Cosmic branes and asymptotic structure

Superrotations of asymptotically flat spacetimes in four dimensions can be interpreted in terms of including cosmic strings within the phase space of allowed solutions. In this paper we explore the implications of the inclusion of cosmic branes on the asymptotic structure of vacuum spacetimes in dimension d > 4. We first show that only cosmic (d-3)-branes are Riemann flat in the neighbourhood of the brane, and therefore only branes of such dimension passing through the celestial sphere can respect asymptotic local flatness. We derive the asymptotically locally flat boundary conditions associated with including cosmic branes in the phase space of solutions. We find the asymptotic expansion of vacuum spacetimes in d=5 with such boundary conditions; the expansion is polyhomogenous, with logarithmic terms arising at subleading orders in the expansion. The asymptotically locally flat boundary conditions identified here are associated with an extended asymptotic symmetry group, which may be relevant to soft scattering theorems and memory effects.Comment: 52 pages; v2, minor additions, published versio

The Mott Metal-Insulator transition in the half-filled Hubbard model on the Triangular Lattice

We investigate the metal-insulator transition in the half-filled Hubbard model on a two-dimensional triangular lattice using both the Kotliar-Ruckenstein slave-boson technique, and exact numerical diagonalization of finite clusters. Contrary to the case of the square lattice, where the perfect nesting of the Fermi surface leads to a metal-insulator transition at arbitrarily small values of U, always accompanied by antiferromagnetic ordering, on the triangular lattice, due to the lack of perfect nesting, the transition takes place at a finite value of U, and frustration induces a non-trivial competition among different magnetic phases. Indeed, within the mean-field approximation in the slave-boson approach, as the interaction grows the paramagnetic metal turns into a metallic phase with incommensurate spiral ordering. Increasing further the interaction, a linear spin-density-wave is stabilized, and finally for strong coupling the latter phase undergoes a first-order transition towards an antiferromagnetic insulator. No trace of the intermediate phases is instead seen in the exact diagonalization results, indicating a transition between a paramagnetic metal and an antiferromagnetic insulator.Comment: 5 pages, 4 figure

Dynamical behavior across the Mott transition of two bands with different bandwidths

We investigate the role of the bandwidth difference in the Mott metal-insulator transition of a two-band Hubbard model in the limit of infinite dimensions, by means of a Gutzwiller variational wave function as well as by dynamical mean-field theory. The variational calculation predicts a two-stage quenching of the charge degrees of freedom, in which the narrower band undergoes a Mott transition before the wider one, both in the presence and in the absence of a Hund's exchange coupling. However, this scenario is not fully confirmed by the dynamical mean-field theory calculation, which shows that, although the quasiparticle residue of the narrower band is zero within our numerical accuracy, low-energy spectral weight still exists inside the Mott-Hubbard gap, concentrated into two peaks symmetric around the chemical potential. This spectral weight vanishes only when the wider band ceases to conduct too. Although our results are compatible with several scenarios, e.g., a narrow gap semiconductor or a semimetal, we argue that the most plausible one is that the two peaks coexist with a narrow resonance tied at the chemical potential, with a spectral weight below our numerical accuracy. This quasiparticle resonance is expected to vanish when the wider band undergoes the Mott transition.Comment: 11 pages, 12 figure

Inferring Synaptic Structure in presence of Neural Interaction Time Scales

Biological networks display a variety of activity patterns reflecting a web of interactions that is complex both in space and time. Yet inference methods have mainly focused on reconstructing, from the network's activity, the spatial structure, by assuming equilibrium conditions or, more recently, a probabilistic dynamics with a single arbitrary time-step. Here we show that, under this latter assumption, the inference procedure fails to reconstruct the synaptic matrix of a network of integrate-and-fire neurons when the chosen time scale of interaction does not closely match the synaptic delay or when no single time scale for the interaction can be identified; such failure, moreover, exposes a distinctive bias of the inference method that can lead to infer as inhibitory the excitatory synapses with interaction time scales longer than the model's time-step. We therefore introduce a new two-step method, that first infers through cross-correlation profiles the delay-structure of the network and then reconstructs the synaptic matrix, and successfully test it on networks with different topologies and in different activity regimes. Although step one is able to accurately recover the delay-structure of the network, thus getting rid of any \textit{a priori} guess about the time scales of the interaction, the inference method introduces nonetheless an arbitrary time scale, the time-bin $dt$ used to binarize the spike trains. We therefore analytically and numerically study how the choice of $dt$ affects the inference in our network model, finding that the relationship between the inferred couplings and the real synaptic efficacies, albeit being quadratic in both cases, depends critically on $dt$ for the excitatory synapses only, whilst being basically independent of it for the inhibitory ones

Off-equilibrium confined dynamics in a glassy system with level-crossing states

We study analytically the dynamics of a generalized p-spin model, starting with a thermalized initial condition. The model presents birth and death of states, hence the dynamics (even starting at equilibrium) may go out of equilibrium when the temperature is varied. We give a full description of this constrained out of equilibrium behavior and we clarify the connection to the thermodynamics by computing (sub-dominant) TAP states, constrained to the starting equilibrium configuration.Comment: 10 pages, 3 figures; longer version with appendi

