Conformal expansions and renormalons

The large-order behaviour of QCD is dominated by renormalons. On the other hand renormalons do not occur in conformal theories, such as the one describing the infrared fixed-point of QCD at small beta_0 (the Banks--Zaks limit). Since the fixed-point has a perturbative realization, all-order perturbative relations exist between the conformal coefficients, which are renormalon-free, and the standard perturbative coefficients, which contain renormalons. Therefore, an explicit cancellation of renormalons should occur in these relations. The absence of renormalons in the conformal limit can thus be seen as a constraint on the structure of the QCD perturbative expansion. We show that the conformal constraint is non-trivial: a generic model for the large-order behaviour violates it. We also analyse a specific example, based on a renormalon-type integral over the two-loop running-coupling, where the required cancellation does occur.Comment: 10 pages, to appear in Phys. Lett.

On the renormalization of multiparton webs

We consider the recently developed diagrammatic approach to soft-gluon exponentiation in multiparton scattering amplitudes, where the exponent is written as a sum of webs - closed sets of diagrams whose colour and kinematic parts are entangled via mixing matrices. A complementary approach to exponentiation is based on the multiplicative renormalizability of intersecting Wilson lines, and their subsequent finite anomalous dimension. Relating this framework to that of webs, we derive renormalization constraints expressing all multiple poles of any given web in terms of lower-order webs. We examine these constraints explicitly up to four loops, and find that they are realised through the action of the web mixing matrices in conjunction with the fact that multiple pole terms in each diagram reduce to sums of products of lower-loop integrals. Relevant singularities of multi-eikonal amplitudes up to three loops are calculated in dimensional regularization using an exponential infrared regulator. Finally, we formulate a new conjecture for web mixing matrices, involving a weighted sum over column entries. Our results form an important step in understanding non-Abelian exponentiation in multiparton amplitudes, and pave the way for higher-loop computations of the soft anomalous dimension.Comment: 60 pages, 15 figure

Next generation flight management system for real-time trajectory based operations

This paper presents the concept of operations, architecture and trajectory optimisation algorithms of a Next Generation Flight Management System (NG-FMS). The NG-FMS is developed for Four Dimensional (4D) Intent Based Operations (IBO) in the next generation Communications, Navigation, Surveillance and Air Traffic Management system (CNS+A) context. The NG-FMS, primarily responsible for the aircraft navigation and guidance task, acts as a key enabler for achieving higher level of operational efficiency and mitigating environmental impacts both in manned and unmanned aircraft applications. The NG-FMS is interoperable with the future ground based 4DT Planning, Negotiation and Validation (4-PNV) systems, enabling automated Trajectory/Intent Based Operations (TBO/IBO). After the NG-FMS architecture is presented, the key mathematical models describing the trajectory generation and optimisation modes are introduced. A detailed error analysis is performed and the uncertainties affecting the nominal trajectories are studied to obtain the total NG-FMS error budgets. These are compared with the Required Navigation Performance (RNP) values for the various operational flight tasks considered

CNS+A capabilities for the integration of unmanned aircraft in controlled airspace

In this paper, the system requirements for the integration of Remotely Piloted Aircraft Systems (RPAS) in controlled airspace regions are discussed. The specificities in terms of Air Traffic Management (ATM) level of service, jurisdiction for deconfliction duties and prevalent traffic characteristics are analysed to support the identification of operational and equipage requirements for RPAS developers. Communication, Navigation, Surveillance, ATM and Avionics (CNS+A) equipment play an essential role in airspace regions characteried by high levels of Air Traffic Services (ATS) and a higher probability of traffic conflicts. A denser route structure and a more frequent occurrence of traffic conflicts mandate high CNS performance, as the deconfliction by ATM crucially relies on accurate and reliable CNS information. Notwithstanding, the reduced jurisdiction of aircraft in deconfliction duties also offers an opportunity to RPAS developers, as it relieves the requirements for on-board expert processing

Fixing the conformal window in QCD

A physical characterization of Landau singularities is emphasized, which should trace the lower boundary N_f^* of the conformal window in QCD and supersymmetric QCD. A natural way to disentangle ``perturbative'' from ``non-perturbative'' contributions to amplitudes below N_f^* is suggested. Assuming an infrared fixed point persists in the perturbative part of the QCD coupling even below N_f^* leads to the condition \gamma(N_f^*)=1, where \gamma is the critical exponent. Using the Banks-Zaks expansion, one gets 4<N_f^*<6. This result is incompatible with the existence of an analogue of Seiberg duality in QCD. The presence of a negative ultraviolet fixed point is required both in QCD and in supersymmetric QCD to preserve causality within the conformal window. Evidence for the existence of such a fixed point in QCD is provided.Comment: 10 pages, 1 figure, extended version of a talk given at the QCDNET2000 meeting, Paris, September 11-14 2000; main new material added is evidence for negative ultraviolet fixed point in QC

Real-time trajectory optimisation models for next generation air traffic management systems

