One dimensional extended Hubbard model: two-particle bound states and resonances.

In questo lavoro di tesi è stato svolto uno studio analitico sul modello di Hubbard esteso unidimensionale al fine di osservare la presenza di eventuali risonanze che possano dare origine alla formazione di stati legati di due particelle. L'esistenza di uno stato legato stabile ha suscitato grande interesse negli ultimi anni, sia in ambito teorico che sperimentale, poichè è alla base di molti fenomeni che vengono osservati nei sistemi a molti corpi a basse temperature, come il BCS-BEC crossover. Pertanto si è ritenuto utile studiare il problema a due corpi nel modello di Hubbard esteso, che in generale non è integrabile. Il modello considerato contiene interazioni a primi e secondi vicini, in aggiunta all'interazione di contatto presente nel modello di Hubbard. Il problema è stato indagato analiticamente attraverso il Bethe ansatz, che consente di trovare tutti gli autovalori e le autofunzioni dell'Hamiltoniana. L'ansatz di Bethe sulla funzione d'onda è stato generalizzato per poter tener conto dei termini di interazione a più lungo raggio rispetto all'interazione di contatto. Si trova che, in questo modello, nel limite termodinamico, possono avvenire delle risonanze (o quasi-risonanze) in cui la lunghezza di scattering diverge, contrariamente a quanto avviene nel modello di Hubbard. Tale fenomeno si verifica quando il livello energetico discreto degli stati legati “tocca” la banda di scattering. Inoltre, con l'aggiunta di nuovi termini di interazione emergono nuovi stati legati. Nel caso in esame, si osservano due famiglie di stati legati, se lo spin totale delle due particelle è 1, e tre famiglie di stati legati, se lo spin totale è 0.

Influence of particle size, density and concentration on bend erosive wear in pneumatic conveyors

Particle concentration is a principal factor that affects erosion rate of solid surfaces under particle impact, such as pipe bends in pneumatic conveyors; it is well known that a reduction in the specific erosion rate occurs under high particle concentrations, a phenomenon referred to as the “shielding effect”. The cause of shielding is believed to be increased likelihood of inter-particulate collisions, the high collision probability between incoming and rebounding particles reducing the frequency and the severity of particle impacts on the target surface. In this study, the effects of particle concentration on erosion of a mild steel bend surface have been investigated in detail using three different particulate materials on an industrial scale pneumatic conveying test rig. The materials were studied so that two had the same particle density but very different particle size, whereas two had very similar particle size but very different particle density. Experimental results confirm the shielding effect due to high particle concentration and show that the particle density has a far more significant influence than the particle size, on the magnitude of the shielding effect. A new method of correcting for change in erosivity of the particles in repeated handling, to take this factor out of the data, has been established, and appears to be successful. Moreover, a novel empirical model of the shielding effects has been used, in term of erosion resistance which appears to decrease linearly when the particle concentration decreases. With the model it is possible to find the specific erosion rate when the particle concentration tends to zero, and conversely predict how the specific erosion rate changes at finite values of particle concentration; this is critical to enable component life to be predicted from erosion tester results, as the variation of the shielding effect with concentration is different in these two scenarios. In addition a previously unreported phenomenon has been recorded, of a particulate material whose erosivity has steadily increased during repeated impacts.

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.