Clustering of Dynamical Systems

In this work, we address the problem of community detection in a graph whose connectivity is given by probabilities (denoted by numbers between zero and one) rather than an adjacency matrix (only 0 or 1). The graphs themselves come from partitions of a dynamical system's state space where the probabilities denote likely transition pathways for dynamics. We propose a modification of the Leicht-Newman algorithm \cite{Leicht2008} which is able to automatically detect communities of strongly intra-connected points in state space, from which information about the residence time of the system and its principal periodicities can be extracted. Furthermore, a novel algorithm to construct the transition rate matrix of a dynamical system which encodes the time dependency of its Perron-Frobenius operator, is developed. Crucially, it overcomes the issue of time-scale separation stemming from the matrix construction based on {\it{infinitesimal}} generators and the exploration of {\it{long-term}} features of the underlying dynamical system. This method is then tested on a range of dynamical systems and datasets

Higher order Laguerre-Gauss mode degeneracy in realistic, high finesse cavities

Higher order Laguerre-Gauss (LG) beams have been proposed for use in future gravitational wave detectors, such as upgrades to the Advanced LIGO detectors and the Einstein Telescope, for their potential to reduce the effects of the thermal noise of the test masses. This paper details the theoretical analysis and simulation work carried out to investigate the behaviour of LG beams in realistic optical setups, in particular the coupling between different LG modes in a linear cavity. We present a new analytical approximation to compute the coupling between modes, using Zernike polynomials to describe mirror surface distortions. We apply this method in a study of the behaviour of the LG33 mode within realistic arm cavities, using measured mirror surface maps from the Advanced LIGO project. We show mode distortions that can be expected to arise due to the degeneracy of higher order spatial modes within such cavities and relate this to the theoretical analysis. Finally we identify the mirror distortions which cause significant coupling from the LG33 mode into other order 9 modes and derive requirements for the mirror surfaces.Comment: 12 pages Submitted to PRD 19/07/201

Subdynamics as a mechanism for objective description

The relationship between microsystems and macrosystems is considered in the context of quantum field formulation of statistical mechanics: it is argued that problems on foundations of quantum mechanics can be solved relying on this relationship. This discussion requires some improvement of non-equilibrium statistical mechanics that is briefly presented.Comment: latex, 15 pages. Paper submitted to Proc. Conference "Mysteries, Puzzles And Paradoxes In Quantum Mechanics, Workshop on Entanglement And Decoherence, Palazzo Feltrinelli, Gargnano, Garda Lake, Italy, 20-25 September, 199

Experimental Scattershot Boson Sampling

Boson Sampling is a computational task strongly believed to be hard for classical computers, but efficiently solvable by orchestrated bosonic interference in a specialised quantum computer. Current experimental schemes, however, are still insufficient for a convincing demonstration of the advantage of quantum over classical computation. A new variation of this task, Scattershot Boson Sampling, leads to an exponential increase in speed of the quantum device, using a larger number of photon sources based on parametric downconversion. This is achieved by having multiple heralded single photons being sent, shot by shot, into different random input ports of the interferometer. Here we report the first Scattershot Boson Sampling experiments, where six different photon-pair sources are coupled to integrated photonic circuits. We employ recently proposed statistical tools to analyse our experimental data, providing strong evidence that our photonic quantum simulator works as expected. This approach represents an important leap toward a convincing experimental demonstration of the quantum computational supremacy.Comment: 8 pages, 5 figures (plus Supplementary Materials, 14 pages, 8 figures

Electric winds driven by time oscillating corona discharges

We investigate the formation of steady gas flows—so-called electric winds—created by point-plane corona discharges driven by time oscillating (ac) electric fields. By varying the magnitude and frequency of the applied field, we identify two distinct scaling regimes: (i) a low frequency (dc) regime and (ii) a high frequency (ac) regime. These experimental observations are reproduced and explained by a theoretical model describing the transport and recombination of ions surrounding the discharge and their contribution to the measured wind velocity. The two regimes differ in the spatial distribution of ions and in the process by which ions are consumed. Interestingly, we find that ac corona discharges generate strong electric forces localized near the tip of the point electrode, while dc corona discharges generate weaker forces distributed throughout the interelectrode region. Consequently, the velocity of the electric winds (>1 m/s) generated by ac discharges is largely independent of the position of the counter electrode. The unified theoretical description of dc and ac electric winds presented here reconciles previous observations of winds driven by dc corona and ac dielectric barrier discharges; insights from the model should also prove useful in the design of other plasma actuators.Chemistry and Chemical Biolog

