Improving Roth's theorem in the primes

Let A be a subset of the primes. Let \delta_P(N) = \frac{|\{n\in A: n\leq N\}|}{|\{\text{$n$ prime}: n\leq N\}|}. We prove that, if \delta_P(N)\geq C \frac{\log \log \log N}{(\log \log N)^{1/3}} for N\geq N_0, where C and N_0 are absolute constants, then A\cap [1,N] contains a non-trivial three-term arithmetic progression. This improves on B. Green's result, which needs \delta_P(N) \geq C' \sqrt{\frac{\log \log \log \log \log N}{\log \log \log \log N}}.Comment: 13 page

Galaxy formation: from primordial fluctuations to structure formation in the Universe

Durante questa tesi studieremo principalmente i modelli di formazione di struttura nel universo di Press & Schechter(1974) e di White & Rees (1978), che spiegano la formazione galattica con un modello gerarchico di formazione di tutte le strutture cosmiche, dalla crescita delle piccole perturbazioni primordiali fino alla formazione della materia, e come essa si evolve per formare stelle e poi sistemi stellari, cioè, galassie. Una parte importante di questa tesi sarà dedicata a studiare la formazione di aloni di materia oscura, che sono vere e proprie buche di potenziale, in cui la materia barionica caderà per formare la galassia. Finalmente, studieremo la formazione di strutture luminose, come sono le stelle, al interno degli aloni di materia oscura ed a cos'è dovuto le diverse morfologie che vediamo in diverse galassie. Confronteremo i risultati più importanti dei modelli teorici studiati con dati osservativi ed esperimentali moderni

Role of Rotations on Surface Diffusion of Water Trimers on Pd\{111\}

Diffusion barriers for a cluster of three water molecules on Pd(111) have been estimated from ab-initio Density Functional Theory. A model for the diffusion of the trimer based in rotations yields a simple explanation of why the cluster can diffuse faster than a single water molecule by a factor $\approx 10^{2}$. This model is based on the differences between the adsorption geometry for the three monomers forming the cluster. One member interacts strongly with the surface and sits closer to the surface (d) while the other two interact weakly and stay at a larger separation from the surface (u). The trimer rotates nearly freely around the axis determined by the d monomer. Translations of the whole trimer imply breaking the strong interaction of the d monomer with the surface. Alternatively, thermal fluctuations exchange the actual monomer sitting closer to the surface with a lower energetic cost. Rotations around different axis introduce a diffusion mechanism where a strong interaction is kept along the diffusion path between the water molecule defining the axis of rotation and the Pd underneath.Comment: water ; monomer ; trimer ; water clusters ; diffusion ; rotation assisted ; Pd\{111\} ; ab-initio ; density functional theor

Firm Location and the Creation and Utilization of Human Capital

This paper presents a theory of location choice that draws on insights from the incomplete contracts and investment flexibility (real option) literatures. We provide conditions under which human capital is more efficiently created and better utilized within industrial clusters that contain similar firms. Our analysis indicates that location choices are influenced by the extent to which training costs are borne by firms versus employees as well as by the uncertainty about future productivity shocks and the ability of firms to increase and decrease the scale of their operations. Extensions of our model allow us to consider, among other things, endogenous technological choices by firms in clusters and how behavioral biases (i.e., managerial overconfidence about their firms' prospects) can affect firms' location choicesLocation choice, Human Capital, Real Options

Patterson Function from Low-Energy Electron Diffraction Measured Intensities and Structural Discrimination

Surface Patterson Functions have been derived by direct inversion of experimental Low-Energy Electron Diffraction I-V spectra measured at multiple incident angles. The direct inversion is computationally simple and can be used to discriminate between different structural models. 1x1 YSi_2 epitaxial layers grown on Si(111) have been used to illustrate the analysis. We introduce a suitable R-factor for the Patterson Function to make the structural discrimination as objective as possible. From six competing models needed to complete the geometrical search, four could easily be discarded, achieving a very significant and useful reduction in the parameter space to be explored by standard dynamical LEED methods. The amount and quality of data needed for this analysis is discussed.Comment: 5 pages, 4 figure

Percus-Yevick theory for the structural properties of the seven-dimensional hard-sphere fluid

The direct correlation function and the (static) structure factor for a seven-dimensional hard-sphere fluid are considered. Analytical results for these quantities are derived within the Percus-Yevick theoryComment: 3 pages, 2 tables, 1 figure; v2: minor changes; to be published in JC

Confinement Effects on Phase Behavior of Soft Matter Systems

When systems that can undergo phase separation between two coexisting phases in the bulk are confined in thin film geometry between parallel walls, the phase behavior can be profoundly modified. These phenomena shall be described and exemplified by computer simulations of the Asakura-Oosawa model for colloid-polymer mixtures, but applications to other soft matter systems (e.g. confined polymer blends) will also be mentioned. Typically a wall will prefer one of the phases, and hence the composition of the system in the direction perpendicular to the walls will not be homogeneous. If both walls are of the same kind, this effect leads to a distortion of the phase diagram of the system in thin film geometry, in comparison with the bulk, analogous to the phenomenon of "capillary condensation" of simple fluids in thin capillaries. In the case of "competing walls", where both walls prefer different phases of the two phases coexisting in the bulk, a state with an interface parallel to the walls gets stabilized. The transition from the disordered phase to this "soft mode phase" is rounded by the finite thickness of the film and not a sharp phase transition. However, a sharp transition can occur where this interface gets localized at (one of) the walls. The relation of this interface localization transition to wetting phenomena is discussed. Finally, an outlook to related phenomena is given, such as the effects of confinement in cylindrical pores on the phase behavior, and more complicated ordering phenomena (lamellar mesophases of block copolymers or nematic phases of liquid crystals under confinement).Comment: 25 pages, 17 figures, to be published in Soft Matte

Crystal structure and electronic states of tripotassium picene

The crystal structure of potassium doped picene with an exact stoichiometry (K3C22H14, K3picene from here onwards) has been theoretically determined within Density Functional Theory allowing complete variational freedom of the crystal structure parameters and the molecular atomic positions. A modified herringbone lattice is obtained in which potassium atoms are intercalated between two paired picene molecules displaying the two possible orientations in the crystal.Along the c-axis, organic molecules alternate with chains formed by three potassium atoms. The electronic structureof the doped material resembles pristine picene, except that now the bottom of the conduction band is occupied by six electrons coming from the ionized K atoms (six per unit cell). Wavefunctions remain based mainly on picene molecular orbitals getting their dispersion from intralayer edge to face CH/pi bonding, while eigenenergies have been modified by the change in the electrostatic potential. The small dispersion along the c-axis is assigned to small H-H overlap. From the calculated electronic density of states we expect metallic behavior for potassium doped picene.Comment: Published version: 8 twocolumn pages, 7 color figures, 2 structural .cif files include