arXiv subjects

Emiliano Cristiani

Publications and source records attributed to Emiliano Cristiani.

At least 19 recordsLinked to original sources

arXiv2026

Roadside units placement for total travel time minimization in I2X-enabled road networks based on a dynamic traffic flow model

This work addresses the problem of locating Road Side Units (RSUs) in vehicular networks with the aim of improving overall traffic efficiency. We propose a heuristic approach for determining the placement of RSUs on a road network, while vehicle dynamics are modeled through a microscopic follow-the-leader interaction in which drivers continuously adapt their speed according to the distance from the vehicle ahead. The RSUs share the collected information among themselves to cooperatively estimate the network state, which is then communicated to vehicles, allowing them to compute their fastest paths. We also assume that not all drivers comply with the provided recommendations, meaning that only a fraction of users follow the suggested routes. Since the aim is to improve network performance while minimizing the number of deployed units, the methodology adopts a nested optimization scheme: an outer module explores the optimal number k of RSUs, while an inner module identifies the best placement configuration for each k. To evaluate the effectiveness and the scalability of the proposed method, we tested two networks with different topologies and sizes. The results show a decrease in Total Travel Time (TTT) compared to the baseline scenario (i.e., without RSUs) of up to 36% on the smaller network and up to 20% on the larger one. Stochastic vehicle origin-destination pairs have also been considered.

math.DS↗

arXiv2026

The Wolf and the Cello: Modelling and design of multiple resonance suppressors in large string instruments

The wolf note is an acoustic instability that occurs in large bowed string instruments when a strong body resonance interacts with the vibrating string, producing amplitude modulation and loss of tonal control. Various wolf suppressors - tuned mass dampers attached to the string or to the instrument body - are used in practice to mitigate this effect. In this paper, we propose a mathematical model describing the coupled dynamics of a string and a two-dimensional body equipped with one or two wolf suppressors. Both string and body include elastic (second-order) and stiffness (fourth-order) contributions and can be excited either by plucking or bowing. Three performance indicators are introduced: The first one perceives the wolf-tone appearance, the second one quantifies the attenuation of the notes possibly caused by the wolf suppressor, and the third one measures the acoustic fidelity (in terms of spectrum) with respect to the original instrument. The proposed numerical tests give insights about optimal tuning and placement of one or two suppressors, achieving effective wolf-note suppression while preserving as much as possible the global tonal balance.

math.DS↗

arXiv2025

A microscopic traffic flow model on network with destination-aware V2V communications and rational decision-making

In this paper we carry out a computational study of a novel microscopic follow-the-leader model for traffic flow on road networks. We assume that each driver has its own origin and destination, and wants to complete its journey in minimal time. We also assume that each driver is able to take rational decisions at junctions and can change route while moving depending on the traffic conditions. The main novelty of the model is that vehicles can automatically and anonymously share information about their position, destination, and planned path when they are close to each other within a certain distance. The pieces of information acquired during the journey are used to optimize the route itself. In the limit case of an infinite communication range, we recover the classical Reactive User Equilibrium and Dynamic User Equilibrium.

math.OC↗

arXiv2025

Numerical computation of generalized Wasserstein distances with applications to traffic model analysis

Generalized Wasserstein distances allow to quantitatively compare two continuous or atomic mass distributions with equal or different total mass. In this paper, we propose four numerical methods for the approximation of three different generalized Wasserstein distances introduced in the last years, giving some insights about their physical meaning. After that, we explore their usage in the context of the sensitivity analysis of differential models for traffic flow. The quantification of models sensitivity is obtained by computing the generalized Wasserstein distances between two (numerical) solutions corresponding to different inputs, including different boundary conditions.

math.AP↗

arXiv2025

A general multi-stratum model for a nanofunctionalized releasing capsule: a computational study

Releasing capsules are widely employed in biomedical applications as smart carriers of therapeutic agents, including drugs and bioactive compounds. Such delivery vehicles typically consist of a loaded core, enclosed by one or multiple concentric coating strata. In this work, we extend over existing mechanistic models to account for such multi-strata structures, and we characterise the release kinetics of the active substance into the surrounding medium. We present a computational study of drug release from a multi-stratum spherical microcapsule, modelled through a non-linear diffusion equation incorporating radial anisotropy and space- and time-discontinuous coefficients. The problem is solved numerically using a finite volume scheme on a grid with adaptive spatial and temporal resolution. Analytical expressions for concentration and cumulative release are derived for all strata, enabling the exploration of parameter sensitivity -- such as coating permeability and internal diffusivity -- on the overall release profile. The resulting release curves provide mechanistic insight into the transport processes and offer design criteria for achieving controlled release. Model predictions are benchmarked against in vitro experimental data obtained under physiologically relevant conditions, showing good agreement and validating the key features of the model. The proposed model thus serves as a practical tool for predicting the behaviour of composite coated particles, supporting performance evaluation and the rational design of next-generation drug delivery systems with reduced experimental effort.