Evidence-based Recommendations on Periodontal Practice and the Management of Periodontal Patients During and After the COVID-19 Era: Challenging Infectious Diseases Spread by Airborne Transmission

Background: Periodontal care, which was completely suspended during the peak of the SARS-Cov-2 pandemic and was delayed and recurrently discontinued during the succeeding waves, must be safely provided in the COVID-19 era. Objectives: The study aimed to provide recommendations on periodontal practice, optimizing safety, ergonomics, and economic resources, and the management of periodontal patients, ensuring continuity, timing, and effectiveness of periodontal care in the COVID-19 era. Methods: Reported protocols for the dental practice in the context of the COVID-19 and current evidence on periodontitis treatment and prevention were reviewed. Results: Evidence-based recommendations on contamination control and ergonomic improvements for periodontal practice and the management of periodontal patients challenging COVID-19 and airborne infectious diseases have been provided. Conclusion: Due to the economic, ergonomic, and ethical concerns raised by limited periodontal care due to the SARS-Cov-2 pandemic, and awareness of other emerging airborne transmitted infections, the periodontal practice should integrate measures minimizing airborne cross-infections and optimizing time-space and economic resources. The management of periodontal patients in the COVID-19 era should comprise less complex treatments and more comprehensive and definitive approaches, reducing emergencies, session length and number, and, concurrently, extending the recall and maintenance intervals. Moreover, it should implement prevention strategies through teledentistry tools and apps, improving periodontal awareness and self-care, and also through the self-reporting of periodontitis and periodontal risk assessment tools, performing both "population-based" and "high-risk" surveillance of periodontitis. Finally, it should enhance inter-professional collaboration, through telehealth networks, especially targeting subjects at high-risk of both periodontitis and systemic disorders, each of the two variously linked to COVID-19 onset and worsening

Survey of Materials for Nanoskiving and Influence of the Cutting Process on the Nanostructures Produced

This paper examines the factors that influence the quality of nanostructures fabricated by sectioning thin films with an ultramicrotome (“nanoskiving”). It surveys different materials (metals, ceramics, semiconductors, and conjugated polymers), deposition techniques (evaporation, sputter deposition, electroless deposition, chemical-vapor deposition, solution-phase synthesis, and spin-coating), and geometries (nanowires or two-dimensional arrays of rings and crescents). It then correlates the extent of fragmentation of the nanostructures with the composition of the thin films, the methods used to deposit them, and the parameters used for sectioning. There are four major conclusions. (i) Films of soft and compliant metals (those that have bulk values of hardness less than or equal to those of palladium, or ≤500 MPa) tend to remain intact upon sectioning, whereas hard and stiff metals (those that have values of hardness greater than or equal to those of platinum, or ≥500 MPa) tend to fragment. (ii) All conjugated polymers tested form intact nanostructures. (iii) The extent of fragmentation is lowest when the direction of cutting is perpendicular to the exposed edge of the embedded film. (iv) The speed of cutting−from 0.1 to 8 mm/s−has no effect on the frequency of defects. Defects generated during sectioning include scoring from defects in the knife, delamination of the film from the matrix, and compression of the matrix. The materials tested were: aluminum, titanium, nickel, copper, palladium, silver, platinum, gold, lead, bismuth, germanium, silicon dioxide ($\textrm{SiO}_2$), alumina ($\textrm{Al}_2\textrm{O}_3$), tin-doped indium oxide (ITO), lead sulfide nanocrystals, the semiconducting polymers poly(2-methoxy-5-(2′-ethyl-hexyloxy)-1,4-phenylene vinylene) (MEH-PPV), poly(3-hexylthiophene) (P3HT), and poly(benzimidazobenzophenanthroline ladder) (BBL), and the conductive polymer poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS).Chemistry and Chemical Biolog

Incoherent dynamics in neutron-matter interaction

Coherent and incoherent neutron-matter interaction is studied inside a recently introduced approach to subdynamics of a macrosystem. The equation describing the interaction is of the Lindblad type and using the Fermi pseudopotential we show that the commutator term is an optical potential leading to well-known relations in neutron optics. The other terms, usually ignored in optical descriptions and linked to the dynamic structure function of the medium, give an incoherent contribution to the dynamics, which keeps diffuse scattering and attenuation of the coherent beam into account, thus warranting fulfilment of the optical theorem. The relevance of this analysis to experiments in neutron interferometry is briefly discussed.Comment: 15 pages, revtex, no figures, to appear in Phys. Rev.