Paolo Freguglia

Proposal of a risk model for vehicular traffic: A Boltzmann-type kinetic approach

This paper deals with a Boltzmann-type kinetic model describing the interplay between vehicle dynamics and safety aspects in vehicular traffic. Sticking to the idea that the macroscopic characteristics of traffic flow, including the distribution of the driving risk along a road, are ultimately generated by one-to-one interactions among drivers, the model links the personal (i.e., individual) risk to the changes of speeds of single vehicles and implements a probabilistic description of such microscopic interactions in a Boltzmann-type collisional operator. By means of suitable statistical moments of the kinetic distribution function, it is finally possible to recover macroscopic relationships between the average risk and the road congestion, which show an interesting and reasonable correlation with the well-known free and congested phases of the flow of vehicles.

Evolution: Geometrical and Dynamical Aspects.

We develop a possible axiomatic approach to the evolution theory that has been previously discussed in Freguglia [2002]. The axioms synthesize the fundamental ideas of evolution theory and allow a geometrical and dynamical interpretation of the generation law. Using the axioms we derive a simple reaction-diffusion model which introduces the species as self-organized stationary distribution of a finite population and simulates the evolution of a phenotypic character under the effect of an external perturbing action. The dynamical properties of the model are briefly presented using numerical simulations.

Emergent Properties and Complexity for Biological Theories

Our aim is to present some ideas about the notion of scientific theory which includes the biological theories. We examine relationships among theories and examples of theoretical situations. In this context we propose definitions of emergent property and complexity. These definitions are exemplified by the development of some biological theories.

A synthetic geometrical approach to betatronic motion: Some remarks

This contribution examines some themes for an easy computer approach to betatronic motion. A synthetic geometrical model of this motion is presented. I shall take the starting-point for my proposal from geometrical optical simulation.

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.

Geometric Calculus and Geometry Foundations in Peano

First, Peano’s geometrical calculus theory is a general theory which is of intrinsic mathematical interest and which is also applied to mechanics and to physics. Peano’s contributions, which come from an elaboration of Grassmann’s ideas, consist in an Euclidean interpretation of relative concepts. Moreover, in this context, Peano proves important fundamental theorems of projective geometry. For this reason, Peano’s geometrical calculus has an implicit foundational interest. In our opinion, the protophysical role of Euclidean geometry in Peano’s works is essential and decisive. He distinguishes position geometry from Euclidean geometry, and from a theoretical point of view, it is appropriate. In his ‘Sui fondamenti della geometria’ the congruence theory is well determined and regulated. Classical geometry constitutes the crucial model for the study of the foundations of geometry. Even Hilbert, deep down, takes Euclid into account20. During this period, we have many proposals of systems with different essential or primitive notions and axioms. Hence, we can observe “equivalent theories” for the foundation of elementary geometry, and in this way we have a “theoretical relativism” regarding the choice of primitive elements and fundamental axioms. This is epistemologically and historiographically21 very important22.

An Optical Geometric Model of the Betatronic Motion

We discuss the analogy between the betatronic motion in a particle accelerator and the geometric optics by using a Lagrangian formalism. We show that each element in a magnetic lattice is equivalent to a an optical lens in the thin lens approximation. We use this analogy to introduce a geometric approach to the description of the betatronic motion and we propose an optical experiment to study the nonlinear effects of the beam Physics.

An Axiomatic Approach to Some Biological Themes

In this paper we continue the enterprise of elaborating an axiomatic framework suitable for modern Biology, started in 1,2,3. We isolate and propose to the attention of the scientific community a few axioms expressing some basic biological facts and their theoretical interpretations. We hope we can foster criticism and contributions from researchers of any field of the Natural Sciences. In fact, we conceive this paper as part of a general research programme on the Foundations of Science, originated in the Eighties by E. De Giorgi at the Scuola Normale Superiore, Pisa and carried on by several researchers after his death in 1996 (see 4,5,6,7,8). The aim of this programme is not to provide safe and unquestionable grounds to scientific activity, but rather to develop conceptual environments where this activity can be carried out naturally and without artificial constraints, and the notions considered in various disciplines can be presented in a simple and clear-cut way, so as to allow for both a deeper analysis by researchers in the field, and a proficuous interdsciplinary debate.

An optical experiment towards the analogic simulation of the betatronic motion

We present the first experiment results of an experiment that simulates the betatronic motion in a FODO cell by using an optical device. The analogy between the hamiltonian mechanics and the geometric optics is discussed in order to define a project of an optical FODO cell. We consider also the possibility of representing an optical path by means of a sequence of quaternion numbers. The experimental results are compared with the simulations of a ray tracing program.

De la perspective à la géométrie projective: le cas du théorème de Desargues sur les triangles homologiques

Le passage d’un outil permettant une representation esthetiquement valable du decor d’un tableau, la perspective, a une science qui permettra a l’Architecte de transmettre ses idees au moyen d’un plan, la geometrie projective, tel est l’enjeu du travail qui suit. Il est remarquable d’observer sur les tableaux peints aux alentours de 1600 un nombre de plus en plus grand de bâtiments.