Sandro Rambaldi

Statistical laws in urban mobility from microscopic GPS data in the area of Florence

The application of Statistical Physics to social systems is mainly related to the search for macroscopic laws that can be derived from experimental data averaged in time or space, assuming the system in a steady state. One of the major goals would be to find a connection between the statistical laws and the microscopic properties: for example, to understand the nature of the microscopic interactions or to point out the existence of interaction networks. Probability theory suggests the existence of a few classes of stationary distributions in the thermodynamics limit, so that the question is if a statistical physics approach could be able to enroll the complex nature of the social systems. We have analyzed a large GPS database for single-vehicle mobility in the Florence urban area, obtaining statistical laws for path lengths, for activity downtimes and for activity degrees. We show also that simple generic assumptions on the microscopic behavior could explain the existence of stationary macroscopic laws, with a universal function describing the distribution. Our conclusion is that understanding the system complexity requires a dynamical database for the microscopic evolution, which allows us to solve both small space and time scales in order to study the transients.

An accurate fractional Brownian motion generator

A new algorithm for the simulation of fractional Brownian motion is suggested. This algorithm has been tested and compared with previous ones. Clear improvements in the statistical and scaling properties of the process, built with our algorithm, are shown. Large improvements have been achieved for short times and for Hursts exponents less then 0.5, i.e. for path with high fractal dimension. A new strategy to generate fractional Brownian motions, based on the use of moments of increasing size blocks, is then described. This numerical method proved to be fast and accurate.

A stochastic model of randomly accelerated walkers for human mobility

Recent studies of human mobility largely focus on displacements patterns and power law fits of empirical long-tailed distributions of distances are usually associated to scale-free superdiffusive random walks called Lévy flights. However, drawing conclusions about a complex system from a fit, without any further knowledge of the underlying dynamics, might lead to erroneous interpretations. Here we show, on the basis of a data set describing the trajectories of 780,000 private vehicles in Italy, that the Lévy flight model cannot explain the behaviour of travel times and speeds. We therefore introduce a class of accelerated random walks, validated by empirical observations, where the velocity changes due to acceleration kicks at random times. Combining this mechanism with an exponentially decaying distribution of travel times leads to a short-tailed distribution of distances which could indeed be mistaken with a truncated power law. These results illustrate the limits of purely descriptive models and provide a mechanistic view of mobility.

Entropic measures of individual mobility patterns

Department of Mathematics, University of BolognaE-mail: rgallotti@gmail.comAbstract. Understanding human mobility from a microscopic point of view mayrepresent a fundamental breakthrough for the development of a statistical physics forcognitive systems and it can shed light on the applicability of macroscopic statisticallaws for social systems. Even if the complexity of individual behaviors prevents atrue microscopic approach, the introduction of mesoscopic models allows the studyof the dynamical properties for the non-stationary states of the considered system.We propose to compute various entropy measures of the individual mobility patternsobtained from GPS data that record the movements of private vehicles in the Florencedistrict, in order to point out new features of human mobility related to the use oftime and space and to de ne the dynamical properties of a stochastic model thatcould generate similar patterns. Moreover, we can relate the predictability propertiesof human mobility to the distribution of time passed between two successive trips.Our analysis suggests the existence of a hierarchical structure in the mobility patternswhich divides the performed activities into three di erent categories, according to thetime cost, with di erent information contents. We show that a Markov process de nedby using the individual mobility network is not able to reproduce this hierarchy, whichseems the consequence of di erent strategies in the activity choice. Our results couldcontribute to the development of governance policies for a sustainable mobility in

Understanding the variability of daily travel-time expenditures using GPS trajectory data

Transportation planning is strongly influenced by the assumption that every individual has a constant daily budget of ≈1 hour for his daily mobility. However, recent experimental results are proving this assumption as wrong. Here, we study the differences in daily travel-time expenditures among 24 Italian cities, extracted from a large set of GPS data on vehicles mobility. To understand these variations at the level of individual behaviour, we introduce a trip duration model that allows for a description of the distribution of travel-time expenditures in a given city using two parameters. The first parameter reflects the accessibility of desired destinations, whereas the second one can be associated to a travel-time budget and represents physiological limits due to stress and fatigue. Within the same city, we observe variations in the distributions according to home position, number of mobility days and a driver’s average number of daily trips. These results can be interpreted by a stochastic time-consumption model, where the generalised cost of travel times is given by a logarithmic-like function, in agreement with the Weber-Fechner law. Our experimental results show a significant variability in the travel-time budgets in different cities, and for different categories of drivers within the same city. This explicitly clashes with the idea of the existence of a constant travel-time budget and opens new perspectives for the modelling and governance of urban mobility.