math.DS↗

arXiv2025

Detection of Anomalous Vehicular Traffic and Sensor Failures Using Data Clustering Techniques

The increasing availability of traffic data from sensor networks has created new opportunities for understanding vehicular dynamics and identifying anomalies. In this study, we employ clustering techniques to analyse traffic flow data with the dual objective of uncovering meaningful traffic patterns and detecting anomalies, including sensor failures and irregular congestion events. We explore multiple clustering approaches, i.e partitioning and hierarchical methods, combined with various time-series representations and similarity measures. Our methodology is applied to real-world data from highway sensors, enabling us to assess the impact of different clustering frameworks on traffic pattern recognition. We also introduce a clustering-driven anomaly detection methodology that identifies deviations from expected traffic behaviour based on distance-based anomaly scores. Results indicate that hierarchical clustering with symbolic representations provides robust segmentation of traffic patterns, while partitioning methods such as k-means and fuzzy c-means yield meaningful results when paired with Dynamic Time Warping. The proposed anomaly detection strategy successfully identifies sensor malfunctions and abnormal traffic conditions with minimal false positives, demonstrating its practical utility for real-time monitoring. Real-world vehicular traffic data are provided by Autostrade Alto Adriatico S.p.A.

cs.LG↗

arXiv2024

Kinetic description and macroscopic limit of swarming dynamics with continuous leader-follower transitions

In this paper, we derive a kinetic description of swarming particle dynamics in an interacting multi-agent system featuring emerging leaders and followers. Agents are classically characterized by their position and velocity plus a continuous parameter quantifying their degree of leadership. The microscopic processes ruling the change of velocity and degree of leadership are independent, non-conservative and non-local in the physical space, so as to account for long-range interactions. Out of the kinetic description, we obtain then a macroscopic model under a hydrodynamic limit reminiscent of that used to tackle the hydrodynamics of weakly dissipative granular gases, thus relying in particular on a regime of small non-conservative and short-range interactions. Numerical simulations in one- and two-dimensional domains show that the limiting macroscopic model is consistent with the original particle dynamics and furthermore can reproduce classical emerging patterns typically observed in swarms.

math-ph↗

arXiv2024

Dissolution of variable-in-shape drug particles via the level-set method

In this work, we deal with a mathematical model describing the dissolution process of irregularly shaped particles. In particular, we consider a complete dissolution model accounting for both surface kinetics and convective diffusion, for three drugs with different solubility and wettability: theophylline, griseofulvin, and nimesulide. The possible subsequent recrystallization process in the bulk fluid is also considered. The governing differential equations are revisited in the context of the level-set method and Hamilton-Jacobi equations, then they are solved numerically. This choice allows us to deal with the simultaneous dissolution of hundreds of different polydisperse particles. We show the results of many computer simulations which investigate the impact of the particle size, shape, area/volume ratio, and the dependence of the interfacial mass transport coefficient on the surface curvature.

math.DS↗

arXiv2024

A macroscopic pedestrian model with variable maximal density

In this paper we propose a novel macroscopic (fluid dynamics) model for describing pedestrian flow in low and high density regimes. The model is characterized by the fact that the maximal density reachable by the crowd - usually a fixed model parameter - is instead a state variable. To do that, the model couples a conservation law, devised as usual for tracking the evolution of the crowd density, with a Burgers-like PDE with a nonlocal term describing the evolution of the maximal density. The variable maximal density is used here to describe the effects of the psychological/physical pushing forces which are observed in crowds during competitive or emergency situations. Specific attention is also dedicated to the fundamental diagram, i.e., the function which expresses the relationship between crowd density and flux. Although the model needs a well defined fundamental diagram as known input parameter, it is not evident a priori which relationship between density and flux will be actually observed, due to the time-varying maximal density. An a posteriori analysis shows that the observed fundamental diagram has an elongated "tail" in the congested region, thus resulting similar to the concave/concave fundamental diagram with a "double hump" observed in real crowds. The main features of the model are investigated through 1D and 2D numerical simulations. The numerical code for the 1D simulation is freely available at https://gitlab.com/cristiani77/code_arxiv_2406.14649

math.DS↗

arXiv2023

An overview of some mathematical techniques and problems linking 3D vision to 3D printing

