New fuzzy spheres through confining potentials and energy cutoffs

We briefly report our recent construction of new fuzzy spheres of dimensions d=1,2 covariant under the full orthogonal group O(D), D=d+1. They are built by imposing a suitable energy cutoff on a quantum particle in D dimensions subject to a confining potential well V(r) with a very sharp minimum on the sphere of radius r=1; furthermore, the cutoff and the depth of the well depend on (and diverge with) a natural number L. The commutator of the coordinates depends only on the angular momentum, as in Snyder noncommutative spaces. When L diverges, the Hilbert space dimension diverges, too; S^d_L converges to S^d, and we recover ordinary quantum mechanics on S^d. These models might be useful in quantum field theory, quantum gravity or condensed matter physics.Comment: Latex file, 13 pages, 2 figures. Contribution to the proceedings of the Corfu Summer Institute "School and Workshops on Elementary Particle Physics and Gravity", 2-28 September 2017, Corfu, Greece. Version 3: some misprints in the published version are correcte

The xix_i-eigenvalue problem on some new fuzzy spheres

We study the eigenvalue equation for the 'Cartesian coordinates' observables $x_i$ on the fully $O(2)$-covariant fuzzy circle $\{S^1_\Lambda\}_{\Lambda\in\mathbb{N}}$ ($i=1,2$) and on the fully $O(3)$-covariant fuzzy 2-sphere $\{S^2_\Lambda\}_{\Lambda\in\mathbb{N}}$ ($i=1,2,3$) introduced in [G. Fiore, F. Pisacane, J. Geom. Phys. 132 (2018), 423-451]. We show that the spectrum and eigenvectors of $x_i$ fulfill a number of properties which are expected for $x_i$ to approximate well the corresponding coordinate operator of a quantum particle forced to stay on the unit sphere.Comment: 28 pages. Version 3: some misprints are correcte

Fuzzy circle and new fuzzy sphere through confining potentials and energy cutoffs

Guided by ordinary quantum mechanics we introduce new fuzzy spheres of dimensions d=1,2: we consider an ordinary quantum particle in D=d+1 dimensions subject to a rotation invariant potential well V(r) with a very sharp minimum on a sphere of unit radius. Imposing a sufficiently low energy cutoff to `freeze' the radial excitations makes only a finite-dimensional Hilbert subspace accessible and on it the coordinates noncommutative \`a la Snyder; in fact, on it they generate the whole algebra of observables. The construction is equivariant not only under rotations - as Madore's fuzzy sphere -, but under the full orthogonal group O(D). Making the cutoff and the depth of the well dependent on (and diverging with) a natural number L, and keeping the leading terms in 1/L, we obtain a sequence S^d_L of fuzzy spheres converging (in a suitable sense) to the sphere S^d as L diverges (whereby we recover ordinary quantum mechanics on S^d). These models may be useful in condensed matter problems where particles are confined on a sphere by an (at least approximately) rotation-invariant potential, beside being suggestive of analogous mechanisms in quantum field theory or quantum gravity.Comment: Latex file, 43 pages, 2 figures. We have added references and made other minor improvements. To appear in J. Geom. Phy

Modules over the Noncommutative Torus and Elliptic Curves

Using the Weil-Brezin-Zak transform of solid state physics, we describe line bundles over elliptic curves in terms of Weyl operators. We then discuss the connection with finitely-generated projective modules over the algebra $A_\theta$ of the noncommutative torus. We show that such $A_\theta$-modules have a natural interpretation as Moyal deformations of vector bundles over an elliptic curve $E_\tau$, under the condition that the deformation parameter $\theta$ and the modular parameter $\tau$ satisfy a non-trivial relation.Comment: 16 pages, no figures; v2: minor correction

Self-similar transport processes in a two-dimensional realization of multiscale magnetic field turbulence

