactions and the van der Waals attraction. In addition to this static result, we proceed to a quasistatic analysis to investigate the variation of the energy when the nuclei move. This paper generalizes a recent work by M. Lewin and the first author in two directions. The first one is that we relax the assumption that the ground state eigenspaces of the submolecules have to fulfill. The second one is that we allow semirelativistic kinetic energy as well

Sea-Level Change along the Emilia-Romagna Coast from Tide Gauge and Satellite Altimetry

Coastal flooding and retreat are markedly enhanced by sea-level rise. Thus, it is crucial to determine the sea-level variation at the local scale in order to support coastal hazard assessment and related management policies. In this work we focus on sea-level change along the Emilia-Romagna coast, a highly urbanized, 130 km-long belt facing the Northern Adriatic Sea, by analysing data from three tide gauges (with data records in the last 25-10 years) and related closest grid points from ESA_CCI monthly gridded satellite altimetry. The results reveal that the rate of sea-level rise observed by altimetry is coherent along the coast (2.8 \ub1 0.5 mm/yr) for the period 1993-2019 and that a negative acceleration of -0.3 \ub1 0.1 mm/yr is present, in contrast with the global scale. Rates resulting from tide gauge time series analysis diverge from these values mainly in consequence of a large and heterogeneous rate of subsidence in the region. Over the common time span, altimetry and tide gauge data show very high correlation, although their comparison suffers from the short overlapping period between the two data sets. Nevertheless, their combined use allows to assess the recent (last 25 years) sea-level change along the Emilia-Romagna coast and to discuss the role of different interacting processes in the determination of the local sea level

On boundedness of isomerization paths for non- and semirelativistic molecules

This article focuses on isomerizations of molecules, i.e. chemical reactions during which a molecule is transformed into another one with the same atoms but in a different spatial configuration. We consider the special case in which the system breaks into two submolecules whose internal geometry is solid during the whole procedure. We prove, under some conditions, that the distance between the two submolecules stays bounded during the entire reaction. This paper generalizes [6] in two directions. The first one is that we relax the assumptions that the ground state eigenspaces of the submolecules have to fulfill. The second one is that we allow semirelativistic kinetic energy as well

Collective dynamics of dense hairy surfaces in turbulent flow

Flexible filamentous beds interacting with a turbulent flow represent a fundamental setting for many environmental phenomena, e.g., aquatic canopies in marine current. Exploiting direct numerical simulations at high Reynolds number where the canopy stems are modelled individually, we provide evidence on the essential features of the honami/monami collective motion experienced by hairy surfaces over a range of different flexibilities, i.e., Cauchy number. Our findings clearly confirm that the collective motion is essentially driven by fluid flow turbulence, with the canopy having in this respect a fully-passive behavior. Instead, some features pertaining to the structural response turn out to manifest in the motion of the individual canopy elements when focusing, in particular, on the spanwise oscillation and/or on sufficiently small Cauchy numbers