Bruno Giorgini

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.

A chronotopic model of mobility in urban spaces

In this paper, we propose an urban mobility model based on individual stochastic dynamics driven by the chronotopic action with a deterministic public transportation network. Such a model is inspired by a new approach to the problem of urban mobility that focuses the attention to the individuals and considers the presence of random components and attractive areas (chronotopoi), an essential ingredient to understand the citizens dynamics in the modern cities. The computer simulation of the model allows virtual experiments on urban spaces that describe the mobility as the evolution of a non-equilibrium system. In the absence of chronotopoi the relaxation to a stationary state is studied by the mean-field equations. When the chronotopoi are switched on the different classes of people feel an attraction toward the chronotopic areas proportional to a power law of the distance. In such a case, a theoretical description of the average evolution is obtained by using two diffusion equations coupled by local mean-field equations.

Dynamics and thermodynamics of a gas of automata

We consider a system of point charges interacting within a cone of vision and confined by an external potential, as a simple model of individuals provided with vision. The non Newtonian nature of the interaction introduces dissipative effects which are balanced by a memory mechanism. The two-body system is amenable to quadrature, whereas the N 1 body system exhibits crystal-like and disordered states with a non-trivial phase diagram if the interaction range and memory persistence are chosen as control parameters.

Hawking evaporation and space-time structure

SummaryThe Vaidya radiating metric is used to model an evaporating black-hole space-time. It is shown that, thus, a wormhole is produced in analogy with the Einstein-Rosen bridge. Its physical consequences are discussed.RiassuntoLa metrica radiante di Vaidya è utilizzata per fare un modello di buco nero evaporante. Si mostra cosí che si produce un «wormhole» in analogia con il «ponte» di Einstein-Rosen. Se ne discutono le implicazioni fisiche.РезюмеИспользуется радиационная метрика Вайдя для получения модели испаряющейся черной дыры. Показывается, что образуется «червячная дыра» по аналогии с «мостом» Эйнштейна-Розена. Обсуждаются физические следствия.

Radiation from a black hole: A Vaidya-metric-based computation

SummaryThe asymptotic behaviour of for a massless scalar field in a two-dimensional Vaidya space-time is investigated. It is shown that a good agreement exists between the quantum-mechanically derived energy-momentum tensor and the classical radiative one.RiassuntoSi studia il comportamento asintotico di per un campo scalare a massa nulla in uno spazio-tempo bidimensionale di Vaidya. Si mostra che esiste un buon accordo tra il tensore energia-impulso calcolato quantisticamente e quello classico di radiazione.РезюмеИсследуется асимптотическое поведение для скалярного поля с нулевой массой в дуумерном пространстве-времени Вайдя. Показывается, что существует хорошее согласие между тензором знергии импульса, вычисленным квантовомеханически, и классическим тензором излучения.

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.

Hamiltonian dynamics with a weak noise and the echo effect for the rotator model

We analyse the effect of a weak noise on the Hamiltonian transport from the analytical and numerical viewpoint. A solvable model, the noisy rotator, is proposed to illustrate the basic phenomena. In the absence of noise, the phase space evolution is a shear flow, whose angular correlations decay following a power law, which depends on the smoothness of the initial action distribution. If the action has a fluctuating component, given by a Wiener process, then the angular correlations decay exponentially according to or faster, where is the noise amplitude. The echo effect is well suited to investigate the competition between the decorrelation due to filamentation and noise. The noisy rotator model allows an exhaustive analytical investigation of the process for a wide class of initial conditions and a generic disturbance. The echo time is proportional to the delay τ of the disturbance and its amplitude is proportional to λτ, where λ is the amplitude of the disturbance. The noise reduces the echo amplitude by , where c depends on the Fourier components of the initial angular distribution, and of the disturbance applied at time τ. The analytical results, derived in the limit λ → 0, τ → ∞, with λτ finite and sufficiently small to justify a first-order expansion, are checked numerically. For more realistic models the analytical procedure would provide qualitative results and scaling laws. Quantitative results are obtained by solving the Fokker–Planck equation with a numerical scheme based on splitting: back propagation and biquadratic interpolation for the integrable part, implicit finite difference scheme for the noise component. The application to a noisy pendulum describing the longitudinal dynamics in a particle accelerator is considered, and we determine the value of the noise amplitude , below which the echo cannot be detected.

Complexity in Physics of an Adhesive Tape

In this paper we show the emergency of a complex dynamics in the peeling of an adhesive tape. In particular we synthetically present some experimental results and theoretical interpretations of the stick-slip regime.

Phase spaces for quantum elementary systems in anti-de Sitter and Minkowski spacetimes

The authors give a phase space description of a massive, spin s, quantum elementary system on the anti-de Sitter spacetime. The latter is associated with a discrete series representation of the kinematical group SO0(3,2) approximately=Sp(4,R)/A2, taken in its Fock-Bargmann realization. When the zero curvature limit (contraction) is carried out, they obtain a Poincare quantum elementary system in its momentum representation (i.e. the usual Wigner representation), at the expense of imposing a polarization condition. This polarization appears as a consequence of the contraction procedure, and it is imposed in order to avoid the appearance of singular terms in the contracted generators.

Aspects of quantum physics in multidimensional spaces

SummarySeveral authors have analysed the possibility that gravity, both at the semi-classical and at the full quantum level, may determine an apparent modification of the quantum evolution equation (QEE). Gross has also suggested that Kaluza-Klein (KK) theories could provide more suitable theoretical laboratories for studying the problems of quantum gravity, and particularly those concerning the QEE, than ordinary fourdimensional gravitation. We indicate here a simple reason why nonzero modes of the metric in KK theories could affect low-energy physics, not only in the sense discussed by Appelquist, and Chodos, but also as far as the QEE is concerned. We also discuss, in terms of a simple model, the circumstances under which the modified QEE may simplify to a Markovian form.RiassuntoDiversi autori hanno analizzato la possibilità che la gravitazione, sia al livello semiclassico sia a quello pienamente quantico, possa determinare un’apparente modifica dell’equazione di evoluzione della meccanica quantistica (QEE).Gross ha inoltre suggerito che teorie alla Kaluza-Klein (KK) possono provvedere un laboratorio teorico per studiare i problemi della gravitazione quantica, ed in particolare quelli riguardanti la QEE, piú adatto della normale gravitazione in quattro dimensioni. In questo lavoro si indica una ragione semplice per la quale i modi non zero della metrica nelle teorie alla KK possono influenzare la fisica delle basse energie non solo nel senso discusso da Appelquist e Chodos, ma anche per quanto riguarda la QEE. Si discute anche, in termini di un semplice modello, le circostanze nelle quali la QEE modificata può assumere una forma semplificata markoviana.РезюмеНекоторые авторы проанализировали возможность, что гравитация на полуклассическом и на квантовом уровнях может определить очевидную модификацию квантового уравнения эволюции. Гросс предположил, что теории Калуца-Клейна представляют более приемлемый теоретический подход для исследования проблем квантовой гравитации и квантового уравнения эволюции, чем обычная четырехмерная гравитация. В этой работе мы указываем причину, почему ненулевые моды метрики в теориях Калуца-Клейна могут изменять физику низких энергий. Мы также обсуждаем, в рамках простой модели, условия, при которых квантовое уравнение эволюции может быть приведено к более простому марковскому виду.