We present the results of a numerical investigation of charged-particle transport across a synthesized magnetic configuration composed of a constant homogeneous background field and a multiscale perturbation component simulating an effect of turbulence on the microscopic particle dynamics. Our main goal is to analyze the dispersion of ideal test particles faced to diverse conditions in the turbulent domain. Depending on the amplitude of the background field and the input test particle velocity, we observe distinct transport regimes ranging from subdiffusion of guiding centers in the limit of Hamiltonian dynamics to random walks on a percolating fractal array and further to nearly diffusive behavior of the mean-square particle displacement versus time. In all cases, we find complex microscopic structure of the particle motion revealing long-time rests and trapping phenomena, sporadically interrupted by the phases of active cross-field propagation reminiscent of Levy-walk statistics. These complex features persist even when the particle dispersion is diffusive. An interpretation of the results obtained is proposed in connection with the fractional kinetics paradigm extending the microscopic properties of transport far beyond the conventional picture of a Brownian random motion. A calculation of the transport exponent for random walks on a fractal lattice is advocated from topological arguments. An intriguing indication of the topological approach is a gap in the transport exponent separating Hamiltonian-like and fractal random walk-like dynamics, supported through the simulation.Comment: 10 pages (including cover page), 7 figures, improved content, accepted for publication in Physica Script

Reduced particle settling speed in turbulence

We study the settling of finite-size rigid spheres in sustained homogeneous isotropic turbulence (HIT) by direct numerical simulations using an immersed boundary method to account for the dispersed solid phase. We study semi-dilute suspensions at different Galileo numbers, Ga. The Galileo number is the ratio between buoyancy and viscous forces, and is here varied via the solid-to-fluid density ratio. The focus is on particles that are slightly heavier than the fluid. We find that in HIT, the mean settling speed is less than that in quiescent fluid; in particular, it reduces by 6%-60% with respect to the terminal velocity of an isolated sphere in quiescent fluid as the ratio between the latter and the turbulent velocity fluctuations is decreased. Analysing the fluid-particle relative motion, we find that the mean settling speed is progressively reduced while reducing the density ratio due to the increase of the vertical drag induced by the particle cross-flow velocity. Unsteady effects contribute to the mean overall drag by about 6%-10%. The probability density functions of particle velocities and accelerations reveal that these are closely related to the features of the turbulent flow. The particle mean-square displacement in the settling direction is found to be similar for all Ga if time is scaled by (2a)/u' (where 2a is the particle diameter and u' is the turbulence velocity root mean square).Comment: Accepted for publication in Journal of Fluid Mechanic

Continuous Growth of Droplet Size Variance due to Condensation in Turbulent Clouds

We use a stochastic model and direct numerical simulation to study the impact of turbulence on cloud droplet growth by condensation. We show that the variance of the droplet size distribution increases in time as t^{1/2}, with growth rate proportional to the large-to-small turbulent scale separation and to the turbulence integral scales but independent of the mean turbulent dissipation. Direct numerical simulations confirm this result and produce realistically broad droplet size spectra over time intervals of 20 minutes, comparable with the time of rain formation.Comment: 5 pages, 3 figures+Supplemental material 6 pages, 5 figure

Recupero di un ex-serbatoio dell’acqua a Medellín, Colombia. Transformation of Medellín Water Reservoir, Colombia