This paper presents models and algorithms for real-time 4-Dimensional Flight Trajectory (4DT) operations in next generation Communications, Navigation, Surveillance/Air Traffic Management (CNS/ATM) systems. In particular, the models are employed for multi-objective optimisation of 4DT intents in ground-based 4DT Planning, Negotiation and Validation (4-PNV) systems and in airborne Next Generation Flight Management Systems (NG-FMS). The assumed timeframe convention for offline and online air traffic operations is introduced and discussed. The adopted formulation of the multi-objective 4DT optimisation problem includes a number of environmental objectives and operational constraints. In particular, the paper describes a real-time multi-objective optimisation algorithm and the generalised expression of the cost function adopted for penalties associated with specific airspace volumes, accounting for weather models, condensation trails models and noise models

Exploiting wind to optimize flight paths for greener commercial flight operations

Trajectory Based Operations (TBO) has been identified by ICAO as a key aviation evolution with significant developments in Next Gen Flight Management Systems (FMS) to communicate with ground based 4DT Air Traffic Management (ATM) system of the future. The Next generation ATM and FMS systems will include the capability of generating 4D trajectories to increase aircraft efficiency and reduce emissions. Natural resources, such as the wind, can be exploited to reduce the aircraft&#039;s fuel usage and travel time while improving its operational efficiency. These benefits are realized if trajectories are formulated to maximise the time in tailwind scenarios. The results presented here quantify the fuel and time savings of a typical Australasian route using a simulated wind field as an input to the optimization problem. Minimum fuel burn and emissions are achieved by minimising flight time at constant cruise speed. The attainable savings appeal to aircraft operators as they reduce operational cost. Optimization algorithms to formulate efficient flight trajectories are hence an essential tool in reducing aviation&#039;s carbon footprint. Future research will focus on the implementation of 4DT operations and associated logistics. Simulations of common commercial and international flight routes from departure to destination using 4DT intent negotiation and validation routines will allow for an accurate evaluation of the potential savings in fuel and reduction in emissions

Automated ATM system enabling 4DT-based operations

As part of the current initiatives aimed at enhancing safety, efficiency and environmental sustainability of aviation, a significant improvement in the efficiency of aircraft operations is currently pursued. Innovative Communication, Navigation, Surveillance and Air Traffic Management (CNS/ATM) technologies and operational concepts are being developed to achieve the ambitious goals for efficiency and environmental sustainability set by national and international aviation organizations. These technological and operational innovations will be ultimately enabled by the introduction of novel CNS/ATM and Avionics (CNS+A) systems, featuring higher levels of automation. A core feature of such systems consists in the real-time multi-objective optimization of flight trajectories, incorporating all the operational, economic and environmental aspects of the aircraft mission. This article describes the conceptual design of an innovative ground-based Air Traffic Management (ATM) system featuring automated 4-Dimensional Trajectory (4DT) functionalities. The 4DT planning capability is based on the multi-objective optimization of 4DT intents. After summarizing the concept of operations, the top-level system architecture and the key 4DT optimization modules, we discuss the segmentation algorithm to obtain flyable and concisely described 4DT. Simulation case studies in representative scenarios show that the adopted algorithms generate solutions consistently within the timeframe of online tactical rerouting tasks, meeting the set design requirements

Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach

We consider the problem of soft gluon resummation for gauge theory amplitudes and cross sections, at next-to-eikonal order, using a Feynman diagram approach. At the amplitude level, we prove exponentiation for the set of factorizable contributions, and construct effective Feynman rules which can be used to compute next-to-eikonal emissions directly in the logarithm of the amplitude, finding agreement with earlier results obtained using path-integral methods. For cross sections, we also consider sub-eikonal corrections to the phase space for multiple soft-gluon emissions, which contribute to next-to-eikonal logarithms. To clarify the discussion, we examine a class of log(1 - x) terms in the Drell-Yan cross-section up to two loops. Our results are the first steps towards a systematic generalization of threshold resummations to next-to-leading power in the threshold expansion.Comment: 66 pages, 19 figure

Novel ATM and avionic systems for environmentally sustainable aviation

Large-scale air transport modernisation initiatives including the Single European Sky Air Traffic Management Research (SESAR), Next Generation Air Transportation System (NextGen) and Clean Sky Joint Technology Initiative for Aeronautics and Air Transport aim to improve the operational efficiency, safety and environmental sustainability of aviation. Scientific advances in Air Transport Management (ATM) and avionic systems are required to achieve the ambitious goals set by national and international aviation organisations. This paper presents the recent advances in ATM and avionic system concepts, integrated architectures and trajectory generation algorithms, to be adopted in Next Generation Avionics Flight Management Systems (NG-FMS) and ground-based 4-Dimensional Trajectory Planning, Negotiation and Validation (4-PNV) systems. Current research efforts are focussed on the development of NG-FMS and 4-PNV systems for Four Dimensional (4D) Trajectory/Intent Based Operations (TBO/IBO), enabling automated negotiation and validation of aircraft intents and thus alleviating the workload of operators. After describing the NG-FMS/4PNV concept of operations, the overall system architecture and the key mathematical models describing the 4DT optimisation algorithms are introduced. Simulation case studies utilising realistic operational scenarios highlight the generation and optimisation of a family of 4DT intents by the NG-FMS corresponding to a set of performance weightings agreed between Air Navigation Service Providers (ANSP) and Airline Operation Centres (AOC). The savings on time, fuel burn and gaseous emissions (CO2 and NOx) associated with the globally optimal 4DT intents are presented. The developed optimisation and negotiation/validation loops meet the timeframe requirements of typical online tactical routing/rerouting tasks