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La varietà stabile: teoria e simulazioni numeriche
Get PDFQuesto lavoro di tesi verte sullo studio di alcune strutture caratteristiche dei sistemi dinamici iperbolici: la variet`a stabile e la variet`a instabile. Focalizzandosi sul caso discreto, sono stati trattati due teoremi fondamenti che descrivono le propriet`a di questi oggetti, il teorema di Hadamard-Perron (o della variet`a stabile locale) ed il teorema di Smale (o della variet`a stabile globale), prestando particolare attenzione alle loro dimostrazioni.
Dallo studio di questi teoremi `e stato evidenziato come la variet`a stabile ed insta- bile possono assumere una struttura molto complessa (rete omoclina) alla quale `e associata una dinamica dal carattere caotico.
E’ stato inoltre trattato un altro teorema, il λ-lemma, vedendo come questo fornisce una base teorica per costruire numericamente le variet`a stabili ed instabili almeno nel caso in cui esse siano unidimensionali. Con questo strumento sono state rea- lizzate delle simulazioni numeriche per due sistemi: la Chirikov standard map ed il pendolo con forzante periodica (quest’ultimo trattato con il metodo delle Mappe di Poincar´e)
Development of a machine learning potential for nucleotides in water
Get PDFRecent experimental research showed that nucleotides, under favorable conditions of temperature
and concentration, can self-assemble into liquid crystals. The mechanism involves the stacking of
nucleotides into columnar aggregates. It has been proposed that this ordered structure can favor the
polymerization of long nucleotide chains, which is a fundamental step toward the so called “RNA
world”. In this thesis, starting from ab initio molecular dynamics simulations, at the density func-
tional theory level, an all-atom potential for nucleotides in water, based on an implicit neural network
representation, has been developed. Its stability and accuracy have been tested and its predictions on
simple model systems have been compared with data generated both ab initio and using currently
available empirical force field for nucleic acids
Electronic properties of twisted bilayer graphene
No full textIn this thesis we will focus on the study of a two-layer graphene system, where a small relative rotation is applied. This system is called twisted bilayer graphene, tBLG.
In the last ten years many experimental works have shown that by twisting two layers of graphene by small angles, one can enhance the conducting properties of the system. Moreover at some specific angles, called “magic angles”, the lowest energy band turns to be very close to the Fermi level and becomes extremely flat.
This is of particular interest in the presence of ordered phases of matter like superconductivity. The densities of charge carriers is orders of magnitude lower than the typical two-dimensional superconductors and the measured critical temperature is however relatively high. This makes tBLG a strong coupling superconductor. The great advantage in tBLG with respect to other systems is the simple and fine tunability of carrier densities, magnetic field and temperature, that enables a complete and fine investigation of the rich phase diagram of such a strongly correlated system. Also the interlayer interactions can be fine-tuned by the modulation of the twist angle and/or the application of perpendicular electric fields and of uniaxial strain induced by non hydrostatic pressure.
In this work we study the tight binding model for the tBLG, which, in the continuum limit, correctly predicts the presence of angles at which the Fermi velocity vanishes, and, therefore, the presence of flat bands near these magic angles. In particular, we show how, in the low energy limit, one gets an analytical expression for the first magic angle, rederiving the effective model and providing all the details useful for the calculation skipped in literature.
Moreover we perform the numerical calculation in order to obtain the full spectrum and the bandwidth for the lowest energy band.
The latter result is useful for us when considering the interacting system. In the presence of electron-electron attractive interaction mediated by the phonons, the system seems to sustain a superconducting phase. By means of a path integral approach we finally derive the corresponding critical temperature
“Arte para aprender las lenguas italianas, franzeses, y españolas” […] de A. Fabre. Recensio y collatio de sus ediciones (1626 - 1664)
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