Network-wide assessment of 4D trajectory adjustments using an agent-based model

This paper presents results from the SESAR ER3 Domino project. It focuses on an ECAC-wide assessment of two 4D-adjustment mechanisms, implemented separately and conjointly. These reflect flight behaviour en-route and at-gate, optimising given (cost) objective functions. New metrics designed to capture network effects are used to analyse the results of a microscopic, agent based model. The results show that some implementations of the mechanisms allow the protection of the network from ‘domino’ effects. Airlines focusing on costs may trigger additional side-effects on passengers, displaying, in some instances, clear trade-offs between passenger- and flight-centric metrics

Correlation, hierarchies, and networks in financial markets

We discuss some methods to quantitatively investigate the properties of correlation matrices. Correlation matrices play an important role in portfolio optimization and in several other quantitative descriptions of asset price dynamics in financial markets. Specifically, we discuss how to define and obtain hierarchical trees, correlation based trees and networks from a correlation matrix. The hierarchical clustering and other procedures performed on the correlation matrix to detect statistically reliable aspects of the correlation matrix are seen as filtering procedures of the correlation matrix. We also discuss a method to associate a hierarchically nested factor model to a hierarchical tree obtained from a correlation matrix. The information retained in filtering procedures and its stability with respect to statistical fluctuations is quantified by using the Kullback-Leibler distance.Comment: 37 pages, 9 figures, 3 table

Inverse cascade in Charney-Hasegawa-Mima turbulence

The inverse energy cascade in Charney-Hasegawa-Mima turbulence is investigated. Kolmogorov law for the third order velocity structure function is shown to be independent on the Rossby number, at variance with the energy spectrum, as shown by high resolution direct numerical simulations. In the asymptotic limit of strong rotation, coherent vortices are observed to form at a dynamical scale which slowly grows with time. These vortices form an almost quenched pattern and induce strong deviation form Gaussianity in the velocity field.Comment: 4 pages, 5 figure

Peripheral mixing of passive scalar at small Reynolds number

Mixing of a passive scalar in the peripheral region close to a wall is investigated by means of accurate direct numerical simulations of both a three-dimensional Couette channel flow at low Reynolds numbers and a two-dimensional synthetic flow. In both cases, the resulting phenomenology can be understood in terms of the theory recently developed by Lebedev and Turitsyn [Phys. Rev. E 69, 036301, 2004]. Our results prove the robustness of the identified mechanisms responsible for the persistency of scalar concentration close to the wall with important consequences in completely different fields ranging from microfluidic applications to environmental dispersion modeling.Comment: 4 pages, 5 figure

Strategic allocation of flight plans in air traffic management: an evolutionary point of view

We present a simplified model of the strategic allocation of trajectories in a generic airspace for commercial flights. In this model, two types of companies, characterised by different cost functions and different strategies, compete for the allocation of trajectories in the airspace. With an analytical model and numerical simulations, we show that the relative advantage of the two populations -- companies -- depends on external factors like traffic demand as well as on the composition of the population. We show that there exists a stable equilibrium state which depends on the traffic demand. We also show that the equilibrium solution is not the optimal at the global level, but rather that it tends to favour one of the two business models -- the archetype for low-cost companies. Finally, linking the cost of allocated flights with the fitness of a company, we study the evolutionary dynamics of the system, investigating the fluctuations of population composition around the equilibrium and the speed of convergence towards it. We prove that in the presence of noise due to finite populations, the equilibrium point is shifted and is reached more slowly

Point-particle method to compute diffusion-limited cellular uptake

We present an efficient point-particle approach to simulate reaction-diffusion processes of spherical absorbing particles in the diffusion-limited regime, as simple models of cellular uptake. The exact solution for a single absorber is used to calibrate the method, linking the numerical parameters to the physical particle radius and uptake rate. We study configurations of multiple absorbers of increasing complexity to examine the performance of the method, by comparing our simulations with available exact analytical or numerical results. We demonstrate the potentiality of the method in resolving the complex diffusive interactions, here quantified by the Sherwood number, measuring the uptake rate in terms of that of isolated absorbers. We implement the method in a pseudo-spectral solver that can be generalized to include fluid motion and fluid-particle interactions. As a test case of the presence of a flow, we consider the uptake rate by a particle in a linear shear flow. Overall, our method represents a powerful and flexible computational tool that can be employed to investigate many complex situations in biology, chemistry and related sciences.Comment: 13 pages, 13 figure

Large-scale confinement and small-scale clustering of floating particles in stratified turbulence

We study the motion of small inertial particles in stratified turbulence. We derive a simplified model, valid within the Boussinesq approximation, for the dynamics of small particles in presence of a mean linear density profile. By means of extensive direct numerical simulations, we investigate the statistical distribution of particles as a function of the two dimensionless parameters of the problem. We find that vertical confinement of particles is mainly ruled by the degree of stratification, with a weak dependency on the particle properties. Conversely, small scale fractal clustering, typical of inertial particles in turbulence, depends on the particle relaxation time and is almost independent on the flow stratification. The implications of our findings for the formation of thin phytoplankton layers are discussed.Comment: 5 pages, 6 figure

Instabilities in multi-asset and multi-agent market impact games

We consider the general problem of a set of agents trading a portfolio of assets in the presence of transient price impact and additional quadratic transaction costs and we study, with analytical and numerical methods, the resulting Nash equilibria. Extending significantly the framework of Schied and Zhang (2019) and Luo and Schied (2020), who considered the single asset case, we prove the existence and uniqueness of the corresponding Nash equilibria for the related mean-variance optimization problem. We then focus our attention on the conditions on the model parameters making the trading profile of the agents at equilibrium, and as a consequence the price trajectory, wildly oscillating and the market unstable. While Schied and Zhang (2019) and Luo and Schied (2020) highlighted the importance of the value of transaction cost in determining the transition between a stable and an unstable phase, we show that also the scaling of market impact with the number of agents J and the number of assets M determines the asymptotic stability (in J and M) of markets

Instabilities in multi-asset and multi-agent market impact games

We consider the general problem of a set of agents trading a portfolio of assets in the presence of transient price impact and additional quadratic transaction costs and we study, with analytical and numerical methods, the resulting Nash equilibria. Extending significantly the framework of Schied and Zhang (2019) and Luo and Schied (2020), who considered the single asset case, we prove the existence and uniqueness of the corresponding Nash equilibria for the related mean-variance optimization problem. We then focus our attention on the conditions on the model parameters making the trading profile of the agents at equilibrium, and as a consequence the price trajectory, wildly oscillating and the market unstable. While Schied and Zhang (2019) and Luo and Schied (2020) highlighted the importance of the value of transaction cost in determining the transition between a stable and an unstable phase, we show that also the scaling of market impact with the number of agents J and the number of assets M determines the asymptotic stability (in J and M) of markets