Phase Space Renormalization and Finite BMS Charges in Six Dimensions

We perform a complete and systematic analysis of the solution space of six-dimensional Einstein gravity. We show that a particular subclass of solutions -- those that are analytic near $\mathcal{I}^+$ -- admit a non-trivial action of the generalised Bondi-Metzner-van der Burg-Sachs (GBMS) group which contains \emph{infinite-dimensional} supertranslations and superrotations. The latter consists of all smooth volume-preserving Diff$\times$Weyl transformations of the celestial $S^4$. Using the covariant phase space formalism and a new technique which we develop in this paper (phase space renormalization), we are able to renormalize the symplectic potential using counterterms which are \emph{local} and \emph{covariant}. We then construct charges which faithfully represent the GBMS algebra and in doing so, settle a long-standing open question regarding the existence of GBMS symmetries in higher dimensional non-linear gravity. Finally, we show that the semi-classical Ward identities for the supertranslations and superrotations are precisely the leading and subleading soft-graviton theorems respectively.Comment: 75 pages, 1 figur

Implementation of a Comprehensive Mathematical Model for Tilt-Rotor Real-Time Flight Simulation

This paper aims at describing the effort performed by the joint research group of Politecnico di Torino and ZHAW (Zurich University of Applied Sciences) in achieving a novel implementation of a mathematical model for real-time flight simulation of tilt-rotors and tilt-wings aircraft. The focus is on the description of the current stage of the project, the achievements of the first version of the model, on-going improvements and future developments. The first part of the work describes the initial development of the overall simulation model: relying on several NASA reports on the Generic Tilt Rotor Simulator (GTRS), the mathematical model is revised and the rotor dynamic model is improved in order to enhance computational performance. In particular, the model uses the conventional mathematical formulation for non-dynamic inflow modelling based on Blade Element Momentum Theory. A novel but simple numerical method is used to ensure the convergence of the non-linear equation in every tested condition. The resulting simulation model and its development and implementation in the MATLAB/Simulink® environment is described. The second part of the work deals with the integration of the model in the ZHAW Research and Didactics Simulator (ReDSim), the replacement of the pilot controls by the introduction of a center stick and the corresponding adjustment of the force-feel system to suitable values for the tilt-rotor model. Subsequently, several pilot tests are carried out and preliminary feedbacks about the overall behaviour of the system are collected. Limits and weaknesses of the first release of the model are investigated and future necessary improvements are assessed, such as the development of a novel generic prop-rotor mathematical model. The third part introduces the novel multi-purpose rotor mathematical model which was developed to improve the overall tilt-rotor simulation model. The multi-purpose rotor model implements non-approximated flapping dynamics and inflow dynamic based on Pitt-Peters formulation. The validation of the novel rotor model is carried out with available data of both the XV-15 Research Aircraft and the UH-60 Helicopter

A methodology for preliminary performance estimation of a hybrid-electric tilt-wing aircraft for emergency medical services

This paper aims to provide a simple methodology to preliminary size a hybrid-electric propulsion system for large scale piloted, optionally piloted or unmanned tilt-wing aircraft. In this work, the author refers to three mission profile representative of an Emergency Medical Service (EMS) operation and estimate the performance of the aircraft along the mission. Thus, based on some assumptions on battery technology, architecture of the hybrid system and mission safety requirements, a methodology for preliminary performance estimation is described and results for a baseline architecture are presented. Based on present and near future battery technology (in terms of charge/discharge rates and energy density), the present study shows how safety requirements can strongly affect the overall size of the power-plant system and impact the feasibility of hybrid-electric technology in aeronautical applications

Design and integration of a tilt-rotor flight simulation platform

This paper introduces a tilt-rotor flight simulation platform for research and teaching purposes implementing a real-time simulation of the Bell XV-15 aircraft. The mathematical model of the XV-15 aircraft has been implemented including simplified models for the aerodynamics of the whole aircraft, rotors, and engine dynamics. Hence, the simulation is performed in a graphic environment to reproduce the simulated flight and to interact with it using commands given by the pilot. The simulation platform is implemented using MATLAB/Simulink®, while the input commands are set using USB peripherals, i.e., a flight stick and a pedal board. Instead, the visualization environment is performed using FlightGear, an open-source and cross-platform software that is widely used in research. The result is a portable tilt-rotor simulator to be executed on a commercial pc, while ensuring real-time performance. The tilt-rotor flight simulator is also validated by a licensed helicopter pilot returning positive feedback regarding the flight experience

Mathematical modelling of gimballed tilt-rotors for real-time flight simulation

This paper introduces a novel gimballed rotor mathematical model for real-time flight simulation of tilt-rotor aircraft and other vertical take-off and landing (VTOL) concepts, which improves the previous version of a multi-purpose rotor mathematical model developed by ZHAW and Politecnico di Torino as part of a comprehensive flight simulation model of a tilt-rotor aircraft currently implemented in the Research and Didactics Simulator of ZHAW and used for research activities such as handling qualities studies and flight control systems development. In the novel model, a new formulation of the flapping dynamics is indroduced to account for the gimballed rotor and better suit current tilt-rotor designs (XV-15, V-22, AW-609). This paper describes the mathematical model and provides a generic formulation as well as a specific one for 3-blades proprotors. The method expresses the gimbal attitude but also considers the variation of each blade’s flapping due to the elasticity of the blades, so that the rotor coning angle can be represented. A validation of the mathematical model is performed against the available literature on the XV-15 Tilt-rotor aircraft and a comparison between the previous model is provided to show the improvements achieved. The results show a good correlation between the model and the reference data and the registered performance allow real-time flight simulation with pilot and hardware in the loop