Collective effects and collisions in halo genesis and growth

For a KV beam the halo is created by test particles, initially out of the core, via nonlinear resonances with the betatron motion. The number of resonances and the related diffusive processes are enhanced by the presence of mismatch oscillations of the core. Numerical (PIC) or physical (collisions) noise modifies the core of a KV beam creating tails on time scales relevant for storage rings. We consider a 2D model defined by N pseudo line‐charges per meter, whose limit N → ∞, at fixed perveance, is the 2D mean field theory for a coasting beam in a constant focusing channel. Using an algorithm of optimal computational complexity we find that the relaxation time scales linearly with N in agreement with Landau’s kinetic theory we have developed for the 2D model.

Frequency map analysis of resonances in a nonlinear lattice with space charge

Abstract In storage rings for heavy ion fusion beam losses must be minimized. During bunch compression high space charge is reached and the reciprocal effects between the collective modes of the beam and the single particle lattice nonlinearities must be considered to understand the problem of resonance crossing and halo formation. We show that the frequency map analysis of particle in core models gives an adequate description of the resonance network and of the chaotic regions where the halo particles can diffuse.

Form-drag instability in a barotropic and a baroclinic atmosphere

We discuss the form-drag instability for a quasi-geostrophic channel flow. We first study the characteristics of this instability in a barotropic flow, considering in detail the influence of the meridional scale and discussing which structure of the perturbation zonal flow must be chosen in order to describe properly this instability.We then consider a continuous quasi-geostrophic channel model in which the topography enters only through the bottom boundary condition, and we discuss how in this case the effects of the form-drag are felt by the mean zonal flow through the ageostrophic mean meridional circulation. Because the meridional structure of the perturbation zonal flow cannot simply be extended from the barotropic to the continuous case, we show how to modify it properly.We then study the baroclinic model in the particular case of constant (in the vertical) basic-state zonal flow and show how this case closely resembles the barotropic, demonstrating the barotropic nature of the form-drag instability.

MODELING TRAFFIC FLUCTUATIONS AND CONGESTION ON A ROAD NETWORK

Statistical mechanics points out as fluctuations have a relevant role for systems near critical points. We study the effect of traffic fluctuations and the transition to congested states for a stochastic dynamical model of traffic on a road network. The model simulates a finite population that moves from one road to another according to random transition probabilities. In such a way, we mimic the traffic fluctuations due to the granular feature of traffic and the dynamics at the crossing points. Then the amplitude of traffic flow fluctuations is proportional to the average flow as suggested by empirical observations. Assuming a parabolic shaped flow-density relation, there exists an unstable critical point for the road dynamics and the system can perform a phase transition to a congested state, where some roads reach their maximal capacity. We apply a statistical physics approach to study the onset congestion and we characterize analytically the relation between the fluctuations amplitude and the appearance of congested nodes. We verify the results by means of numerical simulations on a Manhattan-like road network. Moreover we point out the existence of oscillating regimes, where traffic oscillations back propagate on the road network, whose onset depend sensitively from the traffic fluctuations and that have a strong influence on the hysteresis cycles of the systems when the traffic load is modulated. The comparison between the numerical simulations and the empirical traffic data recorded by an inductive-loop traffic detector system (MTS system) on the county roads of the Emilia Romagna region in Italy is shortly discussed.

A Model for Asystematic Mobility in Urban Space

We present an agent-based model to simulate the citizens mobility in a urban space. The request of mobility is determined by the “chronotopic areas”: i.e. urban areas where time-dependent activities are installed and attract the citizens according to their social categories. The core of the model is a decision mechanism for the agents based on a daily program, which chooses the transportation means and the roads to reach the scheduled chronotopic areas. The decision mechanism depends on some social characters of the agents, on the information at disposal, on the attraction force towards a chronotopos and on some random choices. The daily program can also be upgraded according to the information given to the agents. The finite volume congestion effects are present in the private transportation and in the finite capacity of the public means whereas the crowding in the chronotopic areas causes the extension of the elapsed time in the areas. We present a simulation on the campus of Milano Bicocca University where we take advantage of some experimental observations on the students mobility.