Computer Vision and 3D printing have rapidly evolved in the last 10 years but interactions among them have been very limited so far, despite the fact that they share several mathematical techniques. We try to fill the gap presenting an overview of some techniques for Shape-from-Shading problems as well as for 3D printing with an emphasis on the approaches based on nonlinear partial differential equations and optimization. We also sketch possible couplings to complete the process of object manufacturing starting from one or more images of the object and ending with its final 3D print. We will give some practical examples of this procedure.

cs.CV↗

arXiv2023

Inverting the Fundamental Diagram and Forecasting Boundary Conditions: How Machine Learning Can Improve Macroscopic Models for Traffic Flow

In this paper, we aim at developing new methods to join machine learning techniques and macroscopic differential models for vehicular traffic estimation and forecast. It is well known that data-driven and model-driven approaches have (sometimes complementary) advantages and drawbacks. We consider here a dataset with flux and velocity data of vehicles moving on a highway, collected by fixed sensors and classified by lane and by class of vehicle. By means of a machine learning model based on an LSTM recursive neural network, we extrapolate two important pieces of information: 1) if congestion is appearing under the sensor, and 2) the total amount of vehicles which is going to pass under the sensor in the next future (30 min). These pieces of information are then used to improve the accuracy of an LWR-based first-order multi-class model describing the dynamics of traffic flow between sensors. The first piece of information is used to invert the (concave) fundamental diagram, thus recovering the density of vehicles from the flux data, and then inject directly the density datum in the model. This allows one to better approximate the dynamics between sensors, especially if an accident happens in a not monitored stretch of the road. The second piece of information is used instead as boundary conditions for the equations underlying the traffic model, to better reconstruct the total amount of vehicles on the road at any future time. Some examples motivated by real scenarios will be discussed. Real data are provided by the Italian motorway company Autovie Venete S.p.A.

cs.LG↗

arXiv2022

A generalized mean-field game model for the dynamics of pedestrians with limited predictive abilities

This paper investigates the model for pedestrian flow firstly proposed in [Cristiani et al., DOI:10.1137/140962413]. The model assumes that each individual in the crowd moves in a known domain, aiming at minimizing a given cost functional. Both the pedestrian dynamics and the cost functional itself depend on the position of the whole crowd. In addition, pedestrians are assumed to have predictive abilities, but limited in time, extending only up to $θ$ time units into the future, where $θ\in[0,\infty)$ is a model parameter. 1) For $θ=0$ (no predictive abilities), we recover the modeling assumptions of the Hughes's model, where people take decisions on the basis of the current position of the crowd only. 2) For $θ\to\infty$, instead, we recover the standard mean field game (MFG) setting, where people are able to forecast the behavior of the others at any future time and take decisions on the basis of the current and future position of the whole crowd. 3) For intermediate values of $θ$ we obtain something different: as in the Hughes's model, the numerical procedure to solve the problem requires to run an off-line procedure at any fixed time $t$, which returns the current optimal velocity field at time $t$ by solving an associated backward-in-time Hamilton-Jacobi-Bellman equation; but, differently from the Hughes's model, here the procedure involves a prediction of the crowd behavior in the sliding time window $[t,t+θ)$, therefore the optimal velocity field is given by the solution to a forward-backward system which joins a Fokker-Planck equation with a Hamilton-Jacobi-Bellman equation as in the MFG approach. The fact that a different forward-backward system must be solved at any time $t$ arises new interesting theoretical questions. Numerical tests will give some clues about the well-posedness of the problem.

math.OC↗

arXiv2022

Preventing congestion in crowd dynamics caused by reversing flow

In this paper we devise a microscopic (agent-based) mathematical model for reproducing crowd behaviour in a specific scenario: a number of pedestrians, consisting of numerous social groups, flow along a corridor until a gate located at the end of the corridor closes. People are not informed about the closure of the gate and perceive the blockage observing dynamically the local crowd conditions. Once people become aware of the new conditions, they stop and then decide either to stay, waiting for reopening, or to go back and leave the corridor for ever. People going back hit against newly incoming people who are not yet aware of the blockage or have already decided to stay. This creates a dangerous counter-flow which can easily lead to accidents. We run several numerical simulations varying parameters which control the crowd behaviour, in order to understand the factors which have the greatest impact on the dynamics. We conclude with some useful suggestions directed to the organizers of mass events.