La trasformazione delle riserve idriche di Medellín dimostra come una serie di vecchie infrastrutture dell’acqua, per lo più escluse dai quartieri in cui si trovano, possano diventare al contempo spazi della socialità in grado di rivitalizzare gli agglomerati esistenti, pur conservando la funzione per la quale sono nate. Si tratta del programma municipale Unidades de Vida Articulada (UVA), che prevede lo sviluppo di spazi e attrezzature pubblici nelle aree che ospitano le riserve di acqua dell’acquedotto comunale e i campetti sportivi. Nato nel 2013 e sviluppato dal Grupo EPM Empresas e da INDER, il progetto ha intravisto nel riuso delle vecchie infrastrutture idriche industriali e dei campetti da gioco, circa un centinaio di lotti che popolano la città, l’occasione per far fronte alla carenza di servizi e spazi pubblici.The transformation of Medellin’s water reservoirs demonstrates how a series of old water infrastructures, more isolated from the neighbourhoods in which they are located, can become a space of social interaction with the power to revitalize existing settlements, while conserving their original function. The project is part of the Unidades de Vida Articulada (UVA) municipal program for the development of public spaces and facilities in areas hosting reservoirs serving the municipal aqueduct and playing fields. Created in 2013 and developed by the Grupo EPM Empresas and INDER, the project saw the reuse of old industrial water infrastructures and playing fields – approximately 100 lots across the city – as an occasion to confront a lack of public services and spaces

INVESTIGATION OF CHEMICAL DIFFERENCES IN MEDICATIONS OBTAINED FROM DIVERSE SOURCES USING NOVEL SPECTROSCOPIC AND STATISTIC APPROACHES

Generic medications are those medicines manufactured by a pharmaceutical company without a license from the company that has first invented and patented the same drug, when the related patent and other exclusivity rights have expired. Only studies of bioequivalence are requested as requirements to introduce a new generic medication in clinics, making easier and financially attractive for many pharmaceutical companies to participate in this typology of market. Organised criminality is strongly attracted by this market both for the high profitability, and for the high similarity to the production and trafficking of illegal controlled substances associated to the extreme difficulties faced by the law enforcement authorities in effectively investigating the online market, because of its anonymity. A significant paradigm continuously frequented in pharmacology is the confliction between views on generic medications that can be used interchangeably with the original medicines. Several clinical studies conducted in certain medical areas have shown as the generic medications present an overlapping therapeutic equivalence to the original ones. On the contrary, for certain other generics, both pharmacokinetics and pharmacodynamics issue have been reported. Also, in some cases issues on the stability of generics have been raised. Despite the numerous research articles and reviews published on the matter of clinical equivalence among generic and original medications, no study to the scientific community has been presented on an analytical evaluation of the chemical composition of the different generic drugs that could shed some lights on the reason of the different clinical performances reported. The main aim of this research was to develop a non-destructive quick qualitative analytical methodology to be able to discriminate differences in the chemical composition from generic medicines that have been reported not presenting similar therapeutic equivalence in clinical comparison studies, obtained from authorised pharmacies and non-authorised online sellers. From the cardio-vascular area, digoxin (with the related cardiac glycosides digitoxin and digoxigenin) and amlodipine (in its different salts maleate, mesylate and besylate used in therapies). In the gastroenterology area, omeprazole both in its racemic and isomeric forms, have been selected as samples to be analysed. In the antihistamine area, cetirizine, in its racemic and isomeric forms, equally for the same reasons as before, have been considered. As starting analytical approaches, voltammetry, FT-IR, Raman spectroscopies and NMR have been considered and a statistical data analysis approach of the analytical data obtained based on multivariate analysis such as principal component analysis, cross validation, correlation scatter plots and factor loadings has been implemented. This work has matched the aims initially set, generating novel methods of analysis to investigate differences in the chemical composition within different groups of generic medications. This study has led to the creation and interpretation of new knowledge, through a systematic acquisition and understanding of a substantial body of scientific literature and through original research, and adjusting the project design in the light of unforeseen problems, conceptualizing, designing and implementing the research project for the generation of novel knowledge

The effect of the Basset history force on particle clustering in Homogeneous and Isotropic Turbulence

We study the effect of the Basset history force on the dynamics of small particles transported in homogeneous and isotropic turbulence and show that this term, often neglected in previous numerical studies, reduces the small-scale clustering typical of inertial particles. The contribution of this force to the total particle acceleration is, on average, responsible for about 10% of the total acceleration and particularly relevant during rare strong events. At moderate density ratios, i.e. sand or metal powder in water, its presence alters the balance of forces determining the particle acceleration