math.DS↗

arXiv2021

An all-leader agent-based model for turning and flocking birds

Starting from recent experimental observations of starlings and jackdaws, we propose a minimal agent-based mathematical model for bird flocks based on a system of second-order delayed stochastic differential equations with discontinuous (both in space and time) right-hand side. The model is specifically designed to reproduce self-organized spontaneous sudden changes of direction, not caused by external stimuli like predator's attacks. The main novelty of the model is that every bird is a potential turn initiator, thus leadership is formed in a group of indistinguishable agents. We investigate some theoretical properties of the model and we show the numerical results. Biological insights are also discussed.

nlin.AO↗

arXiv2021

Managing Crowded Museums: Visitors Flow Measurement, Analysis, Modeling, and Optimization

We present an all-around study of the visitors flow in crowded museums: a combination of Lagrangian field measurements and statistical analyses enable us to create stochastic digital-twins of the guests dynamics, unlocking comfort- and safety-driven optimizations. Our case study is the Galleria Borghese museum in Rome (Italy), in which we performed a real-life data acquisition campaign. We specifically employ a Lagrangian IoT-based visitor tracking system based on Raspberry Pi receivers, displaced in fixed positions throughout the museum rooms, and on portable Bluetooth Low Energy beacons handed over to the visitors. Thanks to two algorithms: a sliding window-based statistical analysis and an MLP neural network, we filter the beacons RSSI and accurately reconstruct visitor trajectories at room-scale. Via a clustering analysis, hinged on an original Wasserstein-like trajectory-space metric, we analyze the visitor paths to get behavioral insights, including the most common flow patterns. On these bases, we build the transition matrix describing, in probability, the room-scale visitor flows. Such a matrix is the cornerstone of a stochastic model capable of generating visitor trajectories in silico. We conclude by employing the simulator to increase the number of daily visitors while respecting numerous logistic and safety constraints. This is possible thanks to optimized ticketing and new entrance/exit management.

physics.soc-ph↗

arXiv2021

Macroscopic and multi-scale models for multi-class vehicular dynamics with uneven space occupancy: a case study

In this paper we propose two models describing the dynamics of heavy and light vehicles on a road network, taking into account the interactions between the two classes. The models are tailored for two-lane highways where heavy vehicles cannot overtake. This means that heavy vehicles cannot saturate the whole road space, while light vehicles can. In these conditions the creeping phenomenon can appear, i.e. one class of vehicles can proceed even if the other class has reached the maximal density. The first model we propose couples two first-order macroscopic LWR models, while the second model couples a second-order microscopic Follow-the-Leader model with a first-order macroscopic LWR model. Numerical results show that both models are able to catch some second-order (inertial) phenomena like stop & go waves. Models are calibrated by means of real data measured by fixed sensors placed along the A4 Italian highway Trieste-Venice and its branches, provided by Autovie Venete S.p.A.

math.DS↗

arXiv2021

Two algorithms for a fully coupled and consistently macroscopic PDE-ODE system modeling a moving bottleneck on a road

In this paper we propose two numerical algorithms to solve a coupled PDE-ODE system which models a slow vehicle (bottleneck) moving on a road together with other cars. The resulting system is fully coupled because the dynamics of the slow vehicle depends on the density of cars and, at the same time, it causes a capacity drop in the road, thus limiting the car flux. The first algorithm, based on the Wave Front Tracking method, is suitable for theoretical investigations and convergence results. The second one, based on the Godunov scheme, is used for numerical simulations. The case of multiple bottlenecks is also investigated.

math.DS↗

arXiv2020

Mathematical models and methods for crowd dynamics control

In this survey we consider mathematical models and methods recently developed to control crowd dynamics, with particular emphasis on egressing pedestrians. We focus on two control strategies: The first one consists in using special agents, called leaders, to steer the crowd towards the desired direction. Leaders can be either hidden in the crowd or recognizable as such. This strategy heavily relies on the power of the social influence (herding effect), namely the natural tendency of people to follow group mates in situations of emergency or doubt. The second one consists in modify the surrounding environment by adding in the walking area multiple obstacles optimally placed and shaped. The aim of the obstacles is to naturally force people to behave as desired. Both control strategies discussed in this paper aim at reducing as much as possible the intervention on the crowd. Ideally the natural behavior of people is kept, and people do not even realize they are being led by an external intelligence. Mathematical models are discussed at different scales of observation, showing how macroscopic (fluid-dynamic) models can be derived by mesoscopic (kinetic) models which, in turn, can be derived by microscopic (agent-based) models.

physics.soc-ph↗